HOW WATER MEETS A HYDROPHOBIC SURFACE:
RELUCTANTLY AND WITH FLUCTUATIONS
BY
ADELE POYNOR TORIGOE
B.S., University of Maryland Baltimore Co, 2001
M.S., University of Illinois at Urbana-Champaign, 2003
DISSERTATION
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Physics
in the Graduate College of the
University of Illinois at Urbana-Champaign, 2006
Urbana, Illinois
ii
Abstract
By definition hydrophobic substances hate water.
Water placed on a
hydrophobic surface will form a drop in order to minimize its contact area. What
happens when water is forced into contact with a hydrophobic surface? One theory is
that an ultra-thin low-density region forms near the surface. This depleted region
would have implications in such diverse areas as colloidal self-assembly, and the
boundary conditions of fluid flow. However, the literature still remains divided as to
whether or not such a depleted region exists.
To investigate the existence of this layer, we have employed three surfacesensitive techniques, time-resolved phase-modulated ellipsometry, surface plasmon
resonance, and X-ray reflectivity. Both ellipsometry and X-ray reflectivity provide
strong evidence for the low-density layer and illuminate unexpected temporal
behavior. Using all three techniques, we found surprising fluctuations at the interface
with a non-Gaussian distribution and a single characteristic time on the order of
tenths of seconds. This information supports the idea that the boundary fluctuates
with something akin to capillary waves.
We have also investigated the dependence of the static and dynamic properties
of the hydrophobic/water interface on variables such as temperature, contact angle,
pH, dissolved gasses, and sample quality, among others, in a hope to discover the root
of the controversy in the literature. We found that the depletion layer is highly
dependent on temperature, contact angle and sample quality. This dependence might
explain some of the discrepancies in the literature as different groups often use
hydrophobic surfaces with different properties.
iii
Acknowledgement
This Dissertation would not have been possible without the contributions of
many others. I owe a great deal to my advisor Steve Granick. He not only guided me
through the trials and tribulations of this project but he also helped me realize my
goals and become a fully formed physicist. I would like to thank my committee
members, Dr. Yoshi Oono, Dr. Taekjip Ha, and Dr. Ian Robinson, for providing me
with new perspectives on my project. I would also like to thank Dr. Ian Robinson,
along with Dr. Paul Fenter, Dr. Zhan Zhang and Ms. Meng Liang for our great X-ray
reflectivity collaboration. I would never have been able to do it by myself.
In addition, I would like to thank the past and current postdocs in our group. I
am especially indebted to Dr. Sung Chul Bae, without whom I would never have been
able to perform the dynamic SPR measurements; Dr. Ashis Mukhopdhyay, who
taught me everything about ellipsometry; and Dr. Jiang Zhao, who got me started
with SPR in my first year and taught me how to make thiol monolayers. My group
mates have been a great help to me over the years. I am very grateful to Mr. Liang
Hong, who was learning to teach a physicist chemistry; Ms. Yan Yu who helped to
prepare innumerable hydrophobic monolayers; and Dr. Jeff Turner, who did most of
the work for the SFG experiments. I would also like to thank Liangfang Zhang and
Janet Wong for all the useful discussions and friendship. I have had the privilege to
work with several excellent undergraduate collaborators over the years. I would like
to thank Ms. Jolita Šečkutė for her help with the temperature measurements; Mr.
Brendon Hahn for his work on the OTE monolayers; and Ms. Wina Tjen who with
iv
her questions and excitement over three years of working together taught me more
than I thought possible.
I would like to thank my family for all they have done for me; to my parents
Margaret and Edward Poynor, who fostered my curiosity and instilled in me a love of
science; and my brother, Victor Poynor, who kept me from taking myself too
seriously. Finally, I would like to thank my husband, Eugene Torigoe. He was there
for me from the first day of graduate school and together we have come through this
great adventure.
My funding was provided by U.S. Department of Energy, Division of
Materials Science under contract no. DEFG02-91ER45439 with the Frederick Seitz
Materials Research Laboratory at the University of Illinois at Urbana-Champaign
until this year. My research this summer was supported by Dr. Steve Granick’s
Founder Professorship.
v
Table of Contents
Chapter 1: Introduction ..............................................................................................1
1.1 Theories of Water/Hydrophobic Interfaces .......................................................3
1.2 Simulations of Water/Hydrophobic Interfaces ..................................................6
1.3 Previous Experiments on Water/Hydrophobic Interfaces..................................9
1.4 References........................................................................................................11
1.5 Figures..............................................................................................................14
Chapter 2: Experimental Techniques ......................................................................16
2.1 Ellipsometry.....................................................................................................17
2.2 X-Ray Reflectivity ...........................................................................................25
2.3 Surface Plasmon Resonance ............................................................................28
2.4 Hydrophobic Substrates ...................................................................................34
2.5 References........................................................................................................37
2.6 Figures..............................................................................................................39
Chapter 3: Static Properties of the Water/Hydrophobic Interface.......................44
3.1 Ellipsometric Evidence for the Depletion Layer .............................................44
3.2 X-Ray Reflectivity Evidence for the Depletion Layer ....................................46
3.3 Temperature Dependence ................................................................................50
3.4 Dependence on Dissolved Gases .....................................................................51
3.5 Lateral Properties of the Depletion Layer........................................................53
3.6 Dependence on Sample Quality.......................................................................54
3.7 Conclusions for the Chapter.............................................................................55
3.8 References........................................................................................................56
3.9 Figures..............................................................................................................59
Chapter 4: Dynamic Properties of the Water/Hydrophobic Interface .................74
4.1 Histograms .......................................................................................................74
4.1.1 Dependence of Dynamics on Temperature.............................................77
4.1.2 Dependence of Dynamics on Roughness................................................78
4.1.3 Dependence of Dynamics on Contact Angle ..........................................78
4.1.4 Dependence of Dynamics on Dissolved Gases.......................................80
4.1.5 Dependence of Dynamics on pH ............................................................80
4.2 Power Spectra ..................................................................................................81
4.3 Autocorrelations...............................................................................................82
4.3.1 X-Ray Photon Correlation Spectroscopy................................................83
4.3.2 Surface Plasmon Resonance Correlation Spectroscopy .........................85
4.3.3 Area Dependence ....................................................................................86
4.3.4 Contact Angle Dependence.....................................................................87
4.3.5 Dependence on Dissolved Gases ............................................................87
4.4 Conclusions for the Chapter.............................................................................88
4.5 References........................................................................................................89
4.6 Figures..............................................................................................................91
Chapter 5: Concluding Remarks............................................................................112
5.1 References......................................................................................................115
Appendix A: Use and Maintenance of the Ellipsometer ......................................116
A.1 Alignment and Calibration of the Ellipsometer ............................................116
A.1.1 Aligning the Laser................................................................................116
vi
A.1.2 Finding the p-Polarization....................................................................117
A.1.3 Finding the Analyzer Angles ...............................................................118
A.1.4 Finding the p-Axis of the Phase Modulator .........................................118
A.1.5 Setting Jo(δo) to Zero............................................................................119
A.1.6 Calibration............................................................................................119
A.2 Taking Measurements with the Ellipsometer................................................120
A.2.1 Cleaning and Assembling the Sample Cell..........................................120
A.2.2 Finding the Brewster Angle .................................................................121
A.2.3 Collection and Analysis of Data ..........................................................121
A.3 Figures...........................................................................................................123
Appendix B: Sample Preparation...........................................................................133
B.1 Hydrophilic Silicon .......................................................................................133
B.2 OTE Monolayers ...........................................................................................134
B.3 Thiol Monolayers ..........................................................................................135
Appendix C: Use of the SPR ...................................................................................136
C.1 Cleaning the Sample Cell..............................................................................136
C.2 Mounting the Sample ....................................................................................136
C.3 Taking Measurements ...................................................................................137
C.3.1 Static Measurements ............................................................................138
C.3.2 Dynamic Measurements.......................................................................138
C.4 Figures...........................................................................................................140
Author’s Biography .................................................................................................145
vii
Chapter 1: Introduction
Water is one of the most important and ubiquitous chemicals on earth. It
surrounds and permeates our lives; making up over 60% by volume of our bodies,
and covering over 70% of the earth’s surface. The presence of liquid water is thought
to be essential to the development of life. So much so that on the Mars Exploration
Rover mission, the search for evidence of liquid water was considered equivalent to
the search for previous life [1.1].
Still for all its importance, water is not well understood, and exhibits many
anomalous behaviors when compared to other fluids. For example, hydrogen sulfide
(H2S), which has twice the molecular weight of water, would be expected to have a
higher boiling temperature than water but in fact, its boiling point is 160 oC lower
than water [1.2]. Also, water has a much higher surface tension and heat capacity
than comparable liquids. The origins of many of the unusual aspects of water are due
to its unique liquid structure. In its liquid form, water consists of an ever-changing
three-dimensional network of hydrogen bonds.
Water presents some even more puzzling behaviors near hydrophobic
surfaces. Hydrophobic comes from the Greek roots “hydros” meaning water and
“phobos” meaning fear.
So literally hydrophobic means fearing water, but in
chemistry it is the tendency to of a substance repel to water. On a more microscopic
level, hydrophobic surfaces cannot form hydrogen bonds. When water is placed on a
hydrophobic surface, its hydrogen-bonding network must be disrupted. This causes
the water to want to minimize its contact with the hydrophobic substance. For this
reason, a drop of water placed on a hydrophobic surface will ball up instead of
1
spreading out. The angle made between the solid and the liquid surface at the point
of contact is a good measure of the hydrophobicity of the solid. This angle is called
the contact angle (θ) and is illustrated in Figure 1.1. In this work, surfaces with a
contact angle over 90o will be considered hydrophobic and those with a contact angle
under 90o, hydrophilic.
Water/hydrophobic interfaces surround us. You can see many examples in
day to day life. Examples include a dew drop on a leaf, the folding of proteins in our
bodies and even liquids on stain resistant fabrics. On both leaves and stain resistant
fabrics, water can bead up to minimize its interaction; however for a protein the
hydrophobic amino acids are submerged in water. In this case the disruption of
hydrogen bonds seems more problematic, and exactly what happens here is not clear.
Energetically, we would expect the system to form as many hydrogen bonds as
possible resulting in a preferential ordering of the water. Entropically, we would
expect the system to orient randomly and thus sample the maximum number of states.
Which of these two competing interactions dominates? What effect does the
competition have on the dynamic and equilibrium properties of the system? The
answers to these questions are still hotly debated. To help resolve this debate, I have
preformed a series of experiments looking at the density of water near a hydrophobic
surface.
This Dissertation can be roughly divided into five parts. The first part, this
introduction, deals with the background and motivation for this work. It provides an
overview of past theories, simulations, and experiments done in this area. Chapter 2
introduces the experimental considerations and techniques needed to study the
2
water/hydrophobic interface.
In Chapter 3, evidence for a depletion layer is
presented. The dependence of its static properties on such variables as temperature
and dissolved gasses are also explored. Chapter 4 goes on to look at the dynamic
properties of the depletion layer. A short summary is provided in Chapter 5.
1.1 Theories of Water/Hydrophobic Interfaces
Classically, water molecules were thought to form a rigid ice-like cage
enclosing the hydrophobic particle. This shell preserves hydrogen bonding at the cost
of entropy. The effective attraction between hydrophobic particles was then seen as
an entropic force resulting from the release of some water molecules when two shells
overlapped. However Blokzijl and Engberts [1.3] found no increase in ordering of
water around hydrophobic particles, indicating that a different explanation was
required.
In 1973, Stillinger presented a new theory to qualitatively explain what
happens to water near hydrophobic objects [1.4]. Based on calculations from scaledparticle theory that explicitly includes “the strong and directional hydrogen-bonding
forces in water”, he suggested that large hydrophobic objects will be surrounded by a
“thin film of water vapor”. He predicted that the water in direct contact with the
object would have a density that is only 50,000 times less than that of bulk water.
Furthermore, if the external pressure is close to the saturated vapor pressure for the
given temperature, the film can be thick on the molecular scale because there is
“essentially no driving force to eliminate the vapor film”.
3
Stillinger envisioned quite a different picture of water around small
hydrophobic particles [1.4]. He believed the water would reorganize where possible
to restore a hydrogen-bonding network. So instead of the hydrogen bonds near a
small hydrophobic particle breaking, they would simply go around the particle. This
reorganization costs entropy because the number of accessible states has been
decreased, but it is much less than the cost of breaking hydrogen bonds.
Lum, Chandler and Weeks [1.5] put forth another theory of hydrophobic
interactions. Like Stillinger, they predicted different interactions for hydrophobic
objects at large and small length scales. However their theory does not include
hydrogen bonds; in fact, it is generic to any confined fluid. For small hydrophobic
particles they believe water can reorganize around the voids created in the solvent to
maintain its density. At larger length scales the reorganization is more difficult and
maintaining the density is impossible. As a result, a layer of water with a density less
than bulk is formed at the interface. They predict that the crossover between small
and large behaviors occurs on the nanometer length scale.
If this low density depleted region exists it would be very important. It would
have many implications not only in scientific areas such as protein folding, colloidal
self-assembly, and the boundary conditions of fluid flow; but also in technological
areas such as microfluidics, hard-disk design, and drug delivery.
Another phenomena associated with hydrophobic water interfaces, is the socalled hydrophobic interaction. This is where two or more hydrophobic bodies in
water experience a net attraction over long length scales.
These long range
interactions are observed to occur in surface forces experiments at distances up to 100
4
nm [1.6].
Stillinger’s theory does not explain these long-range hydrophobic
interactions [1.4].
However, Lum, Chandler and Weeks [1.5] do propose a
mechanism for these long-range interactions. As two hydrophobic objects approach
one another, fluctuations in the surrounding low-density layers can expel the
remaining water, creating a low density pocket connecting the two objects. The
resulting pressure imbalance on the objects pushes then together, creating an effective
attraction. If the combined vapor layers are large, as Lum, Chandler and Weeks
believe it is for water at ambient conditions, this effective attraction explains longrange hydrophobic interactions.
Attard and Tyrrell [1.7] suggest long-range hydrophobic attractions are caused
by the presence of nanobubbles. In their view, as two hydrophobic surfaces approach
one another the nanobubbles can bridge the distance and the bridging meniscus then
pulls the surfaces together.
Attard and Tyrrell have imaged nanobubbles using
tapping mode Atomic Force Microscopy (AFM). They report the bubbles to be 20-30
nm high and have such a high surface coverage that it is hard to see the bare substrate.
They note that the height of the nanobubbles is comparable to the height at which the
hydrophobic surfaces jump into contact.
Two major difficulties exist with the nanobubble explanation.
First,
thermodynamics indicates that the bubbles cannot be in equilibrium because their
internal pressure is too high. According to the Laplace equation the internal gas
pressure of a 10 nm bubble would be 140 atm. Such a high pressure should cause the
nanobubbles to quickly dissolve. The second objection is that the AFM techniques
5
used to image these bubbles may in fact be nucleating the bubbles or breaking up a
continuous vapor layer.
The dynamics of the depletion layer are of great interest. Lum, Chandler and
Weeks postulate that it is the fluctuations more than the depletion layer itself that
cause the attraction of large hydrophobic objects [1.5]. Also, these dynamics are of
great importance in understanding the kinetics of protein folding and self-assembly.
Chandler and ten Wolde show that it is solvent fluctuations that cause hydrophobic
polymers to go from an extended coil to a collapsed globule, since the nucleus is
stabilized by the formation of a “vapor bubble” [1.8]. More fundamentally, Chandler
proposes that fluctuations are the key distinguishing factor between wet and dry
interfaces [1.9].
1.2 Simulations of Water/Hydrophobic Interfaces
Many computer simulations have been done to try to uncover the causes of the
different hydrophobic effects. The simulations do not always present a consistent
picture. Many groups have looked at water confined between two hydrophobic
surfaces. In 1995, Wallqvist and Berne [1.10] reported that their constant-pressure
molecular dynamics simulation showed a dewetting transition between large
hydrophobic particles (volume ~ 40 water molecules) when they where brought
closer than two water layers.
Bratko et al. [1.11] also studied the spontaneous
evaporation between large hydrophobic particles. Using an ambient-pressure, Grand
Canonical ensemble simulation, they report the onset of evaporation at three water
layers. Barrat and Bocquet saw a region of depleted density in their molecular
6
dynamics simulation, changing the properties of flow at the interface [1.12]. On the
other hand, Choudhury and Pettitt saw a stabilized water layer, and not dewetting,
when water was confined between graphite surfaces [1.13]. Simulations done for
water inside hydrophobic carbon nanotubes also showed stabilized water structures
[1.14, 1.15].
Others have done simulations looking for a vapor layer without confinement.
In their 2003 paper, Huang et al. observed a vapor layer approximately 0.3-nm thick
forming around a nano-sized hydrophobic object [1.16].
They used a constant
temperature and pressure molecular dynamics simulation. Wallqvist, Gallicchio and
Levy [1.17] also saw a vapor layer form when water was enclosed inside a
hydrophobic cavity. The vapor layer was 0.4 nm thick for purely repulsive waterwall interactions. However when they added a dispersion attraction to the water-wall
interaction, the vapor layer thickness decreased to less than 0.1 nm and the water
seemed to contact the wall.
Research looking at the dynamics of the depletion layer is more rare, although
understanding the dynamic behavior has implications for everything from micelle
formation to protein folding. The simulation done by Huang, Margulis and Berne
showed that a large-scale drying fluctuation was the rate-determining step in
hydrophobic collapse [1.16]. The Janus interface, where water is confined between
hydrophobic and hydrophilic surfaces, was simulated by Thomas McCormick [1.18].
The simulation tests whether the large fluctuations observed by Zhang et al. [1.19]
were caused by fluctuations in the liquid/vapor interface. Using a lattice gas model,
McCormick found that the interface also fluctuates up to twenty-five percent of its
7
mean and displayed similar power spectrum to that found experimentally, although
the power law is less rapidly decaying function of frequency than observed by Zhang
et al. In the simulation, the fluctuations in the mean were caused by fluctuations in
the interface over length scales from 1.5 to 20 nm.
Grunze and Pertsin have recently simulated the Janus interface using the
Grand Canonical Monte Carlo technique (GCMC) [1.20]. They also observed a low
density layer at the hydrophobic wall.
More interestingly, they found giant
fluctuations in the number of particles near this wall.
They referred to this
phenomenon as a “wandering interface” because the liquid/vapor interface changes
position between GCMC runs causing the large fluctuations.
Some of the controversies surrounding simulations of hydrophobic
interactions can be resolved by realizing the strength of the water-solute interaction
drastically changes the properties of the depletion layer. Huang et al. found that the
critical distance (Dc) at which the drying transition occurs changed with contact angle
(θc) [1.21]. See Figure 1.2. Simulations with purely repulsive interactions would
have θc=180o. Those simulations which included idealized attractions in the watersolute interaction would have θc=148o.
The paraffin films as modeled by Huang et
al. have θc=115o, while the graphite films used by Choudhury and Pettitt have θc=83o.
The critical distance for the graphite system would be expected to be much smaller
than one layer of water and therefore should not be observed.
Still not all the discrepancies can be explained by the effect of the water
surface interactions. Furthermore, it is unclear which model to use when simulating
water.
Wernet et al. found that many molecular dynamics simulations deviate
8
significantly from experiment [1.22]. In fact they all yield much higher fractions of
tetrahedrally coordinated water than observed experimentally.
This uncertainty
makes experimental observation all the more important.
1.3 Previous Experiments on Water/Hydrophobic Interfaces
In the years following the theoretical prediction of a low density layer when
water meets a hydrophobic surface, many people have tried to determine whether or
not it exists.
Experimental results have been inconsistent.
Some have been
interpreted in favor [1.23-1.27], some as indicating intimate solid-water contact in
places and ‘nanobubbles’ in others [1.7, 1.28], and some against the existence of the
vapor layer[1.29-1.31].
Using an elegant approach, Sur and Lakshminarayanan
provided experimental evidence for the existence of an interfacial vapor layer [1.23].
They found that electrodes coated with hydrophobic layers demonstrated unusually
low interfacial capacitance in water, which was not present in similar systems with
hydrophilic coatings. They attribute this behavior to a “hydrophobic gap” that in
essence creates an additional capacitor in series with the one created by the film,
effectively lowering the capacitance. Unfortunately, they have not been able to
analyze their results in terms of thickness or density of the vapor layer. Castro et al.
observed a depletion layer at the hydrophobic/water interface, using ellipsometry
[1.26]. On thin polystyrene layer (~65 nm), they found a 5 – 10 Å fully depleted
layer. However they saw no depletion on thicker (~300 nm) polystyrene layers.
Recently, groups have probed the interface using reflection techniques.
Reflection techniques, namely neutron and X-ray reflectivity, are good in that the
9
wavelength employed is on the same order as the predicted thickness of the interfacial
layer. Steitz et al., using neutron reflectivity, observed a non-vanishing scattering
contrast at the interface between deuterated water and polystyrene even though the
materials have matching scattering length densities [1.24]. They explain their result
with the addition of a 2-5 nm region consisting of 88-94% bulk water density. In
another neutron reflectivity experiment, Schwendel et al. found a 2-nm layer
consisting of 9% bulk water density between water-deuterated water mixtures and
alkylated surfaces [1.25]. However they believe that this very low-density layer may
be due to air inclusions. Doshi et al. have seen a reduced density layer adjacent to a
hydrophobic surface using neutron reflectivity [1.27]. They found that the thickness
of the depleted region depended on whether the water contained dissolved gases.
Ambient water produced an 11 Å depletion layer, while degassed water bubbled with
argon had a 2 Å depletion layer.
Using X-ray reflectivity, Jensen et al. were unable to quantitatively establish
the existence of a depletion layer as they had low contrast between their hydrophobic
layer and water [1.30]. Even though they doubt the existence of the layer, they say
that if it does exist they think it would be much thinner than observed by others [1.24,
1.25], with a density near 90% of bulk water and only 0.1 nm thick. Others have also
reported not finding a depleted region. Using ellipsometry, Ducker et al. found that if
the vapor layer was pure air then it would be less than 0.1 nm thick [1.29]. Takata et
al. preformed a very careful ellipsometric study of a hydrophobic alkylsilane
submerged in water and also found no evidence for a vapor layer [1.31].
10
These experimental ambiguities stem partially from different interpretations of
what is means to have a hydrophobic surface.
The effect of dissolved gases,
roughness and surface stability could also be clouding the issue. In Chapter 3, we
explore the static effects different variables have on the depleted region.
There has been less work done on the dynamic properties of the
hydrophobic/water interface. One of the few measurements on the dynamics, an
indirect measurement looking at the change in the force response versus time, was
done by Zhang, Zhu and Granick [1.19]. While studying a Janus interface, they
found films whose viscous response typically fluctuated by twenty-five to fifty
percent of the mean value. They also observed that the power spectrum of the noise
displayed power law behavior, and decayed as 1/f2.
It is surprising that these
fluctuations did not average out over the experimental area of ten microns. A more
direct measurement of the fluctuation themselves, has yet to be made.
1.4 References:
[1.1] “Mars Exploration Rover Mission”
NASA Jet Propulsion Laboratory,
California Institutute of Technology <http://marsrovers.nasa.gov/science/ >, May 23
2006
[1.2] CRC Handbook of Chemistry and Physics: Special Student Edition, 77th Edition
(CRC Press Inc., Boca Raton, FL; 1996)
[1.3] Blokzijl, W., and J.B.F.N. Engberts Angewandte Chemie International Edition
in English 32 1545 (1993)
[1.4] Stillinger, F.H. Journal Solution Chemistry 2 141 (1973)
11
[1.5] Lum, K., D. Chandler and J.D. Weeks Journal of Physical Chemistry B 103
4570 (1999)
[1.6] Israelchvili, J. Intermolecular and Surface Forces; Second Edition (Academic
Press, San Diego, CA; 1992)
[1.7] Tyrrell, J.W.G., and P. Attard Physical Review Letters 87 (17) 176104-1 (2001)
[1.8] ten Wolde, P.R., and D. Chandler Proceedings of the National Academy of
Science 99 6539 (2002)
[1.9] Chandler, D. Nature 437 640 (2005)
[1.10] Wallqvist, A., and B.J. Berne Journal Physical Chemistry 99 2893 (1995)
[1.11] Bratko, D., R.A. Curtis, H.W. Blanch and J.M. Prausnitz Journal of Chemical
Physics 115 (8) 3873 (2001)
[1.12] Barrat, J.-L., and L. Bocquet Physical Review Letters 82 (23) 4671 (1999)
[1.13] Choudhury, N., and B.M. Pettitt Journal of the American Chemical Society 127
3556 (2005)
[1.14] Hummer, G., J.C. Rasaiah and J.P. Noworyta Nature 414 188 (2001)
[1.15] Sansom, M.S.P., and P.C. Biggin Nature 414 156 (2001)
[1.16] Huang, X., C.J. Margulis and B.J. Berne Proceedings of the National Academy
of Science 100 (21) 11953 (2003)
[1.17] . Wallqvist, A., E. Gallicchio and R.M. Levy Journal of Physical Chemistry B
105 6745 (2001)
[1.18] McCormick, T.A. Physical Review E 68 061601 (2003)
12
[1.19] Zhang, X., Y. Zhu and S. Granick Science 295 663 (2002)
[1.20] Grunze, M., and A. Pertsin Journal of Physical Chemistry B 108 (42) 16533
(2004)
[1.21] Huang X., R. Zhou and B.J. Berne Journal of Physical Chemistry B 109 3546
(2005)
[1.22] Wernet, Ph., D. Nordlund, U. Bergmann, M. Cavalleri, M. Odelius, H.
Ogasawara, L.Ǎ. Näslund, T.K. Hirsch, L. Ojamäe, P. Glatzel, L.G.M. Pettersson and
A. Nilsson Science Express Reports (1 April 2004)
[1.23] Sur, U.K. and V. Lakshminarayanan Journal of Colloid and Interface Science
254 410 (2002)
[1.24] Steitz, R., T. Gutberlet, T. Hauss, B. Klösgen, R. Krastev, S. Schemmel, A.C.
Simonsen and G.H. Findenegg Langmuir 19 2409 (2003)
[1.25] Schwendel, D., T. Hayashi, R. Dahint, A. Pertsin, M. Grunze, R. Steitz and F.
Schreiber Langmuir 19 2284 (2003)
[1.26] Castro, L.B.R., A.T. Almeida and D.F.S. Petri Langmuir 20 7610 (2004)
[1.27] Doshi, D.A., E.B. Watkins, J.N. Israelachvili and J. Majewski Proceedings of
the National Academy of Science 102 9458 (2005)
[1.28] Ishida N., T. Inoue, M. Miyahara and K. Higashitani Langmuir 16, 6377
(2000)
[1.29] Mao, M., J. Zhang, R. -H. Yoon and W.A. Ducker Langmuir 20 1843 (2004)
[1.30] Jensen, T.R., M. O. Jensen, N. Reitzel, K. Balashev, G.H. Peters, K. Kjaer and
T. Bjørnholm Physical Review Letters 90 (8) 086101-1 (2003)
[1.31] Y. Takata, J.H.J. Cho, B.M. Law and M. Aratoni Langmuir 22 1715 (2006)
13
1.5 Figures
θ
Figure 1.1 Illustration of Water at a Hydrophobic Surface
Water will bead up when placed on a hydrophobic surface. The degree of
hydrophobicity can be measured by the contact angle, θ. The contact angle is defined
as the angle between the surface and the tangent to the drop.
14
180
148
115
90
Figure 1.2 Critical Distance versus Ellipsoid Radius
The critical distance (Dc) is plotted versus the ellipsoid radius (σ) for different
contact angles (θc). The critical distance decrease with contact angle and is not
expected to be observable at lower contact angles.
Reference 1.21.
15
The figure is taken from
Chapter 2: Experimental Techniques
Since Stillinger’s first prediction of a low-density depletion layer forming at
hydrophobic interfaces [2.1] and especially after Lum, Chandler and Weeks further
advancement of the idea [2.2], many people have tried to test this theory. However
direct measurement of phenomena at the water/hydrophobic interface is not
straightforward in the least.
In fact, studying the depletion layer requires techniques that must meet several
criteria. The first of which is the ability to perform in-situ measurements in an
aqueous environment. With many experimental techniques this means that the probe
beam and resulting signal must travel through the water. In this case it is important to
ensure the beam has sufficient energy to penetrate the bulk water without being
significantly diminished.
Also, a sample cell that keeps the liquid in contact with the substrate must be
employed.
This is more difficult than it first appears as the sample is very
hydrophobic. Hence, one must counteract the tendency of the water to bead up and
roll off the surface. There are two main strategies to overcome this problem. The
first is to completely submerge the sample in water, ensuring that there is too much
water to form a stable drop. The second strategy is to use a hydrophilic surface to pin
a thinner layer of water to the surface.
Secondly, the experimental technique must be able to distinguish the depletion
layer from the bulk. Both the bulk and depletion layer are formed of water and are
thought only to differ in their densities. Accordingly, the technique must be able to
detect differences in density. This can be done by measuring the mass density (as in
16
neutron reflectivity), the electron density (as in X-ray reflectivity), or the optical
density (as in ellipsometry).
Two more requirements arise from the fact that the depletion layer is posited
to be several Angstroms to nanometers in thickness. Obviously, in order to observe
the depletion layer, the technique employed must have sub-nanometer resolution.
This rules out diffraction limited techniques in the optical wavelengths. Also, as the
depletion layer is so much smaller than the bulk layer; the signal from the bulk can
quickly overwhelm the depletion layer’s signal. This is why studying hydrophobic
interfaces requires surface selectivity.
Finally, in order to investigate dynamics at the interface, the experimental
technique needs to be able to collect information over a wide range of time scales.
Very little information exists on the time scales that will be important for
hydrophobic interactions, therefore it is essential to explore as many as possible.
2.1 Ellipsometry
When light is reflected off a planar interface, the polarization of the light
changes.
Exactly how the polarization changes depends on the structure of the
interface and the incident conditions of the light. For example, initially unpolarized
light reflected off a sharp interface will become completely polarized in the direction
perpendicular to the plane of incidence at the Brewster angle.
In ellipsometry, we measure this change in polarization, and use it to
determine the structure of the sample. The quantity ellipsometry measures is called
the ellipticity ( ρ ) and it is equal to the ratio of the parallel to the perpendicular
17
reflection coefficient. Phase-modulated ellipsometry makes use of the Brewster angle
to simplify experimental measurements. At the Brewster angle, the real part of ρ
vanishes making ρ equal to the imaginary part of the reflection coefficient ratio, as
given in Equation 2.1
⎛ rp
⎝ rs
ρ = Im⎜⎜
⎞
⎟⎟
⎠
(2.1)
where rp and rs are the complex reflection amplitudes for the electric field
vectors pointing parallel and perpendicular to the plane of incidence, respectively. At
the Brewster angle, rp (and therefore ρ ) will be zero for a sharp interface between
two semi-infinite slabs of constant dielectric coefficient. However, if a thin layer
with a different dielectric coefficient or a more gradual interface is added to the
system, ρ will be non-zero.
In this case, and assuming the interfacial layers are thin compared to the
wavelength of light, ρ can be interpreted rather simply with the Drude equation
[2.3].
ρ=
π ε 1 − ε 3 [ε 1 − ε ( z )][ε ( z ) − ε 3 ]
dz
λ ε1 + ε 3 ∫
ε ( z)
(2.2)
where ε(z) is the optical dielectric profile at a distance z from the substrate, λ is the
wavelength of light and ε1 and ε3 are the optical dielectric constants of the incident (z
→ ∞) and the substrate (z → - ∞) materials. The Drude equation will only hold if the
imaginary part of the dielectric profile is smaller than the real part. This condition is
satisfied for most materials with the main exceptions being metals, which have a very
18
large imaginary component. The Drude equation also assumes that the interfaces are
roughly parallel and flat to minimize scattering.
Ellipsometry is well suited to studying the hydrophobic/water interface. First,
it is very sensitive to the conditions at the surface. It can distinguish the density
difference between the bulk and depleted layer; since in a multi-component layer, the
dielectric constant is related to volume fraction of each component. As can be seen
from the Drude equation (Equation 2.2) the thickness sensitivity of the ellipsometer
depends on the dielectric coefficient of the layer in question. The highest sensitivity
would be achieved for a depletion layer consisting of pure vacuum, and would
decrease as the layer approached the density of bulk water. Still, even if the density
of water was 90% that of bulk water, we would still have sub-Angstrom sensitivity (~
0.6 Å). By using a special vertical sample cell, described by Mukhopadhyay and Law
[2.4], we can make in situ measurements in an aqueous environment. Also the
vertical configuration allows us to submerge the hydrophobic sample under water.
The greatest advantage of using a phase-modulated ellipsometer is that it allows
dynamic measurements to be made. The phase modulator and lockin amplifier enable
the signal to be averaged over only 30 ms giving us improved time resolution.
Moreover using a phase modulated ellipsometer means that we do not have to vary
the incident angle or wavelength in order to measure ρ . This permits us to repeat
measurements very quickly, on order of 50 Hz.
The vertical sample cell has additional features which allow us to study other
aspects of the hydrophobic/water interface. The sample cell has apertures that allow
19
the introduction of different apparatus; such as a temperature probe, a pH probe or the
inlet and outlet tubing required for in situ fluid exchange.
We have also added a special radiative sample heater, designed by Jim Wentz.
The sample heater works by heating the metal sample holder by conduction. The
sample holder then radiates the heat, symmetrically warming the glass sample cell.
We need symmetric heating for two reasons.
First, we want to minimize any
temperature gradients in the glass as this would distort the light entering and exiting
the sample cell. Second, we want to avoid setting up convection currents within the
sample. The sample heater is capable of keeping the sample cell at temperatures up
to 55 oC stable within 0.1 oC for over an hour.
Cooling the cell has proved more difficult. We have only managed it for
static measurements, where the temperature only needs to remain constant for a few
minutes. For cooling, we start by refrigerating the assembled sample cell before
placing it in the ellipsometer. Also we cool the sample holder by placing it into
contact with ice. In this way we have been able to measure temperatures as low as 10
o
C.
For all its benefits ellipsometry also has its limitations. One restriction is that
not all materials have a real Brewster angle. In order for a material to have a real
Brewster angle, the imaginary component of its dielectric coefficient must be small
compared to the real component.
For example, metals have a large imaginary
component in their dielectric coefficient, and therefore they do not have a real
Brewster angle.
Without a Brewster angle the Drude equation is invalid, and
20
Maxwell’s equations must be solved numerically. For our systems this requires
solving a 4 x 4 complex exponential matrix with six unknowns.
Even when the Drude equation is appropriate, it does not offer a unique
solution for the dielectric profile of the sample from one measurement. We can
overcome this problem to some extent by measuring ρ as the sample is constructed
or by using multiple-index medium technique (MIM) as described by Mao et al. [2.5].
Measuring ρ during construction allows the dielectric profile to be built up step by
step with the sample. MIM makes use of the fact that the Drude equation depends
heavily on the index of the surrounding media, which can be changed without
changing the dielectric profile of the interfacial layers. However there is no way to
find both the thickness and dielectric constant of the depletion layer from our
measurements of ρ . The best we can do is to confine the value to a region of
thickness and index of refraction, and even this depends on how we model the
interface.
Our home-built phase-modulated ellipsometer, pictured in Figure 2.1, is
molded after the one described by Mukhopdhayay [2.6]. It consists of a very stable 2
mW Helium-Neon laser (λ=632.8 nm) which is used as the light source. The initial
polarization of the light is set to p + 45o, where p denotes the direction parallel to the
plane of incidence, by the polarizer. Next, the phase modulator adds a sinusoidally
varying phase shift to the p-component of the electric field. At this stage the electric
field vector (E) can be written as,
E=Eo (s + e iδo sin
ωot
p)
(2.3)
21
where Eo is the amplitude of the electric field, s denotes the direction perpendicular to
the plane of incidence, δo is the amplitude of the phase shift, and ωo is the phase
shift’s angular frequency. The phase modulator is driven with a frequency (ωo/2π) of
50.1 kHz. The light is then reflected off the sample.
Reflection from the sample changes the amplitude and phase of each
component of the electric filed, embedding information on the interface into the light.
The electric field vector can now be written as
E=Eo (rso eiδs s +rpo e i(δp + δo sin
ωot)
p)
(2.4)
where δs/p and rs/po are the phase and amplitude shifts of the s and p components of the
electric field respectively. Next the light is incident on the analyzer. The analyzer is
rotated between two positions, p + 45o and p - 45o. At p + 45o, the electric field is
proportional to the sum of the s and p components of the electric field; while at p 45o, the electric field is proportional to the difference of the s and p components of the
electric field.
Finally the photomultiplier tube (PMT) measures the intensity of the light.
Intensity (I) is proportional to the amplitude squared of the electric filed vector as
written in Equation 2.5.
(
I ≈ rso2 + rpo2
)
⎡ 2 rso rpo
⎤
(
)
cos
δ
sin
ϖ
Δ
+
t
⎢1 ± 2
⎥
o
o
2
⎣⎢ rso + rpo
⎦⎥
(2.5)
where the upper and lower signs refer to p + 45o and p - 45o respectively, and Δ is the
relative phase shift between p and s (i.e. Δ=δp-δs). At the Brewster angle, Δ is
defined to be ± π/2. Using Bessel functions, the cosine term can be expanded as
shown in Equation 2.6.
22
cos (Δ+δo sin ωot)= cos Δ [Jo(δo) + 2 J2(δo) cos 2ωot + . . .]
-sin Δ [2 J1(δo) sin ωot + 2 J3(δo) sin 3ωot + . . .]
(2.6)
We adjust δo with the phase modulator such that Jo(δo) = 0. In this case, Equation 2.6
becomes
I ≈ (rso2 + rpo2 ) [1 ∓ 2 a J 1 (δ ο ) sin (ϖ ο t ) sin Δ ± 2 a J 2 (δ ο ) cos (2ϖ ο t ) cos Δ + …]
(2.7)
where a is given by
a= 2
rso
1
.
rpo 1 + (rso rpo )2
(
)
(2.8)
At the Brewster angle, (rso/rpo) is much less than unity and a can be approximated as
a ≅ 2 (rso rpo ) ,
(2.9)
so
⎛ rp
a sin Δ ≅ 2 Im⎜⎜
⎝ rs
⎞
⎟⎟ = 2 ρ .
⎠
(2.10)
By using circuitry to keep the DC component of the PMT current (IPMT,DC) constant,
the output current of the PMT (IPMT) can be given by Equation 2.11.
IPMT = IPMT,DC [1 ∓ 4 J 1 (δ ο ) ρ sin (ϖ ο t ) ± 2 a J 2 (δ ο ) cos (2ϖ ο t ) cos Δ + …]
(2.11)
After the PMT, the signal is given to the lockin amplifier. The voltage
delivered to the lockin is proportional to the A.C. components of IPMT. The lockin
23
amplifier can easily measure the amplitudes of the components oscillating at ωo (Vωo)
and 2ωo (V2ωo). From Equation 2.11, we see that Vωo and V2ωo can be written as
Vωo = ± (-2 ) b J1(δo) ρ
(2.12)
V2ωo = ± 2 a b J2(δo) cos Δ,
(2.13)
where b is a constant of proportionality, and the upper and lower signs refer to p +
45o and p - 45o respectively.
When taking data with the ellipsometer, V2ωo is used to find the Brewster
angle. In theory, this could be accomplished by making V2ωo zero for both analyzer
polarizations. However in practice there is always some small residual signal that
keeps V2ωo non-zero, due to the non-ideal nature of the phase modulator [2.7]. So
instead, we adjust the incident angle of the light until V2ωo reads the same small value
for p + 45o and p - 45o. At the Brewster angle we can use Vωo to find ρ . From
Equation 2.12 we see,
ρ=
Vϖ ο + + Vϖ ο −
2
∗
1
(2.14)
2ω ocal
where ωocal is given by
ωocal =b*J1(δo)
(2.15)
and Vωo+ and Vωo- refer to Vωo measured at p + 45o and p - 45o respectively. The
value of ωocal is independent of the experiment and is simply a constant determined
during the calibration (see Appendix A for details).
24
During static measurements, a computer program, “Ellipsometer”, is used to
collect Vωo and V2ωo, at both polarizations and calculate ρ . The program measures a
user specified number of ρ ’s (usually between six and ten), and computes the mean
and standard deviation of ρ .
The dynamic measurements are made slightly
differently. First, ρ is measured. Then with the analyzer polarization fixed, Vωo is
measured and recorded continuously by the computer program “Fastpoll” for a user
specified amount of time. The collection speed of “Fastpoll” is determined by the
speed at which the DAC card can query the lockin and record the data. This usually
results in a data collection frequency around 50 Hz. After “Fastpoll” has finished
collecting data, ρ is re-measured.
The file collected is in the form of voltage versus time. In order to convert
this into ellipticity, we must first find the average voltage (V2) from the other
analyzer position, which can be calculated from the average voltage collected and ρ
measured before and after collection. Usually the first and second measurement of
ρ agree and the collected data is flat. If not a linear fit is used to calculate a time
dependent V2. From V2 and the collected voltage the ellipticity can be calculated for
the entire time series.
2.2 X-Ray Reflectivity
The reflection of X-rays from a surface is governed by the same fundamental
physical equations as the reflection of visible light.
The main difference is in
wavelength; visible light has a wavelength on the order of several hundred
25
nanometers while X-rays have wavelengths around several Angstroms. In both cases,
after reflection information on the structure of the surface is embedded in the photons.
For example all photons reflected from a thin film will experience complete
destructive interference if the path lengths of the photons reflected from the two
surfaces differ by an odd multiple half a wavelength. Accordingly, X-rays are able to
probe smaller structures than visible light.
The experimental technique of specular X-ray reflectivity makes use of these
facts to probe interfaces. X-rays with a wave number ki are incident on the surface
with an angle α. The X-rays reflected off the surface with a wave number kf at the
same angle are measured. See Figure 2.2 a. The specular reflectivity, R, is defined as
the ratio of reflected to incident X-ray flux.
In X-ray reflectivity, the specular reflectivity is measured as a function of the
momentum transfer, Q. Q is defined as the vectorial difference between ki and kf. As
can be seen in Figure 2.2 b, it is perpendicular to the sample surface. The momentum
transfer is related to the incident angle of the X-rays. It is given by
Q=
4π
λ
sin(α)
(2.16)
where λ is the wavelength of the X-rays. The reflectivity is directly related to the
electron density profile in the surface-normal direction, ρ(z).
R∝
iQ z
∫ ρ (z )e dz
2
(2.17)
where z is the distance perpendicular to the surface. For a single, perfectly flat, sharp
interface the reflectivity is proportional to Q-4. However, multiple interfaces give rise
to interference, which can be seen as a series of dips and peaks on top of the Q-4
26
decay of the Fresnel reflectivity. These dips are called Kiessig oscillations. The
depth and spacing of the oscillations provide information on the thickness and density
of the different layers. The position of the first dip is a good way to estimate the layer
thickness, D.
D=
π
(2.18)
Qmin
where Qmin is the momentum transfer at which the first dip in the reflectivity occurs.
To analyze our reflectivity data we used a fitting program called Parrot 32,
distributed by the Hans-Meitner Institute, Berlin. It uses the Parratt formalism [2.7]
to make least-squares comparisons between experimental and calculated reflectivities.
Basically, the fitting works by assuming an initial model, calculating a reflectivity
curve, and comparing it to the experimental data. Then the model is changed and if
the change brings the model closer to the data, it is kept. This process iterates until
the fit converges, and until additional changes only worsen the agreement of the
calculated and experimental curves.
Specular X-ray reflectivity meets the requirements for testing the hypothesis
of a depletion layer; it has sub-nanometer resolution, surface selectivity, and high
sensitivity to changes in interfacial density profiles. Using a special sample cell we
were able to keep the water in place over our very hydrophobic samples. In our ‘thinfilm’ cell, the sample was held in by an 8 μm thick Kapton membrane which also
confines a ≈ 2 μm thick water layer [2.8] against the surface. The surfaces were so
hydrophobic that the sample cell had to be assembled underwater. Otherwise either
the water would completely dewet the surface and roll off or air bubbles would be
trapped under the Kapton film.
27
The biggest benefit to X-ray reflectivity over ellipsometry is its ability to
decouple thickness and density. It also provides information on the lateral properties
of the surface, which is averaged out in ellipsometry.
However, X-ray reflectivity also has its limitations. First, it is more difficult
to look at the dynamics of the interface with X-ray reflectivity. One reason for this is
the sample is damaged after continued X-ray exposure. Also, unlike ellipsometry it is
not a table top experiment. In fact the experimental apparatus is over a kilometer in
circumference. The X-ray measurements were performed at the Advanced Photon
Source (BESSRC/XOR beam line 12 BM) at Argonne National Laboratory, in
collaboration with Ian Robinson, Zhan Zhang and Paul Fenter.
2.3 Surface Plasmon Resonance
When light is reflected from an interface between materials with different
dielectric coefficients, the reflected intensity depends on the angle of incidence. This
dependence is described by the Fresnel equations [2.9].
⎛ n cos θ i − n1 cos θ t
R p = ⎜⎜ 2
⎝ n2 cos θ i + n1 cos θ t
⎛ n cos θ i − n2 cos θ t
Rs = ⎜⎜ 1
⎝ n1 cos θ i + n2 cos θ t
⎞
⎟⎟
⎠
2
⎞
⎟⎟
⎠
(2.19)
2
(2.20)
where Rs and Rp denote the reflectivity for light incident with s and p polarizations
respectively, n1 is the index of refraction for the incident media, n2 is the index of
refraction for the transmittive media, θi is the angle of incidence with respect to the
interface normal, and θt is the angle of transmittance with respect to the interface
28
normal, assuming that the permeability of both materials is equal to the vacuum
permeability μo.
As can be seen from the Fresnel equations, if the light is incident from a
region with a higher index of refraction (that is if n1> n2) the reflectivity will be equal
to one for all angles above an angle, θc, given by
sin θc =
n1
.
n2
(2.21)
θc is called the critical angle, and the phenomenon where the reflectivity equals one is
termed total internal reflection.
Even though all the incident light is reflected in total internal reflection, the
intensity of the electromagnetic field in the region of lower refractive index is not
zero.
In fact, it oscillates parallel to the surface and decays exponentially
perpendicular to the surface; such a wave is named an evanescent wave. Griffiths
[2.9] shows that if the incident wave is p-polarized the electric field (E) will have the
form
E=Eo e-(z/l) e(iKxx-ωt)
(2.22)
where Eo is the amplitude of the field, z is the distance perpendicular to the surface
and x is the distance parallel to the surface, t is the time, ω is the angular frequency of
the light, l is the decay length, and Kx is the in-plane wave number. The decay length,
l, determines how far into the medium the evanescent wave penetrates. It depends on
the refractive index of the two media and the incident angle of the light. It is given by
l=
c
1
ϖ
n sin 2 θ i − n22
(2.23)
2
1
29
where c is the speed of light. The in-plane wave number determines how the wave
propagates along the interface. It is given by
K x = n1 ϖ c sin θ i
(2.24)
Evanescent waves have many uses. They can be used to excite dyes close to
the surface in Total Internal Reflection Fluorescence Microscopy. They are used in
Fourier Transform Infrared Spectroscopy in the mode of Attenuated Total Reflection
(FTIR-ATR) to take the vibrational spectrum of molecules near the surface. In
Surface Enhanced Raman Spectroscopy (SERS), they are the source of the
concentrated electric fields used to greatly enhance Raman signals. They can also be
used to excite surface plasmons.
Surface plasmons are longitudinal charge density waves that can be excited at
metal/dielectric interfaces.
Surface plasmons can also be thought of as density
fluctuations at the surface of a theoretical high-density electron liquid or plasma
[2.10].
The evanescent wave induces oscillations in the thin metal film’s free
electrons which in turn create an additional electromagnetic field [2.10]. This field
then propagates into the sample coated onto the film [2.10]. Figure 2.3, taken from
Knoll, depicts the electromagnetic field produced by the surface plasmon [2.11].
There are several conditions required for the excitation of surface plasmons.
First, surface plasmons can only be excited when a surface charge density is induced,
which requires an electric filed component perpendicular to the surface [2.11]. As spolarized light only has an electric field component parallel to the surface, only ppolarized light, which has electric filed components both parallel and perpendicular to
the surface, can be used to excite surface plasmons. Furthermore, the two materials
30
that make up the interface must have dielectric constants whose real parts have
opposite signs to excite surface plasmons [2.12]. Being as the dielectric constants of
metals are generally negative in the visible region, metal/dielectric interfaces are
suitable [2.12]. Finally, light reflected from a surface with an incident angle less than
θc never has sufficient momentum to excite surface plasmons. However, light from
an evanescent wave has higher momentum and under certain conditions can have
sufficient for surface plasmon excitation [2.11]. When all these conditions are met,
resonant coupling between the evanescent wave and surface plasmons can be
obtained. The coupling only occurs when the propagation constant of the surface
plasmon (κx) equals the in-plane wave number of the incoming light (Kx).
κ
2
x
=
ϖ
c
2
2
ε 2 (1 −
(ε
2
ϖ
+1−
2
p
ϖ
ϖ
2
p
2
ϖ
)
2
(2.25)
)
where ε2 is the dielectric coefficient of the sample and surrounding media, ωp is the
plasma frequency, and εg is the dielectric coefficient of the prism. Equation 2.25
assumes the dielectric coefficient of the metal is described by the Drude model. This
is a good approximation in the visible spectrum because the changes due to electronic
loses are small. The experimental technique, Surface Plasmon Resonance (SPR),
uses this condition combined with the Fresnel equations to determine the optical
thickness of the surface layers form the incident angle at which coupling occurs, or
resonance angle. Experimentally, the resonance angle can be determined by looking
at the reflected intensity as a function of incident angle. Since the coupling removes
energy from the evanescent wave, there is a dip in the reflected intensity at the
resonance angle.
31
SPR is another surface technique that is well suited to studying how water
meets a hydrophobic surface. It is capable of real time data collection, over many
time scales [2.13]. SPR has great surface sensitivity. Because the evanescent wave
decays perpendicular to the surface in a distance on the order of 200 nm, it only
interrogates the environment quite close to the surface. It also has a high resolution to
changes in thickness and refractive index in this region, which we saw in ellipsometry,
can be translated into changes in density. A standard SPR setup with a rotating prism
and photodetector typically has a resolution in the resonance angle of 10-2-10-3
degrees [2.14]. Finally, it is a non-intrusive technique, and requires no dye or sample
labeling [2.15].
Only two main modifications are required to use SPR for aqueous systems.
First, a higher refractive index prism was required in order to access the angles need
for resonance by high index aqueous solutions. Also, it is necessary to design a
special fluid cell. With it we can make measurements in fluid environments and
observe in situ monolayer growth. It also allows us to vary the bulk media without
disturbing the sample under investigation. It holds the sample substrate against the
fluid reservoir, and can be completely filled with water to ensure no macroscopic
dewetting occurs.
We built a SPR setup using the Kretschmann geometry with a rotating prism
for resonance angle detection. The setup is depicted in Figure 2.4. Light from a 2
mW helium-neon laser is split by a Glan laser polarizer. The p-polarized light is
transmitted and the s-polarized is reflected. We use the reflected light to remove long
time scale fluctuations of the laser from our dynamics measurements.
32
The p-
polarized light then passes through an iris which is used to control the area probed by
the surface plasmons. The incident angle of the light when it hits the prism is
controlled by the rotation stage. Here the light is totally internally reflected, creating
an evanescent wave which excites surface plasmons in the sample. The intensity of
the reflected light is measured by detector 1. Neutral density (ND) filters are used
before both detectors to prevent saturation and to improve signal-to-noise ratios in
fluctuation measurements.
Static measurements are made by measuring the intensity of reflected light for
a range of incident angles. In this way, we can determine the resonance angle and the
shape of the resonance curve. The resonance curve can then be compared to curves
theoretically calculated curves. In this way we can get some idea of the absolute
values for thickness and refractive index of our samples. True quantitative analysis
can only be done for the relative changes in our samples.
Dynamic measurements are made somewhat differently. As we cannot hope
to measure multiple angles quickly enough to see fluctuations on the time scale
desired, we instead sat at a fixed angle and measured changes in reflectivity. The
changes in reflectivity correspond to changes in resonance angle as illustrated in
Figure 2.5. In order to remove long time scale fluctuations, we added an additional
detector to measure the laser intensity. We can then divide the incident and reflected
intensities to get the reflectivity more accurately. The collection and division of the
signals was done with a lockin amplifier. The data was then transferred into the
computer and recorded. Sung Chul Bae provided immense help and guidance in
33
implementing the dynamic measurements as well as creating the programs to collect
and analyze the data.
2.4 Hydrophobic Substrates
Almost as important as choosing the proper experimental technique is
choosing appropriate hydrophobic surfaces. In order to maximize our chances for
observing the elusive depletion layer, we want to ensure that our surface is as close to
those studied by simulation as possible. We also desire very robust samples to ensure
that any changes in the surface do not mask the presence of the depletion layer.
First, the substrates must be very hydrophobic. Wallqvist et al. showed in
simulations that the strength of the interaction between the water and the surface can
drastically change the thickness of the depletion layer [2.16]. They found that simply
adding a dispersion attraction could decrease the thickness of the vapor layer to 1 Å
from 4 Å. Huang et al. also found a strong dependence of the depletion layer on
contact angle [2.17].
In practice, we use samples with contact angles between 97o
and 110o.
Next, the samples must be well ordered, meaning that they must be fully
coated and densely packed. Surfactant-coated surfaces were used in some earlier
studies, but our selection of a chemically-attached monolayer circumvents the
potential complication that surfactant-coated solid surfaces may reconstruct to form
complex new morphologies when placed in water [2.18, 2.19]. The conformational
changes of loosely packed surfaces make it extremely difficult to decouple the small
34
change due to the depletion layer from the large change due to the substrate
rearrangement.
Also, the sample must be strongly attached to the surface. This helps prevent
rearrangement as noted earlier but it also ensures that the dynamics are stable. If the
surface is not strongly attached to a rigid surface, any fluctuations in the depletion
layer may be coupled into much smaller movements of the layer itself. It would be
extremely difficult to measure these movements.
Finally, the sample must be coated on substrates appropriate for the
experimental technique for which it is used. In the case of ellipsometry and X-ray
reflectivity, silicon wafers are the best choice.
They meet the ellipsometric
requirements for smoothness, dielectric coefficient, and reflectivity. Having a well
defined crystal structure and an electron density about half of water makes them well
suited to X-ray reflectivity. SPR requires a metal-coated transparent substrate that
can be index matched to the prism; therefore we use gold coated high-index flint glass
slides.
On
silicon
wafers
we
use
self-assembled
monolayer
of
n-
Octadecyltriethoxysilane (OTE). OTE is a methyl terminated molecule consisting of
an eighteen carbon chain and a silane head group. It is the head group that allows
OTE to form well packed monolayers that are chemically bound to the silicon
surface. Each head group can form three silicon-oxygen chemical bonds. It can
make theses bonds either with other OTE molecules or with the substrate. So OTE
basically forms a two-dimensional network that is chemically anchored to the silicon
surface. Using the methods described by Hong et al. near perfect, highly hydrophobic
35
monolayer were produced [2.20]. These surfaces have a root mean squared (RMS)
roughness less than 2 Å. The OTE surfaces were characterized using AFM and
contact angle measurements.
One of the large drawbacks in using OTE is that while very good layers are
possible, the process is difficult, as silane chemistry is not fully understood, and the
success rate is low. Another problem is that it is extremely difficult to systematically
vary the roughness or contact angle.
Despite the difficulties in producing OTE monolayers, we believe it is still the
best
monolayer
available
for
silicon
surfaces.
Many
groups
use
octadecyltrichlorosilane (OTS) monolayers as their hydrophobic monolayer but this
surface is less well packed than OTE [2.21]. OTE has an area per molecule of 19.9
Å2 [2.21], while OTS has an area per molecule of 23.5 Å2 on silicon [2.22]. There is
also some evidence that OTS can be swelled by water. Kuhl et al. found that on
silicon an average of 2.9 water molecules per OTS molecules where needed to
account for the scattering length density the observed with neutron reflectivity [2.22].
Mao et al. also reported a change in domain height in OTS in the presence of water;
in air domains where ~ 0.2-0.3 nm and in water they were ~0.3-0.5 nm [2.5].
For SPR, we use thiols to form a monolayer on our metal surfaces. Thiols are
chemically attached to our gold surface through a sulfur-gold chemical bond. For
hydrophobic monolayers we use n-octadecanethiol (ODT), which has a contact angle
of over 100o. One of the big advantages of using thiol chemistry that one can
purchase thiols terminated with any desired end. This allows the systematic control
of many variables such hydrophobicity and surface rigidity. By mixing ODT and 11-
36
mercapto-1-undecanol (R-OH T), we were able to vary the contact angle between
110o and 5o. Also, as the thiol layer takes on the topographical features of the
underlying metal surface, the roughness can be systematically controlled. Thiol
monolayer formation is also much more robust and well understood than OTE
formation, and with very little effort we get nearly 100% success rate. This makes
thiol a great substrate for a physicist. The biggest limitation of the thiols is that they
only form monolayers on coinage metals.
Hence, they cannot be used with
ellipsometry except to get rough qualitative results.
Details of the sample preparation are given in Appendix B.
2.5 References
[2.1] Stillinger, F.H. Journal of Solution Chemistry 2 141 (1973)
[2.2] Lum, K., D. Chandler and J.D. Weeks Journal of Physical Chemistry B 103
4570 (1999)
[2.3] Drude, P. K. L. The Theory of Optics (Dover, New York, 1959), p. 292
[2.4] Mukhopadhyay, A., and B.M. Law Physical Review E 62 (4) 5201 (2000)
[2.5] Mao, M., J. Zhang, R. -H. Yoon and W.A. Ducker Langmuir 20 1843 (2004)
[2.6] Mukhopadhyay, A. (2000), "Ellipsometric Study of Surface Phenomena" PhD
thesis, Kansas State University
[2.7] Parratt, G. Physical Review 95 359 (1954)
[2.8] Fenter, P. Reviews in Mineralology and Geochemistry 49 149 (2003)
[2.9] Grifffiths, D.J. Introduction to Electrodynamics Third Edition (Prentice Hall
New Jersey, 1999) p.384-415
37
[2.10] Salamon, Z., H. A. Macleod and G. Tollin Biochimica et Biophysica Acta 1331
117 (1997)
[2.11] Knoll, W. Annual Review of Physical Chemistry 49 569 (1998)
[2.12] Brockman, J.M., B.P. Nelson and R.M. Corn Annual Review of Physical
Chemistry 51 41 (2000)
[2.13] Green, R.J., R.A. Frazier, K.M. Shakesheff, M.C. Davies, C.J. Roberts and
S.J.B. Tendler Biomaterials 21 1823 (2000)
[2.14] Tao, N.J., S. Boussaad, W.L. Huang, R.A. Arechabaleta and J. D’Agnese
Review of Scientific Instruments 70 (12) 4656 (1999)
[2.15] Homola, J., S.S. Yee and G. Gauglitz Sensors and Actuators B 54 3 (1999)
[2.16] Wallqvist, A., E. Gallicchio and R.M. Levy Journal of Physical Chemistry B
105 6745 (2001)
[2.17] Huang X., R. Zhou and B.J. Berne Journal of Physical Chemistry B 109 3546
(2005)
[2.18] Patrick, H.N., G.G. Warr, S. Manne and I.A. Aksay, Langmuir 15 1685 (1999)
[2.19] Perkin, S., N. Kampf and J. Klein Physical Review Letters 96 038301 (2006)
[2.20] Hong, L., A. Poynor, S. Granick and C. Kessel “Preparation of Smooth
Hydrophobic Self-assembled Monolayers” In preparation
[2.21] Ben Ocko personal communication November 23, 2005
[2.22] Kuhl, T.L., J. Majewski, J.Y. Wong, S. Steinberg, D.E. Leckband, J.N.
Israelachvili and G. S. Smith Biophysical Journal 75 2352 (1998)
38
2.6 Figures
Sample
Holder
Phase
Modulator
Analyzer
Polarizer
Laser
PMT
Figure 2.1 Photograph of the Ellipsometer.
Above is a picture of our home-built phase modulated ellipsometer. Light
from the laser has its initial polarization set by the polarizer. Then a time-dependent
phase difference is added by the phase modulator. The light is reflected off the
sample which changes its polarization, embedding information about the surface into
the light. Next the new polarization is measured by the analyzer and recorded by the
PMT.
39
a
kf
ki
α
α
2α
b
kf
Q
ki
Figure 2.2 Illustration of X-ray Reflectivity
X-rays with an initial wave number (ki) are incident upon the sample surface
at an angle, α, as shown in a. In specular X-ray scattering, the detector is positioned
so that X-rays with a final wave number (kf) are measured.
Part b shows the
definition of the momentum transfer vector, Q. Q is perpendicular to the surface.
40
Figure 2.3 Schematic of a Surface Plasmon
Surface plasmons can be excited at a metal/dielectric interface. The interface
lies in the x-y plane and the plasmon propagates in the x direction. Taken from Knoll
[2.11].
41
Glan Laser
Polarizer
Mirror 1
LASER
Iris
Mirror 2
ND
Detector 2
Prism
Rotation
Stage
ND
Sample
Cell
Detector 1
Figure 2.4 Schematic of SPR Apparatus.
We built our SPR using the Kretschmann Geometry. Here light from the laser
becomes p-polarized after the Glan laser polarizer. The size of the beam is controlled
by an iris and then incident on the prism. It hits the gold layer with an angle above
the critical angle, producing an evanescent wave and thus exciting surface plasmons.
The signal is collected by detector 1. The signal from detector 2 is used to remove
long-time scale fluctuations from the data.
42
1
Reflectivity
0.8
0.6
0.4
0.2
0
50
55
60
65
70
Angle (Degrees)
Figure 2.5 Dynamic SPR Measurements.
A shift in the resonance angle of the system, for example from the blue curve
to the pink curve shown above, indicates the reflectivity at a fixed angle (shown by
the dashed red line) also changes. This allows the shift in resonance angle in time to
be mapped to a shift in reflectivity.
43
Chapter 3: Static Properties of the Water/Hydrophobic Interface
As stated in Chapter 2, what happens at the water/hydrophobic interface is
still hotly debated. This chapter presents evidence both from ellipsometry and X-ray
reflectivity in support of a depletion layer. It also looks at the static dependence of
the depletion layer on such variables as temperature and sample quality.
3.1 Ellipsometric Evidence for the Depletion Layer
In order to look for evidence of the existence of a depletion layer at the water
hydrophobic surface, we first had to build up a model of our system. First, we
measured the contribution to ρ from the silicon substrate and its oxide layer. To do
this the oxide layer was prepared as it would be for OTE functionalization, details can
be found in Appendix B. The silicon wafer was first soaked in Piranha solution for
one hour at 70 oC, and rinsed with copious amounts of deionized water. The wafers
were further cleaned with UV/Ozone for 30 minutes and finally cleaned in an
oxygen-plasma cleaner. This produced bare silicon wafers with a well-defined oxide
layer approximately 2 nm thick. The bare wafers were completely wet by water
(advancing contact angle = 0o). Next the contribution of the OTE layer was measured
in ethanol. We chose ethanol as it has an index of refraction very close to water,
giving it a Brewster angle almost identical to that of water which allows us to
measure ρ for both liquids with the same incident angle. Also, it is not expected to
produce a depletion layer in contact with OTE as the contact angle between ethanol
and OTE is near 15o. Using a simple three-slab model (one slab for the substrate, one
for the OTE and one for the solvent), we found the ellipsometric thickness of the OTE
44
layer in ethanol was 2.47 ± 0.03 nm, which is in good agreement with the expected
chemical structure.
Finally with the sample well-parameterized we were able to measure ρ in
water. Using the vertical sample cell, we were able to make the measurement at the
exact same position in water as we had in ethanol. However if we used the same
model and OTE thickness to calculate the expected value of ρ in water, we found
that the calculated value differed from the measured one by 28%. To better quantify
this difference, we define Δ ρ as the measured value minus the calculated value. In
this case, Δ ρ = -0.0040±0.0001. The physical significance of Δ ρ is illustrated in
Figure 3.1. Since Δ ρ is not zero we know that the three-slab model is not correct.
At first, Occam’s Razor suggested to us that this might reflect some kind of defects in
the monolayers, but swelling of the OTE layer by the water would make Δ ρ
positive. Similarly organic contaminants, which usually have an index of refraction
greater than water, would also make Δ ρ positive.
There are only two ways to get a negative value for Δ ρ . The first requires
the OTE layer to shrink. In our case this would mean that the OTE layer went from
being approximately 2.4 nm thick to being 1.4 nm thick, a decrease of over 40%.
This is would require the tilt angle to change from 24° to 58° or massive layer
disordering, which is physically unrealistic as the OTE layer is already well packed.
To ensure this was not the case, we have also done control experiments to test for
changes in the OTE. Using Sum Frequency Generation (SFG) we examined the OTE
surface both in contact with air and water. The SFG spectra in air and water show no
45
significant differences, as can be seen in Figure 3.2, indicating that no large change in
tilt angle or disordering occurred.
The second reason for a negative Δ ρ requires the addition of another layer
with an index of refraction less than the index of refraction of water. We believe that
our measurement signals the presence of a surface layer of depleted density, directly
from the raw data.
The Drude equation does not yield a unique result for both the thickness and
the density of this depleted zone. Using a four-slab model similar to those used in
neutron reflectivity, we can model the depletion layer, but we cannot uniquely solve
for both the thickness and density. Instead we can relate the values of the thickness
and density as shown in Figure 3.3. As can be seen in Figure 3.3, a fully depleted
layer would have a thickness of 0.180 ± 0.005 nm, while a layer with 90% bulk
density will have a thickness of 2.60 ± 0.07 nm, in agreement with Steitz et al. [3.1].
Alternatively, we can model the vapor layer as a continuous dielectric profile
proportional to the hyperbolic tangent, which is often used in ellispometric modeling.
This provides a more physical, smoothly varying dielectric coefficient that starts out
at the pure vapor value and reaches the bulk value at some distance, L, from the
surface. In this case, L = 0.45 ± 0.01 nm. A comparison of the different models is
shown in Figure 3.4.
3.2 X-Ray Reflectivity Evidence for the Depletion Layer
As stated previously, X-ray reflectivity has an advantage over
ellipsometry in that it can decouple the thickness from the density of the depletion
46
layer. To use this advantage, X-ray measurements were performed at the Advanced
Photon Source (beam line 12 BM) at Argonne National Laboratory, in collaboration
with Ian Robinson, Paul Fenter and Zhan Zhang. The temperature of the sample was
between 23 ºC and 25ºC. The X-ray beam was reflected at incident angles, α,
generally ranging from 0.1° to 2.3°, corresponding to momentum transfers of 0.03 Å-1
to 0.8 Å-1. The incident beam size ranged from 0.04 mm to 0.4 mm so that the
resulting beam footprint remained well within the middle of the surface.
A
monochromatic X-ray beam with energy of 19.0 keV was used to maximize the
transmission through the water layer.
The full incident beam flux was 2x1010
photons/sec. Specular reflectivity measurements took place within 20 minutes for a
given beam spot with two additional scans to probe the background with the sample
angle displaced by ±0.05°, during which time no changes to the reflected intensity
were observed. A correction was applied to the data for angle-dependent attenuation
by the water and Kapton layers [3.2]. A scale factor was used in the analysis, as
beam attenuation prevented measurements near the critical angle. Since reflectivity
varied by 10 orders of magnitude, the data are displayed here as normalized
reflectivities, RQ4, to compensate for the ~Q-4 decay of the Fresnel reflectivity
To fix parameters for subsequent analysis, these organic monolayers were first
studied in air (see Figure 3.5). The reflectivity curve shows Kiessig oscillations
owing to interference between X-rays reflected at the silicon-organic and organic-air
interfaces and thus were highly sensitive to the monolayer thickness, D.
The
thickness estimated from the position of the first intensity dip, using Equation 2.18,
was 24-27 Å. The derived electron density profile corresponding to the best-fit
47
reflectivity is shown in Figure 3.6 and includes contributions from the monolayer
thickness and density, and interfacial oxide and monolayer head-group layers.
Bearing in mind that SAM-coated surfaces never attain 100% surface coverage, and
that they contain grain boundaries and other defects, fits to the data were found to be
most consistent when we assumed a monolayer containing 1% less electron density
than perfectly packed monolayers with 100% coverage, owing to such packing
imperfections. However, the observation of deep intensity minima in Figure 3.5
demonstrates that the monolayers were homogeneous over the large area probed by
the X-ray beam.
After placing these same monolayers in water, reflectivity interference
oscillations continued to be observed but with significant shifts in the dip positions
(Figure 3.5). The estimated monolayer thickness, using Equation 2.18, was 14 -15 Å,
less than two-thirds of the thickness in air, which is physically unrealistic as we
explained in Section 3.1. Rather, this signifies a phase shift of the interference
oscillations owing to non-monotonic changes in the electron density normal to the
silicon. Bearing in mind that the electron density of water is close to that of an
organic monolayer, the observed phase shift indicates that electron density varied
from water to monolayer in a non-monotonic fashion, passing through a region whose
electron density was less than either the water or the monolayer. We emphasize that
this qualitative conclusion, obvious to the eye when one inspects Figure 3.5, holds
independently of the quantitative analysis that follows.
included in Figure 3.6.
48
A schematic sketch is
In fitting the curves, the thicknesses, scattering length densities, and
roughnesses for the silicon oxide and bulk silicon layers were fixed to tabulated
values. A “head group” layer was included following the example of Tidswell et al.
[3.3]. The fit for the monolayer in air served to fix the needed parameters for
subsequent analysis when water was added. The same parameters were used in fitting
the reflectivity of these monolayers immersed in water.
In their influence on the quality of fits, the most important parameter in the
first place was roughness of the organic monolayer, ~7 Å; but this was fixed by the
measurements made in air. In water, fits were made separately to the experiments
where the water was saturated with atmospheric gas, or deaerated, with results
summarized in Figure 3.7.
The best fits are encouragingly consistent for both
ambient and deaerated water, giving for both cases a depletion layer thickness of 2.7
Å, electron density corresponding to 20% water content, and width of the error
function profile (between the depletion layer and bulk water) of 4 Å. However, there
is considerable room to change these parameters and still get an acceptable fit as the
fits in water were very sensitive not only to the thickness of the depletion zone but
also to its electron density relative to that of bulk. The areas of acceptable fits are
shown in Figure 3.7.
How do the values measured for the depletion layer with ellipsometry
compare to those measured with X-ray reflectivity? As stated earlier, ellipsometry
cannot decouple the depletion layers thickness and density, and the best that could be
done was to confine the value to a curve. This curve has been plotted with the
reflectivity results in Figure 3.7. We see remarkably good agreement between the
49
results. This demonstrates that depletion layer is a real effect and is visible to more
than one experimental technique. However, what variables control its properties and
why do not all experiments see the depletion layer?
3.3 Temperature Dependence
The formation of the depletion layer is the result of balancing entropic and
energetic interactions. To more fully understand the relative strengths and influences
of these two aspects, it is useful to look at the temperature dependence of the
depletion layer. In a recent molecular dynamics simulation, Mamatkulov et al. found
that the depletion layer increased in thickness and became more depleted as
temperature was increased [3.4].
We measured the ellipticity from 10oC to 50oC, for OTE in both water and
ethanol. In ethanol we saw no significant change in the ellipticity ( ρ ) while in
water we found that ρ increases with temperature. See Figure 3.8. The increase in
ellipticity was seen for many samples with different contact angles and displayed no
hysteresis. See Figure 3.9. There are two simple ways to represent this change. First,
we can use the hyperbolic tangent model and ascertain how the thickness changes
with temperature; fixing the density while allowing the thickness of the depleted
region to vary. Figure 3.10 depicts this interpretation, where the change in thickness
is plotted versus temperature for several samples. As can be seen the thickness of the
depleted region decreases drastically with temperature. In fact, it decreases by more
than 60% over a forty-degree temperature range. Second, we can employ the fourslab model with a fixed thickness and determine temperature’s effect on the density.
50
This model is displayed in Figure 3.11. In this case, as the temperature is increased
the depleted region becomes more like the bulk. In reality, the thickness and density
of the depleted region probably change simultaneously. Still we can conclude from
these two simple interpretations that the depletion layer dissipates as the temperature
is increased.
This is exactly the opposite result as seen in the simulation [3.4]. What could
be the reason for the depletion layer dissipating with increasing temperature? In bulk
water, as temperature is increased the number of broken hydrogen bonds also
increases.
At a hydrophobic surface this means that few bonds are disrupted
compared to bulk water as the temperature increases. In a sense, this means that
water becomes less “oil-phobic” at higher temperatures [3.5]. Viewed in this way it
is clear that the driving force for creating an interface, namely the minimization of
broken bonds, decreases as temperature is increased and not surprisingly the depletion
layer dissipates [3.6].
3.4 Dependence on Dissolved Gases
Considering that water saturated with dissolved atmospheric gases is reported
to display different hydrophobicity than deaerated water [3.7-3.10], we performed Xray and ellipsometry experiments for both cases. These control experiments were
designed to test the uninteresting possibility that a near-surface layer with density less
than bulk might trivially result from migration to the hydrophobic surface of
dissolved gas.
51
To test this possible influence in ellipsometry, the following control
experiments were performed.
First, the hydrophobic surface was immersed in
ethanol, which wets it, in order to displace any possible absorbed gas. Then, without
exposing the surface to air, ethanol was flushed out of the sample cell with copious
amounts of degassed, deionized water, and finally ellipsometry measurements were
made.
Two methods were employed to degas the water prepared by purification
using a Barnstead Nanopure II deionizing system: (i) water was boiled for 30 minutes
and subsequently cooled to room temperature in a filled, sealed vessel; (ii) water was
freeze-dried at liquid nitrogen temperature and subsequently thawed to room
temperature in a filled, sealed vessel, this process was repeated 5-7 times. We
conclude that, although the hypothetical possibility cannot be excluded that some
residual gas persisted, the greatest care by the means available to us was taken to
exclude it. In the measured ellipticity, there was no significant effect of degassing.
In fact when one position on a sample was measured first in degassed water and then
exposed to air for over an hour and re-measured the change in the thickness of the
depleted region modeled with the hyperbolic tangent was 0.015 ± 0.016 nm.
Similar methods where employed in X-ray reflectivity experiments. As seen
in Figure 3.7, the fits to the reflectivity curves were quite consistent for both ambient
and degassed water.
52
3.5 Lateral Properties of the Depletion Layer
The ellipsometry and X-ray reflectivity data compares favorably with a long
tradition of theory predicting that water forms a depletion layer in the vicinity of
hydrophobic surfaces [3.11-3.15]. However, from recent AFM-based studies the
alternative hypothesis of ‘nanobubbles’ has emerged in which approximately 50% of
a hydrophobic surface is coated with small bubbles around 5-100 nm in height and
100-800 nm in diameter, provided that the water has not been degassed [3.7, 3.16].
The X-ray data reported in Section 3.2 afford a succinct quantitative test of this
hypothesis.
There are two possibilities to consider, depending on whether the
putative bubble size is larger than or less than the coherence length of the X-ray
measurement, as illustrated in Figure 3.12 a. Pershan and coworkers have shown that
the coherence length in X-ray reflectivity along the surface normal direction follows
from geometrical considerations, mainly concerning the detector slit; applied to the
present situation, where the vertical detector aperture was 1 mm at a distance of 750
mm from the sample, it follows that the radial coherence length was approximately
850 Å [3.17]. In the following, we denote the case where the nanobubbles are larger
than this length as the ‘incoherent’ model and the case where they are smaller as the
‘coherent’ model.
In the incoherent model, the measured reflectivity results from a linear
combination of reflectivities for the air/hydrophobic (measured directly) and
water/hydrophobic interfaces, as shown in Figure 3.12 b. This model requires that the
first scattering intensity minimum occur at the same wavevector as when the
monolayer is in air, and it is obvious that the data disagree with this ansatz. A direct
53
comparison (Figure 3.13) for several different hypothetical nanobubble surface
coverages shows explicitly the unfavorable comparison with experimental data.
Alternatively, we suppose that the nanobubble diameter was less than the
coherence length of the X-rays, < 850 Å. Reflectivity in the latter case is calculated
by combining the density profile of the hydrophobic/air interface with an error
function profile for the electron density of water as shown in Figure 3.12 c, giving an
average electron density, intermediate between air and water.
The quantitative
comparison (Figure 3.14) plots RQ4 against Q for several hypothetical nanobubble
surface coverages and shows explicitly the unfavorable comparison to the
experimental data in this case also.
Further evidence against the nanobubble
hypothesis comes from the lack of any significant off-specular diffuse scattering
which would be expected since our lateral spatial resolution (>20 μm) is substantially
larger than the reported lateral size of nanobubbles (~100 nm).
Together these
observations allow us to rule out nanobubbles as playing a significant role in these
measurements.
3.6 Dependence on Sample Quality
One reason why some groups may not observe the depletion layer is that we
saw that it was highly sensitive to sample quality. We found that extreme care is
needed during sample preparation in order to observe a depletion layer. The details
of sample prepatation are given in Appendix B.
Monolayers that have defects or those that are not strongly attached to the
substrate will swell or blister in water. As discussed in Section 3.1, this will make
54
Δ ρ more positive and mask the depleted region (see Figure 3.5). Take for example
one bad sample, when measured in air, its OTE layer was 2.39 ± .01 nm thick but
when measured in ethanol was 3.66 ± .02 nm. This sample gave a depleted region
with a negative thickness (L = -0.06± .01 nm, using the hyperbolic tangent model).
Figure 3.15 displays the difficulty of creating a high quality monolayer that
did not swell. Out of the eleven samples shown six did not show signs of swelling,
and could be used to observe a depletion layer. The other samples showed either zero
or negative depletion layer thicknesses.
The presence of sample swelling probably explains why other groups did not
see the depletion layer on octadecyltrichlorosilane (OTS) monolayers [3.18, 3.19].
Mao et al. also reported a change in domain height in OTS in the presence of water;
in air domains where ~ 0.2-0.3 nm and in water they were ~0.3-0.5 nm [3.18]. This
small change in thickness could easily mask the presence of the depletion layer.
Takata et al. also used OTS and failed to see a depletion layer but did not mention if
they observed any swelling in water [3.19].
3.7 Conclusions for the Chapter
We have observed evidence for the depletion layer with both ellipsometry and
X-ray reflectivity. The evidence for the existence of the depletion layer is very
strong, however pinning down the exact thickness and density is much more difficult.
Both techniques only confine the depletion layer to fall within a certain area. Our
best guess is that the depletion layer is 2.7 Å thick and has a density corresponding to
20% water content.
55
Prior related experiments were controversial. Some ellipsometry experiments
concluded that there is no depletion [3.18, 3.19] while others concluded depletion
exists [3.20].
Experiments based on neutron scattering show effects, but the
magnitudes differ considerably [3.1, 3.9, and 3.21]. X-ray reflectivity measurements
of an organic film floating on an air-water interface showed a density gap < 15 Å in
extent, which in combination with MD simulations was interpreted in terms of 1.2 Å
thick “vacuum” layer [3.22]. Some of these inconsistencies could be due to the
difficulty in properly quantifying the depletion layer. Others are probably due to the
highly sensitive dependence of the depletion layer on sample quality.
Also we have seen no evidence for nanobubbles. This contradicts many AFM
experiments which have observed them [3.7, 3.16].
It is interesting that the
nanobubbles have only been observed during perturbative experiments.
One
possibility is that the tapping motion of the AFM tip may have transformed the
depletion layer into small bubbles.
Many groups have posited that the depletion layer was just the trivial
segregation of dissolved gasses to the surface [3.7, 3.9 and 3.10]. We have seen no
effect of dissolved gasses on the depletion layer. This null result indicates that the
depletion layer is in fact a fundamental property of what happens when water meets a
hydrophobic surface.
3.8 References:
[3.1] Steitz, R., T. Gutberlet, T. Hauss, B. Klösgen, R. Krastev, S. Schemmel, A.C.
Simonsen and G.H. Findenegg Langmuir 19 2409 (2003)
56
[3.2] Fenter P., Reviews in Mineralology and Geochemesitry 49 149 (2003)
[3.3] Tidswell, I.M., T.A. Rabedeau, P.S. Pershan and S.D. Kosowsky Journal of
Chemical Physics 95 2854 (1991)
[3.4] Mamatkulov, S. I., P. K. Khabibullaev and R. R. Netz Langmuir 20 4756 (2004)
[3.5] David Chandler personal communication, June 14 2004
[3.6] Chandler, D. Nature 437 640 (2005)
[3.7] Ishida N., T. Inoue, M. Miyahara and K. Higashitani, Langmuir 16, 6377 (2000)
[3.8] Pashley R. M., J. Phys. Chem. B 107, 1714 (2003)
[3.9] Doshi, D.A., E.B. Watkins, J.N. Israelachvili and J. Majewski., Proceedings of
the National Academy of Science 102 9458 (2005)
[3.10] Stevens, H. R. F. Considine, C. J. Drummond, R. A. Hayes and P. Attard,
Langmuir 21 6399 (2005)
[3.11] Stillinger, F.H. Journal Solution Chemistry 2 141 (1973)
[3.12] Lum, K., D. Chandler and J.D. Weeks Journal of Physical Chemistry B 103
4570 (1999)
[3.13] Huang, X., C.J. Margulis and B.J. Berne Proceedings of the National Academy
of Science 100 (21) 11953 (2003)
[3.14] Dill K.A., T.M. Truskett, V. Vlachy and B. Hribar-Lee Annual Review of
Biophysics & Biomolecular Structure 34 173 (2005)
[3.15] Huang, D. M., and D. Chandler Journal of Physical Chemistry B 106, 2047
(2002)
[3.16] Tyrrell, J.W.G., and P. Attard Physical Review Letters 87 (17) 176104-1
(2001)
57
[3.17] Tamam L., H. Kraack, E. Sloutskin, B.M. Ocko, P. S. Pershan, A. Ulman and
M. Deutsch, Journal of Physical Chemistry B 109, 12534 (2005)
[3.18] Mao, M., J. Zhang, R.-H. Yoon and W.A. Ducker Langmuir 20 1843 (2004)
[3.19] Takata, Y., J.H.J. Cho, B.M. Law and M Aratoni Langmuir 22 1715 (2006)
[3.20] Castro, L.B.R., A.T. Almeida and D.F.S. Petri Langmuir 20 7610 (2004)
[3.21] Schwendel, D., T. Hayashi, R. Dahint, A. Pertsin, M. Grunze, R. Steitz and F.
Schreiber Langmuir 19 2284 (2003)
[3.22] Jensen, T.R., M. O. Jensen, N. Reitzel, K. Balashev, G.H. Peters, K. Kjaer and
T. Bjørnholm Physical Review Letters 90 (8) 086101-1 (2003)
58
3.9 Figures
Δρ > 0
Δρ = 0
d > 2.47 nm
Δρ < 0
Δρ < 0
d < 2.47 nm
Figure 3.1 Schematic Illustration of Δ ρ
Δ ρ is the difference between the measured ellipticity and that calculated
using the OTE thickness measured at the same position on the sample in ethanol.
Δ ρ equal to zero indicates that the three-slab model derived from the ethanol
measurement is correct. While a positive value for Δ ρ suggests that the OTE layer
is swelling. On the other hand, a negative value for Δ ρ points either to a significant
reduction in OTE thickness or to an additional layer with an index of refraction less
than water’s.
59
a
SFG Signal (a.u.)
0.5
0.0
-0.5
-1.0
2850
2900
2950
IR Energy (cm-1)
b
SFG Signal (a.u.)
0.5
0.0
-0.5
-1.0
2850
2900
2950
IR Energy (cm-1)
Figure 3.2: Sum Frequency Spectra
The SFG spectra, taken in collaboration with Jeff Turner using a home-built
SFG setup, for the OTE monolayer/air interface (a) and the OTE monolayer/water
interface (b). There is very little difference between the two spectra indicating the
OTE monolayer did not reorder.
60
Thickness (nm)
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
0.8
1
Notional Water Fraction
Figure 3.3 Depletion Layer Thickness vs. Notional Water Fraction
Ellipsometry cannot uniquely determine the layer thickness and bulk water
volume fraction using the four-slab model. It can only confine these quantities to the
curve shown above.
61
2.2
Dielectric Profile
2.0
1.8
1.6
1.4
1.2
1.0
0
1
2
3
Z (nm)
Figure 3.4 Three Possible Models for the Depleted Region.
The dashed and dot-dashed lines represent the step-like four-slab models for a
region that is completely depleted (Water volume fraction = 0) and 10% depleted,
respectively. The solid line represents the hyperbolic tangent model, which is more
realistic.
62
4
R*Q
1E-7
1E-10
4
R*Q
1E-7
1E-10
1E-13
0.0
0.2
0.4
0.6
0.8
Q(1/A)
Q(1/Å)
Figure 3.5 Reflectivity Curves for OTE Monolayers in Water and Air
X-ray reflectivity is compared in air (black filled symbols) and water (blue
open symbols) for OTE monolayers on <100> silicon wafers for both ambient (upper
set of curves) and degassed (lower set of curves) water. The solid cyan line is the fit
to the water data. Reflectivity RQ4 is plotted against Q on semilogarithmic scales.
63
a
-5
2.0x10
-5
2
ρ (1/Å )
1.5x10
-5
1.0x10
-6
5.0x10
0.0
-10
0
10
20
30
40
50
60
z (Å)
b
Depletion
Layer
ρ(1/Å2)
2.0x10
-5
1.6x10
-5
1.2x10
-5
8.0x10
-6
b
u
l
k
SiOx
O
T
E
Si
Head Group +
roughness
-10
0
10
20
30
40
50
z (Å)
Figure 3.6 Calculated Electron Density Profiles
The calculated electron density profile for a monolayer of OTE is shown in a.
It was used to fix the parameters for the OTE in water. The electron density of OTE
in water is shown in b. The labeled regions are a guide to distinguishing the structure.
The non-monotonic dip for the depletion layer is required to produce the phase shift
seen in Figure 3.5.
64
Precent Bulk Water Density
50
40
30
20
10
0
1
2
3
4
Thickness (Å)
Figure 3.7 Comparison of the Depletion Layer Properties
The best fit from the X-ray reflectivity for the properties of the depletion layer
are marked with a green star. The shaded regions represent acceptable fits found with
X-ray reflectivity for degassed water (red crossed circles, red shading) and ambient
water (black half filled squares, cyan shading).
ellipsometry is shown (blue triangles).
65
The fit curve obtained from
Normalized Ellipticity
0.002
0.0015
0.001
0.0005
0
-0.0005
-0.001
-0.0015
10
20
30
40
50
Temperature (C)
Figure 3.8 Temperature Dependence of the Ellipticity.
The ellipticity, normalized to room temperature, is plotted for both OTE in
ethanol (red triangles) and water (blue squares).
As can be seen there is no
significant change of the ellipticity in ethanol, while in water the ellipticity increases
greatly with increasing temperature.
.
66
Δρ
-0.003
lb28a
wgtime
w924h
w924a
-0.004
30
32
34
36
-0.0032
-0.0034
-0.005
-0.0036
wgtime heating
wgtime cooling
-0.0038
-0.006
10
20
30
40
50
Temperature
Figure 3.9 Temperature Dependence of Δ ρ
The temperature dependence of the ellipticity is plotted for samples with
different contact angles. The squares and diamonds represent a sample with an
advancing water contact angle (θ) of 107 ± 2 in degassed and non-degassed water
respectively. The triangles represent a sample with θ = 104 ± 3, in non-degassed
water. The circles represent a sample with θ = 109 ± 3, in non-degassed water. The
inset shows the reversibility of the measurement on this sample. The filled symbols
are the data series taken while heating the sample and the open symbols where taken
while cooling.
67
T hickness (nm )
0.55
0.5
0.45
0.4
0.35
0.3
0.25
10
20
30
40
50
Temperature (C)
Figure 3.10 Temperature Dependence of Depletion Layer Thickness
The thickness of the depleted region, calculated with hyperbolic tangent
model is plotted versus temperature.
68
Bulk Water Volume Fraction
0.936
0.926
0.916
0.906
0.896
0.886
0.876
10
20
30
40
50
Temperature
Figure 3.11 Temperature Dependence of the Density of the Depletion Layer
The bulk water volume fraction found with the four-slab model and a 2.6-nm
layer thickness is plotted versus temperature.
69
a
Coherent Model
b
Incoherent Model
0 .1
R
1 E -4
1 E -7
1 E -1 0
1 E -1 3
0 .0 0
0 .2 5
0 .5 0
0 .7 5
Q (1 /A )
2x10
-5
1x10
-5
2
ρ (1/Å )
c
0
-2 0
0
20
40
z (Å )
Figure 3.12 Schematic of Coherent and Incoherent Bubble Models
Two models can be used for fitting X-ray reflectivity curves in the presence of
bubbles. If the putative bubbles are large than the coherence length, the incoherent
model applies as illustrated in the left section of a. Then, a linear combination of the
reflectivity curves is taken (b). If the bubbles are smaller than the coherence length,
the coherent model, illustrated in the right section of a, is used. In this case, a linear
combination of the electron densities is taken (c).
70
0%
1E-9
R*Q
4
30%
1E-12 70%
100%
1E-15
0.00
0.25
0.50
0.75
Q(1/Å)
Figure 3.13 Incoherent Model
The measured X-ray reflectivity in degassed water for self-assembled OTE
monolayers shown in Figure 3.5 is compared to a nanobubble model in which
scattering occurs incoherently, in part from OTE in contact with bulk water, in part
from OTE in contact with air.
Reflectivity RQ4 is plotted against Q on
semilogarithmic scales. The open symbols are experimental data. The solid line is
the calculated fit for 0% surface coverage of water. The dotted line, dash-dotted, and
dashed lines are the fits calculated for 30%, 70% and 100% water surface coverage.
The vertical lines are to guide the eye.
71
1E-8
0%
30%
R*Q4
1E-11
70%
100%
1E-14
0.00
0.25
0.50
0.75
Q(1/Å)
Q
Figure 3.14 Coherent Model
The measured X-ray reflectivity in degassed water for self-assembled OTE
monolayers shown in Figure 3.5 is compared to a nanobubble model in which
scattering occurs coherently, in part from OTE in contact with bulk water, in part
from OTE in contact with air.
Reflectivity RQ4 is plotted against Q on
semilogarithmic scales. The open symbols are experimental data. The dashed line is
the calculated fit for 0% surface coverage of water. The solid line, dotted, and dashdotted lines are the fits calculated for 30%, 70% and 100% water surface coverage.
The vertical lines are to guide the eye.
72
Number of Occurences
18
16
14
12
10
8
6
4
2
0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Depletion Layer Thickness (nm)
Figure 3.15 Dependence on Sample Quality
Not all OTE monolayers were good enough to display the depletion layer.
The number of occurrences for each depletion layer thickness, calculated with the
four-slab model assuming a fully depleted region (0% bulk water fraction), are shown
above. The negative values indicate swelling in the OTE layer.
73
Chapter 4: Dynamic Properties of the Water/Hydrophobic Interface
The dynamics of water at a hydrophobic surface has many important
implications especially for protein folding. Yet very few experiments have been done
to probe these dynamics. When we first looked at the depletion layer thickness
versus time with ellipsometry, we noticed that there were fluctuations on many
different time scales, as can bee seen in Figure 4.1. The existence of these large
fluctuations are especially surprising given that ellipsometry inherently averages both
spatially, over a beam size of approximately 10 μm, and temporally, with a time
constant of 30 ms.
It is difficult to really understand the dynamics of the interface by just looking
at the time traces.
We have employed three forms of analysis to get a better handle
on the fluctuations; histograms, autocorrelations, and power spectra. Each technique
provides a different perspective on the fluctuations.
4.1 Histograms
Histograms are created by a three step process. First the measured data is
divided into equally spaced bins. Then the number of data points in each bin is
counted. Finally the results are plotted in a bar chart.
Histograms provided much information on the data analyzed [4.1]. They
show the mean and the distribution about that mean. Also they highlight the presence
of outliers, the skewness of the data and whether multiple modes exist.
According to the Central Limit Theorem, a distribution of N statistically
independent measurements will be Gaussian for large N. As we measured over one
74
hundred thousand points in each time trace, we would expect our histograms to
Gaussian.
Deviations from the expected Gaussian shape can reveal interesting
insights. Two of the main causes for non-Gaussian distributions are underlying
deterministic models, such as sinusoidality in the data, and the mixing of probability
models, due to multiple states [4.1]. With sinusoidal variation, the system spends
more of its time in the extrema of the waveform where the velocity is the slowest than
it does near the mean value, thus producing non-Gaussian distributions. In the case of
a system with multiple states, as the system transitions between the states, their
various distributions will be combined. The resulting distribution will be bimodal for
a two-state system but in general can take on a variety of different non-Gaussian
distributions.
Figure 4.2 shows histograms for three different systems, taken from
ellipsometry measurements. The low amplitude tails seem on all three histograms are
characteristic of all the histograms measured with ellipsometry and probably
represent the distribution of noise convoluted with the signal. The first system, the
hydrophobic/ethanol system, consists of OTE in ethanol (Figure 4.2 a). As stated
earlier, ethanol has a low contact angle with OTE and a depletion layer is not
expected. This system has the expected histogram. It is sharply peaked with a welldefined mean and Gaussian-like distribution around the mean.
In contrast, the
hydrophobic/water system has a very different histogram (Figure 4.2 b). It is not
sharply peaked and has a flattened top. It has a non-Gaussian distribution. This
histogram is especially puzzling when compared to the water/hydrophilic system,
which consists of silicon oxide in water (contact angle = 0o), shown in Figure 4.2 c.
75
The hydrophilic/water histogram looks like the hydrophobic/ethanol histogram, with
a sharply peaked distribution.
What could be the cause of the non-Gaussian distributions in the
water/hydrophobic system? Since the other two systems are not expected to have and
depletion layer, while the water/hydrophobic system is, we believe the distribution is
caused by some property of the depletion layer. As stated above, non-Gaussian
distributions can arise from sinusoidality in the data.
In the water/hydrophobic
system, sinusoidal variation may be arising from capillary waves forming at the
water/depletion layer interface. This kind of fluctuating interface is suggested by
McCormick’s simulation [4.2]. He found that removing spatial Fourier modes with
wavelengths between 1.5 nm and 19 nm significantly changed the temporal Fourier
behavior, indicating the interface fluctuates on many length scales.
Also non-Gaussian distributions can arise from multiple states existing within
the system. In the hydrophobic/water system, multiple states may be evidence for a
wandering interface as described by Grunze [4.3]. His simulations show shifting of
the density distribution between runs. This gives a picture of the depletion layer
jumping between different thicknesses as time goes by.
We have used SPR to confirm the non-Gaussian behavior of the
water/hydrophobic histograms. As shown in Figure 4.3, the histogram of ODT in
ethanol (Figure 4.3 a) has the expected Gaussian shape, while the histogram of ODT
in water is bimodal (Figure 4.3 b). Figure 4.4 also shows the characteristic bimodal
histogram in water and a Gaussian histogram in air.
76
Now that we know the water/hydrophobic interface demonstrates nonGaussian fluctuations we can explore how other factors influence the dynamics of the
depletion layer.
4.1.1 Dependence of Dynamics on Temperature
We saw that temperature had a very large effect on the static properties of the
depletion layer. What effect does it have on the dynamic properties? To test the
temperature dependence, we took time traces for two temperatures separated by 30 oC
at the same spot on the sample. The resulting histograms are plotted in Figure 4.5.
As can be seen in Figure 4.5, the histograms are very similar in appearance. The one
taken at 56 oC is slightly broader; however histograms taken on other samples show
slight broadening with a decrease in temperature.
It is surprising that temperature has such a small effect on the fluctuations
when it had such a large effect on the static properties of the depletion layer. In the
static situation the depletion layer dissipated as temperature was increased, however,
it did not disappear over the temperature range available to us. In 2005, Chandler
proposed that although in some situations the depletion layer may become negligibly
thin its main defining characteristic, the size of its fluctuations, would remain
unchanged [4.4]. It seems this is what is occurring here. The depletion layer is
becoming thinner with increased temperature yet it continues to have the same size
fluctuations.
77
4.1.2 Dependence of Dynamics on Roughness
In the course of our experiments, we found that surface roughness has a
profound effect on the shape of the histogram. Figure 4.6 shows the histogram from a
rough surface taken with ellipsometry. The histogram is obviously very different
form the histograms of the smooth monolayers shown above. It has two widely
spaced narrow peaks and a fairly U-shaped distribution.
How can the roughness cause such a drastic change in the histogram? We
found that a histogram constructed from a single sine wave produces a very similar
U-shaped distribution (see the inset in Figure 4.6). We think that the protrusions on
the monolayer surface may be pinning the capillary waves and creating standing
waves at the interface.
4.1.3 Dependence of Dynamics on Contact Angle
We expect the fluctuations to disappear when the sample is no longer
hydrophobic enough to form a depletion layer. In fact, Huang et al. found that the
strength of the liquid surface interaction strongly affected the characteristics of the
depletion layer [4.5]. With ellipsometry, we preformed a series of experiments on
mixed monolayers of octadecanethiol (ODT) and 11-mercapto-1-undecanol (R-OH T)
to look at the effect of hydrophobicity on the fluctuations. Figure 4.7 shows the
histograms for two different mixtures in water. The surface used in Figure 4.7 a has
the same broadened flat-topped peak as seen with OTE in water.
The second
histogram (Figure 4.7 b) is narrower but surprisingly it still has a flat-topped
distribution even though the water contact angle is only 19o.
78
To get a clearer picture of what was happening; we have plotted the standard
deviation, which is the distance where the distribution drops to approximately 60% of
its maximum value, against the contact angle, as shown in Figure 4.8.
The
distribution becomes narrower as the contact angle decreases. At approximately 50
degrees, the standard deviation drops below that of the OTE/Ethanol system,
indicating that the depletion layer no longer exists. It appears that, as expected, the
distribution becomes more sharply peaked as the contact angle is decreased; however
the fluctuations persist much longer than expected.
Another way to look at the effect of the surface liquid interaction strength on
the fluctuations is to vary the liquid while leaving the surface unaltered.
This
reciprocal situation has an advantage for ellipsometry in that we do not need to use
thiols. The results are shown in Figure 4.9. The fluctuations are not well correlated
to the solvent contact angle.
However, if instead we plot the standard deviation against the relative polarity
of the solvent, we find a much better correlation. See Figure 4.10. The relative
solvent polarity (p) is defined relative to water (i.e. for water p=1), and indicates the
magnitude of the dipole moment of the solvent. We observe that the distribution
becomes much narrower as the solvent becomes less polar.
Why would the fluctuations change with solvent polarity instead of contact
angle? One clue can be found in an experiment done by Cho et al. [4.6]. They found
that the slip length, the extrapolated distance into the solid where the fluid velocity
becomes zero, on a hydrophobic surface correlated not with contact angle as expected
but with solvent polarity. They also found that the more polar liquids had unusually
79
strong repulsions at very slow piezodrive speeds. They believe that this strong
repulsion is due to dipole-dipole image interactions, which in this case are repulsive
and tends to align the dipoles parallel to the surface. Cho et al. posit that it is the
highly structured nature of the dipole liquids that make it more difficult to slip. In our
case if the inherent desire of high polarity liquids to order is frustrated by an
incommensurate surface, there will be a larger incentive to form a second interface
and create a depletion layer. Also the stronger repulsion between the surface and
liquid enhances the formation of a depletion layer.
4.1.4 Dependence of Dynamics on Dissolved Gases
The effect of absorbed gases on hydrophobic surfaces could have implications
on a wide variety of phenomena, such as fluid flow and lubrication. To see what
effect absorbed gas would have on our fluctuations; we first used ellipsometry to
measure the fluctuations in degassed water. Then we allowed the water to equilibrate
with ambient conditions and remeasured the fluctuations. The results are shown in
Figure 4.11. Both histograms are qualitatively the same. This indicates that absorbed
gases have little effect on the fluctuations at a water/hydrophobic interface.
4.1.5 Dependence of Dynamics on pH
We also looked at how changing the pH of the solution would effect the
fluctuations.
Varying the pH will change the surface charge density of the
hydrophobic surface, as explained by Grunze et al. [4.7]. Auto-ionization of water
creates hydronium and hydroxide ions that can then preferentially absorb onto the
80
hydrophobic surface. This creates significant surface charging; for ODT at pH 6 with
10-3 M KCl, there are 1.8x10-2 excess charges per nm2. The literature suggests a pH
dependent surface charging on hydrophobic surfaces with a pKa ≈ 4. We measured
the fluctuations with ellipsometry for a range of pH. Figure 4.12 displays the results.
When we decrease the pH from 8 to 6, that is as the surface becomes less negative,
the histograms take on a more “flat-topped” shape.
This change in shape may
indicate that the surface is going from a wet state (Gaussian shape) to a dry state (flattopped shape) due to decreased absorption of hydroxide ions with decreasing pH.
Absorbed hydroxide ions could allow hydrogen bonding to the surface in effect
decreasing the hydrophobicity of the surface, and therefore reducing the fluctuations.
4.2 Power Spectra
Power spectra are another way to investigate the dynamics at the
water/hydrophobic interface. The power spectrum is made by squaring the Fourier
transform of the time trace and plotting it versus frequency on a logarithmic scale.
This graph indicates the frequencies and the relative amounts of the sine waves
making up the time trace. The power spectrum of a pure sine wave, for example
sin(2πft), will have one spike positioned at the frequency of the sine wave, in this
case f. A linear combination of a series of sine waves will be made up of many
spikes.
However, many power spectra show not spikes but functions that vary
smoothly with frequency. These spectra are a result of time traces made up of nondiscrete frequencies. The power spectrum of white noise is a horizontal line, as it
consists of all frequencies equally.
81
Using ellipsometric time series, we have calculated the power spectra for
many systems. The power spectrum from a water/hydrophilic interface made up of
water on silicon oxide is shown in Figure 4.13. It has the horizontal shape indicative
of white noise. Figure 4.14 displays the power spectrum of water at a hydrophobic
surface of OTE. The power spectrum displays a linear shape with a slope equal to
negative two. At the OTE/ethanol interface a different shape is observed. As seen in
Figure 4.15, the power spectrum is not completely flat as for the water/hydrophilic
system but does not have the slope characteristic of the water/hydrophobic interface.
This slope of – 2 suggests that the fluctuations are due to discrete entities as
smooth variations would decay more rapidly [4.8]. However it could also be a result
of long time scale drift in the data as this often turns up as a slope of negative two.
We found no satisfactory way to remove this possibility from the data. Instead we
switched to a different technique, autocorrelation. The power spectrum and the
autocorrelation function form a Fourier transform pair. Therefore much of the same
information can be gathered from autocorrelation curves that could be found in power
spectra.
4.3 Autocorrelations
Autocorrelations are good at determining whether a data set is random
[4.9, 4.10]. If it is not random, it is also good at determining what type of time series
model would be appropriate for that data set [4.9, 4.10]. Autocorrelations measure
the correlation between measurements in a data set with a specific time lag (τ). The
autocorrelation function, G(τ), can be defined as
82
G (τ ) =
[F (t − τ ) − F (t − τ ) ] [F (t ) − F (t ) ]
F
(4.1)
2
where F(t) is the fluctuation as a function of time, and <F> is the average value of the
fluctuations [4.11] . This equation can be simplified to
G (τ ) =
F (t ) F (t − τ )
F
2
−1
(4.2)
The autocorrelation function is plotted against the time lag to make the
autocorrelation curve. If the autocorrelation curve is flat and very close to zero, then
the system is random [4.9]. Sinusoidal behavior will produce an autocorrelation
curve with an alternating series of positive and negative spikes [4.9]. For a multiple
state system we expect that the system will remain in a single state for a characteristic
amount of time (t1) and then will switch to another state. In this case we would
expect the autocorrelation curve to be roughly step shaped, with positive
autocorrelation up until t1 and then dropping to near zero.
Looking at the shape of the autocorrelation curve could help us determine
which proposed model, capillary waves or wandering interface, best describes the
dynamics at the water hydrophobic interface.
4.3.1 X-Ray Photon Correlation Spectroscopy
Coherent scattering from a disordered surface produces a speckle pattern that
reflects the spatial arrangement of the surface [4.12].
X-ray photon correlation
spectroscopy (XPCS) measures the time variation of the speckle pattern, and
therefore provides information on the dynamics of the interface [4.12].
83
We
used
XPCS
to
attempt
to
observe
the
fluctuations
of
the
water/hydrophobic interface using a thin layer of water sandwiched between Kapton
and the OTE monolayers. We made two types of measurements with XPCS. In the
first set, the static measurements, the entire measurement was collected from one spot
on the sample; leading to an exposure time of approximately one minute. The static
measurements were made five times before moving to a new location on the sample.
In the second set, the moving measurements, the sample was translated during the
collection time; leading to a one to three second exposure time due to the finite size of
the beam. The moving measurements were repeated once before moving to a fresh
area.
The static measurements showed a very weak correlation around of 1.002 at
approximately 175 ms but only for the first set of scans on a sample. See Figure 4.16
a. Subsequent scans on the same sample over ten microns way failed to show this
correlation as displayed in Figure 4.16 b. The photon intensity also showed different
behaviors for the first scan on the sample. It would increase slightly for 30 seconds
and then decrease even more gradually over the next four scans. This did not occur
again when we moved to a new spot on the sample. This strange behavior could be
due to beam damage. As reported by Tidswell, photoelectrons produced in the silicon
wafer could cause widespread damage of the monolayer [4.13]. In this case the
correlations we observed could be of some X-ray induced reaction.
In an attempt to minimize beam damage we switched to moving
measurements.
Autocorrelation curves taken from the moving measurements
84
displayed no correlations as can be seen from Figure 4.17. The series of spikes
displayed in each set of curves is due to the pulsed nature of the electron beam.
What is the meaning of our negative result? Of course it could mean that
there are no characteristic times in the fluctuations to observe. However the amount
of beam damage produced could also be interfering with the observation of such
dynamics. As stated in Section 3.6, the observation of the depleted region is highly
dependent on the sample quality. The much higher flux required for the XPCS
observably damaged the sample within a few seconds and may have destroyed the
depletion layer.
4.3.2 Surface Plasmon Resonance Correlation Spectroscopy
By switching to SPR, we can look at the autocorrelations without having to
worry about damaging the sample. In SPR, the dynamic measurement recorded the
change in reflected intensity versus time. The change in intensity corresponds to a
change in the resonance angle as explained in Chapter 2. As the thickness or density
at the water/hydrophobic interface change, the resonance frequency is shifted.
Therefore, the time-scale of the change in reflected intensity corresponds to the timescales for fluctuation at the interface.
We collected dynamic measurements of ODT in water and in ethanol. The
autocorrelation curve from ODT in ethanol is shown in Figure 4.18 a. At small time
lags, around 1x10-3 s, there is a peak we see in all autocorrelation curves taken with
the SPR. We think it may correspond to some sort of electrical noise. The rest of the
curve is flat and close to zero. This indicates there is no characteristic time for
85
ethanol on ODT. The autocorrelation curve from ODT in water is shown in Figure
4.18 b. Again we see the noise peak at small time scales. However, there is a very
definite step in the correlation in the tenths of seconds region. This indicates that the
water/ODT system has a characteristic time of 0.5-0.6 s.
We did not expect to see a characteristic time that was so long. We would
expect that any fluctuations to occur on the millisecond or microsecond time scales.
Yet the XCPS also showed a slight correlation on the tenths of seconds time scale, so
it seems to be real.
What could this characteristic time indicate? It could mean that the surface
switches between states on the order of two to three times per second. Capillary
waves will also have a characteristic time [4.12]. In this case, the characteristic time
changes with the area interrogated. In order to try to distinguish between these two
possibilities, we looked at how the characteristic time changed with area.
4.3.3 Area Dependence
We used an iris to change the size of the incident laser beam in order to
change the plasmon excitation area. The results are shown in Figure 4.19. Although
the correlation is not as sharp as on other samples, there is no noticeable shift in the
characteristic time for all the areas we where able to employ. However, we were only
able to change the lateral size by less than a factor of 2.5 from 1.9 mm to 4.5 mm,
which may not have been enough to observe the effect.
86
4.3.4 Contact Angle Dependence
We saw that the histograms were effected by changing the contact angle of the
hydrophobic substrate in Section 4.1.3. Does the contact angle have any effect on the
characteristic time?
To answer this question we made a series of mixed thiol monolayers with
contact angles between 102 degrees and 70 degrees. We then collected dynamic
measurements in water. The results are displayed in Figure 4.20.
As can be seen in Figure 4.20, the strength of the correlation decreases with
decreasing contact angle. The correlation has disappeared by the time the contact
angle reaches 70 degrees. Interestingly, the characteristic time does not change with
contact angle.
4.3.5 Dependence on Dissolved Gases
As stated previously, the effected of dissolved gases is thought to have an
effect on hydrophobic interfaces.
To see if there was any dependence of the
autocorrelation curves on dissolved gases, we preformed an experiment where
degassed water was used to measure the time series with SPR than the experiment
was repeated with aerated water. The results are shown in Figure 4.21. Although the
correlation is not very sharp on this sample, there was very little difference between
the two curves.
87
4.4 Conclusions for the Chapter
We have seen that the water/hydrophobic interface fluctuates in unusual ways.
First, using histograms to analyze the time series data collected, we observed that
water/hydrophobic systems have non-Gaussian shapes very different from those
observed in wetting systems. These fluctuations took on more Gaussian shapes as the
contact angle or the dipole moment were decreased. Temperature and degassing had
no effect.
Two possibilities have been put forward to explain the histograms. In the
first, capillary waves forming at the interface were proposed as the origin of the
fluctuations. Secondly, the idea of a wandering interface was suggested. In this case,
the depletion layer shifts between different thicknesses. Unfortunately, the histogram
analysis was not able to support one over the other.
Autocorrelation curves provided another chance at trying to pick between
these two possibilities. The autocorrelation curves of water/hydrophobic systems
were found to have step-like decay indicating a characteristic time in the tenths of
seconds time scale. As contact angle was decreased, the strength of the correlation
decreased but there was no change in the characteristic time scale. Changing the
beam size and degassing the water had little effect on the autocorrelation curves.
At first sight, the results from the autocorrelations make both capillary waves
and a wandering interface seem very unlikely. It is hard to imagine an interface
shifting between different thicknesses only a few times per second. Also the lack of
area dependence seems to rule out capillary waves. However, we only changed the
area of the beam size by a factor less than 2.5; according to Sinha et al., capillary
88
waves logarithmically depend on the interrogated area [4.14].
In this case, the
expected change would have only been a factor of 0.86. Considering this evidence it
seems that capillary waves are the most likely source of fluctuations at the
water/hydrophobic interface.
4.5 References:
[4.1] Section “1.3.3.14 Histograms” NIST/SEMATECH e-Handbook of Statistical
Methods, <http://www.itl.nist.gov/div898/handbook/>, May 4 2006
[4.2] McCormick, T.A. Physical Review E 68 061601 (2003)
[4.3] Grunze, M., and A. Pertsin Journal of Physical Chemistry B 108 (42) 16533
(2004)
[4.4] Chandler, D. Nature 437 640 (2005)
[4.5] Huang X., R. Zhou and B.J. Berne Journal of Physical Chemistry B 109 3546
(2005)
[4.6] Cho, J.-H.J., B. M. Law and F. Rieutord Physical Review Letters 92, 166102
(2004)
[4.7] Chan, Y.-H.M., R. Schweiss, C. Werner and M. Grunze Langmuir 19 7380
(2003)
[4.8] Zhang, X., Y. Zhu and S. Granick Science 295 663 (2002)
[4.9] Section “1.3.3.1 Autocorrelations” NIST/SEMATECH e-Handbook of Statistical
Methods, <http://www.itl.nist.gov/div898/handbook/>, May 9 2006
[4.10] Section “1.3.5.12 Autocorrelations” NIST/SEMATECH e-Handbook of
Statistical Methods, <http://www.itl.nist.gov/div898/handbook/>, May 9 2006
89
[4.11] “Fluorescence Correlation Spectroscopy (FCS) Technical Manual” Third
Edition June 2000 ISS Champaign IL
[4.12] Madsen, A., T. Seydel, M. Tolan and G. Grübel Journal of Synchrotron
Radiation 12 786 (2005)
[4.13] Tidswell, I.M., T.A. Rabedeau, P.S. Pershan and S.D. Kosowsky Journal of
Chemical Physics 95 2854 (1991)
[4.14] Sinha, S.K., E.B. Sirota, S. Garoff and H.B. Stanley Physical Review B 38
2297 (1988)
90
4.6 Figures
Depletion Layer Thickness (nm)
0.56
0.54
0.52
0.56
500.2
500.6
501.0
502
506
510
510
530
550
0.54
0.52
0.56
0.54
0.52
0.56
0.54
0.52
500
1000
1500
Time (s)
Figure 4.1 Time Traces of Ellipsometry Measurement
Times traces calculated using the hyperbolic tangent model are plotted on
many different time scales.
91
a
b
c
Ethanol/Hydrophobic
Δ h (nm)
Water/Hydrophobic
Δ h (nm)
Water/Hydrophilic
Δh (nm)
Figure 4.2 Histograms of Three Systems
The histograms for the change in thickness are shown for three different
systems; ethanol and OTE (a), water and OTE (b), and water and silicon oxide (c).
92
a
4000000
Number
3000000
2000000
1000000
0
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.01
0.02
0.03
ΔR
b
1800000
Number
1500000
1200000
900000
600000
300000
0
-0.03
-0.02
-0.01
0.00
ΔR
Figure 4.3 Histograms Taken with SPR
The histograms were taken with SPR of ODT in ethanol (a) and in water (b).
93
a
1600000
1400000
Number
1200000
1000000
800000
600000
400000
200000
0
-0.010
-0.005
0.000
0.005
0.010
Δ Reflectivity
b
800000
Number
600000
400000
200000
0
-0.010
-0.005
0.000
0.005
0.010
Del Reflectivity
Δ Reflectivity
Figure 4.3 Histograms Taken with SPR in Air and Water.
The histograms were taken with SPR of ODT in air (a) and in water (b).
94
a
12000
Number
10000
8000
6000
4000
2000
0
-0.015 -0.010 -0.005 0.000
0.005
0.010
Δh(nm)
b
12000
Number
10000
8000
6000
4000
2000
0
-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015
Δh(nm)
Figure 4.5 Effect of Temperature on the Histograms
Histograms taken on OTE in water are shown for two different temperatures;
56 oC (a) and 26 oC (b), on the same spot on the sample.
95
Δ h (nm)
Figure 4.6 Effect of Roughness on Histograms
The histogram of fluctuations in height for a rough OTE surface in water was
taken with ellipsometry. The inset shows a 5 x 5 μm height contrast AFM image of
the surface.
96
a
1800
θ = 97.3 ± 1.1
1600
Number
1400
1200
1000
800
600
400
200
0
-0.10
-0.05
0.00
0.05
0.10
Δ h (nm)
b
θ = 19.0 ± 1.4
Number
2000
1500
1000
500
0
-0.10
-0.05
0.00
0.05
0.10
Δ h (nm)
Figure 4.7 Contact Angle Dependence in Histograms
The histograms were taken with ellipsometry for thiols in water. In a, a 2:1
mixture of ODT and R-OH T was used, while in b a pure R-OH T layer was used.
97
40000
2σ
30000
Number
S ta n d a rd D e v ia tio n
0.005
0.004
20000
10000
0
-0.02
0.003
0.00
0.02
Δh (nm)
0.002
0.001
0
50
100
Advancing Contact Angle
Figure 4.8 Standard Deviation versus Substrate Contact Angle
The standard deviation, illustrated in the inset, for histograms taken by
ellipsometry on mixed thiol monolayers in water was plotted against substrate contact
angle. The trend is highlighted by the blue line. The pink line represents the standard
deviation of ethanol/OTE system.
98
Standard Deviation
0.02
0.01
0.00
0
20
100
C ontact Angle
Figure 4.9 Standard Deviation versus Solvent Contact Angle
The standard deviation of histograms taken on OTE with ellipsometry in
different solvents is plotted versus the solvent contact angle.
99
S ta n d a r d D e v ia tio n
0.03
Water
0.02
0.02
Ethanol
0.01
0.01
0.00
-0.1
Toluene
Cyclohexane
0.1
0.3
0.5
0.7
0.9
1.1
Relative Solvent Polarity
Figure 4.10 Standard Deviation versus Relative Solvent Polarity
The standard deviations of histograms taken with ellipsometry for OTE in
various solvents are plotted against relative solvent polarity.
100
a
b
H (nm)
Figure 4.11 Histogram Dependence on Dissolved Gasses
Histograms of OTE in freshly degassed water (a) and then remeasured after
the water was allowed to equilibrate with the atmosphere (b) were taken with
ellipsometry at the same position on a single sample. The hyperbolic tangent model
was used.
101
a
25000
Number
20000
15000
10000
5000
0
-0.005
0.000
0.005
Δh (nm)
b
Number
15000
10000
5000
0
-0.005
0.000
Δh (nm)
c
20000
Number
15000
10000
5000
0
-0.005
0.000
0.005
Δh (nm)
Figure 4.12 Histograms Dependence on pH
Histograms taken with ellipsometry on OTE in aqueous solution for pH equal
to 8.3 (a), 7.7 (b) and 6.4 (c) are displayed. The hyperbolic tangent model was used.
102
0.005
Figure 4.13 Power Spectrum from a Water/Hydrophilic System
The power spectrum was calculated from ellipsometric data for a system
consisting of water and silicon oxide, which is hydrophilic. The line is included as a
guide for the eye.
103
-2
Figure 4.14 Power Spectrum from a Water/Hydrophobic System
The power spectrum was calculated from ellipsometric data for a system
consisting of water and OTE, which is hydrophobic. The line is included as a guide
for the eye.
104
Figure 4.15 Power Spectra from OTE in Water and Ethanol
The power spectra were calculated from ellipsometric data for OTE in water
(blue) and ethanol (red).
105
a
g(τ)
1.02
1.00
50
100
150
200
Time (ms)
b
g(τ)
1.02
1.00
50
100
150
200
Time (ms)
Figure 4.16 X-ray Autocorrelations Static Sample
These X-ray autocorrelations were taken on a static sample. The first time a
scan was taken on the sample a slight correlation of 1.002 was seen at a time lag of
approximately 175 ms (a). Subsequent scans showed no correlation (b).
106
1.10
1.08
1.06
1.04
g(τ)
1.02
1.00
0.98
0.96
0.94
0.92
0.90
50
100
150
200
Time (ms)
Figure 4.17 X-Ray Autocorrelations on Moving Sample
This X-ray autocorrelation was taken on a moving sample, in an effort to
prevent beam damage. The scan shows no autocorrelation. Subsequent scans were
similar.
107
a
0.020
G(τ)
0.015
0.010
0.005
0.000
1E-3
0.01
0.1
1
τ(s)
b
0.004
G(τ)
0.003
0.002
0.001
0.000
1E-3
0.01
0.1
1
10
τ(s)
Figure 4.18 Autocorrelation Curves from SPR
Autocorrelation curves for ODT monolayers with ethanol (a) and water (b) are
shown. The red lines are a guide for the eye.
108
0.1
1
G(τ)
0.003
0.0002
d = 4.5 mm
d = 1.9 mm
d = 2.8 mm
0.002
0.0001
0.0002
0.0001
0.1
1
τ(s)
Figure 4.19 Effect of Beam Size on the Autocorrelation Curves
Autocorrelation curves for ODT in water were taken with different incident
beam sizes. Measured laser beam diameters of 1.9 mm (blue circles), 2.8 mm (red
triangles), and 4.5 mm (black squares) were used.
109
0.003
102 degrees
97 degrees
70 degrees
G(τ)
0.002
0.001
0.000
-0.001
1
10
τ(s)
Figure 4.20 Effect of Contact Angle on Autocorrelation Curves
Autocorrelation curves are shown for monolayers of mixed thiols with
different contact angles in water. The blue squares, green circles and pink triangles
are for thiol layers with contact angles of 102, 97 and 70 degrees respectively. For
clarity, the blue curve was shifted +.0005 and the magenta curve was shifted -.0005
vertically.
110
0.0010
0.1
1
10
G(τ)
0.0005
0.0005
0.0000
0.0000
0.1
1
10
τ (s)
Figure 4.21 Effect of Dissolved Gasses on Autocorrelation Curves
SPR autocorrelation curves taken with on the same ODT sample first with
degassed water (red squares) and then with aerated water (black circles).
111
Chapter 5: Concluding Remarks
Water/Hydrophobic interfaces surrounds us.
You can see many
examples in day to day life for example dew drop on a leaf, the folding of proteins in
our bodies and even liquids on stain resistant fabrics. Yet no well accepted picture of
what happens at such interfaces has been developed.
One theory that has been put forth is that a thin depleted region forms around
extended hydrophobic objects [5.1, 5.2]. If it exists this depletion layer would have
implications in such diverse areas as colloidal self-assembly, and the boundary
conditions of fluid flow. Another idea is that nanobubbles form at the interface [5.3].
Many experiments have seen evidence of the depletion layer [5.4-5.8]. Others have
seen evidence for nanobubbles [5.3, 5.9]. Yet others have no evidence for anything
different at water/hydrophobic interfaces [5.10-5.12].
In an effort to help clarify this situation, we have investigated
water/hydrophobic
surfaces
using
three
different
experimental
techniques;
ellipsometry, X-ray reflectivity, and SPR. These three techniques complement each
other, making up for each others weaknesses. For example, ellipsometry, being a
table top technique, is great for systematically changing variables such as pH and
temperature; however it cannot easily decouple thickness and density. On the other
had X-ray reflectivity can decouple thickness and density but it is impractical to run
an entire series of pH experiments.
In Chapter 3, we saw very strong ellipsometric evidence for the qualitative
existence of a depleted region, but could not quantitatively determine its properties.
Using X-ray reflectivity we also saw qualitative evidence for the existence of a
112
depleted region. The best fit of the reflectivity data gave a thickness of 2.7 Å,
electron density corresponding to 20% water content, and width of the error function
profile (between the depletion layer and bulk water) of 4 Å. However there was still
considerable room to change the parameters and still get an expectable fit. After
combining the ellipsometry data and the reflectivity data, we found they agree quite
well and we can be fairly confident that the depletion layer has a thickness between
1.5 Å and 4 Å, and a density less than 45 % that of bulk water.
We also took advantage of the information on the lateral characteristics of the
interface provided by X-ray reflectivity. Using this information, we were able to rule
out the possibility of nanobubbles forming at the water/hydrophobic interface. This
finding contrast with AFM studies that saw evidence of nanobubbles [5.3, 5.9]. In
truth this result is not too surprising as nanobubbles have only been observed with
tapping mode AFM which may have nucleated the bubbles during the measurement.
We found that the depletion layer is highly dependent on temperature, contact
angle and sample quality. This dependence might explain some of the discrepancies
in the literature as different groups often use hydrophobic surfaces with different
properties.
Additionally, we looked at the dynamics of the hydrophobic/water interface.
Very few experiments have looked at the dynamics in this system despite its
fundamental importance.
In fact, Chandler proposes that fluctuations at the
hydrophobic/water interface are the key distinguishing factor between wet and dry
interfaces [5.13]. We used both histograms and autocorrelation functions to get a
handle on how the interface was varying in time.
113
In Chapter 4, we found that the histograms of time series taken from
water/hydrophobic systems had a strange non-Gaussian shape. While those taken
from wetting interfaces showed the expected Gaussian shape. This was observed
both in time series data collected with ellipsometry and SPR. We proposed two
possible reasons for the non-Gaussian shapes; (1) capillary waves at the boundary
between the water and depleted region, or (2) a wandering interface, where the
depleted region jumps between states with different thicknesses.
To try to distinguish which possibility was more reasonable, we switched to
looking at autocorrelations. We found that the autocorrelations indicated a single
characteristic time of 0.5-0.6 s. This time seems too long to attribute to a wandering
interface. Therefore, we believe the capillary wave model is most likely. However,
we were not able to observe the characteristic time change with area as expected with
capillary waves, most likely because we did not change the area by a large enough
factor.
Finally, we are able to build up a detailed picture of what happens at a
water/hydrophobic interface. We see that the water pulls away from the surface
leaving behind a depletion layer. Also we found that this depletion layer fluctuates
with something akin to capillary waves. All in all, we can say that water meets a
hydrophobic surface reluctantly and with fluctuations.
114
5.1 References
[5.1] Stillinger, F.H. Journal Solution Chemistry 2 141 (1973)
[5.2] Lum, K., D. Chandler and J.D. Weeks Journal of Physical Chemistry B 103
4570 (1999)
[5.3] Tyrrell, J.W.G., and P. Attard Physical Review Letters 87 (17) 176104-1 (2001)
[5.4] Sur, U.K. and V. Lakshminarayanan Journal of Colloid and Interface Science
254 410 (2002)
[5.5] Steitz, R., T. Gutberlet, T. Hauss, B. Klösgen, R. Krastev, S. Schemmel, A.C.
Simonsen and G.H. Findenegg Langmuir 19 2409 (2003)
[5.6] Schwendel, D., T. Hayashi, R. Dahint, A. Pertsin, M. Grunze, R. Steitz and F.
Schreiber Langmuir 19 2284 (2003)
[5.7] Castro, L.B.R., A.T. Almeida and D.F.S. Petri Langmuir 20 7610 (2004)
[5.8] Doshi, D.A., E.B. Watkins, J.N. Israelachvili and J. Majewski., Proceedings of
the National Academy of Science 102 9458 (2005)
[5.9] Ishida N., T. Inoue, M. Miyahara and K. Higashitani, Langmuir 16, 6377
(2000).
[5.10] Mao, M., J. Zhang, R.-H. Yoon and W.A. Ducker Langmuir 20 1843 (2004)
[5.11] Takata, Y., J.H.J. Cho, B.M. Law and M Aratoni, Langmuir 22 1715 (2006)
[5.12] Jensen, T.R., M. O. Jensen, N. Reitzel, K. Balashev, G.H. Peters, K. Kjaer and
T. Bjørnholm Physical Review Letters 90 (8) 086101-1 (2003)
[5.13] Chandler, D. Nature 437 640 (2005)
115
Appendix A: Use and Maintenance of the Ellipsometer
The purpose of this appendix is to explain the use and maintenance of the
ellipsometer so that in the future others can continue to make use of the experimental
apparatus.
A.1 Alignment and Calibration of the Ellipsometer
The alignment and calibration must be done on a regular basis, on average
once a year. Also if the absolute values of the voltages measured at the two analyzer
angles disagree significantly, the ellipsometer needs to be realigned. In the following
I lay out step by step instructions for the alignment and calibration.
A.1.1 Aligning the Laser
The normal operating arrangement of the ellipsometer is shown in Figure A.1.
First, the nut at the center joint of the arms must be removed, and then the arms are
carefully lifted off and oriented parallel to each other. Next, remove all elements
from the incident arm except the laser. Be very careful when moving the phase
modulator. It is very delicate and could break if shaken or jarred. Make sure to sit it
flat on the bench so it cannot fall. Cover the analyzer and the photomultiplier tube
(PMT) with post-it notes. This ensures that the laser cannot shine directly on the
PMT which could burn it. This configuration is shown in Figure A.2. Using two
irises of the same height align the laser. This is done by making sure the laser beam
passes through both openings when one is close to the laser and the other is far away
(i.e. on the second arm). The alignment of the laser can be controlled as shown in
116
Figure A.3. After the laser is aligned put the arms back on the center joint. There is
no need to replace the nut yet.
A.1.2 Finding the p-Polarization
Now align the arms such that the laser hits the silicon sample at 75 degrees
and is reflected at 75 degrees and hits the analyzer. This is shown in Figure A.4. The
sample may need to be rotated to achieve this geometry. This ensures the light is at
the Brewster angle for silicon. In this section it is important to use a fresh and clean
silicon sample. Details of silicon cleaning are given in Appendix B. Replace the
polarizer on the incident arm. Make sure that the light reflected from the polarizer
hits the laser just above or below the incident beam. Adjust the polarization until the
reflected light is extinguished. It is important that the reflected beam is clean (i.e.
very little scattering). If it is not, clean the glass sample holder and make a new
silicon sample. The angle that light is extinguished is the p-polarization angle, p. Do
this step twice and average the values. They may be displaced by 180 degrees; if this
is true, subtract 180 from the larger and then average them. It is important to
remember that the laser itself is also polarized and so this can also cause a minimum
in the reflected light. To avoid this problem, check that the light after the polarizer
but before the sample is still strong when the reflected light is extinguished. If the
only minimum occurs when the light after the polarizer is weak, rotate the laser body
30 degrees. You will have to go back and realign the laser in this case and then find
the p-polarization. Write down the p-polarization angle.
117
A.1.3 Finding the Analyzer Angles
Set the polarizer at p+45o. Remove the arms from the center joint and make
them horizontal. Remove the post-it notes from the analyzer but not from the PMT.
Adjust the polarizer angle until the transmitted light is extinguished. Do this twice.
The average is a. Set the polarizer at p-45o, and find the minimums, the average is a
+ 90o.
A.1.4 Finding the p-Axis of the Phase Modulator
Replace the phase modulator on the incident rail, aligning it such that the
reflected light hits just above the incident beam on the laser, and the beam passes
through the center of the phase modulator. Turn on the power supplies. On the
power supply (large brown box) turn on the power (green light), wait 30 s and then
turn on the high voltage (red light). Then turn on the current controller. See Figure
A.5. Add an n-d filter between the laser and the polarizer. Remove the post-it notes
from the PMT. Set the polarizer at p, and the analyzer at a. Set the lockin harmonic
to 2 and the phase to 2ω. Unlock the set screw on the phase modulator and adjust the
voltage until R is a minimum (X will go negative and positive). Record the angle of
the minimum. Repeat with the analyzer at a + 90o. The average of these two
measurements is the p-axis of the phase modulator. Carefully tighten the set screw
without changing the polarization of the phase modulator.
118
A.1.5 Setting Jo(δo) to Zero
Set the polarizer at p+45o. On the power supply, switch the power supply
from amplifier to supply. Turn the voltage with the large dial until the current on the
current controller reads 0.7. See Figure A.6. Measure the DC voltage by connecting
the coaxial cable to the back of the current controller (labeled DC) and the voltmeter.
Rotate the little dial on the Beaglehole controller until it reads 0.0. Make a chart of
the voltage recorded from each setting of the Beaglehole controller for both a and a +
90o. An example is shown in Figure A.7. The goal is to find the controller position
that makes the voltage the same for both a and a + 90o. Once this position is found
lock the controller and switch the power supply back to constant current mode. To do
this dial the voltage on the power supply until the current reads 0.0, and switch back
to amplifier. This is the end of the alignment.
A.1.6 Calibration
With the analyzer set at a and the polarizer set at p+45o, change the phase on
the lockin until the voltage reads zero. Make sure the harmonic was set at 2. Then
push the – 90o button on the lockin and record the phase and voltage. Repeat with the
analyzer set at a + 90o. The average voltage is V2ω,cal and the average phase is 2ω.
Next we need to find ω. The arms should still be parallel. Put a quarter waveplate after the phase modulator. Make sure the reflected beam is just above the
incident beam, to do this you will have to turn off the power supply and remove the nd filter. Be sure to replace the n-d filter before turning on the PMT. Turn on the
PMT. Find the fast axis of the wave-plate by minimizing the voltage at the two
119
analyzer angles with the harmonic set at 2. Lock the wave-plate. Set the lockin
harmonic at 1. Minimize the voltage with the analyzer set at a. Then push the + 90o
button on the lockin and record the phase and voltage. Repeat with the analyzer set at
a + 90o. The average voltage is Vω,cal and the average phase is ω. This is the end of
the calibration. Replace the arms on the center joint and replace the nut.
A.2 Taking measurements with the Ellipsometer
Taking measurements with the ellipsometer requires several intermediate
steps. The first is cleaning and assembling the sample cell. Next is finding the
Brewster angle. Finally, you can collect and analyze the data.
A.2.1 Cleaning and Assembling the Sample Cell
The parts of the sample cell are pictured in Figure A.8. The glass and Teflon
parts are cleaned by soaking them in base bath overnight and then rinsing with large
amounts of de-ionized water. The base bath is made by adding 1 part KOH to 5 parts
isopropyl alcohol. The glass should not be stored for long periods in the base bath as
this will cause it to become cloudy. The metal part is cleaned by soaking in nitric
acid overnight and then rinsing with large amounts of de-ionized water.
After
cleaning, all parts are dried in the oven for over 30 min and then allowed to cool to
room temperature.
To assemble the sample holder first put the o-ring on the metal part. Next,
mount the sample, as shown in Figure A.9. The sample should be mounted loosely
enough to pull out easily but tightly enough not to shift when held vertically. It is
120
important not to mount the sample too tightly as this will cause stress induced
birefringence and distort the ellipticity. Next, slip the metal part inside the glass
holder and secure it by tightening the bushing. The bushing should only be hand
tightened. The assembled sample cell is shown in Figure A.10.
A.2.2 Finding the Brewster Angle
Next the sample cell is placed inside the sample holder in the ellipsometer.
The set screws can be used to ensure the light is hitting the sample in the center and
reflecting out the sample holder opening toward the PMT. The vertical position of
the sample can be adjusted with the translation stage attached to the backside of the
sample holder. Once the sample is positioned and light is hitting the PMT, turn on
the power supply. Remember not to turn the PMT on if the n-d filter is out. The
lockin should be set with the harmonic at 2 and the phase at 2ω. Rotate the incident
arm until the voltage for both analyzer positions are the same in sign and magnitude.
While you are changing the incident angle, make sure the reflected light is hitting the
PMT. This position is the Brewster angle.
A.2.3 Collection and Analysis of Data
Once the ellipsometer is set at the Brewster angle, you can start data
collection. It is easiest to do this with the computer program “ellipsometer”, but I
will explain how to do it by hand. Set the lockin harmonic to 1 and the phase to ω.
Record the voltage for both analyzer positions. Repeat this procedure several times in
order to find the deviation in the data.
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The ellipticity can be calculated from the above voltages. First take the
absolute values of the voltages. Next take the average of the a and a + 90o voltages
for each measurement. Divide the average by two times Vω,cal, and this quantity
equals the ellipticity.
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A.3 Figures
Sample
Holder
Phase
Modulator
Analyzer
Polarizer
Laser
PMT
N-d filter
Figure A.1 Photograph of the Ellipsometer.
Above is a picture of our home-built phase modulated ellipsometer in its
operating position.
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Figure A.2 Aligning the Laser
This photo shows the geometry for aligning the laser. Post-it notes are used to
protect the PMT.
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Figure A.3 Adjusting the Laser
This photo shows the how to adjust the laser. Turning the top knob moves the
laser left and right (red arrows). The middle knob allows you to adjust the rotational
orientation of the laser (blue arrows). Turning the lower knob moves the laser up and
down (yellow arrows).
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75o
Figure A.4 Finding the p-Polarization
This photo shows the geometry for finding the p-polarization. Both arms are
set at 75 degrees as shown.
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a
b
Figure A.5 Turning on the PMT
This photo shows the current controller (a) and the power supply (b) in regular
operating mode.
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Figure A.6 Supply Mode
This photo shows the power supply in supply mode. The arrow indicates the
knob used for setting the current.
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Controller
0
100
300
500
600
550
525
537
531
534
a
3.3 mV
46 mV
166 mV
.33 V
.52 V
.71 V
.87 V
.79 V
.755 V
.761 V
a+90o
1.48 V
1.45 V
1.35 V
1.19 V
1.01 V
.82 V
.66 V
.74 V
.783 V
.761 V
Figure A.7 Controller Chart
Here is an example chart used to find the proper value for the Beaglehole
controller. We are trying to find the controller value where the voltages are equal. It
helps to start by changing the controller value in large steps and seeing where the
voltages cross each other. Then you can use smaller steps as you close in on the
proper value.
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Metal Part
Bushing
O-Ring
Glass Part
Figure A.8 Components of the Ellipsometer Sample Cell
The components of the sample cell are pictured above. The o-ring is covered
with Teflon.
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Figure A.9 Metal Part/Sample Assembly
This picture shows the correct way to mount the sample on the metal part.
Remember to put the o-ring on the metal part before mounting the sample.
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Figure A.10 Assembled Sample Cell
The fully assembled sample cell is shown. Note when adding liquid do not
fill it above the bottom of the metal piece expect for degassed fluids.
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Appendix B: Sample Preparation
The purpose of this appendix is to provide information on sample preparation
detailed enough so that future students can continue preparing high quality samples.
This appendix is broken into three parts; preparing hydrophilic silicon, preparing
OTE monolayers and preparing thiol monolayers.
B.1 Hydrophilic Silicon
Preparing clean hydrophilic silicon substrates is important not only for use as
hydrophilic surfaces but also as a first step in making OTE monolayers. In order to
produce clean silicon, you need to use clean glassware.
You will need one
scintillation vial per sample and several pipettes. The glassware should be cleaned by
soaking in base bath overnight, rinsing thoroughly with deionized water and drying in
the oven.
Next, the silicon is soaked in Piranha solution heated to 70 oC for at least one
hour. Piranha solution is made by mixing three parts hydrogen peroxide with seven
parts sulfuric acid. This reaction is exothermic and extreme caution should be taken.
Next, the silicon should be rinsed twenty times with deionized water and dried in the
oven for two to three hours.
Then the silicon should be cleaned in the UV/ozone cleaner. Place the silicon
samples shiny side up on to the Teflon o-rings inside the UV/ozone cleaner. Adjust
the lab jack until the samples are approximately a half inch from the UV lamp. Flow
a small amount of oxygen into the cleaner. Close the cleaner, turn it on and let it run
for half an hour.
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The final step is plasma cleaning. Put the sample into the plasma cleaner, and
vacuum it down for 45 minutes. Then add oxygen for 5 minutes. Purge the system
for 1 minute. Add more oxygen for 30 seconds; purge for 15 seconds; add oxygen for
15 seconds and then turn off the oxygen. Immediately turn on the plasma cleaner to
HI. The plasma should be a bright pink or purple color. After 10 minutes, turn off
the plasma. Allow the samples to cool for 30 minutes. Turn off the vacuum then add
oxygen until the samples can be removed.
The samples should now be very
hydrophilic, with a contact angle around zero degrees.
B.2 OTE Monolayers
The best OTE monolayers are formed with vacuum distilled OTE. The first
step is to make a prehydrolysis solution by diluting 0.21g distilled OTE and 0.125g of
1.3 M HCl to a volume of 25mL with THF. Next age the prehydrolysis solution for
approximately 44 hours. Next, make the dipping solution by dissolving 0.6g of the
prehydrolysis solution in 10g cyclohexane. This can be done in a disposable plastic
vial rinsed with acetone several times and blown dry in nitrogen, or in a clean glass
beaker. The clean silicon samples are then submerged in the dipping solution for 35
min. The dipping solutions should be overflowed with cyclohexane to remove a
partial film of excess OTE at the surface. Then the samples can be pulled vertically
and slowly from the solution. This is done to minimize the chances of any surface
layer from attaching to the surface.
After removing the silicon wafers, ultrasonicate them for three minutes each
in cyclohexane, isopropanol, and acetone to remove micelles and any other
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polymerized clusters adsorbed on the surface. Following ultrasonication, blow dry
the samples with pure nitrogen and bake under vacuum at approximately 120°C for
two hours.
Once you have made the OTE monolayers, it is important to characterize them
to see if they are of high quality. The contact angle of good monolayers is high and
steady with time. A contact angle that changes with time indicates that the OTE is
not well attached to the silicon.
B.3 Thiol Monolayers
Making the thiol monolayers is much easier than making the OTE
monolayers.
The first step is to sputter a clean glass slide with a titanium or
chromium adhesion layer, 1-2 nm thick, followed by approximately 60 nm of gold.
The gold layer thickness is not critical; it will work as long as it is between 20 nm and
100 nm thick. Make a 1 mM solution of thiol in ethanol. Place the gold coated slide
in a clean vial and add enough thiol to completely submerge it. Let it sit for 30
minutes.
Then rinse it five times with ethanol.
Fill the vial with ethanol and
ultrasonicate the sample for five minutes. Rinse the sample with ethanol five more
times and then blow it dry. This simple procedure has almost a 100% success rate. If
you want to make mixed thiol monolayers, be sure to mix the thiols together in
solution before adding the glass slide. Otherwise the finished monolayer will have
much more of the first thiol you added than you expected.
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Appendix C: Use of the SPR
The purpose of this appendix is to explain to future graduate students how to
continue experiments with the SPR.
The preparation of samples for SPR was
explained in Appendix B. There is little maintenance or calibration required for the
SPR set-up. The batteries in the photodetectors need to be replaced periodically and
everything should be kept free of dust and fingerprints.
C.1 Cleaning the Sample Cell
The sample cell components are pictured in Figure C.1. The Teflon piece and
the tubing should be cleaned in base bath. The metal pieces do not contact the sample
and therefore do not need to be cleaned. The O-ring is not lined with Teflon and
should only be cleaned with water, unless it was exposed to hydrocarbons in which
case soap may be used followed by very thorough rinsing in water.
C.2 Mounting the Sample
Mounting the sample is more of an art than a science. The flint glass slides
are brittle and often break during the mounting process. I hope that the tips outlined
below will minimize its difficulty.
The first step is to couple the gold coated slide to the prism. The high-index
prism requires we use a high-index optical coupling substance. We use Cargille
“Meltmount” with refractive index of 1.704 and a melting point of 60 oC. The first
time the prism is coupled to a sample you first must melt the coupler and spread a few
drops onto the uncoated side of the sample. Then place the preheated prism on to the
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slide. The heat of the prism should help spread the coupler between the slide and
prism. If it does not, gently heat (~50 oC) the slide until the coupler forms a thin
layer. If the prism is already coupled to a sample and you simply want to change
samples gently heat (~50 oC) the sample/prism. After a few seconds the coupler will
soften enough that the prism can be removed by gently twisting and sliding it off.
The area between the prism and slide will look golden if properly coupled. Silvery
spots indicate trapped air. To remove air bubbles, while the coupler is still warm,
press the prism down onto the slide. You can also try sliding it to remove bubbles
close to the edges. Figure C.2 pictures the prism properly mounted to the slide.
Next the prism/slide must be put into the sample holder. With the thumbscrews fully loosened and one removed, position the slide so that it covers the o-ring
and the prism is centered. Make sure the o-ring is properly seated in its hole. It
should appear level when seen from both sides. Next, making sure the washers are
not touching the slide; gently tighten the thumb-screws until the metal bars just touch
the washers. This should be tight enough to retain water. If not, tighten the screws a
quarter turn more. Be sure to tighten the screws equally during this process, or else
the slide will break. The assembly is shown in Figure C.3.
C.3 Taking Measurements
Now the sample cell can be placed in the SPR set-up. To do this move the
translational stage on the rotation stage all the way back away from the prism holder.
Lower the sample cell into place such that the prism sits in the prism holder.
Advance the translational stage just until the sample cell is held tight. At this point
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the cell can be filled with liquids if desired. You are now ready to begin making
measurements. The final configuration is pictured in Figure C.4.
C.3.1 Static Measurements
Static measurements are made by measuring the reflected intensity versus
angle. We make these measurements by hand. Simply adjust the angle in small
increments and record the intensity. I usually use 1 degree increments until I notice
the intensity starting to change when I switch to 0.1 degree increments.
The
measured curve can be compared to curves calculated on Corn’s website
http://unicorn.ps.uci.edu/calculations/fresnel/fcform.html.
C.3.2 Dynamic Measurements
Dynamic measurements are made by recording the change in reflectivity
versus time at one angle. In this case, it is important to set the angle such that it is
within the linear region of the SPR curve to get maximum contrast between the
different states. Once the angle is chosen the n-d filters should be adjusted such that
the signal from detector 1 is the same magnitude as that from detector 2. See Figure
C.5. Also make sure the photodetectors have not been saturated. A lockin is used to
divide the two signals and also to avoid problems due to impedance mismatching.
The data is then recorded using a program written by Dr. Sung Chul Bae. When
collecting data for long periods of time it is important to ensure that tension from the
coaxial cables does not cause the photodetector to shift. To prevent this pull up slack
138
in the cables before locking down the detector. Also placing pedestals beside the
detector and along the cable can help.
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C.4 Figures
Washer
Metal Bar
Sample Cell
Thumb Screw
Screw
O-Ring
Figure C.1 SPR Sample Cell Components
The sample cell components are shown above. There are four screws, four
thumb screws, and 16 washers. Per screw, three washers go between the metal bar
and the Teflon sample cell and one goes between the Teflon sample cell and the
thumb screw.
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a
Optical Coupling
Prism
Slide
Au Coating
Thiol Layer
b
Figure C.2 Prism/Sample Assembly
The proper way for the prism to be mounted on the sample is illustrated
above. The schematic (a) illustrates the relative orientation of the components. The
photograph shows a mounting free of bubbles.
141
Figure C.3 Mounted SPR Assembly
This figure shows the proper way to assembly the SPR sample cell.
142
Figure C.4 Sample Cell in Place in the SPR
This figure shows the final configuration of the sample cell in the SPR.
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Glan Laser
Polarizer
Mirror 1
LASER
Iris
Mirror 2
ND
Detector 2
Prism
Rotation
Stage
ND
Sample
Cell
Detector 1
Figure C.5 Schematic of SPR Apparatus
We built our SPR using the Kretschmann Geometry. Here light from the laser
becomes p-polarized after the Glan laser polarizer. The size of the beam is controlled
by an iris and then incident on the prism. It hits the gold layer with an angle above
the critical angle, producing an evanescent wave and thus exciting surface plasmons.
The signal is collected by detector 1. The signal from detector 2 is used to remove
long-time scale fluctuations from the data.
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AUTHOR'S BIOGRAPHY
Adele Poynor Torigoe was born in Columbus, Ohio, on December 27,
1978. She received a B.S. in Physics Summa Cum Laude from the University
of Maryland Baltimore County in 2001. She continued her education at the
University of Illinois at Urbana-Champaign, earning her Master of Science in
Physics in 2003. During her time at the University of Illinois, she was a
teaching assistant for two semesters of Physics 112 and one semester of
Physics 213/214, for which she won two UIUC Department of Physics
Excellence in Teaching Awards; the Mavis Memorial Fund Scholarship; and
was twice listed on “The Incomplete list of Teachers Ranked as Excellent by
their Students”. She also received a travel stipend from the Chair’s travel
fund to present at the ACS Meeting in 2004. Following the completion of her
Ph.D., Adele will begin a tenure-track professorship at Allegheny College in
Pennsylvania.
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