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Chemistry
1-1-1985
Self-Diffusion of Water in Polycrystalline Smectic
Liquid Crystals
Frank D. Blum
Missouri University of Science and Technology
Alapat S. Padmanabhan
Rana Mohebbi
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Recommended Citation
F. D. Blum et al., "Self-Diffusion of Water in Polycrystalline Smectic Liquid Crystals," Langmuir, American Chemical Society (ACS),
Jan 1985.
The definitive version is available at http://dx.doi.org/10.1021/la00061a021
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Blum, Padmanabhan, and Mohebbi
128 Langmuir, Vol. 1, No. 1, 1985
liquid crystals can also lead to uncertainties in the interpretation of the PFGSE results.
In this study, we report the results of self-diffusion
measurements on polycrystalline smectic liquid crystals
of sodium 4 41'-heptylnony1)benzenesulfonate (SHBS) and
water. This system was chosen for study because of the
simplicity of the primary structure of the surfactant as
compared to other double-tailed naturally occurring surfactants such as phospholipids. The SHBS-water system
also exhibits structure, thermal behavior, and molecular
dynamics that are quite similar to those found in phospholipid-water systems.17J8 Unlike phospholipids, the
SHBS head group is simple and contains only one hydrophilic moiety. This results in a proton resonance for
water that is narrow enough to use in self-diffusion measurements. In addition, it is possible to prepare the sample
so that the effects of either small domain size or defects
in the liquid crystals are insignificant. It is therefore
possible to estimate the diffusion coefficient of the water
parallel to the surface of the bilayer. For comparison, the
temperature dependence of the self-diffusion coefficients
of water in bulk and an ionic solution is also studied.
Sodium nitrate is the salt chosen for this purpose because
it is similar to the SHBS molecule in that it has the same
cation and a singly charged anion with three oxygens.
Experimental Section
Sodium 441'-heptylnony1)benzenesulfonate was obtained from
the University of Texas and recrystallized from n-butyl alcohol
before use. Samples were prepared for self-diffusion measurements by weighing the dry surfactant in a 5-mm NMR tube and
then adding a known amount of distilled water. The samples were
then annealed at 80-90" C for 2 h to overnight in tightly capped
tubes. This procedure converts almost all of the surfactant into
planar smectic liquid crystal~.~~*'~
The compositionof the liquid
crystals is ca.75 wt % SHBS and 25 w t % water." The solubility
of the surfactant in water at room temperature is only 0.06 wt
%, The sodium nitrate and cyclohexane used were reagent grade
and used without further purification.
The pulsed-field gradient spin-echo (PFGSE) NMR method
was used to measure the self-diffusion coefficients. The measurements were made by proton NMR at 90 MHz on a JEOL
FX-9OQ. The PFGSE pulse sequence used is as previously described21 and is similar to the Stilbs modificationzz of the
Stejskal-Tannerz3method. The advantage of this modification
is that the time between the 90' pulse and echo, 2A, is kept
constant while the field gradient pulse time, 6, is varied. This
also keeps the J-modulation and transverse relaxation effects
constant, so that the effects of diffusion are probed separately.
The resulting equation for the NMR intensity, A , is 21,zz
A = A, exp[-y2G2D,&2(A- 6/31]
(1)
where A. is the intensity with 6 = 0, y is the gyromagnetic ratio
of the nucleus under study, G is the field gradient strength, and
Dlabis the self-diffusion coefficient in the laboratory frame.
For an isotropicdy diffusing species a plot of In A vs. @,where
/3 = P ( A - 6/3), should yield a straight line with a slope of -yzGzD.
Simple exponential behavior was found for cyclohexane,used for
gradient calibration, bulk distilled water, and aqueous sodium
nitrate solutions. The water diffusion in bulk water and 5.3 M
NaNO, solutions was studied for comparison with SHBS dispersions. The 5.3 M NaN03 solution has the same salt/water
(17) Blum, F. D.; Miller, W. G. J . Phys. Chem. 1982,86, 1729.
(18)Blum, F. D. Ph.D. Thesis, University of Minnesota, Minneapolis,
MN, 1981.
(19) Blum, F. D.; Russo, P. E., Neitering, K.; Miller, W. G., unpublished results.
(20) Frames, E. I.; Puig, J. E.; Talmon, Y.; Miller, W. G.; Scriven, L.
E.; Davis, H. T. J. Phys. Chem. 1980,84, 1547.
(21) Cheever, E.; Blum, F. D.; Foster, K. R.; Mackay, R. A. J. Colloid
Interface Sci., in press.
(22) Stilbs, P. J . Colloid Interface Sci. 1982, 87, 385.
(23) Stejskal, E. 0.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288.
W
I/'I
Figure 1. Normal proton NMR spectrum of a 75 wt % SHBS-25
wt %
,+',
water dispersion. The sharp component is the water peak.
I'
<-
Figure 2. Typical PFGSE spectra for a 50 w t % SHBS-50 wt
% water sample at 25 "C. Only the water peak has significant
echo intensity.
mole ratio ( l / l O . l ) as the liquid-crystalline domains. Diffusion
coefficients for the solutions were calculated from the raw data
using log linear least-squares fits. The nonexponentialdecay seen
in the liquid-crystallinedispersions was fitted to the theory by
using the IMSL ZXSSQ routineF4 The criteria for the best fits
were minima in the sums of the squares of the residuals. (In many
cases multiple local minima were found in the fitting process and
the values reported believed to represent the global minima.)
The field gradient used had a value of ca. 0.05 T/m and was
generated using the homospoil accessory. Typical spectra were
taken with a 1000-Hzwindow, 2048 points, and a pulse delay of
4 s. The value of A used was 0.07 s, but the same results were
obtained with A = 0.14 s. The sample temperature was maintained to f 1"C with a JEOL temperature controller. Samples
were dowed to equilibrate for 15 min at each temperature before
the spectra were run. Since most of the samples were biphasic,
the position of the sample tube was kept constant so that the
contribution of water in the isotropic phase was similar for each
temperature studied.
Results and Discussion
A normal proton NMR spectrum of a 75 w t % SHBS-25
wt % water is shown in Figure 1. The sharp resonance
is due to the water. The much broader resonances on
either side of the water peak are due to the aromatic
protons on the phenyl ring and the aliphatic protons on
the tails. The broadness of the surfactant resonances is
due to the anisotropic motion of the surfactant in the
smectic phase and is similar to that observed in the 13C
NMR.17 As can be seen, the water resonance is not completely resolved near the baseline. The spectrum for this
sample is similar to that found for samples with lower
water contents except for the contribution from water in
the isotropic phase.
The results of a PFGSE experiment on a 50 wt %
SHBS-50 wt % water sample at 27 "C are shown in Figure
(24) IMSL Fortran Subroutines Library IMSL, Houston, TX.
Langmuir, Vol. I, No. I , 1985 129
Self-Diffusion of Water in Liquid Crystals
I
-
-
1
L '9
Figure 4. Bilayer fixed axis system showing the orientation of
the director at an angle B with respect to the laboratory (field
gradient) axis.
Table I. Best Fit D and A Values for Water Self-Diffusion
from Ea 4 as a Function of the First B Value Used
p > 3.7 x 10493
p > 2.0 x 10-5 s3
T,"C
D, W 0m2/s
D,
mz/s
10
27
51
68
85
p~io~(~3)
Figure 3. PFGSE data for a 50 wt % SHBS-50 wt % water
sample aa a function of temperature: (e) 10,(M) 27, (A)51,(0)
68,( 0 )85 O C . The curves drawn are the best fits to the model
and the vertical scales are shifted for display purposes. In the
insert is shown the behavior at low p values for the (U) 27 "C SHBS
sample, (---)bulk water, and (---) water in 5.3 M NaN03solution.
2 as a function of p. It is noted that, even though the
surfactant resonances overlapped with the water resonance
in the normal spectrum, the PFGSE experiment yields a
well-resolved peak. This is because the T2'sof the surfactant are short enough that no observable echo is obtained in 2A from the surfactant peaks. The T2value for
the water is long enough so that a strong echo is obtained.
In Figure 3, the data for the PFGSE results for the 50
wt % SHBS-50 wt % water sample as a function of temperature are shown. The plot of In A vs. /3 does not yield
a straight line. This is indicative of anisotropic diffusion.
The dashed and center lines shown in the insert represent
the behavior of water in bulk and sodium nitrate solution
at room temperature, respectively. As can be seen, the
contribution from the bulk water should be negligible at
values of /3 of about 10 X lo4 s3 or possibly less depending
on the amount of bulklike water present. At short gradient
times the contributions from bulklike water in the isotropic
phase varied. For longer gradient times the intensities
were independent of composition for samples from 60 to
25 wt % water, provided that proper annealing conditions
were met. In the annealed samples, most of the liquidcrystalhe material is found in large planar domains.18 The
lack of dependence of the intensities on the amount of
isotropic phase suggests that the liquid-crystalline domains
are planar and static over the PFGSE time scale. Thus
the diffusion behavior of water in the liquid-crystalline
domains is constant over this range. It appears that the
composition of the equilibrium liquid crystal is ca. 75 wt
% SHBS-25 wt % water and the domain size is large
enough that domain boundaries and/or imperfections are
negligible or at least constant. A t higher water contents,
the large fraction of isotropic water, plus the reduced domain size and increased curvature of the crystals, results
in faster reorientation of the domains and the water in
them, making interpretation of the results difficult.
In the analysis of the data, we model the water layers
in the smectic liquid crystals as infinite parallel plates. On
a bilayer fixed coordinate system the diffusion tensor is
diagonal with elements D,, = D, D, = D, and D,, = AD,
where we define D as the diffusion coefficient parallel to
0.46
0.83
1.4
2.1
4.6
0.40
0.74
1.1
1.8
2.6
the bilayer surface. The geometry is shown in Figure 4.
Since the water layer is only about 10 8, thick,lg we can
neglect the restricted diffusion within the water layer
perpendicular to the bilayer surface. However, if the water
can penetrate the bilayer, leave the domain, or pass into
another layer through a crystalline defect, an apparent
perpendicular component will result and is represented by
AD, where A is a constant representing the fraction of the
parallel component seen perpendicular to the bilayer
surface.
In the NMR experiment, spins are labeled along the
direction of the field gradient, which in this case is the
laboratory 2 axis. The relationship between the bilayer
coordinate system and the laboratory system is given by
the Euler angles.2s This results in a laboratory diffusion
coefficient given by
DIab = ZTPDbiPTZ
(2)
where 2 is a unit vector in the 2 direction and extracts the
laboratory 2 component, P is the transformation matrix
containing the Euler angles, and Dbi is the bilayer fixed
diffusion tensor. Insertion of Dlab result into eq 1yields,
for a given domain,
A = A, exp[-y2G2D((sin2e) - A(cos2e))]
(3)
where 6 is the angle between the static field (laboratory
2 axis) and the bilayer director. This is essentially the
same formula derived by Callaghan et a1.26except they
define their parallel and perpendicular diffusion components with respect to the director and ours me with respect
to the bilayer surface. This is also the correct expression
for use in oriented b i l a y e r ~ . ~ J A
~ Jsomewhat
~ - ~ ~ different
approach to the same problem has also been taken by
StejskaL2'3
In our polycrystalline samples the directors of the bilayers are randomly oriented and the appropriate average
of eq 3 is
A = A ( J r exp[-y2G2D((sin2e)
+ A(cos2@)]sin6 dB
(4)
where A,' also contains the appropriate normalization
factors. Since the contribution from isotropic water is
(25) Arfkin, G. 'Mathematical Methods for Physicists"; Academic
Press: New York, 1970.
(26) Callaghan, P. T.; Jolley, K. W.; Lelievre, J. Biophys.J. 1979,28,
133.
(27) Stejskal, E. 0. J. Chem. Phys. 1965, 43,3597.
(28) Stejskal, E. 0. Ado. Mol. Relaxation Process 1972, 3, 27.
130 Langmuir, Vol. 1, No. 1, 1985
Blum, Padmanabhan, and Mohebbi
_a
10
o - ~
-
*
m
E
Y
a
-io
10
-n
10
1.6
d.0
d.2
d.4
3.6
1000/T
Figure 5. Temperature dependence of water self-diffusion
Coefficients for 50 wt % SHBS-50 wt % HzO, ( 0 )p > 20 X lo+
and (A)p > 3.7 X lo4 mz/s. For comparison those for (A)pure
water and (0)
5.3 M NaN03 solutions are shown.
difficult to quantify, the data were fitted first by using fl
values greater than 3.7 X lo4 s3 and then greater than 2.0
X
s3. Intensities from values of p less than 3 X lo4
s3 were believed to contain contributions from bulklike
water. The results are shown in Table I. The best fits
are also drawn in Figure 3 for the fl > 3.7 X lo6 s3 data.
Except for the 10 "C data with = 2.0 X
s3,all of the
data showed "best fits" with A 0. This suggests that the
diffusion perpendicular to the bilayer is negligible. It is
therefore likely that domain boundaries or crystal imperfections are unimportant in these annealed systems.
Water in smaller or imperfect liquid-crystalline domains
will probably escape into the isotropic phase, diffuse rapidly, and only contribute to the intensities for the first few
0 values. As a result the experiment at longer values is
only sensitive to water trapped in a single liquid-crystalline
domain.
The temperature dependence of both sets of data for the
different values is shown in Figure 5 along with the results
for water diffusion in bulk and in 5.3 M NaN03. The large
value of D for the 85 "C data at the shorter value is
probably due to a larger contribution of water which escapes the bilayers and biases the data. If one excluded this
datum point, an energy of activation of 20.2 f 1.2 (SD)
kJ/mol is obtained for both data sets. For comparison the
diffusion coefficients for water in bulk and a 5.3 M NaN03
solutions are shown to be over an order of magnitude
faster. The temperature dependence for pure water was
found to be non-Arrhenius. Between 25 and 65 "C an
apparent energy of activation of 20.3 f 1.1 kJ/mol was
found. This compares with Mills previous results for pure
water from which an energy of activation for diffusion of
19.6 (1-15 OC) and 17.6 (kJ/mol (15-45 "C) was determined.29 For the salt solution the temperature dependence was more or less Arrhenius with an activation energy
of 17.0 f 1.0 kJ/mol. The fact that the diffusion of water
in an aqueous salt solution is much faster than seen in the
dispersions suggests that the geometry plays a major role
in the reduce diffusion coefficients observed and not
binding to the rather mobile counterions.
Comparison with Other Systems. To the authors'
knowledge, this is the first systematic study of the tem(29) Mills, R. J . Phys. Chem. 1973, 77, 685.
perature dependence of water diffusion in smectic liquid
crystals. This is partially due to the fact that many systems only form smectic liquid crystals over a very limited
temperature range. In addition, it is often difficult to
prepare the system so that the domain size is large. Rigaud
et al.30used labeled water to measure the HTO self-diffusion coefficient in lecithin-water systems. Their results
at 30% water suggest D = 0.9 X
m2/s at 22 "C, which
is just slightly higher than our results. The consistency
of their results and ours suggests that the transport in the
lamellar phase must be the dominant mechanism for water
transport in their radiolabeling experiment. Results from
Tiddy et al.13J4on perfluorooctanoates at 23 "C show the
effects of sample preparation but suggest very rapid diffusion of water. Both D,, and D , in their studies on oriented samples are of the same order of magnitude as bulk
water. Callaghan et al.15 have obtained D = 8.5 X 10-lo
m2/s for D20 in a 70/30 potassium palmitate/D20 dispersion at 65 "C. Finally, Ukleja and DoanelGhave also
measured a 70/30 potassium palmitate/H20 sample and
estimated D to be 2.5 X
and 1.6 X
m2/s at 100
and 75 "C, respectively.
These values, even though taken at similar water contents, show significantly faster diffusion than observed in
this study. We suggest that this disagreement could be
due to one of two possibilities. First, it is possible that the
single-tailed surfactants used in the other studies are much
more mobile than SHBS and consequently the aqueous
region is also. This is possible considering that SHBS is
a much larger molecule than single-chain surfactants. This
effect may be seen in the lateral diffusion coefficients of
surfactants at 24 "Ce9 The double-tailed surfactants in
systems with 30-40% water are all about an order of
magnitude slower than the single-tailed ones. Second, it
is also possible that defects in the structure allow the water
molecule to change domains over the course of the NMR
experiment. This results in an apparent diffusion coefficient that is faster than that actually occurring in between
the bilayers.
Finally, we note that for our system we found that the
diffusion perpendicular to the bilayer was negligible compared to that parallel to the bilayer. Results for oriented
potassium palmitate/water (70/30) suggest a very similar
result in that respect. Values of Dli/Dl are on the order
of 25-35.15J6 This would certainly be consistent with our
measurements although it is impossible to put more than
a lower limit of about a factor of 10 on this ratio using
unoriented samples. We believe our A = 0 results suggest
that the water molecules responsible for the intensities at
high fl values do not leave their domains and the domains
do not reorient during the NMR experiment. Results such
as those obtained in the perfluorooctanoate systems13J4are
probably dominated by crystalline defects or small domains because the ratios from these systems are on the
order of 2 or less.
Conclusions
Using the NMR PFGSE technique it is possible to
measure the translational diffusion coefficients of water
in polycrystalline smectic liquid crystals. For the SHBS
system it is found that the self-diffusion coefficients are
much slower than those found in other systems. It is found
that the diffusion perpendicular to the bilayers is negligible
compared to that parallel to the bilayers. The energies of
activation for this diffusion is 20.2 f 1.2 kJ/mol and is
slightly larger than bulk water or sodium nitrate solution.
(30)Rigaud, J.-L.; Gary-Bobo, C. M.; Lange, Y. Biochem. Biophys.
Acta 1972, 266, 12.
Langmuir 1985,1, 131-135
We believe that these results are truly representative of
the two-dimensional diffusion in the planar layers between
the bilayers.
Acknowledgment. We acknowledge the financial
support of the donors of the Petroleum Research Fund,
131
administered by the American Chemical Society, Research
Corporation, National Science Foundation, the Drexel
University Graduate School, and Computer Center. We
also thank Prof. C. Rorris for helpful discussions.
Registry No. SHBS,67267-95-2;water, 7732-18-5.
Kinetics of Displacement and Charge-Transfer Reactions
Probed by SERS: Evidence for Distinct Donor and
Acceptor Sites on Colloidal Gold Surfaces
C. J. SandrofPt and D. R. Herschbach*t
Exxon Research and Engineering Co., Annandale, New Jersey 08801
Received August 17, 1984. In Final Form: October 19, 1984
Both the electron donor W F and the electron acceptor TCNQ give large SERS signals upon adsorption
onto colloidal gold particles, but only TTF displaces previously adsorbed pyridine, indicating that molecular
donors and acceptors ockupy different surface sites. The acceptor (Lewis acid) site probably involves a
reducible metal complex of Au+ while the donor (Lewis base) site may be associated with AuO. The kinetics
for the charge-transfer reaction involving two distinct TTF oxidation states, TTF0.3+ TTF'.O+, can be
explained by migration of the adsorbate from the donor to the acceptor site.
-
Introduction
The degree of charge transfer between certain molecular
adsorbates and metal surfaces can be determined from
vibrational frequency shifts observed by surface-enhanced
Raman scattering.l We have found that electron donors
and acceptors based on tetrathiafulvalene (TTF) and
tetracyanoquinodimethane (TCNQ) form with the noble
metals particularly harmonious adsorbate/metal systems.
These molecules absorb very strongly on silver and gold
surfaces, transfer considerable amounts of charge, and give
rise to large surface-enhanced Raman (SERS)signals. In
experiments with these charge-transfer systems, we observed chemical transformations on gold colloidal surfaces
involving two distinct oxidation states of adsorbed TTF
a partially oxidized TTF species, TTF0.3+,
disappeared in
favor of the radical cation, TTF'.O+. Here we report a
kinetic study of this surface oxidation and competitive
adsorption experiments with pyridine, TTF and TCNQ.
Our results can be rationalized by assuming that molecular donors and acceptors occupy different sites on the
gold colloidal surface. The surface sites which act as acceptors or Lewis acids seem to involve a gold complex with
the metal in a high oxidation state. These sites are readily
reduced by proficient electron donors like 'ITF which have
exceptionally low ionization potentials. The surface sites
that serve as donors or Lewis bases behave like the neutral
metal and readily give up charge to acceptors like TCNQ
with sizable electron affmities. The donor sites, in contrast
to acceptor sites, seem to possess substantial amphoteric
character; they can behave as Lewis acids or bases depending on the difference between the work function of
gold and the electron affinity or ionization potential of the
adsorbate molecule. Thus TTF, when adsorbed as the
partially oxidized TTF0.3+,binds to the Auo site, while
TTF'.O+ attaches strongly to the Au+ site. The relative
populations of
and T"F1.'H
do not remain constant
in time after the initial adsorption onto the gold colloids.
Rather, TTF0.3+converts to the radical cation with a
fmliorder rate constant of 1 X lo4 s-l. The two-site model
suggests that this interfacial charge transfer involves migration from a donor to an acceptor site.
Experimental Section
Aqueous colloidal suspensions consisting of 150-&diametergold
particles at a concentration of 2 X lo1' cm-3 were prepared by
the sodium citrate method of Turkevich et al.2 Adsorbates were
introduced to 20 cm3 of the sol by adding 2 drops of a 5 X
M solution. (Solventswere water for pyridine and acetone for
the charge-transfer compounds.) The colloid turned from red to
blue 30 min after the addition of pyridine, indicating partial
aggregation of the sol particle^."^ Addition of TTF turned the
sol to blue instantly, showing that TTF is much more effective
at reducing the net (negative)charge on the colloidal surface than
is pyridine. The very fast aggregation caused by "Fis consistent
with the flocculation time predicted by Smoluchowski's6theory
of diffusion-limited aggregation. For our dilute colloidal suspension, aggregation should occur in about 1s once the repulsive
interactions between the charged particles are significantly reduced.' As in previous work? only after aggregation had occurred
could strong SERS signals be seen. In contrast to electron donon
like pyridine and TIT, the electron acceptor TCNQ did not cause
any significant aggregation, and SERS spectra of TCNQ were
obtained only after the colloid was aggregated by pyridine or TTF.
(1) Sandroff, C. J.; Weitz, D. A.; Chung, J. C.; Herschbach, D. R. J.
Phvs. Chem. 1983 87. 2127.
12) Turkevich, J.; Stevenson, P. C.; Hillier, J. Discuss. Faraday SOC.
1947. 11. 58.
( 3 ) Creighton, J. A.; Blatchford, C. G.; Albrecht, M. G. J. Chem. SOC.,
Faraday Trans. 2, 1979, 75, 790.
(4) See: Creighton, J. A. In 'Surface Enhanced Raman Scattering";
Chang, R. K., Furtak, T. E., Eds.; Plenum Press: New York, 1982; "Metal
Colloids".
(5) Turkevich, J.; Garton, G.; Stevenson, P. C. J. Colloid Sci., Suppl.
1954, 1, 26.
(6) Von Smoluchowski, M. Physic 2. 1916, 17, 557, 858; Z. Phys.
Chem. 1917,92, 129.
~~
'Present address: Bell Communications Research, Murray Hill,
NJ 07974.
Exxon Faculty Fellow from Harvard University.
*
0743-7463/85/2401-0131$01.50/0
(7) 'Colloid Science"; Kruyt, H. R., Ed.; Elsevier: Amsterdam, 1952;
p 278.
0 1985 American Chemical Society