3228
Langmuir 2008, 24, 3228-3234
Explicit Hydrogen Molecular Dynamics Simulations of Hexane
Deposited onto Graphite at Various Coverages
M. J. Connolly,† M. W. Roth,*,† Paul A. Gray,‡ and Carlos Wexler§
UniVersity of Northern Iowa, Department of Physics, Cedar Falls, Iowa 50614, UniVersity of Northern
Iowa, Department of Computer Science, Cedar Falls, Iowa 50614, and UniVersity of Missouri,
Department of Physics and Astronomy, Columbia, Missouri 65211
ReceiVed October 2, 2007. In Final Form: December 21, 2007
We present results of molecular dynamics (MD) computer simulations of hexane (C6H14) adlayers physisorbed onto
a graphite substrate for coverages in the range 0.5 e F e 1 monolayers. The hexane molecules are simulated with
explicit hydrogens, and the graphite substrate is modeled as an all-atom structure having six graphene layers. At
coverages above about F = 0.9 the low-temperature herringbone solid loses its orientational order at T1 ) 140 ( 3
K. At F ) 0.878, the system presents vacancy patches and T1 decreases to ca. 100 K. As coverage decreases further,
the vacancy patches become larger and by F ) 0.614 the solid is a connected network of randomly oriented islands
and there is no global herringbone order-disorder transition. In all cases we observe a weak nematic mespohase. The
melting temperature for our explicit-hydrogen model is T2 ) 160 ( 3 K and falls to ca. 145 K by F ) 0.614 (somewhat
lower than seen in experiment). The dynamics seen in the fully atomistic model agree well with experiment, as the
molecules remain overall flat on the substrate in the solid phase and do not show anomalous tilting behavior at any
phase transition observed in earlier simulations in the unified atom (UA) approximation. Energetics and structural
parameters also are more reasonable and, collectively, the results from the simulations in this work demonstrate that
the explicit-hydrogen model of hexane is substantially more realistic than the UA approximation.
I. Introduction
Because of its utility, stability, and geometry, much experimental and theoretical work has been completed on systems
involving graphite.1,2 Hexane on graphite has been studied
experimentally3-5 and computationally.6-13 Experimentally,
uniaxially incommensurate (UI) or commensurate herringbone
(HB) phases are seen at low temperatures (depending on
coverage), which transition into a rectangular solid/liquid
coexistence region, melting finally at temperatures ca. 175 K.3-5
At near-monolayer coverages, the melting temperature remains
fairly constant, and as the coverage decreases to about F ) 0.5,
the melting temperature drops to about 150 K.4
Until recently, most computer simulations of hexane on graphite
utilized molecular dynamics (MD) methods and employ the united
atom (UA) approximation. In the UA approximation, methyl
* To whom correspondence should be addressed. E-mail: [email protected].
† Department of Physics, University of Northern Iowa.
‡ Department of Computer Science, University of Northern Iowa.
§ University of Missouri, Columbia.
(1) Bruch, L. W.; Cole, M. W. Zarembam, E. Physical Adsorption: Forces
and Phenomena; Oxford University Press: Oxford, 1997.
(2) Shrimpton, N. D.; Cole, M. W.; Steele, W. A.; Chan, M. H. W. Rare Gases
on Graphite Surface Properties of Layered Structures; Benedek, G., Ed.; Kluwer:
Amsterdam, 1992.
(3) Krim, J.; Suzanne, J.; Shechter, H.; Wang, R.; Taub, H. Surf. Sci. 1985,
162, 446-451.
(4) Newton, J. C. Ph.D. dissertation, University of Missouri-Columbia, 1989.
(5) Taub, H. NATO AdVanced Study Institutes, Series C: Mathematical and
Physical Sciences; Long, G. J., Grandjean, F., Eds.; Kluwer: Dordrecht, The
Netherlands, 1988; Vol. 228, pp 467-497.
(6) Hansen, F. Y.; Taub, H. Phys. ReV. Lett. 1992, 69, 652-655.
(7) Hansen, F. Y.; Newton, J. C.; Taub H. J. Chem. Phys. 1993, 98, 41284141.
(8) Velasco, E.; Peters, G. H. J. Chem. Phys. 1995, 102, 1098-1099.
(9) Peters, G. H.; Tildesley, D. J. Langmuir 1996, 12, 1557-1565.
(10) Peters, G. H. Surf. Sci. 1996, 347, 169-181.
(11) Herwig, K. W.; Wu, Z.; Dai, P.; Taub, H.; Hansen, F. Y. J. Chem. Phys.
1997, 107, 5186-5196.
(12) Roth, M. W.; Pint, C. L.; Wexler, C. Phys. ReV. B 2005, 71, 155427155439.
(13) Pint, C. L.; Roth, M. W.; Wexler, C. Phys. ReV. B 2006, 73, 8542285431.
(CH3) and methylene (CH2) pseudoatoms replace the respective
real functional groups in a molecule. The UA approximation
saves significantly on the computational effort but has significant
shortfalls. The most significant are (i) the lack of in-plane space
occupation due to the missing hydrogens in the UA model, (ii)
the anisotropy introduced by the terminal hydrogens which is
averaged out in the UA model, (iii) the effect of the interaction
of the hydrogens with the graphite substrate which can be
substantially different than that of the UA model, and (iv) the
UA model significantly underestimates the moment of inertia of
the molecule.
Such UA simulations have provided a framework for advancing
our understanding of physisorbed alkanes and are capable of
reproducing the melting temperature at completion (F ) 1) fairly
accurately. In the most recent studies,12,13 at F ) 1 a solid
herringbone phase persists until a transition temperature T1 =
130 K. Then, there is a transition to an orientationally ordered
nematic mesophase up until T2 = 172 K above which there is
an isotropic liquid. In the near-monolayer range13 (0.875 e F e
1.05) a uniaxially incommensurate herringbone (UI-HB) solid
is present.
The simulations in the UA approximation, however, have some
serious pitfalls: for example, at moderate-to-high coverages the
adsorbate molecules are more prominently rolled on their side
perpendicular to the surface of the substrate, which is in significant
disagreement with experiment.4-7 Since the solid-nematic
transition temperature is very sensitive to coverage, an inaccurate
description of molecular rolling may result in erroneous
characterization of both low- and intermediate-temperature
phases.
Because of the three main limitations of the UA model
mentioned earlier, we expect that including explicitely the
hydrogens in the MD simulations will have a significant impact
on the simulation results. First off, since the hydrogens occupy
space through their collision diameters, including them stifles
the molecules’ ability to order and stack as seen in the UA nematic
10.1021/la703040a CCC: $40.75 © 2008 American Chemical Society
Published on Web 03/07/2008
MD Simulations of Hexane on Graphite
Langmuir, Vol. 24, No. 7, 2008 3229
Table 1. Dimensions (X,Y) of the Graphite Substrate for the
Various Coverages Used in This Work and Corresponding
Integer Valuesa
F (monolayer)
X (Å)
Y (Å)
nx ) X/4.26
ny ) Y/2.46
1.000
0.966
0.933
0.878
0.614
0.509
68.16
68.16
68.16
68.16
85.20
93.76
68.88
71.34
73.80
78.72
86.10
98.40
16
16
16
16
20
22
28
29
30
32
35
40
a
Figure 1. Perspective snapshot (allowing distortion of atomic sizes)
for the initial C6/gr herringbone configuration at area density F )
1. Adjacent graphene sheets alternate between purple and gray; hexane
carbons are blue and hydrogens are red.
mesophase. Specifically, the UA model incorporates a spherically
averaged collision diameter for methyl and methylene pseudoatoms, but in the explicit-hydrogen simulations, the presence of
the hydrogens gives rise to an effectively anisotropic methyl/
methylene collision diameter. As a result there are directions
along which the methyl/methylene collision diameter is on the
order of the sum of those for carbon and hydrogen, and this is
how the hydrogens occupy space and prevent close stacking.
Second, since the methyl and methylene constituents of the hexane
molecule are anisotropic, including the hydrogens can help better
represent molecule-substrate interactions, stifling the amount
of rolling and tilting seen in the UA model especially at higher
coverages. Since stacking, rolling, and tilting are significant
transition mechanisms in the UA simulations, the results of the
explicit-hydrogen model may differ significantly from the UA
picture, even though the UA model was meant to represent the
same physics. The main purposes of this work are (i) to simulate
the hexane/graphite (C6/gr) system at various coverages with
explicit hydrogens on the adsorbate molecules and (ii) to compare
the results to experiment and the results of UA simulations. This
allows for a more realistic representation of various physical
aspects of the C6/gr system which in turn will give more
meaningful and relevant insight into its dynamics and behavior
at phase transitions.
II. Computational Method
A. About the Simulation Program: NAMD.14 Since a major
objective of this work is to simulate hexane with explicit hydrogens,
each molecule will now contain more than three times the number
of atoms it did in the UA approximation. Moreover, since the
hydrogen atoms are so light, their simulation usually requires a
smaller time step. As a result, computational time cost increases
considerably. For our simulations we utilized the NAMD code14sa
parallelized MD simulation package which has been carefully and
thoughtfully developed and validated for different systems such as
nucleic acids15 and lipid bilayers.16 The optimizations and parallelization of NAMD permitted us to offset the extra cost of the
hydrogen inclusion by running our simulations in parallel computer
clusters. In addition, we have written pre- and postprocessors in
order to generate system specific input files and to reduce the resulting
output files, respectively.
(14) Kale, L. et al. J. Comp. Phys. 1999, 151, 283-312. See also http://
www.ks.uiuc.edu/Research/namd/.
(15) Jha, S.; Coveney, P. V.; Laughton, C. A. J. Comp. Chem. 2005, 26,
1617-1627.
(16) Benz, R. W.; Castro-Román, F.; Tobias, D. J.; White, S. H. Biophys. J.
2005, 88, 805-817.
The number of hexane molecules is kept constant (N ) 112).
B. Simulation Setup. The hexane molecule definition in our
study was obtained from the Brookhaven Protein Data Bank (PDB).17
A constant N ) 112 hexane molecule system is used for each coverage
in an initial herringbone configuration. Because NAMD currently
does not include an analytical expression for adatom-substrate
interactions, the substrate must be modeled in an all-atom fashion.
The graphite is modeled as six identical stacked graphene sheets,
stacked in the known (-A-B-A-B-) pattern in the z direction.
At the temperatures considered in this work, the dynamics of the
graphite does not contribute appreciably to those of the adlayer and
so the graphite is static, effectively serving as a lattice of interaction
sites for the adsorbed layer. A snapshot of the system’s initial
configuration, including the graphite substrate and a F ) 1 hexane
layer, is shown in Figure 1.
The (x,y) dimensions of the graphite sheets are varied for each
coverage studied, respecting the constraint that the computational
cell must remain commensurate with the graphite substrate. At nearmonolayer densities, the system is in a uniaxially incommensurate
phase and so, in order to mirror such symmetry in the simulations,
only the Y parameter of the computational cell is varied for the four
highest densities studied here. For all densities studied, the initial
configuration was a herringbone lattice expended uniformly in the
y direction that was allowed to equilibrate. At densities where
vacancies begin to form, other initial configurations, such as a
patch in the center of the computational cell were utilized and the
results obtained were not appreciably different from those with the
expended configuration. Appropriate substrate dimensions are shown
in Table 1.
All simulations in this study are constant molecule number,
coverage, and temperature (N ) 112, F, and T, respectively). Periodic
boundary conditions are used in the (x,y) plane and free-boundary
conditions are applied in the vertical z direction. To maintain a
constant temperature, velocity rescaling is utilized. The time step
for all simulations is 1 fs, and each simulation ran for 250 000
equilibration steps and then averages are taken over the next 500 000750 000 time steps.
C. Interaction Potentials. All particle-particle interactions in
the simulations presented here are in the standard CHARMM22
format.18 The internal bonded degrees of freedom consider interactions between atoms within the same molecule created by a chemical
bond. The first internal molecular degree of freedom considered is
two-body C-C bond stretching, whose force arises from the
harmonic potential
ustretch ) k(l - l0)2
(1)
Here k is the bond stiffness and l0 is the equilibrium bond length.
The C-H bonds were held rigid so that as large a time step as
possible could be used and also because such an internal degree of
freedom is probably unimportant to the dynamics of interest in this
study. The three-body bond angle bending is considered
(17) http://www.wwpdb.org/.
(18) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; States, S.;
Swaminathan, S.; Karplus, M. J. Comp. Chem. 1983, 4, 187-217. See also http://
www.charmm.org.
3230 Langmuir, Vol. 24, No. 7, 2008
Connolly et al.
ubend(θ) ) kθ(θ - θ0)2
(2)
Table 2. Bonded Potential Parameters Used in the Simulationsa
parameter
Here θ is the bond angle, θ0 is its equilibrium value, and kθ is the
angular harmonic stiffness constant. Four-body dihedral torsion of
the form
udihed ) kd{1 + cos(nφd - δ)}
K (kcal/mol )
l0 (Å)
kθ (kcal/mol rad2)
[( ) ( ) ]
r0
rij
12
-2
r0
rij
kqiqj
rij
(6)
A. Unit Coverage (F ) 1). The F ) 1 low-temperature solid
is a commensurate herringbone structure where almost all
molecules lie flat to the surface. This can be seen visually in
Figure 2. As temperature is increased for the system, various
order parameters and physical quantities are calculated in order
to quantify and understand its behavior and changes.13 The
herringbone order parameter OPherr gives a measure of the
orientational order of the molecular axis with respect to the
graphite substrate. Here the “molecular axis” is along a molecule’s
smallest principal moment of inertia. OPherr is defined by
〈∑
Nm
i)1
(-1)j sin (2φi)
All values are in CHARMM2218 format; methyl (CH3) groups are
represented by “C3” and methylene groups by “C2”.
Table 3. Nonbonded Potential Parameters Used in the
Simulationsa
parameter
value
-0.055 (C3)
-0.08 (C2)
-0.022 (H)
-0.07 (C)
2.06 (C3)
2.175 (C2)
1.32 (H)
1.9924 (C)
-0.27 (C3)
-0.18 (C2)
0.09 (H)
0 (C)
(kcal/mol)
σ (Å)
III. Results and Discussion
Nm
δ (deg)
(5)
which arises due to the internal charge redistribution between carbons
and hydrogens (even though hexane is not polar, there is a small
charge distribution). The electrostatic interactions are calculated by
the well-known particle mesh Ewald (PME) summation technique
and involves pairs on the same, as well as other, molecules. The
nonbonded potential parameters are given in Table 3.
OPherr t
n (units)
a
are utilized to calculate potential parameters in the cases involving
mixed interactions. All Lennard-Jones lattice sums are taken out
to a pair separation rij ) 7.5 Å and then smoothly diminished to zero
at a separation of rij ) 10 Å. Coulomb interactions are also included
1
kd (kcal/mol)
(4)
1
σij ) (σi + σj)
2
uC )
θ0 (deg)
6
The rij-12 term results in a repulsive force that becomes considerable
when electron clouds of interacting atoms overlap. Ultimately, such
repulsion has its origin in the Pauli Exclusion Principle. The rij-6
dispersion term represents an attractive force and has its origin in
the van der Waals forces arising from fluctuating dipolar interactions.
In eq 4, ij is the potential well depth and σij are the well depth and
collision diameter, respectively, for interactions involving particles
i and j. Lorentz-Bertholot combining rules
ij ) xij,
222.5
1.53
58.00 (C3-C2-C2)
58.35 (C2-C2-C2)
36.00 (H-C3-H)
36.00 (H-C2-H)
115.0 (C3-C2-C2)
113.6 (C2-C2-C2)
115.0 (H-C3-H)
115.00 (H-C2-H)
0.15 (C3-C2-C2-C2)
0.15 (C2-C2-C2-C2)
0.195 (H-C2-C2-H)
0.16 (H-C3-C2-H)
1 (C3-C2-C2-C2)
1 (C2-C2-C2-C2)
3 (H-C2-C2-H)
3 (H-C3-C2-H)
0 (C3-C2-C2-C2)
0 (C2-C2-C2-C2)
0 (H-C2-C2-H)
0 (H-C2-C2-H)
(3)
is also included, where kd is the torsional stiffness constant, n is the
multiplicity, φd is the dihedral angle, and δ is an angular offset. This
expression for torsional energy, and hence the description of gauche
defect formation, differs from that used in previous work6-10,12,13
because in this case the hydrogens also contribute through methyl
torsion. Still, in our simulations gauche defects are calculated as
rotations around bonds in the carbon backbone of the molecule. The
bonded potential parameters used in the simulations are given in
Table 2.
Nonbonded interactions include two-body C-C and C-H
interactions for atom pairs either in different molecules and also
adatom-substrate pair interactions. The first type of nonbonded
interaction is represented by a modified the Lennard-Jones potential
uLJ(rij) ) ij
value
Å2
〉
(7)
where φi is the angle between the axis of greatest moment of
inertia of molecule i and the x axis. The parity of the integer j
q (esu)
a
All values are in CHARMM22 format.18 Like-species interactions
are shown here, and parameters for mixed interactions are given by eq
5. Here data for the graphite carbons are represented with “C”.
accounts for the different orientational herringbone sublattices.
OPherr is equal to unity if all molecular axes are oriented at 45°
and 135° for each sublattice, respectively, and drops as a result
of thermal fluctuations to zero for random in-plane orientations.
Since the F ) 1 static herringbone lattice for the systems studied
here has angles at about 38° and 153°, OPherr has a zerotemperature limiting value of about 0.866 and drops from there.
At low temperatures, the large value of OPherr (Figure 3) along
with the sharp peaks in azimuthal angle probability distributions
P(φ) (Figure 4) characterize a strong herringbone solid. The
microscopic roll angle ψ is defined as
Ψ ) cos-1
{
}
[(b
r j+1 - b
r j) × (b
r j-1 - b
r j)]‚ẑ
|(b
r j+1 - b
r j) × ( b
r j-1 - b
r j)|
(8)
Here b
rj is the position vector for atom j and the expression for
ψ involves the two other atoms that comprise the triplet making
up the bond angle. This roll angle takes on a value of 0° when
the plane consisting of the three molecules in the bond is parallel
to the graphite substrate and takes on a value of 90° when the
plane is perpendicular to the substrate, and it gives an idea of
the degree of rolling of segments of the molecules in the overlayer.
MD Simulations of Hexane on Graphite
Langmuir, Vol. 24, No. 7, 2008 3231
Figure 4. Azimuthal angle probability distributions P(φ) for various
coverages in the solid (black), at the onset of orientational order loss
(blue), at the onset of nematic order loss (green), and in the liquid
(purple). The plot for F ) 0.614 has no color because neither OPHerr
or OPNem show signatures of transitionns. Perspective angles for
various coverages are different in order to better visualize features
at each temperature.
Figure 2. Snapshots of the system at F ) 1 for the low-temperature
solid (T ) 100 K), at the onset of herringbone orientational order
loss (T ) 140 K), at the onset of nematic order loss (T ) 162 K),
and in the isotropic liquid (T ) 180 K). Color scheme is the same
as in Figure 1.
Figure 3. Herringbone order parameter OPHerr (left) and nematic
order parameter OPnem (right) as functions of temperature for
coverages F ) 1 (black), 0.966 (red), 0.933 (green), 0.878 (blue),
and 0.614 (purple).
If the molecules have their carbon backbone flat against the
substrate, ψ ) 0° or 180° and if they are “on their side,” ψ )
90°. Figure 5 shows the microscopic roll angle probability
distributions; it is clear that most of them are flat at low
temperature, consistent with experimental diffraction results.4,6,7
As temperature is increased, it is evident from the data presented
that the herringbone solid loses its orientational order at around
T1 ) 145 ( 2 K. Note however, that all the data presented
suggest that considerable orientational subsists even after the
herringbone disappears. The nematic order parameter shown in
Figure 3 illustrates that the system indeed is in a mesophase,
which persists up until melting into the isotropic fluid at about
T2 ) 160 ( 3 K. The nematic order parameter gives a measure
of the long-range orientational order (and thereby the nematic
character) of the system. It is given by12,13
OPNem t
1
Nm
〈∑
Nm
i)1
〉
cos 2(φi - φdir)
(9)
Figure 5. Microscopic roll angle probability distributions P(ψ) for
various coverages in the same format as Figure 4.
where φi is the angle that the axis of molecule i makes with the
x axis and φdir is a director which is essentially the average
orientation of the system.13 In UA calculations13 the herringbone
phase persists up until about T1 ) 145 K and then changes to
a strong nematic, which in turn persists until about T2 ) 170 K
when the system melts into the isotropic liquid. The nematic is
still present in the fully atomistic simulations, but the degree of
order as indicated by the value of the nematic order parameter
is substantially less than that seen in the UA case, as seen by the
absence of a sharp increase in OPNem after herringbone order is
lost but and in the absence of high peaks in the azimuthal angle
probability distributions in the region T1 < T < T2. The
substantially weakened nematic phase in the all-hydrogen model
is more consistent with experiment3-7 in that no true nematic
phase is observed. Rather a lattice of rectangularly centered islands
mobile in the fluid is inferred from the scattering data. Pair
correlation functions and static structure factors in Figure 6
confirm the two transition temperatures. Still, there is no signature
seen in experimental results for the herringbone-nematic transition
at T1, but rather the melting transition at T2 ≈ 172 K, which is
a few Kelvin higher than calculated in this work.
3232 Langmuir, Vol. 24, No. 7, 2008
Connolly et al.
Figure 6. Pair correlation function (left) and static structure factor
(right) at selected temperatures for F ) 1.
Figure 7. Average Lennard-Jones interaction as a function of
temperature for F ) 1.
In order to understand why the nematic mesophase is
suppressed in the explicit-hydrogen calculations, we also examine
the average adatom-adatom Lennard-Jones interaction as a
function of temperature
〈∑ ∑ [( ) ( ) ]〉
σij
N
U)
4ij
i)1 j>i
rij
12
-
σij
rij
6
(10)
which are shown for unit coverage in Figure 7. The herringbone
to nematic transition was accompanied by a sharp drop in the
molecule-molecule interaction energy in the UA model12,13 (an
increase in |U|). In contrast, here we see a gradual reduction in
|U|. The relative suppression of the nematic phase brought about
by including the hydrogens has to do in one sense with the
hydrogen atoms occupying more in-plane space. In the UA model
the anisotropy of the hydrogens are averaged out and the
interaction centers (pseudoatoms) have the opportunity to sit
very near their equilibrium positions when oriented and stacked
as in the nematic phase. In the explicit-hydrogen picture, however,
the hydrogens are weakly interacting centers but since they are
concentrated at specific spots they are able to prevent the entire
molecules from getting so close together and sampling the steep
repulsive part of the Lennard-Jones interaction potential. Hence,
the carbons are farther apart than in the UA model and their
nonbonded interaction energy does not drop at T ) T1. Hence,
the explicit-hydrogen molecules are simply not allowed to stack
and pack closely together; hence, the Lennard-Jones interactions
are weaker. In addition, the anisotropic interaction of the
hydrogens with the substrate is important, which is evidenced
by the more reasonable rolling behavior afforded in the allhydrogen model.
Figure 8. Snapshots at three submonolayer coverages. Color scheme
is the same as in Figure 1; the graphite substrate for the lower two
coverages is removed for clarity but the approximate size of the
computational cells are shown. To emphasize topological features,
the cells are distorted so the areas do not visually scale.
Table 4. Positions of the Peaks in the Azimuthal Angle
Probability Function P(O) for Various Coverages in the
Low-Temperature Solid
F (monolayer)
peak positions (deg)
1.00
0.966
0.933
0.878
0.614
28, 153
29, 151
31,149
30, 150
0, 35, 61, 104, 153, 172
B. Partial Coverages (F < 1). As the coverage is decreased
slightly below unity, the herringbone transition at T1 shows very
little change. It is interesting to note that, based on the data in
Figure 3, F ) 0.966 actually retains order to slightly higher
temperatures than F ) 1. This is because at F ) 1 there are
vertical atomic fluctuations and ultimately about 1% layer
promotion (Figure 2)which creates in-plane room which in turn
lowers the transition temperatures. At F ) 0.966 the spreading
pressure is somewhat lowered and vertical fluctuations are not
as prevalent. Hence, there is less in-plane mobility and the
transition temperatures are not lowered. Moreover, nematic
mesophase exists over a very short temperature range at F )
0.966, consistent with the conclusion that preventing close
stacking of the molecules weakens the mesophase. However, at
F ) 0.878, T1 decreases dramatically. This decrease is directly
related to the onset of vacancy and vacancy patch formation in
the systemsnot a UI phase any more. Inspection of Figure 8
(left) confirms the presence of vacancy patches and oriented
domains. In fact, by F ) 0.614 the topology is a connected
network and is very similar to that seen at, F ) 0.509, shown
in Figure 8 (right). Below coverages of about 0.5, the system
breaks up into individual patches, as seen in Figure 8. It is
interesting to note that, although more prevalent at F ) 0.878,
all submonolayer systems shown have static gauche defects
usually present at grain boundaries. While the herringbone phase
subsists, the peaks of the azimuthal angle distribution are not
exactly at 30° and 150° but do show a collection of individual
peaks representing many differently oriented domainssa coverage
dependence in reasonable agreement with experiment.4,6,7 Table
4 shows some related numerical data.
The interpretation that the connected network existing at F )
0.509 and 0.614 is comprised of oriented domains is supported
not only visually in Figure 8 but also by the appearance of the
azimuthal angle probability distributions shown in Figure 4.
Inspection of the dihedral angle distributions in Figure 9 suggests
that in this model the herringbone order-disorder transition
depends on the presence of gauche defects, because in the highest
MD Simulations of Hexane on Graphite
Langmuir, Vol. 24, No. 7, 2008 3233
Figure 11. Same as Figure 6 but for F ) 0.614.
Figure 9. Dihedral angle probability distributions P(φd) in the same
format as Figure 4.
Figure 10. Same as Figure 6 but for F ) 0.878.
Figure 12. End-to-end H-H length as functions of temperature at
various coverages. Format is the same as Figure 3.
densities defects are not present until OPHerr starts to drop but
at lower densities they are present in the solid where defects are
evident. In fact the presence of gauche defects at lower
temperatures at lower densities is surprising and suggests that
hexane is not so rigid as previously believed. Moreover, the
presence of gauche defects dynamically reduce the time-averaged
Lennard-Jones nonbonding energy so as to promote the weakness
of the nematic phase with respect to the UA model. For the
highest densities examined, the behavior of OPNem in Figure 3
shows considerable insensitivity of the melting temperature T2
with decreasing coverage until at about F ) 0.9. Since the presence
of vacancies and oriented domains wash out angular order
parmeters, we depend on the pair correlation function and static
structure factors (shown in Figures 10 and 11) to help determine
the location of T2. It is evident that T2 is somewhere between 130
and 140 K, again in reasonable agreement with experimental
values of between 150 and 160 K.4
It is interesting to note that dihedral angle probability
distributions in Figure 9 show the presence of considerable gauche
defects at temperatures that depend on coverage. In fact, inspection
of the left panel of Figure 8 confirms the presence of gauche
defects in the low-temperature submonolayer solid. The presence
of such defects can be seen in the snapshots as molecules whose
backbones are not straight and in all the submonolayer cases are
likely found in the region between two or more grain boundaries.
Furthermore, it can be seen that at low temperature the gauche
defects allow the molecule to conform to the graphite substrate.
Such results strongly suggest that the hydrogens interact strongly
with the graphite substrate vis-a-vis lateral corrugation and the
gauche defects in fact promote the domain formation by relieving
grain boundary stress. So the gauche peaks for F ) 0.878 are
static in nature. Then, they disappear as grain boundary stress
is relieved and reappear dynamically at higher temperatures.
Surprisingly, the end-to-end H-H lengths in Figure 12 seem to
show something contrarysthat, the molecules begin to bend at
nearly the same temperature for all coverages. Inspection of the
end-to-end length distribution (not shown here) shows a single
peak as well. Such results may be understood in that since, at
low temperatures the static submonolayer gauche defects cause
the molecule to conform the substrate, they do so in such a way
that the H-H distances are the same. This is contrary to the
dynamic higher-temperature gauche defects, where methyl torsion
is present. All the dihedral and end-to-end distance results, coupled
with the data in Table 4, suggest that as coverage increases up
to the monolayer there is some strain placed on the molecules
in the herringbone solid which is relieved as coverage is decreased
but at the cost of grain boundary formation. Moreover, this also
explains the insensitivity of the transition temperatures with
decreasing coverage near F ) 1, which is anomalous in simple
physisorbed systems. In turn, this suggests that true monolayer
completion for this interesting system may not occur at the value
previously and usually deemed F ) 1 in this system.
IV. Conclusions
The work presented here allows us to make several important
conclusions about simulating hexane on graphite with explicit
hydrogens:
3234 Langmuir, Vol. 24, No. 7, 2008
(i) Since the hydrogens represent concentrated interaction
centers but are averaged out in the UA model, explicit-hydrogen
molecules are prevented from coming so close together as they
do in UA simulations. Hence, the carbon backbones are prevented
from aligning and stacking closely, as seen in the UA model,
which in turn weakens the explicit-hydrogen nematic. Gauche
defects also promote a dynamic reduction in strength of the
adatom-adatom energy, which further weakens the nematic.
(ii) The herringbone solid-to-nematic phase transition is fairly
insensitive to coverage near completion and begins to become
affected when defects (vacancy islands; percolated networks)
are present in the system. This is in disagreement with previous
work with the UA model,13 where the same transition temperature
(T1) increases with decreasing coverage and vice versa. Since
the molecules in the UA model roll in the solid and have to tilt
in order to form the nematic, decreasing stress through decreasing
density lessens the likelihood for such dynamics to be present.
The explicit hydrogen molecules do not significantly roll or tilt
prior to the transition.
(iii) The loss of herringbone order at higher densities is directly
related to the presence of gauche defects in the explicit-hydrogen
molecules. In previous work with the UA model,13 gauche defects
became prominent throughout the nematic but not so much before.
Connolly et al.
(iv) As coverage is decreased down below about F ) 0.9 some
gauche defects are present in the solid but the end-to-end H-H
distance drops at the same temperature regardless of coverage,
suggesting that the hydrogens are able to notch into the graphite
substrate.
(v) There appears to be strain present in the higher-coverage
systems which is relaxed at lower densities. The strain present
helps explain the insensitivity of the transition temperatures at
the highest densities examined.
(vi) The spreading pressure observed in both the UA and
explicit-hydrogen simulations is comparable. The fact that it is
not zero at F ) 1 indicates that the point of monolayer completion
based on simulations must be further investigated, and work
with larger systems is highly desirable.
Acknowledgment. Acknowledgment is made to the Donors
of The American Chemical Society Petroleum Research Fund
(PRF43277-B5) and the University of Missouri Research Board
for the support of this research. This material is based upon work
supported in part by the Department of Energy under Award No.
DE-FG02-07ER46411. The authors acknowledge fruitful discussions with Haskell Taub and Flemming Hansen.
LA703040A