J . Phys. Chem. 1993,97, 9013-9021
9013
Thin Films of *Octane Confined between Parallel Solid Surfaces. Structure and Adhesive Forces vs Film Thickness from Molecular Dynamics Simulations Yantse Wang, Kirk Hill, and Jonathan G. Harris’ Department of Chemical Engineering, Massachusetts Institute of Technology, 25 Ames St., Room 66-450, Cambridge, Massachusetts 02139 Received: March 15, 1993; In Final Form: May 21, 1993
Molecular fluids in confined spaces exhibit behavior that cannot be properly described by continuum theories. We examine the structure of n-octane confined between crystalline surfaces and in equilibrium with the bulk liquid at 1 atm and 297 K using molecular dynamics simulations of a chemically realistic model of the molecules. We also compute the solvation forces acting upon the surfaces as a function of their separation. The films are studied between solid surfaces separated by gaps of 1.O-2.4 nm. At 297 K, all films exhibit liquid-like dynamics and are strongly layered, although the sharpness of the layering oscillates with gap size. In addition, the solvation forces are oscillatory functions of the surface separations. An especially interesting anomaly appears at a gap size of 1.25 nm, barely enough to allow the molecules to extend lengthwise from one surface to the other. There is a strong tendency of the molecules to orient themselves normal to the solid surfaces, in contrast to molecules in other gap sizes and in similar systems studied by other researchers. Furthermore, the film readily freezes to a solid monolayer when cooled to 250 K in contrast to the 1.S-nm-thick film which remains a liquid at that temperature.
1. Introduction
In problems ranging from adsorption to adhesion and lubrication, one often encounters situations in which molecular liquids are confined to regions with length scales of the order of only a few molecular diameters. In such situations, experimental evidencesuggeststhat the normal continuum treatments of liquids break down, and a molecular level view is needed to understand the behavior of the fluids. One class of experiments which illustrates the importance of such situations to adhesion and forces between particles in a colloidal suspension is adhesive force measurements with the surface force apparatus.’ In a typical surface force apparatus experiment,two cylindrical surfaces formed by bending perfectly cleaved mica sheets around the face of a cylinder are immersed in the liquid with their long axes perpendicular to each other. Sensitive equipment controls the forces acting upon the sheets while interferometryis used to measure the length of the narrowest section of the gap between the cylinders. Because the radii of curvature of the cylinders are much larger than the size of the gap, at a molecular level the walls of the gap appear as two flat surfaces-forming a geometry known to many as a “slit pore”. The idealized “slit pore” is bounded by two flat surfaces of infinite area separated by a distance referred to as a pore width. Hence, simulations or theories of fluids in slit pores are often used to model these systems as well as adsorption phenomena. Many of the earlier simulations and theories of fluids in such pores are reviewed in a recent article by Evans.2 For small spherical molecules, simulations indicate that when the pore width is less than about five atomic diameters, the molecules order in layers perpendicular to the sheets.2-5 Density functional and integral equation theories come to similar conclusions.3~~ These theories and simulations also predict that the layering is associated with an oscillation of the solvation force acting between the plates. While the noble gases, the realistic cousins of the Lennard-Jonesian atoms of the simulations, are not used in experimental measurements, surface force apparatus measurements upon nearly spherical molecules such as OMCTS (octamethylcyclotetrasiloxane)and cyclohexaneshow oscillating solvation forces between microscopically smooth mica surfaces or crystalline surfaces formed by coating the mica with certain surfactant monolayers.9 0022-365419312097-9013$04.00/0
Surface force apparatus experiments have been carried a step further and investigated polymers, oligomers, and a variety of molecules with varying degrees of symmetry. It is found that short linear alkanes (less than length 20) exhibit the oscillatory solvation forces while asymmetrically branched alkanes (excluding symmetricmolecules like neopentane) show few or no oscillations. Most dramatic is the observation that for chains of length of about 12 carbons a single methyl side chain can completely eliminate the oscillations, leaving only an attractive minimum in the forces between the plates.10 These studies can obtain little in the way of the molecular level details of the film structure. Severallattice model simulationsof polymers confined between two solid surfacesl1J2have been published, as well as off-lattice simulationsof bead-spring type chains in slit pores,4J3-’5 of liquid alkanes within structureless pores,16 and of liquid alkanes and of hexadecane” between nickel plates. Also, integral equationtheory has been used to study the structure of linear and star beadspring oligomers within slit pores of smooth walls.’3 All of these suggest the existence of oscillatory density profiles of the fluid confined within the slit pore. Still there have been no published studies examining the effect of the molecular architecture upon the structure and properties of the confined film formed from a liquid between the two solid surfaces. This article is the first of a series of two articles discussing the influence of pore width and branching upon the molecular structure of the film between the surfaces. This article focuses upon the structure of films of the linear alkane, n-octane. A second article will explorethe structure of 2-methylheptane films and compare them with the n-noctane films. The study most similar to the one described here is that of Ribarsky and Landman,” which examined the structure of hexadecane adsorbed between nickel surfaces at 435 K (6.86 elk, where B is the well depth of the CH2 Lennard-Jones interaction) and at constant external loading. Because of this difference in conditions as well as the information sought in our study, we observe new features in the layering not seen in these previous simulations. In addition to the difference in conditions and chemistries of ref 17 and this study, we point out that in ref 17 their thicker films, designed to represent microscopic droplets in an AFM experiment, do not completelycover the solid surface, while ours are designed to be in equilibrium with a bulk liquid 0 1993 American Chemical Society
9014
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993
Wang et al.
TABLE I: Monolayer Lattice Parameters lattice spacing 8,“
0.497 (nm) 28.0 (deg)
Ab
102.0 (deg)
XC
0.0 (deg)
,IAngle between all-transchain axis and surfacenormal. Twist angle between the all-trans molecular plane and the plane formed from the chain axis and the surface Precession angle of the chain axis about the surface normal. phase and have an excess of molecules which bulge out of the pore. Also, by using constant thickness simulations, we can observe film thicknesses that are unstable in constant external load simulations. Such films do occur in porous media or between sections of two surfaces separated by a gap which is nonplanar on length scales much greater than the molecular size. Section 2 of this paper discusses the model used to describe the slit pore surfaces and the alkane molecules which form the fluid between the two surfaces. Section 3 describes the simulation geometry and techniques employed. Of particular concern is the fact that in equilibrium experiments the films must be in mechanical and chemical equilibrium with a bulk fluid (usually the fluid at 1 atm or its vapor pressure). Section 4 illustrates the results of the simulations. Section 5 presents our conclusions in relationship to the experiments and other theoretical work in the area. Preliminary versions of the work have appeared (refs 1821). 2. Model Because slit pores formed from mica surfaces coated with a crystalline surfactant monolayer exhibit behavior similar to that of pores formed from bare mica surfaces9J0 and because surfactant-alkane potentials are well-known, unlike mica-alkane interactions, our slit pores are composed of surfactant monolayers. The surfactant tails are composed of the CH2 and CH3 groups present in the hydrocarbon chain and are modeled using the same interactions assumed for the liquid alkanes. Only the nine outermost hydrocarbon units need to be included, as units closer to the mica are outsideof the 1.O-nm cutoff used in the nonbonded Lennard-Jonesinteractionsof the potential model described below. To save a considerable amount of computer time, we treat the surfactant molecules as forming a static crystalline body. This prevents us from having to compute the interactions between the molecules which form the pore walls at the expense of ignoring effects of the molecular motions within the monolayers upon the pore structure. The reasonability of ignoring internal motions of the surfactant monolayer is supported by the similarities between the solvation forces measured in the surface force apparatus experiments performed on bare mica and mica coated with a crystalline surfactant monolayer.9 The crystal structure is that of the Langmuir-Blodgett monolayer simulated by Hautman and Klein22v23(Table I). Although the monolayer on the mica likely has a different crystal structure, we believe that similar effects should be observed for any crystal phase formed with densely packed alkane units. We use a slightly modified version of Jorgensen’s OPLS model24 to study the alkane, octane. This is identical to the model used in previous work in our laboratory25 and includes rigid bond lengths, flexible bond angles, a torsional potential, and a nonbonded potential. The model of the octane molecules consists of eight united atoms, i.e., the CH2 and CH3 groups. Carboncarbon bond lengths are fixed to 0.153 nm, and the C-C-C bond angles are governed by the harmonicpotentialof Kollman, Weiner, and co-workers26with their equilibrium bond angle of 112.4’
where ke is the force constant and angle. The torsional potential is
u&)
80
is the equilibrium bond
+ c, COS 4i + c2cos24,. + c3cos3 4i ...
= co
(2) where the parameters Ci are given in Table 11. The nonbonded
yFigure 1. Sketch of simulation cell. The grey region represents a static crystalline Langmuir monolayer of the two walls of the slit pore. The wall in the y direction is finite (typically 2.5 nm long). The distance between the walls is H. The wall is infinite in the direction normal to the face of paper ( x ) . The chains of spheres are the octane molecules of the films, which equilibrate with a reservoir outside of the pore at liquid-vapor coexistence.
TABLE 11: Potential Function Parameters €CH&H,/k UcH&H,/k €CH&H,/k UCH~H,
ke 00
59.38 K 0.3905 nm 87.88 K 0.3905 nm 527.184 kJ/mol/rad2 112.4 deg
8.397 29 kJ/mol 16.786 17 kJ/mol c 2 1.133 864 kJ/mol c 3 -26.3 17 36 kJ/mol l g (bond lengths) 0.153 nm C O
c1
interactions between the united atoms are modeled by the Lennard-Jones potential
$(r) = 44(r/a)-12 - ( r / d 4 1
(3) where E is the well depth, c is the core diameter, and all nonbonded interactions (including ones between pore wall atoms and liquid atoms) are truncated at r, = 2 . 5 (1 ~ .O nm). All cross interactions are determined using the geometric mean combining rule. The parameters used in the interactions are shown in Table 11. 3. Methodology and Geometry 3.1. Control of Chemical Potential and System Geometry. In surface force apparatus experiments, the liquid between the two surfaces can be squeezed out to the surrounding bulk liquid when the pore width changes. Therefore, the liquid thin film within the pore can equilibrate with the bulk liquid mechanically and chemically. In such situations, the chemical potential of the fluid between the surfaces is equal to that of the bulk liquid at the temperature and pressure of the experiment (typically 297 K and 1 atm). Of course in some cases, especially when the liquid includes long molecules or there are especially strong liquid-surface interactions, the thin film can glassify or crystallize even when the bulk material is a liquid. In such situations, sticking or significant hysteresis in surface force measurements may result. The study of such nonequilibriumsystemsby molecular dynamics simulations is problematic at best, and hence we focus our efforts on the equilibrium cases. It should also be noted that the small length scale studied with simulations can allow equilibration to occur even though it may be very slow in the experiments. The greatest challenge in this work is carrying out the simulations in the pore at the chemical potential of the bulk liquid at 1 atm. To accomplish this, we used an approach known as the “reservoir” method.27 In this method, the pore is assumed to be finite (typically 2.5 nm long) in one direction (y) and infinite in the other direction ( x ) by imposing periodic boundaries on the surfaces in the x direction, as in Figure 1 . Along the y direction outside of the pore is a reservoir in which liquid and vapor collect. In they direction, periodic boundary conditions are preserved, but the
Alkane Films in Confined Pores
The Journal of Physical Chemistry, Vol. 97, No. 35, I993 9015
TABLE III: Simulation Conditions and Results Summarp set I
I1 I11 IV V
N 48 48 48 48 75 96 96 96 48 48 96 96 96 48 96
T, K 297 297 297 297 297 297 297 297 297 250 297 250 297 297 297
TE,
ns
1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 1 .o 0.7 1 .o 0.7 1 .o 1 .o 1 .o
~,,ns
&nm
5.0 1.5 6.3 5.3 3.9 3.9 2.4 6.0 6.3 7.0 3.9 7.0 2.4 4.0 2.8
2.5 2.5 2.5 2.5 2.5 2.5 2.5
Lz, nm 1 .oo 1.20 1.25 1.40 1.60 1.80 2.00 2.40 1.25 1.25 1.80 1.80 2.00 2.00 2.00
NL
D,,nm
fi, 106Pa
Hp,g/cm3
2 2 2 3 3 4 4 5 2 2 4 4 4 4 4
0.41 0.55 0.61 0.8 1 0.96 1.20 1.39 1.78 0.6 1 0.80 1.18 1.21 1.38 1.37 1.37
86.5(3.1) -19.0(3.0) -16.3(1.8) 32.6(2.9) O.O(l.9) 8.6(2.8) 8 .O( 2 .) 8.3(3.5) -19.0(3.0) 125.2(4.1) 8.6(2.8) -19.4(1.8) 8.0(2.0) lS(O.9) 1.9(1.2)
1.78 1.22 1.10 1.36, 1.06 1.33,0.99 1.25,0.83 1.35,0.97 1.20,0.84,0.73 1.10
VI VI1 VI11 2.5 I11 2.5 IIIa 2.5 crystalline VI 2.5 1.25,0.83 VIa 2.5 1.46, 1.08 VI1 2.5 1.35,0.97 VIIa 2.5 1.31,0.93 VIIb 3.8 1.34,0.94 N is the number of molecules in the simulation, Tis the temperature,T E is the equilibrationtime, T~ is the sampling time used in collecting statistics, L, is the width of the pore in they direction (parallel to the pore walls), Lz is the distance between the pore walls, NLis the number of layers appearing in the film, D, is the distance between the two peaks in the density profile closest to the pore wal1,fi is the solvation force, and H,values are the peak heights listed in order from the wall to the center of the film. Deviations from the normal series of simulations at 297 K are boldface. Entries for sinklations 111, VI, and VI1 are duplicated for convenience. boundaries are at least 4 nm from the center, so the liquid bubble which forms a t the edge of the pore does not interact with the other side of the pore across the boundaries. Only the vapor molecules are allowed to interact with each other across the boundaries. A small number of molecules appear in the vapor during simulations. The direction normal to the pore walls is denoted as 2. Our system can thus be divided into four regions. First, there is a vapor space in the reservoir. Then just outside of the pore a small amount of liquid extends into the reservoir in the form of a bubble. Just inside the pore is a transition region whose properties are influenced by the liquid-vapor interface in the reservoir and the edge of the pore. Finally, the region near the center of the pore should have properties of a fluid of the same chemical potential inside of a slit pore of infinite extent in both directions. From the results presented in the next section, it can be seen that the region 1.5 nm long centered in the middle of the pore appears almost unaffected by the pore edges. If the entire system can equilibrate during the time of the simulation, the chemical potential of the fluid throughout the pore will be the same as that of the liquid at its vapor pressure. For liquid octane, isooctane, and heavier hydrocarbons at room temperature, the liquid structure does not change much as the pressure is varied from their vapor pressure to 1 atm. This approach has the advantage of avoiding difficult and costly insertions. The disadvantages include the extra number of molecules in the system and the presence of the liquid-vapor interface. Also, there is the potential for finite size effects due to the edge of the pore and the finite size of the bubble extending into the reservoir. This is apparent in the Young-Laplace equation, which describes the dependence of droplet vapor pressure upon the droplet radius of curvature.28 Our results in the next section indicate that the finite size effects are small in the center region of the pore. Another potential problem with this approach is that significant amounts of fluid can leave the pore and adsorb on the sides and rear edge of surfaces. This would force us to include extra molecules in the simulation and perhaps make equilibration of the entire system impossible during the time frame of the simulation. We avoid this problem by adding repulsive Gaussian potentials at the back and sides of the slab. The Gaussian is truncated so that it has no influence within the pore. It is important to choose the Gaussian height and width so that the truncation is at low enough energies to avoid significant nonconservation of energy in the microcanonical ensemble but high enough to keep molecules from adsorbing on the back of the slab. 3.2. Computational Methodology. All studies were carried out using the RATTLE molecular dynamics algorithm, specif-
ically the velocity Verlet method with rigid bond length constraints.29 A time step of 0.007 ps was used. Previous experience with the liquid-vapor interface of alkanes suggests that this represents a reasonable trade off between integration accuracy and computational eff0rt.~5 Simulations were started by placing the alkane molecules on a cubic lattice grid at very low density. This system was then simulated while compressing along the z direction (normal to the eventual pore surfaces) until the system equilibrated to a pressure of 1 atm.30 A temperature of 297 K was maintained by coupling with a thermal bath with time constant TT of 3.5 ps.30 After the liquid reached the appropriate density, the boundaries in the y direction were moved to their final position without adjusting the coordinates of any molecules. This formed the liquid-vapor i n t e r f a ~ e .The ~ ~ solid surfaces were then added into the simulation box along the z direction, and the periodic boundaries were moved to eliminate interactions across boundaries in this direction. This was done by performing a series of short simulations in which the surfaces were successively moved along the z direction to their final positions. Subsequent simulations were started from previous simulations by first gradually readjusting the plate positions and then allowing approximately 1 ns for equilibration after the solid surface positions were fixed at the new surface separation. Typical sampling times were 3-6 ns. Most of the calculations were carried out on a Stardent/P3000 work station using a vectorized code. A 350-ps simulation with 48 liquid alkane molecules took approximately 8 h of CPU time. Some simulations were also carried out on a Cray-Y/MP supercomputer, where they ran about 10 times faster than those on the Stardent work station. The conditions and parameters used in the runs are summarized in Table 111. In the property calculations discussed in this paper, separation of the solid plates is defined to be the distance between the centers of the outermost atoms of the surface of the two plates minus 0.153 nm, the C-C bond length. This is about 0.25 nm greater than the separation that would be observed in a corresponding experiment because the experimental surface separations are defined so that a surface separation of zero occurs when the bare surfaces are at contact-a separation of approximately 0.25 nm according to the definition used in these simulations. Density profiles normal to the surface and other properties were computed using only the center region of the pore between y = *0.75 nm, where y = 0 is the center of the pore. As shown for one example in the next section, the effects of the liquid-vapor interface and system size are insignificant in this region. Solvation forces can becalculated using either thedirect average of the forces of liquid molecules upon the plates, the molecular
9016 The Journal of Physical Chemistry, Vol. 97, No. 35, I993
virial, or the atomic virial.3 We did not use the pressure tensor expressions for the solvation force generalized by using the molecular or atomic virials as in ref 25 because they are more time consuming to calculate and more difficult to apply to exclusively the central region of the slab. We chose to use the direct averages as follows because they can be rapidly evaluated from configurations saved during the simulations. The solvation force is thus
where #(r) is the derivative of the Lennard-Jones potential (section 2) with respect tor. The subscript w refers to a particle of the upper surface and u a particle of the lower surface. The ri, is the distance between the carbon i in a liquid molecule and the particle w in the solid monolayer surface. To reduce edge effects, the sums are evaluated over only liquid atoms within the region bl 5 0.75 nm. ( ) is the average taken over the whole samplingperiod. A is the cross sectional area parallel to the pore walls of the volume used in computingf,. The solvation force is the average force normal to the surface per area. 4. Results and Discussion 4.1. Thin Film Structure. Figure 2 shows some samples of snapshots of n-octane thin films in slit pores of several widths. The darker spheres represent the solid surfaces. The chains with lighter spheres are octane molecules. We can see that at pore widths of 1.0 nm the liquid forms a layered structure with molecules lying parallel to the solid surfaces. At larger pore widths, there is always the layered structure on each wall surface and more poorly defined layers in the center of the system. At surface separation of 1.25 nm, a dramatic change in the layered structure is observed. The moleculararrangement becomes more perpendicular to the surfaces. Parts a and b of Figure 2 show the molecular conformations of n-octane in pores 1.O and 1.6 nm wide, respectively. We can see that the n-octane molecules in the 1.0-nm pore are more stretched and oriented parallel to the surfaces. In the wider pore, the strong ordering occurs only near both surfaces. In the middle of the pore, the molecular conformation is closer to random, although the more detailed analysis presented below shows that these regions are still someone ordered. The strong layering observed in the samples may cause one to question whether or not the films are still liquid. We have computeddiffusion coefficients and examinedmolecular motions. Our diffusion coefficients, while rendered less accurate by the presence of the liquid-vapor interface, are similar to those of the bulk alkane liquid. A typical molecule moves a significant fraction of the cell width during the course of the simulation in all systems studied at 297 K. We have also compared samples of the 1.25-nm-thickand the 1.8-nm-thick films after they have been cooled to 250 K. This cooling was accomplished by using Berendsen's external bath with a time constant of 3.5 ps for a 1400-ps equilibration period.30 The initial configurations were the final ones from the T = 297 K simulations. A run with a 7-11s sampling time followed. Parts c-f of Figure 2 show that for such a cooling sequence the film in the 1.25-nm-wide pore freezes to a monolayer oriented at 27O to the surface normal while the film in the 1.8-nm-wide pore still retains structural characteristics similar to those of the liquid film at the higher temperature. The separation between the surfaces in the former case is just enough to allow a molecule to stretch from one face to the other and thus is almost ideal for accommodating the frozen monolayer. It thus appears that confinement can enhance the tendency of the liquid to freeze when the geometry is particularly accommodating to the frozen film. We cannot verify that this observation is purely thermo-
Wang et al. dynamic as opposed to kinetic because there is no computation of the freezing point for our model octane. The orientational characteristics of both the liquid and the solid film in the 1.25-nm-wide pore may seem somewhat at odds with the more conventioinal observation that chain molecules tend to orient parallel to the surface. This latter situation has been observed in most of the samples studied here and in our previous work on the liquid-vapor interface of normal alkanes.25 In that previous work, we found that although in the outermost layer the chains were oriented parallel to the interface there was a region (of much higher density) immediately below in which the chains had a slight tendency to arrange themselves normal to the interface. Recent experimental studies of the liquid-vapor interface of n-alkanes indicate that for certain chain lengths a crystalline monolayer forms at the surface3' of the liquid a few degrees above the melting point. This monolayer is oriented normal to the surface. Furthermore, when the liquid decane surfacesamples studied in our previous work are cooled, they freeze into lamellar structures with the lamellae oriented almost normal to the interface. This occurs because such an orientation exposes the face with minimum surface free energy and lower packing density. 4.2. Density. A total carbon density profile provides a formal approach to characterizingthe degreeof layeringwithin the films. Density profiles in the direction normal to the interface were computed using only the central 1.5 nm in they direction (normal to the porevapor interface). The number of oscillations in the density profiles is the number of layers in the pore. Figure 3 illustrates total carbon density profiles for severalpore diameters. The number of layers varies from two (1 .O-nm-wide pore) to five (2.4-nm-wide pore). Also, the sharpness of the density profiles is not a simple monotonic function of the pore width. The 1.4nm-wide pore has higher peaks than the 1.2-nm-wide pore. This occurs because the former width is ideal for the formation of three complete layers, while the 1.2-nm-wide pore is too narrow to hold three layers but too wide for two layers to fit snuggly in the pore. Figure 3 also compares the densities of the ends and middles in the several pores. Near the wall there is a tendency for the ends to predominate. This effect is similar to that observed in simulation of the liquid-vapor interface of alkanes25 and other types of slit pore arrangement^.^.^ For the 1.25-nm-wide pore, the simulations show a strong peak in the density of the chain middles in the middle of the pore. This unusual pattern has not been observed in other simulations and occurs because the pore width is just large enough to accommodate a molecule extended from one face of the slab to the other. Molecules stretching across the pore in that fashion contribute to the high density of middle groups in the center. In the previous section, we noted that this particular film thickness enhanced the ability of the film to freeze. Parts i and j of Figure 3 also show the density profiles of the 1.25-nm-wide pore and the 1.8-nm-wide pore at 250 K. It is obvious that the film in the 1.25-nm-wide pore has frozen to a crystalline monolayer with the molecular orientation normal to the interface. Figure 4 illustrates the density profile of the 1.O-nm-thick film in the x and y directions. They illustrate the periodicity in these directions imposed by the solid surface structures. 4.3. Chain Operations. The orientations of chains in the pore can be conveniently described by the profile of the orientational order parameter, P,defined by (5) where 8 is defined as the angle formed by the vector between two carbons separated by two bonds (e.g., carbons numbered 1 and 3) and the normal to the pore walls. In the orientational order parameter profiles, P(z), averages ( ) are taken over all C-C
Alkane Films in Confined Pores
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 9017
Figure 2. Snapshots of thin films in slit pores of several widths showing the side views of the molecular structure on the yz cross section. The films is confined (a) within a 1 .O-nm pore at 297 K, (b) within a 1.6-nm pore at 297 K, (c) within a 1.25-nm pore at 297 K, (d) within a 1.25-nm pore at 250 K, (e) within a 1.8-nm pore at 297 K, and (f) within a 1.8-nm pore at 250 K.
vectors between carbons bonded to a third carbon lying in a thin slice parallel to the pore walls centered at z . If the molecules are in the all-trans state, P = 1 when they are perpendicular to the pore walls, P = 0 when they are randomly oriented, and P = -1/2 when they are all parallel to the surfaces. Figure 5 illustrates the orientational order parameters of the n-octane as a function of position along z direction. These profiles show a stratification similarto that observed in the density profiles. We can see that adjacent to the surface of the pore the molecules are highly ordered and parallel to the surface for all pore sizes. In the middle of the slice, the degree of orientational order is greatly reduced, and vectors between the octane layers become perpendicular to the pore walls. The number of oscillations in
the orientational profiles is identical to the number of oscillations in the density profiles, and the valleys in the orientational profile coincidewith the peaks in the density profile, indicating that the orientational order is strongest in the dense layers. Between the layers, the vectors tend to be perpendicular to the walls, because many of the carbons in this region are serving as bridges between the strata. As in the density profile, the degree of orientational order in the profiles is not a monotonic function of pore width. In the wider pores, the greatest variations occur in the middle of the slab, with the samples having the strongest oscillations in the density profiles having the strongest oscillations in the orientational order parameter profile. For example, a 2.0-nmwide pore shows greater orientational order than a 1.8-nm pore
Wang et al.
9018 The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 15 n
"E
