Langmuir 1993,9,1983-1985
1983
Comparison of Branched and Linear Octanes in the Surface Force Apparatus. A Molecular Dynamics Study Yantse Wang, Kirk Hill, and Jonathan G. Harris* Department of Chemical Engineering, Room 66-450, Massachusetts Institutes of Technology, 25 Ames Street, Cambridge, Massachusetts 02139 Received April 19,1993. I n Final Form: June 1I, 1993 Surface force apparatus experiments suggest that small changes in molecular architecture, such as the addition of a methyl side group to a linear alkane chain, can have significant effecta on the structure and properties of molecularly thin films. To explorethese effects, we study the structure and thermodynamics of thin films of n-octane and thin films of 2-methylheptane confined between crystalline surfaces. We use a series of molecular dynamics simulationsall carried out at the chemical potential of the bulk liquid at its vapor pressure. The simulationsshow that even the slight branching present in the 2-methylheptane significantly reduces the ability of the molecules to form discrete layers between the solid surfaces.
Background Essential to understanding lubrication, adhesion, colloidal stability, and swelling of clays is a thorough knowledge of the forces between solid surfaces separated by thin films of a liquid. Experimental measurements carried out with the surface force apparatus indicate that these forces can be extremely sensitive to the molecular architecture of the liquid. One of the most dramatic examples of this sensitivity is the differences between the solvation force curves of branched and linear alkanes.’ The addition of one methyl side chain to a molecule can change the pattern in the measured solvation forces from atrongly oscillatory to nonoscillatory with just one attractive minimum. This pattern is believed to be due to the disruption of a layering that occurs in the alkane film by the side chain. Replacing linear octane with 2-methyloctane reduces the number of such oscillations to one. There has been some skepticism as to whether such small changes in chemical structure can have that great an impact. It is possible that the results of the experiments reflect an inability of the systems to equilibrate. Thus, we have undertaken molecular dynamics simulations of alkane liquids confined between crystalline surfaces to look for significant structural differences between films of linear and branched molecules. The structure of thin films of simple liquids at equilibrium and under shear has been extensively studied for the past decade.”I7 Recently researchers have begun to
publish studies of bead-spring p o l y m e r ~ and l ~ ~linear ~ alkanes2628in confined geometries. In a previous paper we presented structures and solvation forces of thin n-octane films confined between two crystalline solid surfaces.29 This previous paper describes the simulations of the linear octane discussed here. In this work we present the first published molecular dynamics simulationscomparing the structure of thinf h of linear alkanes with thin films of branched alkanes confined between solid surfaces. We have chosen to use n-octane and 2-methylheptane at 297 K as our model compounds. These simulations examine the liquid structure between solid surfaces separated by distances of 1.02.4 nm. We will first summarize our model system and our molecular model. Then we will present our most significant results. A followup article will provide a more detailed structural analysis of our thin films. More details on our potential model can be found in previous work from our laboratory.29
System Geometry and Molecular Model We use as our substrate a static self-assembledfilm with the geometry found by Hautmann and Kleinm This allows us to use the well-studied alkane-alkane interaction parameters instead of the poorly known mica-hydrocarbon interactions in treating the interactions between the solid surfaces and the liquid. Surface force apparatus mea~
(l)Israelachvili, J. N.; Kott, S. J.; Gee, M. L.; Witten, T. A. Macromolecules 1989,22,4247-4253. (2)Ash,S.G.;Everett,D. H.;Radke,C. J. Chem. Soc.,Faraday Trans. 2 1973.69.1256-1277. (3) Ev&, R.; Marini Bettolo Marconi, U.; Tarazona, P. J. Chem. Phys. 1986,84,2376-2399. (4)Evans, R.;Marino Bettolo Marconi, U. J . Chem. Phys. 1987,86, 7138-7148. (5)Evans, R. J. Phys.: Condens. Matter 1990,2,8989-9007. (6)Henderson, D.; Lozado-Caseou, M. J. Colloid Interface Sei. 1986, 114,180-183. (7)Kjellander, R.;Sarman, S . Mol. Phys. 1990,70,215-237. (8)Lane, J. E.; Spurling, T. H. Aust. J. Chem. 1980,33,231-239. (9)Lane, J. E.; Spurling, T. H. A u t . J. Chem. 1981,34,1529-1533. (10)Macdonald, R. A. Znt. J. Thermophys. 1988,9,1061-1067. (11)Schoen, M.; Diestler, D. J.; Cuehman, J. H. J. Chem. Phys. 1987, 87. .5464-5476. ---(12)Schoen, M.; Cuehman, J. H.; Diestler, D. J.; Rhykerd, C. L.J. J . Chem. Phys. 1988,88,1394-1406. (13)Snook, I. K.;van Megen, W. J. Chem. Phys. 1980,72,2907-2913. (14)Sokolowaki, S.;Fiacher, J. Mol. Phys. 1990,71,393-412. (15)Thompson, P. A.; Robbine, M. 0. Phys. Rev. A 1990,41,68306837. ~
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(16)van Megen, W. J.; Snook, I. K. J. Chem. Phys. 1981,74,14091411. (17)Vanderlick, T. K.; Scriven, L. E.; Davis, H. T. J. Chem. Phys. 1988,90,2422-2436. (18)Yethiraj,A.:Hall,C.K.AIC~AnnwlMeeting;AIChE:Chicago, IL,1990;p 268F. (19)Yethirai. A.: Hall. C. K. Macromolecules 1990.23. 186618’72. (20)Yethiri; A.; Hall; C. K. J. Chem. Phys. 1991,‘95,3749-55. (21)Bitsanis, I.; Hadziioannou, G. J . Chem. Phys. 1990, 92,38273847. (22)Kumar, S.K.; Vacatello, M.; Yoon, D. Y. J. Chem. Phys. 1988,89, 5206. (23)Kumar,S.K.;Vacatello, M.; Yoon, D. Y. Macromolecules 1990, 23,2189. (24)ten Brinke, G.; Ausserre, D.; Hadziioannou, G. J. Chem. Phys. 1988,89,4374. (25)Theodorou, D. N.Macromolecules 1988,21,1400. (26)Vacatello, M.; Yoon, D. Y.; Laskoweki, B. Preprint. (27)Vacatello, M.;Yoon,D. Y.; Laskoweki, B. C . J. Chem.Phys. 1990, 93,779-86. (28)Ribarsky, M. W.;Landman, U. J. Chem. Phys. 1992,97,19371949. (29)Wang, Y.; Harris, J. G. J. Phys. Chem., in press. (30)Hautman, J.; Klein, M. L.J. Chem. Phys. 1989,91,4994-6001.
0743-7463/93/2409-1983$04.00/0 0 1993 American Chemical Society
Letters
1984 Langmuir, Vol. 9,No. 8,1993
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Reservoir
y+
Figure 1. Sketch of simulation cell. The gray region represents the static crystalline Langmuir-Blodgett films forming the two walls of the slit pore. The dark spheres are the CH, units of the alkanes. surements carried out on mica coated with a crystalline surfactant and bare mica give very similar patterns in the dependence of the solvation forces on the separation of the surfaces.31 Because the molecules in the crystalline film are longer than 1nm, the cutoff distance in the pair potential, we only need to use the potential functions for alkanealkane interactions. In order to get a meaningful comparison between different surface separations and different molecules, all simulations should be carried out at the chemical potential of the corresponding bulk fluid at 1atm, because in the experiments the liquid between the mica sheets should be in equilibrium with the bulk fluid. A failure to allow for this equilibrium will produce artifacts by placing too many or too few molecules in a fixed simulation cell. We solve this difficulty by making our slit pore (the theorists' term for the region between the solid surfaces) finite in one direction (y) as in the reservoir method of Yethiraj and Hall.32 In this direction the ends of the slit pore are open to a reservoir region where a small drop of liquid extrudes from the pore and sits in equilibrium with the vapor in the rest of the reservoir region. In the x direction periodic boundary conditions generate infinite solid surfaces. Figure 1 illustrates this geometry. Periodic boundary conditions in all directions around the entire simulation cell (reservoirand pore) prevent the depletion of molecules by evaporation. The length of the cell in the y direction is large enough so that both liquid and vapor regions form in the reservoir and molecules in the liquid portion cannot interact across the periodic boundaries. Hence, we simulate the liquid in the split pore in equilibrium with the fluid a t ita bulk vapor pressure. The lack of steady trends in the time evolution of the internal energy and density profiles during the sampling phase of the simulation verifies the equilibration of the fluid in the pore with the vapor in the reservoir. The liquid structure at its vapor pressure (lese than 1 atm) should be almost identical to the liquid structure at 1 atm. One potential problem with this approach is that there are three faces of each crystalline solid which border the reservoir region in addition to the surfaces of the gap. Adding molecules to the system to saturate the adsorption sites a t these surfaces would be prohibitive, so we place Gaussian repulsive potentials at these faces to make such adsorption energetically unfavorable. Careful choice of their width and height ensures that we can truncate the Gaussians so that they have no influence in the slit pore and immediately outside in the reservoir regions, while the discontinuities in the potential energy surface are insignificant. Our slit pores are 2.5 nm wide in they direction and 2.5 nm wide in the x direction, for which periodic boundary (31) Gee, M. L.; Israelachvili, J. N. J. Chem. SOC.,Faraday Trans. 1990,86,4049-4058. (32) Yethiraj, A.; Hall,C. K. Mol. Phys. 1991, 73, 503.
conditions are used. For the pore formed by surfaces separated by 2.0 nm, simulations of a pore of greater surface area indicates that finite size effects are insignificant as far as density profiles and solvation forces are concerned.% Also to minimize finite size artifacts in the comparison of our two liquids, at each surface separation the simulations of octane and isooctane are carried out with the same surface geometry and the same number of molecules, the only difference being the substitution of each octane molecule with 2-methylheptane. We used the intermolecular potential functions described in previouswork.29 These are basicallyJorgensen's OPLS potentials with flexible bond angle^.^^?^ This potential model employs a united atom treatment of the CH, groups, realistic torsional potentials, bond angle bending potentials centered with minima at the C-C-C bond angle, and fixed C-C bond lengths of 0.153 nm. We included the Lennard-Jones-type interactions between united atoms on different molecules or ones separated by more than three bonds on the same molecule. These nonbonded interactions were truncated at a distance of 1.0nm. The treatment of the torsion involvingthe methyl side group will be described in our later paper, but our treatment of this matter is identical to that of Jorgensen. The tertiary CH group in the isooctane is assigned the Lennard-Jones parameters of Jorgensen--E = 0.3347 kJ/ mol and u = 0.3850 nm.
Methodology We included from 48 to 96 liquid molecules in each study depending on the distance between the solid surfaces. Initial configurations were generated as in ref 29. Molecular dynamics were r u n for 1 ns at a fixed solid surfaceseparationbeforestatistics were taken for analysis. The sampling time is 2.5-6 ns for each simulation. The equations of motion were integrated using RATTLE,% the velocity Verlet algorithm with bond length constraints. Our time step was 0.007 ps, and the temperature was maintained at 297 K using Berendsen's external bath approach with a time constant of 3.5 ps." We calculated solvation forces as described in ref 29. This involved calculating the forces between the atoms comprising the solid surfaces and the molecules in the liquid. To minimize edge effects,our calculationof solvationforcesand densityprofiles included liquid atoms only from the region bl
