1072
Langmuir 1996,11, 1072-1074
Orientation of the COOH Headgroup in Stearic Acid Monolayers: Rigid Molecules Organization Calculations Qiang Miao,t?$Ruikang Tang,? Zihou Tai,*>tand Xiangping Qiant Department of Chemistry and State Key Laboratory of Coordination Chemistry, Nanjing University, Nanjing 210093, People’s Republic of China, and Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China Received January 14, 1994. I n Final Form: January 3, 1995@ The atom-atom potential calculations of stearic acid monolayers have been performed to determine orientations of the COOH headgroup. It is shown that the tilt structure of stearic acid monolayers may be due to a leaning of the COOH headgroup’s plane away from vertical with the crossed conformation(see text).
1. Introduction Assemblies of amphiphilic molecules such as stearic acid (CH3(CHz)&OOH) or its salts on water (Langmuir)l or on solid substrate (Langmuir-Bl~dgett)~,~ can form monolayers. The structure of a film and tilt angles of the hydrophobic tails can be adjusted by changing the temperature and the surface p r e ~ s u r e . ~ The characterization of Langmuir-Blodgett films has been carried out using a number of new, highly sensitive experimental technique^.^-^ However, with these techniques, a model is required in order to interpret the experimental result^.^ This has stimulated considerable theoretical activity and makes computer simulation a potential useful adjunct.12 Computer simulation techniques such as energy minimi~ation,~-~ Monte Carlo calculation,10and molecular dynamics9J1J2 allow the study of a film at a molecular level starting from a model of the intermolecular forces and has enhanced the understanding of its behavior. Much of the fundamental interest of investigations has been focused on the two-dimensional structure and correlations between tilt angles of the chains and the area per m ~ l e c u l e , ~but - l ~the nature of the influence of the COOH headgroups on their orientations in monolayers is poorly understood. These simulations were performed by totally ignoring the COOH groups8J1J2or with a simple unitedatom m ~ d e l ~ ,of~ Jthe amphiphilic molecules which approximated the COOH, CH3, and CH2 groups as united pseudoatoms, or spherically symmetry single force sites.
* Author to whom correspondence should be addressed. t Department of Chemistry and State Key Laboratory of Coor-
dination Chemistry. Laboratory of Solid State Microstructures. @Abstract published in Advance ACS Abstracts, March .15, 1995. (1)Kjaer, K.; Als-Nielsen, J.; Helm, C. A.; Tippman-Krayer, P.; Mohwald, H. J . Phys. Chem. 1989, 93, 3200. (2)Roberts, G. G. Adu. Phys. 1985,34, 475. (3) Swalen, J. D.; Allara, D. L.; Andrade, J. D.; Chandross, E. A.; Garoff, S.; Israelachvili, J.;McCarthy, T.J.;Murray, R.; Pease, R. F.; Rabolt, J. F.;Wynne, K. J.; Yu, H. Langmuir 1987, 3, 932. (4) Lin, B.; Shih, M. C.; Bohanon, T. M.; Ice, G. E.; Dutta, P. Phys. Rev. Lett. 1990, 65, 191. (5) Schlossman, M. L.; Schwartz, D. K.; Pershan, P. S.; Kawamoto, E. H.; Kellogg, G. J.; Lee, S. Phys. Rev. Lett. 1991, 66, 1599. (6) For a review see: Knobler, C. M. Adu. Chem. Phys. 1990, 77, 397. (7) Alfimov,M. V.;Bagaturyants,A.A.; Burshtein, K. Ya. Thin Solid Films 1991,200, 165. (8)Eckhardt, C. J.; Swanson, D. R. Chem. Phys. Lett. 1992,194,370. (9) Moller, M. A.; Tildesley, D. J.; Kim, K. S. J. Chem. Phys. 1991,
*
94. - -, 8390. --- -
(10)Yamamoto, T. J . Chem. Phys. 1988, 89, 2356. (11)Cardini,G.;Bareman, J. P.;Klein, M. L. Chem. Phys. Lett. 1988,
-145. . - , 493 .- -.
(12)Bareman, J. P.; Klein, M. L. J. Phys. Chem. 1990, 94, 5202.
We present here results of an energy minimization investigation of COOH group orientations, as a function of the tilt angles of alkyl tails or of the area per chain, in monolayers of close-packed stearic acid molecules using the all-atom representation.lZ 2. Method In our all-atom representation of the molecules, the COOH, CH3, and CH2 groups were split into individual C, H, and 0 atom force sites. Also, the three electronic lone-pairs of the carboxylic acid group, one in OH and two others in (2-0, were modeled as single force centers or pseudoatoms.13 The highly idealized models of rigid-molecule and homoconformation were based on those of Eckhardt et a1.8 and Alfimov et al.7 as used in monolayer or bilayer structure calculations. Since this Letter is concerned only with the orientations of COOH headgroups which anchor to the plane of a subphase, there is no need for consideration of molecular conformation changes in the crystal packing calculations. Our calculations have been performed including two steps: (1)the first was the conformation determination, using Allinger’s MM2&P1,13for a packing free stearic acid molecule in which the planes of the all-trans zigzag alkyl hai in^,^ and the COOH group were fxed parallel (parallel structure, the conformation is antiplanar) or right crossed (crossed of C-C-C-0 structure), as represented in Figure 1;(2) the second was the monolayer energy minimization which simply modeled the molecular backbones as all the same intramolecular conformation (homoconformation) predetermined in the first step. In noncharged polar groups the dipole-dipole interaction energy is the leading term.14 For this reason, the interaction energy between the molecules A and B was calculated according to the atom-atom potential method
V(A,B) = Z,azJ{C, exp{-C$,/(R, + RJI C&R, + RJYRi)+ E n m ( c c , , p mP( ~-~ ~ 3cos a, cos a m ) / ( ~ r n m 3(1) )} The first term in the above is that of the Buckingham and the second is the so-called Jean’s f0rmu1a.l~ For all atoms i in A and all atomsj in B, R, is the distance between atoms i andj and R,and RJare the effective radii of atoms i andj; the mixed interactions u, = (uzzoJ~1‘2, where a,, are empirical parameters related to atoms. And, for (13) Allinger, N. L. J. Am. Chem. SOC.1977,99,8127;MM2&PI 1985 QCPE 1985, No. 395+318. (14) Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982; Chapter 2.
0743-746319512411-1072$09.00/00 1995 American Chemical Society
Langmuir, Vol. 11,No.4, 1995 1073
Letters
Table 2. Calculated Monolayer Parameters for Parallel Structure: The x-0--x Plane of Alkyl Chain Tilted from Surface Normal 4 (deg) a (A) b (A) c (A) r (deg) u (A2) 6 (deg) -E (kcaVmol) 0 5 10 15 20 25 30 35 40
( b>
Figure 1. Molecular Cartesian coordinate: (a) parallel structure; (b) crossed structure. Table 1. Calculated Monolayer Parameters for Parallel Structure: The y-0-z Plane of Alkyl Chain Tilted from Surface Normal 4 (deg) a (A) b (A) c (A) t (deg) u (A2) 6 (deg) -E (kcaVmol) 0 5 10 15 20 25 30 35 40
5.12 5.16 5.26 5.35 5.45 5.53 5.55 5.60 5.76
4.29 4.30 4.28 6.26 4.33 4.58 4.87 5.11 5.34
4.78 4.79 4.79 4.81 4.83 4.82 4.82 4.82 4.92
60.3 60.0 59.2 58.8 57.8 56.0 54.6 53.3 52.4
19.08 19.22 19.34 19.49 19.97 21.00 22.03 22.94 24.37
77.6 80.9 86.5 90.7 91.8 88.7 85.6 85.7 91.2
33.08 32.48 32.59 33.06 32.76 31.38 30.98 31.02 30.34
all dipoles (1pl 2 0.300)n inA and all dipoles (Ipl 2 0.300) m in B, r,, is the distance between dipolar centers n and m , pn and p, are their dipolar moments, /3 is the angle between the two dipoles n and m , and the a's are the angles that the dipoles form with the vector connecting the two. Numerical constants were taken from ref 14: CI = 290 000,CZ= 12.50, C3 = 2.25, and dielectric constant D = 1.5;the units of V were kilocalories per mole and of R and r were angstroms. The energy minimization calculations for every tilt angle of the close-packed array of alkyl chains from vertical include only static contributions to the total energy with respect to four structural parameters: two unit cell axes, a and b; one angle t between the axes; and one orientation angle 8 between the axis of b and the vector of the carboxylic acid head group. All calculations were carried out for infinite ideal two-dimensional crystalline structures using one or two molecules per cell.
3. Results We denoted the molecular Cartesian coordinatesx-y-z (see Figure 1)to illustrate two kinds of tilt manners of molecular backbones for both parallel and crossed structures, tiltingthex-o-z plane and tilting they-o-z plane away from the monolayer's surface normal. We have performed a number of energy minimization calculations for monolayer fdms of stearic acids at different tilt angles of the molecular axis for both tilt manners and both conformation structures. Our calculated results with one molecular per cell appear in Tables 1-4. The lattice parameters a, b, c, and T are defined in Figure 2, u is the area per molecule, 4 is the tilt angle of the molecular tails from the normal, and 8is the COOH headgroup orientation angle that the vector 0 OH forms away from the axis b (counterclockwise in the monolayer plane, see Figure
-
2).
4.29 4.29 4.28 4.28 4.28 4.27 4.28 4.31 4.30
4.78 4.80 4.89 5.03 5.15 5.28 5.51 5.95 6.41
60.3 60.2 60.4 61.1 61.9 63.2 65.9 69.3 70.6
19.08 19.22 19.68 20.32 20.84 21.27 22.02 23.78 25.92
77.6 75.5 75.1 75.4 75.7 75.9 76.1 74.6 74.7
33.08 32.81 31.61 30.87 31.02 31.80 31.76 29.83 29.05
Table 3. Calculated Monolayer Parameters for Crossed Structure: The x-0-2 Plane of COOH Tilted from Surface Normal 4 (deg) a (A) b (A) c (A) t (deg) a(A2) 6 (deg) -E (kcaVmo1)
X
( a>
5.12 5.17 5.29 5.42 5.52 5.58 5.64 5.90 6.39
0 5 10 15 20 25 30 35 40
4.59 4.66 4.79 4.92 5.02 5.11 5.33 5.92 6.32
4.38 4.40 4.42 4.44 4.46 4.48 4.50 4.53 .4.59
5.00 5.06 5.17 5.30 5.42 5.50 5.60 5.71 5.88
67.7 67.8 68.2 68.8 69.4 69.7 68.9 64.6 62.9
18.60 18.98 19.66 20.37 20.96 21.47 22.38 24.23 25.82
28.6 27.3 25.7 24.1 22.6 21.5 20.6 19.2 20.3
34.50 33.36 31.59 30.51 30.43 30.89 30.03 28.28 28.03
Table 4. Calculated Monolayer Parameters for Crossed Structure: The y-0-2 Plane of Alkyl Chain Tilted from Surface Normal 4 (deg) a (A) b (A) c (A) t (deg) a(&) 6 (deg) -E (kcdmol) 0 5 10 15 20 25 30 35 40
4.59 4.60 4.61 4.61 4.61 5.70 5.71 5.81 4.61
4.38 4.36 4.35 4.38 4.53 4.83 5.11 5.38 5.65
5.00 5.14 5.35 5.53 5.73 4.69 4.71 4.84 6.49
67.7 69.9 73.2 75.8 77.6 52.1 51.2 51.1 77.8
18.60 18.83 19.20 19.57 20.40 21.72 22.76 24.31 25.46
28.6 26.2 21.8 16.1 9.6 -1.4 -4.7 -0.8 11.3
34.50 34.06 33.55 33.26 31.76 29.94 29.40 28.10 29.69
The tables show the dependence of the orientation of COOH headgroups on the conformational structure of stearic acid molecules and on the amphiphile tails tilt angle from vertical. It was found within our model, demonstrated in Tables 1 and 4, that the trend of orientations of the COOH group was normal to the nearest neighbor, b, with parallel structure and toward it with crossed structure, following increasing tilt of the y-0-2 plane around the ox axis. These are unexpected results of tilt along a short bond.4 However, leaning the hydrocarbon tail's plane, x-0-2 (see Tables 2 and 31,was always favorable tilted toward the next next nearest neighbor, a or c. The tilt directions of molecular tails with crossed structure are closer to it, where the differences are within 8". This indicates that the B phase in ref 4 may be packed only in the latter tilt manner and influenced by the model's conformation. But we could not get the C phase4 at higher temperature for our energy minimization models perfect lattices at essentially 0 K. The tables also show that our results of molecular areas per chain are in agreement with experimental values4v5 for fatty acid. Calculations with highly ideal conformations and one molecule per unit cell exhibit that the unexpected oblique p l lattice is the most stable monolayer structure of stearic acid at every tilt angle 4. However, it is very shortly deviated from the centered rectangular symmetry a t q5 = 40"tilt along the long bond with parallel structure. Calculations also performed for that of two untilted molecules in the unit cell (see Figure 3). Results show
1074 Langmuir, Vol. 11, No. 4, 1995
Letters LB films, having several close lying local stable structures in which the differences of energy are very small. In this view, the structural parameters of LB films and polar headgroup orientations may be controlled at equilibrium by small perturbations of substrate, temperature, and surface pressure. 4. Conclusions
Figure 2. COOH headgrouporientationsin a parafinicpacking
monolayer.
b Figure 3. COOH headgroup orientations of the parallel
structure in a plural cell.
that the parallel structure with the centered rectangular metry (a = 7.42 A, b = 5.14 A, z = 90.8",u = 19.07 = -33.94 kcal/mol) has the lowest total energy of both structures with untilted and tilted angles. This conclusion from pure computer simulation is the same with the experiment result.15 It indicates that the standing normal parallel structure favors a plural cell and is more stable. However the crossed structure prefers parafinic orientations demonstrated in Figure 2 and always plays a simple cell in any tilt angle. The analysis of potential energy surfaces in both kinds of tilt structures supports the idea of C. J. Eckhardt for
p.
(15) Leveiller, F.; Jacquemain, D.; Leiserowitz, L.; Kjaer, IC; AlsNelsen, J. J. Phys. Chem. 1992, 96, 10380.
As previously stated, this work is only on the molecular monolayer packing. However, it probably should be mentioned that the orientation of head groups in Langmuir or Langmuir-Blodgett films may be influenced by the interaction with the molecules of the subphase especially in the case of the ordered substrate. The orientations of head groups on subphases are some other interesting subjects which we will report in progress. Our calculations indicate that the all-atom representation employed in the energy minimization promises fine tuning of properties of orientation of the head group. Fwthermore, this simplified approach may extend the modeling role of phase diagram of LB films. But as the limit of the computer simulation techniques today, there are some deficiencies of the analysis. Each molecule is isolated while using the MMB&Pl software package to determine its structure. However, the molecules are related with others in the monolayer, so the structure taken from MM2&P1is different from the results of the X-ray diffraction experiment.15J6 The result of the MM2&P1 shows the conformation of C-C-C=O for parallel structure is antiplanar, rather than synplanar as occurs in two-dimensional crystallography. And as we know, the hydrogn bond is not taken into account in the atom-atom potential method and the calculation of the probable molecular packing arrangement in the monolayer was performed by the energy minization. Therefore, the effect of the hydrogen bond is not considered, but it is much affected by intermolecular arrangements.15J6 Despite the fact that this method has some defects in its qualities, it is still a good computer simulation. LA940055C (16)Jacquemain, D.; Wolf, S.; Leveiller, F.; Deutsch, M.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz,L.Angew. Chem., Int. Ed. Engl. 1992, 31, 130.
