J . Phys. Chem. 1988, 92, 5813-5822
5813
Theoretical Examinatlon of Hexanol-Water I iterfaces Jiali Gaot and William L. Jorgensen* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: December 15, 1987; In Final Form: March 31, 1988)
The energetics, structure, and molecular interactions have been examined for model interfacial systems consisting of 1-hexanol/water mixtures in monolayer, bilayer, and double bilayer (biphasic) arrangements. Monte Carlo statistical mechanics simulations were carried out for the three systems in the N I T ensemble at 25 OC and 1 atm. The computations predict minimal water penetration into the hydrophobic regions from the analyses of denisty profiles and radial distribution functions. However, water molecules are found to interact freely with the hydroxyl groups of hexanol in the region ca. 7-14 A from the center of the water unit. Hydrogen-bonding analyses revealed that an average of cx. 2 water molecules are hydrogen bonding with each hexanol molecule in the monolayer, while ca. 1.6 are observed for thi bilayer and biphase. The number of hydrogen bonds between the 1-hexanol pairs is ca. 1.0 in the aqueous interfacial regior +fthe bilayer and biphasic systems and 0.8 in the monolayer. A significant increase in the population of trans conformations adout bonds in the hexanol molecules is also found in the interfacial systems. The population shift helps facilitate the formation of hydrogen bonds in the interfacial regions and helps maintain the dense packing of the amphiphib. Many of the structural findings are consistent with previous experimental and theoretical results that support the picture of relatively narrow interfaces with minimal water penetration beyond the head-group region in amphiphilic aggregates.
Introduction The structures and properties of pure liquids and dilute solutions have been investigated extensively in recent years by using computer simulation techniques.' Though much effort has focused on a broadening range of organic and biochemical systems: interfacial systems such as micelles, monolayers, and bilayers of organic amphiphiles have received limited study. Nevertheless, it is particularly desirable to obtain a better understanding of the interactions and structure in interfacial regions. Such information is a prerequisite to obtaining an atomic level knowledge of important biological processes including transmembrane transport and intercellular recogniti~n.~To this end, Monte Carlo statistical mechanics simulations of model monolayer, bilayer, and biphasic systems in water have been carried out as presented here. The model amphiphile is 1-hexanol, which was chosen owing to its insolubility in water and because its neutral character has computational advantages, especially due to the diminished importance of local polarization and long-range electrostatic forces. At the same time, the hexanol-water system allows the analysis of key issues such as the hydrogen bonding at the interfaces, water penetration into the hydrocarbon region, the surface roughness a t the interfaces, and the effect of the ordered environment on the conformation of the alkyl chains. Previously, structural information has been obtained for phospholipid bilayers from extensive experimental studies using X-ray and neutron diffraction, deuterium magnetic resonance (2H NMR), electron microscopy, and NMR.&'O The conformation of the alkyl chains and the packing of head groups in the interfacial region have begun to be understood for these systems. In particular, the diffraction experiments found the orientation of the head groups of both phosphatidylethanolamine (PE) and phosphatidylcholine (PC) to be parallel to the bilayer surface and not These results are supported to depend on the state of hydrat~n.~?' by N M R studies,* and Seelig and Niederberger have used ZH N M R to provide order parameters for the alkyl groups that also give insights into the chain conformation and p a ~ k i n g .In ~ addition, the long debate on water penetration has been generally resolved by neutron diffraction experiments and other measurements that have shown minimal water penetration into the hydrophobic cores of bilayers and micelles.11.12 However, such data are difficult to obtain experimentally for monolayers for which electron microscopy has revealed only gross features of the amphiphiles' aggregation and surface thickness.1° Moreover, the picture for the interactions between the lipid head groups and Present address: Department of Chemistry, Harvard University, Cambridge, MA 02138
water molecules is still in a primitive state. Some prior computer simulations have also been carried out on water between walls and on bilayers and a m i ~ e l l e . ' ~ -The ~~ (1) (a) Rossky, P. J. Annu. Rev. Phys. Chem. 1985, 36, 321. (b) Jorgensen, W. L. J. Phys. Chem. 1983, 83, 5304. (2) (a) Beveridge, D. L.,Jorgensen, W. L.,Eds. Ann. N . Y.Acad. Sci. 1986,482. (b) Jensen, K. F., Truhlar, D. G., Eds. ACSSymp. Ser. 1987, No. 353. (c) McCammon, J. A.; Harvey, S.C. Dynamics of Proteins and Nucleic Acids; Cambridge University: Cambridge, 1987. (3) Quinn, P. J. The Molecular Biology of Cell Membranes; University Park Baltimore, 1976. (4) Biomembrane Structure and Function; Chapman, D., Ed.; Verlag Chemie: Weinheim, 1984. (5) Seelig, A.; Seelig, J. Biochemistry 1974,13,4839. Zaccai, G.; Buldt, G.; Seelig, A,; Seelig, J. J. Mol. Biol. 1979, 234, 693. (6) Hauser, H.; Pascher, I.; Pearson, R. H.; Sundell, S . Biochim. Biophys. Acta 1981, 650, 21. (7) Worcester, D. L. In Biological Membranes; Chapman, D., Wallach, D. F. H., Eds.; Academic: New York, 1976; Vol. 3. (8) Seelig, J. Biochim. Biophys. Acta 1978,515, 105. Hauser, H.; Phillips, M. C. Prog. Surf. Membr. Sci. 1919, 13, 297. (9) Seelig,J.; Niederberger, W. J. Am. Chem. SOC.1974, 96, 2069. (10) Ries, H. E., Jr.; Matsumoto, M.; Uyeda, N.; Suito, E. Adu. Chem. Ser. 1975, 144, 286. (1 1) (a) Buldt, G.; Galy, H. U.; Seelig, A.; Seelig, J. Nature (London) 1978,272, 182. (b) Dilger, J. A.; Fisher, L.R.; Harplon, D. A. Chem. Phys. Lipids 1982, 30, 159. (c) Bendedouch, D.; Chen, S.-H.; Koehler, W. C. J. Phys. Chem. 1983, 87, 153. Dill, K. A,; Koppel, D. E.; Cantor, R. S.; Dill, J. D.; Bendedouch, D.; Chen, S.-H. Nature (London) 1984, 309, 42. (d) Tabony, J. Mol. Phys. 1984,51,975. (e) Lennox, R. B.; McClelland, R. A. J. Am. Chem. SOC.1986,108,3771. (f) Menger, F. M.; Doll, D. W. J. Am. Chem. SOC.1984, 106, 1109. (12) Tanford, C. The Hydrophobic Effect, 2nd 4.;Wiley-Interscience: New York, 1980. (13) Marchesi, M. Chem Phys. Lett. 1983, 97, 224 Sonnenschein, R.; Heinzinger, K. Chem. Phys. Lett. 1983, 102, 550. Kjellander, R.; Marcelja, S. Chem. Phys. Lett. 1985, 120, 393. (14) Chriaton, N. I.; Whitehouse, J. $.; Dicholson, D.; Parsonage, N. G. Faraday Symp. Chem. SOC.1981, No. 16, 139. Owenson, B.; Pratt, L.R. J. Phys. Chem. 1984,88, 2905, 6048. Woods, M. C.; Haile, J. M.; OConnell, J. P. J. Phys. Chem. 1986, 90, 1875. (15) Lee, C. Y.; McCammon, J. A.; Rossky, P. J. J. Chem. Phys. 1984, 80, 4448. (16) (a) van der Ploeg, P.; Berendsen, H. J. C. J . Chem. Phys. 1982, 76, 3271. van der Ploeg, P.; Berendsen, H. J. C. Mol. Phys. 1983,49, 233. (b) Berendsen, H. J. C.; van Gunsteren, W. F.; Egberts, E.; de Vlieg, J. In Supercomputer Research in Chemistry and Chemical Engineering; Jensen, K. F., Truhlar, D. G., Eds.;ACS Symposium Series 353; American Chemical Society: Washington, DC, 1987; p 106. (c) Cardini, G.; Bareman, J. P.; Klein, M. L. Chem. Phys. Lett. 1988, 145, 493. (17) Scott, H. L., Jr. Chem. Phys. Lett. 1984, 109,570. Scott, H. L.,Jr. Biochim. Biophys. Acta 1985, 814, 327. (18) Kjellander, R.; Marcelja, S.Chem. Scr. 1985, 25, 73. (19) (a) Jonsson, B. Chem. Phys. Lett. 1981, 82, 520. (b) Jonsson, B.; Edholm, 0.;Teleman, 0. J. Chem. Phys. 1986,85, 2259.
0022-3654/88/2092-58 13$01.50/0 0 1988 American Chemical Society
5814
Gao and Jorgensen
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
comprehensive molecular dynamics study of Lee et al. on liquid water between flat surfaces showed that the surfaces induced oscillations in density extending approximately 10 A into the bulk fluid, and the molecular dipole vector preferred an orientation of ca. 5 5 O to the inward-normal of the surfaces.ls The arrangement appeared to represent a balance between the tendencies of maximizing the number of hydrogen bonds and minimizing the packing density of the molecules in the liquid. van der Ploeg and Berendsen have presented their molecular dynamics (MD) simulations of a model bilayer system containing 2 X 64 decane They found that the molecular order parameters were in good accord with experimental results. M D results have also been recently reported for a similarly construed monolayer.'& However, these computations were performed without water; the head groups were confined to the bilayer surface by harmonic forces. The bilayer work has recently been extended to include the water for a mixed sodium decanoate-decanol system.16b The molecular dynamics results indicate a broad interface extending over ca. 10 A with some water penetration well into the interior of the bilayer. Related simulations have been carried out by Scott and co-workers for a series of crude models of PE, PC, and phosphatidylserine (PS) bilayers in which four head groups, each represented as a pair of positive and negative charges, were placed on each side of a slab of 172 TIPS2 water m01ecules.l~ The density, orientation, and hydrogen-bonding profiles of water as a function of distance from the head groups were determined. Kjellander and Marcelja performed similar M D calculations for a model PC-water interface that had charge distributed over more sites on the head groups.'* However, both studies suffer from a lack of molecular detail for the amphiphiles and from the use of small systems. The MD simulation of a sodium octanoate micelle in water by Jonsson et al. should also be noted.Igb Difficulties occurred in keeping the micelle aggregated unless the charges on the ions were reduced to half their real values. This arbitrary scaling reflects the inadequacy of the standard potential functions with fixed charges to describe adequately the energetics in such ionic systems. The present choice of a nonionic system was made in part to reduce these concerns, and, in fact, no stability problems were encountered. In the following, the computational procedures are first summarized. The energetic results are then presented, followed by discussions on the structural findings including density and hydrogen-bonding profiles.
Computational Procedure Monte Carlo Simulations. Statistical mechanics simulations were carried out for monolayer and bilayer systems, each containing 40 1-hexanol and 267 water molecules in a rectangular box with dimensions of ca. 20 X 20 X 41 A as indicated in Scheme I. Similar calculations were also performed on a system of 80 1-hexanol and 267 water monomers in a ca. 20 X 20 X 61 A box, which is referred to here as a biphase. The biphase consisted of two double layers of 1-hexanol molecules as shown in Scheme I. The biphase not only features the interfaces between the alcohol molecules and water but also has an interface between hydroxy groups of 1-hexanol molecules. The three systems were modeled to ascertain the sensitivity of the structural results to these environmental differences. Periodic boundary conditions were employed for the simulations of the bilayer and biphase in all three directions, whereas for the monolayer periodicity was only applied in the x and y directions and not normal to the interface (Scheme I). Thus, the latter form corresponds to infinite sheets of hexanol on both faces of a water slab in vacuum. Standard procedures including Metropolis sampling and the isothermal-isobaric (NPT) ensemble at 25 O C and 1 atm were adopted in all cases.lb New configurations were generated by translating a randomly chosen molecule in all three Cartesian directions, by rotating it about a randomly selected axis, and by altering the dihedral angles for the 1-hexanol molecules. Changes in the volume were attempted every 5000 Configurations (20) Valeau, J. P.; Gardner, A. A. J. Chem. Phys. 1987, 86, 4162
SCHEME I: Schematic Representation of the Interfacial Systems"
WATER
I WATER
OH OH OH OH
WRTER BILRYER
1il 1;I
OH OH OH OH
r\ \ r\ v\
OH OH OH BH
Im OH OH OH
WATER
WATER
w\
BIPHASE
OH OH OH OH
HIYONOLAYER "The open box for the monolayer implies that the periodic boundary conditions are not employed along the z axis. by scaling all of the molecular positions in one randomly chosen Cartesian direction. Thus, the size and shape of the systems adjusted themselves in achieving equilibrium. The ranges for molecular motions and volume changes were chosen to produce an acceptance rate of about 40% for new configurations. Specifically, the ranges were f0.15 A and f15O for water monomers, f0.08 A and *loo for 1-hexanol molecules, and f150 A3 for volume changes. The dihedral angle changes for the alcohol molecules were also restricted to a maximum of f 10'. Umbrella sampling over rotational barriers chopped at 3 kcal/mol was used to enhance the conformational transitions.lb It should be noted that the sampling for the first (H-O-CI-C2) and second (0C1-C2-C3) dihedral angles was not affected by the umbrella potentials because of the low rotational barriers in these cases. Spherical cutoffs, based on atomic separations, were used to truncate the intermolecular interactions at a distance of 8 A for the water-water, water-hexanol, and hexanol-hexanol pairs. Unlike the usual procedure, which is based on roughly the center-of-mass separations,Ibs2' the algorithm used here involved computing all distances between atoms in each of the two interacting monomers. Whenever a distance between any two atoms is found to be shorter than the fixed cutoff separation, the entire interaction energy for the two molecules is included in the total energy of the system. This procedure is particularly favored over the center-of-mass scheme for long molecules such as 1-hexanol. In addition, neighbor lists were employed for computational efficiency. Neighboring molecules within a radius 1 A larger than the cutoff distance were included in the lists and were updated after every 20 attempted moves of a molecule. This was found to increase the speed of calculation by ca. 15%. In each case, 2 X 106-3 X lo6 configurations were discarded in equilibrating the system followed by an additional 5 X lo6 configurations for averaging. The analyses, such as for the density distributions and hydrogen bonding, were made by using configurations saved at intervals of lo4 configurations during the simulations. All computations were run on a Gould 32/8750 computer in our laboratory. Approximately lo6 configurations could be sampled per day. (21) Andrea, T. A,; Swope, W. C.; Andersen, H. C. J. Chem. Phys. 1983, 79, 4576.
Theoretical Examination of Hexanol-Water Interfaces TABLE I: Standard Geometrical Parameters for the Hexanol Molecules bond angle, deg bond length, 8,
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 5815 TABLE 11: Fourier Coefficients and Lennard-Jones Parameters for the Intramolecular Rotational Potential Functions
~
0-H
c-0 c-c
0.945 1.430 1.530
COH
cco ccc
108.5 108.0 112.0
The initial configuration for the biphase simulation was constructed by combining a cell of 80 1-hexanol molecules ordered as in Scheme I, which is reminiscent of crystals of long-chain alcohols,22 and an equilibrated cube (20-A edges) of 267 water monomers. The hexanol region had dimensions of ca. 20 X 20 X 41 A. The figures for the hexanol and water both correspond to the correct densities for the pure Initially, there were 20 alcohol molecules at each water surface. This is consistent with the limiting area of 20 A2 for 1-alkanols observed in force-area diagrams for monolayers on water.24 The dihedral angles for the hexanol molecules all started in the trans form. The initial bilayer configuration was generated by removing the 40 hexanol molecules in the interior region along with the generated free space. Finally, the periodicity along the z direction was eliminated, and the bilayer was separated to become a water slab with an alcohol monolayer on both surfaces. It should be noted that the monolayer model does correspond well to the physical system in film balance experiments (Langmuir-Blodgett films),24 though there is only one water-alcohol interface in the latter case. However, 1-hexanol does not form bilayers or the biphase-type arrangement in water; the two liquids simply separate. The enforced periodicity in the simulations does not allow the separation to occur. So, the latter arrangements are not physically realistic for hexanol; however, they allow the computational study of important model interfacial systems. Intermolecular Potential Functions. The intermolecular potential functions have been reported previously. Specifically, the TIP4P model was adopted for water,2saand the Lennard-Jones and Coulomb parameters for the 1-hexanol molecules are the OPLS set optimized for liquid alcohols.2sb These potential functions have been shown to produce excellent thermodynamic and structural results for the pure liquids with average computed densities and heats of vaporization within ca. 2% of experimental values. The general form for the potential functions (eq 1) includes
Lennard-Jones and Coulomb terms. In eq 1, is the interaction energy between two molecules a and b, and standard and Cij = combining rules are used such that Aij = (AiiAjj)1/2 (CiiCj,)1/2. The A and C parameters may also be expressed in terms of Lennard-Jones u's and e's as Aii = 4eiui'z and Cii = 4eiu:. The interaction sites are located on the nuclei with an exception for water in which the negatively charged point is on the bisector of the HOH angle, 0.15 A from Some further details should be noted. First, a united atom model is used for CH, groups with the interaction site centered on the carbon. However, the hydrogens are explicitly represented on heteroatoms. Secondly, standard bond lengths and angles from experimental studies are used in these simulations for both the hexanol (Table I) and water ( r ( 0 H ) = 0.9572 A, LHOH = 104.52°).25a These remain fixed during the simulations; however, internal rotations are included for the 1-hexanol molecules. Finally, charges are only on the sites for the CHz-0-H units of the hexanol in the OPLS model.25b (22) Abrahamsson, S.; Larsson, G.; van Sydow, E. Acta Crystllogr. 1960, 13, 770. (23) Wilhoit, R. C.; Zwolinski, B. J. J. Phys. Chem. Re$ Data Suppl. 1973, 2. (24) Gaines, G. L. Insoluble Monolayers at Liquid-Gas Interfaces; Interscience: New York, 1966. Shah, D. 0.;Shiao, S. Y. Adu. Chem. Ser. 1975, 144, 153. (25) (a) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J . Chem. Phys. 1983, 79, 926. Jorgensen, W. L.; Madura, J. D. Mol. Phys. 1985.56, 1381. (b) Jorgensen, W. L. J . Phys. Chem. 1986, 90, 1276.
Fourier coefficients, kcal/mol bond C1-0
c,-c2 c-c
VO 0.0 0.0 0.0
interaction C-Ho
c-0 c-c
VI v2 v3 -0.116 0.747 0.834 3.060 0.702 -0.212 1.411 -0.271 3.145 Lennard-Jones parameters 5. 8, c. kcal/mol 2.60 0.008 3.50 0.008 4.00 0.0074
TABLE 111: Thermodynamic Results for the Hexanol-Water Systems at 25 "C" monolayer -12.07 5.62 -0.39 6.62 0.18
Ehw
AEh &nt
+mint
@w
Urn,
AV AHmix
bilayer -10.98 4.13 -0.30 6.13 0.87 -8.3 0.87
biphase -5.32 1.58 -0.25 2.62 1.04 -11.1 1.04
Energies are given in kilocalories per mole of hexanol molecules at the concentration specified in the text. b u n i t s for volume changes are A3 per hexanol molecule for the same concentration.
Intramolecular Potential Functions. Since the torsional motions are included, the corresponding energetics need to be described by torsional potential functions. These are represented by Fourier series for each dihedral angle as given in eq 2. For 1-hexanol, V(@) =
vo + '/ZV,(1 + cos 9)+ XV2( 1 - cos 2@) + Y2V3(1
+ COS 3@) (2)
there are five dihedral angles and five such series. In addition, Lennard-Jones terms are needed to account for the interactions between atoms separated by more than three bonds.Ib Parameters for the torsional potentials of small alcohols have been developed recently.25b For 1-hexanol, the Fourier coefficients for the C,-0 and CI-C2 bonds are taken to be the same as in l - p r o p a n ~ l , ~ ~ ~ whereas the other dihedral angles are treated as in alkanes.26 These parameters were determined by fitting to the rotational potentials obtained from MM2 molecular mechanics calculations27 with full geometry optimization^.^^^^^ The Fourier coefficients and Lennard- Jones parameters for the intramolecular interactions in 1-hexanol are summarized in Table 11.
Results and Discussion Thermodynamics and Energy Distributions. The total energy of the mixture of hexanol and water is defined in eq 3 as the sum (3)
of the intermolecular interaction energies for each species (Ehand E, for the hexanol-hexanol and water-water interactions), the interaction energy between the two constituents (Ehw),and the intramolecular rotational energy for the hexanol molecules (Eht). The energy change on mixing the two constituents from their pure liquid states can be expressed by eq 4 and 5 , where Eh* and E,*
+
AE,,,ix = ET - (Eh* Ei,t*) - E,* = E h w + (Eh - Eh*) + (Eint - Eint*) + AE,,,jx = Ehw + (AEh + AEi,t)
+ AE,
-
(4)
(5)
are the intermolecular energies for the pure liquids, Eint*is the torsional energy for pure hexanol, and (AEh + AEint)and AE, (26) Jorgensen, W. L.; Madura, J. D.; Swenson,C. J. J. Am. Chem. SOC. 1984, 106,6638. (27) Burkert, U.; Allinger, N. L. Molecular Mechanics; ACS Monograph 177; American Chemical Society: Washington, DC, 1982.
Gao and Jorgensen
5816 The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
.-
.lS,
BONDING ENERGY OISTRIBUTIONS I h
I
0
1000
2000
3000
4000
5000
CONFIGURATION I X 1000 I
Figure 1. Total energies for the monolayer, bilayer, and biphasic systems obtained from averages over blocks of 2 X lo5configurations during the Monte Carlo simulations.
-46
-40
-34
I \--BILRYER \
-28
-22
-16
-10
BONDING ENERGY Figure 2. Distributions of total bonding energies (kcal/mol) for the hexanol molecules in the interfacial systems. Units for the ordinate are
mole fraction per kcal/mol.
are the reorganization energies for the pure liquids. The enthalpy of mixing is then given by eq 6 , where AVmixis the difference in volumes of the mixture (V) and the pure liquids (P). The reference values, Eh* + Ei,,* and E,*, have been obtained from separate Monte Carlo simulations of liquid 1-hexanol with 80 monomers and pure TIP4P water at 25 OC and 1 atm. The calculated thermodynamic quantities are listed in Table 111. To ease the comparisons, we divided the total values by the number of hexanol molecules in each case. The uncertainties ( f l u ) for the computed values were determined from separate averages over blocks of 2 X lo5 configurations and are less than f0.1 kcal/mol for the energetic quantities. The volume fluctuates relatively more and leads to uncertainties in AVof ca. f2 A3. For all three interfacial systems, the total energy converged readily and did not show significant drift during the averaging. This is illustrated in Figure 1, which displays the average total energies for each block of 2 X lo5 configurations during the final 5 X lo6 configurations. For all three calculations, the systems appear to be at equilibrium. Although direct measurements of thermodynamic properties relevant to the present mixtures are not available, some experimental results on alcohol-water systems can be noted. 1-Alkanols up to C3 are completely miscible in water, and the process of combining liquid alcohol and water is exothermic at all compositions of the mixture^.^**^^ For alkanols with long carbon chains at high concentrations, the mixture of alkanol and water separates into two phases and the mixing process becomes end other mi^.^^ The present Monte Carlo simulations yield endothermic energies of mixing of 0.2 kcal/mol for the monolayer, 0.9 kcal/mol for the bilayer, and 1.O kcal/mol for the biphase (Table 111). The mole fraction of hexanol for the first two systems is 0.13, while it is 0.23 for the biphase. The experimental results obtained by Marongiu et al. indicated that 1-pentanol exhibited an endothermic excess enthalpy of 0-0.2 kcal/mol in the heterogeneous region.29 The excess enthalpy for mixing hexanol and water should also be positive, particularly so in the present, less than optimal arrangements. Interestingly, Marongiu et al. also found a large, negative value for the excess entropy, indicating increased structural order in the alkanol/water mixtures.lg Some further observations can be made on the calculated energies listed in Table 111. When the interfaces between hexanol and water are formed, some intracomponent hydrogen bonding is destroyed. Consequently, positive disruption energies are observed for each constituent. The larger (AEh Mi,,)for the hexanol in the monolayer is reasonable since the hexanol-hexanol
+
~
~~
~~
~
~
(28) Aveyard, R.; Mitchell, R. W. Trans. Faraday SOC.1968,64, 1757. Aveyard, R.; Lawrence, A. S.C. Trans. Faraday SOC.1964, 60, 2265. (29) Marongiu, B.; Ferino, I.; Monaci, R.; Solinas, V.; Torazza, S. J . Mol Liq. 1984, 28, 229.
I I
I I I I
Figure 3. Distributions of individual interaction energies for the hexanol molecules interacting with water and hexanol in the interfacial systems. Units for the ordinate are molecules per kcal/mol.
contacts have been diminished the most in this case. The smaller value for the biphase partly reflects the existence of the extra hexanol-hexanol interface for this system. The hydrogen bonding in the hexanol region of the biphase may be more favorable than in the pure liquid due to the proximate and ordered state of the head groups. The Ehw values for the bilayer and biphase are consistent since only half of the hexanol molecules in the biphase can hydrogen bond with water. Thus, in both cases the hexanol-water interactions amount to 10-1 1 kcal/mol for each hexanol molecule in the interface. This suggests an average of about 2 hexanol-water hydrogen bonds for each hexanol molecule. The interfacial attraction is even greater (12 kcal/mol per hexanol) for the monolayer, in which fewer hexanol-hexanol interactions need to be accommodated. The greater interfacial attraction is accompanied by greater disruption of both the water (M,)and hexanol (AEh + Mint). The change in the intramolecular rotational energies, mint, is also interesting. For all three systems, it is negative, indicating greater populations for trans conformations than in the pure liquid state. The conformational results will be discussed in detail below. The results for AVindicate some contraction for both the bilayer and biphase relative to the pure liquids. As discussed further below, the hexanol is more ordered in the interfacial systems with some shift in structural character toward the solid including the straightening of the alkyl chains. Consistently, the hexanol is more tightly packed than in the liquid. The volume for the monolayer system is not well defined since it is open in the z direction, so AV cannot be computed. The energy distributions in Figures 2 and 3 can provide further insight into the energetic environment in the mixtures. Figure
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 5817 6
DENSITY DISTRIBUTIONS UONRRYER
9
-
-32
-24
-16
-8
0
8
16
2L)
32
ZIRl
DENS I TY 0 I STR IBUTIONS BILRYER
-21
-15
-9
-3
9
3
15
LIAI
Figure 4. Density profiles for the oxygen atoms of water in the hexanol-water systems. The ordinate gives the density of the oxygen atoms in the interfacial systems relative to that of pure water, Le., p*(z) = p ( z ) / p o ( z ) . Successive plots are offset 0.3 units along the ordinate. OXYGEN DENSITY PROFILE ?
1.
5
r(
>
c3
iW02
d2
K
1
0
-32
-24
-16
-e
o
8
16
2~
32
ZIRl
Figure 6. Density profiles for the hydroxyl and all carbon atoms of hexanol in the monolayer, bilayer, and biphasic systems. Densities relative to liquid hexanol are displayed in the plot. -21
-15
-9
-3
3
9
15
ZlAl
Figure 5. Relative density profiles for the hydrogen atoms of water in the monolayer, bilayer, and biphasic systems. Successive plots are offset 0.3 units along the ordinate. 2 contains the distributions of total intermolecular bonding energies for a hexanol molecule, while the energy pair distributions for an individual hexanol molecule interacting with another monomer (hexanol or water) are displayed in Figure 3. It is apparent from Figure 2 that the hexanol molecules experience a range of energetic environments covering 20-25 kcal/mol. The averages of the energy distributions in Figure 2 correspond to the total intermolecular bonding energies for the hexanol molecules. The more positive bonding energy in the monolayer reflects the reduced interactions due to the removal of the periodicity along the z axis. The bimodal profile for the biphase is similar to that found in simulations of pure liquid alcohols.25b By analogy, the profile results from the overlap of several bands corresponding to hexanol molecules participating in 1, 2, or 3 hydrogen bonds. Qualitatively, the energy pair distributions in Figure 3 consist of 3 or 4 overlapping bands for all three systems. The bands at lowest energy correspond to hydrogen bonds between hexanol molecules, while the region around -5 kcal/mol is consistent with hexanol-water hydrogen bonds. The -3 to -2 kcal/mol regon may
include some interactions with second nearest neighbors, while the spike from -2 to +1 kcal/mol reflects the numerous interactions with more distant molecules. In addition, the smooth transition between the bands indicates a continuous range of interactions and local structure. Though estimated numbers of hydrogen bonds can be obtained by integration of the low-energy bands, thorough analyses of the hydrogen bonding is provided in a subsequent section. Density Profiles and Water Penetration. The atomic density profiles are defined by eq 7 as the average number of atoms in = O"z,z+Gz)) / ( A ~ z ) (7) slabs of area A and thickness 6z along the z direction of the simulation box (Scheme 11). The computed oxygen and hydrogen density profiles for the water molecules are reported in Figures 4 and 5 for the monolayer, bilayer, and biphasic systems. The distribution functions have been normalized relative to liquid water at a density of 0.997 g/cm3, Le., p*(z) = p ( z ) / p " ( z ) .Similar plots for the carbon atoms and the hydroxyl groups of the amphiphiles are presented in Figure 6-9. An important point is that the origin of the z coordinate for each configuration was centered on the average position of the oxygen atoms of the water molecules. This convention has been adopted for all of the analyses presented here that depend on the z coordinates. ~(2)
5818 The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 2.
Gao and Jorgensen
DISTRIBUTIONS MONOLAYER
RTOH
’.&I 2.
-21
-16
-9
-3
3
9
1s
21
-21
Z(R1
-15
-9
3
-3
9
1s
t(R1
Figure 7. Distributions of the hexanol atoms (top from center: 0, C2, C,, and C,; bottom from center: H, C1,C3,and C,) computed for the
Figure 8. Distributions of the hexanol atoms (top from center: 0, C2, C4,and cg; bottom from center: H, C1,C3, and C,) computed for the
monolayer. Relative densities are given in the plot.
bilayer. Relative densities are given in the plot.
SCHEME 11: Simulation Box Divided into Small Volume Units of Area A (xy ) and Thickness bz for Computing the Density and Hydrogen-Bonding Distributions 62
- 2
Figure 4 indicates that the density profiles for the water oxygens show oscillatory behavior for all three systems. The fluctuations extend across the entire aqueous region with a period of about 3 A, as has been observed previously in simulations of water between hydrophobic ~ ~ r f a Experimental ~ e ~ studies . ~ on ~ aqueous solutions between mica surfaces also reveal force oscillations at small separations with a periodicity equal to the diameter of the solvent molecules.30 As Israelachvili states, the force oscillations “reflect the ordering of the liquid molecules into discrete layers when constrained between two surfaces”.Ma It should also be noted that the average density near the centers of the water cells is found to be identical with the value for liquid water. Thus, the present model for liquid interfaces seems reasonable. The hydrogen density profiles in Figure 5 are oscillatory as well. However, the smaller amplitudes can be attributed to the diminished packing requirements and greater orientational freedom (30) (a) Israelachvili, J. N. Acc. Chem. Res. 1987, 20, 415. (b) Israelachvili, J. N.; Pashley, R. M.Nature (London) 1983,306, 249. Christenson, H.K. J . Chem. SOC.,Faraday Trans. I , 1984,80, 1933. (c) Chistenson, H. K.; Horn, R. G. .IColloid . Interface Sci. 1985, 103, SO.
Figure 9. Distributions of the hexanol atoms (top from center: 0, C,, C4, cg, cg, C4, C1, and 0; bottom from center: H, C,, C3,C,, C,, C3, C,, and H) computed for the biphase. Relative densities are given in the
~plot.~
~
~
~
~
~
~
~
~
of the hydrogens in comparison to the oxygens. The density profiles for the 0, Ho, and all carbon atoms of hexanol are shown in Figure 6. The hydroxyl groups are found to be confined to bands about 6-8 A thick. There is no significant difference in the penetration of the hydrogens or oxygens into the water layers. Furthermore, for the bilayer and biphase, diminished intensity for the carbon atoms w u r s in the middle of the hexanol layers. Such reduction in the density profiles has been commonly observed for bilayers by experimental measurements such as X-ray diffraction.” Previous theoretical studies also found similar b e h a v i ~ r . ’ The ~ ~ -confined ~ ~ ~ distributions of the hydroxyl groups (31) Caspar, D. L. D.; Kirschner, D. A. Nature (London) New Biol. 1971, 231, 46. Levine, Y.K.; Bailey, A. I.; Wilkins, M. H. F. Nature (London) 1968, 220, 511.
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 5819
Theoretical Examination of Hexanol-Water Interfaces OO RADIAL DISTRIBUTION FUNCTIONS 3
A
-7
3
---- MONOLRYER BILAYER ------ BIPHASE
HO RADIAL DISTRIBUTION FUNCTIONS
2 W
1
0 1
0 1
3
2
S
4
6
I
0
R
Figure 10. Hexanol oxygen-water oxygen rdfs computed for the monolayer, bilayer, and biphasic interfaces. Distances are in angstroms throughout. OH
5
4
7
6
8
R
Figure 12. Hexanol hydrogen-water oxygen rdfs computed for the interfacial systems. 3
HH
2l
1
RRDIRL DISTRIBUTION FUNCTIONS
3
3
2
RADIAL DISTRIBUTION FUNCTIONS
A
'
_ - - - MONOLAYER ------ BILAYER BIPHASE I
I
1
3
2
5
4
1
6
I
I
8
R
1
2'
Figure 13. Hexanol hydrogen-water hydrogen rdfs computed for the interfacial systems. 3
4
5
6
I
B
R
Figure 11. Hexanol oxygen-water hydrogen rdfs computed for the interfacial systems. reflect the importance of hydrogen-bonding interactions between the head groups of hexanol and the water molecules and the enforced periodicity in the interfacial systems. The greater densities for the hexanol oxygens and hydrogens in the interior region of the biphase results from the presence of the two layers of hydroxyl groups in this region. The relative densities of the Ho and 0 atoms of hexanol in the monolayer are somewhat broader (Figure 6), and the distribution extends farther into the aqueous phase. This reflects greater disorder in the interfacial region for the monolayer. Detailed insight into water penetration into the organic phase can be revealed by further examination of the density profiles. 0, and C atoms of hexanol First, the density profiles for the Ho, in Figure 6 show that the hydroxyl groups are closest to the water phase in all three systems, while the C atoms do not begin to appear for another angstrom. It should also be noted that the distributions of the Ho and 0 atoms near the water interface are essentially the same. The hydroxyl groups are undoubtedly participating in both accepting and donating hydrogen bonds, as discussed further below. Second, from Figures 4-6, it is readily recognized that the overlap between the density profiles of the carbon atoms and the water molecules is small, since there is little water more than 11 A from the centers of the systems. In fact, as indicated in Figures 7-9, the overlapping region is predominantly confined to the a carbon of 1-hexanol. This electrostatically reasonable result is consistent with the picture that has emerged from most recent experimental studies, particularly diffraction work, on amphiphilic systems.11s4 Therefore, this issue, which is fundamentally important to modeling and understanding the structures of micelles and bilayers,11.12*32-34 appears to be well resolved. Proposed deviations from the picture should be carefully analyzed for alternative explanations. In the theoretical area, improper representation of the intermolecular forces could lead to excessive water penetration in simulation work. (32) (a) Dill, K. A.; Flory, P. J. Proc. Nazl. Acad. Sci. U.S.A. 1980, 77, 3115. Dill, K. A.; Flory, P. J. Proc. Nail. Acad. Sci. U.S.A. 1981, 78, 676. (b) Gruen, D. W. R. J . Phys. Chem. 1985, 89, 146. Ibid. 1985, 89, 153. (33) Menger, F. M. Acc. Chem. Res. 1979,12, 111, and references therein. (34) Halle, B.;Carlstrom, G. J . Phys. Chem. 1981, 85, 2142.
-MONOLAYER __--
u
------BILAYER BIPHASE
l
A
I' 2
3
4
,
1
I
5
6
1
I
I
8
R
Figure 14. Hexanol C,-water oxygen rdfs computed for the interfacial systems.
BIPHASE
1
B
9
_ _ - - MONOLRYER BILAYER
2i 1
0 2
3
v
4
5
6
I
R
Figure 15. Hexanol C2-water oxygen rdfs computed for the interfacial systems. Radial Distribution Functionr. The structure in the interfacial regions can be further characterized through radial distribution functions (rdfs), gxy(r),which give the probability of finding an atom of typey a t a distance r from an atom of type x . The rdfs for the H and 0 atoms of water relative to all of the hexanol a t o m were determined during the simulations. However, the focus will be on the rdfs of the C1-O-H units of the hexanol molecules. The results are shown in Figures 10-15. The remaining rdfs are relatively less structured and are not reported here. In each case the first atom in an xy rdf refers to an atom of hexanol, while the second atom is either the oxygen or a hydrogen atom of water. Note that for the present purposes the normalization of the rdfs involved dividing the total number of y atoms in a volume element by the bulk density of hexanol (Nh/v: gxy(r) = (N,,(r,r+ dr))/[47r? dr (Nh/v)]. In Figures 10-15, the actual total volumes were used for the bilayer and biphase systems, while for the monolayer, the limits in the z direction were ca. f21.5 A. Thus,
Gao and Jorgensen
5820 The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
the amplitudes for the rdfs in the biphasic system are the smallest due to the larger density of hexanol. The 00, HO, and O H rdfs are given in Figures 10-12. The hydrogen bonding between the hexanol and water molecules is clearly reflected by the sharp first peaks in these plots. The locations of the first and second peaks in these distributions are nearly invariant in the monolayer, bilayer, and biphase at 2.77 and 4.6 8, for the 00 rdfs, 1.79 and 3.26 8, for OH, and 1.86 and 3.33 for HO. The uncertainties for the principal peaks at separations less than ca. 4 8, are i 0 . 0 4 8,. Integration of the first peaks in the 00 rdfs to the minima at 3.33 8, yields 1.93 water molecules for the monolayer, 1.74 for the bilayer, and 0.82 for the biphase. These may be taken as estimates of the average number of water-alcohol hydrogen bonds.35 However, in the case of the biphase, only half of the 80 hexanol molecules are in contact with the aqueous phase. Thus, there are on average 1.64 water molecules hydrogen bonded to each hexanol molecule at the hexanol-water interface. More diffuse second hydration shells around the oxygens of the hexanol molecules are also notable, centered near 4.6 8, in the monolayer, bilayer, and biphase systems. In the previous simulation of a single methanol molecule in water,35 2.9 water neighbors were found in the first peak of the 00 rdf. Of course, the reduced number in the present cases may be compensated by hexanol-hexanol hydrogen bonding (vide infra). Returning to the OH rdfs in Figure 11, hydrogen bonding is responsible for the sharp first peaks found from 1.5 to 2.5 8,. Their integrals are 1.29 for the monolayer, 0.85 for the bilayer, and 0.92 (2 X 0.46) for the biphase in the regions of the hexanol-water interfaces. These results suggest that of the 1.6-1.9 hexanol-water hydrogen bonds, the water is acting as the hydrogen bond donor 67,49, and 56% of the time for the monolayer, bilayer, and biphase systems, respectively. Moreover, the larger total number of hydrogen bonds for the monolayer comes from this enhanced water donation. Second peaks are also apparent in Figure 11 and contain contributions from both the hydrogens of the donating water molecules and the hydrogens of the water monomer acting as acceptors. In Figure 12, integration of the first peaks of the H O rdfs shows that the hexanol hydrogen atom has ca. 0.7 oxygen of water nearby in all three cases. In this situation, the hexanol molecule is the hydrogen-bond donor. In summary, each hexanol molecule in the monolayer on average participates in ca. 2 hydrogen bonds with water molecules, whereas there are only ca. 1.5-1.7 hydrogen bonds between the hexanol and water molecules in the bilayer and biphase. The HH rdfs are shown in Figure 13. In this case, the first peaks contain the hydrogens of both hydrogen-bond-donating and -accepting water molecules. The locations for the first peaks are all at 2.35-2.42 A, and the integrals to 3.1 8, are 3.7 for the monolayer, 3.0 for the bilayer, and 3.1 for the biphase. These figures are a little higher than expected from the above analyses; however, the bands are broader than in the OH and HO rdfs and probably contain contributions from some slightly more remote water molecules. Finally, the rdfs for the C1 and C2 units of the 1-hexanol molecules are reported in Figures 14 and 15. The broad first peaks of the C,O rdfs in Figure 14 are all centered at 3.6 A for the three systems. Integration of the bands to 4.0 8, yields 2.3-2.5 water molecules, which are presumably mostly the ones in hydrogen bonds with the head groups. There is little structure in Figure 15 for the C 2 0distributions. The small peaks that appear at ca. 5 8,may also be assigned to the water molecules around the head groups. The reduced amplitudes at short range in these rdfs are consistent with the limited water penetration into the hydrocarbon regions. Hydrogen-Bonding Analyses
Hydrogen Bonding across the Interfaces. The hydrogen bonding in the interfacial regions was further analyzed by using ( 3 5 ) Jorgensen, W. L.; Madura, J. D. J . Am. Chem. SOC.1983,105, 1407.
TABLE IV. Results of Hydrogen-Bonding Analyses for the Hexanol-Water Interfaces at 25 OC‘
monolayer no. of hex/H20 no. of hex/hex
AE(hex/ hex)e AEu( hex/ hex) AE,(hex/ hex)
bilayer
1.61
1.42
0.84
1.02
-5.55 -1.92 -3.63
-5.62 -1.53 -4.09
biphase 1.35 0.97 2.08b -5.89 -5.70d -1.73 -0.77d -4.16 -4.92d
“Energies are given in kcal/mol. bNumber of hydrogen bonds for the hexanol molecules in the interior hexanol interface of the biphasic system. e A E is the interaction energy between hydrogen-bonded hexanol pairs. It can be decomposed to Lennard-Jones (LJ) and Coulombic (C) interactions. “Interaction energies between the hexanol molecules in the interior interface of the biphasic system. the configurations saved during the Monte Carlo simulations. The hydrogen-bonding profiles for the water molecules were also computed for the monolayer, bilayer, and biphasic systems. Hydrogen bonds can be defined by an energetic criterion based on the positions of the minima in the energy pair distributions, though geometrical definitions are also available, for example, based on the positions of minima in rdfs.25,36,37For the interfacial systems, a combination of both definitions seems most appropriate due to the mix of intermolecular interactions. Specifically, the energetic criteria that have been used here are -3.25 kcal/mol for the hexanol pairs, -2.25 kcal/mol for the water dimers, and -2.75 kcal/mol for the hexanol-water interactions. These values are consistent with the choices in earlier st~dies.~’ Geometrically, a distance of 2.6 8,or less between the hydrogen and oxygen atoms of hexanol is required for the hexanol-hexanol pairs, while for the water-water and hexanol-water hydrogen bonds a distance of 2.5 8,or less between the hydrogen and oxygen atoms is necessary (cf. Figures 11 and 12). The results for the average number of hydrogen bonds with hexanol and the average interaction energies are listed in Table IV. The total number of hydrogen bonds for a 1-hexanol molecule in the aqueous interfacial regions is nearly constant in all systems. Specifically, there is a total of 2.45 hydrogen bonds including both the hexanol-hexanol and hexanol-water pairs for the monolayer, 2.44 for the bilayer, and 2.32 for the biphase. However, hydrogen bonding between the hexanol and water molecules is more extensive in the monolayer than in the other systems. In particular, there are on average 1.61 water molecules hydrogen bonded to each hexanol monomer in the monolayer, whereas only 1.42 and 1.35 are found in the bilayer and biphase. Simultaneously, the hydrogen bonding between the hexanol pairs in the monolayer is less, with an average of only 0.84 hydrogen bond, whereas there is 1.O interhexanol hydrogen bond in the bilayer and biphase. For the biphasic system, there are also ca. 2.1 hexanol-hexanol hydrogen bonds in the interior interface. This figure is a little higher than the average number of hydrogen bonds (1 -8-1.9) observed in the previous simulations of liquid alcohols:’ but the results are very sensitive to the choice of hydrogen-bonding criteria. Nevertheless, long chains of hydrogen bonds are indicated for all of the alcohol liquids. It should also be noted that the hydrogenbonding analyses yield a somewhat smaller number of hydrogen bonds between the hexanol and water molecules than obtained from the rdfs above. The choice of cutoffs again provides some uncertainty, and not all of the neighbors in the first peaks of the rdfs are necessarily hydrogen-bonded. The average hydrogen-bond energies for the hexanol pairs are also listed in Table IV. The slightly stronger binding in the bilayer and biphasic systems is consistent with somewhat greater disorder at the interface in the monolayer, as noted in the discussion of Figure 6. Another interesting observation is that the Coulombic interactions, AEc, between the hexanol molecules in the inner region of the biphase system are more attractive than in the other ( 3 6 ) Chandrasekhar, J.; Spellmeyer, D. SOC.1984, 106, 903.
C.; Jorgensen, W. L. J . Am. Chem.
(37) Jorgensen, W. L.; Swenson, C. J. J . Am. Chem. SOC.1985,107, 569.
Theoretical Examination of Hexanol-Water Interfaces HYDROGEN BOND PROFILES
r)
TABLE VI: Calculated Internal Energies for the Hexanol Molecules (kcal/mol)
3
H8
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 5821
monolayer
bilayer
biphase
gas
pure liquid
2.31
2.40
2.45
2.15
2.70
Ei,,
DIHEDRAL ANGLE DISTRIBUTILlNS
k 2
b
8
1
HEXRNBL/WATER
2.
0 -21
-15
-3
-9
3
9
-MONOLAYER BILAYER BIPHFISE
---
----
i
15
RIA1
Figure 16. Hydrogen bonding profiles computed for the monolayer,
bilayer, and biphase. Units for the ordinate are number of hydrogen bonds per molecule.
F iJ
1.
TABLE V Calculated Trans and Gauche Percentages for Each Dihedral Angle
@
1 2 3
conformer t 8 t g t
g
4
t
g 5
t
B
gas'
liq'
monolayer
bilayer
biphaseb
54 46 51 49 69 31 65 35 68 32
63 37 43 57 68 32 75 25 73 21
46 54 70 30 91
52 48 65 35 83 17 85 15 74 26
46 54 62 38 87 13 81 19 79 21
9 81 19 82 18
0
60
120
180 240 DIHEDRAL ANGLE
300
31
DIHEDRAL ANGLE DISTRIBUTIONS
MONOLAYER BILAYER BIPHASE
"Obtained from a direct Boltzmann distribution for an isolated 1hexanol molecule and from a Monte Carlo simulation of liquid l-hexanol at 25 OC and 1 atm. bIncludes all hexanol molecules. interfaces. This is more than offset by the increase in the Lennard-Jones energy due to the tighter packing of the hexanol in the interior region. The weaker Coulombic attraction between the hexanol molecules in the monolayer also reflects greater mixing with the water in this case. Hydrogen Bonding in the Aqueous Phase. Hydrogen-bonding profiles for the water molecules in the monolayer, bilayer, and biphasic systems are shown in Figure 16 along with the profiles for the hexanol-water hydrogen bonds. The plots show the average number of hydrogen bonds for a slab of thickness 1 A at a distance z from the center of the water cells, nHB(Z). For the water-water interactions, nHB(Z) rises smoothly to a steady value of 3.5 in the middle of the aqueous region. This figure is exactly the same as the value observed in the pure liquid.25a Hydrogen bonding between the hexanol and water molecules occurs over a ca. 7-A region that terminates sharply about 14 A from the center of the aqueous region. Since the original water cube had 20-A edges, the hexanol and water penetrate each other about 4 A. These figures are averaged over the entire length of the simulation and the entire periodic cells and, consequently, may suggest greater mixing than occurs in individual (instantaneous) configurations owing to roughness of the interfaces rather than true interpenetra tion. Dihedral Angle Distributions and Chain Conformation. The computed conformational populations for the dihedral angles of the hexanol molecules and the intramolecular rotational energies of the monolayer, bilayer, and biphasic systems are compared with the gas-phase and pure liquid values in Table V and VI. The uncertainties ( f l a ) in these results are ca.f l % for the populations and f0.02 kcal/mol for the energies. From Table V it is clear that there are some condensed-phase effects on the conformational distributions. Relative to the gas phase, there is modest change in the populations for rotation about the O-C, bond (3,) in the interfacial systems. There is a 9% increase in the trans population for 3,in the pure liquid, which is coupled with an 8% increase
DIHEDRAL ANGLE
Figure 17. Computed population distributionsfor the HOCIC2(a,, top) and the OC1C2CJ(a2,bottom) dihedral angles of the hexanol molecules in the monolayer, bilayer, and biphase. Units for the ordinate are mole
percent per degree. in the gauche .population for 32. This is presumably reflecting some conformationally dependent preferences for the hydrogenbonding or Lennard-Jones interactions. However, the outstanding observation for the interfacial systems is that there is significant straightening of the alkyl chains beyond 9,. The increase in the trans populations averages 15%. This is clearly a packing effect that reflects the more stringent requirements of the more ordered interfacial environments. Qualitatively similar shifts have been obtained in earlier experimental and theoretical studies.*lc*lsaIn particular, an average increase of 17% for the trans population was found in the MD study of the decane bilayer model.16a Examples of the full dihedral angle distributions, S ( 3 ) , are shown just for 3,and a2in Figure 17. For all three systems, the shape of these distributions are very similar, with predominant trans peaks. The distributions for 3,are uniquely broad, reflecting the comparatively unhindered rotation about this bond. From such plots and Table V, it is also apparent that the 1-hexanol molecules in the monolayer have a greater tendency for trans conformations for three of the dihedral angles. Overall, however, the differences are small. It may also be noted that there is relatively little asymmetry for the gauche+ and gauche- populations in Figure 17. With small numbers of molecules, it is difficult to totally remove the asymmetry even though the energy is well equilibrated.Ib
5822 The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
Gao and Jorgensen
HO
ac CO oc HO
MONOLRYER I
Figure 18. Stereoplot of a configuration from the Monte Carlo simulation of the hexanol-water monolayer. HO
ac CC oc HO
Figure 19. Stereoplot of a configuration from the Monte Carlo simulation of the hexanol-water bilayer.
The average rotational energies for the 1-hexanol molecules are listed in Table VI. The interfacial systems have lower intramolecular rotational energies than in the gas phase and pure liquid. This is, of course, consistent with the greater average trans populations in the interfacial systems. Plots of Configuration. The structural notions discussed above and others are evident in stereoplots of the configurations from the Monte Carlo simulations of the monolayer and bilayer, as shown in Figure 18 and 19. These configurations are the last ones from the simulations and are as arbitrary as any of the 5 X 1O6 configurations. The preiodic boundary conditions should be kept in mind in viewing the stereoplots. Therefore, the molecules near one face interact with monomers near the opposite face, except periodicity was not applied along the z coordinate in the monolayer. Hydrogen bonding is ubiquitous, with the hexanol and water molecules participating in multiple hydrogen bonds in the interfacial regions. Numerous winding chains of hydrogen bonds are apparent, extending from the interfaces into the aqueous region. As indicated in Figure 6, a region of reduced density is apparent between the hexanol layers in the bilayer (Figure 19). Furthermore, as illustrated in Figures 18 and 19 the extent of
Figure 20. CPK plot of a configuration of the hexanol molecules on the interfacial surface of the bilayer. The van der Waals radii were scaled by a factor of ca. 0.7.
water penetration beyond the hexanol head groups is negligible. The boundary between the hexanol and water is very clear in each case, though there is significant roughness to the surface of the head groups. Figure 20 shows the distribution of the 1-hexanol molecules in a configuration of the bilayer over a water surface. Most of the head groups are seen to participate in one hydrogen bond with another head group. Another obvious feature in the plots is the high incidence of trans configurations in the carbon chains, while there are more gauche kinks for the H-O-CI-C2 dihedral angle (cf. Figure 20). Conclusion
The present theoretical study has provided a view of the energetics, structure, and molecular interactions in interfacial regions of model monolayer, bilayer, and biphasic systems. The computations predict minimal water penetration into the hydrophobic regions from the analyses of density profiles and radial distribution functions. It is found that ca. 2 water molecules are involved in hydrogen bonding with each hexanol molecule in the monolayer, while ca. 1.6 are observed in the bilayer and biphase. The number of hydrogen bonds between the 1-hexanol pairs is ca. 1 in the aqueous interfacial region of the bilayer and biphasic systems and 0.8 in the monolayer. A significant increase in the population of trans conformations about bonds in the hexanol molecules is also observed in the interfacial systems. The population shift helps facilitate the formation of hydrogen bonds in the interfacial regions and helps maintain the dense packing of the amphiphiles. Many of the structural findings are consistent with prior experimental and theoretical results that support the picture of relatively narrow interfaces with minimal water penetration beyond the head-group region in amphiphilic aggregates. Acknowledgment. Gratitude is expressed to the National Institutes of Health for support of this research. Registry No. H20,7732-18-5; 1-hexanol, 111-27-3.
