J . Phys. Chem. 1993, 97, 2664-2670
2664
Structure and Energetics of Model Amphiphilic Molecules at the Water Liquid-Vapor Interface. A Molecular Dynamics Study Andrew Pohorille' Department of Pharmaceutical Chemistry, University of California, San Francisco, California 941 43, and NASA-Ames Research Center, Moffett Field, California 94035
Ilan Benjamin' Department of Chemistry, University of California, Santa Crur. California 95064 Received: July 29, 1992
A molecular dynamics study of adsorption of p-n-pentylphenol a t infinite dilution a t the water liquid-vapor interface is reported. The calculated free energy of adsorption is -8.8 f 0.7 kcal/mol, in good agreement with the experimental value of -7.3 kcal/mol. The transition between the interfacial region and the bulk solution is sharp and well-defined by energetic, conformational, and orientational criteria. A t the water surface, the phenol head group is mostly immersed in aqueous solvent. The most frequent orientation of the hydrocarbon tail is parallel to the interface, due to dispersion interactions with the water surface. This arrangement of the phenol ring and the alkyl chain requires that the chain exhibits a kink. As the polar head group is being moved into the solvent, the chain length increases and the tail becomes increasingly aligned toward the surface normal, such that the nonpolar part of the molecule exposed to water is minimized. The same effect was achieved when phenol was replaced by a more polar head group, phenolate. This result underscores the difference between hydrophobic hydration a t the surface and in the bulk solvent, when nonpolar molecular fragments adopt compact conformations.
1. Introduction
In recent years significant theoretical effort has been devoted to molecularly detailed studies of phenomena a t the water liquidvapor interface. This effort has been directed along two lines. On the one hand, the effect of rapid changes in the density and polarity oftheenvironment in theinterfacial region on the behavior of solutes at infinite dilution has been explored. The molecular structure of the energetics and dynamics of adsorption of simple, rigid surface active molecules,* and simple isomerization reactions9 at the water liquid-vapor interface have been investigated. On the other hand, a number of recent molecular dynamics (MD) studies have focused on the structure of dense phases of surfactant molecules, such as monolayerslOslI and bilayzrs,l*-'3at water surfaces. In this work we present the results of molecular dynamics simulations on p-n-pentylphenol (pentylPh), whose chemical structure is shown in Figure 1, at infinite dilution at the water liquid-vapor interface. This study is a continuation of our effort to understand how the competition between the hydrophobicity of the hydrocarbon region and the hydrophilicity of the polar part of a sarfactant molecule determines energetics, orientation, and conformation of this molecule at the water surface. The choice of pentylPh as a model surfactant was motivated in part by the recent second harmonic generation experiments on a homologous series of p-n-alkylphenols and their respective ions a t the water-air interface.ld-Ih From these experiments the free energies of adsorption for the whole series were obtained and, for the neiitral molecules, were found to change linearly with the number of carbon atoms in the alkyl chain. Since the same quantity can also be obtained from the MD simulations, it can serve as a test of accuracy of our calculations. In the previous, closely related, work on the molecular dynamics of pheaol at the liquid-vapor interface of water,g we showed that the calculated and experimental14 free energies of adsorption and tbl: average orientations of phenol at the interface are in very g o d agreement. In addition, a wealth of molecular-level data, not zvailiable experimentally, was obtained from the calculations. 0022-3654/93/2097-2664$04.00/0
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Figure 1. Schematic representation of p-n-pentylphenol. C-C-C-C torsional angles in the alkyl chain are abbreviated C$,, ..., $4.
It was shown that in a well-defined interfacial region the behavior of phenol was distinctly different from that in the bulk water. Its most probable orientation at the interface was such that the aromatic ring was perpendicular to thesurface. In thisorientation the polar OH substituent points toward the liquid, and part of the nonpolar ring remains removed from water. This result 0 1993 American Chemical Society
Adsorption at the Water Liquid-Vapor Interface demonstrates how hydrophobic and hydrophilic portions of the solute influence molecular orientations of the adsorbate at the water surface. One objective of this work is to extend our detailed understanding of adsorbates at water surfaces to model surfactants which contain flexible hydrocarbon chains. In particular, we inquire about the effect of hydrophobic hydration on the conformation and orientation of nonpolar surfactant tails located close to the water surface. In contrast to the behavior of nonpolar species in a bulk aqueous medium, this problem has not been studied so far at the molecular level. In view of our understanding of the hydrophobic effect, it seems quite possible that the effective surfactant-surface interactions display a molecular structure determined by the size of the adsorbate and by the polarity of its head group. Another focus of this paper is to help establish a connection between calculations on surfactants at infinite dilution and in condensed phases. One relevant characteristic of monolayers which can be obtained from molecular dynamics of a single adsorbate molecule at the water liquid-vapor interface is the orientation of the polar head group. Recent second harmonic generation experiments on phenol14 and other amphiphilic molecules17showed that this orientation remains unchanged over a wide range of surface density (a result which is consistent with surface potential measurements). Another characteristic of a surfactant molecule, which is of significant interest, is the location of the head group with respect to the water surface. Theories of the film pressure of surfactants indicate that this quantity is very sensitive to the extent of head group penetration into an aqueous medium.I8 Furthermore, a better understanding of the balance between the hydrophilic and hydrophobic behavior of a surfactant molecule at the water surface may be very helpful in interpreting surface fluctuations of amphiphilic aggregates.19 To address the issues outlined above, we performed three M D calculations. The first calculation was designed to study the energetics and molecular structureof pentylPh at the water liquidvapor interface and during its transfer to the bulk aqueous medium. In the second calculation pentylPh was placed in an enlarged box of bulk aqueous solvent. The purpose of this calculation was to test if the properties considered characteristic of bulk behavior in the previous calculation were not influenced by the presence of water surfaces in the simulation box. In the third calculation p-n-pentylphenolate (pentylPh-) located at the water surface was studied. In this case no attempt was made to calculate the free energy of adsorption. Since the phenolate ring is markedly more hydrophilic than phenol, pentylPh- is only marginally surface a c t i ~ e . The ~ ~ comparison .~~ with pentylPh allows us to examine directly how the behavior of a surfactant molecule at the interface is modified by changing the hydrophilicity of the head group. 11. Methods
The simulations of pentylPh and pentylPh- at or near the water liquid-vapor interface were performed in a box whose dimensions were 24.83 X 24.83 X 75.00 A. The box contained 500 water molecules and 1 solute molecule. The water lamella, prepared as described before,'.8 was perpendicular to the Z-coordinate in the simulation box. Since both solutes considered here are surface active, no constraints were needed to keep them at the interface. In each case, a MD trajectory 1 ns long was obtained after equilibrating for 0.1 ns. The use of a single phenolate ion (without a counterion) corresponds to the experimental situation of a dilute solution in which ion pairing is very rare. In addition, a small counterion is strongly negatively adsorbed at the surface and this further decreases the likelihood of finding such a counterion in thevicinity of pentylPh-. In unconstrained calculations on p-pentylPh only positions close to the water surface were adequately sampled. In order to describe
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2665
TABLE I: Lennard-Jones Parameters and Atomic Charges typeh C
ca ca ca ct oh ho hc hc hc
A'
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789 950.687 50 789 950.687 50 789 950.687 50 789 950.687 50 284 303.500 00 250 183.671 88 8 1.920 33 7 288.000 98 7 288.000 98 7 288.000 98
615.772 249 22 615.772 949 22 615.772 949 22 615.772 949 22 261.214 141 85 387.440 612 79 2.560005 19 17.073 957 44 17.073 957 44 17.073 957 44
0.462 -0.264 -0.002 -0.030 -0.098 -0.528 0.334 0.102 0.064 0.030
Numberingsystemfrom Figure 1. Atom typesasdefined in AMBER (ref 23). ' Parameters for Lennard-Jones potentials A,,/r,112- B,l/r,: between atoms i and j are defined as A,, = (A,,AI,)lI2,B,, = (B,B,,)'12; the same combination rules apply to solute-water interactions; A,, is in kcal/(mol AI2) and B,, is in kcal/(mol Ab). Partial atomic charges in e. e All other carbon atoms in the alkyl chain have the same LennardJones parameters as C7 and all hydrogen atoms the same parameters as H(C7); charges on all these atoms are zero.
the energetics and structure of the solute in a broad interfacial region, a series of calculations had to be performed in which the para carbon atom of the phenol ring was constrained in windows along the Z-coordinate by a biasing potential.20-21The positions of the windows were chosen such that two consecutive windows overlapped by at least 0.5 A. Six windows were needed to transfer pentylphfrom thewater surface tothe bulkliquid. In eachwindow the system was equilibrated for 0.1 ns and then an MD trajectory of 0.5ns was obtained. In each window, the probability density P ( Z ) of finding the para carbon atom at a position Zwasobtained and used to calculate the free energy profile A(Z) from a formula: A ( Z ) = -kT In P ( Z )
where Tis the temperature of the system and k is the Boltzmann constant. To obtain the free energy profile in the full range of 2 , A(Z)'s from consecutive windows were connected in overlapping regions. The details about the biasing potentials, constructing full A ( Z ) and calculating statistical errors, were given in our previous paper.8 The MD calculation of p-pentylPh in the bulk aqueous solvent was performed in a cubic box whose edges were 31.043 A long. The box contained 1 solute molecule and 998 water molecules. This corresponds to the density of water in the bulk, away from the solute, of approximately 1 g/cm2. The length of the MD trajectory after equilibration was 1 ns. In all calculations, periodic boundary conditions were applied in the three directions. MD trajectories were integrated using a time step of 2 fs. Temperature was equal to 300 K. Waterwater intermolecular interactions were described using theTIP4P potential model,2* and solute intramolecular interactions were calculated by the all-atom AMBER potential functions.23 Solutesolvent potentials were obtained from standard combination rules. The parameters for van der Waals potential functions and the partial charges used are given in Table I. The bond stretching, angle bending, and torsional parameters are listed in ref 23. Water-water interactions were truncated smoothly at oxygenoxygen separations between 7.5 and 8 A.24 No correction for the truncation of the long-range interactions was included. These interactions are expected to be important for calculating such macroscopic properties as surface tension and in the treatment of ions near surfaces. However, they are probably less significant in studies of the structure and energetics of hydrophobic species at an interface. All calculations were performed using the COSMOS program of Owenson and P ~ h o r i l l e . ~ ~ 111. Results and Discussion
A. Free Energy of AdsorptionofPentylPh at the Water Surface. In Figure 2 we present the probability density function of finding
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Pohorille and Benjamin
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993
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Figure 2. Probability density of finding the Cq carbon atom of pentylPh (solid line) and of pentylPh- (dashed line) as a function of theZ-coordinate measured from thecenterofthewater lamella. TheGibbsdividingsurface is located at Z = 11.8 A.
the para carbon atoms C4 of the phenol ring in pentylPh and pentylPh- as a function of their Z-coordinates measured from the center of mass of the water lamella. For pentylPh, the maximum of this function is located at Z = 13.8 A, about 2 A above the Gibbs dividing surface, indicating that the solute is surface active. Compared to phenol,s this maximum is shifted 1 A toward the vapor. In contrast, the phenolate ring of pentylPh-, which is markedly more hydrophilic than a neutral phenol ring, penetrates the water surface such that the most probable location of C4 is about 2 A below the Gibbs surface. The free energy profile of adsorption of pentylPh at the water liquid-vapor interface is shown in Figure 3. The interface, defined as a region in which the free energy of adsorption undergoes changes, extends approximately 9 A from the Gibbs surface into the liquid. This is substantially more than in the case of phenol, where the interfacial region was about 4 A wide. The calculated free energy of adsorption is -8.8 f 0.7 kcal/mol, in satisfactory agreement with theexperimental valueof-7.3 kcal/mol. A small activation barrier for the transition from the surface to the bulk was found around Z = 3 A. A similar barrier was also obtained for phenol8 and was attributed, a t least in part, to the increased rotational flexibility of phenol in bulk solvent compared to the one at the interface. B. Orientation of PentylPh and PentylPh- at the Interface. The orientation of pentylPh with respect to the water surface can be conveniently described by the probability distributions of two angles, 8, and &. 8, is formed between the C4-CI vector along the symmetry axis of the phenol ring and the normal to the interface. 8, is the angle between the end-to-end vector of the alkyl chain pointing from C4 to C I I and the normal. In this convention, both angles are zero when the C-0 bond and the alkyl chain point toward bulk water. When pentylPh is located near the surface, the average angle Oris48 f 4°,veryclose to thevalue found for phen01.8.'~However, the probability distribution function of e,, P(O,), shown in Figure 4, is somewhat different from the distribution obtained for phenol. It exhibits a maximum at about 4 5 O , while P(0,) for phenol peaks near 0, = 0 ' . In contrast to phenol, P(0,) for pentylPh changes in the interfacial region. As the phenol ring of pentylPh is moved deeper into the liquid, P(0,) becomes sharper and its maximum
Figure 3. Free energy profile of adsorption of pentylPh at the water liquid-vapor interface as a function of the Z-coordinate measured from the center of the water lamella. 0.3
0.2
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Figure 4. Probability distribution of the angle 8, formed between the C4-Cl vector and the normal to the interface. Solid line is for pentylPh unconstrained at the interface. Dashed line is for pentylPh located such that Cq is approximately 7 A from the Gibbs dividing surface into the liquid. Chained line is for pentylPh-. 8, = 0 when C1-0 bond points toward the liquid.
shifts toward 0, = Oo. This distribution becomes very similar to P(0,) obtained for pentylPh-, which in unconstrained calculations is immersed in water markedly deeper than pentylPh. The relation between the orientation of the chain and the position of the phenol ring with respect to the water surface is also very clear. The probability distribution function of e,, P(&), is shown in Figure 5 . In unconstrained calculations, when the ring is located at the interface, P(&) is quite broad and peaks near 135O. As expected, low values of e,, which would yield extensive hydration of the hydrophobic alkyl chain, are encountered very infrequently. The fraction of chains with the end-
Adsorption at the Water Liquid-Vapor Interface 0.4
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The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2667
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ec Figure 5. Probability distribution of the angle 0, formed between the C4-CI I vector and the normal to the interface. Solid line is for pentylPh unconstrained at the interface. Dashed line is for pentylPh located such that C4 is approximately 7 A from the Gibbs dividing surface into the liquid. Chained line is for pentylPh-. OC = 0 when the alkyl chain points toward the liquid.
to-end vectors in the range 0 f M,, fc(0),which is related to P(0,) by the formula
is the largest for the orientation nearly parallel to the interface. In this orientation, the chain can interact with the water surface via dispersion forces without being appreciably hydrated. Such an orientation requires that the ring is somewhat tilted with respect to the surface normal, explaining the differences between P(0,) for pentylPh and phenol a t the surface, which were discussed above. P(0,) decreased again when the chain points toward the vapor phase, the preferred orientation in dense phases of monolayers of surfactants. Orientational preferences described here are not common to all surfactants with the same alkyl chains, but depend sensitively on the hydrophilicity of the head group. For pentylPh-, whose head group is more hydrophilic than the neutral phenol ring and, therefore, remains buried deeper in water, P(0,) is narrower and shifted toward higher values of 0,. Similar changes are observed when the phenol ring of pentylPh is progressively moved into the liquid. This movement is accompanied by a change in the chain orientation from parallel to perpendicular to the interface. Simultaneously, the range of chain movements decreases markedly. Similar losses of orientational flexibility over the same interfacial region also occur for the phenol ring of pentylPh. Thus, the whole molecule becomes progressively more rigid. Only when Cqis about 9 A from the Gibbs surface does the molecule rapidly regain the rotational flexibility characteristic of a molecule in a bulk solvent. This region of transition from rigid to random orientation coincides with the range of Z where the free energy profile becomes flat. C. Conformation of the Alkyl Chain. The conformation of the alkyl chain of pentylPh is described by four torsional angles denoted +,, ..., 44 in Figure 1. The probability distribution functions for these four angles at the water surface and in a bulk aqueous solvent are shown in Figure 6. The distribution of angle @I exhibits maxima a t 90° and 270°, which correspond to the orientation of the c7-C~bond perpendicular to the phenol ring.
These two maxima do not describe different conformations but simply reflect mirror-image symmetry with respect to the plane of the ring. Since pentylPh adopts only one distinct conformation around 41,we will omit this angle in further discussion of conformational flexibility of the chain. The probability distributions for the remaining three torsional angles exhibit three maxima corresponding to the trans (t) and two gauche (gand g-) conformations. For the fullyextended, all-transchainin thegas phase, theaverage value of the chain end-to-end distance, de,is 6.5 A. Four partially folded conformations, ttg,tgt,gtt, and g t g , yield the average de in a narrow range between 5.4 and 5.8 A. Compact conformations containing at least two bonds in the gauche form, such as tgg,ggt,gtg, and g g g , correspond to de between 4.7 and 5.0 A. Among states which are even more tightly folded, only one conformation, gg-t, with the average de = 4.0 A, is allowed. The remaining conformations are forbidden for steric reasons. On the basis of the simple analysis of the available chain conformations, presented above, we expect that the probability distribution of de should exhibit well-defined peaks, each corresponding to a set of conformations with different degrees of compactness. In Figure 7 we show this probability distribution for pentylPh in the gas phase, in bulk water, at the water surface, and restricted near the interface such that C4is about 7 A away from the Gibbs dividing surface. As expected, the isolated molecule exists predominantly in the all-trans state, which corresponds to the minimum torsional energy. At the water surface, the conformational equilibrium markedly shifts toward the partially folded states. This shift points to the importance of hydrophilic hydration and dispersion interactions between the alkyl chain and the water surface. In the fully extended state, pentylPh cannot simultaneously hydrate the 0-H group of the phenol and retain strong dispersion interactions with the water surface. However, both of these interactions can be simultaneously optimized, a t theexpenseof some increase in the torsional energy, if the alkyl chain kinks. This kink develops mostly by a transition of 42 from the t to the g form. As can be seen in Figure 6, the trans population of this angle at the water surface decreases by more than a factor of 2, compared with the isolated molecule, while trans populations of other angles are not substantially affected. The probability distribution of de for pentylPh in the bulk aqueous solvent is similar to that at the water surface. In both cases the highest peak corresponds to the partially folded states rather than to the extended conformation, as observed for the isolated molecule. There is, however, one subtle but important difference between these two distributions. In the bulk water, the probability distribution exhibits a shoulder at low values of dewhich is absent in thedistribution a t the surface. This shoulder is associated with the increase in population of the compact states from 9% for pentylPh located a t the interface to 20% for the molecule fully immersed in water. This increase arises mainly from the shift from the t to g conformation of 44. The shift in conformational equilibrium of the alkyl chain upon its transfer from the gas phase to liquid water is a result anticipated by theories of the hydrophobic effect. It is usually expected that a flexible nonpolar molecule will tend to adopt in water conformations with reduced surface area exposed to the solvent.26 The microscopic basis for this effect is assumed to be a tendency to minimize the work needed to create a cavity that can accommodate a nonpolar solute. Probably the simplest relevant example of such behavior is the gauche/trans equilibrium in n-butane. Both analytical theoriesZ7.2*and computer simulations29 showed that the fraction of molecules in the more compact gauche conformation increases in the aqueous environment compared to the infinitely dilute gas phase. In the case of pentylPh, it should be noted, however, that the most probable conformations of the chain are not the most compact ones among those which are
2668
The Journal of Physical Chemistry, Vol. 97, No. 11, I993 0.25
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Figure 6. Probability distribution function for torsional angles $ 1 (a), $2 (b), $3 (c), and $4 (d) in the alkyl chain of pentylPh in the gas phase (chained line), in bulk water (dashed line), at the water (solid line), and restricted near the interface such that C4 is about 7 A away from the Gibbs dividing surface (dotted line).
sterically allowed. To account for this, two additional factors should be considered. First, the internal energy of the chain, which usually increases with the number of angles in the gform, also contributes importantly to the conformational preferences of the solute. Second, relations which cannect the work of cavity formation of a nonpolar chain only to its surface area exposed to water may be oversimplifications ignoring molecular structural details associated with the hydrophobic effect. An example of such a structure is the existence of solvent-separated minima in the potential of mean force acting between small hydrophobic solutes in ~ater.~'JO In view of these considerations, it may seem surprising at first sight that the average length of the alkyl chain near the surface progressively increases as the phenol ring is moved into the water. When Cq of pentylPh is located about 7 A below the water surface, the chain conformation more closely resembles the extended
structure of the isolated molecule than conformations adopted at the water surface or in the bulk solvent. The dominance of the extended chain conformation was also observed for pentylPh-, which in unconstrained calculations penetrates water significantly deeper than pentylPh. Only when C.,is moved into the solvent by more than 8 A does the chain collapse into folded or partially folded states similar to those found in a separate calculation on pentylPh in bulk water. The observed orientational and conformational changes in pentylPh near the water liquid-vapor interfacecan be conveniently discussed in terms of the tendency for nonpolar solution components to be sequestered away from an aqueous solution environment. When the phenol head group of pentylPh is located at the water surface, the alkyl chain is almost totally removed from water. Its conformational and orientational preferences are then determined by the balance between a tendency to
Adsorption at the Water Liquid-Vapor Interface
0'3
The Journal of Physical Chemistry, Vol. 97, No. 11 1993 2669 ~
vapor interface. For pentylPh, the free energy of adsorption at the interface was calculated and was found to be in satisfactory agreement with recent experimental results.'5.16 Similar, good agreement with experimental resultsI4was obtained in our previous study on adsorption of phenol at the water surface,* indicating that molecular dynamics is a reliable tool for studying simple amphiphilic molecules at the water liquid-vapor interface. The results of this study lend further support to conclusions reached in our previous work.8 In particular, the width of the interface, defined as a region in which the behavior of the solute is influenced by the presence of the water surface, is determined by the size of the solute. The transition between the interfacial region and the bulk solution is sharp and clearly defined by energetic, conformational, and orientational criteria. Furthermore, the calculations yield detailed information about the effects of different types of interactions on orientational and conformational preferences of the alkyl chain at the interfacial region. At the interface, the alkyl chain is most often oriented parallel to the surface. However, its orientational distribution is broad, reflecting a balance between chain-water dispersion energy, which favors the parallel, kinked arrangement, and the torsional energy of the chain, which reaches the minimum for the extended conformation perpendicular to the surface. As the phenol ring is moved into the liquid in the interfacial region, its symmetry axis and alkyl chains become increasingly aligned toward the surface normal. The same effect can be achieved by replacing phenol by another, more polar head group, e.g., phenolate. These results illuminate differences between the effects of hydrophobic hydration on flexible nonpolar portions of molecules located in the bulk aqueous solvent and at the water surface. In the bulk solvent, the hydrophobic effect drives these nonpolar molecular fragments toward compact states. In contrast, the same molecular fragments near the water surface tend to adopt extended conformations, such that at least some groups or atoms can be removed from the aqueous environment. The observed effect of the balance between the hydrophilicity of the head group and the hydrophobicity of the hydrocarbon chain on the orientation and conformation of a surfactant molecule at the water surface may form a framework for analyzing molecular-scale protrusions of chain molecules into the aqueous phase in monolayers, bilayers, and micelles. Similar ideas have been put forward by Pratt et al.I9 to account for the fact that chain molecules in micelles and bilayers are extended relative to their solution conformations. The fact that the surfactants are stretched may be due to the tendency of their head groups to get into the surrounding aqueous solution in order to be well solvated, while their tails prefer to remain removed from the water. These ideas are supported by results of molecular dynamics simulations of monolayers and bilayers of polar, uncharged surfactants.3'
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Figure 7. Probability distribution function of the chain end-to-end distance, d,, for pentylPh in the gas phase (chained line), in bulk water (dashed line), at the water surface (solid line), and restricted near the interface such that C d is about 7 A away from the Gibbs dividing surface (dotted line).
maximize dispersion interactions with the water surface, which yields kinked conformations oriented parallel to the interface, and a tendency to minimize internal torsional energy, which favors the extended state perpendicular to the surface. As the polar head group is being moved into the water solvent, the accompanying conformational and orientational changes in the solute are mainly governed by a simple principle-to minimize the part of the chain exposed to water. This can be accomplished in two ways, by adopting ring and chain orientations perpendicular to theinterfaceand by increasing chain length. Thus, the surfactant molecule moved from the surface into the aqueous solvent becomes progressively longer and more rigid and reaches the maximum length and rigidity when C4 is located about 7 A from the Gibbs surface. At this distance from the interface, all of the chain but the terminal methyl group remains fully immersed in water. Only when the solvent is moved further from the surface and the whole chain has to become completely hydrated do we observe the transition from the interfacial to bulklike behavior characterized by an increased compactness of the chain and the full rotational freedom of the molecule. From Figure 6 we can see that the probability distributions of the torsional angles in the alkyl chain are not symmetric with respect to 180°, as should be expected for a fully convergent simulation. At this point, it is appropriate to inquire how this lack of symmetry influences the values of d,. One possibility is that distinctly different conformations of the chain are inadequately sampled, yielding skewed distributions of d,. Alternatively, the observed asymmetry may simply reflect unequal sampling of mirror-image conformations. This would have no effect on d,. One way to test these two possibilities is to compare calculated d,, for 42 fixed at g (0-120') and g (240-360') conformations. The same can also be done for 43and &. These comparisons, performed for pentylPh in all four environments considered here, showed that the distributions of d, were quite similar for both gauche conformations. The average values of d, typically differed by 0.1 A and were never larger than 0.2 A. IV. Conclusions In this paper we have presented the results of a molecular dynamics study on pentylPh and pentylPh at the water liquid-
Acknowledgment. This work was supported by the NASA-Ames4.C. Berkeley Intergovernmental Personnel Exchange Agreement NCA-2 315 (A.P.) and by NSF (CHE9015106) (I.B.) and ACS-PRF (22862-G2) grants (I.B.). References and Notes ( I ) Wilson. M. A,; Pohorille. A.; Pratt, L. R. J . Phys. Chem. 1987. 91. 4873. (2) Wilaon. M. A.: Pohorille. A.; Pratt. L. R. J . Chem. fhys. 1988, 88. 3281. ( 3 ) Matsumoto. M.; Kataoka. Y . J. Chem. Phys. 1988, 88, 3233. (4) Motakabbir. K.; Berkowitz. M. Chem. Phys. Lett. 1991, 176, 61. ( 5 ) Townsend. R . M . ; Rice, S. A . J . Chem. Phys. 1991, 94, 2207. ( 6 ) Wilbon, M . A,; Pohorille. A . J . Chem. Phps. 1991. 95. 6005. ( 7 ) Benjamin. I. J . Chem. Phys. 1991. 95. 3698. (8) Pohorille. A,; Benjamin, I . J. Chem. Phys. 1991. 94. 5599. (9) Benjamin. I.:Pohorille, A . J . C'hem.Phys., submitted for publication. ( I O ) Cardini. (3.: Bareman, J . P.; Klein, M. L. Chem. Phy.c. Lett. 1988, 145. 493. Bareman. J. P.; Cardini. C.; Klein, M. L. Phys. Reu. Lett. 1988, 60,2152. Hautman. J.: Klein. M . L. J . C'hem. Phys. 1990.93.7483. Bareman, J. P.; Klein. M . L. J . Phys. Chem. 1990, 94. 5202.
2670 The Journal of Physical Chemistry, Vol. 97, No. 1 1 , 1993 ( I I ) Harris, J.; Rice, S. A. J. Chem. Phys. 1988, 89, 5898. Shin, S.; Collazo, N.; Rice, S.A. J. Chem. Phys. 1992, 96, 1352. Collazo, N.; Shin, S.; Rice, S.A. J. Chem. Phys. 1992, 96, 4735. (12) van der Ploeg, P.; Berendsen, H. J. C. J. Chem. Phys. 1982,76,3271. Egberts. E.; Berendsen, H. J. C. J. Chem. Phys. 1988, 89, 3718. ( I 3) Berkowitz, M. L.;Raghavan, K. fungmuir 1991,7,1042. Raghavan,
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