Conformation and Solvation Structure for an Isolated n-Octadecane

Mountain and Thirumalai carried out molecular dynamics simulations for hydrated ...... Jorgensen, W. L.; Buckner, J. K.; Boudon, S.; Tirado-Rives, J. ...
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J. Phys. Chem. B 2006, 110, 10519-10525

10519

Conformation and Solvation Structure for an Isolated n-Octadecane Chain in Water, Methanol, and Their Mixtures Li Sun,† J. Ilja Siepmann,*,† and Mark R. Schure‡ Departments of Chemistry and of Chemical Engineering and Materials Science, UniVersity of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, and Theoretical Separation Science Laboratory, Rohm and Haas Company, 727 Norristown Road, P.O. Box 0904, Spring House, PennsylVania 19477 ReceiVed: January 13, 2006; In Final Form: March 31, 2006

Configurational-bias Monte Carlo simulations in the isobaric-isothermal ensemble (T ) 323 K and p ) 10 atm) were carried out to probe structural properties of an isolated n-octadecane chain solvated in water, methanol, water-rich, or methanol-rich mixtures and, for comparison, of an isolated chain in the gas phase and for neat liquid n-octadecane. The united-atom version of the TraPPE (transferable potentials for phase equilibria) force field was used to represent n-octadecane and methanol and the TIP-4P model was used for water. In all six environments, broad conformational distributions are observed and the n-octadecane chains are found to predominantly adopt extended, but not all-trans conformations. In addition, a small fraction of more collapsed conformations in which the chain ends approach each other is observed for aqueous hydration, the water-rich solvent mixture and the gas phase, but the simulation data do not support a simple two-state picture with folded and unfolded basins of attraction. For chains in these three “poor” solvent environments, the dihedral angles near the center of the chain show an enhancement of the gauche population. The ensemble of water-solvated chains with end-to-end contacts is preferentially found in a U-shaped conformation rather than a more globular state. An analysis of the local solvation structures in the water-methanol mixtures shows, as expected, an enrichment of the methyl group of methanol near the methylene and methyl segments of the n-octadecane chain. Interestingly, these local bead fractions are enhanced by factors of 2.5 and 1.5 for methyl and methylene segments reflecting the more hydrophobic nature of the former segments.

Introduction Long normal alkanes are often used as model solutes to understand environmental partitioning processes1 and foldingunfolding transitions of biological macromolecules2-6 in aqueous media. A common way to influence aqueous solubilities or folding-unfolding transitions is by adding small amounts of a cosolvent or denaturant.7 Moreover, a loss of retention is commonly observed in reversed-phase liquid chromatography systems when the fraction of organic modifier in the mobile phase falls below a certain threshold; and this is sometimes referred to as phase collapse.8,9 Although it is well-known that neat liquid phases of long n-alkanes show considerable conformational disorder,10-12 there is less and sometimes conflicting information on the conformation of n-alkanes solvated in water or other polar, hydrogenbonding solvents. Recently, the solubilities of n-alkanes with eight to 15 carbon atoms were measured by Tolls et al. using slow-stirring experiments.1 These authors showed that the solubilities correlate very well with computed solvent-accessible surface areas or solvent-accessible volumes of all-trans conformers, and it was, thus, inferred that hydrated n-alkanes prefer the all-trans conformation over folded states.1 This conclusion was also supported by calculations of free energies of transfer using an implicit solvation model.1,13 In contrast, particle-based simulations to obtain the free energies of transfer for ndodecane2 and some smaller alkanes14 point to a less unfavorable * Corresponding author: [email protected]. † University of Minnesota. ‡ Rohm and Haas Co.

air-water transfer energy for folded conformations. Mountain and Thirumalai carried out molecular dynamics simulations for hydrated n-eicosane and found folded conformations in which there is a contact between the chain ends, to be about 12 times more likely than unfolded conformations.5 The Lum-ChandlerWeeks theory of hydrophobic hydration predicts that hydrogenbonding of water persists around small apolar solutes, whereas hydrogen-bonding is depleted near large apolar solutes with the crossover occurring on nanometer length scales.6,15 It is the purpose of this paper to investigate the conformation of n-octadecane and its solvation shell in water, methanol, and their mixtures using particle-based Monte Carlo simulations. Comparisons to chain conformations in the gas phase and in the bulk liquid allow us to elucidate likely reasons for the conflicting results obtained in previous studies. A detailed analysis of hydrogen-bonding and enrichment of methanol around the solute provides further insight on the solvation process. Molecular Models and Simulation Details Six different types of environments were investigated for n-octadecane, including an isolated chain solvated either in neat water (system WAT), in water/methanol solutions with a methanol mole fraction of 33% and 67% (systems 33M and 67M, respectively), and in neat methanol (system MET). In addition, an isolated n-octadecane chain in a vacuum and its bulk liquid were investigated. The latter system consisted of 50 n-octadecane molecules and all four systems for the solvated chain contained 900 solvent molecules (see Table 1). Although

10.1021/jp0602631 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/05/2006

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TABLE 1: Simulation Details and Selected Results: Numbers of n-octadecane and Solvent Molecules, Number of Monte Carlo Cycles for Each Independent Simulation, Average Linear Dimension of the Simulation Box (in Units of Å), Average End-to-End Length (in Units of Å), and the Folding Equilibrium Constant system

NC18

NH2O

WAT 33M 67M MET vacuum bulk

1 1 1 1 1 50

900 600 300

NMeOH

NMC

L

rEE

KUN

300 600 900

2.3 × 105 3.4 × 105 3.2 × 105 3.5 × 105 8.5 × 105 2.9 × 105

30.40 ( 0.06 33.94 ( 0.06 37.05 ( 0.07 39.94 ( 0.07

14.8 ( 0.4 14.1 ( 0.3 15.4 ( 0.2 16.1 ( 0.2 14.54 ( 0.02 15.84 ( 0.07

0.11 ( 0.3 0.13 ( 0.3 0.035 ( 0.013 0.013 ( 0.005 0.080 ( 0.003 0.011 ( 0.003

this number of solvent molecules is sufficient to prevent direct interactions of the two chain ends through the periodic boundaries and to avoid a correlation between changes in chain conformation and fluctuations in system volume, it is well below the actual number of solvent molecules that would be required to reach the extremely low solubility limit for n-octadecane in water (a solubility limit of about 10-11 M in water can be estimated from experiments1 at T ) 298 K). With the exception of the isolated chain in a vacuum, the Monte Carlo simulations for the other five systems were carried out in the isobaric-isothermal ensemble.16 In addition to the usual translational17 and rotational displacements18 and volume moves,16 the conformational degrees of freedom of the noctadecane chain were sampled using a combination of coupleddecoupled configurational-bias Monte Carlo (CBMC) moves for regrowing multiple segments including at least one terminal group19 and self-adapting fixed-end point CBMC moves for regrowing multiple interior segments.20 The simulations were carried out with the program MCCCS (Monte Carlo for complex chemical systems) that is developed by the Siepmann group.21 A user-friendly version of this software (MCCCS-Towhee) maintained by Marcus Martin is freely available via a GNU general public license.22 The united-atom version of the transferable potentials for phase equilibria (TraPPE-UA) force field23-25 was used for n-octadecane and methanol, and water was represented by the TIP4P model.26 It should be noted here that the TraPPE-UA force field uses different Lennard-Jones parameters for methyl and methylene groups: σCH3 ) 3.75 Å, CH3/kB ) 98 K, σCH2 )

30.14 ( 0.02

3.95 Å, and CH2/kB ) 46 K. The Lennard-Jones parameters for all unlike interactions were determined from the LorentzBerthelot combining rules:27 σij ) (σii + σjj)/2 and ij ) (iijj)1/2. A site-site based, spherical cutoff at 14.0 Å and analytical tail corrections28 were used for the Lennard-Jones interactions, and the Ewald summation technique28 was employed to compute the Coulombic interactions arising from the partial charges on the methanol and water molecules (the nonpolar n-octadecane does not contain any partial charges). All simulations were carried out at a temperature of 323.15 K and at a pressure of 1015 kPa (10 atm). These slightly elevated temperature and pressure (compared to standard conditions) were selected for two reasons. To allow for a comparison with liquid n-octadecane, the simulations needed to use a temperature above its triple point at 301 K. Second, the temperature/pressure condition used here is more typical for use in chromatography. For each of the systems, four independent simulations were carried out and the standard deviations were estimated from the results of these independent simulations. The production periods for solvated chains consisted of up to 350 000 Monte Carlo cycles where one cycle involves N randomly selected moves, where N is the total number of molecules. Results and Discussion Conformation of Chains in Different Environments. The evolution of the end-to-end distances, rE, for the solvated n-octadecane chains are shown in Figure 1. The end-to-end distance is a more convenient order parameter for medium-

Figure 1. Evolution of the end-to-end distance of the solvated n-octadecane chains. Data are shown separately for the four independent simulations for each system: WAT (top left), 33M (top right), 67M (bottom left), and MET (bottom right).

Structure of Solvated n-Octadecane Chain

Figure 2. Probability density of the end-to-end distance for noctadecane in six different environments. The black, red, blue, green, magenta, and orange lines show the data for solvation in WAT, 33M, 67M, and MET, in a vacuum and in the bulk liquid, respectively. For clarity, the standard deviations are only shown for systems WAT and MET.

length chains than the radius of gyration. For all four solvents, the following general observations can be made. First, the endto-end distance undergoes rapid, but minor fluctuations and only occasionally undergoes a more dramatic change from an extended to a collapsed conformation with direct contact of the chain ends and vice versa. Second, the end-to-end distances mostly fall into the range from 15 to 20 Å. Third, the end-toend distances cover the full range from about 4 Å for close contact of the two methyl groups to about 22 Å for chains in the all-trans conformation. The probability densities of the end-to-end distances of the solvated n-octadecane chains averaged over the four independent simulations are compared in Figure 2 with the end-to-end distance distributions calculated for a single n-octadecane chain in a vacuum and for bulk n-octadecane chains. A bin width of 2 Å was used for this analysis. For all six cases, the end-to-end distance shows a peak at 17 Å (i.e., for the bin with 16 Å < rE < 18 Å). This corresponds to an unfolded conformation, but is significantly smaller than the 22 Å corresponding to a chain in the all-trans conformation which is only observed with a probability of about 3% in all cases. For all six environments, the main peak is strongly asymmetric with a very extended tail toward shorter end-to-end distances. In addition to the main peak, there is the appearance of a minor peak at 5 Å (i.e., for the bin with 4 Å < rE < 6 Å) for chains solvated in WAT, 33M, and 67M and in a vacuum, whereas the distribution is more unimodal for chains solvated in methanol and the bulk liquid. The average end-to-end distances for the six environments are relatively close with a value of about 14.5 Å for the two water-rich and the vaccuum environments, a value of 15.4 Å for system 67M, and a value close to 15.9 Å for system MET and the bulk liquid (see Table 1). Although the end-to-end distributions do not show a distinct minimum between two states, we followed earlier work by Mountain and Thirumalai5 and computed an equilibrium constant using a two-state model with a folded state with rE e 8 Å and an unfolded state characterized by rE > 8 Å. The equilibrium constants are listed in Table 1, they range from a value of about 0.012 for the nonaqueous solvents (system MET and the bulk liquid) to a value of about 0.12 for the water-rich environments (systems WAT and 33M), where an equilibrium constant below unity signals that unfolded states are preferred. In comparison,

J. Phys. Chem. B, Vol. 110, No. 21, 2006 10521 Mountain and Thirumalai reported an equilibrium constant of 12 for hydrated n-eicosane.5 At this point we need to address likely reasons for the dramatic discrepancies between the earlier work by Mountain and Thirumalai5 and the present work. In the former, the hydrated n-eicosane chain prefers folded conformations with a tight end-to-end contact, whereas in our simulations the chains clearly prefer unfolded conformations with rE≈17 Å. In both simulation studies, a united-atom representation was used for the alkane chains and simple fixed-charge models were used for water. We believe that the different water models (SPC/E vs TIP4P) play only a minor role in explaining the differences and that the source for the discrepancies lies in the alkane models. Since the valence electrons belonging to carbonhydrogen bonds are significantly more polarizable than those belonging to carbon-carbon bonds,29 most united-atom models use different Lennard-Jones parameters for methyl and methylene segments. This is true for the TraPPE-UA model used here (CH3 ) 2.13CH2), and in principle also for the SKS force field30 (CH3 ) 2.43CH2). The latter force field is the basis for the model used by Mountain and Thirumalai,4,5 but unfortunately the SKS parameters for the methyl segment were used for all 20 segments of the n-eicosane chain in their study. Thus, the methylene-methylene interactions are overestimated by a factor of 2.43, and the methyl-methylene and water-methylene LJ interactions are overestimated by a factor of 1.56. If one surmises that chain conformations are similar for a hydrated chain and for a chain in a vacuum (as seen in the present work), then it is straightforward to test the influence of changes in the LJ parameters. The average end-to-end distances for n-octadecane at T ) 323 K in a vacuum computed for the TraPPE-UA model, the SKS model, and the all-methyl model used by Mountain and Thirumalai are 14.54 ( 0.02, 14.39 ( 0.01, and 9.45 ( 0.05 Å, respectively. The corresponding distributions of end-to-end distances are shown in Figure S1 available as Supplementary Information. The differences between the TraPPEUA and SKS models are negligible, whereas the all-methyl model clearly prefers collapsed conformations and its gauche population is increased with an average value of 39% (see next paragraph for the values observed in the present work). Thus, we would argue that the all-methyl model does not provide an acceptable representation for n-eicosane but that folded states may be preferred at significantly lower temperatures or for significantly longer chains, i.e., compensating for the difference between the methyl and methylene parameters. It should be noted here that the main focus of the work by Mountain and Thirumalai5 is to investgate the urea denaturation mechanism which requires a chain model that prefers folded states in neat aqueous solvent. The fractions of gauche defects as a function of the position along the chain backbone are compared in Figure 3. The n-octadecane chains solvated in W and 33M and in a vacuum contain a higher fraction of gauche defects (around 33% averaged over the entire chain) than the chain solvated in 67M (around 30%), and even fewer gauche defects are observed for the chain solvated in methanol and in the bulk liquid (around 28%). Although the changes in the overall fraction of gauche defects are small, there is an interesting difference in the pattern along the chain backbone. For the chains in water-rich solvents or in a vacuum, the gauche defect population increases toward the center of the chain, whereas the gauche defect population is flat throughout the central region of the chain for system 67M and decreases toward the center for the neat methanol solvent and the bulk liquid. Presumably, the reason for this behavior is

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Figure 3. Fraction of gauche defects along the carbon backbone. Line styles are as in Figure 2.

that gauche defects near the chain center are required to allow a chain to fold back on itself and bring the two chain ends into close contact which maximizes favorable self-interactions of chain segments (see next section). It should be noted here that the fraction of gauche defects remains relatively low even for folded chains. This is in marked contrast to the view4 that “in the collapsed state all bonds are expected to be in the gauche conformation.” Actually steric hindrance does not allow for conformations with only gauche defects. Even if nonbonded segment-segment interactions are ignored, the energy difference between trans and gauche conformations would disfavor a gauche defect-rich state. Furthermore, even at infinite temperature the gauche fraction would not exceed 67% because the trans state occupies one-third of the dihedral angle range. A Boltzmann population analysis of the torsional potential11 at T ) 323 K yields a gauche defect fraction of 36%. The fact that the values observed for the n-octadecane chain in the six different environments fall somewhat below the Boltzmann population shows that steric hindrance is more important than the segment-segment attractions, whereas the opposite is true for the all-methyl model with its increased Lennard-Jones well depth. On the basis of experimental measurements of the solubility limit for n-alkanes with 8 to 15 carbon atoms, Tolls et al. inferred that hydrated alkane chains adopt an all-trans conformation.1 This conclusion is based on a very good correlation between the measured solubilities and the solvent-accessible volumes or surface areas calculated for all-trans chain conformations. Further support for this notion was provided by calculations of free energies of hydration at the SM2-AM1 level.13 Although the all-trans conformation is indeed the state of lowest energy for medium-length normal alkanes in the gas phase, it appears unlikely that this conformation dominates the distribution of conformations at a finite temperature, e.g., 298 or 323 K, because there is a huge entropic penalty for limiting all dihedral angles to the trans conformation. Furthermore, recent computational work has shown that common solute descriptors used for continuum solvation models, such as the σ profile, are rather similar for the all-trans or thermally averaged conformations of alkanes.31 Thus, we would like to argue that an equally good correlation should exist between the measured solubilities and thermally averaged solvent accessible surface areas. To support this claim, the solvent-accessible surface areas32 were computed for the all-trans and thermally averaged (T ) 323 K in a vacuum) conformations for n-alkanes with 8 to 18 carbons atoms. In both cases, the solvent accessible surface area is a linear function of chain length (see Figure S2).

Sun et al.

Figure 4. Probability density of the three moments of inertia for the hydrated n-octadecane chains with an end-to-end distance less than 5 Å. The solid, dotted, and dashed lines show the distributions for the smallest, intermediate, and largest moment of inertia, respectively.

Figure 5. Snapshots of hydrated n-octadecane chains with an end-toend distance less than 5 Å. The conformations from 10 system configurations (separated by at least 50 Monte Carlo cycles) were aligned according to their moments of inertia and then plotted together.

Analysis of Folded Chain Conformations in Water. Since water is a poor solvent for nonpolar hydrocarbon chains, it is expected that a compact globular state is preferred for chains that are sufficiently long. Mountain and Thirumalai estimated that collapsed states would be preferentially observed for chains with more than 17 carbon segments.5 As discussed previously, our simulations demonstrate that unfolded conformations are more likely for n-octadecane chains. Nevertheless, there is a minor peak at rE ≈ 5 Å for the hydrated chain. Figure 4 depicts the distributions of the three principal moments of inertia33 for chain conformations with a direct endto-end contact, rE < 5 Å. There is some overlap between the distributions for the smallest and the intermediate moments of inertia, whereas the distribution for the third moment is shifted to significantly larger values. This indicates that hydrated chains with end-to-end contact are not in a globular state with a nearspherical shape characterized by three moments of intertia of about equal magnitude. Snapshots of 10 collapsed chain conformations are overlapped in Figure 5, and it is evident that these chains prefer U-shaped conformations. The potential of mean force (PMF) for the methane dimer in aqueous solution has been the topic of much research since the

Structure of Solvated n-Octadecane Chain

Figure 6. Probability density of the angle formed between the two chain ends and the nearest water oxygen in system WAT. Key: rE e 5 Å (solid), 5 Å < rE e 6 Å (dotted), 6 Å < rE e 7 Å (short dashed), 7 Å < rE e 8 Å (long dashed), 8 Å < rE e 9 Å (dotted dashed), and rE > 9 Å (double dotted dashed).

1970s.34-40 There is general agreement that the PMF exhibits two minima: one for direct methane-methane contacts and another for a pair separated by a single water molecule. It is also of interest for us to know whether the two ends of the n-octadecane chain are water-separated. Figure 6 shows the distribution of the cosine of the angle formed by the vectors from the two methyl groups of the n-octadecane chain to the water oxygen atom which is closest to the two chain ends. The distributions were calculated individually for different rE ranges. For short separations representative of the methane contact pair (rE e 5 Å), the maximum in p(cosθ) is found to be close to cosθ ≈ 0.5, the value representing an equilateral triangle; i.e., on average the methyl-water and methyl-methyl distances are similar. For intermediate separations, 5 Å < rE e 6 Å, representative of the PMF barrier between contact and solventseparated methane pairs, the peak shifts to cosθ ≈ 0.1 (i.e., the

J. Phys. Chem. B, Vol. 110, No. 21, 2006 10523 methyl-water distances are somewhat shorter than the methylmethyl distance), but the probability of finding cosθ < - 0.7 is zero, which indicates that in this case there is no water molecule sitting between the two chain ends. For 6 Å < rE e 7 Å representative of the solvent-separated minimum in the methane PMF, the distribution is further shifted to cosθ ≈ - 0.1, i.e., the closest water molecule does not sit between the two methyl groups but the methyl-methyl distance is on average 50% larger than the methyl-water distance. The distribution shifts further to smaller (more negative) cosine values as rE increases, and for rE > 9 Å, a water molecule is nearly always sandwiched between the two chain ends. Preferential Solvation. To investigate the local solvation environment, radial distribution functions (RDFs) and their corresponding number integrals (NIs) of some solvent functional groups around the methyl or methylene groups of n-octadecane were calculated, as shown in Figure 7. In particular for the two solvent mixtures, the first peak in the CH2(C18)-O(H2O) RDF is depleted, i.e., the n-octadecane chain is “dewetted” as the methanol concentration increases. The opposite behavior is observed for the CH2(C18)-O(MeOH) RDFs for which more structure is observed in the first solvation shell as the methanol concentration decreases. However, the corresponding NIs show that the number of methanol oxygen increases with increasing concentration. Compared to the CH2(C18)-O(MeOH) RDFs, there is considerably more structure in the CH2(C18)-CH3(MeOH) RDFs. Furthermore, for the latter the first peak is shifted to smaller separations. This is a clear indication not only of an enriched methanol environment but also of one with a preferential orientation in which the nonpolar methyl end of methanol surrounds the solute, whereas its polar hydroxyl group points toward the solvent side. This local structuring of methanol molecules is further enhanced around the terminal methyl segments of the solute; i.e., the methyl group is more hydro-

Figure 7. Radial distribution functions and the corresponding number integrals (as inserts) for solute segement-solvent segment pairs: Top left: CH2(C18)-O(H2O). Top right: CH2(C18)-O(MeOH). Bottom left: CH2(C18)-CH3(MeOH). Bottom right: CH3(C18)-CH3(MeOH). Line styles are as in Figure 2.

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TABLE 2: Number of Molecules in the Solvation Shell and Numbers of Acceptor and Donor Hydrogen Bonds per Molecule in Either the Solvation Shell or the Bulk Region system

WAT

33M

67M

Nshell(H2O) Nshell(MeOH) acc (H2O) nshell don nshell (H2O) acc nshell (MeOH) don (MeOH) nshell nacc bulk(H2O) ndon bulk(H2O) nacc bulk(MeOH) ndon bulk(MeOH)

90.0 ( 0.5

32.6 ( 0.6 28.0 ( 0.3 1.50 ( 0.01 1.76 ( 0.01 1.26 ( 0.01 0.91 ( 0.01 1.61 ( 0.01 1.82 ( 0.01 1.34 ( 0.01 0.91 ( 0.01

11.8 ( 0.3 38.3 ( 0.2 1.29 ( 0.01 1.77 ( 0.01 1.08 ( 0.02 0.92 ( 0.01 1.39 ( 0.01 1.81 ( 0.01 1.14 ( 0.01 0.93 ( 0.01

1.80 ( 0.01 1.80 ( 0.01

1.87 ( 0.01 1.87 ( 0.01

phobic (or MeOH-philic) because of its larger nonpolar solvent accessible surface area and higher curvature. Local mole fraction enhancement can provide information on the microheterogeneous nature of the solvent environment.24 The local mole fraction can be calculated from the NIs, it is the average number of particles of a given type up to a distance r around the tagged particle divided by the sum of the average numbers of particles of any type. The local mole fraction enhancement is then defined as the local mole fraction divided by the bulk mole fraction. The local mole fraction enhancements of heavy solvent atoms (including the oxygen atom in water and methanol and the united-atom methyl group in methanol) around solute methyl or methylene groups for systems 33M and 67M are depicted in Figure 8. For both solvent mixtures, the local mole fraction is most enhanced for CH3(C18)-CH3(MeOH), and the enhancement decreases in the following order: CH2(C18)-CH3(MeOH), CH3(C18)-O(MeOH), CH2(C18)O(MeOH), CH3(C18)-O(H2O), and CH2(C18)-O(H2O); with the mole fractions for the latter two being actually depleted, i.e., the enhancements falling below unity. Comparing the enhancements for system 33M with those for 67M, one can notice that the methanol concentration is more enhanced in system 33M, while the water concentration is more depleted in 67M. However, one should be reminded that these plots are normalized by bulk concentration, so the absolute local mole fractions of methanol segments for system 67M are higher than those for system 33M (see Table 2). Hydrogen-Bonding Around the Solute. Other important questions concerning solvation in hydrogen-bonded solvents are whether there are fewer hydrogen bonds in the vicinity of the

Figure 8. Local mole fraction enhancements in the vicinity of the n-octadecane chain for systems 33M (left) and 67M (right). The solid, dashed, dotted-dashed, dotted, long-dashed, and double-dotted dashed lines represent CH2(C18)-CH3(MeOH), CH2(C18)-O(H2O), CH2(C18)O(MeOH), CH3(C18)-CH3(MeOH), CH3(C18)-O(H2O), and CH3(C18)O(MeOH), respectively.

MET 44.5 ( 0.2 0.92 ( 0.01 0.94 ( 0.01

0.94 ( 0.01 0.94 ( 0.01

solute and whether the hydrogen-bonded network is distorted in the solvation shell. To this extent one first needs to find a suitable set of criteria that is required to be satisfied by a pair of molecules for the formation of a hydrogen bond.41,42 Here we use a set of hydrogen bond criteria that was previously applied to water-alcohol mixtures:43,44 rOO e 3.3 Å, rOH e 2.5 Å, cosθOH‚‚‚OL e - 0.1, and Uhead e -13 kJ/mol, where θOH‚ ‚‚OL and Uhead are the hydrogen bond angle and the pair interaction energy, respectively. Furthermore, inspection of the RDFs shown in Figure 7 shows that a distance cutoff at 6 Å between any solute segment and any solvent heavy atom (including the methyl group for methanol and the oxygen atom for both water and methanol) is a suitable definition to define whether a molecule belongs to the solvation shell of noctadecane. Similarly, any solvent molecule that is separated by at least 12 Å from any solute segment is considered to be in a “bulk” solvent environment. As summarized in Table 2, the number of water and methanol molecules in the solvation shell ranges from 90 for system WAT to 45 for system MET, and the total numbers of solvent molecules for the mixtures are 61 and 50 for systems 33M and 67M, respectively. As discussed previously, these solvation shells show an enhanced methanol mole fraction. A water molecule can contribute as donor and acceptor to each two hydrogen bonds, whereas a methanol molecule has two acceptor sites but can donate only to one hydrogen bond. For watermethanol mixtures, this asymmetry leads to water being involved in a higher number of hydrogen bonds as donor than acceptor, whereas the reverse is true for methanol. For all four solvent environments, the data in Table 2 show that molecules in the solvation shell are involved in fewer hydrogen bonds than molecules in the bulklike enviroment. However, the differences are rather small with an average decrease of only 3%; i.e., the hydrogen-bonded network of the solvent molecules is able to wrap around the solute. Following the lead of Mountain and Thirumalai,4 we have also computed the distribution of OOO angles formed by a central solvent molecule as vertex and the two nearest oxygen atoms belonging to two other solvent molecules that are both hydrogen-bonded to the vertex molecule. As can be seen from Figure 9, the distributions for molecules in the solvation shell or in the bulklike environment are remarkably similar with respect to peak position and width. A similar observation was previously made by Mountain and Thirumalai for the solvation of n-octane.4 For water molecules, the maximum is found close to the tetrahedral angle (cosθOOO ≈ -1/3), whereas steric hindrance for methanol results in a shift to a larger OOO angle of about 130°. Both the number of hydrogen bonds and the distribution of OOO angles show clearly that even a hydrocarbon as large as n-octadecane does not yet offer a sufficiently large surface to

Structure of Solvated n-Octadecane Chain

J. Phys. Chem. B, Vol. 110, No. 21, 2006 10525 Supporting Information Available: Figure S1, showing the distributions for end-to-end distances in a vacuum for TraPPEUA, SKS, and all-methyl chains, and Figure S2, showing the linear dependence of the solvent accessible surface area for n-alkanes on the number of carbon atoms is demonstrated for all-trans and thermally averaged conformations. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 9. Distributions of the OOO angle for hydrogen-bonded trimers. The solid, dashed, dotted, and dash-dotted lines depict water trimers with all three molecules being in the solvation shell (system WAT), water trimers with all three molecules being in the bulk solvent phase (system WAT), methanol trimers with all three molecules being in the solvation shell (system MET), and methanol trimers with all three molecules being in the bulk solvent phase (system MET), respectively.

disrupt the hydrogen-bonded network in water or methanol. This finding is in agreement with the prediction of the LumChandler-Weeks theory of hydrophobic hydration that hydrogen bonding would only be significantly disrupted next to apolar solutes with diameters in the nanometer regime.15 Conclusions Simulations of a single n-octadecane chain solvated in water, methanol, and their mixtures, and in a vacuum or its bulk liquid show statistically significant but not dramatic differences in chain conformation. In all cases, the chains prefer unfolded conformations and the distributions of end-to-end distances peak at 17 Å, a value that falls about 20% below the end-to-end distance for the all-trans conformation. The average end-to-end distance decreases with the solvent quality, being largest for the bulk liquid and smallest for the hydrated chain. In relatively poor solvents (water, 33% methanol, and vacuum), a small fraction of chains is observed in folded states with a direct contact of the chain ends. These folded conformations prefer a U-shaped conformation and are not globular. In methanol/water mixtures, the n-octadecane chain is preferentially solvated by methanol with the methanol molecules preferentially oriented with their methyl group toward the solute. This preferential solvation is more pronounced around the methyl group than around the methylene group of the solute. It should be noted that n-octadecane is neither soluble in water nor soluble in methanol under standard conditions nor soluble at temperatures and pressures commonly used in chromatographic separations. Finally, it is found that neither the number nor the geometry of the hydrogen-bonded network formed by the solvent molecules are significantly disrupted by the presence of the n-octadecane chain. Acknowledgment. Financial support from the National Science Foundation (CHE-0213387), a Frieda Martha Kunze Fellowship (L.S.), and the Advanced Biosciences Division of the Rohm and Haas Company is gratefully acknowledged. Part of the computer resources were provided by the Minnesota Supercomputing Institute.

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