Molecular Simulation Study of Water Mobility in Aerosol-OT Reverse

ARTICLE pubs.acs.org/JPCA

Molecular Simulation Study of Water Mobility in Aerosol-OT Reverse Micelles Janamejaya Chowdhary† and Branka M. Ladanyi* Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523-1872, United States ABSTRACT: In this work, we present results from molecular dynamics simulations on the single-molecule relaxation of water within reverse micelles (RMs) of different sizes formed by the surfactant aerosol-OT (AOT, sodium bis(2-ethylhexyl)sulfosuccinate) in isooctane. Results are presented for RM water content w0 = [H2O]/[AOT] in the range from 2.0 to 7.5. We show that translational diffusion of water within the RM can, to a good approximation, be decoupled from the translation of the RM through the isooctane solvent. Water translational mobility within the RM is restricted by the water pool dimensions, and thus, the water mean-squared displacements (MSDs) level off in time. Comparison with models of diffusion in confined geometries shows that a version of the Gaussian confinement model with a biexponential decay of correlations provides a good fit to the MSDs, while a model of free diffusion within a sphere agrees less well with simulation results. We find that the local diffusivity is considerably reduced in the interfacial region, especially as w0 decreases. Molecular orientational relaxation is monitored by examining the behavior of OH and dipole vectors. For both vectors, orientational relaxation slows down close to the interface and as w0 decreases. For the OH vector, reorientation is strongly affected by the presence of charged species at the RM interface and these effects are especially pronounced for water molecules hydrogenbonded to surfactant sites that serve as hydrogen-bond acceptors. For the dipole vector, orientational relaxation near the interface slows down more than that for the OH vector due mainly to the influence of iondipole interactions with the sodium counterions. We investigate water OH and dipole reorientation mechanisms by studying the w0 and interfacial shell dependence of orientational time correlations for different Legendre polynomial orders.

1. INTRODUCTION Aqueous reverse micelles (RMs) are surfactant aggregates that form in water/surfactant/oil systems at high concentrations of the oil phase. The aggregates are surfactant-coated water droplets whose size is determined primarily by the molar ratio1 w0 ¼ ½water=½surfactant

ð1Þ

The dimensions of the water droplets are typically in the nanometer range and are relatively easy to control by varying the water content. RMs have many chemical and biochemical applications. Examples include their use as microreactors in the synthesis of nanoparticles of well-defined sizes and shapes,24 as models of biological compartmentalization in studies of structure and function of biomolecules,5,6 and as media for heterogeneous organic reactions.7 For all of these uses, understanding and predicting the effects of confinement on water pool properties is important and has been the focus of experimental and theoretical studies.810 Water dynamics and hydrogen-bond distribution within RMs have been investigated by several experimental methods for which the observable comes directly or predominantly from water molecules. These include NMR,1113 conventional1416 and time-resolved10,1727 IR, dielectric r 2011 American Chemical Society

relaxation,16,2831 and quasi-elastic neutron scattering.32 In addition, several spectroscopic methods employing probe molecules8,3344 have been used. Molecular dynamics (MD) computer simulation has also proved to be an effective method to study the structure and dynamics of the water pool of model RMs.4562 A surfactant that forms stable RMs over a wide range of w 0 values is aerosol-OT (AOT, sodium bis(2-ethylhexyl)sulfosuccinate).1,63 Numerous experimental studies of its properties have been carried out64 and continue to be an active area of research.8,10,1518,22,24,26,2830,33,34,37,39,43,6570 Given that w0 can be varied over a wide range of values has made RMs formed in water/AOT/oil the systems of choice in studies of nanoconfinement on the properties of water. Several MD studies of the water pool properties of AOT-based RMs using reduced,32,53,54,61,71 coarse-grained,5557 and atomistic5860 models have been carried out. Special Issue: Victoria Buch Memorial Received: February 25, 2011 Revised: April 19, 2011 Published: May 06, 2011 6306

dx.doi.org/10.1021/jp201866t | J. Phys. Chem. A 2011, 115, 6306–6316

The Journal of Physical Chemistry A In this article, we further explore the properties of our atomistic model59 for the water/AOT/isooctane system. The results on the stability, internal organization, and structure of the resulting RMs of different sizes have been presented elsewhere.59 The model has also been applied60 to a simulation study of the observables in ultrafast IR experiments detecting the OD stretch1720 of dilute HOD in the RM water pool. Comparison with experiment showed that the model provides a very good representation of the OD stretch absorption spectrum, the frequency fluctuation and OD bond orientational time correlations, and their changes as w0 varies. By contrast, the spectrum calculated60 using the FaederLadanyi reduced RM model53 does not agree well with experiment. Unlike the reduced model, the present atomistic model allows the RM shape to fluctuate, providing an additional relaxation channel to the water pool species. Furthermore, it represents the hydrophilic portions of the AOT surfactant at the atomic level of detail, making it possible to represent more realistically how the watersurfactant interactions, the proximity to the interface, and the RM size w0 affect water dynamics. We focus here on both the translational and rotational mobilities of the water molecules in water/AOT/isooctane RMs, putting somewhat greater emphasis on translational motion, given that several aspects of rotational relaxation of the HOD IR probe were investigated earlier.60 Understanding translational diffusivity within RMs is important, given that motion of solutes relative to the interface is a significant contributor to reaction dynamics in nanoconfinement.7275 In the water/AOT/isooctane system, water molecules remain within the same surfactant-coated droplet over time scales relevant to our simulations. Thus, the translational displacements are bounded by the RM water pool dimensions. In addition to exploring water mean-squared displacements (MSDs) over distances small compared to the water pool size in order to assess the effects of heterogeneous environments on molecular mobility in different interfacial layers, we investigate how confinement dimensions affect translational motion. We compare our MD results to predictions of models that have been proposed to account for diffusion in confined geometries. Specifically, we investigate the applicability of the “free diffusion in a sphere”76,77 and Gaussian confinement78 models. With respect to orientational relaxation, we consider several aspects of orientational dynamics not addressed in the study of the IR anisotropy decay of the OD stretch.60 First, we examine how the heterogeneous nature of the RM environment affects water orientational dynamics by investigating the behavior of water molecules that solvate several surfactant hydrogen-bonding sites and sodium counterions. We then examine how the orientational relaxation of different vectors embedded in a water molecule is affected by the heterogeneous environment. Finally, we look into the reorientation mechanism for interfacial water. The remainder of the manuscript is organized as follows. In section 2, we specify the system parameters and the simulation methods. The results on translational diffusion within the RM are compared to restricted diffusion models in section 3. In section 4, we present the MD data on survival probabilities for molecules in different interfacial shells and for translational MSDs in different interfacial regions. Our results on orientational relaxation of water OH and dipole vectors are presented in section 5. In section 6, we summarize our main findings and present our conclusions.

ARTICLE

Table 1. System Composition and MD Trajectory Lengths w0

NW

NAOT

NTMP

te (ns)

ts (ns)

2.0

52

26

566

10.0

20.0

5.1

211

42

817

7.5

12.5

7.5

525

70

1403

5.0

10.0

2. MODEL AND SIMULATION DETAILS The details of the simulation protocol are presented elsewhere,59 but we present a brief summary here for the sake of completeness along with specific modifications relevant to the results presented here. AOT RMs with compositions w0 = 2, 5.1, and 7.5 were simulated by selecting NW water, NAOT surfactant, and NTMP isooctane molecules. The numbers of molecules of the three system components in the simulation box are presented in Table 1. In our previous work,59 we used NTMP = 190 in the w0 = 2.0 RM simulation. The number of isooctane molecules was increased here in order to obtain a more realistic representation of the aggregate mobility in isooctane solvent. We have verified that the results on RM structure, presented earlier,59 are not affected by the change in NTMP. All MD simulations were performed using codes developed in our group. The velocity-Verlet algorithm79 was used to propagate the trajectories using a time step of 0.002 ps. The pressure and temperature were maintained at equilibrium values of 1 atm and 298 K, respectively, using Berendsen’s method80 with the barostat and thermostat coupling times of 1 ps. We used the SPC/E model81 for water, the TraPPe force field82,83 for isooctane, a hybrid CHARMM84TraPPe force field for AOT, and the Naþ potential parameters were adopted from Schweighofer et al.85 The MD simulations trajectory lengths were extended beyond those used in ref 59. Table 1 includes the values of equilibration times te and total simulation trajectory lengths ts used to obtain the results that are presented here. Rotational time correlations were obtained from 2 ns portions of the equilibrated trajectories, saved at every second step, while the translational displacements were averaged over the entire (w0 = 7.5) or the remaining portions of (w0 = 2.0 and 5.1) equilibrated trajectories, saved at every fifth step. 3. TRANSLATIONAL DIFFUSION: COMPARISON TO RESTRICTED DIFFUSION MODELS 3.A. Separation of Aggregate and Molecular Translational Diffusion. In order to determine the translational mobility of

water within RMs, our first task is to separate the translational motion of the RM as a whole from water motion within the RM. Because the RM shape fluctuates as the aggregate moves through the solution, this separation is only approximate. We test its accuracy by checking how well it predicts the MSD. Specifically, the MSD of a water molecule in the lab frame may be written as Æ½ΔrL ðtÞ2 æ ¼ Æ½rL ðtÞ rL ð0Þ2 æ ¼ Æ½ΔR CM ðtÞ þ ΔrðtÞ2 æ

ð2Þ

where rL is the molecular position in the lab frame, RCM the position of the RM center of mass (CM), and r the position of the molecule in the CM frame. 6307

dx.doi.org/10.1021/jp201866t |J. Phys. Chem. A 2011, 115, 6306–6316

The Journal of Physical Chemistry A

ARTICLE

Figure 1. MSDs of RM CM, water in CM and laboratory frames, and the MSD sum and cross-correlation indicated by eqs 3 and 4 for w0 = 5.1.

If the CM translation can be approximately decoupled from water motion within the RM, then Æ½ΔrL ðtÞ2 æ = Æ½ΔR CM ðtÞ2 æ þ Æ½ΔrðtÞ2 æ

ð3Þ

or, equivalently, that the RM CM translation is not correlated with water translation within the RM ÆΔR CM ðtÞ 3 ΔrðtÞæ = 0

ð4Þ

Figure 1 illustrates the test of this approximation for the w0 = 5.1 RM. As can be seen from the figure, this approximation is excellent, as tested by both eqs 3 and 4. The results for the other two RM sizes (not shown) indicate that the approximation is just as good for these smaller and larger RMs. From now on, we focus our attention on the water translational mobility in the RM CM frame, paying particular attention to the MSD, Æ[Δr(t)]2æ. Figure 2 illustrates the behavior of Æ[Δr(t)]2æ of water molecules in all three RMs considered here. As is evident from this figure, water translational mobility increases with the increasing RM size. The increase is especially dramatic in going from w0 = 2.0 to 5.1, with the smaller RM showing very low translational mobility compared to that exhibited by molecules in the larger RMs. Analogous trends with w0 have been observed in previous MD studies of MSDs in models for ionic surfactant RMs.53,54,56,58 Water molecules do not escape from the RM interior on the several nanosecond time scale sampled in our simulations. Thus, the maximum distance scale for water translational motion is determined by the size of the interior region. While the MSD plateau has not yet been reached within the 250 ps time scale displayed in Figure 2, the decrease in the slope of Æ[Δr(t)]2æ versus t at longer times signals the approach to this plateau. In order to gain better insight into the effects of confinement on water translational mobility in RMs, we examine how well the observed behavior of the MSD fits some simple models of geometrical confinement. Specifically, we consider the free diffusion in a sphere76,77 and Gaussian confinement78 models. 3.B. Free Diffusion in a Sphere Model. A simple representation of translation within a confining region of approximately spherical shape is that of free diffusion within a sphere, that is, a spherical enclosure with reflecting boundaries. This model has been used in the context of nuclear spin echo76 and quasielastic neutron scattering77 experiments on confined fluids. While this model satisfies the requirement that the maximum MSD be

Figure 2. Water MSD within the RM for the three RM sizes.

limited by the size of the RM, it is not expected to accurately represent the details of translational dynamics, given that the RMs are neither rigid nor perfectly spherical and that translational mobility, even in a rigid sphere model of the RM water pool,53 diminishes near the interface due to watersurfactant interactions. Nevertheless, because this model is expected to have the correct short- and long-time limiting forms, we compare our MD results for translational diffusion to its predictions. In what follows, our notation resembles that in the VolinoDianoux paper.77 In this model, for a sphere of radius Rs, the probability that a particle is at r at time t and was at r0 at t = 0 is given by76,77 pðr, tjr0 Þ ¼

¥

l

Al ðr, r0 , tÞ ∑ Ylm ðθ, φÞYlm ðθ0 , φ0 Þ ∑ l¼0 m¼ l

ð5Þ

where Ylm are spherical harmonics and the radial coefficients Al are given by77 Al ðr, r0 , tÞ ¼

1 ¥ l l ψ ðrÞψl n ðr0 Þ expðDλn tÞ rr0 n ¼ 0 n

∑

ð6Þ

where D is the diffusion coefficient of the molecules within the spherical enclosure, while λln and ψln(r) are, respectively the (nþ1)th eigenvalues and eigenfunctions of the l-dependent radial diffusion equation. The boundary conditions (∂p/∂r)0,Rs = 0 make it possible Rto evaluate λln and, along with the normalization condition R0 s |ψln(r)|2 dr = 1, to determine the functional form of ψln(r). Specifically77 ( ψln ðrÞ ¼ ψ00 ðrÞ ¼

)1=2 2ðxln Þ2 rjl ðxln r=Rs Þ fl, ng 6¼ f0, 0g Rs3 j2l ðxln Þ½ðxln Þ2 lðl þ 1Þ !1=2 3 r fl, ng ¼ f0, 0g Rs3

ð7Þ Here, jl is the spherical Bessel function of order l and xln = Rs(λln)1/2 is determined by solving ljl ðxln Þ xln jl þ 1 ðxln Þ ¼ 0 j1 ðx0n Þ ¼ 0

l>0 l¼0

ð8Þ

For l > 0, xln corresponds to the nth root of ∂jl(x)/∂x = 0. 6308



ARTICLE

Table 2. Parameters in the Fit to Free Diffusion in a Sphere Model D (Å2/ps)

w0

Rs (Å)

Table 3. Parameters for the Fit to the Gaussian Confinement Model

ÆRwæ (Å)

2.0

0.0301

1.99

8.3

5.1 7.5

0.0873 0.133

5.72 8.08

12.1 16.2

b1

a1

a2

1

2

2

w0

(Å )

2 5.1

13.69 5.45 103 90.53 4.07 103

7.5

161.9

(ps )

3.70 103

b2 1

Deff

Æ[Δr(¥)]2æGC

2

(Å )

(ps )

(Å /ps)

(Å2)

0.7915 1.183

0.970 0.827

0.140 0.224

14.5 91.7

1.488

0.542

0.234

163.4

To calculate the MSD ÆðΔrÞ2 æ ¼

Æ½r r0 2 æ ¼ Ær 2 þ r02 2rr0 cos γæ Z Z dr dr0 ½r r0 2 pðr, r0 , tÞpðr0 Þ

¼

x-coordinate, these cross correlations are given by ÆxðtÞxð0Þæ ¼ Æx2 æΓðtÞ

ð9Þ

where Γ(t) is the correlation coefficient, which has the properties Γð0Þ ¼ 1

we use Pl ðcos γÞ ¼

l 4π Y ðθ, φÞYlm ðθ0 , φ0 Þ 2l þ 1 m ¼ l lm

∑

ð10Þ

and77 pðr0 Þ ¼ ¼

3 4πRs3 0

r0 e Rs

ð13Þ

ð11Þ

r0 > Rs

lim ΓðtÞ ¼ 0

t sf ¥

ð14Þ

In the present case, the version of the model corresponding to the same extent of confinement in all three dimensions is appropriate. For the case of isotropic 3-D confinement, the probability distribution for Δr(t) = r(t) r(0) is given by " # 1 ðΔrÞ2 exp 2 pðΔr, ΓÞ ¼ ð15Þ 4Æx æð1 ΓÞ ½4πÆx2 æð1 ΓÞ3=2 where

The result is

" # 1 ¥ 1 expðDλ tÞ 2 n ÆðΔrÞ æ ¼ 6Rs2 2 1 2 1 2 5 n ¼ 0 ðxn Þ ½ðxn Þ 2

∑

Æx2 æ ¼ Æy2 æ ¼ Æz2 æ ¼ Ær2 æ=3 ð12Þ

Volino and Dianoux77 list x1n for n = 17, and the large-n expansion given in ref 86 can be used for larger n values. In practice, we have used the first 50 values of x1n in evaluating the MSD according to eq 12. The values of D and Rs obtained by fitting the simulated MSD over the 250 ps interval to the free diffusion in a sphere model are shown in Table 2. Also included are the average radii ÆRwæ of the water droplet obtained from MD trajectories by calculating the average distance from the AOT head group sulfur atoms to the RM CM.59 As can be seen from the table, the D and Rs values both increase with increasing RM size. However, the Rs values are considerably smaller than the corresponding ÆRwæ values, amounting to one-half or smaller than the actual water pool radius determined from MD simulation. The values of D for all three RMs are appreciably smaller than the bulk SPC/E water value of 0.24 Å2/ps. This shows that diffusion cannot really be thought of as “free” within the water pool and that the effective diffusion constant decreases as w0 decreases, demonstrating that the hydrophilic interface plays an increasingly important role in water dynamics as the droplet size decreases. Thus, a model that includes an attractive well near the repulsive wall, related to the water density enhancement near the surfactant head groups,59 might represent an improvement over free diffusion within the spherical enclosure. The fact that the shape of the confinement region fluctuates is also expected to influence the diffusion of water within it. 3.C. Gaussian Confinement Model. The Gaussian confinement model of Volino et al.78 is intended for systems in which the confining region can fluctuate. The molecular position has a Gaussian distribution, and correlations between positions separated by time interval t decay in time. For confinement along the

ð16Þ

represents the size of the confining region Using eq 15, the result for MSD is Æ½ΔrðtÞ2 æ ¼ 6Æx2 æ½1 ΓðtÞ

ð17Þ

78

Volino et al. give several expressions for the correlation coefficient Γ(t), the simplest of which is ΓðtÞ ¼ expðt=τ0 Þ

ð18Þ

We have tested this form on our MD data and found that it does not provide a satisfactory fit. However, a sum of two exponentials ΓðtÞ ¼

a1 eb1 t þ a2 eb2 t a1 þ a2

ð19Þ

fits our MSD data very well in the range of 1100 ps. Equation 19 can be interpreted as corresponding to the situation where the molecular mobility differs in two parts of the region to which the molecule is restricted. This would correspond to the coreshell model that has been proposed to interpret water IR absorption spectra.20 In this case a1 þ a2 = 6Æx2æ = 2Ær2æ corresponds to the size of the confining region, and the MSD, like in the case of eq 18, is linear in t at short times, now with the slope a1b1 þ a2b2. One might define an effective diffusion coefficien, based on this initial slope a1 b1 þ a2 b2 ð20Þ 6 The model also gives an estimate of the plateau value that the MSD reaches as t f ¥ Deff ¼

lim Æ½ΔrðtÞ2 æ = Æ½Δrð¥Þ2 æGC ¼ a1 þ a2

t sf¥

ð21Þ

The parameters obtained from this fit are summarized in Table 3. The parameters a1 and a2 that correspond, respectively, to the mean-squared dimensions of the core and shell regions 6309



Figure 3. Comparison of MD results and fits to the Gaussian confinement (Gaussian conf.) and free diffusion in a sphere (diff. sph.) models for MSDs of water in RMs.

Figure 4. Intrinsic (relative to the surfactant head groups) density profile of the water oxygen density profile in the w0 = 7.5 RM, divided into interfacial, intermediate, and core regions.

both increase with increasing w0. The estimated plateau values of the MSD, based on the model parameters, are also given. We expect that these quantities provide reasonable estimates of the limiting values that the water MSDs reach within the three RMs. The values of the coefficients b1, which set the time scale for reaching the plateau values, are in the 103 ps1 range, indicating that these values will be reached on the nanosecond time scale. The effective diffusion coefficients, related to the short-time behavior of the MSD (eq 20), increase with increasing w0 and in this model take on values that are of the same order of magnitude as the bulk value, with Deff for w0 = 7.5 now close to the bulk diffusion coefficient value of 0.24 Å2/ps. The quality of the fits is illustrated in Figure 3. The fits to the Gaussian confinement model are excellent, while the fits to the free diffusion in a sphere model are not as good. The latter model does not lead to the correct functional form of the MSD. It predicts an initial slope that is too low and a curvature that is too large.

4. TRANSLATIONAL DIFFUSION IN DIFFERENT INTERFACIAL LAYERS On the basis of previous results from MD simulation of RMs,32,46,48,49,53,54,60 we expect that the mobility of water

ARTICLE

Figure 5. Survival TCF for water in the w0 = 7.5 RM in the three regions defined in Figure 4.

molecules will depend on their location relative to the surfactant interface. In investigating this aspect of water mobility, we divide the molecules according to their proximity to the nearest sulfur site of the AOT sulfonate head group. The regions are divided according to the interfacial shells of the intrinsic water oxygen density profile. This density profile, constructed relative to the surface defined by the S sites,59 is shown in Figure 4 for the w0 = 7.5 RM. Two interfacial layers near the interface followed by a uniform density region closer to the center can be seen and are used to define three regions within this RM. The two interfacial peaks are also present at approximately the same locations for the two smaller RMs. Their heights increase slightly as w0 decreases.59 The w0 = 2.0 RM lacks the core region, while a small core region is present for the w0 = 5.1 RM. In practice, we assign a molecule to the interfacial region if it is within 4.73 Å of the nearest S, to the intermediate region if it is in the range of 4.738.48 Å of the nearest S, and to the core region if it is farther away. The mobility of molecules in a given region is reflected in the population relaxation of molecules in it. To study this population relaxation, we calculate the survival time correlation function (TCF), S(τ), which is the probability that a given molecule remains continuously in a selected region during time interval τ. If N(t,tþτ) is the number of molecules that remain in a given region during the time interval [t,tþτ] and N(t) is the number of molecules in this region at time t, then S(τ) can be calculated as SðτÞ ¼

1 nt NðnΔt, nΔt þ τÞ nt n ¼ 0 NðnΔtÞ

∑

ð22Þ

where nt is the number of time origins considered in the calculation and Δt is the time interval at which trajectory data are saved during the simulation. The behavior of S(t) for water as a function to its location relative to the interface is illustrated in Figure 5. The core and interface regions exhibit the fastest and slowest decay of S(t), respectively. As can be seen from Figure 4, the intermediate region is thinner than the interfacial region, which contributes to the shorter survival time for molecules within it, making its decay almost as fast as that in the core. The water molecules at the interface are less mobile due to strong electrostatic interactions with the surfactant head groups and counterions, the lack of affinity of water for the surfactant hydrophobic tails, and geometric confinement provided by the curved surfactant interface. 6310



Figure 6. Survival TCFs in the interfacial (top) and intermediate (bottom) regions for the three RM sizes.

Figure 7. MSDs of water molecules that remain in the indicated interfacial layers of the w0 = 7.5 RM throughout the time interval displayed.

The effects of the increased curvature and the accompanying decrease in the surface area per head group87 are illustrated in Figure 6, where the w0 dependence of S(t) for the corresponding regions relative to the surfactant interface is shown. As can be seen from the figure, in both regions, S(t) decays more slowly for the smaller RM size. The differences in the decay rates are modest in the case of the w0 = 5.1 and 7.5 RMs, while the decay rates of S(t) in each region are considerably slower in the smallest RM, for which the confinement effects are the strongest. The figure also illustrates that S(t) does not decay exponentially. The deviations are pronounced in both regions for w0 = 2.0, while for the two larger RMs they are more pronounced in the interfacial region. The trends seen in the behavior of S(t) in different interfacial regions and as a function of RM size are mirrored in the behavior

ARTICLE

Figure 8. MSDs of water molecules that remain in the interfacial (top) and in the intermediate (bottom) regions of the RMs of different size.

of the MSDs. We focus first on MSDs of molecules that remain in a given region over the entire time interval under consideration. The MSDs calculated in this way are shown in Figures 7 and 8. The data for w0 = 7.5 in the three RM regions show that water translational mobility increases with the distance from the interface. The mobility in the two inner layers is similar and is considerably higher than that in the outer layer. Figure 8 shows that, in corresponding interfacial layers, the water translational mobility increases with increasing water content w0. As in the case of S(t), the difference in Æ[Δr(t)]2æ is large between w0 = 2 and 5.1 and small between the two larger RMs, w0 = 5.1 and 7.5. This indicates that the interface curvature effects on water mobility diminish, but do not disappear, at w0 = 5.1. Water mobility by region can also be measured by tagging molecules according their location at t = 0 and following their progress, regardless of their subsequent location. This approach was taken in earlier studies of water mobility in RMs53,54 using a reduced RM model and is often employed in studies of interfacial mobility. The relative merits of the two approaches have been discussed in a recent paper by Pinnick et al.88 on water near a lipid bilayer. In Figure 9, we compare these two approaches of calculating MSDs in RM interfacial layers. As can be seen from this figure, the resulting MSDs start diverging from each other at relatively short times, with the molecules that are tagged only initially exhibiting higher mobility in all three regions. The MSDs for these molecules are also closer to being linear in t over the time interval shown, while the MSDs for molecules that remain in a given region show a weaker, “subdiffusive”, t dependence. It is clear from these results that a significant fraction of the molecules leave a given interfacial layer within the 15 ps interval displayed and that, as time progresses, the difference in mobility 6311



Figure 9. Water MSDs in the three regions of the w0 = 7.5 RM. The MSDs calculated for molecules that are tagged according to their initial position (dashed lines) are compared to MSDs of molecules that remain in the region over the entire time interval (full lines). The bulk water MSD is included as a dasheddotted line.

ARTICLE

Figure 10. P2 orientational relaxation of the unit vector along the OH bond in different regions within the w0 = 7.5 RM. The results for bulk water are also shown.

between the molecules that remain in a given layer and all of the molecules that were there initially grows. However, regardless of the way that the MSD in a given region is defined, the difference in water mobility by region persists over a fairly long time interval, as shown in Figure 9. The MSD for bulk water32 is also shown in Figure 9. Because it corresponds to unrestricted motion, it is more properly compared to the MSDs of molecules that are tagged initially according to interfacial region. As can be seen from the figure, water translational mobility in the core region is somewhat lower than that in the bulk, even for the w0 = 7.5 RM. Hummer89 has developed a method to extract diffusion tensor and free-energy interfacial profiles from the analysis of MD trajectories. Given that our results show that diffusivity in RMs varies according to the distance from the surfactant head groups, this approach, which has been applied to a fluid confined in a slit pore,90 might provide an effective way of further analyzing the MD results on translational diffusivity of water confined within RM aggregates.

water molecules that solvate several surfactant hydrogen-bonding sites and sodium counterions. We then examine how the orientational relaxation of different vectors embedded in a water molecule is affected by the heterogeneous environment. Finally, we look into the reorientation mechanism for interfacial water. Orientational relaxation is usually quantified in terms of orientational time correlation functions (TCFs). Most often, these are formulated in terms of reorientation of a unit vector ^ ux in the molecular CM frame

5. WATER ORIENTATIONAL RELAXATION Unlike in the case of the translational MSDs, we consider the orientational time correlation functions of water in the laboratory frame. We do that not only for the sake of simplicity but also because water orientational relaxation measured experimentally corresponds to the laboratory frame result and contains a small contribution from the rotational motion of the RM as a whole. Several aspects of orientational relaxation of the water OH vector in model AOT RMs of different size have already been reported in ref 60, in which time-resolved IR response of HOD dilute in the RM water pool was modeled. In agreement with experiments, it was found that the OH rotational relaxation rate increases with increasing RM size. It was also found that in the RM size range of w0= 2.07.5, the relaxation rate in a given interfacial layer is w0-dependent, increasing with increasing RM size. Here, we focus on several aspects of water orientational relaxation that expand upon this earlier study. First, we examine how the heterogeneous nature of the RM environment affects water orientational dynamics by investigating the behavior of

where ûOH is a unit vector along the molecular OH bond. TCFs of unit vectors along molecular principal axes of inertia are also of interest, although they are not quite as readily experimentally accessible. In addition to Cl,OH(t), we consider here also the molecular dipole TCF

Cl, x ðtÞ ¼ ÆPl ½ûx ð0Þ 3 ûx ðtÞæ

ð23Þ

where Pl is the Legendre polynomial of order l. C1,x(t) and C2,x(t) are the TCFs that are the easiest to access experimentally.91 In the case of water in RMs, the TCF associated with the anisotropy decay of the OD stretch of HOD has served as the main probe of water reorientation in recent experimental studies.17,2026,92 This TCF can be approximated by C2, OH ðtÞ ¼ ÆP2 ½ûOH ð0Þ 3 ûOH ðtÞæ

Cl, μ ðtÞ ¼ ÆPl ½ûμ ð0Þ 3 ûμ ðtÞæ

ð24Þ

ð25Þ

given that the dipole or C2-axis is most interesting in terms of molecular symmetry and iondipole interactions, which influence water rearrangements in cation solvation shells. We start by displaying some of the basic properties of C2,OH(t) in the interfacial shells, shown in Figure 10. C2,OH(t) for bulk water is also shown. In calculating the TCF for water in a given layer, we consider the molecules that are in this layer at t = 0. As can be seen from the figure, there is strong dependence of the C2,OH(t) relaxation rate on the distance of water from the surfactant interface. The slowdown is quite pronounced in the two outermost layers, while the relaxation in the core becomes more rapid, approaching the bulk water rate. It is also worth noting that the deviations from exponential decay become 6312



ARTICLE

Figure 11. Molecular structure of the AOT surfactant. The arrows show the sites on the anion for which the orientational TCFs of the solvation shell water molecules were calculated.

Figure 13. Orientational relaxation of water molecules that remain continuously in the Naþ solvation shells. Depicted are the P2 TCFs for the dipole and OH vectors for molecules in all three RM sizes.

Figure 12. Orientational TCFs of the OH vector for water in solvation shells of several surfactant sites and for all of the water molecules in the interfacial region. Water molecules that remain continuosly in the specified environment are considered.

more pronounced closer to the interface. This is a likely consequence of the heterogeneity of the local environment. The local environment is heterogeneous due to the presence of the surfactant and Naþ counterions. We explore how orientational relaxation of water is influenced by its proximity to surfactant hydrophilic sites and counterions. In the case of the surfactant, we target sulfonate and carbonyl oxygens, all of which make hydrogen bonds with water. Figure 11 illustrates the AOT sites whose solvation shells we consider. Figure 12 illustrates the relaxation rates of interfacial water molecules located in the proximity of different AOT H-bondacceptor sites and in the Naþ coordination shell. The results for the w0 = 5.1 RM are displayed. The results for the other two RM sizes exhibit similar effects of surfactant-site proximity. As can be seen from the figure, water molecules relax at different rates in different interfacial solvation shells, with fastest relaxation for molecules coordinated to Naþ and slowest relaxation for molecules coordinated to the distal carbonyl oxygen. The relaxation rate for all interfacial molecules is somewhat faster than that for the molecules coordinated to the surfactant species. As Figure 4 illustrates, the enhanced density region of the water intrinsic density profile is in its inward portion, where some of the water molecules will have water nearest neighbors. Among the surfactant sites, the most abundant hydrophilic sites are sulfonate

oxygens, and as shown in ref 60, a significant fraction of interfacial water molecules is H-bonded to sulfonate oxygens. The fact that slowest relaxation is observed for the distal carbonyl solvation shell is related to the fact that water molecules in this location are deeply embedded in the surfactant layer and therefore effectively trapped among low-mobility surfactant molecules. Perhaps the most surprising is the relatively fast relaxation of water coordinated to Naþ. Unlike water coordinated to the surfactant anion oxygen sites, molecules next to Naþ are held mainly by iondipole forces that would allow the bond vectors to “wobble” around a fixed dipole orientation without changing the iondipole force. Thus, we would expect that the orientations of dipoles of molecules in the Naþ solvation shell would relax more slowly than the OH vector orientations. As the results presented in Figure 13 illustrate, this is indeed the case. As can be seen from this figure, C2,OH(t) decays considerably faster than C2,μ(t) for molecules that are in the Naþ solvation shell. This figure also illustrates that, even for molecules in the same coordination environment, there is a considerable difference in the orientational relaxation rate in RMs with different water contents. We find the same trend of faster relaxation as that for w0 for molecules coordinated to all of the surfactant species depicted in Figure 12, as well as for the whole interfacial region. The latter result has been reported by Pieniazek et al.60 The trend of faster relaxation in the interfacial region as w0 increases is a consequence of the increased surface area per surfactant head group87 as w0 increases. This means that the interfacial region contains a progressively lower concentration of surfactant and counterion species as w0 increases. Figure 13 shows that water orientational relaxation is anisotropic, at least in the Naþ solvation shells. Different relaxation rates of different vectors defining water orientation are also seen in the bulk liquid.93,94 The extent of anisotropy is l-dependent, as was pointed out by Svishchev and Kusalik93 in the case of the three principal axes of bulk water. As it turns out, the extent of anisotropy in RMs also varies with the location of water molecules relative to the interface. We illustrate this in Figure 14, in which Cl,x(t) for l = 1, 2 and x = OH, μ are depicted for the core and interfacial regions of the w0 = 7.5 RM. As can be seen from this figure, for both l = 1 and 2, Cl,μ(t) experiences a larger slowdown at the interface than does Cl,OH(t). 6313



ARTICLE

Figure 15. A plot of ln Cl,x(t)/[l(l þ 1)] of water for x = OH and μ in the interfacial region (based on the initial location) of the w0 = 7.5 RM.

Figure 14. P1 (top) and P2 (bottom) orientational TCFs of water OH and dipole unit vectors in the interfacial and core regions (based on initial locations) of the w0 = 7.5 RM.

The result is that C1,μ(t), which in the core decays at about the same rate as C1,OH(t), at the interface decays considerably more slowly than the OH vector TCF. The situation is somewhat different for the l = 2 TCFs. In this case C2,μ(t) goes from relaxing considerably faster than C2,OH(t) in the bulk-like core to decaying slightly more slowly than this TCF at the interface. The l dependence of rotational relaxation is related to the reorientation mechanism.95,96 If reorientation occurs by a series of small-angle steps, the angular motion is diffusive. In this case, the quantity that governs the relaxation rate is the rotational diffusion tensor. If the molecule is approximately a spherical rotor, the tensor effectively becomes a scalar Dr, and the decay rate beyond the inertial and librational time scales is Cl, x ðtÞ exp½lðl þ 1ÞDr t

ð26Þ

. This model would predict that ln Cl,x(t)/[l(l þ 1)] is l-independent. However, for many small-molecule liquids, this behavior is not observed.96 In the case of high-torque liquids, ln Cl,x(t)/[l(l þ 1)] decays more slowly as l increases.96 Water is an example of a liquid of this type.97 Water molecules in the bulk reorient by switching H-bond partners, which involves largeangle jumps, and by H-bond network rearrangements.97 The l dependence of the resulting decay rate is well described by a modified jump-diffusion model Cl, OH ðtÞ expðt=τl Þ

ð27Þ

where

1 1 sin½ðl þ 1=2ÞΔθ ¼ 1 ð28Þ þ lðl þ 1ÞDframe r τl τjump ð2l þ 1Þ sinðΔθ=2Þ

Here, Δθ is the jump angle, 1/τjump the jump rate, and Dframe the r rotational diffusion constant of H-bonded molecular pairs.

Although in the interfacial RM region Cl,x does not decay exponentially, the l dependence of its decay would still be indicative of the applicability of the jump-diffusion mechanism. Figure 15 illustrates the behavior of ln Cl,x(t)/[l(l þ 1)] for the OH and dipole vectors. It shows that the decay is clearly l-dependent, with a slower decay rate at higher l, indicative of the jump mechanism. However, the l dependence is considerably stronger for the OH vector than that for the dipole. Although the same trend is seen in the core (cf. Figure 14), it is more pronounced at the interface. This is consistent with the fact that dipole reorientation at the interface is more strongly influenced by the presence of the Naþ ions, which are expected to disrupt the water H-bond network. As a result of this, the H-bond switching mechanism can be expected to apply to a smaller fraction of the interfacial than core region water molecules.

6. SUMMARY AND CONCLUSIONS Translational and rotational mobilities of water molecules in water/AOT/isooctane RMs of varying water content were investigated using MD simulations. We summarize here our main findings. Water stays trapped within the RM over time scales long compared to the scale considered in our simulations. Thus, at long times, its translational diffusion rate is that of the surfactant aggregate. We found that water translational mobility within the RM is, to a very good approximation, decoupled from translational diffusion of the aggregate. Water mobility is limited by the RM size and strongly influenced by the presence of the hydrophilic interface. We have investigated the applicability to water translational MSDs of two models of diffusion in confined geometries, that of free diffusion in a sphere76,77 and Gaussian confinement.78 We found that the first model does not predict well the functional form of the time dependence of the MSD and underestimates the size of the water pool. The Gaussian confinement model could predict well the MSD over the entire time interval considered, provided that a biexponential form of the time correlation of molecular positions was assumed. It also led to a reasonable estimate of the w0 dependence of the effective diffusion coefficient and of the size of the confining region. The success of this model supports a physical picture of a diffusion coefficient that is dependent on the distance from the interface. 6314


The Journal of Physical Chemistry A Our results on MSDs in different interfacial layers also provide support for this physical picture. Water mobility in different interfacial regions was studied by assigning molecules to these regions according to the structural features of the water intrinsic density profile. The times that the molecules spend in different regions were quantified in terms of survival TCFs and their translational and rotational mobilities in terms of MSDs and orientational TCFs, respectively. We find that molecular mobilities are strongly suppressed in the interfacial region and approach their bulk-like values at distances greater than about 9 Å from the surfactant head groups. In the w0 = 2.0 RM, this inner core is absent; therefore, water mobility is suppressed in the entire droplet, as has been concluded in the case of rotational mobility from analysis of time-resolved IR anisotropy data.23 We also find that in a given interfacial layer, water translational mobility increases with increasing w0 as a consequence of decreased interfacial curvature and increased area per surfactant head group,87 the same trend seen earlier for rotational mobility in our model60 as well as in a reduced representation of this system.53 We have investigated how confinement in RMs affects the anisotropy of water reorientation by comparing the TCFs for reorientation of the OH and dipole vectors. We found that the dipole reorientation rate is more strongly affected by the proximity to the interface and showed that suppression of dipole reorientation of molecules coordinated to the Naþ counterion is chiefly responsible for this. We have also examined how coordination to surfactant H-bond-acceptor sites affects water reorientation. This indicates that water molecules orient at different rates when coordinated to sulfonate and to the two distinct carbonyl oxygen sites. IR spectra of AOT sulfonate15 and carbonyls98 have been studied experimentally as a function of w0. It would be interesting to find out through time-resolved IR techniques how the motion of nearby water affects IR absorption in these spectral regions. For the OH and dipole reorientation, we have investigated the reorientation mechanism by examining the dependence of the reorientation rate on the Legendre polynomial order l of the orientational displacement. We found that Cl,μ(t) exhibits weaker l dependence than Cl,OH(t) in the interfacial region, suggesting that the disruption of the H-bond network due to water coordination to Naþ has a greater effect on the dipole than on the OH reorientation mechanism. The latter appears to still be strongly influenced by jumps between H-bonded conformations, the main mechanism for water reorientation in the bulk.97 Further work is needed to clarify this aspect of water reorientation at ionic surfactant interfaces.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Present Addresses †

Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, IL 60637. E-mail: janamejaya.chowdhary@ gmail.com.

’ ACKNOWLEDGMENT This work was supported by the NSF Grants CHE 0608640 and CHE 0911668.

ARTICLE

’ REFERENCES (1) Zulauf, M.; Eicke, H. F. J. Phys. Chem. 1979, 83, 480. (2) Pileni, M. P. J. Phys. Chem. 1993, 97, 6961. (3) Pileni, M. P.; Ninham, B. W.; Gulik-Krzywicki, T.; Tanori, J.; Lisiecki, I.; Filankembo, A. Adv. Mater. 1999, 11, 1358. (4) Eastoe, J.; Hollamby, M. J.; Hudson, L. Adv. Colloid Interface Sci. 2006, 128, 5. (5) Luisi, P. L.; Giomini, M.; Pileni, M. P.; Robinson, B. H. Biochim. Biophys. Acta 1988, 947, 209. (6) Jones, M. N.; Chapman, D. Micelles, Monolayers, and Biomembranes; Wiley: New York, 1995. (7) Holmberg, K. Curr. Opin. Colloid Interface Sci. 2003, 8, 187. (8) Levinger, N. E.; Swafford, L. A. Annu. Rev. Phys. Chem. 2009, 60, 385. (9) Ladanyi, B. M. Properties of Nanoconfined Water. In Water and Life: The Unique Properties of H2O; Lynden-Bell, R. M., Conwey-Morris, S., Barrow, J. D., Finney, J. L., Harper, C., Eds.; CRC Press: Boca Raton, FL, 2010. (10) Fayer, M. D.; Levinger, N. E. Analysis of Water in Confined Geometries and at Interfaces. In Annual Review of Analytical Chemistry; Annual Reviews: Palo Alto, CA, 2010; Vol. 3; p 89. (11) Wong, M.; Thomas, J. K.; Nowak, T. J. Am. Chem. Soc. 1977, 99, 4730. (12) Carlstr€om, G.; Halle, B. Langmuir 1988, 4, 1346. (13) Carlstr€om, G.; Halle, B. J. Phys. Chem. 1989, 93, 3287. (14) Onori, G.; Santucci, A. J. Phys. Chem. 1993, 97, 5430. (15) Freda, M.; Onori, G.; Paciaroni, A.; Santucci, A. J. Mol. Liq. 2002, 101, 55. (16) Fioretto, D.; Freda, M.; Mannaioli, S.; Onori, G.; Santucci, A. J. Phys. Chem. B 1999, 103, 2631. (17) Piletic, I. R.; Tan, H. S.; Fayer, M. D. J. Phys. Chem. B 2005, 109, 21273. (18) Tan, H. S.; Piletic, I. R.; Fayer, M. D. J. Chem. Phys. 2005, 122, 174501. (19) Tan, H. S.; Piletic, I. R.; Riter, R. E.; Levinger, N. E.; Fayer, M. D. Phys. Rev. Lett. 2005, 94, 057405. (20) Piletic, I. R.; Moilanen, D. E.; Spry, D. B.; Levinger, N. E.; Fayer, M. D. J. Phys. Chem. A 2006, 110, 10369. (21) Moilanen, D. E.; Levinger, N. E.; Spry, D. B.; Fayer, M. D. J. Am. Chem. Soc. 2007, 129, 14311. (22) Park, S.; Moilanen, D. E.; Fayer, M. D. J. Phys. Chem. B 2008, 112, 5279. (23) Moilanen, D. E.; Fenn, E. E.; Wong, D.; Fayer, M. D. J. Chem. Phys. 2009, 131, 014704. (24) Moilanen, D. E.; Fenn, E. E.; Wong, D.; Fayer, M. D. J. Phys. Chem. B 2009, 113, 8560. (25) Dokter, A. M.; Woutersen, S.; Bakker, H. J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 15355. (26) Dokter, A. M.; Woutersen, S.; Bakker, H. J. J. Chem. Phys. 2007, 126, 124507. (27) Cringus, D.; Lindner, J.; Milder, M. T. W.; Pshenichnikov, M. S.; V€ohringer, P.; Wiersma, D. A. Chem. Phys. Lett. 2005, 408, 162. (28) D’Angelo, M.; Fioretto, D.; Onori, G.; Palmieri, L.; Santucci, A. Phys. Rev. E 1996, 54, 993. (29) Fioretto, D.; Freda, M.; Onori, G.; Santucci, A. J. Phys. Chem. B 1999, 103, 8216. (30) Freda, M.; Onori, G.; Paciaroni, A.; Santucci, A. J. Non-Cryst. Solids 2002, 307, 874. (31) Venables, D. S.; Huang, K.; Schmuttenmaer, C. A. J. Phys. Chem. B 2001, 105, 9132. (32) Harpham, M. R.; Ladanyi, B. M.; Levinger, N. E.; Herwig, K. W. J. Chem. Phys. 2004, 121, 7855. (33) Riter, R. E.; Undiks, E. P.; Levinger, N. E. J. Am. Chem. Soc. 1998, 120, 6062. (34) Riter, R. E.; Willard, D. M.; Levinger, N. E. J. Phys. Chem. B 1998, 102, 2705. 6315


The Journal of Physical Chemistry A (35) Willard, D. M.; Riter, R. E.; Levinger, N. E. J. Am. Chem. Soc. 1998, 120, 4151. (36) Zhong, Q.; Baronavski, A. P.; Owrutsky, J. C. J. Chem. Phys. 2003, 119, 9171. (37) Sando, G. M.; Dahl, K.; Owrutsky, J. C. J. Phys. Chem. A 2004, 108, 11209. (38) Sando, G. M.; Dahl, K.; Owrutsky, J. C. J. Phys. Chem. B 2005, 109, 4084. (39) Owrutsky, J. C.; Pomfret, M. B.; Barton, D. J.; Kidwell, D. A. J. Chem. Phys. 2008, 129, 10. (40) Maitra, A. Colloids Surf. 1988, 32, 149. (41) Zhang, J.; Bright, F. V. J. Phys. Chem. 1991, 95, 7900. (42) Wittouck, N.; Negri, R. M.; Ameloot, M.; Deschryver, F. C. J. Am. Chem. Soc. 1994, 116, 10601. (43) Dutt, G. B. J. Phys. Chem. B 2008, 112, 7220. (44) Kenez, P. H.; Carlstroem, G.; Furo, I.; Halle, B. J. Phys. Chem. 1992, 96, 9524. (45) Brown, D.; Clarke, J. H. R. J. Phys. Chem. 1988, 92, 2881. (46) Senapati, S.; Berkowitz, M. L. J. Chem. Phys. 2003, 118, 1937. (47) Senapati, S.; Berkowitz, M. L. J. Phys. Chem. B 2003, 107, 12906. (48) Senapati, S.; Berkowitz, M. L. J. Phys. Chem. A 2004, 108, 9768. (49) Linse, P. J. Chem. Phys. 1989, 90, 4992. (50) Linse, P.; Halle, B. Mol. Phys. 1989, 67, 537. (51) Tobias, D. J.; Klein, M. L. J. Phys. Chem. 1996, 100, 6637. (52) Griffiths, J. A.; Heyes, D. M. Langmuir 1996, 12, 2418. (53) Faeder, J.; Ladanyi, B. M. J. Phys. Chem. B 2000, 104, 1033. (54) Faeder, J.; Albert, M. V.; Ladanyi, B. M. Langmuir 2003, 19, 2514. (55) Mudzhikova, G. V.; Brodskaya, E. N. Colloid J. 2006, 68, 729. (56) Mudzhikova, G. V.; Brodskaya, E. N. Colloid J. 2006, 68, 738. (57) Mudzhikova, G. V.; Brodskaya, E. N. Colloid J. 2009, 71, 803. (58) Abel, S.; Sterpone, F.; Bandyopadhyay, S.; Marchi, M. J. Phys. Chem. B 2004, 108, 19458. (59) Chowdhary, J.; Ladanyi, B. M. J. Phys. Chem. B 2009, 113, 15029. (60) Pieniazek, P. A.; Lin, Y. S.; Chowdhary, J.; Ladanyi, B. M.; Skinner, J. L. J. Phys. Chem. B 2009, 113, 15017. (61) Rosenfeld, D. E.; Schmuttenmaer, C. A. J. Phys. Chem. B 2006, 110, 14304. (62) Abel, S.; Waks, M.; Marchi, M.; Urbach, W. Langmuir 2006, 22, 9112. (63) Nave, S.; Eastoe, J.; Heenan, R. K.; Steytler, D.; Grillo, I. Langmuir 2000, 16, 8741. (64) De, T.; Maitra, A. Adv. Colloid Interface Sci. 1995, 59, 95. (65) Nave, S.; Eastoe, J.; Penfold, J. Langmuir 2000, 16, 8733. (66) Boyd, J. E.; Briskman, A.; Colvin, V. L.; Mittleman, D. M. Phys. Rev. Lett. 2001, 87, 147401. (67) Freda, M.; Onori, G.; Paciaroni, A.; Santucci, A. Chem. Phys. Lett. 2001, 348, 311. (68) Boyd, J. E.; Briskman, A.; Sayes, C. M.; Mittleman, D.; Colvin, V. J. Phys. Chem. B 2002, 106, 6346. (69) Kinugasa, T.; Kondo, A.; Nishimura, S.; Miyauchi, Y.; Nishii, Y.; Watanabe, K.; Takeuchi, H. Colloids Surf., A 2002, 204, 193. (70) Freda, M.; Onori, G.; Paciaroni, A.; Santucci, A. Phys. Rev. E 2003, 68, 021406. (71) Harpham, M. R.; Ladanyi, B. M.; Levinger, N. E. J. Phys. Chem. B 2005, 109, 16891. (72) Faeder, J.; Ladanyi, B. M. J. Phys. Chem. B 2005, 109, 6732. (73) Thompson, W. H. J. Chem. Phys. 2004, 120, 8125. (74) Li, S. M.; Thompson, W. H. J. Phys. Chem. B 2005, 109, 4941. (75) Thompson, W. H. J. Phys. Chem. B 2005, 109, 18201. (76) Neuman, C. H. J. Chem. Phys. 1974, 60, 4508. (77) Volino, F.; Dianoux, A. J. Mol. Phys. 1980, 41, 271. (78) Volino, F.; Perrin, J. C.; Lyonnard, S. J. Phys. Chem. B 2006, 110, 11217. (79) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford: New York, 1987.

ARTICLE

(80) Berendsen, H. J. C.; Postma, J. P. M.; Vangunsteren, W. F.; Dinola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684. (81) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (82) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1999, 103, 4508. (83) Kamath, G.; Robinson, J.; Potoff, J. J. Fluid Phase Equilib. 2006, 240, 46. (84) Schlenkrich, M.; Brickmann, J.; Mackerell, A. D., Jr.; Karplus, M. An empirical potential energy function for phospholipids: criteria for parameter optimization and applications. In Biological Membranes: A Molecular Perspective from Computation and Experiment; Merz, K. M., Jr., Roux, B., Eds.; Birkhaeuser: Darmstadt, Germany, 1996; p 31. (85) Schweighofer, K. J.; Essmann, U.; Berkowitz, M. J. Phys. Chem. B 1997, 101, 3793. (86) Handbook of Mathematical Functions; Abramowitz, M.; Stegun, I. A., Eds.; Dover: New York, 1965. (87) Eicke, H. F.; Rehak, J. Helv. Chim. Acta 1976, 59, 2883. (88) Pinnick, E. R.; Erramilli, S.; Wang, F. Mol. Phys. 2010, 108, 2027. (89) Hummer, G. New J. Phys. 2005, 7, 34. (90) Mittal, J.; Truskett, T. M.; Errington, J. R.; Hummer, G. Phys. Rev. Lett. 2008, 100, 145901. (91) McHale, J. L. Molecular Spectroscopy; Prentice Hall: Upper Saddle River, NJ, 1999. (92) Moilanen, D. E.; Fenn, E. E.; Wong, D.; Fayer, M. D. J. Am. Chem. Soc. 2009, 131, 8318. (93) Svishchev, I. M.; Kusalik, P. G. J. Phys. Chem. 1994, 98, 728. (94) Ropp, J.; Lawrence, C.; Farrar, T. C.; Skinner, J. L. J. Am. Chem. Soc. 2001, 123, 8047. (95) Berne, B. J.; Pecora, R. Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics; Wiley-Interscience: New York, 1975. (96) Lynden-Bell, R. M.; Steele, W. A. J. Phys. Chem. 1984, 88, 6514. (97) Laage, D.; Hynes, J. T. Science 2006, 311, 832. (98) Zhou, G. W.; Li, G. Z.; Chen, W. J. Langmuir 2002, 18, 4566.

6316


Molecular Simulation Study of Water Mobility in Aerosol-OT Reverse

Recommend Documents