Hydration Layer of a Cationic Micelle, C10TAB: Structure

J. Phys. Chem. B 2005, 109, 12879-12890

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Hydration Layer of a Cationic Micelle, C10TAB: Structure, Rigidity, Slow Reorientation, Hydrogen Bond Lifetime, and Solvation Dynamics Subrata Pal,† Biman Bagchi,*,† and Sundaram Balasubramanian*,‡ Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India, and Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for AdVanced Scientific Research, Jakkur, Bangalore 560064, India ReceiVed: March 3, 2005; In Final Form: May 4, 2005

We report a theoretical study of the structure and dynamics of the water layer (the hydration layer) present at the surface of the cationic micelle decyltrimethylammonium bromide (DeTAB) by using atomistic molecular dynamics simulations. The simulated micelle consisted of 47 surfactant molecules (and an equal number of bromide ions), in good agreement with the pioneering light scattering experiments by Debye which found an aggregation number of 50. In this micelle, three partially positively charged methyl groups of each surfactant headgroup face the surrounding water. The nature of the cationic micellar surface is found to play an important role in determining the arrangement of water which is quite different from that in the bulk or on the surface of an anionic micelle, like cesium perfluorooctanoate. Water molecules present in the hydration layer are found to be preferentially distributed in the region between the three partially charged methyl headgroups. It is found that both the translational and rotational motions of water exhibit appreciably slower dynamics in the layer than those in the bulk. The solvation time correlation function (TCF) of bromide ions exhibits a long time component which is found to originate primarily from the interaction of the probe with the micellar headgroups. Thus, the decay of the solvation TCF is controlled largely by the residence time of the probe in the surface. The residence time distribution of the water molecules also exhibits a slow time component. We also calculate the collective number density fluctuation in the layer and find a prominent slow component compared to the similar quantity in the bulk. This slow component demonstrates that water structure in the hydration layer is more rigid than that in the bulk. These results demonstrate that the slow dynamics of hydration layer water is generic to macromolecular surfaces of either polarity.

1. Introduction Self-organized molecular assemblies play a crucial role in many natural and biological processes.1 Nanostructures formed by self-assembly are of fundamental importance in drug delivery, molecular recognition, and many other processes.2 Surfactants with polar headgroups and long hydrocarbon tails aggregate in water to form micelles. While water is essential for the formation and stability of the micelles, water molecules present at the interface of micelles, proteins, DNA, and other macromolecular entities show interesting and diverse structures and dynamics that are different from their behavior in the bulk. A complete understanding of these aqueous solutions crucially depends not only on their time-averaged structure but also on the dynamical properties of the hydration layer. Interfacial water molecules are influenced by and influence the shape fluctuations of micelles and the side chain motions of proteins.3-7 An important factor in determining this relationship between the macromolecule and water is the charge on the macromolecular surface. Several workers have studied this problem. Richmond and coworkers have employed vibrational sum frequency studies to examine the orientation of water molecules near charged phospholipid monolayers.10 Vieceli and Benjamin have examined the same issue on chlorine terminated self-assembled * To whom correspondence should be addressed. E-mail: bbagchi@ sscu.iisc.ernet.in (B.B.); [email protected] (S.B.). † Indian Institute of Science. ‡ Jawaharlal Nehru Centre for Advanced Scientific Research.

monolayers and showed that both the dipole vector and the O-H vector of surface water molecules were present in the same plane with respect to the surface normal.11 More recently, Kuo and Mundy reported ab initio molecular dynamics (MD) results on the water/air interface at which both single-donor and acceptoronly species were observed.12 Further, water molecules around an anionic micelle such as sodium dodecyl sulfate (SDS)8 or cesium perfluorooctanoate (CsPFO)9 orient themselves in such a manner as to expose their hydrogen atoms to the surface, enabling the formation of water-headgroup hydrogen bonds. The strength of such hydrogen bonds regulates the phase behavior of aqueous surfactant solutions. Unlike simple micelles which possess polar headgroups of the same kind, the surface of a complex macromolecule such as a protein could be quite different, as the surface offers heterogeneity not only in geometry but also in the sign of the charge locally. To understand the behavior of water near such surfaces which possess variety, one should characterize interfacial water on standard surfaces such as micellar solutions of one kind or the other.13,14 The solvation dynamics study of a newly created ion or a dipole in polar liquids is now a well established method for obtaining molecular level information about the response of solvent molecules (to which both orientational and translational motions contribute) around the probe.15-19 The uniqueness of solvation dynamics as a probe is that it allows, at least partly, for discrimination between the local and global contributions.

10.1021/jp0510793 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/14/2005

12880 J. Phys. Chem. B, Vol. 109, No. 26, 2005 Usually, the contribution by the nearest-neighbor molecules decays at a considerably slower rate than the collective contribution made by all the solvent molecules. This is particularly true for water, where the bulk contribution decays at a time scale of sub-50 fs,20 while the contribution of the nearest-neighbor molecules decays at a rate that can be slower than 1 ps. This separation is expected to be particularly significant if the translational contribution of the solvent molecules is much slower than the rotational part. The success of the solvation dynamics technique in bulk water motivated many such studies on complex systems where water is an important ingredient.21-23 Several important experiments have been carried out to study the solvation dynamics of proteins where the probe is on the surface or buried in the core, thus studying the hydration layer or buried water dynamics, respectively. These experiments have repeatedly found a signature of a slow component which is at least an order of magnitude slower than solvation time in bulk.2,17,24,25 Solvation dynamics in micelles of different surfactants have been studied both experimentally22,23,26-28 and by computer simulations.8,29-32 Experimentally, one often uses the probes Coumarin 480 (C480) and red 4-aminophthalimide (4-AP) because the emission properties of these probes in the micelle are very different from those in bulk water. Sarkar et al.33 and Datta et al.34 studied the solvation dynamics of C480 and 4-AP, respectively, in neutral (TX-100), cationic (CTAB), and anionic (SDS) micelles. It is observed that for SDS, CTAB, and TX100 the average solvation times are respectively 180, 470, and 1450 ps for C48033 and 80, 270, and 720 ps for 4-AP.34 Thus, the solvation dynamics in the Stern layer of a micelle could be 2 orders of magnitude slower than that in bulk water. Vajda et al.21 studied the solvation dynamics of C460 and C480 probes in pure water and also in the cyclodextrin cavity. They found that the solvation dynamics of the probe within the cavity slows down substantially in the long time. This slow is attributed to the quenching of the translational motion of water molecules present in the cavity. Over the past few years, we have focused our attention on the study of interfacial water around the anionic micelle CsPFO. Our results on this system can be summarized as follows. This surfactant contains a carboxylate headgroup whose oxygen atoms can behave as acceptors of hydrogen bonds from neighboring water molecules. Depending on the local geometry, such waters can form two, one, or no hydrogen bonds with the surfactant headgroups. The number of such special hydrogen bonds that an interfacial water molecule possesses determines its character and concentration.9 The higher strength of the water-headgroup hydrogen bonds relative to water-water hydrogen bonds makes the translational and rotational dynamics of the interfacial water slower compared to bulk water. Collective properties of such solutions such as the solvation dynamics of ionic solutes and dielectric relaxation too exhibit signatures of slow dynamics, as a consequence.29,30,35-39 Experiments and simulations performed over the past decade have contributed to our understanding in this area, and a general picture of the processes involved is beginning to emerge now. Recently, a phenomenological model has been proposed, namely, the dynamic exchange model (DEM), which attempts to explain the observed slow dielectric relaxation of aqueous protein solutions.40 The model envisages the existence of interfacial water molecules in two different states: one bound and the other free. The former were assumed to form hydrogen bonds with the hydrophilic groups on the macromolecule, whereas the latter retain their bulk characteristics. They

Pal et al.

Figure 1. (a) Schematic representation of the model surfactant molecule decyltrimethylammonium bromide (DeTAB) with atom labels. (b) Snapshot of the simulated micelle. The red and blue spheres denote the methyl group and nitrogen atom of the headgroup, respectively. The green spheres represent methylene groups along the chain, while the yellow spheres, bromide ions. Water molecules present in the solution are not shown for clarity.

interpreted the dielectric relaxation spectra in terms of a dynamical equilibrium between these two states of water. The slow time constant that emerges is essentially the time constant of transition from the bound water to the free state of water. Thus, the DEM is critically dependent on the assumption of the presence of bound and free water molecules in the layer.40 As discussed earlier, one needs to examine the role of the sign of the charge on the micellar surface in the slow dynamics of interfacial water molecules. This is necessary for its own sake as well as to understand and interpret the structure and dynamics of water present in the hydration layer of proteins containing polar residues and of nucleotides in water. We undertake such a study here. In an exercise to study the behavior of interfacial water in a contrasting environment, we describe here a molecular dynamics (MD) investigation of an aqueous solution of a cationic micelle. The cationic micelle we study is decyltrimethylammonium bromide (DeTAB), C10TAB. This is a homologue of the more common cationic micelle cetyltrimethylammonium bromide (C16TAB). The organization of the paper is as follows. In the next section, we present the details of the system and the details of the MD simulations. Section 3 presents the structural details of the micellar solution, while section 4 contains a description of the dynamics of water molecules near the micellar surface. We close the paper with a few conclusions in section 5. 2. Details of Simulation As mentioned earlier, the surfactant in our simulations is decyltrimethylammonium bromide. A schematic figure is provided in Figure 1a to describe the connectivity of the molecule. The model for the surfactant employs united atom methyl groups that surround the central nitrogen atom in the headgroup. The carbon atom which is adjacent to the nitrogen in the surfactant tail is denoted as CT. CT and the methyl groups in the headgroup each carry a +0.25e charge, while the central nitrogen atom is neutral. Overall charge neutrality of the solution

Hydration Layer of the Cationic Micelle C10TAB

J. Phys. Chem. B, Vol. 109, No. 26, 2005 12881

TABLE 1: Potential Parameters of the Surfactant Molecule and Bromide Iona atom/group

σ (Å)

(K)

charge (e)

CH3 (head) N CT CH2 CH3 (tail) Br

3.96 3.25 3.96 3.93 3.93 4.62

72.97 85.55 72.97 47.00 113.98 45.29

0.25 0 0.25 0 0 -1.0

a σ and correspond to parameters in the standard Lennard-Jones potential. Interaction parameters between any two different atoms/ groups are taken according to the Lorentz-Berthelot rule. The potential is the same as that reported in ref 41.

is achieved by the unit negative charge on each bromide ion that is present in the aqueous phase. The methylene groups and the end methyl group in the tail of the surfactant too were treated as united pseudo-atoms without the explicit presence of hydrogens. The potentials used to model the surfactant as well as its interaction with water have been proposed by Tarek, Tobias, and Klein41 in their work on CTAB bilayers. We provide the same in Table 1 for the sake of completeness. The model for water is the extended simple point charge (SPC/E) model, a rigid one.42 The simulated micelle consisted of 47 surfactant molecules and an equal number of bromide ions. Pioneering light scattering experiments by Debye43 and recent small angle neutron scattering44 and mass spectrometry experiments45 on decyltrimethylammonium bromide solutions have shown that the average molecular weight of the micelles is 10,500, a value which yields an aggregation number of 50. Our micelle, containing 47 amphiphiles is thus representative of the real system, in its size. Each surfactant molecule in our model contains 14 pseudoatoms. To form the initial configuration of the micelle, individual amphiphiles were carefully arranged such that their headgroups were located on the surface of a sphere. Molecular dynamics simulations of short durations were performed starting from this configuration, first with the headgroups fixed in space so as to relax the surfactant tails. These runs were followed by short runs which allowed for the dynamics of the headgroups, while the tail locations were constrained in space. These initial calculations which were carried out in a vacuum removed any artificial hard contacts between the surfactant molecules. The configuration was later soaked in a pre-equilibrated cubic box of water molecules. Water molecules which were within 3 Å of any atom of the surfactant were removed by examination. This procedure resulted in a micelle whose core did not contain any water molecule. The final configuration contained 5834 water molecules in a cubic box of edge length, 58.07 Å. Thus, the solute concentration in our work is 0.4M, which is above the critical micelle concentration (CMC) of DeTAB in water which is 0.067M.46,47 The calculations were performed at a temperature of 300K, using the PINY•MD package.48 The system was then equilibrated for 5 ns, and the micelle was observed to be stable. The micellar solution was simulated under constant temperature and pressure conditions initially, to obtain a simulation box that reproduces zero pressure conditions. Further equilibration and analyses runs were performed under constant temperature and volume conditions. In Figure 1b, we provide a snapshot of the micelle. The micelle is around 36 Å in diameter. Periodic boundary conditions were applied in all three directions. Thus there is a 20 Å thick water slab between the micelle and its closest periodic image, and intermicellar interactions will be negligible. The multiple time step, reference system propagator algorithm

Figure 2. Number density of different species in the DeTAB micellar solution as a function of radial distance from the center of mass of the micelle. Three of the data were multiplied by a factor of 16 (denoted by × 16 in the legend) so as to bring them into the same scale as the rest of the data.

(RESPA) method was used to integrate the equations of motion.49 An outer time step of 4 fs was employed to integrate the long-range nonbonded interactions. Temperature control was achieved using a Nose´-Hoover chain thermostat.50 Particle Mesh Ewald summation method was used to calculate the long-range interactions accurately. A MD trajectory of 9 ns duration was generated, during which atomic coordinates were saved every 1 ps. To compare the residence TCF of interfacial water in the micellar solution with that in bulk water, an independent MD simulation containing 2430 SPC/E water molecules was carried out at the same temperature and at a density of 1.02 g/cm3. Complex systems such as the micellar solution studied here exhibit a variety of dynamics at different time scales. For instance, a quantity such as the dielectric relaxation that exhibits relaxations with time constants of more than 100 ps could be calculated using a coarse time resolution of, say, 1 ps, while faster processes need to be captured with a higher time resolution. Thus, to calculate the reorientational dynamics of water in the micellar solution which shows a faster decay than dielectric relaxation, an analysis run of 900 ps duration was also performed during which the atomic coordinates were dumped every 100 fs. Further, to obtain the ultrafast component of the relaxation in several quantities, we performed MD runs in which the coordinates were saved every 16 fs for a trajectory length of 330 ps. 3. Results and Discussion We shall first discuss the structure of the hydration layer around the micelle. The structure has some unusual features which help in understanding features observed in dynamics. Of particular interest are the density profile of water, the counterions, and their pair correlation functions. We have divided the results and discussion into two parts, namely, structure and dynamics. 3.1. Structure and Energetics. 3.1.1. Density Profile near the Micellar Surface. A profile of the densities of various species in the micellar solution is shown in Figure 2. The densities are calculated for radial distances with respect to the instantaneous center of mass (COM) of the micelle. A note of caution is warranted before an examination of this figure. Such density profiles contain perforce one-dimensional information, and their interpretation needs to be performed with a knowledge of the shape of the micelle. As expected, the last carbon atom in the tail is found to be largely located in the central region of the micelle. The density of all carbon atoms irrespective of their location in the surfactant tail is also shown. There appears to

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Pal et al. TABLE 2: Specific Features of the Different Radial Distribution Functions

Figure 3. Radial distribution functions for (a) nitrogen-bromide ion, (b) methyl group-bromide ion, (c) methyl group-water oxygen, and (d) nitrogen-water oxygen pairs.

be a region (between 6 and 11 Å) where the density is uniform with a value which is close to the density of liquid n-decane at 300 K (0.72 g/cc). The distribution for the location of the CT atom is relatively narrow. Also, water is found to penetrate into the micelle up to the C2 atom. The bulk density of water (0.033 molecules/Å3) is retrieved beyond about 24 Å from the COM. The distributions of the location of the nitrogen atom and of the counterion, Br-, are found to be broad and peaked at around 16.5 and 19 Å, respectively, from the COM. Thus, the average separation between the uncharged nitrogen atom and counterion is just about 2.5 Å. The instantaneous nitrogen position defines the surface of the micelle in the calculations to be described later. 3.1.2. Pair Correlation Functions. A large fraction of the bromide ions are present near the surface of the micelle. This is manifested in the large peak value of the radial distribution functions, gCH3-Br(r) and gN-Br(r). In Figure 3, we show the different radial distribution functions, namely, (a) gN-Br(r), (b) gCH3-Br(r), (c) gCH3-WO(r), and (d) gN-WO(r). gN-Br(r) exhibits a peak around 4.75 Å, and the peak height of the same is around 8 due to the large fraction of the bromide ions present at the surface. It exhibits a minimum at 7.25 Å, which we consider as its first coordination shell. Counterions are also well structured near the surface which is clear from gCH3-Br(r). This could be due to the Coulombic interaction with the CH3 of the headgroup of the micelle. On average, nearly 57% of bromide ions are found to be within the first coordination shell around the central nitrogen atom. This coordination shell of the counterions around the micelle has generally been called the Stern layer.51 With respect to the nitrogen atom of the headgroup, the hydration shell is about 6.3 Å thick. This can be observed from gN-WO(r) which exhibits a peak at 4.5 Å with a first peak minimum at 6.3 Å. The coordination number is around 25. Such a large coordination number arises due to the large size of the methyl groups and the charged CT pseudo-atom which is essentially a methylene group. We thus define an interfacial water molecule as one that is within the first coordination of shell of a nitrogen atom of the micelle, that is, within a distance of 6.3 Å. On average, around 900 water molecules constitute the hydration layer. Table 2 lists specific features of various pair correlation functions. It is important to note that water molecules are structured around the CT atom also (the corresponding g(r) is not shown here). 3.1.3. Spatial Density Functions. The pair correlation function for methyl headgroups surrounding a central interfacial water molecule reveals a first coordination number of 1.35. Every water molecule present at the interface is coordinated on average

type

peak position (Å)

peak minimum (Å)

coordination number at peak minimum

CH3-Br N-Br CH3-WO N-WO

4.05 4.75 3.55 4.55

5.35 7.15 4.65 6.35

0.46 1.07 8.32 24.43

to 1.35 methyl groups. A pair correlation function, however informative, presents only a spherically averaged picture of the local environment. In a heterogeneous environment, it is crucial that such radial information be complemented by data on the orientational aspects of the coordination shell as well. A nice way of capturing this aspect is through atomic probability density maps. Such maps have been of immense help in understanding the structures of bulk fluids and of complex interfaces.41,52,53 The density map showing the locations of water molecules around a surfactant headgroup is shown in Figure 4a. We find that water molecules are preferentially found in locations that, on aVerage, resembles a triple-forked umbrella. Note that this arrangement is time and ensemble averaged and that not every point or branch of this map around a given surfactant need necessarily be occupied by a water molecule. However, such data are very informative and educative. They tell us that the water structure and penetration into the micelle is deep and anisotropic. More importantly, this picture provides us with a clear indication that the hydrogen bond network between interfacial water molecules is likely to be modified relative to that in bulk water. This will have profound implications on their dynamics. The lack of specific hydrogen bonding sites on the headgroups (at least within our interaction model) is likely to play a role in this interfacial water structure. Had the headgroups possessed hydrogen bonding sites (such as in CsPFO), water molecules would have preferred to form hydrogen bonds with them, and the extent of water penetration could be smaller. However, hydrogens of a methyl group are considerably less polar (and hence less capable to form hydrogen bonds) than the polar oxygen atoms of the carboxylate headgroup found in CsPFO. In CsPFO, one finds a regular tetrahedral arrangement of neighboring oxygen atoms (whether from other water molecules or from the headgroup) around a central interfacial water molecule. In DeTAB, water molecules are also found to be “buried” between surfactant headgroups, which could make their dynamics different than what has been found in the aqueous CsPFO solution. Apart from the water density around the headgroup of the surfactant, we have also calculated the densities of different species around a interfacial water molecule which are presented in the Figure 4b. The distribution of neighboring water molecules is similar to that seen in liquid water. The lobe corresponding to the acceptor hydrogen bond (i.e., beneath the interfacial water molecule, as shown in Figure 4b) is likely to arise from those water molecules which are present near the CT atom. The locations for the bromide ions coincide with that of water. Thus, its role could be seen as a “structure breaker”. The methyl groups envelop the central water molecule in a ring. A consequence of the larger penetration of water into the DeTAB micelle is the reduced water-water near-neighbor structure for interfacial water molecules. The corresponding pair correlation function (i.e., for water molecules surrounding an interfacial water molecule) is shown in Figure 5a. The figure shows the usual first neighbor peak at 2.75 Å. However, the first coordination number is reduced from a value of 4.3 seen in bulk water to about 3.75 in the DeTAB solution. This



Figure 5. (a) Radial distribution functions for the presence of a water oxygen atom to surround an interfacial water oxygen (WO) atom in DeTAB micellar solution compared to that of WO-WO in bulk water. Note the reduced coordination number around the interfacial water molecule. (b) Distribution of the total number of hydrogen bonds around a water molecule present at the interface in DeTAB solution and for bulk water.

Figure 4. (a) Atomic probability density map of interfacial water molecules around a surfactant headgroup denoted by the black region. The red spheres represent CH3 groups, the blue sphere represents the nitrogen atom, and the green spheres represent the CH2 and CH3 groups of the surfactant. (b) Environment around an interfacial water molecule. Yellow, green, magenta, and blue denote the most probable locations of the methyl group, nitrogen, bromide ion, and interfacial water, respectively, in the DeTAB micellar solution.

Figure 6. Potential energy distribution of interfacial water molecules in the DeTAB micellar solution compared to that in bulk. The contributions to the monomer energy of the interfacial water molecule from different species present in the system (namely, micelle, bromide ions, and water molecules) are also shown.

reduction in water-water hydrogen bonds at the interface effectively diminishes relaxation mechanisms that depend on the extensive network of such hydrogen bonds. We have also calculated the total number of hydrogen bonds per water molecule, and the distribution is shown in Figure 5b for both surface water and bulk water. The number of hydrogen bonds (donor and acceptor added together) surrounding a given water molecule in the bulk is found to be 3.55, while it is reduced to 3.13 for the molecule at the interface in the DeTAB solution. This reduced coordination number of the surface water can be related to its monomer energy, which we discuss next. In CsPFO, the reduced water-water coordination was adequately compensated by hydrogen bonding to the charged oxygen ions that constituted its carboxylate headgroup. Such

specific hydrogen bonding sites are absent in DeTAB. Consequently, the average potential energy of an individual water molecule that is present at the DeTAB interface is only marginally different from its value in bulk water. This is seen in Figure 6, where the distribution of these monomer energies is provided. The energy is calculated as the sum of potential energies of interaction of the interfacial water with every species in the system. The energy distribution for the interfacial water in DeTAB is slightly more positive (by about 112 K) than that for bulk water. Note also that the distributions possess nearly the same width, implying that the water molecule at the interface sees nearly the same physical heterogeneity in its environment as bulk water. In CsPFO, the energy distributions of most interfacial water molecules were shifted to considerably lower


Pal et al.

energies relative to bulk water. There, only those molecules (which we had christened as IFW, interfacial free water) that were not hydrogen bonded to any surfactant headgroup had nearly the same energy distribution as bulk water. It is remarkable that the overall distribution of this energy in DeTAB is quite similar to that of IFW. The marginal shift of the monomer energy toward the positive side with respect to the bulk water can be understood as follows. The interfacial water molecule is less coordinated at the surface (Figure 5a), and also, it possesses 0.5 less hydrogen bonds (Figure 5b) compared to bulk water. However, the reduced number of water neighbors at the interface is not fully compensated by the interaction with the charged headgroup and the counterions. The same figure shows the contribution of water, bromide ions, and the surfactants to the monomer energy of interfacial water molecules. It is observed that both the micelle and the counterions contribute a significant degree of positive energy to the total potential energy of interfacial water. The shoulder observed in the contribution from bromide ions at around -10 kcal/mol is likely to come from the hydration shell surrounding a counterion. The overall shift in the distribution for the water at the interface can also be rationalized due to the hydrophobic nature of the methyl groups at the interface. 3.2. Dynamics of the Hydration Layer. In the previous section, we provided details on the structure of water around the micellar surface. The different ordering of water molecules around the micellar headgroups relative to that in bulk water profoundly affects their dynamics. Here, we present simulation results on the single particle and the collective dynamics of surface water molecules. 3.2.1. Residence Time Distribution. The residence time distribution of water molecules in the hydration layer provides a quantitative measure of water molecules’ mobility in the layer. We have investigated the residence TCF of indiVidual water molecules at the surface of a DeTAB micelle and also in bulk. The TCF can be defined using the population variables h(t) and H(t), which are Heaviside functions that signify the presence or absence of the water molecule in the hydration layer. h(t) ) 1 if a water molecule is within the shell and zero otherwise. On the other hand, H(t) ) 1 if a water molecule continuously stays within the shell between time 0 and time t and is zero otherwise. Using these definitions, one can define a residence TCF as

Sres(t) )

〈h(τ) H(t + τ)〉 〈h〉

(1)

For surface water, h(t) will be 1 if the water molecule is within 6.3 Å from any headgroup nitrogen and 0 if it is beyond 6.3 Å. The decay of the residence TCF will depend not only on the intrinsic dynamics of the interfacial water molecules but also on the thickness of the interface. Hence, one needs to benchmark the data for the interfacial water against a standard that can be obtained for bulk water. To calculate Sres(t) in bulk water, we constructed a spherical shell in a bath of bulk water which mimics the dimensions of the hydration layer in the micelle system. We repeated these calculations by varying the radii of the spherical shell between 18 and 22 Å to look for any dependence of the result on the radius parameter, and no significant changes were observed. This range of values is comparable to the average radius of the micelle. The thickness of the shell was taken to be the same as that in the micellar solution, that is, 6.3 Å. Thus, for bulk water, h(t) will be 1 if the water molecule is present in the shell defined by the radii 18 and 24.3 Å and zero otherwise.

Figure 7. Residence time correlation function for the interfacial water molecules in the DeTAB micellar solution and for bulk water. The inset shows the log-normal plot of the same functions. The multiexponential fitting parameters of these TCFs are provided in the table.

The computed residence TCFs for both the micellar layer and the bulk water “layer” are presented in Figure 7. The initial decay for both the surface water and bulk water are nearly the same, but they differ significantly at longer times. The parameters of the fit of a multi-exponential function to the TCFs are provided as an inset to the figure. In the inset, the TCFs are also shown on a log-normal scale. The above analysis seems to prove unequivocally that water molecules within the interface are translationally mobile and that the exchange across the interface is robust, although a bit slower than that in bulk water. 3.2.2. Orientational Dynamics of Surface Water Molecules. An important indicator of the dynamics of water molecule is the reorientation of its dipole vector. In a solution containing a molecular assembly or a macromolecule (such as a protein), the reorientational dynamics of water molecules near the macromolecular interface is severely affected. Within the framework of linear response theory, the reorientational motion of water at an interface can also be studied by dielectric relaxation (DR) experiments, although the relationship is somewhat indirect. The time evolution of orientational correlation can be estimated by measuring the dipole-dipole TCF, defined as

Cµ(t) )

〈µ bi(0)‚µ bi(t)〉 〈µ bi(0)‚µ bi(0)〉

(2)

where b µi(t) is the dipole moment vector of the ith water molecule at time t and 〈 ... 〉 denotes averaging over initial times 0 and over the water molecules. Figure 8 shows the dipole-dipole TCF of the surface water molecules in comparison to its relaxation in bulk. The parameters of the fit of a multi-exponential function to the TCFs are provided as an inset to the figure. The graph shows the existence of an intermediate time scale slow decay with a time constant of about 5.1 ps which is somewhat slower than that found for neat water. For neat water, the decay is single exponential with a time constant of about 4 ps. The more interesting and important result of our simulation is that the orientational TCF of surface water (hydration water) exhibits an additional slow decay with a time constant of 111 ps and with an amplitude of 44%. The presence of this slow decay in the reorientational TCF of interfacial water molecules is unequivocal. We are able to capture the full decay of the long time component also. A part



Figure 8. Dipole-dipole time correlation function, Cµ(t), for the interfacial water molecules and for bulk water. The inset shows the multi-exponential fitting parameters to the surface water TCF. The bulk water TCF can be fitted to a single exponential form with a time constant of 4.1 ps.

Figure 9. Mean square displacement of the water molecules at the surface of DeTAB micelle and in bulk water.

than bulk water. From these data, one can obtain the value of the diffusion coefficient using the Einstein relation

〈|b r i(t) - b r i(0)|2〉 ∆tf∞ 2d∆t

D ) lim of this relaxation should come from the slow rotational motion of the micelle itself. The latter, estimated from the decay of the reorientational TCF of the long axis vector of the surfactant, takes place in the time scales of a few nanoseconds. Other contributions to the decay of Cµ(t) of surface water are likely to come from the interaction of the interfacial water molecules with the polar headgroup of the surfactants and from water molecules which are buried between surfactants. The existence of three distinct time scales in the hydration layer orientational dynamics is interesting and deserves further attention. The slow water dynamics owes its origin to the water molecules whose oxygen atoms are in a deep potential energy minimum between the positively charged headgroups. Note that a time constant of 111 ps corresponds to an activation energy of about 3.9 kcal/mol, if one uses the simple, one-dimensional transition state theory expression. The slow component in the reorientation could also come from buried water molecules, in which case the long time relaxation of Cµ(t) would be related to the slow diffusion of these molecules out to the bulk. This argument gains support from the data on residence TCF seen earlier. 3.2.3. Translational Dynamics of Surface Water Molecules. We have calculated the mean square displacement (MSD) of the interfacial water molecules in order to obtain an idea about the surface mobility. MSD is defined as

MSD(t) ) 〈|b r i(t) - b r i(0)|2〉

(3)

where b ri(t) and b ri(0) are the coordinates of the ith water molecule at time t and zero, respectively. The MSD of the molecules on the surface (as well as any other TCFs discussed here) are necessarily a convolution of the MSD (or TCF) and the residence TCF, Sres(t), of water. The MSD (or other TCFs discussed here) was calculated as follows. If the probe stays continuously in the region of interest for the time duration, τ and t + τ, then the probe will contribute to the TCF for time values between zero and t. As in the calculation of any TCF in an equilibrium ensemble, the time origin τ can be arbitrarily chosen. The MSD has been calculated with three different time resolutions, 16 fs, 100 fs, and 1ps. We found the MSD of the surface water to be resolution independent, as expected. In Figure 9, we show the MSD of the surface water with a time resolution of 1 ps and compare it with that of bulk water. As expected, the surface water molecules exhibit a lower mobility

(4)

where d is the dimensionality of the system. Fitting the long time slope of the MSD gives a value for the diffusion constant for surface water (D) of 0.67 × 10-5 cm2/s. This value should be compared with the bulk value of SPC/E water which is 2.5 × 10-5 cm2/s. Note the pronounced slow diffusion of the surface water. Berne and co-workers have recently presented a formulation of obtaining the self-diffusion tensor in anisotropic systems.54 The current estimates for the diffusion constant in the micellar solution assume isotropy and hence should only be considered as a nominal value. However, the fact that the translational diffusion is restricted at the interface relative to the bulk is undisputed. Recently, we have also studied the diffusion of the surface water in the CsPFO micellar solution.37 A similar slow translational dynamics has also been observed there. 3.2.4. Hydrogen Bond Lifetime Dynamics. This is currently an area of great interest because the dynamical response of water is intimately connected with the lifetime of hydrogen bonds. Recent work of Luzar and Chandler55,56 has elucidated many aspects of hydrogen bond lifetime dynamics of neat water, and this has been subsequently extended to explore bond dynamics in complex situations, like electrolytes57 and micellar36 and protein surfaces.58 The lifetime of a hydrogen bond is usually described in terms of the hydrogen bond lifetime correlation functions,57,59-61 denoted by CHB(t) and SHB(t), which are defined by the following expressions:

CHB(t) )

〈h(0) h(t)〉 〈h〉

(5)

SHB(t) )

〈h(0) H(t)〉 〈h〉

(6)

where h(t) is the hydrogen bond lifetime function which is unity if the hydrogen bond between a pair of water molecules is intact at time t and zero if it is broken. H(t), on the other hand, is unity only if the tagged bond has remained continuously unbroken from time t ) 0 to the present time t. Thus, CHB(t) allows hydrogen bonds to be broken and reformed in the time interval t, while SHB(t) does not allow for such reformation. Both of the functions are found to depend on the criteria of hydrogen bond forming/breaking. The definition (distance, angle conditions) of a water-water hydrogen bond was the same as that


Pal et al.

Figure 10. Hydrogen bond lifetime correlation functions (SHB(t) and CHB(t)) for a pair of water molecules at the micellar surface and in the bulk. In the inset, multi-exponential fitting parameters to the TCFs are provided.

used in ref 57. In Figure 10, we show the decay of these TCFs for pairs of water molecules in the interfacial region of the DeTAB micellar solution and for those in bulk water. The parameters of the fit of a multi-exponential function to the TCFs are provided as an inset to the figure. The mean relaxation time according to SHB(t) is about 0.77 ps, whereas for CHB(t) it is 11.7 ps for the interfacial water. Note that, for bulk water, the lifetime of SHB(t) is only about 0.56 ps, while that obtained from CHB(t) is about 6.5 ps.36 The longer lifetime given by CHB(t) is due to the reformation of the bond after it breaks. The limitation of SHB(t) is that it does not take into account the reformation of the H-bond immediately after breaking and thus provides a lower limit of the true lifetime. The increase in the lifetime of the water-water hydrogen bond at the interface is likely to arise from buried water as well as from the reduced water-water coordination number. 3.2.5. Vibrational Dynamics and Power Spectrum. A direct probe of the intermolecular interactions between the water molecules and the surface atoms of the substrate is provided by the shift and line width of the vibrational modes of water at the surface. The interface also affects the intermediate frequency modes, O‚ ‚ ‚O‚ ‚ ‚O bending, and the librational modes of water, that are peaked around 50 and 500 cm-1, respectively, in bulk water. Inelastic neutron scattering data on aqueous membrane and protein solutions62,63 have shown a hardening of the potential energy surface of interfacial water relative to bulk water, which leads to a blue shift in the features of the vibrational spectrum. To understand the vibrational spectrum of the interfacial water molecules, we have calculated the Fourier transform of their velocity auto-TCF (VACF). This function, Cvv(t), is defined as

Cvv(t) )

〈V bi(t + τ)‚V bi(τ)〉 〈V bi(τ)‚V bi(τ)〉

(7)

where b Vi(t) is the velocity of atom i in a water molecule at time t and the angular brackets denote averaging over all atoms of the specific kind and also over the initial time origins, τ. A Fourier transform of the VACF provides a direct measure of the vibrational density of states as a function of frequency. In Figure 11, we present the computed VACF for the oxygen atom ((COvv(t)) and hydrogen atom (CHvv(t)) on an interfacial water molecule, respectively. As expected, for both of the functions, the minimum for surface water is deeper than that for bulk water due to the enhanced rigidity of the environment. Figure 12 shows

Figure 11. Normalized velocity auto-TCF (COvv(t) and CHvv(t)) for the oxygen (top) and hydrogen atom (bottom) of an interfacial water molecule. The data for bulk water are shown for comparison.

Figure 12. Power spectrum (proportional to vibrational density of states) of oxygen (top) and hydrogen (bottom) atoms of interfacial water molecules in the DeTAB solution, compared to their behavior in bulk.

the density of vibrational states obtained by taking the Fourier transforms of COvv(t) and CHvv(t), respectively. We observe a blue shift in the O‚ ‚ ‚O‚ ‚ ‚O mode by ∼20 cm-1 and a blue shift in the librational mode by ∼100 cm-1. These data match reasonably well with the recent incoherent inelastic neutron scattering experiments on aqueous DNA solutions.62,63 3.2.6. Total Moment-Moment TCF. The total dipole moment of a system at time t, M B (t), is defined as N

M B (t) )

b µ i(t) ∑ i)1

(8)

where N is the total number of molecules and b µi is the dipole moment vector of the ith molecule. The total moment of the aqueous micellar system can be split into contributions from water, the micelle, and the ions. Here, we have considered only the contribution from water because the micellar contribution should occur in a much longer time scale (the micelle, due to its possession of a net charge, also poses a problem in defining its dipole moment). We have calculated the normalized moment-moment TCF, defined as

ΦW M (t) )

〈M B W(t)‚M B W(0)〉 〈M B W(0)‚M B W(0)〉

(9)


J. Phys. Chem. B, Vol. 109, No. 26, 2005 12887 around the charged probe. Solvation dynamics is usually monitored by the solvation TCF, S(t), defined as

S(t) )

E(t) - E(∞) E(0) - E(∞)

(10)

where E(t), E(0), and E(∞) are the changes in the energies of the probe at time t, 0, and ∞, respectively, due to the change in its charge distribution. The change in energy comes purely from Coulombic interactions with the solvent, and it is assumed that the geometry of the probe is unaltered upon excitation. The solvation TCF can also be related, by linear response theory, to the auto-TCF of energy fluctuations of the probe ion or dipole, at equilibrium. This is usually denoted by CS(t) and defined as Figure 13. Normalized moment-moment time correlation function for water molecules in the DeTAB micellar solution. The circles are data points (shown infrequently for clarity) obtained from the simulation, and the continuous line is the multi-exponential fit. The inset shows the same function for bulk SPC/E water. The table shows bi-exponential fitting parameters to the surface water TCF. The bulk water TCF can be fitted to a single exponential form with a time constant of 9.2 ps.

where M B W is similar to eq 8 but with the sum extended over the water molecules of the micellar solution. Figure 13 shows the normalized moment-moment TCF of water, both in micellar solution and also in bulk. The parameters of the fit of a bi-exponential function to the TCFs are provided as an inset to the figure. Note that ΦW M (t) of neat water (SPC/E) decays exponentially with a time constant of 9.2 ps. However, the water molecules show a markedly different total moment correlation function in the presence of the micelle, with an average time constant of 16.2 ps. A slow time component of 164 ps has emerged in the contribution of water to dielectric relaxation of the micellar solution, with an amplitude of 4%. This is likely to arise from the interfacial water molecules. A similar long time component attributed to interfacial solvent dynamics, with a time constant of 25 ps, has been observed in dielectric relaxation experiments on several micellar solutions based on CnTAB surfactants.64 The total moment of all of the water molecules in the solution can further be divided into contributions from the interfacial region (i.e., within 6.35 Å) and outside this region. Thus, the total moment TCF defined in eq 9 can be written as the sum of two autocorrelation functions and one cross-correlation function. The surface water-surface water auto-TCF can be fitted to a bi-exponential function of time constants 12 ps (85%) and 123 ps (15%). It is thus seen that the long time component of the relaxation has increased in amplitude for surface waters. Thus, one can safely attribute the 164 ps component in the total moment TCF (as in eq 9) to contributions from water molecules present in the interfacial region. The slow orientational relaxation of the surface water and the observed slow decay in the moment-moment TCF can be correlated by using the well-known micro-macro relation of statistical mechanics.65,66 The 164 ps component observed in the solvent contribution to the dielectric response function is likely to arise from the 111 ps component observed in the single particle reorientational TCF of interfacial water molecules. 3.2.7. SolVation Dynamics in the Hydration Layer. Solvation dynamics usually refers to the time dependent response (measured in terms of energy of the probe) of the solvent to a sudden creation of a charge or dipole in the probe located inside the solvent. The energy change is due to the stabilization of the probe solute due to reorganization of the polar solvent dipoles

CS(t) )

〈δE(t) δE(0)〉 〈δE(0) δE(0)〉

(11)

where δE ) E - 〈E〉 denotes a fluctuation in the solvation energy difference between the excited state and the ground state of the solute and 〈 ... 〉 indicates an equilibrium ensemble average. Within the linear response approximation, S(t) = CS(t). Therefore, we have made no distinction between S(t) and CS(t), although, strictly speaking, these two TCFs may show differences. In our calculations here, we study the solvation dynamics TCF CS(t) of the counterions that are intrinsic to the micellar solution, and E(t) in eq 11 denotes the Coulombic contribution to the potential energy of the counterion at time t. In Figure 14a, the decays of the solvation energy TCF CS(t) of a bromide ion and cesium ion in the respective DeTAB and CsPFO micellar solutions are shown. Bromide and cesium ions which reside continuously within the respective hydration layer for an arbitrary time duration, τ, contribute to CS(t) for values of t starting from zero up to τ. Note the ultraslow component to the relaxation of the solvation energy. To obtain the solvation TCF in bulk water, we have also carried out MD simulations of one bromide ion in a bath of 5711 water molecules within a periodic box at 300 K. Similar calculations were also performed for the cesium ion. The TCF for the bromide ion and cesium ion in the pure water are shown as insets to Figure 14a. The bulk solvation TCF decays within 1-2 ps, as expected. In comparison, the long time part of the solvation dynamics in the micellar surface is slowed by at least 2 orders of magnitude. We have fitted the solvation TCF to a sum of exponential functions. The time constants and the amplitudes are provided in Table 3. We would like to remind the reader here that such an ultraslow component in solvation dynamics has indeed been seen by several studies on solvation with probes located at/ near the micellar surface.22,28,35,37 We now investigate the reason for such slow solvation dynamics on the micellar surface. The energy of a tagged bromide ion consists of contributions from three sources: other bromide ions, the water molecules, and the polar headgroups of the surfactant. The contribution from the micelle to the solvation energy is largely decayed by its rotation which is the leading cause of slow solvation relaxation. Therefore, the total solvation TCF can have contributions from six distinct partial TCFs (three direct and three crosscorrelations). We have computed all these pure and crosscorrelation functions, and the results are shown in Figure 14b. The analysis of the partial TCFs for the micellar system shows several interesting features: (A) The contribution from the interaction of bromide ion with the micellar headgroups is the single most dominant contributor. This partial TCF decays very slowly and is thus the leading cause of slow solvation dynamics. (B) The two cross-correlation functions, both involving bromide


Pal et al.

Figure 14. (a) Solvation time correlation functions for interfacial bromide ions in the DeTAB (cationic micelle) solution compared to those of cesium ions in the CsPFO (anionic micelle) solution. The inset in the middle shows the same functions for short times, in an expanded scale. The insets at the top show that same function for bromide and cesium ions in bulk water. (b) Partial solvation time correlation functions (three direct and three cross) for the interfacial bromide ion. The functions are normalized by 〈δE(0) δE(0)〉, where E(t) is the potential energy of the interfacial bromide ion at time t.

TABLE 3: Parameters of a Multi-exponential Fit to the Normalized Solvation TCF (CS(t)) of Interfacial Bromide Ions in the Micellar Solution τ1 τ2 τ3

time constant (ps)

amplitude (%)

〈t〉 (ps)

0.05 1.1 47.5

62 28 10

5.1

energy as one of the components, also make large contributions. However, the contribution of each of these two terms is negative at t ) 0 and they decay somewhat faster than the dominant 〈δEBr-micelleδEBr-micelle〉 term. Also, they lead to substantial cancellation at all times and make the decay faster, particularly toward the end of the solvation process. Bhattacharyya and co-workers have reported a femtosecond study of solvation dynamics in a related micellar system of cetlytrimethylammonium bromide (C16TAB) in water.71 With a time resolution of 170 fs, they observed components of 0.23 ps (50%), 6.5 ps (26%), and 350 ps (24%). Our simulations agree with the centrality of slow interfacial solvent dynamics that was observed in these experiments, although quantitative differences exist which could arise from the different systems, time resolutions, and probes (and thus their locations in the solution) employed. The absence of a very slow component in our work against the observation of the 350 ps component of experiments can be rationalized as being due to the relatively lighter probe (bromide ion) used in this work as opposed to the DCM molecule used as a probe in experiment. The bromide ion can (and does) diffuse out of the interfacial layer within a

maximum duration of around 100-150 ps. Thus, the maximum residence time forms the upper bound of the longest time component of solvation dynamics, in our work. Our earlier works on the solvation dynamics of cesium ion at the interface of the aqueous micelle CsPFO demonstrated the existence of a long time component, whose time constant was 56 ps at 300 K, with an amplitude of 70%.37 The earlier calculations employed a time resolution of 1 ps. Also, a large, spherical cutoff of 21 Å was used in the calculation of the potential energy of the ion. The latter could introduce artifacts in the form of an enhanced amplitude of the long time component, due primarily to an overestimation of the amplitude of fluctuations in energy from water molecules that are present far away from the probe ion. In Figure 14a, we compared the solvation TCF of interfacial bromide ions in DeTAB with that of cesium ions present in the CsPFO solution. The total potential energy of the ions includes contributions from all of the charged species in the system (i.e., without any interaction cutoff). We observe a slow time component in these solvation TCFs whose magnitude is similar to what was observed earlier, that is, around 40-50 ps. However, its amplitude is considerably smaller, of the order of 5-10%. It is found that the solvation dynamics of bromide in DeTAB is non-negligibly slower than that of cesium in the CsPFO solution. This is primarily due to the larger amplitude of the slow time component in the former. As seen earlier, the long time component in the solvation dynamics arises primarily from the interaction of the probe ion with the polar headgroups of the surfactant. It is surprising that the solvation TCF is slower in DeTAB than in CsPFO, despite the fact that there are no sites on the DeTAB surfactant that water molecules could form hydrogen bonds with (as we use a united atom model for the methyl group). The larger headgroup (which is the only polar component of the surfactant) in DeTAB compared to that in CsPFO is likely to play a role in this difference, apart from the primary reason of the longer residence time of water molecules in the interfacial layer of the DeTAB solution. This needs to be studied further. The above results in DeTAB, when viewed in conjunction with a similar result obtained earlier for the anionic micelle CsPFO, strongly imply that the slow solvation dynamics observed using polar probes located at the surface of micelles is primarily due to the contribution from the micellar headgroups. There could also be other mechanisms, like the selfmotion of the probe itself after the excitation. 3.2.8. Probe of Surface Water Rigidity. The hydration layer around the micelle acquires additional rigidity due to the interaction of water molecules with the charged/polar headgroups at the surface. To understand this feature, we studied the number density fluctuation of water molecules at the surface of cationic micelle and in the bulk. For number density fluctuations in bulk water, we adopted an approach similar to that used for Figure 7. However, note that, while the residence time monitors individual water molecules, the number density fluctuation probes a collective quantity. This is because it is the collective density fluctuation which is expected to be sensitive to the collective potential. The number density function TCF can be defined as

CN(t) )

〈δN(0) δN(t)〉 〈δN(0) δN(0)〉

(12)

where δN(t) ) N(t) - 〈N〉 denotes a fluctuation in the water number density and 〈 ... 〉 indicates an equilibrium ensemble average. The regression of δN(t) should be determined by the barrier that an interfacial water would experience to get out to


Figure 15. Water number fluctuation time correlation function for interfacial water molecules in the DeTAB micellar solution and for bulk water. Data points are shown infrequently for clarity.

the “bulk” (or vice versa). Hence, the rate of decay of this TCF is an indicator of the rigidity of the interface. These results are shown in Figure 15. Note the slower decay of the hydration layer fluctuation indicating the rigidity of the same. The calculated number density fluctuation will give us a collectiVe measure of the rigidity of the water molecules in the hydration shell. One can correlate this TCF with the force constant of the potential energy surface. Note also that this is different from Figure 7 where we have presented the residence TCF of indiVidual water molecules. 4. Conclusions We have employed atomistic molecular dynamics simulations to investigate the microscopic nature of water molecules in the hydration shell of a cationic micelle, decyltrimethylammonium bromide. A characterization of the structure around interfacial water molecules in this system reveals that it could be influenced by the hydrophobicity of the methyl groups67,68 and by the presence of the counterions. Water molecules have been observed to be present predominantly in the regions between two methyl groups. Consequently, these preferential locations, when averaged over time and over the ensemble of configurations, have the appearance of a triple-forked structure. The water molecules near this cationic micelle are less structured relative to bulk water as well as those near the anionic micelle that we have studied earlier (cesium perfluorooctanoate). The reduced structuring near the DeTAB surface need not necessarily be a consequence of the negatively charged surface. It is more likely to arise due to the hydrophobic nature of the methyl groups. It is known that the introduction of a polarizable force field for the headgroups can weaken the association of the counterion with the surfactant and enable the micellar surface to be better hydrated.69 This aspect needs to be studied in our system. Another aspect of micellar solutions that is often neglected is the exchange of monomers between the micelle and bulk solvent. In DeTAB, this process is estimated to occur in the time scale of 10-100 ns.70 Thus, our simulations would be able to capture only the preliminary events of this dissocation. Such an exchange of monomers could decrease the relaxation times of the correlation functions calculated here. This aspect also needs to be addressed in the future. Earlier experimental and computer simulation studies have clearly demonstrated that the dynamics of hydration water molecules is significantly different from that of the bulk. The current study shows a slowing down in the orientational and residence dynamics of water molecules present at the interface. The solvation dynamics of bromide counterions also exhibits a

J. Phys. Chem. B, Vol. 109, No. 26, 2005 12889 slow time component. The slowest component has been observed in the solvation TCF, with the slowest time constant about 2 orders of magnitude slower than that in bulk. Careful analysis allows us to attribute this ultraslow component to the interaction of the anion with the positively charged polar headgroup of the micelles. The contribution of water molecules to the decay of the total moment TCF, which is related to the dielectric response of the micellar solution, has been studied. This function shows two time components, a large, bulklike contribution with a time constant of around 10 ps and a minor component with a time constant of around 164 ps. The latter is likely to arise from the dynamics of interfacial water. It is indeed gratifying that such accurate and long trajectory analyses of a complex system yields the correct time constant of around 10 ps as the major component, which is quite close to the Debye relaxation time of bulk water. The results obtained here demonstrate that the slow dynamics of water molecules near a fluctuating, charged interface such as micelles is generic; we have observed this phenomenon in our earlier calculations on an anionic micelle. The current calculations on a cationic micelle reinforce our earlier conclusions. Micelles, unlike proteins, present a chemically homogeneous surface to water. Hence, a study of the behavior of interfacial water in micellar solutions is expected to help us gain a better understanding of more challenging systems which are biologically relevant.72 Acknowledgment. We thank Mr. M. Krishnan, Ms. Moumita Saharay, and Mr. Sagar Sen for help in the density map calculations and visualizations. The research reported here was supported in parts by grants from the Council of Scientific and Industrial Research (CSIR), Department of Atomic Energy (DAE), and the Department of Science and Technology (DST), Government of India. References and Notes (1) Carvalho, C. M. L.; Cabral, J. M. S. Biochimie 2000, 82, 10631085. (2) Frauchiger, L.; Shirota, H.; Uhrich, K. E.; Castner, E. W., Jr. J. Phys. Chem. B 2002, 106, 7463-7468. (3) Tarek, M.; Tobias, D. J. Phys. ReV. Lett. 2002, 88, 138101-1138101-4. (4) Smith, J. C.; Merzel, F.; Verma, C. S.; Fischer, S. J. Mol. Liq. 2002, 101, 27-33. (5) Melchionna, S.; Briganti, G.; Londei, P.; Cammarano, P. Phys. ReV. Lett. 2004, 92, 158101-1-158101-4. (6) Russo, D.; Hura, G.; Head-Gordon, T. Biophys. J. 2004, 86, 18521862. (7) Bandyopadhyay, S.; Chakraborty, S.; Balasubramanian, S.; Pal, S.; Bagchi, B. J. Phys. Chem. B 2004, 108, 12608-12616. (8) Bruce, C. D.; Senapati, S.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 10902-10907. (9) Pal, S.; Balasubramanian, S.; Bagchi, B. J. Phys. Chem. B 2003, 107, 5194-5202. (10) Watry, M. R.; Tarbuck, T. L.; Richmond, G. L. J. Phys. Chem. B 2003, 107, 512-518. (11) Vieceli, J.; Benjamin, I. J. Phys. Chem. B 2002, 106, 7898-7907. (12) Kuo, I.-F. W.; Mundy, C. J. Science 2004, 303, 658-660. (13) Bandyopadhyay, S.; Tarek, M.; Klein, M. L. Curr. Opin. Colloid Interface Sci. 1998, 3, 242-246. (14) Tarek, M.; Bandyopadhyay, S.; Klein, M. L. J. Mol. Liq. 1998, 78, 1-6. (15) Nandi, N.; Bhattacharyya, K.; Bagchi, B. Chem. ReV. 2000, 100, 2013-2046. (16) Bhattacharyya, K. Acc. Chem. Res. 2003, 36, 95-101. (17) Pal, S. K.; Peon, J.; Bagchi, B.; Zewail, A. H. J. Phys. Chem. B 2002, 106, 12376-12395. (18) Bagchi, B. Annu. Rep. Prog. Chem., Sect. C 2003, 99, 127-175. (19) Tamoto, Y.; Segawa, H.; Shirota, H. Langmuir 2005, 21, 37573764.

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