Vibrational Spectroscopy and Dynamics of Water Confined inside

J. Phys. Chem. B 2009, 113, 15017–15028

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Vibrational Spectroscopy and Dynamics of Water Confined inside Reverse Micelles Piotr A. Pieniazek,† Yu-Shan Lin,† Janamejaya Chowdhary,‡ Branka M. Ladanyi,‡ and J. L. Skinner*,† Theoretical Chemistry Institute and Department of Chemistry, UniVersity of Wisconsin, Madison, Wisconsin 53706, and Department of Chemistry, Colorado State UniVersity, Fort Collins, Colorado 80523 ReceiVed: July 17, 2009; ReVised Manuscript ReceiVed: September 24, 2009

In this work, we combine atomistic molecular dynamics simulations with theoretical vibrational spectroscopy to study the properties of water confined inside bis(2-ethylhexyl)sulfosuccinate (AOT) reverse micelles. This approach is found to successfully reproduce the experimental spectra, rotational anisotropy decays, and spectral diffusion time-correlation functions as a function of micelle size. These results are interpreted in terms of water molecules in different hydrogen bonding environments. One interesting result from our simulation, not directly accessible experimentally, involves the distance from the surfactant headgroup/water interface over which the dynamical properties of water become bulk-like. We find that this distance varies with micelle size, casting doubt on the core/shell model. In particular, the distance increases with decreasing micelle size, and hence decreasing radius of curvature of the interface. We suggest that this arises from curvature-induced frustration. We also find that the dynamics in the smallest micelle studied is extremely slowsrelaxation is still incomplete by 1 ns. As in other glassy systems with collective relaxation, our time-correlation functions can be fit to stretched exponentials, in this case with very small exponents. I. Introduction Water in its various phases has been widely and thoroughly studied. Gas-phase spectroscopy can investigate photodissociation dynamics in the excited states of individual molecules.1 Extremely detailed dimer potentials exist.2-4 On the condensed phase front, numerous studies of ice and liquid water have been performed.5-8 One particularly interesting situation involves water in a confined environment, such that the water pool has a characteristic length on the order of nanometers.9,10 This corresponds to the typical size of cavities found in nanodevices11,12 and porous materials.13-17 Chemical reactivity and dynamics in these size regimes have been found to differ dramatically from those in the bulk phase.18-24 Thus, it is of great interest to understand the structure and dynamics of “confined water”.25-33 There has also been much recent interest in “biological water”34-42swater in the first several hydration shells of biomoleculessuchasproteins,43-63 DNA,63-66 andcarbohydrates.67-69 The structure and dynamics of such biological water affects the stability and function of these biomolecules. It has been found, generally, that the dynamics of biological water is slower than that of bulk water.32,37,59,70,71 One would like to understand the time scales for water dynamics, as a function of the distance from the water/biomolecule interface, and especially how this depends on the nature of the interface. Similar questions apply to water interfaces with composite structures such as lipid membranes.70,72-74 In each case, one can ask, at what distance from the interface does the dynamics of biological water become the same as bulk water?32,43,67 Yet another related problem involves the structure and dynamics of water in aqueous solutions of simple ions. This is intimately related to the Hofmeister series, which, in its original context, has to do with how different ionic solutions stabilize or destabilize proteins.75,76 Surprisingly, the prevailing view is that simple ions do not † ‡

University of Wisconsin. Colorado State University.

Figure 1. The chemical structure of the AOT molecule.

significantly perturb the structure and dynamics of water outside the ions’ first solvation shell,77-80 and so the Hofmeister series results from direct, local interactions. Reverse micelles (RMs), i.e., micelles in which the aqueous phase is in the interior (rather than the exterior), are convenient systems to study confinement effects on water. Additionally, RMs are important in their own right as microreactors and drug delivery vesicles.81-84 RMs are ternary systems formed by a surfactant, a nonpolar solvent, and water, in appropriate ratios. Surfactants are typically classified on the basis of the headgroup charge, into anionic (such as bis(2-ethylhexyl)sulfosuccinate (AOT)), cationic (such as cetyltrimethyl-ammonium bromide (CTAB)), and neutral (such as Igepal and Brij).85 The nonpolar phase is usually a simple alkane, although carbon dioxide and carbon tetrachloride have also been used. Note that RMs also involve aspects of the problems of biological water and “ionic water” (water in the vicinity of ions) described above, since the surfactant molecules and their headgroups are similar to lipid molecules, and for the ionic surfactants there are counterions in, and headgroup ions at the edge of, the water pool. Considering, for example, AOT RMs (the structure of AOT is given in Figure 1), the ratio of water to surfactant concentrations, w0 ) [H2O]/[AOT], which is typically in the 2-20 range, determines the RM size. Linear relationships have been

10.1021/jp906784t CCC: $40.75  2009 American Chemical Society Published on Web 10/20/2009

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established between the w0 parameter and the RM radius, using dynamic light scattering,86 small-angle X-ray87 and neutron88 scattering, compressibility,89 and viscosity90 measurements. The details of the relationship depend on the nature of the nonpolar phase and the surfactant, but generally, the amount of water in each RM ranges from 25 to 100 000 or more molecules. Nuclear magnetic resonance,91,92 dielectric relaxation,93,94 quasi-elastic neutron scattering,95 fluorescence Stokes shift,96,97 and infrared (IR)98-101 spectroscopic techniques have been used to explore the structure and dynamics of confined water in RMs. The latter is vastly different compared to bulk water; for example, time scales up to nanoseconds have been found in the solvation dynamics of fluorescent probes inside RMs.92,96 In recent years, ultrafast IR techniques have been brought to bear on the problem of water dynamics in RMs.102-114 The studies by Wiersma and co-workers focused on the vibrational energy relaxation of pure H2O in AOT RMs.102,103 On the other hand, Fayer and co-workers107-114 considered dilute HOD in H2O (in AOT RMs), performing experiments in the OD stretch region of HOD. In this system, vibrational dynamics is simplified considerably, since now the OD stretch is uncoupled from the other vibrational stretches in the problem, and thus it functions well as a local “chromophore”. These authors performed absorption, pump-probe, and vibrational echo experiments, to measure vibrational lifetimes, rotational dynamics, and spectral diffusion (in this case, the time dependence of the OD stretch chromophore’s fluctuating transition frequency). Bakker and co-workers performed similar experiments on the system of dilute HOD in D2O in AOT RMs,104-106 in which case the OH stretch is the local chromophore. In these experiments105 and also in the later experiments by Fayer and co-workers,112,113 different pump and/or probe frequencies allow the authors to spectrally select different subensembles of molecules, for example, those near the water/surfactant interface, and those in the center of the RMs. All of these experiments show that line shapes blue shift, and rotational and spectral diffusion dynamics slow down, with decreasing RM size, and that the dynamics of interfacial water are the slowest. Many of these results have been understood qualitatively in terms of a “core/shell” model,102,103,105,110,112 in which each micelle has a core of bulk-like water, and a shell of strongly perturbed interfacial water. Within the model, the properties of different sized RMs were interpreted as arising from different ratios of core and shell water. However, some inconsistencies between different experiments,110 and more recent interpretation of the experiments on the small micelles,113 indicate that this model is too simple. In particular, for the smaller micelles (those with w0 below 10), this decomposition does not hold because the water dynamics becomes very collective.113 Several groups have explored the properties of water inside RMs using molecular dynamics (MD) techniques. These approaches can be categorized into two groups. First, there are the reduced models, which represent the micelle as a spherical cavity.71,95,115-120 In these models, only the water, headgroups, and counterions are treated explicitly. Simulations of these models revealed a layered structure of water near the headgroups. Both translational and rotational dynamics of water are slowed down. The second group of models involves atomistic121-127 and coarse-grained128 approaches, which consider the nonpolar phase, surfactant, and water explicitly. These studies showed that the RMs are, in fact, nonspherical, and undergo slow shape fluctuations. The interior surface is very irregular, and as such, water was found to be less layered than in the simplified models. Interestingly (and alarmingly!), a small dependence of the

Pieniazek et al. average structure was found on the initial configuration.124 All simulations are in agreement that, as the size of the water pool increases, its properties approach those of the bulk system. In order to provide a molecular-level interpretation of the steady-state and ultrafast IR spectroscopy experiments discussed above, and to provide a deeper understanding of the structure and dynamics of water confined in RMs, in this paper, we consider several different sized AOT RMs, and calculate, from MD simulations, vibrational spectroscopy observables for the OD stretch of the confined HOD/H2O. We are not aware of any similar calculations, although Rosenfeld and Schmuttenmaer120 calculated near-IR spectra of AOT RMs using MD. Many theorists have calculated spectroscopic observables for bulk HOD/D2O or HOD/H2O. The mixed quantum/classical framework provides a convenient, practical, and popular approach, in which the OH stretch (in the case of HOD/D2O) is treated quantum mechanically, the other vibrations on all water molecules are frozen, and all other degrees of freedom are treated classically.129 Within this approach, at every time step along the MD trajectory, three variables characterizing the OH oscillator are required: (i) the instantaneous transition frequency, (ii) the transition dipole, and (iii) the orientation of the OD bond.130,131 The latter is available in a straightforward way from the atomic positions. Several theoretical approaches are available for the calculation of the instantaneous transition frequency and dipole.129,132-138 Here, we follow the approach developed in our group,131,132,134,139 which is similar in spirit to earlier work of Hermansson and co-workers,140 Buch and co-workers,141 and Cho and coworkers,142 and which involves electronic structure calculations on water clusters, in the electrostatic field of surrounding molecules. The transition frequencies and dipoles of local OH stretches in these clusters are functionals of the nuclear coordinates of all the surrounding molecules in the clusters, including those represented by point charges. This complicated dependence is then replaced by a much simpler dependence on a single collective coordinate, in this case the local electric field, and the best fit to the ab initio results leads to quadratic and linear electric-field “maps” for the transition frequency and dipole, respectively.134 Note that this approach may sound like a simple vibrational Stark effect, but it is not that, since the coefficients in the map come from many-molecule electronic structure calculations, and differ from those for a single water molecule in an external electric field.143 The maps described above have been developed for the OH stretch of HOD/D2O, whereas the experiments to be modeled herein involve the OD stretch of HOD/H2O, and thus, the first step is to modify the maps accordingly. In addition, the microscopic local environments in RMs are clearly more complicated than those in bulk water, and thus, it is not clear that one can simply use the electrostatic map developed for bulk water in RM calculations. A simpler situation intermediate between bulk water and RMs is that of water (actually HOD/ H2O) in salt solutions. In a recent theoretical study of this problem,80 two of us first modified the OH-stretch map for applicability to the OD-stretch problem, and then modified the bulk water maps for ionic solutions, by replacing the actual electric field in the water maps by an effective electric field. This approach worked well for salt solutions,80 and, furthermore, has the nice property that in the absence of ions the maps for bulk water are recovered. There is, of course, no guarantee that these modified maps will work well for the more complicated RM problem, but we implement them herein, nonetheless.

Water Confined inside Reverse Micelles

J. Phys. Chem. B, Vol. 113, No. 45, 2009 15019 TABLE 1: Compositions of the Simulated Reverse Micellesa w0

n H 2O

nAOT

niOCT

2 4 7.5

52 140 525

26 35 70

357 527 1229

a nH2O is the number of water molecules, nAOT is the number of AOT molecules, and niOCT is the number of iso-octane molecules.

Figure 2. Comparison of experimental110 and theoretical HOD/D2O line shapes, in a w0 ) 2 AOT RM.

Armed with a theoretical method for calculating vibrational spectroscopy observables, we next need to decide at what level (reduced, fully atomistic, or coarse-grained, as described above) we should model the RMs. The reduced model of Faeder and Ladanyi71 is clearly the simplest and most convenient, but there are concerns that this model produces water pools that are too ordered, in that micelle shapes are spherical, and they do not have enough surface roughness.124,127 We performed exploratory calculations of HOD/H2O spectra, as described below, using a new atomistic RM model developed by two of us,127 and the reduced Faeder-Ladanyi model.71 The results for a w0 ) 2 micelle are shown in Figure 2. As can be clearly seen, the spectrum obtained using the reduced model is qualitatively different from the experimental result,110 while the atomistic simulation reproduces the experimental spectral features quite well. Thus, in what follows, we solely consider the latter. The paper is constructed as follows. In section II, we describe the computational techniques used to simulate the RMs, and the electrostatic map used in the spectral calculation. The presentation of results and discussion in section III begins with an overview of the system structure and static linear spectroscopy. We then proceed to analyze the spectroscopy and dynamics in terms of the hydrogen bonding properties of the system. In section IV, we conclude. II. Computational Details A. Molecular Dynamics. To perform simulations, we have used the force field and the RM construction procedure developed by Chowdhary and Ladanyi.127 Briefly, water was described by the SPC/E model, and sodium parameters were taken from Schweighofer.144 The TraPPe force field145,146 described the alkyl chains of the AOT and iso-octane. Parameters for the sulfonate headgroup were obtained from the CHARMM force field for lipids.147 All intramolecular electrostatic interactions were excluded, while the Lennard-Jones interactions were scaled by half. Lorentz-Berthelot mixing rules were used. MD simulations were performed using the GROMACS package.148,149 Equations of motion were integrated with time steps of 2 and 1 fs during equilibration and production runs, respectively. The system was maintained at constant temperature (300 K) and pressure (1 atm) by means of the Berendsen algorithm.150 The coupling constants were 1 and 2 ps, respectively. Electrostatic interactions were treated using particle-mesh Ewald summation. Lennard-Jones interactions were smoothly switched to 0 between 1.5 and 1.9 nm. A truncated octahedral box was used, and periodic boundary conditions were applied.

Results from different experimental techniques suggest different micelle compositions for a given w0. The systems studied here are listed in Table 1. These compositions are based on the light scattering experiments by Eicke and Rehak.86 The micelles were assembled as follows. The surfactant shell was constructed by randomly placing the desired number of AOT anions on a grid. Then, a charged sphere was added to the system so as to make it neutral. The size of the sphere was chosen to correspond with the size of the water nanopool. MD simulations were performed until all of the AOT molecules congregated around the sphere. No periodic boundary conditions were used. In a separate simulation, sodium ions and water were placed in a truncated octahedral box with a volume corresponding to the water pool. The system was allowed to equilibrate for 200 ps. The prepared water pool was then placed inside the surfactant shell, and the micelle was inserted into a cavity created in liquid iso-octane. The number of iso-octane molecules was selected so as to have a 1 nm coat around the micelle. Keeping the AOT and iso-octane frozen, the water pool was allowed to equilibrate freely for 200 ps. After this, the entire system was allowed to equilibrate for 25 ns. This was followed by a 10 ns production run, during which configurations of the system, excluding isooctane, were saved every 5 fs. Long-time dynamics was explored using 50 ns trajectories, saving the configurations every 1 ps. An additional 1 ns simulation of a box of 256 water molecules was performed, to provide a bulk water reference. B. Spectroscopy Modeling. Within the linear response formalism and the mixed quantum/classical approximation, the infrared absorption spectrum of an isolated chromophore (in this case the OD stretch) is given by129,130

I(ω) ∼ Re

∫0

∞

dteiωt〈 f µ10(0) ·f µ10(t)e-i

∫ dτω t

0

10(τ)

〉e-t/2T10

(1) where ω is the frequency, t is time, b µ10(t) is the transition dipole moment for the OD stretch fundamental at time t, ω10(t) is the fluctuating transition frequency, and T10 is the vibrational lifetime. In the present work, we did not consider the dependence of the lifetime on the micelle size, or, for example, on instantaneous proximity to salt ions, but rather assumed a bulk value of 1.8 ps.151 The spectra were computed from the trajectory of pure H2O (in the RM). In turn, each H atom was assumed to be a D atom. This produces greatly improved sampling statistics while making only negligible changes to the dynamics. For the calculation of the needed properties, we used the electrostatic maps developed recently for the simulation of vibrational spectroscopy of HOD/ H2O in salt solutions.80 As discussed briefly above, the relationships developed earlier for bulk HOD/D2O134 were first modified for HOD/H2O, and then extended to the case of salt solutions by replacing the actual electric field with an effective field.80 The effective field is a linear combination of the fields from water and from cations and anions,80 as shown in Table 2. In all cases, these scalar electric fields are the projections of the vector electric field along the OD bond direction, evaluated at

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TABLE 2: Electrostatic Maps for the Transition Frequency ω10 (in cm-1), Dipole Derivative µ′ (Normalized by the Gas-Phase Value µg′), and 1-0 Matrix Element of the OD Stretching Coordinate x10 (in Å)a Eeff ) EH2O + 0.81379E+ + 0.92017Eω10 ) 2762.6 - 3640.8Eeff - 56641Eeff2 x10 ) 0.0880 - 1.105 × 10-5ω10 µ′/µg′ ) 0.71116 + 75.591Eeff a EH2O, E+, and E- are the electric fields (in au) on the D atom, projected along the OD bond, from water, cations, and anions, respectively.

the D atom position. This approach worked well for NaCl and NaBr solutions, and is used herein without modification. Note that, in the force field used in the present study, the charge on the sodium counterions is +1, while the charges on each of the AOT sulfonate oxygen atoms is -1/3. The electric field from a given sodium or AOT atom was included, if the distance from the oxygen atom of a given water molecule was less than 7.831 Å, as before.80 The electric field from water molecules was included if the oxygen-oxygen distance was less than 7.831 Å.134 The transition dipole is approximately given by131

f µ10 ) µ′x10uˆ

(2)

where µ′ is the dipole derivative, x10 is the matrix element of the OD stretch coordinate between the ground and first excited vibrational states, and uˆ is the OD bond unit vector. The maps for ω10, x10, and µ′ are given in Table 2. The explicit dependence of µ′ on environment, in this context called a non-Condon effect, has been shown to be important for the linear and nonlinear spectroscopy of bulk water.129,139

Figure 3. Snapshot cross section from a molecular dynamics trajectory of a w0 ) 2 reverse micelle. The iso-octane nonpolar phase is omitted. Atoms are as follows: oxygen (red), hydrogen (white), sodium (blue), sulfur (yellow), and carbon (green).

III. Results and Discussion A. Micellar Structure. A detailed analysis of the RM structures obtained using the current model is presented in ref 127. Here, we focus on those properties needed for understanding vibrational spectroscopy. A snapshot from an MD trajectory of a w0 ) 2 RM is presented in Figure 3. It shows the highly irregular and fragmented nature of the water nanopool. The blue sodium ions are seen to congregate in the vicinity of the negatively charged headgroups. Radial probability distribution functions (PDFs) are shown in Figure 4. They show the probability of finding a given atom a distance r from the center of mass (COM) of the water pool. The normalization is as follows:

4π

∫0∞ p(r)r2 dr ) 1

(3)

Thus, the relative probabilities of finding a given atom at a distance r can be obtained by multiplying by the relative abundances. The distribution functions for sulfur and sulfonate oxygen show that they are distributed around a central cavity and do not penetrate inside it. These are very similar to the sodium distribution functions, with the exception that it is possible to find the sodium cation in the interior of the micelle. Moving toward the micelle interior, the water oxygen and hydrogen probabilities rise, and reach a plateau in close proximity to the headgroup region. Except for the smallest micelle, they do not exhibit much structure, and in this case, the behavior of p(r) around r ) 0 is probably not significant due to poor statistics. The width of the headgroup distribution functions and lack of water structure may arise from an actual lack of structure, or from the nonspherical shape of the micelle (which would tend to wash out any structure). To understand

Figure 4. Atom-water-pool-COM radial probability distribution functions. The curves are as follows: water hydrogen (black), water oxygen (red), sodium (green), sulfur (blue), and sulfonate oxygen (magenta).

this effect, we computed the radii of an ellipsoid having the same moment of inertia and mass as the water pool. Results, along with the maximum of the sulfur PDF, are given in Table 3. The differences between the largest and smallest ellipsoid radii are 3-4 Å, which is similar to the width of the headgroup distribution functions, and the middle radius is roughly the same as the position of the sulfur PDF peak. These results are consistent with a structured water layer, which then becomes washed out by shape fluctuations. This is further confirmed by the intrinsic density profiles in ref 127. It should be noted that


J. Phys. Chem. B, Vol. 113, No. 45, 2009 15021

TABLE 3: Average Radii (〈a〉, 〈b〉, 〈c〉) of the Inertial Ellipsoid and the Maximum (R) of the Sulfur-water-pool-COM Radial Probability Distribution Function (Units Are Angstroms) w0

〈a〉

〈b〉

〈c〉

R

2 4 7.5

9.5 12.0 17.8

7.9 9.9 15.9

6.3 8.7 13.7

8.1 10.7 15.5

the differences between ellipsoid radii are not large, and thus, a spherical micelle is a reasonable zeroth-order approximation. B. Linear Spectroscopy. Two major trends have been observed in the experimental HOD/H2O spectra in RMs.110 As the size of the water pool decreases, the spectrum shifts to the blue. Initially, its width increases but then starts decreasing at about w0 ) 20, finally becoming narrower than that of bulk water at w0 ) 2. How can these changes be rationalized, and do they provide any meaningful information about the water nanopool? Within the linear response theory, the line shape is given by eq 1. Figure 5 compares calculated and experimental110 IR spectra. Note, actually, that, for the intermediate-sized micelles, the theory is for w0 ) 4 and 7.5, while the experiments are from w0 ) 5 and 10, respectively. (Larger micelle sizes become progressively more difficult to simulate, and in this instance, we do not believe these differences are too profound.) The observed agreement between theoretical and experimental line shapes is quite satisfactory, and the increasing blue shift with decreasing micelle size is captured properly. The theoretical and experimental peak positions (ωmax) and full-width-half-maximum (fwhm) line widths are shown in Table 4. One sees that the agreement in the peak positions is excellent, with a maximum deviation between theory and experiment of 12 cm-1, and the agreement between the widths is also quite good, with a maximum deviation of 30 cm-1. The theoretical line shapes correctly show the experimentally observed broadening and then narrowing as w0 decreases. From eq 1, one can deduce that the line shape involves a complex interplay among the static distribution of frequencies and non-Condon effects, and the dynamical effects of motional narrowing caused by spectral diffusion, and broadening caused by rotations and the excited state lifetime. Computer simulations allow us to separate these effects. An ensemble of chromophores with frequencies ω10 and transition dipoles µ′x10 can be characterized by its frequency distribution, P(ω), and spectral density, W(ω), defined as

P(ω) ) 〈δ(ω - ω10)〉

(4)

W(ω) ) 〈µ′ x10 δ(ω - ω10)〉

(5)

2

2

Thus, the spectral density is just the frequency distribution weighted by the square of the transition dipole. Figure 6 compares the spectral densities for the different micelle sizes. As the water pool becomes smaller, the spectral density becomes more asymmetric and shifts to the blue, which indicates the weakening of the hydrogen bonds in the system. The peak positions and fwhm’s of the spectral densities and frequency distributions are also shown in Table 4. Both the frequency distributions and spectral densities show the correct monotonic blue shift with decreasing micelle size, but only those for the latter are in good agreement with experiment (which points out the importance of non-Condon effects). The fhwm of the frequency distribution decreases monotonically with decreasing micelle size, while that of the spectral density shows

Figure 5. Comparison of calculated (solid lines) and experimental110 (dashed lines) HOD/H2O line shapes in reverse micelles and bulk water. Note that, for the curves labeled w0 ) 4 and 7.5, the experimental spectra are actually for w0 ) 5 and 10, respectively. All curves are normalized to a maximum value of 1.

(albeit very weakly!) the experimentally observed broadening and then narrowing. From this, we conclude that we can obtain a qualitative understanding of the observed line shape trends by analyzing the spectral density. C. Spectral Density and Hydrogen Bonding. In bulk water, most researchers believe that on average a molecule is involved in about 3.5 hydrogen bonds, which means that a given H atom will be hydrogen bonded with a probability of between 0.8 and 0.9. This has implications for the OH or OD stretch spectroscopy of HOD/D2O or HOD/H2O, since it is known that, if the H or D atom is not hydrogen bonded, its frequency is significantly blueshifted compared to those that are. Thus, hydrogen bonding has been used to understand and interpret both absorption line shapes and spectral diffusion dynamics in these systems.129,136,138,152-154 Heterogeneous systems like RMs are clearly much more complicated than bulk water, and thus, it is useful to consider a simpler, yet still heterogeneous, system, that of (dilute HOD in) aqueous salt solutions. In this situation, water molecules will be found in many different microscopic environments, including around cations and anions. In terms of spectroscopy, it appears that the largest change in the OD stretch frequency arises when a hydrogen bond to water is replaced with a hydrogen bond to the anion.80 Thus, we could understand the features of the spectrum, and spectral dynamics, by considering three hydrogen bonding classes for a D atom: hydrogen bonded to other water molecules, to anions, or not hydrogen bonded at all. Adopting the same approach here for the case of AOT RMs, three classes can be distinguished: (i) D bound to other water molecules, (ii) D bound to the sulfonate oxygens on the surfactant headgroups, and (iii) free D atoms. A number of hydrogen bonding criteria have been proposed; here, we use one based on charge transfer to the σ*OD(H) orbital of the hydrogen bond donor molecule.134,155 For class ii, we use the position of the first minimum on the sulfonate-oxygen-water-hydrogen radial distribution function, 2.45 Å, as the hydrogen bonding criterion. If both i and ii are satisfied, then the D atom is assigned to class i. Only few such instances are observed. If neither of the criteria is satisfied, then it is in class iii. To quantify the populations, we define an auxiliary function hX, which is 1 when a given D atom is in class X, and 0 otherwise. X can be either (bonded to) H2O or AOT, or free. Results of the hydrogen bond population analysis for pure and confined water are summarized in Table 5. The overall probability of a given D atom being hydrogen bonded changes weakly with confinement, and is approximately 84%. Therefore, water inside an RM does not appear to be less or more

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TABLE 4: Characteristics of the Theoretical HOD/H2O Frequency Distributions, Spectral Densities, and Line Shapes for Water in Reverse Micelles and in the Bulk (Units Are cm-1)a frequency distribution w0 2 4 7.5 bulk

ωmax 2618 2609 2603 2573

fwhm 184 214 230 269

spectral density ωmax 2574 2548 2539 2508

fwhm 194 231 244 243

line shape ωmax 2577 2549 2538 2514

fwhm 171 192 195 169

experiment110 ωmax 2565 2558 2539 2512

fwhm 155 162 177 161

We also show results for the experimental line shapes. Note that for w0 ) 4 and 7.5 we have listed the experimental results for w0 ) 5 and 10, respectively. a

TABLE 5: Hydrogen Bond Probabilities for a D atom on HOD in Reverse Micelles and the Bulk w0

〈hH2O〉

〈hAOT〉

〈hfree〉

2 4 7.5 bulk

0.415 0.588 0.662 0.839

0.423 0.239 0.164

0.162 0.173 0.174 0.161

networked than in the bulk phase. In terms of the relative abundances of different types of hydrogen bonds, for the w0 ) 2 micelle, the ratio of D atom bound to surfactant headgroups to the water-bound species is roughly 1:1. As the size of the water pool increases, this ratio decreases to about 1:3 and 1:4 for w0 ) 4 and 7.5, respectively. Thus, even for the largest micelle studied here, the contribution of D atoms interacting directly with AOT is considerable. The change in the ratio can be interpreted as a decrease of the fractional population of interfacial molecules in the water nanopool due to the increased radius. Figure 7 presents the decomposition of the spectral density into the three hydrogen bonding classes, for different size RMs. Although the two hydrogen bonding peaks each show a weak blue shift with decreasing size, due to the increasing concentration of Na + counterions,80 to a first approximation the shapes and positions of the three spectral densities are independent of micelle size. This indicates that a given hydrogen bonding class is composed of molecules in similar environments in all of the RMs. Therefore, the observed blue shift and broadening of the IR spectra can be interpreted in terms of the shifting populations of different types of hydrogen bonds. The broadest and largest contribution to the spectral density is made by the D atoms bound to other water molecules. D atoms bound to AOT absorb on the blue shoulder of the water distribution. Finally, at the highest frequencies are the contributions from the unbound OD groups. These make only a minor contribution to the spectral density. These distributions appear to develop stronger lowfrequency tails in the micelles. Possibly, this is due to water molecules behind the headgroups, interacting with carboxyl groups (as the present scheme would classify those OD groups as free). This decomposition helps one to understand the observed spectral changes. As the micelle becomes smaller, the population balance between D atoms bound to water and AOT shifts toward the latter. This is accompanied by the rise in intensity on the blue side of the spectrum, and results in a blue shift of the peak frequency. As in salt solutions,80 the blue-shifted spectral density for the hydrogen-bonded-to-anion peak is narrower than the hydrogen-bonded-to-water peak, which produces a more asymmetric line shape for the smaller micelles. A subtle balance between the declining and emerging spectral densities results in an initial broadening and subsequent narrowing of the line shape. From looking at the spectral densities in Figure 7, we can also comment on possible spectral selectivity in pump-probe

experiments.105,112,113 If, for example, one excites below 2400 cm-1, the vast majority of the excited molecules have their D atoms bound to other water molecules. On the other hand, exciting at about 2600 cm-1, for the smallest micelle, shows that a majority of the D atoms are bound to AOT, while a strong minority are bound to other waters. Thus, there should be some selectivity regarding the hydrogen bonding state of the water molecules. Water molecules bound to AOT are most likely to be toward the edge of the micelle, while water molecules bound to other water molecules could be essentially anywhere in the interior. This means that there is a weaker, but still possibly observable, spatial selectivity by exciting on the blue side. Note, also, that the probe pulse can excite the 1-2 transition, whose spectral band overlaps with the red side of the 0-1 transition.113 Therefore, experiments performed on the blue side of the 0-1 transition are easier to interpret.112,113 D. Spectral Diffusion and Rotational Dynamics at Short Times. In addition to the absorption line shapes, Fayer and coworkers also performed ultrafast IR experiments.110 In particular, they measured vibrational echo peak shifts, which provide information about spectral diffusion, and polarization-resolved pump-probe anisotropy decays, which provide information about molecular rotation. These experiments have limited dynamic range due to the relatively short (but longer than that for OH) OD stretch lifetime. In this section, we study the shorttime (up to 5 ps) spectral diffusion and rotational dynamics, for comparison with these experiments. The latest work by the Fayer group presents frequency-resolved anisotropy decay experiments;112,113 we will provide a detailed analysis of these experiments in a future publication. The vibrational echo peak shift experiments were analyzed to obtain the frequency-frequency (time) correlation function (FFCF)

C(t) ) 〈δω10(t)δω10(0)〉

(6)

which characterizes spectral diffusion. In the above, δω10(t) ) ω10(t) - 〈ω10〉. Note that the experimental FFCFs were extracted from the three-pulse echo peak shift data, assuming a second cumulant truncation, and making the Condon approximation, neither of which approximation holds particularly well for water.139,156,157 The experimental110 FFCFs for different RMs are shown in Figure 8. The theoretical FFCFs are also shown in the same figure. One sees that, except for w0 ) 7.5, the agreement is satisfactory (and in the case of w0 ) 7.5, the nearest available experimental data to compare with is for w0 ) 10, which should, and does, decay faster than our theoretical result for w0 ) 7.5). Given the approximations made in obtaining these experimental FFCFs, this general level of agreement between theory and experiment is surprisingly good. Both theory and experiment show that, following an initial drop, the observed dynamics is visibly slower in the RMs than in bulk water. The dynamics of the decay become slower with decreasing pool size. This means that in a smaller micelle the processes that allow


Figure 6. Calculated HOD/H2O spectral densities for water in reverse micelles and in bulk. All curves are normalized to a maximum value of 1.

Figure 7. Decomposition of HOD/H2O spectral density with respect to hydrogen bonding class: bound to water (solid line), bound to AOT (dashed line), and free (dotted line).

J. Phys. Chem. B, Vol. 113, No. 45, 2009 15023

Figure 9. Normalized FFCFs for OD groups hydrogen bonded to AOT (solid lines) and water (dashed lines) at time zero.

Figure 10. Comparison of calculated (solid lines) and experimental (dashed lines) rotational anisotropy decays. Note that experimental data for w0 ) 5 and 10 are shown instead of those for 4 and 7.5, respectively.

below), this is because water molecules hydrogen bonded to other water molecules near the interface are slower than the same class of molecules in the center of the micelle, and the overall decay of these types of molecules is faster in larger micelles because there are more water molecules near the center of the micelle. A similar picture emerges from the study of rotational anisotropydecay,asmeasuredbypolarization-resolvedpump-probe experiments.110 Within some approximations, one can extract from experiment the second-rank anisotropy decay timecorrelation function:

C2(t) ) 〈P2(uˆ(t) · uˆ(0))〉 Figure 8. Comparison of calculated (solid lines) and experimental110 (dashed lines) HOD/H2O FFCFs. Note that experimental data for w0 ) 5 and 10 are shown instead of those for 4 and 7.5, respectively.

the oscillator to sample the different environments, and consequently different frequencies, are slower. The curves are nonexponential; thus, a single time constant cannot be assigned. To understand the origin of the slow dynamics, we calculate FFCFs for subensembles of molecules bound at time t ) 0 to other water molecules, and those bound to AOT. Results, for the normalized FFCFs for the two subensembles, are presented in Figure 9. We see that, on this time scale, spectral diffusion of the OD oscillators bound to AOT is more or less independent of the water pool size. On the other hand, the spectral dynamics of molecules bound to water becomes faster as the water pool becomes larger (but even for w0 ) 7.5 it is still visibly slower than in the bulkssee Figure 8). Presumably (and see

(7)

where, as mentioned above, uˆ(t) is the unit vector in the direction of the OD bond at time t and P2 is the second Legendre polynomial. A comparison between theory and experiment is shown in Figure 10. In all cases, the simulated anisotropy decay is somewhat faster than that in experiment, although the theoretical trends of slower decay with smaller micelles match the experimental trends. In Figure 11, we again divide the molecules into two subensembles, those hydrogen bonded to AOT at time 0 and those hydrogen bonded to water. The results are quite similar to those in Figure 9, with similar conclusions, although here one sees a systematic change with RM size for the molecules bound to AOT: these molecules in the smaller micelles have a slower decay after the initial inertial drop. This result is somewhat surprising, since one might assume that all molecules bound to AOT at the surfactant/water interface would exhibit rotational dynamics that are independent of micelle size. To investigate this a little further, and to answer the question posed in the Introduction about how far from an interface do

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Figure 11. Rotational anisotropy decays for OD groups hydrogen bonded to AOT (solid lines) and water (dashed lines) at time zero. The overlap between solid red and dashed black lines is accidental.

Figure 12. Comparison of rotational anisotropy values at 4 ps at different distances from the headgroups. The distance is defined as that between the water oxygen and the nearest sulfonate oxygen. For each RM, the solid lines are exponential fits, as described in the text.

the dynamical properties of water approach their bulk values, we want to quantify the extent of rotational relaxation a given distance from the interface. There are many ways to do this, and here, we take one simple approach. To quantify the extent of rotational relaxation, we consider the value of C2(t) at t ) 4 ps (an arbitrary but representative time), and to characterize the “distance from the interface”, we consider the distance between the oxygen atom on a given water molecule from the closest AOT oxygen. These values, as a function of distance, for the different micelles, are shown in Figure 12. The surprising result, consistent with the above, is that at eVery distance from the interface rotational relaxation is slower as the micelle gets smaller! Why might this be? Our suggestion is that this is a result of curvature-induced frustration (in the spin-glass sense158). That is, as the concavity of the interface increases, it becomes increasingly difficult, as interfacial water molecules strive to satisfy conflicting local constraints, to find low-energy bifurcated hydrogen bond transition states necessary for rotational motion;159 thus, the system becomes “jammed”. A similar idea was expressed in the recent paper by Moilanen et al.113 Additional possibilities are related to changes in the structure (rather than simply the curvature) of the interface with decreasing RM size.86,113 For instance, the surface area per headgroup is 43, 41, and 31 Å2 for w0 ) 7.5, 4, and 2, respectively. These numbers were obtained by assuming a spherical micelle with a radius equal to the maximum of the sulfur-water-pool-COM radial distribution function. Thus, the surface charge density increases with decreasing RM size.86,113 Possibly related to this is the observed increased water interfacial density with decreas-

Pieniazek et al. ing RM size.127 Either of these effects could also be partly responsible for the slower interfacial dynamics as the RM gets smaller. This finding and the suggested mechanism have several interesting implications. First, this implies that the core/shell model might have limitations, since the dynamics of the “shell” water depends on the size of the micelle. For very large micelles, whose curvature is very large (so that the water/surfactant interface is almost flat), this dependence would be very weak, implying that the core/shell model should work under those circumstances. These two statements are consistent with the recent experimental findings of Moilanen et al.113 These authors state that the core/shell (two-ensemble) model works for large micelles but not for small ones. Second, we can address the question posed in the Introduction regarding the distance from the interface at which water dynamics approaches that of the bulk. In Figure 12, the value of C2(4 ps) for bulk water is shown as the blue line. For w0 ) 7.5, one sees that C2(4 ps) becomes close to the bulk value at about 8 Å (from the AOT oxygen molecules), which is beyond the second solvation shell. For the smaller micelles, there are insufficient molecules at distances larger than 5 or 7 Å, for w0 ) 2 or 4, respectively, to obtain meaningful statistics, and thus, C2(4 ps) never reaches the bulk value. However, the existing data can be extrapolated to longer distances. A simple and physically reasonable form for this extrapolation is an exponential,32 and an exponential fit for each micelle size is shown in Figure 12. One sees that, for w0 ) 4, C2(4 ps) does not become within a few percent of the bulk value until about 10 Å, and for w0 ) 2, this does not occur until about 13 Å. The picture, then, is that the distance from the interface at which water dynamics becomes bulk-like depends on the curvature of the concave interfaces in these reverse micelles, and increases with decreasing radius of curvature. In the limit that the micelles become very large, the radius of curvature becomes infinite, and we can make the connection with a recent simulation study of flat interfaces.32 There are some differences between this study and ours (the interface studied therein is the water/silica surface, and they studied only lateral rotational dynamics), but also some similarities (they are both polar interfaces), and their conclusion was that at about 5 Å from the H atoms at the silica surface (or at about 6 Å from the oxygen atoms), water dynamics becomes bulk-like. The fact that this number is less than our number of 8 Å is consistent with the idea that this distance depends on the curvature of the interface, and increases with decreasing radius of curvature. One can be even more speculative by considering convex polar interfaces, where according to the above ideas of frustration, the critical distance in question might be expected to decrease from the value for the flat interface, since there is even less frustration for a convex interface. If so, one would expect that this distance would decrease with decreasing radius of curvature of the convex interface. One might even consider a limiting case of a convex polar interface to be a single cation or anion! Recent studies have shown that the dynamics of water in the second solvation shell of ions is very similar to that of the bulk,77-80 implying that this critical distance is on the order of 5 Å. This number, being smaller than the number of 6 Å for the flat interface, is consistent with the ideas expressed above about frustration, curvature, and water dynamics. E. Spectral Diffusion and Rotational Dynamics at Long Times.AsdiscussedintheIntroduction,computersimulation32,37,59,70,71 shows that biological, confined, and interfacial water are all significantly slower (sometimes by several orders of magnitude)


J. Phys. Chem. B, Vol. 113, No. 45, 2009 15025 OD groups, and defined the associated functions hX. In order to consider the exchange process among subensembles, we can calculate the hydrogen bonding correlation functions (HBCFs) defined as

CX(t) ) 〈δhX(t)δhX(0)〉

Figure 13. Comparison of normalized HOD/H2O frequency-frequency (black), hydrogen bonding to AOT (green), and hydrogen bonding to water (red) correlation functions, for times up to 1 ns.

Figure 14. Long-time anisotropy decays in different size reverse micelles.

than bulk water. Therefore, it is interesting to examine the FFCF and rotational anisotropy decay on longer time scales than can be measured by ultrafast vibrational spectroscopy. In Figures 13 and 14, we show the normalized FFCF and rotational anisotropy decay for times up to 1 ns, for the different micelle sizes. Remarkably, for the smallest micelle, at 1 ns, these timecorrelation functions are at well over 1% of their initial values; the dynamics in these systems is very slow indeed! Note that spectral diffusion time scales become shorter as the micelle size increases. Also note that in all cases rotational dynamics is faster than spectral diffusion dynamics, and that at long times rotational time scales appear to be independent of micelle size. To understand the long spectral diffusion time scales, we observe that spectral diffusion is complete when frequencies become uncorrelated, or when a subensemble of frequencies has evolved to the equilibrium distribution of frequencies. Thus, this is the time when the subensemble has sampled all possible microscopic environments, including bound to AOT headgroups, in Na+ solvation shells, and well removed from the interface region. If one divides up the ensemble of frequencies into these subensembles, then one can separately consider the times for subensemble populations to exchange and reach equilibrium, and the times for equilibration within each subensemble. Any of these times could, in principle, be the slowest. Above, we considered three subensembles of the frequency distribution, for those D atoms bound to AOT or water, or free

(8)

where δhX(t) ) hX(t) - 〈hX〉. Two HBCFs, for AOT and water, are shown in Figure 13 for each micelle size. One sees, in each case, that the two HBCFs have similar dynamics, which in turn are similar (in time scale but not amplitude) to the FFCFs. This suggests that the physical mechanism for spectral diffusion on these time scales involves equilibration of the populations of the three subensembles. Note that, for this to occur completely, this involves sampling all environments, for example, for boundto-water molecules, including those near the headgroups, and those well away from the interface. Thus, this equilibration involves spatial diffusion of water molecules throughout the micelle, which is why the process is so slow, especially for the smallest, glassiest, micelles. For the larger micelles, the rotational dynamics at a given distance is faster, allowing for faster diffusion and exchange between different environments. As a technical aside, we note that, for an ergodic system, the time average of a certain quantity (for example, the transition frequency or hX) over a trajectory for a single member of the ensemble is equal to the ensemble average of the same quantity. For homogeneous systems with relatively fast relaxation times, this is certainly found to be the case, for finite but accessible simulation times. In our case, however, where the system is very heterogeneous, and relaxation times are very long, even over simulation runs of 10 ns and longer, this is not the case. Therefore, when calculating time-correlation functions where the average is subtracted off (as in the FFCF and HBCFs), for each trajectory, one can subtract either the ensemble average or the average over that trajectory. We have chosen the latter, but it is important to keep in mind that the long-time properties of the correlation functions are sensitive to this choice. The rotational dynamics shown in Figure 14 are faster than the spectral diffusion dynamics because the former is more local, in that molecules can rotate, in principle, without spatial diffusion, whereas spectral diffusion cannot occur without spatial diffusion. As mentioned above, while the amplitudes of the longtime decay decrease with increasing micelle size, the time scales are size-independent. A reasonable interpretation is that the longtime decay is due to molecules near the headgroup interface, in that these rotate the slowest, and the fraction of these molecules decreases as the micelle size increases. Like in other glassy systems with slow relaxation times,160 dynamic processes are very collective and can often be fit with stretched exponentials of the form exp(-(t/τ)β). All of the correlation functions (spectral diffusion, hydrogen bonding, and anisotropy decay) can be fit well, over the range of 0.2 ps to 1 ns, by stretched exponentials. In all cases, the β parameter is very small (from 0.17 to 0.37), which is evidence of extremely collective behavior. IV. Concluding Remarks Using a new atomistic simulation model for AOT reverse micelles, we have calculated structural, dynamical, and spectroscopic properties. Our twofold goal has been to describe and interpret the absorption spectra and ultrafast observables of the OD stretch of dilute HOD in the water pool of AOT reverse micelles, and to provide insight into other aspects of molecular structure and dynamics in these well-controlled model systems for confined and biological water. Regarding the spectroscopy,

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we are able to reproduce, reasonably well, the position and width of the absorption line shape as a function of micelle size. The monotonic blue shift and nonmonotonic broadening and then narrowing as the micelle size decreases can both be understood by considering the spectral densities of different hydrogen bonding classes of HOD molecules. In particular, as the micelle size decreases, strong hydrogen bonds to water are replaced with weaker hydrogen bonds to the oxygen atoms on the sulfonate headgroups, which leads to both spectral trends. Theoretical calculations for two ultrafast observables, the spectral diffusion and rotational anisotropy time-correlation functions, also agree reasonably well with experiment, for different micelle sizes. Both correlation functions slow down with decreasing micelle size, in theory and experiment, and both can be understood roughly as arising from slower interfacial water and faster bulklike water. Given the general validation of the micelle and spectroscopic models by experiment, we can proceed to ask some questions not directly accessible experimentally. The first of these involves dynamics as a function of spatial position in the micelle. We calculated the rotational anisotropy of water molecules a given distance away from the sulfonate headgroup ions, and find that at each distance rotational relaxation depends on the micelle size, with slower relaxation corresponding to the smaller micelles. This finding has clear implications for the validity of the core/shell model, discussed above. In this model, properties in any micelle can be understood as arising from a combination of core and shell water molecules with different weights, and the explicit assumption is that shell water is the same for micelles of different sizes. Thus, the above theoretical observation is in contradiction with this assumption. Note that, for very large micelles, the differences between shell water could be very small, and thus, the core/shell model might hold approximately. The idea that the core/shell model is valid for large micelles but breaks down for smaller micelles was recently suggested by Fayer and co-workers,113 and thus, our work provides theoretical support for this suggestion. An interesting question, relevant to both confined and biological water, is, at what distance from a polarbiomolecule-water interface do the dynamical properties of water become bulk-like? For the largest micelle studied herein, with w0 ) 7.5, we found that the distance is about 8 Å (from the sulfonate ions), which is over two solvation shells. For the smaller micelles, the distance is larger than the micelle radius, but extrapolation of our results shows that the distance increases with decreasing micelle size. This raises the intriguing idea that this critical distance depends on the radius of curvature of a convex polar interface, where the distance increases with decreasing radius, and may not be sensitive to the details of the interface. We suggest that this increasing distance arises from curvature-induced frustration. In the limit of very large micelles, where the radius of curvature goes to infinity, the interface becomes flat. Information from computer simulation on a different, but still polar, interface shows that this critical distance is about 6 Å.32 According to our curvature-induced frustration idea, this length should be smaller than the number for the w0 ) 7.5 reverse micelle, and it is. A second issue, not accessible by vibrational spectroscopy experiments (because of the short vibrational lifetime), involves the long-time dynamics of spectral diffusion and rotation. We find that, over time scales up to 1 ns, neither of these correlation functions have decayed to zero! As in many other systems with glassy dynamics, the correlation functions are fit well by stretched exponential relaxation functions, with very low

Pieniazek et al. exponents (on the order of 0.2 or 0.3). The long-time decay of the spectral diffusion correlation function arises from the spatial diffusion of water molecules that is necessary to sample all molecular environments. Rotational relaxation is slightly faster since it is more local, and its long-time decay is clearly dominated by interfacial water. Because interfacial and bulk water have different (but overlapping) spectral densities, it is possible to obtain spatial selectivity by performing experiments at different pump and probe frequencies, as was recently done by the Bakker and Fayer groups.105,112,113 Thus, these authors come to the conclusions that interfacial water is significantly slower than bulk water. In another recent experimental study, Moilanen et al. compare water dynamics in AOT RMs and AOT lamellar structures.114 Comparing an RM with an internal diameter d, and a lamellar structure with the same interplanar distance d, it was found that rotational dynamics is always slower in the former, consistent again with the idea of slower interfacial dynamics (since the RM has a larger fraction of interfacial water). Molecular dynamics simulation of these lamellar systems would help confirm or refute our idea of curvature-induced frustration. We intend to calculate frequency-dependent anisotropy observables for both the RMs and lamellar structures, using the full infrastructure of third-order response functions,130 with the aim of providing theoretical support for, and interpreting, these exciting experiments. We hope to be able to report on this work shortly. Acknowledgment. The authors are grateful to Steve Corcelli, Shuzhou Li, Ben Auer, and Mohammad Toutounji for some preliminary work in the early stages of this project. We also thank Mark Ediger for helpful conversations. This work was supported by DOE grant DE-FG03-0ZER15376 and NSF grant CHE-0608640 (to B.M.L.) and DOE grant DE-FG02-09ER16110 and NSF grant CHE-0750307 (to J.L.S.). References and Notes (1) Yuan, K. J.; Cheng, Y.; Cheng, L.; Guo, Q.; Dai, D. X.; Wang, X. Y.; Yang, X. M.; Dixon, R. N. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 19148. (2) Keutsch, F. N.; Saykally, R. J. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 10533. (3) Bukowski, R.; Szalewicz, K.; Groenenboom, G. C.; van der Avoird, A. Science 2007, 315, 1249. (4) Huang, X.; Braams, B. J.; Bowman, J. M.; Kelly, R. E. A.; Tennyson, J.; Groenenboom, G. C.; van der Avoird, A. J. Chem. Phys. 2008, 128, 034312. (5) Ball, P. Life’s Matrix: A Biography of Water; Farrar, Straus, and Giroux: New York, 1999. (6) Petrenko, V. F.; Whitworth, R. W. Physics of Ice; Oxford University Press: Oxford, U.K., 1999. (7) Abascal, J. L. F.; Vega, C. J. Chem. Phys. 2005, 123, 234505. (8) Elles, C. G.; Rivera, C.; Zhang, X.; Pieniazek, P. A.; Bradforth, S. E. J. Chem. Phys. 2009, 130, 084501. (9) Levinger, N. E. Science 2002, 298, 1722. (10) Vaitheeswaran, S.; Thirumalai, D. J. Am. Chem. Soc. 2006, 128, 13490. (11) Kim, W.; Javey, A.; Vermesh, O.; Wang, O.; Li, Y. M.; Dai, H. J. Nano Lett. 2003, 3, 193. (12) Karlsson, M.; Davidson, M.; Karlsson, R.; Karlsson, A.; Bergenholtz, J.; Konkoli, Z.; Jesorka, A.; Lobovkina, T.; Hurtig, J.; Voinova, M.; Orwar, O. Annu. ReV. Phys. Chem. 2004, 55, 613. (13) Datta, A.; Das, S.; Mandal, D.; Pal, S. K.; Bhattacharyya, K. Langmuir 1997, 13, 6922. (14) Grunberg, B.; Emmler, T.; Gedat, E.; Shenderovich, J.; Findenegg, G. H.; Limbach, H. H.; Buntkowsky, G. Chem.sEur. J. 2004, 10, 5689. (15) Jennings, H. M. Cem. Concr. Res. 2008, 38, 275. (16) Gulmen, T. S.; Thompson, W. H. Langmuir 2006, 22, 10919. (17) Morales, C. M.; Thompson, W. H. J. Phys. Chem. A 2009, 113, 1922. (18) Raviv, U.; Laurat, P.; Klein, J. Nature 2001, 413, 51.

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