Hydrogen-Bond Dynamics for Water Confined in Carbon Tetrachloride

J. Phys. Chem. B 2008, 112, 10675–10683

10675

Hydrogen-Bond Dynamics for Water Confined in Carbon Tetrachloride-Acetone Mixtures Naga Rajesh Tummala and Alberto Striolo* School of Chemical Biological and Materials Engineering, The UniVersity of Oklahoma, Norman, Oklahoma 73019 ReceiVed: April 22, 2008; ReVised Manuscript ReceiVed: May 29, 2008

In a variety of biological scenarios water is found trapped within hydrophobic environments (e.g., ion channels). Its behavior under such conditions is not well understood and therefore is attracting enormous scientific attention. It is of particular interest to understand how the confining environment affects both the structure and dynamics of water. Within this scenario, we report molecular dynamics simulation results for water trapped in a mixture of acetone and carbon tetrachloride whose composition mimics the one employed in recently reported experiments [Gilijamse, J. J.; et al. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3202]. We show here that the water molecules dissolved in the carbon tetrachloride-acetone mixture assemble in clusters of varying sizes, that the longevity of hydrogen bonds between confined water molecules strongly depends on the cluster size, and that hydrogen bonds last longer for small water clusters in confined water than they do in bulk water. The simulated FT-IR spectra for the confined water are shifted at longer frequencies compared to those observed for bulk liquid water. We discuss the dependence of the FT-IR spectrum on the size of the water clusters dispersed in the carbon tetrachloride-acetone matrix. We also study in detail the rotational orientation of the dispersed water molecules, and we discuss how the composition of the organic matrix affects the results. By enhancing the interpretation of the experimental data, our results contribute to developing a molecular-based understanding of the relationship between environment and water properties. 1. Introduction The investigation of aqueous solutions is a subject of multidisciplinary interest. Although extensive simulation and experimental studies have been conducted over the past decades to unveil the properties of bulk liquid water,1-4 the detailed understanding of such systems still stimulates scientific debates that can only be solved via the synergistic application of sophisticated experimental and theoretical techniques. Molecular dynamics simulations can be employed not only to aid the interpretation of the raw experimental data5 (e.g., from NMR,6,7 spectroscopy,3,8 and other measurements1,9,10), but also to assess structural and dynamic properties at the molecular level (e.g., hydrogen-bond lifetimes11,12). For example, Eaves et al.13 applied two-dimensional Fourier transform infrared (FT-IR) spectra methods (both simulated and experimental) to prove that nonhydrogen-bonded water molecules “are intrinsically unstable and that dangling hydrogen bonds are an insignificant species in liquid water”. Because in many biological14-16 and other systems water is found trapped within hydrophobic environments, several studies have been reported to unveil the properties of confined water.13,17-20 A recent report detailed water in a hydrophobic environment composed of carbon tetrachloride. The results suggest that the confined water molecules have faster rotational correlation times than bulk water molecules do because of the absence of hydrogen bonds (HBs).21,22 We are here interested in understanding how and why the properties of confined water change when the confining organic matrix contains a possible HB acceptor and how they compare to those observed in the bulk. This work was stimulated by a recent experimental study in which femtosecond mid-IR pump-probe measurements were employed to assess the molecular motion and the energy-transfer dynamics of water molecules enclosed in a fluid organic * Author to whom correspondence should be addressed. Phone: (405) 325-5716. Fax: (405) 325-5813. E-mail: [email protected].

matrix.23 The experimental system was carefully prepared to contain water, acetone, and carbon tetrachloride in the molecular ratio 1:10:40, and the measurements were conducted at room temperature.24 Because of the small amount of water, it was assumed that individual water molecules were dispersed within the acetone-carbon tetrachloride mixture. Strong evidence was found according to which the energy transfer in the carbon tetrachloride-acetone mixture is more than 20 times slower than that which occurs in bulk liquid water.23 Long-lived water-acetone HBs were considered responsible for the experimental findings, although the water-acetone HB is much weaker compared to water-water HBs.23 Our detailed simulations provide a complementary description. In our system, the few water molecules are not dissolved uniformly within the mixture, but rather form clusters dispersed within the simulation box. The water clusters, which are not uniform in size, are in general surrounded by acetone molecules. In partial agreement with the experimental data, our results indicate that both rotational dynamics and simulated FT-IR spectra strongly depend on cluster size and differ significantly compared to those observed in bulk liquid water. In addition, our results show that these effects are predominantly due to water-water HBs, and not only to water-acetone HBs, unless the water molecules are individually dispersed in the organic matrix. In the remainder of this paper, after a brief description of the molecular model and algorithms implemented, we discuss our main results and how they both favorably compare and enhance the interpretation of experimental data. 2. Simulation Methods and Algorithms A. Force Fields. The SPC/E model for water25 is suitable to characterize HBs and reorientational average times for water under various conditions.26-28 Because we cannot generate simulated FT-IR spectra with rigid models for water, we

10.1021/jp803511f CCC: $40.75  2008 American Chemical Society Published on Web 08/06/2008

10676 J. Phys. Chem. B, Vol. 112, No. 34, 2008

Tummala and Striolo

TABLE 1: Force Field Parameters for Water, Acetone, and Carbon Tetrachloride, As Implemented in Our Simulationsa Water site

σ (Å)

ε (kcal/mol)

q (e)

O H

3.166 0.000

0.155 402 0.000 000

-0.8476 0.4238 parameters

bond length O-H H-H O-H, H-H O-H, O-H

equation 2 ∑ i)1 De[1

0 - exp(R(rOHi - rOH )]2 i 0 2 0.5kθ(rHH-rHH ) 0 0 2 krθ(rHH - rHH )[∑ i)1 (rOHi - rOH )] i 0 2 (r r ) krr∏i)1 OHi OHi

0 rOH i ) 1.0 Å 0 rHH )1.633 Å

De ) 101.9188 kcal/mol kθ ) 328.645 606 kcal/mol Å2 krθ ) -211.467 20 kcal/mol Å2 krr ) 111.707 65 kcal/mol Å2

R ) 2.567 Å-1

Acetoneb site

σ (Å)

ε (kcal/mol)

q (e)

CH3 C O

3.910 3.750 2.960

0.160 895 0.105 058 0.210 13

0.0620 0.3000 -0.4240

site

σ (Å)

ε (kcal/mol)

q (e)

C Cl

3.410 3.450

0.100 000 0.285 000

-0.1616 0.0404

CCl4

parameters equation bond length (C-Cl) bond angle (Cl-C-Cl)

0 0.5kb(r - rC-Cl )2 0 0.5ka(θ - θCl-C-Cl )2

0 rC-Cl )1.766 0 θCl-C-Cl )109.50

kb ) 630.0 kcal/mol Å2 ka) 149.0 kcal/mol rad2

0 0 ε and σ are Lennard-Jones parameters and q is the partial charge on each site. rx-y is the equilibrium distance between sites x and y. θx-y-z 0 0 b is the equilibrium angle between sites x, y, and z. Fixed bond lengths in acetone are rCH3-C ) 1.507 Å and rC-O ) 1.220 Å. Fixed bond 0 0 angles are θCH 3-C-CH3 ) 116.30° and θCH3-C-O ) 121.86°. a

implemented the flexible version of the SPC/E model used by Praprotnik et al.29 A fully flexible, nonpolarizable, five-site model was chosen to simulate carbon tetrachloride.30 The correct implementation was validated by reproducing structural properties for bulk liquid carbon tetrachloride available in the literature.31,32 The united atom OPLS force field was chosen to simulate acetone.33 The implementation was validated by comparing our simulated radial distribution functions (RDFs) for bulk liquid acetone to experimental and simulated ones.34,35 It should be noted that the available simulation data agree only qualitatively with each other, although they capture some of the main experimentally observed features. This model yields a self-diffusion coefficient of 5.29 × 10-5 cm2/s, which is in semiquantitative agreement with the experimentally observed value of 4.77 × 10-5 cm2/s.36 To describe interactions between nonbonded atoms, 12-6 Lennard-Jones (LJ) potentials were employed. The parameters for not-alike atoms were obtained from those of the pure components via Lorentz-Berthelot mixing rules.37 In Table 1 we report all the parameters used to implement the force fields in our simulations. Mixtures of water and acetone have been studied previously by molecular dynamics (MD) simulations.38-40 In those simulations two models for water (i.e., the SPC/E and the TIP4P) and three models for acetone were considered. The results showed that, although all combinations of force fields reproduce experimental enthalpy, pressure, density, and diffusion coefficients relatively well, the prediction of Kirkwood-Buff integrals strongly depends on the force fields implemented. In particular, when water is described by the SPC/E model and acetone with the OPLS force field, the acetone-water mixture

demixes for acetone mole fractions between 0.3 and 0.7, which disagrees with experimental evidence. However, when the acetone mole fraction is below 0.3 or above 0.7, this combination of force fields seems to appropriately reproduce the Kirkwood-Buff integrals.39 Because our calculations are performed in a system that contains traces of both water and acetone, a flexible SPC/E model for water and the OPLS model for acetone appear to be reasonable choices. B. Algorithms. The simulation was initiated with a simulation box of size 4.5 × 4.3 × 4.5 nm3 which contained 12 SPC/E water molecules. To maintain the experimental molecular ratio, 120 acetone and 480 carbon tetrachloride molecules were inserted within the simulation box. The molecules were inserted within a lattice to avoid overlapping. The initial system density (1.55 g/cm3) was similar to the bulk liquid density of carbon tetrachloride (1.58 g/cm3). MD simulations were conducted within the canonical ensemble (NVT) for 1 ns at 1000 K. In the NVT ensemble the simulation box volume (V), the number of particles (N), and the temperature (T) are maintained constant. The system was then cooled to 300 K. The cooling rate was 100 K every 300 ps. Once the target temperature of 300 K was reached, the system was further simulated for 1.5 ns. The simulation box was at this point replicated twice in each direction. The final system contained 96 water, 960 acetone, and 3840 carbon tetrachloride molecules. Simulations were continued at 300 K for 2 ns in the NVT ensemble. Equilibration was then achieved by conducting MD simulations in the isobaric-isothermal (NPT) ensemble for 8 ns at room conditions. In the NPT ensemble the simulation box volume was allowed to fluctuate to maintain the pressure (P) constant. The

MD of Water in CCl4-Acetone Mixtures

J. Phys. Chem. B, Vol. 112, No. 34, 2008 10677

production phase was then initiated. During the production phase the simulation box maintained the size ∼9.0 × 9.0 × 9.0 nm3, which contained the 96 water molecules. The production phase was carried out for 2 ns, and the results presented here are the average of three 250 ps trajectories separated evenly within the production phase. Additional NPT simulations were performed for bulk liquid flexible SPC/E water at 300 K in a simulation box of 3.0 × 3.0 × 2.0 nm3 with a density of 0.996 g/cm3. Equilibration and production phases lasted 200 ps each. The simulation package LAMMPS41 was employed to integrate the equations of motion within the Nose-Hoover thermostat and barostat using the velocity Verlet algorithm (relaxation time constant of 100 fs).41 The time step used was in the range 0.5-1 fs. A spherical cutoff of 0.9 nm was implemented for both electrostatic and LJ interactions. Longrange electrostatic effects were treated using the Ewald sum method.37 The rigid bond lengths in acetone were constrained using the SHAKE algorithm.42 Periodic boundary conditions were implemented in the X, Y, and Z directions. During production the system configuration was recorded at regular intervals and used for subsequent analysis. The positions of water and acetone were recorded every 25 fs, those of carbon tetrachloride were recorded every 500 fs, and the velocities of waters were recorded every time step. C. Hydrogen-Bond Criteria. The formation of HBs between molecules can be assessed using geometric43 and energetic44 criteria. We adopted the geometric criterion because it best suits the description of HBs at a variety of thermodynamic conditions.45 Two different water molecules, or one water and one acetone molecule, are considered to be hydrogen bonded if their coordinates satisfy three conditions:46 (1) The distance between the oxygen atoms is less than the first minima in the O-O radial distribution function (RDF): 0.36 nm for water-water and 0.376 nm for water-acetone. (2) The distance between oxygen and hydrogen is less than the first minima in the O-H RDF: 0.245 nm for water-water and 0.269 nm for acetone-water. (3) The angle formed between hydrogen-bonded atom and the OH of water is less than 30°. D. Hydrogen-Bond Lifetime. Once the HB has been defined, the mean hydrogen-bond relaxation time (τHB) is accessible.27,47-58 Following Rapaport59 we computed relaxation times from time-dependent correlation functions of hydrogenbonded populations which reflect the existence (or absence) of HBs between each of the possible pairs of molecules in the system. Two types of autocorrelation functions (ACFs) are employed: (1) autocorrelation for molecular pairs bonded continuously over the entire statistical analysis (continuous HB ACF); and (2) autocorrelation for molecular pairs irrespective of intervening interruptions (intermittent HB ACF). The HB ACF is defined as46

C(t) )

〈h(0) h(t)〉 〈h(0) h(0)〉

(1)

Angular brackets indicate ensemble average and h(t) determines whether the pair of molecules considered is hydrogen bonded or not. h(t) is 1 if the considered pair is hydrogen bonded, and is 0 otherwise. For continuous ACFs, h(t) for a molecular pair is 1 when bonded and becomes 0 once the HB breaks. It remains 0 even if the bond forms again. In the intermittent ACFs, h(t) is 0 only when there is no bond between the considered pair of molecules and 1 whenever the bond exists. To estimate HB relaxation times, we report the time taken by the ACFs to decay from 1 to 1/e, 1/e2, and 1/e3. The three relaxation times are

representative of fast, intermediate, and slow relaxations of hydrogen-bonded populations. Molecular reorientational times can be assessed by computing dipole-dipole ACFs. The results can be compared to dielectric and NMR relaxation experiments.27,52,60 The time correlation functions employed here are of the form

Cl,R(t) )

〈Pl(µ ˆR(t) µ ˆR(0))〉 〈Pl(µ ˆR(0) µ ˆR(0))〉

(2)

where Pl is the lth Legendre transform. µˆ R is the unit vector obtained as the normalized sum of the two OH bond vectors in one water molecule. We also computed the correlation function described by eq 2 considering the bond vector connecting oxygen and hydrogen atoms of a water molecule (OH vector), the vector connecting the two hydrogen atoms (HH vector), and also the vector normal to the plane formed by the cross product of the OH and HH vectors (⊥ vector). The reorientational relaxation times, calculated similarly to the relaxation times for HB, are τC2,µ, τC2,OH, τC2,HH, and τC2,⊥, respectively. E. Simulated FT-IR Spectra. The following relation was used to evaluate simulated FT-IR spectra:61

I(ω) ) π-1ω-2

·

·

∫0∞ 〈M(t)/M(0)〉 cos ωt dt

(3)

˙ (t) is the dipole moment velocity. As shown by Martí In eq 3 M et al.,61 the time correlation function of the dipole moment velocity of all the molecules under consideration can be well approximated by the expression ·

·

c 〈M(t)/M(0)〉 ≈ q2VHH (t) ) 〈VH(t) VH(0)〉

(4)

c VXY

In eq 4 is the collective velocity autocorrelation function between atoms X and Y, q is the charge on the atom, and 2N

VH(t) )

∑ VH (t) i)1

i

(5)

In eq 5 VHi is the velocity of the ith hydrogen and N is the number of water molecules. 3. Results and Discussion A. Equilibrium Structure. A typical simulation snapshot is reported in Figure 1. Visual analysis indicates that the water molecules agglomerate into clusters dispersed throughout the system. These clusters are surrounded by acetone molecules, as expected, and embedded within the hydrophobic carbon tetrachloride matrix. However, it should be noted that acetone does not provide a strongly associated shell to the water clusters. Instead, our simulations indicate that, to some extent, carbon tetrachloride also comes into contact with water. Additional results, not shown here for brevity, indicate that the presence of water within the system has the effect of diminishing the association between acetone molecules and also between acetone and carbon tetrachloride, although less significantly. To characterize the system, and to allow the interested reader to calculate thermodynamic properties from Kirkwood-Buff62 integrals, we report in Figure 2 the radial distribution functions (RDFs) for water-water, water-acetone, water-CCl4 (oxygenchlorine), acetone-acetone, acetone-Cl in CCl4, and CCl4-CCl4 (carbon-carbon). Visual inspection confirms that water molecules form clusters within the simulated system and that acetone molecules are more attracted to water than they are to other acetone molecules. Water molecules tend to repel the chlorine atom in CCl4, while acetone molecules are somewhat attracted to them. The CCl4-CCl4 RDF (Figure 2f)


Figure 1. Typical simulation snapshot. Water molecules are enlarged for visualization purposes. White and large red spheres represent hydrogen and oxygen atoms in water, respectively. Small red, gray, and cyan spheres represent oxygen atoms, methyl groups, and carbon atoms in acetone, respectively. Carbon tetrachloride molecules are represented, within the wireframe convention, as green lines. The simulated system consists of 96 water molecules, 960 acetone molecules, and 3840 carbon tetrachloride molecules, for a total of 23 328 atoms.

suggests that the organic matrix is a dense liquid, as expected from the system density. To quantify the average size of the water clusters found within the simulated system, we calculated the frequency at which we observe a cluster of size N during the course of our simulation. To assess whether the simulated system was “evolving” during our simulation, we computed the distance between the centers of mass of different water clusters as a function of time. These results do not indicate any process of aggregation; i.e., the clusters do not come closer during the course of the 2 ns simulation. This does not preclude that the clusters would agglomerate into bigger ones during longer simulations, but because we observed clusters forming and breaking into smaller ones during our analysis, we consider our data to be representative of the equilibrated system. The average size of water clusters is shown in the form of a “population distribution” in Figure 3. Water molecules are considered as belonging to the same cluster when they are connected to each other through a hydrogenbonded network. In Figure 3 we report our results for the population distribution. It helps remembering that the system under investigation is composed of 96 water molecules. Our results indicate that about 30% of the clusters contain one water molecule, and that clusters anywhere in size between 2 and 62 molecules can be observed during the simulation. The largest observed cluster contains 62 water molecules (with 20% probability). The four cluster sizes that are observed more frequently are 62, 22, 11, and 1 molecule. During our simulation we observe only one water molecule completely isolated from the other waters in the system (see snapshot in Figure 1). The remaining 95 water molecules form clusters of various sizes. However, it is also possible that one water molecule near a cluster is momentarily not hydrogen bonded to the cluster. Other cluster sizes in the

Tummala and Striolo population distribution are present because of the temporary breaking of HBs between the water molecules belonging to one large cluster. It should be pointed out that the single water molecule forming an isolated cluster did not form one single HB with other water molecules during the entire 2 ns of production time. Because our results indicate the possible formation of HBs not only between water and acetone, but also between different water molecules, it is interesting to compute the probability of finding different types of HBs during the course of the simulation. The results are presented as follows. For each of the 96 water molecules in the simulation box we evaluate the number of HBs established with another water molecule (nw, X-axis) and that with one acetone molecule (na, Y-axis). The possibility that water molecules form nw HBs with water and na with acetone is denoted by the (nw, na) coordinate, in correspondence of which we report the occurrence probability P in Figure 4. We note that a significant portion of water molecules form HBs with either water or acetone. In other words, although we do not often observe isolated water molecules within the system, we do observe very few nonhydrogen-bonded water molecules in the vicinity of other waters. Our results indicate that the probability of observing 1 water molecule forming only 1 HB with another water [(1, 0) combination] is at most 2%. The probability of finding one water molecule engaged with only one HB to acetone [(0, 1)], ∼0.6%, is similar to the probability of finding one water molecule simultaneously hydrogen bonded to two other waters and two acetones [(2, 2)]. Similarly, the probability of finding one water molecule simultaneously hydrogen bonded to only two acetone molecules [(0, 2)] is ∼0.2%. On the contrary, the probability of observing one water molecule simultaneously engaged in three or more HBs is ∼80%. Thus our results suggest that most of the water molecules are engaged in multiple HBs. From Figure 4 we observe that the probability of the (1, 1) configuration (one HB with water and one with acetone) is greater than that of the (0, 2) configuration (two HBs with acetone). The cumulative probability of all configurations with water molecules having zero HBs to acetone [(nw, 0) configurations] is 73%, whereas that of all configurations with one HB with acetone [(nw, 1) configurations] is 25%. Thus, when possible, waters form HBs among themselves. This may be due to the molecular size of acetone, but also due to the strength of water-water compared to water-acetone hydrogen bonds. The cumulative probability of (nw, 2) configurations, with any nw, is ∼2%, probably not only because of weak water-acetone HBs, but also because (0, 2) configurations are sterically hindered. To appreciate the properties of a system in which water molecules associate only with acetone, we calculated the probability distribution of HBs associated with the water molecule for the cluster of size 1. This water molecule can only form HBs with neighboring acetone molecules. The results are shown in Figure 5. We note that the probability of finding one non-hydrogenbonded water molecule is ∼20% when considering water dispersed as a single molecule in carbon tetrachloride-acetone matrix, while it is ∼0.2% when water clusters with sizes greater than one molecule are considered. The results shown in Figure 5 also indicate that it becomes more probable for water molecules at infinite dilution to form simultaneously two HBs with acetone than it is when multiple water molecules are present. Because water-acetone HBs are not energetically favorable, our results suggest that when other water molecules are not available, multiple bonds are required to stabilize water



Figure 2. Radial distribution functions between various molecules within our system. “Ow” represents the oxygen atom of the water molecule, “Oa” represents the oxygen atom of the acetone, “Cl” and “CCCl4” represent chlorine and carbon atoms of carbon tetrachloride, respectively. In all cases T ) 300 K.

Figure 3. Population distribution of cluster sizes at 300 K. N is the number of water molecules simultaneously hydrogen bonded to each other.

within the hydrophobic environment. From Figures 4 and 5 it is evident that it is more probable for the water molecule to be non-hydrogen bonded when it is surrounded by acetone molecules rather than when it is surrounded by other waters.

Figure 4. Probability P of observing one water molecule hydrogen bonded to either water or acetone. We report on the X-axis the number of HBs with other water molecules (nw) and on the Y-axis the number of HBs with acetone (na).

We also observe that the average number of HBs per water molecule for the isolated water is 1.06, while it is 3.16 for the remaining water molecules. This reinforces the conclusion that, when possible, water molecules trapped in a hydrophobic fluid matrix tend to form hydrogen-bonded water clusters to lower


Figure 5. Probability (P) of finding the isolated water molecule hydrogen bonded to na acetone molecules. For these calculations we considered the cluster with only one water molecule dispersed within the carbon tetrachloride-acetone matrix (see Figure 1).

Tummala and Striolo

Figure 6. Intermittent water-water hydrogen-bond ACFs. The dotted line represents results for water molecules trapped in the carbon tetrachloride-acetone mixture; the continuous line represents those for bulk liquid water.

TABLE 2: Water-Water HB Relaxation Times (ps), Evaluated as the Time Required for the ACFs To Decay from 1 to 1/e, 1/e2, and 1/e3 a τHB(I) (1/e) τHB(I) (1/e2) τHB(I) (1/e3) τHB(C) (1/e) τHB(C) (1/e2) τHB(C) (1/e3)

confined water

bulk water

22.22 (1.5) 88.86 (6.4) >225 4.35 (0.8) 10.61 (1.1) 17.65 (1.8)

25.20 70.10 149.50 5.20 12.90 20.60

a We report data obtained for water in the organic matrix averaged over all 96 water molecules (confined water), and those for bulk liquid water (bulk water). Simulations were conducted at room conditions. The index “I” indicates results obtained from intermittent ACFs and “C” those obtained from continuous ACFs. Values in parentheses are standard deviations from the mean over the three analyses performed.

their free energy. When no other water molecule is available, water can only form weak HBs with acetone. The numbers of water-acetone and water-water HBs averaged over all the 96 confined water molecules are 0.28 and 2.88, respectively, whereas the average number of HBs calculated from independent simulations for bulk flexible SPC/E water is 3.36, which is similar to the value reported by Martí12 (3.5). B. Hydrogen-Bond Lifetime and Reorientation Dynamics. In Table 2 we report the continuous and intermittent HB relaxation times for water-water HBs within the organic matrix and also those for bulk water. The continuous ACF monitors how long HBs that are present at the beginning of the statistical analysis persist during the simulation, whereas the intermittent ACF accounts not only for the HBs present at the beginning of the analysis, but also for those that form during the simulation. It is expected that the continuous ACF decays faster than the intermittent one, as can be observed from our data. The estimated relaxation times for continuous ACF for confined water are significantly shorter than those obtained for bulk liquid water. On the contrary, the intermittent HB ACFs for water in the organic matrix decay more quickly to 1/e, but more slowly to 1/e2 and to 1/e3, than that obtained for bulk liquid water. In Figure 6 we compare the intermittent water-water HB ACF for water trapped within carbon tetrachloride-acetone to that obtained in bulk liquid water. Both simulations are conducted at room conditions. Our data show that at time scales on the

Figure 7. Intermittent water-water HB ACFs for water in carbon tetrachloride-acetone mixtures. Black, blue, and red lines are for water in clusters of size 11, 22, and 62, respectively. The green line is for bulk water.

order of 100 ps the HBs last longer when water molecules are trapped within the carbon tetrachloride-acetone mixture than when they are in the bulk liquid form, but at smaller time scales the confined water HBs show faster decay. For the scopes of comparison, we point out that ACFs such as those in Figure 6 could be described, approximately, by triexponential functions. Following that procedure in the case of the intermittent HB ACF for bulk water, we obtained a relaxation time constant of 0.63 ps for the initial fast decay, slightly larger than that reported in the literature for the rigid TIP3P model of water.63 We point out that it is expected for a flexible model to yield longer relaxation times than rigid models do.64 The advantage of our methodology is that we do not need to assume that the ACFs decay following exponential-type mechanisms. To understand the reasons for the fast decay at short times and the slow decay at long times observed for confined water, we computed intermittent water-water HB ACFs for the individual water clusters. The results are shown in Figure 7, and the estimated relaxation times are reported in Table 3. The ACFs for water in clusters of sizes 11 and 22 decay more slowly than that for the bulk water, but the ACF for water in the cluster of size 62 is different. At short observation times the ACF decays more quickly than that for bulk water, but at long time



TABLE 3: HB Relaxation Times (ps), Evaluated as Time Required for the ACFs To Decay from 1 to 1/ea isolated water molecule cluster of 11 water molecules cluster of 22 water molecules cluster of 62 water molecules bulk water

τHB(I)

τHB(C)

τHB(I)(W-A)

N/A 32.74(6.6) 23.69(2.8) 21.47(2.4) 25.20

N/A 11.78(4.1) 3.33(0.7) 4.30(0.8) 5.20

6.44(1.8) 4.09(0.7) 5.12(0.4) 5.225(0.3) N/A

a

We report results obtained for different cluster sizes and also those obtained for bulk water. Simulations were conducted at room conditions. The index “I” indicates results obtained from intermittent ACFs and “C” those obtained from continuous ACFs. “W-A” denotes the results for water-acetone HBs; all other refer to water-water HBs. Values in parentheses are standard deviations from the mean over the three analyses performed.

scales it decays more slowly than that for bulk water. The continuous water-water HB ACFs, not shown here for brevity, suggest that the ACFs of cluster sizes 22 and 62 decay more quickly compared to that of bulk water, whereas the ACF for water in the cluster of size 11 decays more slowly than that for bulk water. The slow decay of both intermittent and continuous HB ACFs for the water cluster of 11 molecules can be explained in terms of the diffusion of individual water molecules within the cluster. This hypothesis was confirmed through the comparison of the mean square displacement (MSD) of individual water molecules within a cluster as opposed to that of the cluster center of mass. In the cluster with 11 water molecules, the MSD of the center of mass and that of individual molecules show identical behavior. This suggests that the diffusing water molecules cannot escape each other; thus HBs are long-lasting and the ACF decays slowly. In the cluster of 62 water molecules, the MSD of individual water molecules is significantly faster than that of the cluster center of mass. This suggests that individual water molecules are relatively free to move within the cluster, breaking old HBs and forming new ones. Consequently, the ACFs decay quickly. We also computed the distance between the center of mass of a cluster and any individual water molecules within the cluster. The distance as a function of time has an oscillatory behavior going from a minimum of ∼0.1 nm to a maximum of 0.6, 0.8, or 1.0 nm depending on the size of the cluster (11, 22, or 62 water molecules, respectively). This oscillatory behavior suggests that the molecules at the cluster surface find it favorable to be in its core. By moving there, however, they push away the molecules originally at the center of the cluster. This dynamic process is confirmed by the observation that during 250 ps of simulation not even one water molecule exists that did not form at least one HB with acetone. The diffusion of water molecules from the surface to the center of the cluster results in the initial fast decay in intermittent water-water ACF for trapped water and also in the fast relaxation times of continuous HB ACF, especially in large clusters. In small clusters this exchange of water molecules from the cluster surface to the core is not possible, and the ACFs must decay slowly. We explain the slow decay at long time scales observed in the ACF for water molecules in the cluster of size 62 by considering the limitation imposed on diffusion by the surrounding organic matrix. The water molecules do not find it favorable to diffuse beyond the cluster boundary into the hydrophobic matrix. On the contrary, bulk waters do not encounter cluster boundaries. In Figure 8 we compare water reorientational ACFs (i.e., C2OH) obtained as a function of the cluster size. For comparison,

Figure 8. OH reorientation ACF. Black, blue, and red lines are for water in clusters of size 11, 22, and 62, respectively. The green line is for bulk water.

TABLE 4: Water Reorientational Relaxation Times (ps), Expressed as the Time Required for the ACFs To Decay from 1 to 1/ea τC2,OH τC2,HH τC2,µ τC2,⊥

confined water

bulk water

isolated water molecule

3.12(0.14) 3.03(0.12) 2.97(0.18) 1.73(0.13)

9.40 9.70 8.40 5.30

0.25 (0.04) 0.3 (0.19) 0.45 (0.29) 0.175 (0.09)

a We report results obtained for water in the organic matrix averaged over all 96 water molecules, bulk liquid water, and one individually dispersed water molecule in the acetone-carbon tetrachloride system. Simulations were conducted at room conditions. See section 2.D for details. Values in parentheses are standard deviations from the mean over the three analyses performed.

TABLE 5: Water Reorientational Relaxation Times (ps), Expressed as the Time Required for the ACFs To Decay from 1 to 1/ea

τC2,OH τC2,HH τC2,µ τC2,⊥

cluster of 11 water molecules



isolated water molecule

1.72(0.19) 1.47(0.12) 1.65(0.15) 0.78(0.01)

2.62(0.30) 2.67(0.41) 2.33(0.12) 1.30(0.02)

3.70(0.43) 3.66(0.29) 3.63(0.38) 2.18(0.13)

0.25 (0.04) 0.3 (0.19) 0.45 (0.29) 0.175 (0.09)

a We report results obtained for different cluster sizes in the organic matrix. Simulations were conducted at room conditions. The notation is the same as that used in Table 4. Values in parentheses are the standard deviations from the mean over the three analysis performed.

we also report data for bulk water. We found that confined water molecules are always characterized by faster reorientational dynamics than bulk liquid waters (see Table 4). The time for the reorientational ACFs to decay from 1 to 1/e as a function of cluster size is reported in Table 5. The isolated water molecule reorients faster than the water molecules associated in clusters, and the reorientation time in the small water clusters is faster than that in the bigger ones. This is apparently counterintuitive based on the HB ACFs discussed above. Although no experimental NMR data for water in carbon tetrachloride-acetone is available, our data are in quantitative agreement with both NMR and simulation data21,22 for water diluted in carbon tetrachloride. However, the reorientation of water molecules in our system is slower than that observed in carbon tetrachloride. We believe that the presence of acetone around the water clusters determines


Figure 9. Simulated FT-IR spectra. Green, blue, and black lines represent results for bulk liquid water, for confined water, and for one individually dispersed water molecule within the organic matrix, respectively.

these differences. Fast rotation is observed for water in carbon tetrachloride because no HB can form between water and the organic matrix. On the contrary, the rotation of clusters and/or that of individual water molecules is hindered in bulk water because of strong water-water HBs. Our results suggest that weak acetone-water HB can be easily formed and broken, thus allowing the water clusters to rotate within the organic matrix at a speed intermediate between the fast one observed in CCl4 and the slow one observed in water. C. Simulated FT-IR Spectra. We calculated the simulated FT-IR spectra for water molecules confined within the acetone-carbon tetrachloride mixture. These calculations provide a direct link to the experimental data of Gilijamse et al.23 In Figure 9 we report the simulated FT-IR spectra for bulk liquid water, for confined water, and also for one isolated water molecule within the carbon tetrachloride-acetone matrix. The simulated FT-IR spectrum for bulk water features the typical essential modes. The OH-stretching mode is evident at ∼3400 cm-1, whereas we can observe a blue shift of ∼100 cm-1 in the bending mode with respect to experimental data65 at ∼1800 cm-1. The librational mode at ∼720 cm-1 also shows a marginal blue shift compared to its experimental counterpart, but less significant than the blue shift for the bending mode. These differences between simulated and experimental FT-IR spectra are typically observed for flexible SPC/E water models.61 For confined water the OH-stretching mode shows a blue shift (increase in frequency) compared to the bulk water spectrum. The increase in frequency can be attributed to the presence of water-acetone HBs, which affect water-water HBs. The increase in frequency in the stretching mode is due to the frequent breaking of HBs with acetone, as the water-acetone HBs are weaker than water-water HBs typical of bulk water. This result corroborates the relaxation times τHB(I)(W-A) reported in Table 3. With respect to bulk water, the simulated FT-IR spectrum in the 3100-3600 cm-1 region for confined water decreases in intensity, but it becomes stronger in the 3600-3700 cm-1 region. The stronger intensity observed at ∼3600 cm-1 is due primarily to water-acetone HBs, because water-acetone HBs are longer than water-water HBs (see positions of the first peak in the corresponding RDFs in Figure 2). Focusing on the bending mode, the results in Figure 9 indicate that the simulated FT-IR spectrum for confined water is less intense than that for bulk water, but the peak position

Tummala and Striolo does not change. Instead, we observe a strong peak in the simulated FT-IR spectrum for confined water in the librational region (below ∼200 cm-1). This peak is attributed to the change in rotational dynamics for confined water as opposed to bulk water, which induces strong librational motions. By computing FT-IR spectra for water molecules having only either water-water or water-acetone HBs, we confirmed that the major contribution to the librational mode below 200 cm-1 is due to water-water HBs. Because this contribution increases as the size of the water cluster increases, it may be due to those water molecules at the cluster surfaces. To better appreciate the effect of cluster size on the simulated FT-IR spectrum, we also report in Figure 9 the results obtained considering only the water molecule individually dispersed within the organic matrix. We observe a pronounced blue shift in the OH-stretching mode, coupled to a evident band splitting, and a red shift in the bending and librational modes. The decrease in the type and number of HBs available to the isolated water molecule causes the red shift in the bending mode. This mechanism also explains the experimentally observed red shift of the bending mode of water in the vapor phase.65 The shift in the librational mode is due to the reasons discussed above, but in addition we observe multiple peaks. These are due to the increased translational freedom for the individual water molecule.66 Focusing on the OH-stretching mode, the experimental data of Gilijamse et al. help us interpret our results.23 The peak at 3520 cm-1 was attributed to symmetric stretching of OH for water molecules hydrogen bonded to one acetone; the shoulder at 3610 cm-1 was attributed to asymmetric stretching of OH for water bonded to two acetones; the peak at 3690 cm-1 was attributed to the stretching of the free OH group for water molecules hydrogen bonded to one acetone. In agreement, we also observe three pronounced peaks for the isolated water molecule at 3685, 3802, and 3902 cm-1, although the peaks are significantly blue shifted (150-200 cm-1) compared to the experimental ones. Such a deviation compared to experiments is typical for computer simulations, but the observation of three peaks indicating three possible OH-stretching modes for water-acetone HBs, in agreement with experimental observation, suggests that the relatively simple models used here can capture the complicated physics associated with aqueous systems dispersed in organic media. We calculated the simulated FTIR spectrum for confined water with varying contributions of individually dispersed water molecules and found that when the contribution of isolated water molecules reaches 20% of the total, the intensity of the confined water peak at 3400 cm-1 decreases by 80%, indicating that the presence of a few isolated water molecules will dominate the simulated FT-IR spectrum even when the majority of water molecules form clusters. The comparison between the simulated FT-IR spectra in Figure 9 reveals that the experimental data are reproduced semiquantitatively when only the individually dispersed water molecule is considered, but are not when all the water molecules contribute to the spectra. This suggests that water molecules within the experimental system were more finely dispersed than those considered in our simulation. This may be a consequence of the experimental procedure, and our simulation suggests that, given time, the dispersed water molecules may eventually form small clusters within the carbon tetrachloride-acetone matrix. In addition, our detailed results provide information on the properties of the confined water as a function of cluster size. For example, our results suggest that the intensity of the peak at 3685 cm-1, arising due to OH-stretch vibration of water hydrogen bonded to acetone, decreases as the cluster size increases. Our results also document

MD of Water in CCl4-Acetone Mixtures the change of librational and reorientational motions of confined waters as indicated by the peaks in the far-IR region. 4. Concluding Remarks Stimulated by recently reported experimental data, we investigated the properties of water dispersed at low concentration within an organic matrix composed of acetone and carbon tetrachloride. Molecular dynamics simulations conducted on a system of molecular composition equal to that explored experimentally reveal that water molecules tend to form clusters of varying sizes. The properties we computed illustrate the use of simulations in providing insights into the hydrogen-bonding and reorientational mechanism present in this system. Hydrogen-bond autocorrelation functions computed for water molecules within large clusters decay more quickly than those for bulk liquid water at short time scales, whereas they decay more slowly at long time scales. This is attributed to the diffusion of water molecules from the surface to the core of the clusters. There is also a significant difference in the reorientational and rotational mechanism of the water molecules when surrounded by acetone compared to when they are surrounded by water molecules. This seems a consequence of the relative weakness of water-acetone hydrogen bonds compared to water-water ones. Because the structure of the small water clusters dispersed throughout the system differs significantly compared to that of bulk liquid water, our simulations yield FT-IR spectra that depend on cluster size. A significant blue shift in the OH-stretching mode is observed for trapped water in organic media, indicating a frequent breaking of water-acetone hydrogen bonds. The results reported here are important for better understanding the role of hydrogen bonding in determining the properties of water clusters confined within hydrophobic environments, a situation often encountered in systems of biological relevance. Acknowledgment. Financial support was partially provided by the Oklahoma State Regents for Higher Education, by the Vice President for Research at the University of Oklahoma, Norman, through a Junior Faculty Research Program award, and by Oak Ridge National Laboratory (managed and operated by UT-Battelle, LLC) through funding provided by the Divisions of Materials Sciences and Engineering and Chemical Sciences, Geosciences and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract No. DEAC05-00OR22725 to ORNL. Simulation calculations were performed at OSCER, Norman, OK, and at NERSC, Berkeley, CA. The authors wish to thank the group of J. Karl Johnson for help in setting up the algorithm used for FT-IR analysis of the simulated trajectories. References and Notes (1) Gale, G. M.; Gallot, G.; Hache, F.; Lascoux, N.; Bratos, S.; Leicknam, J. C. Phys. ReV. Lett. 1999, 82, 1068. (2) Woutersen, S.; Bakker, H. J. Nature 1999, 402, 507. (3) Fecko, C. J.; Eaves, J. D.; Loparo, J. J.; Tokmakoff, A.; Geissler, P. L. Science 2003, 301, 1698. (4) Asbury, J. B.; Steinel, T.; Stromberg, C.; Corcelli, S. A.; Lawrence, C. P.; Skinner, J. L.; Fayer, M. D. J. Phys. Chem. A 2004, 108, 1107. (5) Luzar, A. J. Chem. Phys. 2000, 113, 10663. (6) Barthel, J.; Bachhuber, K.; Buchner, R.; Hetzenauer, H. Chem. Phys. Lett. 1990, 165, 369. (7) Kindt, J. T.; Schmuttenmaer, C. A. J. Phys. Chem. 1996, 100, 10373. (8) Wulf, A., L. R. ChemPhysChem 2006, 7, 266. (9) Woutersen, S.; Bakker, H. J. Phys. ReV. Lett. 1999, 83, 2077. (10) Smith, D. W. G.; Powles, J. G. Mol. Phys. 1966, 10, 451. (11) Alenka, L. Faraday Discuss. 1996, 103, 29. (12) Martí, J. J. Chem. Phys. 1999, 110, 6876.

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JP803511F

Hydrogen-Bond Dynamics for Water Confined in Carbon Tetrachloride

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