Structural and Dynamic Properties of Water near Monolayer-Protected

J. Phys. Chem. C 2010, 114, 8697–8709

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Structural and Dynamic Properties of Water near Monolayer-Protected Gold Clusters with Various Alkanethiol Tail Groups An-Cheng Yang† and Cheng-I Weng* Department of Mechanical Engineering, National Cheng Kung UniVersity, Tainan, Taiwan, Republic of China, and Fo Guang UniVersity, Jiaushi, Ilan County, Taiwan, Republic of China ReceiVed: October 22, 2009; ReVised Manuscript ReceiVed: February 17, 2010

Molecular dynamics simulations are performed to investigate the structural and dynamic properties of water molecules close to clean gold nanoclusters and four different Monolayer Protected Clusters (MPCs) comprising gold nanoclusters and alkanethiol surfactants with methyl, carboxyl, amine and hydroxyl tail group. The effects of these tail groups on the local structure of water are quantified by the analysis of the reduced density profiles, the average number of hydrogen bonds, and the water orientation distribution. Moreover, the dynamic properties of the water molecules are evaluated by means of diffusion coefficients and residence time. The simulation results indicate that water molecules close to clean gold nanoclusters and nonpolar methyl MPCs form a two-shelled structure in which the molecules in the first shell prefer lying on the surface of the nanocluster or methyl MPCs. The existence of interfacial hydrogen bonds between the water molecules and the tail group of MPCs results in a weakening of the water-water hydrogen bond network. Moreover, the presence of the two water shells constrains the motion of the water molecules close to the clean nanocluster and nonpolar MPC. As a result, the residence time of the water molecules adjacent to the clean nanocluster and nonpolar MPC are significantly longer than those of the molecules close to the three polar MPCs. 1. Introduction Nobel metal nanoclusters have attracted significant interest in recent years due to its exceptional physical1,2 and chemical3,4 properties, which render them ideal for a wild variety of applications in the biology,5,6 medicine,7 and diagnostic8,9 field. As a result, the literature contains many proposals for the preparation of metal nanoclusters using a variety of chemical synthesis methods.10,11 Brust et al. reported that the presence of self-assembled monolayers (SAMs) on the surface of nanoclusters not only improves their stability but also prevents their aggregation with other nanoclusters.10 For such nanoclusters, conventionally referred to as monolayer protected clusters (MPCs), the protecting monolayer has a fundamental effect on the properties of the underlying nanocluster. Thus, many studies have shown that the properties of MPCs can be effectively modified via the use of suitable synthesis methods12-14 or placedexchange reactions15,16 method. The miniature scale of MPCs limits the usefulness of direct experimental methods in observing their behavior in suspension, and thus computer simulations that can provide atomic information about MPCs are largely preferred. Luedtke and Landman performed molecular dynamics (MD) simulations based on united-atom model to investigate the structural and thermodynamic properties of dodecanethiol SAMs on gold nanoclusters.17 The results showed that the disordering mechanisms and melting scenario of SAMs are caused by a temperature-broadened transition. Rupino and Zerbetto investigated the configuration of alkanethiol SAMs on gold nanoclusters and found that the alkanethiol molecules were located primarily in the proximity of the faces edges of the gold nanoclusters.18 Ghorai and Glotzer performed united-atom MD simulations of alkanethiol SAMs * To whom correspondence should be addressed. E-mail: weng@ mail.ncku.edu.tw. Tel: 886-6-2757575 Ext. 62270. Fax: 886-6-2352973. † E-mail: [email protected].

on spherical gold nanoclusters and showed that the monolayer organization depends strongly on the temperature, molecular chain length, and cluster size, respectively.19 Schapotschnikow et al. utilized a steered molecular dynamics (SMD) method to investigate the effects of the temperature, molecular chain length, and choice of solvent on the mean force between two MPCs.20 Zachariah et al. used LAMMPS software to investigate the structure and stability of gold MPCs and showed that the surface of the nanocluster became corrugated as the result of alkanethiol adsorption.21 In addition, it was shown that as the temperature was increased, the alkanethiol dissolved into the nanocluster even at temperature much lower than the melting temperature of gold nanoclusters. Almusallam and Sholl analyzed the transport properties of polymer-stabilized spherical nanoclusters using Brownian dynamics model.22 In their model, hydrodynamic interactions were taken into account to describe the diffusion behavior of polymer-stabilized nanocluster properly. It was shown that the results obtained using the numerical model is in good agreement with the experimental data. Tay and Bresme used MD simulations to investigate the effect of core geometry of MPC on the intercluster force and the structure of self-assembly MPC arrays.23 They found that the core shape has little influence on intercluster force and structure of MPC array, except for the MPC contact with each other. The effects of nanoclusters on the behavior of solvent have attracted particular interest in the literature. For example, Koparde and Cummings performed MD simulations to investigate the adsorption behavior of water molecules near TiO2 nanoclusters of various types and different size under different thermal conditions.24 The results showed that the water molecules formed two hydration shells under all the considered conditions. Moreover, it was found that the water molecules in the first shell exhibited a strong orientational preference. Finally, the residence time of the water molecules at the surface of the nanocluster was shown to be much longer under ambient

10.1021/jp910101t  2010 American Chemical Society Published on Web 04/27/2010

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Figure 1. Snapshots of gold nanocluster MPCs with various tail groups in water. (a) Clean gold nanocluster, (b) methyl MPC, (c) carboxyl MPC, (d) primary amine MPC, (e) hydroxyl MPC. (Note that for clarity, the size of the water molecules is deliberately reduced.)

condition than under hydrothermal condition. Tay and Bresme showed that MPCs induce a large contact angle at the liquid-vapor interface.25,26 The same authors also studied the hydrogen bond structure and vibrational spectrum of water molecules near MPCs and showed that the MPCs had a

hydrophobic characteristic.27 Lal et al. performed MD simulations to investigate the degree of solvation of bare and passivated nanoclusters in subcritical-supercritical fluids.28 The results showed that the degree of solvation of the bare nanoclusters was positive whereas that of the MPCs was negative. In addition,

Properties of Water near Monolayer-Protected Au Clusters it was shown that the nanocluster/solvent affinity was greatly reduced in the presence of a passivating monolayer. In considering the application of MPCs in the biology, medicine, and diagnostic fields, the biocompatibility of the MPCs, that is, their hydrophilic and hydrophobic properties, is of principal concern. To date, however, most of the published literature focused on the structure of MPCs rather than the influence of the MPCs on their surrounding. Accordingly, the present study performs a series of full-atom MD simulations to investigate the structural and dynamic properties of water molecules near clean gold nanocluster and four different types of MPCs with methyl, carboxyl, amine, and hydroxyl tail alkanethiol surfactants. The simulations focus specifically on the effects of the different tail functional groups on the reduced density profiles of the oxygen and hydrogen atoms, the average number of hydrogen bonds, the orientation distribution, the diffusion coefficients, and the residence time of the water molecules, respectively. The interfacial hydrogen bonds formed between water molecules and the different tail functional groups are also analyzed. The results provide useful insights into the behavior of water molecules surrounding MPCs and contribute a further understanding of the microscopic interfacial phenomena of MPCs in water suspensions. 2. Computational Methodology 2.1. Simulation Model. For alkanethiol adsorbed on flat Au(111) surfaces, the alkanethiol molecules form a c(4 × 2) superlattice of the (3 × 3)R30° with an interchain spacing of approximately 5 Å.29,30 However, the arrangement of alkanethiol adsorbed on gold nanoclusters differs notably from that of alkanethiol on flat Au(111) surfaces and depends on the shape of the cluster. For the modeling of MPCs, previous studies have adopted either a crystallographic model or a continuous model.31-33 In models of the former type, the gold nanocluster is assumed to be a polyhedral comprising multiple (111) and (100) facets. Since the facets are locally flat, it is assumed that the arrangement of alkanethiol on these facets is similar to that of alkanethiol on corresponding surfaces. By contrast, in the continuous model the gold nanocluster is assumed to be spherical and the alkanethiol molecules are assumed to extend radially away from the sphere with the sulfur group packed tightly on the surface. The continuous model is suitable for larger nanoclusters (>3 nm) and is therefore adopted as the basis for the simulations performed in the present study. In performing the simulations, a gold nanocluster with diameter of 4 nm is prepared by the simulated annealing method. The cluster is assumed to contain 1956 gold atoms of which 685 lie on the cluster surface. According to the thermogravimetric analysis (TGA) results presented by Murray and co-workers’ study,34 the mass fraction of dodecanethiol in an MPCs χ can be computed as

χ)

MthiolNthiol MthiolNthiol + MAuNAu

(1)

where Mi is the mass of the ith species and Ni is the numbers of the ith species. In the present study, the numbers of dodecanethiol is determined as Nthiol ) 282 by solving eq 1 using χ ) 12.8%.34 The convergence of dodecanethiol (ratio of the numbers of dodecanethiol to the numbers of surface gold atoms) γ is equal to 0.41. The dodecanethiol molecules were randomly placed on the nanocluster with the distance between the sulfur atoms and particle surface specified as 2.38 Å.35 Finally, the MPC was placed at the central of the simulation box with three-dimensional periodic boundary conditions and

J. Phys. Chem. C, Vol. 114, No. 19, 2010 8699 surrounded by sufficient water molecules to avoid the interaction between the MPC and its image in neighboring simulation box. The primary simulation box was assigned dimensions of 132.20 Å × 131.74 Å × 131.79 Å. The water molecules were initially set on a diamond crystal lattice. For the water molecules in the MPC occupied zone, even though only one atom of water molecule was in it, the water was excluded from the simulation. The final density of water in the simulation is 0.973 g/cm3. To clarify the effects of different tail groups on the structural and dynamic properties of the water layer, four different alkanethiol surfactants were considered with tail groups of methyl (CH3), carboxyl (COOH), primary amine (NH2), and hydroxyl (OH). To retain a consistent MPC size as possibly as we can, the whole methyl group was replaced with the carboxyl group, but just one hydrogen atom of the methyl group was replaced with the primary amine and hydroxyl groups. Furthermore, since the dissociation constant of dodecanoic acid in water is quite small (pKa ) 5.7),36 the simulations assumed that the carboxyl groups were not dissociated. Figure 1a-e presents simulation snapshots of equilibrium structures of bare gold nanocluster in water and the methyl, carboxyl, amine, and hydroxyl MPCs in water, respectively. 2.2. Force Field. The intra- and intermolecular interactions between the alkanethiol molecules and the water molecules were modeled using the energy calculation and dynamics force field (ENCAD).37 The potential, U, was given as U)

∑ K (b - b ) i b

i 2 0

i

+

bonds

∑ K (θ - θ ) i θ

∑ K {1 - cos[n (φ - φ )]} +

vdw

torsion 12

[ () Ascεij

r0 rij

+

bends i φ

∑

i 2 0

i

i 0

i

i

()

- 2εij

r0 rij

6

]

A - Svdw (rij) +

∑ els

[

]

qiqj A - Sels (rij) rij

(2)

where the first three terms represent the bonded interactions between the atoms, and the last two terms are the nonbonded interactions. In addition, the parameters Kbi, bi, and b0i in the first term are the bond stretching constant, bond length, and equilibrium bond length, respectively, for the ith bond, while the parameters Kiθ, θi, and θi0 in the second term are the bending angle constant, bending angle, and equilibrium bending angle, respectively, for the ith bending. The third term in eq 2 describes the torsional effect, in which Kφi , φi, φ0i , and ni are the rotation barrier height, torsion angle, equilibrium torsion angle and periodicity, respectively, for ith torsion. The fourth term represents the van der Waals interaction, in which rij is the distance between atoms i and j, r0 is the equilibrium distance, εij is the energy parameter, and Asc is a scale factor used to reduce the truncation error. The fifth term in eq 2 represents the electrostatic interaction, in which qi is the partial charge. A A (rij) and Sels (rij) in the fourth and fifth terms, Note that Svdw respectively, are shift functions which ensures a smooth truncation at cut off distance. (Note that full details of the potential parameters used in the present simulations are presented in Levitt et al.37). The interactions among the gold atoms within the nanocluster were simulated using the tight-binding potential with the second moment approximation (TB-SMA) model,38 that is

U)

∑ [-( ∑ ξ2e-2q(r /r

-1 ij 0 )

i

j*i

)1/2 +

∑ Ae-p(r /r

-1 ij 0 )

]

j*i

(3) where rij is the distance between atoms i and j, r0 is the firstneighbor distance in the lattice, ξ is an effective hopping integral,

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TABLE 1: Force Fields Used in Present Simulations gold cluster gold cluster surfactant water

surfactant

tight binding potential Dreiding force field Sporh potential

38

Dreiding force field ENCAD37 ENCAD

and q describes the dependence of the relative distance between atoms. In addition, the parameters A, p, q, and ξ are fitting to the experimental data relating to the cohesive energy, lattice parameters, and the elastic constants in the appropriate crystal structure at 0 K. In performing the present simulations, the parameters of the tight-binding potential model were taken directly from those given in Cleri et al.39 The interaction between the alkanethiol molecules and the gold atoms in the nanocluster was modeled using the Dreiding force field,40 that is

water 40

Sporh potential42 ENCAD ENCAD

(4)

after, an equilibration process was performed for a duration of 100 ps to obtain equilibrium state. All of the statistical data used in the present analysis (e.g., the density profiles, the water orientation, the hydrogen bond, and so forth) were then collected and averaged over a further 100 ps interval. In implementing each simulation, the equations of motion of the atoms were integrated using the velocity Verlet algorithm45 and the time step, ∆t, was specified as 1 fs. Finally, the cutoff radius for the nonbonding interactions was specified as 12 Å. The results of the present study were obtained using our program compiled with Intel FORTRAN compiler (“-openmp” optimization) and running on Intel Xeon cluster system (E5410, 2.66 GHz, Quadcore*2). It took about 30 days to collect MD data and took about 2 days to compute the structural and dynamic properties.

where D0 is the van der Waals depth, r0 is the equilibrium distance between atom in the alkanethiol molecules and gold atom, rij is the distance between atoms i and j, and z is a dimensionless scaling factor. In the present simulations, the corresponding parameter values were based on those given in Jang et al.41 Finally, the nonbonded interaction between the water molecules and gold atoms in the nanocluster were modeled using the modified Sporh potential,42 that is

3. Results and Discussion 3.1. Reduced Density Profile. In the present study, the effect of surfactants on the structure of the water molecules was quantified via the reduced density profiles of the hydrogen and oxygen atoms of the water molecules near various MPCs. The reduced density, F(r), was determined by averaging the number density of oxygen or hydrogen atoms within a shell of thickness ∆r ) 0.1 Å and normalizing the result by the bulk density, that is

U ) D0

[(z -6 6)exp(z(1 - r )) - (z -z 6)(r ) rij

rij

0

0

-6

U ) S(rij)UAu-O(rij) + UAu-H1(rij) + UAu-H2(rij)

]

(5)

where S(rij) is a switch function, and has the form

{

r e ron 1 2 2 2 2 2 2 S(rij) ) (roff - rij) (roff + 2rij - 3ron) ron e r e roff 2 (roff - r2on)3 (6) and

UAu-O(rij) ) D0{exp[-2βO(rij - rO0 )] 2 exp[-βO(rij - rO0 )]} (7) and

UAu-H(rij) ) γD0 exp[-2βH(rij - rH0 )]

(8)

where ron and roff are the start and end distances of the switch function, D0, γ, and β are adjustable parameters used to obtain an adsorption energy consistent with that obtained experimentally, rij is the distance between atoms i and j, and r0O(r0H) is the equilibrium distance between oxygen (hydrogen) atom and the gold nanocluster surface. Note that in performing the present simulations, the values of all the parameters in eqs 5 to 8 were taken from Dou et al.42 The various force fields used in the present simulations are summarized in Table 1. 2.3. Simulation Details. The effects of the various alkanethiol surfactants on the structural and dynamic properties of the water near clean gold nanocluster and MPCs were investigated by performing canonical MD simulations (NVT MD). During the simulations, the temperature was maintained at 300 K using the Nose´-Hoover chains algorithm.43,44 Each simulation commenced by performing an energy minimization process comprising 1000 conjugate gradient iterations. There-

F(r) )

〈N(r)〉 V(r)F0

(9)

where r is the radial distance between atoms and the center of MPC and N(r) is the number of oxygen or hydrogen atoms in the shell corresponding to r ( 0.5∆r, 〈 · · · 〉 represents the time average, V(r) is the volume of the shell, and F0 is the bulk density. Significantly, the present MPCs do not have an exactly consistent size due to the different tails groups of the alkanethiol surfactants. Thus, when calculating the density profiles of the different MPCs, each profile was computed with setting the center of mass of the tail group comprising the monolayer to zero point such that the effects of the MPCs could be compared on a like-for-like basis. Figure 2a,b shows the reduced density profiles of the hydrogen and oxygen atoms around a clean gold nanocluster and the four MPCs, respectively. Note that the X-axis in each figure represents the distance between the hydrogen or oxygen atoms and the surface of the MPCs (i.e., the center of mass of the tail group) and the Y-axis represents the reduced density. In the case of the unprotected gold nanocluster, two distinct peaks are observed at 3 and 6.4 Å, respectively, in the hydrogen atom density profile and 3.1 and 6 Å, respectively, in the oxygen density profile. These peaks imply the formation of two water shells near the clean gold nanocluster. The water molecules in the first shell are adsorbed on the gold nanocluster directly, while the water molecules in the second shell are bonded to those in first shell via hydrogen bonds (More discussion in Section 3.2). At a distance of more than 10 Å from the nanocluster or MPCs surface, both sets of profiles converge toward unity; implying that the water molecules have a bulklike arrangement. The four surfactants considered in the present simulations can be classified into two types depending on the polarity of

Properties of Water near Monolayer-Protected Au Clusters

Figure 2. Reduced density profiles of (a) hydrogen atoms and (b) oxygen atoms.

the tail group. Specifically, the methyl tail group surfactant is nonpolar, while the carboxyl, amine, and hydroxyl tail group surfactants are all polar. Observing Figure 2a,b for the nonpolar methyl group, it is seen that two distinct peaks exist at 4.3 and 7.7 Å, respectively, in the hydrogen density profile and 4.4 and 7.3 Å, respectively, in the oxygen density profile. This suggests that the water molecules near methyl MPCs also form two shells. However, the two shells are thinner and further from the methyl MPC than those formed near the clean gold nanocluster. It is well-known that water molecules have polar properties due to the difference in electronegativity between the oxygen and hydrogen atoms. A difference in electronegativity also exists between the carbon and hydrogen atoms in the methyl group surfactant. However, in this case, the methyl group is nonpolar due to the symmetrical arrangement of the hydrogen atoms. The interaction between the methyl group and the surrounding water reduces the concentration tendency of the water molecules and repels them from the MPC surface. Thus, as shown in Figure 2a,b, the two water shells are displaced slightly from the MPC surface compared to those formed near the clean gold nanocluster. For the polar tail group MPCs, the hydrogen and oxygen density profiles exhibit a single peak. In other words, two-shelled water structures are not formed near the corresponding MPCs. Furthermore the water molecules can penetrate into the surface

J. Phys. Chem. C, Vol. 114, No. 19, 2010 8701

Figure 3. (a) Definition of dipole vector, normal vector, H-H vector, O-H vector, and vector from center of MPC toward oxygen atom of water molecule. (b) Definition of angles θ and φ in molecule-fixed coordinate frame.

of the polar MPCs. The carboxyl group is bigger than either the hydroxyl or amine group, and thus the water penetration near the carboxyl MPC is less than that near the amine and hydroxyl MPCs. For convenience, the following discussions consider the behavior of the water molecules near the gold nanocluster and the four MPCs within two distinct regions, namely region 1 (near the surface of MPCs, i.e., ∆r < 10 Å) and region 2 (far from the surface of MPCs, i.e., ∆r > 10 Å). To describe the behavior of water in region1 more clearly, we further divided region 1 into two parts A and B which represent the region near first and second peak in density profiles, respectively (if second peak exists). 3.2. Water Orientation Distribution. Further insights into the effects of the various surfactants on the water in the interfacial zone can be obtained by examining the orientations of considering four vectors bound to the each water molecule, bn), the vector namely the dipole vector (r bd), the normal vector (r joining the two hydrogen atoms of the water molecule (r bhh), and the vector pointing from the oxygen atom to either one of the two hydrogen atoms within the same water molecule

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Figure 4. Cosine distributions of angles formed by (top left) dipole vector, (top right) normal vector, (bottom left) H-H vector, and (bottom right) O-H vector of water molecule with vector from center of MPCs orientated toward oxygen atom of water molecule in region 1A.

(r boh)24,46(see Figure 3a). The orientation of the water molecules can be characterized via the angles formed between these four vectors and the vector pointing from the center of the MPC toward the oxygen atom of the water molecule (r bx), denoted as R, β, γ, and χ, respectively. The orientation preference of the water molecules near the MPCs can be quantified via the probability functions P(cos R), P(cos β), P(cos γ), and P(cos χ). The corresponding results in region 1A are presented in Figure 4a-d, respectively and results in region 1B are presented in Figure 5a-d, respectively. It should be noted here that since rhh water molecule have a mirror-like symmetry, vectors b rn and b are indistinguishable in two opposite directions unlike vectors roh. Therefore, cos R and cos χ vary between -1 and 1, b rd and b whereas cos β and cos γ vary between 0 and 1. For the case of the clean gold nanocluster, Figure 4a,b shows that the most preferred values of cos R and cos β are 0 and 1, respectively. This finding indicates that the water molecules close to the unprotected gold nanocluster lie preferentially in a direction perpendicular to the surface of gold nanocluster with rx and b rn parallel to b rx. Meanwhile, from b rd perpendicular to b Figure 4c, the most preferred value of cos γ is 0, which implies r x. that b rhh lies preferentially in a direction perpendicular to b

Finally, the P(cos χ) distribution in Figure 4d shows two preferred orientations of 0 and 105°, respectively, corresponding to the two covalent bonds of the water molecule. In other words, one of the O-H bonds points straight to b rx, while the other lies slightly perpendicularly to b rx. On the other hand, the orientation preference in region 1B is changed. As is seen in Figure 5a-d, the maximum of P(cos R) shifts from positive to negative and the maximum is located at about -0.7. The P(cos β) and P(cos γ) distributions are almost flat. And the P(cos χ) distribution shows two preferred orientations of 180 and 80°, respectively. The above results show that the water molecules in region 1B prefer align parallel to b rx with one of its O-H bonds points straight to the MPCs, whereas the other one slightly perpendicularly to b rx. The analysis of P(cos χ) in region 1A and 1B support the inference made in Section 3.1 that the second layer in the water shell is bonded to the first layer via hydrogen bonds. Observing the results presented in Figure 4a-d and Figure 5a-d for the nonpolar methyl group, it can be seen that the probability functions have a similar distribution to those of the water molecules near the clean gold nanocluster. However,



Figure 5. Cosine distributions of angles formed by (top left) dipole vector, (top right) normal vector, (bottom left) H-H vector, and (bottom right) O-H vector of water molecule with vector from center of MPCs orientated toward oxygen atom of water molecule in region 1B.

the peak values in each distribution are significantly lower than those in the corresponding distributions associated with the clean cluster. The probability functions for the polar tail group surfactants are different. In the case of carboxyl MPCs, the preferred values of P(cos R), P(cos β), and P(cos γ) are 0, 0, and 1. The P(cos χ) distribution shows two preferred values of -0.6 and 0.8. The results imply that the water molecules prefer lying on the surface rx and some of the of carboxyl MPCs with b rd perpendicular to b O-H bonds points down, the others point up. In the case of amine MPCs, the preferred values of P(cos R), P(cos β) are -0.3, 0. The finding suggests that b rd is slightly perpendicular to b rx (R ≈ 100°). The P(cos γ) distribution has two peaks which are located at about 0 and 1. The results imply that b rhh prefer being either perpendicular or parallel to b rx. The P(cos χ) distribution shows two preferred values of -0.8 and 0.5 which means χ ≈ 143 or 60°. Finally, in the case of hydroxyl MPCs, P(cos R) shows two preferred values of -1 and 0.3 which rx (R ≈ 180°) or R ≈ 70°. Both suggests that b rd is opposite to b

P(cos β) and P(cos γ) have an unapparent maximum close to 0. The P(cos χ) distribution shows two preferred values of -0.5 and 0.9 which means χ ≈ 120 or 20°. Although the above analysis of orientational distributions revealed the preferential orientations of the four vectors, it still did not give us enough information about the preferential orientations of entire water molecule. For example, although the preference of R is about 90° and that of γ is about 0° and there is no guarantee that these two orientational preference appear within a single water molecule simultaneously, it can be consistent with some of the water molecules lying preferrx entially on the surface of the MPC with b rd perpendicular to b and others standing on the surface of the MPC with b rhh parallel to b r x. To obtain further insights into the orientation of the water molecules, a bivariate joint distribution of the molecule orientation was constructed using two independent angles θ and φ as the angular polar coordinates of b rx in a molecule-fixed coordinate rhh, and b rn, respectively. As shown in frame consisting of b r d, b

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Figure 6. Bivariate distributions of water molecules in region 1A (a) clean gold nanocluster, (b) methyl MPC, (c) carboxyl MPC, (d) primary amine MPC, (e) hydroxyl MPC.

Figure 3b, the angle θ is identical to angle R, while φ is the rx to the plane angle between b rn and the projection of b perpendicular to b rd. Note that angle φ is equivalent to β when θ ) 90°. Because of the symmetry of the water molecules, φ varies between 0 and 90°. Figures 6 and 7 present the bivariate

distributions P(cos θ,φ) for the water molecules adjacent to the clean gold nanocluster and the four types of MPCs in region 1A and 1B, respectively. It should be noted that uniform spatial configuration of water molecules leads to uniform distribution of P(cos θ,φ).



Figure 7. Bivariate distributions of water molecules in region 1B (a) clean gold nanocluster and (b) methyl MPC.

Figure 8. Schematic of the orientational preference of water (a) clean gold nanocluster and methyl MPC in region 1A, (b) clean gold nanocluster and methyl MPC in region 1B, (c) carboxyl MPC, (d) primary amine MPC, and (e) hydroxyl MPC.

Figure 6a shows that for the clean gold nanocluster in region 1A, the water molecules exhibit a primary orientational preference of approximately cos θ ) 0 and φ ) 0°. In other words, the water molecules lie preferentially with a perpendicular rx. In addition, a minor preference is alignment of b rd relative to b observed for an orientation of cos θ ) 0.5 and φ ) 90°. In this

orientation, b rd points backward the cluster and declines from b rx by about 60. In other words, one of the O-H bonds of the water molecule is orientated virtually parallel to b rx. The orientations of the water molecules corresponding to the two peaks in Figure 6a are shown schematically in Figure 8a. In region 1B, a slight orientational preference appears at about cos θ ) -0.6 and φ

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Figure 9. Illustrations for hydrogen bonding between (a) two water molecules, (b) water molecule and carboxyl group, (c) water molecule and hydroxyl group, and (d) water molecule and primary amine group.

Yang and Weng 6e. The major preference appears at about cos θ ) 0.5 and φ ) 90°. In this preference, the plane of water molecules is parallel to b rx and b rd declines from b rx by about 70°. The minor preference appears at about cos θ ) -1 and φ ) 0°. This means that b rd is rn is perpendicular almost in the opposite direction to b rx and the b to b rx. Figure 8c-e shows the configurations corresponding to the preferences in each case. 3.3. Hydrogen Bonding. To clarify the hydrogen bonding network around the gold nanocluster and the MPCs, a detailed analysis was performed of the hydrogen bond statistics. In characterizing the hydrogen bonding between two water molecules, the following geometrical criteria were applied47 (a) The distance between the two oxygen atoms must be less than 3.6 Å; (b) The distance between the acceptor oxygen atom and the donor hydrogen atom must be less than 2.4 Å; (c) The angle between the O-O direction and the O-H covalent bond direction of the donor must be less than 30°. (Note that H denotes the hydrogen atom which forms the bond.) Similar criteria were also adopted for evaluating the hydrogen bonding between the water molecule and the polar tail group (carboxyl, hydroxyl group, and amine) on MPCs. Figure 9a-d illustrates the hydrogen bonds between water molecule and CdOa, Oa-H, O-Hd, Na-H, N-Hd respectively. Note that the subscript “a” denotes the hydrogen bond acceptor while the subscript “d” denotes the hydrogen bond donor. The average number of hydrogen bonds per water molecule within a certain shell can be computed as

nHB(r) )

Figure 10. Average number of hydrogen bonds per water molecule at five different interfaces.

) 90° in Figure 7a. This preference implies that the water molecules are aligned with one of O-H covalent bonds points rx. The configuration is toward MPCs and b rn perpendicular to b demonstrated in Figure 8b. A similar tendency is observed for the water molecules close to the nonpolar methyl tail group MPC. However, it is noted that the peaks are weaker than those observed for the clean gold nanocluster. In the case of the polar MPCs, the orientational preferences are much different from those in the case of nonpolar MPCs. For the carboxyl MPCs, an orientational preference is observed at about cos θ ) 0 and φ ) 45° in Figure 6c. This preference suggests that the plane of water molecule has a tilt angle of about 45°. For the amine MPCs, two preferences are observed in Figure 6d. The major preference appears at about cos θ ) -0.3 and φ ) 90°. The preference can be characterized by b rd pointing toward MPCs (declining from b rx by about 100°) and a parallel alignment of the plane of water molecules relative to b rx. The minor preference appears at about cos θ ) 0.2 and φ ) 0°. This preference means that the plane of water molecule has an elevation angle of about 10° relative to the interface. In the case of hydroxyl MPCs, two preferences are observed in Figure

〈 〉 h(r) Nw(r)

(10)

where h(r) is the total number of hydrogen bonds in the shell of r ( 0.5∆r, Nw(r) is the number of water molecules in the shell, and 〈 · · · 〉 represents the time average. The average number of hydrogen bonds per water molecule in bulk ENCAD model water at 298K is 3.42. Figure 10 shows the average number of hydrogen bonds per water molecule near the clean gold nanocluster and the four MPCs, respectively. In the case of the clean gold nanocluster, the high value of nHB in the first water shell is the result of the orientational preference of the water molecules. As described in the previous subsection, in the first water shell, the majority of the water molecules lie on the surface of the gold nanocluster with their two O-H bonds orientated perpendicularly to b rx. As a result, the probability of the water molecules forming hydrogen bonds with other water molecules within the first shell are increased, and thus the value of nHB also increase. By contrast, relatively few water molecules exist between the first and the second shell, and thus the value of nHB in this region decreases. At a greater distance from the surface of gold nanocluster, the influence of the cluster on nHB reduces, and thus the value of nHB in region 2 approaches that of bulk water. In Figure 10, the profile corresponding to the nonpolar methyl MPC also contains a peak corresponding to the first water shell and a valley between the first and second shells. However, the concentration of the water molecules adjacent to the methyl MPC is lower than that of the molecules close to the clean gold nanocluster, and thus the maximum value of nHB varies slightly from the bulk value of 3.42. The results presented in Figure 10 show that the water molecules adjacent to the polar tail group surfactants (i.e., carboxyl, hydroxyl, and amine) form fewer hydrogen bonds than those close to the nonpolar methyl MPC. There are two main reasons for



TABLE 2: Hydrogen Bond Populations in Five Different Interfacial Regions navg Au(111) methyl group carboxyl group hydroxyl group amine group

3.496 ( 0.003 3.310 ( 0.005 3.046 ( 0.004 3.119 ( 0.003 3.087 ( 0.004

NW-W 16176.59 15554.38 13425.12 13985.81 14244.32

(100%) (100%) (90.60%) (92.68%) (92.06%)

this. First, the water molecules near polar MPCs are more sparsely spaced than those in the bulk, and thus the probability of the water molecules forming hydrogen bonds is inevitably reduced. Second, in contrast to the nonpolar MPC, the polar MPCs form hydrogen bond with the water molecules. In other words, a competing effect arises between the interwater hydrogen bonding mechanism and the interfacial hydrogen bonding mechanism, and thus the probability of the water molecules forming additional hydrogen bonds with one another is reduced. Table 2 presents an analysis of the resulting hydrogen bonding statistics of the clean gold nanocluster and the four MPCs, respectively in region 1. Note that navg represents the average number of hydrogen bonds per water molecule in the region 1, while NW-W, NW-CO, NW-OH, NW-HO, NW-NH, and NW-HN denote the total number of hydrogen bonds between two water molecules and between each water molecule and CdOa, O-Hd, Oa-H, Na-H, and N-Hd, respectively. Note also that the subscript “a” denotes hydrogen bond acceptor while the subscript “d” denotes the hydrogen bond donor. It can be seen that the values of navg for the case in which interfacial hydrogen bonds are present are lower than those for the case in which the interfacial hydrogen bonds are absent. This finding confirms the validity of the assumption made in the previous hydrogen bond statistics. Furthermore, the results indicate that the hydrogen bond acceptor and donor numbers of the polar function group also affect navg. For example, the carboxyl group provides two acceptors and one donor, the hydroxyl group provides one acceptor and one donor, and the amine group provides one acceptor and two donors. From inspection, it is seen that the hydroxyl MPC results in the highest value of navg (3.11), while the carboxyl MPC results in the lowest value (3.04). 3.4. Diffusion Coefficient of Water. As described in the previous subsection, the water molecules in region 2 have a bulklike characteristic. As a result, the following discussions consider only the water molecules within region 1 (i.e., ∆r < 10 Å). The respective effects of the different tail groups on the dynamic properties of the water molecules can be quantified via the isotropic diffusion coefficient, in accordance with Einstein’s equations

D ) lim tf∞

〈[r(t) - r(0)]2〉 6t

NW-CO

NW-OH (NW-NH)

NW-HO (NW-HN)

687.36 (4.64%)

520.00 (3.51%) 573.00 (3.78%) 740.00 (4.78%)

185.36 (1.25%) 531.59 (3.52%) 488.71 (3.16%)

value is considerably lower than that of bulk water and suggests that the two-shelled water structure formed near the gold cluster constrains the motion of the water molecules. A similar loss in mobility is also observed in the water molecules close to the methyl MPC. However, since the water molecules close to the methyl MPC are concentrated less densely than those adjacent to the clean gold nanocluster, the loss in mobility is less significant, that is, the diffusion coefficient reduces by just 12% compared to 61% for the molecules adjacent to the clean gold nanocluster. As discussed previously in Section 3.1, a two-shelled water structure is not formed adjacent to the polar MPCs. However, the results presented in Table 3 indicate that a reduction in the mobility of the water molecules nevertheless occurs. The diffusion coefficients of the water molecules adjacent to the carboxyl, hydroxyl, and amine MPCs are varied from the bulk value of 2.46 to values of 2.34, 2.43, and 2.37, respectively. It is inferred that the loss in mobility of the water molecules adjacent to the polar MPCs is caused by the formation of interfacial hydrogen bonds between the water molecules and the tail groups of the MPCs 3.5. Residence Time. Further insights into the absorption behavior of the water molecules near the four MPCs can be obtained by computing the value of the residence time correlation function R(t) for the water molecules in region 1 in accordance wit:24,49

R(t) )

〈

N

∑

〉

1 θ (t )θ (t + t) N i)1 i 0 i 0

(12)

where N is the number of water molecules in region 1, and θi has a value of unity if molecule i lies within region 1 in the period t0∼t0 + t, and a value of 0 otherwise. The function decays

(11)

where 〈[r(t) - r(0)]2〉 is the mean-square displacement of mass center of water molecules at a certain time t. Figure 11 shows the mean-square displacement of water molecules in region 1. The delay times in the calculation of mean-square displacement is 50 ps. The isotropic diffusion coefficient of bulk ENCAD model water at 300K is known to be 2.46 × 10-5 cm2 s-1.48 The computed values of the diffusion coefficients for water molecules close to the clean gold nanocluster and the four MPCs, respectively, are presented in Table 3. As shown, the water molecules near the clean gold nanocluster have a diffusion coefficient of 0.95 × 10-5 cm2 s-1. This

Figure 11. Mean square displacement of water molecules in region 1.

8708


Yang and Weng

TABLE 3: Diffusion Coefficients of Water Molecules near Clean Gold Nanocluster and Four MPCs D (10

-5

gold nanocluster

methyl MPC

carboxyl MPC

hydroxyl MPC

amine MPC

0.95

2.15

2.34

2.43

2.37

2

cm /s)

in exponential fashion, and can therefore be expressed as a sum of two exponential functions24

R(t) ) Ae-t/τs + Be-t/τl

(13)

Where A and B are tunable parameters and τs and τl are the short and long residence time constants, respectively. The residence time can be computed by

τ)

∫0∞ R(t)dt

(14)

Figure 12 plots the residence time correlation functions for the water molecules adjacent to the clean gold nanocluster and the four MPCs, respectively. The delay times in the calculation of residence time correlation function is 50 ps. The corresponding fitting parameters, residence time constants, and residence time values are summarized in Table 4. In general, the results show that the water molecules reside at the surface of the clean gold nanocluster and the nonpolar methyl MPC for longer than the water molecules adjacent to the polar MPCs. In addition, the residence times of the water molecules close to the polar MPCs can be ranked as follows: τcarboxyl > τamine > τhydroxyl. The longer residence time of the water molecules adjacent to the clean gold nanocluster and the nonpolar MPC is the result of the two-shelled water structure, which reduces the mobility of the molecules (see Section 3.4) and therefore causes them to

Figure 12. Residence time correlation functions of water molecules in region 1.

linger longer at the nanocluster or methyl MPC surface. Meanwhile, the difference in the residence times of the water molecules close to the polar MPCs reflects a difference in the number of interfacial hydrogen bonds. Specifically, a greater number of interfacial hydrogen bonds (e.g., carboxyl tail group) constrain the motion of the water molecules and therefore increases the time for which they remain at the MPC surface. 4. Conclusion This study has performed a series of molecular dynamics simulations to investigate the structural and dynamic properties of water molecules close to a clean gold nanocluster and four different MPCs consist of methyl, carboxyl, amine, and hydroxyl tail alkanethiol surfactants, respectively. The simulation results obtained for the reduced density profiles of the oxygen and hydrogen atoms have shown that the water molecules close to the clean gold nanocluster and the nonpolar MPC form a twoshelled water structure. However, this structure is absent in the case of the polar MPCs. Comparing the positions of the first peaks in the reduced density profiles of the four MPCs, it has been shown that the methyl tail group repels the water molecules from the surface of the MPC, while the carboxyl, hydroxyl, and amine groups enable the water molecules to approach the MPC surface more closely. Furthermore, the carboxyl group is larger than the hydroxyl or amine groups, and thus the water molecules approach the hydroxyl and amine MPCs more closely than the carboxyl MPC. Thus, ranking the MPCs in terms of the distance d of the water molecules from the MPC surface, it has been shown that dmethyl > dAu > dcarboxyl > damine ≈ dhydroxyl. The molecular orientation analysis results have shown that the tail functional groups of the MPCs have a significant effect on the orientational distribution of the water molecules. And in the second shell, the water molecules stand on the first water shell with one of O-H covalent bonds point toward MPCs. However, in the case of the polar MPCs, several different orientational preferences are observed. The present results also suggest that the two-shelled structure and the presence of interfacial hydrogen bonds have a significant effect on the hydrogen bond network. In the case of clean nanocluster and methyl MPC, nHB in the first peak of two-shelled structure is significantly higher than that in bulk water, whereas that in the region between the two shells is significantly lower. In contrast to the nonpolar MPC, the polar MPCs readily form interfacial hydrogen bonds with the water molecules. A competing effect exists between the interwater hydrogen bonding mechanism and the interfacial hydrogen bonding mechanism. Thus, the formation of interfacial hydrogen bonds reduces the probability of hydrogen bond formation between the water molecules themselves, and thus the value of nHB is also lower than in bulk water.

TABLE 4: Fitting Parameters for Equation 13 and Residence Times of Water Molecules near Clean Gold Nanocluster and Four MPCs A B τs (ps) τl (ps) τ (ps) R-squard

gold nanocluster

methyl MPC

carboxyl MPC

hydroxyl MPC

amine MPC

0.08 0.88 6.88 244.53 217.67 0.999

0.11 0.85 8.01 247.93 211.01 0.998

0.13 0.82 7.34 137.76 114.35 0.999

0.15 0.77 5.18 112.77 87.09 0.997

0.14 0.81 7.68 132.78 108.18 0.998

Properties of Water near Monolayer-Protected Au Clusters Finally, the results obtained for the diffusion coefficients and residence times of the water molecules, have shown that the presence of the two-shelled structure of water adjacent to the clean gold nanocluster and the nonpolar methyl MPC, respectively, results in a notable reduction of the water molecule mobility compared to that of the molecules in bulk water. Furthermore, while the interfacial hydrogen bonds formed at the interface of the polar MPCs also constrain the mobility of the water molecules. The constraining effect of these hydrogen bonds is relatively minor compared to that of the two-shelled structure of water. As a result, the residence time of the water molecules adjacent to the clean gold nanocluster and methyl MPC are significantly longer than those of the water molecules close to the polar MPCs. Acknowledgment. The authors gratefully acknowledge the financial support provided to this study by the National Science Council of the Republic of China under Grant NSC 95-2221E-006-425-MY3. References and Notes (1) Andres, R. P.; Bein, T.; Dorogi, M.; Feng, S.; Henderson, J. I.; Kubiak, C. P.; Mahoney, W.; Osifchin, R. G.; Reifenberger, R. Science 1996, 272 (5266), 1323–1325. (2) Andres, R. P.; Bielefeld, J. D.; Henderson, J. I.; Janes, D. B.; Kolagunta, V. R.; Kubiak, C. P.; Mahoney, W. J.; Osifchin, R. G. Science 1996, 273 (5282), 1690–1693. (3) Green, S. J.; Pietron, J. J.; Stokes, J. J.; Hostetler, M. J.; Vu, H.; Wuelfing, W. P.; Murray, R. W. Langmuir 1998, 14 (19), 5612–5619. (4) Chen, S.; Ingram, R. S.; Hostetler, M. J.; Pietron, J. J.; Murray, R. W.; Schaaff, T. G.; Khoury, J. T.; Alvarez, M. M.; Whetten, R. L. Science 1998, 280 (5372), 2098–2101. (5) Fischer, N. O.; McIntosh, C. M.; Simard, J. M.; Rotello, V. M. Proc. Natl. Acad. Sci. U.S.A. 2002, 99 (8), 5018–5023. (6) You, C.-C.; De, M.; Han, G.; Rotello, V. M. J. Am. Chem. Soc. 2005, 127 (37), 12873–12881. (7) Sahoo, S. K.; Labhasetwar, V. Drug DiscoVery Today 2003, 8 (24), 1112–1120. (8) Xiao, He.; Huang, Lin.; Mya, Y.; Zhang, K. Y. J. Am. Chem. Soc. 2004, 126 (25), 7792–7793. (9) El-Sayed, I. H.; Huang, X.; El-Sayed, M. A. Nano Lett. 2005, 5 (5), 829–834. (10) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. J. Chem. Soc., Chem. Commun. 1994, (7), 801–802. (11) Sarathy, K. V.; Raina, G.; Yadav, R. T.; Kulkarni, G. U.; Rao, C. N. R. J. Phys. Chem. B 1997, 101 (48), 9876–9880. (12) Stellacci, F.; Bauer, C. A.; Meyer-Friedrichsen, T.; Wenseleers, W.; Marder, S. R.; Perry, J. W. J. Am. Chem. Soc. 2002, 125 (2), 328–329. (13) Thomas, K. G.; Kamat, P. V. Acc. Chem. Res. 2003, 36 (12), 888– 898. (14) Stellacci, F.; Bauer, C. A.; Meyer-Friedrichsen, T.; Wenseleers, W.; Alain, V.; Kuebler, S. M.; Pond, S. J. K.; Zhang, Y.; Marder, S. R.; Perry, J. W. AdV. Mater. 2002, 14 (3), 194–198. (15) Templeton, A. C.; Wuelfing, W. P.; Murray, R. W. Acc. Chem. Res. 2000, 33 (1), 27–36. (16) Song, Y.; Huang, T.; Murray, R. W. J. Am. Chem. Soc. 2003, 125 (38), 11694–11701. (17) Luedtke, W. D.; Landman, U. J. Phys. Chem. B 1998, 102 (34), 6566–6572.

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JP910101T

Structural and Dynamic Properties of Water near Monolayer-Protected

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