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Hydrogen-Bond Structure and Dynamics at the Interface between Water and Carboxylic Acid-Functionalized Self-Assembled Monolayers† Nicolas Winter,‡ John Vieceli,§ and Ilan Benjamin* Department of Chemistry and Biochemistry, UniVersity of California, Santa Cruz, California 95064 ReceiVed: May 7, 2007; In Final Form: June 19, 2007
Molecular dynamics computer simulations are used to study hydrogen-bond structure and dynamics at the interface between water and carboxylic acid-functionalized self-assembled monolayers (CAFSAMs). Waterwater, water-CAFSAM, and internal CAFSAM hydrogen bonds are examined. Roughly half of all adjacent carboxylic acid-terminated hydrocarbon chains are hydrogen-bonded to one another. This is consistent with experimental results reflecting two pKa values for CAFSAMs. Hydrogen-bond dynamics are expressed in terms of hydrogen-bond population autocorrelation functions and are found to be nonexponential. The waterwater hydrogen-bond dynamics are slower at the interface than in the bulk, which is similar to what was found at the interface between water and weakly polar liquids such as nitrobenzene. The water-CAFSAM hydrogen bonds are found to be long-lived, on the order of tens of picoseconds. Internal CAFSAM chainchain hydrogen bonds show almost no relaxation on the simulation time scale.
I. Introduction Carboxylic acid-functionalized self-assembled monolayers (CAFSAMs) have been the focus of many recent studies due to their utility in controlling the binding and reactivity of different species.1,2 Recent (and by no means exhaustive) examples include the adsorption of Cu on CAFSAMs studied by high-resolution X-ray photoelectron spectroscopy,3 the immobilization of cytochrome c and the study of electron transfer through CAFSAMs,4 and the use of CAFSAMs to promote the growth of oriented nanowires.5 An important aspect of CAFSAM is the ability to control the charge and reactivity of the surface through a change in the bulk solution pH, taking advantage of the acid-base equilibrium of the terminal COOH headgroups. This equilibrium is in turn dependent on the surface hydrogen-bonding network. Fourier transform infrared-attenuated total reflection (FTIR-ATR) spectroscopic measurements by Gershevitz and Sukenik6 demonstrated the existence of two surface pKa values for the COOH deprotonation: The lower value (around 5) corresponds to COOH groups that are hydrogen-bonded to interfacial water only, while the higher value (around 9) corresponds to COOH headgroups that are hydrogen-bonded to each other. Geiger and co-workers have utilized the “χ(3) second harmonic generation spectroscopy method”, pioneered by Eisenthal and co-workers,7 to arrive at similar results.8 Molecular dynamics studies of SAMs have a long history,9-13 and several molecular dynamics and Monte Carlo computer simulations studies of CAFSAMs have recently been reported. Pei and Ma14 used molecular dynamics simulations to demonstrate the ability of the monolayers to switch conformations reversibly in response to an applied electric field, a result previously observed by Lahann et al.15 Duffy and Harding16 †
Part of the “James T. (Casey) Hynes Festschrift”. Present address: Department of Chemistry, Northwestern University, Evanston, IL 60208. § Present address: Pacific Biosciences, Inc., 1505 Adams Drive, Menlo Park, CA 94025. ‡
used molecular dynamics simulations to investigate the structure of the headgroups of long chain CAFSAMs with even versus odd numbers of carbon atoms. However, no theoretical study of hydrogen-bonding structure and dynamics have been reported. In this paper, we simulate a CAFSAM next to water and consider in particular the structure and dynamics of the hydrogen-bond network at the surface. We show that significant chain-chain hydrogen bonds exist and that they are much longer-lived than chain-water and water-water hydrogen bonds. The water-water hydrogen-bond dynamics are compared to the dynamics of other aqueous/organic interfaces.17 II. Description of System and Potential Energy Functions The system includes 968 water molecules and 100 C17H34COOH molecules covalently attached at one end to a Si-O bond (see Figure 1). The Si atoms are arranged on a twodimensional square lattice, with a distance of 4.3 Å between neighboring atoms.18 This generates a 43 Å × 43 Å surface with a hydrocarbon surface density of 0.054 Å-2. Experimentally, by adjusting the pH of the solution to be well below the pKa value of the acid6,19 (around 5.0), the surface in contact with the water is covered entirely with COOH. In this work, we take all of the COOH headgroups to be protonated. Because of the geometry of our system, periodic boundary conditions are used in the XY plane parallel to the surface but not in the Z direction, normal to the interface. This creates a water liquid/vapor interface on one end. A reflecting wall is placed in the vapor phase at a distance of approximately 30 Å from the water liquid/vapor interface to prevent the escape of gas-phase water molecules and to maintain a fixed vapor pressure. All of the intermolecular interactions calculated are smoothly switched to zero using a force switching function when the distance between two atoms is between 19.5 and 21.5 Å. Corrections due to the long range forces are estimated using a uniform reaction field method20 (by surrounding the water lamella with an infinite medium of dielectric constant equal to 78).
10.1021/jp0734833 CCC: $40.75 © 2008 American Chemical Society Published on Web 08/02/2007
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Winter et al. change the calculated hydrogen-bond lifetimes.31,33,34 Similar definitions are used for the water-CAFSAM hydrogen bonding and for the hydrogen bonding between two COOH headgroups, as illustrated in Figure 1. With a working definition of a hydrogen bond, a dynamical variable, h, is defined as follows: If two tagged water molecules are hydrogen-bonded at t ) 0, h(t) is equal to 1 if these two molecules are still bonded at a later time, t; otherwise, it is equal to 0 (but may become 1 again later if these two water molecules reformed their bond). h(t) is similarly defined for a hydrogen bond between a tagged water molecule and a given CAFSAM molecule or between two COOH headgroups. The dynamics of the random variable, h, can be characterized by the equilibrium correlation function:
Figure 1. Schematic representation of the type of hydrogen bonds involving surface carboxylic acid headgroups considered in this paper. 1 and 2 are bonds between neighboring COOH headgroups, and 3-5 are with interfacial water molecules.
Each hydrocarbon molecule consists of a chain of CH2 groups, modeled as a united atom of mass 14, and is terminated by an explicit atom description of COOH. The intramolecular potential for each hydrocarbon molecule is described by a sum of harmonic bond stretching, harmonic angle bending, and a three-term Fourier series for the torsional energy. Intramolecular nonbonded interactions for two atomic centers separated by three or more bonds are modeled using a sum of Coulomb and Lennard-Jones potentials. This interaction energy is scaled down by a factor of 2 for atoms separated by three bonds. The harmonic stretching and bending terms are taken from AMBER,21 and the parameters for the torsional, Lennard-Jones, and Coulomb potentials are taken from Jorgensen’s OPLS potential.22 The parameters that describe the intramolecular LennardJones and Coulombic potentials, in addition to the intermolecular potential for the hydrocarbons with all other atoms in the system, are given in Table 1. These parameters have been previously used to study wetting behavior, adsorption, and spectroscopy at the water/SAM interface18,23-26 with reasonable agreement with experiments and other simulations. The potential energy of water is described using the SPC model27 and the spectroscopic intramolecular potential of Kuchitsu and Morino.28 The water-chain interactions are modeled using Lennard-Jones and Coulomb potentials with parameters determined using the standard combination rule for mixtures.29 III. Methods The hydrogen-bond dynamics are studied using Yamamoto’s time correlation approach30 extensively used in recent years to examine the hydrogen-bond dynamics in bulk water and aqueous solutions31-36 and at interfaces.17,37-41 We use a similar definition to that of Luzar and Chandler31 and consider two water molecules to be hydrogen-bonded if the distance between their oxygen atoms is less than 3.5 Å (corresponds to the first minimum in the water OO radial distribution function) and the OHO angle is greater than or equal to 150°. The exact choice of these two structural parameters is not expected to significantly
c(t) )
〈h(t) h(0)〉 〈h〉
(1)
where the relation 〈h(0) h(0)〉 ) 〈h〉 has been used. The ensemble average is over all pairs and all time origins. The function c(t) is the probability that a given hydrogen bond exists at time t given that it existed at time zero. c(t) starts at 1 and decays to zero, as any hydrogen bond will eventually break as time progresses. To examine the water-water hydrogen-bond dynamics, the simulation box is divided into adjacent slabs of thickness d ) 3.5 Å along the Z axis (recall the Z axis is parallel to the interface normal). This choice of d approximately corresponds to the thickness of one water “layer”. cn(t) is calculated for the nth slab by including the contributions of all hydrogen bonds between pairs of water molecules where at least one of them belongs to the given slab. If a water molecule changes its initial slab during the simulation, its time history begins to contribute to the average in the new slab. The c(t)’s calculated with this procedure are identical to each other (within the statistical error) in all the bulk slabs and to the c(t) calculated for a bulk system containing 500 water molecules. The hydrogen-bond dynamics and several structural aspects of the system were obtained from a 2.5 ns trajectory at 300 K performed using the velocity version of the Verlet algorithm and an integration time step of 0.5 fs. IV. Results and Discussion A. Interface Structure. The density profile of the water molecules near the CAFSAM surface as well as the carbon atomic density are shown in Figure 2. The marked peak in the water density near the surface signifies that the water wets the surface, as expected. The water reaches its bulk density at a distance of about 10 Å above the top carbon atom (which is located at Z ) 21.0 Å on average). Since the surface is smooth (all the chains are the same length and there are no surface defects) and the chain density is high, there is no water penetration into the layers. Simulations with rough surfaces show that water can get trapped into surface pockets.23,24 Another quantity of interest is the orientation of interfacial water molecules. This is found to be similar to the orientation of water near other SAM and solid uncharged surfaces,23,42 and
TABLE 1: Hydrocarbon Parameters for the Intramolecular and Intermolecular Potentials atom or group
σ (Å)
(kcal/mol)
q (au)
CH2 (in hydrocarbon chain) CH2 (bonded to carbonyl carbon in COOH) C (carbonyl carbon in COOH) O (double bonded to carbonyl carbon in COOH) O (bonded to hydrogen in COOH) H (in COOH)
3.905 3.800 3.750 2.960 3.000 0.000
0.118 0.050 0.105 0.210 0.170 0.000
0.00 0.08 0.55 -0.50 -0.58 0.45
Interface between Water and CAFSAMs
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Figure 4. Bulk (solid line) and interfacial (dotted line) water-water hydrogen-bonding time correlation function. Figure 2. Carbon atom (solid line) and water oxygen (thick solid line) atomic density profiles along the interface normal.
Figure 5. Radial distribution functions for the water oxygen (left panel) and the water hydrogen (right panel) vs different atoms on the COOH headgroup.
Figure 3. Top panel: The probability of a given water molecule to hydrogen bond to n other water molecules in the bulk (solid line) and at the interface (dotted line). Bottom panel: The probability to find n adjacent non-hydrogen-bonded water molecules near a given interfacial or bulk water molecule.
thus, we will just note it here without showing the data. For the fully protonated surface, the water molecules immediately near the surface are oriented with their dipole parallel to the surface with one of the OH bonds pointing directly toward the surface. This orientation is consistent with the expectation that water molecules will hydrogen bond with the COOH headgroups as well as with water molecules located in the second layer. Water in the second and third layers has almost no orientational preference. B. Water-Water Hydrogen Bonding. The hydrogenbonding structure and dynamics for bulk and interfacial water molecules have been extensively studied.17,31-41 The results for the present system are similar. The top panel of Figure 3 shows the probability of a given water molecule hydrogen-bonded to n other water molecules. In bulk water, each water molecule is likely to be hydrogen-bonded to four other water molecules, whereas, for interfacial water molecules (defined as those in the region Z < 27.5 Å), the most likely number is 3. However, both distributions are quite broad. The average number of hydrogen bonds per water molecule at the interface is 2.96 compared with 3.49 in bulk water. The bottom panel of Figure 3 shows the probability to find n adjacent non-hydrogen-bonded water molecules near a given water molecule. These are water molecules that are within the hydrogen-bonding OO distance but with the wrong orientation. The distributions in the bulk and at the interface are very similar. This is similar to what was found for water next to polar and nonpolar liquids.17 Specifically, the distribution P[n(adj)] for bulk water and for water just below the Gibbs dividing surface of these liquids (where the average water density is 50% of the
bulk value) was similar, while water molecules at the Gibbs surface or above it (in the organic phase) shows that almost all adjacent water molecules are hydrogen-bonded. The water molecules at the CAFSAM/water interface seem to behave like water below the Gibbs surface, which is reasonable, since CAFSAM allows water to hydrogen bond to it whereas an organic liquid such as dichloroethane does not. The hydrogen-bond dynamics in the bulk versus at the interface are depicted in Figure 4. c(t) is shown in a semilog plot to demonstrate the non-exponential character of the relaxation. The rapid initial decay represents the breaking of an existing hydrogen bond of a tagged water molecule due to the reorientation and vibration of the O-O vector. The process in the bulk and at the interface follows approximately the same dynamics. The long time relaxation is mainly due to rotational and translational diffusion and takes place when there is a nearby water molecule to form a new bond to the tagged water molecule. This process is slower at the interface due to slower diffusion as well as the fact that at the interface each water molecule is surrounded by fewer water molecules, limiting the number of potential hydrogen-bonding partners, thus causing an increase in the average hydrogen-bond lifetime.36 One may characterize the relaxation rate by the time it takes for c(t) to decay to 1/e. It is about 4.6 ps in bulk water compared with 7.9 ps for interfacial water molecules. This is similar to the behavior of the water molecules on the bulk side of the Gibbs surface at the water/1,2-dichloroethane interface. C. Water-CAFSAM Hydrogen Bonding. The left panel of Figure 5 shows the radial distribution functions for the water oxygen versus different atoms on the COOH headgroup. Note that the asymptotic value of all of these distribution functions is 0.5 due to the fact that half of the configuration space is occupied by the chain molecules (the g(r) are normalized using bulk water density). The well-defined peak in the g(r) between the water oxygen and the O and H atoms of the hydroxyl part of the COOH headgroup is evident. In contrast, significantly less structure is observed with regard to the carbonyl oxygen. A similar picture is indicated by the g(r) between the water hydrogen and the COOH headgroup atoms (right panel). This suggests that the hydroxyl of the COOH group is incorporated
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Figure 6. Top panel: The probability that n interfacial water molecules are hydrogen-bonded to a given carbonyl oxygen (solid line), hydroxyl hydrogen (dashed line), and hydroxyl oxygen (dotted line). Bottom panel: The probability of finding n interfacial water molecules adjacent but not hydrogen-bonded to carbonyl oxygen (solid line) or hydroxyl oxygen (dotted line).
Figure 7. Water-CAFSAM hydrogen-bonding correlation functions for hydrogen bonding with the carbonyl oxygen (solid line), hydroxyl hydrogen (dashed line), and hydroxyl oxygen (dotted line). These correspond to hydrogen bonds types 3, 4, and 5, as illustrated in Figure 1, respectively.
into the water hydrogen-bonding network to a much better degree than the carbonyl part of the headgroup. Figure 6 shows the probability distribution for different types of hydrogen bonds between water and the CAFSAM. The top panel of this figure shows that for a given interfacial water molecule there is 20, 30, or 50% probability for a hydrogen bond with the carbonyl oxygen, hydroxyl hydrogen, or hydroxyl oxygen, respectively. The bottom panel shows that the above situation occurs despite the fact that there are relatively quite a few water molecules in the vicinity of the COOH atoms. For example, there is a 40% probability of finding two water molecules within the hydrogen-bonding distance from a hydroxyl oxygen of the CAFSAM. Apparently, the dense CAFSAM structure enforces orientational constraints that prohibit significantly more water-CAFSAM hydrogen bonds. Figure 7 shows the relaxation dynamics of the three types of hydrogen bonds discussed in Figure 6. First, we note that these functions decay much slower than the water-water hydrogen bonds. This is due to the fact that there are significantly less neighboring water molecules available for hydrogen bonding compared with bulk water. (Compare the bottom panels of Figures 3 and 6.) The number, however, is not negligible, and thus, the relaxation time is still on the few tens of picoseconds time scale. The slight difference in the relaxation time among the different types of water-CAFSAM hydrogen bonds can also be explained with the aid of Figure 6. In particular, the fastest
Winter et al.
Figure 8. Top panel: The probability that a given COOH headgroup will form n hydrogen bonds of the type indicated to other COOH headgroups. Bottom panel: The probability of finding n adjacent but non-hydrogen-bonded pairs of the type indicated between COOH headgroups.
Figure 9. Internal CAFSAM hydrogen-bonding correlation functions for hydrogen bonding of the type indicated.
relaxation is observed for the hydrogen bond with the carbonyl oxygen, which is consistent with the fact that there is a higher probability to find adjacent water molecules that are not hydrogen-bonded. D. Internal CAFSAM Hydrogen Bonding. Finally, we consider the hydrogen bonding between neighboring chain molecules within the CAFSAM. The hydroxyl hydrogen of the COOH headgroup can form a hydrogen bond to the carbonyl oxygen or to the hydroxyl oxygen of a neighboring COOH headgroup (see Figure 1). The probability distributions of observing these bonds per chain molecule are shown in the top panel of Figure 8. This plot shows that about half of the COOH headgroups are hydrogen-bonded to other COOH headgroups. 22% form one bond to a neighboring CO group, 12% are involved with two bonds to two neighboring CO groups, and 14% form bonds to neighboring OH groups. The bottom panel shows that, despite the fact that a given chain molecule is most likely to have zero adjacent but non-hydrogen-bonded neighboring chain molecules, there are still a substantial number of neighboring chain molecules which could potentially participate in a hydrogen bond but the bond is not formed due to orientational constraints (recall that nadj gives the number of OO pairs for which the OO distance is within the hydrogenbond definition, but the OHO angle is outside the acceptable value). Taking into account only hydrogen-bonded COOH headgroups, there are approximately twice as many hydrogen bonds of the type CO-HO than HO-HO. The lifetime correlation functions of these two types of bonds are shown in Figure 9. Note that these H-bonds are significantly longer-lived than the CAFSAM-water or the water-water
Interface between Water and CAFSAMs H-bonds. It is interesting to note that, despite the fact that there are more neighboring non-hydrogen bonds to CO groups than to OH groups, the former are slightly longer-lived. This suggests that the former hydrogen bonds are intrinsically more stable. V. Conclusions The molecular dynamics calculations presented in this paper demonstrate that, at the interface between water (low pH) and carboxylic acid-functionalized self-assembled monolayers, a significant number of the COOH groups are hydrogen-bonded to their neighboring COOH groups, in agreement with recent experiments. Using hydrogen-bond population time correlation functions, we have determined a hierarchy of hydrogen-bond lifetimes at the interface. Chain-chain hydrogen bonds are very long-lived, with a lifetime estimated in the hundreds of picoseconds. Water-chain hydrogen-bond lifetimes are shorter, on the order of tens of picoseconds. The water-water hydrogenbond dynamics at the water/CAFSAM interface are on the order of a few picoseconds, which is slower than in bulk water but comparable to other water/organic liquid interfaces. Acknowledgment. This work has been supported by a grant from the National Science Foundation (CHE-0345361). We are grateful to Professor Franz Geiger for many useful discussions. References and Notes (1) Prime, K. L.; Whitesides, G. M. Science 1991, 252, 1164. (2) Schreiber, F. Prog. Surf. Sci. 2000, 65, 151. (3) Whelan, C. M.; Ghijsen, J.; Pireaux, J.; Maex, K. Thin Solid Films 2004, 464, 388. (4) de Groot, M. T.; Evers, T. H.; Merkx, M.; Koper, M. T. M. Langmuir 2007, 23, 729. (5) Wang, W. L.; Zhai, J.; Bai, F. L. Chem. Phys. Lett. 2002, 366, 165. (6) Gershevitz, O.; Sukenik, C. N. J. Am. Chem. Soc. 2004, 126, 482. (7) Yan, E. C. Y.; Liu, Y.; Eisenthal, K. B. J. Phys. Chem. B 1998, 102, 6331. (8) Konek, C. T.; Musorrafiti, M. J.; Al-Abadleh, H. A.; Bertin, P. A.; Nguyen, S. T.; Geiger, F. M. J. Am. Chem. Soc. 2004, 126, 11754. (9) Hautman, J.; Bareman, J. P.; Mar, W.; Klein, M. L. J. Chem. Soc., Faraday Trans. 1991, 87, 2031. (10) Mar, W.; Klein, M. L. Langmuir 1994, 10, 188.
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