6412
J. Phys. Chem. B 2001, 105, 6412-6419
Organic Monolayers as Mimics of Liquid/Liquid Interfaces: Molecular Dynamics Study of Electronic Spectra and Solvent Dynamics Emilio Squitieri Escuela de Quimica, Facultad de Ciencias, UniVersity Central de Venezuela, Caracas, Venezuela
Ilan Benjamin* Department of Chemistry, UniVersity of California, Santa Cruz, California 95064 ReceiVed: January 17, 2001; In Final Form: April 20, 2001
The electronic spectra and the solvation dynamics following the electronic transition of a chromophore attached to the interface between water and a self-assembled hydrocarbon monolayer are examined by molecular dynamics computer simulations and are compared with the same chromophore undergoing the same electronic transitions at the water/nonane interface. Two different self-assembled monolayers are considered. One is made of only C18H38 molecules giving rise to a smooth surface, and one is made of a 1:1 random mixture of C18H38 and C22H46 molecules giving rise to a rough surface. Different choices of the chromophore charge distribution and its location at the interface are considered and provide insight into different microscopic factors which influence the electronic line shape and the water dynamic response. We find that the electronic spectrum of the chromophore at the interface between water and a self-assembled hydrocarbon monolayer is very similar to the spectrum calculated when the same chromophore is located at the water/nonane interface, with variations which are consistent with the structure of the interface and, in particular, the degree of exposure of the chromophore to interfacial water molecules. The same observation applies to the water dynamic response, with the exception that slow components of water dynamics at the normal liquid/liquid interface (which can be shown to be due to microscopic capillary waves) are missing at the water/self-assembled monolayer interface.
1. Introduction One of the fundamental problems in experimental studies of solvation and reactions at liquid/liquid interfaces is that the buried nature of the interface makes it difficult to obtain high quality data without interference from any signal coming from the two adjoining bulk phases. This problem is compounded by the fact that not much is known about the structure of the interface between two immiscible liquids. Consequently, there is still a debate as to the correct description of the system at the microscopic level,1 and there is no microscopic theory of charge transfer at the interface beyond the simple continuum dielectric model.2 For example, the reorganization free energy for an electron transfer reaction is strongly dependent on the degree of hydration by water at the interface, yet we generally do not know what the degree of hydration is for a solute adsorbed at the liquid/liquid interface. A related issue is the shift in the electronic spectrum of a chromophore adsorbed at the interface.3 One can use this shift to obtain quantitative information about the degree of intermolecular interaction at the interface relative to the bulk, but converting this information to a complete structural characterization is difficult. One major reason for the ambiguity in the structure of the liquid/liquid interface (unlike the solid/liquid interface) is that thermally excited capillary fluctuations and partial mixing of the two liquids add a high degree of uncertainty to the exact nature of the environment experienced by a solute molecule which is adsorbed at the interface. Although molecular dynamics simulations have shown that these capillary fluctuations play an important role in understanding dynamic behavior at the interface, it is useful to understand the contribution of the
intrinsic interface to solvation, spectroscopy, and chemical reactivity without the uncertainty associated with the capillary fluctuations. This is also important as a first step in the development of molecular theories of the interface because the capillary distortions maybe added later as a statistical broadening. Indeed, in many studies of the liquid/vapor interface, comparisons between experimental data and theory involve removing the contribution of the capillary distortions to the experimental data by a procedure based on capillary wave theory.4 One approach to eliminating the complexity associated with the capillary broadening in computer simulations involves adding external field, forcing the interface to remain flat.5 The disadvantage of this procedure is that the resulting system cannot be compared with experimental results. Another approach that we propose here is to study the contribution of the intrinsic structure of the liquid/liquid interface by examining the interface between water and a self-assembled organic monolayer. This system enables us to study spectroscopy, solvation, and reactions at an interface whose microscopic structure is well characterized (like a solid-surface), yet still exhibits many of the unique features of a liquid/liquid interface. By systematically modifying the chemical nature and molecular structure of such an interface, a much better understating of the nature of the interactions at a liquid/liquid interface may be obtained in a system that can be more easily studied experimentally. In addition to the value of these systems for understanding liquid/liquid interfaces they have a huge independent practical importance for many fields of science. Thus, in recent years, significant progress has been made in the design and preparation
10.1021/jp0101716 CCC: $20.00 © 2001 American Chemical Society Published on Web 06/16/2001
Electronic Spectra and Solvent Dynamics of self-assembled monolayers with well characterized molecular structure.6,7 An important class of these are systems made of long-chain hydrocarbons that are either physisorbed on a solid surface like graphite7 or chemically attached to a metal or silica surface.8 The hydrocarbon chains are either unsubstituted or terminated by a variety of small organic groups such as OH, SH, S, Cl, COOH, NH2, and more. As a result, one obtains surfaces with rich structures and varied physicochemical properties. The interface between these systems and water can be investigated by an STM7 (scanning tunneling microscope), an AFM7 (atomic force microscope), neutron reflection,9 electrochemical techniques, and other thermodynamic and surface characterization methods, such as wetting experiments10 and nonlinear spectroscopic techniques.11 Self-assembled monolayers with different electronic and molecular structures have been used in recent years to study a number of different molecular processes such as electron transmission,12 energy transfer, and spectroscopy.13 Significant to our proposed study is the fact that it is possible to synthesize alkane and alkanethiol monolayers terminating with charge-transfer groups such as ferrocene and ruthenium and to study the electron transfer in these systems.14-17 In this paper, we begin a systematic study of the spectroscopy and dynamics of a chromophore attached at the interface between water and a self-assembled organic monolayer. Our main goal is to provide a direct correlation between the structure and the chemical properties of the water/organic interface and the static electronic spectrum and the dynamic solvent response following electronic transition of chromophores that are covalently attached to the interface. This will allow us to remove two uncertainties that currently exist in the study of ordinary liquid/liquid interface systems: the structure of the interface and the location of the solute molecules. Although several molecular dynamics studies of water/ membrane interfaces and of self-assembled monolayers have been reported,18-25 none has been reported for the spectroscopy and reactivity of adsorbed and covalently attached chromophores at the interface between water and the self-assembled monolayers. We consider monolayers which are made up of a mixture of long-chain alkanes of varying lengths attached to a silica surface.26 Mimicking the typical roughness of the water/liquid organic interface is done by changing the ratio of the underlying short vs long-chain hydrocarbons. The alkane chains' terminating CH3 group may be substituted by a number of functional groups in order to generate several “typical” organic/water interface systems. Replacing the CH3 groups by OH will give rise to a hydrogen-bonding polar organic interface. Using a Cl atom instead of the OH group will result in a slightly polar, polarizable interface. Using a COOH group that partially dissociates will allow us to create a charge density at the interface. A covalently attached model chromophore as a terminating group will be the probe in these calculations. This probe will be partially solvated by water to a degree that will depend on the roughness of the surface and the location of the probe. Considering all these factors (surface roughness, probe location, and organic group functionality) involves examining a large number of different molecular systems. Thus, in this paper, we limit ourselves to unsubstitued alkane chains, and we postpone to future publications an examination of more chemically complex surfaces. 2. Systems and Potential Energy Functions A. Organic Monolayers. The structure of the organic part of the system has been previously discussed,27 and we summarize it briefly. The system includes 100 hydrocarbon chain
J. Phys. Chem. B, Vol. 105, No. 27, 2001 6413 molecules, each of which is covalently attached at one end to an Si-O bond. The Si atoms are arranged as a two-dimensional square symmetric lattice, with a distance of 4.3 Å between neighboring Si atoms. Two separate systems are considered: system S (the smooth surface), which is made up of 100 C18H38 molecules, and system R (the rough surface), which is made up of 50 C18H38 molecules and 50 C22H46 molecules randomly attached to the silica surface. This is consistent with the fact that experimentally no self-aggregation of the two different types of molecules occurs.27 Each hydrocarbon molecule consists of a flexible chain of CH2 groups modeled as united atoms of mass 14, terminated by a CH3 group which is modeled as a united atom of mass 15. The intramolecular potential includes harmonic stretching and bending terms, a 3-term Fourier series for the torsional energy28 and nonbonded interactions between two atomic centers separated by three or more bonds. The harmonic force constants, the torsional parameters and the equilibrium bond length and bond angles are taken from the Amber force field29 and Jorgensen’s TIPS parameters.30 The intramolecular nonbonded interactions are modeled using the Lennard-Jones potential with parameters σ ) 4.0 Å, ) 0.1 kcal/mol. (These parameters are slightly different from the intermolecular Lennard-Jones parameters in order to obtain the best fit for the torsional barriers). This interaction is scaled down by a factor of 2 for the 1,4 carbon atoms in each chain.28 The intermolecular interactions between different molecules are modeled as a sum of Lennard-Jones potentials between every pair of united atoms. The Lennard-Jones parameters σij and ij for the interaction between united atoms of types i and j are computed from the standard parameters of the CH2 and CH3 groups, using the relations31
ij ) xij, σij ) (σi + σj)/2
(1)
We take: σCH2 ) σCH3 ) 3.905 Å, CH2 ) 0.118 kcal/mol, CH3 ) 0.175 kcal/mol. The intermolecular interactions are switched smoothly to zero32 when r (the distance between atoms i and j) is in the range between 19.5 Å and 21.5 Å.) B. Water and Water-Organic Monolayer Interactions. The water potential energy function is based on the SPC model,33 including the spectroscopic intramolecular potential of Kuchitsu and Morino.34 This flexible model of water has been shown to give a reasonable representation of bulk and interfacial water properties.5 The water-hydrocarbon interactions are modeled via the Lennard-Jones potential and the mixing rule (eq 1), using the Lennard-Jones parameters σH ) 0, σO ) 3.1655 Å, H ) 0, O ) 0.1554 kcal/mol. C. Chromophore. The chromophore consists of a pair of atoms, the distance between which is held fixed at 6 Å or 8 Å (typical distances for the charge separation in relatively large dye molecules35). It is covalently attached to a top surface atom with parameters that were selected (for simplicity) to be identical to those of a C-C bond in a hydrocarbon chain. This gives rise to three different systems, depending on whether the chromophore is attached to the top atom of: (a) the smooth surface, (b) a long chain molecule of the rough surface, or (c) a short chain molecule of the rough surface. The interaction between each of the solute atoms and the water atoms and the chains atoms is modeled by a Lennard-Jones plus Coulomb potential. The Lennard-Jones interaction parameters for the two solute atoms are taken to be σ ) 5.154 Å and ) 0.1104 kcal/ mol. The charges on the two atoms are (Qn, depending on the electronic state n of the chromophore (see below).
6414 J. Phys. Chem. B, Vol. 105, No. 27, 2001
Squitieri and Benjamin
D. Boundary Conditions. Periodic boundary conditions in the plane parallel to the surface are applied, whereas in the direction normal to the interface, the boundary conditions are free. Thus, liquid water is in equilibrium with the vapor phase. Any water molecule that escapes the box is reflected at a wall set up at a distance larger than the potential cutoff. Our use of a continuous switching function at the largest possible cutoff distance (consistent with the periodic boundary conditions) should minimize adverse effects due to the neglect of long-range forces. An estimate of these forces using a uniform reaction field method (by surrounding the water lamella with an infinite medium with a dielectric constant equal to 78) gives only a small, nearly constant contribution to the chromophorewater interaction energy with an almost indistinguishable effect on the dynamics. Although a more sophisticated, twodimensional Ewald sum36 method can be applied to the geometry of our system, it is not clear what the implications are when the inhomogeneous charge distribution at the interface is extended infinitely, thus magnifying surface fluctuations. An application of the three-dimensional Ewald method to the water/ 1,2-dichloroethan interface shows only minor effects on the reorientation dynamics of interfacial water molecules (unpublished results). Clearly, however, this subject requires additional study.
and thus, the solvent nuclear polarization is not equilibrated to the new solute charge distribution. The solvent will relax to the value appropriate to the new charge distribution (Qnβ). We can observe the relaxation of the solvent to a new equilibrium state by following the dynamical variable Γ[r(t)]. Note that if the solute and/or the solvent are electronically polarizable, then this fast electronic degree of freedom instantaneously equilibrates to the new solute charges, which generally lower the energy of the new state. This contribution is typically much smaller than the contribution due to the solvent permanent dipoles,38 and we neglect it here (i.e., our model solute and solvent are nonpolarizable). The effect due to the contribution of the solvent electronic polarizability has been discussed recently.38,39 The dynamic of Γ[r(t)] is described by the nonequilibrium time correlation function
S(t) )
Un ) U0 + ∆En + QnΓ(r)
(2)
where U0 is the total potential energy for the chains, water, water-chains and the nonelectrostatic interactions between the chromophore atoms and all the other atoms in the system, ∆En is the fixed gas-phase zero point energy of the nth electronic state and
Γ(r) )
∑i qi[(|ri - rA|)-1 - (|ri - rB|)-1]
(3)
where rA and rB are, respectively, the positions of the positively and negatively charged solute atoms, and ri, qi are the position and charge of the i’th liquid atom, respectively. The electronic absorption spectra are calculated for the different systems using the classical Franck-Condon approximation, assuming further that the transition dipole moment is a constant. The absorption spectrum IRβ for the transition nR f nβ corresponds to the energy difference pΩ(r) at fixed nuclear positions r between the system at the state nβ and at the state nR, whereas the solvent degrees of freedom are at equilibrium with respect to the solute in the state nR
IRβ(ω) ) 〈δ[ω - Ω(r)]〉nR )
∫δ[ω - Ω(r)]e-βH ∫e-βH dr
nR
dr (4)
Γ(0) - Γ(∞)
(6)
where Γ(t) is the nonequilibrium ensemble average of Γ[r(t)] at time t. Note that Γ(0) ) 〈Γ〉nR, and Γ(∞) ) 〈Γ〉nβ are the equilibrium averages in the initial and final states. This is closely related to the experimentally derived correlation function
3. Methods The methodology for the spectral shift calculations and the solvent dynamical response has been previously discussed in detail, and we briefly outline it here.5,37 The total potential energy of the system when it is in the n'th electronic state can be written as
Γ(t) - Γ(∞)
Sω(t) )
ω(t) - ω(∞) ω(0) - ω(∞)
(7)
which is determined by following the time-dependent shift of the peak of the emission spectrum ω j (t) from a photochemically excited solute.40,41 Note that ω j (0) is the average equilibrium (static) absorption frequency, and ω j (∞) is the average equilibrium (static) emission frequency. Figure 1 is a schematic diagram showing the different quantities described above. This diagram clearly demonstrates the following: (1) the absorption spectrum shifts to the red (lower energy) relative to the gas phase if ∆µ > 0, and this shift increases with an increase in the polarity of the medium (which raises the energy of the ground state relative to the excited state); (2) the absorption spectrum shifts to the blue (higher energy) relative to the gas phase if ∆µ < 0, and this shift increases with an increase in the polarity of the medium (which lowers the energy of the ground state relative to the excited state). After the system has reached equilibrium in the final (excited) state, the equilibrium fluctuations in Γ(r) can be used to compute the equilibrium time correlation function
C(t) )
〈{Γ[r(t)] - 〈Γ〉e}{Γ[r(0)] - 〈Γ〉e}〉e 〈{Γ[r(0)] - 〈Γ〉e}{Γ[r(0)] - 〈Γ〉e}〉e
(8)
where 〈Γ〉e is the equilibrium average of Γ in the excited state. Under the linear response assumption, when the time evolution of Γ(r) (in the nonequilibrium dynamic) obeys certain conditions42-44 then one obtains the relation
S(t) ) C(t)
(9)
nR
pΩ(r) ) Hnβ - HnR ) ∆Enβ - ∆Enβ + (Qnβ - QnR)Γ(r) (5) where β ) 1/kT, and δ is the Dirac delta function. Immediately following this transition, the solvent atoms' positions r are identical to the positions just before the transition,
which, if correct, suggests that the same solvent dynamic which is responsible for the nonequilibrium decay exists (with the same weighting) in the equilibrium ensemble. 4. Results and Discussion A. Static Spectra. Our previous study27 of water in contact with smooth and rough hydrocarbon surfaces showed that the
Electronic Spectra and Solvent Dynamics
Figure 1. Schematic depiction of the potential energy involved in the electronic absorption and emission spectra in a polar solvent. The ∆µ > 0 and ∆µ < 0 curves correspond to an excited state which is either more polar or less polar, respectively, than the ground state. The vertical arrows correspond to the absorption (solid arrows) and emission (dashed arrows) transitions. The thick arrows superimposed on the energy curves represent solvent relaxation.
Figure 2. Orientational probability distribution for the chromophore attached to the surface. The solid, dashed, and dotted lines correspond to the chromophore attached to the smooth surface, to a short and to a long chain of the rough surface, respectively.
main difference between the two cases is the fact that water better wets the rough surface, creating pockets of enhanced water concentration. The chromophore is an excellent probe of these regions, as the probe location will manifest itself in the spectral shift and the solvation dynamics. The interaction with the water is also influenced indirectly by the constraints imposed by the underlying hydrocarbon surface on the probe orientation. The orientational probability distribution of the probe dipole relative to the interface normal is shown in Figure 2. When the probe is attached to the smooth surface, it forms an angle of about 55 degrees from the normal (solid line). When the probe is attached
J. Phys. Chem. B, Vol. 105, No. 27, 2001 6415
Figure 3. Spectral line shapes (relative to the gas phase) for the chromophore undergoing the transition Qe ) 1.0e f Qg ) 0.5e. In the top panel, the solid, dashed, and dotted lines correspond to the chromophore attached to the smooth surface, to a short and to a long chain of the rough surface, respectively. In the bottom panel, the chromophore is located at the Gibbs surface of the water/nonane interface (solid line), at the organic side of the water/nonane interface (dashed line) and in bulk water (dotted line).
to the short chain, its motion is restricted and it is pointing more toward the normal, the angle now is about 40 degrees. And, as expected, when the probe is attached to the long chain (dashed line), it is protruding into the water phase and has much more freedom of motion. Indeed, the dotted line in Figure 2 which corresponds to this case shows a much wider distribution centered around 70 degrees, with some probability that the probe is parallel to the interface. We now turn to an examination of the static spectrum for the chromophore undergoing several different transitions. Figure 3 corresponds to the case ∆µ ) -14.4 D, and thus, all the spectral lines are shifted to higher energies relative to the gas phase. The top panel depicts the results for the chromophore attached to the three different surfaces (systems A, B, and C). The largest shift is observed when the chromophore is attached to the long-chain of the rough surface (dotted line)s corresponding to the greatest exposure to the water molecules. The smallest shift is observed when the chromophore is attached to the short-chain of the rough surface (dashed line)scorresponding to the least exposure to the water molecules. When the chromophore is attached to the smooth surface, we have an intermediate case (solid line). It is interesting to compare these spectral line shapes (the same electronic transition with the same chromophore) with those determined in bulk water and at the water/nonane liquid/ liquid interface and shown in the bottom panel of Figure 3. As expected, this panel shows that the transition in bulk water is shifted to the blue relative to all the transitions in the top panel. The interesting thing to note is that the spectral line shape at
6416 J. Phys. Chem. B, Vol. 105, No. 27, 2001
Squitieri and Benjamin blue-shiftresulting from the same |∆µ|, because the blue-shift involves a transition from a much more polar ground state. This effect is due to the quadratic dependence of the electrostatic energy of the solute on its charge. A simple demonstration of this fact can be obtained from a continuum electrostatic model calculation for a point dipole in a bulk medium. For example, for a parallel transition in a polar nonpolarizable liquid one finds for the shift relative to the gas phase46,47
∆ωV )
4µg(µg - µe) - 1 +2 a3
(10)
0
Figure 4. Spectral line shapes (relative to the gas phase) for the chromophore undergoing several transitions with the same value of |∆µ| but different values of µg as indicated in the different panels. In each panel, the solid, dashed, and dotted lines correspond to the chromophore attached to the smooth surface, to a short and to a long chain of the rough surface, respectively.
the smooth water/monolayer interface is very similar to that in the normal water/nonane interface when the chromophore is located at the Gibbs surface. Similarly, the spectral line shape at the rough water/monolayer interface (with the chromophore attached to the short chain) is very similar to that in the water/ nonane interface when the chromophore is located in the organic side of the interface. Thus, the environment sensed by the chromophore at different locations of the normal water/nonane interface can be mimicked by locating a probe at different locations of the rough and smooth water/monolayer interface. In addition to the location of the peaks, the widths of the line shapes exhibit interesting behavior. The widths of the three line shapes in the top panel are essentially identical to each other and to the line shapes when the probe is either in bulk water or at the Gibbs surface of the water/nonane interface. However, they are narrower than the line shape when the probe is located on the organic side of the water/nonane interface (dashed line of the bottom panel). This line shape is wider by about 20% because in this case the contribution of the capillary fluctuations (water molecules protruding into the organic phase) at the normal water/nonane interface is most significant when the probe is in the organic phase. We will return to this point later. Figure 4 shows the effect of changing the dipole of the ground state while keeping |∆µ| ) 14.4 D constant.45 The bottom panel is a replot of the data discussed above (in the top panel of Figure 3), shown for easy comparison with the other two cases. First note that the red-shiftdepicted in the top panel (resulting from a ∆µ > 0 transition) is much smaller in absolute value than the
where is the static dielectric constant of the liquid, a0 is the radius of the cavity in which a point dipole of magnitude µg is located in the ground electronic state and µe is the magnitude of the dipole in the excited state. In fact, in our molecularly based calculations the dependence of the spectral shift on the magnitude of the ground state dipole is slightly stronger than quadratic because of partial locking of the solvent dipoles around the charged solute when this charge is big (dielectric saturation). In light of the above considerations, Figure 4 directly demonstrates the degree to which the chromophore probes the interfacial water molecules. Although the bottom panel shows that the interaction with water increases as the chromophore is moved from being attached to the short chain to the smooth surface and to the long chain, the top panel shows the effect of the somewhat reduced ground state dipole. In this case, the probe attached to the smooth surface (solid line) and to the long-chain hydrocarbon (dotted line) experiences similar interactions with water. This interaction clearly diminishes only when the probe is attached to the short chain (buried), indicating that the chromophore is less exposed to water in this location. The fundamental difference between the probe attached to the longchain hydrocarbon and the smooth surface is the degree to which water molecules can interact favorably with the far end of the chromophore (because the other end is equally well exposed to water). The above results suggest that minor differences between theses interactions can be detected with transitions involving a large ground-state dipole. It is interesting to note that electronic transitions involving a zero ground-state dipole (center panel of Figure 4) do not show appreciable differences between the systems, which suggests that despite the difference in the accessibility of the water molecules to the probe, there is little difference between the structure of the hydration shell in the three systems if electrostatic contributions are removed. Figure 5 provides additional insight into the interfacial environment experienced by the probe by considering the dependence of the spectral shifts on the magnitude of ∆µ for three cases where ∆µ > 0. In panel A, we again show the case where ∆µ ) 14.4 D. In panel B, ∆µ ) 19.2 D is achieved by an increase of the ground-state dipole moment by 33%, whereas in panel C the same ∆µ ) 19.2 D is achieved by an increase of the chromophore bond length by 33%. Qualitatively, the results are in agreement with the expected increase of the shift with the increase in the magnitude of ∆µ. However, there is a much larger increase in the spectral shift when the increase in ∆µ is due to a larger charge than when it is due to an increase in the bond length of the chromophore. Equation 10 predicts that the shift will increase by a factor of 1.33/1.00 × (1.33 - 0.667)/ (1.00 - 0.5) ≈ 1.76 when the dipole is changed without a change in the cavity size. By comparing panel B to panel A in Figure 5, we can see that the shift is increased by a factor of 2.0 in the case of the chromophore attached to a shorter hydrocarbon chain and by a factor of 1.9 for the other two
Electronic Spectra and Solvent Dynamics
Figure 5. Spectral line shapes (relative to the gas phase) for the chromophore undergoing several transitions. Panel A: Qe ) 1.0e f Qg ) 0.5e, R ) 6 Å; panel B: Qe ) 4/3e f Qg ) 2/3e, R ) 6 Å; panel C: Qe ) 1.0e f Qg ) 0.5e, R ) 8 Å. In each panel, the solid, dashed, and dotted lines correspond to the chromophore attached to the smooth surface, to a short and to a long chain of the rough surface, respectively.
systems. This is in good agreement with eq 10, considering the simplicity of this equation. In fact, a more exact derivation, which takes into account the dumbbell charge distribution and the dielectric inhomogeneity, is possible with results that depend on the location of the charges relative to the interface.48 For example, when both cavities representing the two charges of the chromophore are on the same side of the interface, the shift is given by
∆ωV ) (Qe - Qg)[f(a,b,R,θ,1,2)Qg + g(a,b,R,θ,1,2)Qe] (11) where (Qg, (Qe are the charges in the ground and excited states, respectively, and f and g are complicated expressions which depend on the diameters of the two cavities (a and b), the distance between them (R), the angle with respect to the interface normal (θ) and the dielectric constant of the two media 1, 2. Unfortunately, applying this expression involves a number of uncertain quantities, but nevertheless, because f . g for reasonable choices of the parameters, we get a similar dependence on the charges and thus, qualitative agreement with the molecular dynamics calculations. Panel C of Figure 5 shows that the increase in ∆ω is much smaller (a factor of 1.2 relative to panel A in all the three systems) when the increase in the dipole is due to the increase in bond length rather than in the charges. A simple continuum model argument based on eq 10 suggests that because the cavity
J. Phys. Chem. B, Vol. 105, No. 27, 2001 6417
Figure 6. Equilibrium (C(t)) and nonequilibrium (S(t)) solvent responses to different electronic transitions in the three different systems considered in this work. In each panel, the thick solid line is for the transition involving a chromophore attached to the smooth surface and the thin solid line and the dotted lines are for the chromophore attached to a short chain and a long chain of the rough surface, respectively. Panels A and B correspond to the transition Qe ) 0.0e f Qg ) 0.1e, R ) 6 Å, Panels C and D correspond to the transition Qe ) 0.0e f Qg ) 4/3e, R ) 6 Å, and Panels E and F correspond to the transition Qe ) 0.0e f Qg ) 1.0e, R ) 8 Å.
size increases by a factor of (8/6)3 ≈ 2.4, the net effect should indeed be much smaller than in case B. A more accurate approach using eq 11 with a reasonable choice of parameters gives a 30% increase in ∆ω which is reasonable. These results suggest that despite the intricate molecular structure at the monolayer/water interface, the qualitative behavior is very similar to the one expected from a boundary between two simple dielectric media. B. Water Solvation Dynamics. We now turn to the nonequilibrium solvation dynamics calculations. Figure 6 summarizes all the data. This includes the electronic transitions from a ground-state charge distribution of Qg ) 0 au to an excitedstate charge distribution of Qe ) 1 au (top panels), or Qe ) 1.33 au (middle panels), or Qe ) 1 au with R ) 8 Å (bottom panels). In each panel, the three lines correspond to the three different adsorption sites, as indicated in the figure caption. The three panels on the left depict the equilibrium correlation C(t) (eq 8), each line calculated from a 200 ps trajectory, whereas the three right panels show the nonequilibrium correlation functions (eq 6), each line calculated from 50, 2 ps trajectories. The obvious feature of the results summarized in Figure 6 is that there is not much variation in the water dynamics among the different systems. This is especially so if we consider the equilibrium fluctuations. The three lines in each panel are almost identical, and there is also small variations among the different panels on the left (corresponding to the different electronic
6418 J. Phys. Chem. B, Vol. 105, No. 27, 2001
Squitieri and Benjamin the overall relaxation is very similar to that at the water/ monolayer interface and almost identical to the case where the chromophore is attached to the smooth surface (thick line in panel B of Figure 6). Figure 7 also shows the dynamics in bulk water (line d) where there is no restriction on the water. This relaxation is faster than in any of the systems we considered here, although the relaxation rate when the probe is 8 Å and attached to the long-chain hydrocarbon (dotted line in panel F of Figure 6) comes very close to this case, as expected. Thus, as in the case of the static spectrum, there is a complete correspondence between the liquid/liquid interface and the water/ monolayer interface with variations due to the lack of capillary excitations at the water/monolayer interface. 5. Conclusions
Figure 7. Comparison of the nonequilibrium solvation dynamics in different systems in which the probe undergoing the transition Qe ) 0.0e f Qg ) 1.0e, R ) 6 Å is (a) located in the nonane side of the normal water/nonane interface; (b) attached to a short chain of the rough self-assembled monolayer surface; (c) located in the nonane side of the water/nonane interface, for which capillary excitations are suppressed; and (d) located in bulk water.
transitions). Most of the variations are observed in the nonequilibrium calculations. In each of the three panels on the right, the water solvation dynamic is slowest for the case where the chromophore is attached to the short chain of the rough surface (thin line). This is consistent with the idea that the water molecules in this region are restricted by the narrow pores created by the nearby longer chains, and it is in agreement with similar experimental observations on water dynamics in restricted environments.49 When the chrompohore is attached to the smooth surface (solid thick line) or to the long-chain molecule of the rough surface (dotted line), the water dynamic is very similar, signaling a comparable influence of the surfaces. The variations among the different electronic transitions is consistent with results obtained in bulk liquids, where a larger change in the dipole moment results in faster dynamics (compare panels B and D). Note that the faster response is observed when the chromophore bond is 8 Å (panel F), and in this case, the difference in the relaxation rate between the different surface locations is not as big as in panel B. This is consistent with the fact that when the bond length is larger, more of the chromophore is exposed to unrestricted water molecules. Somewhat more informative is the comparison of the results discussed in Figure 6 with water solvation dynamics in other systems. This is shown in Figure 7, where the nonequilibrium solvation dynamics following the transition Qe ) 0.0e f Qg ) 1.0e, R ) 6Å is examined. Line b again represents the data shown in panel B (thin line) of Figure 6 (the chromophore is attached to a short chain of the rough self-assembled monolayer surface). In comparison with the same probe undergoing the same transition and located in the nonane side of the normal water/nonane interface (line a), we observe a much slower relaxation in the case of the normal liquid/liquid interface. As discussed elsewhere,50 the very slow component observed in the normal water/nonane interface when the probe is in the organic side is due to slow water fingers interacting via diffusive motion with the chromophore. This type of dynamics does not exist in the water monolayer interface. Indeed, line c shows the results when the capillary excitation at the normal water/nonane interface is suppressed. The slow component is removed, and
The electronic spectrum of a simple probe at the interface between water and a self-assembled hydrocarbon monolayer is remarkably similar to the spectrum calculated when the probe is located at the water/nonane interface and is in qualitative agreement with a simple dielectric picture of the interface. This suggests that self-assembled monolayers with well-defined structures that can be easily constructed and measured may be used to mimic liquid/liquid interfaces. In contrast, solvation dynamics at the water/monolayer interface do not contain slow components which are present at the normal liquid/liquid interface due to capillary waves excitation. This suggests that the systems discussed in this paper are useful for disentangling the effect of dynamic surface roughness on the interactions experienced by a probe molecule at the interface. In general, the dependence of the relaxation rate on the location of the probe is consistent with the degree to which the probe is exposed to freely moving water molecules. We believe that the type of experiments simulated in this paper are feasible to carry out in the laboratory. Very recently, the first solvation dynamics experiments at the liquid/vapor interface have been reported51 with results which agree with simulations published a few years ago.52 These experiments are being carried out now at liquid/liquid interfaces.53 In addition, closely related to the systems discussed above are studies of solvation dynamics at micelle/water interfaces54,49 and water/ solid interfaces. Much of the insight gained by the calculations described above will be directly relevant to these systems. Acknowledgment. This work has been supported by a grant from the National Science Foundation (Grant No. CHE9981847). E.S. would like to acknowledge the support from C.D.C.H de la Universidad Central de Venezuela. References and Notes (1) Girault, H. H. Charge Transfer across Liquid-Liquid Interfaces. In Modern Aspects of Electrochemistry; Bockris, J. O. M.; Conway, B. E.; White, R. E., Eds.; Plenum Press: New York, 1993; Vol. 25; p 1. (2) Benjamin, I. Chem. ReV. 1996, 96, 1449. (3) Wang, H.; Borguet, E.; Eisenthal, K. B. J. Phys. Chem. 1997, 101, 713. (4) Beaglehole, D. Experimental Studies of Liquid Interfaces. In Fluid Interfacial Phenomena; Croxton, C. A., Ed.; Wiley: New York, 1986; p 523. (5) Benjamin, I. Molecular Dynamics Methods for Studying Liquid Interfacial Phenomena. In Modern Methods for Multidimensional Dynamics Computations in Chemistry; Thompson, D. L., Ed.; World Scientific: Singapore, 1998; p 101. (6) Whitesides, G. M.; Laibinis, P. E. Langmuir 1991, 6, 87. (7) Giancarlo, L. C.; Flynn, G. W. Annu. ReV. Phys. Chem. 1998, 49, 297. (8) Brunner, H.; Vallant, T.; Mayer, U.; Hoffmann, H. Surf. Science 1996, 368, 279. (9) Lu, J. R.; Thomas, R. K. J. Chem. Soc., Faraday Trans. 1998, 94, 995.
Electronic Spectra and Solvent Dynamics (10) Olbris, D. J.; Ulman, A.; Shnidman, Y. J. Chem. Phys. 1995, 102, 6865. (11) Eisert, F.; Dannenberger, O.; Buck, M. Phys. ReV. B. 1998, 58, 10 860. (12) Evans, D.; Wampler, R. J. Phys. Chem. B. 1999, 103, 4666. (13) Kaschak, D. M.; Mallouk, T. E. J. Am. Chem. Soc. 1996, 118, 4222. (14) Smalley, J. F.; Feldberg, S. W.; Chidsey, C. E. D.; Linford, M. R.; Newton, M. D.; Liu, Y. P. J. Phys. Chem. 1995, 99, 13 141. (15) Finklea, H. O.; Liu, L.; Ravenscroft, M. S.; Punturi, S. J. Phys. Chem. 1996, 100, 18 852. (16) Feng, Z. Q.; Imabayashi, S.; Kakiuchi, T.; Niki, K. J. Chem. Soc., Faraday Trans. 1997, 93, 1367. (17) Herrero, R.; Moncelli, M. R.; Becucci, L.; Guidelli, R. J. Phys. Chem. B. 1997, 101, 2815. (18) Hautman, J.; Bareman, J. P.; Mar, W.; Klein, M. L. J. Chem. Soc., Faraday Trans. 1991, 87, 2031. (19) Stouch, T. R. Molecular Simulations 1993, 10, 335. (20) Venable, R. M.; Zhang, Y. H.; Hardy, B. J.; Pastor, R. W. Science 1993, 262, 223. (21) Marrink, S. J.; Berkowitz, M.; Berendsen, H. J. C. Langmuir 1993, 9, 3122. (22) Mar, W.; Klein, M. L. Langmuir 1994, 10, 188. (23) Pohorille, A.; Wilson, M. A. Origins Life EVol. Biosphere 1994, 25, 21. (24) Schulten, K.; Zhou, F. J. Phys. Chem. 1995, 99, 2194. (25) Tobias, D. J.; Tu, K. C.; Klein, M. L. Curr. Opin. Colloid Interface Sci. 1997, 2, 15. (26) Trakhtenberg, S.; Naaman, R.; Cohen, S. R.; Benjamin, I. J. Phys. Chem. B. 1997, 101, 5172. (27) Rudich, Y.; Benjamin, I.; Naaman, R.; Thomas, E.; Trakhtenberg, S.; Ussyshkin, R. J. Phys, Chem, A. 2000, 104, 5238. (28) Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, 1982. (29) Weiner, S. J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A. J. Comput. Chem. 1986, 7, 230. (30) Jorgensen, W. L. J. Am. Chem. Soc. 1981, 103, 335. (31) Hansen, J.-P.; McDonald, I. R. Theory of Simple Liquids, 2nd ed.; Academic: London, 1986. (32) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon: Oxford, 1987.
J. Phys. Chem. B, Vol. 105, No. 27, 2001 6419 (33) Berendsen, H. J. C.; Postma, J. P. M.; Gunsteren, W. F. V.; Hermans, J. In Intermolecular Forces; Pullman, B., Ed.; D. Reidel: Dordrecht, 1981; p 331. (34) Kuchitsu, K.; Morino, Y. Bull. Chem. Soc. Jpn. 1965, 38, 814. (35) Reichardt, C. Chem. ReV. 1994, 94, 2319. (36) Hautman, J.; Klein, M. L. Mol. Phys. 1992, 75, 379. (37) Benjamin, I. Molecular Dynamics Simulations in Interfacial Electrochemistry. In Modern Aspects of Electrochemistry; Bockris, J. O. M., Conway, B. E., White, R. E., Eds.; Plenum Press: New York, 1997; Vol. 31; p 115. (38) Bader, J. S.; Berne, B. J. J. Chem. Phys. 1996, 104, 1293. (39) Benjamin, I. Chem. Phys. Lett. 1998, 287, 480. (40) Simon, J. D. Acc. Chem. Res. 1988, 21, 128. (41) Barbara, P. F.; Jarzeba, W. AdV. Photochem. 1990, 15, 1. (42) Carter, E. A.; Hynes, J. T. J. Chem. Phys. 1991, 94, 5961. (43) Stephens, M. D.; Saven, J. G.; Skinner, J. L. J. Chem. Phys. 1997, 106, 2129. (44) Geissler, P. L.; Chandler, D. J. Chem. Phys. 2000, 113, 9759. (45) Note that the top and bottom panels of Figure 4 are not an emission/ absorption pair. (46) McRae, E. G. J. Phys. Chem. 1957, 61, 562. (47) Bakhshiev, N. G. Opt. Spektrosk. 1964, 16, 821. (48) Benjamin, I.; Michael, D. Molecular Dynamics Computer Simulations of Electronic Absorption Line Shapes at Liquid Interfaces. In Laser Techniques for Condensed-Phase and Biological Systems; Scherer, N. F., Hicks, J. M., Eds.; SPIE: Washington, 1998; p 145. (49) Pant, D.; Riter, R. E.; Levinger, N. E. J. Chem. Phys. 1998, 109, 9995. (50) Michael, D.; Benjamin, I. J. Chem. Phys. 2001, 114. (51) Zimdars, D.; Dadap, J. I.; Eisenthal, K. B.; Heinz, T. F. Chem. Phys. Lett. 1999, 301, 112. (52) Benjamin, I. Solvation and Charge Transfer at Liquid Interfaces. In Reaction Dynamics in Clusters and Condensed Phases; Jortner, J., Levine, R. D., Pullman, B., Eds.; Kluwer: Dordrecht, The Netherlands, 1994; p 179. (53) Eisenthal, K. B., personal communication. (54) Weidemaier, K.; Tavernier, H. L.; Fayer, M. D. J. Phys. Chem. B. 1997, 101, 9352.
