Chemical Dynamics Study of Intrasurface Hydrogen-Bonding Effects in

476

J. Phys. Chem. C 2008, 112, 476-490

Chemical Dynamics Study of Intrasurface Hydrogen-Bonding Effects in Gas-Surface Energy Exchange and Accommodation Urosˇ Tasic´ ,† B. Scott Day,‡ Tianying Yan,§ John R. Morris,*,‡ and William L. Hase*,† Department of Chemistry and Biochemistry, Texas Tech UniVersity, Lubbock, Texas 79409-1061, Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, and Institute of New Energy Material Chemistry and Institute of Scientific Computing, Nankai UniVersity, China ReceiVed: June 13, 2007; In Final Form: October 11, 2007

Classical chemical dynamics simulations were performed to compare the efficiency of energy transfer in collisions of Ar with 300 K CH3- and OH-terminated alkyl thiol self-assembled monolayer surfaces (i.e., H-SAM and HO-SAM) and compare with previous experiments (Anal. Chim. Acta 2003, 496, 249). The experiments show that energy is transferred less efficiently to the HO-SAM. The H-SAM has a periodic, ordered surface structure, whereas the surface of the HO-SAM has a disordered, “glassy” structure as a result of “clustering” of the terminal OH groups. The Ar atom has a much stronger physisorption interaction with the HO-SAM, arising from the strong Ar‚‚‚O van der Waals interaction. Though the simulations show that physisorption is more important for Ar atoms colliding with the HO-SAM, energy transfer is less efficient to this surface. The latter results from a significant difference in the energy transfer for direct collisions with the two surfaces. More energy is deposited in the H-SAM for direct collisions. This difference appears to arise from enhanced efficiency to excite interchain intermolecular modes for the H-SAM as compared to the HOSAM. The OH-group clustering enhances surface rigidity and decreases the efficiency of exciting intermolecular modes in direct collisions of Ar atoms with the HO-SAM. Overall, the energy transfer efficiencies determined from the simulations are in excellent agreement with experiment. The simulations suggest that the so-called trapping desorption (TD) component of the experimental translational energy distribution, for Ar + H-SAM scattering, actually consists of both physisorption and direct trajectories.

I. Introduction The fate of a gas colliding with a surface depends on the energy exchange dynamics of the initial impact and the interfacial reactivity. As a species impinges on a surface, it can recoil directly from the outer layer of atoms in an impulsive scattering event or be deflected enough times along a surface to dissipate excess energy and become trapped at the interface. For highly reactive systems, chemistry can occur during the initial collision; however, many processes proceed only after the gas-phase reactant transfers its excess energy to the surface to thermally accommodate with the material. Hence, thermal accommodation efficiencies mediate many reactive processes of environmental and industrial importance. The primary objective of the studies presented below is to explore the energy exchange dynamics that occur when a gas-phase species collides with organic surfaces. Specifically, we aim to develop an atomiclevel understanding of how the chemical and physical properties of an organic surface determine the extent of gas-surface energy transfer and accommodation. Although energy transfer during gas-surface collisions has been explored in detail for atoms and molecules impinging on a variety of single-crystal or polycrystalline inorganic materials,1 relatively few studies have focused on organic substrates due to the challenge of creating well-defined and highly characterized organic surfaces in a reproducible way. This limitation was * To whom correspondence should be addressed. † Texas Tech University. ‡ Virginia Tech. § Nankai University.

addressed in the pioneering work of Cohen, Naaman, and Sagiv, who were the first to employ self-assembled monolayers (SAMs) of amphilic molecules on solid supports to study the energy transfer dynamics of Ar, He, O2, and NO on organic surfaces.2 The initial scattering studies demonstrated that the extent of energy transfer from the gas to the surface is correlated with the rigidity of the monolayer chains and the gas-to-surface mass ratio. They further suggested that the concerted waving motions of the chains and the hindered rotation of the end groups play the dominant role in controlling the energy exchange dynamics. Following the early experiments, several other groups have explored the dynamics of reactive and nonreactive species scattering from organic self-assembled monolayers. In particular, theoretical studies have provided significant insight into the dynamics controlling the outcome of collisions of rare gases with alkanethiol SAMs on gold. Alkanethiol SAMs on gold serve as excellent model systems of organic surfaces because their structure is well-known and they can be reproducibly created in the laboratory. Classical trajectory chemical dynamics simulations by Hase and co-workers3-9 have shown that lowenergy extended motions of monolayer alkane chains play a major role in dissipating the energy of a gas-surface collision, whereas the high-energy C-H motions play a minor role in the dynamics. Complementary work of Troya et al. has highlighted the importance of the gas-surface potential in determining the extent of energy exchange in rare gas collisions on organic surfaces.10,11 They have also revealed that the extent of gas-surface energy exchange decreases as the packing density of alkane chains increases due to restriction of the lowenergy motions within the monolayer.12 Classical trajectory

10.1021/jp074586o CCC: $40.75 © 2008 American Chemical Society Published on Web 12/22/2007

Gas-Surface Energy Exchange and Accommodation simulations have also been combined with experimental studies to reveal new scattering channels in collisions of high-energy Xe atoms with SAMs. Sibener and co-workers have, in addition to studying Ne and Ar collisions on saturated organic SAMs,4,6,13 shown that significant penetration into a monolayer can occur for energetic Xe atoms.4,6,3,14 Furthermore, Kandel et al. have recently followed the structural changes of an octanethiol monolayer upon Xe atom bombardment to find that high-energy atoms can induce structural changes in the film that originate at defects and phase boundaries.15 The work described above and elsewhere has provided important understanding of how the physical properties of a surface affect the scattering dynamics in saturated organic thin films. Additional information about energy exchange in organic systems is emerging from studies that probe how energy exchange and accommodation efficiencies depend on the chemical nature of a surface. Polar functional groups within organic films can have significant effects on the properties of the material relative to analogous saturated hydrocarbon systems, such as increased stability,16-19 altered frictional properties,20-22 and surface free energy.23-26 Recent experiments demonstrate that polar functional groups also influence the outcome of gassurface collisions. Specifically, molecular beam scattering experiments have been employed to study the fractional energy exchange and relative thermal accommodation efficiencies for a variety of gases scattering from alcohol-, amine-, and carboxylic acid-terminated SAMs.27-31 The experiments suggest that intramonolayer hydrogen-bonding plays a major role in determining the rigidity of the SAM by restricting the types of low-energy motions that govern energy transfer in saturated methyl-terminated monolayers. Similar studies have shown that even buried hydrogen-bonding groups within a monolayer affect the relative rigidity of the film.32 The role of hydrogen-bonding groups within organic films has also been explored by Scoles and co-workers, who performed Debye-Waller measurements using He atom scattering on single-crystal organic surfaces.33 These studies demonstrated that a hydrogen-bonding surface is more rigid than a methyl-terminated surface. In contrast, experiments by Wysocki et al. show that hydrogen bonding in OH-terminated alkanethiol SAMs does not change the internal energy distribution of scattered parent molecules in collisions of >20 eV ions with the organic thin films.34 The latter study suggests that the relatively high collision energy used for ionbeam scattering overwhelms the effects that hydrogen bonding has on increasing the rigidity of the SAM. Although scattering studies employing functionalized organic surfaces have provided initial insight into the importance of intrasurface hydrogen bonding in controlling the fate of the incident projectile, it is nearly impossible to completely separate the influences of intrasurface hydrogen bonding from changes in the gas-surface potential when one experimentally compares scattering from polar and nonpolar surfaces. Therefore, we have developed a series of molecular dynamics simulations designed to lend more detailed insight into how gas-surface energy transfer and thermal accommodation efficiencies depend on the hydrogen-bonding nature of an organic thin film. Specifically, we present a detailed classical dynamics study of the energy exchange dynamics for argon atoms scattering from CH3terminated and OH-terminated SAMs of alkanethiols on gold. The results presented below provide new insight into how intrasurface hydrogen bonding in the polar SAM renders the surface more rigid than the analogous nonpolar surface. The increased rigidity reduces the efficiency of gas-surface energy exchange; however, the rigid nature of the hydrogen-bonded SAM is

J. Phys. Chem. C, Vol. 112, No. 2, 2008 477

Figure 1. Single chain structures of optimized (0 K) HO-SAM and H-SAM surfaces with NC ) 10 and 11 chain lengths.

balanced, to some extent, by a more strongly attractive ArOH potential that promotes energy transfer and thermal accommodation relative to the CH3-SAM. We find that the competition between surface stiffness and gas-surface attractive forces ultimately controls the fate of energy transfer and thermal accommodation in atomic scattering from these model organic surfaces. II. Potential Energy Function and Simulation Model Simulations were performed to study the dynamics of Aratom scattering off OH- and CH3-terminated alkyl thiol selfassembled monolayer surfaces (i.e., HO-SAM and H-SAM). The H-SAM was investigated, in addition to the HO-SAM, to determine how replacing the CH3 terminating group with a HO group affects the energy transfer dynamics. Models consisting of alkyl thiol chains with NC ) 10 and 11 carbon atoms were studied for both the HO-SAM and H-SAM surfaces. Single chains of these SAMs are depicted in Figure 1, showing different orientations of their terminal groups. The total potential energy of each Ar + HO-SAM and H-SAM system is written as the sum of the SAM surface potential and the Ar-surface intermolecular potential

V ) Vsurface + VAr-surface

(1)

The VAr-surface and Vsurface potential terms are described below. A. Ar + HO-SAM and H-SAM Intermolecular Potentials. The Ar-surface interactions are described as the sum of Buckingham potentials between Ar and each of the surface atoms

VAr-surface )

∑ (A exp(-Br) + C/rn)

(2)

For the H-SAM surface, there are Ar‚‚‚C and Ar‚‚‚H gassurface interactions. Their Buckingham potential parameters are taken from a previous study,35 and correspond to the Ar/CH4II fit of ab initio potential energy curves for Ar + CH4, calculated at the MP2/aug-cc-pVTZ level of theory. For the HO-

478 J. Phys. Chem. C, Vol. 112, No. 2, 2008

Tasic´ et al.

TABLE 1: Parameters for Models of H-SAM Bonding Potentials potential parametersa potential type harmonic stretch Au-S S-C C-C C-H harmonic bend S-C-C S-C-H C-C-C C-C-H H-C-H torsion C-C-C-C H-C-C-C and H-C-C-H S-C-C-C C-C-C-H

terms

BMYH

b

Troyac

r0, k r0, k r0, k r0, k

2.55, 2.80 1.82, 5.70 1.53, 4.86 1.08, 4.05

θ0, k θ0, k θ0, k θ0, k θ0, k

114.7, 0.68 109.5, 0.54 112.4, 0.85 109.5, 0.54 109.5, 0.54

114.7, 0.70 (-)

φ 1, V 1 φ2, V2 φ3, V3 φ1, V1 φ2, V2 φ3, V3 φ1, V1 φ2, V2 φ3, V3 φ1, V1 φ2, V2 φ3, V3 V0

0.0, 3.705 180.0, -0.135 0.0, 1.571

0.0, 0.0 (0.0, 1.300) 180.0, 0.0 (180.0, -0.05) 0.0, 2.0 (0.0, 0.2) - (0.0, 0.000) - (180.0, 0.000) - (0.0, 0.300) 0.0, 0.0 (-) 180.0, 0.0 (-) 0.0, 2.0 (-) - (0.0, 0.000) - (180.0, 0.000) - (0.0, 0.300)

1.81, 3.08 (-) 1.53, 3.61 (1.53, 3.72) - (1.09, 4.72)

112.4, 0.88 (112.7,0.81) - (110.7, 0.52) - (107.8, 0.46)

0.0, 3.705 180.0, -0.135 0.0, 1.571

3.39

a

this workd 2.55, 2.80 1.81, 3.15 1.53, 4.31 1.09, 4.72 114.7, 0.70 109.5, 0.70 109.5, 0.56 109.5, 0.70 109.5, 0.49 0.0, 1.300 180.0, -0.050 0.0, 2.600

0.0, 2.248 180.0, -0.310 0.0, 1.033

3.39 2

Stretching and bending force constants have units of mdyn/Å and mdyn-Å/rad . Angles are in degrees, distances in angstroms, and torsion potentials in kcal/mol. b Potential developed by Bosio, Meroueh, Yan and Hase, and described in refs 3, 7, and 37. c The OPLS-UA and OPLS-AA force fields (ref 41-43) used by Troya and co-workers, ref 10. The united-atom (UA) values are given first, followed by the explicit-atom or all-atom (AA) values in parentheses. d The Au-S parameters are from BMYH, the harmonic stretch and bend parameters from AMBER95C (ref 44), and the torsion parameters from OPLS-AA (ref 43).

SAM surface, there are additionally Ar‚‚‚C, Ar‚‚‚H(C), Ar‚‚‚O, and Ar‚‚‚H(O) interactions for atoms that constitute the terminal -CH2OH groups. These Buckingham potential parameters are taken from a fit, identified as fit A, of MP2/ccpVTZ potential energy curves calculated for Ar + CH3OH.36 More specifically, the potentials for C and H atoms inside the HO-SAM are the same as those for the H-SAM, and are based on the Ar + CH4 system, but the potentials for the C and H atoms on the top of the HO-SAM are based on the Ar + CH3OH system. Finally, we also included interactions of Ar with the S and Au atoms, both of which are assumed to be like those with the C atom from the fit to Ar + CH3OH. However, at the incident energies considered in this study, the Ar‚‚‚S and Ar‚‚‚Au interactions are unimportant since Ar does not deeply penetrate any of the surfaces; that is. less than 0.5% of the Ar atoms descend to 3.3 Å, the height of the lowermost C atoms (the S atoms reside at a 1.9 Å height), above the middle of the rigid Au-atom layer comprising the Au substrate (see section II.C below). The Ar + HO-SAM and H-SAM analytic intermolecular potentials accurately represent the ab initio Ar + CH4 and Ar + CH3OH potentials. The Ar + CH4 potential energy minimum has an Ar-C separation of 3.68 Å and a well depth of 0.35 kcal/mol. The Ar + CH3OH potential is more attractive and has a well depth of 0.62 kcal/mol. The Ar atom interacts with both the C and O atoms, and the Ar-C and Ar-O separations are 3.68 and 3.69 Å, respectively. A colliding Ar atom interacts with multiple C atoms of the H-SAM and multiple C and O atoms of the HO-SAM. The nature and number of these interactions fluctuate, since the surface atoms have large displacements for their 300 K thermal motions. The average attractive potentials felt by an Ar atom as it interacts with the H-SAM and HO-SAM surfaces are discussed in section V.C.4.

B. H-SAM and HO-SAM Potentials. The potentials for the NC ) 10 and 11 H-SAM and HO-SAM surfaces are described by an explicit-atom (EA) model for which all atoms are represented. The SAMs are built with the same analytic potential functions and parameters, except for the treatment of their -CH3 and -CH2OH terminal groups. The interior -(CH2)n- moieties are represented in the same way for both SAMs. Different models have been used for H-SAMs in previous simulations of rare gas atoms scattering from these surfaces. Bosio, Meroueh, Yan, and Hase (BMYH)3,7,37 investigated both united-atom (UA) and EA models for the H-SAM, following initial work by Klein and co-workers.38,39 The parameters used for the BMYH EA model are summarized by Tasic´ et al.40 Troya and co-workers10,12 have used a EA/UA hybrid model for the H-SAM, for which the CH3-CH2- termini are EAs and the interior -CH2- groups are UAs. The parameters for their H-SAM model are taken from the OPLS UA41,42 and all-atom (AA)43 force fields. Simulations using these potentials indicate the critical feature in obtaining agreement with experiment is the use of an accurate projectile/surface intermolecular potential, with details of the surface potential much less important.7,10 The EA/UA hybrid model gives excellent agreement with experimental studies of Ar + H-SAM scattering13 if the MP2/aug-cc-pVTZ potential,35 described above for the current simulation, is used for the Ar‚‚‚C and Ar‚‚‚H intermolecular interactions. The BMYH UA and EA models have been used in simulations of Ne + H-SAM scattering and they give energy transfer efficiencies which differ from experimentally measured values by only 10%.7 In the current study, a somewhat different EA model was used for the H-SAM, with parameters for the bonding potentials taken from the OPLS43 and AMBER44 force fields. The bonding parameters for this model and for the BMYH model are

Gas-Surface Energy Exchange and Accommodation


TABLE 2: Parameters Unique for the HO-SAMa potential type harmonic stretch C-O O-H harmonic bend C-C-O C-O-H(O) H(C)-C-O torsion C-C-C-O C-C-O-H Lennard-Jones (12-6) C‚‚‚O H‚‚‚O O‚‚‚O electrostatic O H(O) C H

terms

parameters

ref

r0, k r0, k

1.410, 4.45 0.960, 7.68

44 44

θ0, k θ0, k θ0, k

109.5, 0.70 108.5, 0.76 109.5, 0.70

44 44 44

φ1, V1 φ2, V2 φ3, V3 φ1, V1 φ2, V2 φ3, V3

0.0, 1.711 180.0, -0.500 0.0, 3.399 0.0, -0.356 180.0, -0.174 0.0, 1.392

44 44 44 44 44 44

A, B A, B A, B

718443, -551.727 64329.9, -135.559 578581, -627.244

43 43 43

Z Z Z Z

-0.683 0.418 0.145 0.060

43 43 43 43

a Stretching and bending force constants have units of mdyn/Å and mdyn-Å/rad.2 Angles are in degrees, distances in angstroms, and torsion potentials in kcal/mol. Lennard-Jones A and B parameters are in units of kcal-Å12/mol and kcal-Å6/mol, respectively. The electrostatic charges Z are fractional charges.

compared in Table 1. Both models use the same set of nonbonded parameters, described previously.37,39 As shown below in section IV.A, both the current model and the EA/UA hybrid model of Troya give accurate energy transfer efficiencies for Ar + H-SAM scattering, when the MP2/aug-cc-pVTZ potential is used for the Ar + H-SAM intermolecular potential. The same result is expected if the BMYH model is used for the H-SAM. The HO-SAM potential was constructed, from that used in the current study for the H-SAM, by adding additional terms for the -CH2OH terminal groups. The parameters for these additional terms are listed in Table 2. The harmonic stretch, bend, and torsion, parameters are from the AMBER force field,44 and the Lennard-Jones parameters and electrostatic charges are from the OPLSAA force field.43 Electrostatic interactions are only included for the atoms of the -CH2OH terminal groups of the HO-SAM. C. Simulation Model. The model for the HO-SAM and H-SAM surfaces consisted of periodic boundary conditions (PBC)45 with a primary cell of 64 alkyl thiol chains arranged in an 8 × 8 horizontal configuration. For each surface, the 64 chains are uniformly spaced on a one-atomic-layer thick base of frozen Au atoms, representing the top layer of the Au(111) lattice. Previous simulations have shown that a frozen Au surface provides accurate energy transfer results for the collision of rare gas atoms with a SAM/Au surface.7 The root of each chain is an S-atom that is equidistant to three nearest-neighbor Au atoms at the equilibrium. The chains and hollow sites alternate along each horizontal axis producing a hexagonal arrangement with the equilibrium S‚‚‚S separation, i.e., lattice constant of 4.9883 Å along any direction, for each surface. To describe the long-range 1/r electrostatic interactions for the atoms comprising the -CH2OH terminal groups of the HOSAM, as representative of a macroscopic surface, a twodimensional Ewald summation model46 was implemented in the standard manner.45 A conventional 3-dimensional PBC box, with

an elongated cell vector along the surface normal,47 is used to simulate a two-dimensional PBC for the current study. III. Procedure for the Trajectory Simulations The Ar + H-SAM and HO-SAM trajectory simulations were performed with the general chemical dynamics program VENUS.48 As discussed above, the atoms of the SAM surfaces are treated explicitly, the gold atoms are kept frozen, and a PBC is applied, effectively extending the basic 8 × 8 sample cell by eight identical neighbor copies. Furthermore, the PBC is also applied to the Ar projectile, thus ensuring that Ar is always above or inside the surface. For each simulation, an ensemble of trajectories were calculated for a fixed Ar-atom incident kinetic energy Ei of 9.6 or 19.1 kcal/mol and incident polar angle θi, with respect to the surface normal of 30°. These are the conditions for the Ar + HO-SAM experiments of Morris and co-workers.28 The initial azimuthal angle χi is sampled randomly within in the uniform 0°-360° range. This sampling is appropriate to represent the experiments28 for which the beam of Ar atoms overlaps multiple SAM growth domains with different azimuthal angles. The aiming point for the incident Ar atom is also selected randomly on top of the SAM surface, so that the atoms uniformly impact the top of the 8 × 8 sample cell. Consequently, the Ar atom may hit any of the 64 chains, and it may point to it from any side, in semblance to the experiments. Random initial positions and momenta, corresponding to 300 K, are chosen for the surface atoms. For each trajectory initial condition, coordinates of the surface atoms are first taken from a different snapshot of the surface, determined from a previous 200 ps molecular dynamics (MD) simulation at 300 K.45 For each type of SAM, a total of 100 snapshots are selected every 2 ps within the 200 ps interval. Each snapshot provides a surface configuration for choosing initial conditions for 5 or 7 trajectories at Ei of 9.60 or 19.1 kcal/mol, respectively, and θi ) 30°. To choose the trajectory initial condition, the surface atom velocities are first randomly assigned from their Boltzmann distributions. Then, with the snapshot configuration and these initial velocities, the dynamics of the SAM surface is propagated by a 300 K, 2.3 ps MD simulation and finally equilibrated (“annealed”) for another 2.3 ps before the Ar atom is introduced and the simulation begun. The result of this procedure is a completely unique SAM surface configuration, at thermal equilibrium, at the beginning of each trajectory. This procedure ensured the Ar projectiles sample, without bias, a fully thermally equilibrated SAM surface in a variety of its possible configurations. From the 100 snapshots, a total 500 and 700 trajectories where calculated for the simulations at Ei of 9.60 or 19.1 kcal/ mol, respectively. Examination of the data showed that these ensembles are sufficiently large to yield good statistical analyses of the trajectory results. Each trajectory was calculated for up to 42 ps with a sixth order symplectic integrator,50,51 using a constant time step of 3.5 fs. This time step ensures excellent energy conservation for the trajectory, although good energy conservation is also achieved with time steps up to 5.0 fs. The total energy stepto-step fluctuations are less than (0.006 kcal/mol, and the net drift is about -0.002 kcal/mol per 1 ps or less than 0.1 kcal/ mol over the maximum trajectory duration of 42 ps, i.e., typically much less than 0.1 kcal/mol. The symplectic integrator provides a substantial calculation speed-up compared to the previously used40 sixth order Adams-Moulton integrator.52 Each trajectory is initiated with the Ar atom 20 Å from the aiming point and 17 Å above the topmost C-atom layer of the

480 J. Phys. Chem. C, Vol. 112, No. 2, 2008 SAM. Scattering is deemed complete once the Ar atom reaches a height of 35 Å above the gold substrate, corresponding to heights of at least 20 Å above the topmost layer of C-atoms. The final Ar energy Ef and velocity components, i.e., the outgoing polar θf and azimuthal χf angles, are all measured at this point and recorded. Most of the trajectories are complete well before the trajectory is terminated at 42 ps, and less than 3% remain trapped at this time. Because of their long residence times, these Ar atoms are expected to desorb thermally, and their final energy and outgoing polar and azimuthal angles are assigned randomly from their respective Boltzmann, cosine, and uniform distributions. This assumption has been previously justified,5,40 and therefore, this small set of trajectories is also included in the data analysis. The overall change of the azimuthal scattering angle, ∆χ ) χf - χi, ranges from -180° to +180°. The value of ∆χ ) 0° corresponds to in-plane forward scattering, whereas the value of ∆χ ) (180° corresponds to in-plane backward scattering. In the Ar + HO-SAM experiments,28 only events with in-plane forward scattering and θf ) θi ) 30° are detected. Unfortunately, although forward scattering is generally the most likely event, the number of trajectories corresponding to the experimental ∆χ ) 0 ( 1° is prohibitively small for any statistical analysis. Accordingly, all trajectories with ∆χ ) 0 ( 30° were considered as in-plane and compared with experiment. Analysis of the effect of ∆χ on the scattering dynamics suggests this assumption is a reasonable one. Although some scattering properties depend on ∆χ, these dependencies are never very strong. Therefore, we report separately the results for all trajectories and for the subset of trajectories with ∆χ ) 0 ( 30°.

Tasic´ et al.

Figure 2. Comparison of experimental studies13 and current simulations of Ar + decanethiol SAM (i.e., NC ) 10 H-SAM) energy transfer at Ei of 8.42 and 13.4 kcal/mol and θi ) 45°. 9, simulation, total scattering; (, simulation, in-plane scattering; and b, experiment.

IV. Properties of the H-SAM AND HO-SAM Models A. Energy Transfer Dynamics for Different H-SAM Models. In previous work,10,13 chemical dynamics simulations have been used to model energy transfer for Ar + H-SAM collisions, and Troya and co-workers10 have compared the ability of a variety of potential energy surface models to reproduce experimental results.13 They found that a hybrid EA/UA model for the H-SAM, combined with the Ar/CH4-II potential35 for the Ar + H-SAM intermolecular interaction, gives excellent agreement with experiment (see Figure 3 of ref 10). For their EA/UA hybrid surface model, all of the atoms of the CH3CH2termini are treated explicitly by the OPLSAA force field43 and the interior -CH2- groups are represented as UAs by the OPLSUA force field.41,42 For the Ar + H-SAM simulation reported here the same Ar/ CH4-II potential is used for the Ar + H-SAM intermolecular interactions, but combined AMBER44 and OPLSAA43 force fields are used for the H-SAM potential. The same near quantitative agreement with the experiments by Sibener and coworkers,13 for θi ) 45° and Ei of 8.42 and 13.4 kcal/mol (i.e., 365 and 582 meV), is found for this H-SAM model as for the EA/UA hybrid model of Troya and co-workers.10 This is illustrated in Figure 2 where the average final energy of the scattered Ar atoms, 〈Ef〉, is plotted versus the final in-plane polar angle θf (where θf ) 0° is normal to the surface). To have a statistically significant number of trajectory results, scattering events with |∆χ| ) |χf - χi| < 30° were identified as forward in-plane scattering and included in the trajectory analyses. B. Structure of the HO-SAM. An illustration representative of the NC ) 11 HO-SAM surface, obtained from 300 K MD simulations, is given in Figure 3. The NC ) 10 HO-SAM surface exhibits a very similar structure. The surface is disordered, with hydrogen-bonding between the OH groups leading to small

Figure 3. Representative snapshots of the structure of the NC ) 11 HO-SAM surface at 300 K shown with and without the underlying methylene chains and gold atoms. The HO-SAM with a NC ) 10 has a similar structure (see Figure 4).

clusters or chains consisting of a larger number of OH groups. Some of these chains have parallel arrangements, giving the


J. Phys. Chem. C, Vol. 112, No. 2, 2008 481 TABLE 3: Heights of the SAM Surfacesa surface

terminal group

NC ) 10 HO-SAM NC ) 11 HO-SAM NC ) 10 H-SAM NC ) 11 H-SAM

-CH2OH -CH2OH -CH3 -CH3

h,0K

h , 300 K

12.7 13.4 12.8 13.5

14.0 15.2 13.8 14.9

a The height h in units of angstroms, is the average distance between the terminating C-atom and the rigid Au-atom layer comprising the Au-substrate (see section II.C). Values of h are given for both the 0 K optimized structure, and the 300 K equilibrated structure.

TABLE 4: Average Final Ar Energy for the Total Scatteringa non-Boltzmannb Figure 4. Radial distribution functions of the O-O distances in the HO-SAM surfaces and of the terminal C-C distances in the H-SAM surfaces at 300 K equilibrium.

surface local structures which have a striped appearance. Overall, the HO-SAM surface structure found here is very similar to that reported by Klein and co-workers from previous MD simulations.53,54 The disorder and hydrogen-bonding of the HOSAM surface is also apparent in Figure 4, where radial distribution functions are given of the O-O distances for the HO-SAM and of the terminal C-C distances of the H-SAM at 300 K equilibrium. There is strong long-range order for the H-SAM, but not for the HO-SAM. The only predominant peak in the radial distribution function for the HO-SAM occurs at a smaller O-O separation than for the first peak in the C-C separation for the H-SAM. This short O-O separation is a result of the hydrogen-bonding. It is of interest that, though large water clusters have crystalline interiors, they have amorphous surfaces55,56 similar to that found here for the HO-SAM. If the HO-SAM is followed in time, hydrogen-bonds break and reform, but the overall structure remains similar to that in Figure 3. The surface has characteristics of that for a “glassy” system.53 It is of interest that the 0 K optimized structure for the HO-SAM has the same periodic structure as that of the H-SAM, so that the formation of clusters and chains of the OH groups at 300 K arises from thermal fluctuations. At some temperature, or temperature range, the surface undergoes a phase transition from the periodic 0 K structure to the 300 K disordered, glassy structure. Understanding the dynamics of this transition is an interesting topic to pursue in future research. V. Comparison of the H-SAM and HO-SAM Energy Transfer Dynamics For each scattered Ar atom the final energy Ef, the final polar angle θf, the final azimuthal angle χf, the residence time tres, the number of hops Nhop, and the minimum height hmin were collected and analyzed. Additionally, the height, velocity, and energy of the Ar atom was recorded with other essential information every 0.1 ps of the trajectory. The residence time, tres, is the time the Ar atom spends on or inside the SAM surface, defined by the Ar atom having a height of 5 Å or less above the top of the surface, which is considered to be the average height of the C atoms of the terminal -CH3 and -CH2OH groups of the H-SAM and OH-SAM at 300 K. The htop heights of all surfaces are listed in Table 3, for both the optimized 0 and 300 K structures. The Ar height is measured as the vertical distance from the Au substrate. The depth of penetration of the surface is given by the smallest height, hmin, above the Au substrate realized by the Ar atom during a trajectory. A “hop” pertains to the occurrence of an outer turning point followed

total 〈Ef 〉

surface

NC

HO-SAM HO-SAM H-SAM H-SAM

10 11 10 11

Ei ) 9.60 kcal/mol 1.95 ( 0.07 300.0, 0.50, 1.9 1.97 ( 0.07 1.93 ( 0.07 300.0, 0.81, 1.4 1.95 ( 0.07


10 11 10 11

Ei ) 19.1 kcal/mol 2.86 ( 0.09 300.0, 0.67, 2.4 2.95 ( 0.08 2.35 ( 0.07 300.0, 0.85, 1.5 2.40 ( 0.08

TB, f NB, FWHM

TB, f NB, FWHM 297.4, 0.50, 1.9 484.9, 0.06, 0.4

390.6, 0.43, 2.8 453.6, 0.35, 2.3

a Energies are in kcal/mol and temperature in Kelvin. The error bar is the standard deviation of the mean. b Fit to the simulation P(Ef) by eq 3. The temperature of the Boltzmann component, TB, was both fixed at 300 K and allowed to vary. FWHM is the full-width at half-maximum of the non-Boltzmann (NB) component in the fit and fNB is the fraction of this component.

by an inner turning point in the vertical motion of the Ar atom, so that the number of hops Nhop equals the number of inner turning points. If the Ar atom scatters directly off the SAM, Nhop ) 0. The trajectories were calculated for fixed Ar atom incident kinetic energies Ei of 9.6 and 19.1 kcal/mol and an incident polar angle θi of 30°, with respect to the surface normal. These are the conditions for the Ar + HO-SAM and H-SAM experiments of Morris and co-workers.28 A. Probability of Energy Transfer. Comparison between Simulation and Experiment. In the following section, the efficiency of energy transfer is compared for the H-SAM and HO-SAM surfaces. The experiments for the H-SAM were performed with a NC ) 12 alkylthiol chain,28 whereas chains with NC ) 10 and 11 were used for the simulations. This difference is expected to be insignificant since earlier experiments57 have found a threshold of NC ) 7-8 where the energy transfer becomes independent of further increase in the chain length (aside from a minor odd-even chain-length effect). In addition, the present simulations show no significant or systematic differences between the NC ) 10 and 11 surfaces for either the HO-SAM or H-SAM. 1. AVerage Energy 〈Ef〉 of Scattered Ar atoms. The average energy of the scattered Ar atoms, with no restrictions on the final scattering angles θf and χf, is listed in Table 4 for the different simulations. The 〈Ef〉 values for the H-SAM and HOSAM surfaces are similar at Ei ) 9.60 kcal/mol, but at the higher Ei, the 〈Ef〉 value is ∼ 0.5 kcal/mol larger for the HO-SAM. The 〈Ef〉 values with |∆χ| < 30° to model experimental inplane scattering,49 and with no restriction on the final θf, are listed in Table 5. At the higher incident energy, 〈Ef〉 is ∼0.751.0 kcal/mol larger for the HO-SAM than for the H-SAM. In addition, though the statistics are poor, there is an indication that 〈Ef〉 is slightly larger for the HO-SAM at the lower Ei. Thus,


Tasic´ et al.

TABLE 5: Average Final Ar Energy for Forward In-Plane Scattering. Comparison of Experiment and Simulationa simulation |∆χ| < 30° surface

NC


10 11 10/12e 11


10 11 10/12e 11

total

1.9 ( 0.1 1.5 ( 0.1

3.3 ( 0.1 2.1 ( 0.1

θf ∼ 30°

θf : 0-90°

experiment NBb

direct

totalc

directd

Ei ) 9.60 kcal/mol 2.5 3.1 ( 0.1 2.5 2.4 ( 0.1 2.4 2.3

3.4 2.9 2.7 2.7

2.1 ( 0.3 1.3 ( 0.3 1.4 ( 0.3 1.9 ( 0.3

2.9 ( 0.4 1.7 ( 0.5 1.8 ( 0.4 2.4 ( 0.5

Ei ) 19.1 kcal/mol 3.8 4.4 ( 0.1 4.1 3.3 ( 0.1 3.1 3.1

4.4 5.1 3.3 3.3

3.2 ( 0.5 3.8 ( 0.8 2.2 ( 0.3 2.4 ( 0.3

3.6 ( 0.5 4.5 ( 0.9 2.4 ( 0.4 2.5 ( 0.4

total

a All energies are in kcal/mol. Error bar is the standard deviation of the mean. b In the experiments,28 the NB-component as identified as the impulsive scattering (IS) component. c Average final energy for trajectories with θf ) 30(5° and |∆χ| < 30°. d Trajectories with Nhop ) 0. e NC is 10 for the simulations and 12 for the experiments. Experiments have shown that H-SAM surfaces with NC of 10 and 12 give statistically the same results.55

the trajectory simulations recover the experimental result28 that more energy is transferred to the H-SAM as compared to the HO-SAM. For a direct comparison with experiment, it is necessary to obtain simulation results for in-plane scattering with θf ∼ 30°. To accomplish this, the simulation results for |∆χ| < 30° were further delineated for 25° < θf < 35° to approximate in-plane scattering with θf ) 30°. Listed in Table 5 are values of 〈Ef(30)〉∆χ∼0 for all types of scattering events and those for direct scattering with Nhop ) 0. A comparison is also given with the experimental 〈Ef〉 values for |∆χ| ) 0° and θf ) 30°. The experimental and simulation 〈Ef〉 values for in-plane scattering and θf ) 30° are in overall good agreement. Given the statistical uncertainties in the simulations, the largest difference between experiment and simulation is 0.3 kcal/mol for the HO-SAM at Ei ) 9.60 kcal/mol. In comparing energy transfer for the HO-SAM and H-SAM surfaces, 〈Ef〉 is ∼ 1 kcal/ mol larger for the HO-SAM at the higher Ei, with no statistical differences in 〈Ef〉 for the two surfaces at the lower Ei. The experiments28 find an 〈Ef〉 for the HO-SAM that is ∼0.4 and ∼1.1 kcal/mol larger than that for the H-SAM at the lower and higher Ei, respectively. The simulations do not recover the small difference in the energy transfer efficiencies at the lower Ei. However, overall the simulations agree with the experiments,28 in that they predict less energy transfer to the OH-SAM. Also listed in Table 5 are simulation values of 〈Ef〉 for direct, in-plane scattering with Nhop ) 0. With no restriction on θf, 〈Ef〉 for the HO-SAM is larger than that for the H-SAM at both Ei. However, restricting θf to ∼ 30° results in similar energy transfer efficiencies for the two surfaces at the lower Ei, and more efficient energy transfer to the H-SAM at the higher Ei, i.e., a result akin to that described above for total in-plane scattering. It is of interest that, for both the total and direct inplane trajectories, 〈Ef〉 is substantially larger if no restriction is placed on θf as compared to restricting it to ∼30°. 2. Energy Transfer Distribution P(Ef). The probability distribution, P(Ef), of the final Ar translational energy is plotted in Figure 5 for collisions with the HO-SAM and H-SAM surfaces at Ei of 9.60 and 19.1 kcal/mol. All of the trajectories are included in P(Ef) regardless of their final polar and azimuthal angles. For both surfaces, the NC ) 10 and 11 chain lengths give the same P(Ef) within statistical uncertainties (see the 〈Ef〉 values in Tables 4 and 5), and the data for the two NC are combined to give the composite P(Ef) in Figure 5. At Ei ) 9.60 kcal/mol, the P(Ef) are similar for the two surfaces, consistent with their similar 〈Ef〉 values given in Table 4. As discussed

above, it is at the higher Ei that there are significant differences in the energy transfer for the two surfaces. At this energy, the initial rising part of P(Ef) is nearly the same for the two surfaces. The peak in P(Ef) occurs at a slightly lower Ef for the HOSAM, but it is past this peak that the P(Ef) differ significantly. The H-SAM P(Ef) is initially broader but then decays fast, whereas the HO-SAM P(Ef) is initially narrower but then decays more slowly with a quite distinctive tail. The overall effect is more energy transfer to the H-SAM (see Table 4). The extent of thermalization is often measured by the fraction of P(Ef) that may be represented by a Boltzmann energy distribution. Different values of the Boltzmann component fB for two surfaces are assumed to represent different efficiencies for these surfaces to equilibrate the incident projectile. A value for fB is determined by fitting the low-energy part of P(Ef) with the Boltzmann distribution for thermal desorption, so that P(Ef) is given by

P(Ef) ) PNB + PB )

{

} ( )

m[(2Ef/m)1/2 - V2]2 fNBA Ef exp + 2kBT2 -1

fB(kBTS)-2Ef exp -

Ef (3) kBTB

where PNB is the non-Boltzmann component and fNB and fB are respectively the non-Boltzmann and the Boltzmann components with fNB + fB ) 1. The temperature of the Boltzmann component, TB, is either fixed at the surface temperature or allowed to vary. For the non-Boltzmann component, T2 and V2 are fitting parameters, and A ) ∫∞0 Ef exp{-{m[(2Ef/m)1/2 V2]2}/{2kBT2}} dEf is the normalization constant of the nonBoltzmann component which is integrated numerically during the fitting process. Following previous work,4,5,7,8,40 the P(Ef) were fit, as shown in Figure 5, with TB either fixed at the surface temperature of 300 K or allowed to vary. The parameters for the fits are listed in Table 4. For the lower Ei, the HO-SAM has a larger Boltzmann component than the H-SAM if TB is fixed at 300 K, but a smaller Boltzmann component than the H-SAM if TB is allowed to vary. With a variable TB, the HO-SAM has a smaller TB and a larger NB component, as compared to the H-SAM. These effects become more pronounced at the higher Ei. If TB is constrained to the 300 K surface temperature for this Ei, then both surfaces have a small Boltzmann component,



Figure 5. Probability density distribution P(Ef), for final Ar translational energy with Ei ) 9.60 kcal/mol (top) and 19.1 kcal/mol (bottom). The P(Ef) distributions for the NC ) 10 and 11 surfaces are statistically the same, and are combined to give the plotted distributions. P(Ef) distributions for the HO-SAM (left) and H-SAM (right) are compared. The P(Ef) includes all trajectories. In each case, the distribution is deconvoluted, eq 3, into Boltzmann (PB) and non-Boltzmann (PNB) components, using two methods: (a) the surface temperature of 300 K to yield PB(300) and PNB(300), and (b) the variable T temperature to yield PB(T) and PNB(T).

i.e., 0.33 for the H-SAM and 0.15 for the HO-SAM. However, if TB is allowed to vary, the result is a near Boltzmann distribution for the H-SAM with fB ) 0.65 and TB ) 453.6 K. However, for the HO-SAM, fB ) 0.57 and TB equals 390.6 K. Thus, with TB allowed to vary, the HO-SAM has a smaller Boltzmann component at a lower temperature. This is consistent with the experiments28 which also find a smaller thermal component for the HO-SAM (fB ) 0.43) than for the H-SAM (fB ) 0.61). Properties of the NB component of the P(Ef) distributions are summarized in Table 4. For Ei ) 19.1 kcal/mol, the FWHM for the HO-SAM’s NB component is 2.4 kcal/mol and larger than the 1.5 kcal/mol for the H-SAM. Though this result is for the full P(Ef), which includes all the trajectories, it agrees with the experiments for restricted in-plane scattering and θf ) 30°. The experimental FWHM of the NB component is 4.4 and 3.2 kcal/mol for the HO-SAM and H-SAM, respectively. As discussed in the next section and shown in Table 6, the HO-SAM has a larger fraction of physisorption trajectories than does the H-SAM. However, this does not result in more thermal desorption for the HO-SAM. Apparently, some of the direct Nhop ) 0 trajectories for the H-SAM have efficient energy transfer and contribute to its Boltzmann component. This type of dynamics has been observed previously for Ne + H-SAM scattering,9 where nearly all the trajectories are direct but there is an appreciable Boltzmann component in P(Ef). As described above, with a variable TB, P(Ef) for the H-SAM is nearly Boltzmann-like, which is not the case for the HO-SAM. Thus,

TABLE 6: Fractions of Different Trajectory Typesa top

penetrate

surface

NC

direct direct top physisorb inside physisorb Pincomplete Pin-plane


10 11 10 11

0.44 0.49 0.64 0.58

Ei ) 9.60 kcal/mol 0.50 0.03 0.03 0.46 0.01 0.04 0.30 0.03 0.02 0.36 0.05 0.02

0.05 0.06 0.02 0.02

0.26 0.24 0.24 0.24


10 11 10 11

0.54 0.56 0.63 0.67

Ei ) 19.1 kcal/mol 0.34 0.06 0.06 0.32 0.06 0.06 0.19 0.11 0.08 0.18 0.09 0.06

0.04 0.03 0.01 0.01

0.28 0.29 0.24 0.25

a “Direct” trajectories have Nhop ) 0, whereas “physisorb” trajectories are those with Nhop > 0. For “top” trajectories, hmin g htop, whereas for “penetrate” trajectories, hmin < htop. For “incomplete” trajectories, Ar does not desorb within 42 ps. The “in-plane” trajectories scatter forward with |∆χ| < 30° and have no restriction on θf. The fractions of “top” and “penetrate” trajectories add up to one.

for Ar atom collisions at Ei ) 19.1 kcal/mol, the H-SAM is better for thermalization, whereas the OH-SAM surface is both harder and stickier. C. Atomistic Details of the Energy Transfer Dynamics. The simulation results presented above show that, in accord with experiment,28 the H-SAM is a more efficient absorber of the Ar-atom collision energy than the HO-SAM. Here, the origin of this difference is probed by investigating the atomic-level dynamics of the Ar + surface collisions.


Tasic´ et al.

TABLE 7: Average Final Energies 〈Ef〉 of Ar for Different Trajectory Typesa top surface

a

NC

total

direct

penetrate physisorb


10 11 10 11

1.95 ( 0.07 1.97 ( 0.07 1.93 ( 0.07 1.95 ( 0.07

Ei ) 9.60 kcal/mol 2.63 1.41 2.51 1.44 2.20 1.32 2.14 1.59


10 11 10 11

2.86 ( 0.09 2.95 ( 0.08 2.35 ( 0.07 2.40 ( 0.08

Ei ) 19.1 kcal/mol 3.83 1.79 3.82 1.83 2.59 1.84 2.60 1.62

direct

physisorb

in-plane

1.61 2.31 2.11 2.30

1.31 1.26 2.05 1.70

2.48 ( 0.17 2.52 ( 0.16 2.42 ( 0.17 2.34 ( 0.17

1.77 2.18 2.21 2.83

1.31 1.54 1.91 1.88

3.82 ( 0.21 4.12 ( 0.19 3.07 ( 0.18 3.09 ( 0.20

Energies are in kcal/mol, and error bars are standard deviations of the means. The trajectory types are defined in Table 6.

1. Trajectory Types and Their Energy Transfer. As done previously,40 four different trajectory types were identified in the simulations, and their fractions are listed in Table 6. The trajectories either scatter off the top or penetrate the surface. These events may occur directly with only one inner turning point in the Ar surface perpendicular motion (i.e., Nhop ) 0) or by physisorption with multiple inner turning points with Nhop g 0. For both Ei’s of 9.60 and 19.1 kcal/mol, the dominant event is scattering off the top of the surface. For collisions with the HO-SAM at Ei ) 9.60 kcal/mol, the direct and physisorption events on the top have nearly equal probabilities. However, for the H-SAM, the direct events dominate. The probability of scattering directly off the top increases for the higher Ei. The fraction of penetrating trajectories is small and increases from ∼0.05 at Ei ) 9.60 kcal/mol to as large as ∼0.2 at Ei ) 19.1 kcal/mol. In summary, the dominant characteristic of the dynamics is Ar-atom scattering off the top of the surface, with physisorption on the top being more important for the HO-SAM than for the H-SAM. Also listed in Table 6 are probabilities for forward in-plane scattering, with |∆χ| < 30°, and for Ar atoms remaining physisorbed when the trajectory is terminated at 42 ps, i.e., Pin-plane and Pincomplete. A trajectory with | ∆χ| < 30° is significantly more likely than a trajectory scattering sideways into the same solid angle. Pin-plane varies from ∼0.25-0.30, with an apparent small increase in its value for the HO-SAM when Ei is elevated to 19.1 kcal/mol. The number of incomplete trajectories is small, ranging from 1 to 6% of all of the trajectories. It is interesting to note they are more common at the lower collision energy and also more common for the HOSAM than the H-SAM. These trends are reflective of trends in the residence times, discussed below. The average energy of the scattered Ar atoms, 〈Ef〉, is given in Table 7 for the different trajectory types. For the top-direct events, there is a substantial difference between the two surfaces’ energy transfer. The H-SAM surface absorbs more energy, and this effect becomes more pronounced at the higher Ei. For trajectories that scatter off the top with physisorption, there are no clear differences between the two surfaces, whereas for the penetration-physisorption trajectories, the average final energies follow a trend opposite to that for the top-direct trajectories; that is, more energy is transferred to the HO-SAM. For complete accommodation with the surface, 〈Ef〉 ) 2RT ) 1.2 kcal/mol. The final energies approach this value for the top-physisorption scattering events for both surfaces at Ei ) 9.60 kcal/mol, and for the penetration-physisorption trajectories on the HO-SAM surface at both the low and high Ei. The 〈Ef〉 values for the penetrating trajectories are larger for the H-SAM as compared to the HO-SAM. Large nonthermal 〈Ef〉 values for the H-SAM have been previously explained9,14 by a repulsive energy release

TABLE 8: Average Number of Ar Atom Hops 〈Nhop〉a surface

total

top

penetrate


10 11 10 11

Ei ) 9.60 kcal/mol 3.3 ( 0.2 3.3 3.2 3.3 ( 0.2 3.2 5.4 1.0 ( 0.1 1.0 1.1 1.1 ( 0.1 1.1 1.4


10 11 10 11

Ei ) 19.1 kcal/mol 2.7 ( 0.3 2.4 5.5 2.2 ( 0.2 2.1 2.9 1.2 ( 0.2 0.7 3.6 0.8 ( 0.1 0.7 1.5

physisorb

Pdirect

6.2 ( 0.4 6.6 ( 0.4 3.2 ( 0.2 2.9 ( 0.3

0.47 0.50 0.67 0.63

6.8 ( 0.5 5.8 ( 0.3 4.5 ( 0.8 3.4 ( 0.3

0.60 0.62 0.74 0.76

a “Top” and “penetrate” refer to trajectories with hmin greater and smaller than htop, respectively. “Physisorb” trajectories have Nhop > 0. Pdirect is the fraction of trajectories with Nhop ) 0.

as the rare gas atom is ejected from the surface and the H-SAM relaxes to its equilibrium geometry. This process may be less important for the HO-SAM as a result of its surface hydrogenbonding and enhanced rigidity, which would explain the smaller 〈Ef〉 values for the HO-SAM’s penetrating trajectories. Table 8 compares the average number of hops, 〈Nhop〉, for the different surfaces at both collision energies. Values of 〈Nhop〉 are given for the total trajectories, those that scatter off the top, those that penetrate, and those that physisorb (i.e., Nhop > 0) either on the surface’s top or in its interior. Also listed is Pdirect, the fraction of trajectories with 〈Nhop〉 ) 0. These trajectories consist of both the “top” and “penetrating” types. The two pronounced results in Table 8 are the smaller values of Pdirect and larger total 〈Nhop〉 for the HO-SAM surfaces. For each trajectory type identified in Table 8, 〈Nhop〉 is larger for the HOSAM surface. 〈Nhop〉, for the total ensemble of trajectories, decreases with increase in Ei for the HO-SAM but not for the H-SAM. The importance of different trajectory types for the two surfaces, and correlations in their energy transfer dynamics, may be studied by scatter plots. Figure 6 gives scatter plots of Ef and the trajectory duration time, which closely corresponds to the residence time, versus the minimum height attained by the Ar atom. The calculations are for the NC ) 10 surfaces and at Ei ) 19.1 kcal/mol. The Ar atom penetrates the surface for trajectories with hmin less than htop. The value of htop is 13.8 and 14.0 Å for the H-SAM and HO-SAM, respectively. For the H-SAM, the trajectories are concentrated at lower Ef and shorter residence times and also more spread out along the hmin axis. For both SAMs, there are three groups of trajectories: (i) those that do not penetrate and quickly desorb with a wide range of Ef, some preserving much of the initial energy Ei; (ii) those that reside for a wide range of times in the vicinity of the surface top and transfer most of Ei; and (iii) a small group of trajectories



Figure 6. Scatter plots of the final Ar energy Ef (kcal/mol), and of the trajectory duration ttraj (ps) versus the minimum height hmin (Å) attained by the trajectory. Calculations for the HO-SAM and H-SAM surfaces with NC ) 10 and Ei ) 19.1 kcal/mol.

Figure 7. (Top) Probability distributions of the final polar angle θf and of the absolute change in the azimuthal angle |∆χ|. (Bottom) The average final kinetic energy 〈Ef〉 of the Ar atoms as a function of the θf and |∆χ| angles. The results are for Ei ) 19.1 kcal/mol. Energy is in kcal/mol and scattering angles in degrees.

that penetrate the SAM, and spend a period of time on/in the SAM before desorbing with a moderate amount of energy in E f. 2. Role of the Scattering Angles θf and ∆χ. A number of the scattering properties show significant and systematic dependencies on the final polar angle, θf, and the absolute change

in azimuthal angle, |∆χ|, at the higher Ei of 19.1 kcal/mol. These effects are illustrated in Figures 7-9. The probability of a collision with a particular θf or |∆χ| and values of 〈Ef〉 versus θf and |∆χ| are plotted in Figure 7. It is seen that in-plane scattering with |∆χ| ) 0 is the most probable, and that scattering perpendicular or parallel to the


Tasic´ et al.

Figure 8. Average of minimum height hmin (Å) of the Ar atom realized in a trajectory versus θf and |∆χ| angles in degrees. Results are for Ei ) 19.1 kcal/mol.

Figure 9. The average number of Ar-atom hops 〈Nhop〉 versus the final polar angle θf in degrees. Results are for Ei ) 19.1 kcal/mol.

surface (θf of 0° or 90°) is quite improbable. For thermal desorption, and scattering collected at all azimuthal angles, P(θf) equals sin θ cos θ and is peaked at 45°.9 The scattering for both the HO-SAM and H-SAM only approximately resemble this distribution. For the HO-SAM, P(θf) appears bimodal with a specular scattering peak at θf ∼ 30° and a second peak at 45°-60°. For the H-SAM, there is a single peak in P(θf) near 30°. For thermal desorption P(∆χ) is uniform. For both surfaces the higher probability of forward scattering, with ∆χ = 0, reflects some memory of the incident collision, which is more pronounced for the HO-SAM. Figure 7 illustrates that 〈Ef〉 increases for larger θf or smaller |∆χ|, with the largest 〈Ef〉 for scattering in-plane and parallel to the surface. 〈Ef〉 is the smallest for perpendicular scattering, θf ) 0°, or backward scattering with |∆χ| ) 180°. Representative error bars are included for only one surface and signify the standard deviation of the mean. The chain length does not appear to play any role in either P(θf), P(∆χ), or values of 〈Ef〉 versus θf and |∆χ|. This is significant because, if the terminal group alignment (as defined by whether the chain length is even or odd) is important, then the probability distribution for the outgoing Ar atom would depend on the chain length. Figure 8 displays the minimum Ar height, hmin, versus θf and |∆χ| and Figure 9 the average number of Ar-atom hops for all the trajectory types, 〈Nhop〉, versus θf. For each surface, there is a general trend for hmin to increase with increase in θf or decrease in |∆χ|. The value of hmin is largest, with the least amount of penetration, for in-plane scattering and θf ) 90°. One feature

of the hmin versus θf and |∆χ| plots is that, for the same C-atom chain length, there is less penetration of the HO-SAM; see the discussion below. There is an interesting “dip” in the hmin versus |∆χ| plot, for both the NC ) 10 HO-SAM and H-SAM surfaces at |∆χ| ∼ 120°, which may warrant future study. Note the hmin values are necessarily larger for the thicker NC ) 11 SAMs. Figure 9 shows the 〈Nhop〉 for the H-SAM surfaces is small, less than 2, and independent of θf. 〈Nhop〉 is larger for the HOSAM than H-SAM surfaces, except for θf near 90°. For small θf values 〈Nhop〉 is substantially larger for the HO-SAM surfaces, particularly for the NC ) 10 surface. For the 9.60 kcal/mol lower collision energy, the dynamics are similar to those illustrated in Figures 7-9. However, overall the trends are less pronounced. At this lower energy, the plots of 〈Ef〉 versus θf and |∆χ| are indistinguishable for the different SAMs. As at the higher Ei, the probability P of θf is peaked at a smaller θf for the H-SAMs. However, the P versus | ∆χ| plots are indistinguishable for the two SAMs. The following trends in the hmin versus θf plots are also observed at the lower Ei: (1) deeper penetration is correlated with a smaller θf; (2) the H-SAM is penetrated more deeply than the HO-SAM, with shallower penetration at the smaller Ei, particularly for the H-SAM; and (3) the dependence of hmin on θf is more pronounced for evenlength chains (i.e., NC even) as compared to odd-length chains. As found from the hmin versus |∆χ| plots at the higher Ei, deeper penetration is associated with a larger |∆χ|. The relationship between 〈Nhop〉 and θf is preserved at the lower Ei for both surfaces, but with increased “hopping”. However, compared to the higher Ei, where hopping is more important for the even chain-length HO-SAM, hopping for this surface is unaffected by the chain-length at the lower Ei. 3. Surface Penetration. Penetration may be investigated by comparing hmin and htop, where the former is the minimum height the Ar atom attains in the course of a trajectory and the latter the average height of the outermost C-atom layer. Physisorption can be better understood by studying 〈Nhop〉, the average number of hops the Ar atom executes during its residence on/in the surface. Table 9 lists the average minimum height, 〈hmin〉, for the four trajectory types and for collisions with the different surfaces. For each Ei and for all of the surfaces, 〈hmin〉 for all of the trajectories is about 1-2 Å larger than the htop values given in Table 3. The extent of penetration of the different surfaces may be studied by comparing the 〈hmin〉 - htop values for the penetrating trajectories. Using this criterion, one sees that on average the H-SAM surfaces are penetrated deeper than the HO-



Figure 10. Probability of observing the Ar atom at a particular height, h (Å), above the plane of the gold-surface at any time during the trajectory. Calculations are for Ar collisions at Ei ) 19.1 kcal/mol. with the NC ) 10 HO-SAM and H-SAM surfaces.

TABLE 9: Average Minimum Height of the Ar Atom for Different Trajectory Typesa top surface

NC

Total

direct physisorb direct physisorb


10 11 10 11

Ei ) 9.60 kcal/mol 15.67 ( 0.04 15.96 15.70 16.82 ( 0.04 17.02 16.87 15.23 ( 0.05 15.36 15.40 16.29 ( 0.05 16.33 16.67


10 11 10 11

Ei ) 19.1 kcal/mol 15.34 ( 0.06 15.82 15.60 16.53 ( 0.04 16.90 16.77 14.51 ( 0.06 15.05 15.24 15.78 ( 0.07 16.26 16.15

a

penetrate

13.68 13.64 13.38 14.25

12.80 14.30 10.96 12.96

12.90 14.47 12.65 13.99

11.77 13.85 10.94 12.19

Average minimum height 〈hmin〉 is in angstroms.

SAM surfaces by 0.2-0.6 Å, with deeper and more probable penetration of both surfaces at the higher collision energy. The minimum height reached by an Ar atom does not provide a complete picture of its penetration dynamics. Figure 10 provides additional information about penetration and gives the probability that Ar has a particular height for the NC ) 10 HOSAM and H-SAM surfaces at Ei ) 19.1 kcal/mol. The height of the surface top, htop, defined by the terminal C atoms, is nearly the same for the two surfaces, and it is seen that the probability of finding Ar decreases as one moves deeper into the SAM and becomes near zero until close to the SAMs bottom. There is a relatively small but significant and “unexpected” presence of Ar atoms very deep in the SAM, near the SAM bottom at h ) 3.1 Å. For comparison, the heights of the S and bottom-most C atoms are 1.9 and 3.3 Å. This feature indicates there is a “pocket”, near the bottom of the SAM, in which the Ar atom may reside. To further examine penetration, the fraction of trajectories in which Ar has penetrated the surface, versus time, was studied. Figure 11 gives plots versus time of the probability, Ppenetrate, of finding the Ar atom anywhere below htop. The plots are for the NC ) 10 surfaces and Ei ) 19.1 kcal/mol. From the Ppenetrate(t) plot, one sees that, if penetration occurs, it does so initially. Once Ar penetrates, it takes a range of times for it to resurface. The decay of Ppenetrate(t) is non-exponential suggesting there are at least two mechanisms/time-scales for release of Ar, which may be related to the depth of penetration, energy transfer effects, etc. Although penetration lasts very long for a few trajectories, i.e., the rare event when Ar gets trapped in the

Figure 11. Plot of the penetration probability Ppenetrate(t) versus time t in ps. Penetration probability is a probability of finding the Ar atom below the top of the surface htop, defined as the average height of the terminal C atoms. Results are for the Ar scattering with the NC ) 10 HO-SAM and H-SAM surfaces at Ei ) 19.1 kcal/mol.

pocket near the surface bottom, for the vast majority of Ar atoms penetration lasts less than 8 ps. At 8 ps, there are essentially no Ar atoms underneath the SAM’s top, but there is still a significant fraction that have not desorbed. It is plausible that some of Ar atoms remain trapped on the top after resurfacing, but it is not clear whether Ar atoms typically tend to be ejected completely out of the surface as they resurface, or to stay on the top. The 〈Ef〉 values for penetrating collisions suggest both mechanisms are operative. The major difference between the two surfaces is that penetration is more extensive for the H-SAM and, thus, more permeable to Ar. For Ei ) 19.1 kcal/mol and the NC ) 10 surfaces, the average residence time of Ar on/in the HO-SAM is 4.3 ( 0.3 ps but only 2.7 ( 0.2 ps for the H-SAM. For the penetrating trajectories, the average penetration times are similar, i.e., 2.3 ( 0.8 and 2.5 ( 0.6 ps for the HO-SAM and H-SAM, respectively. The error bars signify standard deviations of the mean. Thus, although penetration is less common for the HOSAM, the actual duration of penetration is the same for both surfaces. This is not surprising given that the two surfaces are only different in their terminal groups, and their interiors are the same. In future work it will be important to investigate more accurately the role of the “pocket”, near the bottom of the SAM, in trapping Ar and other rare gas atoms. For the current study, approximate Ar‚‚‚S and Ar‚‚‚Au interatomic potentials were used by assuming they are the same as for Ar‚‚‚C (see section II.A). In reality, S and Au are larger than C, with relative C, S, and Au atomic radii of 0.79, 1.04, and 1.34 Å,58 respectively, and the Ar‚‚‚S and Ar‚‚‚Au repulsive potentials are longer range than for Ar‚‚‚C. This may make it more difficult for Ar to become trapped near the Au-surface than as found for the current model simulations. 4. Physisorption. Differences in the physisorption dynamics of the H-SAM and HO-SAM surfaces are identified by the probability that the Ar atom resides on top of the surface. Figure 10 shows that the Ar atom spends most of its time above the surface top, peaking at about 3.8 Å and 3.5 ( 0.5 Å above htop for the HO-SAM and H-SAM, respectively. The two surfaces differ in their population distributions at the peak above htop, which is substantially higher and narrower for the HO-SAM. This suggests that the HO-SAM has a more spatially welldefined interfacial region. For the HO-SAM, the Ar atom is tightly held at a particular, well-defined height above the SAM, whereas for the H-SAM, the Ar atom is more loosely bonded and explores a broader height region. This is consistent with


Tasic´ et al.

Figure 12. The average potential energy V(h) of interaction between the Ar atom and surface versus the height h (Å) of the Ar atom. The potential energy is the time-average for all of the trajectories. The calculations are for the NC ) 10 HO-SAM and H-SAM surfaces at Ei ) 19.1 kcal/mol.

Figure 13. Plot of the desorption probability Pdesorb(t) versus time t in ps. Desorption probability is a probability of finding the Ar atom more than 5 Å above the top of the surface, htop. Results are for Ar scattering with the NC ) 10 HO-SAM and H-SAM surfaces at Ei ) 19.1 kcal/ mol.

the stronger interfacial intermolecular potential for the HO-SAM as compared to that for the H-SAM. In addition, the probability of finding an Ar atom below htop is 0.06 for the HO-SAM but 0.14 for the H-SAM, reflecting the Ar-atom’s smaller preference for penetrating the HO-SAM. This is consistent with a more rigid HO-SAM surface. A consequence of the Ar atom’s ability to more easily penetrate the H-SAM is a larger peak in its P(h) distribution, near the surface bottom, than for the HO-SAM. A more detailed explanation for the Ar atom’s preference to remain on top of the HO-SAM as compared to the H-SAM is given in Figure 12. Plotted in this figure is the average interaction potential between the Ar atom and all of the surface atoms as a function of h, for the NC ) 10 HO-SAM and H-SAM surfaces. The potential energy is plotted only in the region above the surface, where there is sufficient information to obtain good statistics. It is seen that the Ar atom has a much stronger attractive interaction with the HO-SAM. Comparison of Figures 10 and 12 shows that for the Ar + HO-SAM system the peak in P(h) at 17.8 Å is near the outer minimum in 〈V(h)〉 at 17.2 Å. A somewhat larger h is expected for the P(h) distribution because of entropic effects. It is also of interest to compare average potentials experienced by Ar in contact with the NC ) 10 HO-SAM and H-SAM surfaces, for collisions at Ei ) 19.1 kcal/mol. The average most attractive potential encountered in the course of a trajectory is 〈Vmin〉 ) -1.9 kcal/mol and -1.6 ( 0.8 kcal/mol for the HOSAM and H-SAM, respectively. The average most repulsive potential encountered is 〈Vmax〉 ) 2.7 kcal/mol and 2.4 kcal/ mol for the two respective surfaces. The average potential value felt by an Ar atom is 〈V〉 ) -0.27 kcal/mol for the HO-SAM and -0.17 kcal/mol for the H-SAM. The standard deviation of the mean for these average energies is quite small and not listed. These values pertain to calculations with Ei ) 19.1 kcal/mol and the NC ) 10 surfaces. However, the same relationships between the average energies are found for the NC ) 11 surfaces and the lower Ei. Thus, in collisions with HO-SAM, the Ar atom accesses more attractive and repulsive regions of the potential surface and is typically more strongly bound to the surface than for the H-SAM. It would be of interest to investigate the extent of lateral motions of Ar atoms physisorbed on the top of the SAM surfaces, to see if they are relatively mobile or are locally trapped. However, this information was not obtained and would be an important topic to address in future studies. The fraction of trajectories in which Ar has desorbed, versus time, was determined to further examine physisorption. Figure 13 gives plots versus time of the probability Pdesorb of finding

Ar at a height larger than 5.0 Å + htop. The plots are for the NC ) 10 HO-SAM and H-SAM surfaces and Ei ) 19.1 kcal/mol. In Pdesorb(t), the Ar atoms reach h ) 5.0 Å within 1.0-1.3 ps, where substantial gas-surface interactions begin. Most trajectories, i.e., ∼70% for the HO-SAM and ∼80% for the H-SAM, scatter immediately. The remaining Ar atoms are physisorbed for a wide range of times, but gradually they desorb. Some have very long residence times. Comparison of the two SAMs shows that (i) the Ar atoms that depart immediately do so faster for the HO-SAM, which is consistent with transferring less energy, (ii) significantly more trajectories remain physisorbed for the HO-SAM, and (iii) the rate of Ar desorption is slower for the HO-SAM. The last two features are consistent with more attractive ArsHO-SAM interactions. The Pdesorb probabilities in Figure 13 were analyzed for exponential kinetics and found to be biexponential. For the 4-18 ps time interval, kdesorb is 0.15 and 0.085 ps-1 for the H-SAM and HO-SAM, respectively, whereas for the 18-40 ps time interval, kdesorb is the same for the two surfaces and 0.06 ps-1. Analyses of the trajectories show that that the longer time desorption from the H-SAM is dominated by trajectories which penetrated the surface. For the HO-SAM, the longer time desorption arises from trajectories that first penetrated the surface and then physisorbed on the top of the surface when they emerged from the interior. For both surfaces, the longer time kinetics is strongly influenced by diffusion out of the SAM, which may explain their similar kdesorb of 0.06 ps-1. The shorter time desorption kinetics is dominated by physisorption on the top of the surface, and the ratio of the rate constants 0.15 and 0.085 ps-1 gives a physisorption well depth 0.34 kcal/mol deeper for the HO-SAM, if it is assumed the Arrhenius A-factor for desorption is the same for both surfaces. This 0.34 kcal/mol difference in well depths is consistent with the potential energy plots in Figure 12. VI. Summary Chemical dynamics simulations were performed to study the dynamics of energy transfer in 9.60 and 19.1 kcal/mol collisions of Ar atoms with CH3- and OH-terminated alkanethiol SAM surfaces, i.e., H-SAM and HO-SAM. Molecular dynamics simulations were performed to study differences in the structures of the HO-SAM and H-SAM surfaces. The global potential minimum for both surfaces has a periodic structure. At 300 K, the H-SAM retains features of this structure and has long-range order. In contrast, the HO-SAM is disordered, with thermal

Gas-Surface Energy Exchange and Accommodation fluctuations resulting in hydrogen bonding and the formation of small clusters of OH groups or chains consisting of a larger number of OH groups. The hydrogen bonding leads to enhanced rigidity of the HO-SAM, with a structure characteristic of a “glassy” system. The simulation results are in overall good agreement with previous experiments at the same collision energies,27-31 showing the H-SAM is a more efficient absorber of the collision energy. For the 9.60 kcal/mol collision energy, the simulations give average final translational energies of the scattered Ar atoms, 〈Ef〉, that are statistically the same for the two surfaces and do not identify the 0.4 kcal/mol higher 〈Ef〉 found experimentally for the HO-SAM surface. However, for the higher collision energy of 19.1 kcal/mol, the experimental 〈Ef〉 is 1.2 kcal/mol larger for the HO-SAM, and this difference is observed in the simulations. Also, the P(Ef) distributions found from the simulations are in qualitative agreement with those found experimentally. An understanding of the different energy transfer efficiencies for the H-SAM and HO-SAM surfaces is obtained by studying and characterizing the trajectories. Four different trajectory types were identified, and the most important are events that scatter off the top of the surface, without surface penetration. They may occur by a direct collision, with only one inner turning point in the Ar atom’s motion with respect to the surface plane, or by physisorption in which the Ar atom “hops” on the top of the surface. Penetration of the surface is relatively unimportant and constitutes ∼10% of the trajectories or less, except for Ar + H-SAM scattering at 19.1 kcal/mol, for which penetration comprises 15-20% of the trajectories. Physisorption on the top of the surface is more important for the HO-SAM surface, because of the strong Ar‚‚‚O attractive potential; that is, for the 19.1 kcal/mol collisions, physisorption comprises 33% of the HO-SAM trajectories but only 18% of those for the H-SAM. Since the physisorption trajectories have a much smaller 〈Ef〉 value than do the direct trajectories and the 〈Ef〉 values are nearly the same for physisorption on the HOSAM and H-SAM, considering physisorption alone indicates 〈Ef〉 should be smaller for the HO-SAM. What leads to less efficient energy transfer for the HO-SAM is the HO-SAM’s much larger 〈Ef〉 for the direct trajectories. This less efficient energy transfer to the HO-SAM for direct-top trajectories is attributed to the enhanced rigidity33 of the HO-SAM, arising from hydrogen-bonding. This diminishes the ability to excite interchain intermolecular modes as compared to the H-SAM.6 The competing influences of surface rigidity (caused by terminal group hydrogen-bonding interactions) and gas-surface attraction (the result of the relatively deep Ar-OH potential energy well) are the primary factors responsible for the experimentally observed trends in rare gas scattering from the H-SAM and HOSAM. Finally, the trajectory simulations indicate that one cannot attribute the TD component in the experimental P(Ef) distribution to only trajectories which trap (i.e., physisorb) on the surface. The simulations show more trajectories physisorb on/ in the HO-SAM than the H-SAM, whereas the experimental TD component is larger for the H-SAM. Furthermore, we find that direct-top trajectories for the H-SAM with efficient energy transfer appear to contribute to the TD component for this surface. Acknowledgment. The research at Texas Tech University was supported by the AFOSR/MURI Grant F49620-01-1-0335, administered through the University of Chicago with Steve

J. Phys. Chem. C, Vol. 112, No. 2, 2008 489 Sibener as the Principal Investigator, and the Robert A. Welch Foundation by Grant No. D-0005. The research at Virginia Tech was supported by a National Science Foundation Grant CHE0549647. Yuxing Peng assisted in the data analysis and figure preparation. References and Notes (1) Harris, J. Dynamics of Gas-Surface Interactions; Royal Society of Chemistry: Cambridge, U.K., 1991. (2) Cohen, S. R.; Naaman, R.; Sagiv, J. Phys. ReV. Lett. 1987, 58, 1208. (3) Bosio, S. B. M.; Hase, W. L. J. Chem. Phys. 1997, 107, 9677. (4) Isa, N.; Gibson, K. D.; Yan, T.; Hase, W.; Sibener, S. J. J. Chem. Phys. 2004, 120, 2417. (5) Yan, T. Y.; Hase, W. L.; Tully, J. C. J. Chem. Phys. 2004, 120, 1031. (6) Yan, T. Y.; Isa, N.; Gibson, K. D.; Sibener, S. J.; Hase, W. L. J. Phys. Chem. A 2003, 107, 10600. (7) Yan, T. Y.; Hase, W. L. J. Phys. Chem. B 2002, 106, 8029. (8) Yan, T. Y.; Hase, W. L.; Barker, J. R. Chem. Phys. Lett. 2000, 329, 84. (9) Yan, T. Y.; Hase, W. L. Phys. Chem. Chem. Phys. 2000, 2, 901. (10) Day, B. S.; Morris, J. R.; Troya, D. J. Chem. Phys. 2005, 122, 214712. (11) Alexander, W. A.; Troya, D. J. Phys. Chem. A 2006. (12) Day, B. S.; Morris, J. R.; Alexander, W. A.; Troya, D. J. Phys. Chem. 2006, 110, 1319. (13) Gibson, K. D.; Isa, N.; Sibener, S. J. J. Chem. Phys. 2003, 119, 13083. (14) Gibson, K. D.; Isa, N.; Sibener, S. J. J. Phys. Chem. A 2006, 110, 1469. (15) Fogarty, D. P.; Kandel, S. A. J. Chem. Phys. 2006, 124, 111101. (16) Nuzzo, R. G.; Zegarski, B. R.; Dubois, L. H. J. Am. Chem. Soc. 1987, 109, 733. (17) Dubois, L. H.; Nuzzo, R. G. Ann. ReV. Phys. Chem. 1992, 43, 437. (18) Brewer, N. J.; Foster, T. T.; Leggett, G. J.; Alexander, M. R.; McAlpine, E. J. Phys. Chem. B 2004, 108, 4723. (19) Cooper, E.; Leggett, G. J. Langmuir 1999, 15, 1024. (20) Ruths, M.; Granick, S. J. Phys. Chem. B 1998, 102, 6056. (21) Ruths, M.; Granick, S. J. Phys. Chem. B 1999, 103, 8711. (22) Mugele, F.; Salmeron, M. J. Chem. Phys. 2001, 114, 1831. (23) Houssiau, L.; Graupe, M.; Colorado, R.; Kim, H. I.; Lee, T. R.; Perry, S. S.; Rabalais, J. W. J. Chem. Phys. 1998, 109, 9134. (24) Weinstein, R. D.; Moriarty, J.; Cushnie, E.; Colorado, R.; Lee, T. R.; Patel, M.; Alesi, W. R.; Jennings, G. K. J. Phys. Chem. B 2003, 107, 11626. (25) Alloway, D. M.; Hofmann, M.; Smith, D. L.; Gruhn, N. E.; Graham, A. L.; Colorado, R.; Wysocki, V. H.; Lee, T. R.; Lee, P. A.; Armstrong, N. R. J. Phys. Chem. B 2003, 107, 11690. (26) Colorado, R.; Lee, T. R. Langmuir 2003, 19, 3288. (27) Shuler, S. F.; Davis, G. M.; Morris, J. R. J. Chem. Phys. 2002, 116, 9147. (28) Day, B. S.; Davis, G. M.; Morris, J. R. Anal. Chim. Acta 2003, 496, 249. (29) Day, B. S.; Shuler, S. F.; Ducre, A.; Morris, J. R. J. Chem. Phys. 2003, 119, 8084. (30) Lohr, J. R.; Day, B. S.; Morris, J. R. J. Phys. Chem. B 2005, 109, 15469. (31) Lohr, J. R.; Day, B. S.; Morris, J. R. J. Phys. Chem. A 2006, 110, 1645. (32) Ferguson, M. K.; Lohr, J. R.; Day, B. S.; Morris, J. R. Phys. ReV. Lett. 2004, 92, 073201. (33) Bracco, G.; Acker, J.; Ward, M. D.; Scoles, G. Langmuir 2002, 18, 5551. (34) Smith, D. L.; Selvan, R.; Wysocki, V. H. Langmuir 2003, 19, 7302. (35) Sun, L.; de Sainte Claire, P.; Meroueh, O.; Hase, W. L. J. Chem. Phys. 2001, 114, 535. (36) Tasic´, U. S.; Alexeev, Y.; Vayner, G.; Crawford, D.; Windus, T. L.; Hase, W. L. Phys. Chem. Chem. Phys. 2006, 8, 4678. (37) Meroueh, O.; Hase, W. L. Phys. Chem. Chem. Phys. 2001, 3, 2306. (38) Hautman, J.; Klein, M. L. J. Chem. Phys. 1989, 91, 4994. (39) Mar, W.; Klein, M. L. Langmuir 1994, 10, 188. (40) Tasic´, U. S.; Yan, T. Y.; Hase, W. L. J. Phys. Chem. B 2006, 110, 11863. (41) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc. 1984, 106, 6638. (42) Jorgensen, W. L.; Tirado-Rives, J. J. Am. Chem. Soc. 1988, 110, 1657. (43) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225.

490 J. Phys. Chem. C, Vol. 112, No. 2, 2008 (44) Cornell, W. D.; Cieplak, P.; Bayley, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. J. Am. Chem. Soc. 1995, 117, 5179. (45) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford: New York, 1987. (46) Ewald, H. Ann. Phys. 1921, 64, 253. (47) Alejandre, J.; Tildesley, D. J.; Chapela, G. A. J. Chem. Phys. 1995, 102, 4574. (48) Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornicki, A.; Lim, K. F.; Lu, D.-H.; Peslherbe, G. H.; Swamy, K. N.; Vande Linde, S. R.; Zhu, L.; Varandas, A.; Wang, H.; and Wolf, R. J. Quantum Chem. Program Exch. (QCPE) Bull. 1996, 16, 671. (49) Reference to Morris Ar + HO-SAM scattering experiments. (50) Schlier, Chapter.; Seiter, A. J. Phys. Chem. A 1998, 102, 9399.

Tasic´ et al. (51) Schlier, Chapter.; Seiter, A. Comp. Phys. Commun. 2000, 130, 176. (52) Bunker, D. L. Meth. Comp. Phys. 1971, 10, 287. (53) Hautman, J.; Bareman, J. P.; Mar, W.; Klein, M. L. J. Chem. Soc. Faraday Trans. 1991, 87, 2031. (54) Sprik, M.; Delamarche, E.; Michel, B.; Ro¨thlisberger, U.; Klein, M.; Wolf, H.; Ringsdorf, H. Langmuir 1994, 10, 4116. (55) Steinbach, C.; Anderson, P.; Buck, U.; Buch, V.; Beu, T. A. J. Phys. Chem. A 2004, 108, 6165. (56) Buch, V.; Bauerecker, S.; Devlin, J. P.; Buck, U.; Kazimirski, J. K. Int. ReV. Phys. Chem. 2004, 23, 375. (57) Day, B. S.; Morris, J. R. J. Phys. Chem. B 2003, 107, 7120. (58) Berry, R. S.; Rice, S. A.; Ross, J. Physical Chemistry; Wiley: New York, 1980.

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