On the Mechanism of Surfactant Adsorption on Solid Surfaces: Free

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On the Mechanism of Surfactant Adsorption on Solid Surfaces: Free-Energy Investigations Zhijun Xu, Xiaoning Yang,* and Zhen Yang State Key Laboratory of Material-Orientated Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing UniVersity of Technology, Nanjing 210009, China ReceiVed: June 22, 2008; ReVised Manuscript ReceiVed: August 25, 2008

The adsorption free-energy of surfactant on solid surfaces has been calculated by molecular dynamics (MD) simulation for a model surfactant/solvent system. The umbrella-sampling with the weight histogram analysis method (WHAM) was applied. The entropic and enthalpic contributions to the full potential of mean force (PMF) were obtained to evaluate the detailed thermodynamics of surfactant adsorption in solid/liquid interfaces. Although we observed that this surfactant adsorption process is driven mainly by a favorable enthalpy change, a highly unfavorable entropic contribution still existed. By decomposing the free energy (including its entropic and enthalpic components) into the solvent-induced contribution and the surfactant-wall term, the effect of surface and solvent on the adsorption free-energy has been distinguished. The contribution to the PMF from the surface effect is thermodynamically favorable, whereas the solvent term displays an obviously unfavorable component with a monotonic increase as the surfactant approaches to the surface. The impact of various interactions from the surfaces (both solvent-philic and solvent-phobic) and the solvent on the adsorption PMF of surfactant has been compared and discussed. Compared to the solvent-philic surface, the solventphobic surface generates more stable site for the surfactant adsorption. However, the full PMF profile for the solvent-phobic system shows a clear positive maximum value at the bulk-interface transition region, which leads to a considerable long-range free-energy barrier to the surfactant adsorption. These results have been analyzed in terms of the local interfacial structures. In summary, this comprehensive study is expected to reveal the microscopic interaction mechanisms determining the surfactant adsorption on solid surfaces. I. Introduction Surfactant adsorption on solid surfaces is of great interest in diverse applied fields.1-5 The adsorption process of surfactant in solid-liquid interfaces controls the surfactant self-assembly structures on surfaces and determines the performance of prepared materials.1,3 The adsorption process is mainly determined by complicated interactive effects of solvent and surface.6,7 Molecular-level knowledge of the interaction mechanism is of large benefit to the understanding of adsorption process. Presently, the rapid time scale associated with the adsorption process of a surfactant in solid/liquid interfaces has prevented accurate experimental investigation of the adsorption mechanism,8 even though the development of optical techniques, such as optical reflectometry and ellipsometry, has made it possible to study the kinetics of adsorption and desorption processes.9,10 Computer simulation can provide a microscopic level picture of surfactant adsorption. The microscopic morphology of selfassembled surfactants on solid surfaces has been extensively simulated,11-17 whereas it is relatively lacking in assessing the kinetic information on surfactant adsorption. One fundamental measure of the interaction responsible for surfactant adsorption process containing the kinetic information is the potential of mean force (PMF), i.e., the free energy as a function of the separation between the center of mass of surfactant and solid surface. At present, the PMF simulation has been accepted as an effective tool in studying the microscopic mechanism of various adsorption processes. Striolo et al.18 have reported the PMF profile for the homopolymer near the solid surface by the method of conformation-average. They obtained the segment* To whom correspondence should be addressed. E-mail: Yangxia@ njut.edu.cn.

density profile derived from the PMF data and observed a polymer-segment depletion layer near the surface when there is no attraction between the wall and the polymer. Recently, Sun et al.19 explored the interaction behavior between various peptides and a functionalized hydrophobic surface by investigation of the PMF. The free-energy for the metal ion adsorbed on the calcite surface has been calculated by Kerisit et al.20,21 They found that the free energy profile is correlated with the solvent density. Girardet et al.22 studied the transfer of small molecules through a thin liquid water film supported on ionic surfaces (MgO and NaCl) based on the free energy profile. They observed that the solvent layer on the solid surfaces induces an obvious free-energy barrier for the small molecule adsorption. To our best knowledge, no systematic PMF simulation study has been reported for the surfactant adsorption on solid surfaces. Surfactant molecules possess the unique head/tail structure with different affinities to surface. Meanwhile, the solvent layer structure forming on surface has an obvious influence on the surfactant adsorption process.7,13 The PMF profile for surfactant adsorption can be applied to identify the complex interaction mechanism, including diverse surface and solvent effects, in the adsorption process of surfactant/solvent systems, and to provide the information on the kinetics of adsorption/desorption process, such as adsorption/desorption rate constant,23,24 as the position and height of the free-energy barrier are the main ingredients needed to apply the transition-state theory.24,25 Also, the PMF is very helpful in determining the most favorite position, orientation and configuration of absorbed surfactants near solid surfaces based on the shape of the free energy profile. In this work, a comprehensive molecular simulation has been carried out to study the adsorption free-energy of single surfactant on solid surface with the umbrella sampling26 and

10.1021/jp8055009 CCC: $40.75  2008 American Chemical Society Published on Web 10/10/2008

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the weight histogram analysis methods,27 which have been successfully used to study the macromolecule transfer in complex interfacial regions.19,28,29 The adsorption process of a single surfactant can provide the first step toward understanding the adsorption and self-assembly of surfactants on solid surfaces. The details of enthalpy and enthalpic contributions to the PMF of surfactant adsorption, which represent the thermodynamic driving force of adsorption, will be thoughtfully investigated. This study will identify the various effects of solvent and surface on the adsorption process. Because the PMF based on all-atom simulation is not easily separated into various contributions,30 it is acceptable to use a simplified coarse-grained model, which eliminates the details but preserves the main features of the system of interest. The coarse-grained model permits one to systematically study the influence of various interactions on the adsorption PMF. In this study, the solvent is chosen to be CO2-like Lennard-Jones model and the relatively simple coarse-grained model for the surfactant molecule is adopted. A series of MD simulations with different strengths of the surface-surfactant and solvent-surfactant interactions are designed. It is expected that the adsorption PMF will help to shed some light on the general adsorption mechanism of the surfactant molecule. This study will serve as the initial step in exploring the microscopic adsorption behavior and mechanism for the complicated surfactant/Supercritical CO2 (Sc-CO2) systems. The rest of the paper is organized as follows. The simulation models and methods are provided in section II. The results and discussions are presented in section III, and finally, we conclude with a brief conclusion in section IV. II. Model and Methodology Models. In the coarse-grained model, a single-point model,31 widely used to represent the CO2 molecule in the simulation of supercritical CO2 solution, was adapted as the solvent for the reason of computational economy.32,33 The model surfactant used here7 was described by a chain of spherical beads (h4t4) connected via the harmonic potential, in which four CO2-philic units, identified as the “tail” (t), show stronger affinity to the solvent than other four CO2-phobic units, identified as the “head” (h). The bending potential with the 180° equilibrium bond angle was used to prevent the surfactant chain from producing any sharp bend and to increase an effective length of the surfactant.7 A cut and shifted Lennard-Jones potential was used for the intermolecular and intramolecular (a pair of atoms three hops away in the surfactant chain) nonbonding interactions as follows: cut Uij(rij) ) φijLJ(rij) - φijLJ(rijcut) rij e rij Uij(rij) ) 0 rij > rijcut

(1)

where φijLJ(r) ) 4εij((σij/r)12 - (σij/r)6). εij and σij are the well depth and the size parameters of the Lennard-Jones potential, respectively. The parameters for the surfactant-CO2 interaction should be selected to mimic the pressure dependence of surfactants solubility in Sc-CO2 solvent. In the previous study,7 this surfactant model has been proved to be reasonable and effective in representing the surfactant/Sc-CO2 system. Bilayer aggregate structure has been found to form on the solvent-philic surfaces, similar to the behaviors observed from other simulations.11,15 Finally, the solid surface was the ordered silica surface, which was generated by fracturing the β-cristobalite structure on the [001] crystallographic faces.34 At first, a reference simulation system was chosen, in which the interaction parameters between the fluid molecules and the silica surfaces

Figure 1. Snapshot of a typical initial configuration in a biased MD simulation. White and pink spheres represent the tail and head particles of the surfactant, respectively. The green sphere is the solvent.

was adopted directly from the CO2-philic system in the previous report.7 The detailed potential parameters of the reference system are given in Table 1 of the Supporting Information. To explore the effect of various types of interactions on the adsorption free-energy of surfactant, a series of designed MD simulations, with different potential parameters, were performed. The interaction parameters between the surfactant (tail and head groups) and surface (or solvent (C)) were adjusted in a systematical way according to the parameters in the reference system. For example, if the interaction parameters between the head and tail groups of the surfactant (S) and the surface (W) are increased by 1.2 times as many as the corresponding parameters in the reference system, this designed system is denoted as “Us-w ) 1.2” in the following illustrations and it represents an enhanced interaction between the surfactant and surface as compared with the reference system. The complete parameter information in this study is summarized in Table 2 of the Supporting Information. Simulation Details. For each system, the free energy profile for surfactant to adsorb from the bulk solution onto the surface was calculated on the basis of the biased umbrella-sampling simulations. Each simulation cell consists of a solvent phase (density 0.8 g/cm3) with dimensions of 35 (x) Å × 35 (y) Å × 60 (z) Å over the ordered silica surface and a single surfactant molecule, as shown in Figure 1. The initial system configuration was taken from an equilibrated simulation of the solvent/surface system so as to accelerate the equilibrium achievement of the biased simulations. All MD simulations were performed under constant temperature (310 or 330 K) and constant volume (NVT) using the Nose-Hoover thermostat with a relaxation time of 0.5 ps. The two different temperatures were used to separate the free energy into entropic and enthalpic contributions (see eqs 8-11). The periodic boundary condition was applied to all directions. The trajectories were generated using the velocityVerlet algorithm with a time step of 2.0 fs. Finally, the snapshots from the MD simulations were saved every 4 fs in the production run. In a typical MD run, 4 ns simulation was

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required with 400 ps equilibration time. There is a total of 120-240 ns simulation for each PMF run. In a biased MD simulation, the surfactant molecule was restrained to move in a narrow region (a sampling window) along the direction perpendicular to the surface but was allowed a free motion in other directions. To obtain a sufficient sampling in each window region, a quadratic biased potential was applied:26

V(h) ) 1/2Kumb(h - h0)2

(2)

where h is the distance between the center of mass of the surfactant and the surface and h0 denotes the designed distance of the sampling window from the surface. To construct the potential of mean force between the surfactant and surface as a function of the separation h, a series of biased simulations were performed with various h0 values spanning the entire range of interest on the surface. Typically, the 30 starting structures corresponding to the 30 windows were created to cover the interfacial range from 3.5 to 18 Å (21.5 Å in some cases) with a gap distance 0.5 Å. In this research, the whole interfacial simulation coordinate for surfactant adsorption was chosen to be wide enough, ranging from the bulk solution phase to the solid surface. The umbrella potential with Kumb ) 4 kcal/(mol Å2) was initially applied to all the windows, providing a significant overlapping between windows. In some cases (especially near the surface), Kumb )16 kcal/(mol Å2) with the separated distance 0.25 Å between windows was used to examine the validity of the calculated results. Usually, during the same simulation time, the PMF generated by the umbrellasampling simulations for a large number of narrow windows is more advantageous to the precision than that with a smaller number of wider windows.35 Processing of Simulation Results. Calculation of the PMF. The data from all windows of the biased MD simulation were postprocessed using the weighted histogram analysis method27,36,37 to obtain the unbiased probability Pumb(h), which was then used to evaluate the PMF (W(h)) using the equation38

W(h) ) -1/β ln Pumb(h) + W0

(3)

where β ) 1/kBT. W0 is an undetermined constant, because only the relative free energies can be obtained in this approach. The WHAM selected here was designed to combine the distributions of the variables of interest calculated from all overlapping umbrella-sampling simulation windows so as to minimize the errors in the resulting distribution (Pumb). Usually, the WHAM considerably simplifies the task of recombining the various windows, and moreover, no cumulative error propagation in matching adjacent windows is generated for a large number of windows.37,39 For each biased simulation i, the distribution of the counts (Ni(h)) of finding the single surfactant in a particular bin was determined. An estimate of the (unnormalized) unbiased probability histogram Pumb(h) was given by37 R

∑ Ni(h) i)1

Pumb(h) )

R

n

∑ exp(Fi - βVi(h))

(4)

i)1

where R is the window number and n is the number of the obtained configurations for a biased simulation. The quantity Fi is considered as the dimensionless free energy corresponding to the window i, and it can be determined by the following equation:37

exp(-Fi) )

∑ Pumb(h) exp(-βVi(h))

(5)

h

Because the unbiased probability Pumb(h) itself depends on the value of Fi, the set of eqs 4 and 5 was iteratively solved until the dimensionless free energy attains the self-consistency within a tolerance of 10-4. The bin dimension was chosen to be 0.1 Å for all systems on the basis of the convergence. Finally, we assumed that the resulting PMF is zero at the bulk phase. The region a certain distance (16.0-21.5 Å) beyond the surface, where the surfactant can be considered to be in the bulk phase, was used as a baseline to superimpose all the PMFs calculated by the WHAM. A pilot study using the reference system was first conducted to evaluate the dependence of the PMF, using the umbrellasampling/WHAM method, on the simulation time for each window (corresponding to the configuration number collected from each window). As illustrated in Figure S1 of the Supporting Information, the satisfactory convergence can be achieved for the long simulation time (4 ns) in terms of the positions and values of the free-energy barrier. In the whole free-energy calculations, the 4 ns simulation time was used for each window. Decomposition of the PMF. The full free energy W(h) for surfactant adsorption is composed of the contribution from the direct surfactant-wall interaction, Ws-w(h), and the solventinduced contribution, Wsol(h),

W(h) ) Ws-w(h) + Wsol(h)

(6)

In the previous reports on the contacting free-energy simulation between two isotropic solute molecules,40,41 the interaction energy between solutes was considered as the enthalpic portion of free-energy. However, in this work, the interaction energy between the surfactant and the surface cannot be treated as the surfactant-wall contribution, Ws-w(h). Additionally, the Ws-w(h) cannot be determined on the basis of the umbrella-sampling/ WHAM procedure, as described above, by simply removing the solvent in the simulation system.42 This is because this simple treatment may produce a quite unreasonable result for the long-chain anisotropic surfactant molecule due to the orientation effect in the dense solvent system. The wall contribution to the full PMF, Ws-w(h), was obtained by integrating the average force fz(h), which is perpendicular to the surface and arises from the surface-surfactant interaction,

Ws-w(h) )

∫hh 〈fz(h)〉 dh 0

(7)

where the average of the restraining force fz(h) acting on the whole surfactant molecule situating at a distance h ( ∆h (∆h ) 0.05 Å) can be easily calculated from the MD trajectory. Finally, the solvent-induced contribution, Wsol(h), was determined as the difference between the full PMF (W(h)) and the contribution (Ws-w(h)) from the surfactant-wall interaction, as given in eq 6. Here we present a test on the validity of the force averaging (FA) method in evaluating the Ws-w(h) contribution. Figure S2 in the Supporting Information displays two PMF profiles obtained with the methods of the WHAM and the FA method, respectively, for the particularly designed system, which is the same as the reference system but without the surfactantsolvent interaction. Because there is no interaction between the surfactant and the solvent, the full adsorption PMF is only from the surface influence. As seen in Figure S2, the full PMF using the weighted histogram method is in good agreement with that from the FA method. This indicates that the FA method can produce a reasonable result for the contribution to the PMF from the surfactant-wall interaction.

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The entropic (-T∆S(h)) and enthalpic (∆H(h)) components of the free energy can be obtained through the dependence of free energy on temperature:28,43

dW T ≈ (W(h,T+∆T) - W(h,T)) dT ∆T ∆H(h) ) ∆W(h) + T∆S(h)

-T∆S(h) ) T

(8) (9)

where values of T and ∆T are chosen to be 310 and 20 K,43 respectively. As the free energy portion, the Ws-w(h), and Wsol(h), can also be spitted into the enthalpic and entropic contributions according to the eq 8, respectively.

∆Hs-w(h) ) ∆Ws-w(h) + T∆Ss-w(h)

(10)

∆Hsol(h) ) ∆Wsol(h) + T∆Ssol(h)

(11)

Orientation Distribution of the Surfactant. Because the surfactant structure is quite anisotropic, its orientation in the process of approaching the surface is affected by the surface and solvent interactions. Here the surfactant orientation at a fixed position, based on the center of mass of surfactant, is represented by the order parameter S(h), defined as44 Nh

S(h) )

∑

1 (3〈cos 2 θ 〉 -1) 2Nh i)1

(12)

where θ is the angle between the surfactant (the vector from the last tail to the first head) and the normal to the surface. Nh is the total number of surfactant configurations obtained from all biased simulations at the distance h from the surface. If the surfactant molecule is parallel to the surface, then the order parameter S ) -0.5. A value of 1.0 indicates that the surfactant is preferably perpendicular to the surface. III. Results and Discussion A. PMF on the Solvent-philic Surface. A representative PMF of surfactant adsorption as a function of distance from the surface is shown in Figure 2a for the reference system. The free energy profile shows an oscillating performance and it approaches to zero beyond 15 Å from the surface. The PMF is associated with the solvent density distribution with the freeenergy barrier coinciding with the valley of solvent density. As shown in Figure 2a, the PMF curve has three distinctive minima located around at 3.8, 6.8, and 11 Å, respectively, relative to the surface, corresponding to the three interfacial solvent layers. The first two deep minima near the surface are usually referred to as the contact minimum (CM) between the surfactant and surface as well as the solvent layer-separated minimum (SLSM). However, there appears a noticeable free-energy barrier of adsorption at about 5.2 Å from the surface between the CM and SLSM positions. The third minimum (TM) in the PMF curve is positioned at the bulk-interface transition region, where the surfactant molecule weakly interacts with the surface. For the solvent-philic surface, the free-energy of surfactant in the interfacial region is obviously lower than the bulk phase, suggesting that the surfactant has stronger tendency to approach the surface. It is observed from Figure 2a that there are two free-energy barriers, 0.1 and 0.5 kcal/mol, for a single surfactant to transfer from the bulk phase to the surface, and also two free-energy barriers, 1.1 and 1.3 kcal/mol, for the surfactant to go back. Each free-energy barrier represents a separated adsorption/desorption process step. For example, Figure 2a suggests that the adsorption of the surfactant is a two-step process involving the first passage from the TM position to the SLSM adsorption state and the second course from the SLSM to the CM states.

Figure 2. (a) PMF and solvent density (F, in g/cm3) profiles as a function of the surfactant distance from the surface for the reference system with the solvent-philic surface. (b) Contribution to the surfactant adsorption PMF from the surfactant-wall interaction (Ws-w(h)) and the solvent-induced contribution (Wsol(h)). (c) Enthalpic contribution (∆H(h)) and the entropic contribution (-T∆S(h)) to the full PMF.

The solvent and wall contributions to the PMF for the reference system are depicted in Figure 2b, in which the surface effect is the dominative factor. The PMF portion from the wall-surfactant interaction provides a strong attractive contribution to the PMF. However, the solvent contribution Wsol(h) displays a nearly monotonic increase as the separation decreases, quite different from that between two solute molecules in aqueous solution.42 This repulsive/unfavorable nature of Wsol(h) includes the direct effect of the solvent-surfactant interaction and the indirect effects of the solvent-surface and solventsolvent interactions (solvent structure rearrangement), which is closely associated with the interfacial solvent layer distribution.45 Figure 2c shows the entropic contribution -∆TSfull(h) and the enthalpic contribution ∆Hfull(h) to the full PMF. Attention is first paid to the “mirror symmetry” characteristic28,43 between the unfavorable entropic and favorable enthalpic terms. From a thermodynamics point of view, the surfactant transfer from bulk phase to the surface is mainly driven by the enthalpy effect. However, the minimum and barrier points in the PMF are caused jointly by the different shapes of the entropic and enthalpic profiles. We also note that the calculated enthalpy and entropy are relatively large (-10 and 8 kcal/mol, respectively), almost canceling each other, in comparison with to the adsorption freeenergy (-2 kcal/mol). The large entropic change is similar to the observation on the transportation of hexane in the lipid bilayer.28

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Figure 3. (a) Entropic portion, -T∆Sfull(h) to the full PMF and the solvent (-∆TSsol(h)) and wall (-T∆Ss-w(h)) contributions to the entropic portion for the reference system. (b). Enthalpic portion ∆Hfull(h) to the full PMF and the corresponding solvent (∆Hsol(h)) and wall (∆Hs-w(h)) contributions. The inset in (b) is the solvent coordination numbers (CN) as a function of surfactant position.

In the PMF profile, the entropic (-T∆Sfull(h)) and enthalpic (∆Hfull(h)) contributions can be further split into the two components of solvent and wall effects: -T∆Ssol(h), -T∆Ssw(h), and ∆Hsol(h), ∆Hs-w(h), respectively. Figure 3a displays the solvent (-T∆Ssol(h)) and wall (-T∆Ss-w(h)) contributions to the entropic portion of the full PMF. The wall contribution, -T∆Ss-w(h), contributes a repulsive component of the entropic PMF, which is due to a reduction in the translational freedom of the surfactant and the number of available surfactant conformations during the surface adsorption process.18 This can be illustrated from the dynamical snapshots of the interfacial surfactants, as shown in Figure 4, where the snapshots of surfactants for four typical positions, marked in Figure 2a, are presented. Because of the surface interaction, the spatial orientation of the surfactant shows greater ordering as it approaches to the surface. For example, at the position of 3.5 Å from the surface (point 4 in Figure 4), the surfactant molecule almost lies flat on the surface with no obvious variation in the orientation pattern. This indicates that the surfactant very near the surface has lower conformational entropy, which offers a negative contribution to the PMF. However, for the solvent-induced portion, -T∆Ssol(h), a positive contribution near the surface (less than 6.5 Å) is observed. This is owing to a breaking of the complete solvation shell structure around the surfactant with approaching the surface, which leads an increase in the solvation entropy of the surfactant.46 The change in the solvation shell structure can be shown in the inset of the Figure 3b, where the coordination number (CN) of the solvent molecules around the surfactant decreases with the surfactant approaching to the surface. The CN was obtained by integrating the distribution functions of the solvent relative to the center of mass of surfactant. Figure 3b shows the solvent (∆Hsol(h)) and wall (∆Hs-w(h)) contributions to the enthalpic portion of the full PMF. The

Xu et al. component from the surface effect (∆Hs-w(h)) shows a relatively larger preferable contribution to this enthalpic portion, whereas the solvent component (∆Hsol(h)) gives an adverse effect. As the surfactant approaches to the surface, the surfactant-wall interaction gradually becomes much stronger, resulting in the attractive contribution to the PMF. Nevertheless, the reduced contact extent between the surfactant and solvent in the interfacial region can result in an unfavorable component, ∆Hsol(h), as seen in Figure 3b. It is interesting to note that the small attractive contribution in the region of 6.5-11 Å for the ∆Hsol(h) curve is consistent with the convex shape in the CN profile (see the inset of Figure 3b). In summary, for the surfactant adsorption on the solventphilic surface (reference system), the contribution to the PMF from the surface effect is thermodynamics favorable, whereas the solvent plays an unfavorable role. The surfactant-wall interaction is the major controlling factor to both the entropic portion and the enthalpic portion in the total adsorption PMF for the surfactant on the solvent-philic surface. To further investigate the effect of surfactant-wall interaction on the adsorption PMF near the solvent-philic surface, three additional cases with different interactions between the surfactant and the surface (Us-w ) 0.6, 0.8, and 1.2 in Table S2, Supporting Information) were simulated. The PMF profile for each case is shown in Figure 5, along with that in the reference system. With an increase in the interaction strength, the well-defined CM becomes deeper, except for the smallest interaction case (Us-w ) 0.6), in which the CM disappears and a shoulder is formed, showing a large impeditive barrier for the surfactant adsorption. Furthermore, with the interaction strength increasing, the SLSM gradually becomes unclear, and finally, for the largest interaction case (Us-w ) 1.2), the adsorption free-energy barrier also vanishes. The positions and heights of the TMs in the PMF plots seem to be relatively insensitive to a change in the surfactant-surface interaction, owing to a negligible influence from the surface in this position. The solvent and surface contributions to the PMFs, Wsol(h) and Ws-w(h), are depicted in Figure 6, for the four surfacesurfactant interaction cases investigated. The overall behavior is that, as the interaction decreases, the dominating part in the PMF is changed from the surface contribution (Ws-w(h)) to the solvent-induced contribution (Wsol(h)). In Figure 6a, the negative repulsive contribution Wsol(h) is weakly dependent on the surface interaction. Figure 6b shows that the favorable contributions to the PMF given by Ws-w(h) display an evident enhancing trend with the surfactant-wall interaction increasing. This is due to the enhancing enthalpic contribution (∆Hs-w(h)) to the Ws-w(h) from the surface interaction. The CM positions in the profiles for all the four systems are lightly shifted toward the surface with the interaction increasing, possibly due to the influence of surface structure. From Figure 6a, it is observed that there is a crossover point (around 6 Å from the surface) in the Wsol(h) curves. With the surfactant-wall interaction increasing, Wsol(h) decreases in the interface region below 6 Å from the surface, whereas Wsol(h) increases in the region of 6-12 Å. This crossover behavior is most likely due to the different solvent layer influences in the two interfacial regions. To understand this crossover phenomenon, the orientation order parameter distributions of the surfactant for the four interaction cases are shown in Figure 7. In the interfacial region of 6-12 Å, the surfactant tends to be perpendicular to the surface with an increase in the surface interaction. This orientation behavior can be clearly seen in the configuration snapshots of the surfactant located at the distance

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Figure 4. Orientation snapshots of surfactants at the four positions marked in Figure 2a. Each configuration of the surfactant is taken from the equilibrated 4 ns simulations with separated by 200 ps. Blue and red spheres represent the tail and head particles of the surfactant, respectively. All configurations are overlaid at the mass center of surfactant by translating them in the plane parallel to the solid surface without rotation.

Figure 5. PMF profiles as a function of the distance from the solventphilic surface for four designed surfactant-wall interactions: Us-w ) 0.6, 0.8, 1.0 and 1.2. For comparison, solvent density profile (in g/cm3) is also presented.

of 8 Å, as shown in Figure 8, where the surfactant shows more obvious trend toward the perpendicular orientation with an increase in Us-w. Especially, for the case of Us-w ) 1.2, the surfactant is observed to stand straight with the tail group toward the surface. This vertical orientation of the surfactant may result in a decline of the complete solvation shell of the surfactant, thereby increasing the repulsive enthalpic contribution ∆Hsol(h) to the Wsol(h). Conversely, in the interfacial region below 6 Å, the enhancing surface interaction will enlarge the parallel inclination to surfactant orientation (as shown in the inset of Figure 7), thereby enlarging the interaction between the surfactant and the solvent. Thus, it gives a less unfavorable solvent contribution to the PMF. B. Adsorption PMF on Solvent-phobic Surface. We have also investigated the surfactant adsorption PMF on the solventphobic surface, which is geometrically the same as the above solvent-philic surface, but with a purely repulsive interaction between the solvent and the surface. In the typical solventphobic system (i.e., Us-w ) 1.0, see the second row of Table 2 in the Supporting Information), the other interaction parameters were the same as the reference system. The obtained PMF for surfactant adsorption is shown in Figure 9a, together with the solvent density distribution. In the interfacial region, weak

Figure 6. (a) Solvent-induced contributions (Wsol(h)) to the full PMFs for the four systems. The inside picture shows details of the regions (marked with the ellipse) in an enlarged scale. (b) Contributions to the full PMFs from the surfactant-wall interactions (Ws-w(h)). Arrows indicate the direction of surfactant-wall interaction increasing. The color scheme is the same as that in Figure 5.

solvent layer is formed with only two smaller peaks locating at the farther distances (3.8 and 7.5 Å from the surface). It is clearly observed that, in the PMF profile, the depth of the CM (about -5.7 kcal/mol) is much larger than that for the solvent-philic surface (-1.8 kcal/mol in Figure 2a). Another feature is the occurrence of a shoulder (around 8 Å) in the PMF for the solvent-phobic system. These observations indicate that the free energy near the solvent-phobic surface seems to be more advantageous for the surfactant adsorption. The more favorable surfactant-adsorption behavior induced by the solvent-phobic surface is in good agreement with the previous studies,47,48 in which the hydrophobic (CH3-terminated) self-assembled monolayer (SAM) enhances protein adsorption in aqueous solution, as compared with the hydrophilic (OH-terminated) SAM. It is interesting to note that here, although the PMF profile very near the solvent-phobic surface displays a thermodynamically favorable behavior for surfactant approaching, the full PMF at the

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Figure 7. Orientation order parameters (S(h)) as a function of distance from the surface. Arrows indicate the direction of surfactant-wall interaction increasing. The color scheme is the same as that in Figure 5.

bulk-interface transition region (around 10 Å away from the surface) shows a visible positive maximum value, as shown in the Figure 9a, which produces an adsorption barrier with approximately 1.0 kcal/mol. This behavior will be addressed in the following section. The solvent and surface induced contributions to the PMF: Wsol(h), Ws-w(h) are depicted in Figure 9b. As compared with the solvent-philic system, the surface effect on the surfactantadsorption PMF becomes more favorable, owing to an enhanced interaction between the surfactant and the surface in the solventrepelling interface. Furthermore, the influencing region from

Xu et al. the solvent-induced contribution becomes more extensive. For example, for the solvent-phobic system, the solvent-induced term Wsol(h) can produce the unfavorable contribution to the PMF in a wider region as far as 17 Å from the surface. Comparatively, for the solvent-philic surface (cf. Figure 2), the influencing region of Wsol(h) is only below 11 Å with respect to the surface. This distinguishing long-range behavior gives rise to the appearance of a free-energy barrier in the intermediate vicinity near the solvent-phobic surface, which is closely related to the depleting solvent distribution. The corresponding entropic and enthalpic contributions to the PMF are shown in Figure 9c. In the interfacial region between 9 and 18 Å from the surface, there are a favorable entropic contribution and an unfavorable enthalpic contribution to the PMF, which are obviously in contrast with the corresponding entropic and enthalpic effects in the same interfacial region for the solvent-philic system (c.f. Figure 2c). Figure 10 gives the relevant decomposition of the full PMF into the solvent (-T∆S sol(h), ∆Hsol(h)), and wall (-T∆Ss-w(h), ∆Hs-w(h)) contributions for the solvent-phobic system. It was observed that, in Figure 10a,b, both the favorable entropic contribution and the unfavorable enthalpic contribution, in the region above 9 Å from the surface, are largely induced by the solvent effect. When the surfactant initially approaches to the surface from the bulk phase, the weak solvent layer in this interface region offers more available space volume to fit the surfactant molecule and therefore brings about the positive entropy influence. Furthermore, such a decrease in the solvent

Figure 8. Orientation snapshots of surfactants at the distance 8.0 Å away from the surface for the four designed systems, with the same method depicted in Figure 4.

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J. Phys. Chem. B, Vol. 112, No. 44, 2008 13809

Figure 10. (a) Entropic portion (-T∆S full(h) to the full PMF and the solvent (-T∆S sol(h)) and wall (-T∆S s-w(h)) contributions to the entropic portion for the same system as in Figure 9. (b) Enthalpic portion ∆Hfull(h) to the full PMF and the corresponding solvent (∆Hsol(h)) and wall (∆Hs-w(h)) contributions.

Figure 9. (a) PMF and solvent density (F, in g/cm3) profiles for the solvent-phobic surface with Us-w ) 1.0. (b). Contribution to the adsorption PMF from the surfactant-wall interactions (Ws-w(h)) and the solvent-induced contribution (Wsol(h)). (c) Enthalpic contribution (∆H(h)) and the entropic contribution (-∆TS(h)).

layer in the interfacial region may reduce the interaction between the surfactant and the surrounding solvent molecules. This also enhances a thermodynamically unfavorable contribution (∆Hsol(h), in Figure 10b). In Figure 9a, the occurring PMF barrier in the intermediate region may lead to resistance against surfactant movement toward the surface. To clarify the effect of various surface interactions on the adsorption barrier, three extra PMF simulations were carried out with the further enhanced interaction strengths between the surfactant and surface (Us-w ) 2.0, 4.0, and 10.0). The results are shown in Figure 11a, along with the solvent-phobic system of Us-w ) 1.0. Each of the obtained PMFs exhibits a distinct adsorption barrier, and the free-energy barrier decreases with the interaction increasing. Figure 11b shows that the solvent contribution plays a key role in controlling the free energy barrier in the intermediate region. C. Effect of Surfactant-Solvent Interaction on the Adsorption PMF. From the discussions above, the interfacial solvent layer usually provides a repulsive component to the PMF. Especially, for the solvent-phobic surface, the solventinduced contribution can produce a free-energy barrier in the bulk-interface transition region. Thus, it is essential to investigate how various surfactant-solvent interactions affect the adsorption PMF. Figure 12a shows the PMF profiles for the solvent-philic systems, with four different surfactant-solvent interactions: Us-c ) 0.6, 0.8, 1.0 and 1.2. As seen from Figure 12a, with the

Figure 11. (a) Full PMF profiles as a function of the distance from the solvent-phobic surface for four different surfactant-wall interactions. (b) Contributions to the full PMFs from the surfactant-wall interactions (Ws-w(h)) and the solvent-induced contributions (Wsol(h)) for the range marked with the ellipse in (a).

interaction strength decreasing, the surfactant adsorption freeenergy is more beneficial. Figure 12b depicts the decomposition of the full PMFs: Wsol(h) and Ws-w(h). It could be observed that an obvious decline in the repulsive solvent-induced contribution

13810 J. Phys. Chem. B, Vol. 112, No. 44, 2008

Figure 12. (a) PMF profiles on the solvent-philic surface for four different surfactant-solvent interactions. (b) Contributions to the full PMFs from the surfactant-wall interactions (Ws-w(h)) and the solventinduced contributions (Wsol(h)).

Xu et al. solvent interaction mainly decreases the disadvantageous contribution of the enthalpic effect from the solvent (∆Hsol(h)). The effect of various surfactant-solvent interactions on the adsorption PMF for the solvent-phobic system is presented in Figure 13a. The overall PMF performance is comparable to that in the solvent-philic systems, except with more favorable adsorption free energy. Here, our attention is mainly focused on the free-energy barriers in the bulk-interface transition region (around 10 Å from the surface). As indicated from Figure 13a, the free-energy barrier reduces as the surfactant-solvent interaction decreases and it nearly becomes flat for the case of Us-c ) 0.6. It seems to forecast that the solvent-induced repulsive contribution to the PMF on the solvent-phobic surface would disappear once the solvent-surfactant interaction declines to some extent. Figure 13b shows the corresponding contributions of Wsol(h) and Ws-w(h). As expected, the negative solventinduced contributions to the total PMFs decrease with the surfactant-solvent interaction decreasing. However, the decreasing extent is more significant, as compared with the solventphilic systems (Figure 12b). It is interesting to note that, for the surfactant-solvent interaction of Us-c ) 0.6, the solvent contributes a weak attractive component of the full adsorption PMF in the interfacial region owing to a considerable decrease in the ∆Hsol(h) effect in this case. According to the adsorption PMF profile, the free-energy barrier in the intermediate region may impede the adsorption or self-assembly of surfactants on the solvent-phobic surface. The interaction strength between surfactant and solvent can modify this free-energy barrier, that is, with the interaction decreasing the free-energy barrier reduces. This understanding may explain why in the previous simulation researches, different adsorption phenomena have been observed for various surfactant/solvent systems on the so-called solvent-phobic surfaces.7,13 For example, in the previous simulation7 about the adsorption of surfactant/Sc-CO2 system on the CO2-phobic surface, the surfactant depletion phenomenon on the surface has been observed. This surfactant-repelling feature on the surface is due to the existence of the adsorption free-energy barrier, which is too high for surfactant to overcome. Moreover, the stronger interaction between the surfactant and the CO2 solvent in this simulation enlarges the barrier. Conversely, in the earlier simulation studies of the surfactant adsorption from aqueous solution on hydrophobic surfaces,49,50 obvious adsorption/selfassembly behavior on surfaces can be found. The interaction between the surfactant and the water solvent is comparatively smaller because the pure repulsive feature of the hydrophobic groups of surfactant was usually adopted in these simulation studies. This weak solvent-surfactant interaction may lower the so-called adsorption barrier. Therefore, in the simulation of surfactant adsorption from solution, it is very important to reasonably determine the effect of interfacial solvent layer, especially for solvent-phobic system, which is crucial to the surfactant adsorption performance.51 IV. Conclusion

Figure 13. (a) PMF profiles on the solvent-phobic surface for three different surfactant-solvent interactions: Us-c ) 0.6, 0.8 and 1.0. (b) Contributions to the full PMFs from the surfactant-wall interactions (Ws-w(h)) and the solvent-induced contributions (Wsol(h)).

with a decrease in the interaction intensity. On the other hand, the PMF portions from the surface effect are relatively insensitive to a change in the surfactant-solvent interaction. On the basis of the preceding analysis, this reduction in the surfactant-

In this paper, we have performed MD simulations to investigate the free energy profiles for a single surfactant to transfer from bulk solution phase to solid surfaces. A coarsegrained surfactant/solvent system with both the solvent-philic surface and the solvent-phobic surface was studied. The thermodynamics features of surfactant adsorption were clarified on the basis of the free-energy analysis. The free energy profile for surfactant approaching the surface is determined by a remarkably fine balance between the

Surfactant Adsorption on Solid Surfaces opposing entropy and enthalpy terms. The stabilization of surfactant adsorption behavior is mainly enthalpically dominated. Decomposing the full PMF (and its entropic and enthalpic components) into the solvent-induced contribution and the surface-surfactant interaction contribution has distinguished the effect of surface and solvent on the PMF. The solvent-induced term to the full PMF is found to show a monotonic increase as the surfactant approaches surface, indicating a highly repulsive contribution. This unfavorable solvent contribution can be interpreted in terms of the interfacial solvent layer effect. The interplay of the repulsive solvent component and the attractive surface component of the full PMF is responsible for the microscopic adsorption behavior of surfactant on the surfaces. For both the solvent-philic surface and the solvent-phobic surface, the adsorption PMF for the surfactant becomes more favorable with increasing surfactant-surface interaction (Usw). However, the solvent-surfactant interaction (Us-c) shows a contrasting influence on the adsorption PMF; i.e., an increase in the interaction (Us-c) leads to a less favorable contribution to the PMF. Compared to the solvent-philic surface, the PMF on the solvent-phobic surface displays the more thermodynamicsfavorable CM position to the surfactant adsorption.47 However, an evident long-range adsorption free-energy barrier appears in the bulk-interface transition region for the solvent-phobic surface. This presence of the free-energy barrier is surely due to the depletion of the solvent layer on the surface and it may induce impediment to the surfactant adsorption on the solventphobic surface. When the surfactant-solvent interaction is reduced to a certain degree, the negative solvent contribution may become an attractive action on the surfactant adsorption, which could cause a disappearance of the free-energy barrier in the intermediate region on the solvent-phobic surface. In summary, the free-energy profile can be used to clarify the effect of various interactions on the surfactant adsorption. Moreover, it can provide the information on adsorption kinetics. The detailed understanding of this surfactant adsorption on solid surfaces is very critical for developing the surfactant candidates applied in solid/liquid interfaces. Acknowledgment. This study is supported by the National Natural Science Foundation of China under Grant 20776066, the Special Scientific Research Foundation (20060291002) for Doctoral Discipline Area of the Institution of Higher Learning, and the Innovation Funding for Doctorate Dissertation of Nanjing University of Technology (BSCX200712). Supporting Information Available: Interaction parameters for the reference system and other systems investigated in this study are listed in Tables 1 and 2, respectively. The dependence of the PMF for the surfactant adsorption on the simulation time is shown in Figure S1. Two PMF profiles using the WHAM method and the FA method are given in Figure S2. These materials are available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Yu, K. M. K.; Steele, A. M.; Zhu, J.; Fu, Q.; Tsang, S. C. J. Mater. Chem. 2003, 13, 130–134. (2) Ghosh, K.; Vyas, S. M.; Lehmler, H. J.; Rankin, S. E.; Knutson, B. L. J. Phys. Chem. B 2007, 111, 363–370. (3) Hanrahan, J. P.; Copley, M. P.; Ryan, K. M.; Morris, M. A.; Spalding, T. R.; Holmes, J. D. Chem. Mater. 2004, 16, 424.

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