Role of Solvent Selectivity in the Equilibrium Surface Composition of

Jun 21, 2010 - The dimensionless exchange parameter χij z/(kT)[wij - (wii Ч ..... fit parameters of the model are then the degree of incompatibility...
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Role of Solvent Selectivity in the Equilibrium Surface Composition of Monolayers Formed from a Solution Containing Mixtures of Organic Thiols Folusho T. Oyerokun,* Richard A. Vaia, John F. Maguire, and Barry L. Farmer Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson AFB, Ohio 45433-7132 Received April 13, 2010. Revised Manuscript Received May 22, 2010 We have developed a simple model to quantify the effect of solvent selectivity on the surface composition of twocomponent self-assembled monolayers formed from solutions containing mixtures of organic thiols. The coarse-grained molecular model incorporates the relevant intermolecular interactions in the solution and monolayer to yield an expression for the free energy of monolayer formation. Minimization of the free energy results in a simple and analytically tractable expression for the monolayer composition as a function of solvent selectivity (defined as the difference in the Flory-type interaction parameters of the two organic thiols in the solution) and the degree of incompatibility between the adsorbate molecules. A comparison of our theory to experiments on the formation of twocomponent self-assembled monolayers from solution indicates that the coarse-grained molecular model captures the trends in the experimental data quite well.

Introduction Multicomponent monolayers, in which two or more distinct organic thiol molecules are adsorbed onto an interface provide a suitable means of controlling the physicochemical properties of the surface.1,2 When the attached thiol molecules are highly incompatible with each other, either because of a size mismatch or unfavorable intermolecular interactions between specific chemical groups on the molecules, the adsorbate molecules can phase segregate into domains within the monolayer.3-7 Recent studies on multivalent nanoparticles (i.e., nanoparticles with two or more attached organic thiols) have suggested that the phase-separated structure can form “striped” or “Janus” patterns on the surface depending on the nanoparticle size.8-11 It has been postulated that microphase separation to stripelike patterns arises because of a gain in conformational entropy resulting from the adjacent placement of alkyl thiols of unequal lengths or bulkiness on the curved nanoparticle surface.10 Two-component monolayers with phase-separated structures are desirable in a variety of biosensing applications.8,12,13 In general, the spatial organization of the adsorbate molecules and the ensuing properties of the *To whom correspondence should be addressed. E-mail: folusho. [email protected]. (1) Love, J. C.; Estroff, L. A.; Kriebel, J. K.; Nuzzo, R. G.; Whitesides, G. M. Chem. Rev. 2005, 105, 1103. (2) Schreiber, F. Prog. Surf. Sci. 2000, 65, 151. (3) Folkers, J. P.; Laibinis, P. E.; Whitesides, G. M. Langmuir 1992, 8, 1330. (4) Stranick, S. J.; Parikh, A. N.; Tao, Y.-T.; Allara, D. L.; Weiss, P. S. J. Phys. Chem. 1994, 98, 7636. (5) Tamada, K.; Hara, M.; Sasabe, H.; Knoll, W. Langmuir 1997, 13, 1558. (6) Siepmann, J. I.; McDonald, I. R. Mol. Phys. 1992, 75, 255. (7) Shevade, A. V.; Zhou, J.; Zin, M. T.; Jiang, S. Langmuir 2001, 17, 7566. (8) Jackson, A. M.; Myerson, J. W.; Stellacci, F. Nat. Mater. 2004, 3, 330. (9) Jackson, A. M.; Hu, Y.; Silva, P. J.; Stellacci, F. J. Am. Chem. Soc. 2006, 128, 11135. (10) Singh, C.; Ghorai, P. K.; Horsch, M. A.; Jackson, A. M.; Larson, R. G.; Stellacci, F.; Glotzer, S. C. Phys. Rev. Lett. 2007, 99, 226106. (11) DeVries, G. A.; Brunnbauer, M.; Hu, Y.; Jackson, A. M.; Long, B.; Neltner, B. T.; Uzun, O.; Wunsch, B. H.; Stellacci, F. Science 2007, 315, 358. (12) Mrksich, M.; Grunwell, J. R.; Whitesides, G. M. J. Am. Chem. Soc. 1995, 117, 12009. (13) Frederix, F.; Bonroy, K.; Laureyn, W.; Reekmans, G.; Campitelli, A.; Dehaen, W.; Maes, G. Langmuir 2003, 19, 4351.

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multicomponent monolayers are intimately tied to the equilibrium surface coverage. The most common protocols for synthesizing two-component self-assembled monolayers of alkyl thiols exploit competitive adsorption between the two organic ligand molecules from solution.3,14-16 The preferential adsorption of one alkyl thiol over the other from the solution can occur either because of a difference in size of the respective molecules or as a result of the selectivity of the solvent. Milner has studied the kinetics and equilibrium of adsorption of two competing species of endadsorbing polymer chains onto a flat interface from solution as a function of size and the degree of stickiness of the end groups.17 He found that the size mismatch (i.e., the degree of bidispersity) between the homopolymers was more influential in determining the final coverage than the binding strength of the end groups. Short-chain homopolymers readily adsorb in the presence of an existing layer of longer chains; the adsorption of short chains is accompanied by an enhanced desorption of the original chains. The introduction of invading chains of identical size, but with stronger stickers at their end groups, was found not to be as effective in modifying the surface composition of the original layer. In contrast, the role of solvent selectivity in the final composition of two-component monolayers is less well understood. A study of the formation of two-component self-assembled monolayers from ethanol onto a gold surface by three separate pairs of alkanethiols of identical chain length but consisting of polar and nonpolar terminal groups found that the alkanethiol terminated with the nonpolar group is always preferred on the gold substrate, presumably because of its lower solubility in the solvent.14 Similar studies carried out on mixed monolayers of alkanethiols on silver substrate18 and disulfides on gold15 also find significant deviations (14) Bain, C. D.; Whitesides, G. M. J. Am. Chem. Soc. 1988, 110, 6560. (15) Bain, C. D.; Biebuyck, H. A.; Whitesides, G. M. Langmuir 1989, 5, 723. (16) Folkers, J. P.; Laibinis, P. E.; Whitesides, G. M.; Deutch, J. J. Phys. Chem. 1994, 98, 563. (17) Milner, S. T. Macromolecules 1992, 25, 5487. (18) Laibinis, P. E.; Fox, M. A.; Folkers, J. P.; Whitesides, G. M. Langmuir 1991, 7, 3167.

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between the monolayer composition and solution concentration. In their study on the formation of mixed self-assembled monolayers of rigid biphenyl thiols on gold from different solvents, Kang and co-workers found that the final composition of the biphenyls in the monolayer depends on the polarity of the solvent.19 Despite these observations, to our knowledge, no systematic study has been embarked upon to quantify the effect of solvent selectivity on the surface composition of multicomponent self-assembled monolayers. The objective of this communication is the development of a simple theoretical model to quantify the role of solvent selectivity in the equilibrium surface coverage in two-component monolayers formed from a solution containing a mixture of organic thiols. Our molecular approach, built upon lattice-based descriptions of both the solution and monolayer phases, directly incorporates the details of the intermolecular interactions between the organic thiols and the solvent. The resulting expression for the equilibrium surface composition is both simple and analytically tractable. It contains explicit terms for the solvent selectivity and the degree of incompatibility between the adsorbate molecules. Most importantly, the predictions of our model are quantitatively testable with experiments and may be extended readily to a large variety of systems.

Theoretical Model In this section, we present our theoretical model for the determination of the equilibrium surface composition of monolayers formed from a solution containing two distinct organic thiols. The objective of our model is modest: we seek to ascertain how the fractional composition of the adsorbates in the monolayer vary with solvent selectivity and the degree of incompatibility between the organic thiol molecules. Specifically, we propose to demonstrate that significant deviation in the surface composition of adsorbates in a two-component monolayer from their relative concentration in the solution can arise if the interaction between the solvent molecules and one of the organic thiol molecules is highly unfavorable. Usually, the presence of one dissimilar chemical moiety (for instance, substitution of a terminal polar group with a nonpolar group) is sufficient to affect the relative solubilities of organic thiols in solution drastically. In formulating our model, we incorporate several ideas from a simple theoretical model developed by Folkers, Laibnis, Whitesides, and Deutch to investigate the role of incompatibility between adsorbate molecules in the phase behavior of two-component self-assembled monolayers in contact with solutions of end-adsorbing alkanethiols.16 First, we assume that both the solute and adsorbate molecules are structureless. This heavily coarsegrained description ignores the conformational flexibility of the organic thiol molecules and replaces the intermolecular interactions between the different chemical units on the thiol molecules by a single “effective” interaction parameter. As formulated, our model is particularly suitable for short-chain organic thiols (where the simplification introduced by the neglect of conformation flexibility is not as severe) and should be useful in the determination of the surface composition in two-component monolayers where there are no appreciable differences in the size of the two adsorbate molecules. Notwithstanding the above simplifications, we believe that insights gleaned from the coarse-grained model have broader applicability beyond very short chain alkyl thiols. The second major idea introduced by Folkers and co-workers, which we have also incorporated into the current theory, is to (19) Kang, J. F.; Liao, S.; Jordan, R.; Ulman, A. J. Am. Chem. Soc. 1998, 120, 9662.

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model the formation of the two-component monolayer simply as a change of state:16 Asoln þ Bsoln f ASAM þ BSAM

ð1Þ

In other words, the formalism ignores the subtleties of the underlying adsorption mechanism, such as the effect of the substrate on adsorption kinetics, and adopt a strictly thermodynamic description of monolayer formation. Consequently, other issues that might be important for understanding the formation of twocomponent monolayers, such as the presence of intermediate and “kinetically trapped” structures, are also omitted from consideration. Notwithstanding its apparently simplistic treatment of monolayer formation, the model provides reasonable predictions of the phase behavior of two-component monolayers. A summary of the thermodynamic model of Folkers and co-workers is given in Appendix A. Our current approach and that of ref 16 differ in that we have adopted a lattice fluid model in describing the thermodynamic states of both the solution and the monolayer. The introduction of a lattice-based description has enabled us to model explicitly the relevant solvent-solute and adsorbate-adsorbate interactions necessary to capture the role of solvent selectivity in surface composition unambiguously. Although in principle more sophisticated off-lattice molecular models can be formulated to describe the thermodynamic state in both phases, the advantage of latticebased models rests on their simplicity and analytical tractability. A major drawback of lattice-based models, however, is the difficulty in capturing pressure-volume (equation of state) effects.16,20 Following Folkers and co-workers, we shall neglect the difference between the enthalpy and internal energy of the structureless molecules. The molar change in the (Gibbs) free energy during monolayer formation at constant temperature and pressure is Δf ¼

1 ½ðμA SAM - μA soln ÞxA þ ðμB SAM - μB soln ÞxB  kT

ð2Þ

where k is the Boltzmann constant and xi is the mole fraction of is the chemical potential of adsorbate i in the monolayer. μsoln i is the chemical potential of the solute i in the solution, and μSAM i corresponding adsorbate in the monolayer. The determination of the appropriate expressions for the chemical potentials of both the solutes and adsorbates requires the invocation of a statistical mechanical model for the solution and monolayer phases. We shall represent the monolayer by a two-component lattice that is entirely populated by the adsorbate molecules (i.e., there are no solvent molecules or voids present) so that xA þ xB = 1. If we further assume that each molecule on the lattice interacts only with its z nearest neighbors, then the chemical potential of adsorbate A in the two-component layer is20 μSAM zwAA A ¼ þ log xA þ xB 2 χAB kT 2kT

ð3Þ

where wij is the contact energy between molecules of adsorbates i and j. The dimensionless exchange parameter χij  z/(kT)[wij - (wii þ wjj)/2] quantifies the strength of interaction between species i and j. When χAB < 0, the interaction between dissimilar adsorbate molecules is more preferable than interactions between similar (20) Dill, K. A.; Bromberg, S. Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology; Garland Science: New York, 2003.

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molecules. Above a critical χAB, the adsorbates will segregate into A-rich and B-rich domains within the monolayer. In eq 3, the first term on the right-hand side is the (reference) chemical potential in a single-component monolayer (i.e., in a monolayer comprising only molecules of adsorbate A). The third term, proportional to the square of the mole fraction of the B adsorbates, is the contribution of the A-B intermolecular interactions to the chemical potential of adsorbate A. A similar expression to eq 3 holds for the chemical potential of adsorbate B in the monolayer: μSAM zwBB B ð4Þ ¼ þ log xB þ xA 2 χAB kT 2kT The determination of the chemical potentials of the organic thiols in the solution requires the generalization of the lattice model to a ternary mixture. The derivation of the chemical potential of a three-component solution is given in Appendix B. We shall simply summarize the key results in this section. The appropriate expressions for the chemical potentials of organic thiols A and B in the solution are μsoln zwAA A ¼ þ log yA þ yB 2 χAB þ yB yS ðχAB þ χAS - χBS Þ þ yS 2 χAS kT 2kT μsoln zwBB B ¼ þ log yB þ yA 2 χAB þ yA yS ðχAB þ χBS - χAS Þ þ yS 2 χBS kT 2kT ð5Þ where yA, yB, and yS are the mole fractions of solutes A and B and solvent S, respectively. We have assumed in the derivation of the chemical potentials that the contact energies between the adsorbate molecules in the monolayer are the same as the contact energies between the corresponding solute molecules in the soln 21 solution so that χSAM AB = χAB  χAB. Note that, in addition to χAB, the chemical potential of the organic thiols (eq 5) contains two new interaction parameters χAS and χBS reflecting the additional solute-solvent intermolecular interactions present in the solution. Exchange parameters χAS and χBS can be determined from the Hildebrand solubility parameters of the organic thiols22,23 Vref χij ¼ ð6Þ ðδi - δj Þ2 RT where Vref is a reference molecular volume (usually the solvent’s molar volume) and R is the gas constant. The Hildebrand solubility parameter, also known as the cohesive energy density, is often estimated from the enthalpy of vaporization, δi = (ΔEv/vm)1/2. The molar volumes (vm), enthalpies of vaporization (ΔEv), and solubility parameters of a variety of organic solvents and adsorbing solute molecules are listed in several thermophysical and chemical handbooks. (See, for example, the comprehensive handbook by Yaws.24) It is worthwhile to point out that the determination of an exchange parameter based on the Hildebrand solubility parameter approach works well only when the molecules of the solvent (21) In principle, the degree of incompatibility between the A and B solutes in the solution is not the same as the incompatibility in the monolayer (i.e., χSAM AB 6¼ soln χAB ). In the formation of mixed monolayers of alkanethiolates from a solution containing alkanethiols, the chemisorption of alkanethiols onto noble metal surfaces results in the displacement of the terminal H atom so that the resulting adsorbate molecule (alkanethiolate) is quite different from its solution counterpart (alkanethiol). However, because most organic thiols of practical interest usually consist of six or more backbone atoms, the difference between these two values is negligible. (22) Hildebrand, J. H.; Scott, R. L. Regular Solutions; Prentice-Hall: Englewood Cliffs, NJ, 1962. (23) van Krevelen, D. W.; te Nijenhuis, K. Properties of Polymers, 4th ed.; Elsevier: Amsterdam, 2009. (24) Yaws, C. L. Chemical Properties Handbook; McGraw-Hill: New York, 1999.

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and the organic thiols of interest are nonpolar or weakly polar.25 For a mixture in which the dominant interactions between the solute and solvent molecules involve polar groups, the Hilderbrand technique breaks down and gives poor estimates for the exchange parameters. Several refinements to the Hildebrand techniques have been proposed for studying solutions involving specific interactions. The interested reader is referred to the comprehensive monographs by Coleman, Graf, and Painter25 and van Krevelen and te Nijenhuis23 for more details. Substitution of the chemical potential expressions from eqs 3-5 into eq 2 yields the free energy of formation in terms of the mole fraction of the organic thiols in solution and the monolayer as well as intermolecular interactions: Δf ¼ - xA log yA - ð1 - xA Þlog yB þ χAB ½xA ðyA - yB Þ SAM - yA ð1 - yB Þ þ χAS yS ðyA - xA Þ þ χBS yS ðxA þ yB - 1Þ þ Δfmix

ð7Þ Here, Δf SAM mix is the free energy of mixing in the two-component monolayer: SAM ¼ xA log xA þ ð1 - xA Þlogð1 - xA Þ þ χAB xA ð1 - xA Þ Δfmix

ð8Þ Minimization of eq 7, with respect to adsorbate mole fraction xA, yields a transcendental equation for equilibrium surface composition in the two-component monolayer   xA þ χAB ½1 - 2xA þ ð2φA - 1Þyt  þ Rð1 - yt Þ log 1 - xA   φA ð9Þ ¼ log 1 - φA where yt is the total mole fraction of the organic thiols in the solution and φA = yA/yt is the relative mole fractions of A in solution. The solvent selectivity parameter, R, is defined as the difference between the solute-solvent exchange parameters, R  χBS - χAS. On the basis of this convention, a positive R always signifies that the solvent is selective to organic thiol A. On the contrary, R < 0 implies that species B is more soluble in the solution. Equation 9 is solved numerically to determine the equilibrium composition of adsorbate A as a function of the total mole fractions of the thiols (yt), the solvent selectivity (R), and the degree of incompatibility between the adsorbate molecules (χAB) It is possible to obtain an explicit relationship between the fractional composition of adsorbates within the monolayer (xi) and the relative solution concentration of the organic thiols (φi) by considering the dilute solution limit of eq 9 (i.e., when yt , 1). Within this limit, the surface coverage expression simplifies to     xA φA þ χAB ð1 - 2xÞ þ R ¼ log ð10Þ log 1 - xA 1 - φA The inversion of eq 10 yields an analytical expression for the dependence of φA on xA:   xA exp½χAB ð1 - 2xA þ RÞ 1 - xA   ð11Þ φA ¼ xA exp½χAB ð1 - 2xA þ RÞ 1þ 1 - xA Equation 11 gives very good estimates of the surface composition provided the total mole fraction of the organic thiols in the (25) Coleman, M. M.; Graf, J. F.; Painter, P. C. Specific Interactions and the Miscibility of Polymer Blends; Technomic Publishing Company: Lancanster, PA, 1991.

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Figure 1. Role of solvent selectivity (R  χBS - χAS) in equilibrium surface composition of two-component monolayers of noninteracting adsorbate molecules (i.e., χAB = 0). Variation of the mole fraction of adsorbate A in the monolayer (xA) with the relative mole fraction of organic thiol A in the solution (φA): R = -1 ( 3 3 3 ), 0 (-), 0.5 (---), and 1 ( 3 - 3 ). The total mole fraction of the thiols in the solution [yt = yA þ yB = 10-3, χAB = 0, and φA = yA/(yA þ yB)] is the relative mole fraction of organic solute A in the solution (i.e., minus the solvent).

solution is not too high, yt < 10-2. Because the total thiol concentration is 1 mM or lower in most experiments, eq 11 is often a valid approximation to eq 9.

Results and Discussion Role of the Selectivity of the Solvent in Surface Composition. We now investigate the role of solvent selectivity in monolayer composition. For purpose of illustration, we first consider the ideal case in which the organic thiol molecules are noninteracting (i.e., χAB = 0) but have different solubilities in the solvent. (This is true, for example, when both organic thiols have an identical number and chemical composition of backbone atoms and nearly compatible end groups.) Figure 1 shows the variation of the fractional composition of adsorbate A (xA) with the relative mole fraction of solute A in the solution (φA) at different solvent selectivity, R = -1, 0, 0.5 and 1; the total solute concentration yt is 10-3. The fractional coverage of the adsorbates in the monolayer increases linearly (solid line in Figure 1) with the initial relative concentration of the corresponding organic solute when the solvent is nonselective (i.e., R = 0). However, for all other values of R, the model predicts a preponderance of molecules from the less-soluble species in the monolayer. The fact that the relationship between xA and φA is nonlinear when R 6¼ 0 suggests that the mole fraction of an adsorbate in the monolayer is not always equal to its relative fraction in the solution. In fact, the equality of these two values will occur only for the unique case of R = χAB = 0. Another useful indicator of the effect of the solvent selectivity on the surface composition in two-component monolayers is the relative solute concentration, φ*, A corresponding to equal mole fractions of adsorbates (i.e., xA = xB = 0.5). For organic thiols dissolved in a nonselective solvent (R = 0), an equimolar concen* = 0.5. It is possible to derive tration in the monolayer occurs at φA a simple relation for how φ*A varies with the solvent selectivity R for very dilute concentrations of organic thiols. By setting xA = 0.5 in eq 11, one obtains eR  ð12Þ φA ¼ 1 þ eR Figure 2 illustrates the variation of φA * with solvent selectivity (R) in a two-component monolayer formed from a solution containing mixtures of organic thiols. Equation 12 can serve as a useful 11994 DOI: 10.1021/la101464j

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Figure 2. Variation of the relative mole fractions of solute A corresponding to equimolar concentrations of adsorbates in the monolayer (φA *) as a function of solvent selectivity. For a nonselective solvent, φ*(R = 0) = 0.5. A

rule of thumb in experiments because it provides an estimate of how the relative solubility of the organic thiols will impact the surface composition. Role of Incompatibility between Adsorbate Molecules in Surface Composition and Phase Behavior. We now consider the role of incompatibility (χAB) in equilibrium surface coverage. First, we rewrite eq 10 in the form !   xA Rsoln þ χAB ð1 - 2xÞ ¼ log  ð13Þ log 1 - xA Rsoln where Rsoln = φA/(1 - φA) and the parameter R*soln = eR. Recasting eq 10 into eq 13 has allowed us to absorb the explicit dependence of surface composition on solvent selectivity into ratio Rsoln/R*soln and thereby obtain a universal expression for its variability with the degree of incompatibility between adsorbate molecules. Figure 3 shows the variation of surface composition xA with the relative thiol concentration, expressed in the form of Rsoln/R*soln, at different degrees of incompatibility between the adsorbate molecules. Below a critical incompatibility (χAB e χcrit AB = 2.0), the adsorbates in the monolayer are mixed together into a single homogeneous phase. (Note that the compositions of the adsorbates in this phase are not necessarily equal to their relative concentrations in the solution.) Phase separation occurs in the monolayer above the critical incompatibility, χAB >χcrit AB. A twophase coexistence region consisting of A-rich and B-rich domains occurs in a very narrow window in the neighborhood of Rsoln/ R*soln = 1. Equation 13 bears a striking resemblance to the surface coverage expression derived by Folkers and co-workers in ref 16 (see also eq 18 in Appendix A). The key difference between the two expressions is that the phenomenological parameter R‡soln (in eq 18 of Appendix A) has now been replaced by the solvent selectivity term R*soln = exp(χBS - χAS), which incorporates all of the molecular details of the solute-solute and solute-solvent interactions. Hence, not surprisingly, both models give an identical prediction of the role of incompatibility between the adsorbate molecules in the final coverage. Within the Folkers et al. model, phenomenological parameter R‡soln quantifies the preference of one component over the other in the monolayer (e.g., as a result of solvent selectivity or favorable surface energetics). For instance, the equimolar concentration of the adsorbates in the monolayer (xA = xB = 0.5) occurs when Rsoln = R‡soln. For R‡soln > 1, the model predicts that a higher concentration of the solute A is needed in the solution (Rsoln > 1) in order to maintain an equimolar concentration in the monolayer. Langmuir 2010, 26(14), 11991–11997

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Figure 3. Role of the degree of incompatibility between the adsorbate molecules in the variation of surface composition (xA) with solute concentration (Rsoln/R*soln) computed using the dilute solution approximation, eq 13: χAB = 0 (-), 1 (- 3 -), 2 (---), and 3 ( 3 3 3 ). Rsoln = φA/φB is the ratio of the mole fractions of solutes in the solution. The parameter R*soln = exp(χBS - χAS) quantifies the solvent selectivity.

Although R‡soln provides some qualitative insight into the role of solvent selectivity in coverage, its experimental determination is problematic. In contrast, R*soln, can be determined from a knowledge of the solubility parameters of the organic thiols and solvent via eq 6. Comparison with Experiment on a Two-Component Monolayer of Alkanethiols. Our theory can be compared to experiments on the formation of two-component monolayers in two ways. If the solvent selectivity and incompatibility are known for the solutes and adsorbates of interest, then we can determine the dependence of the adsorbate fraction as a function of the mole fraction of the organic thiols in the solution by using eq 11. However, if the solvent selectivity and/or the incompatibility are not known a priori, which is often the case in practical situations, then eq 11 can be used to fit xA versus φA data. In this instance, the fit parameters of the model are then the degree of incompatibility (χAB) and the solvent selectivity term (R). The computed incompatibility or solvent selectivity can then be used to estimate the solubility parameters of the organic thiols. We illustrate by applying our theoretical model to the experimental data of Bain and Whitesides on the formation of twocomponent self-assembled monolayers of organic thiols from ethanol on flat gold substrates.14 The authors studied three binary systems of alkanethiols of identical size, but with terminal groups of varying polarity. One of the alkanethiols has a nonpolar terminal group [HS(CH2)10CH3], and the other three organic thiols have a polar component at one of their ends [HS(CH2)10CH2Br, HS(CH2)10COOH and HS(CH2)10CH2OH]. Figure 4 shows the variation of the surface composition of the polar-group-terminated alkanethiols as a function of their relative mole fraction in the ethanol solution. The open symbols are the experimental data, and the lines are fits to the data based on eq 11. Again, the two fit parameters of the model are χAB and R. Somewhat surprisingly, the simple model captures the trends in the experimental data quite well. The predicted values of incompatibility and solvent selectivity are in the legend of Figure 4. According to Figure 4 and the fitted values of χAB and R, HS(CH2)10CH2Br is the most compatible organic thiol with HS(CH2)10CH3. This observation is also confirmed by the estimated value of φ*A (based on eq 12): 0.59 [HS(CH2)10CH2Br], 0.7 [HS(CH2)10COOH], and 0.62 [HS(CH2)10CH2OH]. An independent determination of the solvent selectivity parameter and incompatibility can be made using eq 6 if the solubility Langmuir 2010, 26(14), 11991–11997

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Figure 4. Variation of the surface composition of polar-groupterminated alkanethiols in a two-component monolayer with its relative fraction in the solution from ref 14. Three binary systems of alkanethiol molecules of identical size but with different terminal groups were considered in the experimental study. The polargroup-terminated organic thiols are HS(CH2)10CH2Br (O), HS(CH2)10CH2OH (4), and HS(CH2)10COOH (0). The second organic thiol molecules (alkanethiol B) in the solution is HS(CH2)10CH3. The lines are theoretical fits to the data using eq 11. The two fit parameters of the model, degree of incompatibility between adsorbate molecules (χAB), and solvent selectivity (R) are displayed in the table.

parameters of the organic thiols are known. According to Yaws, the solubility parameters of ethanol and 1-undecanethiol are 25.42 and 17.29 (J/cm3)1/2, respectively.24 Regrettably, we were unable to locate any data regarding the solubility parameters of polar-group-terminated alkanethiols in the literature. Consequently, a quantitative comparison between our predicted values of R and χAB for the three binary systems of a self-assembled monolayer of alkanethiolates is not possible at this time. Nonetheless, we can use the solubility parameters of ethanol and 1-undecanethiol to estimate χBS (i.e., the exchange parameter of 1-undecanethiol in ethanol). Substituting the molar volume of ethanol vm = 58.52 cm3 mol-1 for Vref in eq 6 yields χBS = 1.56 at room temperature. Once χBS is known, it is straightforward to determine the exchange parameters of the polar-terminated alkyl thiols (χAS) from the estimated values of R given in the legend of Figure 4. Hence, at room temperature χAS = χBS - R = 1.2 [HS(CH2)10CH2Br], 0.7 [HS(CH2)10COOH], and 1.07 [HS(CH2)10CH2OH]. Note that the model predicts that the four organic thiols under study are soluble in ethanol (i.e., χAS < 2). This is an important prediction because ethanol is known to solvate a variety of alkanethiols with varying degrees of polarity.1 It is instructive to compare the estimated interaction parameters (χAS) of the alkyl thiols in the Bain and Whitesides experiment with those corresponding to ethanol solutions of analogous hydrocarbons whose terminal moiety contains a methyl (CH3) group instead of a thiol group (SH). An advantage of this comparison is that the solubility parameters of an alkanethiol and analogous nonthiolated hydrocarbons are very similar; in the case of 1-undecanethiol and dodecane, the difference is actually within 10%. Furthermore, the energy of vaporization and the molar volumes that are necessary for the determination of the solubility parameters are documented for these compounds. According to the Yaws’ Handbook, the solubility parameters of dodecane [CH3(CH2)10CH3], 1-bromodecane [CH3(CH2)10CH2Br], dodecanoic acid [CH3(CH2)10COOH], and dodecanol [CH3(CH2)10CH2OH] are 15.91, 16.49, 20.49, and 19.48 in units of (J/cm3)1/2, respectively. The calculated values of the interaction parameters of these hydrocarbon compounds in ethanol at room temperature, based on eq 6, are χAS = 1.88 [CH3(CH2)10CH2Br], 0.57 [CH3(CH2)10COOH], and 0.83 [CH3(CH2)10CH2OH]. The fact that the trends in the variation of the predicted values of χAS for DOI: 10.1021/la101464j

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the alkyl thiols and the calculated values for analogous nonthiolated hydrocarbons based on experimentally determined solubility parameters are similar is indeed very encouraging and suggests that the predictions of our model are at least qualitatively correct. So far in our discussion, we have focused entirely on binary systems of alkanethiols of identical size but with different chemical moieties at their termini. In a variety of applications, it is often desirable to introduce a size mismatch in the organic thiols decorating the surface. As already pointed out by Ligoure and Leibler in their adsorption of end-functionalized homopolymers on flat interfaces and also by Milner in his competitive adsorption studies, the absolute value of surface coverage depends on the size of the molecule.17,26 We expect that the incorporation of the entropic effects associated with the differences in the conformational flexibility of the two molecules would lead to both qualitative and quantitative modifications of the surface composition in a two-component monolayer. However, such effects are beyond the scope of our heavily coarse-grained model.

Summary and Conclusions We have developed a statistical mechanical model to investigate the role of solvent selectivity in the surface composition in two-component monolayers formed on a solid substrate from a solution containing end-adsorbing organic molecules. The coarse-grained lattice fluid model incorporates the relevant solute-solute, solute-solvent, and adsorbate-adsorbate intermolecular interactions to yield an expression for the free energy of formation of the monolayers at constant temperature and volume. Minimization of the free energy results in an expression for the monolayer composition that is both simple and analytically tractable (eq 11). It contains explicit terms for the solvent selectivity (R) and degree of incompatibility between the adsorbate molecules in the monolayer (χAB). The model is easily generalizable to the study of multicomponent monolayers formed from solutions containing three or more kinds of organic solutes. According to the model, the relationship between xA and φA is nonlinear except for the unique case of R = χAB = 0 (Figure 1). For R ¼ 6 0, the theory predicts a preponderance of molecules of the less-soluble organic thiol in the two-component monolayer. We have quantified the tendency toward increasing the fractional mole fraction of the less-soluble constituent via a parameter φ*A, the relative mole fraction of the organic thiols in the solution corresponding to equimolar coverage in the monolayer (xA = xB = 0.5). Our theory predicts that the more selective the solvent, the larger the deviation of φ*A from φ*A(R = 0) = 0.5 (eq 12 and Figure 2). Our treatment yields identical predictions to the simple thermodynamic model in ref 16 regarding the role of the incompatibility of the adsorbate molecules in their phase behavior and surface composition.16 Below a critical incompatibility (χAB e χcrit AB = 2.0), the model predicts that the adsorbates in the monolayer are mixed together into a single homogeneous phase (Figure 3). However, for χAB > χcrit AB, the adsorbate molecules in the monolayer segregate into A-rich and B-rich domains. According to both theories, the coexistence region of the phase-separated domains occurs in a very narrow range in the solution concentration of the organic thiols. Although the above conclusion seems to suggest the near impossibility of experimentally observing phase segregation in two-component monolayers in contact with a solution of adsorbing thiols at equilibrium, we expect a quantitative modification of the (26) Ligoure, C.; Leibler, L. J. Phys. (Paris) 1990, 51, 1313.

11996 DOI: 10.1021/la101464j

phase behavior when there is a significant size mismatch between the ligand molecules. This is because entropic effects, due to the conformational flexibility of the molecules that hitherto have been neglected, could considerably impact the spatial organization of the adsorbate molecules in the monolayer, resulting in stripelike or Janus patterns depending on the curvature of the solid interface. We have compared the predictions of our model to the experimental data of Bain and Whitesides for three binary systems of self-assembled monolayers of polar- and nonpolar-group-terminated alkanethiols from ethanol onto flat gold substrates. Data from the experiment were fitted using the surface coverage expression derived from the analytic theory (Figure 4). The fit parameters of the model are the solvent selectivity (R) and the degree of incompatibility between the adsorbate molecules (χAB). Surprisingly, the coarse-grained model captures the trends in the experimental data quite well and provides reasonable estimates of the interaction parameters between the organic thiols and the solvent. Acknowledgment. This research was performed while F.T.O. held the National Research Council Associateship Award at the Air Force Research Laboratory. We thank the Air Force Office for Scientific Research for funding.

Appendix A: Simple Thermodynamic Model of Phase Behavior in Two-Component Monolayers In this section, we briefly summarize the thermodynamic theory of Folkers and co-workers.16 The objective of the model is to determine the phase behavior of the two-component monolayer in contact with the solution of end-adsorbing organic thiols as a function of the solution concentration of the organic thiols and the incompatibility between the adsorbate molecules in the monolayer. Specifically, the model seeks to determine under which equilibrium conditions the adsorbate molecules in the monolayer will phase segregate into islands. The change in the molar (Gibbs) free energy during the formation of a two-component monolayer, as described by eq 1, at constant temperature and pressure is Δf ¼

1 SAM ½ðμSAM - μsoln - μsoln A ÞxA þ ðμB B ÞxB  kT A

ð14Þ

where, as in the Theoretical Model section, xi signifies the mole fraction of alkanethiolate i in the monolayer. The chemical , is obtained potential of the alkanethiol i in the solution, μsoln i by assuming a dilute (and ideal) solution of noninteracting organic thiols: ¼ μ†i þ kT log yi μsoln i

ð15Þ

Here, yi and μ†i are the solution concentration and the reference chemical potential at infinite dilution of thiol i, respectively.27 An expression for the chemical potential of structureless adsorbate molecules is derived by assuming only nearest-neighbor interactions in a solvent-free two-component lattice representing the monolayer. By adopting the Bragg-Williams approximation, the chemical potential of an adsorbate i in the mixed monolayer is given by 

¼ μi þ kT½log xi þ χAB ð1 - xi Þ2  μSAM i

ð16Þ

(27) Kirkwood, J. G.; Oppenheim, I. Chemical Thermodynamics; McGraw-Hill: New York, 1961.

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Here, μ*i is the reference chemical potential of the adsorbate in a single-component lattice. Substitution of the expressions for the chemical potentials of the alkanethiols (eq 15) and the alkanethiolates (eq 16) into molar free energy (eq 14), after algebraic manipulation, yields the final expression for the molar Gibbs free energy of formation of the monolayer ! Rsoln ‡ þ xA log xA Δf ¼ ΔμB - log yB - xA log ‡ Rsoln þ xB log xB þ xA xB χAB Δμi‡

ð17Þ

μ†i)/kT

where = (μ*i and Rsoln = yA/yB is the ratio of the mole fractions of the two organic solute molecules in the solution. The phenomenological parameter R‡soln  exp(Δμ‡A - Δμ‡B) quantifies the difference in the reference chemical potentials of solutes and the adsorbates of organic species A and B. Minimization of the molar free energy with respect to the composition, after the rearrangement of terms, leads to a transcendental equation for the equilibrium surface coverage: !   xA Rsoln þ χAB ð1 - 2xA Þ ¼ log ‡ ð18Þ log xB Rsoln

Appendix B: Lattice Model of Three-Component Mixtures We give a brief treatment of the extension of the lattice model to a three-component mixture. The derived expressions for the chemical potential of the solutes (organic thiols) as a function of concentration and intermolecular interactions in the solution are used in the Theoretical Model section to aid in the determination of the equilibrium surface composition. Consider a lattice that is entirely populated by solute molecules (A and B) and solvent (S). Let the number of molecules of species i in the solution be designated as Ni. In the absence of voids within the lattice, the entropy of mixing in the solution, as represented by the above lattice, is simply Smix NA NB NS ¼ log N log NA log NB log NS Nk N N N ¼ - yA log yA - yB log yB - yS log yS ð19Þ where the total number of sites on the lattice is N = NA þ NB þ NS and yi = Ni/N is the mole fraction of each species in the solution. We shall assume that intermolecular interactions occur only between nearest neighbors on the lattice upon contact. Denoting the contact energy between two molecules i and j as wij, the (internal) energy of mixing in the lattice is the sum of all pair interactions between nearest neighbors in the three-component mixture Umix ¼ mAA wAA þ mAB wAB þ mAS wAS þ mBB wBB þ mBS wBS þ mSS wSS ð20Þ where mij is the number of i-j contacts or interactions between pairs i and j. In general, mij is not known a priori. A convenient

Langmuir 2010, 26(14), 11991–11997

approximation, known as the mean-field or Bragg-Williams approximation, is to assume that the molecules are randomly and uniformly mixed within the lattice. Although the mean-field approximation ignores correlations that can become important in situations where certain interactions (e.g., self-interactions) are more preferable than others, it is nonetheless a reasonable approximation in the study of multicomponent solutions especially at low solute molecule concentration.20 Within the Bragg-Williams approximation, the number of interacting pairs mij is20 mij ¼

zNi Nj N

mii ¼

zNi 2 2N

ð21Þ

Here, z is the coordination number of the lattice. By adopting the Bragg-Williams approximation, the internal energy of mixing (eq 20) now takes the form Umix z ¼ ½wAA NA 2 þ wBB NB 2 þ wSS NS 2 þ 2ðNA NB wAB 2N 2 kT NkT z þ NA NS wAS þ NB NS wBS Þ ¼ ½wAA yA 2 þ wBB yB 2 2kT þ wSS yS 2 þ 2ðyA yB wAB þ yA yS wAS þ yB yS wBS Þ

ð22Þ

The free energy of mixing is obtained by combining the expression for the entropy of mixing (eq 19) and the internal energy of mixing (eq 22): Fmix Umix Smix ¼ NkT NkT Nk z ½wAA yA 2 þ wBB yB 2 þ wSS yS 2 þ 2ðyA yB wAB ¼ 2kT þ yA yS wAS þ yB yS wBS Þ þ yA log yA þ yB log yB þ yS log yS ð23Þ Subsequently, the chemical potential of species i in the solution phase is determined from the partial derivative of the free energy with respect to its mole fraction. The resulting expressions for the chemical potentials of solutes A and B, after algebraic manipulation, are28 μsoln zwAA A ¼ log yA þ þ yB 2 χAB þ yB yS ðχAB þ χAS - χBS Þ þ yS 2 χAS kT 2kT μsoln zwBB B ¼ log yB þ þ yA 2 χAB þ yA yS ðχAB þ χBS - χAS Þ þ yS 2 χBS kT 2kT ð24Þ where the dimensionless exchange parameter is χij  z/(kT)[wij (wii þ wjj)/2]. (28) As discussed in the Theoretical Model section, we have ignored pressurevolume effects and assumed in the derivation of eq 22 that the changes in enthalpy and internal energy are effectively equal, Δh ≈ Δe = xAxBχAB.

DOI: 10.1021/la101464j

11997