Structural Rearrangements in Self-Assembled Surfactant Layers at

J. Phys. Chem. B 2010, 114, 3847–3854

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Structural Rearrangements in Self-Assembled Surfactant Layers at Surfaces Maria L. Sushko* and Jun Liu Pacific Northwest National Laboratory, Richland, Washington 99352 ReceiVed: NoVember 17, 2009; ReVised Manuscript ReceiVed: January 22, 2010

The transition from compact to extended configuration in ionic surfactant layers under the influence of salt, surfactant surface density, and temperature is studied using the classical density functional theory (cDFT). The increase in ionic strength of an aqueous salt solution or in the surfactant surface density leads to the transition from the hemicylindrical to the perpendicular monolayer configuration of the molecules. Although producing the same structural rearrangement in the surfactant layer, the origin of the effect of salt and surface density is different. While the addition of salt increases the out-of-plane attractive interactions with the solvent, the increase in density results in the increase in the in-plane repulsion in the surfactant layer. The temperature effects are subtler and are mainly manifested in the reduction of the solution structuring at elevated temperatures. 1. Introduction 1-5

the Since the discovery of self-assembled monolayers, modification of inorganic surfaces with organic layers proved to be a powerful method for controlling their physical and chemical properties. Moreover, organic layers can serve as a template for nucleation and growth of inorganic materials with well-controlled architecture. The latter mechanism is widely used in nature, where biomolecules direct the growth of mollusk shells, skeletal plates of echinoderms, eggshells, and many other amorphous, polycrystalline, and single-crystal biominerals.6-10 This ability of organic molecules to determine the architecture of inorganic materials has been recently utilized to synthesize mesoporous and mesostructured materials on surfactant templates.11-15 To further advance this important area of research with wide-ranging applications in catalysis,16 sensing and separation,17 energy conversion, and storage,18 it is crucial to gain a fundamental understanding of the mechanism of surfactant self-assembly at surfaces. Experimental studies have revealed that the analogues of many regular structures observed in surfactant solutions can form at surfaces.19-21 However, the forces governing the selfassembly at surfaces differ from those acting in the bulk solution. Apart from surfactant-solvent interactions, the interactions with the surface play a key role. For example, the structures formed on a hydrophilic neutral silica surface are quite different to those formed on a weakly charged mica or hydrophobic graphite.19 Molecular dynamics modeling of ionic and nonionic surfactant layers at surfaces confirmed the possibility of the hemicylinders’ formation on graphite.22-26 These simulations revealed that the nonionic surfactants with long tails form hemicylinders, while surfactants with shorter tails form monolayers on a graphite surface.23 Simulations of ionic surfactant layers on graphite in pure water showed the transition from the hemicylindrical configuration at low surface coverage to full cylinders at high coverage.25 While giving semiatomistic information on the structure of surfactant layers, coarse-grained molecular dynamics has several limitations. Force fields for organic/ inorganic interfaces are scarce and, therefore, often have to be fitted.27 Also, the complexity of the system usually limits the * To whom correspondence should be addressed. E-mail: maria. [email protected].

representation of the solvent to either pure water or water with self-counterions of ionic surfactants. It is too computationally expensive to consider a finite medium to high ionic strengths even on a coarse-grained level. An alternative coarse-grain method used to model surfactants at surfaces is the Monte Carlo (MC) method, which is generally more efficient with sampling the configurational space of aqueous salt solutions.28 However, sampling of the configurations of surfactant layers is more challenging in this approach, and the MC simulations are limited to short, up to about 10 coarse-grained monomers, surfactants.29 On the other end of the simulation spectrum are the meanfield models, which, in general, allow consideration of larger length and time scales via omitting the atomistic details of the system. The early attempts to access the full phase diagram of block copolymers and surfactants at surfaces employed the phenomenological Landau expansions30 or the self-consistent field theory (SCFT).31 Both approaches have been applied to model the thickness-dependent phase diagrams of di- and triblock copolymer films.32-40 The serious limitation of these approaches is a very loose connection between the parameters of the models with the intermolecular interactions in the systems. A compromise between the efficiency of the mean-field models and the details of coarse-grained models can be achieved in the framework of the classical density functional theory (cDFT). First introduced by Chandler, McCoy, and Singer (CMS),41,42 this method is based on the minimization of the freeenergy functional with respect to the densities of the components of the system. The original approach uses the quadratic density expansion of the free energy with respect to the ideal system. The CMS requires as an input the direct correlation functions from the polymer integral equation theory43 and the intramolecular correlation functions from a single-chain Monte Carlo simulation.41 The second flavor of the cDFT is based on the exact formalism for the ideal system and the generalized firstorder perturbation theory. The ideal part retains the details of bond connectivity, while all short-range interactions and chain correlations are treated using the weighted density approximation and first-order perturbation theory, respectively.44-46 Therefore, this approach retains the segmental level intermolecular forces as in the coarse-grained models. However, these interactions are derived analytically in the cDFT, rather than fitted for each particular system. The resulting high transferability of the cDFT

10.1021/jp910927b  2010 American Chemical Society Published on Web 02/25/2010

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J. Phys. Chem. B, Vol. 114, No. 11, 2010

and its computational efficiency render it a method of choice for modeling complex polymeric and surfactant systems to address such problems as phase transitions in polymeric melts,47 polyelectrolyte adsorption onto surfaces,48 properties of thin films,49-51 and vapor-liquid nucleation of amphiphiles.52,53 In this study, we use the extended cDFT model to elucidate the role of in-plane and out-of-plane forces in structural rearrangements in surfactant layers at surfaces. Although the adsorption of surfactants is mainly governed by the out-of-plane forces, the experimental evidence suggests the important role of surfactant surface density54 and, therefore, of the in-plain interactions between surfactant molecules. It has been found that spontaneous adsorption often results in low, well below the critical micellar concentration (cmc), surfactant concentrations at surfaces.21,55,56 Under these conditions, the hydrophobic interactions between the surfactants and surfaces prevail, which results in the orientation of surfactant tails parallel to the surface.57 However, achieving higher surface coverages (above the cmc) produces either vertical monolayer58 or hemicylindrical19 arrangement of the molecules. In this study, we investigate the possibility of the transitions between these two surface architectures of ionic surfactants under the influence of the ionic strength, surfactant density, and temperature. We aim to decouple the influence of the interactions with the solvent and the surface, the in-plain interactions in the surfactant layer, and the solvent structuring effects.

Fid ) kT

∫ dRbF

b

M(R)[ln

b) - 1] + FM(R

kT

∫ dRbF

b

b +

M(R)Vb(R)

r (b)[ln r F (b) r - 1] ∑ ∫ dbF R

R

(1)

R)+,-

b) is a multidimensional density profile of surfactant where FM(R b2, segments as a function of surfactant configuration b R ≡ (r b1,r b) are the density profiles of small ions. ..., b rM) and FR(R The excess free energy is not known exactly, and certain approximations have to be made. In our model, the hard-sphere repulsion, electrostatic correlation, direct Coulomb, chain connectivity, segment/segment, and segment/surface attraction or repulsion terms have been included in the expression for the excess Helmholtz functional ex ex Fex ) Fhs + Felex + FCex + Fex ch + Fatt

(2)

The hard-sphere repulsion was calculated using the Fundaex ) mental Measure Theory.60 The corresponding free energy (Fhs can then be expressed as an integral of the functional of b)) weighted densities (nω(r

Fex ha ) kT

r b r ∫ Φhs[nω(b)]d

(3)

The electrostatic correlation term (Fex el ) can be derived using the Mean Spherical Approximation61,62

2. Methods Classical Density Functional Theory (cDFT). To determine the equilibrium configuration of a multicomponent system of surfactants at surfaces in aqueous salt solution, we use classical DFT.29,59 In our model, the surfactant molecules are approximated as chains of spherical segments or monomers of types A and B. Surfactant monomers have the same diameter, σs ) 0.6 nm, while their charges and attractive/repulsive interaction potentials (see below) depend on the type. The surface is approximated as a flat hard wall and the aqueous salt solution as a dielectric medium with ε ) 78 and a certain density of spherical positively and negatively charged particles, representing the ions. In this work, we considered aqueous NaCl solutions. Therefore, the diameters of the mobile ions were σ+ ) 0.23 nm and σ- ) 0.33 nm, and their charges were q+ ) 1 and q- ) -1, which corresponds to ionic diameters and charges of Na+ and Cl-, respectively. To determine the equilibrium configuration of the system, the total Helmholtz free-energy functional is minimized with respect to the densities of all of the species. It is convenient to partition the total free energy of the system into so-called ideal (Fid) and excess parts (Fex). The ideal free energy corresponds to the free energy of noninteracting surfactant molecules in solution. It is determined by the contributions from surfactant and small ion configurational entropies and the surfactant b). The latter is defined intramolecular bonding potential, Vb(R as

b)/kT) ) exp(-Vb(R

Sushko and Liu

kT 2

r b′ r ∑ A dbd

σs)/4πσs2)

∫ dbr ∑

∆C(2)el r ij (| b

∆C(1)el r - Fbulk R (FR(b) R )-

R)+,-

- b′|)(F r r - Fbulk )(Fj(b′) r i(b) i

i,j)+,-

Fbulk ) j

(4)

where the first- and second-order direct correlation functions are defined as

∆C(1)el ) -µelR /kT R

(5)

∆C(2)el r - b′|) r ) ij (| b

{

qiqje2 1 κ - 4κ2(| b r - b′|) r kTε (| b r - b′|) r 0

[

]

(| b r - b′|) r e σij (| b r - b′|) r > σij

(6)

In these equations µelR is the chemical potential of the mobile ions, κ is the inverse Debye length, and σij ) (σi + σj)/2. The direct Coulomb term is calculated exactly, giving the following free-energy contribution

FCex )

M-1

∏ (δ(|br i+1 - br i| -

ex bulk Fex el ) Fel [{FR }] - kT

kTlB 2 i,j)B,+,-

∑ A

qiqjFi(b)F r j(b′) r dbd r b′ r |b r - b′| r

(7)

i)1

where M is the total number of segments in each surfactant molecule and δ is the Dirac delta function. The ideal free energy can be calculated exactly as

where qi(j) are the valences of the charged species and the Bjerrum length is defined as lB ) e2/kTε. The formation of bonds between surfactant segments leads to the loss in entropy of the system, which can be expressed using the first-order perturbation theory63 as

Structural Rearrangements in Surfactant Layers

Fex ch ) kT

1-M M

J. Phys. Chem. B, Vol. 114, No. 11, 2010 3849

∫ n0 ln(y(σi, nω))dbr

(8)

In this expression, M is the number of segments in the chain. The expression for the contact value of the cavity correlation function, y(σi,nω), is given elsewhere.64-66 We use simple square-well potentials to describe the attraction/repulsion interactions between surfactant segments and between the segments and the surface in the form

{

∞ r γσs

(9)

{

εij 0 < r < σs 0 otherwise

φiw(r) )

(10)

where indexes i,j run over all surfactant monomers, w stands for wall, r is the distance between the surfaces of the spheres or the sphere and the wall, respectively, and γ ) 1.2 as in ref 29. The corresponding mean-field approximation for the free energy for these nonbonded interactions is then ex Fatt )

1 2

r b′ r ∑ ∫ ∫ dbd

Fi(b)F r j(b)φ r ij(| b r - b′|) r +

i,j∈A,B

r iw(r) + ∫ dr ∑ Fj(b)φ r jw(r) ∫ dr ∑ Fi(b)φ i∈A

(11)

j∈B

For surfactants at surfaces, the density profiles are only changing in the direction normal to the surface. Therefore, in the following, we will consider a one-dimensional case. We choose the coordinate system with the z-axis normal to the surface with the origin at the surface. Then, the minimization of the grand potential leads to the following set of equations for the density profiles of surfactant segments and small ions29,65

[

FR(z) ) exp

µR - λR(z) kT

[ ]∑

GLi (z) exp -

[ ]∑

GLi (z) exp -

FA(z) ) exp

FB(z) ) exp

µM kT

µM kT

i∈A

i∈B

]

(12)

[

λi(z) i GR(z) kT

]

(13)

[

λi(z) i GR(z) kT

]

(14)

where the left and right recurrence functions are calculated as

GLi (z) )

1 2σs

z+σ ∫z-σ

GRi (z) )

1 2σs

z+σ ∫z-σ

s

s

s

s

[

λi-1(z) i-1 GR (z)dz kT

[

λi+1(z) i+1 GR (z)dz kT

exp -

exp -

]

(15)

]

(16)

with GL1(z) ) 1 and GRM(z) ) 1. Index i ) 1, 2, ..., M. In these expressions, the effective field λk is defined as

λk(z) )

∂Fex + ψk(z) ∂Fk(z)

(17)

where ψk(z) is the external potential. The chemical potential of mobile ions, µR, in eq 10 is calculated using the overall electroneutrality condition. Equations 12-14 can be solved selfconsistently using a Picard iteration method. The output densities were constructed from the input densities using the mixing parameter of 0.005. The convergence was considered to be achieved when the difference between the input and the output density profiles became smaller than 10-6. We used a grid of 500 points along the z-direction equally spaced by distances of σs/10. The model was implemented in a Fortran code, which was used in all calculations reported here. The electrostatic component of the code was extensively tested earlier on the examples of polyelectrolyte brushes and DNA monolayers.67 Therefore, it would be sufficient to test only the nonelectrostatic part here. We will use the example of AB-type nonionic surfactants in a pure aqueous solution for the purpose. 3. Results and Discussion 3.1. Nonionic Surfactants: Testing the Method. The rich phase behavior of nonionic surfactants at surfaces has been extensively probed using experimental and theoretical methods. Coarse-grained molecular dynamics (MD),22,23 Monte Carlo (MC), and cDFT simulations29 showed the dependence of the structure of the surfactant layer at surfaces on the interactions between the blocks and the blocks with the surface. To test the cDFT method, we have considered block AAABBB surfactants in aqueous solution at a wall with two sets of short-range interaction parameters: (i) Short-range interactions between similar blocks are attractive and larger than attractive interactions between dissimilar blocks (εAA ) -4.525 eV, εBB ) -4.360 eV, εAB ) -1.962 eV), short-range interactions between block A and the wall are weakly attractive (εAW ) -0.3085 eV), while the interactions of block B with the wall are weakly repulsive (εBW ) 0.02 eV). The values of the parameters for these interactions correspond to the values in the coarse-grained model reported in ref 23. (ii) A qualitatively similar case, but blocks A and B repel each other. The parameters, corresponding to those used in ref 29, are εAA ) -1.0 eV, εBB ) -0.5 eV, εAB ) 0.5 eV, εAW ) -0.5 eV, εBW ) 0.5 eV. For direct comparison, in both cases, the initial surfactant surface density was 0.0216 nm-2. The calculations of the equilibrium configurations of these nonionic surfactants at the surface revealed very different molecular arrangements (Figure 1). The densities of blocks B span the region of 0.3-1.2 nm above the surface in the first case, while these blocks are confined to the region [0.6 nm, 1.2 nm] in case (ii). The density profiles of blocks A are, on the contrary, very similar due to a similar qualitative character of their interactions with the wall and themselves. The density profile of blocks B for case (i) is consistent with the hemicylindrical configuration of the molecules observed in molecular dynamics simulations and AFM experiments.19,23 Indeed, for this configuration, the density of blocks B should have two regions, the region close to the surface with a lower density and a region above the A blocks with a higher density (see inset to Figure 1a). Our calculations show that a change in the short-range interaction parameters (case (ii)) leads to the change in the

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Figure 1. Density profiles of nonionic AAABBB surfactant segments as a function of distance from the surface. Densities of segments A and B are shown as solid and dashed lines, respectively. The attraction/ repulsion parameters are as those in ref 23 (a) and as those in ref 29 (b) (see text for details). The cross sections of surfactant layers corresponding to the density profiles are shown in the insets. Blocks A are shown as blue spheres and blocks B as yellow spheres.

equilibrium surfactant layer structure (Figure 1b). Now, the density peaks for A and B blocks are almost separated in space, with blocks A at the surface and blocks B further away. These density distributions correspond to the case of molecules forming a monolayer with the molecules standing at a certain angle to the surface (see inset to Figure 1b). The average monolayer height is 1.1 nm, which corresponds to an average 72° tilt angle of the molecules. The monolayer structure is not perfect, as indicated by the asymmetry of the block B density profile. Therefore, the tilt angle and the tilt direction of the molecules may vary. The data obtained for cases (i) and (ii) are in line with the results of the MD23 and the MC/cDFT29 literature data, respectively, which validates the use of the method for other surfactant systems. In particular, in the next section, the model is applied to ionic surfactant layers at surfaces and is used to elucidate the influence of in-plane and out-of-plane forces on their structure.

Sushko and Liu

Figure 2. Schematic representation of out-of-plane forces acting on ionic AAAAAAB surfactants at high (a) and low (b) bulk ionic strength. Red arrows show the attractive force between the charged blocks B (red spheres) and counterions in solution (gray spheres). The blue arrows show the cumulative force acting between blocks B and blocks A (blue spheres) in the direction to the surface.

3.2. Ionic Surfactants. 3.2.1. Effect of Bulk Ionic Strength. To probe the effect of the ionic strength of the solvent on the structure of surfactant layers at surfaces, we have considered the AAAAAAB surfactants with a neutral block A and charged block B with charge equal to -1. The short-range interactions of block A with the wall are attractive (εAW ) 0.5 eV), while they are repulsive for block B (εBW ) -0.5 eV). The interactions between dissimilar blocks are attractive (εAB ) 0.05 eV). We considered the solutions of a 1:1 electrolyte and the diameters of the co- and counterions corresponding to the ionic diameters of Cl- (σco ) 0.23 nm) and Na+ (σctr ) 0.33 nm), respectively. The change in ionic strength of the solvent influences the balance of surfactant group B attractive and repulsive interactions with other components of the system. Namely, group B has two opposing forces acting on it in the direction perpendicular to the surface, the attraction to counterions in solution and the attraction to blocks A, which are, in turn, attracted to the surface (see Figure 2). Our calculations show that there are three regimes with different structures of the surfactant layer and different distributions of ions in solution. In the regime of low ionic strength, the attractive interactions between groups B and solution are weaker than those with blocks A (Figure



Figure 4. Density profiles of ionic AAAAAAB surfactant segments (a) and co- and counterions (b) as a function of the distance from the surface. The following parameters were used: surfactant surface density 0.02 nm-2, bulk salt content 0.01 M NaCl, temperature 298 K. The same notations as those in Figure 3 were used.

Figure 3. Density profiles of ionic AAAAAAB surfactant segments (a) and co- and counterions (b) as a function of the distance from the surface. The following parameters were used: surfactant surface density 0.02 nm-2, bulk salt content 0.001 M NaCl, temperature 298 K. The density profiles of blocks A (a) and the co-ions (b) are shown as solid lines, and the density profiles of blocks B (a) and the counterions (b) are shown as dashed lines. The possible structures of the surfactant layer are shown schematically in (c) and (d). The 1-3 regions in (a) correspond to the 1-3 regions in (c). The same notations as those in Figure 2 were used. Note that the solid line in part (b) is very close to the horizontal axis.

2b). This results in a compact structure of the surfactant layer with blocks A close to the surface and blocks B further away (Figure 3a). To compensate for the energetically unfavorable in-plane repulsion between like-charged B groups, the counterion density around these groups is significantly increased (Figure 3b). Moreover, there is an excess of counterions at the surface, which further increases the force acting on groups B in the direction toward the surface. This redistribution of counterions, leading to the increase in their density near the surface, also results in the decrease in their density above the surfactant layer. The latter leads to the decrease in attractive interactions between groups B and solution. The three-peak density distribution of groups B is consistent with a hemicylindrical arrangement of surfactants. However, contrary to the case of the nonionic surfactants, discussed above, blocks B are not present at the surface. Therefore, the suggested structure can be as shown in Figure 3c. The surfactant molecules do not form a whole half-cylinder but a smaller section of the cylinder. Alternatively, the structure of the surfactant layer may

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Sushko and Liu

Figure 5. Density profiles of ionic AAAAAAB surfactant segments (a, c) and co- and counterions (b, d) as a function of the distance from the surface. The following parameters were used: surfactant surface density 0.02 nm-2, bulk salt content 0.03 M (a, b) and 0.05 M NaCl (c, d), temperature 298 K. The same notations as those in Figure 3 were used.

be similar to the structure of a monolayer with three preferential tilt angles of the molecules (Figure 3d). However, the two-peak density profile for the counterions points to a hemicylindrical configuration. Indeed, in this configuration, counterions can be accommodated in the “gaps” between the cylindrical sectors, giving rise to the first narrow peak at the surface. The latter would not be possible in a disordered monolayer configuration. The increase in the bulk concentration of the 1:1 electrolyte results in a stronger electrostatic correlation between counterions. This effect is manifested in a more complex counterion distribution in the system (Figure 4). Apart from several peaks in the density profile of counterions in the vicinity of charged groups B, the long-range solution structuring is also observed (Figure 4b). The distribution of surfactant groups is very similar to that in a low salt regime. The only change is in the relative peak heights for groups B, which suggests small structural changes in the surfactant layer. However, these quantitative changes do not affect the qualitative structure of the layer up to salt concentrations of 0.03 M. We observe a phase transition in the structure of the surfactant layer at a 1:1 electrolyte concentration of 0.03 M (Figure 5). At this salt content, strong electrostatic interactions between

charged groups B and solution shift the balance of forces toward repulsion from the surface. Although blocks A are still attracted to the surface, most molecules assume a fully stretched configuration normal to the surface, while the rest form a small angle with the surface, similar to that in Figure 4. The distribution of the mobile ions also splits into two bands, the band with two peaks closer than 1 nm to the surface and the band with several peaks in the region of 3.5-4.2 nm. This allows for the screening of electrostatic interactions between groups B in this dual character system. For even higher salt content, the molecules become fully stretched, forming a perfect monolayer (Figure 5c). In this regime, the counterion density has two peaks, one just below and one just above groups B for the effective screening of inplane repulsive forces (Figure 5d). It is noteworthy that our results are in line with experimental observations.54 However, the salt-induced transition have not been observed in atomistic molecular dynamics simulations.26 One of the possible reasons for this difference is that global rearrangement of the surfactant layer may not happen on the nanosecond time scales accessible for the atomistic simulations.



Figure 6. Schematic of AAAAAAB surfactant monolayer structures for low (top) and high (bottom) surfactant surface densities. The same notations as those in Figure 2 were used.

3.2.2. Effect of Surfactant Concentration. To investigate the relation between the structure and the density of the surfactant layer at the surface, we have considered AAAAAAB surfactants in a 0.001 M NaCl solution with surfactant densities of 0.005-0.05 nm-2. Our cDFT calculations showed that upon the increase in surface surfactant density, the structure of the layer changes from compact to fully stretched, similar to that presented in Figure 5c,d (Figure 6). The transition takes place at 0.03 nm-2. At this surfactant density, molecules form a monolayer with zero tilt angle. The distribution of the counterions in the system also changes accordingly; at low surfactant density, the counterion density profile has two peaks centered at 0.2 and 0.85 nm from the surface (as in Figure 3b), while for high density, the peak of the distribution shifts to 3.8 nm. This structural transition in the surfactant layer is associated with the increase in electrostatic repulsion between charged B groups. As the density of the surfactant layer increases, the inplane electrostatic repulsion become stronger due to the reduction of the distance between charges. The stretched configuration becomes more energetically favorable as it maximizes the distance between the charges and allows for better access to these groups by the counterions. At the transition point, the average distance between groups B is approximately equal to 3.2 nm if we assume a hexagonal arrangement of the molecules. The latter distance is significantly larger than the maximum distance between these groups in a hemicylindrical configuration, equal to 2.6 nm (for a hemicylinder with a cross section of six fully stretched molecules). 3.2.3. Effect of Temperature. To investigate the effect of temperature on the structure of the surfactant layers, we have studied AAAAAAB surfactants with an initial surface density of 0.02 nm-2 in solutions of 0.001 and 0.01 M NaCl. The results reported in two previous sections suggest that the structural properties of the surfactant layers in 0.001 M solutions are mainly determined by the balance of electrostatic and short-range attractive/repulsive interactions. Both types of interactions do not depend on temperature, that is, they give a purely enthalpic contribution to the excess free energy (see eqs 7, 9-11). Therefore, one would expect the temperature changes not to influence the structure of the surfactant layer. Our calculations for the AAAAAAB surfactant at a wall in a 0.001 M NaCl solution for temperatures varying between 298 and 500 K confirm this conclusion. For all temperatures studied, the surfactant and mobile ion density profiles were the same. It is noteworthy, that the density profiles calculated using our one-dimensional model represent the densities averaged over the x-y planes. Therefore, our model is not sensitive to the

Figure 7. Density profiles of co- and counterions inside and outside of an ionic AAAAAAB surfactant layer as a function of the distance from the surface. The following parameters were used: surfactant surface density 0.02 nm-2, bulk salt content 0.01 M NaCl, temperature 500 K. The same notations as those in Figure 3 were used.

local variations of the in-plane distributions of ions and surfactant segments. The entropic effects, however, are often local. For example, in self-assembled monolayers, the elevation of temperature causes the increase in the number of rotational and gauche defects without significantly influencing its global structure, defined by the average tilt angle of the molecules.68,69 For a higher bulk concentration of the salt, ion correlation forces also become important. The strength of these interactions changes with temperature since both entropy and enthalpy contribute to Fex el . Calculations for the surfactants in a 0.01 M NaCl solution show a decrease in the long-range solvent structuring at elevated temperatures (Figure 7). However, hardly any changes in the surfactant structure at the surface were found up to the temperatures of 500 K. 4. Conclusions We have investigated the structural transitions in ionic surfactant layers at surfaces using classical density functional theory. The method allows an efficient calculation of the equilibrium properties of complex surfactant systems in a wide range of surfactant concentrations and solvent compositions. While retaining the segment-level details of the system, cDFT does not require a force field fitting as it uses the analytically derived expressions for inter- and intramolecular interactions in the system. The model has been tested against the available literature data for nonionic surfactants at surfaces. The study of the effect of bulk salt content in the solvent on the structure of ionic surfactant layers revealed the transition from the hemicylindrical to monolayer configurations at 0.03 M NaCl. The transition was induced by the shift of the balance of out-of-plane interactions in the system toward the attraction to bulk solution. A qualitatively similar transition was observed upon the increase of surfactant density on the surface. However, the driving force for this transition is the change in the strength of in-plane repulsive forces in the surfactant layer. The investigation of the temperature effect on the equilibrium properties of the system confirmed the dominant role of in- and out-of-plane van der Waals and Coulomb interactions in determining the structure of the surfactant layer. It also revealed

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the decrease in solution structuring at elevated temperatures caused by the weakening of the ion correlation interactions between the mobile ions. Acknowledgment. The development of the cDFT software is supported by the Laboratory-Directed Research and Development Program at Pacific Northwest National Laboratory (PNNL). The study of surfactant self-assembly at surfaces is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award KC020105-FWP12152. PNNL is a multiprogram national laboratory operated for DOE by Battelle under contract DE-AC05-76RL01830. References and Notes (1) Nuzzo, R. G.; Allara, D. L. J. Am. Chem. Soc. 1983, 105, 4481. (2) Finklea, H. O.; Avery, S.; Lynch, M.; Furtsch, T. Langmuir 1987, 3, 409. (3) Bain, C. D.; Whitesides, G. M. Science 1988, 240, 62. (4) Strong, L.; Whitesides, G. M. Langmuir 1988, 4, 546. (5) Troughton, E. B.; Bain, C. D.; Whitesides, G. M.; Nuzzo, R. G.; Allara, D. L.; Porter, M. D. Langmuir 1988, 4, 365. (6) Meldrum, F. C.; Colfen, H. Chem. ReV. 2008, 108, 4332. (7) Aizenberg, J.; Black, A. J.; Whitesides, G. M. Nature 1999, 398, 495. (8) Aizenberg, J.; Weaver, J. C.; Thanawala, M. S.; Sundar, V. C.; Morse, D. E.; Fratzl, P. Science 2005, 309, 275. (9) Evans, J. S. Chem. ReV. 2008, 108, 4455. (10) Killian, C. E.; Wilt, F. H. Chem. ReV. 2008, 108, 4463. (11) Liu, J.; Kim, A.; Wang, L. Q.; Palmer, B. J.; Chen, Y. L.; Bruinsma, P.; Bunker, B. C.; Exarhos, G. J.; Graff, G. L.; Rieke, P. C.; Fryxell, G. E.; Virden, J. W.; Tarasevich, B. J.; Chick, L. A. AdV. Colloid Interface Sci. 1996, 69, 131. (12) Antonietti, M. Curr. Opin. Colloid Interface Sci. 2001, 6, 244. (13) Xiao, F. S. Curr. Opin. Colloid Interface Sci. 2005, 10, 94. (14) Goltner-Spickermann, C. Curr. Opin. Colloid Interface Sci. 2002, 7, 173. (15) Brinker, C. J.; Dunphy, D. R. Curr. Opin. Colloid Interface Sci. 2006, 11, 126. (16) Taguchi, A.; Schuth, F. Microporous Mesoporous Mater. 2005, 77, 1. (17) Liu, N. G.; Dunphy, D. R.; Atanassov, P.; Bunge, S. D.; Chen, Z.; Lopez, G. P.; Boyle, T. J.; Brinker, C. J. Nano Lett. 2004, 4, 551. (18) Liu, J.; Cao, G. Z.; Yang, Z. G.; Wang, D. H.; Dubois, D.; Zhou, X. D.; Graff, G. L.; Pederson, L. R.; Zhang, J. G. ChemSusChem 2008, 1, 676. (19) Manne, S.; Gaub, H. E. Science 1995, 270, 1480. (20) Manne, S.; Cleveland, J. P.; Gaub, H. E.; Stucky, G. D.; Hansma, P. K. Langmuir 1994, 10, 4409. (21) McDermott, D. C.; McCarney, J.; Thomas, R. K.; Rennie, A. R. J. Colloid Interface Sci. 1994, 162, 304. (22) Nielsen, S. O.; Srinivas, G.; Lopez, C. F.; Klein, M. L. Phys. ReV. Lett. 2005, 94, 228301. (23) Srinivas, G.; Nielsen, S. O.; Moore, P. B.; Klein, M. L. J. Am. Chem. Soc. 2006, 128, 848. (24) Bandyopadhyay, S.; Shelley, J. C.; Tarek, M.; Moore, P. B.; Klein, M. L. J. Phys. Chem. B 1998, 102, 6318. (25) Dominguez, H. J. Phys. Chem. B 2007, 111, 4054. (26) Dominguez, H. Langmuir 2009, 25, 9006.

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