Bridge Structure: An Intermediate State for a ... - ACS Publications

From lattice Monte Carlo simulations, we found that an intermediate state, which is called the bridge structure, may exist during the phase transition...
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J. Phys. Chem. C 2007, 111, 7144-7151

Bridge Structure: An Intermediate State for a Morphological Transition in Confined Amphiphile/Water Systems Fengxian Zheng, Xianren Zhang,* and Wenchuan Wang DiVision of Molecular and Materials Simulation, Key Lab for Nanomaterials, Ministry of Education, Beijing UniVersity of Chemical Technology, Beijing 100029, China ReceiVed: January 7, 2007; In Final Form: March 19, 2007

From lattice Monte Carlo simulations, we found that an intermediate state, which is called the bridge structure, may exist during the phase transition of confined amphiphile/water systems, such as a transition from the monolayers on each solid surface to bilayer structures between the adsorbed monolayers. Extensive simulation results show that the occurrence of the bridge phase during the monolayer/bilayer transitions depends on the transition path and surfactant architecture. In addition, it is suggested that the bridge structure found in this work may be one possible origin for long-range hydrophobic forces.

Introduction Atomic force microscopy (AFM) perhaps has made the greatest advance in our understanding of the aggregate morphology of adsorbed surfactants on solid-/liquid interfaces in the past decade. However, several studies showed that significant changes in adsorption might occur upon the approach of the AFM tip apex to the substrate. Wanless et al. demonstrated that the approach of the AFM tip would result in an attractive interaction that precludes the imaging of interfacial structures.1-2 Ducker et al.3,4 demonstrated that the magnitude of a change in surface excess was significant for the cationic surfactants adsorbed to silica surfaces, due to the change of the nature of the interaction force between the AFM tip and the surface. Therefore, the confinement space between the AFM tip and the substrate exerts a strong influence on interfacial structures. In addition, surfactants in confined spaces are also important because they can influence colloidal stability, which is relevant to many applications where surfactants are used as additives (e.g., ceramic processing, wastewater treatment, and formulation of personal products). Recently, the effects of confinement on various complex systems have been studied extensively.5-15 The phase behavior of a symmetrical binary AB polymer bend confined into a thin film was studied by self-consistent theory.5,6 Various phenomenological theories15-19 and Monte Carlo (MC) simulations15,20-21 were also used to study the phase diagram of symmetric diblock copolymer thin films between two hard surfaces. However, only a few experimental22-29 and theoretical30-33 studies have been reported on the morphology of surfactants in confined spaces. Leermakers et al.32 used the self-consistent field theory (SCF) to investigate surfactant adsorption in confined spaces. A confinement-induced first-order phase transition was observed and was accompanied by a discontinuous change in the surface excess, which occurs upon increasing or decreasing the distance between the hydrophobic surfaces. They also applied this theory to consider a solution of positively charged surfactants up to its critical micelle concentration adsorbed onto two amphiphilic surfaces. Similarly, a confinement-induced first-order phase transition of a surfactant layer adsorbed on a charged amphipolar * Corresponding author. E-mail: [email protected].

surface was investigated in detail. At the transition, the adsorbed surfactant layer changed from a monolayer to a bilayer structure, and the interaction force jumped from a weak electrostatic repulsion at large distances to a strong electrostatic attraction at short distances.33 SCF theory is simple and very efficient to study surfactant adsorption both in wide gaps and in confined spaces. However, because the theory is based on the mean field approximation, composition fluctuations are not considered. Using the Landau-Ginzburg model of microemulsions, Hołyst et al.34 studied the behavior of the surfactant/oil/water system confined to two parallel walls. They found35 various structural changes in the internal surface, which occur in a confined surfactant/oil/water system, as a function of the boundary conditions and the size of the system. Most interestingly, it was found that confinement of the lamellar phase induces topological fluctuations of its interface in the form of passages in the system. Because wormhole passages were observed to form and disappear spontaneously, they were called fluctuations. Inspired by the works of Hołyst and his coworkers,34,35 we want to determine that besides the phase transition and fluctuation in the interface, as is pointed out by Hołyst et al., whether there are any morphology changes of the surfactant layers induced by confinement in the amphiphile/ water system. The Landau-Ginzburg model is no longer appropriate here because we focus on the subtle structure changes of the surfactant layers, rather than treating the interfaces as structureless layers. In this work, thus, the lattice Monte Carlo (LMC) method is used. It is noted that SCF is an alterative way to study phase behavior; however, as compared with SCF, molecular simulations (MC and molecular dynamics) are more efficient to observe topological fluctuations. In this work, we concentrated on various topological changes, which occur in a confined surfactant solution system, as a function of the distance between the walls as well as the surfactant concentration. An interesting bridge structure may appear during the morphology transition from the structure of monolayers adsorbed on each solid surface to the formation of a bilayer between the adsorbed monolayers, depending on the transition path and surfactant architecture. To identify the existence of the bridge structure in a confined space, phase

10.1021/jp070124z CCC: $37.00 © 2007 American Chemical Society Published on Web 04/25/2007

Bridge Structure: Transition in Amphiphile/Water

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Figure 1. Typical snapshots of the systems of H4T4 in confined space for different distances between the walls. (a) Two adsorbed monolayers for Lz ) 10; (b) bridges between two monolayers for Lz ) 13; and (c) bilayer between adsorbed monolayers for Lz ) 17. In these snapshots, only tail groups are shown for clarity. The surfactant concentration in volume fraction is approximately 88.9%.

diagrams of different surfactant structures were determined from extensive simulations. Models and Methods In this work, the MC method based on Larson’s lattice model36,37 was used to simulate the behavior of surfactant solutions confined in two parallel hydrophobic surfaces. The model uses a fully occupied simple cubic lattice, in which a site interacts equally with all 26 sites that are located within one lattice spacing in each of the three directions. Amphiphiles are constructed by linking together a number of water-like (heads) and oil-like sites (tails). Each lattice site is occupied by one segment of a surfactant molecule or a solvent molecule. The energy of the surfactant system is defined as the sum of all nearest-neighbor contacts. The behaviors of surfactant systems, such as the micellization and phase equilibria of surfactant systems38-41 and micelle formation dynamics,42,43 were widely studied by using the model. Panagiotopoulos and co-workers used the model and MC method to investigate the behavior of confined cylindrical micelle-forming surfactants under the influence of shear stress.44,45 Gubbins and his co-workers also

Figure 2. Density profiles corresponding to the cases in Figure 1: (a) Figure 1a, (b) Figure 1b, and (c) Figure 1c, respectively. Statistical uncertainties are smaller than the symbol size.

used this model to study the phase separation and self-assembly in supercritical solvent-surfactant46-48 and the surfactantinorganic-solvent systems.49,50 In our previous work,51 we used the model to study the morphological transition of surfactants adsorbed on solid surfaces. In this work, the simulation box is of the dimension Lx × Ly × Lz with the periodic boundary conditions in the x and y directions. Hard walls are located in the layers z ) 0 and z ) Lz + 1. The abbreviation HxTy is used to denote an amphiphile, which has x hydrophilic head groups and y hydrophobic tail groups. The volume fraction for the surfactant concentration is defined as φ ) (x + y)N/V, where N is the number of amphiphiles and V is the lattice volume. In the present paper,

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Figure 3. Minkowsiki functionals as a function of Lz. (a) Average surface area (S/Lx2), (b) mean breath (B/Lx, proportion to mean curvature), (c) average Euler characteristic 〈χ〉, (d) its variance 〈χ2〉 - 〈χ〉2, (e) average total energy per lattice site, and (f) heat capacity per lattice site. Solid lines are for the system with artificial treatment, and dashed lines are for the system without artificial treatment. The surfactant (H4T4) concentration in volume fraction is approximately 88.9%.

the simulation box sizes in the x and y directions were 30 lattice sites (i.e., Lx ) Ly ) 30). To control the computing time, Lx ) Ly ) 20 was used to obtain phase diagrams. The length in the z direction was changed to study the effect of confinement on the surfactant solution. The bottom and upper surfaces of the simulation box in the z direction were both hydrophobic surfaces. Three kinds of surfactant solutions: H4T4, H4T3, and H2T4 were studied in this work at a reduced temperature of 7.0 as used by Mackie et al.38 Nearest-neighbor pairs of sites (head, tail, and solvent) have interaction energies as follows: HH, TT, HT, WW, HW, and TW, where the subscript W stands for water molecules. The interaction parameters were chosen in this work as follows: HH ) 0, TT ) 0, HT ) 1, WW ) 0, HW ) 0, and TW ) 1. The interaction parameters are equivalent to those used by Pana-

giotopoulos and co-workers.40,41 The interactions between solid, surfactant chain monomers, and water are represented by HS, TS, WS, respectively, where S denotes the solid surface. In this work, these parameters were set to HS ) 9,TS ) -9,WS ) 0. The reason to choose TS ) -9 is that the surfaces in simulation boxes are hydrophobic. Here HS ) 9 is chosen somewhat arbitrarily to represent the unfavorable interaction between a hydrophilic head group and the hydrophobic surface. Note that the effects of HS ) 9 on the adsorption structure are negligible. As for all the simulated systems, initial configurations were generated by placing amphiphilic chains to replace water sites at random positions on a lattice. To avoid configurations with overlaps, the Rosenbluth and Rosenbluth algorithm52 was used to obtain the initial chain conformations. An amphiphile is considered to be a part of a cluster if any of its tail segments is

Bridge Structure: Transition in Amphiphile/Water in contact with any tails of another surfactant in the cluster. To sample the phase space efficiently, it is necessary to consider the moves for both monomers and aggregates. Reptation and chain regrowth moves were implemented in addition to the cluster move to explore the phase space efficiently, as done by Mackie et al.38,39 A typical mix of the Monte Carlo moves used was 80% reptations, 19.99% regrowth, and 0.01% cluster moves, as was used by Mackie et al.39 Simulations were carried out for at least 6 × 106 MC cycles, in which 3 × 106 was used to equilibrate the system. One MC cycle is defined as each surfactant moving once on average. To obtain statistical uncertainties, the production part of a simulation run was divided into five sub-blocks. The statistical uncertainties were obtained as the standard deviations of results from the five sub-blocks. To determine the mechanisms in the structure transition in confined surfactant systems, modern integral geometry morphological measures, which are called Minkowski functionals, were used in this work. For a three-dimensional system, there are four independent Minkowski functionals: the volume V, the surface area S, the average mean curvature H of the surface, and the Euler characteristic χ. Euler characteristics can be effectively used in such simulations to identify different phases and topological fluctuations, as suggested by Hołyst and Gozdz.53 The Minkowski functionals were computed according to the algorithm described by Michielsen and De Raedt.54,55 This procedure described in the literature55 is valid for the coexisting phases consisting of pure components only.56 For systems in which the composition of the coexisting phases is not 1 and 0, one has to apply the procedure described by Aksimentiev et al.57 In our work, in order to adapt the confined system of the surfactant solutions to the procedure, we translated the lattice sites into segments of type A (1), when 50% or more of their 26 nearest and next-nearest neighbors were segments tails. Otherwise, the lattice site was translated into segment B (0). With this kind of transitions, we can also exclude the effects of small aggregates on the Euler characteristic. Results and Discussion Effects of Distance between Walls. First, simulations were performed for the surfactant solutions of 88.9% H4T4 confined between two parallel hydrophobic surfaces with the increase of their distance Lz from 10 to 20 by an increment of 1. It was found that there existed three morphologies of the systems. Besides the two expected morphologies (i.e., the type of two adsorbed monolayers and the structure of the bilayer between the adsorbed monolayers), the structure of the bridges between the two adsorbed monolayers was observed (as intuitively shown in Figure 1b). The snapshots for the three typical morphologies are shown in Figure 1a-c, respectively. To confirm these structures, their corresponding segment density profiles are presented in Figure 2a-c, respectively. For the system of Lz ) 10, two monolayers of the adsorbed surfactants were formed due to hydrophobicity of the surfaces, as shown in Figure 1a. This observation is supported by the segment density profiles of surfactant and solvent in Figure 2a. This type of morphology is called a monolayer for simplicity hereafter. An interesting morphological structure was found for the system with the larger pore size, Lz ) 13, in which there were many bridges connecting the two adsorbed monolayers (see Figure 1b). For simplicity, we called the morphology the bridge structure. Because of the existence of the bridges, the tail segment density in Figure 2b increased in the middle of the simulation box accordingly. As the distance between the two walls increased further, besides the two adsorbed monolayers, there was still one layer in the

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Figure 4. Euler characteristic as a function of time (MC cycle) in 88.9% H4T4 solution with Lz ) 15.

middle of the system, as shown in Figure 1c. Two peaks of the head groups in Figure 2c indicated that the layer in the middle of the system possessed the bilayer stucture. Therefore, the morphology in Figure 1c is called the bilayer structure, and the morphological transition from monolayer structure to bilayer structure is called the monolayer-bilayer transiton. To identify and investigate different phases, the Euler characteristic χ is a more convenient tool. In general, χ depends on the number of the separated domains (micellar structure), holes or droplets, and handles. For example, the presence of the separated domains and droplets results in a positive χ, whereas the presence of holes and handles can lead to a negative χ. In this study, it was found that the occurrence of the bridge structure was usually related to the deformation of the adsorbed monolayers (i.e., the formation of the holes on the monolayers). To take into account and to separate the effects of these variables, two different methods for solving χ were applied for comparison. First, the site of the solid surface was artificially treated as a tail group. By artificial treatment, the effects of deformation (holes) of the monolayer were effectively eliminated. Thus, we can focus on the main structure transition (i.e., the bridge structure). Then, the effects of the holes on the adsorbed monolayer were investigated by removing the artificial treatment. In addition to the Euler characteristic, the average values of the internal energies, and the heat capacities in these systems, were also calculated to better understand the morphology transitions. As the distance between the two walls increased, the morphologies of the monolayer, bridge, and bilayer were obtained in turn. In Figure 3, we show the average surface area (S/Lx2) (Figure 3a), the mean breath (B/Lx, proportion to mean curvature) (Figure 3b), the average Euler characteristic 〈χ〉 (Figure 3c), its variance 〈χ2〉 - 〈χ〉2 (Figure 3d), the average total energy per lattice site (Figure 3e), and the heat capacity per lattice site (Figure 3f) as a function of Lz. First, we focused on the main morphology transition for the system by using the artificial treatment; thus, the fluctuations of adsorbed monolayer on each side were excluded from the calculations of the mean curvature, χ, and its variance. It can be seen from Figure 3c that the Euler characteristic χ remained basically unchanged with a value of +2 for Lz varied from 10 to 12, which is supported by the zero variance of χ (Figure 3d). This indicates that the monolayers remain in the small range of Lz from 10 to 12. However, when Lz increases to 13, the Euler characteristic becomes negative, which indicates that the morphology of the systems changes from two separated monolayers to a highly interconnecting bridge structure with a negative χ. This morphology transition can also be found from their corresponding

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Figure 5. Average Euler characteristic 〈χ〉 (a), its variance 〈χ2〉 - 〈χ〉2 (b), the average total energy per lattice site (c), and the heat capacity per lattice site (d) as a function of the surfactant (H2T4) concentration in a fixed simulation box of the 30 × 30 × 14 lattice. All the results are for the system with artificial treatment.

snapshots (Figure 1). χ reached its minimum value while its variance and the average energy reached their maximum for Lz ) 14 (Figure 3d,e). Then, χ began to increase with a further increase of the distance between the walls, which meant that the number of bridges decreased. It was found from snapshots that the new layer was introduced in this process, with the decrease of the number of the bridges. At last, it reached a fixed value of +3 (i.e., the typical value of the bilayer when Lz ) 17). From the previous discussion, it was concluded that the systems for Lz ) 14-20 formed the structure of the bilayer, although only a small part of the bilayer structure was formed for Lz ) 14 and 15. Another reason for us to consider the morphological structure as the bilayer type is that these morphologies are not stable. The time evolution for Lz ) 15 is shown in Figure 4, where χ exhibits the behavior of noises, which indicates that bridges between the monolayers are created or removed very quickly. It is shown in Figure 3a that the surface area increases slowly for the small pore size and then increases very quickly and finally remains basically constant for the large pore size. The drastic increase in surface area corresponds to the morphology transition from monolayer to bridge structure. It is obvious that the structure of the bridge possesses a larger surface area due to the existence of many bridges connecting the adsorbed monolayers. As the bilayer structure is formed for the larger distance between two walls, the surface area decreases slightly. To consider the structure fluctuations of the adsorbed monolayers, the surface area, mean curvature, Euler characteristic, and its fluctuation were calculated again for the systems without applying the artificial treatment. Thus, by comparing the results by applying the artificial treatment as discussed before, we can identify the fluctuations of the two adsorbed monolayers (i.e., the holes in our work) as the distance between the two walls increases. As expected, the holes in the surfaces

alter χ significantly, while they have not affected significantly the other variables. By comparing the Euler characteristic curves for the two cases, it was found that both the χ values of the systems without the artificial treatment and their variances increased or decreased much more quickly than those of its counterpart, due to the existence of each hole changing χ by -1. More importantly, the peaks in the average Eluer characteristic and in its variance both shifted from the point at Lz ) 14 to Lz ) 13. By comparing the results for these two cases, we concluded that for the system with Lz ) 13, where the bridge structure occurs, the number of holes on the adsorbed layers fluctuated strongly. In other words, holes were frequently formed or sealed in the system. The occurrence of the holes increased the mean curvature inevitably, as shown in Figure 3b for Lz ) 13 and 14. The simulations were also performed for a surfactant solution of 66.7% H2T4 confined between two parallel hydrophobic surfaces. It was found that the morphologies of the confined H2T4 systems also experienced the monolayer, the bridge structure, and the bilayer structure as the distance between the walls increased. From the previous discussion, it was concluded that there existed three topological structures in both the H4T4 and the H2T4 solutions confined in two parallel hydrophobic walls as the distance between the walls was in the range of 10-20. They are the adsorbed monolayers, the bridge structure, and the bliayer structure, respectively. In other words, if the transition from bilayer to monolayer occurs along the transition path in which the confinement becomes strong at a constant surfactant concentration, the bridge structure would appear as an intermediate state. The occurrence of the bridge structure is often accompanied by strong fluctuations of the monolayers (i.e., the frequent formations and seals of the pores). Next, to consider the effects of surfactant concentration, we will discuss the

Bridge Structure: Transition in Amphiphile/Water

Figure 6. Snapshots of H2T4 confined in the fixed simulation box of the 30 × 30 × 14 lattice at different surfactant concentrations: (a) C ) 47.6%, (b) C ) 52.4%, and (c) C ) 85.7%. For C ) 47.6%, the system has the type of two adsorbed monolayers. For C ) 52.4%, the bridge structure is formed. For C ) 85.7%, the bilayer structure is formed.

structure changes in the H2T4 solutions in the confined space of the 30 × 30 × 14 lattice, as the surfactant concentration increased from 47.6 to 85.7% by an increment of 4.8%. Effects of Surfactant Concentration. Simulations were performed for H2T4 solutions confined between two parallel hydrophobic surfaces. The system size was a 30 × 30 × 14 lattice with periodic boundary conditions in the x and y directions. The number of H2T4 varied from 1000 to 1800 in the fixed simulation box, and their corresponding volume fraction changed from 47.6 to 85.7%. In Figure 5, we show in turn the results for the average Euler characteristic 〈χ〉, its variance 〈χ2〉 - 〈χ〉2, the average energy, and the heat capacity as a function of the surfactant concentration with artificial treatment. It can be seen from the snapshot in Figure 6a that the structure of the two adsorbed monolayers is formed at C ) 47.6%, which is consistent with the corresponding positive χ in Figure 5a. As the surfactant concentration increases from C ) 52.4%, the value of the heat capacity increases, and the Euler characteristic becomes negative. Because the effects of holes and small micelles on the Euler characteristic are excluded, the increase of heat capacity and the decrease of χ are attributed to the interconnected structure. This can be proven by the snapshot in Figure 6b, from which the bridge structure is clearly observed. In general, when the

J. Phys. Chem. C, Vol. 111, No. 19, 2007 7149 volume fraction increases from 57.1 to 71.4%, a continuous decrease of χ with an increase of its variance takes place. These observations indicate that the number of bridges increases to accommodate the increasing number of surfactants. Then, when the surfactant concentration increases to 76.2%, the layer in the middle of the simulation box exhibits a bilayer structure. However, the bilayer still connects with the two adsorbed monolayers (Figure 6c). If we continue to increase the surfactant concentration, the bilayer in the middle of the box grows gradually, inducing a nearly constant average energy and a decrease of heat capacity (Figure 5c,d). From the snapshot for C ) 85.7% in Figure 6c, more parts of the layer in the middle of the system are observed to contact the opposing absorbed monolayers as compared with that for C ) 52.4% in Figure 6b. The reason for the decrease of the Euler characteristic is that some local interconnection structures like that for C ) 85.7% are formed. In summary, in this section, we investigated the morphology of the H2T4 solution confined within the parallel hydrophobic surfaces in the 30 × 30 × 14 lattice box with an increase in the number of surfactants (i.e., the surfactant concentration). Similar to the system discussed previously at constant surfactant concentrations, this system undergoes three structures (i.e., the two adsorbed monolayers, the bridge, and the bilayer structures, respectively), with an increase of the surfactant concentration from 47.6 to 85.7%. However, because the confinement is so strong that the system cannot accommodate a complete bilayer structure, at high surfactant concentrations, the bilayer structures were still interconnected with the two adsorbed monolayers on the solid surfaces. From the previous discussion, it is concluded that the bridge structure always appears as an intermediate state during the monolayer-bilayer transition for surfactants H2T4 and H4T4, at least for the two transition paths (i.e., the increase of the distance between two confining walls at a fixed surfactant concentration and the varied surfactant concentration at a fixed confined space). However, a fundamental question remains unsolved: is the bridge structure necessary for any transition path and different surfactants? To clarify this question, we determined the phase diagrams in the surfactant concentrationLz plane for different surfactants H2T4, H4T4, and H4T3. Phase Diagrams of Surfactants with Different Architectures. Figure 7a-c shows the surfactant concentration versus Lz phase diagrams for confined systems of H4T4, H2T4, and H4T3, respectively. The states, where the morphologies are explicitly simulated, are marked in the figure. The morphologies of the systems are mostly determined by combining the corresponding snapshots with the Euler characteristics. The phase boundaries are approximately determined by the obtained morphologies and drawn as guides for the eyes. It is seen from Figure 7a that four kinds of morphologies (i.e., monolayer, bridge, micelle, and bilayer) are observed in the whole phase diagram. Note that the micelle structure is defined for the system, in which all kinds of micelles, such as globular and cylindrical, are formed between two absorbed monolayers. Although the bridge structure exists for confined H4T4 solutions, it is limited to a small region. Only when Lz increases to 13 and the surfactant concentration is larger than 0.8 is the bridge structure observed. Hence, the occurrence of the intermediate states for the phase transition of the confined H4T4 systems depends on the transition path. However, when we substitute H2T4 for H4T4 (Figure 7b), the region of the bridge structure becomes increasingly wider, and more importantly, the region spans the whole range we studied, which means that the

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Zheng et al. molecular shape (architecture). For example, in bulk solution, the theory can explain the observations that roughly cylindrical molecules tend to form bilayers, while wedge-shaped molecules form aggregates with significant spontaneous curvatures such as cylinders or spheres. According to the theory, Kabalnov and Wennerstro¨m60 demonstrated that surfactants with bulky alkyl chains and small head groups stabilize W/O emulsions due to the packing constraints at the oil-water interface of an emulsion drop, while the single tailed surfactants with large polar heads stabilize O/W emulsions for similar reasons. In a similar way, we can use the oriented wedge theory to interpret the effects of the surfactant architecture on the appearance of the bridge region in the phase diagrams. To create a bridge on the monolayer, one has to pay a monolayer bending energy penalty because the surface must be strongly curved at the corner where the bridge and the monolayer cross. This penalty is dramatically different between H2T4 and H4T3, according to the oriented wedge theory. This determines the size of the bridge phase region and even the existence of the region. From the previous discussion, we can conclude that the existence of the bridge structure depends on the transition paths and surfactant architectures. The hydrophobic interaction plays a significant role in biological and many colloidal systems. Although several mechanisms on the hydrophobic interaction have been proposed over 20 years, no single theory is able to explain all of the forces observed between the many different surfaces studied so far.61 Suggested mechanisms for the long-range attraction include electrostatic charge or correlated dipole-dipole interactions,62-68 water structure,69,70 phase metastability,71,72 preexisting submicroscopic bubbles that bridge the surfaces,73-75 and molecular rearrangement into patchy blilayers.76-78 From the previous discussion, we can find that when two surfaces approach each other very closely, the adsorbed layers of surfactants may connect to each other by the bridge structure, which would inevitably result in a long-range attractive interaction between the two surfaces; thus, the bridge structures as an intermediate state are likely to be responsible for the origin of the longrange hydrophobic interaction, at least in some cases. Conclusion

Figure 7. Phase diagrams for surfactant concentration vs Lz in different surfactant solutions confined between two hydrophobic surfaces: (a) H4T4, (b) H2T4, and (c) H4T3.

intermediate phase would appear for any phase transitions between monolayer and bilayer in the range of parameters we studied. To further verify whether the bridge structure exists or not for different surfactants in a confined space, we also studied the phase behavior of confined H4T3 solutions. In Figure 7c, it can be obviously seen that the bridge structure is not observed in the given surfactant concentration versus Lz plane. The effects of surfactant architecture on the existence of the bridge structure can be qualitatively interpreted in the framework of the oriented wedge theory. The oriented wedge theory was first developed by Harkins et al. and Langmuir58,59 and then revisited recently by Kabalnov and Wennerstro¨m,60 to correlate the monolayer bending energy and emulsion stability. This theory provides an intuitive and useful idea to correlate the geometry of aggregates and their

In this paper, we have performed extensive LMC simulations of the morphologies for the surfactant solutions confined between parallel hydrophobic surfaces. The morphologies are affected by many factors. However, the effects of the size of confined space, surfactant concentration, and surfactant structure are mainly investigated in this work. Several variables, including surface area, mean curvature, total energy, heat capacity, and the Euler characteristic and its fluctuations, were used to distinguish these different morphologies. The simulation results show that an interesting bridge structure appears during the morphology transition from the monolayers adsorbed on each solid surface to a bilayer between the adsorbed monolayers. The occurrence of the bridge structure is often accompanied by strong fluctuations of the monolayers (i.e., the frequent formations and seals of the pores on the monolayers). To identify the existence of the bridge structure in a confined space, phase diagrams for different surfactant structures are determined from extensive simulations. In general, the occurrence of the bridge structure during the monolyer-bilayer transition depends on the transition paths and surfactant architectures. The bridge structure as an intermediate state is likely to be responsible for the origin of truly hydrophobic short-range force regimes for long-range hydrophobic interactions, at least in some cases.

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