Phase equilibria of a lattice model for an oil–water–amphiphile mixture

Predicting solubilisation features of ternary phase diagrams of fully dilutable lecithin linker microemulsions

Fully dilutable microemulsions (μEs), used to design self-microemulsifying delivery system (SMEDS), are formulated as concentrate solutions containing oil and surfactants, without water. As water is added to dilute these systems, various μEs are produced (water-swollen reverse micelles, bicontinuous systems, and oil-swollen micelles), without the onset of phase separation. Currently, the formulation dilutable μEs follows a trial and error approach that has had a limited success. The objective of this work is to introduce the use of the hydrophilic-lipophilic-difference (HLD) and net-average-curvature (NAC) frameworks to predict the solubilisation features of ternary phase diagrams of lecithin-linker μEs and the use of these predictions to guide the formulation of dilutable μEs. To this end, the characteristic curvatures (Cc) of soybean lecithin (surfactant), glycerol monooleate (lipophilic linker) and polyglycerol caprylate (hydrophilic linker) and the equivalent alkane carbon number (EACN) of ethyl caprate (oil) were obtained via phase scans with reference surfactant-oil systems. These parameters were then used to calculate the HLD of lecithin-linkers-ethyl caprate microemulsions. The calculated HLDs were able to predict the phase transitions observed in the phase scans. The NAC was then used to fit and predict phase volumes obtained from salinity phase scans, and to predict the solubilisation features of ternary phase diagrams of the lecithin-linker formulations. The HLD-NAC predictions were reasonably accurate, and indicated that the largest region for dilutable μEs was obtained with slightly negative HLD values. The NAC framework also predicted, and explained, the changes in microemulsion properties along dilution lines.

Simulating the formation of surfactant-templated mesoporous silica materials: a model with both surfactant self-assembly and silica polymerization

We have used Monte Carlo simulations to study the formation of the MCM-41 mesoporous silica material, with a new lattice model featuring explicit representations of both silicic acid condensation and surfactant self-assembly. Inspired by experimental syntheses, we have adopted the following two-step "synthesis" during our simulations: (i) high pH and low temperature allowing the initial onset of mesostructures with long-range order; (ii) lower pH and higher temperature promoting irreversible silica condensation. During step (i), the precursor solution was found to spontaneously separate into a surfactant-silicate-rich phase in equilibrium with a solvent-rich phase. Lamellar and hexagonal ordering emerged for the surfactant-silicate-rich mesosphases under different synthesis conditions, consistent with experimental observations. Under conditions where silica polymerization can be neglected, our simulations were found to transform reversibly between hexagonal and lamellar phases by changing temperature. During step (ii), silica polymerization was simulated at lower pH using reaction ensemble Monte Carlo to treat the pH dependence of silica deprotonation equilibria. Monte Carlo simulations produced silica-surfactant mesostructures with hexagonal arrays of pores and amorphous silica walls, exhibiting Q(n) distributions in reasonable agreement with (29)Si NMR experiments on MCM-41. Compared with bulk amorphous silica, the wall domains of these simulated MCM-41 materials are characterized by even less order, larger fractions of 3- and 4-membered rings, and wider ring-size distributions.

Model shape transitions of micelles: spheres to cylinders and disks

We present a microscopic analysis of shape transitions of micelles of model linear nonionic surfactants. In particular, symmetric H(4)T(4) and asymmetric H(3)T(6) surfactants have been chosen for the study. In a previous work, it has been observed that symmetric surfactants have a strong tendency to prefer spherical micelles over a wide range of chemical potentials, while asymmetric surfactants undergo shape transitions between a spherical micelle at low concentration to other forms, mainly finite cylindrical micelles. This study combines the application of a two-dimensional single-chain mean-field theory (SCMFT) with Monte Carlo (MC) simulations of exactly the same systems. On the one hand, the characteristics of the SCMFT make this method suitable for free energy calculations, especially for small surfactants, due to the incorporation of relevant microscopic details in the model. On the other hand, MC simulations permit us to obtain a complete picture of the statistical mechanical problem, for the purpose of validation of the mean-field calculations. Our results reveal that the spherical shape for the symmetric surfactant is stable over a large range of surfactant concentrations. However, the asymmetric surfactant undergoes a complex shape transition that we have followed by calculating the standard chemical potential as a function of the aggregation number. The results indicate that the system forms prolate spheroids prior to developing short capped cylinders that gradually grow in length, with some oscillations in the energy of formation. The most important result of our work is the evidence of a bifurcation where, together with the elongated objects, the system can develop oblate aggregates and finally a torus shape similar to a red blood cell.

Coarse-grained molecular dynamics simulations of the sphere to rod transition in surfactant micelles

Surfactant molecules self-assemble in aqueous solutions to form various micellar structures such as spheres, rods, or lamellae. Although phase transitions in surfactant solutions have been studied experimentally, their molecular mechanisms are still not well understood. In this work, we show that molecular dynamics (MD) simulations using the coarse-grained (CG) MARTINI force field and explicit CG solvent, validated against atomistic MD studies, can accurately represent micellar assemblies of cetyltrimethylammonium chloride (CTAC). The effect of salt on micellar structures is studied for aromatic anionic salts, e.g., sodium salicylate, and simple inorganic salts, e.g., sodium chloride. Above a threshold concentration, sodium salicylate induces a sphere to rod transition in the micelle. CG MD simulations are shown to capture the dynamics of this shape transition and support a mechanism based on the reduction in the micelle-water interfacial tension induced by the adsorption of the amphiphilic salicylate ions. At the threshold salt concentration, the interface is nearly saturated with adsorbed salicylate ions. Predictions of the effect of salt on the micelle structure in different CG solvent models, namely, single-site standard water and three-site polarizable water, show qualitative agreement. This suggests that phase transitions in aqueous micelle solutions could be investigated by using standard CG water models which allow for 3 orders of magnitude reduction in the computational time as compared to that required for atomistic MD simulations.

A Monte Carlo study of crowding effects on the self-assembly of amphiphilic molecules

In this work, lattice Monte Carlo was used to study the effects of crowding on the self-assembly of surfactants. Simulation results show that crowding strongly shifts the critical micelle concentration (CMC) of surfactants from the bulk value. Two effects originated from crowding are found to govern the CMC shift: one is the depletion effect by crowding agents and the other is the available volume for micelle formation. The depletion effects inevitably result in the enrichment of surfactants in crowding-free regions and cause the decrease in CMC. On the other hand, the appearance of crowding agents decreases the available volume for micelle formation, which reduces the conformational entropy and impedes the micelle formation. Three factors, including the radius of crowding agents, the arrangement of crowding agents, and the volume fraction of crowding agents, are considered in this work to study the crowding effects. The trends of CMC shifts are interpreted from the competition between the depletion effects and the available volume for micelle formation.

Computer simulation of adsorption kinetics of surfactants on solid surfaces

Adsorption kinetics of surfactants on solid surfaces has been studied by using computer simulation. Both bulk surfactant concentration and diffusion region are explicitly integrated in our model. Depending on the head-surface interaction, our simulation results indicate that there exist two different kinetic modes in adsorption process of surfactants on solid surfaces. One is the four-regime mode and the other is step-wise mode. For the strongly attractive head-surface interaction, four distinct regimes of surfactant adsorption are found: a diffusion-controlled regime, a self-assembly controlled regime, an intermediate coverage regime and a saturated regime. In particular, the adsorption in second regime displays a power-law time dependence with an exponent unrelated to bulk concentrations and diffusion coefficients. While for the weaker adsorption surfaces, the step-wise mode is found. The mode includes a low-coverage nucleation regime and the saturated regime after a sudden aggregation of surfactants on the substrates which occurs stochastically. Besides the head-surface interaction, in this work, the effects of surfactant diffusivity, bulk concentration, the length of diffusion zone and surfactant architecture on the adsorption kinetics are also considered. The simulated adsorption kinetics is compared qualitatively with experimental results.

Adsorption and morphology transition of surfactants on hydrophobic surfaces: a lattice Monte Carlo study

In this work, we first show that there are only five independent interchange parameters in the surfactant-solvent-interface system in Larson's model, and then adsorption and morphology transition of surfactants on hydrophobic surfaces are studied by extensive lattice Monte Carlo simulations. In our simulations, we found that there exist six adsorbed morphologies: (1) premature admicelle, (2) hemisphere, (3) hemisphere-hemicylinder mixture, (4) wormlike hemicylinder, (5) perforated monolayer, and (6) monolayer. The surface morphologies and the amount of adsorption on hydrophobic surfaces are found to be affected obviously by two interchange parameters. One is the attractive interaction between tail groups and surface (chiTS), and the other is the solubility of head groups in bulk (chiHW). Phase diagrams in chiHW versus chiTS planes for surfactants with different hydrophobicities (chiTW) and for surfactants with different molecular structures are determined in this work, from which the transitions of surface morphologies and adsorption behaviors are discussed.

Effects of solvent immiscibility on the phase behavior and microstructural length scales of a diblock copolymer in the presence of two solvents

We employ self-consistent mean-field theory to study the phase behavior and the microstructural sizes of AB diblock copolymers in the presence of a neutral solvent S1 and a slightly B-selective solvent S2. In particular, the effects of copolymer volume fraction phiC, the solvent ratio, and the immiscibility parameter between two solvents chiS1S2, are examined. We find that increasing chiS1S2 not only enlarges the ordered microphase region in the concentrated solutions, but also induces a less concentrated homogeneous solution to form an ordered structure and even undergo a macrophase separation. This is due to the fact that increasing chiS1S2 enhances the preferentially of S1 for A and S2 for B and, thereafter, the effective segregation between A and B. Hence, we observe that the structural length results obtained by varying chiS1S2 resemble a consequence of varying the solvent selectivity in the diblock copolymer solutions when only one solvent is added. For example, when chiS1S2 is small, the domain spacing decreases with decreasing phiC while at larger values of chiS1S2, it first shows a decreasing trend and then an increasing behavior with decreasing phiC.

Effect of stiffness on the micellization behavior of model H4T4 surfactant chains

The micellization behavior of a series of model surfactants, all with four head and tail groups (H4T4) but with different degrees of chain stiffness, was studied using grand canonical Monte Carlo simulations on a cubic lattice. The critical micelle concentration, micellar size, and thermodynamics of micellization were examined. In all cases investigated, the critical micelle concentration was found to increase with increasing temperature as observed for nonionic surfactants in apolar or slightly polar solvents. At a fixed reduced temperature and increasing chain stiffness, in agreement with previous observations, it was found that the critical micelle concentration decreased and the average micelle size increased. This behavior is qualitatively consistent with that experimentally observed when comparing hydrogenated and homologous fluorinated surfactants. Thermodynamic considerations based on the analysis of the temperature dependence of the critical micelle concentration indicated that both effects could be interpreted as arising from an increased number of heterocontacts between hydrophobic portions of stiff surfactants and a lower entropic cost on packing rigid chains. Structural analysis that was also based on considering the inner micellar radial dependence of the surfactant head and tail site fraction distributions suggested that, on stiffening the molecular backbone, the resulting micellar aggregates grew, without appreciable deviations from spherical symmetry. Stiffer surfactants led to a slightly denser micellar core because of better packing.

Complementary use of simulations and molecular-thermodynamic theory to model micellization

Molecular-thermodynamic descriptions of micellization in aqueous media can be utilized to model the self-assembly of surfactants possessing relatively simple chemical structures, where it is possible to identify a priori what equilibrium position they will adopt in the resulting micellar aggregate. For such chemical structures, the portion of the surfactant molecule that is expected to be exposed to water upon aggregate self-assembly can be identified and used as an input to the molecular-thermodynamic description. Unfortunately, for many surfactants possessing more complex chemical structures, it is not clear a priori how they will orient themselves within a micellar aggregate. In this paper, we present a computational approach to identify what portions of a surfactant molecule are hydrated in a micellar environment through the use of molecular dynamics simulations of such molecules at an oil/water interface (modeling the micelle core/water interface). The local environment of each surfactant segment is determined by counting the number of contacts of each segment with the water and oil molecules. After identifying the hydrated and the unhydrated segments of the surfactant molecule, molecular-thermodynamic modeling can be performed to predict: (i) the free-energy change associated with forming a micellar aggregate, (ii) the critical micelle concentration (CMC), and (iii) the optimal shape and size of the micellar aggregate. The computer simulation results were found to be sensitive to the atomic charge parameters utilized during the simulation runs. Two different methods of assigning atomic charges were tested, and the computer simulation and molecular-thermodynamic modeling results obtained using both sets of atomic charges are presented and compared. The combined computer simulation/molecular-thermodynamic modeling approach presented here is validated first by implementing it in the case of anionic (sodium dodecyl sulfate, SDS), cationic (cetyltrimethylammonium bromide, CTAB), zwitterionic (dodecylphosphocholine, DPC), and nonionic (dodecyl poly(ethylene oxide), C12E8) surfactants possessing relatively simple chemical structures and verifying that good predictions of CMCs and micelle aggregation numbers are obtained. In the case of C12E8, the challenges and limitations associated with simulating a single, polymeric E8 moiety at the oil/water interface to model its behavior at the micelle/water interface are discussed. Subsequently, the combined modeling approach is implemented in the case of the anionic surfactant 3-hydroxy sulfonate (AOS) and of the nonionic surfactant decanoyl-n-methylglucamide (MEGA-10), which possess significantly more complex chemical structures. The good predictions obtained for these two surfactants indicate that the combined computer simulation/molecular-thermodynamic modeling approach presented here extends the range of applicability of molecular-thermodynamic theory to allow modeling of the micellization behavior of surfactants possessing more complex chemical structures.

Lattice Monte Carlo simulations of phase separation and micellization in supercritical CO2/surfactant systems: effect of CO2 density

Lattice Monte Carlo simulations are used to study the effect of nonionic surfactant concentration and CO2 density on the micellization and phase equilibria of supercritical CO2/surfactant systems. The interaction parameter for carbon dioxide is obtained by matching the critical temperature of the model fluid with the experimental critical temperature. Various properties such as the critical micelle concentration and the size, shape, and structure ofmicelles are calculated, and the phase diagram in the surfactant concentration-CO2 density space is constructed. On increasing the CO2 density, we find an increase in the critical micelle concentration and a decrease in the micellar size; this is consistent with existing experimental results. The variation of the micellar shape and structure with CO2 density shows that the micelles are spherical and that the extension of the micellar core increases with increasing micellar size, while the extension of the micellar corona increases with increasing CO2 density. The predicted phase diagram is in qualitative agreement with experimental phase diagrams for nonionic surfactants in carbon dioxide.

Methodology of predicting approximate shapes and size distribution of micelles: illustration for simple models

We propose an efficient methodology for predicting approximate shapes and size distribution of micelles. The methodology is a judicious combination of a conventional thermodynamic approach, the reference interaction site model (RISM) theory, and the Monte Carlo (MC) simulated annealing technique. Solvent effects are fully incorporated using the RISM theory with our robust and very efficient algorithm for solving the RISM equations, and the MC technique is applied only to surfactant molecules. The methodology is potentially applicable to realistic models of surfactant and solvent molecules with all-atom potentials. As the first step, however, it is illustrated for simplified models having only essential characteristics of the amphiphiles. We estimate the critical micelle concentration, approximate shapes, and size distributions at some surfactant concentrations. Roles of the solvent and effects due to the type of the surfactant molecule are discussed in detail.

Importance of Micellar Kinetics in Relation to Technological Processes

The association of many classes of surface-active molecules into micellar aggregates is a well-known phenomenon. Micelles are in dynamic equilibrium, constantly disintegrating and reforming. This relaxation process is characterized by the slow micellar relaxation time constant, tau(2), which is directly related to the micellar stability. Theories of the kinetics of micelle formation and disintegration have been discussed to identify the gaps in our complete understanding of this kinetic process. The micellar stability of sodium dodecyl sulfate micelles has been shown to significantly influence technological processes involving a rapid increase in interfacial area, such as foaming, wetting, emulsification, solubilization, and detergency. First, the available monomers adsorb onto the freshly created interface. Then, additional monomers must be provided by the breakup of micelles. Especially when the free monomer concentration is low, which is the case for many nonionic surfactant solutions, the micellar breakup time is a rate-limiting step in the supply of monomers. The Center for Surface Science & Engineering at the University of Florida has developed methods using stopped flow and pressure jump with optical detection to determine the slow relaxation time of micelles of nonionic surfactants. The results showed that the ionic surfactants such as SDS exhibit slow relaxation times in the range from milliseconds to seconds, whereas nonionic surfactants exhibit slow relaxation times in the range from seconds (for Triton X-100) to minutes (for polyoxyethylene alkyl ethers). The slow relaxation times are much longer for nonionic surfactants than for ionic surfactants, because of the absence of ionic repulsion between the head groups. The observed relaxation times showed a direct correlation with dynamic surface tension and foaming experiments. In conclusion, relaxation time data of surfactant solutions correlate with the dynamic properties of the micellar solutions. Moreover, the results suggest that appropriate micelles with specific stability or tau(2) can be designed by controlling the surfactant structure, concentration, and physicochemical conditions (e.g., salt concentration, temperature, and pressure). One can also tailor micelles by mixing anionic/cationic or ionic/nonionic surfactants for a desired stability to control various technological processes.

Mixing Properties of Two-Dimensional Lattice Solutions of Amphiphiles

Lattice Monte Carlo simulations of two-dimensional amphiphile solutions are used to examine the accuracy of the mixing properties predicted by lattice theories such as the Flory-Huggins theory, random-solution approximation, and quasichemical approximation. The internal energy, Helmholtz free energy, and entropy of mixing have been calculated from the configurational energy data obtained from the simulations, and the effect of nonrandom mixing on these properties has been determined. The quasichemical approximation predicts the entropy and Helmholtz free energy of mixing accurately for the amphiphile solution, but fails to predict the energy of mixing, due to the presence of microphase (self-aggregation) separation, which is beyond the reach of the quasichemical approximation, a mean-field theory. Helmholtz free energy of mixing is predicted accurately, and the shielding of the solvophobic segments in the microphase leads to small energies of mixing compared to the entropy of mixing. Copyright 2000 Academic Press.