A molecular, mean-field theory of chain packing statistics in aggregates of amphiphilic molecules is applied to calculate the conformational properties of the lipid chains comprising the hydrophobic cores of dipalmitoyl-phosphatidylcholine (DPPC), dioleoyl-phosphatidylcholine (DOPC), and palmitoyl-oleoyl-phosphatidylcholine (POPC) bilayers in their fluid state. The central quantity in this theory, the probability distribution of chain conformations, is evaluated by minimizing the free energy of the bilayer assuming only that the segment density within the hydrophobic region is uniform (liquidlike). Using this distribution we calculate chain conformational properties such as bond orientational order parameters and spatial distributions of the various chain segments. The lipid chains, both the saturated palmitoyl (-(CH2)(1)4-CH3) and the unsaturated oleoyl (-(CH2)(7)-CH=CH-(CH2)(7)-CH3) chains are modeled using rotational isomeric state schemes. All possible chain conformations are enumerated and their statistical weights are determined by the self-consistency equations expressing the condition of uniform density. The hydrophobic core of the DPPC bilayer is treated as composed of single (palmitoyl) chain amphiphiles, i.e., the interactions between chains originating from the same lipid headgroup are assumed to be the same as those between chains belonging to different molecules. Similarly, the DOPC system is treated as a bilayer of oleoyl chains. The POPC bilayer is modeled as an equimolar mixture of palmitoyl and oleoyl chains. Bond orientational order parameter profiles, and segment spatial distributions are calculated for the three systems above, for several values of the bilayer thickness (or, equivalently, average area/headgroup) chosen, where possible, so as to allow for comparisons with available experimental data and/or molecular dynamics simulations. In most cases the agreement between the mean-field calculations, which are relatively easy to perform, and the experimental and simulation data is very good, supporting their use as an efficient tool for analyzing a variety of systems subject to varying conditions (e.g., bilayers of different compositions or thicknesses at different temperatures).

The interaction free energy between a hydrophobic, transmembrane, protein and the surrounding lipid environment is calculated based on a microscopic model for lipid organization. The protein is treated as a rigid hydrophobic solute of thickness d(P), embedded in a lipid bilayer of unperturbed thickness d(L)o. The lipid chains in the immediate vicinity of the protein are assumed to adjust their length to that of the protein (e.g., they are stretched when d(P) > d(L)o) in order to bridge over the lipid-protein hydrophobic mismatch (d(P) - d(L)o). The bilayer’s hydrophobic thickness is assumed to decay exponentially to its asymptotic, unperturbed, value. The lipid deformation free energy is represented,as a sum of chain (hydrophobic core) and interfacial (head-group region) contributions. The chain contribution is calculated using a detailed molecular theory of chain packing statistics, which allows the calculation of conformational properties and thermodynamic functions (in a mean-field approximation) of the lipid tails. The tails are treated as single chain amphiphiles, modeled using the rotational isomeric state scheme. The interfacial free energy is represented by a phenomenological expression, accounting for the opposing effects of head-group repulsions and hydrocarbon-water surface tension. The lipid deformation free energy DELTAF is calculated as a function of d(P) - d(L)o. Most calculations are for C-14 amphiphiles which, in the absence of a protein, pack at an average area per head-group a0 congruent-to 32 angstrom2 (d(L)o congruent-to 24.5 angstrom), corresponding to the fluid state of the membrane. When d(P) = d(L)o, DELTAF > 0 and is due entirely to the loss of conformational entropy experienced by the chains around the protein. When d(P) > d(L)o, the interaction free energy is further increased due to the enhanced stretching of the tails. When d(P) < d(L)o, chain flexibility (entropy) increases, but this contribution to DELTAF is overcounted by the increase in the interfacial free energy. Thus, DELTAF obtains a minimum at d(P) - d(L)o congruent-to 0. These qualitative interpretations are supported by detailed numerical calculations of the various contributions to the interaction free energy, and of chain conformational properties. The range of the perturbation of lipid order extends typically over few molecular diameters. A rather detailed comparison of our approach to other models is provided in the Discussion.

The two successive fluid-fluid phase transitions in surfactant Langmuir monolayers are described using a highly simplified molecular model: a ‘reactive’ mixture of inter-converting squares of two different sizes. The model is solved by a mean-field lattice approach and by Monte Carlo simulations. The mean-field scheme involves a re-division of the original lattice into ‘cells’ which can contain either one large square representing the (projection on the lattice of) an amphiphilic molecule in a conformationally disordered (’expanded’) state, or clusters consisting of 1-4 small squares, each representing an ordered (’stretched’) molecule. This procedure circumvents some of the difficulties associated with the size disparity of the adsorbed particles. In spite of its simplicity, the model can explain some major, as well as some subtle, characteristics of experimental monolayer phase diagrams. These include the conditions under which the monolayer exhibits one phase transition, two or none; the decrease of the triple point temperature with increasing chain length, and the gradual decrease with temperature of the liquid-condensed phase density.

We consider the effect of shear velocity gradients on the size (L) of rodlike micelles in dilute and semidilute solution. A kinetic equation is introduced for the time-dependent concentration of aggregates of length L, consisting of ‘‘bimolecular’’ combination processes L + L’ –> (L + L’) and ‘‘unimolecular’’ fragmentations L –> L’ + (L - L’). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shear-induced coalescence of emulsions, and the latter by incorporating the tension-deformation effects due to flow. Steady-state solutions to the kinetic equation are obtained, with the corresponding mean micellar size (LBAR) evaluated as a function of the Peclet number P, i.e., the dimensionless ratio of flow rate-gamma and rotational diffusion coefficient D(r). For sufficiently dilute solutions, we find only a weak dependence of LBAR on P. In the semidilute regime, however, an apparent divergence in LBAR at P congruent-to 1 suggests a flow-induced first-order gelation phenomenon.

In this paper we present a rigid-rod model (involving a restricted set of orientations) which is solved first with mean-field theory and then by Monte Carlo simulation. It is shown that both interparticle attractions and anisotropic adsorption energies are necessary in order for two successive fluid-fluid transitions to occur. The first is basically a gas-liquid condensation of ‘‘lying down’’ rods in the plane of the surface, and the second involves a ‘‘standing up’’ of the particles. A close qualitative correspondence is established between the results obtained in the mean-field and Monte Carlo descriptions. The role of biaxial states, i.e., in-plane orientational ordering, is also discussed in both contexts. To this end, we develop an analogy between our one-component rod monolayer and a bidisperse system of interconverting isotropic particles.

We present a statistical-thermodynamic theory that associates fracture of a solid with the approach of a spinodal upon increasing stress. This formulation is illustrated by a one-dimensional model, and the temperature dependence of the nonlinear stress-strain relation and fracture stress is obtained. A two-dimensional network model is treated by both effective-medium theory and Monte Carlo simulations, showing metastability and the nucleation of microcracks.

Within the framework of two complementary models, we show that the densities and patterns of defects in amphiphile-water systems with lamellar organization are coupled to the strength of the bilayer-bilayer interactions and hence to the overall surfactant concentration. We consider defects which introduce curvature (i.e., larger head-group area per molecule) while preserving the integrity of stacked bilayers at surfactant volume fractions of several tenths. These features are favored if the molecules comprising the lamellae are preferentially packed with a nonplanar aggregate-water interface: curvature defects lower the local free energy in systems constrained by aggregate-aggregate interactions to lamellar geometry. As the amphiphile volume fraction is increased-and the bilayer-bilayer spacing thereby decreased-we predict phase transitions between lamellar phases of different defect patterns on the bilayer surface, with concurrent decrease in the defect area fraction per bilayer. Specifically, there is a progression from a stripe-like pattern of parallel channels to a random network of line defects to a pore phase, with the latter appearing at the highest amphiphile concentrations but characterized by the lowest density of defects. Connection is made with experimental work which has recently suggested various departures from classical lamellar structure.

The steady-state bimolecular annihilation reaction A + B –> 0 on two-dimensional surfaces is studied via computer simulations. In the simulations A and B are randomly adsorbed on vacant sites, and reaction takes place whenever A and B reach nearest-neighbor sites, either directly following adsorption or through diffusion. It is found that both with and without diffusion the reactants segregate into separate islands of A’s and B’s. The islands vary in size and exhibit highly ramified shapes. Moreover, the islands are self-similar with a fractal dimension D = 1.89 (similar to percolation, but also other clusters). D is found to be independent of the diffusion rate K. Other fractal dimensions, e.g., of the ‘‘hull’’ differ from those of percolating clusters. The steady-state coverage theta* = theta*A + theta*B decreases with K, as expected (theta*A = theta*B, corresponding to equal fluxes of A and B is the only physical solution). For systems with immobile particles (K = 0) we find theta* congruent-to 0.59 and theta* congruent-to 0.49 for the square and the triangular lattices, respectively, similar to the percolation thresholds on these lattices. The long-time characteristics of the system (D, theta*, etc.) are independent of the initial conditions of the simulation, indicating that the system reaches a stable steady state. Furthermore, for the large systems simulated (typically 500 x 500 lattice sites) it was found that the long-time behavior is independent of the input mode. Namely, the same results are obtained for conserved (i.e., exactly balanced) and nonconserved (statistically balanced) A,B input mechanisms, indicating that on the time scale of the simulations (approximately 10(4) Monte Carlo steps) the apparent steady state (for nonconserved input) is essentially identical with the true steady state (for the conserved input).

A mean field theory of chain packing in amphiphilic aggregates is used to calculate conformational and thermodynamic properties of the inverse hexagonal phase. These properties are compared with those for planar bilayers and curved monolayers. Calculated bond order parameters reveal that chains packed in the hexagonal arrangement have more conformational freedom than chains packed in a bilayer. The calculated order parameters are in good agreement with recent experimental results. Free energy calculations are also presented. It is found that for small areas per head group the packing free energy of amphiphiles in a bilayer is considerably higher than in the hexagonal phase.