ALBERT

Notes: 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 coalesence 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 (L¯) evaluated as a function of the Peclet number P, i.e., the dimensionless ratio of flow rate γ(overdot) and rotational diffusion coefficient Dr. For sufficiently dilute solutions, we find only a weak dependence of L¯ on P. In the semidilute regime, however, an apparent divergence in L¯ at P(approximately-equal-to)1 suggests a flow-induced first-order gelation phenomenon.

Notes: We develop a microscopic-level formulation for the curvature elasticity of monolayer and bilayer systems of typical surfactant molecules. It is argued that both the bending and saddle-splay force constants k and k¯ are determined primarily by the conformational entropy of the flexible hydrocarbon chain rather than by the electrostatic interactions associated with hydrophilic head groups. A priori estimates of the chain contributions are made for the first time, without the use of any adjustable parameters. Both k and k¯ are shown to be calculable wholly from the conformational statistics describing the planar film. In particular, these constants are expressed in terms of the derivatives and moments of the lateral pressure profile characterizing chain packing in the unbent layers. By considering the dependence of the curvature elasticity on chain length, area per molecule, and composition in mixed films, we are able to account for the order-of-magnitude variations in k observed in a variety of different surfactant systems. The replacement of long chain molecules by short ones is shown to be especially efficient in lowering the bending energy from 10's of kBT to kBT. The effect of "free'' vs "blocked'' exchange are also presented and contrasted with the case of fixed area-per-molecule bending deformation. Finally, monolayer vs bilayer results are compared and the calculated signs and magnitudes of k and k¯ are discussed in the context of planar bilayer stability.

Notes: 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.

Notes: We treat the isotropic-to-nematic transition in polydisperse suspensions of micellar rods. By generalizing an early theory of Onsager, we obtain a first-order transition in which the ordered rods are significantly longer than those in the (coexisting) isotropic phase. We show that this "growth'' is driven by the free energy term arising from loss of orientational entropy upon alignment. For large aggregates the product ρ¯L¯2D (where L¯ is a number-averaged length, D the diameter of the rods, and ρ¯ the number density of aggregates) is roughly constant for each phase at coexistence. The transition value of the (nematic) order parameter ((approximately-equal-to)〈P2(cos θ)〉) first increases linearly with aggregation number s (for small rods) and approaches unity asymptotically (for large s). We compare our results to those of an earlier, monodisperse treatment of this system and interpret the nematic-induced growth in terms of coupling between rod size and alignment in micellar solutions.

Notes: We study the two-dimensional (2-D) structural and thermodynamic changes in smectic-A/lamellar phases of self-assembling surfactant systems, in which the rim associated with a bilayer edge has a preferred curvature. This property was not considered in previous studies of 2-D aggregation, where an infinite bilayer emerges already at very low concentrations. A lattice Hamiltonian is used to describe the bending energy of the rim: An occupied lattice site corresponds to a minimum, disklike, micelle, and a bending energy penalty is associated with corners and straight edges depending on the value of the spontaneous curvature. When the spontaneous radius of curvature of the rim is small and the bending modulus is large, we find that the "condensation'' transition—i.e., the "collapse'' of the finite aggregates into a continuous bilayer—is postponed to high concentrations. At low concentrations the bending energy leads to an effective repulsive interaction between the aggregates, which in turn can result in ordered (modulated) structures for not too large ratios of thermal energy to bending energy (which is the expected situation in most systems of interest). Our model should be applicable to the systems of decylammonium chloride and cesium perflourooctanoate studied by Boden and co-workers (NMR and conductivity measurements) and Zasadzinski and co-workers (freeze fracture), where monodisperse micellar disks are observed to layer in stacked planes. In the latter system a 2-D order of disk-shaped aggregates appears within the smectic-A layers, which is also consistent with our theory. Experimental studies of the structural evolution under further condensation of the system are not yet available.

Notes: A two-dimensional lattice model, originally introduced by Granek et al. [J. Chem. Phys. 101, 4331 (1994)], is used to demonstrate the intricate coupling between the intramicellar interactions that determine the optimal aggregation geometry of surfactant molecules in dilute solution, and the intermicellar interactions that govern the phase behavior at higher concentrations. Three very different scenarios of self-assembly and phase evolution are analyzed in detail, based on Monte Carlo studies and theoretical interpretations involving mean-field, Landau–Ginzburg, Bethe–Peierls, and virial expansion schemes. The basic particles in the model are "unit micelles'' which, due to spontaneous self-assembly or because of excluded area interactions, can fuse to form larger aggregates. These aggregates are envisaged as flat micelles composed of a bilayerlike body surrounded by a curved semitoroidal rim. The system's Hamiltonian involves one- through four-body potentials between the unit micelles, which account for their tendency to form aggregates of different shapes, e.g., elongated vs disklike micelles.Equivalently, the configurational energy of the system is a sum of micellar self-energies involving the packing free energies of the constituent molecules in the bilayer body and in rim segments of different local curvature. The rim energy is a sum of a line tension term and a 1D curvature energy which depends on the rim spontaneous curvature and bending rigidity. Different combinations of these molecular parameters imply different optimal packing geometries and hence different self-assembly and phase behaviors. The emphasis in this paper is on systems of "curvature loving'' amphiphiles which, in our model, are characterized by negative line tension. The three systems studied are: (i) A dilute solution of stable disklike micelles which, upon increasing the concentration, undergoes a first-order phase transition to a continuous bilayer with isolated hole defects. An intermediate modulated "checkerboard'' phase appears under certain conditions at low temperatures. (ii) A system of unit micelles which in dilute solution tend to associate into linear micelles. These micelles are rodlike at low temperatures, becoming increasingly more flexible as the temperature increases. Upon increasing the concentration the micelles grow and undergo (in 2D) a continuous transition into nematic and "stripe'' phases of long rods. At still higher concentrations the micellar stripes fuse into continuous sheets with line defects. (iii) A system in which, already in dilute solution, the micelles favor the formation of branched aggregates, analogous to the branched cylindrical micelles recently observed in certain surfactant solutions. As the concentration increases the micelles associate into networks ("gels'') composed of a mesh of linear micelles linked by "T-like'' intermicellar junctions. The network may span the entire system or phase separate and coexist with a dilute micellar phase, depending on the details of the molecular packing parameters. © 1995 American Institute of Physics.

Notes: A comparison between a mean field theory of chain packing in membranes and micelles and Monte Carlo simulations is presented for model lipid bilayers. In both approaches the "lipids" are modeled as freely jointed (but self-avoiding) chains of spherical segments. The first segment of the chain represents the head group, anchored to the bilayer interface by a harmonic binding potential. The simulations are performed for symmetric bilayers composed of 200 chains, with periodic boundary conditions. Both pure and mixed bilayers (composed of long and short chains) are analyzed. In the simulation nonbonded segments interact via Lennard-Jones potentials, ensuring nearly uniform segment density in the bilayer core, as assumed in the mean field theory. The lateral pressure profiles governing the probability distribution of chain conformations in the mean field theory are related and compared to the tangential pressure profiles calculated from the simulations using Kirkwood–Buff's molecular theory. The two pressure profiles show very good agreement. We also calculate two conformational chain properties: end-segment distributions and orientational bond order parameters. The end-segment distributions calculated by the two approaches show excellent agreement. The order parameters compare somewhat less satisfactorily, yet we found that the order parameters derived from the simulations depend rather sensitively on the details of the interaction potential. In general, the results of the simulations support the use of the mean field theory as a (simple) tool for studying conformational chain statistics in confined environments and related thermodynamic properties, such as membrane curvature elasticity. © 1997 American Institute of Physics.