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We outline a connection between recent mean-field theories of short-chain packing in micellar systems and earlier approaches developed for treating phase separation in polymer blends. These theories are easily unified on the basis of a common variational principle, thereby allowing a single route for deriving lateral pressures, local ordering, and thermodynamic properties. In this approach the search for conformational probability distribution functions is mapped into a constrained random walk problem, using the monomer propagator formalism first exploited by Edwards. As an application, the case of a compact (uniform density—‘‘dry’’) amphiphilic bilayer is studied in detail. We show that the ‘‘core’’ free energy can be described via a single reduced variable relevant to both short and long chains: convenient scaling relations are proposed and discussed. [ABSTRACT FROM AUTHOR]

Starting from the partition function of a micellar aggregate, the various assumptions involved in decomposing the aggregate’s standard chemical potential into surface and core terms are explicitly stated and discussed. The conformational statistics of the amphiphiles’ hydrocarbon chains (tails) composing the hydrophobic core is assumed to be governed by the hard core repulsive interactions between chain segments. The density within the core is assumed uniform and liquid-like. By appropriate expansion of the aggregate’s configurational integral, explicit expressions are derived for the (singlet) distribution function of chain conformations and the chain’s conformational partition function (free energy). These quantities depend on the thickness and curvature (geometry) of the hydrophobic core via the lateral pressures representing the geometric packing constraints. (The same distribution function has been previously derived by us using the maximal entropy formalism.) It is argued that the variations in the conformational contribution to the aggregate’s chemical potential may be comparable to those due to the surface term. (In the prevailing models of amphiphile aggregation only the latter are included.) Detailed numerical analyses for model chains packed in spherical, cylindrical, and planar aggregates are presented in the subsequent paper (part II). One of the major conclusions from the calculations is that geometric packing constraints rather than internal energy (gauche–trans) effects are the dominant factors determining chain statistics. [ABSTRACT FROM AUTHOR]

Based on the theory presented in part I (preceding paper) we calculate molecular and thermodynamic properties of model chains packed in micellar aggregates of three typical geometries: spheres, cylinders, and planar bilayers. Each possible conformation of a model chain is equivalent to a sequence of walks on a regular cubic lattice. The internal energy of a given conformation is proportional to the number of ‘‘kinks’’ (π/2 bond angles). The kink (gauche) energy measures the inherent flexibility of the chain. We calculate bond order parameter profiles for chains packed in aggregates of various curvature and radius, and find that in all cases the degree of conformational freedom increases from the chain head towards its end. The same qualitative behavior is observed for entirely flexible (zero kink energy) chains. This implies that the internal energy of the chain plays only a secondary role, compared to that of the packing constraints in determining chain conformational statistics in micellar aggregates. In accordance with this conclusion we also find that the geometry dependence of the conformational free energy is dominated by the entropic contribution. The differences between the minimal free energies of chains in different geometries are generally small. Yet, they may be comparable in magnitude to the changes associated with the surface (‘‘opposing forces’’) contributions to the geometry dependence of the micelle’s free energy. [ABSTRACT FROM AUTHOR]

The liquid crystalline phase diagrams for aqueous solutions of the homologous series of surfactants CF3(CF2)nCO-2Cs+ (n=5–8) have been determined. They all exhibit the classical isotropic (I)-to-discotic nematic (ND) and ND-to-smectic lamellar (L) sequences of transitions with increasing concentration, as previously established for the n=6 system [N. Boden, S. A. Corne, and K. W. Jolley, J. Phys. Chem. 91, 4092 (1987)]. The effect of increasing n is to displace the transitions to higher temperatures. The behavior of all of the surfactant systems can be represented on a universal phase diagram. Both the I-to-ND and the ND-to-L transitions at corresponding concentrations are found to occur when the axial ratio of the disklike micelles attains a singular value in each case, irrespective of the value of n. The form of the experimental phase diagrams can be qualitatively understood in terms of a simple ‘‘zeroth’’ order theory which uses the results of Onsager’s theory [L. Onsager, Ann. NY Acad. Sci. 51, 627 (1949)] applied to disks to find the critical axial ratios in the coexisting isotropic and nematic phases and, separately, a dilute solution, self-assembly theory of disklike micelles [W. E. McMullen, A. Ben-Shaul, and W. M. Gelbart, J. Colloid Interface Sci. 98, 523 (1984)] to determine the temperatures at which these axial ratios are achieved at each concentration. The same treatment is also shown to account for the experimental phase behavior of mixed-chain-length systems. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The conformational and thermodynamic characteristics of molecular organization in mixed amphiphilic aggregates of different compositions and geometries are analyzed theoretically. Our mean-field theory of chain conformational statistics in micelles and bilayer membranes is extended from pure to mixed aggregates, without invoking any additional assumptions or adjustable parameters. We consider specifically binary aggregates comprised of long-chain and short-chain surfactants, packed in spherical micelles, cylindrical rods, and planar bilayers. Numerical results are presented for mixtures of 11- and 5-carbon chain amphiphiles. The probability distribution functions (pdfs) of the (different types of) chains are determined by minimizing the conformational free energy, subject to packing constraints which reflect the segment density distribution within the hydrophobic core. In order to analyze the relative thermodynamic stabilities of mixed aggregates of different compositions (long/short chain ratios) and different geometries, the aggregate’s free energy is expressed as a sum of conformational, surface, and mixing contributions. The conformational free energy is determined by the pdfs of the chains and the surface term is modeled in terms of the ‘‘opposing forces’’ operative at the hydrocarbon–water interface. An interesting coupling between these terms arises from the special geometric (surface/volume) limitations associated with packing short and long chains in a given ratio within a given aggregate. In particular, it is found that the minimal area per surfactant head group in a mixed spherical micelle is significantly lower than that in a pure micelle (similarly, though less drastically so, for cylindrical micelles). The most important qualitative conclusion of our thermodynamic analysis is that the preferred aggregation geometry may vary with composition. For example, we find that under certain conditions (areas per... [ABSTRACT FROM AUTHOR]

A recently developed mean field (‘‘single-chain’’) theory for amphiphile chain organization and thermodynamics in micellar aggregates is applied to rotational isomeric state, model chains. The theory provides explicit, simple expressions for the probability distribution of chain conformations and related molecular and thermodynamic properties applicable to aggregates of arbitrary geometries. Bond order parameter profiles calculated from the theory for a planar bilayer, assuming a compact hydrophobic core, show very good agreement with experimental data and molecular dynamics simulations. For small spherical micelles comparison between theory and experiment suggest the existence of a somewhat rough (few angstroms wide) hydrocarbon–water interfacial region. Cylindrical aggregates reveal intermediate behavior. The extent of ‘‘surface roughness’’ is introduced into the theory via a density profile of the hydrophobic core which decreases gradually from the bulk liquid (compact core) density to zero. A series of calculations is presented to analyze the effects of internal chain (gauche/trans) energy and micellar geometry on the conformational and thermodyamic properties of the hydrocarbon chains. It is found that the internal energy plays only a secondary role, compared to the primary role of the packing constraints. (This is qualitatively consistent with our previous findings for approximate, ‘‘cubic,’’ model chains.) The conformational free energy cost associated with chain packing in aggregates is shown to depend on the micellar geometry (i.e., on the curvature of, and the average area per head group at, the hydrocarbon–water interface) and to be comparable with the surface (head group) contributions treated exclusively in the prevailing theories of surfactant self-assembly. Finally, a ‘‘corresponding-states’’ behavior is demonstrated for... [ABSTRACT FROM AUTHOR]