Precise calculations are made of the scattering intensity I(q) from an oriented stack of lipid bilayers using a realistic model of fluctuations. The quantities of interest include the bilayer bending modulus K c , the interbilayer interaction modulus B, and bilayer structure through the form factor F(q z ). It is shown how K c and B may be obtained from data at large q z where fluctuations dominate. Good estimates of F(q z ) can be made over wide ranges of q z by using I(q) in q regions away from the peaks and for q r 0 where details of the scattering domains play little role. Rough estimates of domain sizes can also be made from smaller q z data. Results are presented for data taken on fully hydrated, oriented DOPC bilayers in the L ␣ phase. These results illustrate the advantages of oriented samples compared to powder samples.
We use self-consistent mean field methods and analytical theory to determine the behavior of AB copolymers at the interface between two incompatible homopolymers, A and B. We calculate the reduction in interfacial tension, γ, resulting from the copolymers localizing at the A/B interface. We examine the effects of chain length, composition, and molecular architecture on the efficiency of the copolymers. In particular, we compare the interfacial behavior of different linear copolymers (random, alternating, and diblock) and various branched copolymers (stars and combs). At fixed molecular weight, the diblock copolymers are the most efficient at reducing γ. However, when we compare random and comb copolymers with diblocks at different molecular weights, we observe that the longer random or comb copolymers are more efficient than short diblocks. These studies allow us to predict the reduction in interfacial tension produced by a wide variety of copolymers and, thereby, permit a rational design of cost-effective and efficient compatibilizers.
To model the phase behavior of polymer−clay composites, we develop a free energy
expression for a mixture of polymers and solid, thin disks. The free energy expression is adopted from
the Onsager model for the equilibrium behavior of rigid rods. Thus, our theory takes into account the
possible nematic ordering of the disks within the polymer matrix. By minimizing this free energy and
calculating the chemical potentials, we construct phase diagrams for the polymer−disk mixtures. The
findings provide guidelines for tailoring the polymer molecular weight and the volume fraction of the
different components to fabricate thermodynamically stable mixtures with the desired morphology.
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