A new theory of inhomogeneous multicomponent systems is developed, starting from the functional integral representation of the partition function. The theory can be used to determine the interfacial properties and microdomain structures of a combination of homopolymers, block copolymers, monomers, and solvents.For the case of no polymers present, our theory reduces to that of Cahn and Hilliard for small molecules.In our approach, the general free energy functional is optimized by the saddle-function method, subject to constraints of no volume change with mixing and constancy of the individual particle numbers, to obtain new equations for the mean fields acting on the polymers. We are thus able to restrict density fluctuations in the system, without introducing an "ad hoc" term involving a vanishing compressibility into the free energy. In addition, by using the gradient expansion for the interaction energy, we demonstrate explicitly the absence of all "kinetic" terms involving the (inverse) degree of polymerization from the mean-field equations, when we choose to introduce the local, homogeneous Flory-Huggins free energy for reference. The mathematical formalism is worked out in detail for the multicomponent homopolymer-solvent system, and it is shown how to extend the theory to include block copolymers. Finally, in order to give a definite example, the variation of the interfacial properties with molecular weight and interaction parameter is worked out numerically for the simplest case of a homopolymer-solvent system. The numerical method is discussed in detail. Applications to more complicated systems will be given in the future.

Interpenetrating polymer networks (IPNs) have been the subject of extensive study since their advent in the 1960s. Hydrogel IPN systems have garnered significant attention in the last two decades due to their usefulness in biomedical applications. Of particular interest are the mechanical enhancements observed in "double network" IPN systems which exhibit nonlinear increases in fracture properties despite being composed of otherwise weak polymers. We have built upon pioneering work in this field as well as in responsive IPN systems to develop an IPN system based on end-linked poly-(ethylene glycol) (PEG) and loosely crosslinked poly(acrylic acid) (PAA) with hydrogen bond-reinforced strain-hardening behavior in water and high initial Young's moduli under physiologic buffer conditions through osmotically induced pre-stress. Uniaxial tensile tests and equilibrium swelling measurements were used to study PEG/PAA IPN hydrogels having second networks prepared with varying crosslinking and photoinitiator content, pH, solids content, and comonomers. Studies involving the addition of non-ionic comonomers and neutralization of the second network showed that template polymerization appears to be important in the formation of mechanically enhanced IPNs.

A simple model of AB diblock copolymer micelles in solution is presented. A spherical shape is assumed, with a completely uniform inner core formed from the insoluble B blocks and a uniform outer shell composed of the soluble A blocks. The interaction parameters, as well as the molecular weight, composition, and overall volume fraction of the copolymers, are assumed to be given. All energetic and entropic contributions to the free energy can be written down simply, with the exception of the interfacial tension y of the asymmetric interphase. An approximation for y is developed, and the free energy is minimized to obtain the equilibrium size of the micelle. Good agreement with the small-angle X-ray scattering data on the polystyrene/ polybutadiene / n-heptane system is obtained. Numerical results, as well as scaling arguments, indicate that the size of the micelle, even for different block copolymer compositions, is characterized by power law functions of the total molecular weight of the block copolymer.

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A preaveraged topological parameter, TV, is introduced to provide a criterion for the presence of entanglements in polymer melts. The theory predicts a geometrical transition from the entangled to the unentangled state in agreement with experimental data. A generalized Rouse theory is used to describe polymer dynamics in both states.PACS numbers: 61.41.+e, 36.20.Ey, 62.10.+S In the reptation model for entangled polymers, 1,2 a polymer diffuses in a dense network of entanglements formed by the surrounding chains. The model assumes that the entanglements are sufficiently long-lived that diffusional motion is essentially one dimensional in a confining tube. The detailed conformation of the polymer chain is replaced by a connected sequence of freely jointed links corresponding to equal-sized segments of polymer, whose length is equal to the mean number of monomers between entanglements, N e , which then evolves in a stochastic earthworm fashion creating and destroying the tube at the ends. The phenomenological parameter N e is assumed to be a property of the entangled chains and independent of the chain length. A direct calculation of N e , for a particular system, has not been accomplished because of the difficulty of topological classification of entanglements. In practice, N e is used as an experimental fitting parameter.In this paper, we introduce a reformulation of the tube Ansatz. The parameter N e is replaced by a new parameter, TV, called the coordination number, whose value is expected to be universal. In the present theory, TV is a geometrical property of the entangling chains and can be related to N e and TV r , the critical chain size for the presence of long-lived entanglements. Polymer dynamics, in the entangled state, can then be described by a suitable projection of the Rouse equation onto a tube axis. Several scaling properties of polymer melts and concentrated solutions followed directly from this theory.Our system of interest consists of Gaussian monodisperse chains with TV skeletal bonds, bond length /, and bond number density p m . Focusing on one chain, hereafter called the test chain, we inscribe a subsection of the chain, with N e bonds, in a sphere of diameter A^1 /2 /, i.e., the mean distance spanned by the N e bonds (see Fig. 1). For the moment N e will be some arbitrary number less than TV. In a high-density system, several other polymers will thread through this sphere and may be involved in forming entanglements with the test chain segment, or may restrict the lateral degrees of freedom of the chain. With the help of Fig. 1 we can see that the probability of this situation occurring is not independent of chain lengths. For example, if we rescale all polymer lengths according to TV-* N/2 by simply cutting all polymers at their midpoints (Fig. 1, lower part), some of our scissions will occur within the test sphere. The new polymer ends produced by this cutting will lessen the probability of forming entanglements or having lateral constraints, and increase the mean spacing between entang...