The influence of stoichiometry on the elastic modulus of eight-functional end-linked poly-(dimethylsiloxane) (PDMS) networks was investigated by extensional rheometry with extensions up to more than 100%, and the stress-strain relation was found to be almost linearsa characteristic property for a network structure with an eight-functional cross-linker. The experimental data were compared to a stochastic model taking into account entanglements and to Monte Carlo simulations. The Mooney-Rivlin model was furthermore used to fit the data, and the dependency of C 1 and C2 parameters on the stoichiometric ratio was investigated in order to clarify especially the influence of trapped entanglements acting either as chemical cross-links or as sliding links. It was found that including a locking factor dividing trapped entanglements into locked entanglements and slip-links could explain our data obtained for the Mooney-Rivlin constants. It was furthermore found that trapped entanglements dominate when there is an excess of cross-linker, ensuring that all long difunctional DMS chains are bound to the infinite network in both ends.

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We compute phase diagrams for dilute AB diblock copolymers in poor solvent in the strong segregation limit (SSL), as function of the copolymer volume fractions, from physics derived directly from the properties of the single diblock copolymer and the interfacial surface tension between the solvent and the copolymer. We allow both volumetric as well as stiffness asymmetry between the two diblock components. We also allow for the possibility of reversion of the morphologies, which represent a system that is continuous in polymer rather than solvent. Thereby, we can map transitions between various phases with, e.g., bicontinuous and continuous structures in either solvent or copolymer. We show that the energetically favorable morphologies in the SSL are different from the morphologies in the more studied weak segregation limit (WSL). Transitions from spherical to cylindrical and from cylindrical to bicontinuous phases are observed with increased asymmetry. A remarkable result is that spherical micelles are not favored for very asymmetric polymers except when the solvent−copolymer interaction is very low.

We study the melt rheology of randomly branched polymers in the hyperbranched polymer (HBP) class which are formed by the co-condensation of AB and AB2 type monomers. Specifically, we study the effect of branch length M x on the entanglement transition in the HBP class. To this end, two series of HBPs were prepared using AB2 mole fractions of 10% and 1% respectively. This allowed us to vary M x from just below to just above M e, the entanglement molecular weight for linear chains of the same chemistry. For the 10% branched samples (M x < M e), we were able to quantitatively model the low and intermediate frequency rheology data using a Rouse model for unentangled chains. For the 1% branched samples (M x > M e), there is a clear entanglement plateau for the higher molecular weight samples and we were able to quantitatively model the rheology around the entanglement plateau region using the tube model. Our data demonstrate conclusively that the entanglement transition for randomly branched polymers in the HBP class is controlled by M x and the transition occurs around M x ≈ M e. These conclusions are the same as for randomly branched polymers in the percolation class. We are able to explain these results using either the Colby−Rubinstein model or double reptation model for entanglements if we assume that whole molecules and side branches with Rouse times less than the Rouse time of an entanglement do not contribute to entanglement formation.

Neuroeconomics has the potential to fundamentally change the way economics is done. This article identifies the ways in which this will occur, pitfalls of this approach, and areas where progress has already been made. The value of neuroeconomics studies for social policy lies in the quality, replicability, and relevance of the research produced. While most economists will not contribute to the neuroeconomics literature, we contend that most economists should be reading these studies.