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Abstract:

Detailed physical and mechanical characterization of the matrix as well as the interphases of polymer matrix composites can lead to a more complete understanding of failure mechanisms in polymer matrix composite (PMC). This study illustrates mechanical damage of polymers in both the bulk, as well as around the interphase region through integrated computation & experimentation approach. We have developed a quantum mechanics-molecular dynamics framework, which has enabled the prediction of bond scission under load, creation of intermittent free radicals, and exploration of the potential energy surface for possible secondary reactions immediately following bond scission. In parallel, we have conducted experiments with epoxy systems with varying molecular weight and cross-linker density at different load conditions to benchmark the simulation findings of the chemical species present on fracture surfaces of the polymer. In order to evaluate experimentally molecular level effects of mechanical load in epoxy-systems, detail characterizations were conducted combing spectroscopy (X-ray photoelectron spectroscopy, FT-Infrared spectroscopy), microscopy (HRTEM, AFM-IR, SEM), X-ray diffraction (SAXS) and mechanical testing (3-point bending). Similarly, the nanoscopic nature of interphases of PMCs in terms of topography, chemical mapping/bonding, fractography, and modulus are also studied in order to find a bridge between nanoscopic, microscopic and macroscopic mechanical properties.

Abstract:

We consider the statistical mechanics of a class of models involving close-packed loops with fugacity n on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretizations of CPn-1 σ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the σ model, and we discuss the relationship between loop properties and σ model correlators. On large scales, loops are Brownian in an ordered phase and have a nontrivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for n=1,2,3 and first order transitions for n≥4. We also give a renormalization-group treatment of the CPn-1 model that shows how a continuous transition can survive for values of n larger than (but close to) 2, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including SU(n) quantum magnets in (2+1) dimensions, Anderson localization in symmetry class C, and the statistics of random curves in three dimensions. © 2013 American Physical Society.

Abstract:

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using $CP^{n-1}$ or $RP^{n-1}$ and O(n) $σ$ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter $θ$ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.