Efficient enhancement of the toughness of epoxy resins has been a bottleneck for expanding their suitability for advanced applications. Here, polysulfone (PSF) was adopted to toughen and modify the epoxy. The influences of PSF on the mechanical and thermal properties of the epoxy resin were systematically studied by optical microscopy, Fourier transform infrared spectrometer (FT-IR), differential scanning calorimetry (DSC), thermogravimetric analyzer (TG), dynamic mechanical thermal analyzer (DMA), mechanical tests and scanning electron microscope (SEM). The dissolution experimental results showed that PSF presents a good compatibility with the epoxy resin and could be well dissolved under controlled conditions. The introduction of PSF was found to promote the curing reaction of the epoxy resin without participating in the curing reaction and changing the curing mechanism as revealed by the FT-IR and DSC studies. The mechanical properties of PSF/epoxy resin blends showed that the fracture toughness and impact strength were significantly improved, which could be attributed to the bicontinuous phase structure of PSF/epoxy blends. Representative phase structures resulted from the reaction induced phase separation process were clearly observed in the PSF/epoxy blends during the curing process of epoxy resin, which presented dispersed particles, bicontinuous and phase inverted structures with the increase of the PSF content. Our work further confirmed that the thermal stability of the PSF/epoxy blends was slightly increased compared to that of the pure epoxy resin, mainly due to the good heat resistance of the PSF component.

Abstract.In general, when a quasi-Newton method is applied to solve a system of nonlinear equations, the quasi-Newton direction is not necessarily a descent direction for the norm function. In this paper, we show that when applied to solve symmetric nonlinear equations, a quasi-Newton method with positive definite iterative matrices may generate descent directions for the norm function. On the basis of a Gauss-Newton based BFGS method [D. H. Li and M. Fukushima, SIAM J. Numer. Anal., 37 (1999), pp. 152-172], we develop a norm descent BFGS method for solving symmetric nonlinear equations. Under mild conditions, we establish the global and superlinear convergence of the method. The proposed method shares some favorable properties of the BFGS method for solving unconstrained optimization problems: (a) the generated sequence of the quasi-Newton matrices is positive definite; (b) the generated sequence of iterates is norm descent; (c) a global convergence theorem is established without nonsingularity assumption on the Jacobian. Preliminary numerical results are reported, which positively support the method.

The nonlinear Poisson-Boltzmann equation (PBE) is a widely-used implicit solvent model in biomolecular simulations. This paper formulates a new PBE nonlinear algebraic system from a mortar finite element approximation, and proposes a new minimization protocol to solve it efficiently. In particular, the PBE mortar nonlinear algebraic system is proved to have a unique solution, and is equivalent to a unconstrained minimization problem. It is then solved as the unconstrained minimization problem by the subspace trust region Newton method. Numerical results show that the new minimization protocol is more efficient than the traditional merit least squares approach in solving the nonlinear system. At least 80 percent of the total CPU time was saved for a PBE model problem.

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