Surface Scaling Analysis of a Frustrated Spring-network Model for Surfactant-templated Hydrogels

We propose and study a simplified model for the surface and bulk structures of crosslinked polymer gels, into which voids are introduced through templating by surfactant micelles. Such systems were recently studied by Atomic Force Microscopy [M. Chakrapani et al., e-print cond-mat/0112255]. The gel is represented by a frustrated, triangular network of nodes connected by springs of random equilibrium lengths. The nodes represent crosslinkers, and the springs correspond to polymer chains. The boundaries are fixed at the bottom, free at the top, and periodic in the lateral direction. Voids are introduced by deleting a proportion of the nodes and their associated springs. The model is numerically relaxed to a representative local energy minimum, resulting in an inhomogeneous, ``clumpy'' bulk structure. The free top surface is defined at evenly spaced points in the lateral (x) direction by the height of the topmost spring, measured from the bottom layer, h(x). Its scaling properties are studied by calculating the root-mean-square surface width and the generalized increment correlation functions C_q(x)= . The surface is found to have a nontrivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales. As the vacancy concentration approaches the site-percolation limit, both the crossover length and the saturation value of the surface width diverge in a manner that appears to be proportional to the bulk connectivity length. This suggests that a percolation transition in the bulk also drives a similar divergence observed in surfactant templated polyacrylamide gels at high surfactant concentrations.Comment: 17 pages RevTex4, 10 imbedded eps figures. Expanded discussion of multi-affinit

Thermal activation of rupture and slow crack growth in a model of homogenous brittle materials

Slow crack growth in a model of homogenous brittle elastic material is described as a thermal activation process where stress fluctuations allow to overcome a breaking threshold through a series of irreversible steps. We study the case of a single crack in a flat sheet for which analytical predictions can be made, and compare them with results from the equivalent problem of a 2D spring network. Good statistical agreement is obtained for the crack growth profile and final rupture time. The specific scaling of the energy barrier with stress intensity factor appears as a consequence of irreversibility. In addition, the model brings out a characteristic growth length whose physical meaning could be tested experimentally.Comment: To be published in : Europhysics Letter

Plasticity of thinwalled beam modeled by spring network

Příspěvek představuje dynamický systém využívající fyzikální diskretizaci pomocí pružinové sítě. Popisuje jednotlivé fáze diskretizačního postupu na praktické, ale zároveň výpočetně náročné nelineární úloze. Všímá si současných aspektů modelu a rovněž demonstruje využití paralelních výpočtů prostřednictvím platformy Nvidia CUDA.The paper represents dynamical system with use of physical discretization method based on spring networks. It describes every phase of used discretization process on practical but also timeconsuming non-linear task. It observes contemporary model aspects and demonstrates use of parallel computation technique by Nvidia CUDA platform

Slow crack growth : models and experiments

The properties of slow crack growth in brittle materials are analyzed both theoretically and experimentally. We propose a model based on a thermally activated rupture process. Considering a 2D spring network submitted to an external load and to thermal noise, we show that a preexisting crack in the network may slowly grow because of stress fluctuations. An analytical solution is found for the evolution of the crack length as a function of time, the time to rupture and the statistics of the crack jumps. These theoretical predictions are verified by studying experimentally the subcritical growth of a single crack in thin sheets of paper. A good agreement between the theoretical predictions and the experimental results is found. In particular, our model suggests that the statistical stress fluctuations trigger rupture events at a nanometric scale corresponding to the diameter of cellulose microfibrils.Comment: to be published in EPJ (European Physical Journal