Modelling the time evolution of the structure factor during polymeric spinodal decomposition using dynamic mode decomposition Matthew Jones and Nigel Clarke Department of Physics and Astronomy, University of Sheffield, UK Scattering experiments are a powerful way to probe the evolution of the microstructure in heterogeneous materials [1], for example immiscible polymer blends. In spinodal decomposition – the process of spontaneous phase separation – information about the microstructure can be deduced from measurements of the structure factor [1], defined as the Fourier transform of the two-point correlation function of the composition fluctuations. While the time evolution of the structure factor can be measured relatively easily, modelling it has proved to be much more difficult [2]. Embracing this duality, we model the time evolution of the structure factor in simulated polymer blends using dynamic mode decomposition [3] – a data-driven method for constructing approximate linear models of high-dimensional, non-linear dynamical systems. We assess the accuracy and range of the predictions and investigate the parameter choices required to build good models. Our findings suggest that dynamic mode decomposition could be used practically and effectively to make future predictions of the structure factor in an experimental setting. References 1. J. S. Higgins and H. C. Benoit,Polymers and Neutron Scattering,Oxford University Press, 1994 2. A. Z. Akcasu et al., Theoretical and Experimental 3. Study of Dissolution of Inhomogeneities Formed During Spinodal Decomposition in Polymer
4. Mixtures, The Journal of Chemical Physics, 97(8):5782-5793, 1992 5. S. L. Brunton and J. N. Kutz, Dynamic Mode Decomposition,SIAM, 2016
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