Eur. Phys. J. E 8, 15-31 (2002)
DOI: 10.1140/epje/i2002-10089-9

Theoretical and finite-element investigation of the mechanical response of spinodal structures

D.J. Read¹, P.I.C. Teixeira², R.A. Duckett³, J. Sweeney⁴ and T.C.B. McLeish<sup>3

1</sup>  Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK
²  Faculdade de Engenharia, Universidade Católica Portuguesa, Estrada de Talaíde, P-2635-631 Rio de Mouro, Portugal and Departamento de Engenharia de Materiais e Instituto de Ciência e Engenharia de Materiais e Superfícies, Instituto Superior Técnico, Avenida Rovisco Pais, P-1049-001 Lisbon, Portugal
³  IRC in Polymer Science and Technology, Department of Physics, University of Leeds, Leeds, LS2 9JT, UK
⁴  IRC in Polymer Science and Technology, Department of Mechanical and Medical Engineering, University of Bradford, Bradford, BD7 1DP, UK

d.j.read@leeds.ac.uk

(Received 21 January 2002 and Received in final form 9 April 2002)

Abstract
In recent years there have been major advances in our understanding of the mechanisms of phase separation in polymer and copolymer blends, to the extent that good control of phase-separated morphology is a real possibility. Many groups are studying the computational simulation of polymer phase separation. In the light of this, we are exploring methods which will give insight into the mechanical response of multiphase polymers. We present preliminary results from a process which allows the production of a two-dimensional finite-element mesh from the contouring of simulated composition data. We examine the stretching of two-phase structures obtained from a simulation of linear Cahn-Hilliard spinodal phase separation. In the simulations, we assume one phase to be hard, and the other soft, such that the shear modulus ratio is large ( ). We indicate the effect of varying composition on the material modulus and on the distribution of strains through the stretched material. We also examine in some detail the symmetric structures obtained at 50% composition, in which both phases are at a percolation threshold. Inspired by simulation results for the deformation of these structures, we construct a "scaling" theory, which reproduces the main features of the deformation. Of particular interest is the emergence of a lengthscale, below which the deformation is non-affine. This length is proportional to , and hence is still quite small for all reasonable values of this ratio. The same theory predicts that the effective composite modulus scales also as , which is supported by the simulations.

PACS
61.41.+e - Polymers, elastomers, and plastics.
62.25.+g - Mechanical properties of nanoscale materials.
61.43.Hv - Fractals; macroscopic aggregates (including diffusion-limited aggregates).


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002