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Abstract
Growth, shape and texturing dynamics of single 2D spherulites are
analyzed using the Landau-de Gennes (LdG) liquid crystal model of
isotropic-nematic phase ordering. Direct numerical simulation shows
that non-circular nucleation due to anisotropy in the interfacial
tension results in non-circular shapes in the early stages of
growth. However, interfacial heterogeneities in growth and structure
then lead to interfacial defect nucleation and shedding and a
reshaping of the interface into a circular shape. The formulated
dynamics show that a growing spherulite in the early stage of phase
ordering also acquires topological higher charges than expected from
the well-known Kibble mechanism. In agreement with experiments
under strong quenching, the predicted growth dynamics of a
spherulite of characteristic radius R is linear: $R $~$ t$. To
better understand these computational results, a dynamic shape
equation is obtained from the LdG model and is shown to have the
same form as the growth and shape equations of crystal growth. The
shape equation is used to reveal the mechanisms involved in shape
transformations, interfacial defect shedding, and growth dynamics
computed by direct numerical simulation of the bulk LdG equations.
Mathematics Subject Classification: Primary: 70K99, 00A00; Secondary: 00A00.
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