Hard-Needle Elastomer in One Spatial Dimension

Autor(es)

Liarte, Danilo B. ; Petri, Alberto ; Salinas, Silvio R.

• Tipo de documento: Artigo Científico
• Fonte: Brazilian Journal of Physics; v. 53, n. 3, p. 7-pg., 2023-06-01.

Resumo

We perform exact statistical mechanics calculations for a system of elongated objects (hard needles) that are restricted to translate along a line and rotate within a plane, and that interact via both excluded-volume steric repulsion and harmonic elastic forces between neighbors. This system represents a one-dimensional model of a liquid crystal elastomer, and has a zero-tension critical point that we describe using the transfer-matrix method. In the absence of elastic interactions, we build on previous results by Kantor and Kardar, and find that the nematic order parameter Q decays linearly with tension sigma. In the presence of elastic interactions, the system exhibits a standard universal scaling form, with Q/|sigma| being a function of the rescaled elastic energy constant k/|sigma|(Delta), where Delta is a critical exponent equal to 2 for this model. At zero tension, simple scaling arguments lead to the asymptotic behavior Q similar to k(1/Delta), which does not depend on the equilibrium distance of the springs in this model. (AU)

• Processo FAPESP: 22/09615-7 - Geometria, topologia e fluidos complexos: aplicações a cristais líquidos e sistemas elásticos desordenados
• Beneficiário: Danilo Barbosa Liarte
• Modalidade de apoio: Bolsas no Brasil - Jovens Pesquisadores
• Processo FAPESP: 21/14285-3 - Geometria, topologia e fluidos complexos: aplicações a cristais líquidos e sistemas elásticos desordenados
• Beneficiário: Danilo Barbosa Liarte
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores