Hard-Needle Elastomer in One Spatial Dimension

• Autor(a) principal: Liarte, Danilo B. [UNESP]
• Data de Publicação: 2023
• Outros Autores: Petri, Alberto, Salinas, Silvio R.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s13538-023-01289-7; http://hdl.handle.net/11449/248728
• topic: Elastomers; Exact solvable models; Liquid crystals; Rigid rotors

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 σ. In the presence of elastic interactions, the system exhibits a standard universal scaling form, with Q/|σ| being a function of the rescaled elastic energy constant k/|σ|Δ, where Δ is a critical exponent equal to 2 for this model. At zero tension, simple scaling arguments lead to the asymptotic behavior Q∼k1/Δ, which does not depend on the equilibrium distance of the springs in this model.