Hard-needle elastomer in one spatial dimension

Abstract

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 $Q\sim k^{1/\Delta }$, which does not depend on the equilibrium distance of the springs in this model.

arXiv comment6 pages, 4 figures, to appear in a special issue of the Brazilian Journal of Physics in honor of Prof. Silvio R. Salinas

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Cited by in corpus (1)

• Ordering properties of anisotropic hard bodies in one-dimensional channels