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Deposition and evaporation of infinitely thin hard rods (needles) is studiedin two dimensions using Monte Carlo simulations. The ratio of deposition toevaporation rates controls the equilibrium density of rods, and increasing itleads to an entropy-driven transition to a nematic phase in which both staticand dynamical orientational correlation functions decay as power laws, withexponents varying continuously with deposition-evaporation rate ratio. Ourresults for the onset of the power-law phase agree with those for a conservednumber of rods. At a coarse-grained level, the dynamics of the non-conservedangle field is described by the Edwards-Wilkinson equation. Predicted relationsbetween the exponents of the quadrupolar and octupolar correlation functionsare borne out by our numerical results. We explore the effects of spatialinhomogeneity in the deposition-evaporation ratio by simulations, entropy-basedarguments and a study of the new terms introduced in the free energy. Theprimary effect is that needles tend to align along the local spatial gradientof the ratio. A uniform gradient thus induces a uniformly aligned state, asdoes a gradient which varies randomly in magnitude and sign, but acts only inone direction. Random variations of deposition-evaporation rates in bothdirections induce frustration, resulting in a state with glassycharacteristics.Comment: modified version, Accepted for publication in Physical Review

physical review. e, statistical, nonlinear and soft matter physics

Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in two dimensions: A study using deposition-evaporation kinetics