Microscopic theory for the glass transition in a system without static correlations

We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a.We approximate the influence of the surrounding rods onto dynamics of a pair of rods by introducing an effective rotational diffusion constant D(l),l=L/a. We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at l_c, if v(l_c)=1. We present a variational and a numerically exact evaluation of v(l).Close to l_c the diffusion constant decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a glass transition in the absence of any static correlations, in contrast to present form of mode coupling theory.Comment: 6 pages, 3 figure

Glass transition in systems without static correlations: a microscopic theory

We present a first step toward a microscopic theory for the glass transition in systems with trivial static correlations. As an example we have chosen N infinitely thin hard rods with length L, fixed with their centers on a periodic lattice with lattice constant a. Starting from the N-rod Smoluchowski equation we derive a coupled set of equations for fluctuations of reduced k-rod densities. We approximate the influence of the surrounding rods onto the dynamics of a pair of rods by introduction of an effective rotational diffusion tensor D and in this way we obtain a self-consistent equation for D. This equation exhibits a feedback mechanism leading to a slowing down of the relaxation. It involves as an input the Laplace transform v_0(l/r) at z=0, l=L/a, of a torque-torque correlator of an isolated pair of rods with distance R=ar. Our equation predicts the existence of a continuous ergodicity-breaking transition at a critical length l_c=L_c/a. To estimate the critical length we perform an approximate analytical calculation of v_0(l/r) based on a variational approach and obtain l_c^{var}=5.68, 4.84 and 3.96 for an sc, bcc and fcc lattice. We also evaluate v_0(l/r) numerically exactly from a two-rod simulation. The latter calculation leads to l_c^{num}=3.45, 2.78 and 2.20 for the corresponding lattices. Close to l_c the rotational diffusion constant decreases as D(l) ~ (l_c - l)^\gamma with \gamma=1 and a diverging time scale t_\epsilon ~ |l_c - l|^{-\delta}, \delta=2, appears. On this time scale the t- and l-dependence of the 1-rod density is determined by a master function depending only on t/t_\epsilon. In contrast to present microscopic theories our approach predicts a glass transition despite the absence of any static correlations.Comment: 22 pages, 7 figures (minor revisions in the text, corrected figures

Towards a gm/Id design methodology for polymer-based organic thin film transistors

In this paper we show based on experiments that an invariant representation exists for various polymer-based solution processable organic thin film transistors (OTFTs). Despite the fact that this technology suffers from a non-negligible spread of parameters, all experimental data exhibit low dispersion when represented in a gm/Id versus Id diagram. This result is important for circuit design strategy based on the gm/Id representation, giving more insight into analogue design methodology. In addition, the gm/Id invariant can also be used to extract the gale voltage mobility dependence that is inherent to organic field effect transistor