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Updated: May 26, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
One-dimensional diffusion: discrepancy between exact results and Monte Carlo calculations
J J Torrez Herrera1, G A Ranzuglia, S J Manzi
1Departamento de Física, Instituto de Física Aplicada (INFAP)-Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional de San Luis, San Luis, Argentina.
Abstract:
The exact expression for the collective diffusion coefficient in one dimension, obtained by Payne and Kreuzer [Phys. Rev. B. 75, 115403 (2007)], is compared with Monte Carlo simulation. Different hopping kinetics are analyzed. For initial- and final-state interaction kinetics no anomalies are observed. However, for the so-called interaction kinetics where both initial- and final-state interactions are involved, it is shown that even when the transition rates satisfy the principle of detail balance, additional constraints are necessary to guarantee the diffusion of particles. These restrictions give rise to a phase diagram that determines the regions where the exact solution of the diffusion coefficient seem to be not physically sound. The Monte Carlo simulation allows us to analyze the mechanism of diffusion in these regions, where in some cases the simulation does not match the exact solution. A possible explanation is presented.
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