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We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules. The theory is an application of Jayne's maximum entropy principle, which allows the statistical treatment of systems away from equilibrium. In particular, neither temperature nor atomic fractions are required to be uniform but instead are allowed to take different values from particle to particle. In addition, following the Coleman-Noll method of continuum thermodynamics we derive a dissipation inequality expressed in terms of discrete thermodynamic fluxes and forces. This discrete dissipation inequality effectively sets the structure for discrete kinetic potentials that couple the microscopic field rates to the corresponding driving forces, thus resulting in a closed set of equations governing the evolution of the system. We complement the general theory with a variational meanfield theory that provides a basis for the formulation of computationally tractable approximations. We present several validation cases, concerned with equilibrium properties of alloys, heat conduction in silicon nanowires and hydrogen desorption from palladium thin films, that demonstrate the range and scope of the method and assess its fidelity and predictiveness. These validation cases are characterized by the need or desirability to account for atomiclevel properties while simultaneously entailing time scales much longer than * Corresponding author E-mail address: ortiz@caltech.edu (M. Ortiz). September 27, 2014 those accessible to direct molecular dynamics. The ability of simple meanfield models and discrete kinetic laws to reproduce equilibrium properties and long-term behavior of complex systems is remarkable. Preprint submitted to Journal of the Mechanics and Physics of Solids

A procedure to obtain homogeneous free-standing polypyrrole (ppy) films 10−20 μm thick is described. The resulting films have mechanical characteristics good enough to be used as a working electrode for electrochemical measurements and applications. Structures and uniformity of both film surfaces and the cross section were studied by SEM. Three different procedures were used to determine the film thickness. The free-standing film can be reduced in aqueous solution up to −3.0 V without any presence of hydrogen release or polymer degradation. Voltammetric experiments show the usual voltammograms, but they only involve a partial oxidation and reduction of the film capabilities:  voltammetric charges increase for decreasing sweep rates. A deep reduction of the film is achieved by polarization times longer than 300 s at −0.6 V or more cathodic potentials. The second cathodic maximum, appearing on the voltammograms between −0.7 and −0.9 V, is related to slow kinetic and structural processes since the film reduction is completed by long polarization time at −0.6 V; the concomitant equilibrium potential is then more anodic than −0.6 V. All of these results are consistent with the electrochemically stimulated conformational relaxation (ESCR) model. The swelled and oxidized film shrinks progressively along the voltammetric reduction. Around −1.0 V the polymeric structure is closed when still 35% to 60% (depending on the scan rate) of the material remains oxidized. The reduction is then completed by slow migration of the counterions through the increasingly compacted polymeric entanglement by stimulating conformational relaxation processes of the ppy chains. A constant and low cathodic current is observed on the voltammograms up to −3.0 V. Oxidation potentials higher than +0.6 V promote the electrochemical degradation of the ppy. Three potential windows are distinguished for these films in aqueous solutions:  from potentials as low as −3.0 to −0.6 V they are a compacted semiconductor electrode without hydrogen release; from −0.6 to +0.5 V they are a progressively more oxidized and swelled conducting polymer electrode; and potentials higher than +0.6 V bring on ppy over-oxidation processes and degradation of the electrochemical activity.

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