Publications

A theoretical and computational framework for systematically calculating the macroscopic polarization density as a field variable from molecular dynamics simulations is presented. This is done by extending the celebrated Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)10.1063/1.1747782] procedure, which expresses macroscopic stresses and heat fluxes in terms of the atomic variables, to the case of electrostatics. The resultant macroscopic polarization density contains molecular dipole, quadrupole, and higher-order moments, and can be calculated to a desired accuracy depending on the degree of the coarse-graining function used to connect the molecular and continuum scales. The theoretical and computational framework is verified by recovering the dielectric constant of bulk water. Finally, the theory is applied to calculate the spatial variation of the polarization vector in the electrical double layer of a 1:1 electrolyte solution. Here, an intermediate asymptotic length scale is revealed in a specific region, which validates the application of mean field Poisson-Boltzmann theory to describe this region. Also, using the existence of this asymptotic length scale, the lengths of the diffuse and condensed/Stern layers are identified accurately, demonstrating that this framework may be used to characterize electrical double layers over a wide range of concentrations of solutions and surface charges. © 2013 AIP Publishing LLC.

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We present a rigorous Green-Kubo methodology for calculating transport coefficients based on on-the-fly estimates of: (a) statistical stationarity of the relevant process, and (b) error in the resulting coefficient. The methodology uses time samples efficiently across an ensemble of parallel replicas to yield accurate estimates, which is particularly useful for estimating the thermal conductivity of semi-conductors near their Debye temperatures where the characteristic decay times of the heat flux correlation functions are large. Employing and extending the error analysis of Zwanzig and Ailawadi [Phys. Rev. 182, 280 (1969)]10.1103/PhysRev.182.280 and Frenkel [in Proceedings of the International School of Physics Enrico Fermi, Course LXXV (North-Holland Publishing Company, Amsterdam, 1980)] to the integral of correlation, we are able to provide tight theoretical bounds for the error in the estimate of the transport coefficient. To demonstrate the performance of the method, four test cases of increasing computational cost and complexity are presented: the viscosity of Ar and water, and the thermal conductivity of Si and GaN. In addition to producing accurate estimates of the transport coefficients for these materials, this work demonstrates precise agreement of the computed variances in the estimates of the correlation and the transport coefficient with the extended theory based on the assumption that fluctuations follow a Gaussian process. The proposed algorithm in conjunction with the extended theory enables the calculation of transport coefficients with the Green-Kubo method accurately and efficiently. © 2012 American Institute of Physics.

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