Correlation factor, velocity autocorrelation function and frequency-dependent tracer diffusion coefficient

Abstract

Abstract. The correlation factor, defined as the ratio between the tracer diffusion coefficient in lattice gases and the diffusion coefficient for a corresponding uncorrelated random walk, is known to assume a very simple form under certain conditions. A simple derivation of this is given with the aid of the Green-Kubo formula for the tracer diffusion coefficient and it is generalised to a frequency-dependent correlation factor. The application to lattice gases with nearly vanishing vacancy concentration is critically discussed. The derivation is also extended to more complex hopping processes where the correlation factor is a tensor. The velocity autocorrelation function of the tracer particle is demonstrated to exhibit a P 2 -' ) long-time tail. in agreement with mode-coupling predictions.

Silicon-Based Anodes for Li Batteries: Thermodynamics, Structural Analysis, and Li Diffusion

“…39 To estimate Li mobility, the diffusion coefficient has been calculated from the AIMD-obtained autocorrelation function (see eq 10 of the Supporting Information), as shown in Table 3. 40 The diffusion coefficients are in line with those measured using cyclic voltammetry, electrochemical impedance spectroscopy, and galvanostatic intermittent titration measurements (ranging from ∼10 −13 to ∼10 −12 cm 2 /s) and calculated by kinetic Monte Carlo calculations (1.38 × 10 −13 cm 2 /s) and within the range of values calculated by AIMD (4.92 × 10 −14 and 1.05 × 10 −11 cm 2 /s). 41−43 The diffusion coefficient of Li + decreases with an increase in lithium concentration, indicating that diffusion becomes increasingly hindered as the electrode becomes more lithiated due to the scarcity of available interstitial sites near full capacity.…”

Tracer counterpermeation analysis of diffusivity in finite-length nanopores with and without single-file dynamics

“…Furthermore, it is reasonable to expect that the site-approximation estimate, D tr (site) = D 0 (1 − X 0 ), for SFD from (5) provides an upper bound on all D tr (j,j + 1), and in particular on D tr (max) = max D tr (j,j + 1) = D tr (1,2). The factor 1 − X 0 simply reflects blocking of hopping by empty sites, but this formulation neglects any "back-correlation" in diffusion which generally produces lower values of D tr [32]. In fact, for large L, we find that…”

Tracer diffusion in concentrated lattice gas models. Rectangular lattices with anisotropic jump rates

“…6 (2) where the inverse Laplace transform ~(t) of ~(s) is defined as the probability density for an actual random walk as defined above, but with an absorbing boundary at p~ = 0 and with starting point p = a~ at time 0, to first arrive at p=-a~ at time t. 4 In analogy to (I.3), ~ can be expressed as with …”