Dispersive diffusion transport and noise, time-dependent diffusion coefficient, generalized Einstein-Nernst relation, and dispersive diffusion-controlled unimolecular and bimolecular reactions

Ngai, K. L.; Fu-Sui, Liu

doi:10.1103/physrevb.24.1049

Cited by 76 publications

(17 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The coherent as well as the incoherent intermediate scattering functions for diffusion and for these other relaxations are different. This difference is evident from results of mean squared displacement obtained previously for diffusion by the CM (45,(51)(52)(53)(54).…”

Section: D? Id? = D L (Q)id S (Q)contrasting

confidence: 33%

“…The mean-square displacement corresponding to equation 12 has been calculated before from the CTRW formalism analytically in limiting time regimes (51) and numerically for all times (52). The numerical result obtained for all times t>t c agree with the analytical results which consists of two stages: a(co) -co 2 lirn^o J~(r 2 (t))e i( "~adt and the three time regimes of <A^(f)> given by equations 11,13 and 14 correspond to the three frequency regimes of a(co)= o 0 for (fl£(*c)"\ a(G))occo n for (f )* 1 «aK<(r c )" 1 , and a(©)=<Jdc for (f ) _1 »co that have been discussed in a previous subsection.…”

Section: D? Id? = D L (Q)id S (Q)mentioning

confidence: 99%

See 1 more Smart Citation

Basic Physics of the Coupling Model: Direct Experimental Evidences

Ngai

Rendell

1997

ACS Symposium Series

Self Cite

View full text Add to dashboard Cite

The fundamental results of the Coupling Model, i.e. crossover from independent relaxation at short-times to slowed down cooperative relaxation at a temperature independent time t c , are represented by three equations. They are shown to be in accord with experimental data in molecular glass formers, glass-forming, glassy or crystalline ionic conductors, and concentrated colloidal suspensions. Emphasis is given in this work to the colloidal suspensions which have the advantage of the absence of vibrational contributions and the experimentally measured intermediate scattering function is attributed entirely to diffusion dynamics. Direct evidences of such crossover are demonstrated. These, together with the many successful applications of the predictions to several fields and many materials have led us to believe that the Coupling Model has captured the basic physics of relaxation in materials with many-body interactions. We mention in passing that the theoretical basis of the Coupling Model is closely related to chaos in Hamiltonian dynamical systems.The coupling model (CM) (1-3) is a general approach to dynamics of constrained or interacting systems, that has been shown to be applicable in depth to many problems of relaxation in different materials (4-6). Interaction between relaxing units implies cooperativity between them and vice versa. Thus, the effect of the many-body interactions on relaxation can be rephrased as cooperativity in the context of the CM. Several approaches to this problem have been proposed. Recent versions of the coupling theory are This chapter not

show abstract

Section: D? Id? = D L (Q)id S (Q)contrasting

confidence: 33%

Section: D? Id? = D L (Q)id S (Q)mentioning

confidence: 99%

Basic Physics of the Coupling Model: Direct Experimental Evidences

Ngai

Rendell

1997

ACS Symposium Series

Self Cite

View full text Add to dashboard Cite

show abstract

“…Substituting Eqs. (5) and (6) into this expression and introducing the "Laplace frequency" S = LCOE~ (8) one arrives at the following equation for the electrostatic potential:…”

Section: The Macroscopic Model and Its Discretizationmentioning

confidence: 99%

Universal low-temperature ac conductivity of macroscopically disordered nonmetals

Dyre

1993

Phys. Rev. B

151

View full text Add to dashboard Cite

This paper discusses a macroscopic model for ac conduction in electronically or ionically conducting disordered solids. The model considers ac conduction in an inhomogeneous solid that is characterized by a spatially randomly varying thermally activated (frequency-independent) conductivity. Discretizing Maxwell s equations leads to an equivalent electrical circuit that is a simple-cubic lattice where each pair of nodes are linked by a resistor and a capacitor in parallel. The values of the resistors are determined by the local resistivity while the capacitors are all equal, given by the infinite-frequency dielectric constant. It is shown that the capacitor currents are Maxwell's displacement currents. Assuming uncorrelated resistances, the model is solved analytically at low temperatures in the effective-medium approximation (EMA) and in a naive percolation-path approximation.Both approximations predict similar universal ac responses as T~O, where the macroscopic frequency-dependent conductivity becomes independent of the activation-energy probability distribution. The universality represents an unusual type of regularity appearing in the extreme disorder limit. The universality prediction is tested by computer simulations of 200X200 lattices in two dimensions and of 50XSOX50 lattices in three dimensions. The computer simulations show that the EMA works very well in two dimensions in the whole temperature range studied; in particular, the low-temperature universality prediction is confirmed. In three dimensions the universality prediction is confirmed as wellĨ

show abstract

“…Also, time dependence of the diffusion coefficient has been introduced in another theoretical approach in [4]. It can be seen that relations 1-2 predict lower values of the diffusion coefficients, as compared with the values corresponding to the conventional Einstein relation.…”

Section: Modified Einstein-nernst Relationmentioning

confidence: 95%

“…This is in accordance with the model presented in the recent paper, claiming that the ratio of ion diffusivity to ion mobility in electrolytes is time dependent during the transient process to equilibrium. Also, time-dependent diffusion and mobility coefficients have been introduced in [4] to generalize the Einstein-Nernst formula. Polyelectrolyte solutions have also been examined experimentally [5,6] and the results have shown that the measured diffusion coefficients have lower values than the values deduced from the Einstein relation, whereas the discrepancy increases with temperature rise.…”

Section: Introductionmentioning

confidence: 99%

A modified Einstein–Nernst relation between mobility and diffusion of charges to evaluate the non-equilibrium, transient processes of ions in electrolytes

Tankovsky

Syrakov

2008

Ionics

View full text Add to dashboard Cite

Transient correction terms to the nonlinear differential equations, describing the dynamics of migration and diffusion of the ion charges in electrolytes, have been recently defined and numerically evaluated. The system of equations has been modified in accordance with the obtained non-equilibrium corrections and the system variables have been evaluated in the case when the corrections are space-averaged. The purpose of the present work is to obtain a general solution when both the time and space dependencies of the correction terms are preserved i.e. without space-averaging of the corrections. The obtained, under these conditions, set of dynamical equations has been analytically transformed to a simpler form, which is easier to be tackled numerically. The corrected results, in contrast to the results of uncorrected equations, show much faster convergence to equilibrium of the physical system and manifest the presence of characteristic pre-electrode maxima of the transient ion currents.

show abstract

Dispersive diffusion transport and noise, time-dependent diffusion coefficient, generalized Einstein-Nernst relation, and dispersive diffusion-controlled unimolecular and bimolecular reactions

Cited by 76 publications

References 40 publications

Basic Physics of the Coupling Model: Direct Experimental Evidences

Basic Physics of the Coupling Model: Direct Experimental Evidences

Universal low-temperature ac conductivity of macroscopically disordered nonmetals

A modified Einstein–Nernst relation between mobility and diffusion of charges to evaluate the non-equilibrium, transient processes of ions in electrolytes

Contact Info

Product

Resources

About