Hopping models of charge transfer in a complex environment: coupled memory continuous-time random walk approach.

Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard kinetic approach in description of the system is addressed either in the framework of continuous-time random walks (CTRWs) or fractional diffusion. In this paper the power of the CTRW approach is illustrated by use of the probabilistic formalism and limit theorems that allow one to rigorously predict the limiting distributions of the paths traversed by charges and to derive effective relaxation properties of the entire system of interest. In particular, the standard CTRW scenario is generalized to a new class of coupled memory CTRWs that effectively can lead to the well known Havriliak-Negami response. Application of the method is discussed for nonexponential electron-transfer processes controlled by dynamics of the surrounding medium.

[1]  W. Coffey,et al.  Microscopic models for dielectric relaxation in disordered systems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  T. Geisel,et al.  Particle dispersion on rapidly folding random heteropolymers. , 2003, Physical review letters.

[3]  Joseph Klafter,et al.  Probability Distributions for Continuous-Time Random Walks with Long Tails , 1994 .

[4]  Dennis A. Siginer,et al.  Advances in the flow and rheology of non-Newtonian fluids , 1999 .

[5]  R. Cole,et al.  Dielectric Relaxation in Glycerol, Propylene Glycol, and n‐Propanol , 1951 .

[6]  Bernd Giese,et al.  Direct observation of hole transfer through DNA by hopping between adenine bases and by tunnelling , 2001, Nature.

[7]  Marcin Kotulski,et al.  Asymptotic distributions of continuous-time random walks: A probabilistic approach , 1995 .

[8]  X. Xie,et al.  Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer , 2003, Science.

[9]  S. Havriliak,et al.  A complex plane analysis of α‐dispersions in some polymer systems , 2007 .

[10]  G. Papp,et al.  DISORDER EFFECTS IN DIMERIZED BRIDGED MOLECULAR SYSTEMS , 1998 .

[11]  J. Ulstrup.  Charge Transfer Processes in Condensed Media , 1979 .

[12]  K. Cole,et al.  Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics , 1941 .

[13]  I M Sokolov,et al.  Solutions of a class of non-Markovian Fokker-Planck equations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Two-level system with noise: Blue's function approach , 1997, cond-mat/9701187.

[15]  A. Blumen,et al.  Disorder Effects on Relaxational Processes , 1994 .

[16]  W. Schmickler.  J. Berthiers et al. (Eds.): Lecture Notes in Chemistry, Vol. 10: J. Ulstrup: Charge Transfer Processes in Condensed Media. Springer Verlag, Berlin, Heidelberg, New York 1979. 419 Seiten, Preis: DM 39,- , 1980 .

[17]  V. Pande,et al.  ELECTRON TRANSPORT IN DISORDERED POLYMERIC AND BIOLOGICAL SYSTEMS , 1997 .

[18]  Ilya A. Balabin,et al.  Dynamically controlled protein tunneling paths in photosynthetic reaction centers. , 2000, Science.

[19]  A. Weron,et al.  Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes , 1993 .

[20]  D. Matyushov.  A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region. , 2005, The Journal of chemical physics.

[21]  G. Weiss,et al.  Transport properties of the continuous-time random walk with a long-tailed waiting-time density , 1989 .

[22]  A. K. Jonscher,et al.  The ‘universal’ dielectric response , 1977, Nature.

[23]  V. May,et al.  On the theory of nonadiabatic bridge-mediated electron transfer , 2003 .

[24]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[25]  A. Płonka.  4 Dispersive kinetics , 2001 .

[26]  A. Stuchebrukhov,et al.  Effect of protein dynamics on biological electron transfer. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[27]  H. Mcconnell,et al.  Intramolecular Charge Transfer in Aromatic Free Radicals , 1961 .

[28]  I. Sokolov.  Lévy flights from a continuous-time process. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Graham Williams,et al.  Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function , 1970 .

[30]  K. Weron,et al.  On the Cole-Cole relaxation function and related Mittag-Leffler distribution , 1996 .

[31]  D. Stein,et al.  Biological transport processes and space dimension. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[32]  R. Marcus,et al.  Electron transfers in chemistry and biology , 1985 .

[33]  E. Montroll,et al.  Anomalous transit-time dispersion in amorphous solids , 1975 .

[34]  J. Hynes.  Outer-sphere electron-transfer reactions and frequency-dependent friction , 1986 .

[35]  J. Friedrich,et al.  Trehalose effect on low temperature protein dynamics: fluctuation and relaxation phenomena. , 2001, Biophysical journal.

[36]  Karina Weron,et al.  Random walk models of electron tunneling in a fluctuating medium. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  V. Zolotarev.  One-dimensional stable distributions , 1986 .

[38]  Igor Sokolov,et al.  Lévy flights in external force fields: from models to equations , 2002 .