Rate statistics and thermodynamic analogies for relaxation processes in systems with static disorder: Application to stretched exponential

Journal of Chemical Physics

Volumn 106, Issue 10, 1997, Pages 4157-4167

  Vlad, Marcel O ^a,b   Huber, David L ^c   Ross, John ^a  

^a STANFORD UNIVERSITY   (United States)

^b ACADEMY OF ROMANIAN SCIENTISTS   (Romania)

^c University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTIVATION ENERGY; ENERGY TRANSFER; ENTROPY; FOURIER TRANSFORMS; LAPLACE TRANSFORMS; PROBABILITY; REACTION KINETICS; STATISTICAL MECHANICS; THERMODYNAMICS;

DECAY RATES; RANDOM CHANNEL MODELS; RANDOM RATE MODELS; STATIC DISORDER; STRETCHED EXPONENTIAL RELAXATION; THERMAL ACTIVATION;

RELAXATION PROCESSES;

EID: 0031559205     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.473100     Document Type: Article

References (41)

1. E. W. Montroll and J. T. Bendler, J. Stat. Phys. 34, 129 (1984), and references therein.
2. A. Blumen, J. Klafter, and G. Zumofen, in Optical Spectroscopy of Glasses, edited by I. Zschokke (Reidel, Amsterdam, 1986), pp. 199-265, and references therein.
3. M. F. Shlesinger, Annu. Rev. Phys. Chem. 39, 269 (1988), and references therein.
4. A. Plonka, Time-Dependent Reactivity of Species in Condensed Media, Lecture Notes on Chemistry (Springer, Berlin, 1986), Vol. 40; Progr. React. Kinetics 16, 157 (1991); Annu. Rep. Prog. Chem. Sect. C Phys. Chem. 89, 37 (1992).
5. A. Plonka, Time-Dependent Reactivity of Species in Condensed Media, Lecture Notes on Chemistry (Springer, Berlin, 1986), Vol. 40; Progr. React. Kinetics 16, 157 (1991); Annu. Rep. Prog. Chem. Sect. C Phys. Chem. 89, 37 (1992).
6. A. Plonka, Time-Dependent Reactivity of Species in Condensed Media, Lecture Notes on Chemistry (Springer, Berlin, 1986), Vol. 40; Progr. React. Kinetics 16, 157 (1991); Annu. Rep. Prog. Chem. Sect. C Phys. Chem. 89, 37 (1992).
7. R. G. Palmer, D. Stein, E. S. Abrahams, and P. W. Anderson, Phys. Rev. Lett. 53, 958 (1984).
8. T. Förster, Z. Naturforsch. A 4, 321 (1949).
9. A. Blumen, Nuovo Cimento B 63, 50 (1981), and references therein.
10. M. F. Shlesinger and E. W. Montroll, Proc. Natl. Acad. Sci. USA 81, 1280 (1984).
11. G. F. Cerofolini and N. Re, Riv. Nuovo Cimento 16, 1 (1993), and references therein; W. Rudzinski and H. D. Evrett, Adsorption of Gases on Heterogeneous Surfaces (Academic, London, 1992); S. Dattagupta, Relaxation Phenomena in Condensed Matter Physics (Academic, Orlando, 1987).
12. G. F. Cerofolini and N. Re, Riv. Nuovo Cimento 16, 1 (1993), and references therein; W. Rudzinski and H. D. Evrett, Adsorption of Gases on Heterogeneous Surfaces (Academic, London, 1992); S. Dattagupta, Relaxation Phenomena in Condensed Matter Physics (Academic, Orlando, 1987).
13. G. F. Cerofolini and N. Re, Riv. Nuovo Cimento 16, 1 (1993), and references therein; W. Rudzinski and H. D. Evrett, Adsorption of Gases on Heterogeneous Surfaces (Academic, London, 1992); S. Dattagupta, Relaxation Phenomena in Condensed Matter Physics (Academic, Orlando, 1987).
14. R. H. Austin, K. W. Beeson, L. Einsestein, H. Frauenfelder, and I. C. Gunsalas, Biochem. 14, 5355 (1975); J. Berendzen, S. F. Browne, H. Frauenfelder, T. B. Sauke, E. Shyamsunder, and R. D. Young, Proc. Natl. Acad. Sci. USA 82, 5000 (1985); H. Frauenfelder and R. D. Young, Comments Mol. Cell. Biophys. 3, 347 (1986); A. Ansari, J. Berendzen, D. Braunstein, B. R. Cowen, H. Frauenfelder, M. K. Hong, I. E. T. Iben, JU. B. Jonson, P. Ormos, T. B. Sauke, R. Scholl, P. J. Steinbach, J. Vittitov, and R. D. Young, Biophys. Chem. 26, 337 (1987); L. Edman, Ü. Mets, and R. Rigler, Proc. Natl. Acad. Sci. USA 93, 6710 (1996).
15. R. H. Austin, K. W. Beeson, L. Einsestein, H. Frauenfelder, and I. C. Gunsalas, Biochem. 14, 5355 (1975); J. Berendzen, S. F. Browne, H. Frauenfelder, T. B. Sauke, E. Shyamsunder, and R. D. Young, Proc. Natl. Acad. Sci. USA 82, 5000 (1985); H. Frauenfelder and R. D. Young, Comments Mol. Cell. Biophys. 3, 347 (1986); A. Ansari, J. Berendzen, D. Braunstein, B. R. Cowen, H. Frauenfelder, M. K. Hong, I. E. T. Iben, JU. B. Jonson, P. Ormos, T. B. Sauke, R. Scholl, P. J. Steinbach, J. Vittitov, and R. D. Young, Biophys. Chem. 26, 337 (1987); L. Edman, Ü. Mets, and R. Rigler, Proc. Natl. Acad. Sci. USA 93, 6710 (1996).
16. R. H. Austin, K. W. Beeson, L. Einsestein, H. Frauenfelder, and I. C. Gunsalas, Biochem. 14, 5355 (1975); J. Berendzen, S. F. Browne, H. Frauenfelder, T. B. Sauke, E. Shyamsunder, and R. D. Young, Proc. Natl. Acad. Sci. USA 82, 5000 (1985); H. Frauenfelder and R. D. Young, Comments Mol. Cell. Biophys. 3, 347 (1986); A. Ansari, J. Berendzen, D. Braunstein, B. R. Cowen, H. Frauenfelder, M. K. Hong, I. E. T. Iben, JU. B. Jonson, P. Ormos, T. B. Sauke, R. Scholl, P. J. Steinbach, J. Vittitov, and R. D. Young, Biophys. Chem. 26, 337 (1987); L. Edman, Ü. Mets, and R. Rigler, Proc. Natl. Acad. Sci. USA 93, 6710 (1996).
17. R. H. Austin, K. W. Beeson, L. Einsestein, H. Frauenfelder, and I. C. Gunsalas, Biochem. 14, 5355 (1975); J. Berendzen, S. F. Browne, H. Frauenfelder, T. B. Sauke, E. Shyamsunder, and R. D. Young, Proc. Natl. Acad. Sci. USA 82, 5000 (1985); H. Frauenfelder and R. D. Young, Comments Mol. Cell. Biophys. 3, 347 (1986); A. Ansari, J. Berendzen, D. Braunstein, B. R. Cowen, H. Frauenfelder, M. K. Hong, I. E. T. Iben, JU. B. Jonson, P. Ormos, T. B. Sauke, R. Scholl, P. J. Steinbach, J. Vittitov, and R. D. Young, Biophys. Chem. 26, 337 (1987); L. Edman, Ü. Mets, and R. Rigler, Proc. Natl. Acad. Sci. USA 93, 6710 (1996).
18. R. H. Austin, K. W. Beeson, L. Einsestein, H. Frauenfelder, and I. C. Gunsalas, Biochem. 14, 5355 (1975); J. Berendzen, S. F. Browne, H. Frauenfelder, T. B. Sauke, E. Shyamsunder, and R. D. Young, Proc. Natl. Acad. Sci. USA 82, 5000 (1985); H. Frauenfelder and R. D. Young, Comments Mol. Cell. Biophys. 3, 347 (1986); A. Ansari, J. Berendzen, D. Braunstein, B. R. Cowen, H. Frauenfelder, M. K. Hong, I. E. T. Iben, JU. B. Jonson, P. Ormos, T. B. Sauke, R. Scholl, P. J. Steinbach, J. Vittitov, and R. D. Young, Biophys. Chem. 26, 337 (1987); L. Edman, Ü. Mets, and R. Rigler, Proc. Natl. Acad. Sci. USA 93, 6710 (1996).
19. Yu. A. Berlin, N. I. Chekunaev, and V. Goldanski, Chem. Phys. Lett. 197, 81 (1992); A. Plonka, Chem. Phys. Lett. 151, 466 (1988); A. Plonka, J. Kroh, and Yu. A. Berlin, ibid. 153, 533 (1988); A. Plonka, Yu. A. Berlin, and N. I. Chekunaev, ibid. 158, 380 (1989).
20. Yu. A. Berlin, N. I. Chekunaev, and V. Goldanski, Chem. Phys. Lett. 197, 81 (1992); A. Plonka, Chem. Phys. Lett. 151, 466 (1988); A. Plonka, J. Kroh, and Yu. A. Berlin, ibid. 153, 533 (1988); A. Plonka, Yu. A. Berlin, and N. I. Chekunaev, ibid. 158, 380 (1989).
21. Yu. A. Berlin, N. I. Chekunaev, and V. Goldanski, Chem. Phys. Lett. 197, 81 (1992); A. Plonka, Chem. Phys. Lett. 151, 466 (1988); A. Plonka, J. Kroh, and Yu. A. Berlin, ibid. 153, 533 (1988); A. Plonka, Yu. A. Berlin, and N. I. Chekunaev, ibid. 158, 380 (1989).
22. Yu. A. Berlin, N. I. Chekunaev, and V. Goldanski, Chem. Phys. Lett. 197, 81 (1992); A. Plonka, Chem. Phys. Lett. 151, 466 (1988); A. Plonka, J. Kroh, and Yu. A. Berlin, ibid. 153, 533 (1988); A. Plonka, Yu. A. Berlin, and N. I. Chekunaev, ibid. 158, 380 (1989).
23. J. Klafter and M. F. Shlesinger, Proc. Natl. Acad. Sci. USA 83, 848 (1986).
24. D. L. Huber, Phys. Rev. B 31, 6070 (1985).
25. M. O. Vlad and M. C. Mackey, J. Math. Phys. 36, 1834 (1995).
26. M. O. Vlad, B. Schönfisch, and M. C. Mackey, Phys. Rev. E 53, 4703 (1996).
27. D. L. Huber and M. O. Vlad, Physica A (to be published).
28. T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Waugh, Rev. Mod. Phys. 53, 385 (1981).
29. R. D. Levine, Adv. Chem. Phys. 70, 53 (1988).
30. R. F. Greene and H. B. Callen, Phys. Rev. 83. 1231 (1951); H. Callen, in Nonequilibrium Thermodynamics, Variational Techniques and Stability, edited by R. J. Donnelly, R. Hermann, and I. Prigogine (University of Chicago, Chicago, 1966), p. 227; M. O. Vlad and J. Ross, J. Chem. Phys. 100, 7295 (1994).
31. R. F. Greene and H. B. Callen, Phys. Rev. 83. 1231 (1951); H. Callen, in Nonequilibrium Thermodynamics, Variational Techniques and Stability, edited by R. J. Donnelly, R. Hermann, and I. Prigogine (University of Chicago, Chicago, 1966), p. 227; M. O. Vlad and J. Ross, J. Chem. Phys. 100, 7295 (1994).
32. R. F. Greene and H. B. Callen, Phys. Rev. 83. 1231 (1951); H. Callen, in Nonequilibrium Thermodynamics, Variational Techniques and Stability, edited by R. J. Donnelly, R. Hermann, and I. Prigogine (University of Chicago, Chicago, 1966), p. 227; M. O. Vlad and J. Ross, J. Chem. Phys. 100, 7295 (1994).
33. G. H. Weiss and R. J. Rubin, Adv. Chem. Phys. 52, 363 (1983), and references therein.
34. B. H. Lavenda, Thermodynamics of Extremes (Albion, Chichester, 1995).
35. M. O. Vlad, Phys. Scr. 49, 389 (1994).
36. R. Zwanzig, Acc. Chem. Res. 23, 148 (1990); N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 2nd ed. (North-Holland, Amsterdam, 1992) Chap. 16; A. Plonka and A. Paszkiewicz, J. Chem. Phys. 96, 1128 (1992).
37. R. Zwanzig, Acc. Chem. Res. 23, 148 (1990); N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 2nd ed. (North-Holland, Amsterdam, 1992) Chap. 16; A. Plonka and A. Paszkiewicz, J. Chem. Phys. 96, 1128 (1992).
38. R. Zwanzig, Acc. Chem. Res. 23, 148 (1990); N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 2nd ed. (North-Holland, Amsterdam, 1992) Chap. 16; A. Plonka and A. Paszkiewicz, J. Chem. Phys. 96, 1128 (1992).
39. D. L. Huber, Phys. Rev. E 53, 6544 (1996); M. O. Vlad, J. Ross, and M. C. Mackey, J. Math. Phys. 37, 803 (1996); M. O. Vlad, R. Metzler, T. Nonnenmacher, and M. C. Mackey, ibid. 37, 2279 (1996).
40. D. L. Huber, Phys. Rev. E 53, 6544 (1996); M. O. Vlad, J. Ross, and M. C. Mackey, J. Math. Phys. 37, 803 (1996); M. O. Vlad, R. Metzler, T. Nonnenmacher, and M. C. Mackey, ibid. 37, 2279 (1996).
41. D. L. Huber, Phys. Rev. E 53, 6544 (1996); M. O. Vlad, J. Ross, and M. C. Mackey, J. Math. Phys. 37, 803 (1996); M. O. Vlad, R. Metzler, T. Nonnenmacher, and M. C. Mackey, ibid. 37, 2279 (1996).