TY - JOUR
T1 - Shear-transformation-zone theory of linear glassy dynamics
AU - Bouchbinder, Eran
AU - Langer, J. S.
N1 - Division of Materials Science and Engineering, Office of Basic Energy Sciences, Department of Energy through Oak Ridge National Laboratory [DE-AC05-00OR-22725]; Harold Perlman Family Foundation; Robert Rees Applied Research FundWe thank M. Siebenburger for sending us the data shown in Fig. 2, and M. Falk for especially useful comments on an earlier draft of this paper. J.S.L. was supported in part by the Division of Materials Science and Engineering, Office of Basic Energy Sciences, Department of Energy, DE-AC05-00OR-22725, through a subcontract from Oak Ridge National Laboratory. He benefited from discussions with M. Cates, P. Sollich, M. Fuchs, D. Durian, D. Rodney, and C. Schuh, among others at the program on glass physics at the Kavli Institute for Theoretical Physics in the spring of 2010. E.B. was partially supported by the Harold Perlman Family Foundation and by a grant from the Robert Rees Applied Research Fund.
PY - 2011/6/15
Y1 - 2011/6/15
N2 - We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both metallic glasses and soft glassy materials such as colloidal suspensions. We find that the frequency-dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an α peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.
AB - We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both metallic glasses and soft glassy materials such as colloidal suspensions. We find that the frequency-dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an α peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.
UR - http://www.scopus.com/inward/record.url?scp=79961054464&partnerID=8YFLogxK
U2 - https://doi.org/10.1103/PhysRevE.83.061503
DO - https://doi.org/10.1103/PhysRevE.83.061503
M3 - مقالة
SN - 1539-3755
VL - 83
JO - Physical Review E
JF - Physical Review E
IS - 6
M1 - 061503
ER -