Comment on ‘‘Relaxation Kinetics of Nanoscale Indents in a Polymer Glass’’ Structural relaxation of amorphous materials is usually described as resulting from the contribution of microscopic transitions covering a spectrum of activation
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چکیده
Structural relaxation of amorphous materials is usually described as resulting from the contribution of microscopic transitions covering a spectrum of activation energies, gðEÞ [1,2]. When gðEÞ is flat, the relaxation kinetics follows a logðtÞ dependence [2,3]. Thus, it is quite surprising that Knoll et al. [4] do not rely on this classic model to describe their experimental results. Their model, relating the activation energy to the relaxation degree, is very appealing. However, their good fitting to experiment, with 0 depending on the annealing temperature, cannot be an argument for the model validity because (a) before annealing the state is always the same and (b) the number of free parameters is too high to deliver meaningful values [5]. First, let us show that the experimental points can be fitted to the classical model [1,2]. According to it, a particular state d=d0 is reached when the transitions with a given activation energy Eðd=d0Þ take place, i.e., at time t 1 0 exp1⁄2Eðd=d0Þ=kT , where 0 is the attempt frequency [1]. For d=d0 1⁄4 0:6, we obtain 2.0 eV and 0 2 10 s 1 for t 1⁄4 120, 100, and 80 C (inset of Fig. 1) [6]. Furthermore, the observed logarithmic dependence of d=d0 on time is consistent with a flat spectrum between Emin and Emax. We can thus fit the experimental points to the theoretical dependence [2,3]:
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