ABSTRACT
Polymer physics is a mature branch of chemistry and industry (e.g., plastics, nylon, rubber), and of biochemistry (DNA, RNA, microtubules). The theoretical description of polymers is a major branch in theoretical physics, to which many excellent books and reviews have been devoted, see, e.g., de Gennes [1979]; Doi & Edwards [1986]. There are many forms of polymers: linear polymers, cross-linking polymers, and, of particular interest in biophysics, heterogeneous polymers. The first aging experiments were performed on polymers [Struik, 1978], but
mostly the phenomenon of aging has been investigated in different systems. Solvable models for aging in heteropolymer systems exist, see, e.g., Montanari et al. [2004]; Mu¨ller et al. [2004] and references therein. The glass transition is caused by the appearance of a multitude of long-lived
states, which prevents exploration of the whole phase space. These effects are so strong that, in practice, one can only observe precursor effects. Experimentally, one observes a dynamical freezing around the tunable glass temperature Tg, see Sec. 1.1, set by the cooling rate. The ergodic theorem says that time-averages may be replaced by ensemble
averages. It is widely believed that the inherent dynamical nature of the glass transition implies that there is neither need nor chance for a thermodynamic explanation. However, since so many decades in time are involved, this is an unsatisfactory point of view. In previous chapters we have discussed exactly solvable models with glassy behavior. Here we discuss this picture of the glassy transition in a polymer model, introduced by Nieuwenhuizen [1997b]. We consider a linear monomeric polymer, in an idealized geometry and in the presence of a disordered substrate. This setup induces important simplifications in the statics and dynamics. As in the two previous chapters, the model is designed with a simple statics and a glassy dynamics and can be solved analytically.
