The crack-lattice trapping phenomenon introduce by R. Thomson et al[1] is studied for the conditions of the Frenkel-Kontrova-type experiment. By using a new method, which allows further model extension for a finite temperature case we are able to describe an equilibrium crack energetics for arbitrary externa conditions and ascertain the crack propagation conditions. Specifically, the system free energy F as a function of nonlinear bond displacement ul for an external forces P and for a finite temperature T is found. The equilibrium values for the displacement ul = ul* and for G* = G(ul*), are obtained. The free-energy barrier height G = Gmax − G* dependence upon P and T is determined. With the help of the exact solution of the equilibrium equations we obtained the free energy as function of crack length G(l,T,P). We found that local free energy barriers take place for every crack length l, which is in contrast to the Thomson model. From the microscopic viewpoint it means that crack advance is controlled by local free energy barriers. We found that near the equilibrium length the crack energy barrier is relatively high, while far from equilibrium crack position, energy barrier height decreases to a finite value. It is worth to note that the barrier height monotonically decrease with the increase of the environment temperature. On the basis of our model the temperature dependence of the crack surface energy will be found, the global energetics of the crack will be described.
Free-energy cost of localizing a single monomer of a confined polymer
