Characteristics of Polymer Deformation

The Brownian motion of a polymer chain for self-diffusion is carried out by the integration of Brownian motions of monomers. Therefore, the entropic elasticity of chain conformation in a random coil allows a large-scale deformation, with its extent subject to the external stress for polymer deformatiOTi and flow, and hence exposes the characteristic feature of a mbber state in a temperature window between the glass state and the fluid state. 

Small molecules display both glass and fluid states, but not the mbber state. The mbber state is a unique feature for non-crystalline or semi-crystalline polymers in the intermediate temperature regime between the glass and the fluid states. With the decrease of temperature from the fluid state, various modes of polymer motions will be gradually frozen, corresponding to their different scales of length and time (a dynamic stmcture). First, the fluid-mbber transition occurs, which freezes the 

Fetters et al. examined for a series of non-crystalline polymers (Fetters et al. 1999) and found that 

Here p is the density of the polymer, and is an empirical parameter that reflects how many interpenetrated chains on average are required for displaying entanglement effects, tit = 21.3 7.5 %, is the Avogadro constant, and p is the packing length, which is defined as 

Clearly, p is the ratio of the occupied volume of each chain to its radius of gyration. Here, n is the number of chain units in each polymer. Using the simple freely-jointed-chain model with a chain unit holding the length I and the width w, we can obtain 

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