Irreversible statistical mechanics of polymer chains. III. A dynamic model of vinyl polymers

Computational works are made of the dynamic rotational isomer model of vinyl polymers, of which theoretical foundation has been given in the first paper of this series. First, a concept of ``simple elementary mode'' is newly introduced, based on the assumption of short-range order of vinyl polymers, and 2317 simple elementary modes for ν ≤ 14 (where ν is the length of local chains) are found with the aid of a computer. Langevin equations for local chains rotating in a viscous medium are introduced to derive transition probabilities for these modes. They are given as functions of the monomer size (Rm), the free volume (νf) of the system, and a hydrodynamic parameter (ε). Two kinds of systems, dilute polymer solutions and bulk polymers (including concentrated polymer solutions), are discussed separately. Two dimensionless quantities, [Da] (intrinsic diffusion coefficient) and [Ta] (intrinsic relaxation time) for normal coordinates Qa, are newly defined and they are computed numerically for various ε, Rm, νf, and gauche state energy (Eg). The following are found in the present work. (1) [Dα] strongly depends on νf both in the range 0≤α̃≤ 0.3 and 0.8≤α̃≤ 1, but not on 0.4 ≤α̃≤ 0.75, where α̃=α/N. (2) [Dα] is almost independent of Rm and Eg in the whole range 0≤α̃≤ 1. (3) In dilute solutions (i.e., νf=∞) all the (2317) elementary modes participate in the Brownian motion of the polymer chains, but with the increase in polymer concentration (i.e., with the decrease in νf the larger elementary modes begin to freeze up and, near the glass-transition temperature, the only two smallest modes, (4,1)S and (6,2)S remain unfrozen. (4) Even in dilute solutions, the Brownian motion of the normal coordinate with a large α̃(0.3≤α̃≤ 1) is determined by several small elementary modes alone. (5) [τα̃] takes its minima [τα]min in the range 0.4≤ α ≤ 0.75. (6) [τα] strongly depends on both νf and Eg, but [τα]min depends only on Eg. The following subjects are also discussed: The superposition of time and temperature changes, behaviors of long elementary modes, and the glass-transition phenomena.