Quantitative Theory of the Globule-to-Coil Transition. 1. Link Density Distribution in a Globule and Its Radius of Gyration

In this series of papers new results and a brief review of the current state of mean-field theories of the condensed globular state and of the globule-to-coil transition in the θ-region for a linear, homogeneous, noncharged macromolecule are presented. As a basis of our consideration, we use both Lifshitz's theory and interpolation Flory-type theory. Complete quantitative theoretical results are obtained and compared with experimental data. In this first paper of the series the unary characteristics of a polymer chain are considered. It is shown that the density distribution of monomers inside a globule depends on parameters of a polymersolvent system in the combination t = N^1/2BC^−1/4(a²/6)^−3/4 ~ N^1/2(T - θ)/θ only (a stands for the distance between neighboring links along the chain, N is the total number of links in the chain, T stands for temperature, and B and C are the second and third virial coefficients of quasimonomer interactions, respectively). The form of the t-dependence (or of the (T - θ)N^1/2-dependence) of a macromolecule expansion factor is determined by the polymer rigidity parameter √C/a³. The question of the bimodality of macromolecular states in the transition region is discussed.