Nonideality Factor in the Thermodynamic Analysis of Real Polymer Solutions

The generalized nonideality factor of systems g is introduced in Rényi and Tsallis information entropy equations describing self-organized structures of high molecular weight compounds in solution. This relative thermodynamic characteristic relates ideal and real models of the system in which one can distinguish two processes opposite in sign and effect: order (–) ↔ chaos (+); attraction (–) ↔ repulsion (+); compression (–) ↔ expansion (+), etc. The value of g =1 – βord + αnord, where βord and αnord are statistically averaged characteristics of opposite processes, varies in the interval 0 ≤ g ≤ 2 and depends on which of competitive processes prevails. At αnord = 0 factor g → 0, at βord = 0 factor g → 2, and at g = 1 the behavior of system elements is ideal. New entropy expressions with parameter g_th ≡ g are obtained for quasi-equilibrium structures in the Rényi formalism $$S_{{{{g}_{{{th}}}}}}^{{{M} - {Rn}}} = {R}{{{{g}_{{{th}}}}}}{ln}( { ∑ i = 1N(ε ) pᵢ^{{{{g}_{{{th}}}} - 1}}} )$$ and nonequilibrium open systems in the Tsallis formalism $$S_{{{{g}_{{{th}}}}}}^{{{M} - {Ts}}}( p ) = {{R(1 - ∑ _iN(ε ) pᵢ^{{1 - {{g}_{{{th}}}}}})}}{{{{g}_{{{th}}}}}}$$ . A relationship is found between the generalized nonideality factor and the scaling indices $${{a}η},{{b}_{{D}}}$$ , and cS. The thermodynamic functions of solutions of branched natural and synthetic high molecular weight compounds (dioxane lignins, polystyrenes, polyglycerols, pyridine-containing polyphenylene dendrimers) are calculated from the experimental data derived by hydrodynamic methods. The results are discussed in terms of both classical quasi-equilibrium and modern nonequilibrium thermodynamics.