Statistical mechanics of temporary polymer networks I. The equilibrium theory
Copyright policy )Statistical mechanics of temporary polymer networks I. The equilibrium theory
This work treats the equilibrium state of temporary polymer networks in which the junctions are allowed to decay and to form. The network is described as an open system and a modified spring-bead model is assumed. The decaying and reforming beads bring about the viscous behaviour in addition to the elastic behaviour of the permanent network. The total physical system consists of both solvent and polymer network. However the solvent is considered as an external system to the network and is treated as a heat bath with which the polymer network is in contact. The system is analyzed within the framework of the classical equilibrium thermodynamics and statistical mechanics and the basic equation is a reduced form of Liouville's equation. The grand-canonical probability density function and some of the equations of state, particularly the mean junction number, are derived. It is found that the probability density function for the length of a network chain connecting two junctions is of Wien's type.
- University of Stuttgart Germany
- Max Planck Society Germany
second moments, polymer solution, Wien type probability density for length of chain, mean junction number, nonequilibrium, equations of state, distribution functions, transcendental formula, incomplete gamma function, viscous behaviour, solvent, transition probabilities, equilibrium statistics, polymer networks, Statistical thermodynamics, reformation of junction, junctions are allowed to decay and to form, relaxation-time approach, Viscoelastic fluids, one-junction approximation, Classical and relativistic thermodynamics, reduced form of Liouville's equation, chain lengths, generalized diffusion equation, modified spring-bead model, elastic behaviour, generalized spring-bead model, grand-canonical probability density function, local elastic energy, equilibrium state of temporary polymer networks, open system, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
second moments, polymer solution, Wien type probability density for length of chain, mean junction number, nonequilibrium, equations of state, distribution functions, transcendental formula, incomplete gamma function, viscous behaviour, solvent, transition probabilities, equilibrium statistics, polymer networks, Statistical thermodynamics, reformation of junction, junctions are allowed to decay and to form, relaxation-time approach, Viscoelastic fluids, one-junction approximation, Classical and relativistic thermodynamics, reduced form of Liouville's equation, chain lengths, generalized diffusion equation, modified spring-bead model, elastic behaviour, generalized spring-bead model, grand-canonical probability density function, local elastic energy, equilibrium state of temporary polymer networks, open system, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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