Viscoelasticity in concentrated polymer solutions

While all liquid media are viscoelastic, concentrated polymer solutions are characterized by an especially rich distribution of relaxation processes. In order to consider this phenomenon, the pure shear deformation will be employed. Consider an equilibrium concentrated polymer solution and identify the absolute location of every atom in the sample. Now deform the sample such that the new x-coordinate of each atom is increased by a constant multiple of its y-coordinate. This affine deformation might be difficult in the laboratory, but it can be executed for a computer sample of a concentrated polymer solution. Now allow the sample to evolve in time in contact with a heat bath. After a long time, the sample will reach equilibrium, with the new shape determined by the initial shear deformation. 

The sample as a whole is characterized by a shear-relaxation modulus G(f) that is equal to the instantaneous stress induced in the sample divided by the fixed shear deformation. It is convenient to represent the actual shear-relaxation modulus in terms of a distribution of relaxation times p(x). The relationship can then be expressed as  

There will be relaxation processes on many time scales. The most rapid changes will occur between chemically bonded atoms. Chemical bonds lhat have been stretched or compressed will relax to some excited vibrational level and eventually will therm ize and return to the ground vibrational state. Bond angles will also thermalize and return to the ground vibrational state. Internal torsional angles will initially thermalize within the rotational isomeric state that has been achieved after the deformation. The internal relax- 

The chain molecule solution will be characterized by a set of rotational isomeric states. After the initial thermalization, this set will still be in a nonequilibrium state due to the overall shear deformation. For the internal torsional angle distribution to relax to equilibrium, it is necessary for the solution liquid structure to relax and the solvent molecule distribution to reach equilibrium. In a concentrated polymer solution, these processes are highly coupled. Rotational isomeric state changes depend on both internal potentials and the local viscosity and are often in the nanosecond range, well above the glass transition for the solution. Total stress relaxation cannot occur any faster than the chains can change their local rotational isomeric states. 

This overview of the range of time scales that are important for the description of a concentrated polymer solution emphasizes the complexity of these systems. More than 15 decades of time are often involved in the dynamics of concentrated polymer solutions. The dynamics can be organized into groups of relaxation times associated with specific types of relaxations. The local fluid structure and local rotational isomeric state dynamics are most closely associated with the phenomenon known as the glass transition and will be considered in more detail in CTiapter 8. 

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