Polymer solution characteristic length

Investigation of viscoelastic behaviour of linear polymer solutions and melts shows that there are universal laws for dependencies of the terminal characteristics on the length of macromolecules, which allows to interpret these phenomena on the base of behaviour of a single macromolecule in the system of entangled macromolecules (Ferry 1980, Doi and Edwards 1986). The validity of the mesoscopic approach itself rests essentially on the fundamental experimental fact that quantities that characterise the behaviour of a polymer system have a well-defined unambiguous dependence on the length of the macromolecule. 

Although a network is not present in a concentrated solution, there exists a characteristic length, which had earlier been assumed the distance between neighbouring network sites. The characteristic length is a dynamic one. There are no temporary knots in a polymer system, though there is a characteristic time, which is the lifetime of the frozen large-scale conformation of a macromolecule in the system. So, the conceptions of intermediate length and characteristic time are based on deeper ideas and are reflected in the theory. 

In a comparison study of the values of flow birefringence An and the viscosity t of a polymer solution it is often possible to simplify the experimental procedure so as to avoid the determinations of the characteristic values of [n] and [tj] by determining the quantity An/g (i - tjq) at finite solution concentration instead of the ratio [n]/[7j]. Here is the viscosity of the solvent and the value of g(rj - t o) - At characterizes the effective shearing stress in solution introduced by the dissolved polymer. Many experimental data show that for a flexible-chain polymer in the absence of the macroform effect the ratio An/At, which may be called the shear optical coefficient , is independent of solution concentration, and, also, over a wide range of molecular weights, of chain length ... 

Nierlich M, Boue F, Lapp A, Oberthur R. Characteristic lengths and the structure of salt free polyelectrolyte solutions. A small angle neutron scattering study. Colloid Polymer Sci 1985 63 955-964. 

As was shown by Kirkwood,13 if dynamical measurements are carried out on polymers in dilute solutions, a new characteristic length appears, the hydro-dynamic radius ftH. By definition... 

A number of important characteristics of polymers, such as molecular weight, chain length, branching, and chain stiffness, can be explored when the individual molecules are separated froni each other. Such studies therefore employ dilute solutions of polymers. However, the dissolution of a polymer also brings with it many new problems. For a correct interpretation of the behavior of polymer solutions it is essential to understand the thermodynamics of polymer-solvent interaction. We will therefore explore some of the basic underlying thermodynamic principles of polymer solutions in this chapter. A major part of the chapter will be concerned with methods of studying polymer solutions that deal with equilibria and can be fully described by thermodynamic relations. These include vapor pressure, osmotic pressure, and phase separation in polymer-solvent systems. 

We have introduced three characteristic lengths 1, i e> and to describe the effects of chain overlap on the density fluctuation correlation, the intrachain excluded-volume interaction, and the intrachain hydrodynamic interaction, respectively. In the following chapters, we will illustrate the important roles played by them in understanding the static and dynamic behavior of polymer solutions. 

When C > C, similar to the treatment of neutral polymers in semi-dilute solutions, we can use the blob model to describe the polyelectrolyte segment holding the electrostatic repulsion in semi-dilute solutions. Assuming the blob size as a characteristic length to maintain the chain rigidity, with reference to the critical overlap concentration C, ... 

The given information affords to define more precisely the developed semiempirical turbulent theory of polymer solutions [4,53. In this case it is necessary to connect the length of the mixing path or of turbulence viscosity with the increased longitudinal solution viscosity in the presence of macromolecules, and the last - with molecular characteristics of a polymer and with its solution concentration. 

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