Entanglement molecular weight concentration dependence

The new information necessary to make this approach quantitative is the dependence of the effective entanglement molecular weight on the concentration, (j) of unrelaxed segments. This is known from experiments on dilution of polymer melts by theta-solvents to be approximately which corre-... 

The local viscosity also depends on concentration and temperature, but the details depend on the polymer and the solvent. Experiments carried out with high-molecular-weight chains as a function of chain length verify the 1 /N dependence for the self-diffusion coefficient in well-entangled solutions. The concentration dependence is much harder to verify because of the issue of local viscosity, but the decrease of the self-diffusion coefficient with concentration is dramatic for all solutions in tiiis regime. 

When the molecular weight and concentration dependences of the structural parameters S2, E, n, and v are inserted (S2ocM, E oc cM, nocAf, voc c/M), an expression for viscosity in highly entangled linear molecules is obtained. 

This allows one to write the dependencies of the characteristic quantities on the concentration of polymer and on the thermodynamic rigidity, if the dependence on molecular weight of the macromolecule, for example, is known. With help of the result of Section 3.3.4 (see formulae (3.30)), one can obtain for the strongly entangled systems... 

For the weakly entangled system, the steady-state modulus depends on the molecular weight of polymer as M 1, while for strongly entangled system, the steady-state modulus does not depend on the molecular weight of polymer, which is consistent with typical experimental data for concentrated polymer systems (Graessley 1974). The expression for the modulus is exactly the same as for the plateau value of the dynamic modulus (equations (6.52) and (6.58)) Expressions (9.42) lead to the following relation for the ratio of the normal stresses differences... 

It can be shown that the pore size of an entangled polymer solution does not depend on the degree of polymerization, only on its concentration. This means also that two solutions of the same type of polymer and with the same concentration but different molecular weights may have the same pore size as long as they are entangled. However, the viscosity of the two solutions is different because viscosity depends on the molecular weight. This has important consequences for the choice of the appropriate polymer solution. The pressure with CE instrumentation needed to displace the buffer solutions is limited, therefore the viscosity should not exceed a certain value. Explicit descriptions can be found in literature [16] for the selection of appropriate polymers and their concentrations for DNA analysis. 

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