Undiluted Polymers of Low Molecular Weight

A useful principle was proposed by Bueche in 1952 the character of molecular motions and configurational changes as described for dilute solutions is much the same in concentrated solution or even undiluted polymer as long as the molecular weight is sufficiently low so that the coupling entanglements discussed qualitatively 

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For undiluted polymers of low molecular weight to which the Rouse theory is applicable, the X factors are actually determined entirely by fo- Comparison of equations 4, 6, 21, and 23 shows that... 

Rouse Theory for Undiluted Polymer of Low Molecular Weight... 

For the restricted case of low molecular weights and no coupling entanglements, the viscoelastic properties of star-branched undiluted polymers can be described by a special case of the Zimm-Kilb theory o in which there is no hydrodynamic interaction. Calculations were made by Ham i by use of a method which is somewhat different from that of Rouse but yields the same results for unbranched molecules. Stars with arms of unequal length were included. For such a branched molecule, the terminal relaxation time ti, the viscosity r/o, and the steady-state compliance are always smaller than for an unbranched molecule of the same molecular weight the more branches and the more nearly equal their lengths, the... 

FIG. 17-1. Glass transition temperatures of polystyrene solutions with various diluents of low molecular weight, plotted against weight fraction of diluent. The Tg for the undiluted polymer is somewhat lower than that usually accepted (Table 11-11). (Jenckel and Heusch. )... 

The softening dispersions of entangled low-molecular-weight polymers are often modeled by the Rouse modes modified for undiluted polymers. From their very definition only involving the coordinates of a single chain, the Rouse modes are not intermolecularly coupled, and their relaxation times, t/ /, are proportional to the monomeric friction coefficient, fo that is. 

A quite different type of observation which leads also to the concept of an entanglement network is the dependence of viscosity on molecular weight in undiluted polymers or at constant concentration in concentrated solutions, as advanced by Bueche. This is illustrated in Fig. 10-10 for fractions of polystyrene. At low molecular weights, rjo increases only slightly more rapidly than directly proportional to Af, and its magnitude is actually predicted by the Rouse theory, in accordance with the principle of Bueche. Thus, from equations 4 and 6, rjo is given by... 

In making these comparisons, it is assumed that the characteristic length a is independent of molecular weight, and this will not be the case if excluded volume must be taken into account. However, it is clear that molecular weight distribution has a very large effect on [G ]/ at low frequencies, and also on the steady-state compliance through the relation = lim< -.o[G ]fi/[G"]. These features also appear in concentrated solutions and undiluted polymers (for which the effect of molecular weight distribution was first derived ). 

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