Chain end mobility

If one could assign an "effective volume" to each highly mobile chain end and another "effective volume" to each branch point, the free volume of a network could be described conveniently as that of a (three dimensional) three component copolymer ... 

On the other hand, the mobile chain-end blocks may be identified as chain sections not subject to entanglements so that they move in a whip-like fashion. In view of the critical molecular mass Me indicating the minimum... 

Among the complications that can interfere with this conclusion is the possibility that the polymer becomes insoluble beyond a critical molecular weight or that the low molecular weight by-product molecules accumulate as the viscosity of the mixture increases and thereby shift some equilibrium to favor reactants. Note that we do not express reservations about the effect of increasing viscosity on the mobility of the polymer molecules themselves. Apparently it is not the migration of the center of mass of the molecule as a whole that determines the reactivity but, rather, the mobility of the chain ends which carry the reactive groups. 

By linking the chain ends of different molecules they form a type of network structure as long as the domains remain glassy. As the polymer is heated above the of the domain polymer block the domain molecules become mobile and on application of a stress the material flows like a thermoplastic. On cooling, new domains will be formed, thus regenerating the elastic state. 

Polymerizations Above Tg. Let the polymerization begin in pure monomer. As the concentration of polymer chains increases initially one observes a relatively small increase in the termination rate constant. This is related to the effect of polymer concentration on coil size. A reduction in coil size increases the probability of finding a chain end near the surface and hence causes an increase in k-. Soon thereafter at conversions 15-20 polymer chains begin to entangle causing a dramatic reduction in radical chain translational mobility giving a rapid drop in k-j. ... 

Table II shows Tgs obtained from DSC traces. (Footnotes a and b in Table II show T s values of three reference polymers two PIBs, whose Mns are similar to the Mns of MA-PIB-MA used in the network synthesis, and a PDMAAm the difference in the Tg for the Mn=4,000 and 9,300 PIBs is due to the dependence of Tg on Mn(72)). The DSC traces of the networks exhibited two Tgs, one in the range of -63 to -52 °C (PIB domains) and another in the range of 90 to 115 °C (PDMAAm domains) indicating microphase separated structures. The Tgs associated with the PIB phase in the PDMAAm-1-PIB networks were higher than those of the reference homoPIBs which may be due to PIB chain-ends embedded in the glassy PDMAAm phase restricting segmental mobility. The Tg of the PIB phase in the PDMAAm-1-PIB increases by increasing the PIB content which may be due to an increase in crosslink density. In contrast, the Tg for the PDMAAm phase in the network decreases upon increasing the PIB content. Interaction of the (-CH2-CH-) moiety of the PDMAAm with the flexible PIB and thus the formation of a more flexible structure may explain this phenomenon.

Figure 31 compares the dynamic structure factors obtained from the crosslinks and the chain ends for two different Q-values. Without any analysis a strong reduction of the cross-link mobility compared to that of the chain end is obvious. A closer inspection also shows that the line-shape of both curves differs. While S(Q,t)/S(Q, 0) from the chain end decays continuously, S(Q,t) from the cross-links appears to decay faster at shorter than at longer times. This difference in line shape is quantified via the line shape parameter p. For the end-labelled chains, p is in close agreement with the p = 1/2 prediction of the... 

The papers of Mallon and Ray [98, 123] can be regarded as the state of the art in understanding and modelling solid-state polycondensation. They assumed that chain ends, catalysts and by-products exist solely in the amorphous phase of the polymer. Because of the very low mobility of functional groups in the crystalline phase, the chemical reactions are modelled as occurring only in the amorphous phase. Additionally, the diffusion of by-products is hindered by the presence of crystallites. The diffusivity of small molecules was assumed to be proportional to the amorphous fraction. Figure 2.32 shows the diffusion coefficients for the diffusion of EG and water in solid PET. 

The thickness of the interphase is a similarly intriguing and contradictory question. It depends on the type and strength of the interaction and values from 10 Ato several microns have been reported in the hterature for the most diverse systems [47,49,52,58-60]. Since interphase thickness is calculated or deduced indirectly from some measured quantities, it depends also on the method of determination. Table 3 presents some data for different particulate filled systems. The data indicate that interphase thicknesses determined from some mechanical properties are usually larger than those deduced from theoretical calculations or from extraction of filled polymers [49,52,59-63]. The data supply further proof for the adsorption of polymer molecules onto the filler surface and for the decreased mobility of the chains. Thermodynamic considerations and extraction experiments yield data which are not influenced by the extent of deformation. In mechanical measurements, however, deformation of the material takes place in all cases. The specimen is deformed even during the determination of modulus. With increasing deformations the role and effect of the immobilized chain ends increase and the determined interphase thickness also increases (see Table 3) [61]. 

The above models describe a simplified situation of stationary fixed chain ends. On the other hand, the characteristic rearrangement times of the chain carrying functional groups are smaller than the duration of the chemical reaction. Actually, in the rubbery state the network sites are characterized by a low but finite molecular mobility, i.e. R in Eq. (20) and, hence, the effective bimolecular rate constant is a function of the relaxation time of the network sites. On the other hand, the movement of the free chain end is limited and depends on the crosslinking density 82 84). An approach to the solution of this problem has been outlined elsewhere by use of computer-assisted modelling 851 Analytical estimation of the diffusion factor contribution to the reaction rate constant of the functional groups indicates that K 1/x, where t is the characteristic diffusion time of the terminal functional groups 86. ... 

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