The Effect of Coil Size

It soon became evident that the correlation between the termination rate coefficients and viscosity was much more complex than it had seemed to be at first. This complexity arises from the fact that if one solvent is replaced by another (or, alternatively, as soon as some polymer has been formed), the thermodynamic properties of the solution change simultaneously. Poor solvents, for instance, will decrease the radii of gyration of polymer coils and hence also the segment densities of these solvated macromolecules. Consequently, the dynamics of polymer coils in general (including the translational and segmental motions) will be affected by the solvent properties. This was actually already the case in some of the MM A studies in different solvents as mentioned above [40, 66-71, 73, 77] as not all these solvents dissolve pMMA equally well [95]. 

D represents the diffusion of a polymer chain due to Brownian or thermal motion, while is a coefficient that characterizes the relaxation of a concentration gradient being present in a solution. At zero percent conversion, these two diffusion coefficients are identical. 

Several other groups have confirmed the experimental findings of North and Reed. Ludwico and Rosen [79, 80] found a similar behavior in the polymerization of styrene (S) in the presence of either polybutadiene or polystyrene. Also these workers found an increase in kt, depending upon the molar mass of the polymer being dissolved and/or the chain lengths of the terminating radicals (small radicals being less affected by the dissolved polymer) [80]. 

Mahabadi and O Driscoll also studied the effect of dissolved polymer upon the termination rate coefficient [82, 83]. They derived a theoretical relationship for the dependence of kt upon conversion [82], based on a previously derived segmental diffusion model [100] that allowed for a concentration dependent linear expansion coefficient and polymer-solvent interactions. Also Mahabadi and O Driscoll pointed out that the rate of segmental diffusion would increase if the segment density gradient was increased as a result of coil shrinkage. In a simplified form, the dependence of kt upon polymer concentration, C, could be represented by  

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The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

A More Refined View on the Effect of Coil Size... 

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