The complex damped orientational diffusion model of polymer local, main chain motion in moderately dilute solution is extended to include the effects of attached probes and periodic side chains on the dynamics. In the case of an appended probe attached to the main chain, a prescription is given for extracting the contribution of the probe to the local, main chain dynamics and thereby allows one to determine when the probe essentially exerts a minor influence on the character of the local motions and when it does not. In the case of a polymer containing a periodic array of side chains (as is normally the case), we demonstrate that to an excellent approximation in the context of the complex damped orientational diffusion model, side chains merely modify the effective damping constant of an equivalent polymer lacking any side chains. This is an important conclusion that requires experimental verification. Finally, we demonstrate that the complex damped diffusion model in general remains invariant to the particular kind of short-wavelength cutoff employed (either soft or hard) to represent the fact that the fundamental motional unit is of finite extent. In conjunction with the previous conclusion (Macromolecules 1982,15,1041) that the model is insensitive to the particular form of the long-wavelength cutoff, this implies a certain robustness of the basic orientational diffusion picture of polymer local motion. In a series of we have developed a damped orientational diffusion model of the local, main chain motion of polymers in solution and have shown that NMR and dielectric relaxation processes can be adequately de- scribed by such models. We have also extended the ori- entational diffusion model to include chain-chain inter- actions in an averaged way through the use of a complex damping constant? thus enabling it to be applied to more concentrated polymer solutions. In addition, the model has been extended to the case of restricted rotational diff~sion.~ Recently, Viovy, Monnerie, and Brochon5 presented a detailed comparison of the ability of a variety of diffusional models of polymer local, main chain motion to fit their measured fluorescence depolarization mea- surements on polystyrene and found that these models fit the measured autocorrelation function very well. It has become increasingly evident as more experimental results are reported and compared to theory that local polymer motion as probed by typical relaxation measurements can be well described by an orientational diffusion picture. Encouraged by the above, we shall extend the range of applicability of the damped diffusion model of polymer motion to include the effect of spatial inhomogeneties. In particular two cases are explicitly treated. In the first case a polymer chain contains a probe molecule attached to it. Examples include spin-labels required in ESR measure- ments and dyes required in fluorescence depolarization measurements. Here, we present a procedure for deter- mining whether the probe moiety is essentially benign, that is, it does not change the intrinsic relaxation characteristics of the polymer local motion, and if so, a method is given for extracting the intrinsic motional parameters of the polymer chain. The second case we shall treat is the be- havior of a polymer that contains a periodic array of side chains appended to the main chain. Here we shall examine how the power spectrum of the polymer (and hence its relaxation properties) is modified by the presence of the side chains. In the damped diffusional model, orientational diffusion down the polymer chain is treated as a superposition of damped diffusional waves. In the context of this model an inhomogeneity is treated as an isolated change in the
Read full abstract