Polymer Self-Diffusion in Entangled Systems

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Abstract
This article has focused on work in the last several years, a period during which theoretical insights and experimental techniques pertaining to polymer self-diffusion in entangled systems have advanced enormously. The point has been to lay out for the reader the means by which this information has been developed and to lay out the available information itself. The objective has been to facilitate comparisons regarding use and applicability of techniques, quality, and interpretations of data and the trends present in the various data. Presentation of the information in this style leads to a few definite conclusions and a larger number of problems which come more sharply than before into focus as ripe for continued study. Specific conclusions which seem reasonable at this point are: The molecular weight dependence of Ds is, in entangled systems, an inverse square law, consistent with the prediction of the reptation model. The self-diffusion coefficient becomes quite insensitive to the matrix molecular weight Mm at sufficiently high Mm. The variation of Ds with concentration in entangled solution is very strong, considerably higher than the c−3 law suggested by scaling arguments with the reptation model. Free volume effects on the monomeric friction coefficient are at the root of this. Outstanding problems include the following areas and questions: It is necessary to ascertain why there is, in melt Ds data, a reproducible discrepancy between NMR data and those data obtained via other methods. Is NMR sensing the slowest translational mode of motion? Is the marking which is necessary for all the other techniques affecting the measurements? In solution data, the origin of the QELS “slow mode” and the marked disparity between these data and those from other methods must be determined. Critical conditions for the onset of entangled or reptation behavior (in terms of M and c) in Ds must be studied and defined more clearly both experimentally and theoretically. Is the observation that Ds∼M−2 down to unexpectedly low molecular weight an indication that diffusion proceeds via a reptation-like mechanism even for molecular weights which show no other manifestation of entanglement, OI is there another set of conditions which produce Ds∼M−2 scaling? Incisively designed experiments to study matrix and molecular architecture effects seem likely to be most fruitful. Stars, combs, rings, and polydisperse samples hold new information on diffusion mechanisms. A comprehensive experimental and theoretical picture of polymer self-diffusion will advance the state of practice of a wide range of technological applications. The current status of available diffusion information is good enough that the time scales of many practical processes can be predicted approximately. More precise predictions of, for example, diffusion-controlled reaction rates, await the availability of more extensive data and of the resolution of some of the remaining questions and discrepancies highlighted here.

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