Chapter

Light Scattering from Polymers

Volume 48 of the series Advances in Polymer Science pp 1-124

Date:

Static and dynamic light scattering from branched polymers and biopolymers

  • Walther BurchardAffiliated withInstitute of Macromolecular Chemistry, Hermann-Staudinger-Haus, University of Freiburg

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Abstract

The striking properties of synthetic polymers and biological macromolecules are largely determined by their shape and the internal mobility. Both quantities are closely related to the architecture of the molecules. This article deals with branched macromolecules in dilute solution, where the individual molecules are observed. The common technique for determining the shape of macromolecules is static light scattering. Information on the internal mobility and the translational motion of the mass centre can be obtained from the more recent technique of quasi-elastic or dynamic light scattering.

As a result of the mostly statistical mechanism of reaction, many different isomeric structures and a broad molecular weight distribution are obtained on polymerizing monomers with more than two functional groups. An interpretation of the quantities measured by the two light scattering techniques, i.e. the z-averages of the mean square radius of gyration 〈S2z, of the particle scattering factor Pz(q), of the translational diffusion coefficient Dz and of the reduced first cumulant Γ/q2, as function of the weight average molecular weight Mw is not possible without a comparison with special well defined models.

Starting with simple regularly branched structures and ascending to the more involved randomly branched structures, the article presents various techniques for the calculation of the measurable quantities and concentrates on the polydispersity. The representation of the molecules by rooted trees is shown to be most adequate for an extension of the theory of regularly branched chains to randomly branched polymers where statistical means have to be applied. In the Flory-Stockmayer theory and the further developed cascade branching theory all average quantities which are measured by the two light scattering techniques, i.e. Mw, 〈S2z, Pz(q), Dz etc., are uniquely determined by the extents of reaction of the various functional groups which, statistically speaking, are link probabilities. The basis of the cascade branching theory and their rules for analytical calculations are displayed and elucidated with many examples.

The second part of the article compares theory and experiment. In general, good agreement is found with the behavior predicted by the cascade theory. An interpretation for the static and dynamic light scattering behavior is given, and new structure sensitive parameters are introduced by combination of the static with the dynamic light scattering data. In particular, the dimensionless parameter ϱ=[〈S2z]1/2 〈R h −1 z is shown to be a quantity of great relevance.

Finally, the applicability of the cascade theory to rather complicated systems with unequal functional groups, substitution effect, vulcanization of chains and long rang correlation as a result of directed chain reactions is shown. The limitation of the theory to essentially tree-like molecules and their unperturbed dimensions is outlined and the consequence of this error for the prediction of real systems is discussed.