Light scattering and the absolute characterization of macromolecules

We propose a model giving the conformation of a star shaped polymer by taking into account the radial variation of the monomer concentration ϕ( r). For an isolated star when increasing r (at the centre of the star r = 0), the variation of ϕ (r) is first given by a constant value (r f1/2 ν-1 l); wh ere f is the number of branches, N the number of monomers in a branch and ν and l are the excluded volume and the length associated to a monomer. For all these cases, it is shown that the size of a branch is always larger than that of a linear polymer made of N monomers. Beyond the overlapping concentration the star conformation is obtained from two characteristic lengths essentially : χ(c ) a radius inside which the branches of the other stars do not penetrate, this radius defines a domain where the conformation of a star is similar to that of an isolated one. Beyond χ(c) the interpenetration of branches is characterized by a screening length ξ(c) very similar to that found for semi-dilute solutions of linear polymers. For all these regimes the variation of the size of a star is predicted as a function of N, f, v and c.

https://hal.archives-ouvertes.fr/jpa-00209423/document

Star shaped polymers : a model for the conformation and its concentration dependence

http://static.sif.it/SIF/resources/public/files/va2012/likos_0710.pdf

Effective interactions in soft condensed matter physics

“Life is branched” was the motto of a special issue of Macromolecular Chemistry and Physics1 on “Branched Polymers”, indicating that branching is of similar importance in the world of synthetic macromolecules as it is in nature. The significance of branched macromolecules has evolved over the last 30 years from just being considered as a side reaction in polymerization or as a precursor step in the formation of networks. Important to this change in perception of branching was the concept of “polymer architectures”, which formed on new starand graft-branched structures in the 1980s and then in the early 1990s on dendrimers and dendritic polymers. Today, clearly, controlled branching is considered to be a major aspect in the design of macromolecules and functional material. Hyperbranched (hb) polymers are a special type of dendritic polymers and have as a common feature a very high branching density with the potential of branching in each repeating unit. They are usually prepared in a one-pot synthesis, which limits the control on molar mass and branching accuracy and leads to “heterogeneous” products with a distribution in molar mass and branching. This distinguishes hyperbranched polymers from perfectly branched and monodisperse dendrimers. In the last 20 years, both classes of dendritic polymers, dendrimers as well as hb polymers, have attracted major attention because of their interesting properties resulting from the branched architecture as well as the high number of functional groups.2 The challenging synthesis of the dendrimers attracted especially scientists with a strong organic chemistry background and led to beautifully designed macromolecules, which allowed a deeper insight into the effect of branching and functionality. Dendrimers have been considered as perfect “nano-objects” where one can control perfectly size and functionality, which is of high interest in nanotechnology and biomedicine. hb polymers, however, were considered from the beginning as products suitable for larger-scale application in typical polymer fields like coatings and resins, where a perfect structure is sacrificed for an easy and affordable synthetic route. Thus, the first structures that were reported paralleled the chemistry used for linear polymers like typical polycondensation for polyester synthesis. More recently, unconventional synthetic methods have been adopted also for hb polymers and related structures. Presently, a vast variety of highly branched structures have been realized and studied regarding their properties and potential application fields. Excellent reviews appeared covering synthesis strategies, properties, and applications, like the very recent tutorial by Carlmark et al.,3 the comprehensive book on hyperbranched polymers covering extensively synthesis and application * E-mail: voit@ipfdd.de; lederer@ipfdd.de. Chem. Rev. 2009, 109, 5924–5973 5924

/pdf/hyperbranched-and-highly-branched-polymer-architectures-4fgsgtfpcd.pdf

Hyperbranched and highly branched polymer architectures--synthetic strategies and major characterization aspects.

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.

Diffusion in disordered media

Formulas for the mean square radii of various branched and ringed polymer molecules are developed under the usual assumptions regarding the statistics of chain configuration. For branched molecules, the mean square radii vary less rapidly with molecular weight than for strictly linear molecules, while for systems containing only rings and unbranched chains the variation is more rapid than for the linear case. These results show that in principle the quantity of branches or of rings can be determined from light‐scattering measurements.

The Dimensions of Chain Molecules Containing Branches and Rings

This discussion is concerned with the excluded volume effect in polymer chains, i.e., the mathematical problem of random flights with correlations between the flights, which is of importance in relating the mean size of a chain to its structure. A general formulation of the problem is set up and compared with the theory of Markoff processes. It is shown that although an integral equation of the Markoff form for the distribution function exists, it contains a complicated function whose exact evaluation is difficult. Since the same function occurs in the problem of the osmotic second virial coefficient, it is natural to relate the excluded volume effect to the second virial coefficient. The results of preliminary numerical calculations for the relation between the mean square radius of the chain and the second virial coefficient, in good agreement with experiment, are given. It is concluded that the volume effect is certainly not negligible for real chains, except when the second virial coefficient is zero, and that the effect increases with increasing chain length.

Walter H. Stockmayer

Papers

The Dimensions of Chain Molecules Containing Branches and Rings

Excluded Volume in Polymer Chains

When polymer science looked easy.

Polymerization Kinetics and Polymer Properties