Renormalization group theory polymers

Freed KF (1987) Renormalization group theory of macromolecules. John Wiley, New York des Cloizeaux J, Jonnink G (1990) Polymers in solution Clarendon Oxford... 

In good solvents, the mean force is of the repulsive type when the two polymer segments come to a close distance and the excluded volume is positive this tends to swell the polymer coil which deviates from the ideal chain behavior described previously by Eq. (1). Once the excluded volume effect is introduced into the model of a real polymer chain, an exact calculation becomes impossible and various schemes of simplification have been proposed. The excluded volume effect, first discussed by Kuhn [25], was calculated by Flory [24] and further refined by many different authors over the years [27]. The rigorous treatment, however, was only recently achieved, with the application of renormalization group theory. The renormalization group techniques have been developed to solve many-body problems in physics and chemistry. De Gennes was the first to point out that the same approach could be used to calculate the MW dependence of global properties... 

M. Bishop, J. H. R. Clarke, and J. J. Freire, /. Cbem. Phys., 98, 3452 (1993). Computer Simulation Study of the Validity of Scaling and Renormalization Group Theories for Two-Dimensional Star Polymers. 

Recently, Oono [119] and Oono and Kohmoto [120] applied the renormalization group theory to polymer hydrodynamics of the Kirkwood-Riseman scheme. They computed and Pe to first order in e, where e = 4 — d with d being the dimensionality of space, and obtained in three dimensions... 

Renormalization group theory (see, e.g., [35]) lies at the heart of this theory, justifying the use of scaling laws in the asymptotic limit, i.e., for infinitely long polymer chains and for dilute solutions. For semidilute solutions, however, this criterion is not so crucial because the polymer chains are overlapping and many properties, e.g., osmotic pressure, are independent of the chain length. 

Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca Freed KF (1987) Renormalization group theory of macromolecules. Wiley, New York Freed KF, Dudowicz J, Stukalin EB, Douglas JF (2010) General approach to polymer chains confined by interacting boundaries. J Chem Phys 133 094901 Fuoss RM, Katchalsky A, Lifson S (1951) The potential of an infinite rod-like molecule and the distribution of the counter ions. Proc Natl Acad Sci USA 37 579-589 Golestanian R, Kardar M, Liverpool TB (1999) Collapse of stiff polyelectrolytes due to counterion fluctuations. Phys Rev Lett 82 4456-4459 Guggenheim FA (1952) Mixtures. The Clarendon Press, Oxford... 

Renormalization group theory. The mean field theory neglects the fact that the collisions between the segments in the polymer are strongly correlated a collision of any pair of segments is likely to induce other collisions since the segments are connected. To take into account such... 

Experimental values of g and pg are considerably influenced by the polydispersity of polymer samples used however, both g and pg are universal to a first approximation, the former being mostly found to be in the range (2.0 - 2.7) X lO mor and the latter in the range 1.25-1.35 (6.15-5.70 for Fg). Recently, Oono and Kohmoto [10,11] applied renormalization-group theory to the polymer hydrodynamics of the Krikwood-Riseman scheme and computed the values of g =2.36 x lO moP and Fg = 6.20, which compares rather favorably with experimental values. 

This book offers a detailed account of the renormalization group theory. The book contains an excellent review of many experimental data on the thermodynamic properties of polymer solutions. 

The development of adsorption theory provides the explanation of the macromolecule behavior in the adsorption layer and provides the basis of arguments on the experimental results. A few theoretical models, describing the adsorbed macromolecule, are widely used now. Self-consistent field theory or mean field approach is used to calculate the respective distribution of trains, loops, and tails of flexible macromolecule in the adsorption layer [22-26]. It allows one to find the segment density distribution in the adsorption layer and to calculate the adsorption isotherms and average thickness of the adsorption layer. Scaling theory [27-29] is used to explain the influence of the macromolecule concentration in the adsorption layer on the segment density profile and its thickness. Renormalization group theory [30-33] is used to describe the excluded volume effects in polymer chains terminally attached to the surface. The Monte Carlo method has been used for the calculation of the density profile in the adsorption layer [33-35]. 

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