Theory of Random Copolymer Fractionation in Columns

  • Sabine EndersEmail author
Part of the Advances in Polymer Science book series (POLYMER, volume 238)


Random copolymers show polydispersity both with respect to molecular weight and with respect to chemical composition, where the physical and chemical properties depend on both polydispersities. For special applications, the two-dimensional distribution function must adjusted to the application purpose. The adjustment can be achieved by polymer fractionation. From the thermodynamic point of view, the distribution function can be adjusted by the successive establishment of liquid–liquid equilibria (LLE) for suitable solutions of the polymer to be fractionated. The fractionation column is divided into theoretical stages. Assuming an LLE on each theoretical stage, the polymer fractionation can be modeled using phase equilibrium thermodynamics. As examples, simulations of stepwise fractionation in one direction, cross-fractionation in two directions, and two different column fractionations (Baker–Williams fractionation and continuous polymer fractionation) have been investigated. The simulation delivers the distribution according the molecular weight and chemical composition in every obtained fraction, depending on the operative properties, and is able to optimize the fractionation effectively.


Continuous thermodynamics Fractionation in column Theory of copolymer fractionation 



Segment-molar activity coefficient




Reciprocal to the uniformity, see (15)


Number of stages in the fractionation-column




Segment number


Ideal gas constant




Nonuniformity (30)


Number of volume increments in the Baker–Williams column


Intensive two-dimensional distribution function


Extensive two-dimensional distribution function


Segment fraction


Chemical composition of statistical copolymers


Segment fraction of the solvent in the solvent + nonsolvent mixture





Continuous polymer fractionation


Continuous spin fractionation


Extraction agent


Ethylene vinyl acetate copolymer


Feed in continuous polymer fractionation


Gel permeation chromatograph


Size exclusion chromatography


Successive precipitation fractionation


Successive solution fractionation

Greek Symbols


Segment-molar chemical potential


Gamma function


Parameter defined in (5)


Flory–Huggins interaction parameter


Parameter of the Stockmayer distribution function (15) describing the broadness of the chemical heterogeneity


Quotient of the total amount of segments in phase II and in phase I


Abbreviation, defined in (9) and (11)


Parameter of the Baker–Williams column in (45)


Parameter of the Baker–Williams column in (45)


Parameter of the Baker–Williams column in (45)


Parameter of the Baker–Williams column in (45)





Excess quantity




Number of stages in the fractionation-column


Number of maximal stage in CPF-column


Component i in the mixture


Number-average quantity


Number of volume increment in the Baker–Williams column


Mass-average quantity



Phase I


Phase II


Feed phase



Sincere thank is given to Dr. Heike Kahl for support in preparation of the manuscript.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Fachgebiet “Thermodynamik und Thermische Verfahrenstechnik”TU BerlinBerlinGermany

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