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Theory of Random Copolymer Fractionation in Columns

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

Abstract

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.

Keywords

Continuous thermodynamics Fractionation in column Theory of copolymer fractionation 

Symbols

f

Segment-molar activity coefficient

F

Fraction

k

Reciprocal to the uniformity, see (15)

m

Number of stages in the fractionation-column

P

Pressure

r

Segment number

R

Ideal gas constant

T

Temperature

U

Nonuniformity (30)

v

Number of volume increments in the Baker–Williams column

W

Intensive two-dimensional distribution function

w

Extensive two-dimensional distribution function

X

Segment fraction

y

Chemical composition of statistical copolymers

Z

Segment fraction of the solvent in the solvent + nonsolvent mixture

Abbreviations

CF

Cross-fractionation

CPF

Continuous polymer fractionation

CSF

Continuous spin fractionation

EA

Extraction agent

EVA

Ethylene vinyl acetate copolymer

FD

Feed in continuous polymer fractionation

GPC

Gel permeation chromatograph

SEC

Size exclusion chromatography

SPF

Successive precipitation fractionation

SSF

Successive solution fractionation

Greek Symbols

μ

Segment-molar chemical potential

Γ

Gamma function

γ

Parameter defined in (5)

χ

Flory–Huggins interaction parameter

ε

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

φ

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

ρ

Abbreviation, defined in (9) and (11)

η

Parameter of the Baker–Williams column in (45)

τ

Parameter of the Baker–Williams column in (45)

θ

Parameter of the Baker–Williams column in (45)

λ

Parameter of the Baker–Williams column in (45)

Subscripts

A

Solvent

E

Excess quantity

M

Mixture

m

Number of stages in the fractionation-column

Max

Number of maximal stage in CPF-column

i

Component i in the mixture

N

Number-average quantity

n

Number of volume increment in the Baker–Williams column

W

Mass-average quantity

Superscripts

I

Phase I

II

Phase II

F

Feed phase

Notes

Acknowledgment

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

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Authors and Affiliations

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

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