Making Floryr–Huggins Practical: Thermodynamics of Polymer-Containing Mixtures

  • Bernhard A. WolfEmail author
Part of the Advances in Polymer Science book series (POLYMER, volume 238)


The theoretical part of this article demonstrates how the original Flory–Huggins theory can be extended to describe the thermodynamic behavior of polymer-containing mixtures quantitatively. This progress is achieved by accounting for two features of macromolecules that the original approach ignores: the effects of chain connectivity in the case of dilute solutions, and the ability of polymer coils to change their spatial extension in response to alterations in their molecular environment. In the general case, this approach leads to composition-dependent interaction parameters, which can for most binary systems be described by means of two physically meaningful parameters; systems involving strongly interacting components, for instance via hydrogen bonds, may require up to four parameters. The general applicability of these equations is illustrated in a comprehensive section dedicated to the modeling of experimental findings. This part encompasses all types of phase equilibria, deals with binary systems (polymer solutions and polymer blends), and includes ternary mixtures; it covers linear and branched homopolymers as well as random and block copolymers. Particular emphasis is placed on the modeling of hitherto incomprehensible experimental observations reported in the literature.


Modeling Mixed solvents Phase diagrams Polymer blends Polymer solutions Ternary mixtures Thermodynamics 



Exponent of Kuhn–Mark–Houwink relation (29)


Intramolecular interaction parameter (47) for blend component A


Constants of (13)

A2, A3

Second and third osmotic virial coefficients


Activity of component i


Intramolecular interaction parameter (47) for blend component B


Concentration in moles/volume


Constant of interrelating α and ζλ (34)


Gibbs free energy – free enthalpy


Integral interaction parameter




Constant of the Kuhn–Mark–Houwink relation (29)


Lower critical solution temperature


Molar mass


Number-average molar mass


Weight-average molar mass


Number of segments


Number of moles


Vapor pressure


Ideal gas constant




Molecular surface


Absolute temperature


Ternary interaction parameter (61)


Melting point


Upper critical solution temperature




Molecular volume


Weight fraction


Mole fraction


Parameter relating the conformational relaxation to β (53)

Greek and Special Characters

\(\overline \omega \)

Parameter quantifying strong intersegmental interactions (42)


Intrinsic viscosity


Volume fraction of polymer segments in an isolated coil (27)


Theta temperature


Parameter of (23), first step of dilution


Degree of branching (52)


Flory–Huggins interaction parameter


Parameter of (57)


Parameter of (57)


Surface-to-volume ratio of the segments in binary mixtures (24)


Segment fraction, often approximated by volume fraction


Constant of (30)


Intramolecular interaction parameter (23)


Chemical potential


Parameter of (23)


Any parameter of (23)


Osmotic pressure




Parameter of (44)


Differential Flory–Huggins interaction parameter for the polymer


Conformational relaxation (second step of dilution) (23)


1, 2, 3 …

Low molecular weight components of a mixture

A to P

High molecular weight components


Branched oligomer/polymer


Critical state


Conformational relaxation


Fixed conformation




Enthalpy part of a parameter

i, j, k

Unspecified components i, j, k


Linear polymer


Linear oligomer/polymer




Entropy part of a parameter




Quantity referring to a pure component, to an isolated coil, or to high dilution


Molar quantity


Segment-molar quantity


Excess quantity


Residual quantity (with respect to combinatorial behavior)

Infinite molar mass of the polymer



The author is grateful to Dr. John Eckelt (WEE-Solve AG, Mainz, Germany) and to Prof. Spiros Anastasiadis (University of Crete, Greece) for their constructive criticism, which has certainly improved the readability of this contribution.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Institut für Physikalische Chemie der Johannes Gutenberg-Universität MainzMainzGermany

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