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polymer science Polymer science or macromolecular science is a subfield of materials science concerned with polymers, primarily synthetic polymers such as plastics and elastomers. The field of polymer science includes researchers in multiple disciplines includ ...
Flory–Rehner equation is an equation that describes the mixing of
polymer A polymer (; Greek ''poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic and ...
and
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, an ...
molecules A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioc ...
as predicted by the equilibrium swelling theory of Flory and Rehner. It describes the equilibrium swelling of a lightly crosslinked polymer in terms of crosslink density and the quality of the
solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
. The Flory–Rehner equation is written as: : -\left \ln+\nu_2+ \chi_1 \nu_2^2 \right= V_1 n \left(\nu_2^\frac-\frac\right) where, \nu_2 is the volume fraction of polymer in the swollen mass, V_1 the molar volume of the solvent, n is the number of network chain segments bounded on both ends by crosslinks, and \chi_1 is the Flory solvent-polymer interaction term. In its full form, the Flory–Rehner equation is written as: : -\left \ln+\nu_2+ \chi_1 \nu_2^2 \right= \frac \left(1-\frac\right) \left(\nu_2^\frac-\frac\right) where, \bar is the
specific volume In thermodynamics, the specific volume of a substance (symbol: , nu) is an intrinsic property of the substance, defined as the ratio of the substance's volume () to its mass (). It is the reciprocal of density (rho) and it is related to the ...
of the polymer, M is the primary
molecular mass The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quant ...
, and M_c is the average molecular mass between crosslinks or the network parameter.


Flory–Rehner theory

The Flory–Rehner theory gives the change of free energy upon swelling of the polymer gel similar to the
Flory–Huggins solution theory Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing. The result is an equatio ...
: :\Delta F = \Delta F_\mathrm + \Delta F_\mathrm. The theory considers forces arising from three sources: # The
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
change \Delta S_\mathrm caused by mixing of polymer and solvent # The heat of mixing of polymer and solvent \Delta U_\mathrm, which may be positive, negative, or zero so, that \Delta F_\mathrm=\Delta U_\mathrm-T\Delta S_\mathrm # The entropy change caused by reduction in numbers of possible chain conformations via swelling \Delta F_\mathrm The Flory–Rehner equation was used to model the cooking of steaks in a journal article in 2020


References


Bibliography

* * *{{cite book, last = Alger, first = Mark , title = Polymer Science Dictionary, publisher =
Chapman & Hall Chapman & Hall is an Imprint (trade name), imprint owned by CRC Press, originally founded as a United Kingdom, British publishing house in London in the first half of the 19th century by Edward Chapman (publisher), Edward Chapman and William Hall ...
, year = 1997, edition = 2nd, isbn = 978-0-412-60870-4, location =
London London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...
, ref = Alger Polymer physics Soft matter Materials science Polymers Equations Rubber properties