In polymer science Flory–Rehner equation is an equation that describes the mixing of polymer and liquid molecules as predicted by the equilibrium swelling theory of Flory and Rehner.[1] It describes the equilibrium swelling of a lightly crosslinked polymer in terms of crosslink density and the quality of the solvent.
The Flory–Rehner equation is written as:
\( {\displaystyle -\left[\ln {\left(1-\nu _{2}\right)}+\nu _{2}+\chi _{1}\nu _{2}^{2}\right]=V_{1}n\left(\nu _{2}^{\frac {1}{3}}-{\frac {\nu _{2}}{2}}\right)} \)
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.[2]
In its full form, the Flory–Rehner equation is written as[3]:
\( {\displaystyle -\left[\ln {\left(1-\nu _{2}\right)}+\nu _{2}+\chi _{1}\nu _{2}^{2}\right]={\frac {V_{1}}{{\bar {\nu }}M_{c}}}\left(1-{\frac {2M_{c}}{M}}\right)\left(\nu _{2}^{\frac {1}{3}}-{\frac {\nu _{2}}{2}}\right)} \)
where, \( {\bar {\nu }} \) is the specific volume of the polymer, M is the primary molecular mass, and \( M_c \) is the average molecular mass between crosslinks or the network parameter.[3]
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:
\( {\displaystyle \Delta F=\Delta F_{\mathrm {mix} }+\Delta F_{\mathrm {elastic} }}. \)
The theory considers forces arising from three sources:[2]
The entropy change \( {\displaystyle \Delta S_{\mathrm {mix} }} \) caused by mixing of polymer and solvent
The heat of mixing of polymer and solvent \( {\displaystyle \Delta U_{\mathrm {mix} }} \), which may be positive, negative, or zero so, that \( {\displaystyle \Delta F_{\mathrm {mix} }=\Delta U_{\mathrm {mix} }-T\Delta S_{\mathrm {mix} }} \)
The entropy change caused by reduction in numbers of possible chain conformations via swelling \( {\displaystyle \Delta F_{\mathrm {elastic} }} \)
The Flory–Rehner equation was used to model the cooking of steaks in a journal article in 2020[4]
References
Flory and Rehner 1943
Sperling 2006, p. 472
Alger 1997, p. 202
Nelson, H.; Deyo, S.; Granzier-Nakajima, S.; Puente, P.; Tully, K.; Webb, J. (2020). "A mathematical model for meat cooking". The European Physical Journal Plus. 135 (3): 322. arXiv:1908.10787. doi:10.1140/epjp/s13360-020-00311-0. ISSN 2190-5444.
Bibliography
Flory, Paul; Rehner, John (1943). "Statistical mechanics of cross-linked polymer networks II. Swelling". J. Chem. Phys. 11 (11): 521–526. Bibcode:1943JChPh..11..521F. doi:10.1063/1.1723792.
Sperling, Leslie H. (2006). Introduction to Physical Polymer Science (4th ed.). Bethlehem, PA: John Wiley & Sons. ISBN 978-0-471-70606-9.
Alger, Mark (1997). Polymer Science Dictionary (2nd ed.). London: Chapman & Hall. ISBN 978-0-412-60870-4.
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
