Extension of the Flory-Rehner theory of swelling to an anisotropic polymer system

Abstract

The Flory-R eimer t heor y for isotropic swelling of rubber crosslinked in t he dry state is extended to an anisotropic system crosslinked in t he dry, oriented state . The new parameters introduced into t he equation can be readily determined from dimensional changes of the fib er in a s ui table solvent using a photomicrographic te::hnique. Unlike other method3, s uch as the cathetometric and weight methods, t his technique enable3 t he attainment of s welling equilibrium usually within 30 minutes. Good agreement is obtained bet ween the equivalents of crosslinks calculated from chemical a nalyses and from swelling meas urements, respecti vely. I . IntroductionAn important objective in Lhe propcr evn,lwtLion of.lletwork structufes is the determination of the V swelling equilibrium. volume raLio q",= V o ' an d the calculation 01' the average molecular weight between fcrosslinks (l\1c). Tb ere arc two classical methods for the determination of the swelling equilibrium volume ratios: (a) the weight method, and (b) the linear method with a catheto metel'. Usin g the weight method one obtains the ratio of the weight of the swollen n etwork at equilibrium to the weight of the unswo11en crosslinked polym er, and from a knowledge o[ the densities of th e solven t and polymer, one can calculate q",=~, (where V = volume o[ Lhe swollen network at equilibrium and Vo = volume of tlte unslvollen crosslinked network) . Using the linear method one meas ures the length of the fib er at swelling equilibrium (L), and the length of the original fib er in th e dry state (L o) . The equilibrium volume swelling ratio, qm, will then be equalWith rela tiv ely highly crosslinked n etworks, especially in case of oriented fib ers, neither of the above-mentioned m ethods is practical. Swelling equilibrium in this case is reached very slowly (up to several weeks) because of surface effects of the fiber. Also, b ecause the system is anisotropic, q", is noIt is the obj ect of this pap er to present a modification of the Flory-Rehner theory of swelling and to describ e a photomicrogr aphic technique for the rapid determina tion of swellin g equilibrium volume ratios in crosslinked fibers. The Flory-Rehner th eory for isotropic swellin g of rubber crosslinked in the dry state is extended to an anisotropic system crosslinked in the dry, oriented state. It is shown that good agreement is obtained between the equivalents of crosslinks calculated from ch emical analyses and from swelling measurements, respectively. -On ( 1 -V2m)+V2m + X1V~m] = wher e v2m = 1/qm, which is Lhe raLio of the voluill e of the unswollen n etwork (Vo) to the volum e of th e swollen n etwork at eq uilibrium (V); VI = moht r volume of solvent ; v = specific volume of swollen polymer ; j\1c= nurnber average molecular weigh t between crosslinks; M = primary number average molecular weight of polymer (before crosslinking); x, = interaction p arameter which is a measure of tlte interaction energy of solvent molecules with polY1ner .According to Flory [4] the term 1 /v2m = ...

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