Chapter 38 Polyelectrolyte Chains in Swollen Gels
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S. Sasaki, H. Ojima, and H. Maeda Department of Chemistry, Faculty of Science, Kyushu University, 33, Hakozaki Higashi-ku Fukuoka 812, Japan
Our previous approach describing the swelling behavior of polyion gels in terms of the dimensionality d of the chain extension space is applied to the analysis of the expansion behavior ofpoly(acrylicacid) gels neutralized to various degrees in equilibrium with external salt solutions of different concentrationsCs.The results showed that d remained constant to be about 2.2 in the range ofCsbetween 10 and 50 mM while it reached about 3 atC of 0.1 M. Light scattering data on fully ionized gels also showed corresponding changes in a narrower range ofCsbetween 60 and 80 mM with respect to both the apparent diffusion constants and the scattered light intensities. A structural change of sodium polyacrylate gels was suggested in this range of Cs. s
Ionic polymer gels expand tremendously at high ionization degrees and the degree of expansion depends strongly on the salt concentration (I). The gel volume is determined by a balance among the conformational contractile force, the electrostatic expanding force and the mixing free energy (2 - 5). We have proposed a novel approach according to which the expansion behavior of the gels can be related to the dimensionality d of the space for the microbrownian motion of cross-linked chains(
s
e
It is necessary to express π in terms of n ' rather than n since it is not % but n ' that is experimentally controlled. In contrast with the ideal Donnan equilibrium, % is related to n^ through a more exact Donnan equilibrium in Manning's theory as follows. 0 8
s
s?
s
Y n ±
f
s
(n +n ) = ( n ) e
s
2
s
It is not easy, however, to solve eq 14 for n since the mean activity coefficient γ is given as a function of ξ and X (= n^ / %). It is not easy to express ft in terms of ης' in Manning's approach, although it provides a better approximation than the values in this study. This is the reason why we calculate n according to eq 6. s
±
os
os
This work was partially supported by a Grant-in-Aid (No. 02403004)fromthe Ministry of Education, Science and Culture of Japan. Literature Cited 1) Kuhn, W.; Hargitay, B.; Katchalsky, Α.; Eisenberg, H. Nature 1950, 165, 514 2) Katchalsky, Α.; Lifson, S.; Eisenberg, H. J. Polym. Sci. 1951, 7, 571 3) Katchalsky, Α.; Michaeli, I. J. Polym. Sci. 1955, 15, 69 4) Flory, P. J. Principles of Polymer Chemistry ; Cornell University Press: 1953
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37, 579. 9) Lifson, S.; Katchalsky, A. J. Polym. Sci. 1953 13, 43 10) de Gennes, P. -G. Scaling Concepts in Polymer Physics, Cornell Univ. Press
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12) Oosawa, F. Polyelectrolytes, Marcel Dekker, Inc: 1971, Chap. 2. 13) Manning, G. J. Chem. Phys., 1969
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September 7, 1993
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