Abstract
The kinetics of particle growth in lead zirconate titanate sol gel precursor solutions has been investigated. It was found that chemical reaction limited aggregation was responsible for most of the sol aging, followed by diffusion limited aggregation in the later stage. At the beginning, particles grow by reaction between initial polymers and particles. As the particle number-density increases, a particle-particle aggregation characterised by an exponential growth law becomes the predominant mechanism. When particles grow larger, towards gel formation, the aggregation changes to diffusion limited. Mathematical models derived according to the above mechanisms agreed well with experimentally measured particle growth profiles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S.R. Gurkovich and J.B. Blum, in Ultrastructure Processing of Glasses, Ceramics and Composite, edited by L.L. Hench and D.R. Ulrich (John Wiley, New York, 1984), p. 152.
K.C. Chen, A. Janah, and J.D. Mackensie, in Better Ceramics Through Chemistry II, Materials Research Society Symposium Proceedings, edited by C.J. Brinker, D.E. Clark, and D.R. Ulrich (MRS, Pittsburgh, PA, 1986), Vol. 73, p. 731.
C. Hsueh and M.L. Mecartney, J. Mater. Res. 6(10), 2208 (1991).
K.Kushida, K.R. Udayakumar, S.B. Krupanidhi, and L.E. Rhine, J. Am. Ceram. Soc. 76(5), 1345 (1989).
R.W. Schwartz, B.C. Bunker, D.B. Dimos, R.A. Assink, B.A. Tuttle, R. Tallant, and I.A. Weinstock, Int. Ferroelectrics 2, 243 (1992).
R.W. Schwartz, J.A. Voigt, B.A. Tuttle, D.A. Payne, T.L. Reichert, and R.S. DaSalla, J. Mater. Res. 12(2), 444 (1997).
Q. Zhang, M.E. Vickers, R.W. Whatmore, and A. Patel, J. Sol-Gel. Sci. & Tech. 11, 141 (1998).
Q. Zhang, R.W.Whatmore, M.E.Vickers, and A. Patel, J.Korean Phys. Soc. 32, S572 (1998).
T.A. Witten and L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981).
M. Kolb, R. Botet, and R. Jullien, Phys. Rev. Lett. 51, 1123 (1983).
D.A.Weitz, J.S. Huang, M.Y. Lin, and J. Sung, Phys. Rev. Lett. 53, 1657 (1984).
D.A.Weitz, J.S. Huang, M.Y. Lin, and J. Sung, Phys. Rev. Lett. 54(13), 1416 (1985).
R.C. Ball, D.A. Weitz, T.A. Witten and F. Leyvraz, Phys. Rev. Lett. 58(3), 274 (1987), and the references therein.
M. von Smoluchowski, Phys. Z. 17, 593 (1916).
R.M. Ziff, M.H. Ernst, and E.M. Hendriks, J. Phys. A: Math. Gen. 16, 2293 (1983).
P.G.J. van Dongen and M.H. Ernst, J. Phys. A: Math. Gen. 18, 2779 (1985).
P.J. Flory, Principles of Polymer Chemistry (Ithaca, New York, 1953).
W.H. Stockmayer, J. Chem. Phys. 11, 45 (1943).
P. Meakin, Phys. Rev. Lett. 51, 1119 (1983).
R. Jullien and M. Kolb, J. Phys. A: Math. Gen. 17, L639 (1984).
W.D. Brown and R.C. Ball, J. Phys. A: Math. Gen. 18, L517 (1985).
D.A. Weitz and M.Y. Lin, Phys. Rev. Lett. 57, 2037 (1986).
Q. Zhang, Z. Huang, and R.W. Whatmore, J. Sol-Gel Sci. & Tech. 23, 135 (2002).
G. Yi, Z. Wu, and M. Sayer, J. Appl. Phys. 75(5), 2717 (1988).
C. Sanchez, F. Babonneau, S. Doeuff, and A. Leaustic, in Ultrastructure Processing of Advances Ceramics, edited by J.D. Mackenzie and D.R. Ulrich (Wiley, New York, 1988).
R.A. Assink and R.W. Schwartz, Chem. Mater. 5, 511 (1993).
Q. Zhang, Z. Huang, M.E. Vickers, and R.W. Whatmore, Int. Ferroelectrics 23, 215 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Huang, Z., Zhang, Q. & Whatmore, R. Studies of Lead Zirconate Titanate Sol Aging Part II: Particle Growth Mechanisms and Kinetics. Journal of Sol-Gel Science and Technology 24, 49–55 (2002). https://doi.org/10.1023/A:1015161532663
Issue Date:
DOI: https://doi.org/10.1023/A:1015161532663