Small-angle X-ray Scattering; Gaussian random fields; Gels
Abstract :
[en] Time-resolved small-angle x-ray scattering (SAXS) is used to follow the formation of resorcinol-formaldehyde (RF) gels. An existing morphological model based on Gaussian random fields, and validated on RF aerogels, is generalized to analyze the data. The generalization is done in two different ways, one being relevant to colloid aggregation and the other to microphase separation. The SAXS data do not enable discrimination between the two mechanisms of gel formation, which shows that aggregation and microphase separation can generate very similar morphologies at the length scales explored by SAXS. Furthermore, physical arguments
suggest that, in the case of RF gels, aggregation and microphase separation can be regarded as two idealizations of the same complex physical process.
Disciplines :
Mathematics Materials science & engineering
Author, co-author :
Gommes, Cédric ; Université de Liège - ULiège > Département de chimie appliquée > Génie chimique - Génie catalytique
Roberts, Anthony
Language :
English
Title :
Structure development of resorcinol-formaldehyde gels: either microphase separation or colloid aggregation
Publication date :
2008
Journal title :
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
ISSN :
1539-3755
eISSN :
1550-2376
Publisher :
American Physical Society, College Park, United States - Maryland
D. W. Schaefer and K. D. Keefer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53.1383 53, 1383 (1984).
D. R. Vollet, D. A. Donatti, and A. Ibanez Ruiz, J. Non-Cryst. Solids 81, 288 (2001). 0022-3093
P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
V. I. Raman and G. R. Palmese, Langmuir LANGD5 0743-7463 10.1021/la048393t 21, 1539 (2005).
A. Serrano Aroca, M. Monleón Pradas, and J. L. Gómez Ribelles, Colloid Polym. Sci. 285, 753 (2007). 0303-402X
H. Tanaka, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.787 76, 787 (1996).
R. W. Pekala, J. Mater. Sci. JMTSAS 0022-2461 10.1007/BF01139044 24, 3221 (1989).
S. A. Al-Muhtaseb and J. A. Ritter, Adv. Mater. (Weinheim, Ger.) ADVMEW 0935-9648 10.1002/adma.200390020 15, 101 (2003).
R. W. Pekala and D. W. Schaefer, Macromolecules MAMOBX 0024-9297 10.1021/ma00072a029 26, 5487 (1993)
D. W. Schaefer, R. Pekala, and G. Beaucage, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/0022-3093(95)00043-7 186, 159 (1995).
T. Yamamoto, T. Nishimura, T. Suzuki, and H. Tamon, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/S0022-3093(01)00619-6 288, 46 (2001).
A. P. Roberts, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.R1286 55, R1286 (1997).
N. Job, R. Pirard, J. Marien, and J.-P. Pirard, Carbon CRBNAH 0008-6223 10.1016/j.carbon.2003.12.072 42, 619 (2004).
O. Glatter and K. Kratky, Small-Angle X-ray Scattering (Academic, London, 1982).
S. Ciccariello, J. Goodisman, and H. Brumberger, J. Appl. Crystallogr. JACGAR 0021-8898 10.1107/S0021889887010409 21, 117 (1988).
J. Rouquerol, D. Avnir, C. W. Fairbridge, D. H. Everett, J. H. Haynes, N. Pernicone, J. D. F. Ramsay, K. S. W. Sing, and K. K. Unger, Pure Appl. Chem. PACHAS 0033-4545 10.1351/pac199466081739 66, 1739 (1994).
S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer, New York, 2001).
S. Ciccariello, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.28.4301 28, 4301 (1983).
Y. Jiao, F. H. Stillinger, and S. Torquato, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.031110 76, 031110 (2007).
J. S. Pedersen, Adv. Colloid Interface Sci. ACISB9 0001-8686 10.1016/S0001-8686(97)00312-6 70, 171 (1997).
J. Serra, Image Analysis and Mathematical Morphology (Academic, Orlando, FL, 1983).
J. Ohser and F. Mücklich, Statistical Analysis of Microstructures in Materials Science (Wiley, Chichester, U.K., 2000).
M.Y. Lin, H.M. Lindsay, D.A. Weitz, R.C. Ball, R. Klein and P. Meakin, Proc. R. Soc. London, Ser. A PRLAAZ 0950-1207 423, 71 (1989).
B. Mohanty and H. B. Bohidar, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10338-7 76, 965 (2006).
T. P. M. Beelen, W. H. Dokter, H. F. Van Garderen, and R. A. Van Santen, Adv. Colloid Interface Sci. ACISB9 0001-8686 10.1016/0001-8686(94)80023-5 50, 23 (1994).
A. Hasmy and R. Jullien, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/0022-3093(95)00079-8 186, 342 (1995).
D. Posselt, J. S. Pedersen, and K. Mortensen, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/S0022-3093(05)80441-7 145, 128 (1992).
C. J. Gommes, S. Blacher, B. Goderis, R. Pirard, B. Heinrichs, C. Alié, and J.-P. Pirard, J. Phys. Chem. B JPCBFK 1089-5647 10.1021/jp049568a 108, 8983 (2004).
O. Malcai, D. A. Lidar, O. Biham, and D. Avnir, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.56.2817 56, 2817 (1997).
M. Kolb and H. J. Herrmann, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/18/8/007 18, L435 (1985).
R. Jullien and A. Hasmy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.4003 74, 4003 (1995).
H.-S. Ma, R. Jullien, and G. W. Scherer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.041403 65, 041403 (2002).
F. W. Billmeyer, Textbook of Polymer Science, 3rd ed. (Wiley-Interscience, New York, 1984).
N. F. Berk, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.44.5069 44, 5069 (1991).
J. W. Cahn, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1695731 42, 93 (1965).
N. F. Berk, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.2718 58, 2718 (1987).
M. Teubner, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/14/5/003 14, 403 (1991).
H. Jinnai, T. Hashimoto, D. Lee, and S.-H. Chen, Macromolecules MAMOBX 0024-9297 10.1021/ma960486x 30, 130 (1997).
P. Levitz, Adv. Colloid Interface Sci. 76-77, 71 (1998). 0001-8686
A. P. Roberts and M. A. Knackstedt, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.2313 54, 2313 (1996).
A. P. Roberts and M. Teubner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.51.4141 51, 4141 (1995).