Abstract
Large deformation, nonlinear stress relaxation modulus G(t, γ) was examined for the SiO2 suspensions in a blend of acrylic polymer (AP) and epoxy (EP) with various SiO2 volume fractions (ϕ) at various temperatures (T). The AP/EP contained 70 vol.% of EP. At ϕ ≤ 30 vol.%, the SiO2/(AP/EP) suspensions behaved as a viscoelastic liquid, and the time-strain separability, G(t, γ) = G(t)h(γ), was applicable at long time. The h(γ) of the suspensions was more strongly dependent on γ than that of the matrix (AP/EP). At ϕ = 35 vol.% and T = 100°C, and ϕ ≥ 40 vol.%, the time-strain separability was not applicable. The suspensions exhibited a critical gel behavior at ϕ = 35 vol.% and T = 100°C characterized with a power law relationship between G(t) and t; G(t) ∝ t − n. The relaxation exponent n was estimated to be about 0.45, which was in good agreement with the result of linear dynamic viscoelasticity reported previously. G(t, γ) also could be approximately expressed by the relation \(G(t,\gamma) \propto t^{-n^{\prime}}\) at ϕ = 40 vol.%. The exponent n ′ increased with increasing γ. This nonlinear stress relaxation behavior is attributable to strain-induced disruption of the network structure formed by the SiO2 particles therein.
Similar content being viewed by others
References
Amari T, Watanabe K (1983) Rheological properties of disperse systems of pigment. Poly Eng Rev 3:277–321
Aoki Y (2007) Rheological characterization of carbon black/varnish suspensions. Colloids Surf A 308:79–86
Aoki Y, Watanabe H (2004) Rheology of carbon black suspensions. III. Sol–gel transition System. Rheol Acta 43:390–395
Aoki Y, Hatano A, Tanaka T, Watanabe H (2001) Nonlinear stress relaxation of ABS polymer in the molten state. Macromolecules 32:3100–3107
Aoki Y, Hatano A, Watanabe H (2003) Rheology of carbon black suspensions. I. Three types of viscoelastic behavior. Rheol Acta 42:209–216
Chambon F, Winter HH (1987) Linear viscoelasticity at the gel point of a crosslinking PDMS with imbalanced stoichiometry. J Rheol 31:683–697
Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon, London
Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, New York
Grant MC, Russel WB (1993) Volume fraction dependence of elastic moduli and transition temperatures colloidal silica gels. Phys Rev E 47:2606–2614
Guth E, Gold O (1938) On the hydrodynamic theory of the viscosity of suspension. Phys Rev 53:322
In M, Prud’homme PK (1993) Fourier transform mechanically spectroscopy of the sol–gel transition in zirconium alkoxide ceramic gels. Rheol Acta 32:556–565
Isaki T, Takahashi M, Urakawa O (2003) Biaxial damping function of entangled monodisperse polystyrene melts: comparison with the Mead–Larson–Doi model. J Rheol 47:1201–1210
Jokinen M, Gyorvary E, Rosenholm JB (1998) Viscoelastic characterization of three different sol–gel derived silica gels. Colloids Surf A 141:205–211
Onogi S, Matsumoto T (1981) Rheological properties of polymer solutions and melts containing suspended particles. Polym Eng Rev 1:45–87
Osaki K, Kishizawa K, Kurata M (1982) Material time constant characterizing the non-linear viscoelasticity of entangled polymeric systems. Macromolecules 15:1068–1071
Pham KN, Petekidis G, Vlassopoulos D, Egelhaaf SU, Poon WCK, Pusey PN (2006) Yielding of colloidal glasses. Europhys Lett 75:624–630
Pham KN, Petekidis G, Vlassopoulos D, Egelhaaf SU, Pusey PN, Poon WCK (2008) Yielding behavior of repulsion- and attraction-dominated colloidal glasses. J Rheol 52:649–676
Pontom A, Barboux-Douuff S, Sanchez C (1999) Rheology of titanium oxide based gels: determination of gelation time versus temperature. Colloids Surf A 162:177–192
Rueb CJ, Zukoski CF (1997) Viscoelastic properties of colloidal gels. J Rheol 42:197–218
Rueb CJ, Zukoski CF (1998) Rheology of suspensions of weakly attractive particles: approach to gelation. J Rheol 42:1451–1476
Schwarzl FR (1975) Numerical calculation of stress relaxation modulus from dynamic data for linear viscoelastic materials. Rheol Acta 14:581–590
Soskey PR, Winter HH (1984) Large step strain experiments with parallel-disk rotational rheometers. J Rheol 28:625–645
Tokumoto MS, Santilli CV, Pulcinelli SH (2000) Evolution of the viscoelastic properties of SnO2 colloidal suspensions during the sol–gel transition. J Non-Cryst Solids 273:116–123
Trappe V, Weitz DA (2000) Scaling of the viscoelasticity of weakly attractive particles. Phys Rev Lett 85:449–452
Uematsu H, Aoki Y, Sugimoto M, Koyama K (2010) Rheology of SiO2/(acrylic polymer/epoxy) Suspensions. I Linear viscoelasticity. Rheol Acta 49:299–304
Winter HH, Chambon F (1986) Analysis of linear viscoelasticity of a crosslinking polymer at the gel point. J Rheol 30:367–382
Wu H, Morbidelli M (2001) A model relating structure of colloidal gels to their elastic properties. Langmuir 17:1030–1036
Yanez JA, Laarz E, Bergstroem L (1999) Viscoelastic properties of particle gels. J Colloid Interface Sci 209:162–172
Yoshikawa K, Toneaki N, Moreki Y, Takahashi M, Masuda T (1990a) Dynamic viscoelasticity, stress relaxation and elongational flow behavior of high density polyethylene melts. Nihon Reoroji Gakkaishi (J Soc Rheol Jpn) 18:80–86
Yoshikawa K, Toneaki N, Moreki Y, Takahashi M, Masuda T (1990b) Dynamic viscoelasticity and stress relaxation of column-fractionated high density polyethylene melts. Nihon Reoroji Gakkaishi (J Soc Rheol Jpn) 18:87–92
Acknowledgements
The authors are grateful to Dr. T. Inada and T. Iwakura at Hitachi Chemical Co., Ltd. for support of this work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Uematsu, H., Aoki, Y., Sugimoto, M. et al. Rheology of SiO2/(acrylic polymer/epoxy) suspensions. II. Nonlinear stress relaxation. Rheol Acta 49, 1187–1196 (2010). https://doi.org/10.1007/s00397-010-0495-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00397-010-0495-0