Evolution of the viscoelastic properties of SnO2 colloidal suspensions during the sol–gel transition
Introduction
Traditionally, the rheological characterization of gels is limited to the analyses of the coefficient of viscosity and of flow curves [1], [2]. In the specific case of gelation processes, oscillatory experiments have been used to determine the linear response of the storage, , and loss, , moduli. By measuring these moduli at different frequencies of oscillation (ω), the critical point of gel, from which the extent of the transformation [3], [4], [5] can be described, has been experimentally defined. Near the gel point, a distribution of relaxation times can be fit with a power law frequency variation of the complex modulus, [3] and the gel point is an intermediate state between a liquid and a solidwhere the gel strength (S) depends on the cross-linking density and of the molecular chain flexibility.
At the gel point both and can be fit with a power law dependence, with the same exponent (Δ), on the frequency of oscillation [3]Therefore, the loss angle (δ) does not depend on ωfrom which the gel time is determined for . The Δs corresponding to the gel time depend on the stoichiometry, concentration, and mean molar weight of molecular species, resulting [6].
Otherwise, the percolation threshold describes the sol–gel transition by a power law dependence on the Newtonian viscosity, η0, equilibrium shear modulus, G0, and equilibrium steady-state shear compliance, J0, with the relative distance of the gel point, ε:where , with p the transformation extent and pc its critical value, and the critical exponents s and z are related by [5]Often, for experimental work, it has been assumed [3], [4], [5], [6] that ε changes linearly with time , with the gelation time, tg, determined empirically). A few studies determining the transformation extent show that p is not proportional to the gelation time excepted over an interval near the critical point [5].
Two theoretical approaches concerning the mechanical properties of such elastic systems have been postulated [7], [8]. The scalar percolation transition takes account of an analogy between the elastic bonds between the rigid objects composing the network (particles, aggregates or chains) with the electrical conductivity of a random network of isolating and conducting bonds. From this approach Eq. (4) is an universal scaling law, with and . Otherwise, the vector percolation transition assumes that the objects are totally rigid and forces are transmitted through bending of the weakest link. In this case, the elasticity is vectorial and the critical exponents are always larger than in scalar percolation.
Besides, the simplicity of applying the above theory, the oscillatory rheological measurements present some practical difficulties. The main one is the time required for probing a range of oscillatory frequencies, hindering the analysis of the faster kinetic processes. Moreover, the measurements have to be done in the linear regime and not cause any perturbation on the gelation process. These constraints impose contradictory requirements, i.e., to keep the angular amplitude of deformation as small as possible and to be able to measure the shear stress.
From the creep and creep-recovery tests both the elastic and viscous components of the system under conditions close to equilibrium can be determined. This feature makes available the structural conformation and some of the structural parameters of macromolecules or aggregates that constitute the gel [9]. Moreover, the magnitude of the applied stress in the creep test does not perturb the gel's structure. From this experiment the steady-state viscosity at zero shear rate, η0, the equilibrium steady-state shear compliance, J0, and the relaxation time, τ, are obtained quite directly. The relaxation time is obtained from the recovery of the strain, γ, when the external stress constraint is released by the relation [9]in which, for and, for the function must decay much faster than a power law (exponentially, for instance).
Earlier studies involving SnO2 colloidal suspensions [10], [11] make evident that the sol–gel transition occurs by physical aggregation of primary particles permitting the secondary polycondensation reaction by oxolation reaction between OH groups at the surface of adjacent particles. This reaction produces interparticle chemical bonds, which increase the stiffness of chains constituting the network [10]. The kinetics of these processes may be followed if some parameters, which control aggregation and gelation, such as particle and electrolyte concentrations, pH, and temperature, could be adjusted to provide adequate time to carry out in situ tests. In this study, creep and oscillatory measurements have been used to observe the structural evolution involved during aggregation and gelation processes in SnO2 colloidal suspensions. The effect of the concentration of electrolyte and pH on the kinetics of aggregation and gelation has been analyzed.
Section snippets
Experimental
SnO2 aqueous colloidal suspensions (1.0M) have been prepared from SnCl4 · 5H2O as described elsewhere [10]. After dialysis a stable sol is obtained at and electrolyte concentration (NH4+, Cl−) less than 0.01 mM. The pH of an aliquot of this suspension was increased to 7.5 by adding aqueous ammonium hydroxide solution (0.01M). Then, the concentration of electrolyte was adjusted by adding aqueous ammonium chloride solution (1M). Suspensions containing concentration of electrolyte equal to
Results
The results show that samples have three different responses, so that the following terminology was adopted: fast transformation (FT) for samples prepared at and mM; slow transformation (ST) for samples prepared at and mM and gel transformation (GT) for samples prepared at and mM.
The effects of the pH and the concentration of electrolyte on the time evolution of the apparent viscosity measured at constant shear stress (0.4 Pa) are shown in Fig. 1.
Discussion
The slower increase of viscosity observed in Fig. 1 for GT samples is characteristic of a developing structure of the system due to aggregation of colloidal particles. In this sample we observed the formation of a transparent gel after 1 h. Meanwhile, from the simple observation of the viscosity change we cannot determine the gelation time. On the other hand, the more rapid increase of viscosity, observed after 10 min for ST samples is similar to gelation observed for gelling systems [4], [5].
Conclusions
The creep and creep-recovery experiments appear as a well-suited technique to probe structural changes during aggregation and gelation of colloidal suspensions. The simple analysis of the time dependence of the data provides information on growth and interactions of aggregates. From the changes of the instantaneous compliance we can resolve the different steps of the sol-gel transition, i.e., aggregate growth, interconnection between aggregates, and the gel point.
An open aggregate growth was
Acknowledgements
This work has been supported by CAPES/COFECUB, CNPq and FAPESP (Brazil).
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