Gelation of polymer solutions under shear flow

doi:10.1016/S0927-7757(03)00319-4

Colloids and Surfaces A: Physicochemical and Engineering Aspects

Volume 225, Issues 1–3, 15 September 2003, Pages 37-48

https://doi.org/10.1016/S0927-7757(03)00319-4 Get rights and content

Abstract

Gelling a polymer solution under constant shear rate was recently found to be an attractive procedure for preparing size-controlled microgels. In the theoretical approach developed in this paper, the microgels formed during gelling are modelled as non-covalent ‘star’ polymers. This approach provides scaling laws to predict the effects of the shear rate applied during gelation on: (1) the gelling kinetics in three flow regimes; (2) the microgel size dependence in weak and strong flows; and (3) the rheological and elastic properties of the microgel solutions. The reported experiments were carried out by gelling semi-dilute high molecular weight polymer solutions by a crosslinker small enough to diffuse inside macromolecules and thus able to form both intra and intermolecular cross-links. All available experimental results are in agreement with our theoretical predictions, but further experiments are needed for a complete validation of the proposed theory.

Introduction

The gelation of a polymer solution results from the formation of intermolecular cross-links that can be formed by various mechanisms: attractive interactions between a few hydrophobic groups [1], temperature-induced attraction between monomers [2] or formation of organo-metallic complexes [3]. Whatever the mechanism is, the imposition of a constant shear flow during the crosslinking process prevents the formation of a true gel, i.e. macromolecule aggregates having an infinite size, even if the initial polymer solution is semi-dilute. Instead, we obtain a solution of non-linked aggregates with finite size we refer to as microgels.

Gelling a polymer solution with crosslinker under constant shear rate flow has been proposed recently as an attractive new method for preparing soft size-controlled microgels [4], [5], [6]. In Refs. [4], [5], the four steps of the crosslinking process have been described and we proposed to consider the microgels thus formed as soft supra-macromolecular fractal aggregates. In these investigations, the polymer is a terpolymer of acrylamide bearing acrylate groups and the crosslinker an organo-metallic complex of zirconium (zirconium lactate) which is a non-toxic product. The crosslinking occurs by ligand exchange between lactates and acrylate functional groups. When gelling occurs in the semi-dilute regime, the microgels overlap significantly so that the solutions can become extremely viscous and their rheology is similar to that of concentrated particles. In more recent studies [6], [7], [8], the microgels could be isolated and stabilised over long periods of time so that their sizes could be measured directly by photon correlation spectroscopy. After stabilisation, these microgels were found to be quasi-insensitive to pH, salinity and temperature and able to propagate very easily in porous media without any sign of plugging. The main advantage of preparing microgels by crosslinking under shear is that the polymer, the crosslinker and gelling conditions can be selected in order to reach the properties required for a given application.

In this paper we propose a new theoretical approach to model the gelling process and to predict the viscoelastic properties of the microgels and their solutions. This approach assumes that the microgels obtained at the end of the process can be modelled either as fractal aggregates of soft, partially draining spheres or as ‘star’ polymers.

When applied shear stresses are too small to induce any polymer deformation, the assimilation of microgels to aggregates of hard partially draining colloidal particles is straightforward. However, when the applied shear stresses are high enough to induce polymer conformation changes, predicting gelling kinetics, microgel size and the viscoelastic properties of their solutions, requires to use an approach combining the theories of colloidal dispersions with that of star polymers.

In the first section of this paper, we propose a theoretical approach to model the formation of microgels and the viscoelastic properties of their solutions at the end of formation process. This approach proposes some modifications to existing models (colloidal particle aggregation and star polymer theories) to take into account the conformational changes induced by shear stresses during gelation. These modifications allow to predict the shear rate sensitivity of aggregation kinetics as well as the effects of the non-Newtonian character of the initial polymer solution on the rupture of the aggregates by shear stresses and, consequently, on the variation of microgel size versus applied shear rate. Some rheological characteristics including elastic properties of the microgel solutions obtained are predicted. In the second section, the experimental system selected as well as the rheological equipment used is described. In the third section, the experimental results are reported and discussed on the basis of the comparison with the theoretical approach proposed in the first section. Good agreement between the proposed theory and experimental results suggests that the dual approach proposed in this paper, which combines theories for colloidal dispersions together with a theory of star polymers, is a good way to describe the properties of microgel solutions prepared by gelling under shear.

Section snippets

Shear-rate dependence of gelling kinetics

Potanin [9] argued that the most probable mechanism of aggregation of colloidal hard spheres is of hierarchical type. In other terms, aggregation starts by the formation of doublets which are then cross-linked, so that clusters of higher order are progressively formed. By extending this result to the case of the gelling of polymers in good solvent, we expect that, if the mixture of the polymer solution with the cross-linker is homogeneous at the beginning of gelation, the system should remain

Experimental

The polymer used is a statistical terpolymer of acrylamide bearing 2% of zirconium-reactive acrylate side groups and 2% of sulfonated groups to prevent syneresis. Its molecular weight is around 2×10⁶ Da. When dissolved in distilled water containing 20 g/l of NaCl at pH 7, its zero shear intrinsic viscosity is [μ]_p=950 cm³/g at 30 °C with a low value of the Huggins constant ( k′=0.34) showing that the polymer is in a good solvent [6].

For gelling experiments the polymer concentration was fixed at C

Rheology of initial polymer solution

First of all the viscosity of the initial polymer solution was measured as a function of shear rate. The log–log plot on Fig. 1 shows that the specific viscosity depends on shear rate as expected for semi-dilute solutions displaying clearly a Newtonian regime at low shear rates followed by a shear-thinning regime. The crossover between these two regimes occurs at a critical shear rate γ_a* close to 20 s⁻¹. Beyond this value, the viscosity (or the specific viscosity) decrease as γ_a^−0.33.

Gelation kinetics

The

Conclusions

The gelation of a polymer solution under shear has been modelled by using a new theoretical approach which considers the microgels formed during gelation as star polymers. The experimental validation of this theory is only partial but quite promising. The main conclusions derived from this study are:

(1) Three kinetic regimes are theoretically expected as the applied shear rate increases: (i) at very small applied shear rates (P_e≪1), the gelation kinetics is entirely governed by thermal

Acknowledgements

The authors wish to tank IFP for permission to publish this work and are indebted to Prof. W.B. Russel for his pertaining remarks and his suggestions.

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