Diffusing probe measurements in Newtonian and elastic solutions☆
Introduction
The use of colloidal particles as probes in polymer solutions and gels is not new. A significant number of studies have measured the diffusion of colloidal probes in a wide variety of polymer solutions in both aqueous [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18] and non-aqueous solvents. The probe particles are thought to sense their local environment in the polymer or polyelectrolyte solution and thus probe the internal structure of the solution. Our interest in these measurements has arisen from the non-purturbative nature of the measurements in examining polyelectrolyte solutions and gels. The measured diffusion coefficient of the probe particles is generally interpreted as a microviscosity using the Stokes–Einstein (S–E) equation. The microviscosity is simply the viscosity of the particle environment in the polymer or polyelectrolyte solution which has been shown to deviate from the macroscopic viscosity in a number of cases. For Newtonian solvents the micro- and macroviscosities generally appear to be the same while for polymer and polyelectrolyte solutions significant differences have been observed. In polyelectrolyte solutions the solution viscosity may not be uniform on the length scales of the diffusive fluctuations of the particles and differences between the micro- and macroviscosities may be measured to yield structural information pertaining to the polymer/polyelectrolyte solution.
The (S–E) equation is used to relate the measured diffusion coefficients to the solvent viscosity;where D is the diffusion coefficient, k Boltzmann's constant, T the absolute temperature, η the solution viscosity and Rh the hydrodynamic radius of the particle. The S–E relation may be used to interpret the measured diffusivity as a viscosity. Prior work has used the normalization of the viscosity and diffusivity by the product Dη/D0η0 where D0 and η0 are the diffusivity of the probe in the solvent and the solvent viscosity, respectively. Positive and negative deviations from (S–E) behaviour are defined as the product being greater than or less than 1, respectively. The number of papers in the area is significant and are well summarized in the work of Won et al. [1]. Both positive and negative deviations are observed in a number of solvents and probe/polymer mixtures. A significant number of papers show adherence to S–E behaviour such that Dη/D0η0=1. A positive deviation from S–E behaviour corresponds to a microviscosity which is less than the macroscopic viscosity of the solution. The viscosities of the polymer solutions are often not Newtonian and therefore the normalization used above is often not valid. Many of the prior works have relied on capillary viscometry for the measurement of viscosity without specification of the shear rate. Given that most polymer or polyelectrolyte solutions show visco-elastic behaviour, this normalization procedure may be prone to error. However, there currently exists no method, other than capillary viscometry, known to the authors for measuring the viscosity-shear rate behaviour of truly dilute polymer and polyelectrolyte solutions.
This study reports the measurement of the diffusion of latex tracer particles in Newtonian glycerol/water mixtures and both latex and hematite in highly elastic polyacrylamide and polyacrylate solutions (Separan AP30 and Alclar 665). The observed increase in the measured apparent fast diffusion coefficients in the polyelectrolyte solutions is discussed with reference to the visco-elastic nature of these solutions.
Section snippets
Experimental section
Triply distilled water was used in all experiments. AR glycerol obtained from BDH was used after centrifugation to remove all dust.
The lattices used were obtained from Interfacial Dynamics Corporation, USA, and used without further purification. Sulfate lattices of 0.2 μm diameter and amidine lattices of 0.068 μm diameter had negative and positive surface charges, respectively. Surface charge densities of −0.8 μC/cm2 and +4.8 μC/cm2 for the sulfate and amidine lattices were obtained from
Results and discussion
Fig. 3 shows the measured diffusion coefficients vs. viscosity for the 0.2 μm latex particles in glycerol/water solutions. Within experimental error, the S–E equation is obeyed over a range of Newtonian solvent viscosities. The measured diffusion coefficient varies inversely with the viscosity for the Newtonian glycerol/water solutions.
Fig. 4 shows the measured diffusion coefficients of the particle vs. temperature divided by the viscosity for the 0.2-μm latex particles in water over the range
Conclusions
The S–E equation is obeyed for colloidal particles over a range of Newtonian solvent viscosities and temperatures. Measured diffusion coefficients in elastic solutions are greater than those in water at finite polyelectrolyte concentrations where a maximum concentration is observed. This behaviour is not fully understood and is postulated as due to either the elasticity of the polyelectrolyte solutions where an elastic fluctuation is present, or a caged local motion of the probe particles. The
Acknowledgements
D.D. would like to acknowledge the support of the CRC for Industrial Plant Biopolymers during this work. K.B. would like to thank the Australian Research Council and the Advanced Mineral Products Research Centre. We would like to thank Jason Stokes for performing the rheological measurements on the AP30.
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Dedicated to Professor M. Almgren on the occasion of his 60th Birthday.