Journal of Colloid and Interface Science 247, 303–309 (2002) doi:10.1006/jcis.2001.8150, available online at http://www.idealibrary.com on Particulate Hematite Diffusion in Sodium Polyacrylate Solutions. The Effect of Ionic Strength Kristen E. Bremmell, David E. Dunstan, 1 Peter J. Scales, and Thomas W. Healy CRC for Bioproducts and Particulate Fluids Processing Center, Department of Chemical Engineering, The University of Melbourne, Parkville, VIC 3010 Australia Received May 5, 2000; accepted December 10, 2001 The diffusion coefficients of hematite particles in polyelectrolyte solution have been investigated using dynamic light scattering. Two apparent diffusion coefficients, a fast and a slow diffusional mode, are observed for the hematite particles in high-molecular-weight sodium polyacrylate solution at pH 10.5. The slow diffusion co- efficient (D slow ) shows a decrease with increase in polyelectrolyte concentration. The fast diffusion coefficient (D fast ) shows an in- crease to a maximum with increasing polyelectrolyte concentration and then a rapid decrease as the polyelectrolyte concentration in- creases further. With an increase in ionic strength from 10 -4 to 0.1 M NaNO 3 , the maximum value of D fast increased in magnitude, while the polyacrylate concentration at which the maximum occurs is seen to increase. The dependence of D fast on the measurement an- gle indicates that it is coupled to the fluctuations of the chains. The observed behavior is attributed to the hematite probe particle sens- ing both macroscopic (viscous) and elastic fluctuations associated with the polyelectrolyte motion. C  2002 Elsevier Science (USA) Key Words: dynamic light scattering; hematite diffusion; poly- electrolytes; ionic strength. INTRODUCTION This investigation follows from our interest in flocculation and the behavior of polyelectrolytes in particulate suspensions, which is fundamental to a diverse range of processes from the minerals industry to water treatment, pharmaceutical, and food industries. Understanding the flocculation processes in which polymers are used to effect aggregation of particles in suspen- sions can be assisted by analysis of the diffusion of particles in polymer solutions. Probe diffusion studies have been used to investigate both the adsorbed layer thickness of polyelectrolyte molecules (1) and the rheological dynamics of the macromolec- ular solution in which they are dispersed (2). Polyacrylate-type flocculants are commonly used in the mineral processing indus- try as a result of their high molecular weight and stability in a range of chemical environments. As such they have found appli- cation in the alumina industry where they are used in flocculating Bayer process solids (referred to as red mud). Red mud primar- 1 To whom correspondence should be addressed. Fax: +61 3 8344 4153. E-mail: davided@unimelb.edu.au. ily consists of iron oxide (3, 4) so for the present study we have chosen hematite and sodium polyacrylate as our model system. The diffusion of colloidal particles in solution is typically discussed in terms of the Stokes–Einstein equation, D = k B T 6πη R h , [1] where D is the diffusion coefficient of the particles in solu- tion, k B is Boltzmann’s constant, T is absolute temperature, η is the solution viscosity, and R h is the hydrodynamic radius of the particle. Derivation of the Stokes–Einstein equation as- sumes the suspending medium to be continuous, so the validity of the equation depends on the relative size of the solute and sol- vent molecules and of the probe particles. Systems that consist of non-interacting spheres diffusing through a solvent of small molecules are well defined by the Stokes–Einstein equation (5). However, for spherical probe diffusion in macromolecular so- lutions this relationship may not be followed. A range of so- called ternary systems have been studied previously where the probe and matrix consist of random coil polymers (6, 7) and also where the probe is a spherical solid particle (9–16). Both positive and negative deviations from Stokes–Einstein behavior have been observed for various probe/polymer/solvent systems. In these studies a positive deviation is usually referred to as one where, as a function of the polymer concentration, the diffusiv- ity decreases less than the viscosity increases. In general, ionic systems have shown greater deviation than neutral solutions. Polymer scaling theories (17, 18) have been applied to the- oretically model probe studies. An alternative theory is the hy- drodynamic scaling model of Phillies (19, 20) that assumes that interchain hydrodynamic interactions dominate macromolecu- lar entanglements. Ngai et al. (21, 22) developed a coupling model where the process of relaxation in these complex systems is described as the “co-operative process of motions coupled together by interactions” (22). Here the coupling between poly- mer chains plays an important role in the relaxation processes. In dilute solutions there is almost no coupling and the degree of coupling increases with increasing polymer concentration. A characteristic length scale which is often used when dis- cussing polymer solutions is the correlation length, ξ , which 303 0021-9797/02 $35.00 C  2002 Elsevier Science (USA) All rights reserved.