Temperature dependence of the diffusion coefficient of polystyrene latex spheres

Abstract

and its extensions, i.e., hydrodynamic properties of dilute solutions of macromolecules scale linearly with temperature and antilinearly with solvent viscosity. The accuracy of this rule was extensively studied by Longsworth,' who used a Rayleigh interference technique to measure the diffusion coefficient of materials with molecular weights of 20-68,000. While one cannot show the universal applicability of a rule, over the temperature range of 1-37C, the diffusion coefficients of the macromolecular solutes studied in Ref. 1 were found to deviate from Eq. (1) by only f4%. Recently, Crossley et a1.2 used quasielastic light scattering (QELS) to measure the diffusion coefficient of polystyrene latex and low-density lipoprotein over the temperature range 25-50°C, finding large deviations (-0.6%/K) of D from Walden's rule. These workers also obtained the drag coefficient f of low-density lipoprotein by ultracentrifugation, finding a similar anomaly in the temperature dependence off. The paper of Crossley et aL2 thus joins a series of papers3 suggesting that QELS may not always measure the conventional mutual diffusion coefficient. It is somewhat difficult to understand how such a large effect could have been overlooked in earlier work. The anomaly found by Crossley et al.2 is smallest near room temperature, measured and calculated values for D being in near agreement a t 25°C. Since there have been relatively few studies of the temperature dependence of QELS spectra of macromolecule s ~ l u t i o n s , ~ ~ ~ it is conceivable that the agreement between light-scattering spectroscopy and other methods is in part a coincidence that unfortunately occurs a t the standard measurement temperature. Alternately, polystyrene latex spheres might be subject to a hitherto unnoticed change in diameter with temperature. Since these spheres are a calibration standard in light-scattering spectroscopy, an unnoticed dependence of their radius on T could lead to systematic errors in other experiments. In order to test these hypotheses, we made extensive measurements on the diffusion of 0.038-pm carboxylate-modified polystyrene latex spheres (Dow Diagnostics) over the temperature range 0-50°C. The spheres were suspended in 14 M a deionized water a t a concentration of -5 X by volume. At this concentration, multiple scattering and sphere-sphere forces are negligible. Our instrumentation and data-analysis techniques are unchanged from our earlier ~ o r k . ~ , 5 The observed spectra, S(k , t ) , were fit to a cumulant expansion.6 The best fit was usually obtained with a secondor, rarely, a third-order fit. The variance V