Mössbauer Study of Brownian Motion in Liquids: Colloidal Cobaltous Hydroxy Stannate in Glycerol, Ethanol-Glycerol, and Aqueous-Glycerol Solutions

We have measured the resonant absorption of the 23.9-keV $\gamma$ rays of ${\mathrm{Sn}}^{199m}$ in a colloidal suspension of CoSn${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_6$ in glycerol in the temperature range 110-323 °K. We measured the colloidal-particle radii with a scanning electron microscope, and found them to be 650±150 Å. We have also studied the fixed-temperature Mössbauer line broadening of our glycerol-based colloid, as a function of ethanol and water dilution. We find that the diffusive broadening of the Mössbauer line is proportional to the absolute temperature divided by the viscosity. The constant of proportionality is the same within the experimental errors, whether the sample viscosity is changed by varying the sample temperature, or by diluting the sol with ethanol or water. These results are in good agreement with the Singwi-Sjölander theory and the Einstein-Stokes relation. For this system we observed a rapid falloff in the recoil-free fraction in the temperature region where diffusive broadening effects were observed, similar to other earlier observations of this effect. Attempts to prepare large-particle sols of FeSn${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_6$ in glycerol were made to try to see a breakdown in the Singwi-Sjölander theory. Some evidence for a failing in the theory was found for particle sizes of 1500 Å, but these results were not conclusive, as the sols were always unstable for these large colloidal particles.