A Different Interpretation of Einstein's Viscosity Equation Provides Accurate Representations of the Behavior of Hydrophilic Solutes to High Concentrations

摘要

Viscosities of aqueous solutions of many highly soluble hydrophilic solutes with hydroxyl and amino groups are examined with a focus on improving the concentration range over which Einstein's relationship between solution viscosity and solute volume, V, is applicable accurately. V is the hydrodynamic effective volume of the solute, including any water strongly bound to it and acting as a single entity with it. The widespread practice is to relate the relative viscosity of solute to solvent, η/η0, to V/V_(tot), where V_(tot) is the total volume of the solution. For solutions that are not infinitely dilute, it is shown that the volume ratio must be expressed as V/V0, where V0 = C_(tot) - V. V0 is the volume of water not bound to the solute, the "free" water solvent. At infinite dilution, V/V0 = V/V_(tot). For the solutions examined, the proportionality constant between the relative viscosity and volume ratio is shown to be 2.9, rather than the 2.5 commonly used. To understand the phenomena relating to viscosity, the hydrodynamic effective volume of water is important. It is estimated to be between 54 and 85 cm~3. With the above interpretations of Einstein's equation, which are consistent with his stated reasoning, the relation between the viscosity and volume ratio remains accurate to much higher concentrations than those attainable with any of the other relations examined that express the volume ratio as V/V_(tot).