ISSN: 2574-187X
Authors: Osuga T*
The sphere radii H2Oaw and D2Oaw of H2O and D2O performing rotational Brownian motion (RBM) in the liquid state were calculated to be H2Oaw =1.44±0.01 Å at 0℃ and D2Oaw =1.45±0.01 Å at 10℃, respectively, by substituting the previously measured dielectric relaxation time τrel into the dielectric relaxation formula (DRF), where 0℃ and 10℃ are close to the maximum density temperatures of 3.98℃ for H2O and 11.6 ℃ for D2O, respectively. The sphere radii H2Oawb and D2Oawb of H2O and D2O in the vapour state were calculated to be H2Oawb = 1.4445 Å and D2Oawb = 1.4532 Å of H2O and D2O, respectively, using the van der Waals b constant. The sphere radius performing RBM in the liquid state was found to be similar to that of a single molecule in the vapor state because H2Oaw and D2Oaw determined by τrel are close to H2Oawb and D2Oawb of H2O and D2O, respectively, which is supported by the specific heat showing a sufficient rotational freedom in the liquid state. The liquid density decreasing with temperature from 0 to 50℃ can be used to determine the thermal expansion rate vol= 7.9×10-5/℃ of the water sphere radius. The radius H2OawS of H2O (Stokes radius) performing the translational Brownian motion is calculated by substituting the diffusion coefficient into the Stokes-Einstein equation (SEE). The radius expansion rates of rot of H2Oaw and trans of H2OawS were calculated to be 3.0×10-4/℃ and 2.0×10-3/℃ using the DRF and SEE, respectively. The DRF was found to yield better expansion rate than the SEE does in the water sphere radius evaluation because rot / vol is 4 while trans / vol is 23.
Keywords: Stokes Radius; Einstein–Smoluchowski Relation; Stokes-Einstein-Sutherland Equation; Langevin Equation; Van Der Waals Equation; Oseen Equation
