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 H2Oaw b and D2Oaw b of H2O and D2O in the vapour state were calculated to be H2Oaw b = 1.4445 Å and D2Oaw b = 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 D2Oaw b and D2Oaw b 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 H2Oaw S 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 H2Oaw S 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
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