234 H. K. SCHACHMAN AND R. C. WILLIAMS 



where rj^plc is termed the reduced viscosity. At infinite dilution, the second 

 and higher terms in the power series become negligible and Equation (6) 

 results. 



]im{7jJcl_^, = A=[rj] (6) 



This serves as definition of the intrinsic viscosity, [t]]. 



Note that it has the units of reciprocal concentration. If, as is rarely the 

 case, the concentration, c, is in volume units, i.e. milliliters of solute per 

 milliliter of solution, then [rj] would be dimensionless. According to Einstein, 

 [77]= 2.5 for spherical particles if the concentration of the solute is expressed 

 as volume fraction. It should be recognized that Einstein's result is a limiting 

 form of Equation 4 and that the higher terms represent interparticle inter- 

 actions. If the concentration is in grams per milliliter, the intrinsic viscosity 

 will have the units of milliHters per gram. However, the literature often 

 contains intrinsic viscosities as deciliters per gram because the concentration 

 was expressed as gm./lOO ml. In order to evaluate the experimental data in 

 terms of the desired intrinsic viscosity, the quantity rj^^lc should be plotted 

 against c to give a curve whose intercept at c = is the intrinsic viscosity. 

 Unfortunately such plots usually show wide scattering of the points, especi- 

 ally at low concentrations, and it is often difficult to derive a reliable value 

 of the intercept by extrapolation. For such situations the data should be 

 plotted as t]^^ versus c. In this way curves are obtained wliich are almost 

 straight lines near the origin. The slope at c = then gives the intrinsic 

 viscosity directly. Although this method of treating the data works satis- 

 factorily, the former is preferred because it shows any trends in the data 

 such as those resulting from concentration dependent equilibria. Plots of 

 this type were used to demonstrate the dissociation of aggregates of 

 tobacco mosaic virus into the characteristic monomeric miits (Schachman, 

 1947). 



As already indicated, both the Einstein equation and the Simha extension 

 of it to ellipsoids of revolution require that the concentration be expressed 

 as volume fraction. If the jjarticles w^ere analogous to glass beads, the con- 

 version of weight to volume concentration would be straightforward since 

 the volume of a bead is its weight divided by its density. With molecules 

 which interact with water by virtue of strong attractive forces such a calcu- 

 lation is meaningless. This poses a problem that is not as yet satisfactorily 

 resolved. Some workers have proposed that the volume fraction of solute 

 be defined as Vc where V is the partial specific volume of the solute. Its 

 reciprocal is the analog of the density, but only in the absence of interactions 

 can these be equated. The term, Vc, refers, of course, to the dry volume of 

 the solute. Since many macromolecules are presumed to be swollen in 

 solution, imbibing appreciable amounts of solvent, some correction for this 



