This model assumes the solvent is weakly perturbed by the string of beads. Each bead independently exerts a frictional force on the solvent. The result is
[eta] proportional to M1 + Delta
which is not compatible with the typical experimental results for polymer coils, which find the exponent for M is smaller than 1.
This model assumes solvent is trapped within the interior of the polymer coil, and the trapped solvent moves with the polymer. Although the instantaneous conformation of a polymer chain does not have spherical symmetry, for the sake of simplicity we will assume that the "particle" (polymer + trapped solvent) moving through the solution can be approximated by a sphere. This assumption lets us start with Einstein's expression for the viscosity of a suspension of spheres with volume fraction Phi.
etarel = 1 + 2.5 Phi
Converting to concentration expressed as mass/volume, and introducing the hydrodynamic volume, Vh, associated with one polymer molecule, the limiting form as c goes to zero is
[eta] = 2.5 VhL/M
where L denotes Avogadro's number. We now postulate a proportionality between Vh and the volume defined by the mean square radius of gyration, <s2>,
V' = (4 pi/3) <s2>3/2
Since <s2> is proportional to alpha2M, where alpha is the expansion factor,
[eta] = K'M1/2alpha3
which leads to the Mark-Houwink-Sakurada equation,
[eta] = KMa
The two constants in this equation can be obtained by measurements using standards of known molecular weight, preferably of very low polydispersity, PC Fig. 10.16. After the constants have been determined, the molecular weight of an unknown sample of the same polymer can be determined by measuring [eta], at the same temperature and in the same solvent.
The value of a is
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