Page 119 - Carrahers_Polymer_Chemistry,_Eighth_Edition

82 Carraher’s Polymer Chemistry

2.0 for rigid polymer chains extended to their full contour length and 0 for spheres. When “a” is 1.0,
the Mark–Houwink equation (3.26) becomes the Staudinger viscosity equation.

a
LVN = KM (3.26)
Values of “a” and “K” have been determined and complied in several polymer handbooks and are
dispersed throughout the literature. Typical values are given in Table 3.7. With known “a” and
“K” values, molecular weight can be calculated using Equation 3.26. As noted before, viscosity
is unable to give absolute molecular weight values and must be calibrated, that is, values of “a”
and “K” determined using polymer samples where their molecular weights have been determined
using some absolute molecular weight method such as light-scattering photometry. It is custom-
ary in determining the “a” and “K” values to make a plot of log LVN versus log M since the log
of Equation 3.26, that is, Equation 3.27, is a straight line relationship where the slope is “a” and
intercept “K.” In reality, “a” is determined from the slope but “K” is determined by simply select-
ing a known LVN–M couple and using the determined “a” value to calculate the “K” value.

log LVN = a log M + log K (3.27)
The intrinsic viscosity or LVN, like melt viscosity, is temperature-dependent and decreases as
temperature increases as shown in Equation 3.28.

LVN = Ae E/RT (3.28)

However, if the original temperature is below the theta temperature, the viscosity will increase when
the mixture of polymer and solvent is heated to a temperature slightly above the theta temperature.
Viscosity measurements of dilute polymer solutions are carried out using a viscometer, such as
any of those pictured in Figure 3.24. The viscometer is placed in a constant temperature bath and

the time taken to flow through a space measured.
Flory, Debye, and Kirkwood showed that [η] is directly proportional to the effective hydrodynamic
volume of the polymer in solution and inversely proportional to the molecular weight, M. The effective
2 3/2
hydrodynamic volume is the cube of the root-mean-square end-to-end distance, (r ) . This propor-
tionality constant, N, in the Flory equation for hydrodynamic volume, Equation 3.29, has been consid-
ered to be a universal constant independent of solvent, polymer, temperature, and molecular weight.

TABLE 3.7
Typical “K” Values for the Mark–Houwink Equation
5
Polymer Solvent Temperature (K) K × 10 dL/g
Low-density polyethylene Decalin 343 39
High-density polyethylene Decalin 408 68
i-Polypropylene Decalin 408 11
Polystyrene Decalin 373 16
Poly(vinyl chloride) Chlorobenzene 303 71
Poly(vinyl acetate) Acetone 298 11
Poly(methyl acrylate) Acetone 298 6
Polyacrylonitrile Dimethylformamide 298 17
Poly(methyl methacrylate) Acetone 298 10
Poly(ethylene terephthalate) m-Cresol 298 1
Nylon-66 90% aqueous formic acid 298 110

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