Page 117 - Carrahers_Polymer_Chemistry,_Eighth_Edition

80 Carraher’s Polymer Chemistry

“relative” molecular weight. The molecular weight is referred to as “relative” since viscosity mea-
surements have not been directly related, through rigorous mathematical relationships, to a specifi c
molecular weight. By comparison, measurements made using light-scattering photometry and the
other methods covered before are relatable to specific molecular weight values and these techniques

are said to give us “absolute” molecular weights.
The relationship between the force “f” necessary to move a plane of area “A” relative to another
plane a distance “d” from the initial plane (Figure 3.22) is described in Equation 3.24.

A
f
(3.24)
d
To make this a direct relationship a proportionality factor is introduced. This factor is called the
coeffi cient of shear viscosity or simply viscosity.
 A 
f = η  
 d  (3.25)

Viscosity is then a measure of the resistance of a material to flow. In fact, the inverse of viscos-
ity is given the name fl uidicity. As a material’s resistance to fl ow increases, its viscosity increases.
Viscosities have been reported using a number of different names. The CGS unit of viscosity is
called the poise, which is a dyne seconds per square centimeter. Another widely used unit is the
pascal (or Pa.), which is Newton seconds per square centimeter. In fact, 1 Pa = 10 poise.
Table 3.5 contains the general magnitude of viscosity for some common materials. It is impor-
tant to note the wide variety of viscosities of materials from gases such as air to viscoelastic solids
as glass.
In polymer science we typically do not measure viscosity directly, but rather we look at relative
viscosity measures by determining the flow rate of one material relative to that of a second material.

Viscosity is one of the most widely used methods for the characterization of polymer molecular
weight because it provides the easiest and most rapid means of obtaining molecular weight-related
data that requires minimal instrumentation. A most obvious characteristic of polymer solutions is
their high viscosity, even when the amount of added polymer is small. This is because polymers
reside in several flow planes (Figure 3.22b) acting to resist the flow of one plane relative to another

fl ow plane.
The ratio of the viscosity of a polymer solution to that of the solvent is called the relative
viscosity (η ). This value minus 1 is called the specifi c viscosity (η ), and the reduced viscosity
r sp
(η ) or viscosity number is obtained by dividing η by the polymer concentration c; that is,
red sp
η /c. The intrinsic viscosity or LVN is obtained by extrapolating η /c to zero polymer concen-
sp sp
tration. These relationships are given in Table 3.6 and a typical plot of η /c and In η /c is given
sp r
in Figure 3.23.
Staudinger showed that the intrinsic viscosity of a solution ([η]) or LVN is related to the molec-
ular weight of the polymer. The present form of this relationship was developed by Mark–Houwink

Area = A f
d

(a) (b)

FIGURE 3.22 (a) Representation of Equation 3.24 (b) Illustration of a polymer chain between two fl ow planes.

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