Influence of the Processes Parameters on the Properties of The ...

Chapter 3.
Analytical Methods and Designs <strong>of</strong> Experiments
To describe <strong>the</strong> glass transition, <strong>the</strong> temperature <strong>of</strong> half-vitrification, T g , should be specified, i.e.,
<strong>the</strong> temperature at which <strong>the</strong> heat capacity is midway between that <strong>of</strong> <strong>the</strong> liquid and glassy states (cf. Figure
3.3). This temperature usually corresponds closely to <strong>the</strong> point <strong>of</strong> inflection in <strong>the</strong> heat capacity, and also to
<strong>the</strong> breaks in <strong>the</strong> enthalpy or volume versus temperature curves at <strong>the</strong> glass transition. The onset
temperature, T onset , is <strong>of</strong>ten given.
2 Intrinsic Viscosity
2.1 Molecular Mass <strong>of</strong> Polymer and Viscosity
The M n number average molecular mass is <strong>the</strong> simple arithmetical average <strong>of</strong> each molecule as a
summation, divided by <strong>the</strong> number <strong>of</strong> molecules. Ano<strong>the</strong>r measurement <strong>of</strong> average is <strong>the</strong> M w ‘weight’
average, and is an expression <strong>of</strong> <strong>the</strong> fact that <strong>the</strong> higher molecular mass fractions <strong>of</strong> a polymer play a greater
role in determining <strong>the</strong> properties than do <strong>the</strong> fractions <strong>of</strong> lower molecular mass.
Ma<strong>the</strong>matically, this is given by:
Mw
w M
1 1
(3.2)
w1
where, w 1 represents <strong>the</strong> overall weight <strong>of</strong> molecules <strong>of</strong> molecular mass M 1 . The M w weight
average molecular mass is invariably greater than <strong>the</strong> M n number average as its real effect is to square <strong>the</strong>
weight.
Several methods <strong>of</strong> measuring molecular weight are used and are summarized here:
Osmometry. This is a vapour pressure method, useful for polymers <strong>of</strong> molecular mass up to about
25 000; membrane osmometry is used for molecular mass from 20 000 to 1 000 000. These are
number average methods.
Light scattering. This is a weight average method.
Gel permeation chromatography. This is a direct fractionation method using molecular mass. It is
relatively rapid and has proved to be one <strong>of</strong> <strong>the</strong> most valuable modern methods.
Viscometry. This is a relative method, but <strong>the</strong> simplest, and its application is widespread in industry.
Viscometry is <strong>the</strong> technique to measure <strong>the</strong> viscosity <strong>of</strong> materials noting <strong>the</strong> flow rate/efflux time by
using different kinds <strong>of</strong> viscosimeters [Warson and Finch, 2001].
The absolute value <strong>of</strong> M w (molecular mass average) can only be determined by complex analytical
methods such as light scattering. For linear and un-branched polymers, <strong>the</strong> viscosity average <strong>of</strong> molecular
weight (M vis ) is approximately equal to <strong>the</strong> demi-sum <strong>of</strong> <strong>the</strong> M w molecular mass average and <strong>the</strong> M n number
average molecular mass.
2.2 General Principle <strong>of</strong> Viscosity Measurement
Intrinsic viscosity, which is measured from <strong>the</strong> flow time <strong>of</strong> a solution through a simple glass
capillary, has considerable historical importance for establishing <strong>the</strong> very existence <strong>of</strong> polymer molecules.
The most useful kind <strong>of</strong> viscometer for determining intrinsic viscosity is <strong>the</strong> “suspended level” or Ubbelohde
viscometer, sketched Figure 3.4.
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