Page 123 - Carrahers_Polymer_Chemistry,_Eighth_Edition

86 Carraher’s Polymer Chemistry

Shear stress is measured in terms of the required torque needed to achieve a fi xed-rotation rate
for a specific radius differential between the radius of the bob and cup. The Brookfi eld viscom-

eter is a bob and cup viscometer. The Mooney viscometer, often used in the rubber industry,
measures the torque needed to revolve a rotor at a specified rate. In the cone and plate assem-

blies, the melt is sheared between a flat plat and a broad cone whose apex contacts the plate

containing the melt.
A number of capillary viscometers or rheometers have been employed to measure melt viscosity.
In some sense these operate on a principle similar to the simple observation of a trapped bubble
moving from the bottom of a shampoo bottle when it is turned upside down. The more viscous the
shampoo, the longer it takes for the bubble to move through the shampoo.

3.10 SUMMARY

1. Some naturally occurring polymers such as certain proteins and nucleic acids consist of mol-
ecules with a specific molecular weight and are called monodisperse. However, many other

natural polymers, such as cellulose and natural rubber, and most synthetic polymers consist of
molecules with different molecular weights and are called polydisperse. Many properties of
polymers are dependent on their chain length. Since the melt viscosity increases exponentially
with chain length, the high-energy costs of processing high molecular weight polymers are not
often justifi ed.
2. The distribution of chain lengths in a polydisperse system may be represented on a typical proba-
bility-like curve. The M is the smallest in magnitude of the typically obtained molecular weights
n
and is a simple arithmetic mean that can be determined using any technique base on colligative
properties, such as osmotic pressure, boiling point elevation, freezing point depression, and end-
group determination. M is larger than M and is referred to as the second power relationship
w n
for disperse polymer chains. This value is most often determined by light-scattering photometry.
Light-scattering photometry and the colligative-related values are referred to as absolute molec-
ular weight values because there is a direct mathematical connection between molecular weight
and the particular property used to determine molecular weight.
3. For monodisperse samples, M = M . For polydisperse samples the ratio of M /M is a measure
n w w n
of the polydisparity and is given the name polydispersity index. The viscosity molecular weight
must be calibrated using samples whose molecular weight has been determined using an absolute
molecular weight determination technique, thus it is not an absolute molecular weight determin-
ing technique, but it requires simple equipment, and is easy to measure. The Mark–Houwink
a
relationship, LVN = KM is used to relate molecular weight and viscosity.
4. The number-average molecular weight is dependent on the number of polymer chains, while
the weight-average molecular weight is dependent on the size of the chains. Thus, there is a
correlation between the way the molecular weight is obtained and the type of molecular weight
obtained.
5. MWD is most often measured using some form of chromatography. In GPC, cross-linked poly-
mers are used in a column and act as a sieve allowing the larger molecules to elute fi rst. After
calibration, the molecular weight of the various fractions of the polymer can be determined.
Combinations such as chromatography coupled with light-scattering photometry are used to
obtain the molecular weight of the various fractions in a continuous manner.
6. While some techniques such as membrane osmometry and light-scattering photometry give
absolute molecular weight, other techniques such as viscometry give only relative molecular
weights unless calibrated employing a technique that gives absolute molecular weight. After cal-
ibration between viscometry values and chain length through some absolute molecular weight
method, viscometry is a fast, inexpensive, and simple method to monitor molecular weight.
7. In general, polymers are soluble in less solvents and to a lower concentration than similar smaller
molecules. This is because entropy is the driving force for solubility and smaller molecules have

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