Page 108 - Carrahers_Polymer_Chemistry,_Eighth_Edition
P. 108
Molecular Weight of Polymers 71
3.6.2 END-GROUP ANALYSIS
In cases where the end groups are known and their concentration can be determined, knowledge
of their abundance allows a determination of M . The sensitivity of this method decreases and the
n
chain length becomes greater. Some end groups can be determined using spectroscopic techniques
and other through titration.
3.6.3 EUBLLIOMETRY AND CRYOMETRY
Raoult’s law works for small polymers as well as small molecules. Determination of M is based
n
for both eublliometry (boiling point elevation) and cryometry (freezing point lowering) on the
Clausius–Clapeyron equation:
RT V C
2
M n = ∆ ∆ T (3.12)
H C→ 0
By use of sensitive thermocouples and care, molecular weights to about 50,000 Da can be
determined.
3.7 LIGHT-SCATTERING PHOTOMETRY
Ever watch a dog or young child chase moonbeams? The illumination of dust particles is an illustration
of light scattering, not of refl ection. Reflection is the deviation of incident light through one particular
angle such that the angle of incidence is equal to the angle of reflection. Scattering is the radiation of
light in all directions. Thus, in observing the moonbeam, the dust particle directs a beam toward you
regardless of your angle in relation to the scattering particle. The energy scattered per second (scat-
tered flux) is related to the size and shape of the scattering particle and to the scattering angle.
Scattering of light is all about us—the fact that the sky above us appears blue, the clouds white,
and the sunset in shades of reds and oranges is a consequence of preferential scattering of light from
air molecules, water droplets, and dust particles. This scattered light caries messages about the scat-
tering objects.
The measurement of light scattering is the most widely used approach for the determination of
M . This technique is based on the optical heterogeneity of polymer solutions and was developed
w
by Nobel Laureate Peter Debye in 1944.
Today, modern instruments utilize lasers as the radiation source because they provide a mono-
chromatic, intense, and well-defined light source. Depending upon the size of the scattering object,
the intensity of light can be essentially the same or vary greatly with respect to the direction of the
oncoming radiation. For small particles the light is scattered equally independent of the angle the
observer is to the incoming light. For larger particles the intensity of scattered light varies with
respect to the angle of the observer to the incoming light. For small molecules at low concentrations
this scattering is described in terms of the Raleigh ratio.
In 1871, Rayleigh showed that induced oscillatory dipoles were developed when light passed through
gases and that the amount (intensity) of scattered light (τ) was inversely proportional to the fourth power
of the wavelength of light. This investigation was extended to liquids by Einstein and Smoluchowski in
1908. These oscillations reradiate the light energy producing turbidity, that is, the Tyndall effect. Other
sources of energy, such as X-rays or laser beams, may be used in place of visible light sources.
For light-scattering measurements, the total amount of the scattered light is deduced from the
decrease in intensity of the incident beam, I , as it passes through a polymer sample. This can be
o
described in terms of Beer’s law for the absorption of light as follows:
I − tl
= e (3.13)
I
0
9/14/2010 3:36:42 PM
K10478.indb 71 9/14/2010 3:36:42 PM
K10478.indb 71
