Page 112 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Molecular Weight of Polymers 75

Rod (slope = 1)

log r g Coil (slope about 0.5−0.6)

Sphere (slope=1/3)

log M

FIGURE 3.18 Standard plot of the log of the mean radium of gyration versus log smolecular weight for
different-shaped macromolecules. Essentially, for a sphere the radius is proportion to the root-mean-square
1/3
radius, rms radius, and M with a slope in the log r g versus log M of 1/3; for rod-shaped polymers, length is
proportional to rms radius and M with a slope of 1; and for random coils the end-to-end distance is propor-
1/2
tional to the rms radius and M with a slope of about 0.5–0.6.
∑ rm
2
r = i i (3.19)
2
g
∑ m i
One of the most important advances in polymer molecular weight determination is the “cou-

pling” of SEC and light-scattering photometry, specifically LALLS or MALS. As noted in
Section 3.5, SEC allows the determination of the MWD. In its usual operational confi guration,
it does not itself allow the calculation of an absolute molecular weight but relies on calibration
with polymers of known molecular weight. By coupling HPLC and light-scattering photometry,
the molecular weight of each fraction can be determined giving an MWD and various molecular
weight values (M , M , M ).
w
n
z
The LALLS or MALS detector measures τ-related values, a differential refractive index (DRI)
detector is used to measure concentration, and the SEC supplies samples containing “fractionated”
polymer solutions allowing both molecular weight and MWD to be determined. Further, polymer
shape can be determined. This combination represents the most powerful, based on ease of oper-
ation, variety of samples readily used, cost, means to determine polymer size, shape, and MWD
available today.
A general assembly for a SEC-MALS instrument is given in Figure 3.19. A typical three-dimen-
sional plot obtained from such an assembly is shown as Figure 3.20.
Dynamic light scattering is similar in principle to typical light scattering. When several particles
are hit by oncoming laser light, a spotted pattern appears, the spots originating from the interfer-
ence between the scattered light from each particle giving a collection of dark (from destructive
interference) and light (from constructive interference) spots. This pattern of spots varies with time
because of the Brownian motion of the individual scattering particles. The rate of change in the
pattern of spots is dependant on a number of features, including particle size. In general, the larger
the particle the slower the Brownian motion and, consequently, the slower the change in the pattern.

Measurement of these intensity fluctuations with time allows the calculation of the translational dif-
fusion constant of the scattering particles. The technique for making these measurements is given
several names, including DLS emphasizing the fact that it is the difference in the scattered light with

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