Page 114 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Molecular Weight of Polymers 77

Intensity

2
3
4
5
6
7
Detector # (scattering angle)
8
9
10
11
12
13
14
15
16
17
18
Elution volume (mL)
FIGURE 3.20 Three-dimensional plot of scattering intensity as a function of scattering angle and elu-
tion volume for a broad MWD polystyrene (NITS standard reference 706). (Used with permission of Wyatt
Technology Corporation, Santa Barbara, CA 93117; wyatt@wyatt.com)
including small conformational changes. The assembly also allows good molecular determination
to occur even when there are small dn/dc values, low molecular weight fractions, absorbing and

fluorescent polymers, copolymers with varying dn/dc values, and chiral polymers that depolarize
the incident beam.
Figure 3.21 contains data on myoglobin obtained using a triple detection setup. A molecular
weight of 21,100 is found with a viscosity of 0.0247 dl/g and from this a hydrodynamic radius of
2.06 nm that is essentially the same as the Stokes value of 2.0 nm reported for myoglobin.
3.8 OTHER TECHNIQUES
3.8.1 ULTRACENTRIFUGATION

Since the kinetic energy of solvent molecules is greater than the sedimentation force of gravity,
polymer molecules remain suspended in solution. However, this gravitational field, which permits

Brownian motion, may be overcome by increasing this force by use of high centrifugal forces, such
as the ultracentrifugal forces developed by Nobel Laureate The Svedberg in 1925.
Both M and M may be determined by subjecting dilute polymer solutions to high centrifugal
w
z
forces. Solvents with densities and indices of refraction different from the polymers are chosen to
ensure polymer motion and optical detection of this motion. In sedimentation velocity experiments,
the ultracentrifuge is operated at extremely high rotational speeds up to more than 70,000 rpm to
transport the denser polymer molecules through the less-dense solvent to the cell bottom or to the
top if the density of the solvent is greater than the density of the polymer. The boundary movement
during ultracentrifugation can be followed using optical measurement to monitor the sharp change
in refractive index (n) between the solvent and the solution.
The rate of sedimentation is defined by the sedimentation constant s, which is directly propor-

tional to the polymer mass m, solution density ρ, and specific volume of the polymer V, and inversely

proportional to the square of the angular velocity of rotation ω, the distance from the center of rota-
tion to the point of observation in the cell r, and the fractional coeffi cient f, which is inversely related

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