Download (direct link):
in which n0 is the refractive index of the solvent, dn/dc is the specific refractive index _ of the polymer, and NA is Avogadro’s number.
Re, the excess Rayleigh ratio, is the scattered light intensity of the polymer (the scattered intensity of the solution minus the solvent), normalized relative to the incident beam intensity and the scattered volume geometry.
Ð(â) is the particle-scattering function at the angle of measurement that takes into account angular dissymmetry of scattered light. If the hydrodynamic diameter of the polymer is <0.05Ë, P(0) is unity; at values > 0.05A, P(0) is less than unity, and must be evaluated. A2 is the second virial coefficient of the polymer solution that is related to polymer-solvent interaction. In a typical SEC light-scattering experiment, the A2c term is close to zero and usually can be ignored.
There are now several different SEC light-scattering detectors available that differ in terms of cell design and measurement angles (see Appendix C). In general, however, if measurements are made at relatively low angles relative to the forward direction (i.e., less than about 15°), P(6) is close to unity and Eq. (26) becomes
Size Exclusion Chromatography
and M can be calculated readily at each elution volume increment.
If scattered intensities are made at angles greater than 15°, at least several higher angles must be used. In this case, Kc/Re is plotted against sin2(fl/2) and measurements extrapolated to zero angle; the correct molecular weight is obtained from the intercept. The molecular size (radius of gyration) of a polymer across the molecular weight distribution can also be obtained from the slope of this plot. The lower radius of gyration limit, however, is approximately 10 nm, which corresponds to approximately 1 X 105 g mol-1 relative to polystyrene in a good solvent. Multiangle light-scattering instruments use a diode-array detector configuration in which scattered intensities are measured simultaneously from various angles, depending on the number of diodes surrounding the cell [59,60]. (See Ref.  for a listing of other uses and applications of SEC light scattering.)
3. Light Scattering-Viscometry
For molecular-weight-sensitive detectors, the most useful system is the combination of both light-scattering and viscometry. in conjunction with a concentration-sensitive detector, some-times referred to as a “triple detection system” [61-64]. In this manner, the molecular weight and intrinsic viscosity distributions of a polymer are determined simultaneously without the need of universal calibration. With this approach, Mark-Houwink coefficients, branching in-dices, and molecular size parameters can be calculated.
With existing HPLC instrumentation and appropriate data acquisition and processing software, an SEC system can be set up easily. For organosoluble polymers, any appropriate good solvent may be used for the mobile phase, and cross-linked polystyrene is usually suitable for the packing. For synthetic water soluble polymers, however, mobile-phase optimization and SEC column evaluation may be required.
As an entropically controlled separation process, SEC has a peak capacity that is ap-proximately an order of magnitude lower than that of gradient elution HPLC . However, SEC is a useful method for screening complex, multicomponent oligomeric and polymeric materials. Because the elution order of components is directly related to molecular size, peak identification is facilitated.
Provided that the SEC system is properly calibrated, all the statistical average molecular weights of a polymer can be determined readily. In most laboratories, SEC has supplanted traditional methods of molecular weight measurements, such as osmometry and light scattering. Furthermore, if molecular-weight-sensitive detectors (light-scattering or viscometry) are employed, molecular parameters of a polymer, including branching an chain conformation, can be determined . Lastly, by including an on-line composition-sensitive detector, for example an FT-IR, mass spectrometer, or NMR, compositional heterogeneity of polymeric materials can be obtained.
SUPPLIERS* Appendix A: Polymer Standards
American Polymer Standards, P.O. Box 901, Mentor, OH 44061 National Institute of Standards and Technology, Gaithersburg, MD 20899
*Please note that these appendices list major suppliers and that this is by no means a comprehensive listing.
Polymer Laboratories Inc., 160 Old Farm Rd., Amherst, MA 01002
Polymer Standards Service, 13531 Cedar Creek Ln., Silver Spring, MD 20904
Polysciences, Inc., 400 Valley Rd., Warrington, PA 18976
Pressure Chemical Co., 3419-25 Smallman St., Pittsburgh, PA 15201
TosoHaas, 156 Keystone Dr., Montngomeryville, PA 18936
Waters Corporation, 34 Maple St., Milford, MA 01757
Appendix B: SEC Columns
Beckman Instruments, 2500 Harbor Blvd., Fullerton, CA 92634 Asahi Chemical, Kawasaki, Japan