# International Polymer Analysis in New Orleans

27 June 2013 No Comment

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In case you missed it, Malvern exhibited and presented at the International Symposium on Polymer Analysis and Characterization ISPAC in New Orleans earlier this month. The symposium started on the 9th of June and ended on the 12th of June. Malvern’s Mark Pothecary presented on Monday with a talk titled “Advances in Polymer Characterization Using Multi-Detector GPC and Light Scattering” and he was also the first author on a poster titled “Using DLS Microrheology to Fully Characterize the Dynamic Spectrum and Viscoelastic Properties of Macromolecules in Solution” together with co-authors John Duffy, Steve Carrington, Paul Clarke. Additionally, Dr. Wei-Sen Wong gave a presentation on “Application Of Malvern Polyolefin Characterization Technologies For The Process Control Of UHMW Polyethylene Resins And Fibers”. All in all Malvern was strongly represented at this meeting.
Mark’s slides on polymer characterization advances contained some interesting points on what multi-detector chromatography [which was defined as concentration + light scattering + viscometry] can do.

A unique aspect of the combination of light scattering and differential viscometry is that it can provide access to 4 molecular size parameters which were listed as:

• Rg from light scattering
• Rg(FF) from light scattering/viscometer
• Rh from light scattering/viscometer
• Rh from DLS

To clarify these different parameters, here are a few brief details with mathematics:

1. The radius of gyration Rg, or root mean square radius (or sometimes called simply the RMS radius), can be obtained directly from the angular dependence of the scattering intensity. In a typical implementation, the Rayleigh ratio Kc/RΘ is plotted versus sin(Θ/2)^2 and (in a most common Zimm approximation, extrapolated to zero concentration) linearly fit to

$\frac{K c}{R_\Theta}=\frac{1}{M_W} (1+\frac{q^2 R_G^2}{3 }) \;\; \textrm{ with } \; q=\frac{4 \pi n}{\lambda} sin(\Theta /2)$

where λ is the laser wavelength, Θ the scattering angle, n the refractive index and Mw the weight average molecular mass of the sample and the square root of the slope leads to Rg.

2. Rg(FF) stands for the radius of gyration obtained from a Flory-Fox approximation. In the Flory-Fox equation the intrinsic viscosity [η] and molecular weight Mw are related to the root mean square radius via

$M_W [\eta] = \Phi R_G^3$

where Φ is called the Flory constant which is known for hard spheres and lower for polymer coils, i.e. it is shape dependent.

3. In Universal Calibration one can take advantage of the fact that the product of molecular weight and instrinsic viscosity are directly proportional to the hydrodynamic volume of the molecule, and thus the hydrodynamic size as well:

$M_W [\eta] \propto V_h \propto R_h^3$

This relation has the major advantage that no shape assumptions are made, it simply holds true regardless of the type of molecule under investigation.

4. An additional measurement method to obtain the hydrodynamic size is dynamic light scattering, where the diffusion coefficient is measured by analysing the scattered light intensity fluctations due to Brownian motion. The measured translational diffusion coefficient is then transformed into a size which corresponds to the equivalent size of a sphere with the same diffusion behavior as observed experimentally.

$D_T = \frac{k_B T}{6 \pi \eta R_h}$

where the kB is the Boltzmann constant, T the absolute temperature in Kelvin, and η the solvent viscosity.