Molar Mass Determination -- PSS-USA

Molar Mass determination (Theoretical background )

Liquid Chromatography: Gel Filtration, Gel Permeation, Size Exclusion Chromatography

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Molar mass averages and molar mass distribution

Synthetic materials, polysaccharides, and also some proteins do not exhibit a single definite molar mass, unlike low-molecular-weight substances. They consist of mixtures of chains with different numbers of repeating units, with each chain having its own molar mass.

Molar mass distribution for a narrow and broad Poly(styrene), molar mass averages are also given.

The molar mass of a macromolecule is obtained by averaging the molar mass of the different chains by number (Mn) or by weight (Mw). However, even if values for Mn, Mw and Mw/Mn — the polydispersity index (PDI) — are available, macromolecules are still not characterized comprehensively.
MW, Mn and PDI Formulae

Macromolecules can have the same averages but still show significantly different physical properties. This is because they have a different molar mass distribution (MMD) which means the fractions of the defined molar masses are different.

The molar mass averages and the MMD influence the macroscopic properties of the materials. Therefore reliable, precise, and fast determination of the averages and the MMD is required for QC/QA and R&D alike.

What is the difference between a GPC/SEC chromatogram and a molar mass distribution?

GPC/SEC chromatograms show the fractions and the concentration change with molecular size in solution for the sample, but this information is superimposed by the parameters of the analytical equipment. For example, if the same sample is measured in two separate laboratories on two different instruments using different-sized columns, the resulting chromatograms will obviously be different. Without previous knowledge nobody will assume that the chromatograms represent the same sample. If the instrument is properly calibrated, using any kind of calibration (for example, conventional, universal, light scattering), and the samples are correctly evaluated, the influence of the equipment is eliminated. MMDs are obtained that are independent from the instrument and allow inter-laboratory comparison.

Overlay of the true MMD (green) and the molar mass scaled elugram (red). Green obtained with WinGPC Unity software, red obtained with a HPLC software with GPC-option. For red, the y-axis is not correctly transformed

Unfortunately, many high performance liquid chromatography (HPLC) data systems that also perform GPC/SEC calculate “molar mass diagrams”, that do not eliminate the influence of the instrument. The difference between a molar mass diagram and a molar mass distribution is mainly the y-axis. MMDs have a y-axis w(log M), where the mass fractions w in constant molar mass increments (log (M)) are shown. “Molar mass diagrams” have the same y-axis as the chromatogram, normally the detector signal intensity. This can make an inter-laboratory comparison extremely difficult. The determination of fractions above or below certain molar masses, for example below 500 g/mol, can also be faulty. The figure clearly shows that both, peak position, which relates to the molar mass, and peak width, which relates to the PDI, can be wrong.

Why is conventional GPC/SEC a relative method?

Overlay PSS ReadyCal samples green, red, and white (each with 4 different molecular weight samples from 2 540 000 down to 376 Da) and the resulting PS calibration curve (fit: polynomial 3rd order)

Since GPC/SEC separates according to the hydrodynamic volume and not to molar mass, the resulting calibration curve is only valid for chemically matching unknown samples. For example a Poly(styrene) calibration curve constructed from Poly(styrene) molar mass standards is only valid for Poly(styrene) samples and unknowns. For Poly(methyl methacrylate) unknowns conventional GPC/SEC with a Poly(styrene) calibration curve yields apparent molecular weights. These molar masses can be compared to each other providing valuable information, but a precise and absolute molar mass determination is not possible.

Several approaches have been developed to overcome this limitation and to allow accurate molar mass determination for all samples:

calibrate with matching molar mass standards.
use GPC/SEC-viscometry and evaluate data using a universal calibration curve (see: H. Benoît, Z. Grubisic, P. Rempp, D. Decker, J.G. Zilliox, J. Chem. Phys. 63, 1507 (1966)). A universal calibration curve is valid for all types of unknowns.
use GPC/SEC-light scattering to measure the molar mass of homopolymers on-line

What does GPC/SEC-light scattering offer?

GPC/SEC-light scattering is an absolute method. The light scattering detector allows the direct measurement of the molar mass, when the refractive index increment (dn/dc) is known. For highest precision of light scattering experiments PSS recommends to measure the dn/dc off-line using dn/dc instruments

GPC/SEC-light scattering signals for a SLD7000 MALLS detector (only three signals shown) and an RI detector. The signal shift between RI and MALLS and between the three different MALLS signals is real (inter-detector delay is corrected) and due to the fact that different detectors see different information.

There are several static light scattering techniques, that are used on-line coupled to GPC/SEC or as stand-alone (off-line, batch) techniques:

Technique		Comments
LALLS (LALS)	Low angle (laser) light scattering	Molar mass information based on a single angle
RALLS (RALS)	Right angle (laser) light scattering	Molar mass information for isotropic scatterers (Macromolecules up to molar masses about 150 000 Da (high molar mass part) or many proteins; use viscometer to overcome this limitation (Triple detection)
MALLS (MALS)	Multi angle (laser) light scattering	Molar mass information, radius of gyration, branching information based on the simultaneous measurement of multiple angles at the same time

A comparative overview can help to select the best method for the application.