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Molar Mass
determination (Theoretical background )
Liquid Chromatography: Gel Filtration, Gel Permeation, Size Exclusion
Chromatography
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Click
picture for close up view
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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.
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.
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.
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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?
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
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There
are several static light scattering
techniques, that are used on-line coupled to GPC/SEC or as stand-alone
(off-line, batch) techniques:
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Technique
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Comments
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LALLS (LALS)
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Low angle
(laser) light scattering
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Molar mass
information based on a single angle
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RALLS (RALS)
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Right angle
(laser) light scattering
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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)
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MALLS (MALS)
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Multi angle
(laser) light scattering
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Molar
mass information, radius of gyration, branching information based on
the simultaneous measurement of multiple angles at the same time
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A comparative
overview can help to select the best method for the application.
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