In the early history of polymer sciences, the measurement of molecular weights
was the key experimental evidence proving the presence of macromolecules. In the
following decades, many methods have been invented to measure the molecular
weights of polymers. The stoichiometric methods include the end-group titration.
The thermodynamic methods make use of the colligative properties of polymer
dilute solutions, such as the rise of solvent boiling points, the depression of polymer
melting points, the vapor-phase osmometry, the isothermal distillation, and the
osmotic pressure. The scattering methods include the small-angle scattering of
visible light (or enhanced with laser beams), X-ray and neutron beams. The
microscopy methods include the electron microscopy. The fluid mechanics
methods include the viscosity of dilute solutions, the melt index (MI, or melt flow
rate MFR, are often used in industry for a fast identification of molecular weights of
polymer products, and are defined as the grams of melt mass flowing through a hole
within 10 min under a specific pressure and a specific temperature. In recent years,
the melt volume flow rate MVR is also used with the unit of cm^3 /10 min), the
sedimentation equilibrium, the sedimentation diffusion, and the GPC method.
Some methods measure the molecular-weight distributions as well.
In the modern chemistry laboratories, the technology ofgel permeation chroma-
tography(GPC) has been well commercialized for the characterization of polymer
molecular weights and their distributions. In principle, GPC is a kind of volume-
exclusion chromatography, because the molecular-weight fractionation is based
upon volume exclusion. The porous silica beads are filled in the column of
chromatography. In each pore, the low molecular weight fractions get into the
deeper region and stay longer upon fluid-washing, while the high molecular weight
fractions stay shorter upon fluid-washing, as demonstrated in Fig.2.5a. Therefore,
under the detection of the ultraviolet spectroscopy, we obtain the adsorption curve
on the outflow volume. The first signal corresponds to the fraction of the highest
molecular weights. The adsorption strengthHcorresponds to the total weight of the
fraction, and the efflux volumeVecorresponds to the molecular weight of that
fraction. The latter is calibrated by a standard curve obtained from the standard
polystyrene samples, as demonstrated in Fig.2.5b, c. Therefore,
MW¼
SHiMi
SHi(2.24)
Fig. 2.5 Illustration of the principle of GPC. (a) The volume exclusion chromatography for the
selection of chain lengths; (b) the efflux curve of a polydisperse polymer sample; (c) the standard
curve based on the standard polystyrene samples
26 2 Structure–Property Relationships