Molar Mass Distribution - Measurement

Measurement

These different definitions have true physical meaning because different techniques in physical polymer chemistry often measure just one of them. For instance, osmometry measures number average molar mass and small-angle laser light scattering measures weight average molar mass. M_v is obtained from viscosimetry and M_z by sedimentation in an analytical ultracentrifuge. The quantity a in the expression for the viscosity average molar mass varies from 0.5 to 0.8 and depends on the interaction between solvent and polymer in a dilute solution. In a typical distribution curve, the average values are related to each other as follows: M_n < M_v < M_w < M_z. Polydispersity of a sample is defined as M_w divided by M_n and gives an indication just how narrow a distribution is.

The most common technique for measuring molecular weight used in modern times is a variant of high-pressure liquid chromatography (HPLC) known by the interchangeable terms of size exclusion chromatography (SEC) and gel permeation chromatography (GPC). These techniques involve forcing a polymer solution through a matrix of cross-linked polymer particles at a pressure of up to several thousand psi. The limited accessibility of stationary phase pore volume for the polymer molecules results in shorter elution times for high-molecular-weight species. The use of low polydispersity standards allows the user to correlate retention time with molecular weight, although the actual correlation is with the Hydrodynamic volume. If the relationship between molar mass and the hydrodynamic volume changes (i.e., the polymer is not exactly the same shape as the standard) then the calibration for mass is in error.

The most common detectors used for size exclusion chromatography include online methods similar to the bench methods used above. By far the most common is the differential refractive index detector that measures the change in refractive index of the solvent. This detector is concentration-sensitive and very molecular-weight-insensitive, so it is ideal for a single-detector GPC system, as it allows the generation of mass v's molecular weight curves. Less common but more accurate and reliable is a molecular-weight-sensitive detector using multi-angle laser-light scattering - see Static Light Scattering. These detectors directly measure the molecular weight of the polymer and are most often used in conjunction with differental refractive index detectors. A further alternative is either low-angle light scattering, which uses a single low angle to determine the molar mass, or Right-Angle-Light Laser scattering in combination with a viscometer, although this latter technique does not give an absolute measure of molar mass but one relative to the structural model used.

The molar mass distribution of a polymer sample depends on factors such as chemical kinetics and work-up procedure. Ideal step-growth polymerization gives a polymer with polydispersity of 2. Ideal living polymerization results in a polydispersity of 1. By dissolving a polymer an insoluble high molar mass fraction may be filtered off resulting in a large reduction in M_w and a small reduction in M_n thus reducing polydispersity.