Polymer Molecular Weight Distribution Using TD-NMR

Knowing the molecular weight/molecular weight distribution is crucial to understanding polymeric properties and performance, such as polymer size and chain conformation. Chromatography is a well-known method suited for determining molecular weight distribution. However, it requires special sample preparation, a large amount of solvent, and is time-consuming.

TD-NMR using pulsed field gradients (PFG) has proved to be a powerful, non-destructive method to obtain the molecular weight/molecular weight distribution via the diffusion coefficient. It is easily implemented routinely since it requires easy sample preparation, a flexible choice of solvent, and a broad range of operating temperatures.

Diffusion coefficient data acquired with the MQC-R equipped with pulsed field gradients for dilute monodisperse polyethene glycol (PEG) standards (molecular weights 1,970 – 21,300 mg.mol⁻¹) in deuterated water (D₂O) is shown in the figures. The attenuation of log-normal signal intensity of monodisperse PEG by incrementing the gradient strength (g) follows a mono-exponential trend, as indicated by the least mean square fit-dashed line in figure (a). Therefore, each monodisperse PEG sample is represented by a single diffusion coefficient, as predicted.

γ represents the nuclear gyromagnetic ratio, g is the gradient strength, δ is the gradient pulse duration, and Δ is the diffusion time.

A multi-exponential decay would be obtained for a polydisperse polymer, indicating multiple diffusion coefficients, and in that case, the inverse Laplace transform (ILT)-based numerical method is used to determine the diffusion coefficient distribution curve. Furthermore, under dilute conditions, the diffusion coefficient (D) correlates to the molecular weight (Mw) according to the equation D=kMw⁻α.

Figure (b) shows the linear correlation of log-D and log-M_w obtained for the monodisperse PEG samples. By creating a calibration curve between D and M_w for a set of monodisperse polymer standards in a dilute condition, the scaling parameters related to the polymer type (k and α) can be determined. Knowing the parameters K and α, it becomes possible to determine the distribution of molecular weights from the distribution of diffusion coefficients for an unknown polydisperse polymer. Other methods, based on relaxation, may be used on the MQC-R to measure polymer properties such as amorphous/crystalline content, cross-linking density as well as fluorine content in fluoropolymers.