A Simple Access to the (Log/Normal) Molecular Weight Distribution Parameters of Polymers Using PGSTE NMR

Abstract

A log/normal MWD is characterized by two parameters, its mean molecular weight M0 and width σ. It is demonstrated how these parameters can be obtained by model fitting a stretched exponential function (SEF), as characterized by two parameters β and DS, to the PGSTE response curve. Based on simulations, two general empirical equations relating β and DS to M0 and σ are found. The model enables the MWD characteristics to be determined if the scaling law between diffusivity and molecular weight is known. The sensitivity and relative error of σ and M0 are discussed and the applicability of the model is illustrated by analyzing experimental NMR response curve of some PEO samples. The key advantages of this technique are its simplicity, numerical robustness, and reliability. magnified image

The gamma distribution model for pulsed-field gradient NMR studies of molecular-weight distributions of polymers

“…However, the relation between spread and the value of the beta parameter is complicated [20]. However, the stretched exponential model does not correspond to an actual distribution of self-diffusion coefficients.…”

“…a phenomenological relationship which is able to express polydispersity to some extent through the 'stretch' parameter b [18,19], and some attempt have been made to interpret this in terms of polydispersity [20]. However, the relation between spread and the value of the beta parameter is complicated [20].…”

Scaling exponent and dispersity of polymers in solution by diffusion NMR

“…However, the scaling parameters of Eq. (1) specific to that polymersolvent system must be found by measuring ⟨D⟩ on fractionated samples of the polymer with known M. Therefore, currently all PGSE NMR-based methods which convert from D to M cannot independently measure the absolute molecular mass distribution [12,13,14,15,16,17,18,19,20,21,22,23,24,25].In this paper we show that ν in Eq.(1) can be directly estimated from a single PGSE experiment in which the extremity (end-group) polymer signal can be spectrally resolved by a chemical shift from the polymer main-chain signal. The scaling exponent, ν, is a measure of the polymer conformation as well as solvent quality [3,26], with bounds of ν = 1/3 for a perfectly coiled, impenetrable, polymer ball and ν = 1 for a perfectly straight polymer rod [17].…”

Molecular Weight Distribution Characteristics (of a Polymer) Derived from a Stretched‐Exponential PGSTE NMR Response Function—Simulation

“…It is well known, however, that this is an illposed numerical problem of particular complexity. However, it is known that the ILT of an SEF can be expressed explicitly by a series expansion, [ 7 ] which then bypass the numerical problem of performing an ILT of a SEF.We recently presented an alternative approach to overcome the above numerical problem [ 8 ] whereby a numerical Laplace transform of a log-normal distribution (LND) function was performed and the resulting transform was fi tted to an SEF. By applying the well-known relation between the molecular weight and molecular diffusivity, two empirical equations relating the two SEF parameters of the PGSTE NMR response function and the two corresponding parameters of the log-normal molecular weight distribution (LNMWD) were derived.…”

“…We recently presented an alternative approach to overcome the above numerical problem [ 8 ] whereby a numerical Laplace transform of a log-normal distribution (LND) function was performed and the resulting transform was fi tted to an SEF. By applying the well-known relation between the molecular weight and molecular diffusivity, two empirical equations relating the two SEF parameters of the PGSTE NMR response function and the two corresponding parameters of the log-normal molecular weight distribution (LNMWD) were derived.…”