Molecular Weight Distribution Characteristics Of Polymers Obtained From A Stretched Exponential Representation Of A PFG NMR Response Function

Pulsed Field Gradient Nuclear Magnetic Resonance (PFG NMR) experiment is an important, alternative technique to determine the molecular weight distribution (MWD) of polymers, as it's independent on the type of solvent and does not affect the solute: Moroever, it can differentiate between the MW of various components in a mixture. To overcome the ill-posed numerical problems of performing an Inverse Laplace Transform (ILT) of a PFG NMR response curve, which is a prerequisite to derive a reliable MWD, a stretched-exponential response function (SEF:y=exp(-(xDs)β),0<β<1) is introduced to represent the observed PFG NMR response curve. Based on the well-known empirical relation (scaling law) between molecular weight M and diffusivity D of a polymer (D=KM-α), any diffusion coefficient can be transformed into a molecular weight M. A brief summary of the main findings in this thesis are summarized:[1]. A large number of diffusion-distributions were calculated from known log-normal (LN) MWDs. Each distribution was Laplace transformed (using MATLAB) and added random noise (1%) in order to mimic real PFG NMR response curves. After fitting a SEF to each synthesized response function, two empirical equations relating the width and the median of the log-normal MWD and the two parameters characterizing the SEF were proposed, showing that the ILT of a SEF possesses many of the characteristics of a LNMWD (NMR-M1).[2]. In order to pin down the quantitative differences between a LNMWD and the corresponding MWD properties derived from the ILT of a SEF, a detailed synthetic/theoretical investigation was performed showing that:The average molecular weights, the distribution width and the PDI can be calculated from the so-called moments (m1,m0,m-1) of the distribution. Unfortunately, it was found that one of the moments m-1, diverges, implying that a cut-off in the low molecular weight had to be defined form-1to exist. [3]. By varying the exponent a in the scaling law, which is a most important property parameter of a polymer solution, the MWD as derived from the ILT technique, is shown to be significantly affected. Hence, a second "Master" equation (Equation5.7) relating the distribution width σ to α and the parameter β of the SEF was obtained (NMR-M2). It was noted that the shape of the MWD, as obtained from the ILT of a SEF, deviated from a LNMWD by becoming flatter and more skewed with increasing β and decreasing a.[4]. NMR-M1/NMR-M2are both calculated from the SEF representation of the PFG NMR response function, but compare to NMR-M1which is asuming there is a LNMWD of the polymer sytem NMR-M2is more general. A comparison between the MWD of real systems and the NMR-M1/NMR-M2models show that the two models are comparable.The important aspect of the present work is that a PFG NMR response function that can be well fitted to a SEF (assuming implicitly that the MWD is reasonably well represented by the ILT of the SEF) enables the MWD characteristics, like the average molecular weight and the PDI to be directly and easily derived from the two SEF parameters (in combination with the scaling-law).All the results presented suggest that the technique is fast and robust and has a potential to be applied in other fields, like in the analysis of NMR relaxation times and to probe the distribution of diffusivities within porous materials. Actually, we believe that the technique may find application in other fields of science in which distribution characteristics are of importance.