A user‐friendly program has been developed to estimate copolymerization reactivity ratios based on a nonlinear minimization algorithm. The use of an optimal experimental design for copolymerization when the Mayo–Lewis model applies is presented. The applicability of the program is demonstrated using actual and simulated experimental data.
In order to obtain the correct calibration of molecular-weight sensitive detectors (such as on-line viscometers or light scattering detectors) in size-exclusion chromatography, it is necessary to account for the (molecular) non-uniformity of the calibration standards. This is true even in the case of the narrow molecular weight distribution standards typically commercially available for calibration. Methods of taking this non-uniformity into consideration are presented. For a multidetector size-exclusion chromatography system calibrated in this way, independent calibration curves can be established for each detector. Thus, at a given hydrodynamic volume, corresponding signals from the different detectors can be obtained. This eliminates the need to estimate additional parameters such as interdetector volumes or lag times for matching signals from different detectors. The practicability of this approach in the analysis of (molecularly) nonuniform polymers is demonstrated by combining on-line viscometer and concentration signals (to obtain intrinsic viscosity versus molecular weight information) for two different polymers, viz. polystyrene and poly(methy1 methacrylate). The resultant intrinsic viscosity versus molecular weight data is then compared to that predicted from the literature.
The viscosity distribution of a polymer sample can be obtained by using an on-line viscometer as a detector in size-exclusion chromatography. This newly defined viscosity distribution is closely related to the molecular weight distribution and expresses weight fraction times intrinsic viscosity of species i as a function of the corresponding molecular weight times intrinsic viscosity (w, [q,] vs. MI [ql I). The intrinsic viscosity ([q]) and number-average molecular weight (M,) can be obtained directly from a viscosity distribution. If the Mark-Houwink exponent a is known (or approximately known) for non-homogeneous polymer the Mw/M, can be estimated from the viscosity distribution when the molecular weight distribution is approximated with a known distribution function. These estimates are independent of any other detector and are valid even for nonhomogeneous polymer samples. The relation between the moments of the viscosity distribution and the &?,/an is presented for two widely used distribution functions, the Log-Normal and the Generalized Exponential Distributions. Polymer characterization based on the viscosity distribution is shown to be a robust technique. It is particularly attractive in characterizing non-homogeneous polymers since it is solely obtained from on-line viscometer.
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