Differential Molecular Weight Distribution Research Articles

GPC data interpretation

AbstractA rigorous procedure for reducing gel permeation chromatography elution data to differential molecular weight distribution curves is discussed and demonstrated by two sample calculations. The errors introduced by failure to correct the ordinates of the elution curve by means of a differential calibration curve are identified, and a simple graphical conversion procedure is illustrated.

Column fractionation of polymers. VII. Computer program for determination of molecular weight distributions from gel permeation chromatography

AbstractGel permeation chromatography produces a type of differential molecular weight distribution directly and rapidly. Conversion of these data to conventional molecular weight distributions and plots of distributions is time‐consuming. A computer program is described to perform these operations readily. Input data from the automated chromatograph, elution volume, and recorder deflection are converted to unit sensitivity and base line corrections applied. The curve is then numerically integrated and a calibration curve used to convert elution volumes into molecular weights. Various calibration curves can readily be introduced into the program. The output, in addition to tabulation of cumulative and differential molecular weight distributions, contains values of M̄n, M̄v, M̄w, M̄z, and M̄z+1. Importantly, a reduced absolute area, i. e., area computed for unit sensitivity on a unit concentration basis, is tabulated. An additional time‐saving eature is the printing out of differential and cumulative molecular weight distribution curves and of a differential histogram.

Tailored heterogeneity indices in anionic polymerization

AbstractEquations are derived for the differential molecular weight distribution curve and for the heterogeneity index for several types of delayed initiator addition in anionic polymerization. All the results are in closed and easily used form, and depend only upon the product of the rate constant of the propagation reaction, the total initiator concentration, and a parameter representative of the rate of initiator addition. The results are plotted versus the above‐mentioned product, so that one can determine the heterogeneity index to be expected under a wide range of the variables involved.

Column fractionation of polymers. IV. Large‐scale polyester column fractionation

AbstractA small‐scale fractionation of 9 g. and a large‐scale fractionation of 90 g. of a polyester were carried out. The polymer was prepared by condensation of isophthalic acid, maleic anhydride, and propylene glycol in the mole ratio 1:2:3. Results from the two fractionations were in good agreement despite different fractionation conditions. By proton magnetic resonance measurements the fractions were found to have nearly constant chemical compositions. The Huggins' constant and the Staudinger relation for this polyester were determined from data on fractions in chloroform at 30°C. Integral and differential molecular weight distributions as well as various molecular weight averages for the polyester were obtained by a computer program. The fractionation data were applied to several popular distribution correlations. The experimental distribution was found to be in good agreement with that expected from the theory of polycondensation kinetics.

THE FRACTIONATION OF POLYTHENE

An apparatus is described for fractionating large quantities (400 g) of polythene into five roughly equal fractions using a fractional precipitation technique. Application of this method of fractionation to a linear polythene has shown that the width of the molecular-weight distribution of the successive fractions decreases as the fractionation proceeds. Consequently, the initial high-molecular-weight fractions require refractionation to produce equally narrow distributions in them as are found in later fractions. Good agreement is obtained with the experimentally determined values of the number-average and weight-average molecular weight for the parent polymer when the measured values of Mn and Mw for each fraction are used to calculate the values for the parent. The differential molecular-weight distribution function of the parent polymer was calculated on a Bendix G-15 computer from the data for the fractions by using the weight, number-average and weight-average molecular weight, measured for each fraction in conjunction with an assumed log-normal or negative binomial molecular-weight distribution function in each fraction.

Molecular weight distribution of a vinylidene cyanide/vinyl acetate copolymer

AbstractA copolymer of VCVA (vinylidene cyanide/vinyl acetate) was fractionated into twenty‐five fractions ranging in Mn values from 7,000 to 535,000. The differential weight molecular weight distribution curve for this copolymer exhibited two maxima, one occurring at a Mn value of 100,000 and the other at 340,000. The original copolymer had a Mn value of 89,000 and after extraction with acetone the Mn value was increased to 137,000. Molecular weights varying from 7,000 to 24,000 were determined for the acetone‐soluble fractions. At 25.00°C. the relationship between intrinsic viscosity measurements in DMF and molecular weight is given by the equation [η]0 = 1.536 × 10−4 M0.78. Using the equations of Huggins, a μ1 value of 0.373 ± 0.019 and a k′ value of 0.373 ± 0.025 were determined for the VCVA fractions solubilized in DMF at 25.00°C. The μ1 values decreased slightly with decreasing molecular weight, indicating a small change in chemical structure or composition of the VCVA molecules as a function of decreasing molecular weight. Approximately 23% of the original VCVA copolymer was in the molecular weight range of 84,600 to below 7,000 and here with decreasing molecular weight the VA component (per mole of VC) present in the copolymer increased from 1.075 to 2.32 moles. Using the Flory equation, root mean square end‐to‐end values of the VCVA fractions in DMF at 25.00°C. were calculated. Assuming the absence of branching or crosslinking, the degree of coiling of the VCVA chain appeared to increase as the molecular weight increased. The cohesive energy density of the VCVA copolymer was calculated to be 122.8 cal./cc.