| The molecular weight distributions generated by Ziegler-Natta catalyzed polymerizations are examined. Only those catalysts with one type of catalytic species are considered. From the rate laws for propagation and elimination, a series of coupled differential equations result which define the rate of formation of polymer chains composed of i monomer units. Solving these differential equations yields a time-dependent molecular weight distribution function with the observed rate constants for propagation function with the observed rate constants for propagation and elimination as parameters. Careful analysis of this distribution function shows that it predicts a transition from a Poisson to Schulz-Flory distribution with time. This transition is known for both the Ziegler-Natta catalyzed polymerization of olefins and the Fischer-Tropsch catalyzed hydrogenation of carbon monoxide. Hence, this time-dependent distribution function may apply to coordination catalyzed polymerizations in general.; Analysis of this distribution function shows that the weight fraction distribution becomes bimodal just before the limiting Schulz-Flory form of the distribution is reached. This bimodal behavior provides an insight into the effect of propagation and elimination rates on the molecular weight distribution. Qualitatively, this behavior may be explained as follows. Before many eliminations occur, the molecular weight distribution obeys the Poisson distribution function, shifting to higher molecular weights with time. At longer times, the catalyst increasingly eliminates chains and starts to grow new chains. This results in a decrease in the number of surviving chains representative of the Poisson distribution and an increase in the lower molecular weight material. These new chains are generated at different times and represent a broad, truncated Schulz-Flory distribution. Eventually, the Poisson peak passes the time-independent peak of the truncated Schulz-Flory distribution and a bimodal distribution is obtained. Since the Poisson distribution decreases with time, it eventually disappears into the high molecular weight tail of the Schulz-Flory distribution. This predicted behavior is confirmed experimentally by analyzing the molecular weight distributions of polypropylene prepared at low temperatures with a vanadium (III) trisacetylacetonate/diethyl aluminum chloride catalyst.; In addition, functions describing the time-dependence of the number-average and weight-average degrees of polymerization are derived from the rate laws. These functions are in excellent agreement with the available experimental data. |
