| Abstract: | The molecular weight distributions in two-stage step-growth polymers are investigated. A two-stage polymer is produced when polymer chains from two or more different polymerization reactions are mixed together and, in a second stage, are polymerized further to obtain the final polymer. The theoretical molecular weight distribution functions of two-stage polymers are developed using a probabilistic approach. The final distributions are best described by means of matrix equations. The use of matrices simplifies the final form of these distribution functions. The molecular weight distribution functions of two-stage step-growth polymers are also found by solving the kinetic rate equations of each molecular species present. The solution of these rate equations is shown to be equivalent to the solution by probabilistic arguments. The molecular weight distributions which are described by the theoretical equations can be thought of as a linear combination of several one-stage distribution functions. These theoretical equations are compared to the distribution obtained in several two-stage polyurethane polymers measured by gel permeation chromatography (GPC). The quantitative agreement between the measured and calculated distributions is fairly good, although a limited number of two-stage polymers were made. Along with the molecular weight distributions, the theoretical sequence-length distributions in copolymers made by a two-stage process is also investigated. It is found that the sequence-length distribution can be radically altered by using a two-stage process. This sequence-length distribution should have a great effect on the phase properties of the final polymer. |
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