Polymerization degree against reaction

To start the experiment all the tubes are placed in a rack at the same time and allowed to warm to room temperature finally they are placed in a thermostat at 50 °C.The tubes are removed at intervals of 1 h and immediately cooled in an acetone/dry ice bath.The samples that are still fluid are diluted with approximately 50 ml of chloroform and dropped into about 500 ml of stirred heptane or petroleum ether. For the very viscous or solid samples 1-2 g are dissolved in 50-100 ml of chloroform and the solution is added dropwise to 500-1000 ml of heptane or petroleum ether with stirring.The polymers are filtered off and dried to constant weight in vacuum at 50 C.The yield, the limiting viscosity number (measured in chloroform at 20 °C) and the degree of polymerization are plotted against reaction time. 

Equation 20.17 puts the kinetic expression entirely in terms of the initial concentration of monomer, Cq, and is in the form useful for following the rates of linear (only bifunctional monomers) self-catalyzed polycondensations. If 1/p is plotted against t one gets a straight line. Under self-catalyzed conditions, the reaction is third order, and the degree of polymerization (DP, or Xn) is approximately proportional to t. This third-order dependency of the rate of self-catalyzed polycondensations also means that the rate of increase in the molecular weight (degree of polymerization) slows down quite rapidly as the reaction proceeds. 

The concept of generating functions is useful to obtain the distribution and averages of the degree of polymerization in the course of polymerization reactions and polycondensation reactions. Most of the material described in the literature deals with branched systems. In these systems, classical statistical methods often run against walls and only advanced methods like the application of generating functions will be successful. 

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