No abstract

The penetration theory equations representing diffusion with a generalized, reversible chemical reaction of the form γAA + γBB ⇌ γMM + γNN are solved by a finite‐difference method. Many solutions are presented in graphical form. Approximate solutions to several limiting cases are obtained analytically by means of a steady state representation and are useful for estimating results of the solution to the penetration theory equations.

The final stages of condensation polymerization are characterized by a rapid rise in molecular weight, as the condensation product is formed and diffuses out of the polymer. The process occurring is one of desorption accompanied by a chemical reaction. The penetration theory equations for a generalized condensation polymerization reaction have been solved and some solutions are presented. The penetration theory solution, obtained by finite-difference computations, is compared with an analytical solution for the special case of no diffusional resistance.In many instances, the rate at which a polymerization reaction proceeds is controlled or strongly affected by diffusional resistances. The high viscosities encountered in polymeric media are partly responsible for this. Even if the reaction is infinitely rapid, the diffusional processes required to bring about the reaction may be so slow as to have a dominant effect on the overall rate of polymexization. Under these circumstances, a mathematical representation is necessary if an adequate understanding of condensation polymerization is to be achieved.Condensation polymerization proceeds by the reaction of two functional groups, usually with the formation of a volatile by-product. This by-product must be removed in order to drive the polymerization reaction toward completion, with the formation of polymers having high molecular weights. The desorption process is often controlled by the rate at which the volatile by-product can diffuse out of the reaction medium.The mathematical representation and analysis of problems in which a diffusing species is simultaneously consumed or produced by a chemical reaction have received considerable attention in the literature. Recently, many special cases that had previously been solved were brought together in a single mathematical model of wide applicability, that yields penetration-theory solutions by digital computation ( 5 ) . The purpose of this paper is to demonstrate how the general model can be used to represent condensation polymerization.Examples of condensation polymerizations in which diffusion is important are the synthesis of polyamides:and the synthesis of polyesters such as polyethylene terephthalateThe general mathematical model that has been developed for diffusion with reaction ( 5 ) can be adapted readily to the representation of condensation polymerization. That model was developed for absorption with reaction, while we are dealing here with desorption accompanied by chemical reaction.The Higbie penetration theory ( 4 ) is appropriate for the mathematical representation of condensation polymerization since the high viscosities encountered effectively suppress convection. MATHEMATICAL DEVELOPMENTwritten in terms of reactive groups as follows:A general condensation polymerization reaction can be ka ki

A microinterferometric method was used to measure the diffusion coefficient as a function of concentration in the system dimethylformamide‐polyacrylonitrile at 25°C. The diffusion coefficient increases with increasing polymer concentration up to the maximum employed, 17.72% by weight. The theoretical basis for this type of behavior is explained. The diffusion coefficient in the limit as the polymer concentration approaches zero was calculated from theory to be 0.30 × 10−6 sq.cm./sec. This value is consistent with the diffusion coefficients obtained experimentally.

A mass transfer model was developed to represent the desorption of a volatile species from a molten polymer in an extruder consisting of co‐rotating twin screws in a figure‐eight bore. The melt undergoes a series of alternating exposure and mixing processes while being transported axially through the device. The model relates the ratio of entrance to exit concentrations of the volatile species to the dimensions of the screws, the rate of their rotation, the rate of polymer flow, and the diffusion coefficient of the volatile species in the polymer. Experimental data, obtained with a halocarbon‐polybutene system in a twin‐screw extruder, were compared with predictions of the model. For the observed performance, the model predicts a process screw length about 14 percent below the actual screw length in the experimental extruder.