Effect of molecular weight distribution on viscoelastic properties of polymers. 2. Terminal relaxation time and steady-state compliance

1984 ◽  
Vol 17 (4) ◽  
pp. 895-898 ◽  
Author(s):  
Michio Kurata
Keyword(s):  
Molecular Weight ◽  
Relaxation Time ◽  
Steady State ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Viscoelastic Properties ◽  
State Compliance

Peculiarities of flow and viscoelastic properties of solutions of polymers with a narrow molecular-weight distribution

1973 ◽  
Vol 9 (11) ◽  
pp. 1231-1249 ◽  
Author(s):  
G.V. Vinogradov ◽  
A.Ya. Malkin ◽  
N.K. Blinova ◽  
S.I. Sergeyenkov ◽  
M.P. Zabugina ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Viscoelastic Properties ◽  
Narrow Molecular Weight Distribution

Analysis of Polymerization Kinetics and the Use of a Digital Computer

1961 ◽  
Vol 34 (4) ◽  
pp. 995-1133 ◽  
Author(s):  
Shean-lin Liu ◽  
Neal R. Amundson
Keyword(s):  
Molecular Weight ◽  
Steady State ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Digital Computer ◽  
Continuous Process ◽  
Monomer Concentration ◽  
Batch Process ◽  
Active Species ◽  
Rate Equations

Abstract The design of chemical reactors for polymerization and degradation processes requires the consideration of the kinetics of reaction systems which may contain several hundred or even thousand consecutive and simultaneous reactions. The problem is further complicated by the fact that the kinetic mechanisms for these processes are not well established. The present paper is a theoretical analysis of addition polymerization, copolymerization and degradation systems occurring in both continuous stirred tank and batch reactors for a number of kinetic models reported in the literature. Analytical solutions are derived for the steady state continuous process. In the batch process a steady state is not assumed and approximately 200 simultaneous first order differential equations for species concentrations are solved numerically. The paper is divided into three parts. Addition polymerization is discussed in the first part for each of the special cases of monomer, spontaneous, combination and disproportionation termination. For the continuous process, the steady state concentrations of the polymers arc obtained and the molecular weight distribution function and the optimum isothermal operating temperature are discussed. For the batch process, the rate equations are solved numerically by the Runge-Kutta method on a digital computer and the effects of the system parameters on the monomer concentration profile and the molecular weight distribution are examined. By the use of numerical methods with a digital computer it is possible to obtain the concentration of each of a large number of polymer species during the course of polymerization. The result of computation shows that the steady state assumption for active polymer species is not accurate, especially in early stage of reaction, and as well, is inaccurate also for high molecular weight active species. In the case of spontaneous termination, the rate of monomer consumption is slower than that in the case of monomer termination, because the monomer is reproduced by the termination process of the active polymer, P1. The profiles of monomer concentration and molecular weight distribution are the same for the cases of no termination and combination termination. Essentially the same treatment is made for copolymerization in the second part. This time the two simultaneous algebraic equations for the monomer concentrations are solved by the Newton-Raphsom method and these are then used to obtain the steady state concentrations of the copolymer species as functions of the system parameters. The analysis of the batch case involves the numerical solution of 194 simultaneous nonlinear first order differential equations. It is shown that the steady state approximation for the active copolymer concentrations cannot be made. There is a little delay in the formation of the dead species relative to that of the corresponding active copolymer. This is expected, because the dead species are produced by the termination reactions of the corresponding active species. In the third part, degradation is considered as random scission, as a chain reaction, and as a reverse polymerization. The rate equations describing the random scission process in a batch reactor arc shown to be linear so that they may be solved by methods of straightforward integration and by matrixes, while the chain reaction and reverse polymerization mechanism require the same numerical techniques as used for polymerization.

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