Kinetic Analysis of "Living" Polymerization Processes Exhibiting Slow Equilibria. 2. Molecular Weight Distribution for Degenerative Transfer (Direct Activity Exchange between Active and "Dormant" Species) at Constant Monomer Concentration

1995 ◽  
Vol 28 (22) ◽  
pp. 7335-7338 ◽  
Author(s):  
Axel H. E. Mueller ◽  
Deyue Yan ◽  
Galina Litvinenko ◽  
Rugang Zhuang ◽  
Hai Dong
Keyword(s):  
Molecular Weight ◽  
Kinetic Analysis ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Monomer Concentration ◽  
Living Polymerization

Controlled and Efficient Polymerization of Methyl Methacrylate Catalyzed by Pyridinylidenaminophosphines Based Lewis Pairs

2021 ◽  
Author(s):  
Fang Ge ◽  
Sun Li ◽  
Zhe Wang ◽  
Wenzhong Zhang ◽  
Xiaowu Wang
Keyword(s):  
Molecular Weight ◽  
Methyl Methacrylate ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Living Polymerization ◽  
Narrow Molecular Weight Distribution ◽  
Synthetic Approaches ◽  
Lewis Pairs

Developing different synthetic approaches to realize controlled or living polymerization are aspirational to achieve polymers with defined molecular weight, narrow molecular weight distribution and unambiguous structures by polymer chemists. Herein,...

Controlled/‘living’ polymerization methods

2004 ◽  
Author(s):  
Wayne Hayes ◽  
Steve Rannard
Keyword(s):  
Molecular Weight ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Chain Transfer ◽  
Living Polymerization ◽  
Degree Of Polymerization ◽  
Polymer Chains ◽  
Chain Growth ◽  
Living Polymerizations ◽  
Living Nature

Chain-growth polymerizations such as free-radical polymerizations are characterized by four key processes:(i) initiation, (ii) propagation, (iii) chain transfer, and (iv) termination. If it is possible to minimize the contribution of chain transfer and termination during the polymerization, it is possible to achieve a level of control over the resulting polymer and achieve a predetermined number average molecular weight and a narrow molecular weight distribution (polydispersity). If such an ideal scenario can be created, the number of polymer chains that are produced is equal to the number of initiator groups; the polymerization will proceed until all of the monomer has been consumed and the polymer chain ends will remain active so that further addition of monomer will lead to continued polymerization. This type of polymerization was termed a ‘living’ polymerization by Szwarc in 1956 and represents one of the ultimate goals of synthetic polymer chemists. Flory determined that in the absence of termination, the number of propagating polymer chains must remain constant and that the rate of polymerization for each growing chain must be equal. In this situation, the number average degree of polymerization (DPn) and hence the molecular weight of the polymer can be predicted by simple consideration of the monomer to initiator ratio (see eqns (1) and (2), respectively). Several key criteria are used to elucidate the ‘living’ nature of a polymerization. For a polymerization to be considered ‘living’, the rate of initiation must exceed the rate of propagation. Therefore, all the propagating polymer chains are formed simultaneously and grow at the same rate. If this situation did not occur, the first chains formed would be longer than those initiated later and the molecular weight distribution of the propagating chains would broaden. In addition, an ideal ‘living’ or ‘immortal’ polymerization must not exhibit any termination of the propagating polymer chains over the lifetime of the reaction. Consequently, ‘living’ polymerizations are characterized by very narrow molecular weight distributions (Mw/Mn < 1.2).

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.

Sign in / Sign up

Export Citation Format

Share Document