The polymerization of styrene by sulphuric acid - III. The molecular weight distribution

The theory of the molecular weight distribution in polystyrenes initiated by sulphuric acid, described in part I, has been tested by preparation and fractionation of suitable low-yield polymer samples. The expected ‘most probable’ distribution is found in these samples, but not in a high-conversion polymer. The characteristic parameters of the distributions the relative probability of chain growth—agree with values calculated from the kinetic con­stants measured in part II.

2016 ◽  
Vol 1819 ◽  
Author(s):  
Ramiro Infante-Martínez ◽  
Enrique Saldívar-Guerra ◽  
Odilia Pérez-Camacho ◽  
Maricela García-Zamora ◽  
Víctor Comparán-Padilla

ABSTRACTThis work shows the development of several models for chain-growth polymerizations that admit the direct calculation of the complete molecular weight distribution of the polymer. The direct and complete calculation implies that no statistical mean values are employed as in the moments method neither numerical approximations like in the minimum-squared based methods. The free radical polymerization of ethylene (LDPE) and the coordination via metallocenes polymerization of ethylene (HDPE) are taken as examples for analysis.In the free radical polymerization case, the conventional scheme for chain-growth polymerization is adopted, with steps for initiation, propagation, chain transfer to small species and the additional step of chain transfer to dead chains [1]. The kinetic parameter are obtained from the open literature. Two kind of reactors were modelled: batch and continuous stirred tank reactor. For this last case, a simulation strategy was considered in which the run started from an initial known population of dead chains. Results show that typical non-linear polymerization profiles for the molecular weight distribution are obtained. For the coordination polymerization of ethylene via metalocenes, the standard coordination model was employed [2]. A two-site catalyst was considered and kinetic parameters reported in the open literature were used. For this study an experimental program in a lab-scale reactor was undertaken in order to obtain modelling data [3]. Results show that the standard model adequately reproduces the experimental data in the kinetic and molecular attributes of the polymer.


Author(s):  
Wayne Hayes ◽  
Steve Rannard

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).


2015 ◽  
Vol 1767 ◽  
pp. 87-91
Author(s):  
Ramiro Infante-Martínez ◽  
Enrique Saldívar-Guerra ◽  
Odilia Pérez-Camacho ◽  
Maricela García-Zamora ◽  
Víctor Comparán-Padilla

ABSTRACTThis work presents results on the prediction of the molecular weight distributions (MWD) of chain growth polymerization using conventional software and hardware tools. The investigation focuses on two kinds of polymerization processes: free radical batch and continuous polymerization processes with application to low density polyethylene synthesis (LDPE); and coordination polymerization via metallocenes with application to high density polyethylene synthesis (HDPE). For both processes, kinetic models, consisting of sets of differential equations describing the dynamic behavior of all the chemical species in the reaction media, are presented. From these sets is possible to obtain the molecular weight distribution of the polymer1,2,4Strategies for the simulation of the polymerization models were developed and results of these simulations are presented. On the free radical polymerization case, the next results are highlighted: i) It was confirmed that the chain transfer to polymer step produces strong asymmetries on the MWD as well as a high polydispersity index; ii) It’s possible to calculate the MWD in the CSTR process through a simulation strategy that permits the decoupling of the live and dead chains populations. On the metallocene polymerization case, it was demonstrated that the coordination standard model represents well the system experimentally studied and it can be employed to directly calculate the molecular weight distribution.These results confirm the idea that the complete MWD can be directly calculated with conventional hardware and software tools.


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