Recent progresses in the development of more reliable predictions of average molecular weights and chain-lenght distributions for complex irreversible non-linear polymerizations

Prediction of the structure of branched polymers is a challenging problem, for which only more or less clumsy mathematical solutions have been made available for a long time in the case of kinetically controlled polymerizations. The matter has, nevertheless, considerable economic significance. For instance, a controlled amount of long branching is known to have many benefits on the rheologic properties the widely used polyolefins (Nele et al., 2003). Development of processes and their optimization could benefit a lot with models with better predictive capacities. Progresses in applied mathematics could at last bring about a considerable improvement in this situation. This paper reviews recent methods (Costa and Dias, 2003; Dias and Costa, 2003, 2005) allowing the direct computation of moments (i. e. avoiding Hulburt-Katz closures) of polymer chain length distributions, even in the presence of gel, overcoming past difficulties in their computational implementation. Description of non-linear free radical polymerizations is now possible, thanks to the development methods for solving highly stiff two point boundary value problems (Cash et. al., 2001). Chain length distributions are obtained by adapting algorithms better known with Laplace transform inversion (Papoulis, 1956; Weeks, 1966; Durbin, 1974). Numerous past inconsistencies leading to unwanted errors are now avoided through the use of well-founded chemical and mathematical principles

Overcoming performance and convergence issues of discrete transform based modeling of crosslinking classical and reversible deactivated radical polymerizations

Population balances of polymer species in terms 'of discrete transforms with respect to counts of groups lead to tractable first order partial differential equations when ali rate constants are independent of chain length and loop formation is negligible [l]. Average molecular weights in the absence ofgelation are long known to be readily found through integration of an initial value problem. The extension to size distribution prediction is also feasible, but its performance is often lower to the one provided by methods based upon real chain length domain [2]. Moreover, the absence ofagood starting procedure and a higher numerical sensitivity hás decisively impaired its application to non-linear reversibly deactivated polymerizations, namely NMRP [3].This work was financially supported by: Project POCI-01-0145-FEDER-006984 – Associated Laboratory LSRE/LCM funded by FEDER funds through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI)

520b Dynamic prediction of microstructure and molecular size in coordination terpolymerizations including cross-linking and branching

The production of terpolymers using coordination catalysts is a subject with a great industrial importance, being the ethylene-propylene-diene (EPDM) the most representative chemical system within this class of polymers[1-4]. For technical reasons, only a very low content (less than 2 mol %) of diene monomer (such as ethylidene norbornene (ENB)) can usually be incorporated in the terpopolymer. Chain branching and cross-linking, leading eventually to gel formation are important limiting factors to increase the diene content as desired to obtain products with improved properties.FCT European Communit

Semibatch operation and primary cyclization effects in homogeneous free-radical crosslinking copolymerizations

A theoretical analysis is presented on the use of semibatch reactors for producing non-linear copolymers through the homogeneous free-radical polymerization of mono- and divinyl-monomers. The kinetic scheme distinguishes two kinds of pendant double bonds and five kinds of polymer radicals, as it also takes into account the primary cyclization of terminal divinyl units. In spite of the fairly large number of groups and reactions, the generating function of vector chain length distribution of polymer species can still be accurately computed by a numerical implementation of the method of characteristics and thus average molecular weights before and after gelation can be reliably obtained. The influence of feed policies of the monomers, initiator and transfer agent on gelation, average chain lengths and weight fraction of sol is discussed, as well as their sensitivity to some kinetic parameters

Grafting of functional brushes on the surface of 5-Fluorouracil molecularly imprinted polymer particles through RAFT polymerization

The grafting of functional brushes on the surface of molecularly imprinted polymer (MIP). particles hás been explored in the last few years to synthesize materiais combining high molecular recognition capabilities and stimulation triggered by changes in the surrounding environment [1, 2]. In the present work, MIP particles for 5-fluorouracil (a drug used in câncer treatment) were produced by precipitation polymerization in acetonitrile, using either MAA or HEMA as imprinting fünctional monomers, and m the presence of different kinds of RAFT agents. In a second step, taking advantage of the RAFT groups present in the surface of the particles, different kinds of fiinctional polymer brushes were grafted on the MIPs considering a "grafting from" process in the presence of a RAFT agent.This work was financially supported by: Project POCI-01-0145-FEDER-006984 – Associated Laboratory LSRE/LCM funded by FEDER funds through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI)

Prediction of sol fraction and average molecular weights after gelation for non-linear free radical polymerizations using a kinetic approach

Mass balance equations in terms of the moment generating function of the distribution of mole concentrations of polymer species for free radical copolymerizations of mono/divinyl monomers could be numerically solved after gel point using open source code ACDC, needed for extremely stiff two-point boundary value problems. For the first time, it became possible to compare the error of earlier well-known approximated estimation methods for the weight fraction of sol and average molecular weights to this accurate mathematical solution. It turns out that predictions by the pseudo-kinetic method are reasonable only when equal reactivity of double bonds prevails, causing early gelation in the batch reactor. Otherwise the discrepancies between the exact and approximate solutions are quite important

Branching and crosslinking in coordination terpolymerizations

A general kinetic method, based upon population balances of generating functions, is applied to the prediction of the microstructure and molecular size of non-linear terpolymers obtained through the coordination polymerization of two monovinyl monomers and a non-conjugated diene. A rather complex kinetic scheme involving crosslinking and long-chain branching is considered. It is shown that even in these conditions it is possible to carry out the prediction of molecular size and mass distributions, sequence size distributions, and z-average mean-square radius of gyration of the polymers. The influence of some kinetic parameters on the properties of the products is studied, considering a homogeneous operation in a semi-batch reactor. The used simulation method is able to predict these properties before and after gelation whenever it occurs.Fundação para a Ciência e a Tecnologia (FCT), Ministry of Science and Technology of Portugal; Grant Number: POCI/EQU/44784/2002 European Community through FEDER; Grant Number: POCI/EQU/60483/200

Prediction of mean square radius of gyration of tree-like polymers by a general kinetic approach

This paper describes a kinetic method to predict the z-average molecular mean square radius of gyration of tree-like polymers formed by irreversible reactions, assuming Gaussian chains. It is based on the population balance equations for the two-sided molecular distributions of pendant chains associated with every chemically distinguishable kind of bonds. An automated method for the solution of those equations is valid both before as well as after gelation for complex kinetic schemes. Examples of its use are presented with polycondensation systems leading to hyperbranched polymers, the anionic polymerization of mono- and divinyl monomers and a radical polymerization with terminal branching and transfer to polymer.FCT European Communit

A general kinetic method to predict sequence length distributions for non-linear irreversible multicomponent polymerizations

A method to predict the sequence length distribution (SLD) for homogeneous non-linear irreversible multicomponent polymerizations is described. With more than two monomers, it also predicts chain length distributions of the sub-domains containing a prescribed sub-set of the repeating units, but in all possible orderings. Its goal is the analysis of polymerization systems involving complex kinetic schemes in an automated way. The radical terpolymerization of two vinyl monomers with a divinyl monomer and a radical copolymerization including branching by transfer to polymer and by propagation on terminal double bonds are considered as case studies showing the interest of our approach. Finally, the concept of gelation of sequences is presented and discussed in comparison with the related and better known gelation of the population of polymer molecules.FCT European Communit

An improved method of moments as a more reliable alternative for prediction of average molecular weights of irreversible non-linear polymerizations and reversible polycondensations

An improved method of moments as a more reliable alternative for prediction of average molecular weights of irreversible non-linear polymerizations and reversible polycondensation