The Termination Reaction

The termination press in free-radical polymerization is caused, as was shown early in this chapter, by one of three types of reactions: (1) a second order radical-radical reaction, (2) a second order radical-molecule reaction, and (3) a first order loss of radical activity. The first reaction can be either one of combination or of disproportionation. In a combination reaction, two unpaired spin electrons, each on the terminal end of a different polymer-radical, unite to form a covalent bond and a large polymer molecule. In disproportionation, on the other hand, two polymer-radicals react and one abstracts an atom from other one. This results in formation of two inactive polymer molecules. The two differ from each other in that one has a terminal saturated structure and the other one has a terminal double bond. Usually ,the atom that is transferred is hydrogen. It was suggested [111] that a basic rule of thumb can be applied to determine which termination reaction predominates in a typical homopolymerizations. Thus, polymerizations of 1,1-disubstituted olefins are likely to terminate by disproportionation because of steric effects. Polymerizations of other vinyl mono mer, however, favor terminations by combination unless they contain particularly labile atoms for transferring. Higher activation energies are usually required for termination reactions by disproportion ation. This means that terminations by combination should predominate at lower temperatures. For a polymer radical that simply grows by adding monomeric units and still possesses an active center after the growth, the number of monomeric units (r) added to a radical center during the time interval t, according to Tobita [112], conforms to the following Poisson distribution:

where θ is the expected number of monomeric units added to a radical center, given by

Where k_p is the propagation rate coefficient and [M]is the monomer concentration. If the number of the added monomeric units, r, is large enough, one can approximate that r≡θ. For bimolecular termina tion reactions that are independent of chain length, the required time for bimolecular termination between a particular radical pair is also given by the following most probable distribution [112]:

Where E=kt/(kp[M]nNA), and kt is the bimolecular termination rate coefficient. The imaginary time for chain stoppage by bimolecular termination must be considered for all radical pairs that exist in the reaction medium [112]. The third type of a termination reaction is chain transferring. Premature termination through transferring results in a lower molecular weight polymer than can be expected from other termination reactions. The product of chain transferring is an inert polymer molecule and, often, a new free radical capable of new initiation. If, however, the new radical is not capable of starting the growth of a new chain, then this is degenerative chain transferring. It is also referred to as a first-order termination reaction. The molecules that accept the new radical sites (participate in chain transferring) can be any of those present in the reaction medium. This includes solvents, monomer molecules, inactive polymeric chains, and initiators. The ease with which chain transferring takes place depends upon the bond strength between the labile atoms that are abstracted and the rest of the molecule to which they are attached. For instance, chain transferring in methyl methacrylate polymerization to the solvent occurs in the following order [115]:

benzene < toluene < ethyl benzene < cumene The rate of a chain transferring reaction is,

R_tr = k_tr (M)(XA)

Where, ktr is the chain transferring constant in areaction:

Examples of molecules that have particularly labile atoms and contribute readily to chain transferring are mercaptans and halogen compounds ,such as chloroform ,carbon tetrachloride , etc. A polymer that was prematurely terminated in its growth by chain transferring may be a telomer In most cases of telomer formation, the newly formed radical and the monomer radical are active enough to initiate new chain growth. Thus , the life of the kinetic chain is maintained. An illustration of a telome rization reaction can befree-radical polymerization of ethylene in the presence of chloroacetyl chloride:

Chain transferring is affected by temperature but not by changes in the viscosity of the reaction medium [115].When a transfer takes place to a monomer, it is independent of the polymerization rate [116,117].When ,however, transfer takes place to the initiator, the rate increases rapidly[118]. A chain transferring reaction to a monomer can be illustrated as follows:

A transfer reactioncanalsooccurfromtheterminalgroupofthepolymer-radicaltoalocationon the polymeric back bone. This is known as backbiting:

The new free-radical site on the polymer backbone starts chain growth that results in formation of a branch. The same reaction can take place between a polymer-radical and a location on another polymer chain. In either case, fresh chain growth results in formation of a branch. Whether chain transferring can take place to an initiator depends upon the initiator’s chemical structure. It was believed in the past that chain transferring to a,a0-azobisisobutyronitrile does not occur. Later it was shown that chain transferring to this initiator does occur as well, at least in the polymerizations of methyl methacrylate [118, 119]. The amount of chain transferring that takes place to monomers is usually low because the reaction requires breaking strong carbon-hydrogen bonds. Monomers, however, such as vinyl chloride and vinyl acetate have fairly large chain transferring constants. In the case of vinyl acetate, this is attributed to the presence of an acetoxy methyl group. This explanation, however, cannot be used for vinyl chloride. The chain transferring constants, are usually defined as:

CM =k_tr.M/kp for monomers

CS =k_tr.S /kp for solvents

C_I = k_tr.I /k_P for initiators,

The values can be found in handbooks and other places in the literature. Presence of chain transferring agents in a polymerization reaction requires redefining the degree of polymerization to include the chain termination terms. The number average degree of polymerization has to be written as follows:

It can also be expressed in terms of the chain transferring constants as follows:

This can also be written in still another form:

Whenapolymerizationreactionisconductedinaconcentratedsolution,orincompleteabsenceofa solvent, the viscosity of the medium increases with time, (unless the polymer precipitates out). This impedes all steps in the polymerization process, particularly the diffusions of large polymer-radicals [54]. The decreased mobility of the polymer-radicals affects the termination process. It appears that this is common to many, though not all, free-radical polymerizations. All molecular processes in the termination reactions are not fully understood, particularly at high conversions [119] This is a complex process that consists of three definable steps. These can be pictured as follows. First, two polymer radicals migrate together by means of translational diffusion. Second, the radical sites reorient toward each other by segmental diffusion. Third, the radicals overcome the small chemical activation barriers and react. The termination reaction is, therefore, diffusion controlled. At low concentrations, this will be segmental diffusion while at medium or high concentrations it will be translational diffusion. Present theories of terminations suggest that at intermediate conversions, terminations are dominated by interactions between short chains formed by transfer and entangled long chains [121]. When terminations are diffusion controlled, most termination events involve two highly entangled chains whose ends move by the “reaction-diffusion” process [119]. In this process, terminations occur because of the propagation-induced diffusion of the chain ends of growing macroradicals. This means that the rates of terminations depend upon the chain lengths [113]. Diffusion theories have been proposed that relate the rate constant of termination to the initial viscosity of the polymerization medium. The rate-determining step of termination, the segmental diffusion of the chain ends, is inversely proportional to the microviscosity of the solution [123]. Yokota andItoh [124] modified the rate equation to include the viscosity of the medium. According to that equation, the overall polymerization rate constant should be proportional to the square root of the initial viscosity of the system. The number average termination rate constants in a methyl methacrylate polymerization were measured with an in-line ESR spectrometer. This was done by observing the radical decay rates [120]. The results are in disagreement with the concept of termination by propagation-diffusion that is expected to be dominant at high conversion rates. Instead, the termination rate constants decrease dramatically in the posteffect period at high conversions. Actually, a fraction of the radicals were found trapped during the polymerization. Thus, there are two types of radicals in the reaction mixture, trapped and free radicals. In the propagations and termination reactions, the two types of radical populations have very different reactivities [120]. Shipp and coworkers [120] described a method for analyzing the chain length dependence of termination rate coefficients of the reacting radicals in low conversion free radical polymerizations. Their method involves comparing experimental molecular weight distributions of polymers formed in pulsed laser photolysis experiments with those predicted by kinetic simulation. The method is enabled by direct measurements of the concentration of radicals generated per laser pulse. Knowledge of the radical concentrations should mean that the only unknowns in the simulations are the termination rate coefficients. They concluded that the analysis demonstrates the need for chain length dependent termination rate constants in describing polymerization kinetics. Free-radical photopolymerizations (see Chap. 10) of multifunctional acrylic monomers result in cross-linked polymeric networks. The kinetic picture of such polymerizations varies from ordinary linear polymerization because the diffusion of free radicals and functional groups becomes severely restricted. This causes growing polymer chains to rapidly cyclize and cross-link into clusters (microgels). The clusters become linked up into networks. Many free radicals become trapped, but terminations take place by combinations and by chain transferring. The cumulative chain length in such polymerizations can be calculated from the following equation [125]:

where, X is the conversion of functional groups and nm0 is the initial number of functional groups and nrg is the total number of radicals generated.

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مواضيع ذات صلة

Steric Control in Free-Radical Polymerization

The rmal Polymerization

Inhibition and Retardation

Ring Forming Polymerization

Polymerization of Monomers with Multiple Double Bonds

Methods for Measuring Molecular Weights of Polymers

Radius of Gyration

Solutions of Polymers

Orientation of Polymers

The Mesomorphic State, Liquid Crystal Polymers

Kinetics of Crystallization

Thermodynamics of Crystallization