Chain polymerization polymer thermodynamics

This is a theoretical study on the entanglement architecture and mechanical properties of an ideal two-component interpenetrating polymer network (IPN) composed of flexible chains (Fig. la). In this system molecular interaction between different polymer species is accomplished by the simultaneous or sequential polymerization of the polymeric precursors [1 ]. Chains which are thermodynamically incompatible are permanently interlocked in a composite network due to the presence of chemical crosslinks. The network structure is thus reinforced by chain entanglements trapped between permanent junctions [2,3]. It is evident that, entanglements between identical chains lie further apart in an IPN than in a one-component network (Fig. lb) and entanglements associating heterogeneous polymers are formed in between homopolymer junctions. In the present study the density of the various interchain associations in the composite network is evaluated as a function of the properties of the pure network components. This information is used to estimate the equilibrium rubber elasticity modulus of the IPN. 

At the transfer of the polymeric chain from the ideal into the real solution its conformational volume is deformed with the transformation of the spherical Flory ball into the conformational ellipsoid elongated or flattened along the axis connecting the begin and the end of a chain 26, that leads to decrease of the conformational volume and accordingly to the Eq. (8) to decrease of X. at any deformations of the Flory ball X became less than the one. That this why the effects related with the notions hardness of the polymeric chain and the thermodynamic quality of the solvent can be quantitatively estimated via the multiplicity of the volumetric deformation X <. The indicated effects are visualized in the adsorption layer weaker than in the solution firstly, because the conformational volume in the adsorption layer equal to //2, is less, than in solution. This increases the elastic properties of the conformational volume of polymeric chain and thereafter increases the deformation woik. Moreover, the concentrated adsorption layer corresponding to the quasi-plateau on the adsorption isotherm is more near to the ideal than the diluted real solution. That is why under other equal conditions X > X. This means, that the adsorption of polymer from the real solution is more than ftom the ideal one. 

It should be noted that, whereas the preceding discussion has been cast in terms of free-radical polymerizations, the thermodynamic argument is independent of the nature of the active species. Consequently, the analysis is equally valid for ionic polymerizations. A further point to note is that for the concept to apply, an active species capable of propagation and depropagation must be present. Thus, inactive polymer can be stable above the ceiling temperamre for that monomer, but the polymer will degrade rapidly by a depolymerization reaction if main chain scission is stimulated above T.. 

Detailed analytical and numerical studies of the above questions are in progress, and a very rich and nonadditive dependence of the phase behavior on the precise nature of the attractive potentials, single chain architecture, and thermodynamic state is found [67, 72]. A full understanding of these issues would provide a scientific basis for the rational molecular design of polymeric alloys. The influence of asymmetries on the spinodal phase boundary of simple model polymer alloys using analytic PRISM theory with molecular closures has been derived by Schweizer [67]. In this section a few of these results are briefly discussed. 

More modem approaches borrow ideas from the liquid state theory of small molecule fluids to develop a theory for polymers. The most popular of these is the polymer reference interaction site model (PRISM) theory " which is based on the RISM theory of Chandler and Andersen. More recent studies include the Kirkwood hierarchy, the Bom-Green-Yvon hierarchy, and the perturbation density functional theory of Kierlik and Rosinbeig. The latter is based on the thermodynamic perturbation theory of Wertheim " where the polymeric system is composed of very sticky spheres that assemble to form chains. For polymer melts all these liquid state approaches are in quantitative agreement with simulations for the pair correlation functions in short chain fluids. With the exception of the PRISM theory, these liquid state theories are in their infancy, and have not been applied to realistic models of polymers. 

Like all other chemical reactions, polymer syntheses may be subdivided into two categories, namely into kinetically controlled (KC) polymerizations and thermodynamically controlled (TC) polymerizations. KC polymerizations are characterized by irreversible reaction steps, equilibration reactions are absent, and the reaction products may be thermodynamically stable or not. TC polymerizations involve rapid equilibration reactions, above all formation of cyclics by back-biting of a reactive chain end (see Formula 5.1), and the reaction products represent the thermodynamic optimum at any stage of the polymerization process. Borderline cases also exist, which means that a rapid KC polymerization is followed by slow equilibration. This combination is typical for many Ring-opening polymerizations (ROPs). 

The ring-opening polymerization of is controUed by entropy, because thermodynamically all bonds in the monomer and polymer are approximately the same (21). The molar cycHzation equihbrium constants of dimethyl siloxane rings have been predicted by the Jacobson-Stockmayer theory (85). The ring—chain equihbrium for siloxane polymers has been studied in detail and is the subject of several reviews (82,83,86—89). The equihbrium constant of the formation of each cycHc is approximately equal to the equihbrium concentration of this cycHc, [(SiR O) Thus the total... 

Viscoelastic polymers essentially dominate the multi-billion dollar adhesives market, therefore an understanding of their adhesion behavior is very important. Adhesion of these materials involves quite a few chemical and physical phenomena. As with elastic materials, the chemical interactions and affinities in the interface provide the fundamental link for transmission of stress between the contacting bodies. This intrinsic resistance to detachment is usually augmented several folds by dissipation processes available to the viscoelastic media. The dissipation processes can have either a thermodynamic origin such as recoiling of the stretched polymeric chains upon detachment, or a dynamic and rate-sensitive nature as in chain pull-out, chain disentanglement and deformation-related rheological losses in the bulk of materials and in the vicinity of interface. 

Tethering may be a reversible or an irreversible process. Irreversible grafting is typically accomplished by chemical bonding. The number of grafted chains is controlled by the number of grafting sites and their functionality, and then ultimately by the extent of the chemical reaction. The reaction kinetics may reflect the potential barrier confronting reactive chains which try to penetrate the tethered layer. Reversible grafting is accomplished via the self-assembly of polymeric surfactants and end-functionalized polymers [59]. In this case, the surface density and all other characteristic dimensions of the structure are controlled by thermodynamic equilibrium, albeit with possible kinetic effects. In this instance, the equilibrium condition involves the penalties due to the deformation of tethered chains. 

A detailed description of AA, BB, CC step-growth copolymerization with phase separation is an involved task. Generally, the system we are attempting to model is a polymerization which proceeds homogeneously until some critical point when phase separation occurs into what we will call hard and soft domains. Each chemical species present is assumed to distribute itself between the two phases at the instant of phase separation as dictated by equilibrium thermodynamics. The polymerization proceeds now in the separate domains, perhaps at differen-rates. The monomers continue to distribute themselves between the phases, according to thermodynamic dictates, insofar as the time scales of diffusion and reaction will allow. Newly-formed polymer goes to one or the other phase, also dictated by the thermodynamic preference of its built-in chain micro — architecture. 

The interactions between bulky phenyl substituents in the polymer chain can give more steric hindrance than the deformation of the valency angles in the four membered ring. Similar interactions prevent the polymerization of 1,1-diphenylethylene and 2,2-diphenyloxirane (16). Thus, octaphenylcyclotetrasilane can be thermodynamically more stable than linear perphenylpolysilane and no initiator exists capable of converting this cycle to the linear polymer. 

Cyclosilazanes are found to be reluctant to polymerize by the ring-opening process, probably for thermodynamic reasons. On the other hand, six- and eight-membered silazoxane rings are able to undergo anionic polymerization under similar conditions to those which have been widely used for cyclosiloxane polymerization provided there is no more than two silazane units in the cyclic monomer. They can also copolymerize with cyclosiloxanes however, the chain length of the linear polymer formed is substantially decreased with increasing proportion of silazane units. 

Polymerization occurs very quickly and the process is controlled via kinetic effects rather than thermodynamic ones. The net result is that the molecular weight distribution of the product does not match the thermodynamically stable one. If the chains were not capped with monofunctional phenols, the polymer chains would depolymerize, allowing the monomers to rearrange themselves at elevated temperature to approach the thermodynamically stable... 

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