Step polymerization thermodynamics

Polymerization thermodynamics has been reviewed by Allen and Patrick,323 lvin,JM [vin and Busfield,325 Sawada326 and Busfield/27 In most radical polymerizations, the propagation steps are facile (kp typically > 102 M 1 s l -Section 4.5.2) and highly exothermic. Heats of polymerization (A//,) for addition polymerizations may be measured by analyzing the equilibrium between monomer and polymer or from calorimetric data using standard thermochemical techniques. Data for polymerization of some common monomers are collected in Table 4.10. Entropy of polymerization ( SP) data are more scarce. The scatter in experimental numbers for AHp obtained by different methods appears quite large and direct comparisons are often complicated by effects of the physical state of the monomei-and polymers (i.e whether for solid, liquid or solution, degree of crystallinity of the polymer). 

Kricheldorf and coworkers [2001a,b,c] have stressed that step polymerizations can proceed either with kinetic control or thermodynamic control. Polymerizations under thermodynamic control proceed with an equilibrium between cyclic and linear products. Polymerizations under kinetic control proceed without an equilibrium between cyclic and linear products. 

Table 2-8 shows values of some kinetic and thermodynamic characteristics of typical step polymerizatiosn [Bekhli et al., 1967 Chelnokova et al., 1949 Fukumoto, 1956 Hamann et al., 1968 Malhotra and Avinash, 1975, 1976 Ravens and Ward, 1961 Saunders and Dobinson, 1976 Stevenson, 1969 Ueberreiter and Engel, 1977]. These data have implications on the temperature at which polymerization is carried out. Most step polymerizations... 

Many thermosets are inhomogeneous. This may be the result of the polymerization mechanism (chemically induced inhomogeneities, such as those produced by the free-radical crosslinking polymerization of multifunctional monomers or by the step polymerization of three different monomers), or of the decrease of solubility of reaction products (thermodynamic driving force) or of both factors acting simultaneously, such as the case of several UP formulations. Inhomogeneities formed in the course of polymerization are fixed by the crosslinking reactions. 

The possibility of synthesizing a polymer network containing chemical (topological) clusters by using three monomers of different sizes during a step polymerization was described. In the absence of thermodynamic effects, cluster formation is fully controlled by the initial composition of the system, the relative reactivities of functional groups, and the network-formation history (Nabeth et al, 1996 Cuney et al., 1997). 

Other variables can also be used to influence the thermodynamics of a polymerization. For example, most step polymerizations involve equilibrium reactions, which may be driven to completion by removing the small molecule by-product in an open system. Addition polymerizations are influenced by the solvent used. That is, [ML depends on both the nature of the solvent and on [M]o- For example, the equilibrium monomer concentration of THF increases as the acidity of the solvent increases due to complex formation. In other cases, solvation of a polymer segment may be more exothermic than monomer solvation, resulting in a more exothermic AHP compared to the bulk polymerization. 

More recent experiments proving the presence of very large rings in step reactions and a discussion of the role of ring formation in step polymerization are summarized by Kricheldorf HR (2003) The Role of Ring-ring Equilibria in Thermodynamically Controlled Polycondensation, Macromol Symp 199 15-22 see also other papers in the same issue and the introduction What Does Polycondensation Mean Ibid pp 1-13. 

Thermodynamics of Step Polymerization Many step polymerizations involve equilibrium reactions. Consider a simple polyesterification where carboxyl groups and hydroxyl groups react to form a polyester and water see Section 1.4.2. The equilibrium constant, K, is given schematically by... 

The Fischer glycosidation may be described as a process in which, in a first step, the dextrose reacts relatively quickly and an ohgomer equilibrium is reached. This step is followed by slow degradation of the alkyl polyglycoside. In the course of the degradation, which consists of dealkylation and polymerization steps, the thermodynamically more stable polydextrose is formed substantially irreversibly in increasing concentrations. Reaction mixtures which have exceeded an optimal reaction time may be described as overreacted. ... 

The initiators which are used in addition polymerizations are sometimes called catalysts, although strictly speaking this is a misnomer. A true catalyst is recoverable at the end of the reaction, chemically unchanged. Tliis is not true of the initiator molecules in addition polymerizations. Monomer and polymer are the initial and final states of the polymerization process, and these govern the thermodynamics of the reaction the nature and concentration of the intermediates in the process, on the other hand, determine the rate. This makes initiator and catalyst synonyms for the same material The former term stresses the effect of the reagent on the intermediate, and the latter its effect on the rate. The term catalyst is particularly common in the language of ionic polymerizations, but this terminology should not obscure the importance of the initiation step in the overall polymerization mechanism. 

Another factor in step-growth polymerizations is cyclization versus linear polymerization.1516 Since ADMET is a step-growth polymerization, most reactions are carried out in the bulk using high concentrations of the reactant in order to suppress most cyclic formation. A small percentage of cyclic species is always present but is dependent upon thermodynamic factors, typical of any polycondensation reaction. 

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 industrial process for which this methodology was developed comprised polymerizing a monomer in the presence of a mixed solvent, the catalyst and other Ingredients. Once the batch polymerization is complete, the product requires removal of the solvents to a specified level. The solvents, an aromatic Cy and aliphatic Cy compounds, are removed by a two-step process schematically shown in Figure 1. As shown, the polymer slurry is initially flashed to a lower pressure (Pj ) in the presence of steam and water. The freely available solvent in the polymer-solvent mixture is removed by the shift in thermodynamic equilibrium. Solvent attached to the surface of the polymer particle is removed by the steam. In this first step, 90% of the total solvents are recovered. The remaining solvents are recovered in the second flash, where the effluent is almost all water with very low concentrations of the solvents. 

The actual SFE extraction rate is determined by the slowest of these three steps. Identification of the ratedetermining step is an important aspect in method development for SFE. The extraction kinetics in SFE may be understood by changing the extraction flow-rate. Such experiments provide valuable information about the nature of the limiting step in extraction, namely thermodynamics (i.e. the distribution of the analytes between the SCF and the sample matrix at equilibrium), or kinetics (i.e. the time required to approach that equilibrium). A general strategy for optimising experimental parameters in SFE of polymeric materials is shown in Figure 3.10. 

When a compound that can form several modifications crystallizes, first a modification may form that is thermodynamically unstable under the given conditions afterwards it converts to the more stable form (Ostwald step rule). Selenium is an example when elemental selenium forms by a chemical reaction in solution, it precipitates in a red modification that consists of Se8 molecules this then converts slowly into the stable, gray form that consists of polymeric chain molecules. Potassium nitrate is another example at room temperature J3-KN03 is stable, but above 128 °C a-KNOs is stable. From an aqueous solution at room temperature a-KN03 crystallizes first, then, after a short while or when triggered by the slightest mechanical stress, it transforms to )3-KN03. 

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