Polymerization free enthalpy

The dissolution reaction (change in free enthalpy Ag1 ) implies the breaking of too Si-O-Si bonds ( per silicon atom) and the formation of four silanol groups (Kith disappearance of tno Hater molecules). On the other hand the polymerization reaction (change in free enthalpy AG) corresponds to the formation of a Si-0-Si bond (and a Hater molecule) and to the disappearance of tno silanol groups. It can thus be nritten to a first approximation ... 

Formation of polymers is governed by thermodynamic and kinetic factors (see also Section 2.3). The free enthalpy of polymerization is an important parameter, which is known for various monomers. Tables with values for AH° and AS are given in literature [4]. Several values for AH for the formation of some polymers having in the backbone chain only carbon atoms are given in Table 2.2.1 (1 cal = 4.1868 J international, 1 cal = 4.184 J thermochemical). Some of the values are given for ideal gas phase, although few monomers and no polymers are in gas phase. Since in a reaction the reactant and the product can be in different aggregation states, the state of both participants must be indicated. 

Basically, the free enthalpy of polymerization from ethene up to n-olefin is obtained ... 

The ability to generate groups (intermediates) with high free enthalpy to drive polymerization or growth processes, e.g., by formation of H2O. 

For the understanding of thermal analysis, it is necessary to recognize that most encountered polymeric systems are not in equilibrium, may be micro- or nanophase separated, and could even be not homogeneous. In order to describe such situations, one has to turn to nonequdibrium, irreversible thermodynamics. Functions of state such as entropy and free enthalpy are defined for systems in global equilibrium. Some others, such as mass, volume, and total energy, on the other hand, are largely indifferent to equilibrium. They need special treatment to be used for the description of nonequilibrium situations which arise when deviating from the free enthalpy minimum characteristic for equilibrium, as shown in Fig. 2.79. The four possible functional forms of the free enthalpy lead to stable, metastable, neutral, and labile equilibria. 

In case the reverse of the polymerization, the depolymerization, is significant, a more complicated kinetics describes the chain reactions. Figure 3.30 shows the scheme. If rates of the forward and reverse reactions become the same, equilibrium is reached. The equilibrium temperature is called the ceiling temperature, T (at a given concentration or vapor pressure [A]). Standard thermodynamics applies to this equilibrium (see Chap. 2). On depolymerization, the entropy of the system, S, increases because the number of molecules increases. With a positive AS, a T must exist at sufficiently high temperature, since one can write AG = AH - TAS, where AG is the Gibbs function or free enthalpy and AH, the enthalpy of the reaction. 

Polyethylene data are shown in Fig. 2.23. At the equilibrium melting temperature of 416.4 K, the heat of fusion and entropy of fusion are indicated as a step increase. The free enthalpy shows only a change in slopes, characteristic of a first-order transition. Actual measurements are available to 600 K. The further data are extrapolated. This summary allows a close connection between quantitative DSC measurement and the derivation of thermodynamic data for the limiting phases, as well as a connection to the molecular motion. In Chaps. 5 to 7 it will be shown that this information is basic to undertake the final quantitative step, the analysis of nonequilibrium states as are common in polymeric systems. 

Basic to the thermodynamic description is the heat capacity which is defined as the partial differential Cp = (dH/dT)n,p, where H is the enthalpy and T the temperature. The partial differential is taken at constant pressure and composition, as indicated by the subscripts p and n, respectively A close link between microscopic and macroscopic description is possible for this fundamental property. The integral thermodynamic functions include enthalpy H entropy S, and free enthalpy G (Gibbs function). In addition, information on pressure p, volume V, and temperature T is of importance (PVT properties). The transition parameters of pure, one-component systems are seen as first-order and glass transitions. Mesophase transitions, in general, were reviewed (12) and the effect of specific interest to polymers, the conformational disorder, was described in more detail (13). The broad field of multicomponent systems is particularly troubled by nonequilibrium behavior. Polymerization thermodynamics relies on the properties of the monomers and does not have as many problems with nonequilibrium. 

A chain polymerization implies that the active species formed upon addition or insertion of the last monomer molecule is of the same nature as the original one. Such chain growth also entails the formation of at least two covalent bonds between other monomer units. In view of the previously mentioned thermodynamic constraints, a negative variation of the free enthalpy of polymerization is another imperative to fulfill. These two conditions considerably restrict the variety of the organic compounds that can be polymerized, and only two main categories of monomers meet these criteria ... 

As for the reactivity (polymerizability), the situation is different from that of initiation. Indeed, the new free radical active center formed after monomer insertion in the polymeric chain is roughly identical to the last formed one. Thus, its formation does not entail an increase of stability. The negative variation of the free enthalpy is only due to the exothermic transformation of the monomer molecule into a monomeric unit. The stabilizing power of the substituent A carried by the double bond is exerted not only on the active center formed after addition but also on the monomer molecule. Logically, a progressive decrease of kp is observed with the increase of the stabilizing power of substituents A (see Table 8.5). 

The formal thermodynamic criterion of a given monomer polymerizability is related to a sign of the free enthalpy (called also Gibbs energy) of polymerization (cf. Equation 1.1) ... 

The free enthalpy of polymerization (AGp) may be ejcpressed as a sum of standard enthalpy of polymerization (AG°) and a term related to instantaneous monomer molecules and growing macromolecules concentrations ... 

In the kinetically controlled regime, the chain propagation reaction is predominant and a high molecular-weight polymer (P ) is formed (Equation 12.1). The monomer-polymer equiUbrium (Equation 12.2) is characterized by the equilibrium constant (K) which is approximately equal to the inverse equilibrium monomer concentration ([M]e) (Equation 12.3). Equation 12.4 relates the equilibrium monomer concentration and the free enthalpy of polymerization (AG°). For standard conditions ([M]o = 1 mol L ) and above a critical temperature, no polymer is obtained. The critical temperature is defined as ceihng temperature (Tc) when both AH° and AS° are negative (Equation 12.5). 

Nxylylene system, substituents affect it only to a minor extent. AH parylenes are expected to have a similar molar enthalpy of polymerization. An experimental value for the heat of polymerization of Parylene C has appeared. Using the gas evolution from the Hquid nitrogen cold trap to measure thermal input from the polymer, and taking advantage of a peculiarity of Parylene C at — 196°C to polymerize abmptiy, perhaps owing to the arrival of a free radical, a = —152 8 kJ/mol (—36.4 2.0 kcal/mol) at — 196°C was reported (25). The correction from — 196°C to room temperature is... 

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