Heat-of-transition rule

As indicated in Figs 2.3-2.5, A// and AG are usually positive, and it is assumed that the H curves do not intersect. Also as discussed above, the G curves intersect only once. This set of circumstances leads to a statement of the heat-of-transition rule (Grunenberg et al. 1996 Burger and Ramberger 1979a)  

If an endothermic phase change is observed at a particular temperature, the transition point hes below that temperature, and the two polymorphs are enantiotropically related. If an exothermic transition is observed, then there is no thermodynamic transition point below that transition temperature. This can occur when the two modifications are monotropicaUy related or when they are enantiotropically related and the thermodynamic transition point is higher than the measured transition temperature. 

Burger and Ramberger (1979ft) claim that this rule is observed in at least 99 per cent of the cases examined. 

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A number of empirical rules have been proposed to deduce the relative order of stability of polymorphs and the nature of the process that interconverts these (i.e., enantiotropy vs. monotropy). Among the better known are the Heat of Transition Rule, which states that if an endothermic transition is observed at some temperature, it may be assumed that there must be a transition point located at a lower temperature where the two forms bear an enantiotropic relationship. Conversely, if an exothermic transition is noted at some temperature, it may be assumed that there is no transition point located at a lower temperature. This in turn implies that either the two forms bear a monotropic relationship to each other or that the transition temperature is higher than the temperature of the exotherm. 

Heat of transition rule If an endothermic transition is observed at some temperature below the melting point, it may be assumed that there are two forms related enantiotropically. If an exothermic transition is observed below the melting point, it may be assumed that there are two forms related monotropically or the transition temperature is higher. 

To help decide whether two polymorphs are enantiotropes or monotropes. Burger and Ramberger developed four thermodynamic rules [14]. The application of these rules was extended by Yu [15]. The most useful and applicable of the thermodynamic rules of Burger and Ramberger are the heat of transition rule and the heat of fusion rule. Figure 11, which includes the liquid phase as well as the two polymorphs, illustrates the use of these rules. The heat of fusion rule states that, if an endothermic polymorphic transition is observed, the two forms are enantiotropes. Conversely, if an exothermic polymorphic transition is observed, the two forms are monotropes. 

The above conditions, that are implicit in the thermodynamic rules, are summarized in Table 4. The last two rules in Table 4, the infrared rules, and the density rule, were found by Burger and Ramberger [14] to be significantly less reliable than the heat of transition rule and the heat of fusion rule and are therefore not discussed here. 

The heat of transition rule states that, if an endothermic phase transition is observed at a particular temperature, the... 

The second group involves polymers with three-dimensional ordering of side branches (e.g., those forming Mj-phaseXTable 5). On X-ray patterns of these polymers 3-4 narrow reflexes at wide angles are observed. As a rule, the authors define this type of structure as crystalline, or ascribe a smectic type of structure, characteristic for ordered smectics in SE or SH phases. The heats of transition from anisotropic state to isotropic melt are usually small and do not exceed the heats of transition smectic liquid crystal — isotropic melt . The similarity of structural parameters of three-dimensionally ordered smectics and that of crystalline polymers of the type here considered, make their correct identification quite a difficult task. 

General Rules for Thermal Analysis Testing Methods of Plastics by Thermogravimetry Testing Methods for Transition Temperatures of Plastics Testing Methods for Heat of Transition of Plastics Testing Methods for Specific Heat Capacity of Plastics... 

Primary explosives are substances which unlike secondary explosives show a very rapid transition from combustion (or deflagration) to detonation and are considerably more sensitive towards heat, impact or friction than secondary explosives. Primary explosives generate either a large amount of heat or a shockwave which makes the transfer of the detonation to a less sensitive secondary explosive possible. They are therefore used as initiators for secondary booster charges (e.g. in detonators), main charges or propellants. Although primary explosives (e.g. Pb(N3)2) are considerably more sensitive than secondary explosives (e.g. RDX), their detonation velocities, detonation pressures and heat of explosions are as a rule, generally lower than those of secondary explosives (Tab. 2.1). 

In Section A.l, the general laws of thermodynamics are stated. The results of statistical mechanics of ideal gases are summarized in Section A.2. Chemical equilibrium conditions for phase transitions and for reactions in gases (real and ideal) and in condensed phases (real and ideal) are derived in Section A.3, where methods for computing equilibrium compositions are indicated. In Section A.4 heats of reaction are defined, methods for obtaining heats of reaction are outlined, and adiabatic flame-temperature calculations are discussed. In the final section (Section A.5), which is concerned with condensed phases, the phase rule is derived, dependences of the vapor pressure and of the boiling point on composition in binary mixtures are analyzed, and properties related to osmotic pressure are discussed. 

V. Rothmund showed that in the general case of solid soln., the effect of a solute on the transition temp, of the solvent is analogous to the cryoscopic effect of a liquid soln., and the depression of the transition temp, is given by Oq—Oi =RT IQ(C2 Ci), where 6q and 61 denote the transition temp, of ammonium nitrate before and after the addition of potassium nitrate T, the absolute transition, temp, of ammonium nitrate alone Cq and Oi, the mol, cone, of potassium nitrate in 100 grms. of the two modifications of ammonium nitrate, and Q is the heat of transformation of ammonium nitrate. The results with potassium and ammonium nitrates are in accord with V. Rothmund s rule, and, at 32°, there is a change of quadruple into triple molecules 3(NH4N03)4= 4(NH4N03)3. 

In selective separation of hydrocarbons from their mixtures with air or from their aqueous solutions, it makes sense to use membranes based on rubbery polymers, whose permeability increases with the decrease in glass transition point. Permselectivity of rubbery polymers is dominated by the sorption component, which increases with condensability of the hydrocarbon penetrant. Higher activity of the component being separated in the feed mixture results in plasticization of the membrane and can make it swell. This can produce a non-monotonic dependance of selective properties of the membrane on activity of the component being separated. As a rule, permselectivity for mixtures of penetrants is significantly lower than their ideal values. Negative values of sorption heat of easily condensable hydrocarbons can result in existence of non-monotonic temperature dependencies of mass transfer coefficients. 

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