Nucleation enthalpy

Availability change to form embryo Initial bubble diameter Frequency factor in nucleation Enthalpy of vaporization Rate of formation of critical-sized embryos per unit volume Jacob numter [Eq. (17)] Boltzmann s constant or thermal conductivity... 

Physical properties of the acid and its anhydride are summarized in Table 1. Other references for more data on specific physical properties of succinic acid are as follows solubiUty in water at 278.15—338.15 K (12) water-enhanced solubiUty in organic solvents (13) dissociation constants in water—acetone (10 vol %) at 30—60°C (14), water—methanol mixtures (10—50 vol %) at 25°C (15,16), water—dioxane mixtures (10—50 vol %) at 25°C (15), and water—dioxane—methanol mixtures at 25°C (17) nucleation and crystal growth (18—20) calculation of the enthalpy of formation using semiempitical methods (21) enthalpy of solution (22,23) and enthalpy of dilution (23). For succinic anhydride, the enthalpies of combustion and sublimation have been reported (24). 

Since a can be separated from the propagation step only because it is independent of temperature, additional influences which may exist remain undiscovered as far as they are connected with a gain or a loss of enthalpy (forces between the single chains and interactions with solvent). A possibly appearing effect of enthalpy, which occurs only during nucleation is then distributed among the propagation steps. 

The melt mixed 80/20 PS/iPP blend displays a set of exotherms, where the amount of the iPP component that was heterogeneously nucleated is substantially reduced as indicated by the decrease of the crystallization enthalpy in the temperature region where the iPP crystallizes in bulk, i.e., at 109-111 °C (exotherm labeled A). This effect is due to the confinement of iPP into a large number of droplets. If the number of droplets of iPP as a dispersed phase is greater than the number of heterogeneities present in the system, fractionated crystallization occurs. The number of droplets for this composition is known (by scanning electron microscopy observations) to be of the order of 1011 particles cm-3 and polarized optical microscopy (POM) experiments have shown that this iPP contains approximately 9 x 106 heterogeneities cm-3. In fact, it can be seen in Fig. 1 that the fractionated crystallization of the iPP compon-... 

Nucleation is defined as the point where the protonucleus is sufficiently large that its surface area to volume ratio exceeds a critical point, and further growth results in a reduction in global free energy surface effects are now small compared to the inside of the crystal. This is the point where enthalpy dominates over entropy. Subsequent crystal growth and further nucleation events will occur until thermodynamic equilibria is reached, as defined by Eq. 3. The rate of nucleation is defined as the rate at which clusters grow through this critical point. 

As is well known (Morse and Berner, 1972) even very small concentrations of HPO (and some organic solutes) inhibit nucleation of CaC03, most likely because these adsorbates block essential surface sites on the substrate or on the mineral clusters. Mg2+ is known to inhibit many nucleation processes, especially also the nucleation of Mg bearing minerals. The water exchange rate of Mg2+ is slower than that of many cations, such as Pb2+, Cu2+, Zn2+, Cd2+, Ca2+. The inhibition effect of Mg2+ may be due to its sluggishness to (partial) dehydration. (Mg2+ has among the bivalent ions a very large enthalpy (-AHj,) of hydration.)... 

Once a particular class of unit has been decided upon, the choice of a specific unit depends on initial and operating costs, the space available, the type and size of the product, the characteristics of the feed liquor, the need for corrosion resistance and so on. Particular attention must be paid to liquor mixing zones since the circulation loop includes many regions where flow streams of different temperature and composition mix. These are all points at which temporary high supersaturations may occur causing heavy nucleation and hence encrustation, poor performance and operating instabilities. As Toussaint and Donders(72) stresses, it is essential that the compositions and enthalpies of mixer streams are always such that, at equilibrium, only one phase exists under the local conditions of temperature and pressure. 

A second-order phase transition is one in which the enthalpy and first derivatives are continuous, but the second derivatives are discontinuous. The Cp versus T curve is often shaped like the Greek letter X. Hence, these transitions are also called -transitions (Figure 2-15b Thompson and Perkins, 1981). The structure change is minor in second-order phase transitions, such as the rotation of bonds and order-disorder of some ions. Examples include melt to glass transition, X-transition in fayalite, and magnetic transitions. Second-order phase transitions often do not require nucleation and are rapid. On some characteristics, these transitions may be viewed as a homogeneous reaction or many simultaneous homogeneous reactions. 

The classical theory [50,52,53,55] expresses the change in free enthalpy (A/x) resulting from the nucleation phenomena Equation 1 has a positive contribution from the interface free energy (ySg, which takes into account the generation and stabilization of an interface), and a negative contribution... 

The isothermal crystallization of PEO in a PEO-PMMA diblock was monitored by observation of the increase in radius of spherulites or the enthalpy of fusion as a function of time by Richardson etal. (1995). Comparative experiments were also made on blends of the two homopolymers. The block copolymer was observed to have a lower melting point and lower spherulitic growth rate compared to the blend with the same composition. The growth rates extracted from optical microscopy were interpreted in terms of the kinetic nucleation theory of Hoffman and co-workers (Hoffman and Miller 1989 Lauritzen and Hoffman 1960) (Section 5.3.3). The fold surface free energy obtained using this model (ere 2.5-3 kJ mol"1) was close to that obtained for PEO/PPO copolymers by Booth and co-workers (Ashman and Booth 1975 Ashman et al. 1975) using the Flory-Vrij theory. 

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