Melting isotherm

The dashed line represents an idealized process in which all solid is heated to the freezing point and then all the sample is melted isothermally. The two lines, QO and OS, are thus separate specific-heat and melting components for the actual process. The flat line, OS, represents the melting of the two substances, solvent and solute, with different heats of fusion. However, for most substances studied, the amount of solute is always small so that on the central part of the curve, which is used for analysis, the fraction of material melted is proportional to the distance along OS. 

But, when the curvature of the interface becomes very strong the Gibbs-Thomson effect close to the crucible wall has to be taken into account [55]. The consequence is that the phase boundary must not follow completely the melting isotherm and an extended undercooled region exists in front of the solid/liquid interface that also increases the probability for defect formation as shown in Fig. 5.17. The extension of the undercooled region can be expressed by, for example, increasing the temperature gradient in front of the solid/liquid interface. 

Fig. 5.17 Schematic view of the interface shape close to the crucibie waii. For a strong curvature of the melting isotherm, the Gibbs-Thompson effect may be of importance. Therefore, the phase boundary is not identicai to the melting isotherm and an undercooied region ciose to the crucible wall may develop.

Thermodynamic Properties. The thermodynamic melting point for pure crystalline isotactic polypropylene obtained by the extrapolation of melting data for isothermally crystallized polymer is 185°C (35). Under normal thermal analysis conditions, commercial homopolymers have melting points in the range of 160—165°C. The heat of fusion of isotactic polypropylene has been reported as 88 J/g (21 cal/g) (36). The value of 165 18 J/g has been reported for a 100% crystalline sample (37). Heats of crystallization have been determined to be in the range of 87—92 J/g (38). 

Other crystallization parameters have been determined for some of the polymers. The dependence of the melting temperature on the crystallization temperature for the orthorhombic form of POX (T = 323K) and both monoclinic (T = 348K) and orthorhombic (T = 329K) modifications of PDMOX has been determined (284). The enthalpy of fusion, Aff, for the same polymers has been determined by the polymer diluent method and by calorimetry at different levels of crystallinity (284). for POX was found to be 150.9 J/g (36.1 cal/g) for the dimethyl derivative, it ranged from 85.6 to 107.0 J/g (20.5—25.6 cal/g). Numerous crystal stmcture studies have been made (285—292). Isothermal crystallization rates of POX from the melt have been determined from 19 to —50 C (293,294). Similar studies have been made for PDMOX from 22 to 44°C (295,296). 

Based on differences in melting points and Hquid-phase solubilities four modes of operation possible drown-out, isothermal evaporation, adiabatic evaporation, and cooling (choice depends on stream characteristics). 

Zone refining is one of a class of techniques known as fractional solidification in which a separation is brought about by crystallization of a melt without solvent being added (see also Crystallization) (1 8). SoHd—Hquid phase equiUbria are utilized, but the phenomena are much more complex than in separation processes utilizing vapor—Hquid equiHbria. In most of the fractional-solidification techniques described in the article on crystallization, small separate crystals are formed rapidly in a relatively isothermal melt. In zone refining, on the other hand, a massive soHd is formed slowly and a sizable temperature gradient is imposed at the soHd—Hquid interface. 

We developed a sensor for determination of content of phosphorars in metallurgical melts. In quality of ion conductor used orthophosphate of calcium which pressed in tablets 010 mm. Tablets (mass 1-2 g) annealed at a temperature 400°C during 7-10 h. Tablets melts then in a quartz tube and placed the alloy of iron containing 1 mass % P. Control of sensor lead on Fe - P melts. Information on activities (effective concentration) of phosphorars in Fe - P melts was received. It is set that the isotherm of activity of phosphorars shows negative deviations from the Raouls law. Comparison them with reliable literary inforiuation showed that they agree between itself. Thus, reliable data on activities (effective concentration) of phosphorars in metallic melts it is possible to received by created electrochemical sensor for express determination. 

As discussed in the previous section, it is convenient to consider the output from the extruder as consisting of three components - drag flow, pressure flow and leakage. The derivation of the equation for output assumes that in the metering zone the melt has a constant viscosity and its flow is isothermal in a wide shallow channel. These conditions are most likely to be approached in the metering zone. 

In practice there are a number of other factors to be taken into account. For example, the above analysis assumes that this plastic is Newtonian, ie that it has a constant viscosity, r). In reality the plastic melt is non-Newtonian so that the viscosity will change with the different shear rates in each of the three runner sections analysed. In addition, the melt flow into the mould will not be isothermal - the plastic melt immediately in contact with the mould will solidify. This will continuously reduce the effective runner cross-section for the melt coming along behind. The effects of non-Newtonian and non-isothermal behaviour are dealt with in Chapter 5. 

Example 5.4 Eight polypropylene mouldings, each weighing 10 g are to be moulded using the runner layout shown in Fig. 5.19. If the injection time is 2 seconds and the melt temperature is 210°C, calculate the pressure at each cavity if the injection pressure at the sprue is 80 MN/m. The density of the pwlypropylene is 909 kg/m3 and the volume of the sprue is 5000 mm. Assume that the flow is isothermal and ignore the pressure losses at comers. 

Solution (a) Isothermal Situation. If the volume flow rate is Q, then for any increment of time, dt, the volume of material injected into the cavity will be given by Qdt). During this time period the melt front will have moved from a radius, r, to a radius (r -I- dr). Therefore a volume balance gives the relation... 

However, in the non-isothermal case the pressure is also high at low injection rates. This is because slow injection gives time for significant solidification of the melt and this leads to high pressures. It is clear therefore that in the non-isothermal case there is an optimum injection rate to give minimum pressure. In Fig. 5.28 this is seen to be about 3.0 x 10 m /s for the situation considered here. This will of course change with melt temperature and mould temperature since these affect the freeze-off time, //, in the above equations. 

A polymer melt is injected into a circular section channel under constant pressure. What is the ratio of the maximum non-isothermal flow length to the isothermal flow length in the same time for (a) a Newtonian melt and (b) a power law melt with index, n = 0.3. 

CORCON initially assumes that the molten core debris is stratified as a dense oxidic layer on the bottom and a less dense metallic layer on the top. Later, when molten concrete slag dilutes the heavy oxide layer, the lighter oxide layer than the metal layer rises to the top. Each layci is assumed to be isothermal and heat is exchanged between (1) the melt and the concrete, (2) layers of the melt, and (3) the top surface of the melt and the atmosphere above it. When the concrete heats up to about 2500 F, CORCON predicts the release of steam and COj from concrete decomposition. Tile lieat of reaction of the gases reacting with the materials of the melt are calculated. 

Figure 4 DSC melting endotherms of P7MB after isothermal crystallization at 135°C, starting from the isotropic melt [10]. The curves correspond to 0, 3,6, and 35 min of crystallization time, from bottom to top. Scanning rate 5°C/min.

Mass-transfer deposits can lead to blockages in non-isothermal circulating systems, cis in the case of liquid-metal corrosion. In fused salts, the effect can be reduced by keeping contamination of the melt by metal ions to a minimum e.g. by eliminating oxidising impurities or by maintaining reducing conditions over the melt . 

For example, in the case of the reversible isothermal transformation of ice to water at the melting point (273 K), the heat gained by the ice will be the latent heat of fusion (A//f = 6(X)6 J mol" ) and a corresponding quantity of heat will be lost by the surrounding, and... 

Molten salt investigation methods can be divided into two classes thermodynamic and kinetic. In some cases, the analysis of melting diagrams and isotherms of physical-chemical properties such as density, surface tension, viscosity and electroconductivity enables the determination of the ionic composition of the melt. Direct investigation of the complex structure is performed using spectral methods [294]. 

Physicochemical properties of molten systems have an applied significance due to their wide use in both technological process planning and in production equipment design. Analysis of various melt properties versus different parameters of the melt enables to infer the interaction mechanism between the initial components, and in some cases, even to estimate the possible composition of the main complex ions formed in the melt [312]. From this point of view, the analysis of isotherms of physicochemical properties versus melt composition and of the magnitude of their deviation from ideal conditions is of most interest. 

The results were presented in the form of isotherms, in which the properties are plotted versus the concentration. Nevertheless analysis of the isotherms was made based on available melting diagrams approach that the melts consist of TaFg3 and TaF7Cl3 complex ions. However, according to this general conception [312-314], the isotherm of the surface tension must, in such a case, have either a minimum or at least display prominence of the dependence in the direction of the concentration axis. 

Fig. 60. Isotherms (800°C) of molar volume (top) (after Agulyansky et al. [322]) and specific conductivity (bottom) (after Agulyansky et al. [3241) of the melts KF- K2TaF7 (I) andKCl - K2TaF7 (2).

Such a model of the melt structure does not contradict conductivity data [324], if plotted against the composition of the KF - TaF5 system. Fig. 63 presents isotherms of molar conductivity, in which molar conductivity of the ideal system was calculated using Markov s Equation [315], and extrapolation... 

The specific concave shape of the isotherms of the properties of KC1 -K2TaF7 melts can be explained by the following ligand-replacement interaction ... 

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