Melting first-order

Tra.nsitions and Relaxations. Only one first-order transition is observed, the melting poiat. Increasing the pressure raises mp. At low pressure, the rate of iacrease ia the melting poiat is ca 1.74°C/MPa (0.012°C/psi) at high pressures this rate decreases to ca 0.725°C/MPa (0.005°C/psi). Melting iacreases the volume by 8%. la the preseace of the HFP comonomer, crystal distortioa occurs with an iacrease ia iatramolecular distance that, ia turn, reduces the melting poiat (54). 

Decompositions may be exothermic or endothermic. Solids that decompose without melting upon heating are mostly such that can give rise to gaseous products. When a gas is made, the rate can be affected by the diffusional resistance of the product zone. Particle size is a factor. Aging of a solid can result in crystallization of the surface that has been found to affect the rate of reaction. Annealing reduces strains and slows any decomposition rates. The decompositions of some fine powders follow a first-order law. In other cases, the decomposed fraction x is in accordance with the Avrami-Erofeyev equation (cited by Galwey, Chemistry of Solids, Chapman Hall, 1967)... 

Organic Solids A few organic compounds decompose before melting, mostly nitrogen compounds azides, diazo compounds, and nitramines. The processes are exothermic, classed as explosions, and may follow an autocatalytic law. Temperature ranges of decomposition are mostly 100 to 200°C (212 to 392°F). Only spotty results have been obtained, with no coherent pattern. The decomposition of malonic acid has been measured for both the solid and the supercooled liquid. The first-order specific rates at 126.3°C (259.3°F) were 0.00025/min for solid and 0.00207 for liquid, a ratio of 8 at II0.8°C (23I.4°F), the values were 0.000021 and 0.00047, a ratio of 39. The decomposition of oxalic acid (m.p. I89°C) obeyed a zero-order law at 130 to I70°C (266 to 338°F). 

Ammonium nitrate decomposes into nitrous oxide and water. In the solid phase, decomposition begins at about I50°C (302°F) but becomes extensive only above the melting point (I70°C) (338°F). The reaction is first-order, with activation energy about 40 kcal/g mol (72,000 Btii/lb mol). Traces of moisture and Cr lower the decomposition temperature thoroughly dried material has been kept at 300°C (572°F). All oxides of nitrogen, as well as oxygen and nitrogen, have been detected in decompositions of nitrates. 

Figure 13.6 shows the influence of temperature on specific volume (reciprocal specific gravity). The exaet form of the eurve is somewhat dependent on the crystallinity and the rate of temperature change. A small transition is observed at about 19°C and a first order transition (melting) at about 327°C. Above this temperature the material does not exhibit true flow but is rubbery. A melt viseosity of 10 -10 poises has been measured at about 350°C. A slow rate of decomposition may be detected at the melting point and this increases with a further inerease in temperature. Processing temperatures, exeept possibly in the case of extrusion, are, however, rarely above 380°C. 

In another study Milehev and Landau [27] investigated in detail the transition from a disordered state of a polydisperse polymer melt to an ordered (liquid erystalline) state, whieh oeeurs in systems of GM when the ehains are eonsidered as semiflexible. It turns out that in two dimensions this order-disorder transition is a eontinuous seeond-order transformation whereas in 3d the simulational results show a diseontinuous first-order transformation. Comprehensive finite-size analysis [27] has established... 

The Pink model is found to exhibit a gel-fluid transition for lipids with sufficiently long chains, which is weakly first order. The transition disappears in bilayers of shorter lipids, but it leaves a signature in that one observes strong lateral density fluctuations in a narrow temperature region [200,201]. In later studies, the model has been extended in many ways in order to explore various aspects of gel-fluid transitions [202]. For example, Mouritsen et al. [203] have investigated the interplay between chain melting and chain crystallization by coupling a two-state Doniach model or a ten-state Pink model to a Potts model. (The use of Potts models as models for... 

An intrinsic surface is built up between both phases in coexistence at a first-order phase transition. For the hard sphere crystal-melt interface [51] density, pressure and stress profiles were calculated, showing that the transition from crystal to fluid occurs over a narrow range of only two to three crystal layers. Crystal growth rate constants of a Lennard-Jones (100) surface [52] were calculated from the fluctuations of interfaces. There is evidence for bcc ordering at the surface of a critical fee nucleus [53]. 

Many metals and metallic alloys show martensitic transformations at temperatures below the melting point. Martensitic transformations are structural phase changes of first order which belong to the broader class of diffusion js solid-state phase transformations. These are structural transformations of the crystal lattice, which do not involve long-range atomic movements. A recent review of the properties and the classification of diffusionless transformations has been given by Delayed... 

Melting of ECC involving transition into the isotropic melt was shown by Flory to be a first-order process. It can be seen in Fig. 18 b that there occurs a transition from a complete order to a fully random chain arrangement in the isotropic melt (Fig. 16, point 4). 

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

Following three phase transformations [951] (>298 K), NH C decomposition begins [915] in the solid phase at 423 K but only becomes extensive well above the melting point ( 440 K). Decomposition with the evolution of N20 and H20 from the melt is first order [952,953] (E = 153—163 kJ mole-1), the mechanism suggested involving intermediate nitramide formation. Other proposed schemes have identified NOj [954] or the radical NH2NO [955] (<473 K) as possible participants. Studies [956,957] have been made of the influence of additives on NH C decomposition. 

The heat loss to the melting polymer was assumed (for a first order approximation) to be negligible compared to the heat loss by convection. This is one area of the model which could profit from more study to determine the exact magnitude of energy exchange with the polymer. 

Dm (and Du) vary inversely with reciprocal temperature (Fig. 15). For mantle solidus garnets the correlation is reasonably good and can be used to make a first-order estimate of Dm- A more comprehensive model for Du and Dm, as a function of pressure, temperature and melt composition is provided by Salters et al. (2002). Their full expressions (for the molar partition coefficients, D ) are ... 

Pure parathion is a pale yellow, practically odorless oil, which crystallizes in long white needles melting at 6.0° C. (17). It is soluble in organic solvents, except kerosenes of low aromatic content, and is only slightly soluble in water (15 to 20 p.p.m. at 20° to 25° C.). Peck (35) measured its rate of hydrolysis to diethyl thiophosphate and nitro-phenate ions in alkaline solutions. He found that the reaction kinetics are first order with respect to the ester and to hydroxyl ion. In normal sulfuric acid the rate of hydrolysis was the same as in distilled water. Peck concluded that hydrolysis takes place by two mechanisms—a reaction catalyzed by hydroxyl ions and an independent uncatalyzed reaction with water. He calculated that at a pH below 10 the time for 50% hydrolysis at 25° C. is 120 days in the presence of saturated lime water the time is 8 hours. The over-all velocity constant at 25° C. is k = 0.047 [OH-] + 4 X 10-6 min.-1... 

It has to be noticed that no isothermal volume contraction on cooling or volume expansion on heating is associated with Tg, contrary to crystallisation or melting. The latter is a true first-order transition exhibiting a discontinuity in... 

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