Melting points, models

Fig. 3.4. Biichi Melting Point Apparatus. Biichi Melting Point Models B-540 and B-545 can determine melting points on routine and non-routine substances in research and quality control labs of pharmaceutical and chemical companies. Both models have a temperature range from ambient to 400°C and a selection of nine heating speeds. Heating (from 50 to 350°C) takes approximately 7 min and cooling (from 350 to 50°C) takes approximately 10 min. The units can simultaneously determine melting points of three samples or two...

Source Data from K. J. Burch and E. G. Whitehead, Melting Point Models of Alkanes, Journal of Chemical and Engineering Data 49(4) 858-863 (2004). 

In order to develop a melting point model a dataset was created from prior published sources. Melting points from the PHYSPROP database [40] and from the work of Karthikeyan and coworkers [41] were combined. However, we had to find out that this combined dataset contains a significant amount of noise, plainly speaking basically questionable entries. Thns, suspect data points were ranoved or corrected resulting in a dataset containing the melting point and SMILES of more than 12,(XX) compounds. 

For this specific melting point model 14 variables have been selected by iterative forward selection (Fig. 9.4), yielding an overall accuracy (RMSE) after fivefold cross-validation of 41.2 K (Table 9.4). 

Melting points modeling of complex halides of AsBX type 0.356 0.816... 

In the previous chapters, the dissolution and micellization of surfactants in aqueous solutions were discussed from the standpoint of the degrees of freedom as given by the phase rule. The mass-action model for micelle formation was found to be better for explaining the phenomena of surfactant solutions than the phase-separation model. Two models have similarly been used to explain the Krafft point, one postulating a phase transition at the Krafft point and the other a solubility increase up to the CMC at the Krafft point. The most recent version of the first approach is a melting-point model for a hydrated surfactant solid. The most direct approach to the second model of the Krafft point rests entirely on measurements of the solubility and CMC of surfactants with temperature. From these mesurements the concept of the Krafft point can be made clear. This chapter first reviews the concepts used to relate the dissolution of surfactants to their micellization, and then shows that the concept of a micelle temperature range (MTR) can be used to elucidate various phenomena concerning dissolution... 

Another approach to the Krafft point is the melting-point model of a hydrated solid surfactant. In this model, the solubility curve represents the hydrated surfactant solid below the Krafft point and the melted surfactant phase above it. If the micelle is regarded as a phase, the system must be invariant (/ = 0) at the Krafft point because four phases (intermicellar bulk phase, hydrated surfactant solid phase, melted surfactant phase, and micellar phase) coexist for two components. However, experimental evidence shows that the CMC changes with pressure. 

Even if the micelle is regarded as a chemical species, the melting-point model is not correct. In this case, the system is monovariant (/= ), and the Krafft point is determined automatically at 1 atm pressure. That seems reasonable for a single surfactant solution, but when the model is applied to a mixed surfactant solution, it is found to be incorrect. Figure 6.2 shows the phase diagram of a water/sodium dodecyl sulfate (SDS)/manganese (II) dodecyl sulfate [Mn (08)2] system, with temperature as the ordinate. The CMC of the surfactant mixture gives a curved surface between the... 

Consider point P in Fig. 6.2. If the melting-point model is applied, five phases coexist at point P [micellar solution, SDS solid, melted SDS, Mn(DS)2 solid, melted Mn(DS)2], and the number of degrees of freedom is zero. If this were true, phase diagrams like Fig. 6.2 could be drawn only at 1 atm pressure. In fact, the solubility and CMC of surfactants have been measured from one to several thousand atmospheres. 

Bivalent metal dodecyl sulfates or sulfonates are typical hydrated surfactant solids, for example, Cu(DS)2 4H2O and Cu(DSo)2 2H2O. For both of these compounds, the Krafft point and the phase transition temperature are not the same (Krafft points 19.0 and 53.5 C respectively phase transition temperatures 44 and 66 C, respectively ), indicating that the melting-point model is wrong. There are cases, however, in which the phase transition temperature of the hydrated surfactant solid happens to be very near the Krafft point of the surfactant. ... 

This section will describe the current status of research in two different aspects of nanocrystal phase behaviour melting and solid-solid phase transitions. In the case of melting, thennodynamic considerations of surface energies can explain the reduced melting point observed in many nanocrystals. Strictly thennodynamic models, however, are not adequate to describe solid-solid phase transitions in these materials. 

The simplest approach to understanding the reduced melting point in nanocrystals relies on a simple thennodynamic model which considers the volume and surface as separate components. Wliether solid or melted, a nanocrystal surface contains atoms which are not bound to interior atoms. This raises the net free energy of the system because of the positive surface free energy, but the energetic cost of the surface is higher for a solid cluster than for a liquid cluster. Thus the free-energy difference between the two phases of a nanocrystal becomes smaller as the cluster size... 

Thermal Properties at Low Temperatures For sohds, the Debye model developed with the aid of statistical mechanics and quantum theoiy gives a satisfactoiy representation of the specific heat with temperature. Procedures for calculating values of d, ihe Debye characteristic temperature, using either elastic constants, the compressibility, the melting point, or the temperature dependence of the expansion coefficient are outlined by Barron (Cryogenic Systems, 2d ed., Oxford University Press, 1985, pp 24-29). 

The first commercial fluidized bed polyeth)4eue plant was constructed by Union Carbide in 1968. Modern units operate at 100°C and 32 MPa (300 psig). The bed is fluidized with ethylene at about 0.5 m/s and probably operates near the turbulent fluidization regime. The excellent mixing provided by the fluidized bed is necessary to prevent hot spots, since the unit is operated near the melting point of the product. A model of the reactor (Fig. 17-25) that coupes Iduetics to the hydrodynamics was given by Choi and Ray, Chem. Eng. ScL, 40, 2261, 1985. 

These super-alloys are remarkable materials. They resist creep so well that they can be used at 850°C - and since they melt at 1280°C, this is 0.72 of their (absolute) melting point. They are so hard that they cannot be machined easily by normal methods, and must be precision-cast to their final shape. This is done by investment casting a precise wax model of the blade is embedded in an alumina paste which is then fired the wax bums out leaving an accurate mould from which one blade can be made by pouring liquid super-alloy into it (Fig. 20.4). Because the blades have to be made by this one-off method, they are expensive. One blade costs about UK 250 or US 375, of which only UK 20 (US 30) is materials the total cost of a rotor of 102 blades is UK 25,000 or US 38,000. 

The various densification mechanisms at different temperatures can be modelled and displayed in HIP diagrams, in which relative temperature is plotted against temperature normalised with respect to the melting-point (Arzt el al. 1983). This procedure relates closely to the deformation-mechanism maps discussed in Section 5.1.2.2. 

Melting point, 193, 203, 528 Meslin s theorem, 229 Metastable states, 181 Mixed liquids, 380 Mixture rule, 263 Mobile equilibrium, 304, 340 Model, thermodynamic, 240 Mol, 20, 135... 

A very recent application of the two-dimensional model has been to the crystallization of a random copolymer [171]. The units trying to attach to the growth face are either crystallizable A s or non-crystallizable B s with a Poisson probability based on the comonomer concentration in the melt. This means that the on rate becomes thickness dependent with the effect of a depletion of crystallizable material with increasing thickness. This leads to a maximum lamellar thickness and further to a melting point depression much larger than that obtained by the Flory [172] equilibrium treatment. 

In a review of the subject, Ubbelohde [3] points out that there is only a relatively small amount of data available concerning the properties of solids and also of the (product) liquids in the immediate vicinity of the melting point. In an early theory of melting, Lindemann [4] considered that when the amplitude of the vibrational displacements of the atoms of a particular solid increased with temperature to the point of attainment of a particular fraction (possibly 10%) of the lattice spacing, their mutual influences resulted in a loss of stability. The Lennard-Jones—Devonshire [5] theory considers the energy requirement for interchange of lattice constituents between occupation of site and interstitial positions. Subsequent developments of both these models, and, indeed, the numerous contributions in the field, are discussed in Ubbelohde s book [3]. 

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