Depression of the melting point

Very small particles of a substance have a depressed melting point relative to the bulk due to the curvature of their surfaces, which may be expressed as [137, 138]  

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The cryoscopic constant Kj gives the depression of the melting point AT (in degrees Celsius) produced when 1 mol of solute is dissolved in 1000 g of a solvent. It is applicable only to dilute solutions for which the number of moles of solute is negligible in comparison with the number of moles of solvent. It is often used for molecular weight determinations. 

In more recent times, naphthalene has been used in condensation products from naphthalene sulfonic acids, utili2ing formaldehyde as additives to improve the flow properties of concrete these are referred to as superplastici2ers. Another newer appHcation is the production of diisopropylnaphthalenes. The mutual depression of the melting points in the mixture gives a Hquid which is used as a solvent for dyes in the production of carbonless copy paper. 

It yields a hydrochloride melting at 35° to 37°, which when treated with aniline regenerates the same hydrocarbon, which is identical in all respects -with isopinene. The admixture of this fenchene hydrochloride with that prepared from isopinene causes no depression of the melting-point, and Komppa regards the identity of inactive a-fenchene and isopinene as established. He assigns the following constitution to a-fenchene (isopinene) —... 

The derivation of the quantitative relationship between this equilibrium temperature and the composition of the liquid phase may be carried out according to the well-known thermodynamic procedures for treating the depression of the melting point and for deriving solubility-temperature relations. The condition of equilibrium between crystalline polymer and the polymer unit in the solution may be restated as follows ... 

The nature of the heat of fusion AHu deserves particular attention, for it represents the heat required to melt one mole of crystalline units it does not refer to the latent heat AJT required to melt such crystallinity as may occur in a given semicrystalline polymer. The depression of the melting point Tm, already defined as the maximum temperature at which crystalline regions may coexist with amorphous poly-... 

The DSC thermograms of several triblock copolymers and homopolymer HB are coiq>ared to that of a low density polyethylene in Figure 2. The thermograms are those of the first run on quenched samples. Their behavior is similar except that the temperature of the maximum in the DSC melting peak, Tm, for LDPE (110 C) is higher than that of HB (102°C). The depression of the melting point brought about by the presence of 5 to 8 mole percent... 

Evidence for these equilibria comes from the Raman spectra, which show an absorption peak (or unresolved peaks), probably attributable to Cu,Clj. Addition of CuCI or Cl causes this peak to increase or decrease as expected by the above equilibria. The system thus probably contains at least four anionic species, and the impurities account for the depression of the melting point. In accordance with this interpretation is the fact that the material is oily and never forms a crystalline solid with a true freezing point, but congeals to a glass. it about 0 °C. 

Figure 2.43 Mechanism for the solvent-induced depression of the melting point. Reprinted with permission from J. E. Mark, Physical Chemistry of Polymers, ACS Audio Course C-89, American Chemical Society, Washington, DC, 1986. Copyright 1986, American Chemical Society.

Information about the combinability of dyes is obtained from dye suppliers. Moreover, dye producers offer premixed disperse dyes whose components are selected in such a manner that the mixture is absorbed evenly at relatively low temperature and, consequently, makes fewer demands on the dispersion stability. At the same time, the depression of the melting point of mixtures should not be overlooked [119], When using mixed dyes, differences in the fastness of the components must be accepted. 

As shown in Equation 10.4, the depression of the melting point of a given confined solvent is related to the geometry of the pores of the confining material. In principle, measurement of AT can give access to the pore size. Three main techniques have been developed to measure porosity in solids via the use of the Gibbs-Thomson equation thermoporosimetry, NMR cryporometry and surface force apparatus. These techniques are secondary methods since they require pre-... 

Flory (1953,1978) derived the following useful equation for the depression of the melting point by lower molecular constituents of the polymer ... 

The depression of the melting point of a crystalline polymer in blends can be used to measure the Flory-Huggins interaction parameter of the mixture. The melting points on heating, or crystallisation points on cooling, can be measured using techniques such as differential scanning calorimetry or by turbidity measurements. 

However, one can already mention that the introduction of dissymmetry had two positive effects on the mesomorphic properties a depression of the melting points was observed and ferrocene derivatives exhibiting smectic C and smectic A phase were obtained for the first time. 

As occurs with other crystalline substances, the melting temperature of polymers decreases in the presence of solvents (melting point depression). Thermodynamic arguments lead to expressions that relate the depression of the melting point to the solution concentration. The equation that gives the melting temperature of a polymer solution as a function of the concentration (17) can be written as... 

The depression of the melting point of a polymer by the presence of small amounts of comonomer is described by Flory and Eby Flory suggested that the comonomer is relegated to the amorphous regions of the polymer, its presence thus reducing the extension of the crystalline regions. Flory s equation for the melting point depression caused by comonomer B in polymer A reads ... 

The reactions of triphenylmethanol are dominated by the ease with which it dissociates to form the relatively stable triphenylmethyl carbocation. When colorless triphenylmethanol is dissolved in concentrated sulfuric acid, an orange-yellow solution results that gives a fourfold depression of the melting point of sulfuric acid, meaning that four moles of ions are produced. If the triphenylmethanol simply were protonated only two moles of ions would result. 

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