A new method of calculation of the melting temperatures of crystals of Group 1A metal halides and francium metal

A new method of calculation of melting temperatures of binary ionic crystals has been suggested. The method is based on finding a matrix relation between the ionic radii (the lattice energy U) and melting temperature of ionic crystals of the MX type, where M is a Group 1A metal, and X is a halogen. From the equation for the lattice energy U, a new equation has been derived for calculation of the melting temperature of ionic crystals with the use of only the ionic radii and the degree of bond ionicity ?: T _m = f(U, ?). The average error of determination of T _m for alkali-metal halides is 2.80%. The melting temperatures of francium halides and alkali-metal astatides (including FrAt) have been calculated. It has been shown that the accuracy of calculation of the melting temperature of ionic crystals depends on the degree of bond ionicity: the error increases with an increase in the covalent contribution. On the basis of the melting temperatures of metal halide crystals, a method has been developed for the calculation of the melting temperatures of corresponding metals. The melting temperature of francium has been calculated to be 24.861 ± 0.517°C.     

Correlations between parameters of melting and conductivity of solid lonic compounds

Analysis of the literature data allows one to correlate the melting parameters and the activation enthalpy H₀ of the charge carrier formation in an ionic crystal. The melting enthalpy H_m and H₀ values are connected by the basic relation H₀ = 9.2 H_m. The well-known Barr-Lidiard relation is shown to be a particular case of this basic relation. It is demonstrated that the conductivity jump at the melting temperature of an ionic crystal may be predicted from the melting entropy. Correlations of the form mentioned above may be useful in predicting the conductivity values of ionic crystals as well as in looking for new types of superionic conductors.     

Melting behaviour of a series of diamides

The melting behaviour of diamides of general formula (n — C_pH_2p+1)CONH-(CH₂)_qNHCO(n — C_pH_2p+1) has been investigated by calorimetric, dilatometric and IR techniques. The conformational contribution to the melting entropy, calculated from the hypothesis of complete conformational freedom of the molecules at the melting point, has been compared with the experimental data. The higher melting points of the diamides, as compared with those of the linear hydrocarbons having the same number of conformationally flexible chain bonds, are attributed to a reduction of conformational freedom of the chain segments in the liquid state (caused by the large fraction of hydrogen bonds maintained in the melt).     

Die ermittlung des schmelzpunktes von kristallinen polymeren mittels wärmeflusskalorimetrie (DSC)

Small and imperfect crystals in polymers reorganize during slow heating. This leads to an increase of their melting point T_m. In order to measure the melting point of the original crystals, high heating rates are needed. This is possible with the modern heat-flow-calorimeters, which work with very small samples. The thermal lag of a DSC cell causes a shift of the melting peak by ΔT to higher temperature. From the theory of a heat-flow-calorimeter, it follows that the error ΔT is proportional to the square root of heating rate. heat of fusion and sample mass. Measurements with sharp melting low molecular weight compounds confirm that this square root relation is quantitatively followed. In order to measure the true melting point of the crystals present in a polymer sample, one has to use different high heating rates and constant sample mass. By plotting the melting peak temperatures as a function of the square root of heating rate and linear extrapolation to zero heating rate, the true melting point is found. This method is applied to HDPE, LDPE and some polyamides.     

Molecular dynamics study of orientational order and rotational melting in clusters of TeF6

Molecular dynamics simulations of the behavior of molecules in crystalline clusters of TeF₆ were carried out on systems of 100, 150, 250, and 350 molecules. Several diagnostic functions were applied to investigate whether rotational melting occurred before translational melting. These functions included the coefficient of rotational diffusionD _θ(T), the “orientational Lindemann index” δ_θ(T), the “orientational angular distribution function”Q(θ,T), and the “orientational pair-correlation function”g _θ(r, T). All indicators implied that rotational melting occurred before translational melting, that it began with the outermost molecules, and that its onset for smaller clusters was at lower temperatures than for larger clusters. Results also showed that the rotational transition coincided with the transition from a lower symmetry phase (monoclinic) to cubic, a phenomenon that had been noted by others to occur with some regularity for systems of globular molecules.     

DSC study of charge-transfer complexes of polynuclear aromatic hydrocarbons with nitroaromatic acceptors

Charge-transfer, crystalline complexes of 1,3,5-trinitrobenzene (TNB), 2,4,7- trinitro-9-fluorenone (TNF). and 2,4,5,7-tetranitro-9-fluorenone (TENF) with eleven polynuclear aromatic hydrocarbons were compared for thermal stability, ΔH and ΔS of melting. Factors possibly influencing the above parameters are discussed.Melting does not induce separation of the components; these complexes can be repeatedly crystallized and melted without variation of the ΔH of melting, thereby indicating high thermal stability.With a few exceptions, melting temperatures of the complexes increase in the order TNB<TNF<TENF: so do ΔH and ΔS of melting. A number of crystal transitions were observed.     

Alternating melting points,heats and entropies of fusion of linear aliphatic polyesters

Heats of fusion of polyethylene-adipate, pimelate, suberate and azelaate have been determined by two methods, viz. DTA and the pressure dependence of the melting point up to 6000 bar. Degrees of crystallization were measured dilatometrically. Entropies of fusion were divided into volume and conformational entropy terms, only the latter alternates. Alternation of melting points depends on enthalpy of fusion ΔH_m, entropy of fusion ΔS_m and volume change Δυ on melting; influence of the functions increases thus ΔV_m < ΔH_m < ΔS_m and ΔS_m is dominant. Entropy and heat of fusion alternation is explained by the conformational change on melting governed by the driving force of maximum H-bridge formation.     

Melting temperature evolution of non-reorganized crystals. Poly(3-hydroxybutyrate)

In the present study the correlation between the melting behaviour of poly(3-hydroxybutyrate) (PHB) original, non-reorganized crystals and the crystallinity increase during isothermal crystallization is presented and discussed. Since the reorganization processes modify the melting curve of original crystals, it is necessary to prevent and hinder all the processes that influence and increase the lamellar thickness. PHB exhibits melting/recrystallization on heating, the occurring of lamellar thickening in the solid state being excluded. The first step of the study was the identification of the scanning rate which inhibits PHB recrystallization at sufficiently high T_c. For the extrapolated onset and peak temperatures of the main melting endotherm, which is connected to fusion of dominant lamellae, a double dependence on the crystallization time was found. The crystallization time at which T_onset and T_peak change their trends was found to correspond to the spherulite impingement time, so that the two different dependencies were put in relation with primary and secondary crystallizations respectively. The increase of both T_onset and T_peak at high crystallization times after spherulite impingement was considered an effect due to crystal superheating and an indication of a stabilization process of the crystalline phase. Such stabilization, which produces an increase of the melting temperature, is probably connected with the volume filling that occurs after spherulite impingement.     

Application of recurrence relations to melting points of homologs

The previously established recurrence equations A(n + 1) = aA(n) + b characterizing variations in the majority of physicochemical constants of organic compounds in homologous series and relating the properties of adjacent homologs with n + 1 and n carbon atoms are applicable in the modified form [T _m(n + 2) = aT _m + b] to the melting points. This second-order recurrence is observed with a high accuracy, despite significant alternations in the melting points of even and odd homologs. The method for calculating melting points, based on this recurrence, has no analogs among the previously suggested methods and makes it possible, in particular, to reveal errors in reference data, originating in most cases from the low purity of the samples dealt with.     

Melting behaviour of a series of monoamides

The melting behaviour of the monoamides of general formula (n-C_pH_2p+1)CONH-(n-C_qH_2p+1) is investigated by differential scanning calorimetry (DSC) and infrared spectroscopy. The lower values of melting entropies, compared to those for linear hydrocarbons with the same number of conformationally flexible chain bonds, is attributed to a reduction in the number of conformations available to the hydrocarbon portion of the molecule, because of the large amount of hydrogen bonding maintained in the melt. The melting behaviour of the monoamides is compared with that of the diamides discussed in a previous paper [1]. The persistence of a network of hydrogen bonds in the melt of the diamides reduces the conformational freedom of the chain segments more than for the monoamides.     

Ionic conductivity of some alkaline earth halides

The ionic conductivity above and below the melting temperature has been measured for the fluorides, chlorides, and bromides of calcium, strontium, and barium and for magnesium chloride. The observed behavior is of three types: I (MgCl₂, CaCl₂, CaBr₂, BaBr₂), there is an increase in conductivity of several orders of magnitude on melting; II (BaCl₂, SrBr₂), there is a solid-solid transition accompanied by a large increase in conductivity with little subsequent change on melting; and III (CaF₂, SrF₂, BaF₂, SrCl₂), the conductivity of the solid is continuous and changes only slightly on melting.     

Multiple melting behavior of poly(butylene succinate)

The multiple melting behavior of poly(butylenes succinate) (PBS) isothermally crystallized from the melt was investigated using differential scanning calorimetry (DSC), temperature modulated DSC (MDSC) and polarized optical microscopy. PBS exhibits at most four melting endotherms (denoted as T_m1, T_m2, T_m3, and T_m4 from high to low temperatures) and a crystallization exotherm (denoted as T_re) in the DSC heating trace. Multiple melting endotherms were observed even at high heating rates. The origins of each endothermal and exothermal peak were discussed in detail. It is suggested that: (i) the crystallization exothermic peak, T_re, relates to the recrystallization of the melt of the crystallites with lower thermal stability; (ii) the T_m1 is ascribed to the melting of crystallites formed through recrystallization; (iii) two crystal populations with different thermal stability are responsible for the T_m2 and T_m3; (iv) the T_m4, which is the annealing peak, represents the transition of the rigid amorphous fraction (RAF) from solid-like RAF into liquid-like amorphous fraction.     

Melting behavior of isotactic polystyrene revealed by differential scanning calorimetry and transmission electron microscopy

The triple melting behavior and lamellar morphologies of isotactic polystyrene isothermally crystallized from the glassy state have been investigated by differential scanning calorimetry (DSC), temperature-modulated DSC and transmission electron microscopy (TEM). The combination of thermal analysis measurements and morphological observations indicates that: (1) The lowest endothermic peak, the so-called “annealing peak” (T_a), is not associated with the melting of the subsidiary crystals formed by secondary crystallization as often suggested in the literature, but probably with a constrained interphase between the amorphous and crystalline regions; (2) Within spherulites two lamellar populations with different degrees of perfection (or thermal stability) are confirmed by direct TEM observations following partial melting experiments, which are responsible for the so-called double melting peaks (T_m,1 and T_m,2) at higher temperatures observed in DSC curves; (3) The highest endothermic peak (T_m,2) is partially originated from the melting of the recrystallized lamellae formed during heating process in DSC.     

Poly(dithiotriethylene adipate): Melting behavior, crystallization kinetics and morphology

The melting behavior and the crystallization kinetics of poly(dithiotriethylene adipate) (PSSTEA) were investigated by differential scanning calorimetry and hot-stage optical microscopy. The observed multiple endotherms, commonly displayed by polyesters, were influenced by the crystallization temperature (T_c) and ascribed to melting and recrystallization processes. Linear and nonlinear theoretical treatments were applied to estimate the equilibrium melting temperature for PSSTEA, using the corrected values of the melting temperature; the nonlinear estimation yielded a higher value by about 15 °C. Isothermal crystallization kinetics were analyzed according to the Avrami’s theory. Values of the Avrami’s exponent n close to 3 were obtained, independently of T_c, in agreement with a crystallization process originating from predeterminated nuclei and characterized by three-dimensional spherulitic growth. As a matter of fact, space-filling spherulites were observed by optical microscopy at all T_c’s. The rate of crystallization became lower as T_c increased, as usual at low undercooling, the crystallization process being controlled by nucleation.     

Preparation and some properties of diamine-diacid type alternating copolyamides

The polycondensations of N,N′-bis-(6-aminohexyl)oxamide, N,N′-bis-(6-aminohexyl) succinimide and N,N′-bis(6-aminohexyl)-sebacamide, with p-nitrophenyl adipate in 1,2,4-trichlorobenzene solution, using relatively low temperature (100°) to avoid the amide exchange reactions, gave alternating copolyamides corresponding to (6-6) (6-2), (6-6) (6-4) and (6-6) (6–10) nylons. These copolymers have melting points between those of their corresponding homopolyamides, whereas the random copolymers melt lower than either of the homopolymers. The microstructure of the copolymers seems to be modified by heat treatment below the melting points. Amide exchange reactions occur when they are heated to melting. C¹³ spectra allowed differentiation between the CO groups of the two constituent units of the copolymers, but not between the alternating and the random copolymers.     

Molecular-dynamics simulation of the structural stability,energetics, and melting of Cu n(n = 13–135) clusters

Cluster properties of copper have been investigated using the Molecular-Dynamics md technique. The structural stability and energetics of spherical Cu_n (n = 13–135) clusters have been investigated at temperatures T = 1 K and T = 300 K. It has been found that the average interaction energy per atom in the cluster decreases and reaches an asymptotic value as cluster size increases. The melting behaviour of clusters n = 13 and n = 55 have been investigated. It has been found that the melting temperature decreases as cluster size increases, and for clusters with multishell structures melting starts from the outermost shell. In the simulation an emprical potential energy function (PEF) proposed by Erkoç has been used, which contains two-body atomic interactions.     

Corresponding states theory and thermodynamic properties of liquid alkali metals

According to phenomenological scaling and the law of corresponding states, reduced coordinates F ^*-T ^*, where F* represents the reduced thermodynamic properties (enthalpy of vaporization, speed of sound, surface tension, saturated liquid density) and T ^* is the reduced temperature, are introduced for the prediction of the thermodynamic properties of alkali metals. Values of the thermodynamic properties from the melting point up to boiling point are correlated. It has been shown that the correlation between reduced thermodynamic properties, as well as with the reduced temperature, can be expressed as a unique straight-line plot with a linear correlation coefficient of 0.9998. The proposed correlation has a simple form for easy calculation, requires only the melting and boiling point parameters, which are usually easy to acquire, and can predict the thermodynamic properties from the melting temperature up to the boiling temperature accurately.     

Die stereoisomeren bicyclo[4.2.0]octan-cis-Diole-(7,8)

The stereochemical assignment of the bicyclo[4.2.0]octane-cis-7,8-diols is reinvestigated. It is shown that the cis-diols prepared by different routes are indeed stereoisomers, the lower melting being the exo-isomer (1), the higher melting the endo-isomer (2). The synthesis of the previously unknown trans-fused bicyclo[4.2.0]octane-cis-7,8-diol (3) via photosensitized cycloaddition of vinylene carbonate to cyclohexene is described.     

Crystallization and melting behaviors of polystyrene-b-poly(ethylene-co-butene) block copolymers

Non-isothermal and isothermal crystallization behaviors of polystyrene-b-poly(ethylene-co-butene) (PSt-b-PEB) block copolymers with different compositions and chain lengths were investigated by differential scanning calorimetry (DSC). The results show that crystallization of PEB block is strongly dependent on the composition. Crystallization temperature (T_c), melting temperature (T_m) and fusion enthalpy (ΔH_f) increase rapidly with PEB volume fraction (V_E) for block copolymers with V_E below 50%, but there is little change when PEB block becomes the major component. Glass transition temperature (T_g) of the PSt block and order-disorder transition temperature (T_ODT) of block copolymers also have a weak effect. The isothermal crystallization kinetics results show that Avrami exponent (n) was strongly dependent on the composition and crystallization temperature. For the block copolymers with V_E below 38.7 vol%, the values of n vary between 0.9 and 1.3, indicating that crystallization is confined. For the PSt-b-PEB block copolymers with V_E higher than 50%, fractionated crystallization behavior is usually observed. A two-step isothermal crystallization procedure is applied to these block copolymers. It is found that breakout crystallization occurs at higher T_c, but confined at lower T_c. Two overlapped melting peaks are observed for the block copolymers with fractionated crystallization behavior after two-step crystallization, and only the higher melting peak corresponding to breakout crystallization can be used to derive equilibrium melting temperature.     

β-Modification of polypropylene and its two-component systems

β-modification and multi-component systems ofβ-polypropylene were prepared both under laboratory and processing conditions. Characteristic features of crystallization, melting, and annealing ofβ-PP are summarized. The very distinct memory effect in the melting and annealing ofβ-PP is also presented. The existence of a lower and an upper limit temperature ofβ-PP formation is demonstrated. The structural stability and the orientation-inducedβα-recrystallization ofβ-PP are analyzed. Preparation and properties of polymer blends and filled composites fromβ-PP are introduced, too.