Melting Entropy Research Articles

Why Is Gyroid More Difficult to Nucleate from Disordered Liquids than Lamellar and Hexagonal Mesophases?

Block copolymers, surfactants, and biomolecules form lamellar, hexagonal, and gyroid mesophases. Across these systems, the nucleation of lamellar from the disordered liquid is the easiest and the nucleation of gyroid the most challenging. This poses the question of what are the factors that determine the rates of nucleation of the mesophases and whether they are controlled by the complexity of the structures or the thermodynamics of nucleation. Here, we use molecular simulations to investigate the nucleation and thermodynamics of lamellar, hexagonal, and gyroid in a binary mixture of particles that produces the same mesophases as those of surfactants and block copolymers. We demonstrate that a combination of averaged bond-order parameters q̅2 and q̅8 identifies and distinguishes the three mesophases. We use these parameters to track the microscopic process of nucleation of each mesophase and investigate the existence of heterogeneous nucleation (cross-nucleation) between mesophases. We estimate the surface tensions of the liquid/mesophase interfaces from nucleation rates using classical nucleation theory and find that they are comparable for the three mesophases with values that are about a third of those expected for liquid-crystal interfaces. The driving forces for nucleation, on the other hand, are quite different and increase in the order gyroid < hexagonal < lamellar at any temperature. We find that the nucleation rates of the mesophases follow the order of their driving forces. We conclude that the difficulty to nucleate the gyroid originates in its lower temperature of melting and extremely low entropy of melting compared to those of the hexagonal and lamellar mesophases.

Determining solid/liquid interfacial energies in Al-Cu by curvature controlled melting point depression

An experimental method for determining solid/liquid interfacial energies of alloys is presented. Spherical intermetallic particles of Al2Cu with diameters down to 50 nm were generated as ”divorced eutectic” in an initially homogeneous solid solution of 4 wt% Cu in Al by short-term annealing (t < 10 s) in a temperature gradient. Particle size distributions were analyzed using transmission electron microscopy (TEM) after dissolving the Al matrix of a representative part of the sample in dry butanol. During heating of the remaining sample part in a highly sensitive power-compensating differential scanning calorimeter, the onset of eutectic melting was measured. The expectation value of the narrow size distributions and the respective curvature undercooling were correlated on the basis of the Gibbs-Thomson equation. For deriving the solid/liquid interfacial energy, the temperature and concentration dependent melting entropy were calculated under the assumption of thermodynamic equilibrium at the solid/liquid interface using a CALPHAD type database. In thermodynamic equilibrium, at a constant temperature the solid and the liquid phase have different concentrations at the interface leading to an interfacial energy that is higher than the value for pure Al derived from maximum supercooling experiments, and lower than the value for Al-Cu determined using the grain boundary groove method. The extension of the method to other alloy systems is discussed.

Insights into Melting Behavior of Propyl-Bridged Di(cyanate ester) Monomers through Crystal Packing, Thermal Characterization, and Computational Analysis

Four isomeric propyl-bridged di(cyanate ester) monomers having an unexpectedly wide range of melting points were analyzed using X-ray crystallography, thermal analysis, and both empirical and semiempirical modeling, in order to examine the structure–property relationships that determine the melting characteristics. The four monomers’ crystal structures were determined, and intermolecular contacts and packing were examined. Enthalpies and entropies of melting were determined experimentally via differential scanning calorimetry and compared against two empirical models. Computational insights were provided by examining the monomers’ energetic rotational barriers. Significant effects that could not be accounted for within the framework of either the empirical or semiempirical models altered the entropy of melting over a range spanning about 40% of the average value, while the enthalpy of melting varied over a range equivalent to 50% of the average value. These large variations, even within an isomeric series...

Thermal Shift as an Entropy-Driven Effect.

Thermal shift assays (TSAs) are among the most commonly used biophysical approaches in drug discovery in both academic and industrial settings. However, the most common interpretation of the data generated by a TSA is purely qualitative, using only the change in melting temperature (ΔTm) as a metric. This has left many questions surrounding the interpretation of the data as well as whether the TSA truly correlates with other assays. TSAs also lack theoretical descriptions of the melt behavior of proteins in the presence of multiple ligands. Here we describe a novel simplified analytical framework based on "pseudoisothermal" models as well as exact thermodynamic descriptions of protein-ligand melt behavior rooted in changes in the entropy of melting. We show how the models are broad and independently applicable, in that they can describe the behavior of any macromolecule such as a protein or DNA and demonstrate good correlations with other techniques. These models are shown to give good descriptions of assay systems containing single or multiple ligands and can determine the mechanism of interaction. The models are derived from first principles, and the theoretical justification is discussed.

The isobaric heat capacities and thermodynamic properties of ionic liquid 1-ethylpyridinium bis(trifluoromethylsulfonyl)imide

Ionic liquid 1-ethylpyridinium bis(trifluoromethylsulfonyl)imide ([C2py][NTf2]) was synthesized and characterized by 1H NMR spectroscopy, 13C NMR spectroscopy and thermal gravity analysis. The molar heat capacities of [C2py][NTf2] were measured using a heat-flow calorimeter with “3D Calvet” calorimetric sensor from (293 to 312) K. The experiment value of molar heat capacity 502.15 J K−1 mol−1 at 298.15 K was obtained. Moreover, the estimation values of molar heat capacity were calculated by using 4 methods at 298.15 K, and the result showed the Paulechka et al.’s method was more appropriate for predicting the molar heat capacity of IL [C2py][NTf2], and the error was less than 2%. In addition, the freezing point T * was calculated by freezing point depression, which was approximately equal to experimental value 305.08 K. The molar enthalpy of fusion Δf H m = 26.77 kJ mol−1, molar melting entropy Δde S m = 90.60 J mol−1 K−1 and the freezing constant K f were also calculated.

Estimating the Physicochemical Properties of Polysubstituted Aromatic Compounds Using UPPER

The UPPER model (Unified Physicochemical Property Estimation Relationships) has been used to predict 9 essential physicochemical properties of pure compounds. It was developed almost 25 years ago and has been validated by the Yalkowsky group for almost 2000 aliphatic, aromatic, and polyhalogenated hydrocarbons. UPPER is based on a group of additive and nonadditive descriptors along with a series of well-accepted thermodynamic relationships. In this model, the 2-dimensional chemical structure is the only input needed. This work extends the applicability of UPPER to hydrogen bonding and non-hydrogen bonding aromatic compounds with several functional groups such as alcohol, aldehyde, ketone, carboxylic acid, carbonate, carbamate, amine, amide, nitrile as well as aceto, and nitro compounds. The total data set includes almost 3000 compounds. Aside from the enthalpies and entropies of melting and boiling, no training set is used for the calculation of the properties. The results show that UPPER enables a reasonable estimation of all the considered properties.

Molecular structure, configurational entropy and viscosity of silicate melts: Link through the Adam and Gibbs theory of viscous flow

The Adam and Gibbs theory depicts the viscous flow of silicate melts as governed by the cooperative re-arrangement of molecular sub-systems. Considering that such subsystems involve the silicate Qn units (n=number of bridging oxygens), this study presents a model that links the Qn unit fractions to the melt configurational entropy at the glass transition temperature Tg, Sconf(Tg), and finally, to its viscosity η. With 13 adjustable parameters, the model reproduces η and Tg of melts in the Na2O-K2O-SiO2 system (60≤[SiO2]≤100mol%) with 1σ standard deviations of 0.18 log unit and 10.6°, respectively.The model helps understanding the links between the melt chemical composition, structure, Sconf and η. For instance, small compositional changes in highly polymerized melts generate important changes in their Sconf(Tg) because of an excess of entropy generated by mixing Si between Q4 and Q3 units. Changing the melt silica concentration affects the Qn unit distribution, this resulting in non-linear changes in the topological contribution to Sconf(Tg). The model also indicates that, at [SiO2]≥60mol%, the mixed alkali effect has negligible impact on the silicate glass Qn unit distribution, as corroborated by Raman spectroscopy data on mixed Na-K tri- and tetrasilicate glasses. Such model may be critical to link the melt structure to its physical and thermodynamic properties, but its refinement requires further high-quality quantitative structural data on silicate and aluminosilicate melts.

Microstructural and mechanical characterization of melt spun process Sn-3.5Ag and Sn-3.5Ag-xCu lead-free solders for low cost electronic assembly

This paper aims to investigate the reliability of mechanical and creep behavior for the eutectic Sn-Ag and Sn-Ag-Cu Solder joints rapidly solidified after hot compressing (HC) in terms of structural changes and its relationship with thermal behavior, which has been discussed and compared with their properties before HC process by Mustafa et al. (2016) [1]. These solder joints were prepared by melt-spinning technique and tested by HC at 30MPa pressure and 150°C for 90min, their structural, mechanical and thermal properties after HC process have been investigated by X-ray diffraction (XRD), dynamic resonance techniques (DRT) and differential scanning calorimetry (DSC) techniques respectively and compared with these solders before HC. The results revealed that the pressure caused some fractures on the solders morphology surfaces. But some benefits for these solders have been occurred, like eliminating the internal stresses through recrystallization process whose evidence by the particle size increases after they HC, stabilized structure after HC was due to the metastable phases rearrangements, new intermetallic compounds (IMCs) formation, decreasing, melting temperature range (∆T), lattice strains (ƹ) and entropy change (S). These sequential benefits are considered to be the main reasons which lead to decreasing energy loss (Q−1), creep rate (ɛ) and thermal stability enhancement. Elastic modulus increment might be due to low elastic lattice distortions after HC, while the stress exponent (n) reduction refers to viscous glide mechanism of deformation after HC instead of climb deformation mechanism before HC.

Enthalpy relaxation studies of memory effect in various glass formers in the vicinity of glass transition

The glass is in a non-equilibrium state in nature, and relaxation might occur towards the equilibrium state at a certain temperature. When heating a quenched glass, relaxation can be resolved as temperature approaches to the glass transition, and further heating leads to enthalpy recovery as the system turns into an equilibrium supercooled liquid. The released energy involving the relaxation relative to the original quenched state is, in magnitude, identical to the gained energy in enthalpy recovery, showing a memory effect. In this paper, we discuss the enthalpy behaviors involved in a cooling and reheating cycle around the glass transition in various glass forming systems such as oxides, metal alloys, and small molecular systems. The cooling and heating rates are fixed to be -/+ 20 K/min with the related cooling and heating heat capacity curves being determined. It is found that the relaxation enthalpy involved in the cooling/heating cycles is closely related to the enthalpy of fusion for the glass forming materials, and the basically linear correlation implies the similarity between the glass transition and melting behaviors with regard to the atomic rearrangements involved in the relaxation and solidification processes. The determining of the cooling and heating heat capacity curves also helps establish the enthalpy relaxation/recovery spectra of various glasses, and the symmetry of the spectrum is associated with the fragility of glass-forming material. For the material of low or medium fragilities, the symmetry of the enthalpy relaxation spectrum is observed to be somehow dependent on the fragility, while for the high fragility glass, the symmetry keeps almost constant. The dependence of fragility on the glass transition thermodynamics is also discussed, and low melting entropy and high fragility are shown to reduce effectively the liquid-crystal Gibbs free energy difference. Using the correlation between the relaxation enthalpy and kinetic fragility reported in our previous studies, the glass transition thermodynamics for the case of the most fragile glass with m= 175 is evaluated, especially compared with the second phase transition of thermodynamics. The results provide a new understanding of the thermodynamics of the relaxation in glassy material and the glass transition.

Thermochemistry of Evaporation and Sublimation of 2,4,6‐Triazido‐1,3,5‐triazine

AbstractSaturated vapor pressure over cyanuric triazide melt was measured in the temperature range 393.15–453.15 K using glass membrane Bourdon pressure gauges. Measured evaporation heat and evaporation entropy are equal to 61.1±3.3 kJ mol–1 and 111.3±6.1 J mol–1 K–1, respectively. According to DSC data, melting heat and melting entropy of cyanuric triazide are 22.2±1.3 kJ mol–1 and 60.5±3.5 J mol–1 K–1, respectively. Based on the results obtained, the following dependence was found for the saturated vapor pressure over solid cyanuric triazide: Ps [Pa]=1014.0⋅exp[(–83300±3300)/RT]. Concequently, sublimation heat and sublimation entropy of cyanuric triazide are equal to 83.3±3.3 kJ mol–1 and 171.8±9.6 J mol–1 K–1, respectively. Saturated vapor pressure over solid cyanuric triazide at room temperature is equal to 0.25 Pa (1.9×10−3 Torr). It is concluded that high volatility of cyanuric triazide is caused by its low sublimation heat.

Melting entropy and its connection to kinetic fragility in glass forming materials

The connections of liquid dynamics to thermodynamics are proven to facilitate understanding the glass transition in liquids. Here, we investigated the melting entropies ΔSm of various materials with the emphasis on its relation to kinetic fragility. The vibrational entropy ΔSvib-ex in ΔSm is determined and, a correlation between the ratio of ΔSvib-ex/ΔSm and fragility is shown. The correlation basically reproduces the results determined at glass transition temperatures, Tg, showing the sluggish variation of ΔSvib-ex/ΔSm from Tg up to the melting point Tm. ΔSvib-ex/ΔSm is also found to be related to the ionicity for ionic crystals and to Tm for metals.

Calculating the Threshold Energy of the Pulsed Laser Sintering of Silver and Copper Nanoparticles

In this study, in order to analyze the low-temperature sintering process of silver and copper nanoparticles, we calculate their melting temperatures and surface melting temperatures with respect to particle size. For this calculation, we introduce the concept of mean-squared displacement of the atom proposed by Shi (1994). Using a parameter defined by the vibrational component of melting entropy, we readily obtained the surface and bulk melting temperatures of copper and silver nanoparticles. We also calculated the absorption cross-section of nanoparticles for variation in the wavelength of light. By using the calculated absorption cross-section of the nanoparticles at the melting temperature, we obtained the laser threshold energy for the sintering process with respect to particle size and wavelength of laser. We found that the absorption cross-section of silver nanoparticles has a resonant peak at a wavelength of close to 350 nm, yielding the lowest threshold energy. We calculated the intensity distribution around the nanoparticles using the finite-difference time-domain method and confirmed the resonant excitation of silver nanoparticles near the wavelength of the resonant peak.

Effects of size and shape on the specific heat, melting entropy and enthalpy of nanomaterials

A simple theory is proposed to study the size- and shape-dependent specific heat, melting entropy and enthalpy of nanomaterials. The particle size and shape are demonstrated to affect the specific heat, melting entropy and enthalpy of nanomaterials. The model is applied to Ag, Cu, In, Se, Au and Al nanomaterials in spherical, nanowire and nanofilms shapes. The specific heat is observed to increase with the decrease in particle size, whereas the melting entropy and enthalpy decrease as the particle size decreases. Our theoretical predictions agree well with available experimental and computer simulation results, thereby supporting the validity of formulation developed.

Size- and shape-dependent melting enthalpy and entropy of nanoparticles

A theoretical model free of any adjustable parameter was derived based on the relation between Gibbs energy change and size to describe the size- and shape-dependent behavior of the melting enthalpy and entropy of nanoparticles. For the melting enthalpy and entropy of vanadium (V), silver (Ag), and copper (Cu) nanoparticles, the results of pure theoretical calculation are in good agreement with available molecular dynamic results. The effect of size on the melting enthalpy and entropy of nanoparticles is greater compared to that of shape effect. The melting enthalpy and entropy decrease with particle size decreasing and the smaller the particle size, the greater the size and shape effects. Furthermore, at the same equivalent diameter, the more the shape of nanoparticles deviates from that of the sphere, the smaller the melting enthalpy and entropy. The thermodynamic relations derived herein can quantitatively describe the influence regularities of size and shape on the melting thermodynamic properties of nanoparticles.

Thermophysical properties of model compounds of the lignin structural unit

Sixteen lignin related aromatic compounds formed by the thermal degradation of lignin and being potentially valuable products of the processing of renewable raw materials were studied using differential scanning calorimetry. The temperatures, enthalpies, and entropies of melting were determined. The temperature dependences of isobaric heat capacities for the studied compounds were obtained. The relationship between the structures of the lignin related compounds and their thermochemical properties is considered.

Solubility of cefoxitin acid in different solvent systems

Cefoxitin acid is one kind of important pharmaceutical intermediate. Its solubility is crucial for designing and optimizing the crystallization processes. In this work, the solubility of cefoxitin acid in organic solvents (methanol, acetonitrile, ethanol, isopropanol, n-propanol and ethyl acetate), water and water-methanol mixtures was measured spectrophotometrically using a shake-flask method within the temperature range 278.15–303.15K. PXRD data and the Karl Fischer method were used to verify the crystal form stability of cefoxitin acid in the solubility measuring process. The melting points, the enthalpy and entropy of fusion were estimated. Results showed that the solubility of cefoxitin acid increases with the increasing temperature in all tested solvents in this work, and the solubility of cefoxitin acid increases with the increasing methanol concentration in water-methanol mixtures. The experimental solubility values were well correlated using the modified Apelblat equation, NRTL model and CNIBS/R-K model. An equation proposed by Williamson was adopted to calculate the molar enthalpy during the dissolution process.

Nanoscopic Thermodynamics.

Conventional thermodynamics for bulk substances encounters challenges when one considers materials on the nanometer scale. Quantities such as entropy, enthalpy, free energy, melting temperature, ordering temperature, Debye temperature, and specific heat no longer remain constant but change with the crystal dimension, size, and morphology. Often, one phenomenon is associated with a variety of theories from different perspectives. Still, a model that can reconcile the size and shape dependence of the thermal properties of the nanoscaled substances remains one of the goals of nanoscience and nanotechnology. This Account highlights the nanoscopic thermodynamics for nanoparticles, nanowires, and nanofilms, with particular emphasis on the bond energy model. The central idea is that the atomic cohesive energy determines the thermodynamic performance of a substance and the cohesive energy varies with the atomic coordination environment. It is the cohesive energy difference between the core and the shell that dictates the nanoscopic thermodynamics. This bond energy model rationalizes the following: (i) how the surface dangling bonds depress the melting temperature, entropy, and enthalpy; (ii) how the order-disorder transition of the nanoparticles depends on particle size and how their stability may vary when they are embedded in an appropriate matrix; (iii) predictions of the existence of face-centered cubic structures of Ti, Zr, and Hf at small size; (iv) how two elements that are immiscible in the bulk can form an alloy on the nanoscale, where the critical size can be predicted. The model has enabled us to reproduce the size and shape dependence of a number of physical properties, such as melting temperature, melting entropy, melting enthalpy, ordering temperature, Gibbs free energy, and formation heat, among others, for materials such as Pd, Au, Ag, Cu, Ni, Sn, Pb, In, Bi, Al, Ti, Zr, Hf, In-Al, Ag-Ni, Co-Pt, Cu-Ag, Cu-Ni, Au-Ni, Ag-Pt, and Au-Pt on the nanometer scale. Furthermore, this model predicts the phenomena of the thermal stability of metal particles on graphene, the superheating of embedded nanoparticles, the order-disorder transition of nanoalloys, the size-temperature phase diagram for low-dimensional solids and the alloying ability on the nanoscale. Extensions of this model may lead to the design of new functional nanomaterials.

4He glass phase: A model for liquid elements

The specific heat of liquid helium confined under pressure in nanoporous material and the formation, in these conditions, of a glass phase accompanied by latent heat are known. These properties are in good agreement with a recent model predicting, in liquid elements, the formation of ultrastable glass having universal thermodynamic properties. The third law of thermodynamics involves that the specific heat decreases at low temperatures and consequently the effective transition temperature of the glass increases up to the temperature where the frozen enthalpy becomes equal to the predicted value. The glass residual entropy is about 23.6% of the melting entropy.

Organic Crystal Engineering of Thermosetting Cyanate Ester Monomers: Influence of Structure on Melting Point

Key principles needed for the rational design of thermosetting monomer crystals, in order to control the melting point, have been elucidated using both theoretical and experimental investigations of cyanate esters. A determination of the thermodynamic properties associated with melting showed that the substitution of silicon for the central quaternary carbon in the di(cyanate ester), 2,2-bis(4-cyanatophenyl)propane, resulted in an increase in the entropy of melting along with a decrease in the enthalpy of melting, leading to a decrease in the melting temperature of 21.8 ± 0.2 K. In contrast, the analogous silicon substitution in the tri(cyanate ester), 1,1,1-tris(4-cyanatophenyl)ethane, resulted in no significant changes to the enthalpy and entropy of melting, accompanied by a small increase of 1.5 ± 0.3 K in the melting point. The crystal structure of 1,1,1-tris(4-cyanatophenyl)ethane was determined via single crystal X-ray diffraction, and the structures of these four di(cyanate esters) and tri(cyanate ...

On the size dependence of melting parameters for silicon

Using the dependences of melting point Tm and crystallization point Tc on the number of atoms (N) in a spherical silicon crystal that were calculated elsewhere [6] by the method of molecular dynamics, (i) the number of atoms at which the latent heat of the solid–liquid phase transition disappears and (ii) temperature T0 = Tm(N0) = Tc(N0) below which solidifying nanoclusters remain noncrystalline are estimated. These values are found to be N0 = 22.8156 and T0 = 400.851 K. The N dependences for silicon melting parameters, namely, a jump of entropy of melting, latent melting heat, slope of the melting line, and jumps in the surface energy and volume, are derived.