Ion calorimetry: Using mass spectrometry to measure melting points

Calorimetry measurements have been used to probe the melting of aluminum cluster cations with 63 to 83 atoms. Heat capacities were determined as a function of temperature (from 150 to 1050 K) for size-selected cluster ions using an approach based on multicollision-induced dissociation. The experimental method is described in detail and the assumptions are critically evaluated. Most of the aluminum clusters in the size range examined here show a distinct peak in their heat capacities that is attributed to a melting transition (the peak is due to the latent heat). The melting temperatures are below the bulk melting point and show enormous fluctuations as a function of cluster size. Some clusters (for example, n = 64, 68, and 69) do not show peaks in their heat capacities. This behavior is probably due to the clusters having a disordered solid-like phase, so that melting occurs without a latent heat.     

Second-order phase transitions in amorphous gallium clusters

Ion mobility and calorimetry measurements have been used to probe the nature of the phase transitions in gallium clusters with 29-55 atoms. While most clusters appear to undergo a first-order transition between solidlike and liquidlike phases, a few show the signature of melting without a significant latent heat. These transitions appear to be the finite size analogue of a second-order phase transition, and they presumably occur for some cluster sizes because their solidlike phase is amorphous.     

Melting of alloy clusters: effects of aluminum doping on gallium cluster melting

Calorimetry measurements have been performed as a function of temperature for size-selected Ga(n-1)Al+ clusters with n = 17, 19, 20, 30-33, 43, 46, and 47. Heat capacities determined from these measurements are compared with previous results for pure Ga(n)+ clusters. Melting transitions are identified from peaks in the heat capacities. Substituting an aluminum atom appears to have only a small effect on the melting behavior. For clusters that show melting transitions, the melting temperatures and latent heats for the Ga(n-1)Al+ clusters are similar to those for the Ga(n)+ analogs. For Ga(n)+ clusters that do not show first-order melting transitions (n = 17, 19, and 30) the Ga(n-1)Al+ analogs also lack peaks in their heat capacities. The results suggest that the aluminum atom is not localized to a specific site in the solid-like Ga(n-1)Al+ clusters.     

The effect of heating rate on the melting of polytetrafluoroethylene

When virgin polytetrafluoroethylene is heated at intermediate rates, two melting peaks are observed. As the heating rate is increased, the higher-temperature peak grows at the expense of the lower-temperature one without any significant change in the total heat of fusion. It is suggested that the higher-temperature peak represents a transition to a strained melt which subsequently changes to the more stable equilibrium melt. After recrystallization from the melt, there is only a single melting peak which occurs at a lower temperature than peaks for the virgin polymer. All of these transitions are subject to superheating.     

Breathing mode dynamics and elastic properties of gold nanoparticles

We present calculations of the bulk modulus, heat capacity, and the period of the breathing mode for spherical nanoparticles following excitation by ultrafast laser pulses. The bulk modulus and heat capacities both exhibit clear transitions upon bulk melting of the particles. Equilibrium calculations of the heat capacity show that the melting transition is sharper and occurs at a lower temperature than one would observe from an ultrafast experiment. We also observe an intriguing splitting in the low-frequency spectra of the nanoparticles and analyze this splitting in terms of Lamb's classical theory of elastic spheres. We conclude that the particles either (1) melt during the observation period following laser excitation or (2) melt an outer shell while maintaining a crystalline core. Both mechanisms for melting are commensurate with our observations.     

Gallium cluster "magic melters"

Calorimetry measurements (using a method based on multicollision induced dissociation) have been performed for unsupported gallium clusters, Gan+ (n = 30-50 and 55). Melting transitions have been identified from spikes in the heat capacities recorded as a function of temperature. There are enormous fluctuations in the melting temperatures and the heats of fusion with cluster size. Clusters with n = 31, 33, 37, and 45-47 are "magic melters" with particularly well-defined melting transitions. There is a strong correlation between the heats of fusion, entropies of fusion, and the stabilities of the clusters. However, these quantities are not strongly correlated with the melting temperatures.     

Heating-induced freezing and melting transitions in charged colloids

We examine influence of temperature on the phase behavior of dilute aqueous dispersions of charged colloidal silica and polystyrene particles. They undergo either freezing or melting transitions with increasing temperature. Freezing occurs in the case of low-charge, low-salt colloids, and melting is observed in the case of high-charge, high-salt colloids. All of these phase transitions are thermoreversible. These intriguing behaviors can be qualitatively explained in terms of the decrease in the permittivity of water at elevated temperatures.     

Specific heat and Lindemann-like parameter of metallic clusters: mono- and polyvalent metals

The Brownian-type molecular dynamics simulation is revisited and applied to study the thermal and geometric properties of four mono- and two polyvalent metallic clusters. For the thermal property, we report the specific heat at constant volume CV and study the solid-liquid-like transition by scrutinizing its characteristic. For the geometric property, we calculate the root mean square relative bond-length fluctuation delta as a function of increasing temperature. The thermal change in delta reflects the movement of atoms and hence is a relevant parameter in understanding the phase transition in clusters. The simulated results for the CV of alkali and aluminum clusters whose ground state structures exhibit icosahedral symmetry generally show one phase transition. In contrast, the tetravalent lead is quite often seen to exhibit two phase transitions, a premelting process followed by a progressive melting. In connection with the premelting scenario, it is found here that those (magic number) clusters identified to be of lesser stability (among other stable ones) according to the second energy difference are clusters showing a greater possibility of undergoing premelting process. This energy criterion applies to aluminum clusters nAl=28 and 38. To delve further into the thermal behavior of clusters, we have analyzed also the thermal variation of deltaT and attempted to correlate it with CV(T). It turns out that the premelting (if exist) and melting temperatures of the smaller size clusters (n less, similar 50) extracted from CV do not always agree quantitatively with that deduced from delta.     

Quality of Brazilian vegetable oils evaluated by (modulated) differential scanning calorimetry

Vegetable oils are increasingly replacing fossil-oil-based polymers, and therefore aimed at being used in polymerization reactions from ?20 to 100?°C. Therefore, phase transitions and heat capacities in this temperature range should be well characterized to optimize processing conditions and energy inputs. By using the DSC analysis, only small primary correspondence or divergence between different oil types are seen as a function of their degree of unsaturation, but it does not clearly distinguish detailed features such as shoulder bands related to the separate melting processes of single fatty acid components. By using modulated DSC analysis, the combined analysis of reversing and non-reversing heat signals provides better results. The latter confirms that the melting is not a physical one-step process, but equilibrates between phase transitions and enthalpic reorganizations of the fatty acids that can be monitored separately. The specific heat capacities measured during modulated DSC are somewhat lower than traditional calorimetric measurements, but relate to the degree of unsaturation. The thermal behavior of palm-, soy-, sunflower-, corn-, castor-, and rapeseed-oil is discussed in relation to their composition, by applying a first or second heating scan.     

Isomerisation and phase transitions in small sodium clusters

Using a distance-dependent tight-binding hamiltonian, we have studied the influence of the temperature on the geometries of small alkali clusters (Na₄, Na₈, and Na₂₀). We have applied a Monte-Carlo thermodynamical method which consists in performing canonical samplings for various temperatures, these samplings being reexpressed in the microcanonical ensemble. This method provides thermodynamical values such as the entropy and the specific heat. Their behaviour shows one phase transition in the case of Na₄ and Na₈, and two phase transitions for Na₂₀. As concerns Na₄ and Na₈, the transition occurs at 200 K, between a solid-like phase and a phase for which the geometry of these clusters oscillates between numerous shapes. In the case of Na₂₀, the two observed phase transitions can be described as a melting of the surface atoms (at 200 K) preliminarily to the fluctuation of an inner icosahedron seed (at 300 K).     

Low-temperature heat capacities and derived thermodynamic functions of cyclohexane

The low-temperature heat capacities of cyclohexane were measured in the temperature range from 78 to 350 K by means of an automatic adiabatic calorimeter equipped with a new sample container adapted to measure heat capacities of liquids. The sample container was described in detail. The performance of this calorimetric apparatus was evaluated by heat capacity measurements on water. The deviations of experimental heat capacities from the corresponding smoothed values lie within ±0.3%, while the inaccuracy is within ±0.4%, compared with the reference data in the whole experimental temperature range. Two kinds of phase transitions were found at 186.065 and 279.684 K corresponding solid-solid and solid-liquid phase transitions, respectively. The entropy and enthalpy of the phase transition, as well as the thermodynamic functions {H_(T)-H _{298.15 K}} and {S _(T)-S_{298.15 K}}, were derived from the heat capacity data. The mass fraction purity of cyclohexane sample used in the present calorimetric study was determined to be 99.9965% by fraction melting approach. This revised version was published online in July 2006 with corrections to the Cover Date.     

Metal clusters that freeze into high energy geometries

Heat capacities measured for isolated aluminum clusters show peaks due to melting. For some clusters with around 60 and 80 atoms there is a dip in the heat capacities at a slightly lower temperature than the peak. The dips have been attributed to structural transitions. Here we report studies where the clusters are annealed before the heat capacity is measured. The dips disappear for some clusters, but in many cases they persist, even when the clusters are annealed to well above their melting temperature. This indicates that the dips do not result from badly formed clusters generated during cluster growth, as originally suggested. We develop a simple kinetic model of melting and freezing in a system consisting of one liquidlike and two solidlike states with different melting temperatures and latent heats. Using this model we are able to reproduce the experimental results including the dependence on the annealing conditions. The dips result from freezing into a high energy geometry and then annealing into the thermodynamically preferred solid. The thermodynamically preferred solid has the higher freezing temperature. However, the liquid can bypass freezing into the thermodynamically preferred solid (at high cooling rates) if the higher energy geometry has a larger freezing rate.     

An off-lattice Wang-Landau study of the coil-globule and melting transitions of a flexible homopolymer

The Wang-Landau Monte Carlo approach is applied to the coil-globule and melting transitions of off-lattice flexible homopolymers. The solid-liquid melting point and coil-globule transition temperatures are identified by their respective peaks in the heat capacity as a function of temperature. The melting and theta points are well separated, indicating that the coil-globule transition occurs separately from melting even in the thermodynamic limit. We also observe a feature in the heat capacity between the coil-globule and melting transitions which we attribute to a transformation from a low-density liquid globule to a high-density liquid globule.     

Molecular simulation of gas hydrate nanoclusters in water shell: Structure and phase transitions

Gas hydrate nanoclusters surrounded by water shells are studied by the molecular dynamic method. Hydrates of methane (sI structures) and krypton (sII structures), as well an ice nanocluster in a supercooled water shell, are considered. The main attention was focused on studying the local structure and phase transitions. Variations in local partial densities with an increase in temperature are monitored. Melting points of nanosized samples of gas hydrates are determined using caloric curves. Additional information on the behavior of the considered systems is obtained from the temperature dependences of diffusion coefficients and the Lindemann criterion. Two-phase transitions are revealed for gas hydrate nanoclusters. The first phase transition at 210 K can be assigned to the melting of the ice shell. The second transition at 230–235 K is identified as the phase transition in the hydrate core. The melting of ice cluster is observed at 215 K, which corresponds to the melting point of bulk crystal upon the use of the SPC/E water model.     

Ab initio molecular dynamical investigation of the finite temperature behavior of the tetrahedral Au19 and Au20 clusters

Density functional molecular dynamics simulations have been carried out to understand the finite temperature behavior of Au19 and Au20 clusters. Au20 has been reported to be a unique molecule having tetrahedral geometry, a large HOMO-LUMO energy gap, and an atomic packing similar to that of the bulk gold (Li, J.; et al. Science 2003, 299, 864). Our results show that the geometry of Au19 is exactly identical with that of Au20 with one missing corner atom (called a vacancy). Surprisingly, our calculated heat capacities for this nearly identical pair of gold clusters exhibit dramatic differences. Au20 undergoes a clear and distinct solid-like to liquid-like transition with a sharp peak in the heat capacity curve around 770 K. On the other hand, Au19 has a broad and flat heat capacity curve with continuous melting transition. This continuous melting transition turns out to be a consequence of a process involving a series of atomic rearrangements along the surface to fill in the missing corner atom. This results in a restricted diffusive motion of atoms along the surface of Au19 between 650 to 900 K during which the shape of the ground state geometry is retained. In contrast, the tetrahedral structure of Au20 is destroyed around 800 K, and the cluster is clearly in a liquid-like state above 1000 K. Thus, this work clearly demonstrates that (i) the gold clusters exhibit size sensitive variations in the heat capacity curves and (ii) the broad and continuous melting transition in a cluster, a feature that has so far been attributed to the disorder or absence of symmetry in the system, can also be a consequence of a defect (absence of a cap atom) in the structure.     

Heat capacities and thermodynamic functions of d-ribose and d-mannose

The heat capacities of d-ribose and d-mannose have been studied over the temperature range from 1.9 to 440 K for the first time using a combination of Quantum Design Physical Property Measurement System and a differential scanning calorimeter. The purity, crystal phase and thermal stability of these two compounds have been characterized using HPLC, XRD and TG–DTA techniques, respectively. The heat capacities of d-Mannose have been found to be larger than those of d-ribose due to its larger molecular weight, and the solid–liquid transition due to the sample melting has also been detected in the heat capacity curve. The heat capacities of these two compounds have been fitted to a series of theoretical models and empirical equations in the entire experimental temperature region, and the corresponding thermodynamic functions have been derived based on the curve fitting in the temperature range from 0 to 440 K. Moreover, the phase transition enthalpy and melting temperature of these two compounds have also been determined from the heat flows obtained in DSC measurements.

     

Neon scattering off Sodium clusters at finite temperatures

We present findings from computer simulations of collisions of neon atomic beams with Na20 atomic clusters at different internal temperatures. A functional form for the double differential cross section is determined, and no simple signature of a phase transition is seen, even though the clusters undergo a melting phase transition in the temperature range investigated (100 K–400 K). However, such experiments can be used effectively to measure the internal cluster temperature.     

Direct observation of phase transitions of polyethylene under high pressure by a PSPC x-ray system

A position-sensitive proportional counter (PSPC) x-ray measuring system is employed to observe directly phase transition processes of polyethylene at high temperature and high pressure. X-ray diffraction measurements reveal important new experimental data. First, an irreversible crystal transition from the hexagonal to the orthorhombic structures occurs in the critical region where the hexagonal structure begins to appear at a pressure of 350 MPa. That is, the (100) hexagonal reflection is observed only on cooling at 350 MPa. At pressures above about 400 MPa, however, the hexagonal phase is stable and the phase transitions melt ? hexagonal ? orthorhombic occur reversibly. Second, during cooling at pressures above 400 MPa, the (100) hexagonal reflection can be observed at temperatures below the hexagonal ? orthorhombic transition temperature. This behavior suggests that all the crystal morphologies of polyethylene, from “highly-extended-chain” crystals to crystals with a low melting point, are formed by the transitions melt → hexagonal → orthorhombic. Third, in heating at elevated pressures above 500 MPa, a shoulder in the peak intensity versus temperature plot for the (100) hexagonal reflection is observed at a higher temperature than the large maximum which occurs immediately after the crystal transition. This behavior indicates melting in two stages of hexagonal structures with different thermal stabilities, and the shoulder at higher temperature may be due to the fusion of the hexagonal phase annealed either below or above the transition point.     

自由表面的Ni原子团簇的熔化

采用分子动力学模拟技术研究了不同尺寸的Ni原子团簇的熔化过程.团簇的最初构型为FCC结构.研究结果表明,原子团簇的熔化温度与原子团簇中原子的个数有关,团簇的熔化首先从表面开始,当外层原子成为液态后,整个团簇的熔化从液态层开始,直至核心区域.该熔化过程可以被称为非均质熔化,自由表面充当非均质形核位置.作为对比,对无自由表面的大块固态Ni的熔化过程也进行了模拟,其熔化温度高于实验温度约400 K.表明对无自由表面的大块固态的熔化过程,液相形成无非均质形核位置,熔化的本质过程受均质形核机理控制.     

Detection of obscured glass transitions by QiDSC

Determination of compatibility in the amorphous phase for a two component blend is usually accomplished by analyzing for whether one notes one or two glass transitions. This can be complicated when one of the components is semicrystalline and its melting peak obscures the second glass transition. Quasi-isothermal differential scanning calorimetry (QiDSC) can be used to detect an obscured glass transition by allowing the semicrystalline component to melt and relax revealing the underlying glass transition of the other component. QiDSC is accomplished by performing a modulated temperature DSC experiment at a particular temperature and step ramping through the transitions of interest. For this study two systems are investigated. The first system is a model system based on a blend of polystyrene (PS) and a copolymer of vinylidene fluoride and hexafluoropropylene, P(VF₂/HFP). The glass transition for the PS occurs at the same temperature as the melting point for the fluoro-copolymer. The second system is a fluoro-copolymer/acrylic dried latex. In both cases the hidden glass transition can be noted in the reversing heat capacity of the QiDSC analysis.