Gibbs-Thomson Relationship Research Articles

Polymorphic Phase Transformation Pathways under Nanoconfinement: Flufenamic Acid

Flufenamic acid (FFA) is a highly polymorphic compound, with nine forms to date. When melt crystallization was performed under nanoscale confinement in controlled pore glass (CPG), the formation of the extremely unstable FFA form VIII was favored. Under confinement, form VIII was sufficiently stable to allow the measurement of its melting point, which decreased with decreasing pore size in accord with the Gibbs–Thomson relationship, enabling determination of the otherwise elusive melting point of the bulk form. Moreover, the transformation pathways among the various polymorphs depended on pore size, proceeding as form VIII → form II → form I for nanocrystals embedded in 30–50-nm diameter pores, and form VIII → form IV → form III in 100–200 nm pores. In contrast, form VIII converts directly to form III in the bulk. Whereas previous reports have demonstrated that nanoconfinement can alter (thermodynamic) polymorph stability rankings, these results illustrate that nanoscale confinement can arrest and alter phase transformations kinetics such that otherwise hidden pathways can be observed.

Interface stability, interface fluctuations, and the Gibbs-Thomson relationship in motility-induced phase separations.

Minimal models of self-propelled particles with short-range volume exclusion interactions have been shown to exhibit the signatures of phase separation. Here I show that the observed interfacial stability and fluctuations in motility-induced phase separations (MIPS) can be explained by modeling the microscopic dynamics of the active particles in the interfacial region. In addition, I demonstrate the validity of the Gibbs-Thomson relationship in MIPS, which provides a functional relationship between the size of a condensed drop and its surrounding vapor concentration. As a result, the late-stage coarsening dynamics of MIPS at vanishing supersaturation follows the classic Lifshitz-Slyozov scaling law.

Population Balance Modeling with Size-Dependent Solubility: Ostwald Ripening

In this work, we present a detailed population balance model for Ostwald ripening. The model is based on a size-dependent growth rate expression incorporating the Gibbs–Thomson relationship between particle size and solubility, and is solved numerically. The effect of parameters such as average initial particle size, initial width of the particle size distribution, and initial mass as well as solubility are investigated in simulations. This analysis focuses on understanding how the ripening phenomenon can be exploited in a crystallization process. The simulations are compared to the predictions of classical Lifshitz, Slyozov, Wagner (LSW) theory. Using our results, we assess the advantages and disadvantages of the full numerical simulation compared to the LSW model.

Controlled Synthesis and Up-Conversion Emission of Rare-Earth Tri-Doped NaYF<SUB>4</SUB> Nanocrystals Under Femtosecond-Laser Excitation

Cubic nanocrystal and hexagonal micro-rods NaYF4, with predictable size, shape and phase, have been successfully synthesized through hydrothermal reaction. The growth mechanism and the effect of mass transfer on the morphology of hexagonal micro-prism are both discussed in detail. The increase of tri-doping lanthanide ion concentration decreased the size of crystal particle, which was explained by the Arrhenius rate equation together combined with the Gibbs-Thomson relationship. Furthermore, the dopants did not only affect the sizes of tri-doped NaYF4 micro-rods, but also impacted upon fluorescence intensity. The fluorescence of tri-doped NaYF4: Nd3+/Yb3+/Er3+ system, excited by an 800 nm femtolaser, was intensified with the increase of doped lanthanide ions concentration. Nevertheless owing to the fluorescence quenching, the other two systems (NaYF4: Nd3+/Ho3+/Er3+ and NaYF4: Nd3+/Tm3+/Er3+) did not show the same phenomenon.

A 2H nuclear magnetic resonance study of the state of water in neat silica and zwitterionic stationary phases and its influence on the chromatographic retention characteristics in hydrophilic interaction high-performance liquid chromatography

2H NMR has been used as a tool for probing the state of water in hydrophilic stationary phases for liquid chromatography at temperatures between −80 and +4 °C. The fraction of water that remained unfrozen in four different neat silicas with nominal pore sizes between 60 and 300 Å, and in silicas with polymeric sulfobetaine zwitterionic functionalities prepared in different ways, could be determined by measurements of the line widths and temperature-corrected integrals of the 2H signals. The phase transitions detected during thawing made it possible to estimate the amount of non-freezable water in each phase. A distinct difference was seen between the neat and modified silicas tested. For the neat silicas, the relationship between the freezing point depression and their pore size followed the expected Gibbs–Thomson relationship. The polymeric stationary phases were found to contain considerably higher amounts of non-freezable water compared to the neat silica, which is attributed to the structural effect that the sulfobetaine polymers have on the water layer close to the stationary phase surface. The sulfobetaine stationary phases were used alongside the 100 Å silica to separate a number of polar compounds in hydrophilic interaction (HILIC) mode, and the retention characteristics could be explained in terms of the surface water structure, as well as by the porous properties of the stationary phases. This provides solid evidence supporting a partitioning mechanism, or at least of the existence of an immobilized layer of water into which partitioning could be occurring.

Phase Equilibria and Thermodynamic Modeling of Ethane and Propane Hydrates in Porous Silica Gels

In the present study, we examined the active role of porous silica gels when used as natural gas storage and transportation media. We adopted the dispersed water in silica gel pores to substantially enhance active surface for contacting and encaging gas molecules. We measured the three-phase hydrate (H)-water-rich liquid (L(W))-vapor (V) equilibria of C(2)H(6) and C(3)H(8) hydrates in 6.0, 15.0, 30.0, and 100.0 nm silica gel pores to investigate the effect of geometrical constraints on gas hydrate phase equilibria. At specified temperatures, the hydrate stability region is shifted to a higher pressure region depending on pore size when compared with those of bulk hydrates. Through application of the Gibbs-Thomson relationship to the experimental data, we determined the values for the C(2)H(6) hydrate-water and C(3)H(8) hydrate-water interfacial tensions to be 39 +/- 2 and 45 +/- 1 mJ/m(2), respectively. By using these values, the calculation values were in good agreement with the experimental ones. The overall results given in this study could also be quite useful in various fields, such as exploitation of natural gas hydrate in marine sediments and sequestration of carbon dioxide into the deep ocean.

Structured Water in Porous Solids and Bio-Objects

The interfacial behaviour of water and mixtures of water and organic compounds adsorbed onto carbon and oxide adsorbents and bio-objects (proteins, cells, tissues) was analyzed using 1H NMR spectroscopy with layer-by-layer freezing-out of the bulk and structured water at 190-280 K and the NMR cryoporometric method based on the Gibbs-Thomson relationship for the freezing point depression for adsorbed liquids.

Neutron Diffraction Cryoporometry—A measurement technique for studying mesoporous materials and the phases of contained liquids and their crystalline forms

Neutron diffraction is a standard method for determining the structure of matter on an atomic scale; NMR cryoporometry is a recent widely applicable technique for characterising structure on a 2 nm to 2 μ m scale. An extension of these techniques is described, Neutron Diffraction Cryoporometry (NDC). The information from a set of neutron diffraction measurements of liquids and their crystalline forms in meso-pores, as a function of temperature, is displayed as a cryoporometry graph. The data may then be conveniently interpreted using the Gibbs–Thomson relationship by analogy with the existing technique, NMR cryoporometry. Clear information is thus obtained on the relationship between phase and nano-structure, in a form well suited to further analysis. This method is applied to an equilibrium study of water/ice in SBA-15 templated silicas, as model nano- to meso-structured systems. The method described here uses global pattern matching (a one-dimensional morphing algorithm inside a linear least-squares fitting algorithm) applied to the full range of the diffraction data. This is a rapid method by comparison with the conventional method of fitting individual (overlapping) peaks, and has already led to NMR observations indicating plastic (rotator phase) ice in the same system.

Electrochemical Response of Nanocrystalline Tetragonal Manganese Dioxides Prepared by Spray Vapor Pyrolysis and Ball Milling

The electrochemical and microstructural properties of nanometric tetragonal β-MnO 2 (MD) prepared by high-energy ball milling (BM) and spray pyrolysis (nano-β) were studied in comparison with the original volumetric phase (micro-β). The microstructure was characterized by X-ray diffraction and transmission electron microscopy. Electrochemical properties were studied by step linear voltametry in 1 M KOH. Both the equilibrium potential and the incremental capacity at high potential of the MnO 2 electrode increase when the crystallite size decreases. Ball-milled MD and nano-β both become insertion materials but only the later presents a good cyclability. The increase in electrode potential in 1 M KOH measures the decrease in Gibbs free energy due to the surface energy contribution (1.3 J/m 2 ) generated by the nanometric size of the particles at the solid-liquid interface. Thermogravimetric analysis measurements in the 300-1200 °C range show for all samples a decrease in MnO 2 -Mn 2 O 3 transition temperature which also leads to a calculation of the surface energy of nanometric samples, according to the Gibbs-Thomson relationship. At the solid-gas interface, nano-β has a surface energy a three times larger than BM samples: 0.6 J/m 2 for BM samples and 1.9 J/m 2 for nano-β ones. That illustrates the main differences between both synthesis processes: crystal growth under equilibrium for nano-β, size decrease by striking, and lamination leading to unstable nanometric BM samples.

Compositional pathways and capillary effects during isothermal precipitation in a nondilute Ni–Al–Cr alloy

For a Ni–5.2Al–14.2Cr at.% alloy with moderate solute supersaturations, the compositional pathways, as measured with atom-probe tomography, during early to later stage γ′(L1 2)-precipitation ( R = 0.45–10 nm), aged at 873 K, are discussed in light of a multi-component coarsening model. Employing nondilute thermodynamics, detailed model analyses during quasi-stationary coarsening of the experimental data establish that the γ/γ′ interfacial free-energy is 22–23 ± 7 mJ m −2. Additionally, solute diffusivities are significantly slower than model estimates. Strong quantitative evidence indicates that an observed γ′-supersaturation of Al results from the Gibbs–Thomson effect, providing the first experimental verification of this phenomenon. The Gibbs–Thomson relationship for a ternary system, as well as differences in measured phase equilibria with CALPHAD assessments, are considered in great detail.

Crystallization and melting behaviour of poly(m-xylene adipamide)

The melting and crystallisation behaviour of poly(m-xylene adipamide) (MXD6) are investigated by using the conventional DSC, X-ray diffraction and polarised light microscopy. Triple, double or single melting endotherms are obtained in subsequent heating scan for the samples after isothermal crystallisation from the melt state at different temperatures. The lowest melting peak can be ascribed to the melting of secondary crystals. The melting of primary crystals causes the medium melting peak and the highest melting peak is attributed to the melting of recrystallised species formed during heating. Following the Hoffman–Weeks theory, the equilibrium melting temperature is equal to 250°C and the equilibrium melting enthalpy ΔH m 0 to 175 J g–1. Then, using the Lauritzen–Hoffmann theory of secondary crystallisation, the analyse of the spherulitic growth shows that the temperature of transition between the growing regimes II and III is equal to 176°C. Finally the Gibbs-Thomson relationship allows the determination of the distribution function of crystalline lamellae.

Gibbs–Thomson relationship for the precipitation in Cu–Ti alloys

A diffusion-couple Cu/Cu–Ti alloy was prepared in order to obtain a macroscopic composition gradient in the Cu–Ti alloy system. This couple was solution treated subsequently water quenched and aged at 837 K for 600 s. The precipitation process was analyzed with an EDS-TEM. The Gibbs–Thomson relation was used to analyze the precipitation of the metastable and semicoherent β′ phase in Cu–Ti alloys and this relationship enabled us to estimate the interfacial free energy between matrix and precipitates to be about 0.31 ± 0.02 J m − 2 .

Crystallization, melting, and morphology of a poly(ethylene oxide) diblock copolymer containing a tablet-like block of poly{2,5-bis[(4-methoxyphenyl)oxycarbonyl]styrene}

A poly(ethylene oxide) diblock copolymer containing a short block of poly{2,5-bis[(4-methoxyphenyl)oxycarbonyl]styrene} (PEO- b-PMPCS) has been successfully synthesized via atom transfer radical polymerization (ATRP) method. The number average molecular weights ( M n) of the PEO and PMPCS blocks are 5300 and 2100 g/mol, respectively. Combining the techniques of differential scanning calorimetry (DSC), optical microscopy (OM), wide angle X-ray diffraction (WAXD), and small angle X-ray scattering (SAXS), we have found that the PMPCS blocks, which are tablet-like, can significantly affect the crystallization and melting of the diblock copolymer. The sample studied can form the crystals with a monoclinic crystal structure identical to that of the homo-PEO. The melting temperature ( T m) of the diblock copolymer increases monotonically with crystallization temperature ( T c), which is remarkably similar to the behavior of long period. On the basis of Gibbs–Thomson relationship, the equilibrium T m ( T m 0 ) of the diblock copolymer is estimated to be 65.4 °C. In a wide undercooling (Δ T) range (14 °C<Δ T<30 °C), the isothermal crystallization leads to square-shaped crystals. The PEO- b-PMPCS crystallization exhibits a regime I→II transition at Δ T of 19 °C. The PEO blocks are non-integral folded (NIF) in the crystals, and the PMPCS blocks rejected to lamellar fold surfaces prevent the NIF PEO crystals from transforming to integral folded (IF) ones. Furthermore, the PMPCS tablets may adjust their neighboring positions up or down with respect to the lamellar surface normal, forming more than one PMPCS layer to accompany the increase in the PEO fold length with increasing T c.

Crystal growth science between the centuries

The major framework of crystal growth concepts and technologies was built during the 20th century. This solid framework, however, does not have enough predictive power. The lack of fundamental constants, multi-parametric experimental conditions, and complex chemistry in many systems remain obstacles to the quantitative confrontation of many key concepts with experiment, to make them predictive and to develop these concepts further. In addition, at least several generic issues should be addressed. For instance, the BCF theory is based on the assumption that thermodynamic fluctuations at steps are fast enough to generate a sufficient density of kinks for growth. However, for strongly polygonized steps this is not always the case. Also, for these steps, the Gibbs–Thomson relationship may be valid only within a very low supersaturation range. These problems are considered here. The Kossel model should be generalized for the lattices of which unit cells include several, say, n identical molecules, atoms, or ions in crystallographically inequivalent positions. In this case, only the unit cell as a whole makes a self-reproducible kink while the building blocks in the liquid or gas are the component molecules, atoms or ions. Because of this, the driving force for crystallization takes the same form as that in a system of n components. Therefore even the kink rate is proportional to Cn-Cne rather than to C-Ce where C and Ce are actual and equilibrium concentrations, respectively. Finally, the challenges of biomacromolecular crystallization are discussed. © 2001 Kluwer Academic Publishers

Thermodynamics of calcite growth: baseline for understanding biomineral formation

The complexity of biomineralized structures suggests the potential of organic constituents for controlling energetic factors during crystal synthesis. Atomic force microscopy was used to investigate the thermodynamic controls on carbonate growth and to measure the dependence of step speed on step length and the dependence of critical step length on supersaturation in precisely controlled solutions. These data were used to test the classic Gibbs-Thomson relationship and provided the step edge free energies and free energy barriers to one-dimension nucleation for calcite. Addition of aspartic acid, a common component in biomineralizing systems, dramatically affected growth morphology and altered the magnitude of the surface energy.