The essence of phase transitions in condensed matter by an information theoretic approach.

Our information theoretic considerations suggest that the essence of phase transitions in condensed matter is the change in entropy as reflected in the change in the number of isomers between two phases. The explicit number of isomers as a function of size is computed using a graph theoretic approach that is compared to a direct count for smaller systems. This allows us to apply a common approach to both nanosystems and their macroscopic limit. The entropy increases very rapidly with size with the results that replacing the actual distribution over size by an average is not an accurate approximation. That the phase transition is a sharp function of the temperature is due to the high heat capacity of both the solid and liquid phases. The difference in entropy at the transition is related to the Trouton-Richards considerations. The finite width of the boundary between two phases of a finite system is related to the inherent uncertainty product that is derived from the maximum entropy formalism and that is a result of the fluctuations about equilibrium. As the system size increases, the boundary becomes sharper and one recovers the usual thermodynamic description.

Understanding Organic Photovoltaic Materials Using Simple Thermal Analysis Methodologies.

Large strides have been made in designing an ever-increasing set of modern organic materials of high functionality and thus, often, of high complexity, including semiconducting polymers, organic ferroelectrics, light-emitting small molecules, and beyond. Here, we review how broadly applied thermal analysis methodologies, especially differential scanning calorimetry, can be utilized to provide unique information on the assembly and solid-state structure of this extensive class of materials, as well as the phase behavior of intrinsically intricate multicomponent systems. Indeed, highly relevant insights can be gained that are useful, e.g., for further materials-discovery activities and the establishment of reliable processing protocols, in particular if combined with X-ray diffraction techniques, spectroscopic tools, and scanning electron microscopy enabled by vapor-phase infiltration staining. We, hence, illustrate that insights far richer than simple melting point- and glass-transition identification can be obtained with differential scanning calorimetry, rendering it a critical methodology to understand complex matter, including functional macromolecules and blends.

Theoretical Study on the Structures and Electronic Properties of Tungsten Fluorides at High Pressures.

Transition metal fluorides are a series of strong oxidizing agents. Tungsten (W) fluorides, particularly WF6, have shown broad applications such as luminescence and fluorinating agent. However, other stoichiometries of W fluorides have rarely been studied. It is well-known that pressure can induce structural phase transition, stabilize new compounds, and produce novel properties. In this work, the high-pressure phases of W-F were searched systematically at the pressure range of 0-200 GPa through first-principles swarm-intelligence structural search calculations. A new stoichiometry of WF4 has been predicted to be stable under high pressures. On the other hand, two new high-pressure phases of WF6 with the symmetries of P 2 1 ${{P2}_{1}}$ /m and P ${P}$ -1 were found with decahedral structural units. The electronic properties of the W-F compounds were then investigated. The predicted stable WF6 high-pressure phases maintain semiconducting features, since the W atom provides all its valence electrons to fluorine. We evaluated the oxidizing ability of WF6 by calculating its electron affinity potential. The high pressure P 2 1 ${{P2}_{1}}$ /m WF6 molecular phase shows higher oxidation capacity than the ambient phase. The built pressure-composition phase diagram and the theoretical results of W-F system provide some useful information for experimental synthesis.

Elastic Properties of Alloyed Cementite M3X (M = Fe, Cr; X = C, B) Phases from First-Principle Calculations and CALPHAD Model.

Fe-Cr-C-B wear-resistant steels are widely used as wear-resistant alloys in harsh environments. The M3X (M = Fe, Cr; X = C, B) cementite-type material is a commonly used strengthening phase in these alloys. This study investigated the mechanical properties of cementite (Fe, Cr)3(C, B) using the first-principle density functional theory. We constructed crystal structures of (Fe, Cr)3(C, B) with different concentrations of Cr and B. The bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and hardness of the material were calculated, and a comprehensive mechanical property database based on CALPHAD modeling of the full composition was established. The optimal concentrations of the (Fe, Cr)3(C, B) phase were systematically evaluated across its entire composition range. The material exhibited the highest hardness, shear modulus, and Young's modulus at Cr and B concentrations in the range of 70-95 at% and 40 at%, respectively, rendering it difficult to compress and relatively poor in machinability. When the B content exceeded 90 at%, and the Cr content was zero, the shear modulus and hardness were low, resulting in poor resistance to deformation, reduced stiffness, and ease of plastic processing. This study provides an effective alloying strategy for balancing the brittleness and toughness of (Fe, Cr)3(C, B) phases.

The Chromatin Regulator HMGA1a Undergoes Phase Separation in the Nucleus.

The protein high mobility group A1 (HMGA1) is an important regulator of chromatin organization and function. However, the mechanisms by which it exerts its biological function are not fully understood. Here, we report that the HMGA isoform, HMGA1a, nucleates into foci that display liquid-like properties in the nucleus, and that the protein readily undergoes phase separation to form liquid condensates in vitro. By bringing together machine-leaning modelling, cellular and biophysical experiments and multiscale simulations, we demonstrate that phase separation of HMGA1a is promoted by protein-DNA interactions, and has the potential to be modulated by post-transcriptional effects such as phosphorylation. We further show that the intrinsically disordered C-terminal tail of HMGA1a significantly contributes to its phase separation through electrostatic interactions via AT hooks 2 and 3. Our work sheds light on HMGA1 phase separation as an emergent biophysical factor in regulating chromatin structure.

PtOx Cly (OH)z (H2 O)n Complexes under Oxidative and Reductive Conditions: Impact of the Level of Theory on Thermodynamic Stabilities.

Platinum-based catalysts with Cl- , OH- , O2- and H2 O ligands, are involved in many industrial processes. Their final chemical properties are impacted by calcination and reduction applied during the preparation and activation steps. We investigate their stability under these reactive conditions with density functional theory (DFT). We benchmark various functionals (PBE-dDsC, optPBE, B3LYP, HSE06, PBE0, TPSS, RTPSS and SCAN) against ACFDT-RPA. PBE-dDsC is well adapted, although hybrid functionals are more accurate for redox reactions. Thermodynamic phase diagrams are determined by computing the chemical potential of the species as a function of temperature and partial pressures of H2 O, HCl, O2 and H2 . The stability and nature of the Pt species are highly sensitive to the activation conditions. Under O2 , high temperatures favour PtO2 while under H2 , platinum is easily reduced to Pt(0). Chlorine modifies the coordination sphere of platinum during calcination by stabilizing PtCl4 and shifts the reduction of platinum to higher temperatures under H2 .

Multicomponent Chiral Quantification with Ultraviolet Circular Dichroism Spectroscopy: Ternary and Quaternary Phase Diagrams of Levetiracetam.

Chiral molecules are challenging for the pharmaceutical industry because although physical properties of the enantiomers are the same in achiral systems, they exhibit different effects in chiral systems, such as the human body. The separation of enantiomers is desired but complex, as enantiomers crystallize most often as racemic compounds. A technique to enable the chiral separation of racemic compounds is to create an asymmetry in the thermodynamic system by generating chiral cocrystal(s) using a chiral coformer and using the solubility differences to enable separation through crystallization from solution. However, such quaternary systems are complex and require analytical methods to quantify different chiral molecules in solution. Here, we develop a new chiral quantification method using ultraviolet-circular dichroism spectroscopy and multivariate partial least squares calibration models, to build multicomponent chiral phase diagrams. Working on the quaternary system of (R)- and (S)-2-(2-oxopyrrolidin-1-yl)butanamide enantiomers with (S)-mandelic acid in acetonitrile, we measure accurately the full quaternary phase diagram for the first time. By understanding the phase stabilities of the racemic compound and the enantiospecific cocrystal, the chiral resolution of levetiracetam could be designed due to a large asymmetry in overall solubility between both sides of the racemic composition. This new method offers improvements for chiral molecule quantification in complex multicomponent chiral systems and can be applied to other chiral spectroscopy techniques.

Thermodynamic anomalies, polyamorphism and all that.

The appearance and evolution of thermodynamics anomalies, and related properties, are studied for two classes of system, modelling those dominated by covalent and ionic interactions, respectively. Such anomalies are most familiar in the density but are also present in other thermodynamics variables such as the compressibility and heat capacity. By systematically varying key model parameters the emergence and evolution of these anomalies can be tracked across the phase space. The interaction of the anomalies can often be rationalized by thermodynamics 'rules'. The emergence of these anomalies may also be correlated with the appearance of polyamorphism, the existence of multiple amorphous states which differ in density and entropy. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.

Two-Component Rare-Earth Fluoride Materials with Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in 50 RF3-R'F3 (R = La-Lu) Systems.

The formation of materials with negative thermal expansion (NTE) based on a phase transition-type mechanism (NTE-II) in 50 T-x (temperature-composition) RF3-R'F3 (R = La-Lu) systems out of 105 possible is predicted. The components of these systems are "mother" RF3 compounds (R = Pm, Sm, Eu, and Gd) with polymorphic transformations (PolTrs), which occur during heating between the main structural types of RF3: ß-(ß-YF3) → t-(mineral tysonite LaF3). The PolTr is characterized by a density anomaly: the formula volume (Vform) of the low-temperature modification (Vß-) is higher than that of the high-temperature modification (Vt-) by a giant value (up to 4.7%). In RF3-R'F3 systems, isomorphic substitutions chemically modify RF3 by forming R1-xR'xF3solid solutions (ss) based on both modifications. A two-phase composite (ß-ss + t-ss) is a two-component NTE-II material with adjustable parameters. The prospects of using the material are estimated using the parameter of the average volume change (ΔV/Vav). The Vav at a fixed gross composition of a system is determined by the ß-ss and t-ss decay (synthesis) curves and the temperature T. The regulation of ΔV/Vav is achieved by changing T within a "window ΔT". The available ΔT values are determined using phase diagrams. A chemical classification (ChCl) translates the search for NTE-II materials from 15 RF3 into an array of 105 RF3-R'F3 systems. Phase diagrams are divided into 10 types of systems (TypeSs), in four of which NTE-II materials are formed. The tables of the systems that comprise these TypeSs are presented. The position of Ttrans of the PolTr on the T scale for a short quasi-system (QS) "from PmF3 to TbF3" determines the interval of the ΔTtrans offset achievable in the RF3-R'F3 systems: from -148 to 1186 ± 10 °C. NTE-II fluoride materials exceed known NTE-II materials by almost three times in this parameter. Equilibrium in RF3-R'F3 systems is established quickly. The number of qualitatively different two-component fluoride materials with the giant NTE-II can be increased by more than ten times compared to RF3 with NTE-II.

Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF3-TbF3 System.

Multicomponent fluorides of rare earth elements (REEs-R) are phase transition-type negative thermal expansion (NTE-II) materials. NTE-II occurs in RF3-R'F3 systems formed by "mother" single-component dimorphic RF3 (R = Pm, Sm, Eu, and Gd) with a giant NTE-II. There are two structural types of RF3 polymorphic modifications: low-temperature ß-YF3 (ß-) and high-temperature LaF3 (t-). The change in a structural type is accompanied by a density anomaly: a volume of one formula unit (Vform) Vß- >Vt-. The empirical signs of volumetric changes ΔV/V of NTE-II materials were considered. For the GdF3-TbF3 model system, an "operating-temperature window ΔT" and a two-phase composition of NTE-II materials follows from the thermodynamics of chemical systems: the phase rule and the principle of continuity. A necessary and sufficient sign of NTE-II is a combination of polymorphism and the density anomaly. Isomorphism in RF3-R'F3 systems modifies RF3 chemically by forming two-component t- and ß- type R1-xR'xF3solid solutions (ss). Between the two monovariant curves of ss decay, a two-phase area with ΔTtrans > 0 (the "window ΔT") forms. A two-phase composite (t-ss + ß-ss) is an NTE-II material. Its constituent t-ss and ß-ss phases have different Vform corresponding to the selected T. According to the lever rule on a conode, Vform is calculated from the t-ss and ß-ss compositions, which vary with T along two monovariant curves of ss decay. For the GdF3-TbF3 system, ΔV/V = f(T), ΔV/V = f(ΔT) and the "window ΔT" = f(x) dependencies were calculated.

Lanthanide Contraction in LnF3 (Ln = Ce-Lu) and Its Chemical and Structural Consequences: Part 1: Location of YF3 in the LnF3 Series According to Its Chemical and Structural Characteristics.

A lanthanide contraction(LC) of 14 lanthanides (Ln) from 58Ce to 71Lu consists of the interaction of Ln nucleus with 4f-electrons. Rare earth elements (REEs-R) include Sc, Y, La, and 14 Ln. They are located in 4-6th periods of the subgroup of group III. The electronic structure divides R into short (d- Sc, Y, La) and long (14 f-elements Ce-Lu) homologous series. The most important chemical consequence of LC is the creation of a new conglomerate of 16 RF3 by mixing fluorides of d- (Y, La) and f-elements. This determines the location of YF3 among LnF3. The location of YF3 depends on the structural (formula volumes-Vform) and thermochemical (temperatures and heats of phase transformations, phase diagrams) properties. The location of YF3 between HoF3 and ErF3 was determined by Vform at a standard pressure (Pst) and temperature (Tst). The location of YF3 according to heats of phase transformations ΔHfus and ΔHtrans is in a dimorphic structural subgroup (SSGr) D (Ln = Er-Lu), but without the exact "pseudo ZY". According to the temperatures of phase transformations (Ttrans) in LnF3 (Ln = Dy-Lu), YF3 is located in the SSGr D between ErF3 and TmF3. The ErF3-YF3 and YF3-TmF3 phase diagrams show it to be between ErF3 and TmF3. The crystals of five ß-LnF3 (Ln = Ho-Lu) and ß-YF3 were obtained in identical conditions and their crystal structures were studied. Vform (at Pst and Tst) with "pseudo" atomic numberZY = 67.42 was calculated from the unit cell parameters, which were defined with ±5 × 10-4 Å accuracy. It determines the location of YF3 between HoF3 and ErF3.

Economic Separations of Organic Acidic or Basic Enantiomeric Mixtures-A Protocol Suggestion.

In this review, we aim to present new concepts for the revisited separation of enantiomers from racemic compounds and a protocol worth to be followed in designing the preparation of pure enantiomers. We have taken into account not only the influence of the properties (eutectic composition) and characteristics of the reactants (racemic compound, resolving agent), but also the behavior of the resulting diastereomers and the different conditions (e.g., crystallization time, solvents used, solvate-forming compounds, achiral additives, etc.). The examples discussed are resolutions developed by our research team, through which we will try to illustrate the impact of all these considerations, presenting the methodological investigations interpreting recent discoveries and observations. Some special solid-state analytical and structural investigations assisting us in the elucidation and invention design of the resolution processes of some active pharmaceutical ingredients, such as Tetramisole, tofisopam, and Amlodipine, are also shown.

Critical Influence of Water on the Polymorphism of 1,3-Dimethylurea and Other Heterogeneous Equilibria.

It is shown that the presence of hundreds of ppm of water in 1,3-dimethylurea (DMU) powder led to the large depression of the transition temperature between the two enantiotropically related polymorphic forms of DMU (Form II → Form I) from 58 °C to 25 °C, thus explaining the reported discrepancies on this temperature of transition. Importantly, this case study shows that thermodynamics (through the construction of the DMU-water temperature-composition phase diagram) rather than kinetics is responsible for this significant temperature drop. Furthermore, this work also highlights the existence of a monohydrate of DMU that has never been reported before with a non-congruent fusion at 8 °C. Interestingly, its crystal structure, determined from X-ray powder diffraction data at sub-ambient temperature, consists of a DMU-water hydrogen bonded network totally excluding homo-molecular hydrogen bonds (whereas present in forms I and II of DMU).

Solid-Liquid Equilibrium in Co-Amorphous Systems: Experiment and Prediction.

In this work, the solid-liquid equilibrium (SLE) of four binary systems combining two active pharmaceutical ingredients (APIs) capable of forming co-amorphous systems (CAMs) was investigated. The binary systems studied were naproxen-indomethacin, naproxen-ibuprofen, naproxen-probucol, and indomethacin-paracetamol. The SLE was experimentally determined by differential scanning calorimetry. The thermograms obtained revealed that all binary mixtures investigated form eutectic systems. Melting of the initial binary crystalline mixtures and subsequent quenching lead to the formation of CAM for all binary systems and most of the compositions studied. The experimentally obtained liquidus and eutectic temperatures were compared to theoretical predictions using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state and conductor-like screening model for real solvents (COSMO-RS), as implemented in the Amsterdam Modeling Suite (COSMO-RS-AMS). On the basis of the obtained results, the ability of these models to predict the phase diagrams for the investigated API-API binary systems was evaluated. Furthermore, the glass transition temperature (Tg) of naproxen (NAP), a compound with a high tendency to recrystallize, whose literature values are considerably scattered, was newly determined by measuring and modeling the Tg values of binary mixtures in which amorphous NAP was stabilized. Based on this analysis, erroneous literature values were identified.

Droplet Microfluidics for the Label-Free Extraction of Complete Phase Diagrams and Kinetics of Liquid-Liquid Phase Separation in Finite Volumes.

Liquid-liquid phase separation of polymer and protein solutions is central in many areas of biology and material sciences. Here, an experimental and theoretical framework is provided to investigate the thermodynamics and kinetics of liquid-liquid phase separation in volumes comparable to cells. The strategy leverages droplet microfluidics to accurately measure the volume of the dense phase generated by liquid-liquid phase separation of solutions confined in micro-sized compartments. It is shown that the measurement of the volume fraction of the dense phase at different temperatures allows the evaluation of the binodal lines that determine the coexistence region of the two phases in the temperature-concentration phase diagram. By applying a thermodynamic model of phase separation in finite volumes, it is further shown that the platform can predict and validate kinetic barriers associated with the formation of a dense droplet in a parent dilute phase, therefore connecting thermodynamics and kinetics of liquid-liquid phase separation.

A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids.

Clarifying the factors that control the contact angle of a liquid on a solid substrate is a long-standing scientific problem pertinent across physics, chemistry, and materials science. Progress has been hampered by the lack of a comprehensive and unified understanding of the physics of wetting and drying phase transitions. Using various theoretical and simulational techniques applied to realistic fluid models, we elucidate how the character of these transitions depends sensitively on both the range of fluid-fluid and substrate-fluid interactions and the temperature. Our calculations uncover previously unrecognized classes of surface phase diagram which differ from that established for simple lattice models and often assumed to be universal. The differences relate both to the topology of the phase diagram and to the nature of the transitions, with a remarkable feature being a difference between drying and wetting transitions which persists even in the approach to the bulk critical point. Most experimental and simulational studies of liquids at a substrate belong to one of these previously unrecognized classes. We predict that while there appears to be nothing particularly special about water with regard to its wetting and drying behavior, superhydrophobic behavior should be more readily observable in experiments conducted at high temperatures than at room temperature.

Fragile Pressure-Induced Magnetism in FeSe Superconductors with a Thickness Reduction.

The emergence of high transition temperature (Tc) superconductivity in bulk FeSe under pressure is associated with the tuning of nematicity and magnetism. However, sorting out the relative contributions from magnetic and nematic fluctuations to the enhancement of Tc remains challenging. Here, we design and conduct a series of high-pressure experiments on FeSe thin flakes. We find that as the thickness decreases the nematic phase boundary on temperature-pressure phase diagrams remains robust while the magnetic order is significantly weakened. A local maximum of Tc is observed outside the nematic phase region, not far from the extrapolated nematic end point in all samples. However, the maximum Tc value is reduced associated with the weakening of magnetism. No high-Tc phase is observed in the thinnest sample. Our results strongly suggest that nematic fluctuations alone can only have a limited effect while magnetic fluctuations are pivotal on the enhancement of Tc in FeSe.

Phase-field Determination of NaSICON Materials in the Quaternary System Na2 O-P2 O5 -SiO2 -ZrO2 : The Series Na3 Zr3-x Si2 Px O11.5+x/2.

Two types of solid electrolytes have reached technological relevance in the field of sodium batteries: ß/ß"-aluminas and NaSICON-type materials. Today, significant attention is paid to room-temperature stationary electricity storage technologies and all-solid-state Na batteries used in combination with these solid electrolytes are an emerging research field besides sodium-ion batteries. In comparison, NaSICON materials can be processed at lower sintering temperatures than the ß/ß"-aluminas and have a similarly attractive ionic conductivity. Since Na2 O-SiO2 -ZrO2 -P2 O5 ceramics offer wider compositional variability, the series Na3 Zr3-x Si2 Px O11.5+x/2 with seven compositions (0≤x≤3) was selected from the quasi-quaternary phase diagram in order to identify the predominant stability region of NaSICON within this series and to explore the full potential of such materials, including the original NaSICON composition of Na3 Zr2 Si2 POl2 as a reference. Several characterization techniques were used for the purpose of better understanding the relationships between processing and properties of the ceramics. X-ray diffraction analysis revealed that the phase region of NaSICON materials is larger than expected. Moreover, new ceramic NaSICON materials were discovered in the system crystallizing with a monoclinic NaSICON structure (space group C2/c). Impedance spectroscopy was utilized to investigate the ionic conductivity, giving clear evidence for a dependence on crystal symmetry. The monoclinic NaSICON structure showed the highest ionic conductivity with an optimum ionic conductivity of 1.22×10-3 at 25 °C for the composition Na3 Zr2 Si2 PO12 . As the degree of P5+ content increases, the total ionic conductivity is initially enhanced until x=1 and then decreases again. Simultaneously, the increasing amount of phosphorus leads a decrease in the sintering temperatures for all samples, which was confirmed by dilatometry measurements. The thermal and microstructural properties of the prepared samples are also evaluated and discussed.

An industrial perspective on co-crystals: Screening, identification and development of the less utilised solid form in drug discovery and development.

Active pharmaceutical ingredients are commonly marketed as a solid form due to ease of transport, storage and administration. In the design of a drug formulation, the selection of the solid form is incredibly important and is traditionally based on what polymorphs, hydrates or salts are available for that compound. Co-crystals, another potential solid form available, are currently not as readily considered as a viable solid form for the development process. Even though co-crystals are gaining an ever-increasing level of interest within the pharmaceutical community, their acceptance and application is still not as standard as other solid forms such as the ubiquitous pharmaceutical salt and stabilised amorphous formulations. Presented in this chapter is information that would allow for a co-crystal screen to be planned and conducted as well as scaled up using solution and mechanochemistry based methods commonly employed in both the literature and industry. Also presented are methods for identifying the formation of a co-crystal using a variety of analytical techniques as well as the importance of confirming the formation of co-crystals from a legal perspective and demonstrating the legal precedent by looking at co-crystalline products already on the market. The benefits of co-crystals have been well established, and presented in this chapter are a selection of examples which best exemplify their potential. The goal of this chapter is to increase the understanding of co-crystals and how they may be successfully exploited in early stage development.

Biodegradable Amphoteric Surfactants in Titration-Ultrasound Formulation of Oil-in-Water Nanoemulsions: Rational Design, Development, and Kinetic Stability.

Amphoteric amphiphilic compounds, due to their unique properties, may represent a group of safe and biocompatible surface-active agents for effective colloidal stabilization of nanoformulations. For this reason, the aim of this work was to develop and characterize the oil-in-water nanoemulsions based on two betaine-derived surfactants with high biodegradability, i.e., cocamidopropyl betaine and coco-betaine. In the first step, we investigated ternary phase diagrams of surfactant-oil-water systems containing different weight ratios of surfactant and oil, as the betaine-type surfactant entity (S), linoleic acid, or oleic acid as the oil phase (O), and the aqueous phase (W) using the titration-ultrasound approach. All the received nanoemulsion systems were then characterized upon droplets size (dynamic light scattering), surface charge (electrophoretic light scattering), and morphology (transmission electron as well as atomic force microscopy). Thermal and spinning tests revealed the most stable compositions, which were subjected to further kinetic stability analysis, including turbidimetric evaluation. Finally, the backscattering profiles revealed the most promising candidate with a size <200 nm for potential delivery of active agents in the future cosmetic, pharmaceutical, and biomedical applications.