Excess Free Energy Research Articles

Impact of ceftriaxone sodium on tetradecyltrimethylammonium bromide & cetyltrimethylammonium bromide mixture: Conductivity and theoretical investigation

The formation of mixed micelle of tetradecyltrimethylammonium bromide (TTAB) & cetyltrimethylammonium bromide (CTAB) mixture has been carried out in appearance of ceftriaxone sodium trihydrate (CTS) drug having different concentrations over a temperature range of 298.15 to 323.15 K, keeping a break of 5 K. The CMC of pure and mixture of surfactants were observed to be reliant on the concentration of drug. The CMC values of TTAB + CTAB mixture lie in between that of pure TTAB & CTAB. The larger deviation of CMC of TTAB & CTAB mixture from the corresponding ideal CMC (CMCid) at higher mole fraction (α1) of CTAB signify stronger interaction amid TTAB and CTAB at higher bulk α1 of CTAB. The negative excess free energy (ΔGexRub) values reveal the stable form of micelle and the stability was attained to be enhanced by the rise of α1 of CTAB. The interaction parameter (β) also reveals the attractive interaction amongst the studied species of surfactants. The micellar mole fraction (X1Rub), as well as its ideal (X1id) values, experience an augmentation by the rise of α1, which reveal that the contribution of CTAB increase with the raise of α1. The Gibbs free energy of micellization (ΔGm0) reveals a spontaneous association of both pure and mixed systems. The enthalpy (ΔHm0) and entropy (ΔSm0) of micellization reveal that the micellization is exothermic in nature, while the recommended forces are hydrophobic interaction, along with weak electrostatic interactions. The values of intrinsic enthalpy also reveal the micelle’s stability, thereby, formed. Degree of dissociation (g), compensation temperature, etc., were also reported.

The Balance of Thermodynamic Potentials in Solar Cells Investigated by Numerical Device Simulations

This article presents an extension of the classical gain/loss analysis of Brendel et al. based on the balance of free energy in a solar cell. We consider the full balance of all thermodynamic potentials by separating the excess free energy into excess chemical and excess electrostatic potentials. A layer-by-layer analysis of an exemplary silicon solar cell shows that the different functionalities of different parts of the solar cell, e.g., the neutral base and the space charge regions, are well reflected in the different pictures provided by looking at the thermodynamic potentials separately. Additionally, we investigate fill factor losses by insufficient majority carrier collection at the back contact of the solar cell with two prototypical passivation layers. Here we show that resistive losses, i.e., losses in the electrostatic potential can be distinguished from kinetic losses, i.e., losses in the chemical potential.

Salt Effect on Donnan Equilibrium in Montmorillonite Demonstrated with Molecular Dynamics Simulations.

Donnan equilibrium governs the distribution of ions in many systems such as ion exchange membranes and biological cells in contact with an external electrolyte. Herein, Donnan equilibrium between bulk salt solution and bihydrated montmorillonite was investigated because such a system is of great importance for many nuclear waste disposal concepts. Specifically, we used molecular dynamics simulations to determine the partition coefficient of chloride, which was achieved by calculating the free-energy difference of chloride in the interlayer and the bulk using enhanced sampling methodology. Montmorillonite in equilibrium with either NaCl or CaCl2 was examined to elucidate the general difference between 1:1 and 2:1 salts. The concentration dependence of the partition coefficient for each salt was determined using three and four concentrations for NaCl and CaCl2, respectively. In the case of NaCl, we found that the partition coefficient increased linearly with the concentration, while for CaCl2, the increase was proportional to the square root of the concentration. A derivation of the partition coefficient using general Donnan theory that includes excess free energy contributions beyond the electrostatic Donnan potential is also presented. For both salts, the agreement between the partition coefficient from the simulations and Donnan theory was excellent. Although Donnan theory is a continuum theory derived without any reference to atomistic details, the present results justify its application to systems with nanoscale pores.

Theoretical Analysis of the Thermodynamic, Structural, Surface and Transport Properties of PbSn Liquid Alloys at 1050 K

The thermodynamic, structural, surface and transport properties of PbSn eutectic alloys at 1050 K have been analyzed employing self association model. The model parameters have been evaluated on utilizing the experimental data of free energy of mixing of PbSn liquid alloys at 1050 K. For the validation of the model parameters, the calculated values of the excess free energy of mixing and activity of the components of PbSn liquid alloys have been compared with the experimentally measured data. Further, the estimated model parameters have been used to determine the thermodynamic functions i.e. the free energy of mixing, thermodynamic activity, entropy of mixing and heat (or enthalpy) of mixing, and the structural properties such as the concentration fluctuations and shortrange order parameter. The theoretical and experimental values are compared. A good agreement is observed. Again, the surface properties of PbSn liquid alloys at 1050 K have been investigated using the Butler model in the framework of self association model. The calculated values of surface tension of PbSn liquid alloys at 1050 K are in reasonable agreement with the data available in the literature. The transport properties like the diffusivity and viscosity of PbSn liquid alloys at 1050 K have been theoretically analyzed. For the computation of viscosity, the simple formula developed by Moelwin- Hughes has been used in conjunction with self association model. The present study reveals that PbSn eutectic liquid alloys at 1050 K are segregating in nature. Further, the model parameters are found to depend on temperature.Keywords: Gibbsfree energy; concentration fluctuations; short-range order parameter; surface tension; diffusivity; viscosity

Assembly nature and physicochemical variables of a mixture of cetyltrimethylammonium bromide + tetradecyltrimethylammonium bromide in aq. levofloxacin hemihydrate drug medium: A conductivity and theoretical approach

This study describes the development of mixed micelles between two cationic surfactants of different chain lengths, hexadecyltrimethylammonium bromide (CTAB) and tetradecyltrimethylammonium bromide (TTAB), in an aqueous solution of levofloxacin hemihydrate (LFH). The LFH is, an antibiotic drug, used to treat many bacterial infections. The conductivity method was used in this investigation at varying temperatures and concentrations of CTAB. From the conductivity versus [surfactant] plots, the critical micelle concentration (CMC) and degree of ionization (g) were determined. The differences between the experimental CMC and its ideal value (CMCid) revealed the presence of interactions amid two employed amphiphiles in creating the mixed micelles. The CMC of the TTAB + CTAB mixed system decreased as the mole fraction (α1) of CTAB was increased at a specific temperature. The values of X1Rub and X1id were larger than the corresponding stoichiometric mole fraction of CTAB (α1), which indicated that CTAB substituted the TTAB molecules from the mixed micelles, and the contribution of CTAB increased in the mixed micelles with increase of α1. The activity coefficients (f1Rub and f2Rub) also showed the contribution of CTAB in the mixed micellization. Thermodynamic variables including excess free energy (ΔGexRub) were computed. The enthalpy (ΔHm0) and entropy (ΔSm0) of the association process indicated the presence of electrostatic (ion–dipole, ion–ion) interactions as well as hydrophobic interactions between the constituents of the study system.

Exponential Temperature-Dependent Parameters for Thermodynamic and Structural Properties of Al-Ti Melt

Thermodynamic and structural properties of Al-Ti melt have been estimated in the framework of Redlich-Kister (R-K) polynomial using linear temperature-dependent (T-dependent) interaction parameters above melting temperatures. These calculations show the existence of the artificial inverted miscibility gaps (artifacts) at temperatures 2000 K, 2500 K, and 2700 K. Therefore, interaction parameters are assumed to vary exponentially with temperature and have been optimised for excess free energy of mixing. The artifacts do not appear in the calculation of these properties of the concerned alloy when these optimized parameters are used. BIBECHANA 19 (2022) 75-82

Theory of charge asymmetric electrolytes. Onsager’s approach revisited

Onsager made corrections to the Poisson–Boltzmann equation, to more correctly describe interactions in asymmetric electrolytes (those which have different charges, in absolute value, for the cation and the anion). The equations established by Onsager allow the calculation of symmetric total correlation functions, such that hij(r)=hji(r). In this article it has been shown that these correlation functions, describing in particular asymmetric electrolytes, can also be deduced from the Ornstein Zernicke integral equations by considering a nonlinear closure relation of the HNC type. The excess free energy deduced from these correlation functions has been found similar to that obtained in Mayer’s theory. Relations with the electrostatic association models on the one hand, and with the dressed ions theory on the other hand, are recovered.

Vapor-liquid equilibrium predictions of refrigerant systems using COSMO based Gex-EoS methods

Combining COSMO-based excess Gibbs free energy models with the Peng-Robinson (PR) equation-of-state (EoS) via mixing rules has recently been shown as a promising method for satisfied VLE predictions on refrigerant systems by Mambo-Lomba and Paricaud. An extension is provided in this work for more systematic and dedicated evaluations focusing on a significantly larger refrigerant database and comparisons between different VLE modeling approaches. In particular, the COSMO-SAC-dsp model is combined with via the original Huron-Vidal (HVO), the modified Huron-Vidal (MHV1) and the Wong-Sandler (WS) mixing rules. Comprehensive model evaluation is performed on the basis of 447 vapor-liquid-equilibrium (VLE) experimental datasets for 233 refrigerant pairs. The results show that the combination of the COSMO-SAC-dsp with the PR yields satisfied and comparable prediction accuracy on the VLE in most cases comparing to the well-established group-contribution based Gex-EoS methods VTPR and PSRK. The performance of the three mixing rules on the studied database follows a decreasing order of MHV1 > HVO > WS but without qualitative difference. Large VLE prediction errors can appear between halogenated hydrocarbons and hydrocarbons. Moreover, errors become more significant and the VLE calculation cannot converge at all for mixtures involving R717 and R744 respectively. Improved predictive accuracy can be achieved by re-optimizing the atomic dispersion parameters of F and =O to 35.5 and 74.0 respectively.

Influence of ternary solute additions on nanocrystalline stability and mechanical behavior

The addition of a ternary solute to reduce the accompanying loss in hardness in a Ni-Cu-P alloy is reported. Here, P serves as the stabilizing addition by its partitioning to the grain boundaries (GBs). In a Ni-40Cu-0.6P (at.%) alloy, nanocrystalline (NC) stability is achieved thermodynamically, i.e., the P solute rapidly diffuses from the matrix to wet the GBs reducing the excess interfacial free energy. In a Cu-19.4Ni-0.6P and a Cu-19.8Ni-0.2P alloy, the P precipitates nanoscale Ni3P in the GBs but such kinetic pinning precipitates where less effective in providing NC stabilization as both the phosphate phase and grains coarsened. For a Ni-40Cu-0.3P alloy, the Ni3P phase also precipitated in the GBs but did not coarsen. Rather, as the GBs broke free from these phosphate precipites they became incorporatedwithin the grains’ interior as evidenced by in situ TEM annealing characterization studies. Nanoindentation confirmed that the addition of the tenary element was effective in mitigating the loss of strength as the stabilizing solute partitions to the GBs as compared to a binary stabilized NC alloy using the same stabilization solute. The collective outcomes of this work concretely demonstrate the need to achieve a sufficient concentration of the stabilizing solute to the GBs and their associated mechanisms by which NC stability is achieved; the influence of a tenary element on solute partitioning diffusivity; and the mechanical tunability offered through ternary alloying in NC alloys.

Thermodynamics of trimethyltetradecylammonium bromide – Sodium deoxycholate binary mixed micelle formation in aqueous solution: Regular solution theory with mutual compensation of excess configurational and excess conformational entropy

A binary mixture of trimethyl(tetradecyl)ammonium bromide = TB-SD = sodium deoxycholate surfactants forms non-ideal binary mixed micelles that have molar excess Gibbs free energy described with the Margules function of the first order. Strong synergistic interactions exist between TB and SD particles (interaction coefficient with a magnitude of 10). Based on the temperature dependence of interaction coefficient and temperature dependence of TB and SD micellar molar fractions product logarithm, it follows that the molar excess entropy is zero. Therefore, although the surfactants TB and SD are structurally very different, their binary mixed micelles can still be described with regular solution theory (random mixing of TB and SD). However, the 2D ROESY spectrum indicates that the binary micellar pseudophase is not random in terms of the spatial distribution of TB and SD particles. Namely, intermolecular interactions between deoxycholic acid anions are missing in the binary mixed micelle. This results in the appearance of excess configuration entropy. However, a zero value of the total molar excess entropy and the existence of the first order Margules function for the molar excess Gibbs free energy means that the molar excess configurational entropy is compensated with the molar excess conformational entropy and that there are correlation effects between the excess configurational enthalpy and entropy as well as between the excess conformational enthalpy and entropy.

Intersubjectivity as an antidote to stress: Using dyadic active inference model of intersubjectivity to predict the efficacy of parenting interventions in reducing stress-through the lens of dependent origination in Buddhist Madhyamaka philosophy.

Intersubjectivity refers to one person’s awareness in relation to another person’s awareness. It is key to well-being and human development. From infancy to adulthood, human interactions ceaselessly contribute to the flourishing or impairment of intersubjectivity. In this work, we first describe intersubjectivity as a hallmark of quality dyadic processes. Then, using parent-child relationship as an example, we propose a dyadic active inference model to elucidate an inverse relation between stress and intersubjectivity. We postulate that impaired intersubjectivity is a manifestation of underlying problems of deficient relational benevolence, misattributing another person’s intentions (over-mentalizing), and neglecting the effects of one’s own actions on the other person (under-coupling). These problems can exacerbate stress due to excessive variational free energy in a person’s active inference engine when that person feels threatened and holds on to his/her invalid (mis)beliefs. In support of this dyadic model, we briefly describe relevant neuroimaging literature to elucidate brain networks underlying the effects of an intersubjectivity-oriented parenting intervention on parenting stress. Using the active inference dyadic model, we identified critical interventional strategies necessary to rectify these problems and hereby developed a coding system in reference to these strategies. In a theory-guided quantitative review, we used this coding system to code 35 clinical trials of parenting interventions published between 2016 and 2020, based on PubMed database, to predict their efficacy for reducing parenting stress. The results of this theory-guided analysis corroborated our hypothesis that parenting intervention can effectively reduce parenting stress if the intervention is designed to mitigate the problems of deficient relational benevolence, under-coupling, and over-mentalizing. We integrated our work with several dyadic concepts identified in the literature. Finally, inspired by Arya Nagarjuna’s Buddhist Madhyamaka Philosophy, we described abstract expressions of Dependent Origination as a relational worldview to reflect on the normality, impairment, and rehabilitation of intersubjectivity.

Carbon Nanoparticle-Induced Changes to Lipid Monolayer Structure at Water-Air Interfaces.

Surface specific vibrational spectroscopy experiments together with surface tension measurements and spectroscopic ellipsometry data were used to characterize the effects of soluble carbon particulates on compressed and partially compressed lipid monolayers adsorbed to the water-air interface. The lipid monolayers consisted of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DPPC), and measurements were made for both tightly packed monolayers (40 Å2/molecule) and monolayers in their liquid condensed state (55 Å2/molecule). Langmuir trough data show that very small amounts of PHF (0.0075 mg/mL or 6.4 × 10-6 M) decrease lipid film compressibility. This finding supports a cooperative adsorption mechanism whereby the soluble PHFs are drawn to the surface and associate with the insoluble DPPC monolayer. Excess free energies (ΔGmixE) were positive, consistent with the cooperative adsorption mechanism, and although the excess free energies are small (≤1 kJ/mol), adsorbed PHF has measurable effects on monolayer structure. Further support for the cooperative adsorption mechanism at the water-air interface comes from vibrational sum frequency generation (VSFG) experiments. Low PHF concentrations (≤0.06 mg/mL) increase DPPC acyl chain ordering in liquid condensed lipid films and decrease DPPC acyl chain ordering and film thickness in tightly packed lipid films.

Multi-technique approach to explore the mixed micellization behavior of promazine hydrochloride drug and cetyltrimethylammonium bromide surfactant in aqueous glycine, glycylglycine (dipeptide) and glycylglycylglycine (tripeptide) solutions

The aggregation properties of amphiphiles and their mixtures are of theoretical and applied importance. Therefore, mixed micellization behavior of promazine hydrochloride (PMZ) drug and cetyltrimethylammonium bromide (CTAB) surfactant at different mole fractions, α PMZ = (0.2, 0.4, 0.6 and 0.8) has been scrutinized in water and (0.025, 0.050 and 0.100) mol·kg −1 aqueous solutions of glycine, glycylglycine (dipeptide) and glycylglycylglycine (tripeptide) at T = (298.15 to 318.15) K, by means of multiple techniques. Thermodynamic parameters of micellization (ΔG°m, ΔH°m, and ΔS°m) along with excess Gibbs free energy of mixing (ΔG m ex), the molecular interaction parameter (β int), and the degree of ionization (α), have been attained from the conductivity measurements. The partial specific volumes (φ v), partial specific isentropic compression (φ κ) as well as isentropic compressibilities (κ s) were computed from the measured density and speed of sound data. UV-Visible absorption, fluorescence emission and proton (1H) NMR spectra were recorded for the pure PMZ and mixed (PMZ + CTAB) system in the presence of glycine(aq), glycylglycine(aq) and glycylglycylglycine(aq) solutions. Dynamic light scattering (DLS) study was carried out to measure the hydrodynamic diameters (D H) of mixed micellar systems. The prevalence of hydrophobic-hydrophobic interactions amid the hydrophobic groups of PMZ drug (tricyclic scaffolding), CTAB (–C16H33), glycine, di- and tri-peptides (–CH2), and electrostatic interactions amid the hydrophilic/ionic groups of PMZ{tertiary amine part and +NH (CH3)2, Cl−}, CTAB (–N (CH3)3 +, Br‒) and glycine, di- and tri-peptides {zwitterion (NH3 +, COO−} have been depicted from the aforementioned studies.

Interaction between Triton X100 and Brij 58 in their binary mixed micelles: Micellization in aqueous solution and aqueous solution of Poloxamer 188 at the range of temperature T = (273.15–323.15) K

The micellization of the binary mixture of surfactants Triton X100 – Brij 58 in an aqueous solution (with and without Poloxamer 188) was investigated using a spectrofluorimetric method with pyrene as a probe molecule. There are synergistic interactions between the micellar building units in the binary mixed micelles Triton X100 – Brij 58, which increase with increasing temperature. The analyzed binary mixed micelles possess molar excess entropy. The molar excess Gibbs free energy is a first-order Margules function from the surfactant (Triton X100 or Brij 58) molar fraction in the binary mixed micelles Triton X100 – Brij 58. Poloxamer 188, in the temperature range T = (273.15–323.15) K, does not form micelles. Poloxamer 188 in an aqueous surfactant solution (0.01 w/w) reduces the thermodynamic stabilization of the binary mixed micelle Triton X100 – Brij 58 concerning the state of the same binary mixed micelle when this polymer is not present in an aqueous solution. In the presence of Poloxamer 188, the thermodynamic destabilization of the binary mixed micelle Triton X100 – Brij 58 increases with increasing temperature.

Effect of slag composition on the distribution and separation behavior of arsenic between CaO-based slag and liquid copper

To determine the effects of slag basicity and oxygen potential on the distribution of arsenic (As) between slag and liquid copper, high-temperature experiments were conducted using a Kanthal-Super electric furnace. The thermodynamic driving force of As removal from liquid copper was found to increase as the slag basicity increased because the excess free energy of As2O3 decreased with increasing basic oxide content in the slag. The addition of a small amount of Na2O improved As removal efficiency from the liquid copper. In the case of acidic (i.e., low basicity) slag, the As was minimally distributed to slag phase due to the low activity of CaO in the slag. As a result, the basicity of slag should be carefully controlled for the efficient removal of As. In addition, As was segregated and stabilized in the (Mg,Fe)O monoxide as well as in crystalline phases (magnesium arsenate, Mg3(AsO4)2 and ferric arsenate, FeAsO4) formed due to the high contents of MgO and FeO in the slag, from which it was concluded that As enrichment and separation can be achieved during cooling process.

A temperature-independent prediction model predicts the vapor-liquid equilibrium of CO2-based binary mixtures

CO2-based binary mixtures are considered good alternative working fluids in the refrigeration and power cycle due to their excellent performance and environmental friendliness. The vapor-liquid phase equilibrium of CO2-based binary mixtures is the basis for calculating mixing enthalpy and heat capacity, which is essential for thermodynamic analysis. In this work, based on the vdW mixing rules, we proposed a kij model (kij=θjki-θikj). In the proposed model, ki and kj are defined as pure interaction factors of the pure components, θj is the influence factor of component j to component i, and θi is the influence factor of component i to component j. After continuous fitting and trial calculation, we developed a semi-empirical formula, which is called a temperature-independent prediction model. The model does not have any adjustable parameters, which are only related to the physical properties (critical pressure (kPa), critical temperature (K), and acentric factor) and molecular structure (carbon-carbon double bonds, carbon-fluorine, chlorine, iodine, and oxygen atoms) of the components. The temperature-independent prediction model can predict the bubble-point pressures, vapor phase molar fractions, and relative volatilities very well, which is better than the prediction model based on the vdW mixing rules by others and the group contribution model based on the excess free energy (GE) mixing rules (PR+MHV1+UNIFAC). The total average absolute relative deviation of pressures, the total average absolute deviation of vapor phase molar fractions, and the total average absolute relative deviation of relative volatilities by the temperature-independent prediction model are 2.23%, 0.0095, and 5.21%, respectively.

The Interaction of Gb3 Glycosphingolipids with ld and lo Phase Lipids in Lipid Monolayers Is a Function of Their Fatty Acids.

The glycosphingolipid Gb3 is a specific receptor of the bacterial Shiga toxin (STx). Binding of STx to Gb3 is a prerequisite for its internalization into the host cells, and the ceramide's fatty acid of Gb3 has been shown to influence STx binding. In in vitro studies on liquid ordered (lo)/liquid disordered (ld) coexisting artificial membranes, Shiga toxin B (STxB) binds solely to lo domains, thus harboring Gb3 concomitant with an observed lipid redistribution process. These findings raise the question of how the molecular structure of the fatty acid of Gb3 influences the interaction of Gb3 with the different lipids preferentially either found in the lo phase, namely, sphingomyelin and cholesterol, or in the ld phase. We addressed this question by using a series of synthetically available and unlabeled Gb3 glycosphingolipids carrying different long chain C24 fatty acids (saturated, monounsaturated, and α-hydroxylated). In conjunction with surface tension experiments on Langmuir monolayers, we quantified the excess of free energy of mixing of the different Gb3 species in monolayers composed of either sphingomyelin or cholesterol or composed of a fluid phase lipid (DOPC). From a calculation of the total free energy of mixing, we conclude that mixing of the saturated Gb3 species with the ld lipid DOPC is energetically less favorable than all other combinations, while the unsaturated species mix equally well with the lo phase lipids sphingomyelin and cholesterol and the ld phase lipid DOPC. Furthermore, we found that STxB partially penetrates in mixed lipid monolayers (DOPC/sphingomyelin/cholesterol) containing the Gb3 sphingolipid with a saturated or a monounsaturated C24 fatty acid. The maximum insertion pressure, as a measure for protein insertion, is >30 mN/m for both Gb3 molecules and is not significantly different for the two Gb3 species.

Thermodynamic properties of binary systems containing 1-allyl-3-methylimidazolium dicyanamide [Amim][DCA] with short chain alcohols and prediction of surface tension based on molar surface Gibbs free energy

BackgroundAllyl functionalized ionic liquids (ILs) are widely used because of their excellent properties, to increase their applications in industry and academic community, preparing binary mixtures containing ILs and organic solvents is an effective way, and it is essential to further explore the thermodynamic properties of them. MethodsHere, we reported the synthesis and characterization of the ILs 1-allyl-3-methylimidazolium dicyanamide [Amim][DCA]. Then, in the temperature range of 288.15 K–318.15 K, the values of density and surface tension of 1-allyl-3-methylimidazolium dicyanamide, methanol, ethanol, propanol and corresponding binary systems were measured at every 5 K in the full molar concentration. The values of surface tension deviation Δγ, excess molar volume VE and molar surface Gibbs free energy gs of the mixtures were calculated. In addition, the modified Eӧtvӧs equation is derived based on gs, and the values of surface tension of binary mixtures are estimated. Significant findingsThe results show VE are negative, which is mainly due to the tight packing and hydrogen bond, the formation of hydrogen bond has been confirmed by infrared spectroscopy. The Δγ values of 1-allyl-3-methylimidazolium dicyanamide + methanol are positive, while that of the other two are negative. The modified Eӧtvӧs equation has a clear physical meaning. Moreover, the predicted values are in good agreement with the measured ones.

Atomic-Level Description of Thermal Fluctuations in Inorganic Lead Halide Perovskites.

A comprehensive microscopic description of thermally induced distortions in lead halide perovskites is crucial for their realistic applications, yet still unclear. Here, we quantify the effects of thermal activation in CsPbBr3 nanocrystals across length scales with atomic-level precision, and we provide a framework for the description of phase transitions therein, beyond the simplistic picture of unit-cell symmetry increase upon heating. The temperature increase significantly enhances the short-range structural distortions of the lead halide framework as a consequence of the phonon anharmonicity, which causes the excess free energy surface to change as a function of temperature. As a result, phase transitions can be rationalized via the soft-mode model, which also describes displacive thermal phase transitions in oxide perovskites. Our findings allow to reconcile temperature-dependent modifications of physical properties, such as changes in the optical band gap, that are incompatible with the perovskite time- and space-average structures.

Reversible cross-linking facilitates the formation of critical nucleus in binary polymer blends.

Using self-consistent field theory, we study the effect of reversible cross-linking on the nucleation behavior of a binary polymer blend where only one of the components is able to form cross-links. To control the total number of cross-links and their distribution, we introduce a position-dependent cross-linking probability function that is characterized mainly by two parameters, the magnitude and the width. In the weakly cross-linked region, where the product of the magnitude and width, I, is small, the nucleation behavior is classical-like and the profile of the free energy excess is unimodal. In contrast, in the strongly cross-linked region, the profile of the free energy excess becomes bimodal, and the free energy minimum specifies a metastable nucleus. In a certain I, the free energy barrier for the metastable nucleus turns to be negative, which means it becomes more stable. In both cases, the free energy barrier of the critical nucleus is lower than that without cross-linking, indicating that cross-linking always facilitates nucleation although the dynamic behavior may be different when a metastable nucleus is involved during the nucleation process. The free energy analysis demonstrates that the interaction energy rather than the entropy is responsible for the properties of the critical nucleus. Our study provides an easy alternative way for the control of the nucleation behavior and may attract practical interest.