Statistical Thermodynamic Analysis Research Articles

Remarkable Stabilities of Trimetallic Nitride Clusterfullerenes MSc2N@C70 (M = Sc, Y, Dy) with Three Pentagon Adjacencies: A Theoretical Survey

A MSc2N@C70 (M = Sc, Y, Dy) family has been systematically investigated by density functional calculations in conjunction with statistical thermodynamic analyses for the first time. The results revealed that C2v(7854)-C70 is the most predominant carbon cage when encapsulating DySc2N, YSc2N, and Sc3N clusters. In addition, endohedral structures based on C1(7852)-C70 and C1(7851)-C70 are also stable with large concentrations in the temperature region of fullerene formation. All these three isomers are non-IPR structures with three pentagon adjacencies (PA) and related by Stole-Wales transformation. The interaction energies (INT) of MSc2N@C2v(7854)-C70, MSc2N@C1(7852)-C70, and MSc2N@C1(7851)-C70 are much more negative than those of the IPR structures MSc2N@D5h(8149)-C70, revealing a stabilizing effect of the MSc2N (M = Sc, Y, Dy) clusters toward the PAs. On the basis of the ionic model of (MSc2N)6+@C706–, which is confirmed by the frontier orbital analyses, the electron back-donation from C706– to (MSc2N)6+ ...

New Insight into U@C80: Missing U@D3(31921)-C80 and Nuanced Enantiomers of U@C1(28324)-C80.

Triplet U@C1(28324)-C80, violating the isolated pentagon rule, is experimentally recognized as the stable isomer for uranium-based endohedral monometallofullerene U@C80. Here we first verified that triplet U@D3(31921)-C80, following the isolated pentagon rule, was to be another thermodynamically stable isomer via density functional theory in conjunction with statistical thermodynamic analysis. U@D3(31921)-C80 was probably missing in the previous experiment and would be a promising isomer in the to-be experiment because of its excellently thermodynamic stability. In addition, the anomalous metal position was revealed in U@D3(31921)-C80 and U@C1(28324)-C80. Four-electron transfer from U to C80 was also revealed for the two isomers. Thus, two unpaired 5f electrons were still in the U for U@D3(31921)-C80 and U@C1(28324)-C80. Moreover, the covalent interactions between U and C80 in U@D3(31921)-C80 were stronger than those in U@C1(28324)-C80. The electrostatic interactions preponderated in the interaction energy ΔEint between U and C80 for U@C1(28324)-C80, and the orbital interactions dominated in the ΔEint for U@D3(31921)-C80. The electrophilic and nucleophilic reactivities were also analyzed for U@D3(31921)-C80 and U@C1(28324)-C80. Electronic circular dichroism spectra were simulated to distinguish the two enantiomers of U@C1(28324)-C80. We are hopeful that this investigation will be valuable for further identification of the two enantiomers in future experiments.

Pivotal Role of Nonmetal Atoms in the Stabilities, Geometries, Electronic Structures, and Isoelectronic Chemistry of Sc3X@C80 (X = C, N, and O)

The thermodynamic and dynamic stabilities of Sc3 X@C80 (X = C, N, and O) are explored via density functional theory combined with statistical thermodynamic analysis and ab initio molecular dynamics. It is the first time to comprehensively consider the effect of nonmetal atoms on trimetallic endohedral clusterfullerenes. Relative to Sc3 X@Ih (31924)-C80 (X = N and O) with general six-electron transfer, an intriguing electronic structure of unexplored Sc3 C@D5h (31923)-C80 with thermodynamic and dynamic stabilities is clearly disclosed. Natural bond orbitals and charge decomposition analysis simultaneously suggest that one unpaired electron appears on the cage for neutral Sc3 C@D5h (31923)-C80 , which could be prospectively stabilized by effective exohedral derivatization and ionization in the future. Moreover, isoelectronic endohedral clusterfullerenes, (Sc3 C@C80 )- , Sc3 N@C80 , and (Sc3 O@C80 )+ , are also uniquely taken into account. The geometries, electronic structures, reactivities, and reactive sites of isoelectronic species are examined, and it turns out that all the three isoelectronic species would rather electrophilic than nucleophilic reactions. © 2019 Wiley Periodicals, Inc.

Encapsulation of Monometal Uranium into Fullerenes C2n (2n = 70-74): Important Ionic U4+C2n4- Characters and Covalent U-Cage Bonding Interactions.

By using density functional theory calculations combined with statistical thermodynamic analyses, the stabilization performance of a series of fullerene cages C2n (2n = 70-74) via encapsulating monometal uranium was systematically and thoroughly investigated. Results indicate that fullerene cages D5h(8149)-C70 and D3h(14246)-C74 obeying the isolated pentagon rule and C2(10612)-C72 featured with one pentalene moiety were the most promising candidates to encage uranium. Subsequent Mulliken spin density distribution and frontier molecular orbital analyses suggest that four formal electron transfer occurs from monometal U to above the carbon cages. There also exists a high degree of covalent character between the atom U and fullerenes C2n based on Mayer bond order and quantum theory of atoms in molecule (QTAIM) analyses, indicative of the cooperative stabilization by both ionic and covalent bonding interactions. In addition, investigations on the above-mentioned U@C2n isomers and other favorable candidates (U@Cs(8094)-C70, U@C1(10610)-C72, U@C1(13393)-C74, and U@C1(14049)-C74) reveal that these isomers could be closely linked via simple C2 addition and Stone-Wales transformation. These results will provide a systematic understanding on U-based endohedral metallofullerenes (EMFs) and also might be helpful for further exploration of EMF growth mechanisms.

In-Depth Theoretical Probe into Novel Mixed-Metal Uranium-Based Endohedral Clusterfullerenes Sc2UX@Ih(31924)-C80 (X = C, N).

Mixed-metal uranium-based endohedral clusterfullerenes, Sc2UX@C80 (X = C, N), which were recently reported in experiments, have been investigated considering heptagon-containing isomers by density functional theory calculations in conjunction with statistical thermodynamic analysis. The triplet Sc2UC@Ih(31924)-C80 and quartet Sc2UN@Ih(31924)-C80, named after the spiral number (31924), are found to be thermodynamically stable and satisfy aromaticity rules. Furthermore, the restricted movements of the Sc2UX (X = C, N) cluster in Ih(31924)-C80 have been demonstrated via ab initio molecular dynamics simulations. The six-electron transfer from the inner cluster to the cage results in the electronic structures (Sc2UX)6+@C806- (X = C, N), which were also confirmed by natural bond orbital analysis. On the basis of the frontier molecular orbitals, the oxidation states of uranium in Sc2UC@C80 and Sc2UN@C80 are +IV and +III, respectively, with residual electrons in 5f orbitals of U. The chemical bond between U and C (N) of the inner cluster is characterized as a double bond (single bond) by an analysis of the Mayer bond orders. There are covalent interactions between the inner cluster and outer cage, which is clarified by the quantum theory of atoms in molecules. IR spectra of the optimal isomers have also been simulated, which show the clear difference between Sc2UX@C80 (X = C, N). These findings, together with simulated results, are expected to supply useful information in future experiments of mixed-metal uranium-based endohedral clusterfullerenes.

Genoprotection by complexation: The case of Phyllanthus orbicularis K extract

The aqueous extract of the herb Phyllanthus orbicularis Kunth inhibits the mutagenicity of certain aromatic amines (m-phenylendiamine (m-PDA), 4-aminobiphenyl (4-ABP), and 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP)). Meanwhile, the phenolic compound 2–6 di-sec-butylphenol (DSBP) was isolated from this plant’s extract. Computational evidence is presented to support the possibility of a direct complexation between DSBP and each one of these three amines. This complexation is proposed as a possible mode of genoprotective action of the active ingredient(s) present in this extract. Semiempirical dispersion-corrected PM6-D and dispersion-corrected density functional theory (DFT) calculations, corrected for basis set superposition error (BSSE), and followed by statistical thermodynamics analysis demonstrate that the phenol-amines complexes are stable in the following order of decreasing stability: PhIP > m-PDA > 4-ABP. This complexation between the phenol (protector) and each one of the environmentally hazardous amines may interfere with their metabolic bioactivation preventing their conversion into ultimate mutagens. Results from multiple quantum chemical methods, including statistical mechanical analysis, are consistent which lends stronger support to the mechanism than would occur from any one method alone.

Preferential extraction of Ni(II) over Co(II) by arylsulphonic acid in the presence of pyridinecarboxylate ester: Experimental and DFT calculations

Selective extraction of Ni(II) from base metals is a critical step in the direct nickel synergistic extraction process. Significant synergistic effect and preferential extraction of Ni(II) over Co(II) were observed by using the synergistic extractant containing dinonylnaphthalene sulfonic acid (HDNNS) and 2-ethylhexyl 4-pyridinecarboxylate ester (ligand L) in Escaid 110. The selectivity sequence followed the order: Ni(II) > Co(II) > Al(III) > Mg(II) > Fe(III). In order to elucidate the separation difference between Ni(II) and Co(II) which had similar chemical properties, statistical thermodynamics analysis and relativistic density functional theory (DFT) calculations were applied to provide the selective mechanism from both macroscopic and microscopic perspectives. The synergistic extraction diagrams showed that the optimum molar ratio of HDNNS and the ligand L was at 1:2 for Ni(II) and Co(II) extraction, and statistical thermodynamics analysis indicated that the overall extraction process was endothermic. According to DFT calculation results, the optimized geometries of the Ni(II) and Co(II) complexes were in accordance with the crystallographical data. The thermodynamical examination for the Ni and Co extraction was further conducted using a thermodynamical cycle. The difference in the change of Gibbs free energies for the formation of the Ni(II) complex was more negative than that of the Co(II) complex, which was in agreement with the experimental data. It could be concluded that the synergistic extractant had a higher affinity for Ni(II) than Co(II), which might account for the preferential extraction of Ni(II) over Co(II). The results established a computational model capable of predicting the selectivity order of metal ions, which would provide new insights into the separation mechanism of Ni(II) and Co(II) with synergistic extractants.

Toward Rational Design of Selective Molecularly Imprinted Polymers (MIPs) for Proteins: Computational and Experimental Studies of Acrylamide Based Polymers for Myoglobin.

Molecularly imprinted polymers (MIPs) have potential as alternatives to antibodies in the diagnosis and treatment of disease. However, atomistic level knowledge of the prepolymerization process is limited that would facilitate rational design of more efficient MIPs. Accordingly, we have investigated using computation and experiment the protein-monomer binding interactions that may influence the desired specificity. Myoglobin was used as the target protein and five different acrylamide-based monomers were considered. Protein binding sites were predicted using SiteMap and binding free energies of monomers at each site were calculated using MM-GBSA. Statistical thermodynamic analysis and study of atomistic interactions facilitated rationalization of monomer performance in MIP rebinding studies (% rebind; imprinting factors). CD spectroscopy was used to determine monomer effects on myoglobin secondary structure, with all monomers except the smallest monomer (acrylamide) causing significant changes. A complex interplay between different protein-monomer binding effects and MIP efficacy was observed. Validation of hypotheses for key binding features was achieved by rational selection of two different comonomer MIP combinations that produced experimental results in agreement with predictions. The comonomer studies revealed that uniform, noncompetitive binding of monomers around a target protein is favorable. This study represents a step toward future rational in silico design of MIPs for proteins.

Dehydrated Na6[AlSiO4]6 sodalite as a promising SO2 sorbent material: A first principles thermodynamics prediction

AbstractThe capture of sulfur dioxide (SO2) using dehydrated Na6[AlSiO4]6 sodalite was investigated using the first principles density functional theory calculations and thermodynamics analysis. The adsorption geometries, energetics, and electronic structures were predicted with the increasing number of SO2 adsorbates. Upon adsorption, the S atom of single SO2 molecule tends to align to the framework O2− and the two oxygen atoms are oriented to the framework Na+, through electrostatic interactions and with a minor charge transfer. Increasing the number of SO2 adsorbates, the Na6[AlSiO4]6 sodalite framework shrinks first and then expands. Statistical thermodynamics analysis suggests that the capture reaches its saturation limit of four SO2 molecules per Na6[AlSiO4]6 formula (~300 mg/g) at room temperature and a low SO2 partial pressure of 0.001 atm, indicating that dehydrated Na6[AlSiO4]6 can be an efficient SO2 sorbent even at its extremely low concentrations. Higher SO2 partial pressures lead to a higher capture capacity. A low baking temperature of 100‐150°C can efficiently release the adsorbed SO2 and hence restore the capture capacity of Na6[AlSiO4]6.

Thermodynamic mixing properties of alunite supergroup minerals: Quantum-mechanical modeling and thermodynamic analysis of sulfate, chromate, selenate, phosphate, and arsenate solid solutions, as well as uranyl incorporation

Abstract In various geological settings, alunite supergroup minerals, including the end members alunite [KAl3(SO4)2(OH)6] and jarosite [KFe3(SO4)2(OH)6], occur in extensive solid solution on the cation and anion sites, enabling them to accommodate a variety of elements. Jarosite is known for scavenging heavy metals on the K site (e.g., Pb in solid solution between jarosite and plumbojarosite) in acid mine drainage settings, while both jarosite and alunite can be important in controlling toxic anions such as selenate, chromate, or arsenate. However, there is no thermodynamic information on the solubility of these important cations and anions as a function of temperature, in part because this information is difficult to obtain experimentally. In this study, thermodynamic mixing properties of sulfate-chromate (S-Cr), sulfate-selenate (S-Se), and sulfate-phosphate-arsenate (S-P-As) solid solutions in alunite supergroup minerals are investigated based on quantum-mechanical modeling and statistical thermodynamic analysis. S-Cr and S-Se solid solutions in alunite and jarosite are due to the mixing of anions with equivalent charges on the sulfate site. The enthalpy of mixing ( Δ H mix ) is lowest at 0 K (−273 °C) and increases with increasing temperature; it also depends on the arrangement of atoms on the sulfate site (i.e., atomic ordering). Δ H mix is almost constant at −70 °C and higher temperatures. These findings imply that S-Cr and S-Se solid solutions tend to be complete at room temperature and no ordering is acquired at or above ambient conditions. The Gibbs free energy of mixing ( Δ G mix ) indicates that jarosite is more flexible to accommodate chromate and selenate at the sulfate site than the alunite structure and that complete solid solution can be formed between jarosite and both Se- and Cr-analogues at temperatures above −80 °C. Our modeling results of solid solutions in jarosite and alunite demonstrate the critical role of alunite supergroup minerals in controlling toxic elements for long-term immobilization including the relatively favorable incorporation of uranyl (UO22+) into plumbojarosite. The S-P-As solid solution is also explored between alunite family minerals [DAl3(TO4)2(OH, H2O)6] (D is K+, Na+ or Ca2+; TO4 is SO42−, PO43− or AsO43−). The energetic barrier for mixing (reflected by the peak enthalpy of mixing) between ions with different charges (i.e., S-P and As-S solid solution; ∼2–3 kJ/mol of exchangeable atoms) is higher by a factor of two or three compared to anions with the equal charge (P-As solid solution; 1–1.5 kJ/mol of exchangeable atoms). Below 700 °C, ternary S-P-As mixing over a range of compositions in ternary space having alunite, crandallite [CaAl3(PO4)6(OH)5(H2O)], and arsenocrandallite [CaAl3(AsO4)6(OH)5(H2O)] as end members shows large miscibility gaps at compositions close to the ratio of S:P:As = 4:1:1 and 1:1:1 at the TO4 site. Ternary S-P-As mixing between woodhouseite, arsenowoodhouseite, and either alunite or natroalunite shows that arsenate is more compatible with sulfate in natroalunite than sulfate in alunite, whereas substitution of sulfate with phosphate is energetically more favorable in alunite than natroalunite. Our computed phase diagrams of S-P-As mixing suggest that binary solid solutions between pairs of sulfate, phosphate and arsenate in alunite family minerals scarcely occur below 100 °C, is limited at temperatures from 100 to 300 °C and become extensive or complete above 300 °C.

Theoretical analysis of the explosion limits of hydrogen-oxygen mixtures and their stability

We present here a novel explanation for the explosion limits phenomenon, based on the concept of thermodynamic stability analysis of the fuel-oxidizer mixture. This concept is demonstrated by a detailed statistical thermodynamic analysis of the explosion limits of the H2–O2 system. It is shown that while the magnitude of the relative fluctuations in the number of molecules is very small, the reactants approach their thermodynamic stability limit at the explosion limit, thus contributing to the onset of self-ignition. It is also found out that the products (H2O) behave in an opposite manner, being on the verge of stability in the non-explosive region, and becoming stable above the explosion limit. The different chain-carriers are on the verge of thermodynamic stability over the complete range (both explosive and non-explosive regions), a fact that sits well with their short residence time as known from chemical kinetics and experiments. We conclude that the unique nature of the branching limits phenomenon can be considered as a thermodynamic stability problem, promoting the idea that a universal self-ignition criterion can be developed.

The Excess Chemical Potential of Water at the Interface with a Protein from End Point Simulations.

We use end point simulations to estimate the excess chemical potential of water in the homogeneous liquid and at the interface with a protein in solution. When the pure liquid is taken as the reference, the excess chemical potential of interfacial water is the difference between the solvation free energy of a water molecule at the interface and in the bulk. Using the homogeneous liquid as an example, we show that the solvation free energy for growing a water molecule can be estimated by applying UWHAM to the simulation data generated from the initial and final states (i.e., "the end points") instead of multistate free energy perturbation simulations because of the possible overlaps of the configurations sampled at the end points. Then end point simulations are used to estimate the solvation free energy of water at the interface with a protein in solution. The estimate of the solvation free energy at the interface from two simulations at the end points agrees with the benchmark using 32 states within a 95% confidence interval for most interfacial locations. The ability to accurately estimate the excess chemical potential of water from end point simulations facilitates the statistical thermodynamic analysis of diverse interfacial phenomena. Our focus is on analyzing the excess chemical potential of water at protein receptor binding sites with the goal of using this information to assist in the design of tight binding ligands.

Sc2O@Cs(126339)-C92: Di-scandium oxide cluster encapsulated into a large fullerene cage

The geometric, electronic structure and thermodynamic stability of Sc2O@C92 has been characterized by using hybrid density functional theory calculations combined with statistical thermodynamic analyses. Results indicate that the isolated pentagon rule (IPR) isomers Sc2O@Cs(126339)-C92, Sc2O@C1(126367)-C92 and Sc2O@C1(126390)-C92 are favorable. Noteworthy, it is the first time to declare that fullerene isomer Cs(126339)-C92 could be considered as the suitable cage to encapsulate metallic cluster. The electronic properties of these three isomers were performed with frontier molecular orbital (HOMO and LUMO) analyses and bond order calculations. Finally, 13C NMR and UV-vis-NIR spectra were simulated to provide valuable information for future experiments.

Insight into the thermodynamically preferred V3N@Ih(31924)-C80 and acknowledged VxSc3-xN@Ih(31924)-C80 (x=0, 1 and 2)

Very recently, the endohedral clusterfullerenes VxSc3-xN@C80 (x = 1 and 2) have been successfully prepared. Herein, the novel entire family of VxSc3-xN@C80 (x = 0, 1, 2 and 3) were systematically investigated via density functional theory combined with statistical thermodynamics methods. The isomer of Ih(31924)-C80 was unambiguously proved as the most suitable hollow cage to entrap the clusters VxSc3-xN (x = 0, 1, 2 and 3) at the range of endohedral fullerenes form-temperature through statistical thermodynamics analysis considering the influence of entropy-enthalpy. Both the interaction between cluster, VxSc3-xN (x = 0, 1, 2 and 3), and empty cage Ih(31924)-C80 and electronic properties of VxSc3-xN@Ih(31924)-C80 (x = 0, 1, 2 and 3) were explored. IR and Raman spectra of VxSc3-xN@Ih(31924)-C80 (x = 0, 1, 2 and 3) were simulated to distinguish the different structure of these isomers. The Raman absorption spectra of the vibration of inner moieties showed a similar strength interactions between each inner moiety and Ih(31924)-C80. The possibility of existence for V3N@Ih(31924)-C80 is strongly supported by thermodynamic and chemical stability. It is believed that this work will provide valuable information to further explorations of VxSc3-xN@Ih(31924)-C80 (x = 0, 1, 2 and 3) in experiments and applications.

Thermodynamic Quantities and Defect Chemical Properties of La0.8Sr0.2FeO3-δ

In this work, the defect structure analysis of La0.8Sr0.2FeO3-δ (LSF82) was presented. Thermogravimetric measurements were performed to determine change in oxygen nonstoichiometry (Δδ) with oxygen partial pressure in 10−19⩽ ⩽0.21 and 750⩽(T/°C)⩽900 range. LSF82 showed a clear electronic stoichiometric point around δ≈0.1. The negative sign of partial molar enthalpy and entropy indicated that the incorporation of oxygen was an exothermic process and showed that the experimentally observed variations in and with δ fitted well with the statistical thermodynamic analysis. The defect diagram analysis showed that in n-type regime Fe/Fe concentration varied with whereas in p-type regime Fe•Fe concentration varied with . The electrical conductivity relaxation (ECR) experiments were performed to extract partial ionic conductivity and oxygen self diffusivity. The oxygen self-diffusivity (DO) increased from 1.20 × 10−8 cm2⋅s−1 at 800°C to 3.54 × 10−8 cm2⋅s−1 at 900°C with an activation energy of 1.17 ± 0.23 eV. Dilatometry was performed for expansion measurements as function of and temperature. The chemical expansion model based on the relative change in mean ionic radius vs. δ showed that Fe3+ existed as a mixture of high-spin and low-spin states and made a transition from low-spin to high-spin state with increasing δ.

Dynamics of Hydration Water Plays a Key Role in Determining the Binding Thermodynamics of Protein Complexes

Interfacial waters are considered to play a crucial role in protein–protein interactions, but in what sense and why are they important? Here, using molecular dynamics simulations and statistical thermodynamic analyses, we demonstrate distinctive dynamic characteristics of the interfacial water and investigate their implications for the binding thermodynamics. We identify the presence of extraordinarily slow (~1,000 times slower than in bulk water) hydrogen-bond rearrangements in interfacial water. We rationalize the slow rearrangements by introducing the “trapping” free energies, characterizing how strongly individual hydration waters are captured by the biomolecular surface, whose magnitude is then traced back to the number of water–protein hydrogen bonds and the strong electrostatic field produced at the binding interface. We also discuss the impact of the slow interfacial waters on the binding thermodynamics. We find that, as expected from their slow dynamics, the conventional approach to the water-mediated interaction, which assumes rapid equilibration of the waters’ degrees of freedom, is inadequate. We show instead that an explicit treatment of the extremely slow interfacial waters is critical. Our results shed new light on the role of water in protein–protein interactions, highlighting the need to consider its dynamics to improve our understanding of biomolecular bindings.

Entropy effects at dimerisation equilibrium in hard-sphere fluids with different diameters

Statistical-thermodynamic analysis for the calculation of chemical equilibrium in the case of dimerization of hard-sphere monomer species of different sizes into an asymmetric dumbbell was considered. The description of the dimerization was carried out within two models: a) the simplest yet analytical description of the van der Waals type in order to take into account excluded volume effects, and b) the approach of the Largo and Solana type for more accurate description of hard-body mixtures with the effective form factor. Deviations of dimerization equilibrium from ideality depending on the ratio of the reacting monomers' diameters and their overlapping in the dimer were analyzed. It was shown that the reduction in entropy of the resulting hard-body mixture is more noticeable with a larger difference in the diameters but with less fusion of spheres in the dimer.

Characterizing Atomic Interactions in Interstitial Non-Stoichiometric Compounds by Statistical Thermodynamics: Engineering Usage of Estimated Values of Statistical Thermodynamic Parameters

Statistical thermodynamics allows us to estimate atomistic interactions in interstitial non-stoichiometric compounds MXx through analysis of experimentally determined pressure-temperature-composition (PTC) relationships for MXx being in equilibrium with X2 in gaseous state (X=H,N,P or S) or for non-stoichiometric carbide MCx being in equilibrium with excess C. In case of analysis for MCx, chemical activity a(C) of C in place of partial pressure p(X2) of X2 gas must be known. On statistical modelling of crystal lattice structure for MXx, an a priori assumption of constant nearest-neighbour X-X interaction energy E(X-X) within a homogeneity composition range at arbitrary temperature T was accepted to determine number θ of available interstitial sites for occupation by X atoms per M atom. Values of interaction parame-ters estimated as such appear rational and realistic noting consistency of the values for M’s in the same group in the Periodic Table of the Elements and compatibility with enthalpy values evaluated by conventional thermodynamic approach. Engineering insights gained for MXx through analysis of atomistic interaction parameter values evaluated by the statistical thermodynamics are reviewed comprehensively in this paper. M might be substitutional alloy A1-yBy composed of constituents, A and B, or MZz containing another interstitial constituent Z besides X. Insights acquired from this line of statistical thermodynamic analysis appear to be of pragmatic use for advanced alloy design as shall be demonstrated hereafter.

Statistical thermodynamics unveils the dissolution mechanism of cellobiose.

In the study of the cellulose dissolution mechanism opinion is still divided. Here, the solution interaction components of the most prominent hypotheses for the driving force of cellulose dissolution were evaluated quantitatively. Combining a rigorous statistical thermodynamic theory and cellobiose solubility data in the presence of chloride salts, whose cations progress in the Hofmeister series (KCl, NaCl, LiCl and ZnCl2), we have shown that cellobiose solubilization is driven by the preferential accumulation of salts around the solutes which is stronger than cellobiose hydration. Yet contrary to the classical chaotropy hypothesis, increasing salt concentration leads to cellobiose dehydration in the presence of the strongest solubilizer ZnCl2. However, thanks to cellobiose dehydration, cellobiose-salt interaction still remains preferential despite weakening salt accumulation. Based on such insights, the previous hypotheses based on hydrophobicity and polymer charging have also been evaluated quantitatively. Thus, our present study successfully paved a way towards identifying the basic driving forces for cellulose solubilization in a quantitative manner for the first time. When combined with unit additivity methods this quantitative information could lead to a full understanding of cellulose solubility.

Dimerization of hard sphere fluid in inert solvent

Statistical-thermodynamic analysis of the dimerization equilibrium within a hard sphere model in the presence of an inert solvent was carried out. Calculation of the dimerization equilibrium at constant temperature and pressure requires the solution of two equations: the mass action law (MAL) and the equation of state (EOS). Both positive and negative deviations from ideality in a dimerizing hard sphere system with an inert solvent can be simply described by using the minimum number of parameters that characterize the ratio of the components' sizes in the mixture. The enthalpy of mixing varies from the pure endothermic to that of alternating with the exothermic effect at moderate and high concentrations, which are dependent on the ratio of the dimerizing species and the solvent hard-sphere diameters.