Equilibrium Correlation Research Articles

Equilibrium Solubility Determination and Correlation of Isobutoxyphenylboronic Acids in Organic Solvents

The solubility of three isomers of isobutoxyphenylboronic acid in several organic solvents (chloroform, 3-pentanone, acetone, dipropyl ether, and methylcyclohexane) has been determined experimental...

Density dynamics in the mass-imbalanced Hubbard chain

We consider two mutually interacting fermionic particle species on a one-dimensional lattice and study how the mass ratio $\eta$ between the two species affects the (equilibration) dynamics of the particles. Focussing on the regime of strong interactions and high temperatures, two well-studied points of reference are given by (i) the case of equal masses ${\eta = 1}$, i.e., the standard Fermi-Hubbard chain, where initial non-equilibrium density distributions are known to decay, and (ii) the case of one particle species being infinitely heavy, ${\eta = 0}$, leading to a localization of the lighter particles in an effective disorder potential. Given these two opposing cases, the dynamics in the case of intermediate mass ratios ${0 < \eta < 1}$ is of particular interest. To this end, we study the real-time dynamics of pure states featuring a sharp initial non-equilibrium density profile. Relying on the concept of dynamical quantum typicality, the resulting non-equilibrium dynamics can be related to equilibrium correlation functions. Summarizing our main results, we observe that diffusive transport occurs for moderate values of the mass imbalance, and manifests itself in a Gaussian spreading of real-space density profiles and an exponential decay of density modes in momentum space. For stronger imbalances, we provide evidence that transport becomes anomalous on intermediate time scales and, in particular, our results are consistent with the absence of strict localization in the long-time limit for any ${\eta > 0}$. Based on our numerical analysis, we provide an estimate for the "lifetime" of the effective localization as a function of $\eta$.

The separation of isopropyl alcohol from diisopropyl ether system using glycols: Phase equilibrium and rigorous correlation

The liquid-liquid equilibria data for the (diisopropyl ether + isopropyl alcohol + ethylene glycol or 1,3-propanediol ternary) system were measured at 303.2 K and 323.2 K under 101.3 kPa. The tie-line data for both systems are displayed in the phase diagram with typical type-I behaviour. The distribution coefficient and separation factor were calculated according to the measured tie-line data. The calculated results suggest that both the two solvents can separate the diisopropyl ether and isopropyl alcohol mixture. Ethylene glycol possesses much better separation efficiency for low concentration extraction. The non-random two liquids (NRTL) and universal quasi-chemical (UNIQUAC) models were applied to obtain the binary interaction parameters of pure components with all the root-mean-square deviation values less than 1.0%, indicating the deviation of regression process can be acceptable. Based on Gibbs stability criteria, the topological analysis with a graphical user interface confirmed the binary interaction parameters from data regression were well consistent with the experimental tie-line data.

Selected applications of typicality to real-time dynamics of quantum many-body systems

Abstract Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the dynamics of quantum many-body systems, called dynamical quantum typicality (DQT). In this paper, we give a brief overview of selected applications of DQT, where particular emphasis is given to questions on transport and thermalization in low-dimensional lattice systems like chains or ladders of interacting spins or fermions. For these systems, we discuss that DQT provides an efficient means to obtain time-dependent equilibrium correlation functions for comparatively large Hilbert-space dimensions and long time scales, allowing the quantitative extraction of transport coefficients within the framework of, e. g., linear response theory (LRT). Furthermore, it is discussed that DQT can also be used to study the far-from-equilibrium dynamics resulting from sudden quench scenarios, where the initial state is a thermal Gibbs state of the pre-quench Hamiltonian. Eventually, we summarize a few combinations of DQT with other approaches such as numerical linked cluster expansions or projection operator techniques. In this way, we demonstrate the versatility of DQT.

Equilibrium Solubility Determination and Correlation of Monobenzone in Fifteen Monosolvents at a Series of Temperatures

This study reports the equilibrium solubility for monobenzone in methanol, ethanol, n-propanol, isopropanol, n-butanol, acetonitrile, ethyl acetate, acetone, 1,4-dioxane, cyclohexane, N,N-dimethylf...

Direct ionization and solubility of chitosan in aqueous solutions with acetic acid

A better understanding of the physicochemical phenomena underlying the direct solubilization of solid chitosan in an aqueous acetic acid medium without the addition of salt is needed. These phenomena have been studied using an inverse approach in which the chitosan is treated as a poly-acid and not as poly-base, and the macrophenomenon observed represents the aggregation of the macromolecules of chitosan instead of their solubilization. The purpose of this study is to present an overview of the physicochemical phenomena underlying this direct solubilization in an aqueous acetic acid medium without the addition of salt through a mathematical model based on equilibrium equations, mass balances, and correlations between experimental data. This model allowed us to model dilute chitosan/acetic acid/water systems without the addition of salt with an adequate fit (R2 > 0.9951) to the trend of the experimental data, enabling the calculation of the pH, degree of ionization, apparent dissociation constant, and the concentrations of the smaller molecules $$\left( {{\text{CH}}_{3} {\text{COOH}}, {\text{CH}}_{3} {\text{COO}}^{ - } ,{\text{H}}_{3} {\text{O}}^{ + } } \right)$$ , with only a priori knowledge of the initial concentration of acetic acid, initial concentration of amine groups, and the dissociation constant of acetic acid. The main finding of this study was that the diluted systems lacking salt studied here showed a tendency toward an apparent dissociation constant of $$pK_{1/2} \to 6.44$$ as the polymer concentration increased. This value is similar to the values reported in the literature for systems containing salt and a degree of deacetylation $$\left( {f_{\text{D}} \sim 0.7} \right)$$ similar to the chitosan evaluated here.

Liquid–Liquid Equilibrium Measurement and Correlation for the Ternary Systems (Dimethyl Succinate + 1,4-Butanediol)/(Dimethyl Glutarate + 1,5-Pentanediol)/(Dimethyl Adipate + 1,6-Hexanediol) + Water at Different Temperatures

Liquid–liquid equilibria (LLE) data for esters + diols + water ternary systems were measured at 101.3 kPa at four different temperatures, namely, 293.15, 303.15, 313.15, and 323.15 K. The Othmer–To...

Vapour-liquid equilibrium measurements and correlation for separating azeotropic mixture (ethyl acetate + n-heptane) by extractive distillation

Since ethyl acetate and n-heptane can form the lowest azeotropic mixture, p-xylene and butyl butyrate were selected as extracting agents to separate the azeotrope (ethyl acetate + n-heptane) using extractive distillation. The binary isobaric vapour-liquid equilibrium (VLE) data for the binary systems (ethyl acetate + p-xylene), (ethyl acetate + butyl butyrate) and (n-heptane + butyl butyrate) were determined at 101.3 kPa using a Rose-Williams still. The measured experimental data were checked by the van Ness method and Herington test. Besides, the determined VLE data were fitted by the NRTL, UNIQUAC and Wilson thermodynamic models. The calculated root-mean-square deviation values of the temperature and vapour phase mole fraction are no more than 0.19 K and 0.0053, respectively. The results showed that three thermodynamic models can be used to correlate the determined experimental data for the three binary systems. Meanwhile, the binary interaction parameters for the three thermodynamic models were optimized, which are a great help for the optimization and simulation of separating the azeotropic mixture (ethyl acetate + n-heptane).

Finite Speed of Quantum Scrambling with Long Range Interactions.

In a locally interacting many-body system, two isolated qubits, separated by a large distance r, become correlated and entangled with each other at a time t≥r/v. This finite speed v of quantum information scrambling limits quantum information processing, thermalization, and even equilibrium correlations. Yet most experimental systems contain long range power-law interactions-qubits separated by r have potential energy V(r)∝r^{-α}. Examples include the long range Coulomb interactions in plasma (α=1) and dipolar interactions between spins (α=3). In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large α. This result parametrically improves previous bounds, compares favorably with recent numerical simulations, and can be realized in quantum simulators with dipolar interactions. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems, and improve bounds on environmental decoherence in experimental quantum information processors.

Solid-liquid phase equilibrium determination and correlation of ternary systems NH4Cl+AlCl3+H2O, MgCl2+AlCl3+H2O and SrCl2+AlCl3+H2O at 298 K

The equilibrium data (solubility, density and refractive index) of three aqueous ternary systems NH4Cl + AlCl3+H2O, MgCl2+AlCl3+H2O, and SrCl2+AlCl3+H2O at 298 K were measured by isothermal dissolution method, and the corresponding diagrams were plotted. The phase diagram shows that these three systems are simple eutectic type, and neither double salt nor solid solution formed. Three ternary systems all have one ternary invariant point, two isothermal dissolution curves and two crystallization fields. The equilibrium thermodynamics data of three aqueous ternary systems at 298 K were correlated by using the Pitzer thermodynamic model. Result shows that the calculated values are consistent well with the experimental ones.

Adaptive cluster expansion for Ising spin models

We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we use the Adaptive Cluster Expansion method, originally developed to solve the inverse Ising problem, that is, to infer the interactions from the equilibrium correlations. The method consists in iteratively constructing and selecting clusters of spins, computing their contributions to the free energy and discarding clusters whose contribution is lower than a fixed threshold. The properties of the cluster expansion and its performance are studied in detail on one dimensional, two dimensional, random and fully connected graphs with homogeneous or heterogeneous fields and couplings. We discuss the differences between different representations (Boolean and Ising) of the spin variables.

Non-hysteretic functional form of capillary pressure in porous media

Models of flow of two immiscible fluids in a porous medium overwhelmingly involve use of an equilibrium correlation between what is identified as capillary pressure and the saturation of one of the fluids. This correlation is said to be hysteretic with the functional relation depending on which of the two fluids has displaced the other in a flow scenario. This correlation was proposed when abilities to investigate porous medium systems experimentally for the distribution of fluids or using computer simulation were limited. Because of advances, we can now assert that the quantity called capillary pressure is ambiguously defined and the alleged hysteretic behaviour, even at equilibrium, is actually due to incompleteness in the functional dependence. We provide a path forward for a theoretically sound formulation that corrects the assertion that capillary pressure is a hysteretic function of saturation, and we advocate for moving beyond ingrained erroneous notions.

Quantum criticality in Ising chains with random hyperuniform couplings

We study quantum phase transitions in transverse-field Ising spin chains in which the couplings are random but hyperuniform, in the sense that their large-scale fluctuations are suppressed. We construct a one-parameter family of disorder models in which long-wavelength fluctuations are increasingly suppressed as a parameter $\alpha$ is tuned. For $\alpha = 0$, one recovers the familiar infinite-randomness critical point. For $0 < \alpha < 1$, we find a line of infinite-randomness critical points with continuously varying critical exponents; however, the Griffiths phases that flank the critical point at $\alpha = 0$ are absent at any $\alpha > 0$. When $\alpha > 1$, randomness is a dangerously irrelevant perturbation at the clean Ising critical point, leading to a state we call the critical Ising insulator. In this state, thermodynamics and equilibrium correlation functions behave as in the clean system. However, all finite-energy excitations are localized, thermal transport vanishes, and autocorrelation functions remain finite in the long-time limit. We characterize this line of hyperuniform critical points using a combination of perturbation theory, renormalization-group methods, and exact diagonalization.

Measurement, correlation and modelling of high-pressure phase equilibrium of PLGA solutions in CO2

Poly (lactic-co-glycolic acid) (PLGA) is a copolymer used as drug carrier in controlled release systems as microparticles or scaffolds. Foamed structures are industrially obtained by injecting gas at temperatures above the melting point of the polymer that may promote PLGA degradation. High temperatures are avoidable in this foaming process if a polymer dissolution is used. Ethyl acetate and ethyl lactate are suitable solvents for the PLGA since the polymer is easily solubilised, is environmentally friendly and highly recommendable for medical purposes. CO2 is proposed as antisolvent because is environmentally benign, non-flammable and non-toxic. The knowledge of the solubility of these solvents in CO2 is essential to find the most appropriate working conditions for the foaming process. In this work, the solubility of ethyl acetate and ethyl lactate in CO2 in the presence of different initial concentrations of PLGA has been studied at 298.15 K and at pressures up to 150 bar using a high-pressure variable volume view cell.

Correction to “Design of a Salt-Free Aqueous Two-Phase System Containing Butanol, n–Butylpyridine Dicyanamide, and Water: Equilibrium Data and Correlation”

ADVERTISEMENT RETURN TO ISSUEPREVAddition/CorrectionNEXTORIGINAL ARTICLEThis notice is a correctionCorrection to “Design of a Salt-Free Aqueous Two-Phase System Containing Butanol, n–Butylpyridine Dicyanamide, and Water: Equilibrium Data and Correlation”Shuai XuShuai XuMore by Shuai Xu, Qi ZhuQi ZhuMore by Qi Zhu, Tiantian NieTiantian NieMore by Tiantian Nie, Chong HeChong HeMore by Chong He, Yuliang Li*Yuliang LiMore by Yuliang Lihttp://orcid.org/0000-0002-7803-5073, and Xuliang LinXuliang LinMore by Xuliang Linhttp://orcid.org/0000-0003-2170-5985Cite this: J. Chem. Eng. Data 2019, 64, 10, 4605Publication Date (Web):September 10, 2019Publication History Published online10 September 2019Published inissue 10 October 2019https://doi.org/10.1021/acs.jced.9b00786Copyright © 2019 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views439Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (289 KB) Get e-Alerts Get e-Alerts

Experimental measurement, correlation and COSMO-SAC prediction of liquid-liquid equilibrium for MIPK + dimethylphenols + water mixtures

Liquid-liquid equilibrium (LLE) data for ternary systems of methyl isopropyl ketone (MIPK) + 2,3-/3,4-/3,5-dimethylphenol + water was determined from 298.15 K to 338.15 K under 101.3 kPa in this work. Distribution coefficient and selectivity were calculated to investigate solvent extraction efficiency of dimethylphenol from water and their high values indicated that MIPK could extract dimethylphenols well. The NRTL and UNIQUAC models were applied to correlate experimental LLE data and related root-mean square deviations (RMSDs) were less than 0.5%. Additionally, the experimental data was predicted by COSMO-SAC model, and the corresponding RMSD values demonstrated that COSMO-SAC model can be applied as a predictive tool to calculate LLE data of the investigated ternary systems.

Can the distinguishable cluster approximation be improved systematically by including connected triples?

The Distinguishable Cluster (DC) approximation to the coupled cluster (CC) doubles, proposed by Kats and Manby [J. Chem. Phys. 139, 021102 (2013)], can semiquantitatively describe multiple bond dissociation (which is traditionally considered a paradigm of strongly correlated electronic structure methods based on the multideterminant approach) without leaving the single-reference coupled cluster framework. DC is just one of many internally corrected (CC) methods that improve on the parent CC method by approximation. To build on the success of the DC methods, it is important to probe whether they can be systematically improved. To answer this question, we considered a set of methods in the distinguishable cluster family, culminating in the DC singles, doubles, and triples (DCSDT), a DC modification of the parent CC singles, doubles, and triples that maintains exactness for 3-electron systems. Inclusion of the complete treatment of triples leads to systematic improvement over the DCSD for equilibrium correlation energy estimates. However, this improvement is not matched by enhanced accuracy for multiple bond breaking processes.

Measurement and correlation of isobaric vapour-liquid equilibrium for the (acetonitrile + water) system containing different ionic liquids at atmospheric pressure

Isobaric vapour-liquid equilibrium (VLE) for the (acetonitrile + water) system containing 1-hexyl-3-methylimidazolium chloride ([HMIM][Cl]), 1-butyl-3-methylimidazolium chloride ([BMIM][Cl]), 1-allyl-3-methylimidazolium chloride ([AMIM][Cl]) and 1-butyl-3-methylimidazolium acetate ([BMIM][OAC]) are measured at atmospheric pressure (101.30 kPa). The experimental results show that the addition of ionic liquids (ILs) can improve the separation of acetonitrile and water and eliminate the azeotrope when the content of ILs reaches a certain value. The separation ability of ILs is [BMIM][OAC] > [AMIM][Cl] > [BMIM][Cl] ≈ [HMIM][Cl]. A crossover effect of salting-in and -out of acetonitrile in different concentration ranges is observed. The experimental VLE data are satisfactorily correlated with the non-random two liquid (NRTL) model. Additionally, COSMO-SAC is employed to predict the phase behaviours of the investigated systems and good trends are obtained.

Correlations and forces in sheared fluids with or without quenching

Spatial correlations play an important role in characterizing material properties related to non-local effects. Inter alia, they can give rise to fluctuation-induced forces. Equilibrium correlations in fluids provide an extensively studied paradigmatic case, in which their range is typically bounded by the correlation length. Out of equilibrium, conservation laws have been found to extend correlations beyond this length, leading, instead, to algebraic decays. In this context, here we present a systematic study of the correlations and forces in fluids driven out of equilibrium simultaneously by quenching and shearing, both for non-conserved as well as for conserved Langevin-type dynamics. We identify which aspects of the correlations are due to shear, due to quenching, and due to simultaneously applying both, and how these properties depend on the correlation length of the system and its compressibility. Both shearing and quenching lead to long-ranged correlations, which, however, differ in their nature as well as in their prefactors, and which are mixed up by applying both perturbations. These correlations are employed to compute non-equilibrium fluctuation-induced forces in the presence of shear, with or without quenching, thereby generalizing the framework set out by Dean and Gopinathan. These forces can be stronger or weaker compared to their counterparts in unsheared systems. In general, they do not point along the axis connecting the centers of the small inclusions considered to be embedded in the fluctuating medium. Since quenches or shearing appear to be realizable in a variety of systems with conserved particle number, including active matter, we expect these findings to be relevant for experimental investigations.

Liquid–Liquid Equilibrium for Ternary Systems of N-Methylformamide + Pyrrole/Indole + Alkanes at 298.15 K: Phase Equilibrium Measurement and Correlation

For the purpose of separating nitrogen compounds, pyrrole and indole, N-methylformamide (NMF) was selected as the extractive solvent. The liquid–liquid equilibrium (LLE) data for {NMF + pyrrole/indole + alkanes} systems were measured at 298.15 K under atmospheric pressure of 101.3 kPa. The triangular diagrams of the above eight systems, {NMF + pyrrole/indole + n-hexane/n-heptane/n-decane/n-dodecane}, were classified as Treybal’s type I. Meanwhile, the nonrandom two-liquid (NRTL) and universal quasi-chemical (UNIQUAC) activity coefficient models were applied to correlate the LLE data, and the UNIQUAC model shows better agreement than the NRTL model. In addition, the distribution constant and selectivity factor were calculated on the basis of the experimental data and utilized to investigate the extraction capabilities of NMF for pyrrole and indole.