Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.     

Ionothermal Synthesis of Imide-Linked Covalent Organic Frameworks

Covalent organic frameworks (COFs) are an extensively studied class of porous materials, which distinguish themselves from other porous polymers in their crystallinity and high degree of modularity, enabling a wide range of applications. COFs are most commonly synthesized solvothermally, which is often a time-consuming process and restricted to well-soluble precursor molecules. Synthesis of polyimide-linked COFs (PI-COFs) is further complicated by the poor reversibility of the ring-closing reaction under solvothermal conditions. Herein, we report the ionothermal synthesis of crystalline and porous PI-COFs in zinc chloride and eutectic salt mixtures. This synthesis does not require soluble precursors and the reaction time is significantly reduced as compared to standard solvothermal synthesis methods. In addition to applying the synthesis to previously reported imide COFs, a new perylene-based COF was also synthesized, which could not be obtained by the classical solvothermal route. In situ high-temperature XRPD analysis hints to the formation of precursor–salt adducts as crystalline intermediates, which then react with each other to form the COF.     

Isotope‐Filtered 4D NMR Spectroscopy for Structure Determination of Humic Substances

Humic substances, the main component of soil organic matter, could form an integral part of green and sustainable solutions to the soil fertility problem. However, their global‐scale application is hindered from both scientific and regulatory perspectives by the lack of understanding of the molecular make‐up of these chromatographically inseparable mixtures containing thousands of molecules. Here we show how multidimensional NMR spectroscopy of isotopically tagged molecules enables structure characterization of humic compounds. We illustrate this approach by identifying major substitution patterns of phenolic aromatic moieties of a peat soil fulvic acid, an operational fraction of humic substances. Our methodology represents a paradigm shift in the use of NMR active tags in structure determination of small molecules in complex mixtures. Unlike previous tagging methodologies that focused on the signals of the tags, we utilize tags to directly probe the identity of the molecules they are attached to.     

Mixing and decomposition behavior of {[4bmpy][Tf2N] + [emim][EtSO4]} and {[4bmpy][Tf2N] + [emim][TFES]} ionic liquid mixtures

Mixing ionic liquids (ILs) has been revealed as a useful way to finely tune the properties of IL-based solvents. The scarce available studies on IL mixtures have shown a quasi-ideal behavior of their physical properties. In this work, we have performed a thermophysical characterization of two binary IL mixtures, namely {4-methyl-N-butylpyridinium bis(trifluoromethylsulfonyl)imide ([4bmpy][Tf₂N]) + 1-ethyl-3-methylimidazolium ethylsulfate ([emim][EtSO₄])} and {[4bmpy][Tf₂N] + 1-ethyl-3-methylimidazolium 1,1,2,2-tetrafluoroethanesulfonate [emim][TFES]}. Both binary IL mixtures have been recently proposed as promising solvents in the (liquid + liquid) extraction of aromatic hydrocarbons from mixtures with alkanes. Densities, viscosities, refractive indices, thermal stability, and specific heats of the {[4bmpy][Tf₂N] + [emim][EtSO₄]} and {[4bmpy][Tf₂N] + [emim][TFES]} IL mixtures have been measured as a function of both temperature and composition. Dynamic viscosities, refractive indices, and thermal stability of the {[4bmpy][Tf₂N] + [emim][EtSO₄]} mixture have exhibited strong deviations from the ideality, in contrast with the quasi-ideal properties of the {[4bmpy][Tf₂N] + [emim][TFES]} mixture and the behavior of the imidazolium and pyridinium-based IL mixtures studied hitherto. The reliability of predictive methods of the thermophysical properties of the mixtures has also been evaluated.     

Isopropanol dehydration via extractive distillation using low transition temperature mixtures as entrainers

Low transition temperature mixtures (LTTMs), also known as deep eutectic solvents, show properties that make them suitable as entrainers for extractive distillation. Two different low transition temperature mixtures were considered as potential entrainers for the extractive distillation of the azeotropic mixture (isopropanol + water). (Lactic acid + choline chloride) (2:1) and (glycolic acid + choline chloride) (3:1) were selected for this work. (Vapor + liquid) equilibrium measurements of the pseudo-binary systems (isopropanol + LTTM) and (water + LTTM) were measured at different concentrations of LTTM in a pressure range of 10 to 100 kPa. (Vapor + liquid) equilibrium data of the pseudo-ternary system (isopropanol + water + LTTM) were also measured at constant pressure (100 kPa) and constant LTTM molar fraction of 0.05 and 0.1. It was found that these LTTMs cannot break the azeotrope at those concentrations. However, the azeotrope was displaced to a much higher isopropanol concentration. The NRTL model was successfully applied to fit the experimental data.     

Phase behavior and interfacial properties of diblock copolymer-homopolymer ternary mixtures: Influence of volume fraction of copolymers and interaction energy

We use a Monte Carlo method to study the phase and interfacial behaviors of A-b-B diblocks in a blend of homopolymers, A and B, which are confined between two asymmetric hard and impenetrable walls. Our results show that, when the interaction strength is weak, the block copolymersare uniformly distributed in the ternary mixtures under considered concentrations. Under strong interaction strength, distribution region of the block copolymers changes from a single smooth interface to a curved interface or multi-layer interface in the ternary mixtures. Furthermore, our findings show that with increasing volume fraction of A-b-B diblock copolymer(фC), copolymer profiles broaden while фC≥ 0.4, a lamellar phase is formed and by further increasing фC, more thinner layers are observed. Moreover, the results show that, with the increase of фC, the phase interface first gradually transforms from plane to a curved surface rather than micelle or lamellar phase while with the increase of the interaction between A and B segments(ε_(AB)), the copolymer chains not only get stretched in the direction perpendicular to the interface, but also are oriented. The simulations also revealthat the difference between symmetric and asymmetric copolymers is negligible in statistics if the lengths of two blocksare comparable.     

Fast-switching effect using viscous chiral-nematic materials

We report on chiral-nematic mixtures containing viscous chiral dopants, composed of rigid rod-like chiral molecules, in order to solve the problem of backflow in the middle layers of the liquid crystal cells. During the study, the viscoelastic properties of the liquid crystal compositions have been optimised, as well as the helical twisting power of the chiral compounds, the anchoring energy and the pre-tilt angle of alignment materials, the ratio between the cell gap and the helical pitch (d/P₀). After optimisation, we prepared test cells with low operating voltage – from 1.5 till 5.0 V, fast response time (τ_on + τ_off) – less than 1 ms, wide operating temperature range from ?40°C till +100°C, and good thermal stability. It should be noted that the response time of the new electro-optical mode does not strongly depend on the cell gap, which is in contrast to other known operating modes. We have achieved rather linear than quadratic dependence of the response time when changing the thickness of the cell.     

Solubility of phenobarbital in aqueous cosolvent mixtures revisited: IKBI preferential solvation analysis

The preferential solvation parameters of phenobarbital in aqueous binary mixtures of 1,4-dioxane, t-butanol, n-propanol, ethanol, propylene glycol and glycerol were derived from solution thermodynamic properties by using the IKBI method. This drug is sensitive to preferential solvation effects in all these mixtures. The preferential solvation parameter by the cosolvent (δx_1,3) is negative in almost all the water-rich mixtures but positive in mixtures with similar proportions of solvents and cosolvent-rich mixtures, except in 1-propanol + water mixtures, where negative values are also found in mixtures with x₁ ≥ 0.70. Hydrophobic hydration around the non-polar ethyl and phenyl groups of this drug in water-rich mixtures could play a relevant role in drug solvation. Otherwise, in mixtures of similar solvent compositions and in cosolvent-rich mixtures the preferential solvation by cosolvent could be due to the acidic behaviour of the drug.     

Condensation from steam—air mixtures in a horizontal annular flow channel

Experiments were performed on the condensation of steam from steam-air mixtures in annular flow at a cooled inner tube. The range of investigation was varied for laminar and turbulent flow for 1.5 × 10³ Re 1.3 × 10⁴ and inlet concentrations 0.59 p_steam/p_total 0.95. The measurements, performed at an open test loop at p_total ≈ 0.96 bar, allowed local heat and mass transfer coefficients to be evaluated for various inlet lengths in the 2 m long annulus. The steam concentration was measured locally inside the annulus with a newly developed dew-point probe. The heat flux was measured locally using the temperature gradient in the cooled inner tube.

Near the inlet region the experiments showed a slightly higher heat flux at the bottom of the tube compared to the top, although it is expected to be smaller there owing to a thicker liquid film. Far downstream from the inlet region the heat transfer at the top was higher than at the bottom. The reasons for these effects are discussed, yielding a better understanding of the thermal and fluid processes involved in condensation from vapor-gas mixtures. The measured data allow the development of correlations for predicting the local Nusselt and Sherwood numbers in a horizontal annular-flow chanbel.     

A variational approach to a micro-structured theory of solid-fluid mixtures

Summary In this paper, we present a micro-structured model for describing global deformations of heterogeneous mixtures. In particular, for a saturated solid-fluid mixture, we regard the solid volume fraction as a microstructural parameter so as to enlarge the space of admissible deformations with respect to the classical theory of mixtures. According to the variational approach, the governing equations are obtained as the stationarity of a suitable action functional. The micro-structured model is then forced to establish a second-gradient mixture theory, by introducing among the considered state parameters a suitable internal constraint. Finally, we determine under which (integrability) conditions the additional balance laws, typically employed to close the theory of porous media endowed with the volume fraction, can fit the variational framework. The authors wish to thank Prof. Francesco dell'Isola from University of Rome La Sapienza for his constructive criticism about the variational approach to continuum mechanics and the interpretation of the volume-fraction balance law.