Properties Of Solutions Research Articles

Effect of Pyrrolidinium Based Ionic Liquid on Thermo Physical and Electrochemical Properties of Binary Aqueous Solutions of Benzylamine and Benzamide at Different Equidistant Temperatures (288.15 K to 318.15 K)

Effect of Pyrrolidinium Based Ionic Liquid on Thermo Physical and Electrochemical Properties of Binary Aqueous Solutions of Benzylamine and Benzamide at Different Equidistant Temperatures (288.15 K to 318.15 K)

An Analytical Framework for In-Plane Two-Impulse Transfers Between Lissajous Orbits

AbstractThis paper presents an analytical framework for in-plane two-impulse transfers between two Lissajous orbits around a single collinear libration point in the linearized circular restricted three-body problem. Based on the categorization of orbits near a collinear libration point in the linearized dynamics, we formulate two-impulse transfers as a two-point boundary value problem with a fixed time of flight (ToF). We explicitly derive and numerically verify the solution, along with its subsets corresponding to transfers involving asymptotic invariant manifolds. Additionally, we derive some general properties of solutions, including the inherent constraints arising from the limited distribution of invariant manifolds are identified and compared to their single-impulse counterparts. We further investigate the relation between the performance and the constraints of two-impulse transfers by numerically evaluating the cost of maneuvers for amplitude-decreasing transfers. Our main results demonstrate improved feasibility compared to the single-impulse transfers with minimum additional cost for a relatively large ToF, regardless of the size of the amplitude size, as well as the existence of a lower bound on the cost similar to the one found in the single-impulse case.

Microfluidic Bubble-Templating Multinozzle 3D Printing for Preparations of Macroporous Hydrogels with Ordered Pores of Large Size Ranges.

A strategy for fabrication of macroporous hydrogels through 3D printing assisted by molding and multiple microfluidic bubble-templating nozzles is proposed here. This approach aims to address the challenges faced by methods for 3D printing macroporous hydrogels, such as difficulties in precisely controlling the spatial distribution of macropores, limited porosity, and low resolution of external boundaries due to the poor mechanical properties of hydrogel solutions as printing ink. In this method, fast-switching microfluidic bubble-templating nozzles of varying sizes allowed for precise control of target pore sizes over a wide range. Cavities of polydimethylsiloxane (PDMS) molds were used to define the overall external shape of the hydrogels and enhance the resolution of the boundaries. During the printing process, the laminar shear force generated by a coaxial microfluidic system generated microbubbles which were then injected into the PDMS mold cavities. The spatial distribution of the microbubble clusters within the cavities was controlled by a 3D motion module. Finally, macroporous hydrogels with a pore size range of 238-930 μm were fabricated while avoiding millimeter round corners on the boundaries. A control precision of pore sizes was about 60 μm. Most importantly, this strategy broke through the space occupancy limitations of pores in traditional 3D printing methods for macroporous hydrogels. The space occupancy of pores could reach a maximum of about 87% within a single layer.

Schouten-Codazzi Gravity

Abstract We propose a new phenomenological second order gravity theory to be denoted as ''Schouten-Codazzi' Gravity'' (SCG), as it is based on Schouten and Codazzi tensors. The theory is related, but is clearly distinct from Cotton Gravity. By assuming as source the energy momentum of General Relativity, we form a second order system with its geometric sector given by the sum of the Schouten tensor and a generic second order symmetric tensor complying with the following properties: (i) it must satisfy the Codazzi differential condition and (ii) it must be concomitant with the invariant characterization based on the algebraic structure of curvature tensors for specific spacetimes or classes of spacetimes. We derive and briefly discuss the properties of SCG solutions for static spherical symmetry (vacuum and perfect fluid), FLRW models and spherical dust fluids. While we do recognize that SCG is ``work in progress'' in an incipient stage that still requires significant theoretical development, we believe that the theory provides valuable guidelines in the search for alternatives to General Relativity

Mixed Adsorption Mono- and Multilayers of ß-Lactoglobulin Fibrils and Sodium Polystyrene Sulfonate

The formation of beta-lactoglobulin (BLG)/sodium polystyrene sulfonate (PSS) complexes decelerates the change in the surface properties of the mixed solutions with the surface age and increases the steady-state dilational surface elasticity in a narrow PSS concentration range. At the same time, the changes in the surface properties are accelerated in the dispersions of BLG fibrils with and without PSS due to the influence of small peptides coexisting with fibrils. A decrease in the peptide concentration as a result of the dispersion purification leads to slower changes in the surface properties at low PSS concentrations. The increase in the polyelectrolyte concentration results in an increase in the steady-state surface elasticity due to the fibril/PSS complex formation and in very slow changes in the surface properties if the polyelectrolyte exceeds a certain critical value. The latter effect is a consequence of the formation of large aggregates and of an increase in the electrostatic adsorption barrier. The consecutive adsorption of BLG fibrils and PSS leads to the formation of regular multilayers at the liquid–gas interface. The multilayer properties change noticeably with an increase in the number of layers from four to six in agreement with previous results on the multilayers of PSS with an oppositely charged synthetic polyelectrolyte, presumably due to the heterogeneity of the first PSS layer. The dynamic elasticity of the multilayers approaches 250 mN/m, indicating that they can effectively stabilize foams and emulsions.

Stabilizing effect of the spacetime expansion on the Euler-Poisson equations in Newtonian cosmology

Abstract The validity of the cosmic no-hair theorem for polytropic perfect fluids has been established by Brauer, Rendall, and Reula [Classical and Quantum Gravity, 11(9), 1994: 2283] within the context of Newtonian cosmology, specifically under conditions of exponential expansion. This paper extends the investigation to assess the nonlinear stability of homogeneous Newtonian cosmological models under general accelerated expansion for perfect fluids. With appropriate assumptions regarding the expansion rate and decay properties of the homogeneous solution, our results demonstrate that the Euler-Poisson system admits a globally classical solution for initial data that are small perturbations to the homogeneous solution. Additionally, we establish that the solution asymptotically approaches the homogeneous solution as time tends to infinity. The theoretical framework is then applied to various types of perfect fluids, including isothermal gases, Chaplygin gases, and polytropic gases.

Effects of Moisture Content and Heat Treatment on the Viscoelasticity and Gelation of Polyacrylonitrile/Dimethylsulfoxide Solutions

Polyacrylonitrile (PAN) gels create significant obstacles in industrial fiber spinning by forming insoluble networks that compromise solution stability and uniformity. This study investigates the rheological properties of PAN/dimethyl sulfoxide (DMSO) solutions, examining how aging time, moisture content, and polymer concentration affect gelation behavior. Dynamic rheological analysis revealed that both physical and chemical crosslinks play crucial roles in gel formation, with gelation accelerating markedly when moisture content exceeds 3% and aging progresses. Under heat treatment at 80 °C, samples with increased moisture content demonstrated rapid transitions to solid-like states, indicating a critical moisture threshold for enhanced gelation kinetics. Additionally, reductions in polymer concentration disrupted physical crosslink density, thereby mitigating gel formation. These results underscore the importance of precisely controlling moisture and concentration parameters in PAN solutions to stabilize solution properties and minimize gel formation, thus enhancing process efficiency and quality in PAN-based carbon fiber production.

Achieving Color‐Tunable Solid‐State Fluorescence by Adjusting the Molecular‐State Chromophores on Carbonized Polymer Dots

Carbon dots (CDs) have attracted great interest in recent years due to their excellent fluorescent properties, convenient synthetic methods, and wide availability of source materials. However, although most CDs exhibit excellent luminescent properties in solution, achieving solid‐state fluorescence (SSF) CDs is still difficult due to aggregation‐caused quenching, and realizing color‐tunable SSF‐CDs remains a serious challenge. Herein, the SSF‐carbonized polymer dots (CPDs) are successfully obtained by one‐step hydrothermal of polyethyleneimine (PEI) and citric acid. The photoluminescence centers of these CPDs are molecular‐state chromophores, which are proved as imidazo [1,2‐a] pyridine‐7‐carboxylic acid, 1,2,3,5‐tetrahydro‐5‐oxo‐ (IPCA) derivatives by NMR. Further investigation reveals that the formation and distribution of IPCA derivatives would affect the bandgaps when CPDs particles aggregate, which is also verified by density functional theory calculations. Based on the above conclusion, the blue, green, yellow, and orange SSF CPDs are successfully obtained, and the multicolor and white emission light emitting diodes are effectively fabricated by these CPDs.

Molecular diffusion in aqueous methanol solutions: The combined influence of hydrogen bonding and hydrophobic ends.

Although the nonmonotonic variation in the diffusion coefficients of alcohol and water with changing alcohol concentrations in aqueous solutions has been reported for many years, the underlying physical mechanisms remain unclear. Using molecular dynamics simulations, we investigated the molecular diffusion mechanisms in aqueous methanol solutions. Our findings reveal that the molecular diffusion is co-influenced by hydrogen bonding and the hydrophobic ends of methanol molecules. A stronger hydrogen bond (HB) network and a higher concentration of hydrophobic ends of methanol molecules both enhance molecular correlations, thereby slowing molecular diffusion in the solution. As methanol concentration increases, the HB network weakens, facilitating molecular diffusion. However, the increased concentration of hydrophobic ends counteracts this effect. Consequently, the diffusion coefficients of water and methanol molecules exhibit nonmonotonic changes. Previous studies have only focused on the role of HB networks. For the first time, we have identified the impact of the hydrophobic ends of alcohol on molecular diffusion in aqueous alcohol solutions. Our research contributes to a better understanding and manipulation of the properties of aqueous alcohol solutions and even liquids with complex compositions.

Qualitative analysis of fourth-order hyperbolic equations

We investigate the qualitative properties of weak solutions to the boundary value problems for fourth-order linear hyperbolic equations with constant coefficients in a plane bounded domain convex with respect to characteristics. Our main scope is to prove some analog of the maximum principle, solvability, uniqueness and regularity results for weak solutions of initial and boundary value problems in the space L2. The main novelty of this paper is to establish some analog of the maximum principle for fourth-order hyperbolic equations. This question is very important due to natural physical interpretation and helps to establish the qualitative properties for solutions (uniqueness and existence results for weak solutions). The challenge to prove the maximum principle for weak solutions remains more complicated and at that time becomes more interesting in the case of fourth-order hyperbolic equations, especially, in the case of non-classical boundary value problems with data of weak regularity. Unlike second-order equations, qualitative analysis of solutions to fourth-order equations is not a trivial problem, since not only a solution is involved in boundary or initial conditions, but also its high- order derivatives. Other difficulty concerns the concept of weak solution of the boundary value problems with L2 – data. Such solutions do not have usual traces, thus, we have to use a special notion for traces to poss correctly the boundary value problems. This notion is traces associated with operator L or L-traces. We also derive an interesting interpretation (as periodicity of characteristic billiard or the John's mapping) of the Fredholm's property violation. Finally, we discuss some potential challenges in applying the results and proposed methods.

On the linearized Eringen–Cattaneo–Christov–Straughan model: Some qualitative properties of solutions

AbstractIn this paper the Eringen–Cattaneo–Christov–Straughan linearized model is investigated, studying for it in particular: (i) the well‐posedness in Hadamard's sense of the related initial‐boundary value problem, by resorting to the semigroup theory; and (ii) the type of decay the solutions are subject to. This study contributes to strengthening the theoretical basis of a recent model capable of describing thermoporoacoustic phenomena.

Varying the Core Topology in All-Glycidol Hyperbranched Polyglycerols: Synthesis and Physical Characterization.

In the present study, low molecular weight cyclic polyglycidol is used as a macroinitiator for hypergrafting glycidol and producing cyclic graft hyperbranched polyglycerol (cPG-g-hbPG) in the molecular weight range of 103-106gmol-1. Linear graft hyperbranched polyglycerol (linPG-g-hbPG) and hyperbranched polyglycerol (hbPG) are prepared as reference samples. This creates a family of hbPG structures with cyclic, linear, and star cores, allowing to evaluate their properties in solution and in bulk. The morphology study of the high molecular weight structures using atomic force microscopy revealed a spherical shape for cPG-g-hbPG and hbPG, and a cylindrical shape for linPG-g-hbPG in the nanometric range. Small angle X-ray scattering confirmed the compact particle-like structure of this family of hbPG architectures. Interestingly, the glass transition temperature showed a structure dependence, with cPG-g-hbPG having the highest values and hbPG having the lowest values for the same molecular weight. This study is a step forward in the generation of water-soluble polymers with tailored structure and functionality for advanced applications.

Two new Mn-LMOF based on an AIEgens ligand for selective detection of Al3+ and other ions in aqueous solution

Two novel multifunctional chemical sensor Mn-LMOF, namely, [Mn2(TPPE)(ndc)2(H2O)]n (LMOF-1) and [Mn2(TPPE)(oba)2]n (LMOF-2) were solvothermally synthesized by introducing an AIE luminogens (AIEgens) ligand, 1,1,2,2-tetra[4-(pyridin-4-yl)phenyl]ethylene(TPPE), and analyzed by single crystal X-ray diffraction, thermogravimetric and powder X-ray diffraction and other methods. LMOF-1 and LMOF-2 have high stability and strong luminescence properties in solutions. The sensing experiments testify that LMOF-1 can be used as a selectively sensor for Al3+, with the limit of detection is 1.83 × 10−5 M. And LMOF-1 and LMOF-2 can identify Fe3+, CrO42− and Cr2O72− ions in aqueous solution, and LMOF-1 has a higher Ksv for all three ions than LMOF-2.

Optimal regularity and the Liouville property for stable solutions to semilinear elliptic equations in ℝn with n ≥ 10

Optimal regularity and the Liouville property for stable solutions to semilinear elliptic equations in ℝn with n ≥ 10

Variational inequalities of multilayer elastic contact systems with interlayer friction: Existence and uniqueness of solution and convergence of numerical solution

Inspired by the layered structure models in pavement mechanics research, in this study, a class of multilayer elastic contact systems with interlayer frictional contact conditions and deformable supporting frictional contact conditions on the foundation has been constructed. Based on the nonlinear elastic constitutive equations, the corresponding system of partial differential equations and variational inequalities are respectively introduced. Under the framework of variational inequalities, the existence and uniqueness of solutions for such models, along with the approximation properties of finite element numerical solutions, are proven and analyzed. The aforementioned conclusions provide fundamental and broadly applicable theoretical support for addressing mechanical problems in multilayer elastic contact systems within the framework of variational inequalities. Finally, the numerical experimental results based on the mixed finite element method also substantiate our theoretical conclusions.

Unusual Dielectric Properties of NaCl Solutions within Confined MoS2 Monolayer Nanochannels

Unusual Dielectric Properties of NaCl Solutions within Confined MoS2 Monolayer Nanochannels

Understanding the mechano-fluorochromic enhancement in a cyanoethylene-functionalized pyrene-based luminogen: an experimental and theoretical study

Pyrene-based luminogens have attracted wide attention due to their promising applications in organic electronics, chemical sensing, and bioimaging. In this study, a cyanoethylene-functionalized pyrene-based luminogen CNPyCH3 was designed and synthesized. Experimental results show that CNPyCH3 exhibits distinct photophysical properties in dilute solution and various solid states. The mechano-fluorochromic (MFC) property is more attractive and interesting, as a red shift with enhanced emission was observed upon mechanical stimulation. The intriguing MFC enhancement behavior was further investigated by in-depth theoretical calculations combining Monte Carlo simulations, quantum mechanics/molecular mechanics calculations, and time-dependent density functional theory. It was found that the calculated emission wavelengths for both pristine and ground CNPyCH3 are in good agreement with the experimental values, and that the ground CNPyCH3 has a greater oscillator strength. From the perspective of intermolecular interactions, the weakened π-π interactions induced by the half-switched “face-to-edge” packing modes are beneficial for achieving brighter emission upon grinding. In terms of intramolecular structures, the ground CNPyCH3 has a more planar conformation around the cyanoethylene moiety in the excited-state equilibrium geometry than the pristine CNPyCH3, resulting in the grinding-induced red-shifted emission. Our study provides a unique insight into the MFC enhancement behavior of the pyrene-based luminogens.

Determination of the modified exterior Steklov eigenvalues via the reciprocity gap method

The modified exterior Steklov eigenvalues (MESEs) arise from the inverse scattering problem for inhomogeneous media with a cavity and may serve as potential target signatures in nondestructive testing. In this paper we are interested in the determination of the MESEs from the measured Cauchy data of the total field on some manifold inside the cavity due to interior point sources. To this end, the reciprocity gap (RG) method based on a linear integral equation is employed. We provide the related theory and show that the blow-up property of the approximate solution to the integral equation can be used to characterize the MESEs. Numerical examples are presented to demonstrate the viability of our method.

Shape reconstruction of a cavity with impedance boundary condition via the reciprocity gap method

We consider an interior inverse scattering problem of reconstructing the shape of a cavity with impedance boundary condition from measured Cauchy data of the total field. The incident point sources and the measurements are distributed on two different manifolds inside the cavity. We first prove that the boundary of the cavity and the surface impedance can be uniquely determined by the scattered field data on the measurement manifold. Then we develop a reciprocity gap (RG) method to reconstruct the cavity. The theoretical analysis shows the uniquely solvability and existence of the approximate solution for the linear integral equation constructed in the RG method. We also prove that the shape of the cavity can be characterized by the blow-up property of the approximate solution of the proposed integral equation. Numerical examples are presented to verify the feasibility of the RG method.

Quantitative uniqueness of solutions to a class of Schrödinger equations with inverse square potentials

This paper is devoted to proving the quantitative unique continuation property for solutions to a class of Schrödinger equations with inverse square potentials. The argument is to introduce a frequency function and show an almost monotonicity formula and three-ball inequalities by combining the Hardy's inequality.