Intermediate Plateau Research Articles

Equilibrium loadings and adsorption isotherm model parameters estimated from multi-component breakthrough curves

Quantitative knowledge of competitive adsorption isotherms is essential for the design and optimization of adsorption based separation processes. Since the experimental determination of these thermodynamic functions is complicated and time consuming, there is a need for fast and easy to apply methods. In particular attractive are methods that evaluate measured breakthrough curves (BTC). Key features of these curves can be predicted with the equilibrium theory, which ignores kinetic effects that cause band broadening. If the adsorption equilibria can be described by the classical competitive Langmuir isotherm model, outlet concentration profiles can be calculated analytically. The paper summarizes and illustrates well-known classical results for N-component systems. The theory is applied to analyze experimentally determined BTC for a ternary mixture fed into an initially fully regenerated column under constant flowrate and under isothermal conditions. It is demonstrated that the retention times and intermediate plateau concentrations, which are observable for example in a single ternary BTC experiment, allow estimating a defined number of characteristic equilibrium loadings. These loadings can be directly used for easy estimation of the parameters of an assumed isotherm model. Various possibilities to use a reduced number of loadings and to include complementary results of standard pulse experiments are described. The isotherms generated from the ternary BTC are successfully validated by results of single component and ternary BTC experiments carried out subsequently. Options to generalize the method to determine isotherm model parameters from measured BTC to initially preloaded columns and to more complex mixtures are finally outlined.

The energy spectrum and magnetization profile of the decorated spin ladder systems

The peculiarities of the energy spectrum of the decorated mixed spin two-leg ladder system having three spin unit cells have been studied by the perturbation theory in the limit of dominant spin coupling in ladder rungs. It is shown, that despite the singlet ground state, this spin ladder may have an intermediate plateau in a low-temperature magnetization profile. The existence of a similar plateau was shown also in the case of some intermediate values of coupling parameters by means of exact diagonalization study of small ladder clusters and by the density-matrix renormalization group calculations. We also found that the Ising type of interactions in ladder rungs may lead to the disappearance of the above intermediate magnetization plateau for the corresponding isotropic spin ladder.

Strength vs temperature for refractory complex concentrated alloys (RCCAs): A critical comparison with refractory BCC elements and dilute alloys

To support the development of refractory complex, concentrated alloys (RCCAs), a clear understanding of the effect of temperature on strength is needed. Body-centered cubic (BCC) refractory metals and dilute refractory alloys show a strong temperature dependence of yield stress (σy) at low and high temperatures, with a relatively temperature-independent regime in between. RCCAs may introduce important changes in deformation and strengthening mechanisms, so it is not clear if RCCAs will show the same thermal dependencies. The objective of this work is to answer the question, “Is the temperature dependence of strength similar or different for RCCAs compared to BCC refractory elements and dilute refractory alloys ?” We evaluate σyvs. temperature for 61 RCCAs by analyzing data curated from the literature. We find that σy increases progressively from refractory BCC elements, to dilute alloys, to single- and multi-phase RCCAs. Single-phase RCCAs show the same three thermal regimes, but the stresses are higher and the intermediate plateau is shorter and is sometimes steeper. The thermal dependence of σy in multi-phase RCCAs shows more substantial differences. Six factors that contribute to the higher σy of RCCAs are discussed: (i) higher solute concentration; (ii) dispersion in atomic sizes; (iii) the shear modulus magnitude; (iv) the type of principal elements; (v) the solvus temperature of predicted secondary phases; and (vi) microstructure. Based on the present observations and analyses, suggestions for future research are made, especially regarding improved models for the effect of temperature on strength.

A comparative study between Monte Carlo entropic sampling method and local mean field investigations of thermal properties of spin-crossover nanoparticles based on Ising-like model

The thermally induced transitions between low-spin (LS) and high-spin (HS) configurations of spin-crossover (SCO) nanoparticles are simulated, focusing on the effects of localized surface and bulk interactions on the average magnetization of 2D square lattices. The thermal behaviors and hysteresis cycles are investigated within the framework of the Ising model Hamiltonian and are conducted following two approaches: local mean field approximation (LMFA) and Monte Carlo entropic sampling (MCES) techniques. The results obtained by these two methods are compared for the two square lattice sizes, 6 $$ \times $$ 6 and 7 $$ \times $$ 7. Thus, when the bulk-surface interaction term is set to zero, the two approaches lead to identical values of the surface and bulk transition temperatures separated by a long intermediate plateau in both cases. Although hysteresis curves exhibit a similar shape, LMFA shows slightly larger widths $$ \Delta T $$ than MCES. On increasing bulk-surface interaction term, the two methods lead to different shifts in equilibrium temperature values for both bulk and surface components, respectively, to lower and higher values by MCES. In general, it is found that LMFA shifts surface equilibrium temperature differently to lower values and enhances the hysteresis effect, particularly for surface molecules. On the other hand, for the 7 $$ \times $$ 7 square lattice, the equilibrium temperatures are slightly higher by 1.5% and 3.2% for bulk and surface molecules, respectively, with a narrower hysteresis width in the surface. Moreover, with the MCES method, an abrupt transition instead of a hysteresis transition is calculated for surface molecules ($$ \Delta T_{surf}^{MCES}=0 $$ K).

Energy spectrum and magnetic properties of the decorated spin ladder models of nanomagnets on the base of polymeric transition metal compounds

The work is devoted to the theoretical study of the energy spectrum and low-temperature magnetic properties of the decorated spin-ladder model with the polyacene topology and the three types of the site spins. On the base of cluster expansion technique an approximate analytical treatment of lowest part of the energy spectra of two isomeric ladder structures was given. It is shown that the ladder model with singlet ground state is more stable than its isomeric analog with the macroscopic ground state spin. In addition, the numerical study of field dependence of low-temperature magnetization of 8- spin clusters of both ladder models was performed by means of exact diagonalization method. On the base of these results, it was shown the presence of an intermediate plateau in low-temperature magnetization profile of the above spin ladder models.

The energy spectrum and low-temperature magnetic properties of the decorated two-leg mixed spin ladder

The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.

Surface-Bulk 2D Spin-Crossover Nanoparticles within Ising-like Model Solved by Using Entropic Sampling Technique

We model the thermal effects in different 2D spin-crossover (SCO) square lattices within the frame of the Ising-like model using Monte Carlo entropic sampling (MCES) method to enhance the scan of macrostates beyond the most probable thermal ones. In fact, MCES allows access to the metastable states, and it is then well adapted to study thermal hysteresis properties. In this contribution, we distinguish, for the first time, the interaction between molecules located in bulk at the surface and those connecting the bulk and surface regions of an SCO lattice. In addition, an extra ligand field contribution is assigned to surface molecules through an interaction parameter L. In the absence of environmental effects on surface nanoparticles, a single thermal hysteresis loop increasing with the lattice size is simulated with a unique bulk and surface equilibrium temperature Teq=Teqbulk= Teqsurf. When environmental effects are accounted for, a two-step behavior associated with two hysteresis loops of widths ΔTS (for the surface) and ΔTB (for the bulk) with an intermediate plateau 14 K wide is obtained in the thermal dependence of the high-spin (HS) fraction for the 6 × 6 lattice. The surface and bulk equilibrium temperatures are then different, both decreasing towards lower values, and the L parameter controls the three states’ behavior as well as the hysteresis loop interval. Size effects show that the equilibrium temperature is governed by the surface atoms for a small lattice size (5 × 5) and by the bulk atoms for a large lattice size (7 × 7). Moreover, a change in the size of the lattice results in a variation of the order–disorder (or Curie) temperature, TO.D., and the surface equilibrium temperature, Teq, while only TO.D. changes in bulk.

Half-Integer Conductance Plateau at the ν=2/3 Fractional Quantum Hall State in a Quantum Point Contact.

The ν=2/3 fractional quantum Hall state is the hole-conjugate state to the primary Laughlin ν=1/3 state. We investigate transmission of edge states through quantum point contacts fabricated on a GaAs/AlGaAs heterostructure designed to have a sharp confining potential. When a small but finite bias is applied, we observe an intermediate conductance plateau with G=0.5(e^{2}/h). This plateau is observed in multiple QPCs, and persists over a significant range of magnetic field, gate voltage, and source-drain bias, making it a robust feature. Using a simple model that considers scattering and equilibration between counterflowing charged edge modes, we find this half-integer quantized plateau to be consistent with full reflection of an inner counterpropagating -1/3 edge mode while the outer integer mode is fully transmitted. In a QPC fabricated on a different heterostructure which has a softer confining potential, we instead observe an intermediate conductance plateau at G=(1/3)(e^{2}/h). These results provide support for a model at ν=2/3 in which the edge transitions from a structure having an inner upstream -1/3 charge mode and outer downstream integer mode to a structure with two downstream 1/3 charge modes when the confining potential is tuned from sharp to soft and disorder prevails.

A pH-triggered reinforcement of transient network of wormlike micelles by halloysite nanotubes of different charge

Soft viscoelastic nanocomposites based on entangled linear wormlike micelles of cationic surfactant erucyl bis(hydroxyethyl)methylammonium chloride and aluminosilicate clay halloysite nanotubes with a surface charge triggered by pH were prepared and studied by rheometry, ξ-potential measurements, thermogravimetric analysis, and cryo-TEM. It was shown that the nanotubes induce an increase of viscosity, which can be attributed to their incorporation into the network of entangled wormlike surfactant micelles via the attachment of micellar endcaps to the surfactant double layer on the surface of the nanotubes. The junctions between the micelles and the nanotubes were visualized by cryo-TEM. The soft nanocomposites demonstrate peculiar flow curves with two shear thinning regions and a plateau between them. The two slopes were attributed to the orientation of the nanotubes (at lower shear rates) and then of the micellar worms (at higher shear rates) along the direction of flow. The intermediate viscosity plateau may represent a stable flow when all nanotubes are oriented, while the micellar worms are not. The nanocomposite system was shown to be pH responsive. Its viscosity increases by 30 times with increasing pH from 4 to 9, which was explained by increasing surface charge of the nanotubes favoring the interaction with oppositely charged WLMs. Such soft materials with easily triggered rheological properties are very promising for various applications.

Insight into ground-state spin arrangement and bipartite entanglement of the polymeric coordination compound [Dy[formula omitted]Cu[formula omitted]][formula omitted] through the symmetric spin-1/2 Ising–Heisenberg orthogonal-dimer chain

The ground-state spin arrangement and the bipartite entanglement within Cu2+-Cu2+ dimers across the magnetization process of the 4f-3d heterometallic coordination polymer [Dy(hfac)2(CH3OH)2Cu(dmg)(Hdmg)2]n (H2dmg = dimethylglyoxime, Hhfac = 1,1,1,5,5,5-hexafluoropentane-2,4-dione) are theoretically examined using the symmetric isotropic spin-1/2 Ising–Heisenberg orthogonal-dimer chain. The numerical results point to five possible ground states of the compound with three different degrees of the quantum entanglement within Cu2+-Cu2+. Besides the standard ferrimagnetic and saturated phases without quantum entanglement of Cu2+ ions, which are manifested in low-temperature magnetization curve as wide plateaus at the non-saturated magnetization 16.26μB and at the saturation value 20.82μB, respectively, one also finds an intriguing singlet-like phase with just partial entanglement within Cu2+-Cu2+ and two singlet phases with fully entangled Cu2+-Cu2+ dimers. The former quantum phase can be identified in the low-temperature magnetization process as very narrow intermediate plateau at the magnetization 9.27μB per unit cell, while the latter ones as zero magnetization plateau and intermediate plateau at the magnetization 18.54μB. Non-monotonous temperature variations of the concurrence, through which the entanglement within cooper dimers is quantified, point to the possible temporary thermal activation of the entangled states of Cu2+-Cu2+ also above non-entangled ferrimagnetic and saturated phases.

Tomonaga-Luttinger Spin Liquid and Kosterlitz-Thouless Transition in the Spin-1/2 Branched Chains: The Study of Topological Phase Transition.

In the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction is antiferromagnetic and intra-chain interaction is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when is ferromagnetic and is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz–Thouless transition from a gapful phase to a gapless spin liquid phase.

Rheology of Poly(glycidyl methacrylate) Macromolecular Nano Assemblies.

A recently reported combined polymerization process of glycidyl methacrylate, mediated by homometallic and heterobimetallic aluminium complexes, naturally produces nano-sized macromolecular assemblies. In this work, the morphological features and the rheological properties of these novel nanoassemblies are studied. The hydrodynamic sizes of the nanoparticles in the solution range from 10 to 40 nm (in numbers), but on a flat surface they adopt a characteristic thin disk shape. The dynamic moduli have been determined in a broad range of temperatures, and the time—temperature superposition applied to obtain master curves of the whole viscoelastic response from the glassy to the terminal regions. The fragility values obtained from the temperature dependence are of m ~40, typical of van de Waals liquids, suggesting a very effective packing of the macromolecular assemblies. The rheological master curves feature a characteristic viscoelastic relaxation with the absence of elastic intermediate plateau, indicating that the systems behaved as un-entangled polymers. The analysis of the linear viscoelastic fingerprint reveals a Zimm-like dynamics at intermediate frequencies typical of unentangled systems. This behaviour resembles that observed in highly functionalized stars, dendrimers, soft colloids and microgels.

Pressure-induced multi-step and self-organized spin states in an electro-elastic model for spin-crossover solids

Isotropic applied pressure inducing two-step transitions with labyrinth self-organized spin states in the intermediate plateau regions.

Magnetic properties of generalized polyallyl spin chain

The work is devoted to the theoretical simulation of low-temperature magnetic properties of generalized polyallyl spin chain with the antiferromagnetic coupling of the neighboring spins (GPSC) - spin model of a family of quasi-one dimensional molecular ferrimagnets. First, the exact energy spectra of Heisenberg spin Hamiltonians of the finite lattice clusters of GPSC with the spins of the main chain s=1/2 and pendant spins š=1 have been studied by means of the exact diagonalization method. The calculations were performed for different positive values of the coupling parameters for neighboring spins of the main chain of GPSC clusters. On the base of the above exact energy spectra and the Boltzmann distribution law the field dependencies of magnetization of finite lattice clusters are calculated numerically at different temperatures. In the result, for low temperatures the presence of intermediate plateau in field dependencies of the cluster magnetization has been shown. These calculations demonstrated the stabilization of the intermediate magnetization plateau with the growth of the spin coupling along the main chain of GPSC clusters. In addition, the numerical study of temperature dependence of zero field magnetic susceptibility of 12- spin clusters of GPSC gives the results which are similar to the 1D model of molecular ferrimagnets like necklace spin ladder. Similar calculations of the magnetization profile were performed for infinite Heisenberg –Ising GPSC model with Ising type of the antiferromagnetic interactions between the neighboring spins of the main chain. The classical transfer- matrix method was used for this purpose. In the result, it was shown the presence of an intermediate plateau in the low-temperature magnetization profile of infinite chain model and the increase of the plateau size with increasing of the Ising coupling between the spins of the main chain.

Magnetic properties of 1D spin systems with compositional disorder of three-spin structural units

Abstract The exact diagonalization (ED) approach and Quantum Monte-Carlo (QMC) method were used for the study of the lowest energy states and low-temperature magnetic properties of some disordered 1D Heisenberg spin-1/2 systems formed by two types of three-spin structural units. For the system with a singlet ground state and the random distribution of structural units along the chain system, a significant decrease of the size of the intermediate magnetization plateau in comparison to the corresponding uniform spin system was found. For the “polyallyl” spin chain with a macroscopic value of the ground state spin, a transition to the singlet ground state due to the effect of compositional disorder was observed.

Influence of a spatial anisotropy on presence of the intermediate one-half magnetization plateau of a spin-1/2 Ising–Heisenberg branched chain

A spin-1/2 Ising–Heisenberg branched chain constituted by regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is exactly solved in a magnetic field by the transfer-matrix method. The spin-1/2 Ising–Heisenberg branched chain involves two different Ising and one Heisenberg coupling constants. The overall ground-state phase diagram is formed by three different ground states emergent depending on a mutual interplay between the magnetic field and three considered coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. It is shown that the interaction anisotropy connected to two different Ising coupling constants substantially influences a breakdown of the intermediate one-half magnetization plateau, which represents a macroscopic manifestation of the quantum ferrimagnetic phase.

Unifying disparate rate-dependent rheological regimes in non-Brownian suspensions.

A typical dense non-Brownian particulate suspension exhibits shear thinning (decreasing viscosity) at low shear rate or stress followed by a Newtonian plateau (constant viscosity) at intermediate shear rate or stress values which transitions to shear thickening (increasing viscosity) beyond a critical shear rate or stress value and finally undergoes a second shear thinning transition at extremely high shear rate or stress values. In this study, we unify and quantitatively reproduce all the disparate rate-dependent regimes and the corresponding transitions for a dense non-Brownian suspension with increasing shear rate or stress. We employ discrete particle dynamics simulations based on the proposed mechanism to elucidate its accuracy. We find that a competition between interparticle interactions of hydrodynamic and nonhydrodynamic origins and the switching in the dominant stress scale with increasing the shear rate or stress lead to each of the above transitions. Inclusion of traditional hydrodynamic interactions, attractive or repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions the interparticle contact interactions, and a constant friction (or other constraint mechanism) reproduces the initial thinning as well as the shear thickening transition. However, to quantitatively capture the intermediate Newtonian plateau and the second shear thinning, an additional nonhydrodynamic interaction of non-DLVO origin and a decreasing coefficient of friction, respectively, are essential, thus providing an explanation for the presence of the intermediate Newtonian plateau along with reproducing the second shear thinning in a single framework. Expressions utilized for various interactions and friction are determined from experimental measurements and hence result in excellent quantitative agreement between the simulations and previous experiments.

On the energy spectrum and thermodynamics of decorated quasi-one-dimensional magnetic systems with uniaxial anisotropy

This paper is devoted to the study of thermodynamics of the quasi-1D spin models with Ising interaction between complex unit cells by transfer-matrix method. The field and the temperature dependences of the main thermodynamic characteristics have been investigated. It is shown that the field dependence of the magnetization at low temperatures for the models of “comb” and “decorated comb,” and decorated triangles structures have an intermediate magnetization plateau in case of antiferromagnetic Ising interactions. The temperature dependence of the heat capacity may have several maxima in zero magnetic field. For the chain model of triangles decorated by Ising spins through the one vertex and for the “double decorated comb” some kind of the pseudo-phase transitions in the critical magnetic field is found.

Two step micro-rheological behavior in a viscoelastic fluid.

We perform micro-rheological experiments with a colloidal bead driven through a viscoelastic worm-like micellar fluid and observe two distinctive shear thinning regimes, each of them displaying a Newtonian-like plateau. The shear thinning behavior at larger velocities is in qualitative agreement with macroscopic rheological experiments. The second process, observed at Weissenberg numbers as small as a few percent, appears to have no analog in macro-rheological findings. A simple model introduced earlier captured the observed behavior and implied that the two shear thinning processes correspond to two different length scales in the fluid. This model also reproduces oscillations, which have been observed in this system previously. While the system under macro-shear seems to be near equilibrium for shear rates in the regime of the intermediate Newtonian-like plateau, the one under micro-shear is thus still far from it. The analysis suggests the existence of a length scale of a few micrometres, the nature of which remains elusive.

Nature of intermediate magnetization plateaus of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice.

The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.