Closed-packed lattice model for polymer solution systems considering the chain length dependence effect: Correlating LLE,VLE, and gel swelling behaviors using identical interaction energy parameters

We propose a new Helmholtz energy of mixing equation following the original Flory–Huggins (F–H) closed-packed lattice model. Also, to overcome F–H mean-field approximation, we introduce new universal constants to consider chain length dependence of polymer in solvent and consider specific interactions to describe strongly interacting polymer systems. Our proposed model successfully describes liquid–liquid equilibria (LLE) for binary polymer–solvent systems using identical interaction parameters which do not depend on the polymer molecular weight. We also describe vapor–liquid equilibria (VLE) for polymer/solvent systems and swelling equilibria of thermosensitive hydrogel systems using the same energy parameters obtained from LLE calculations.     

Solvent effect of ionic liquids on the distribution constant of 2-thenoyltrifluoroacetone and its nickel(II) and copper(II) chelates and the evaluation of the solvent properties based on the regular solution theory

Distribution constants of 2-thenoyltrifluoroacetone (Htta) and its Ni(II)and Cu(II) chelates between 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (C_nmimTf₂N; n = 4, 6, and 8) as ionic liquid (IL) and an aqueous phase were determined. The enol fraction of Htta in ILs was spectrophotometrically measured to calculate the distribution constant of the enol form (K_D,HE) of Htta. The K_D,HE values in ILs were evaluated by comparing those in various molecular solvents such as alkanes, aromatic hydrocarbons, chlorohydrocarbons, ethers, ketones, and esters previously reported on the basis of the regular solution theory (RST). It was elucidated that the IL solutions of Htta (enol) can be taken as apparently regular solutions as expected in the organic solvents. On the other hand, the effect of ILs on the distribution constant of metal(II) chelates (K_D,M) was fairly complicated. The Cu(tta)₂-IL solutions behaved like the alkane and aromatic hydrocarbon solutions but the Ni(tta)₂-IL (C₄mimTf₂N) like ether and ketone solutions. In the Ni(II) case, some specific interactions between the Ni(II) chelate and IL was suggested. Finally, the solubility parameters of ILs were calculated using K_D,HE by RST and were in good agreement with the literature values obtained by the enthalpy of vaporization.     

Molecular thermodynamics approach for polymer-polymer miscibility

We extended the previous lattice model for polymer solution systems to binary polymer blend systems. Based on Müller’s Monte-Carlo simulation data for symmetric system (r₁ = 32 and r₂ = 32), the energy of mixing is correlated as a function of temperature and composition using an empirical expression. In addition, we introduce new universal functions which reflect the characteristics of polymer-polymer miscibility behaviors. In associated blend systems, specific interactions between polymer segments are considered by using a secondary lattice. Using only one or two adjustable parameters, the proposed model satisfactory correlates the experimental data of real polymer blend systems with greater accuracy than those of other models.     

The influence of sulfur substitution on the atomic displacement in Bi2Ti2O7

To clarify the role of A₂O′ and B₂O₆ networks on cation displacement observed in Bi₂Ti₂O′O₆, we used density functional theory calculations to examine the effect of sulfur substitution on the O′ and O sites on lone pair formation and resulting atomic displacement observed in Bi₂Ti₂O′O₆. Cation displacement in bismuth titanate is suppressed only when S is substituted on the O′ site. Analysis of the electronic structure shows that S substitution on the O′ site suppresses the formation of the asymmetric p-type lone pair by modifying the Bi-anion hybridization. Lone pair formation is favored in Bi₂Ti₂O′S₆ and the atomic displacement is larger than that observed in Bi₂Ti₂O′O_6. This enhanced displacement is due to weaker Bi-S versus Bi-O interactions leading to significantly stronger hybridization between the Bi and O′ states in Bi₂Ti₂O′S₆. We also induced lone pair formation in a metallic bismuth pyrochlore oxide (Bi₂Ru₂O′O₆) by modifying the Bi-O interactions through S substitution on the B₂O₆ network, indicating atomic displacement on the A₂O′ network may be achieved by modifying the B₂O₆ network.     

Non-local theory solution of two collinear mode-I cracks in piezoelectric materials

In this paper, the basic solution of two collinear cracks in a piezoelectric material plane subjected to a uniform tension loading is investigated by means of the non-local theory. Through the Fourier transform, the problem is solved with the help of two pairs of integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the integral equations, the jumps of displacements across the crack surfaces are directly expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the interaction of two cracks, the materials constants and the lattice parameter on the stress field and the electric displacement field near crack tips. Unlike the classical elasticity solution, it is found that no stress and electric displacement singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to using the maximum stress as a fracture criterion in piezoelectric materials.     

Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian

We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.     

On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.     

A time-reversal lattice Boltzmann method

In this paper we address the time-reversed simulation of viscous flows by the lattice Boltzmann method (LB). The theoretical derivation of the reversed LB from the Boltzmann equation is detailed, and the method implemented for weakly compressible flows using the D2Q9 scheme. The implementation of boundary conditions is also discussed. The accuracy and stability are illustrated by four test cases, namely the propagation of an acoustic wave in a medium at rest and in an uniform mean flow, the Taylor–Green vortex decay and the vortex pair–wall collision.     

Fabrication and characterization of Zn1−xAlxO nanoparticles by DC arc plasma

In this paper we have introduced a simple method for the fabrication of aluminum doped zinc oxide (AZO) nanoparticles. The Zn_1−xAl_xO nanoparticles with different concentrations of Al (x=0.01, 0.03, 0.06, 0.09, 0.12) were fabricated successfully by this method. The samples were analyzed by the use of several techniques such as SEM, EDX, XRD, PL and UV-vis spectroscopy. The SEM images showed that the fabricated nanoparticles had spherical shapes. The XRD patterns of the samples indicated that the Al atoms substituted in the Zn positions in the crystal lattice of ZnO and there were some changes in the lattice parameters. A blue shift in the λ_max of the absorption and a red shift in the λ_max of the emission were observed. The results also indicated that the amount of shifts had a direct relationship with the changes in the lattice parameters.     

Synthesis and optical properties of Cr doped ZnS nanoparticles capped by 2-mercaptoethanol

Nanoparticles of Zn_1−xCr_xS (x=0.00, 0.005, 0.01, 0.02 and 0.03) were prepared by a chemical co-precipitation reaction from homogenous solutions of zinc and chromium salts. These nanoparticles were sterically stabilized using 2-mercaptoethanol. Here a study of the effect of Cr doping on structural, morphological and optical properties of nanoparticles was undertaken. Elemental analysis, morphological, structural and optical properties have been investigated by energy dispersive analysis of X-rays (EDAX), scanning electron microscopy (SEM), X-ray diffraction (XRD), transmission electron microscopy (TEM) and UV-visible spectroscopy .EDAX measurements confirmed the presence of Cr in the ZnS lattice. XRD showed that ZnS:Cr nanoparticles crystallized in zincblende structure with preferential orientation along (1 1 1) plane. The average sizes of the nanoparticles lay in the range of 3-6 nm and lattice parameters were in the range of 5.2-5.4 Å. Lattice contraction was observed with an increase of Cr concentration. The particle size and lattice parameters obtained from TEM and SAED images were in agreement with the XRD results. The absorption edge shifted to lower wavelengths with an increase in Cr concentration as per UV-Vis spectroscopy. The band gap energy values were in the range of 3.85-4.05 eV. This blueshift is attributed to the quantum confinement effect.