Anisotropic Interaction Parameters Research Articles

Crystal step edges with alternating rows of growth units: 1D nucleation and step velocity

Crystals with asymmetric growth units present a ubiquitous challenge for modeling crystal growth. We derive the crystal step edge velocity for steps with alternating rows of growth units (i.e., a row of A followed by a row of B growth units). We construct a free energy model for 1D nucleation of this two-tiered row and show that a single anisotropic interaction parameter and the supersaturation characterize the edge stability. A Fokker–Planck model captures the kinetics of nucleation and seamlessly connects the stable and unstable regimes, whereas previous models diverge near the transition between these cases. The 1D nucleation model leads to an expression that predicts the step velocity as a function of supersaturation and edge stability. We show that the model is in excellent agreement with kinetic Monte Carlo simulations.

Generalized van der Waals theory for phase behavior of two-dimensional nematic liquid crystals. II. Phase coexistence and adsorption.

Adsorption of asymmetric particles or molecules into monolayers is important for many biological and technologically relevant physical systems. In-plane ordering can drastically affect adsorption and phase behavior. In this work, a generalized van der Waals theory previously developed [M. V. Zonta and E. R. Soulé, Phys. Rev. E 100, 062703 (2019)10.1103/PhysRevE.100.062703] is used to calculated phase behavior and adsorption isotherms in a system of hard-core rodlike particles with in-plane nematic order, as a function of the model parameters (aspect ratio L/B, isotropic and anisotropic interaction parameters χ and ν,and adsorption constant K_{ads}). For small L/B, isotropic-nematic and/or (depending on χ) isotropic liquid-gas coexistence is observed; as L/B increases, coexistence between two different nematic phases appears at low temperature, and liquid-gas equilibrium ceases to be observed for large enough L/B; this is understood considering that as aspect ratio increases, the range of stability of the nematic phase becomes larger. Adsorption isotherms are found to significantly deviate from Langmuir behavior, and are strongly affected by ordering and interactions (surface density in the adsorbed layer increases as interaction parameters and ordering increase). Phase coexistence is observed as discontinuous transitions in adsorption isotherms, where adsorption-desorption hysteresis cycles are possible.

Generalized van der Waals theory for phase behavior of two-dimensional nematic liquid crystals: Phase ordering and the equation of state.

Liquid crystalline ordering of anisotropic particles in two dimensions is important in many physical and biological systems and their phase behavior is still a topic of interest. A generalized van der Waals theory is formulated, accounting for repulsive excluded volume and attractive van der Waals and Maier-Saupe interactions, for rectangles confined to two dimensions. The phase ordering transitions and equation of state are analyzed as a function of the model parameters (aspect ratioL/B and isotropic and anisotropic interaction parameters χ and ν). Different phase transitions are observed: continuous isotropic-nematic (high L/B and ν), first-order isotropic-nematic (intermediate L/B and small ν), and continuous isotropic-tetratic (small L/B and ν) followed by a continuous tetratic-nematic transition at higher densities. Increasing L/B decreases the pressure, and this effect is more pronounced in the nematic than in the isotropic phase. Increasing both interaction parameters decreases pressure and can lead to phase separation.

Solid-state 23Na NMR spectroscopy studies of ordered and disordered cellulose nanocrystal films

Cellulose nanocrystal films with either disordered or chiral nematic structures of varying helical pitch were investigated using 23Na solid-state nuclear magnetic resonance (NMR) spectroscopy. Spin lattice relaxation of 1H correlated with 23Na analyzed by indirect observation using polarization transfer from 1H nuclei to 23Na nuclei showed that the Na+ cations are well hydrated in the cellulose nanocrystal films. Linewidth analysis in solid-state 23Na NMR showed that the Na+ cations move in confined spaces, and that the Na+ cations in the film having disordered structure are more dynamic than in the films having ordered structure. From lineshape analysis of the 23Na 2D nutation NMR spectra, we can distinguish the Na+ environments within the ordered and disordered films, and find trends in anisotropic interaction parameters between ordered samples with different pitches. These are the first detailed 23Na NMR spectroscopic studies of CNC-Na+ films, and they show that this technique may be a powerful probe for characterizing the extent of order in nanocellulose samples.

Mixing-Induced Anisotropic Correlations in Molecular Crystalline Systems

We investigate the structure of mixed thin films composed of pentacene and diindenoperylene using x-ray reflectivity and grazing incidence x-ray diffraction. For equimolar mixtures we observe vanishing in-plane order coexisting with an excellent out-of-plane order, a yet unreported disordering behavior in binary mixtures of organic semiconductors, which are crystalline in their pure form. One approach to rationalize our findings is to introduce an anisotropic interaction parameter in the framework of a mean field model. By comparing the structural properties with those of other mixed systems, we discuss the effects of sterical compatibility and chemical composition on the mixing behavior, which adds to the general understanding of interactions in molecular mixtures.

First-principles study of magnetic interactions in cupric oxide

Cupric oxide (CuO) has been described as belonging to the quasi-one-dimensional antiferromagnetic compounds. It has also been suggested that cupric oxide possesses strong magnetic anisotropy, which is possibly related to the observed ferroelectricity in this material. In this paper, the magnetic interactions of CuO are investigated using the embedded cluster approach. Accurate wave-function-based methods have been employed to describe the interactions along all copper-oxygen chain directions. Both two-center and three-center clusters are considered in our calculations. The antisymmetric anisotropic interaction parameters are also calculated for the two-center clusters by applying an effective Hamiltonian theory. Our results show that the magnetic interactions are dominated by the antiferromagnetic coupling between copper ions along the chain of largest Cu-O-Cu angles in agreement with experiment. The results for the interplane magnetic interactions reveal competition between nearest-neighbor ferromagnetic coupling and second-nearest-neighbor antiferromagnetic interaction along the direction where two copper ions are connected via doubly bridged oxygen ligands. We also find nonnegligible Dzyaloshinskii-Moriya interactions with magnitude comparable to the weak isotropic interchain interactions.

Thermodynamics of the model of equal spin-spin interactions

We consider the thermodynamics of the model of equal spin-spin interactions. We obtain exact expressions for the correlation functions and heat capacity of finite clusters applicable in the entire range of temperature and external fields. We analyze the obtained thermodynamic characteristics depending on the interaction parameters, the external magnetic field, and the number of particles in the cluster. We find an anomalous behavior of the heat capacity and other thermodynamic quantities due to elementary spin gap excitations occurring in the spectrum. The absence of a long-range order in the system is ensured by the presence of topological excitations (solitons). We study the effect of an anisotropic interaction parameter on the soliton structure.

Depletion interactions of non-spherical colloidal particles in polymer solutions

We consider anisotropic colloidal particles immersed in a solution of long, flexible, andnon-adsorbing polymers. For the dumbbell shapes of recently synthesized particlesconsisting of two intersecting spheres, and for lens-shaped particles with spherical surfaces,we calculate the isotropic and anisotropic interaction parameters that determine theimmersion free energy and the orientation-dependent depletion interaction betweenparticles that are induced by the polymers. Exact results are obtained for ideal (randomwalk) polymer chains.

MAS NMR with and without double-quantum filtration at and near the n = 0 rotational resonance condition

Spectral lineshapes of MAS NMR spectra of dipolar (re)coupled spin pairs exhibiting considerable chemical shielding anisotropies at and near the so-called n = 0 rotational resonance ( R 2) condition are considered. The n = 0 R 2 condition is found to be not extremely sharp. Anisotropic interaction parameters such as chemical shielding tensor orientations and the magnitude of the dipolar coupling constant remain sensitively encoded in such lineshapes even when differences in isotropic chemical shielding values of up to 400 Hz (corresponding to ca. half the size of the dipolar coupling constant) are present. Additional double-quantum filtration (DQF) may enhance the sensitivity of spectral lineshapes to anisotropic interaction parameters for even larger differences in isotropic chemical shielding values. The dependence of the DQF efficiency on spin-system parameters as well as on external parameters (Larmor and MAS frequencies) is investigated. Away from R 2 conditions a trend to lower DQF efficiencies is found whereas some spin-system parameters are more sensitively encoded in the corresponding spectral lineshapes. Our study is based on numerical simulations, with the known parameters of the 31P spin pair in Na 4P 2O 7 · 10H 2O representing our model case.

Measurement of the Gd-Gd exchange and dipolar interactions inGd0.01Y0.99Ba2Cu3O6

The microscopic parameters of the Gd-Gd pair interaction are measured in single crystals of the ${\mathrm{Gd}}_{0.01}{\mathrm{Y}}_{0.99}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6}$ cuprate using high-frequency (225 GHz) ${\mathrm{Gd}}^{3+}$ electron-spin resonance. In addition to the fine-structure spectrum of single ${\mathrm{Gd}}^{3+}$ ions, a series of low intensity resonance transitions are resolved at high magnetic fields and low temperatures which arise from Gd-Gd pairs. From the resonance line positions of nearest-neighbor Gd-Gd pairs we determine an isotropic exchange energy of $J=156\mathrm{mK}$ and an anisotropic (mainly dipolar) interaction energy of $D=51.7\mathrm{mK}.$ The anisotropic interaction parameters of second, third, and fourth neighbors correspond to the values expected for dipolar interaction only.

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor Sij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region.

Nuclear relaxation and molecular motion of 1,3,5-trifluorobenzene- d3 in liquid solutions

The 2D and 19F spin-lattice relaxation times of 1,3,5-trifluorobenzene- d 3 in 0.15 mol fraction solutions in various solvents have been measured over the temperature range 270–400 K. The relationship between the reorientational correlation times, τ θ, and the angular momentum correlation times, τ J , obtained from the nuclear relaxation data has been compared with the theoretical relationships predicted by the J-diffusion limit of the extended diffusion (ED J) model and the Fokker-Planck-Langevin (FPL) model for symmetric top molecules. It was found that the rotational motion of 1,3,5-trifluorobenzene- d 3 in most solutions was better described by the FPL model with frictional anisotropy τ ‖/τ · in the range 1–2. (τ ‖ and τ · are the correlation times for the angular velocity components along the axes parallel and perpendicular to the molecular symmetry axis.) The viscosity and temperature dependence of τ θ has been analyzed in terms of a modified Debye equation and values for the anisotropic interaction parameter, κ, in each solvent are reported. The variation in κ with solvent is attributed mainly to the variation in the dipole moment of the solvent molecules. The frictional anisotropy (τ ‖/τ ·) is found to decrease as κ increases. This is interpreted in terms of the effects of molecular shape and electrostatic interactions between CF bond dipole moment and solvent dipole moments.

ESR line shape studies of N-(4-n butyl benzilidine) 4-amino 2,2,6,6-tetramethyl piperidine 1-oxide (BBTMPO) in toluene

BBTMPO was synthesized by a condensation of 4-n butyl benzaldehyde and 4-amino 2,2,6,6-tetramethyl piperidine N-oxide (4-tempamine). The shape of the resulting spin probe, estimated using the Dreiding models, is a spherocone of length 10.7 Å capped by hemispheres of radii 6.6 and 4.0 Å, respectively. The magnetic parameters of BBTMPO in toluene at 77 K were determined. Variable temperature ESR line shape studies in the temperature range of 142–211 K revealed that BBTMPO exhibited anisotropic rotational diffusion in toluene along the long axis of the spherocone and in the direction parallel to the N–O bond. Rotational diffusion along the long axis was found to be 3±0.5 and 7±0.5 times faster for frozen and liquid toluene, respectively, than the other two axes. The line shapes have been simulated by using the stochastic Liouville theory of slow-motional effects on ESR spectrum. The slow tumbling spectrum (158 K) in the model-sensitive region showed good agreement for a Brownian model. The plot of τR vs 1/T over the whole temperature range yield a good linear fit with two slopes, with the activation energy for reorientation process of 4.9 kcal/mol in the liquid state, and 9.9 kcal/mol in the solid state. The higher activation energy of rotational reorientation coupled with a lower anisotropy of molecular reorientation (N) in the solid state, indicates that the rotational degrees of freedom is more restricted in the frozen state than in the liquid state. Molecular reorientation for BBTMPO in toluene was analyzed in terms of the hydrodynamic free space model for molecular relaxation in liquids. The stickiness factor S was found to be 0.6 while the anisotropic interaction parameter κ which measures the coupling of rotation to translation was found to be 0.7. For perdeuterated 2,2,6,6-tetramethyl-4-piperidine N-oxide (PD-Tempone) in toluene the stickiness factor was calculated to be 0.3, and κ was 0.4. The doubling in size and weight in going from PD-Tempone to BBTMPO increases the stickiness factor and κ from 0.3 to 0.6, and 0.4 to 0.7, respectively. The similarity in the structure of BBTMPO to that of liquid crystal methoxy benzilidine butyl aniline (MBBA) and its potential use as a spin probe for MBBA is discussed.

Anomalous relaxation in low-dimensional magnets with anisotropic interactions

Anomalies of the angle-dependent EPR line spectrum and its satellites due to the long-time tails in one-and two-dimensional Heisenberg paramagnets with anisotropy terms are treated in the high-temperature limit by making use of a new mode-coupling theory. A normal lorentzian EPR line spectrum is also expected for some particular combinations of the anisotropic interaction parameters due to the competition between them.

A Study of the Effect of Solvent and Temperature on the Electron Paramagnetic Resonance Parameters and Linewidths of Copper(II)bis(Diethyldithiocarbamate)

The effect of varying solvent and temperature on the e.s.r. parameters and linewidths of copper(II) bis(diethyldithiocarbamate) has been studied. The temperature and solvent dependences of the isotropic hyperfine coupling constant (a0) have been interpreted in terms of vibronic and axial ligation effects. The rotational correlation time, τR, of Cu(DEDC)2 has been measured in the solvents employed. The values of τR measured at 300 K have been used to obtain the anisotropic interaction parameter, κ, which is found to correlate roughly with the dipole moment and molar refractivity of the solvent.

ESR linewidths in solution. VI. Variation with pressure and study of functional dependence of anisotropic interaction parameter, κ

Measurements have been made on the ESR linewidths of vandyl acetylacetonate (VOAA) in a number of nonhydrogen-bonded solvents. The X-band spectra were taken over a wide range of temperatures and at pressures ranging up to 4.5 kbar. The high pressure measurements were carried out in a high pressure bomb containing a slow-wave helix, instead of a resonant cavity, and a pair of 100 kHz modulation coils; the sample was placed in a Teflon holder which also surrounded the helix and could be sealed after the sample was deoxygenated. The reorientation correlation time τθ, is written as τθ=43π r03κ(η/kT), where η is the coefficient of shear viscosity, T the absolute temperature, r0 the hydrodynamic radius determined by translational diffusion experiments, and κ the anisotropic interaction parameter. κ is proportional to the ratio of the mean square intermolecular torques to the mean square intermolecular force where the interaction is between VOAA and solvent molecules. The values of κ determined from these experiments are independent of pressure, temperature, and density. However, κ varies from solvent to solvent and an analysis of the data indicates, but not unambiguously, that κ decreases with solvent size and it increases with solvent dipole moment. The results are compatible with a quasirotational diffusion model, with the assumption that the autocorrelation functions for intermolecular forces and torques have the same time dependence, and with the assumption that the dependence of torques on intermolecular separation is nearly equivalent to that of forces. The single adjustable parameter, κ, is sufficient to explain all the spectra at low (η/T) for a given solvent regardless of pressure and temperature, but at high values of (η/T) unexplained discrepancies between theory and experiment occur. A discussion of anisotropic diffusion is also given; however, the anisotropic contributions are probably negligible for VOAA.