Repulsive Soft Core Research Articles

Phase diagram of two-dimensional binary Yukawa mixtures

ABSTRACTWe have used Ramakrishnan–Yussouff (RY) density functional theory (DFT) to explore the topology of the phase diagram of two-component charge stabilised colloidal suspensions confined to a two-dimensional plane. The particles of the system interact via purely repulsive soft core Yukawa potential. Pair correlation functions (PCFs) used as input informations in DFT were calculated by solving both the hypernetted chain (HNC) and Percus–Yevick (PY) integral equation theories. To test the relative performance of the HNC and PY theories in the context of phase transitions, we have also studied the corresponding one-component systems. We found that RY DFT with HNC PCFs does not stabilise solid in both the one- and two-component cases, whereas the PY theory does. By considering the freezing into the substitutionally disordered triangular solid, we found that the temperature-composition phase diagrams of the binary mixture are narrow spindles whose thickness depends on the symmetry of the mixture components and the value of the screening constant of the Yukawa potential. Although the phase diagram obtained by RY DFT with structural inputs calculated by the PY theory is found to be shifted to higher temperature region in the temperature-composition plane, however, it captures qualitatively all the essential features of the phase diagram. Our results are in principle verifiable through computer simulations and experiments.

Phase diagram of the uniaxial and biaxial soft–core Gay–Berne model

Classical molecular dynamics simulations have been used to explore the phase diagrams for a family of attractive-repulsive soft-core Gay-Berne models [R. Berardi, C. Zannoni, J. S. Lintuvuori, and M. R. Wilson, J. Chem. Phys. 131, 174107 (2009)] and determine the effect of particle softness, i.e., of a moderately repulsive short-range interaction, on the order parameters and phase behaviour of model systems of uniaxial and biaxial ellipsoidal particles. We have found that isotropic, uniaxial, and biaxial nematic and smectic phases are obtained for the model. Extensive calculations of the nematic region of the phase diagram show that endowing mesogenic particles with such soft repulsive interactions affect the stability range of the nematic phases, and in the case of phase biaxiality it also shifts it to lower temperatures. For colloidal particles, stabilised by surface functionalisation, (e.g., with polymer chains), we suggest that it should be possible to tune liquid crystal behaviour to increase the range of stability of uniaxial and biaxial phases (by varying solvent quality). We calculate second virial coefficients and show that they are a useful means of characterising the change in effective softness for such systems. For thermotropic liquid crystals, the introduction of softness in the interactions between mesogens with overall biaxial shape (e.g., through appropriate conformational flexibility) could provide a pathway for the actual chemical synthesis of stable room-temperature biaxial nematics.

Resonance states in 16O+16O, 12C+16O, α+16O and α+12C with modified Morse potentials

The resonance states in 16O+16O, 12C+16O, α+16O and α+12C are described using modified Morse potential proposed earlier whose success has already been demonstrated in the case of 12C+12C system. The general validity of such a potential with long range, shallow depth and repulsive soft core determined from the resonance data itself is being examined through the present study of the resonances in the above four systems. In each system, the experimental data of a large number of states have been successfully described with a modified Morse potential. The success points out a common mechanism of the origin of these states, and reaffirms authentically the diatomic-like rotational and vibrational picture of the nuclear molecular resonances proposed previously. The close resemblance between the physics of diatomic molecules and nuclear molecular resonances extending to the level of potential which is Morse type in both the cases — although belong to two different areas of physics — is further strengthened through the present study.

NN interaction derived from the Nambu–Jona-Lasinio model

The nucleon–nucleon potential is calculated within the Nambu–Jona-Lasinio (NJL) model. The effect of the quark–meson coupling constant, g, on the energy per baryon in quark matter, medium quark mass, medium pion and sigma meson masses and finally on the nucleon–nucleon potential is investigated. It is found that the potential obtained is attractive and the attraction raises with increasing coupling constant g, due to the increases in the scalar interaction. The medium and long range parts of the potential are well reproduced with g=4.6, where a better agreement with the phenomenological Paris potential is obtained. When the short range part is added to the NJL potential, through the one gluon exchange potential, the potential obtained exhibits all the qualitative features of the distance-dependence of the nucleon–nucleon interaction viz., a repulsive soft core followed by an attractive part at the right positions.

Repulsive step potential: a model for a liquid-liquid phase transition.

In the framework of the perturbation theory for fluids we study the model with the isotropic repulsive step potential which in addition to the hard core has a repulsive soft core of a larger radius. It is shown that this purely repulsive potential is sufficient to explain a liquid-liquid phase transition and liquid anomalies.

Models for a liquid–liquid phase transition

We use molecular dynamics simulations to study two- and three-dimensional models with the isotropic double-step potential which in addition to the hard core has a repulsive soft core of larger radius. Our results indicate that the presence of two characteristic repulsive distances (hard core and soft core) is sufficient to explain liquid anomalies and a liquid–liquid phase transition, but these two phenomena may occur independently. Thus liquid–liquid transitions may exist in systems like liquid metals, regardless of the presence of the density anomaly. For 2D, we propose a model with a specific set of hard core and soft core parameters, that qualitatively reproduces the phase diagram and anomalies of liquid water. We identify two solid phases: a square crystal (high density phase), and a triangular crystal (low density phase) and discuss the relation between the anomalies of liquid and the polymorphism of the solid. Similarly to real water, our 2D system may have the second critical point in the metastable liquid phase beyond the freezing line. In 3D, we find several sets of parameters for which two fluid–fluid phase transition lines exist: the first line between gas and liquid and the second line between high-density liquid (HDL) and low-density liquid (LDL). In all cases, the LDL phase shows no density anomaly in 3D. We relate the absence of the density anomaly with the positive slope of the LDL–HDL phase transition line.

Molecular Dynamics and Hypernetted Chain Equation Studies of Soft Core Repulsions in Electrolyte Solutions

Abstract Effects of the repulsive soft core pair potential r−v in 1:1 electrolytes (1 molar concentration) are studied by molecular dynamics (MD) simulations and by the hypernetted chain (HNC) integral equations. Comparisons on the electrolyte structure and dynamical properties are made between a (a) soft ion (SI) model and a (b) soft ion in solution (SIS) model of electrolyte. In the SI model, there is no solvent, whereas the SIS model has ions and neutral solvent molecules at liquid density. Inclusion of the solvent imparts liquid-like structure to the ion-ion pair correlation functions and, if v ≠ ∞, gives rise to substantial back scattering oscillations in the velocity autocorrelation functions with a consequent reduction in the particle self diffusion coefficient. Larger values of v reduce the back scattering in the velocity autocorrelation functions. The dynamical behavior of the ions in the SI model is similar to that of the primitive model electrolyte (θ = ∞) when v ≥ 9. In the SIS fluid, all the ...

NUCLEON-NUCLEON POTENTIAL FROM THE QUARK MODEL

Assuming the nucleon to consist of three valence quarks and a large number of sea quarks and gluons at high temperature, the nucleon-nucleon potential is deduced. This potential exhibits all the qualitative features of the r dependence of the nucleon-nucleon potential viz., a repulsive soft core followed by an attractive well.

-Nucleon Tensor Force in Hypertriton

The hypertriton ~H is the lightest and loosely bound hypernucleus and is of fundamental impor­ tiillce to get the knowledge of the A -nucleon interaction. Thereupon we examine the effect of A-N tensor force in the bound state of the hyper­ triton by solving the Faddeev equation in the coordinate .space, considering the fact that the neutron-proton tensor force plays an inportant role to make the realistic estimate of the binding energy in the hypertriton. The meson theoretical A-N potential due to one boson exchange (OBE) has been proposed by N agels et al. I) in order to reproduce the available nucleon-nucleon and hyperon-nucleon scattering data, where the latest ones are the model D and F. Since the tensor force of the model D is stronger than that of the model F, it is more effective to examine a local A-N potential including the tensor force with repulsive soft core based on this OBE model D potential, where the explicit AN-2:N coupling is not introduced. We previously estimated the A -separation energy BA of the hypertriton using the effective central A -N potential with three term Yukawa form including the repulsive soft core and the Reid soft core n-p potential including the tensor force 2 ) by solving the Faddeev equation in the coordinate space and obtained the BA value of 0.17 MeV. 3 ) It was then pointed out that the n-p tensor force is important for the bound state of the hypertriton. Gibson and Lehman re-evaluat­ ed the A -separation energy BA of ~H using the A-N separable central potential and also n-p separable potential including the tensor force by solving the Faddeev equation in the momentum space.') Their results for BA were 0.13 MeV

Bogoliubov approximation as a second-order approximation in the spectral-density method.—II

We discuss a method, based on the second-order approximation in the spectral-density approach, which avoids the difficulties which appear in the Bogoliubov approximation for an interacting Bose system. We indicate the prescriptions under which, starting from the original number-conserving Hamiltonian, the known Bogoliubov results and the possibility to obtain corrections to those results emerge in a natural way. Explicit calculations are made at zero temperature for a high-density Bose model with a repulsive soft core and a strong attraction between the particles and the self-consistence of the above prescriptions is explicitly proved.