Structural and thermodynamic properties of a multicomponent freely jointed hard sphere multi-Yukawa chain fluid

The product-reactant Ornstein-Zernike approach, represented by the polymer mean-spherical approximation (PMSA), is utilized to describe the structure and thermodynamic properties of the fluid of Yukawa hard sphere chain molecules. An analytical solution of the PMSA for the most general case of the multicomponent freely jointed hard sphere multi-Yukawa chain fluid is presented. As in the case of the regular MSA for the hard sphere Yukawa fluid, the problem is reduced to the solution of a set of nonlinear algebraic equations in the general case, and to a single equation in the case of the factorizable Yukawa potential coefficients. Closed form analytical expressions are presented for the contact values of the monomer-monomer radial distribution function, structure factors, internal energy, Helmholtz free energy, chemical potentials and pressure in terms of the quantities, which follows directly from the PMSA solution. By way of illustration, several different versions of the hard sphere Yukawa chain model are considered, represented by one-Yukawa chains of length m, where m = 2, 4, 8, 16. To validate the accuracy of the present theory, Monte Carlo simulations were carried out and the results are compared systematically with the theoretical results for the structure and thermodynamic properties of the system at hand. In general it is found that the theory performs very well, thus providing an analytical route to the equilibrium properties of a well defined model for chain fluids.     

Cluster formation in binary charge-stabilized colloidal suspensions confined to a two-dimensional plane

Hypernetted chain (HNC) integral equation theory has been used to study the structural features of binary charged stabilized colloidal suspensions confined to a two-dimensional plane. The particles interact via purely repulsive Yukawa intermolecular potential, the inverse screening length scaled by the average distance between strongly interacting components of the mixture (dimensionless screening parameter) being 1, 3 and 5. Results of HNC theory for one-component systems are found to be in very good agreement with that of simulation, in the parameter range of our study. Binary Yukawa systems with dimensionless screening parameters 1 and 3 are found to exhibit diffuse clusters of the weakly interacting particles, marked by the emergence of a cluster peak in the corresponding partial structure factor curves. No cluster peak is found in the system with the screening parameter 5. For the entire range of mixture parameters, the strongly interacting particles remain homogeneously distributed.     

Structure factor of a hard-core fluid with short-range Yukawa attraction: analytical FMSA theory against Monte Carlo simulations

ABSTRACT

Analytical solution of the first-order Ornstein–Zernike equation known as the first-order mean spherical approximation (FMSA) theory due to Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] is used to write down a closed equation for the static structure factor of the hard-sphere fluid with a short-range Yukawa attraction. Calculations are performed for a Yukawa decay exponent that corresponds to a range of attraction that does not exceed the first coordination shell of Lennard-Jones-like simple fluids. By comparison with Monte Carlo simulation data it is shown that the analytical FMSA equation for the static structure factor is of the same or even of superior accuracy as that within the seminumerical mean spherical approximation theory.     

Analytic presentation of a solution of the Schrödinger equation

High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schrödinger equation is cast into the nonlinear Riccati equation, which is solved analytically in first iteration of the quasi-linearization method (QLM). The zeroth iteration is based on general features of the exact solution near the boundaries. The approach is illustrated on the Yukawa potential. The results enable accurate analytical estimates of effects of parameter variations on physical systems.     

Solution of the Ornstein-Zernike equation for a soft-core Yukawa fluid

A model for simple fluids is proposed in which the radial distribution function has a parametric form appropriate to a soft-core fluid for interparticle separationr R, whereR is some range parameter. Forr > R, the direct correlation function is assumed to be of Yukawa form. The Ornstein-Zernike equation is solved for this system, yielding the radial distribution and the total correlation function for the entire range of interparticle separation. Methods of relating the model fluid to a real fluid by assigning values to the parameters are discussed.Supported by ARGC grant No. B7715646R.     

Eigen solutions of the D-dimensional Schrӧdinger equation with inverse trigonometry scarf potential and Coulomb potential

The approximate analytical solutions of the D-dimensional space of the Schrӧdinger equation is studied with a newly proposed potential model. The proposed potential is a combination of Coulomb potential and inverse trigonometry scarf-type potential. The energy equation and the corresponding wave function are obtained using parametric Nikiforov–Uvarov method. The energy equations for Coulomb potential and inverse trigonometry scarf-type potential are respectively obtained by changing the numerical values of the potential strengths. It is found that the results obtained are equivalent to that previously obtained for Hellmann potential which is a combination of Coulomb potential and Yukawa potential. It is also found that the results for inverse trigonometry scarf potential are equivalent to the results previously obtained for Yukawa potential. Also, the Onicescus information energy of a system under the influence of the newly proposed potential is investigated in detail.     

Polydisperse fluid in contact with a semipermeable membrane

Using density functional theory developed by Rosefeld, a model polydisperse fluid has been studied in contact with a membrane permeable to some components of the fluid. Calculations were carried out for three kinds of polydisperse fluid, each characterized by a different distribution of particle sizes. The structure of fluid has been evaluated on both sides of the membrane, plus the distribution of the particles in bulk fluid and in the surface layers. The adsorption and osmotic pressure in the system have been calculated.     

A New Uniform Phase Bridge Functional: Test and Its Application to Non-uniform Phase Fluid

A new bridge functional as a function of indirect correlation function was proposed, which was basedon analysis on the asymptotic behavior of the Ornstein-Zernike (OZ) equation system and a series expansion whoserenormalization resulted in an adjustable parameter determined by the thermodynamics consistency condition. Theproposed bridge functional was tested by applying it to bulk hard sphere and hard core Yukawa fluid for the predictionof structure and thermodynamics properties based on the OZ equation. As an application, the present bridge functionalwas employed for non-uniform fluid of the above two kinds by means of the density functional theory methodology, theresulting density distribution profiles were in good agreement with the available computer simulation data.     

An Extension of the Analytical Solution of the Ornstein–Zernike Equation with the Yukawa Closure

The analytical solution of the Ornstein–Zernike equation with one Yukawa closure of the factorizable-coefficient case is extended from the scalar-factorization case to the vector-factorization case. As a result, the scaling parameter is extended from a scalar quantity to a matrix quantity, and the scaling matrix      

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces, respectively. Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations. We study the influence of the inter-particle potentials. The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields. Moreover, the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles. These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

Study on analytical solutions and their simplification for one-component multi-Yukawa fluids and test by Monte-Carlo simulation

Using the mean spherical approximation, an explicit analytical equation of state with non-dimensional variables for one-component multi-Yukawa fluids is established based on the work of Blum and Ubriaco. Two simplified calculation methods (one is the linear summation method and the other is the negligible entropy method) are proposed. The compressibility factors for one-component 1–4 Yukawa fluids are simulated with the Monte-Carlo method. Comparisons between various methods under different range parameters are listed and discussed for 1–4 Yukawa fluids. These indicate that our methods are reliable for a wide range of parameters and can be used conveniently.     

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces,respectively.Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations.We study the influence of the inter-particle potentials.The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields.Moreover,the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles.These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

Renormalization group and relations between scattering amplitudes in a theory with different mass scales

In the Yukawa model with two different mass scales, the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. By considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives the possibility to reduce the problem to the scattering of light particles in the “external field” substituting a heavy virtual state. Applications of the results to problems of searches for new physics beyond the Standard Model are discussed.     

Amplitude Instability in Two-Dimensional Hexagonal Clusters

The conditions for the formation of amplitude instabilities in two-dimensional Yukawa systems consisting of seven charged particles have been investigated. An analytical approach to searching for a criterion of the development of such instabilities based on the determination of the inflection point of a system’s potential energy when the particles deviate from their equilibrium positions is considered. The results obtained are compared with the melting criteria for extended two-dimensional systems.     

DKP equation under a vector Yukawa-type potential

Approximate analytical solutions of the Duffin-Kemmer-Petiau equation are obtained for a vector Yukawa potential. The solutions are reported for any J state. The results are obtained based on an exponential approximation as well as the NU analytical technique. Energy solutions are numerically discussed for various quantum numbers and different η, α.     

Approximate solution of the spin-one Duffin-Kemmer-Petiau (DKP) equation under a non-minimal vector Yukawa potential in (1+1)-dimensions

We solve the Duffin-Kemmer-Petiau (DKP) equation with a non-minimal vector Yukawa potential in (1+1)-dimensional space-time for spin-1 particles. The Nikiforov-Uvarov method is used in the calculations, and the eigenfunctions as well as the energy eigenvalues are obtained in a proper Pekeris-type approximation.     

Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.     

The compressibility theorem for quantum simple fluids at equilibrium

An extension of the compressibility theorem for quantum simple fluids within the pathintegral approach is presented. First, it is demonstrated that in the absence of quantum exchange, the isothermal compressibility can be formulated in an exact manner with the use of the pair radial correlation function of the path-integral centroids corresponding to the particles of the fluid. This adds up to the two known formulations based on the pair correlations between true quantum particles, namely the instantaneous and the pair linear response correlations. To complement this extension, an exact Ornstein-Zernike equation for pair centroid correlations is derived, which permits accurate estimates for the isothermal compressibility to be obtained. Several fluids are studied, new numerical results for the latter quantity are reported to support the theoretical points, and some difficulties present in this sort of calculation are discussed. The systems studied are the following: the quantum hard sphere fluid with and without attractive Yukawa interaction, liquid helium-4 and liquid para-hydrogen. Finally, the possibilities of extending the theorem to deal with quantum exchange are considered, and it is shown that the extension and its computational Ornstein-Zernike scheme also hold for a Bose fluid.     

A new model for calculating the binding energy of the lithium nucleus under the generalized Yukawa potential and Hellmann potential

In this paper, the Schrodinger equation for a 6-body system is studied. We solve this equation for the lithium nucleus by using a supersymmetry method with several specific potentials. These potentials are the Yukawa potential, the generalized Yukawa potential and the Hellmann potential. The results of our model for all calculations show that the ground state binding energy of the lithium nucleus with these potentials is very close to that obtained experimentally.