Approximating the Radial Distribution Function of the Electron in a Hydrogen Atom by a Normal Distribution Suggests That Magnetic Confinement Fusion Would Be Less Energy Efficient than Inertial Confinement Fusion

Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma.

A prediction model for the effective thermal conductivity of nanofluids considering agglomeration and the radial distribution function of nanoparticles

Conventional heat transfer fluids usually have low thermal conductivity, limiting their efficiency in many applications. Many experiments have shown that adding nanosize solid particles to conventional fluids can greatly enhance their thermal conductivity. To explain this anomalous phenomenon, many theoretical investigations have been conducted in recent years. Some of this research has indicated that the particle agglomeration effect that commonly occurs in nanofluids should play an important role in such enhancement of the thermal conductivity, while some have shown that the enhancement of the effective thermal conductivity might be accounted for by the structure of nanofluids, which can be described using the radial distribution function of particles. However, theoretical predictions from these studies are not in very good agreement with experimental results. This paper proposes a prediction model for the effective thermal conductivity of nanofluids, considering both the agglomeration effect and the radial distribution function of nanoparticles. The resulting theoretical predictions for several sets of nanofluids are highly consistent with experimental data.

Three Semi-empirical Analytic Expressions for the Radial Distribution Function of Hard Spheres

Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan-Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of PercusYevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.

Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.

Molecular simulation study of the microstructures and properties of pyridinium ionic liquid[HPy][BF_(4)]mixed with acetonitrile

The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this work.The following properties were determined:density,self-diffusion coefficient,excess molar volume,and radial distribution function.The results show that with an increase in the mole fraction of[HPy][BF_(4)],the self-diffusion coefficient decreases.Additionally,the excess molar volume initially decreases,reaches a minimum,and then increases.The rules of radial distribution functions(RDFs)of characteristic atoms are different.With increasing the mole fraction of[HPy][BF_(4)],the first peak of the RDFs of HA1-F decreases,while that of CT6-CT6 rises at first and then decreases.This indicates that the solvent molecules affect the polar and non-polar regions of[HPy][BF_(4)]differently.

Molecular Dynamic Simulation of Melting Points of Trans-1,4,5,8- tetranitro-1,4,5,8-tetraazadacalin （TNAD） with Some Propellants

Molecular dynamic simulation was employed to predict the melting points Tm of TNAD/HMX, TNAD/RDX, TNAD/DINA, and TNAD/DNP systems （tans-1,4,5,8- tetranitro-1,4,5,8-tetraazadacalin （TNAD）, dinitropiperazine （DNP）, cyclotetramethylenetetranitroamine （HMX）, cyclotrimethylenetrinitramine （RDX）, and N-nitrodihydroxyethylaminedinitrate （DINA））. Tm was determined from the inflexion point on the curve of mean specific volume vs. temperature. The result shows that the Tm values of TNAD/HMX, TNAD/RDX, and TNAD/DINA systems are 500, 536, and 488 K, respectively. The TNAD/DNP system has no obvious Tm value, which shows the system is insoluble. Using Tm, the solubility of the four systems was analyzed. The radial distribution functions of the four systems were analyzed and the main intermolecular forces between TNAD and other energetic components are short-range interactions. The better the solubility is, the stronger the intermoleenlar interaction is. In addition, the force field energy at different temperature was also analyzed to predict Tm of the four systems.

Molecular Dynamics Study on Microstructure of Potassium Dihydrogen Phosphates Solution

Molecular dynamics simulations were carried out to study the internal energy and microstructure of potassium dihydrogen phosphates （KDP） solution at different temperatures. The water molecule was treated as a simple-point-charge model, while a seven-site model for the dihydrogen phosphate ion was adopted. The internal energy functions and the radial distribution functions of the solution were studied in detail. An unusually large local particle number density fluctuation was observed in the system at saturation temperature. It has been found that the specific heat of oversaturated solution is higher than that of unsaturated solution, which indicates the solution experiences a crystallization process below saturation temperature. The radial distribution function between the oxygen atom of water and the hydrogen atom of the dihydrogen phosphate ion shows a very strong hydrogen bond structure. There are strong interactions between potassium cation and oxygen atom of dihydrogen phosphate ion in KDP solution, and much more ion pairs were formed in saturated solution.

Molecular dynamics simulation of structure H clathrate-hydrates of binary guest molecules

Molecular dynamics （MD） simulations are performed to study the stability of structure H clathrate-hydrates of methane＋large-molecule guest substance （LMGS） at temperatures of 270, 273, 278 and 280 K under canonical （NVT-） ensemble condition in a 3×3×3 structure H unit cell replica with 918 TIP4P water molecules. The studied LMGS are 2-methylbutane （2-MB）, 2,3-dimethylbutane （2,3-DMB）, neohexane （NH）, methylcyclohexane （MCH）, adamantane and tert-butyl methyl ether （TBME）. In the process of MD simulation, achieving equilibrium of the studied system is recognized by stability in calculated pressure for NVT-ensemble. So, for the accuracy of MD simulations, the obtained pressures are compared with the experimental phase diagrams. Therefore, the obtained equilibrium pressures by MD simulations are presented for studying the structure H clathrate-hydrates. The results show that the calculated temperature and pressure conditions by MD simulations are consistent with the experimental phase diagrams. Also, the radial distribution functions （RDFs） of host-host, host-guest and guest-guest molecules are used to analysis the characteristic configurations of the structure H clathrate-hydrate.

Molecular Dynamics Simulation on Scale Inhibition Mechanism of Polyepoxysuccinic Acid to Calcium Sulphate

Molecular dynamics simulation has been performed to simulate the interaction between PESA and the （001） face of anhydrite crystal CaSO4 at different temperatures with the presence of various number of H2O molecules. The results show that PESA can effectively prevent the growth of CaSO4 scale at 323-343 K. At the same temperature, the binding energy between PESA and the （001） face of CaSO4 for systems with various number of H2O has the order of E-bind（OH2O）〉Ebind（200-400H2O）〉E, bind（lOOH2O）. For the same system at different temperatures the binding energies are close and are mainly contributed from the Coulomb interaction, including ionic bonds. The bonds are formed between the calcium atoms of anhydrite scale crystal and the Hydrogen bonds are formed between the O oxygen atoms of the carboxyl group of PESA. atoms of the carboxyl group of PESA and the H atoms of H2O. van der Waals interaction is conducive to the stability of the system of PESA, H2O, and CaSO4. The radial distribution functions of O（carbonyl of PESA）-H（H2O）, O（CaSO4）-H（H2O）, and O（CaSO4）-H（PESA） imply that solvents have effects on the anti-scale performance of PESA to CaSO4.

Structure of MgSO_4 in Concentrated Aqueous Solutions by X-Ray Diffraction

Detailed time-and-space-averaged structure of MgSO4 in the concentrated aqueous solutions was investigated via X-ray diffraction with an X’pert Pro θ-θ diffractometer at 298 K, yielding structural function and radial distribution function（RDF）. The developed KURVLR program was employed for the theoretical investigation in consideration of the ionic hydration and ion association. Multi-peaks Gaussian fitting method was applied to deconvolving the overlapping bands of Differential radial distribution function（DRDF）. The calculation of the geometric model shows that octahedrally six-coordinated Mg（H2O）62＋, with an Mg2＋…OW bond length of 0.201 nm dominates in the solutions. There exists contact ion-pair（CIP） in the more concentrated solution（1：18, H2O/salt molar ratio） with a coordination number of 0.8 and a characteristic Mg…S distance of 0.340 nm. The result indicates the hydrated SO42– ion happens in the solution. The S…OW bond distance was determined to be 0.382 nm with a coordination number of 13. The fraction of CIP increases significantly with the increasing concentration. The symmetry of the hydration structure of sulfate ion is lowered by forming complex with magnesium ion.

Molecular dynamics studies of the inhibitory mechanism of copper(Ⅱ) on aggregation of amyloid β-peptide

The inhibitory mechanism of copper（Ⅱ） on the aggegation of amyloid β-peptide （Aβ） was investigated by molecular dynamics simulations. The binding mode ofcopper（Ⅱ） with Aβ is characterized by the imidazole nitrogen atom, Nπ, of the histidine residue H 13, acting as the anchoring site, and the backbone＇s deprotoned amide nitogen atoms as the main binding sites. Drove by the coordination bonds and their induced hydrogen bond net, the conformations of Aβ converted from β-sheet non-β-sheet conformations, which destabilized the aggregation of Aβ into fibrils.

Size effect in the melting and freezing behaviors of Al/Ti core-shell nanoparticles using molecular dynamics simulations

The thermal stability of Ti@A1 core/shell nanoparticles with different sizes and components during continuous heating and cooling processes is examined by a molecular dynamics simulation with embedded atom method. The thermodynamic properties and structure evolution during continuous heating and cooling processes are investigated through the character- ization of the potential energy, specific heat distribution, and radial distribution function （RDF）. Our study shows that, for fixed Ti core size, the melting temperature decreases with A1 shell thickness, while the crystallizing temperature and glass formation temperature increase with A1 shell thickness. Diverse melting mechanisms have been discovered for different Ti core sized with fixed A1 shell thickness nanoparticles. The melting temperature increases with the Ti core radius. The trend agrees well with the theoretical phase diagram of bimetallic nanoparticles. In addition, the glass phase formation of A1-Ti nanoparticles for the fast cooling rate of 12 K/ps, and the crystal phase formation for the low cooling rate of 0.15 K/ps. The icosahedron structure is formed in the frozen 4366 A1-Ti atoms for the low cooling rate.

Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid

In this work, a bridge density functional approximation （BDFA） （J. Chem. Phys. 112, 8079 （2000）） for a nonuniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa （HCRY） fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.

Vapor-Liquid Equilibrium Simulation of Binary and Ternary Mixtures of CH_4,C_2H_4 and iso-C_4H_(10)

The vapor-liquid equilibrium(VLE) properties for the binary and ternary mixtures of CH4,C2H4 and isoC4H10 are of great importance in the recovery of ethylene from mixture containing CH4 and C2H4 with iso-C4H10 as solvent.Hence,Gibbs ensemble Monte Carlo(GEMC) simulations were used to estimate vapor-liquid equilibrium for the binary and ternary mixtures of CH4,C2H4 and iso-C4H10 with the united atom potential NERD model.The selected simulation conditions are based on the experiment in the literature.The results of this work were shown to be in satisfactory agreement with available experimental data and predictions of Peng-Robinson equation of state.The structure of simulated liquid phase is also characterized by radial distribution function(RDF),which contributes to further understanding of the VLE curve of these systems.RDF is not sensitive to the pressure and temperature range.With the increase of pressure or the decrease of temperature,the molecules tend to gather together.

Short-range structural change in indium melt by Gaussian peaks decomposing of RDF

Liquid indium's structure was studied at 280, 390, 550, 650, and 750 deg Crespectively by using an elevated temperature X-ray diffractometer, and its radial distributionfunction (RDF) at different temperatures was decomposed into 4 Gaussian peaks in the range of0.2-0.6nm. Positions of the decomposed Gaussian peaks were compared with the nearest and the secondnearest neighbor atomic distances, respectively. It is shown that the position of the firstdecomposed Gaussian peak is similar to the nearest neighbor atomic distance in liquid In at thecorresponding temperature, and that of the third decomposed Gaussian peak is similar to the secondnearest neighbor atomic distance. Moreover, the first and the third Gaussian peaks correspond to thefirst and the second atom shells of liquid In at the corresponding temperatures, respectively.Therefore, the position and the area of Gaussian peaks can represent the position and atom number ofcorresponding shells. Based on this result, short-range structural changes in liquid In wasstudied. It was found that the first and the second shells are close to the referred atom, and theatom number at the shells decreases with the increasing temperature from 280 to 750 deg C. Indifferent ranges of temperature, structural changes in the first and the second shells showdifferent features.

Transformation of the Angular Power Spectrum of the Cosmic Microwave Background(CMB)Radiation into Reciprocal Spaces and Consequences of This Approach

A formalism of solid state physics has been applied to provide an additional tool for the research of cosmological problems. It is demonstrated how this new approach could be useful in the analysis of the Cosmic Microwave Background (CMB) data. After a transformation of the anisotropy spectrum of relict radiation into a special two-fold reciprocal space it was possible to propose a simple and general description of the interaction of relict photons with the matter by a “relict radiation factor”. This factor enabled us to process the transformed CMB anisotropy spectrum by a Fourier transform and thus arrive to a radial electron density distribution function (RDF) in a reciprocal space. As a consequence it was possible to estimate distances between Objects of the order of ~102 [m] and the density of the ordinary matter ~10-22 [kg.m-3]. Another analysis based on a direct calculation of the CMB radiation spectrum after its transformation into a simple reciprocal space and combined with appropriate structure modelling confirmed the cluster structure. The internal structure of Objects may be formed by Clusters distant ~10 [cm], whereas the internal structure of a Cluster consisted of particles distant ~0.3 [nm]. The work points in favour of clustering processes and to a cluster-like structure of the matter and thus contributes to the understanding of the structure of density fluctuations. As a consequence it may shed more light on the structure of the universe in the moment when the universe became transparent for photons. On the basis of our quantitative considerations it was possible to derive the number of particles (protons, helium nuclei, electrons and other particles) in Objects and Clusters and the number of Clusters in an Object.

Spatial Correlation in Typical Binary Polycondensation Systems: An Essential Extension of the Kirkwood-Buff Theory

We present the isothermal susceptibility(XT)for the typical binary polycondensation system of Af-Bg type,and relate XT to the weight-average degree of polymerization in terms of the Kirkwood-Buff(KB)theory.The investigation is based on a new expression of XT for mixtures,which is still expressed by the KB integrals(KBIs)but endowed with an explicit physical interpretation.For polymerization systems,it is proposed that the KBIs can be further decomposed according to whether there exists a bond between particles when conversions(extents of reaction)of functional groups are incorporated into the KBIs.In this way,XT is directly decomposed into its relevant components as well.This is especially useful to reveal the relationship between local structures and average properties of various polymerization systems.As a consequence,the effect of polymerization on XT is greatly simplified in comparison with the free energy route.Therefore,we have provided a very simple method to carry out some thermodynamic properties of polymerization systems.

Molecular simulation of the CH_4/CO_2/ H_2O adsorption onto the molecular structure of coal

Clarification of the molecular mechanism underlying the interaction of coal with CH4, CO2, and H2 O molecules is the basis for an in-depth understanding of the states of fluid in coal and fluid-induced coal swelling/contraction. In terms of instrumental analysis, molecular simulation technology based on molecular mechanics/dynamics and quantum chemistry is a powerful tool for revealing the relationship between the structure and properties of a substance and understanding the interaction mechanisms of physical-chemical systems. In this study, the giant canonical ensemble Monte Carlo（GCMC） and molecular dynamics（MD） methods were applied to investigate the adsorption behavior of a Yanzhou coal model（C222H185N3O17S5）. We explored the adsorption amounts of CH4, CO2, and H2 O onto Yanzhou coal, the adsorption conformation, and the impact of oxygen-containing functional groups. Furthermore, we revealed the different adsorption mechanisms of the three substances using isosteric heat of adsorption and energy change data.（1） The adsorption isotherms of the mono-component CH4, CO2, and H2 O were consistent with the Langmuir model, and their adsorption amounts showed an order of CH4CO2〉CH4. In addition, at higher temperatures, the isosteric heat of adsorption decreased; pressure had no significant effect on the heat of adsorption.（3） CH4 molecules displayed an aggregated distribution in the pores, whereas CO2 molecules were cross arranged in pairs. Regarding H2 O molecules, under the influence of hydrogen bonds, the O atom pointed to surrounding H2 O molecules or the H atoms of coal molecules in a regular pattern. The intermolecular distances of the three substances were 0.421, 0.553, and 0.290 nm, respectively. The radial distribution function（RDF） analysis showed that H2 O molecules were arranged in the most compact fashion, forming a tight molecular layer.（4） H2 O molecules showed a significantly stratified distribution around oxygen-containing functional groups on the coal surface, and the bonding strength showed a descending order of hydroxyl〉 carboxyl〉carbonyl. In contrast, CO2 and CH4 showed only slightly stratified distributions.（5） After the adsorption of CH4, CO2, and H2 O, the total energy, the energy of valence electrons, and the non-bonding interaction of the system in the Yanzhou coal model all decreased. The results regarding the decrease in the total energy of the system indicated an order of H2O〉CO2〉CH4 in terms of the adsorption priority of the Yanzhou coal model. The results regarding the decrease in the energy of valence electrons showed that under certain geological conditions, a pressure-induced “coal strain” could lead to a structural rearrangement during the interaction of coal with fluid to form a more stable conformation, which might be the molecular mechanism of coal swelling resulting from the interaction between fluid and coal. An analysis of the contribution of Van der Waals forces, electrostatic interactions and hydrogen bonds to the decrease in non-bonding interactions revealed the mechanism underlying the interactions between coal molecules and the three substances. The interaction between coal molecules and CH4 consisted of typical physical adsorption, whereas that between coal molecules and CO2 consisted mainly of physical adsorption combined with weak chemical adsorption. The interaction between coal molecules and H2 O is physical and chemical.

The compatibility of polylactic acid and polybutylene succinate blends by molecular and mesoscopic dynamics

The compatibility of polylactic acid(PLA)/polybutylene succinate(PBS)blends was studied by molecular dynamics and mesoscopic dynamics,which is a controversial issue in experiments.Six simulation models of PLA/PBS with different composition ratios(100/0,90/10,80/20,70/30,60/40,0/100)were constructed.The radial distribution function,hydrogen bond,free energy density,order parameter and iso-density surface morphology of the PLA/PBS systems were simulated and analyzed.Due to the formation of hydrogen bonds and van der Waals bonds between different elements of PLA chains and PBS chains,the PLA/PBS blends exhibit good compatibility at all composition ratios.

Dynamics Simulation on the Associative Properties of Amphiphilic Functional Monomer Modified Polyacrylamide Copolymers

A kind of amphiphilic functional monomer was selected to modify polyacrylamide （PAM） or partially hydrolyzed polyacrylamide （HPAM）. The relative properties of the modified polyacrylamide （HM-PAM） and modified partially hydrolyzed polyacrylamide （HM-HPAM） such as radius of gyration （Rg）, hydrodynamic radius （RH）, and radial distribution functions （RDFs） have been studied to find the intrinsic relation between the microstructure of the polymer chain and the intrinsic viscosities with changing the amotmt of modified monomers from 1% to 4%. The simulation results show that, compared to HPAM, HM-HPAM has a better performance in increasing viscosity when the percentage of modified monomers is 2% and has a stronger salt tolerance when the modified monomers is 4%. Furthermore, a complex hydrogen bonding network was revealed with the analysis of radial distribution functions （RDFs） and the pair correlation function was used to investigate the diffusivity of Na^＋ and carbon atoms in the COO^- group.