Repulsive Part Research Articles

Brownian Dynamics Simulations of Polyelectrolyte Adsorption onto Topographically Patterned Surfaces

The effect of patterned surface topography on the adsorption of single polyelectrolyte molecules is explored using Brownian dynamics simulations. The polyelectrolyte is modeled as a free-draining, freely jointed bead-rod chain, and electrostatic interactions are incorporated using a screened Coulombic potential with excluded volume interactions accounted for by the repulsive part of a Lennard-Jones potential. Topography consisting of periodically spaced valleys of square cross section separated by flat hills is considered. Chain conformations are characterized for a wide range of valley widths, depths, and spacings as well as for several different types of surface charge distributions. Depending on the parameter values describing the topography, the chains are found to adopt conformations ranging from flat and extended to those associated with bridge-, brush-, or semi-bridge-like structures. The formation of these structures is rationalized on the basis of a free-energy model that takes into account the increase in free energy due to entropic confinement, excluded volume interactions, and chain stretching as well as the decrease in free energy due to bead-surface electrostatic attraction. The results of this work are expected to be useful in designing patterned surface topography to control the conformations of adsorbed polyelectrolyte molecules.

Transferable step potentials for perfluorinated hydrocarbons

The step potential equilibria and discontinuous molecular dynamics (SPEADMD) model is adapted for characterizing the interaction potentials of perfluorocarbons and their mixtures with n-alkanes. We seek to explain the peculiar behavior of these systems, especially with regard to the unfavorable mixing behavior. The methodology is based on discontinuous molecular dynamics (DMD) and second order thermodynamic perturbation theory (TPT). DMD simulation is applied to the repulsive part of the potential. The effects of disperse attractions and hydrogen bonding are treated by TPT, discretizing the attractive potential into four distinct wells of variable depth. This approach accelerates the molecular simulations in general and the parameterization of the transferable potentials in particular. C 3–C 8 straight chain perfluorocarbons are characterized along with perfluorobenzene, perfluorocyclobutane, and heptafluoropropane applying explicit atom models for all fluorine atoms. Each compound is simulated at 21 densities. Interpolation with density combines with TPT to give a complete equation of state. The depths of the attractive wells are optimized by iterating on their values until the vapor pressures computed by the resulting equation of state provide the minimum deviation from experimental data. Step potentials offer the prospect of setting the step depths without preconceived notions regarding the shape of the potential. In the case of perfluorocarbons, it is found that the minimum of the potential is reached at roughly 1.8 σ, with the range from σ to 1.8 σ acting as a soft “shoulder” region which is weakly attractive, where σ designates the site diameter. This shoulder region can explain the unusually low heat of vaporization of perfluorocarbons and high vapor pressures relative to compounds with similar molecular volume. Application of this approach results in average absolute deviations of 8% in vapor pressure and 3% in liquid density. Coincidentally, the soft shoulder also explains the weak mixture interactions between perfluorocarbons and n-alkanes. The Lorentz–Berthelot combining rule assumed to describe site–site interactions between corresponding steps leads to ɛ ijk ∼ ( ɛ iik ɛ jjk ) 1/2, where ɛ ijk is the depth of the potential well between sites i and j in the kth step. For steps at short range, the alkane steps are at their deepest, but the perfluorocarbon interactions are weak, making the mixed interaction weak. For steps at long range, the perfluorocarbon steps are deeper, but the alkane interactions are weak, again making the mixed interaction weak.

Rigorous conditions for the existence of bound states at the threshold in the two-particle case**Dedicated to Walter Greiner on his seventieth anniversary.

In the framework of non-relativistic quantum mechanics and with the help of Green's functions formalism, we study the behaviour of weakly bound states in a non-central two-particle potential as they approach the continuum threshold. Through estimating Green's function for positive potentials we derive rigorously the upper bound on the wavefunction, which helps us to control its falloff. In particular, we prove that for potentials whose repulsive part decays slower than 1/r2 the bound states approaching the threshold do not spread and eventually become bound states at the threshold. This means that such systems never reach supersizes, which would extend far beyond the effective range of attraction. The method presented here is applicable in the many-body case.

Combining molecular dynamics and chemical process simulation: the SPEAD model

AbstractDiscontinuous molecular dynamics simulation and thermodynamic perturbation theory have been used to study the thermodynamic and transport properties of a large number of organic compounds. The fundamental basis of the approach relies on a stepwise characterization of the disperse interactions and blister potentials for hydrogen bonding. It has been demonstrated that these types of attractive interactions can be quantitatively treated by thermodynamic perturbation theory (TPT). The vapor pressure is predicted to roughly 10% average error with reduced temperatures generally extending to 0.45 while applying transferable characterizations of the molecular interaction potentials. For branched, aromatic, and naphthenic compounds, it is necessary to distinguish between primary, secondary, and tertiary bonding of the attached group as well as the branched site. One key to this accuracy is the distinction between isomers at the molecular level by the rigorous molecular dynamics simulation of the repulsive part of the potential. The molecular dynamics simulations also permit predictions of transport properties. The transport results account for the repulsive structure, branching, bond angles, etc. through rigorous molecular simulation but there is no theory for transport properties comparable to TPT. Therefore, predictions for transport properties are semiempirical in the sense that attractive forces have been correlated with experimental data. The accuracy for diffusivity is within 30% for non‐associative species. Disperse attractions appear to play a significant role in transport properties. Copyright © 2007 Curtin University of Technology and John Wiley & Sons, Ltd.

Accurate Pair Interaction Energies for Helium from Supermolecular Gaussian Geminal Calculations

Nonrelativistic clamped-nuclei pair interaction energy for ground-state helium atoms has been computed for 12 interatomic separations ranging from 3.0 to 9.0 bohr. The calculations applied the supermolecular approach. The major part of the interaction energy was obtained using the Gaussian geminal implementation of the coupled-cluster theory with double excitations (CCD). Relatively small contributions from single, triple, and quadruple excitations were subsequently included employing the conventional orbital coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)] and the full configuration interaction (FCI) method. For three distances, the single-excitation contribution was taken from literature Gaussian-geminal calculations at the CCSD level. The orbital CCSD(T) and FCI calculations used very large basis sets, up to doubly augmented septuple- and sextuple-zeta size, respectively, and were followed by extrapolations to the complete basis set limits. The accuracy of the total interaction energies has been estimated to be about 3 mK or 0.03% at the minimum of the potential well. For the attractive part of the well, the relative errors remain consistently smaller than 0.03%. In the repulsive part, the accuracy is even better, except, of course, for the region where the potential goes through zero. For interatomic separations smaller than 4.0 bohr, the relative errors do not exceed 0.01%. Such uncertainties are significantly smaller than the expected values of the relativistic and diagonal Born-Oppenheimer contributions to the potential.

Perturbation theory for classical solids with vacancy defects

We present a density functional model for the thermodynamic properties of a Lennard-Jones system in the crystalline state having a small fraction of vacancies present in the lattice. The test density function is modified from its usual form to take into account the presence of vacancies in the lattice structure. The repulsive part of the Lennard-Jones potential is treated in terms of an equivalent hard sphere (EHS) system while the contribution from the long attractive part is treated perturbatively. The properties of the EHS in the inhomogeneous state is obtained with the weighted density functional approach. The thermodynamic behavior is studied by locating the state of minimum free energy. The dependence of the vacancy concentration on temperature at the coexistence of crystal and liquid is obtained.

Comparative study of cascade damage in Fe simulated with recent potentials

Considerable quantitative uncertainty has remained regarding the amount and structure of defects produced in molecular dynamics simulations of collision cascades in Fe. The problem is most likely related to the description of interstitial energetics in the interatomic potentials. Three potentials have recently been developed for Fe, which, even though they have different physical motivations and functional forms, describe the interstitial energetics well. Using these potentials, we simulate recoil collision cascades in Fe in the recoil energy range 0.5–20keV. Prior to the cascade simulations a realistic high-energy repulsive part was added to two of the potentials, adjusting the fit to reproduce the experimentally obtained threshold displacement energies. The results show that the total Frenkel pair production, as predicted by the three potentials, is the same within the statistical uncertainty, but also that some differences remain in the fraction of clustered defects. However, these differences are smaller than those predicted by previous potentials.

Alkylation Effects on Strong Collisions of Highly Vibrationally Excited Alkylated Pyridines with CO2

The role of alkylation on the energy partitioning in strong collisions with CO2 was investigated for highly vibrationally excited 2-ethylpyridine (2EP) and 2-propylpyridine (2PP) prepared with E(vib) approximately 38,570 and 38,870 cm(-1), respectively, using lambda = 266 nm light. Nascent energy gain in CO2 (00(0)0) rotation and translation was measured with high-resolution transient absorption spectroscopy at lambda approximately 4.3 microm and the results are compared to earlier relaxation studies of pyridine (E(vib) = 37,950 cm(-1)) and 2-methylpyridine (2MP, Evib = 38,330 cm(-1)). Overall, the alkylated donors impart less rotational and translational energy to CO2 than does pyridine. 2PP consistently imparts more translational energy in collisions than does 2EP and has larger energy transfer rates. Of the alkylated donors, 2MP and 2PP have larger probabilities for strong collisional energy transfer than does 2EP. Two competing processes are discussed: donors with longer alkyl chains have lower average energy per mode and fewer strong collisions but longer alkyl chains increase donor flexibility, leading to higher state densities that enhance energy loss via strong collisions. A comparison of state density effects based on Fermi's Golden Rule shows that 2PP has more strong collisions than predicted while 2EP has fewer. The role of torsional motion in the hot donors is considered. Comparison of effective impact parameters shows that the alkylated donors undergo strong collisions with CO2 via a less repulsive part of the intermolecular potential than does pyridine.

Ultrafast shape recognition for similarity search in molecular databases

Molecular databases are routinely screened for compounds that most closely resemble a molecule of known biological activity to provide novel drug leads. It is widely believed that three-dimensional molecular shape is the most discriminating pattern for biological activity as it is directly related to the steep repulsive part of the interaction potential between the drug-like molecule and its macromolecular target. However, efficient comparison of molecular shape is currently a challenge. Here, we show that a new approach based on moments of distance distributions is able to recognize molecular shape at least three orders of magnitude faster than current methodologies. Such an ultrafast method permits the identification of similarly shaped compounds within the largest molecular databases. In addition, the problematic requirement of aligning molecules for comparison is circumvented, as the proposed distributions are independent of molecular orientation. Our methodology could be also adapted to tackle similar hard problems in other fields, such as designing content-based Internet search engines for three-dimensional geometrical objects or performing fast similarity comparisons between proteins. From a broader perspective, we anticipate that ultrafast pattern recognition will soon become not only useful, but also essential to address the data explosion currently experienced in most scientific disciplines.

Spectroscopy of the 11 u(5 1P 1) and [formula omitted] singlet electronic states of cadmium dimer: Bond lengths and verification of ab initio potentials

A method of supersonic free-jet expansion beam combined with techniques of laser spectroscopy was used in investigation of vibrational and rotational structures in the 1 0 u + ( 5 1 P 1 ) and 11 u(5 1P 1) electronic energy states of Cd 2. Laser induced fluorescence (LIF) excitation and dispersed fluorescence spectra recorded at the 1 0 u + - X 1 0 g + and 1 1 u - X 1 0 g + transitions provided spectroscopic characteristics of the excited and ground states as well as a shape of the repulsive part of the ground-state potential energy curve (PEC). Rotational structures of the 228Cd 2 isotopomer recorded in the ( υ′, υ″) = (45,0) and (38,0) bands of the 1 0 u + ← X 1 0 g + and 1 1 u ← X 1 0 g + transitions, respectively, were used for a direct determination of the ground- and excited-state bond lengths. Moreover, the 11 u-state interatomic potential was obtained numerically using an inverted perturbation approach (IPA). The position and height of the 11 u-state potential barrier was determined and compared with results of ab initio calculation. Analysis of Condon-internal-diffraction (CID) profiles in the bound-free dispersed fluorescence spectrum resulted in determination of a degree of repulsion between two ground-state Cd atoms in the dimer, supporting a hypothesis of a covalent admixture to the dominant van der Waals (vdW) bonding.

Structure and thermodynamics of discrete potential fluids in the OZ–HMSA formalism

We study the structural and thermodynamic properties of three discrete potentialfluids: the square well (SW), the square well–barrier (SWB), and the squarewell–barrier–well (SWBW) fluids by means of the Ornstein–Zernike (OZ) integralequation and the HMSA (hybrid mean spherical approximation) closure relation.The radial distribution functions, structure factors, and pressure of the systemsare calculated as a function of the strength of the attractive and repulsive partsof the potential in an extended range of densities, mainly covering the range0.1 ≤ ρ* ≤ 0.9. We find that far away from the liquid–vapour coexistence region the HMSA theory is anaccurate approach that compares well with Monte Carlo simulations. We also find that when theattractive parts of the potential dominate over the repulsive part the structure factor at lowq values shows a considerable increase, which suggests the formation of large-scale domainsthat locally exhibit fluid-like structure.

Study of fusion cross-sections of 16O + 208Pb and 28Si + 208Pb reactions by effective soft-core nucleon-nucleon interaction

In this paper, the cross-sections of fusion reactions 16O + 208Pb, 28Si + 208Pb, 40C + + 40Ca, 40Ca + 48Ca, 58Ni + 58Ni, and 16O + 154Sm at bombarding energies above and near the fusion barrier have been investigated. The fusion cross-sections have been studied by means of the Monte Carlo method and effective soft-core nucleon-nucleon interaction. One adjustable parameter was used in these calculations. This parameter can change the strength and repulsive parts of soft-core potential values. It has to be adjusted, so that the analytical results are in acceptable agreement with the experimental data. In our calculations, we have taken the range of the nucleon-nucleon soft-core interaction to be constant and equal to that of the M3Y-Raid potential. Results show that the higher values for the diffusion parameter in the Woods-Saxon potential obtained from a careful analysis of 16O + 208Pb and 28Si + 208Pb reactions are due to the many particle effects on the nucleon-nucleon potential.

Vapour-liquid equilibria of the two- and three-dimensional monoatomic classical fluids interacting via double Yukawa potential

We have carried out Monte Carlo simulations in Gibbs ensemble for two-and three-dimensional double Yukawa fluid. We have compared liquid-vapour equilibrium curve with that of Lennard-Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. The role of repulsive and attractive contributions for the potential on the liquid-vapour coexistence region as well as on critical temperature and critical density has been studied. The critical temperature is found to be more sensitive than the critical density to the variation in repulsive and attractive parts of the potential. Also, the range of the attractive interaction directly influences range of the liquid vapour coexistence region. It has been found that smaller the values of the attractive parameter, larger is the coexistence region.

Density anomaly and liquid-liquid transition from perturbation theories

We report on theoretical results concerning the relation between the liquid-liquid transition and the density anomaly for a family of ramp potentials (hard-core plus linear short range repulsion and linear long range attraction). Using first order perturbation, we have studied the influence of the range of the attractive interactions, taking the repulsive part of the interaction as the reference system. Two different mechanisms of liquid-liquid coexistence have been predicted: attraction and compression. The attractive case is attributed to long ranged potentials, while the second one is obtained when the interaction is shortened. The density anomaly appears linked to regions where the temperature derivative of the density derivative of the energy is bigger (in absolute value) than a limit. This condition is fulfilled when the range of the attractive part of the potential is short enough.

A molecular dynamics study on the role of attractive and repulsive forces in internal energy, internal pressure and structure of dense fluids

Isotherms of experimental data of internal pressure of dense fluids versus molar volume, V m are shown to have each a maximum point at a V max below the critical molar volume. In this study, we investigated the role of attractive and repulsive intermolecular energies on this behavior using a molecular dynamics simulation technique. In the simulation, we choose the Lennard-Jones (LJ) intermolecular potential energy function. The LJ potential is known to be an effective potential representing a statistical average of the true pair and many-body interactions in simple molecular systems. The LJ potential function is divided into attractive and repulsive parts. MD calculations have produced internal energy, potential energy, transitional kinetic energy, and radial distribution function (RDF) for argon at 180 K and 450 K using LJ potential, LJ repulsive, and LJ attractive parts. It is shown that the LJ potential function is well capable of predicting the inflection point in the internal energy-molar volume curve as well as maximum point in the internal pressure-molar volume curve. It is also shown that at molar volumes higher than V max, the attractive forces have strong influence on determination of internal energy and internal pressure. At volumes lower than V max, neither repulsive nor attractive forces are dominating. Also, the coincidence between RDFs resulting from LJ potential and repulsive parts of LJ potential improves as molar volume approaches V max from high molar volumes. The coincidence becomes complete at V max ⩾ V.

Density Functional Theory Model of Adsorption on Amorphous and Microporous Silica Materials

We present a novel quenched solid density functional theory (QSDFT) model of adsorption on heterogeneous surfaces and porous solids, which accounts for the effects of surface roughness and microporosity. Within QSDFT, solid atoms are considered as quenched component(s) of the solid-fluid system with given density distribution(s). Solid-fluid intermolecular interactions are split into hard-sphere repulsive and mean-field attractive parts. The former are treated with the multicomponent fundamental measure density functional. Capabilities of QSDFT are demonstrated by drawing on the example of adsorption on amorphous silica materials. We show that, using established intermolecular potentials and a realistic model for silica surfaces, QSDFT quantitatively describes adsorption/desorption isotherms of Ar and Kr on reference MCM-41, SBA-15, and LiChrosphere materials in a wide range of relative pressures. QSDFT offers a systematic approach to the practical problems of characterization of microporous, mesoporous, and amorphous silica materials, including an assessment of microporosity, surface roughness, and adsorption deformation. Predictions for the pore diameter and the extent of pore surface roughness in MCM-41 and SBA-15 materials are in very good agreement with recent X-ray diffraction studies.

Modification of a new potential model used for calculation of the second virial coefficient and zero density transport properties

A new hard-core potential model was recently used to calculate thermodynamic properties of some model fluids, including equilibrium properties, such as compressibility factor and internal energy. A Lennard–Jones (LJ) like potential has been used to modify the repulsive part of the potential. The modified potential contains five parameters, namely, α, R, ε, σ, and σHS. The parameter α is the tail of the attractive branch whose value changes from zero to one. In this work, we have chosen α = 1 to make the potential continuous at separation r = Rσ, where the parameter R is the well width. R lies in the range 1.2 to 2.5, and R = 1.3 was found to be the best value for all real gases studied. The parameter ε is the well depth of potential function, and σ is the separation at which the potential function is zero. σHS is the effective hard sphere diameter, which depends on temperature and an additional parameter. Using statistical mechanics along with the Boltzmann factor criterion (BFC) for the effective hard sphere diameter, an analytical expression has been derived for the reduced second virial coefficient in terms of the reduced temperature. Fitting experimental data to expression derived for the second virial coefficient, the potential parameters ε and σ are obtained. Since this potential is spherical (depending only on distance), three types of species are chosen, namely Ar and He (monoatomic), N2and O2 (diatomic), and methane (spherical molecule), to show how appropriate this potential model is for them. This model predicts an inversion temperature for the second virial coefficient (temperature at which the second virial coefficient pass through a maximum) at , where T 1 is the inversion temperature, and TB is the Boyle temperature. The predicted value is better than that of the L–J model (for which ). The maximum percentage deviation of the second virial coefficient is about 2%, except around the Boyle temperature. Then the transport properties of the fluids at the zero density limit, including viscosity, thermal conductivity, and self-diffusion coefficients, are calculated using the same values of the potential parameters. Maximum percentage deviation of transport properties at the zero density limit is about 3% for viscosity (except for Ar, with 5%), about 2.5% for thermal conductivity (except for N2 and Ar, at 8 and 5%, respectively), and about 8% for the self-diffusion coefficient. In comparison with experimental data, the modified potential model gives more accurate results than those obtained from the hard-core and modified hard-core potential models, especially at high temperatures.

Density functional theory of homopolymer mixtures confined in a slit

A density functional theory (DFT) is developed for polymer mixtures with shorted-ranged attractive interparticle interactions confined in a slit. Different weighting functions are used separately for the repulsive part and the attractive part of the excess free energy functional by applying the weighted density approximation. The predicted results by DFT are in good agreement with the corresponding simulation data indicating the reliability of the theory. Furthermore, the center-of-mass profiles and the end-to-end distance distributions are obtained by the single chain simulation; the predictions also agree well with simulation data. The results reveal that both the attraction of the slit wall and the temperature has stronger effect on longer chains than on shorter ones because the intrasegment correlation of chains increases with increasing chain length.

Do Inverse Monte Carlo Algorithms Yield Thermodynamically Consistent Interaction Potentials?

We numerically verify a statistical mechanics theorem which shows that there is a one-to-one equivalence between the structure of a liquid (i.e., the pair correlation function) and its pairwise additive intermolecular potential. Specifically, we show for three systems interacting with simple spherically symmetric pairwise additive potentials that inverse Monte Carlo (IMC) simulations can obtain the underlying potentials by only using the target pair correlation functions. The convergence of potentials obtained by the standard IMC procedure is, however, extremely slow. Interestingly, we find that the repulsive part of the potential converges rapidly, consistent with the well-accepted notion that it essentially determines the structure of condensed liquids. We show that additional information about the system, such as thermodynamic properties (e.g., average energy and or pressure) can be included in a modified IMC procedure. Because internal energy and pressure are primarily sensitive to the attractive part...

Sequential quenching of randomly deposited ellipsoids: Anisotropy and spatial patterns

We studied the sequential quenching of prolate ellipsoids on a homogeneous surface by using our proposed pair potential whose repulsive part was that of hard ellipses and attractive part was the r −6 pairwise attraction. Both the strength and range parameters for the attraction were functions of the orientations of the pair of ellipses and related by ε ∝ σ − λ . The parameter λ determines the relative strength of the side-by-side and end-to-end attractions and thus plays an important role in determining the alignment of the particles. We adopted the value λ = 2.19 by using point-energy additivity to compute the minimum energies for both of these configurations for a pair of ellipsoids of revolution with aspect ratio of 2:1. We investigated the effect of temperature and the parameter λ on the alignments of ellipses. Both radial distribution function, g ( r ) , and orientational correlation function, G ( r ) , show the expected longer ranges of orientational correlation at lower temperatures and show higher degree of orientational order for λ = 3.5 than λ = 2.19 and 0.10. This can also be seen in the examples of configurations showing that for λ = 3.5 , ellipses are more aligned than λ = 2.19 and 0.1.