Extraction of Force Laws from Measured Liquid Structure via Decoupling of Triplet Direct Correlation Function

Abstract

Extraction of a pair potential from measured structure data on monatomic liquids is proposed by combining work of Hernando and the writers with a recent decoupling of the triplet direct correlation function by Barrat et al.     

Flow Injection Analysis of Hydrogen Peroxide,Sulfite, Formaldehyde and Hydroxymethanesulfonic Acid in Precipitation Samples

Abstract

Hydroxymethanesulfonic acid (HMSA), the reaction product of sulfite and formaldehyde plays an important part in the aqueous phase conversion of sulfite to sulfate. HMSA is fairly stable under acidic conditions and in presence of hydrogen peroxide. Sulfite is unstable under these conditions.

A flow injection set-up was developed, which allows the determination of H₂O₂, sulfite, formaldehyde and hydroxymethanesulfonic acid.

H₂O₂ analysis by amperometric detection offers the possibility of a simple, robust field instrument. The detection limit is 5μg/l and the method is linear up to 5mg/l.

Based on the 4,4-dithiodipyridine/sulfite reaction selective and sensitive spectrophotometric detections were developed for sulfite, formaldehyde and hydroxymethanesulfonic acid. The detection limit of these compounds is 50μg/l and the method is linear up to 5mg/l.

A large fraction of S(IV) is present as HMSA in fog, dew and precipitation samples in The Netherlands.     

On the quantum chemical origin for the nonvalidity of Koopmans' theorem in transitionmetal compounds

The quantum chemical origin for the nonvalidity of Koopmans' theorem in transitionmetal compounds of the 3d series is analyzed by means of the Green's function formalism applied in the framework of a semiempirical INDO Hamiltonian. In the case of ferrocene (1), cyclobutadiene iron tricarbonyl (2) and irontetracarbonyl dihydride (3) the self-energy part of a geometric approximation has been partitioned into relaxation and correlation (pair removal, pair relaxation) increments. The breakdown of Koopmans' theorem for strongly localized MOs with large Fe 3d amplitudes is predominantly the result of electronic relaxation lowering the calculated ionization potentials. On the other hand the variation of the pair correlation energy in the cationic hole-state is by no means negligible and acts into the opposite direction as the relaxation increment. These significant pair relaxation contributions explain the wellknown failtures of the ΔSCF approach in combination with large scaleab initio bases. The loss of ground state pair correlation in the outer valence region is small in comparison to relaxation and pair relaxation. The magnitude of the aforementioned reorganization increments has been studied as a function of the localization properties of the MOs and as a function of the one-electron energies of the available particle- and hole-states. The computational findings derived with the INDO model are compared with recentab initio studies.     

Structure of colloids and macroionic solutions with soft,long-range interactions

The structure of strongly interacting, charged dispersions is examined using the Ornstein-Zernike integral-equation formalism with thermodynamic consistency conditions (i.e., with the so-called HMSA closure conditions). It is shown that for highly charged dispersions interacting through screened Coulombic (Yukawa) interactions this integral-equation approach predicts the static structure factorS(q) in excellent agreement with Monte Carlo results and that it is better than the rescaled mean-spherical approximation. The Sogaimi potential (which predicts Coulombic attraction under identical physicochemical conditions) is also considered here as a model potential for representing soft, long-ranged interactions with an attractive component. None of the integralequation formalisms, including the HMSA theory and the reference hypernetted-chain (RHNC) theory, leads to a sufficient level of thermodynamic consistency for the latter potential, and the results deviate noticeably from the Monte Carlo results. We further demonstrate that fitting the experimentally observed structure factors in the neighborhood and beyond the primary peak inS(q) could lead to inaccurate conclusions concerning the nature of interparticle forces, particularly in the case of soft, long-range interactions.     

Pair Function and Structure Factor of an Interacting Electron Liquid

Abstract

Recent work on small angle scattering from liquid metals has caused renewed interest in the electron pair function in the uniform interacting electron liquid, jellium. Therefore we have re-examined this problem, starting from an analysis of the exchange hole, in which the only correlations are due to the Pauli Principle and solely therefore between parallel spin electrons. The pair function g(r) of noninteracting Fermions is expressed in terms of the density of the p-component in the free electron density matrix. This motivates the treatment of the Coulomb repulsion via a potential energy V(r) To close the theory, one must either invoke self-consistency to determine V(r), or relate it to the (direct) correlation function c(r) as in classical liquids. Both methods are briefly considered; the second has the advantage that here the collective plasma oscillations can be introduced through their zero-point energy.     

Structural properties of some liquid transition metals

This article addresses the computation of structural properties of liquid transition metals, namely, 3d (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn), 4d (Zr, Pd, Ag and Cd) and 5d (Pt, Au and Hg). We have calculated the structure factor S(q), pair distribution function g(r), interatomic distance r ₁, coordination number n ₁, long wavelength limit of structure factor S(0) and isothermal compressibility χ_T for liquid transition metals. To describe electron–ion interaction, we have used our own model potential along with one component plasma reference system. To see the influence of exchange and correlation effect, Sarkar et al.'s [Mod. Phys. Lett. B12, 639 (1998)] local field correlation function is used. Thus, our newly constructed model potential has successfully generated the structural properties (structure factor S(q), pair distribution function g(r), interatomic distance r ₁, coordination number n ₁, long wavelength limit of structure factor S(0) and isothermal compressibility χ_T ) for liquid transition metals.     

Exact Self-consistent Integral Equations for the Distribution Functions of Classical Fluids

Abstract

The source particle method (SPM) due to Percus and Verlet of obtaining the single particle density, and the pair and triplet distribution functions of classical fluids (as well as in the variational theory of Bose liquids) is studied. Generalizations of hypernetted chain (HNC) equations are generated by holding fixed the coordinates of the definite group of source particles. Special attention is paid to the triplet distribution function and to the self-consistent calculation of the bridge function (elementary diagram) contribution in the pair distribution function. A comparison with the other exact integral equation theories including the BBGKY-equations is discussed.     

Effect of repulsive interaction on the structural and dynamic features of liquid water. The role of molecular polarizability

The effect of variation of the potential function on the structural and dynamic properties of model water when the surface of pair interactions is invariant is studied by the molecular dynamics method. Variations for the rigid and polarizable models are compared. Translated fromZhurnal Strukturnoi Khimii, Vol.40, No. 2, pp. 296–303, March–April, 1999.     

三嗪基苯胺桥联双环糊精的合成及其对染料分子的选择键合

通过N,N-二乙基-4-(二氯代-1,3,5-三嗪-2-基)苯胺分别与单-[6-(乙二胺基)-6-脱氧]-β-环糊精和单-[6-(二乙烯三胺基)-6-脱氧]-β-环糊精反应合成了两种三嗪基苯胺桥联双环糊精, 采用荧光和紫外光谱滴定方法测定了它们在磷酸缓冲溶液中(25 ℃, pH＝7.2)与几种具有不同形状和电子密度的染料分子包结配位的稳定常数. 结果表明, 三嗪基苯胺桥联双环糊精不但对具有较大电子密度的三角形客体结晶紫给出了6～26倍于天然环糊精的配位稳定常数, 而且对结晶紫/中性红分子对给出了高的分子选择性(K_CV/K_NR＝23～31). 分子力学研究表明, 桥联双环糊精对客体分子的强键合能力主要源于两个环糊精空腔及桥链基团对客体分子的协同键合, 特别是桥链中三嗪基苯胺基团与客体之间的p-p相互作用.     

On the conformational effects of intermolecular interactions in nematics

Abstract

A perturbation expansion of the pair correlation function is used to derive the molecular field self-consistency equations for non-rigid molecules. The order parameters and the thermodynamic functions are expressed directly in terms of the segmental interaction coupling constants. The values of these constants for the 4-n-alkyl-4'-cyanobiphenyis (NCB) are determined by analysing the orientational order parameters observed by N.M.R. in the nematic phase; they are in reasonable agreement with values obtained from calculations of the nematic-isotropic transition temperatures. It is found that contributions of the isotropic intermolecular interactions to the conformational energy of the alkyl chain are comparable in magnitude to the direct intramolecular contributions.     

Méthode des Biorbitales: Application Préliminaire au Calcul de l'Energie de l'Etat Fondamental de l'Atome de Beryllium

The ground-state electronic energy of Be is calculated using the method of biorbitals (SCF –BI ). In this method the wave function is represented by an antisymmetrized product of identical pair functions. The basic set used to develop the biorbitals consists of the Watson s and p orbitals. The pair function is presumed to describe a singlet pair state. The energy associated with this function is minimized using a steepest descent procedure. A value of 0.0414 a.u. was found for the correlation energy, which is 44% of the total correlation energy. The SCF –BI method is compared with the CI method. The relationships are established between the expansion coefficients of both methods. The occupation numbers of orbitals are calculated.     

IR spectroscopic study of ion-molecular interactions in the methanesulfonic acid—N,N-dimethylformamide system

Complex formation in the methanesulfonic acid (MSA)-DMF system was studied by Multiple Attenuated Total Reflectance (MATR) IR spectroscopy at 30°C within the composition range from neat MSA up to neat DMF. Depending on the ratio of components, two types of complexes with a strong quasi-symmetrical H bond (1 and2) are formed. The uncharged complex1 is a quasi-ion pair with the (O…H…O) bridge. Complex2 is formed by a protonated DMF molecule and the (A…H…A)⁻ anion bound as an ion pair. It is established that complexes1 are solvated by DMF molecules in an excess of a base. Solvation or2 in an excess of an acid corresponds to a change from contact to contact-separated ion pairs. Continuous absorption spectra of charged and uncharged complexes1 and2 were obtained. The schemes of acid-base interactions in the MSA-DMF and HCl-DMF systems were compared. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2484–2489, December, 1998.     

Liquid‐like structure of polymer solutions near the overlap concentration

The light scattering structure factor S( q , c) has been measured for a series of concentrations near the overlap value c* for solutions of high molecular weight poly(α‐methyl styrene) in the good solvent toluene. Scattering functions near and above overlap are characterized by a maximum as a function of scattering vector q . Scattering functions have also been calculated for these conditions using the measured second virial coefficient and radius of gyration, as reported previously for dilute solutions. The scattering function is factored into an intramolecular part that is described by a Debye function with no adjustable parameters and an intermolecular part that depends on the coil–coil pair correlation function, as suggested by Flory and Bueche. The pair correlation function is calculated using the Percus–Yevick theory of liquids and the Flory–Krigbaum potential for coil–coil interactions, as suggested by Frank Stillinger. Good agreement is obtained for the most concentrated dilute solutions, but as the overlap concentration is approached significant discrepancies are observed. The thermodynamic value of the scattering function, S(0, c), is overestimated by the theory. This discrepancy is discussed in terms of the importance of three‐body interactions, the failure of the Flory–Krigbaum potential in semidilute solutions and the limited precision of the standard protocol for calculating the measured scattering function in nondilute solutions. The observed maximum in the scattering function near overlap is not quantitatively reproduced by the theory. This discrepancy is discussed in terms of the failure of the shape of the Flory–Krigbaum potential to accurately reflect the energy of overlap for chains separated by distances near twice the radius of gyration. The mean‐field nature of the potential ignores the increased probability of interactions of linear neighboring segments. Well into the overlap region, the calculated scattering function poorly describes the observed results. The failure of the Flory–Bueche approximation in semidilute solutions is discussed as well as the effect of a changing radius of gyration as a function of concentration on the intramolecular scattering function. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 703–710, 2006     

N.M.R. study of segmental molecular interactions in liquid crystals

Abstract

A simple statistical model of interacting non-rigid molecules, based on a perturbation expansion of the pair correlation function and the additivity of segmental interactions, is applied to the study of orientational order as measured by N.M.R. in the nematic and S_A phases of 4-n-alkyl-4′-cyanobiphenyls (N-CB, N = 5 to 8), the nematic and S_C phases of 4-n-alkyloxybenzoic acids (N-OBA, N = 7, 8) and the D _h0 columnar discotic phase of hexa-alkyloxytriphenylenes (N-THE, N = 5 to 8). The order parameters of each homologous series are correctly described in terms of two isotropic and two anisotropic segmental coupling constants. The model predicts certain relations among coupling constants pertaining to different homogous series. These predictions are supported by the results obtained for the three types of compounds studied.     

Effect of the state of h-b-1 hydrogen bond on the character of some atom vibrations in guanine-cytosine pair of the DNA molecule

For the first hydrogen bond of the guanine-cytosine (G-C) pair, the potential function V(r, R) is found for the nonequilibrium bond length R. A new form of the semiempirical potential function, Clementi's calculations for V(r, R₀) and some experimental data are used. New wave functions and energy levels as a function of the H-bond length for the ground and several excited states are obtained. This allows one to obtain frequencies and amplitudes of some vibrations of the G-C pair side groups involved in the formation of the hydrogen bond when the latter is not excited and when it is excited to the first energy level. © 1996 John Wiley & Sons, Inc.     

Statistical–mechanical models with separable many-body interactions: especially partition functions and thermodynamic consequences

We start from a classical statistical–mechanical theory for the internal energy in terms of three- and four-body correlation functions g ₃ and g ₄ for homogeneous atomic liquids like argon, with assumed central pair interactions f(r_ij){\phi(r_{ij})} . The importance of constructing the partition function (pf) as spatial integrals over g ₃, g ₄ and f{\phi} is stressed, together with some basic thermodynamic consequences of such a pf. A second classical example taken for two-body interactions is the so-called one-component plasma in two dimensions, for a particular coupling strength treated by Alastuey and Jancovici (J Phys (France) 42:1, 1981) and by Fantoni and Tellez (J Stat Phys 133:449, 2008). Again thermodynamic consequences provide a particular focus. Then quantum–mechanical assemblies are treated, again with separable many-body interactions. The example chosen is that of an N-body inhomogeneous extended system generated by a one-body potential energy V(r). The focus here is on the diagonal element of the canonical density matrix: the so-called Slater sum S(r, β), related to the pf by pf(b) = òS(r, b)d[(r)\vec]{{\rm pf}(\beta) = \int {S({\bf r}, \beta)}d\vec {r}}, β = (k _B T)⁻¹. The Slater sum S(r, β) can be related exactly, via a partial differential equation, to the one-body potential V(r), for specific choices of V which are cited. The work of Green (J Chem Phys 18:1123, 1950), is referred to for a generalization, but now perturbative, to two-body forces. Finally, to avoid perturbation series, the work concludes with some proposals to allow the treatment of extended assemblies in which regions of long-range ordered magnetism exist in the phase diagram. One of us (Z.D.Z.) has recently proposed a putative pf for a three-dimensional (3D) Ising model, based on two, as yet unproved, conjectures and has pointed out some important thermodynamic consequences of this pf. It would obviously be of considerable interest if such a pf, together with conjectures, could be rigorously proved.     

Evaluation of Multivariate Calibration Using a Tikhonov Regularization Approach and the Generalized Pair‐Correlation Method with Nonlinear Data

Abstract

In order to reduce data nonlinearity and overfitting with the multivariate calibration model y=Xb, a modified Tikhonov regularization (TR) algorithm is evaluated for selecting key variables from an X augmented with extra columns that contain the original measured variables (x _ij ) as squared terms (x _ij ²) and other orders. The TR approach simultaneously develops the multivariate calibration model. The new generalized pair‐correlation method (GPCM) is also studied for variable selection followed by partial least squares (PLS) for multivariate calibration. Results from synthetic spectral data are compared when using the modified TR approach, GPCM, and PLS without variable selection. The GPCM usually performs slightly better than the TR approach for tabulated bias and variance measures and in some cases, at a sacrifice to parsimony. The method of PLS without variable selection performs the worst. By using synthetic spectral data sets, how the methods work could be studied. Thus, results from this study will aid investigators of real spectral data sets exhibiting nonlinear behavior.     

A Comparative Analysis of the Rice-Allnatt and Square-Well Liquid Transport Theories

Abstract

The Yvon-Born-Green pair correlation function theory is discussed from the viewpoint of its role as theoretical data input for the Rice-Allnatt liquid transport theory. The general behavior of the Rice-Allnatt theory is shown to compare favorably with that of the square-well transport theory of Davis, Rice, and Sengers, although the former is not as quantitative. The predictive ability of the Rice-Allnatt theory is improved by a systematic adjustment of the Lennard-Jones parameters used in the YBG pair correlation functions, based on the critical point locus.     

Polymerization induced phase separation (PIPS) in a polymer dispersed liquid crystal (PDLC) system: A Monte-Carlo simulation approach

Abstract

The polymerization induced phase separation (PIPS) process in a polymer dispersed liquid crystal (PDLC) system was studied by using Monte-Carlo (MC) simulation methods. In particular, the dependence of the phase separation between liquid crystal and polymer on the parameters, such as temperature γ = ?/kT, polymerization reactivity p and curing time t _c, was examined. It was found that the pair correlation function G(a, t) decreases with the decrease of temperature when the polymerization reactivity p is fixed. Our results also revealed that at a constant temperature, the final value of G(a) first increases with the increasing of p, and finally approaches a constant value. This observation provides us an effective way of controlling the size of liquid crystal droplets as well as their distributions. It was observed that the equilibrium value of G(a) increases as the curing time increases when both temperature and p are kept constant. This is another way of controlling the size of liquid crystal droplets.     

Interparticle Correlations and Magnetic Properties of Concentrated Ferrocolloids

A statistical mechanical model was proposed for describing magnetic properties of highly concentrated ferrocolloids and dielectric properties of polar liquids. The model is based on a relationship between the magnetization and the pair correlation function of a spatially homogeneous ferroparticle system. The advantage of the proposed method is that the determination of the pair distribution function, with an accuracy of the powers of the concentration n ^k and the powers of the interparticle dipole-dipole interaction potential U _d ^k , leads to an expression for the magnetization of the order of n ^{k +1} and U _d ^k+1, respectively. Relations for the magnetization and the magnetic susceptibility of a ferrofluid and also for the permittivity of a polar liquid taking into account interparticle correlations with an accuracy of terms U _d ² were derived. The results obtained within the framework of this model agree closely with the numerical calculations and experimental data.