Kirkwood Equation Research Articles

Towards optimizing cooling rate, microstructure, and compressive strength in rapidly solidified Cu–20Fe alloy

There is currently interest in the development new Cu–Fe alloys with higher Fe content (>5 wt%), a low-cost element. In order to improve electrical, thermal and mechanical properties, there is a need to decrease the size of the Fe-rich phase and improve its distribution, whose possibilities rely on adding alloying third elements and heat treatments. However, the prospect of controlling the size of the phase through dendritic spacing control by means of rapid solidification processes may be feasible and deserves to be explored, as is the case in the present study. The following methods were employed to evaluate the round stepped cast samples of the Cu-20 wt% Fe alloy: centrifugal casting in a Cu mold, optical microscopy, CALPHAD, Scanning Electron Microscopy/Energy Dispersive Spectroscopy (SEM/EDS), X-ray Diffraction (XRD), Vickers hardness, and compressive tests, in samples corresponding to different coarsening microstructures. Finally, dendritic growth is modelled using the Kirkwood equation. The results demonstrate a promising processing route with control of the secondary dendrite arm spacing (SDAS), whose methodology and modeling can serve as a basis for other alternative processes with the Cu–Fe alloys, allowing suitable size and distribution of Fe phase to be attained. It is further demonstrated that the Kirkwood model is able to match experimental SDAS in both slowly and rapidly solidified Cu–Fe samples. While Fe (BCC) is expected to increase strength, this is only slightly observed in the hardness results for smaller SDAS, as the loads are more superficial. In the case of compressive yield strength, SDAS in the observed range (1.4 μm–2.2 μm) is found to have no effect.

Demystifying the Stern layer at a metal-electrolyte interface: Local dielectric constant, specific ion adsorption, and partial charge transfer.

Electric double layer (EDL) represents one of the most basic concepts in electrochemistry and is pertinent to diverse engineering applications ranging from electrocatalysis to energy storage. Whereas phenomenological and coarse-grained models have been long established to describe ionic distributions in the diffuse layer, a faithful prediction of the physicochemical properties of the electrode-electrolyte interface from a molecular perspective remains a daunting challenge. In this work, we investigate the charging behavior of an Ag (111) electrode in NaF aqueous solutions leveraging experimental results and theoretical calculations based on the classical density functional theory for ion distributions in the diffuse layer and on the joint density functional theory (JDFT) for the electronic structure. When the Ag electrode is applied with a negative voltage, the surface charge density can be reasonably described by assuming a neutral Stern layer with the dielectric constant dependent on the local electric field as predicted by the Kirkwood equation. However, the specific adsorption of F- ions must be considered when the electrode is positively charged and the fluoride adsorption can be attributed to both physical and chemical interactions. Qualitatively, F- binding and partial charge transfer are supported by JDFT calculations, which predict an increased binding energy as the voltage increases. Our findings shed insight on the molecular characteristics of the Stern layer and the charge behavior of adsorbed species not specified by conventional EDL models.

An electronic properties investigation to interpret the substituent constants of monosubstituted benzene derivatives

In the present work, the π and π∗-electronic nature of substitution constants (σ) of the twenty-two monosubstituted benzene derivatives (MSBDs) are estimated in terms of the para-delocalization index (PDI) and total non-Lewis structure (TNLS), respectively. Since these compounds are aromatic, the other descriptors of aromaticity such as nuclear independent chemical shifts and aromatic stabilization energy have been examined. Because of no considerable variation for the π and π∗-electron delocalization in the ring systems, a very weak correlation has been demonstrated between all aromaticity indices. Also, none of these descriptors has a linear correlation with the values of σ for both electron-donating groups (EDGs) and electron-withdrawing groups (EWGs) in a simultaneous relationship. We now propose the usage of the dipole moments values of molecules, considering their directions, by multiplying the PDI and TNLS values as probes to interpret σ values for benzene and MSBDs since the dipole moment can affect the π and π∗-electron delocalization. It is interesting to note that there is a remarkable linear correlation between our suggested probes, ±μPDI and ±μTNLS, and σp, σm, and σ+/σ− for EDGs and EWGs in simultaneous linear relationships. Also, these probes have a relative relationship with Kirkwood and Westheimer equation. Additionally, the regression coefficient between ±μPDI and ±μTNLS is 0.989.

Generation of Pairwise Potentials Using Multidimensional Data Mining.

The rapid development of molecular structural databases provides the chemistry community access to an enormous array of experimental data that can be used to build and validate computational models. Using radial distribution functions collected from experimentally available X-ray and NMR structures, a number of so-called statistical potentials have been developed over the years using the structural data mining strategy. These potentials have been developed within the context of the two-particle Kirkwood equation by extending its original use for isotropic monatomic systems to anisotropic biomolecular systems. However, the accuracy and the unclear physical meaning of statistical potentials have long formed the central arguments against such methods. In this work, we present a new approach to generate molecular energy functions using structural data mining. Instead of employing the Kirkwood equation and introducing the "reference state" approximation, we model the multidimensional probability distributions of the molecular system using graphical models and generate the target pairwise Boltzmann probabilities using the Bayesian field theory. Different from the current statistical potentials that mimic the "knowledge-based" PMF based on the 2-particle Kirkwood equation, the graphical-model-based structure-derived potential developed in this study focuses on the generation of lower-dimensional Boltzmann distributions of atoms through reduction of dimensionality. We have named this new scoring function GARF, and in this work we focus on the mathematical derivation of our novel approach followed by validation studies on its ability to predict protein-ligand interactions.

Dielectric permittivity, polarizability and dipole moment of refrigerants R1234ze(E) and R1234yf determined using a microwave re-entrant cavity resonator

Abstract Dielectric permittivities (er) have been measured using a microwave re-entrant resonator at temperatures from (248 to 365) K and pressures up to 11 MPa for the alternative refrigerants 1,3,3,3-tetrafluoropropene (R1234ze(E)) and 2,3,3,3-tetrafluoropropene (R1234yf) in the liquid and vapour phases. Values of er were also measured for liquid CO2 at temperatures below 274 K, extending the data available for this fluid. Molecular polarizability, dipole moment, and the dielectric virial coefficients of each hydrofluoroolefin (HFO) refrigerant were determined by applying the dielectric virial expansion and Kirkwood equation to the measured permittivity data. The experimental results for the vapour phase lead to dipole moments with relative standard uncertainties around 5% that are in reasonable agreement with values from molecular modelling. The measured dipole moment for R1234ze(E) of 1.13 D is about 12% smaller than predicted, while the measured dipole moment for R1234yf of 2.24 D is about 11% smaller than predicted. In the compressed liquid region, the two refrigerants exhibited quite different dependencies on temperature and density. The polarizability of liquid R1234ze(E) could be predicted within 4.2% using the gas phase parameters (measured dipole moment and molecular polarizability). In contrast, the temperature dependence of the polarizability of R1234yf was twice as large in the liquid phase as in the gas phase. The density dependence of the polarizability for liquid R1234yf is at least 10 times that of liquid R1234ze(E). Liquid phase data were also used to estimate effective Kirkwood correlation factors, g, by assuming them to be temperature independent over the range of measurements. The results indicate g ≈ 2.4 for R1234yf and g ≈ 1.2 for R1234ze(E).

Prediction of the surface tension of cesium in the whole liquid range

ABSTRACTSurface tension is an important quantity, both as physical and technological features. We applied the general form of Lennard-Jones potential model, LJ (m-n), and some thermodynamic arguments in the Kirkwood and Buff equation to calculate the surface tension of liquid cesium. To find out the surface tension in a wide temperature range, only pVT data are required. By this method, we investigated the influence of the potential model on the surface tension. For two selected potential models [LJ (6–3) and LJ (8.5–4)], the values of the calculated surface tension and the predicted surface energy agree with the experimental values.

Characterisation and mechanistic study of the oxidative addition reactions of [Ir(cod)(sacac)

[Ir(cod)(sacac)] (sacac = thioacetyl acetonato) complexes were successfully synthesized and characterised using 1H and 13C NMR, IR and micro elemental analyses. The formation of isosbestic points in different solvents clearly indicate the formation of only one product, while the kinetic results for all of the complexes (except for chlorobenzene) showed simple second order kinetics with a zero intercept (within experimental error). The rate of oxidative addition showed little or no change with a solvent variation even with a large difference in polarity for the selected solvents, varying between 1.78 × 10−3 and 5.2(3) M−1 s−1 for chlorobenzene and acetonitrile respectively. Activation volumes were determined in four of the solvents, which varied between +10.2(9) for chloroform to −18(1) cm3 mol−1 for acetonitrile. This solvent variation obeyed the Kirkwood equation with an intrinsic volume of activation of −21(3) cm3. A DFT analysis of the oxidative addition reaction shows that the trans addition is energetically favoured and that the trans [Ir(cod) (sacac) (CH3) (I)]-alkyl product is more stable than the four possible cis [Ir(cod) (sacac) (CH3) (I)]-alkyl products.

PHYSICOCHEMICAL QUALITY CONTROL OF BEE HONEYS FROM CAMPOS GERAIS REGION OF PARANÁ – BRAZIL

Bee (Apis mellifera L.) honeys have been widely used for therapeutic and nutritional proposes. For evaluating the honey production, physicochemical approaches have been extensively performed to ensure that this hive product is authentic in respect to the legal requirements. The aim of this paper was to discuss the quality control of 93 samples of honey from Campos Gerais region of Paraná State – South Brazil by physicochemical parameters. Moisture, reducing sugars, sucrose, water-insoluble solids, ash, free acidity, pH, activity of diastase, hydroxymethylfurfural content and colour were performed by the standard usual methods. Samples were also classified in floral honeys or honeydew honeys according to the Kirkwood equation. A total of 71 samples (76.34%) showed values in accordance with the Brazilian legal requirements for all the achieved physicochemical parameters. Otherwise, all the studied honeys were likewise within the legislation limits only for water-insoluble solids and colour. For pH, an additional parameter that has not been provided in honey legislation, samples showed values ranging from 3.60 to 5.35. By the Kirkwood equation, 61 honeys were considered as floral products.

Prediction of a structural transition in the hard disk fluid

Starting from the second equilibrium equation in the BBGKY hierarchy under the Kirkwood superposition closure, we implement a new method for studying the asymptotic decay of correlations in the hard disk fluid in the high density regime. From our analysis and complementary numerical studies, we find that exponentially damped oscillations can occur only up to a packing fraction η(∗)∼0.718, a value that is in substantial agreement with the packing fraction, η∼0.723, believed to characterize the transition from the ordered solid phase to a dense fluid phase, as inferred from Mak's Monte Carlo simulations [Phys. Rev. E 73, 065104 (2006)]. Next, we show that the same method of analysis predicts that the exponential damping of oscillations in the hard sphere fluid becomes impossible when λ=4nπσ(3)[1+H(1)]≥34.81, where H(1) is the contact value of the correlation function, n is the number density, and σ is the sphere diameter in exact agreement with the condition, λ≥34.8, which is first reported in a numerical study of the Kirkwood equation by Kirkwood et al. [J. Chem. Phys. 18, 1040 (1950)]. Finally, we show that our method confirms the absence of any structural transition in hard rods for the entire range of densities below close packing.

Thermodynamic description of equilibria in mixed fluids (H2O-nonpolar gas) in a wide range of temperatures (25–700°C) and pressures (1–5000 bar)

A new method is proposed for calculating equilibria in mixed multicomponent systems H2O-nonpolar gas at high temperatures and pressures. The method is based on calculation of electrostatic interactions between a solute component and surrounding molecules of a solvent (H2O). The SUPCRT98 database and the Helgeson-Kirkham-Flowers equation of state for components of an aqueous solution were used for computer realization of the method. The thermodynamic properties of solute gases at elevated temperatures and pressures are calculated by the Redlich-Kwong equation. The dielectric properties of a mixed solvent are determined using the modified Kirkwood equation. The proposed method was approved in description of the available set of experimental data on constants of H2O and NaCl dissociation, as well as data on solubility of both covalent and ionic crystals [SiO2, AgCl, Ag2SO4, Ca(OH)2, CaCO3] in mixed solvents H2O-nonpolar component [1,4-dioxane (C4H4O2), Ar, CO2]. The calculation and experimental data agree in a wide range of PTx conditions (temperatures up to 500°C, pressures up to 5000 bar, and mole fractions (x) of a nonpolar component in fluid up to 0.3). The proposed approach can be used for assessing the Born parameters of solute components. The calculation algorithm developed allows us not only to consider separate reactions but also to study equilibria in hydrothermal systems as a whole. Hence, the proposed approach can be used for constructing thermodynamic models of evolution of fluids rich in volatile components and vital to natural processes of mineral formation.

Swelling behavior of PDMS–PMHS pervaporation membranes in ethyl acetate–water mixtures

AbstractPervaporation composite membranes were prepared with a three‐layer structure: a PP support, a PEI microporous structure, and a PDMS–PMHS selective layer. Swelling tests were performed in water, ethyl acetate, and four different ethyl acetate–water mixtures, to calculate the diffusional and swelling parameters. Moreover, the dynamic–mechanical properties of the membranes were obtained before and after the swelling experiments, and their relaxation spectra were characterized with the Fuoss–Kirkwood equation and analyzed in terms of the free volume parameter. It was found that the ethyl acetate possesses high affinity with the composite membranes and that the absorption of these small molecules substantially modifies the viscoelastic behavior and structure of the active layer. The combination of swelling experiments and the study of the mechanical relaxations proved to be an appropriate technique to investigate the behavior of pervaporation membranes immersed in different mixtures. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1384–1393, 2004

Temperature dependence of local density augmentation around exciplex in supercritical carbon dioxide

To clarify the temperature dependence of local density augmentation around short-lived species, the pressure dependence of the formation and decay processes of exciplex between two neutral species, acetophenone (AP) and N, N, N′, N′-tetramethylbenzidine (TMB), in supercritical carbon dioxide was investigated by a transient absorption technique at 40, 55, and 70 °C. In the high-density (>0.6 g cm −3) region, the decay rate constant could be described by the Kirkwood equation. However, in the low-density (0.35–0.6 g cm −3) region, the exciplex was more stable than that predicted by Kirkwood analysis, which means that strong influence of local density augmentation around the exciplex occurred. The local density augmentation can be described in terms of an excess density which is defined as a difference between local and bulk density. The excess density was derived from the difference between experimental results and Kirkwood analysis and exhibited a maximum at near-critical density. The excess density decreased with increasing temperature and became negligible at high temperatures and high bulk densities.

Dissipative particle dynamics simulation of polymer drops in a periodic shear flow

The steady-state and transient shear flow dynamics of polymer drops in a microchannel are investigated using the dissipative particle dynamics (DPD) method. The polymer drop is made up of 10% DPD solvent particles and 90% finite extensible non-linear elastic (FENE) bead spring chains, with each chain consisting of 16 beads. The channel’s upper and lower walls are made up of three layers of DPD particles, respectively, perpendicular to Z-axis, and moving in opposite directions to generate the shear flow field. Periodic boundary conditions are implemented in the X and Y directions. With FENE chains, shear thinning and normal stress difference effects are observed. The “colour” method is employed to model immiscible fluids according to Rothman–Keller method; the χ-parameters in Flory–Huggins-type models are also analysed accordingly. The interfacial tension is computed using the Irving–Kirkwood equation. For polymer drops in a steady-state shear field, the relationship between the deformation parameter ( D def) and the capillary number ( Ca) can be delineated into a linear and nonlinear regime, in qualitative agreement with experimental results of Guido et al. [J. Rheol. 42 (2) (1998) 395]. In the present study, Ca<0.22, in the linear regime. As the shear rate increases further, the drop elongates; a sufficiently deformed drop will break up; and a possible coalescence may occur for two neighbouring drops. Dynamical equilibrium between break-up and coalescence results in a steady-state average droplet-size distribution. In a shear reversal flow, an elongated and oriented polymer drop retracts towards a roughly spherical shape, with a decrease in the first normal stress difference. The polymer drop is found to undergo a tumbling mode at high Schmidt numbers. A stress analysis shows that the stress response is different from that of a suspension of solid spheres. An overshoot in the strain is observed for the polymer drop under extension due to the memory of the FENE chains.

Influence of previous annealing on first stage of degradation of blends of low‐density polyethylene and Mater‐Bi AF05H aged in soil: Comparative thermal analysis study

AbstractSamples of low‐density polyethylene (LDPE) filled with a commercial biodegradable material (Mater‐Bi AF05H) were subjected to an accelerated soil burial test in a culture oven. In addition, another series of these blends was subjected to thermal treatment and afterward buried in soil under the same conditions. Comparative studies of the changes in the thermal stability and the structural and morphological properties of the samples were carried out by means of differential scanning calorimetry, dynamic mechanical thermal analysis, and thermogravimetric analysis. The morphological properties under study were the melting temperature, the crystalline content, and the lamellar thickness distribution. The αI relaxation zone of the mechanical spectra was characterized in terms of tan δ, whereas the αII and relaxation zones were characterized in terms of E″ according to the Fuoss–Kirkwood equation and with the help of a deconvolution method. Finally, the kinetics of each thermodegradation process was studied using the Broido integral method. The Mater‐Bi hindered the uniform growth of crystallites in PE and facilitate molecular motions, but the thermal treatment seemed to rearrange the crystallites in the crystalline phase of PE and promote segregation of the crystallite sizes. These molecular reorganizations affected the degradation process so that the degradation of the polymeric matrix seemed to be obstructed by the annealing during the first 120 days of aging in soil and only the Mater‐Bi degradation could be observed. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 3359–3373, 2003

Classificação do mel em floral ou mel de melato

O mel e um produto natural de abelhas fabricado a partir do nectar das flores (mel floral) e de secrecoes de partes vivas das plantas, ou de excrecoes de insetos sugadores de partes vivas das plantas (mel de melato). O melato e uma fonte alternativa de alimento bastante utilizada pela abelha. Em Santa Catarina, o mel de melato e muito conhecido, sendo produzido nos meses de janeiro a abril, em ciclos bianuais. Foram colhidas aleatoriamente 25 amostras de mel, no periodo de janeiro/93 a junho/96, de diferentes apiarios e datas de colheita. Foram determinados os teores de umidade, pH, cinzas e acucares redutores. Os resultados foram utilizados na aplicacao da equacao de Kirkwood para classificar o mel como floral ou de melato. As amostras tambem foram analisadas quanto a rotacao optica para classificacao de acordo com White. Das 25 amostras analisadas, 11 foram classificadas como mel de melato de acordo com Kirkwood e White. O estudo estatistico, feito pela aplicacao do teste exato de Fisher, indicou que, apesar da divergencia em 4 amostras, estes metodos sao equivalentes e ambos podem ser usados.

The dielectric constant of polarizable fluids from the renormalized perturbation theory

A perturbation theoretical equation for the dielectric constant of polarizable dipolar fluids is proposed. For the fluctuation of the dipole moment, namely for the Kirkwood g-factor, a formula is given on the basis of Wertheim's renormalized perturbation theory. Using this formula, a series expansion for ε(p) is suggested on the basis of the Kirkwood equation, which gives an implicit function for ε as a function of ¶. The same series expansion can be derived from the Clausius-Mosotti equation—thus it proves to be independent of the boundary conditions. The resulting equation gives excellent results for the dielectric constant of the polarizable Stockmayer fluid producing good agreement with computer simulation data. The series expansion gives better results than the Kirkwood equation itself.

Dynamic mechanical and dielectric relaxation behaviour of poly(methacrylate)s containing saturated rings with seven and eight members in the side‐chains

AbstractDynamic mechanical and dielectric behaviour of poly(cycloheptyl methacrylate), poly(cycloheptylmethyl methacrylate) and poly(cyclooctyl methacrylate) have been investigated. The study was performed by determining the components of the complex relaxation modulus E* and the complex dielectric permittivity ϵ*. Results are discussed in terms of the effect of the size and structure of the side ring. The saturated ring group shows mechanical and dielectric activity at low temperature that is analyzed in terms of the Fuoss–Kirkwood equation. The free volume for the three polymers was determined. The conductive and interfacial phenomena were studied by MacDonald and Coelho models, where the dipolar contribution was introduced.© 2002 Society of Chemical Industry

Degradation studies of LDPE–Mater‐Bi blends annealed and aged in soil

AbstractBlends of low‐density polyethylene (LDPE) and a commercial biodegradable material commonly used as an additive, Mater‐Bi AF05H, were subjected to thermal treatment followed by an accelerated soil burial test in a culture oven. The effect of the degradation process on the structural and morphological properties of the samples was studied by differential scanning calorimetry and dynamic mechanical thermal analysis. The morphological properties studied in this work were the melting temperature, the crystalline content, and the lamellar thickness distribution. The αI relaxation zone of the mechanical spectra was characterized in terms of tan δ and the αII and β relaxations were characterized in terms of E″ according to the Fuoss–Kirkwood equation and using a deconvolution method. It was found that the thermal treatment rearranges the crystallites in the crystalline phase and promotes a segregation of the crystallite sizes. However, the annealing seems rather to hinder than to improve the degradation of the samples. Moreover, the degradation process in the blends apparently starts in the Mater‐Bi. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 405–413, 2002

Dielectric relaxations of poly(2-norbornyl methacrylate) and poly(3-methyl-2-norbornyl methacrylate)

Dielectric behaviour of poly(2-norbornyl methacrylate) (P2NBM) and poly(3-methyl-2-norbornyl methacrylate) (P3M2NBM) was studied. The effect of the methyl substituent on the norbornyl ring is to decrease the temperature of the dynamic glass transition about 50K. Moreover, weak secondary relaxations are observed in the two polymers under study. The secondary process of P3M2NBM has been conveniently analysed in terms of the empirical Fuoss–Kirkwood (F–K) equation.

Viscoelastic behavior of degradable polyolefins aged in soil

Samples of polypropylene and a high density polyethylene/polypropylene blend filled with different biodegradable additives (rice starch/iron oxide mixture, Bioefect 72000 and Mater-Bi AF05H) have been subjected to an outdoor soil burial test for 21 months. Changes on the morphology of the samples have been studied by differential scanning calorimetry. The degradation process also has been analyzed in terms of the mechanical behavior of the polymers. The three characteristic relaxation zones α, β, and γ (in order of decreasing temperature) of the dynamic-mechanical relaxation spectra of the samples have been characterized according to the Fuoss–Kirkwood equation. When two relaxations were overlapped, a deconvolution method was applied. It has been observed that the degradation process affects just to a small extent the amorphous phase of the polymers. That the β relaxation is the most sensitive to the exposure time suggests that degradation starts in the crystalline–amorphous interface. However, the crystalline phase is also affected significantly by the degradation process. The mechanical results are in good agreement with the calorimetric measurements, proving that degradation takes place in two stages with different time scales depending on the additive used. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1707–1720, 2000