THEORETICAL STUDIES ON SOLVATION: PART II. NEW THEORY FOR EVALUATION OF IONIC SOLVATION NUMBER FOR DIVALENT IONS AT 25 °C

1960 ◽  
Vol 38 (6) ◽  
pp. 993-1002 ◽  
Author(s):  
A. M. Azzam
Keyword(s):  
Present Theory ◽  
Water Molecules ◽  
Solvation Number ◽  
Divalent Ions ◽  
Ionic Solvation ◽  
Solvation Numbers ◽  
Aquo Complex ◽  
Solvent Molecules ◽  
Definition Of ◽  
Good Agreement

The concepts of ionic solvation are discussed and the definition of four types are suggested. Utilizing Webb's theory, values of the dielectric constant of water in terms of distance from a divalent ion are evaluated. The statistical mechanics of the distribution of solvent molecules round a divalent ion in aqueous solution has been worked out.The present theory shows that all divalent ions with radius less than 1.6 Å can have a saturated envelope of eight water molecules in excess of the Goldschmidt co-ordination number have to be accounted for as inner primary solvation number. The concept of catonium is suggested for such a stable aquo-complex entity. The catonium entity is further hydrated electrostatically in the normal way by primary and secondary solvation types. The conditions governing all types of solvation and their possible termination boundaries are discussed and evaluated.The theoretically calculated values of the ionic solvation numbers are in good agreement with the experimental results.

STUDIES ON IONIC SOLVATION: PART III. NEW THEORY FOR CALCULATING HEATS OF HYDRATION OF MONOVALENT IONS AT 25 °C

1960 ◽  
Vol 38 (11) ◽  
pp. 2203-2216 ◽  
Author(s):  
A. M. Azzam
Keyword(s):  
Alkali Metals ◽  
Ionic Radius ◽  
Present Theory ◽  
Ionic Solvation ◽  
Positive Ions ◽  
Monovalent Ions ◽  
Ionic Size ◽  
Monovalent Ion ◽  
Experimental Values ◽  
Good Agreement

From Part I of this series, the structure of solution around a completely hydrated monovalent ion could be visualized. On the basis of this picture, the ionic heats of hydration is to be due to three terms. These three terms are critically discussed and evaluated for the case of alkali metals and halide ions.The present theory shows that the Born–Bjerrum term contributes a significant part to the heat and that the ionic radius value included in this term must be dependent only on the charge and not on the ionic size. The most probable value is 2.4 Å for the positive ions and 2.9 Å for the negative ions.The calculated ionic heats of hydration, which are in good agreement with the experimental values, are compared with those of previous theories.

scholarly journals Optimal Relabeling of Water Molecules and Single-Molecule Entropy Estimation

Biophysica ◽  
2021 ◽  
Vol 1 (3) ◽  
pp. 279-296
Author(s):  
Federico Fogolari ◽  
Gennaro Esposito
Keyword(s):  
Single Molecule ◽  
Degrees Of Freedom ◽  
Water Molecules ◽  
Maximum Information ◽  
Nearest Neighbours ◽  
Biomolecular Simulations ◽  
Solvent Molecules ◽  
Solvation Entropy ◽  
Dynamics Simulations ◽  
Internal Degrees Of Freedom

Estimation of solvent entropy from equilibrium molecular dynamics simulations is a long-standing problem in statistical mechanics. In recent years, methods that estimate entropy using k-th nearest neighbours (kNN) have been applied to internal degrees of freedom in biomolecular simulations, and for the rigorous computation of positional-orientational entropy of one and two molecules. The mutual information expansion (MIE) and the maximum information spanning tree (MIST) methods were proposed and used to deal with a large number of non-independent degrees of freedom, providing estimates or bounds on the global entropy, thus complementing the kNN method. The application of the combination of such methods to solvent molecules appears problematic because of the indistinguishability of molecules and of their symmetric parts. All indistiguishable molecules span the same global conformational volume, making application of MIE and MIST methods difficult. Here, we address the problem of indistinguishability by relabeling water molecules in such a way that each water molecule spans only a local region throughout the simulation. Then, we work out approximations and show how to compute the single-molecule entropy for the system of relabeled molecules. The results suggest that relabeling water molecules is promising for computation of solvation entropy.

Ionic solvation numbers from compressibilities and ionic vibration potentials measurements

1972 ◽  
Vol 76 (15) ◽  
pp. 2140-2151 ◽  
Author(s):  
J. O'M. Bockris ◽  
P. P. S. Saluja
Keyword(s):  
Ionic Solvation ◽  
Solvation Numbers

ALTERNATIVE COEFFICIENT OF CONCORDANCE IN CASE OF CONNECTED RANKS

2021 ◽  
pp. 40-45
Author(s):  
Ю.В. Лубенец
Keyword(s):  
Expert Opinion ◽  
Special Kind ◽  
Statistical Characteristics ◽  
Expert Survey ◽  
Complete Consistency ◽  
Expert Opinions ◽  
Coefficient Of Concordance ◽  
Definition Of ◽  
Two Stages ◽  
Good Agreement

Рассматривается оценка согласованности мнений экспертов при проведении экспертного опроса. Наиболее часто в качестве такой оценки применяется коэффициент конкордации Кендалла. Однако этот коэффициент не может в полной мере применяться для установления хорошей согласованности мнений экспертов, поскольку он показывает только отклонение от случаев полной несогласованности. Для устранения данного недостатка может рассматриваться альтернативный коэффициент конкордации, оценивающий близость сумм рангов альтернатив к случаю полной согласованности. Здесь дается определение этого коэффициента при наличии связанных рангов. Сложность определения заключается в том, что в этом случае наблюдается несколько случаев полной согласованности с различными суммами рангов. Определение альтернативного коэффициента конкордации при наличии связанных рангов проводится в два этапа. Сначала вводится его определение для упорядоченных таблиц специального вида и показывается его совпадение с коэффициентом конкордации Кендалла в этом случае. После дается определение альтернативного коэффициента конкордации в общем случае и показывается более простая формула его вычисления. Далее приводятся некоторые примеры сравнений значений рассматриваемых коэффициентов конкордации, их статистических характеристик и гистограмм The article considers evaluation of expert opinion consistency when conducting an expert survey. The most commonly used score is Kendall's coefficient of concordance. However, this coefficient cannot be fully applied to establish good agreement of expert opinions, as it only shows deviations from cases of complete inconsistency. To eliminate this drawback, an alternative concordance coefficient can be considered, which estimates the proximity of the sums of the ranks of the alternatives to the case of complete consistency. The article gives the definition of this coefficient in the presence of connected ranks. The difficulty of this definition lies in the fact that in this case there are several cases of complete consistency with different sums of ranks. Definition of the alternative coefficient of concordance in the presence of tied ranks is carried out in two stages. First, its definition for ordered tables of a special kind is introduced and its coincidence with Kendall's coefficient of concordance in this case is shown. After that, the definition of the alternative coefficient of concordance in the general case is given and a simpler formula for its calculation is shown. Below are some examples of comparisons of the values of the considered concordance coefficients, their statistical characteristics, and histograms

Neutral 4-phenyl-1-[phenyl(pyridin-2-yl)methylidene]semicarbazide and its salt forms with inorganic anions

2019 ◽  
Vol 75 (1) ◽  
pp. 1-7
Author(s):  
Vinicius Oliveira Araujo ◽  
Bárbara Tirloni ◽  
Lívia Streit ◽  
Vânia Denise Schwade
Keyword(s):  
Solid State ◽  
Spectroscopic Characterization ◽  
Water Molecules ◽  
Keto Form ◽  
Chloride Dihydrate ◽  
Ir And Nmr Spectroscopy ◽  
Tautomeric Forms ◽  
Counter Ions ◽  
Salt Forms ◽  
Good Agreement

Semicarbazones can exist in two tautomeric forms. In the solid state, they are found in the keto form. This work presents the synthesis, structures and spectroscopic characterization (IR and NMR spectroscopy) of four such compounds, namely the neutral molecule 4-phenyl-1-[phenyl(pyridin-2-yl)methylidene]semicarbazide, C19H16N4O, (I), abbreviated as HBzPyS, and three different hydrated salts, namely the chloride dihydrate, C19H17N4O+·Cl−·2H2O, (II), the nitrate dihydrate, C19H17N4O+·NO3 −·2H2O, (III), and the thiocyanate 2.5-hydrate, C19H17N4O+·SCN−·2.5H2O, (IV), of 2-[phenyl({[(phenylcarbamoyl)amino]imino})methyl]pyridinium, abbreviated as [H2BzPyS]+·X −·nH2O, with X = Cl− and n = 2 for (II), X = NO3 − and n = 2 for (III), and X = SCN− and n = 2.5 for (IV), showing the influence of the anionic form in the intermolecular interactions. Water molecules and counter-ions (chloride or nitrate) are involved in the formation of a two-dimensional arrangement by the establishment of hydrogen bonds with the N—H groups of the cation, stabilizing the E isomers in the solid state. The neutral HBzPyS molecule crystallized as the E isomer due to the existence of weak π–π interactions between pairs of molecules. The calculated IR spectrum of the hydrated [H2BzPyS]+ cation is in good agreement with the experimental results.

scholarly journals Asymptotic analysis for personalized Web search

2010 ◽  
Vol 42 (02) ◽  
pp. 577-604 ◽  
Author(s):  
Yana Volkovich ◽  
Nelly Litvak
Keyword(s):  
Web Search ◽  
Power Laws ◽  
User Preference ◽  
Importance Measure ◽  
Web Documents ◽  
Original Definition ◽  
Theoretical Predictions ◽  
Heavy Tailed ◽  
Definition Of ◽  
Good Agreement

PageRank with personalization is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equationwhere theRis are distributed asR. This equation is inspired by the original definition of the PageRank. In particular,Nmodels the number of incoming links to a page, andBstays for the user preference. Assuming thatNorBare heavy tailed, we employ the theory of regular variation to obtain the asymptotic behavior ofRunder quite general assumptions on the involved random variables. Our theoretical predictions show good agreement with experimental data.

scholarly journals A Cylindrical Wideband Conformal Fractal Antenna for GPS Application

2017 ◽  
Vol 6 (3) ◽  
pp. 64
Author(s):  
R. Sahoo ◽  
D. Vakula
Keyword(s):  
Conformal Geometry ◽  
Ground Plane ◽  
Antenna Design ◽  
Fractal Antenna ◽  
Frequency Range ◽  
Bandwidth Enhancement ◽  
Conformal Antenna ◽  
Operating Frequency Range ◽  
Definition Of ◽  
Good Agreement

In this paper, a novel wideband conformal fractal antenna is proposed for GPS application. The concepts of fractal and partial ground are used in conformal antenna design for miniaturization and bandwidth enhancement. It comprises of Minkowski fractal patch on a substrate of Rogers RT/duroid 5880 with permittivity 2.2 and thickness of 0.787mm with microstrip inset feed. The proposed conformal antenna has a patch dimension about 0.39λmm×0.39λmm, and partial ground plane size is 29mm×90mm.The proposed antenna is simulated, fabricated and measured for both planar and conformal geometry, with good agreement between measurements and simulations. The size of the fractal patch is reduced approximately by 32% as compared with conventional patch. It is observed that the conformal antenna exhibits a fractional bandwidth(for the definition of -10dB) of 43.72% operating from 1.09 to 1.7GHz, which is useful for L1(1.56-1.58GHz), L2(1.21-1.23GHz), L3(1.37-1.39GHz), L4(1.36-1.38GHz), and L5(1.16-1.18 GHz) in GPS and Galileo frequencies: E=1589.742MHz(4MHzbandwidth), E2=1561. 098MHz(4MHzbandwidth), E5a=1176.45MHz(=L5),E5b= 1207.14MHz, and E6=1278.75MHz(40MHz bandwidth). The radiation pattern exhibits an omnidirectional pattern, and gain of proposed antenna is 2.3dBi to 3.5dBi within operating frequency range.

scholarly journals Solvent influence on intramolecular interactions and aromaticity in meta and para nitroanilines

2020 ◽  
Vol 31 (5) ◽  
pp. 1717-1728
Author(s):  
Krzysztof K. Zborowski ◽  
Halina Szatyłowicz ◽  
Tadeusz M. Krygowski
Keyword(s):  
Cluster Model ◽  
Density Functional ◽  
Intramolecular Interactions ◽  
Water Molecules ◽  
Amino Groups ◽  
Functional Theory ◽  
Hydration Effect ◽  
Solvent Influence ◽  
Solvation Models ◽  
Solvent Molecules

Abstract Theoretical density functional theory (B3LYP/6-31G**) was used to study the intra- and intermolecular interactions of nitrobenzene, aniline, and meta and para nitroaniline in various solvation models. The studied molecules were solvated by one or two water molecules in the presence of continuum solvation (the PCM model) or without it. Finally, the studied molecules were surrounded by a cluster of water molecules. For comparison, calculations were also made for separated molecules. Geometries, energies, hydrogen bonding between solutes and solvent molecules, atomic charges, and aromaticity were examined. The analysis was based on the Atoms in Molecules methodology and the Harmonic Oscillator Model of Aromaticity (HOMA) index. As a result, an extensive description of the solvation of nitro and amino groups and the effect of solvation on mutual interactions between these groups in meta and para nitroanilines is provided. It was found that in general, the PCM description of the hydration effect on the electronic structure of the studied systems (substituents) is consistent with the approach taking into account all individual interactions (cluster model).

scholarly journals Molecular Dynamics Modellization and Simulation of Water Diffusion through Plant Cutin

1999 ◽  
Vol 54 (11) ◽  
pp. 896-902 ◽  
Author(s):  
Antonio Matas ◽  
Antonio Heredia
Keyword(s):  
Experimental Data ◽  
Molecular Dynamics ◽  
Structural Information ◽  
Md Simulations ◽  
Water Molecules ◽  
Plant Cuticle ◽  
X Ray Diffraction ◽  
Cross Link ◽  
X Ray ◽  
Good Agreement

Abstract A theoretical molecular modelling study has been conducted for cutin, the biopolyester that forms the main structural component of the plant cuticle. Molecular dynamics (MD) simulations, extended over several ten picoseconds, suggests that cutin is a moderately flexible netting with motional constraints mainly located at the cross-link sites of functional ester groups. This study also gives structural information essentially in accordance with previously reported experimental data, obtained from X -ray diffraction and nuclear magnetic resonance experiments. MD calculations were also performed to simulate the diffusion of water mole­cules through the cutin biopolymer. The theoretical analysis gives evidence that water perme­ation proceedes by a “hopping mechanism”. Coefficients for the diffusion of the water molecules in cutin were obtained from their mean-square displacements yielding values in good agreement with experimental data.

scholarly journals The Frequency of YY Orionis Objects among the T Tauri Stars

1977 ◽  
Vol 42 ◽  
pp. 80-87 ◽  
Author(s):  
I. Appenzeller
Keyword(s):  
Statistical Analysis ◽  
Present Theory ◽  
T Tauri Stars ◽  
Early Evolution ◽  
Low Mass Stars ◽  
T Tauri ◽  
Uv Excess ◽  
Low Mass ◽  
Good Agreement

A list of 24 T Tauri stars belonging to the YY Orionis subclass is presented. From a statistical analysis it is estimated that at least 75% (and possibly all) UV-excess T Tauri stars are YY Orionis stars. Since about 50% of all known T Tauri stars show a strong UV-excess, the percentage of YY Orionis stars among the T Tauri stars is estimated to be 40 - 50%. This relative high percentage is in good agreement with the present theory of the formation and early evolution of low mass stars.

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