Study of θϕ Networks via Zagreb Connection Indices

Graph theory can be used to optimize interconnection network systems. The compatibility of such networks mainly depends on their topology. Topological indices may characterize the topology of such networks. In this work, we studied a symmetric network θϕ formed by ϕ time repetition of the process of joining θ copies of a selected graph Ω in such a way that corresponding vertices of Ω in all the copies are joined with each other by a new edge. The symmetry of θϕ is ensured by the involvement of complete graph Kθ in the construction process. The free hand to choose an initial graph Ω and formation of chemical graphs using θϕΩ enhance its importance as a family of graphs which covers all the pre-defined graphs, along with space for new graphs, possibly formed in this way. We used Zagreb connection indices for the characterization of θϕΩ. These indices have gained worth in the field of chemical graph theory in very small duration due to their predictive power for enthalpy, entropy, and acentric factor. These computations are mathematically novel and assist in topological characterization of θϕΩ to enable its emerging use.

Sharp Bounds of First Zagreb Coindex for F -Sum Graphs

Let G = V E , E G be a connected graph with vertex set V G and edge set E G . For a graph G, the graphs S(G), R(G), Q(G), and T(G) are obtained by applying the four subdivisions related operations S, R, Q, and T, respectively. Further, for two connected graphs G 1 and G 2 , G 1 + F G 2 are F -sum graphs which are constructed with the help of Cartesian product of F G 1 and G 2 , where F ∈ S , R , Q , T . In this paper, we compute the lower and upper bounds for the first Zagreb coindex of these F -sum (S-sum, R-sum, Q-sum, and T-sum) graphs in the form of the first Zagreb indices and coincides of their basic graphs. At the end, we use linear regression modeling to find the best correlation among the obtained results for the thirteen physicochemical properties of the molecular structures such as boiling point, density, heat capacity at constant pressure, entropy, heat capacity at constant time, enthalpy of vaporization, acentric factor, standard enthalpy of vaporization, enthalpy of formation, octanol-water partition coefficient, standard enthalpy of formation, total surface area, and molar volume.

Some Bounds on Bond Incident Degree Indices with Some Parameters

It is considered that there is a fascinating issue in theoretical chemistry to predict the physicochemical and structural properties of the chemical compounds in the molecular graphs. These properties of chemical compounds (boiling points, melting points, molar refraction, acentric factor, octanol-water partition coefficient, and motor octane number) are modeled by topological indices which are more applicable and well-used graph-theoretic tools for the studies of quantitative structure-property relationships (QSPRs) and quantitative structure-activity relationships (QSARs) in the subject of cheminformatics. The π -electron energy of a molecular graph was calculated by adding squares of degrees (valencies) of its vertices (nodes). This computational result, afterwards, was named the first Zagreb index, and in the field of molecular graph theory, it turned out to be a well-swotted topological index. In 2011, Vukicevic introduced the variable sum exdeg index which is famous for predicting the octanol-water partition coefficient of certain chemical compounds such as octane isomers, polyaromatic hydrocarbons (PAH), polychlorobiphenyls (PCB), and phenethylamines (Phenet). In this paper, we characterized the conjugated trees and conjugated unicyclic graphs for variable sum exdeg index in different intervals of real numbers. We also investigated the maximum value of SEIa for bicyclic graphs depending on a > 1 .

Generalized Pitzer Correlation for Density Calculations of Ionic Liquids

The density of ionic liquids is an important design parameter for its utilization as a chemical process solvent. In this study, a generalized Pitzer-type correlation for calculating the density of ionic liquids with the use of reduced temperature (TR), reduced pressure (PR), and acentric factor (ω) as parameters is proposed. Experimental density data were obtained from several references through the IUPAC Ionic Liquids Database. Expansion of the terms as well as integrating the ionic liquid molecular weight was attempted to determine the accuracy improvement of the model in predicting densities at 0.1 MPa. Then, the obtained model was modified by further truncation to include the pressure effects for densities at higher pressures. MATLAB software was used to determine the optimal virial coefficients for the proposed correlations. The percent average absolute deviation (%AAD) was applied to calculate the variation between the experimental and calculated density values. It was concluded that the eight (8) coefficient correlation equation with molecular weight for densities at 0.1 MPa had a %AAD of 4.7537%. Upon modifying the correlation to include pressure effects, the resulting modified equation had an overall %AAD of 4.7174%.

Supercritical Pseudo Boiling in Cubic Equations of State

Today, modern combustion systems and advanced cycles often reach operating pressures exceeding the working fluid’s or fuel’s critical pressure. While the liquid-gas coexistence line is the dominant feature in the fluid state space at low pressures, a supercritical analog to boiling, pseudo boiling, exists at supercritical pressures. Pseudo boiling is the transcritical state transition between supercritical liquid states and supercritical gaseous states, associated with peaks in heat capacity and thermal expansion. This transition occurs across a finite temperature interval. So far, the relation between the pseudo boiling line of tabulated hi-fi p-v-T data and the behavior of efficient engineering cubic equations of state (EOS) is unclear. In the present paper, we calculate the slope of the pseudo boiling line analytically from cubic equations of state. The Redlich-Kwong EOS leads to a constant value for all species, Peng-Robinson and Soave-Redlich-Kwong EOS yield a cubic dependency of the slope on the acentric factor. For more than twenty compounds with acentric factors ranging from −0.38 to 0.57 calculated slopes are compared with NIST data and vapor pressure correlations. Particularly the Peng-Robinson EOS matches reference data very well. Classical empirical values of Guggenheim or Plank & Riedel are obtained analytically. Then, pseudo boiling predictions of the Peng Robinson EOS are compared to NIST data. Deviations in transition temperature interval, and nondimensional parameters of the distributed latent heat are compared. Especially the different caloric behavior of tabulated fluid data for H2, N2, CO2, and H2O cannot be reproduced by the Peng Robinson EOS. These results may open the way towards new EOS with specific emphasis on Widom line and supercritical transition behavior.

Non-Equilibrium Molecular Dynamics Study of the Influence of Branching on the Soret Coefficient of Binary Mixtures of Heptane Isomers

Equimolar mixtures composed of isomers were firstly used to investigate the molecular branching effect on thermal diffusion behavior, which was not disturbed by factors of molecular mass and composition in this work. Eight heptane isomers, including n-heptane, 2-methylhexane, 3-methylhexane, 2,2-dimethylpentane, 2,3-dimethylpentane, 2,4-dimethylpentane, 3,3-dimethylpentane and 3-ethylpentane, were chosen as the researched mixtures. A non-equilibrium molecular dynamics (NEMD) simulation with enhanced heat exchange (eHEX) algorithm was applied to calculate the Soret coefficient at T = 303.15 T=303.15 K and P = 1.0 atm P=1.0\hspace{0.1667em}\text{atm} . An empirical correlation based on an acentric factor was proposed and its calculation coincides with the simulated results, which showed the validity of the NEMD simulation. It is demonstrated that the isomer with higher acentric factor has a stronger thermophilic property and tends to migrate to the hot region in the heptane isomer mixture, and the extent of thermal diffusion is proportional to the difference between the acentric factors of the isomers.

Surface Tension of Liquid Organic Acids: An Artificial Neural Network Model

An artificial neural network model is proposed for the surface tension of liquid organic fatty acids covering a wide temperature range. A set of 2051 data collected for 98 acids (including carboxylic, aliphatic, and polyfunctional) was considered for the training, testing, and prediction of the resulting network model. Different architectures were explored, with the final choice giving the best results, in which the input layer has the reduced temperature (temperature divided by the critical point temperature), boiling temperature, and acentric factor as an independent variable, a 41-neuron hidden layer, and an output layer consisting of one neuron. The overall absolute percentage deviation is 1.33%, and the maximum percentage deviation is 14.53%. These results constitute a major improvement over the accuracy obtained using corresponding-states correlations from the literature.

Analysis of various approaches to accurately prediction of phase equilibrium of binary helium systems based on the Peng-Robinson equation of state

The paper presents a detailed algorithm for calculating the vapor-liquid phase equilibrium for multicomponent systems based on the Peng-Robinson equation of state. Various approaches are considered that make it possible to improve the quality of predicting phase equilibrium by the example of eight binary helium systems containing nitrogen, argon, carbon dioxide, methane, ethane, propane, isobutane, and n-butane. The influence of the acentric factor and the binary interaction parameter on the accuracy of the helium systems phase behavior predicting is analyzed. The optimal interaction coefficients for the presented systems are found under the assumption that this parameter does not depend on temperature. The temperature range of applicability of various approaches is determined, which makes it possible to maximize the description of the phase behavior of helium systems.