Corresponding State Research Articles

The Weil correspondence and universal special geometry

The Weil correspondence states that the datum of a Seiberg-Witten differential is equivalent to an algebraic group extension of the integrable system associated to the Seiberg-Witten geometry. Remarkably this group extension represents quantum consistent couplings for the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 QFT if and only if the extension is anti-affine in the algebro-geometric sense. The universal special geometry is the algebraic integrable system whose Lagrangian fibers are the anti-affine extension groups; it is defined over a base B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{B} $$\\end{document} parametrized by the Coulomb coordinates and the couplings. On the total space of the universal geometry there is a canonical (holomorphic) Euler differential. The ordinary Seiberg-Witten geometries at fixed couplings are symplectic quotients of the universal one, and the Seiberg-Witten differential arises as the reduction of the Euler one in accordance with the Weil correspondence. This universal viewpoint allows to study geometrically the flavor symmetry of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFT in terms of the Mordell-Weil lattice (with Néron-Tate height) of the Albanese variety AL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {A}_{\\mathbbm{L}} $$\\end{document} of the universal geometry seen as a quasi-Abelian variety YL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Y}_{\\mathbbm{L}} $$\\end{document} defined over the function field L≡ℂB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathbbm{L}\\equiv \\mathbb{C}\\left(\\mathcal{B}\\right) $$\\end{document}.

A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)

The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one ignores normalizations, of positive operators. On the CFT side of the correspondence, any two positive operators A, B will satisfy the trace inequality Tr(AB) ≤ Tr(A)Tr(B). This relation holds on any Hilbert space H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document} and is deeply associated with the fact that the algebra B(H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}) of bounded operators on H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document} is a type I von Neumann factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate below. In particular, we argue that the Euclidean gravitational path integral respects this inequality at all orders in the semi-classical expansion and with arbitrary higher-derivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for Jackiw-Teitelboim gravity and we also motivate it for more general theories.

An improved corresponding states principle model for orthohydrogen thermal conductivity from the triple point to 300 K and 20 MPa

There is a notable scarcity of reference data on the thermal conductivity of orthohydrogen in both vapor and liquid phases within the open literature, compared to parahydrogen and normal hydrogen. An improved corresponding states principle (CSP) model is proposed to predict the thermal conductivity of orthohydrogen by employing an optimized shape factor, which is expressed as a correlation with respect to pressure and temperature from the triple point to 300 K and at pressures up to 20 MPa. Critical parameters, ideal state thermal properties, and eccentricity factor are involved in the calculation as input parameters. The feasibility and accuracy of the proposed CSP model is verified by using experimental data of parahydrogen and some theoretical data of orthohydrogen. The estimated uncertainty of the model against high-precision experimental data of parahydrogen is within ±2.82 %. When the model is applied to dilute gas orthohydrogen, the predictions exhibit a deviation of less than ±5 % compared to other methods found in the literature. In addition, a correlation for thermal conductivity of parahydrogen, presented as a single function of temperature, is also proposed along the vapor-liquid equilibrium at temperatures from the triple point to the critical point, with an uncertainty of ±3 %.

The evaluation of density and diffusion properties in hydrogen/oxygen mixture modelled by Lennard-Jones fluid

This paper examines the satisfaction of the principle of corresponding states (PCS) on thepressure–density–temperature relation and the binary diffusion coefficient of hydrogen/oxygen mixture modelled as binary Lennard–Jones (LJ) fluid especially in a supercritical region. The hydrogen/oxygen mixture properties were computed by molecular dynamics simulation and compared with simulation results for a nitrogen/oxygen mixture as well as while using the Peng–Robinson (PR) equation of state (EOS) for both mixture types and a mono-component LJ-EOS. The Fuller–Schettler–Giddings model with the PR-EOS and Takahashi’s EOS were used for binary diffusion coefficient comparison. The pseudocritical point concept of a fluid mixture was applied for PCS reduction and PCS satisfaction was conducted over a wide temperature range above the pseudocritical pressure with changing hydrogen molar fraction. PCS satisfaction for hydrogen/oxygen mixture properties was confirmed at reduced temperature of 1.5 or above. At reduced temperature of 1.0 or below, the hydrogen/oxygen mixture properties disagree with those of the comparison mixture because phase separation occurs. We conclude that the properties of hydrogen/oxygen mixtures can be estimated using the pseudocritical point concept and the investigated EOSs based on the PCS in the supercritical region at reduced temperature of1.5 or above.

Topological phenomena in honeycomb Floquet metamaterials

Being driven by the goal of finding edge modes and of explaining the occurrence of edge modes in the case of time-modulated metamaterials in the high-contrast and subwavelength regime, we analyse the topological properties of Floquet normal forms of periodically parameterized time-periodic linear ordinary differential equations ddtX=Aα(t)Xα∈Td\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ \\frac{d}{dt}X = A_\\alpha (t)X\\right\\} _{\\alpha \\in {\\mathbb {T}}^d}$$\\end{document}. In fact, our main goal being the question whether an analogous principle as the bulk-boundary correspondence of solid-state physics is possible in the case of Floquet metamaterials, i.e., subwavelength high-contrast time-modulated metamaterials. This paper is a first step in that direction. Since the bulk-boundary correspondence states that topological properties of the bulk materials characterize the occurrence of edge modes, we dedicate this paper to the topological analysis of subwavelength solutions in Floquet metamaterials. This work should thus be considered as a basis for further investigation on whether topological properties of the bulk materials are linked to the occurrence of edge modes. The subwavelength solutions being described by a periodically parameterized time-periodic linear ordinary differential equation ddtX=Aα(t)Xα∈Td\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ \\frac{d}{dt}X = A_\\alpha (t)X\\right\\} _{\\alpha \\in {\\mathbb {T}}^d}$$\\end{document}, we put ourselves in the general setting of periodically parameterized time-periodic linear ordinary differential equations and introduce a way to (topologically) classify a Floquet normal form F, P of the associated fundamental solution Xα(t)=P(α,t)exp(tFα)α∈Td\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ X_\\alpha (t) = P(\\alpha ,t)\\exp (tF_\\alpha )\\right\\} _{\\alpha \\in {\\mathbb {T}}^d}$$\\end{document}. This is achieved by analysing the topological properties of the eigenvalues and eigenvectors of the monodromy matrix Xα(T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_\\alpha (T)$$\\end{document} and the Lyapunov transformation P(α,t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P(\\alpha ,t)$$\\end{document}. The corresponding topological invariants can then be applied to the setting of Floquet metamaterials. In this paper these general results are considered in the case of a hexagonal structure. We provide two interesting examples of topologically non-trivial time-modulated hexagonal structures.

Criticality points on the phase diagram of substances as scaling parameters in the law of corresponding states: alkali metals

The law of corresponding states (LCS), based on a generalized van der Waals equation of state (gvdWEoS) has been formulated by rescaling its thermodynamic variables with liquid- vapour critical—point parameters, the spinodal, the thermodynamic limit of superheat (TLS) and the supercritical (SC) point. This gvdWEoS differs from the known van der Waals equation of state (vdWEoS) by the modified attractive term. The scaling properties have been derived on the basis of the gvdWEoS. The expressions for the isothermal compressibility, a derivate of Gibbs free energy, have been derived. In all the cases of rescaling, the gvdWEoS has the similar functional form and the expression for isothermal compressibility has a similar functional form. This shows that the parameters of any spinodal-point on the phase diagram, including the TLS as a particular case, and the SC point, characteristic point on the quasispinodal, provide the alternate scales of parameterizing the thermodynamic properties of substances other than the liquid-vapour critical point. Moreover, an isothermal compressibility regularity is formulated on the basis of the gvdWEoS and it is found to satisfactorily trace the literature data for saturated liquid alkali metals.

PENGEMBANGAN APLIKASI NASKAH DINAS ELEKTRONIK PADA BAG TIK KORLANTAS POLRI

This study aims to create a system that can recap the state of correspondence in the form of a desktop-based application that can manage correspondence management quickly, accurately, relevantly, and effectively. This correspondence management administration system is designed using the SDLC (Software Development Life Cycle) method, as a software development method and built using Netbeans IDE 8.2 software which uses the Java programming language and MySQL as its database. This research produces an administrative system that can help the admin personnel of the ICT Korlantas Polri in managing mail data in a fast and efficient time. And with this application, it is hoped that it will help work activities that require accurate information and be able to minimize human errors that often occur in the data collection process for correspondence management when using a manual system.

Hard-core attractive Yukawa fluid global isomorphism with the lattice gas model.

In this work, we study the global isomorphism between the liquid-vapor equilibrium of the hardcore attractive Yukawa fluid (HCAYF) and that of the Lattice Gas (LG) model of the Ising-like type. The applicability of the global isomorphism transformation and the dependence of its parameters on the screening length of the Yukawa potential are discussed. These parameters determine both the slope of the rectilinear diameter of the liquid-vapor binodal and the Zeno-element, which are the core ingredients of the fluid-LG isomorphism. We compare the Zeno-element parameters with the virial Zeno-line parameters, which are commonly used in the literature for the formulation of generalized law of the correspondent states. It is demonstrated that the Zeno-element parameters appear to be sensitive to the liquid state instability when the interaction potential becomes too short-ranged, while the virial ones do not show any peculiarities connected with this specific of the HCAYF.

Corresponding-state principle model for the correlation of temperature dependent difference of coexisted densities of refrigerants at equilibrium

A simple and new correlation model based on the corresponding state principle is proposed for the difference of coexisted densities (DCD) of the saturated refrigerants fluids. It requires three physical properties as inputs. They are the critical temperature Tc, the minimal temperature Tmin at which data of the DCD is available in the NIST database, and the corresponding DCD value at Tmin. This proposed correlation has a simple analytical expression and includes only one adjustable parameter. It can accurately reproduce the DCD data in the NIST database in the temperature range from the triple point to the critical point with AAD values less than 1.92% for 47 out of 48 refrigerants considered. Large deviations only stand in a tiny temperature range very close to the critical point.

Corresponding-states model for the correlation and prediction of the surface tension of hydrocarbons

In this paper, a new corresponding state principle (CSP)-based model is proposed to calculate the surface tension of hydrocarbons based on the National Institute of Standards and Technology (NIST) database. This model requires the critical point temperature, the lowest temperature available for surface tension data and the corresponding maximum surface tension value as inputs. It includes two adjustable coefficients which are fitted by using NIST data of three hydrocarbons. To test the applicability of this model, we applied it to predict the surface tension values of other 16 hydrocarbons. For all the 19 hydrocarbons available in NIST database, the average absolute deviations of 16 hydrocarbons are less than 5%. We also compared this new proposed model with other three existing corresponding state models, and found that this model is the best in predicting the surface tension data of hydrocarbons.

Subcritical and supercritical thermodynamic geometry of Mie fluids

The Thermodynamic Geometry (TG) of Mie fluids in the subcritical and supercritical region is studied using a third order thermodynamic perturbation theory equation of state (EOS). The R-crossing method of TG is applied to reproduce the coexistence curves related to Mie fluids and it is found that the validity of this methodology is range dependent. Besides, defining the R-Widom line, as the curve obtained from the extreme of the isotherms of the scalar curvature in the (P,T) plane, the behavior of this Widom line is analyzed varying the range and stiffness of Mie potentials and it is compared to the locus of the maxima of some response functions. A strong dependence of the R-Widom line is found with respect to stiffness and range potential for the Mie fluids. Besides, a kind of correspondence states principle it is found for the R-Widom line, and a Clausius–Clapeyron-type relation near the critical point in the supercritical region is fulfilled.

Permutohedra for knots and quivers

The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this correspondence is not a bijection: more than one quiver may be assigned to a given knot and encode the same information. In this work we study this phenomenon systematically and show that it is generic rather than exceptional. First, we find conditions that characterize equivalent quivers. Then we show that equivalent quivers arise in families that have the structure of permutohedra, and the set of all equivalent quivers for a given knot is parametrized by vertices of a graph made of several permutohedra glued together. These graphs can be also interpreted as webs of dual three-dimensional $\mathcal{N}=2$ theories. All these results are intimately related to properties of homological diagrams for knots, as well as to multicover skein relations that arise in the counting of holomorphic curves with boundaries on Lagrangian branes in Calabi-Yau three-folds.

A new prediction equation of compressed liquid isochoric heat capacity for pure fluids and mixtures

In this paper, a new prediction equation for compressed liquid isochoric heat capacity (cv) was developed based on the corresponding states principle (CSP). By knowing acentric factor (ω), critical parameters (Tc, pc and vc) and ideal gas isochoric heat capacity (cv,0), the new equation could predict cv for pure fluids and mixtures (including polar and nonpolar fluids) at 0.25 < Tr < 1 and 0.5 < pr < 10. The overall average absolute relative deviation (AARD) of the new equation for 25 pure fluids and 10 mixtures are 2.21% and 1.62%, respectively. A comparison was conducted between the new equation and other models (PR EoS, Helmholtz energy EoSs, generalized equation (GE) of Zhong et al. [1] and corresponding states equation (CSE) of Sheng et al. [2]). The new equation significantly improves the prediction performance for the heat capacity of important fluids, such as halogenated hydrocarbons, carbon dioxide, water and so on, compared with the existing models. Although the prediction performance of the new equation is slightly worse than that of the Helmholtz energy EoS, the new equation has a simpler form and more powerful prediction performance than the Helmholtz energy EoS for mixtures.

Vaporization enthalpy of silanes fluids: A new correlation based on the corresponding states principle

A new and simple correlation based on the corresponding-states principle is proposed for the relation of the vaporization enthalpy with the temperature for saturated silanes. The primary accepted data for 7 silanes obtained from the most recent version of the DIPPR database are used as reference to define the model. Then predictions are made for other 29 silanes and compared with DIPPR data. The proposed correlation reproduces these data with average absolute deviations (AAD) lower than 1% for 8 silanes, AAD<5% for 30 fluids and AAD<10% for 35. The predictive power of the model is also checked by considering vaporization enthalpy data available for other 9 silanes not included in DIPPR. In this case, the mean AAD is 2%. Comparison with other previously published corresponding-states correlations is made, the here proposed being simpler, accurate, and predictive.

Empirical correlations for second virial coefficients of associated and quantum fluids covering a wide temperature range

Characterizing interactions between two molecules, the second virial coefficient is of great value in calculating the effect of the real-fluid imperfection. The corresponding-state principle followed, the second-virial-coefficient correlation proposed in our previous work was extended to associated and quantum fluids. The effects of hydrogen bonds were carefully analyzed and the new associated polar terms gave physically reliable results for alcohols, amines, ammonia and water. Taking the reduced de Broglie wavelength as the characteristic parameter, a new corresponding-state treatment for quantum fluids was established. The new quantum term was applicable for all quantum fluids except for Neon and was in good agreement with the ab initio and experimental data when the reduced temperature is higher than 0.33. The second virial coefficients of Neon can be calculated by the simple spherical term formula. For the requirement of high-precision calculation, this paper also proposed the specific correlations of the second virial coefficients for He-3, He-4, Neon and water. Together with previous correlations for nonpolar and non-associated polar fluids, a second-virial-coefficient model for most common fluids in a wide temperature range was completed in this work.

Tracking spatial dynamics of functional connectivity during a task

Functional connectivity (FC) measured from functional magnetic resonance imaging (fMRI) provides a powerful tool to explore brain organization. Studies of the temporal dynamics of brain organization have shown a large temporal variability of the functional connectome, which may be associated with mental status transitions and/or adaptive process. Most dynamic studies, e.g. functional connectome and functional network connectivity (FNC), have focused on the macroscopic FC changes, i.e. the changes of temporal coherence across various brain network sources, nodes and/or regions of interest, where it is assumed within the network or node that the FC is static. In this paper, we develop a novel method to examine the spatial dynamics of FC, without the assumption of its intra-network stationarity. We applied our approach to fMRI data during an auditory oddball task (AOD) from twenty-two subjects, in an attempt to capture/validate the approach by evaluating whether spatial connectivity varies with task condition. The results showed that connectivity networks exhibit spatial variability over time, in addition to participating in conventional temporal dynamics, i.e. cross-network variability or dynamic functional network connectivity (dFNC). Furthermore, we studied the relationship of spatial dynamic in FC to cognitive processes, by performing a cluster analysis to evaluate an individual's functional correspondence towards the ‘target’ (oddball) detection from AOD task, and extracting cognitive task correspondence states as well as their dynamic FC spatial maps segregated by such states. We found a clear trend in different task-guided states, particularly, a prominent reduction of task stimulus synchrony state along with strong anticorrelation between default mode network (DMN) and cognitive attentional networks. We also observed an increasing occurrence of the task desynchrony state which showed an absence of DMN anticorrelation. The results highlight the impact of a well-studied cognitive task on the observed spatial dynamic structure. We also showed that the FC spatial dynamic pattern from our method largely corresponds to macroscopic dFNC patterns, but with more details and specifications over space, meanwhile the connectivity within the source itself provides novel information and varies over time. Overall, we demonstrate clear evidence of the presence of the (usually ignored) spatial dynamics of connectivity, its links to the task and implications of cognition/mental status.

Evaluation of material property estimating methods for n-alkanes, 1-alcohols, and methyl esters for droplet evaporation calculations

Modeling of heat and mass transfer in liquid fuel combustion requires several material properties in a wide temperature and pressure range. The unavailable data are commonly patched with various estimation methods. In this paper, group contribution methods (GCM) and law of corresponding states (LCS) were analyzed for estimating material properties of n-alkanes (up to C10H22 and C12H26), 1-alcohols (up to C10H22O), and methyl esters (up to C19H38O2 and C19H36O2). These were compared to reference data to evaluate their applicability. LCS suggested by Poling et al. provides proper estimation for the acentric factor. GCM of Joback accurately estimates normal boiling point, critical properties, and specific heat capacity of the vapor-phase, the latter was corrected for methanol, however, GCM of Constantinou is more accurate for critical pressure of methyl esters. GCM of Ruzicka is suitable for estimating liquid-phase specific heat capacity. This method was updated for methanol. GCM of Elbro gives a proper estimation for liquid-phase density, while LCS of Lucas estimates vapor-phase viscosity properly. LCS of Chung and the modified Eucken method for vapor-phase and GCM of Sastri for liquid-phase thermal conductivity are appropriate. Considering the gas-phase mutual diffusion coefficient, the method of Fuller provides the best estimation, while LCS methods of Riedel and Chen are suitable for the enthalpy of vaporization at the normal boiling point.

Empirical correlations for second virial coefficients of nonpolar and polar fluids covering a wide temperature range

Being of great value in calculating the effect of the vapor-phase nonideality, second virial coefficients can be accurately described by the corresponding-state principle. Based on the corresponding-state principle, the new generalized second-virial-coefficient correlations of simple, nonpolar and non-associated polar fluids were proposed in this work. Four mathematical criterions for second-virial-coefficient models were summarized on the basis of the temperature-dependent characteristics of molecular interactions and macroscopic properties. Covering a wide temperature range which had never been reached before, the new-form correlations met the four mathematical criterions strictly. Ab initio values, together with the carefully selected high-quality experimental data, were used to define the “perfect” simple fluid and fitted satisfactory with the present simple spherical and nonpolar terms. More experimental data of second virial coefficients for non-associated polar fluids were collected and the refitted polar term yielded more reliable and physically-reasonable results.

Prediction of Surface Tension of Heavy Oil Based on Principle of Corresponding States Combined with Detailed Composition and Molecular Structure Analysis

Prediction of Surface Tension of Heavy Oil Based on Principle of Corresponding States Combined with Detailed Composition and Molecular Structure Analysis

A new method for predicting the isobaric heat capacity of biodiesel-related esters based on the corresponding states principle

In this work, a new model based on the three-parameter corresponding states principle (CSP) is proposed for estimating the isobaric heat capacity of biodiesel-related esters in the liquid state. This model is an updated version of that proposed by Poling-Prausnitz-O’Connell (2001). The model's parameters were fitted to 95 experimental heat capacity data of 5 biodiesel-related esters covering a temperature range from 270 K to 393 K. Then, 344 experimental data points of 25 esters in a slightly wider temperature interval (250 K–393 K) were used to test the model. The absolute average relative deviation obtained for the correlation and prediction datasets were 0.78% and 0.83%, respectively. The method proposed in this work was critically compared to the eight most consolidated models available in the literature for the same property (5 based on the group contribution concept and 3 based on the CSP). For all comparisons, we used a rigorous procedure that considered the accuracy and the physical consistency of the estimated values. In view of all criteria, we recommend the use of our model in future applications.