scholarly journals Condensed-matter equation of states covering a wide region of pressure studied experimentally

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Elijah E. Gordon ◽  
Jürgen Köhler ◽  
Myung-Hwan Whangbo
Keyword(s):  
Strain Energy ◽  
Equations Of State ◽  
Interatomic Potential ◽  
Condensed Matter ◽  
Mathematical Functions ◽  
Wide Region ◽  
Equation Of States ◽  
Cubic Polynomial ◽  
Temperature And Pressure ◽  
Fitting Parameters

Abstract The relationships among the pressure P, volume V, and temperature T of solid-state materials are described by their equations of state (EOSs), which are often derived from the consideration of the finite-strain energy or the interatomic potential. These EOSs consist of typically three parameters to determine from experimental P-V-T data by fitting analyses. In the empirical approach to EOSs, one either refines such fitting parameters or improves the mathematical functions to better simulate the experimental data. Despite over seven decades of studies on EOSs, none has been found to be accurate for all types of solids over the whole temperature and pressure ranges studied experimentally. Here we show that the simple empirical EOS, P = α 1 (PV) + α 2 (PV) 2  + α 3 (PV) 3 , in which the pressure P is indirectly related to the volume V through a cubic polynomial of the energy term PV with three fitting parameters α 1 –α 3 , provides accurate descriptions for the P-vs-V data of condensed matter in a wide region of pressure studied experimentally even in the presence of phase transitions.

scholarly journals Erratum: Condensed-matter equation of states covering a wide region of pressure studied experimentally

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Elijah E. Gordon ◽  
Jürgen Köhler ◽  
Myung-Hwan Whangbo
Keyword(s):  
Condensed Matter ◽  
Wide Region ◽  
Equation Of States

A NEW SIMPLE CORRELATION FOR CALCULATING SOLUBILITY OF DRUGS IN SUPERCRITICAL CARBON DIOXIDE

2013 ◽  
Vol 12 (07) ◽  
pp. 1350062 ◽  
Author(s):  
ALI ZEINOLABEDINI HEZAVE ◽  
MOSTAFA LASHKARBOLOOKI
Keyword(s):  
Carbon Dioxide ◽  
Supercritical Carbon Dioxide ◽  
Equations Of State ◽  
Mixing Rules ◽  
Simple Correlation ◽  
The Past ◽  
Different Temperatures ◽  
Temperature And Pressure ◽  
Fitting Parameters ◽  
Supercritical Carbon

During the past 20 years, supercritical fluid (SCF) based technologies have been gaining an increasing attention through the academic and industrial communities due to its advantages. One of the most important parameter for any supercritical-based technologies is the knowledge of the solute solubility at different pressures and temperatures. But, due to several concerns e.g. time and expense, measuring the solubility of all compounds in wide ranges of temperature and pressure is not possible. Respect to this, a new empirical correlation with four fitting parameters has been proposed to correlate the solubility of pharmaceuticals in different temperatures and pressures. The obtained results compared with four widely used density based correlations including Mendez-Santiago and Teja (MST), Bartle et al., Chrastil, Kumar and Johnston (KJ) revealed rather good capability of the proposed simple correlation for predicting the solubility of solutes in supercritical carbon dioxide (SC- CO 2). At last, the obtained results compared with the results of three Equations of State (EoS's) with three different mixing rules.

Hydrolytic Aging in Rubber-Like Materials: A Micro-Mechanical Approach to Modeling

2019 ◽  
Author(s):  
Amir Bahrololoumi ◽  
Roozbeh Dargazany
Keyword(s):  
Strain Energy ◽  
Chain Scission ◽  
Good Choice ◽  
Mullins Effect ◽  
Cross Link ◽  
Original Matrix ◽  
Mechanical Responses ◽  
Permanent Set ◽  
Mechanical Approach ◽  
Fitting Parameters

Abstract The effect of hydrolytic aging on mechanical responses of Rubber likes materials, in particular, Mullins effect and the permanent set has been modeled. Hydrolytic aging is considered as the result of the competition between two phenomena (1) chain scission and (2) cross-link scission/reformation. Both phenomena were modeled and thus, the strain energy of the polymer matrix is written with respect to three independent mechanisms; i) the shrinking original matrix which has not been attacked by water, ii) conversion of the first network to a new network due to the reduction of the crosslinks, and iii) energy loss from network degradation due to water attacks to ester groups. The model is validated with respect to a set of experimental data. Besides accuracy, the simplicity and few numbers of fitting parameters make the model a good choice for further implementations.

Automating the Flexible Lofting Spline for Reusable Forming Devices

1998 ◽  
Vol 120 (4) ◽  
pp. 695-701
Author(s):  
K. R. Hardman ◽  
J. J. Cox
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Mechanical Systems ◽  
Elastic Strain Energy ◽  
Large Deflections ◽  
Test Device ◽  
Cubic Polynomial

A flexible lofting spline is presented as an actuated component in mechanical systems requiring the forming of continuous shapes. The spline is modeled with a piece-wise, cubic polynomial, based on minimum elastic strain energy, and nonlinear, large deflections. A flexible spline test device is explained and used to evaluate accuracy, limitations, and general issues. Conclusions and recommendations are provided.

scholarly journals Group additivity calculation of the standard molal thermodynamic properties of aqueous amino acids, polypeptides and unfolded proteins as a function of temperature, pressure and ionization state

2005 ◽  
Vol 2 (5) ◽  
pp. 1515-1615 ◽  
Author(s):  
J. M. Dick ◽  
D. E. LaRowe ◽  
H. C. Helgeson
Keyword(s):  
Amino Acids ◽  
Thermodynamic Properties ◽  
Equations Of State ◽  
Reference Model ◽  
Accurate Determination ◽  
Group Additivity ◽  
Unfolded Proteins ◽  
Ionization State ◽  
Degree Of Ionization ◽  
Temperature And Pressure

Abstract. Thermodynamic calculation of the chemical speciation of proteins and the limits of protein metastability affords a quantitative understanding of the biogeochemical constraints on the distribution of proteins within and among different organisms and chemical environments. These calculations depend on accurate determination of the ionization states and standard molal Gibbs free energies of proteins as a function of temperature and pressure, which are not generally available. Hence, to aid predictions of the standard molal thermodynamic properties of ionized proteins as a function of temperature and pressure, calculated values are given below of the standard molal thermodynamic properties at 25°C and 1 bar and the revised Helgeson-Kirkham-Flowers equations of state parameters of the structural groups comprising amino acids, polypeptides and unfolded proteins. Group additivity and correlation algorithms were used to calculate contributions by ionized and neutral sidechain and backbone groups to the standard molal Gibbs free energy (Δ G°), enthalpy (Δ H°), entropy (S°), isobaric heat capacity (C°P), volume (V°) and isothermal compressibility (κ°T) of multiple reference model compounds. Experimental values of C°P, V° and κ°T at high temperature were taken from the recent literature, which ensures an internally consistent revision of the thermodynamic properties and equations of state parameters of the sidechain and backbone groups of proteins, as well as organic groups. As a result, Δ G°, Δ H°, S° C°P, V° and κ°T of unfolded proteins in any ionization state can be calculated up to T~-300°C and P~-5000 bars. In addition, the ionization states of unfolded proteins as a function of not only pH, but also temperature and pressure can be calculated by taking account of the degree of ionization of the sidechain and backbone groups present in the sequence. Calculations of this kind represent a first step in the prediction of chemical affinities of many biogeochemical reactions, as well as of the relative stabilities of proteins as a function of temperature, pressure, composition and intra- and extracellular chemical potentials of O2 and H2, NH3, H2PO4 and CO2.

AN EQUATION OF STATE FOR GASES AT LOW DENSITIES

1932 ◽  
Vol 6 (6) ◽  
pp. 596-604 ◽  
Author(s):  
D. LeB. Cooper ◽  
O. Maass
Keyword(s):  
Carbon Dioxide ◽  
Equation Of State ◽  
Equations Of State ◽  
Absolute Temperature ◽  
Viscosity Function ◽  
Temperature And Pressure ◽  
New Equation ◽  
Molecular Radius ◽  
Expanded Form ◽  
Density Results

An equation of state for gases at low densities is developed, using a new function for the change in viscosity with temperature, also developed herein.The gas law equation takes the form[Formula: see text]or V(1 + KT)(PV − RT) = λT − a where a and b are constants corresponding to those of the Van der Waals' equation, and K is a constant derived from the proposed viscosity function which is, for carbon dioxide,[Formula: see text]where K is a constant and η is the viscosity at an absolute temperature T.In the case of carbon dioxide the equation was found to follow density results with an accuracy of from 0.01% to within experimental limits, and the viscosity function was found to agree with Sutherland's (10) results between −78.5 and 20 °C.Comparisons with several other equations of state are made. These show that the new equation is probably more accurate than any other.An expanded form of the new equation, namely:[Formula: see text]permits calculations of the slopes of isothermals for any temperature. Comparisons are made with experimental data.The expanded form of the equation may be solved for K, giving the expression:[Formula: see text]where [Formula: see text] and [Formula: see text] and ξ = Rb0, and since the equation enables the calculation of the molecular radius r, the viscosity may be calculated for any temperature and pressure over which the equation holds.

Modeling Approaches to Hydration Properties of Aqueous Nonelectrolytes at Elevated Temperatures and Pressures

2008 ◽  
Vol 73 (3) ◽  
pp. 322-343 ◽  
Author(s):  
Josef Sedlbauer
Keyword(s):  
Elevated Temperatures ◽  
Equations Of State ◽  
Environmental Chemistry ◽  
Hydrothermal Systems ◽  
Organic Solutes ◽  
Hydration Properties ◽  
New Developments ◽  
Elevated Pressures ◽  
Temperature And Pressure ◽  
Temperature Correlations

Thermodynamic models describing temperature and pressure evolution of Henry's law constant and related properties of hydration of aqueous nonelectrolyte solutes are reviewed. The included models cover a broad range spanning from simple van't Hoff-like equations used in environmental chemistry over the more elaborate empirical or semiempirical temperature correlations favored for engineering purposes to complete equations-of-state for hydration properties originating in the theory of near-critical phenomena and developed for modeling of hydrothermal systems. For aqueous organic solutes, the methods are often coupled with the group additivity approximation, leading to complex tools for predicting the properties of solutions containing organic species. The various models were subjected to tests documenting their expected range of applicability at elevated pressures (for acid gases) or at high temperatures (for hydrocarbons and oxygen-containing organic solutes). New developments in the field are discussed and some future needs are envisioned.

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