A critical evaluation of Lennard–Jones and Stockmayer potential parameters and of some correlation methods

Mourits, F.M.; Rummens, F. H. A.

doi:10.1139/v77-418

Cited by 340 publications

(193 citation statements)

References 10 publications

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“…Mourits and Rummens [57] review intermolecular potentials based upon viscosity measurements, and discuss the fact that many combinations of the potential parameters, ε i and ζ i , can be used to calculate viscosities of acceptable precision (2% or less) for species i, even for a range of temperatures. Kim and Ross [58] had previously pointed out that at a given temperature, there is a curve in (ε , ζ) along which the viscosity is constant, and they determined the shape of the curve for some special cases of reduced temperature for which analytical approximations for the collision integral are available.…”

Section: Pure Speciesmentioning

confidence: 99%

Transport properties for combustion modeling

Brown

Bastien

Price

2011

Progress in Energy and Combustion Science

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This review examines current approximations and approaches that underlie the evaluation of transport properties for combustion modeling applications. Discussed in the review are: the intermolecular potential and its descriptive molecular parameters; various approaches to evaluating collision integrals; supporting data required for the evaluation of transport properties; commonly used computer programs for predicting transport properties; the quality of experimental measurements and their importance for validating or rejecting approximations to property estimation; the interpretation of corresponding states; combination rules that yield pair molecular potential parameters for unlike species from like species parameters; and mixture approximations. The insensitivity of transport properties to intermolecular forces is noted, especially the non-uniqueness of the supporting potential parameters. Viscosity experiments of pure substances and binary mixtures measured post 1970 are used to evaluate a number of approximations; the intermediate temperature range 1 < T* < 10, where T* is kT/ε, is emphasized since this is where rich data sets are available. When suitable potential parameters are used, errors in transport property predictions for pure substances and binary mixtures are less than 5 %, when they are calculated using the approaches of Kee et al.; Mason, Kestin, and Uribe; Paul and Warnatz; or Ern and Giovangigli. Recommendations stemming from the review include (1) revisiting the supporting data required by the various computational approaches, and updating the data sets with accurate potential parameters, dipole moments, and polarizabilities; (2) characterizing the range of parameter space over which the fit to experimental data is good, rather than the current practice of reporting only the parameter set that best fits the data; (3) looking for improved combining rules, since existing rules were found to under-predict the viscosity in most cases; (4) performing more transport property measurements for mixtures that include radical species, an important but neglected area; (5) using the TRANLIB approach for treating polar molecules and (6) performing more accurate measurements of the molecular parameters used to evaluate the molecular heat capacity, since it affects thermal conductivity, which is important in predicting flame development. (1) revisiting the supporting data required by the various computational approaches, and updating the data sets with accurate potential parameters, dipole moments, and polarizabilities; (2) characterizing the range of parameter space over which the fit to experimental data is good, rather than the current practice of reporting only the parameter set that best fits the data; (3) looking for improved combining rules, since existing rules were found to under-predict the viscosity in most cases; (4) performing more transport property measurements for mixtures that include radical species, an important but neglected area; (5) using the TRANLIB approach for treating polar...

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Section: Pure Speciesmentioning

confidence: 99%

Transport properties for combustion modeling

Brown

Bastien

Price

2011

Progress in Energy and Combustion Science

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“…Mourits and Rummens [4] review intermolecular potentials based upon viscosity measurements, and point out that many combinations of the potential parameters, ε i and σ i , can be used to calculate viscosities of acceptable precision (2% or less) for species i. The nonuniqueness or indeterminacy of the potential parameters has not been recognized in many disciplines like the combustion and chemical physics communities that use transport properties in various applications.…”

Section: -Non Uniqueness Of the Potential Parametersmentioning

confidence: 99%

“…Fitted potential parameters, potential parameters obtained from different combining rules, and the slope of the line representing the trough for twelve different binary mixture systems. [37] CF 4 [3] SF 6 [3] Binary Mixtures [3] Table IV and experimental values. …”

Section: -Conclusionmentioning

confidence: 99%

“…Mourits and Rummens [4] review intermolecular potentials based upon viscosity measurements, discuss the problem of indeterminacy inherent to the calculations, but do not characterize the nature of the indeterminacy. Indeterminacy in this context implies that many combinations of the potential parameters, ε i and σ i , can be used to calculate viscosities of acceptable precision (2% or less) for species i.…”

Section: -Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Intermolecular potential parameters and combining rules determined from viscosity data

Bastien

Price

Brown

2010

Int J of Chemical Kinetics

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The Law of Corresponding States has been demonstrated for a number of pure substances and binary mixtures, and provides evidence that the transport properties viscosity and diffusion can be determined from a molecular shape function, often taken to be a Lennard-Jones 12-6 potential, that requires two scaling parameters: a well depth ε ij and a collision diameter σ ij , both of which depend on the interacting species i and j. We obtain estimates for ε ij and σ ij of interacting species by finding the values that provide the best fit to viscosity data for binary mixtures, and compare these to calculated parameters using several "combining rules" that have been suggested for determining parameter values for binary collisions from parameter values that describe collisions of like molecules. Different combining rules give different values for σ ij and ε ij and for some mixtures the differences between these values and the best-fit parameter values are rather large.There is a curve in (ε ij, σ ij ) space such that parameter values on the curve generate a calculated viscosity in good agreement with measurements for a pure gas or a binary mixture. The various combining rules produce couples of parameters ε ij , σ ij that lie close to the curve and therefore generate predicted mixture viscosities in satisfactory agreement with experiment. Although the combining rules were found to underpredict the viscosity in most of the cases, Kong's rule was found to work better than the others, but none of the combining rules consistently yields parameter values near the best-fit values, suggesting that improved rules could be developed.Keywords: viscosity, transport properties, combining rules, intermolecular potential parameters 3 I -IntroductionMany important phenomena that occur in gas mixtures depend on molecular transport processes including viscosity, diffusion, and thermal conductivity. Transport properties are often critically important in engineering applications and for understanding phenomena like combustion processes, hypersonic flows, and chemical vapor deposition. A recent trend in engineering design is to use modeling to reduce design times, and combustion is an area benefitting from this approach. Modeling combustion processes requires accurate values of transport properties over a wide range of temperatures and pressures. It is not possible to measure all the requisite transport properties, so we must have models to calculate them. This requires adequate information about the intermolecular potential and the underlying dynamics. The shape function, φ, is frequently taken to be a Lennard-Jones 12-6 potential, where the energy scaling parameter ε ij is the well depth, and σ ij is the length scaling parameter that defines the intermolecular separation at which the potential is zero. Viscosity measurements of a single chemical species allow direct estimation of the parameters that describe the interaction between two molecules of the same species, ε ii and σ ii . The situation is more complicated for even the si...

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“…61 The bath gas was N 2 at 298 K, with Lennard-Jones parameters of σ ) 3.74 Å and ) 82 K. 62,63 Following the same procedures [64][65][66][67] used in our study of isoprene ozonolysis, 68 we estimated Lennard-Jones parameters of σ ) 4.31 Å and ) 297 K for the •C 2 H 5 O 3 minima and transition structures.…”

Section: Iib Rrkm/master Equation Calculationsmentioning

confidence: 99%

Computational Studies of Intramolecular Hydrogen Atom Transfers in the β-Hydroxyethylperoxy and β-Hydroxyethoxy Radicals

et al. 2007

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The -hydroxyethylperoxy (I) and -hydroxyethoxy (III) radicals are prototypes of species that can undergo hydrogen atom transfer across their intramolecular hydrogen bonds. These reactions may play an important role in both the atmosphere and in combustion systems. We have used density functional theory and composite electronic structure methods to predict the energetics of these reactions, RRKM/master equation simulations to model the kinetics of chemically activated I, and variational transition state theory (TST) to predict thermal rate constants for the 1,5-hydrogen shift in I (Reaction 1) and the 1,4-hydrogen shift in III (Reaction 2). Our multi-coefficient Gaussian-3 calculations predict that Reaction 1 has a barrier of 23.59 kcal/mol, and that Reaction 2 has a barrier of 22.71 kcal/mol. These predictions agree rather well with the MPW1K and BB1K density functional theory predictions but disagree with predictions based on B3LYP energies or geometries. Our RRKM/master equation simulations suggest that almost 50% of I undergoes a prompt hydrogen shift reaction at pressures up to 10 Torr, but the extent to which I is chemically activated is uncertain. For Reaction 1 at 298 K, the variational TST rate constant is ∼30% lower than the conventional TST result, and the microcanonical optimized multidimensional tunneling (µOMT) method predicts that tunneling accelerates the reaction by a factor of 3. TST calculations on Reaction 2 reveal no variational effect and a 298 K µOMT transmission coefficient of 10 5 . The Eckart method overestimates transmission coefficients for both reactions.

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A critical evaluation of Lennard–Jones and Stockmayer potential parameters and of some correlation methods

Cited by 340 publications

References 10 publications

Transport properties for combustion modeling

Transport properties for combustion modeling

Intermolecular potential parameters and combining rules determined from viscosity data

Computational Studies of Intramolecular Hydrogen Atom Transfers in the β-Hydroxyethylperoxy and β-Hydroxyethoxy Radicals

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