TABLE 2-335 Thermophysical Properties of Selected Nonmetallic Solid Substances
Density, Specific heat, Thermal conductivity, Thermal diffusivity,
Material kg/m3 Emissivity kJ/(kg⋅K) W/(m⋅K) m2/s×106
Alumina 3975 0.765 36 11.9
Asphalt 2110 0.920 0.06 0.03
Bakelite 1300 1.465 1.4 0.74
Beryllia 3000 0.82 1.030 270 88
Brick 1925 0.93 0.835 0.72 0.45
Brick, fireclay 2640 0.93 0.960 1.0 0.39
Carbon, amorphous 1950 0.86 0.724 1.6 1.13
Clay 1460 0.91 0.880 1.3 1.01
Coal 1350 0.80 1.26 0.26 0.15
Cotton 80 1.30 0.06 0.58
Diamond 3500 0.509 2300 1290
Granite 2630 0.775 2.79 1.37
Hardboard 1000 1.38 0.15 0.11
Magnesite 3025 0.38 1.13 4.0 1.2
Magnesia 3635 0.72 0.943 48 14
Oak 770 0.90 2.38 0.18 0.10
Paper 930 0.83 1.34 0.011 0.01
Pine 525 0.84 2.75 0.12 0.54
Plaster board 800 0.91 0.17
Plywood 540 1.22 0.12 0.18
Pyrex 2250 0.92 0.835 1.4 0.74
Rubber 1150 0.92 2.00 0.2 0.09
Rubber, foam 70 0.90 0.03
Salt 0.34 0.854 7.1
Sandstone 2150 0.59 0.745 2.9 1.8
Silica 0.79 0.743 1.3
Sapphire 3975 0.48 0.765 46 15
Silicon carbide 3160 0.86 0.675 110 230
Soil 2050 0.38 1.84 0.52 0.14
Teflon 2200 0.92 0.35 0.26 0.34
Thoria 4160 0.28 0.71 14 4.7
Urethane foam 70 1.05 0.03 0.36
Vermiculite 120 0.84 0.06 0.60
NOTE: Difficulties of accurately characterizing many of the specimens mean that many of the values presented here must be regarded as being of order of magnitude only. For some materials, actual measurement may be the only way to obtain data of the required accuracy. To convert kilo- grams per cubic meter to pounds per cubic foot, multiply by 0.062428; to convert kilojoules per kilogram-kelvin to British thermal units per pound-degree Fahrenheit, multiply by 0.23885.
INTRODUCTION
Physical property values, sufficiently accurate for many engineering applications, can be estimated in the absence of reliable experimental data. The purpose of this subsection is to provide a set of recom- mended prediction methods for general engineering use; it is not a comprehensive review, and many alternative methods are available in the literature. Methods recommended were selected on the basis of accuracy, generality, and, in most cases, simplicity. They generally cor- respond to the methods tested and given priority in the DIPPR®801 database project.†
Properties included in this subsection are divided into 10 categories:
(1) physical constants: critical properties, normal melting and boiling points, acentric factor, radius of gyration, and dipole moment; (2) vapor
pressure: liquid and solid; (3) thermal properties: enthalpy and Gibbs’
energy of formation and ideal gas entropy; (4) latent enthalpy: vaporiza- tion, fusion, and sublimation; (5) heat capacity: ideal gas, gas, liquid, and solid; (6) density: gas, liquid, and solid; (7) viscosity: gas and liquid; (8) thermal conductivity: gas and liquid; (9) surface tension; and (10) flam- mability properties: flash point, flammability limits, and autoignition temperature. Each of the 10 subsections provides a definition of the rel- evant properties and a description of one or more recommended predic- tion methods. Each description lists the type of method, its uncertainty, its limitations, and the expected uncertainty of the predicted value. A numerical example is also given to illustrate use of the method. For brevity, symbols used for physical properties and for variables and con- stants in the equations are defined under Nomenclature and are not gen- erally defined after their use except where doing so clarifies usage. A list of equation and table numbers in which variables appear is included in the Nomenclature section for quick cross-referencing. Although empha- sis is on pure-component properties, some mixture estimation tech- niques have been included for physical constants, density, viscosity, thermal conductivity, surface tension, and flammability. Correlation and estimation of properties that are inherently multicomponent (e.g., diffu- sion coefficients, mixture excess properties, activity coefficients, etc.) are treated elsewhere in the Handbook.
PREDICTION AND CORRELATION OF PHYSICAL PROPERTIES*
*Some material in this subsection has been retained from the corresponding subsection in the Seventh Edition, which was coauthored by Thomas E.
Daubert and Evan Buck.
†The Design Institute for Physical Properties (DIPPR®) is an industrial con- sortium under the auspices of AIChE; Project 801, Evaluated Process Design Data, is a pure-component database of industrially important compounds.
UNITS
The International Metric System (SI) of units has been used through- out this subsection. Where possible, the estimation equations are set up in dimensionless groups. This makes transparent any conversion factors that should be applied to obtain the property in a desired set of units and eliminates the requirement of specific units for variables.
For example, rather than use Pcas a variable with defined units, the dimensionless group Pc/ Pa is used. When a value for Pcexpressed in
any units (say, Pc= 6.53 MPa) is inserted into this group, the result is dimensionless with an explicit indication of conversion factors that must be included:
= = =6.53106
Section 1 of this handbook should be used for appropriate unit con- version factors.
106Pa MPa 6.53 MPa Pa 6.53 MPa
Pa PC
Pa 2-464 PHYSICAL AND CHEMICAL DATA
Nomenclature
Physical constants Definition Value
h Planck’s constant 6.62610−34Js
k Boltzmann’s constant 1.380610−23J/(moleculeK)
NA Avogadro’s number 6.0221026molecule/kmol
R Gas constant 8.3143 Pam3/(kmolK)
Properties Definition Typical units
A, B, C Molecular principal moments of inertia kgm2
B, B(T) Second virial coefficient m3/kmol
Bm Second virial coefficient for a mixture m3/kmol
CP Constant-pressure molar heat capacity J/(kmolK)
Cop Ideal gas constant-pressure molar heat capacity J/(kmolK)
Cv Constant-volume molar heat capacity J/(kmolK)
Hi Enthalpy of compound i J/kmol
k Thermal conductivity W/(mK)
kb Thermal conductivity at Tb W/(mK)
LFL Lower flammability limit %
M Molecular weight kg/kmol
P Pressure Pa
P Parachor unitless
Pc Critical pressure Pa
Pr Reduced pressure; Pr=P/Pc unitless
P* Vapor pressure Pa
P*meas Measured vapor pressure value Pa
Pr* Reduced vapor pressure; Pr*=P*/Pc unitless
Pt* Vapor pressure at triple point Pa
Rg Radius of gyration m
So Ideal gas entropy J/(kmolK)
Ss Standard state entropy J/(kmolK)
Sr Rotational contribution to entropy J/(kmolK)
Svib Vibrational contribution to entropy J/(kmolK)
T Temperature K
Tb Normal boiling point temperature K
Tbr Reduced temperature at Tb;Tbr= Tb/Tc unitless
Tc Critical temperature K
Tm Melting temperature K
Tmeas Tat which a dependent property was measured K
Tr Reduced temperature; Tr=T/Tc unitless
Tt Triple point temperature K
UFL Upper flammability limit %
V Molar volume m3/kmol
Vm Mixture molar volume m3/kmol
Vr Reduced volume; Vr=ZTr/Pr unitless
wi Mass fraction of component i unitless
xi Mole fraction of component i unitless
yi Mole fraction of component iin vapor phase unitless
Z Compressibility factor; Z=PV/RT unitless
Zc Critical compressibility factor; Zc=PcVc/RTc unitless Zi Compressibility factor of reference fluid i unitless Gfo Ideal gas standard Gibbs energy of formation J/kmol Gfs Standard state Gibbs energy of formation J/kmol Hfo Ideal gas standard enthalpy of formation J/kmol
Hfs Standard state enthalpy of formation J/kmol
Hfus Enthalpy of fusion J/kmol
Hrxn Enthalpy change per mole of reaction as written J/kmol
Hsub Enthalpy of sublimation J/kmol
Hv Enthalpy of vaporization J/kmol
Sfs Standard state entropy of formation J/(kmolK)
Sfo Ideal gas entropy of formation J/(kmolK)
Sfus Latent entropy of fusion J/(kmolK)
Zv Change in compressibility factor upon vaporization unitless
Molar density; =V−1 kmol/m3
c Critical molar density; c=Vc−1 kmol/m3
PREDICTION AND CORRELATION OF PHYSICAL PROPERTIES 2-465
Nomenclature(Continued)
Properties Definition Typical units
r Reduced molar density; r=/c unitless
Acentric factor unitless
Viscosity Pas
o Viscosity at low pressure Pas
Surface tension mN/m
m Surface tension of mixture mN/m
Complementary reduced temperature (=1−Tr) unitless b Complementary reduced normal boiling
temperature (=1−Tbr) unitless
Dipole moment D
r Reduced dipole moment [defined in Eq. (2-62)] unitless
Eq. variables Definition (Equations), [Tables]
a EoS constant (2-66), [2-354]
a, b, c, . . . GC values for Cpand (2-51), (2-52), (2-53),
(2-97), [2-356]
a, b, c Correlation coefficients (2-21), (2-23)
ai GC values (2-43), (2-97), [2-346, 2-356]
a, b Terms in second virial correlation (2-61)
a, b Chickos correlation parameters (2-39), (2-40), (2-41)
ai, bi, di GC values for liquid Cp (2-51), [2-348]
a–– EoS constant for mixture (2-76)
A, B, C, . . . Correlation constants/parameters (2-2), (2-20), (2-22), (2-34), (2-36), (2-50), (2-65), (2-68), (2-83), (2-85), (2-87), (2-88), (2-95), (2-96), (2-101), above (2-114)
A Factor in liquid kcorrelation (2-108), [2-358]
Ai Constants in Copcorrelation (2-45), (2-46)
b EoS constant (2-66), [2-354]
bi, ci, . . . Reference EoS constants (2-65), [2-353]
bi GC value for AIT (2-124), [2-363, 2-364]
b–
EoS constant for mixture (2-75)
B(i) Second virial expansion terms (2-58), (2-59), (2-60), (2-61)
C Number of components in mixture (2-55), (2-72), (2-73),
(2-74), (2-75), (2-76), (2-77), (2-80), (2-81), (2-82), (2-98), (2-113), (2-119)
Ci GC values for Tbor (2-15), (2-87), [2-341, 2-355]
Ci,int Sum of intramolecular group-group interactions (2-16)
Cij Group-group intramolecular interaction pair (2-16), [2-342]
(Cop)i GC values for ideal gas heat capacity (2-49), [2-347]
Csj Chickos: GC value for C—H group (2-41), [2-344]
Ctj Chickos: GC value for functional group (2-41), [2-345]
fi Halogen correction for ∆Hsubcorrelation (2-43), [2-346]
f(i) Vapor pressure deviation function (2-25)
F Factor in surface tension equation (2-116), (2-117)
Gij Adjustable mixture viscosity parameter (2-98) gEc UNIFAC combinatorial excess Gibbs energy (2-99)
gEr UNIFAC residual excess Gibbs energy (2-99)
h Parameter in Riedel vapor pressure equation following (2-24) K Parameter in Riedel vapor pressure equation following (2-24)
LFLi GC contribution (2-122), [2-361, 2-362]
n Number of nonhydrogen atoms (2-15)
nA Number of atoms in molecule (2-1), (2-30), (2-31), (2-48)
nE Number of occurrnces of element Ein compound (2-54)
ni Number of occurrences of group i (2-27), (2-43), (2-49), (2-51), (2-53), (2-87), (2-109), (2-115), (2-122), (2-123), (2-124) nf Chickos: no. of different functional groups (2-41) ns Chickos: no. of different nonring or aromatic (2-41)
C—H groups bonded to functional groups
nx Total no. of halogen and H atoms attached (2-43) to C and Si atoms for Hsubcorrelation
N Total number of groups in molecule (2-12), (2-15) (2-16), (2-43), (2-49), (2-51), (2-53), (2-54), (2-87), (2-97), (2-109), (2-115)
NC Number of C atoms (2-121)
Nfi Chickos: no. of functional groups of type i (2-41) Ngi Chickos: no. of C—H groups of type ibonded (2-41)
to other C atoms
NH Number of H atoms (2-121)
2-466 PHYSICAL AND CHEMICAL DATA
Nomenclature(Continued)
Eq. variables Definition (Equations), [Tables]
NCR Chickos: no. of CH2groups in nonaromatic (2-40) ring to form cyclic paraffin of same ring size
NO Chickos: Number of O atoms (2-121)
NR Chickos: no. of nonaromatic rings (2-40)
NS Chickos: Number of S atoms (2-121)
Nsi Chickos: no. of C—H groups of type ibonded (2-41) to at least one functional group
NX Number of halogen atoms (2-121)
P–
c Pseudocritical pressure for mixture (2-73)
Pc,ij Cross term in mixing rule (2-79)
q Rackett equation power for Zc (2-69), (2-70), (2-81)
qi UNIFAC molecular surface area following (2-100)
Qk UNIFAC group surface area following (2-100)
ri UNIFAC molecular volume following (2-100)
r* Dimensionless separation distance (2-4)
Rk UNIFAC group volume following (2-100)
(So)i GC value for entropy (2-27), [2-343]
t Chickos: total no. of functional groups (2-41) tm1,i First-order GC contribution for Tm (2-13), [2-339]
tm2,i Second-order GC contribution for Tm (2-13), [2-340]
T–
c Pseudocritical temperature for mixture (2-72), (2-73), (2-80)
Tc,ij Cross term in mixing rule (2-78), (2-80)
xP Term in Pailhes method = log(1 atm/P) (2-14) U* Dimensionless intermolecular potential (2-4)
UFLi GC contribution (2-123), [2-361, 2-362]
Vc,ij Cross term in mixing rule (2-78), (2-79)
Z(0) Compressibility factor of simple fluid (2-63), (2-64), [2-351]
Z(1) Acentric deviation term for Z (2-63), (2-64), [2-352]
Zc,ij Cross term in mixing rule (2-78), (2-79)
ZRA Modified Rackett correlation parameter (2-70) Z⎯
RA Modified Rackett parameter for mixture (2-82)
,, , . . . Correlation parameters for k (2-106), (2-107), (2-108), (2-109), [2-358]
(Tr) EoS temperature-dependent function (2-66), [2-354]
c Parameter in Riedel vapor pressure equation following (2-24) mn Viscosity group-group interactions (2-100), [2-357]
Reference EoS constant (2-65), [2-353]
Stoichiometric coefficient in FP correlation (2-120), (2-121)
i Nonlinear correction term in correlation (2-43), (2-53), [2-346, 2-349]
Reference EoS constant (2-65), [2-353]
=0 for nonlinear molecules; =1 for linear (2-1), (2-48)
EoS parameter (2-66), [2-354]
E Contribution of element Eto heat capacity (2-54), [2-350]
P GC contribution to Pc (2-7), (2-10), [2-336, 2-337]
T GC contribution to Tc (2-6), (2-9), [2-336, 2-337]
V GC contribution to Vc (2-8), (2-11), [2-336, 2-337]
(Hfo)i GC value for enthalpy of formation (2-27), [2-343]
ki GC for thermal conductivity at Tb (2-109), [2-359]
Pi GC for parachor (2-115), [2-360]
si Chickos: GC value for group i (2-41), [2-344, 2-345]
Lennard-Jones well depth parameter following (2-4)
EoS parameter (2-66), [2-354]
UNIFAC molecular volume fraction following (2-100)
i Volume fraction of component i (2-80), following (2-100), (2-113) i Stoichiometric coefficient (+ for product (2-28), (2-29), (2-30)
and−for reactant) for compound iin reaction
j Frequency of vibrational mode j (2-47)
UNIFAC molecular surface fraction following (2-100)
UNIFAC group surface fraction following (2-100)
A,B,C Characteristic rotational Tof molecule before and following (2-31) j Characteristic vibrational Tof mode j (2-1), (2-31), (2-48)
Lennard-Jones size parameter (2-4)
Rotational external symmetry number following (2-31)
r* Modified reduced dipole moment (2-85), (2-86)
Parameter in Riedel vapor pressure equation following (2-24) Parameter in correlation of kfor gases (2-106)
mn UNIFAC interaction factor (2-100)
ξ Viscosity dedimensionalizing factor (2-89), (2-90), (2-91), (2-92), (2-93), (2-94)
– Pseudoacentric factor for mixture (2-74)
ij Cross term in mixing rule (2-79)
Acronyms and abbreviations Definition
CC Computational chemistry
CS Corresponding states
DIPPR® Design Institute for Physical Properties
EoS Equation of state
PREDICTION AND CORRELATION OF PHYSICAL PROPERTIES 2-467
Nomenclature(Concluded)
Acronyms and abbreviations Definition
GC Group contributions
LJ Lennard-Jones
MC Monte Carlo
MD Molecular dynamics
QSPR Quantitative structure-property relationships
TRC Thermodynamics Research Center
GENERALREFERENCES
(a) Prediction methods:
[PGL4] Reid, R. C., J. M. Prausnitz, and B. E. Poling,The Properties of Gases and Liquids,4th ed., McGraw-Hill, New York, 1987.
[PGL5] Poling, B. E., J. M. Prausnitz, and J. P. O’Connell,The Properties of Gases and Liquids,5th ed., McGraw-Hill, New York, 2001.
(b) Property databases:
[DIPPR] Rowley, R. L., et al.,DIPPR®Data Compilation of Pure Chemicals Properties,Design Institute for Physical Properties, AIChE, New York, 2007.
[TRC] TRC Thermodynamic Tables—Non-Hydrocarbons, Thermodynamics Research Center, The Texas A&M University System, College Station, Tex., extant 2004;TRC Thermodynamic Tables—Hydrocarbons, Thermodynamics Research Center, The Texas A&M University System, College Station, Tex., extant 2004.
[JANAF] Chase, M. W., Jr., et al., “JANAF Thermochemical Tables,” J. Phys.
Chem. Ref. Data,14, suppl. 1, 1985.
[SWS] Stull, D. R., F. F. Westrum, Jr., and G. C. Sinke, The Chemical Thermo- dynamics of Organic Compounds, John Wiley & Sons, New York, 1969.
CLASSIFICATION OF ESTIMATION METHODS
Physical property estimation methods may be classified into six gen- eral areas: (1) theory and empirical extension of theory, (2) corre- sponding states, (3) group contributions, (4) computational chemistry, (5) empirical and quantitative structure property relations (QSPR) correlations, and (6) molecular simulation. A quick overview of each class is given below to provide context for the methods and to define the general assumptions, accuracies, and limitations inherent in each.
Theory and Empirical Extension of Theory Methods based on theory generally provide better extrapolation capability than empirical fits of experimental data. Assumptions required to simplify the theory to a manageable equation suggest accuracy limitations and possible improvements, if necessary. For example, the ideal gas iso- baric heat capacity, rigorously obtained from statistical mechanics under the assumption of independent harmonic vibrational modes, is [Rowley, R. L., Statistical Mechanics for Thermophysical Property Calculations, Prentice-Hall, Englewood Cliffs, N.J., 1994]
+
j=1 3nA6δ
2
δ{ 0 1 nonlinear molecules linear molecules (2-1) whereΘjis the characteristic temperature for the jth vibrational fre- quency in a molecule of nAatoms. The temperature dependence of this equation is exact to the extent that the frequencies are harmonic.
Corrections for anharmonicity can be applied (albeit with difficulty) where warranted.
Extension of theory often requires introduction of empirical models and parameters in lieu of terms that cannot be rigorously calculated.
Good accuracy is expected in the region where the model parameters were fitted to experimental data, but only limited accuracy when an empirical model is extrapolated to other conditions. For example, a simplified theory suggests that vapor pressure should have the form
lnP*A (2-2)
where the empirical parameter B is given by
B ∆Hv (2-3)
R∆Zv
B T
eΘj T (eΘj T1)2 Θj
T 8δ
2 CoP
R
and ∆Hv and ∆Zv are differences between the vapor and liquid enthalpies and compressibility factors, respectively. Vapor pressures over a narrow temperature range can be effectively correlated using Eq. (2-2), but this equation should not be used to extrapolate vapor pressures over a wide range of temperatures.
Corresponding States (CS) The principle of CS applies to con- formal fluids [Leland, T. L., Jr., and P. S. Chappelear, Ind. Eng.
Chem.,60(1968): 15]. Two fluids are conformal if their intermolecu- lar interactions are equivalent when scaled in dimensionless form. For example, the Lennard-Jones (LJ) intermolecular pair potential energy Ucan be written in dimensionless form as
U*4[(r*12r*6)] (2-4)
wherer*rσ,U*Uε,σis the LJ size parameter, and εis the LJ attractive well depth parameter. At equivalent scaled temperatures kTε(k is Boltzmann’s constant) and pressures Pσ3ε, all LJ fluids will have identical dimensionless properties because the molecules inter- act through the identical scaled intermolecular potential given by Eq.
(2-4). Generalization of this scaling principle is commonly done using critical temperature Tcand critical pressure Pcas scaling factors. At the same reduced coordinates (Tr=T/TcandPr=P/Pc) all conformal fluids will have the same dimensionless properties; for example, Z= Z(Tr,Pr) where the compressibility factor is defined as Z=PV/RT. A correlation of experimental data for one fluid can be used as the ref- erence for the properties of all conformal fluids. Nonconformality is the main accuracy limitation. For instance, interactions between non- spherical or polar molecules may not be adequately represented by Eq. (2-4), and so the scaled properties of these fluids will not conform to those of a fluid with interactions well represented by Eq. (2-4). A correction for nonconformality is usually made by the addition of one or more reference fluids whose deviations from the first reference fluid are used to characterize the effect of nonconformality. For example, in the Lee-Kesler method [Lee, B. I., and M. G. Kesler, AIChE J.,21(1975): 510] n-octane is used as a second, nonspherical reference fluid, and deviations of n-octane scaled properties from those of the spherical reference fluid at equivalent reduced conditions are assumed to be a linear function of the acentric factor. An extended Lee-Kesler method [Wilding, W. V., and R. L. Rowley, Int. J. Thermo- phys.,7(1986): 525] uses three reference fluids: n-octane to correct for size-shape nonconformality relative to methane and water to cor- rect for polar effects. Some CS methods [e.g., Teja, A., S. I. Sandler, and N. C. Patel, Chem. Eng. J.,21(1981): 21] utilize different refer- ence fluids for different classes of fluids to maintain close conformal- ity between the fluid whose properties are to be estimated and the reference fluids.
Group Contributions (GC) Chemical and physical properties generally correlate well with molecular structure. GC methods assume a summative behavior of the structural groups of the con- stituent molecules. For example, ethanol (CH3—CH2—OH) proper- ties would be obtained as the sum of contributions from the
—CH3,—CH2, and —OH groups. The contribution of each group is obtained by regression of experimental data that include as many dif- ferent compounds containing that group as possible. Structural groups must be used exactly as defined in the original correlation. A general priniciple in deciding how to make the groupings is to give the more specific group priority. For example, although the structural piece —COOCH3is ambiguous in a methyl ester, a more specific group value available for an ester —COO— would take precedence over a combination the two smaller groups —(C苷O)— and
2-468 PHYSICAL AND CHEMICAL DATA
—O— whose values were most likely regressed only from ketone and ether data, respectively. Excellent accuracy can usually be expected from GC methods when group values were regressed from large quantities of experimental data. However, if the ratio of number of groups to regressed experimental data is large, significant errors can result when the method is applied to new compounds (extrapolation).
Such excessive specificity in the group definitions leads to poor extrapolation capabilities even though the fit of the regressed data may be excellent.
Computational Chemistry (CC) Commercial software is avail- able that solves the Schrửdinger equation for approximate forms of the wave function. Various levels of sophistication (termed model chemistry) for the wave function can be chosen at the expense of com- putational time. Results include structural information (bond lengths, bond angles, dihedral angles, etc.), electron/charge distribution infor- mation, internal vibrational modes (for ideal gas properties), and energy of the molecule, valid for the chosen model chemistry.
Because calculations are performed on individual molecules, they are primarily suited for ideal gas properties. Relative energies for the same model chemistry are more accurately obtained than absolute energies, so enthalpies and entropies of reaction are common indus- trial uses of CC predictions in addition to individual structural and ideal gas properties.
Empirical QSPR Correlations In quantitative structure prop- erty relationship (QSPR) methods, physical properties are correlated with molecular descriptors that characterize the molecular and elec- tronic structure of the molecule. Large amounts of experimental data are used to statistically determine the most significant descriptors to be used in the correlation and their contributions. The resultant cor- relations are simple to apply if the descriptors are available. Descrip- tors must generally be generated by the user with computational chemistry software, although the DIPPR®801 database now contains a table of molecular descriptors for most of the compounds in it.
QSPR methods are often very accurate for specific families of com- pounds for which the correlation was developed, but extrapolation problems are even more of an issue than with GC methods.
Molecular Simulations Molecular simulations are useful for predicting properties of bulk fluids and solids. Molecular dynamics (MD) simulations solve Newton’s equations of motion for a small number (on the order of 103) of molecules to obtain the time evolution of the system. MD methods can be used for equilibrium and transport properties. Monte Carlo (MC) simulations use a model for the poten- tial energy between molecules to simulate configurations of the mole- cules in proportion to their probability of occurrence. Statistical averages of MC configurations are useful for equilibrium properties, particularly for saturated densities, vapor pressures, etc. Property esti- mations using molecular simulation techniques are not illustrated in the remainder of this section as commercial software implementations are not generally available at this time.
PHYSICAL CONSTANTS