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Ind. Eng. Chem. Res. 2004, 43, 1788-1793
GENERAL RESEARCH Transferable Step Potentials for the Straight-Chain Alkanes, Alkenes, Alkynes, Ethers, and Alcohols Ozlem Unlu, Neil H. Gray, Zeynep N. Gerek, and J. Richard Elliott* Chemical Engineering Department, The University of Akron, Akron, Ohio 44325-3906
Discontinuous molecular dynamics simulation and thermodynamic perturbation theory have been used to study thermodynamic and transport properties for hydrocarbons and oxygenated compounds. The fundamental basis of the method relies on a stepwise characterization of the disperse interactions and Wertheim potentials for the hydrogen bonding. The study on the transferable step potential energies, which are used to correlate the physical properties, the vapor pressure and liquid density, from available experimental data in the literature for straightchain alkanes is extended to straight-chain alkenes, alkynes, ethers, and alcohols. The transferable multistep potentials for the new training set of pseudo-atoms governed by two transferable square-well depths and diameters are introduced, being transferable for the selected model compounds in each family. Those transferable parameters are applied to a set of validation compounds, and the results are analyzed. Overall, the vapor pressures and liquid densities are correlated to within 5% error with reduced temperatures extending to 0.45 for n-alkanes, alkenes, alkynes, ethers, and alcohols while applying transferable characterizations of the individual pseudo-atoms’ molecular interaction potentials. I. Introduction Reliable molecular modeling requires identification of transferable intermolecular potential models. To achieve this, it is necessary to infer the energetics of each molecular interaction. In the past, these have been modeled typically by continuous potentials such as the Lennard-Jones model. As an alternative, one can suggest the use of discontinuous potential models, like square-well or step potentials. The simplicity of a discontinuous potential model provides several advantages.1 Among these are the clean separation between attractive and repulsive effects and the faster execution of dynamics described by the ultimate multiple time step method. The combination of discontinuous molecular dynamics (DMD) with thermodynamic perturbation theory (TPT) builds a bridge between theoretical and experimental work in the sense that it enables a detailed study of the molecular interactions by relating them directly to the macroscopic physical properties. Previous work demonstrated that second-order TPT provided quantitative agreement of coexistence properties with the simulation of the full potential.2 The advantage of DMD/TPT becomes more apparent when one considers the increase in efficiency when the attractive potential need not be simulated. Because the computation time goes as the number of neighbor interactions, and the number of neighbors goes as the cube of the range of the potential, shortening the potential by a factor of 2-2.5 leads to a 1 order of magnitude improvement in computational efficiency. Noting that DMD inherently includes information about dynamic properties such as diffusivity and viscosity, we refer to this combined methodology as the step potential equilibria and dynamics (SPEAD) model.
In previous work, we have modeled the intermolecular potentials by applying the DMD/TPT formalism to n-alkanes and benzene.3 Because the attractive part of the potential comprises the perturbation computed from theory, applied after the simulation is over, the characterization of the attractive wells can be optimized very efficiently. The physical properties of concern, primarily the vapor pressure and liquid density, are sensitive in the sense that the details of the attractive potential are distinguishable. This sensitivity to various parts of the intermolecular potential (diameter and inner and outer well depths) means that a more conventional “group contribution” approach ultimately faces limitations that can be avoided by the approach of transferable potentials. Although related to group contributions at a certain level, the transferable potentials provide clear physical insights, and they offer the prospect for further refinement through quantum mechanical analysis of deviations from the assumption of transferability. As shown by Chapela and co-workers4 years ago, we have also convinced ourselves that the multistep united-atom potential model can be an accurate substitute for the Lennard-Jones potential. Thus, the optimized resulting potentials follow understandable trends and promise to be transferable in the sense of providing identical characterization of CH3- and -CH2- groups for ethane, butane, hexane, octane, and other n-alkanes. Finally, we demonstrated for methane a methodology of varying the well widths and depths in the manner of a nonlinear regression to achieve representation of vapor pressure, density, and internal energy to better than 1% accuracy.5 In the present work, the DMD/TPT formalism is applied to a broader range of n-alkanes, alkenes,
10.1021/ie034036m CCC: $27.50 © 2004 American Chemical Society Published on Web 02/28/2004
Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 1789
alkynes, alcohols, and ethers with some modifications in the multistep potential to enhance the transferability of the potential by decreasing the number of transferable parameters. The roles of qualitative variations in the potential function are also probed relative to physical properties. For this purpose, a set of model compounds has been selected. The alkanes include methane, ethane, propane, n-butane, n-pentane, n-hexane, nheptane, n-octane, n-nonane, n-decane, n-dodecane, and n-hexadecane. Alkenes include ethylene, propylene, 1-butene, trans-2-butene, cis-2-butene, 1,5-hexadiene, and 2-methyl-2-butene. Alkynes include acetylene, 1-butyne, 2-butyne, 2-pentyne, vinylacetylene, and 2-hexyne. Alcohols include methanol, ethanol, n-propanol, nbutanol, and n-pentanol. Ethers include dimethyl ether, ethyl methyl ether, diethyl ether, di-n-propyl ether, and tetrahydrofuran. While it is essentially desired to be able to determine and reproduce the thermodynamic properties for hydrocarbons and oxygenated compounds, the secondary goal has been to minimize the number of different site types needed to characterize any molecule of concern. In this way, the same set of parameters for any particular site can be used in all types of molecules. Intermolecular interactions are considered to be the basis of the site-type definitions. The next section describes the details of the perturbation contribution formulation and postsimulation analysis. Then, the results for the transferable parameters for n-alkanes, alkenes, alkynes, alcohols, and ethers are presented with a comparison of the vapor pressure and liquid density with the experimental data. The last section presents the conclusions. II. Perturbation Contributions for Multistep Potentials The algorithm for simulation (DMD) is fundamentally different from the algorithm for continuous potentials and generally much more efficient. TPT enhances this efficiency because it allows the use of the simulation results for reference potentials for quantitative representation of the statistical mechanics of the full potential. Because the DMD/TPT methodology provides an efficient yet rigorous treatment of the molecular dynamics, it allows the simultaneous treatment of thermodynamic and transport properties. Although the details of performing the DMD simulations and the formalism have been given previously,6 it would be desirable to review the basic formulas for computing perturbation contributions. The perturbation theory formalism applied in this work follows the work of Barker and Henderson (BH).7 Basically, BH perturbation theory suggests that the attractive part can be divided into an infinite series of wells, with each well width small enough that the energy of each step can be treated as a constant. Also, the Helmholtz free energy can be decomposed into a reference contribution and an attractive contribution in the form of a power series in β, where β ≡ 1/kBT, with kB ≡ Boltzmann’s constant. If the first well depth is designated as the base value, -, all of the other well depths can be designated as fractions of the first well depth. Therefore, the Helmholtz energy can be formalized as follows: ig A - Aig A0 - A ) + A1*β + A2*β2 NkBT NkBT
(1)
A1* )
∑j 〈Nj〉0uj/N
∑i ∑j (〈NiNj〉0 - 〈Ni〉0〈Nj〉0)uiuj/2N2
A2* ) -
(2) (3)
where the first term, A0, is the Helmholtz energy of the repulsive fluid, Aig is the Helmholtz energy of the ideal gas, j means the jth well, 〈Nj〉 is the ensemble average of the interaction site pairs inside the jth well, uj is the potential of the jth well, Nj is obtained from the reference fluid simulation, and 〈 〉0 denotes an ensemble average of the reference fluid. A1* and A2*, in eqs 2 and 3, represent what are called the first- and second-order perturbation terms. It is necessary to note that the above formulas for A1* and A2* are only applicable when all sites on the molecule are identical. For methane, ethane, ethylene, and acetylene, this constraint is of no concern because they are composed of a single site type, CH3-, CH2d, and tCH, respectively. For the other chain and branched compounds in each alkane, alkene, alkyne, alcohol, and ether family, however, the assumption of a single site type is an oversimplification. By analysis of the trends in the potential parameters proceeding from ethane to octane, insight has been gained about the changes in the molecular interactions as the weighting on the -CH2- group increases.3 In the extended study for model molecules of concern in each alkene, alkyne, alcohol, and ether family, the same method has been followed to understand the behavior of the different site types and the changes in intermolecular attractions, which are reflected as different transferable site parameters. Equation 4 shows the energy of interaction between those two sites or groups of type i and j, which is the geometric mean of the group potentials, .
ij ) xij
(4)
The BH formalism is advantageous because it permits one to dissect the potential into multiple steps with variable width and depth and, moreover, to define the shape of the potential function. The well widths and depths can be obtained by fitting experimental data with no additional simulation step. As discussed in the previous work of n-alkanes and benzene,3 we used four disperse attraction wells because they are sufficient to describe the physical properties, the vapor pressure and density. Our notation 2580 designates that separate attractive wells exist at r/σ ) 1.2, 1.5, 1.8, and 2.0, not mentioning the discontinuity at r ) σ. In the present work, when the number of wells is kept as four, the number of adjustable parameters is decreased to three, being σ, (/k)1, and (/k)4, instead of five when all well depths are varied independently. Here, the second and third disperse attraction well depths are determined from the first (deepest) and the fourth (shallowest) well depths according to the following relation:
2 ) 4 + 2(1 - 4)/3
(5)
3 ) 4 + (1 - 4)/3
(6)
Therefore, linear well depths impose the shape of the potential. This modification has helped to overcome multiparameter optimization difficulties when too many coupled parameters are varied independently. With three parameters per site type, the SPEAD method can
1790 Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 Table 1. Transferable Parameters for SPEAD pseudo-atom CH3CH3CH3-CH2-CH2dCH2 dCH2 dCHdCH-OtCH tCtC-OH -OH -OH -OH(1′) -OH(2′)
sample molecule n-alkane, R-olefin methyl ether methanol n-alkane, R-olefin, primary alcohol, alkyne, ether ethanol propylene R-olefin R-olefin dienes ether 1-alkyne 2-alkyne vinylacetylene methanol ethanol n-propanol primary alcohol secondary alcohol
(/kB)1 (/kB)4 σ (nm) 90.90 108.00 69.50 25.60
16.20 11.00 25.97 23.50
0.363 0.363 0.363 0.357
32.90 90.90 65.00 25.60 40.00 52.00 99.91 51.40 81.50 172.50 108.50 176.00 171.50 124.80
19.60 7.10 20.00 22.50 19.00 39.00 4.50 11.50 5.80 26.40 21.30 4.10 10.90 95.60
0.357 0.350 0.350 0.350 0.350 0.270 0.330 0.350 0.350 0.285 0.285 0.285 0.285 0.285
be compared to the TraPPE8 and NERD9 models, with two parameters per site type, and the Errington and Panagiotopoulos10 model, with three or more parameters. III. Results and Discussion The vapor pressure is an extremely important physical property in chemical processing. Because it represents the vapor-liquid equilibria of the pure fluid, accurate treatment of mixture phase equilibria is closely tied to vapor-pressure accuracy. Although it is relatively easy to measure the fluid density experimentally, it provides an important metric of molecular size. Therefore, SPEAD, at its developmental stage, focuses mainly on the vapor-pressure and liquid-density prediction while trying to keep the model transferable to minimize the number of different site types. The site types are defined based on the intermolecular interactions. Table 1 shows the different site types and sample molecule(s) along with the optimized SPEAD transferable parameters. For example, the CH3 site interacting with the CH3 or CH2 group in ethane, n-alkanes, n-alkenes, or alkynes assumes the same field of molecular interactions in all cases. However, a new methyl group definition is necessary for a CH3 site connected to an OH site, as in the case of methanol because the attractive interactions in the methyl group may be affected by the nearby hydroxyl group. Following the same argument, the CH2 sites in alcohols or ethers are expected to have different transferable sets of potential energies.8 The energy potential is illustrated in Figure 1, which shows the step potential function for the sites for -CH3, -CH2-, and tC-. To study alkenes and alkynes, new site types with double and triple bonds, -CHd, CH2d, >Cd, -Ct, and CHt, were introduced. To minimize the number of site types, the CH3 groups connected to -Cd or -Ct sites were assumed to be the same as the methyl groups in a straight-chain alkane. The bond lengths were assumed to follow standard values in all cases (e.g., 0.154 nm for CH2-CH2). For alcohols, we found it necessary to consider alcohols with more than two carbons before a transferable characterization of the -OH type was feasible. For methanol and ethanol, -OH sites with special parameters were used. Also, for ethers, an -Osite was defined for the straight-chain ether linkage. For vinylacetylene, where both triply and doubly bonded
Figure 1. Step potential function for -CH3, -CH2-, and ≡Csites. Table 2. Vapor-Pressure and Liquid-Density Prediction Accuracy of the SPEAD Model for n-Alkanes % AAD P % AAD F rms error (%) n-butane n-hexane n-hexadecane methane ethane propane n-pentane n-heptane n-octane n-nonane n-decane n-dodecane overall
Tmin r
ηmax
1.32 2.45 5.53
Training Set 1.31 2.67 5.62
1.65 2.81 6.22
0.45 0.51 0.475 0.51 0.525 0.5
2.89 3.73 3.31 2.91 5.87 10.32 4.92 4.38 3.64 4.54
Validation Set 1.96 1.11 0.63 1.7 5.55 3.26 3.43 4 4.13 3.10
2.84 2.84 3.13 2.9 7.77 7.97 4.79 4.42 4.15 4.53
0.45 0.525 0.45 0.5 0.525 0.45 0.5 0.525 0.525 0.50
0.45 0.52 0.5 0.5 0.52 0.52 0.51 0.49 0.5 0.50
sites are present, a special set of parameters was necessary owing to the influence of the double-bonded site on the triple-bonded one. The MinPack implementation of the LevenbergMarquardt algorithm was used to regress the step depths. Because of the coupling effects between the step depths and the repulsive diameter, the MinPack program had some difficulties in simultaneous regression of the depths and diameters. This led us to the determination of the diameters by a systematic trial-anderror approach. Diameters were varied in increments of 0.01 nm, and optimization was performed over the step depths until the overall root-mean-square (rms) % error was minimized. The experimental data for the vapor pressure and density for each compound were taken from the DIPPR compilation.11 Tables 2-6 show the vapor-pressure and liquid-density prediction accuracy of the SPEAD model for n-alkanes, alkenes, alkynes, alcohols, and ethers, respectively, in terms of absolute average deviations from the experimental data. Here, there are two sets of compounds listed as the training and validation sets. The training set compounds represent the compounds analyzed during the optimization of the transferable parameters, whereas the validation compounds are the compounds used to verify the transferability of the optimized potential parameters. The minimum achieved reduced temperature (Tmin r ) and the maximum corresponding packing fraction (ηmax) values as well as the
Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 1791 Table 3. Vapor-Pressure and Liquid-Density Prediction Accuracy of the SPEAD Model for Alkenes
% AAD P
% AAD F
rms error (%)
Tmin r
1-butene 1-pentene 1-hexene 1,3-pentadiene (T) 2,4-hexadiene (C, T) 2-butene trans-2-pentene trans-2-heptene 2-hexene trans-3-heptene trans-2-octene
5.35 2.13 2.89 3.14 4.30 16.82 4.04 3.62 8.52 5.20 6.04
0.50 0.50 0.50 0.45 0.45 0.45 0.45 0.45 0.53 0.45 0.45
0.49 0.50 0.50 0.52 0.53 0.51 0.50 0.52 0.50 0.52 0.52
cis-2-butene cis-2-pentene cis-2-heptene 3-hexene propylene 1,5-hexadiene 1-octene 1,3-pentadiene (C) 2,4-hexadiene (T, T) overall
Validation Set 19.23 0.65 7.89 2.18 7.13 1.11 15.04 2.67 0.72 0.61 2.71 0.95 3.06 4.43 5.48 2.82 6.66 1.15 7.19 1.61
13.73 6.79 5.42 10.90 1.07 2.33 4.77 4.51 5.81 5.87
0.45 0.45 0.45 0.53 0.40 0.53 0.53 0.45 0.45 0.47
0.50 0.51 0.52 0.50 0.52 0.49 0.51 0.52 0.52 0.51
Table 4. Vapor-Pressure and Liquid-Density Prediction Accuracy of the SPEAD Model for Alkynes
1-butyne 1-pentyne 1-hexyne 1-nonyne 2-hexyne 3-hexyne vinylacetylene
7.62 11.39 9.39 10.79 3.21 3.54 3.09
Training Set 1.46 2.23 1.09 1.2 5.47 6.43 3.27
1-decyne 2-butyne 2-pentyne overall
11.76 6.27 5.84 7.29
Validation Set 1.34 10.63 7.83 4.10
ηmax
7.14 8.72 7.36 8.9 4.63 6.02 3.49
0.45 0.45 0.45 0.45 0.45 0.45 0.45
0.526 0.533 0.529 0.529 0.517 0.513 0.528
8.84 9.44 7.16 7.17
0.45 0.45 0.45 0.45
0.529 0.515 0.514 0.52
Table 5. Vapor-Pressure and Liquid-Density Prediction Accuracy of the SPEAD Model for Alcohols % AAD P methanol ethanol n-propanol n-hexanol n-heptanol n-octanol
3.15 2.84 3.09 11.29 8.89 8.01
n-butanol n-pentanol n-nonanol n-decanol overall
18.65 15.04 8.86 10.24 9.01
Tmin r
ηmax
3.33 2.89 3.19 9.72 7.42 7.34
0.4 0.45 0.475 0.475 0.45 0.45
0.52 0.51 0.528 0.527 0.538 0.51
Validation Set 4.45 14.07 3.73 13.69 1.85 7.21 1.87 8.64 2.49 7.75
0.45 0.475 0.45 0.45 0.45
0.536 0.54 0.534 0.533 0.53
% AAD F
rms error (%)
Training Set 0.65 2.55 2.63 2.26 2.95 1.94
rms error (%)
Tmin r
ηmax
dimethyl ether diethyl ether di-n-propyl ether
Training Set 1.25 2.5 9.32 1.43 7.8 1.77
2.2 7.21 6.93
0.45 0.45 0.45
0.523 0.529 0.535
methyl propyl ether ethyl propyl ether ethyl methyl ether overall
Validation Set 3.54 2.57 2.86 1.7 7.71 0.994 5.41 1.83
3.45 2.83 6 4.77
0.45 0.45 0.45 0.45
0.528 0.533 0.525 0.53
% AAD P
ηmax
Training Set 5.31 0.76 2.44 1.28 2.89 2.44 3.66 1.12 3.57 1.34 23.39 1.92 4.39 1.56 4.56 1.02 11.49 1.96 6.21 1.03 7.91 1.28
% AAD P % AAD F rms error (%) Tmin r
Table 6. Vapor-Pressure and Liquid-Density Prediction Accuracy of the SPEAD Model for Ethers
rms error values in percentage are tabulated. Table 7 summarizes those individual results and shows the overall percent average absolute deviation (% AAD) for the vapor pressure and density for each hydrocarbon and oxygenated compound family as well as the rms % error of the optimal potential. Here, we also compare the % AADs for the vapor pressure and density to the TraPPE force field.8,12 Although the number of empirical parameters in the SPEAD method is slightly greater than the number in other potentials, the average
% AAD F
deviations of the SPEAD model for the vapor pressure are 1 order of magnitude smaller than those of the TraPPE-UA model, and the temperature range also extends much lower for the SPEAD model. The purecomponent association parameters used for alcohols, the bonding volume and the energy of hydrogen bonding, are tabulated in Table 8. Generally, the % AADs are less than 5%. Figure 2 shows the temperature-liquid-density projection for n-alkanes. Figure 3 illustrates the semilog vaporpressure curve for alkenes. The trend in the results for the liquid density and vapor pressure are typical for all of the compounds studied. Figure 4 illustrates the transferability analysis in detail, conveying the isomer effects for selected alkenes in comparison with n-hexane. This analysis was initially carried out (Figure 4a) by using n-alkane parameters with the alkene well distributions from DMD simulations. Note that the trend predicted using alkane parameters is opposite from that of the experimental data. The predicted vapor pressure naturally decreases simply because of the shortening of the bonds and the decrease in molecular volume. Optimizing the potential parameters resulted in a set of transferable parameters for alkenes (Figure 4b) that were necessarily less attractive than those for alkanes. The deviations in the vapor pressure are barely discernible in Figure 3 because of the log scale, but systematic deviations in the liquid density are apparent. At high temperatures, a systematic error in the density is expected because the perturbation theory cannot represent the nonanalytical behavior in the critical region. This limitation explains why the temperatures considered were constrained to be less than 90% of the critical temperature. Away from the coexistence curve but in the critical region, we favor the application of a crossover equation as demonstrated for square-well spheres by Kiselev and Ely.13 Because all properties of the current study were on the coexistence curve, the crossover equation is not discussed here. It is necessary to point out that larger density errors were observed in the case of 2- and 3-alkynes. These resulted from a compromise between the vapor pressure and density errors. In principle, the density error can be reduced by decreasing the diameter of the triple bond site, -Ct. However, this was found to undermine the transferability of the potentials. This problem may arise from the rigid nature of the alkynes in general. The -CtC-CHx bond should be 180°, but the vibrating nature of the DMD model results in an average value of ∼160° for this angle. The results for 1-alkynes are anomalous in the sense that the diameter for the CH≡ site is smaller than that of the -C≡ site. Normally, the diameters increase as more hydrogen atoms are included. We found that smaller diameters than 0.35 nm
1792 Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 Table 7. Overall Prediction Accuracy for the Vapor Pressure and Density for the SPEAD Model in Comparison with the TraPPE United-Atom Model SPEAD
TraPPE-UA
no. of comp.
% AAD P
% AAD F
rms error (%)
Tmin r
ηmax
no. of comp.
% AAD P
% AAD F
Tmin r
12 3 9 20 11 9 10 7 3 10 6 4 6 3 3
4.27 3.10 4.66 7.19 6.89 7.51 7.29 7.00 7.79 9.01 6.21 13.20 5.41 6.12 4.70 6.63
2.95 3.20 2.86 1.61 1.43 1.82 4.10 3.02 5.97 2.49 2.16 2.98 1.83 1.90 1.75 2.59
4.29 3.56 4.53 5.87 5.64 6.12 7.17 6.61 8.15 7.75 5.65 10.90 4.77 5.45 4.09 5.97
0.49 0.48 0.49 0.47 0.47 0.47 0.45 0.45 0.45 0.45 0.45 0.46 0.45 0.45 0.45 0.46
0.50 0.51 0.50 0.51 0.51 0.51 0.52 0.53 0.52 0.53 0.52 0.54 0.53 0.53 0.53 0.52
7
25.83
0.53
0.617
8
30.02
0.57
0.569
9
28.00
5.12
0.565
27.95
2.07
0.58
n-alkanes training validation alkenes training validation alkynes training validation alcohols training validation ethers training validation overall
Table 8. Pure-Component Parameters for a Number of Alcohols According to the SPEAD Model component
bonding volume (nm3/mol)
HB (kcal/mol)
methanol ethanol n-propanol primary alcohol secondary alcohol
0.00100 0.00070 0.00060 0.00070 0.00050
5.00 5.30 5.20 5.10 5.00
for the -C≡ site led to large errors in the vapor pressure and diminished transferability. This occurs because the shortness of the triple bond leads to substantial overlap between the -C≡ site type and covalently bound neighbors. If the -C≡ site diameter is small, its molecular interactions are screened substantially. The CH≡ site is not subject to so much overlap, and its diameter has a stronger effect on the density because it occupies the end of the chain. The 1-alkynes are also instructive regarding what may be the limit of transferability because a very simple change in the outermost well depth is sufficient to strongly alter the vaporpressure deviations while leaving the density deviations
Figure 2. Liquid densities of n-alkanes correlated by the SPEAD potential models.
relatively unchanged. When the outermost well is fixed at /k ) 1.5 K, the vapor-pressure deviations for 1-pentyne and 1-hexyne drop to less than 3% while the deviations for 1-butyne, 1-nonyne, and 1-decyne rise to roughly 20%. The situation reverses when the outermost well is fixed at /k ) 4.5 K, with vapor-pressure deviations for 1-pentyne and 1-hexyne rising to 20% and the other 1-alkynes dropping to 4%. To obtain a single characterization of this interaction that transfers to all compounds similarly, it is necessary to compromise on an intermediate value within this small range of possibilities. This observation highlights the sensitivity of the vapor pressure to details of the potential and the challenge of identifying globally transferable characterizations of the potential. Therefore, by stepwise optimization of the diameter for the CH≡ site, the vapor-pressure deviations are overcome with a slight compromise in the liquid-density predictions. Even so, SPEAD’s predictions for alkynes are similar in accuracy to the correlations from the training set (Table 4). In the analysis of alcohols, methanol, ethanol, and
Figure 3. Vapor pressures of alkenes correlated by the SPEAD potential models.
Ind. Eng. Chem. Res., Vol. 43, No. 7, 2004 1793
Figure 4. Vapor pressures of several alkenes correlated by the SPEAD potential models (a) with alkane parameters and (b) with alkene transferable parameters.
n-propanol are regressed individually but longer primary alcohols share transferable parameters. We hope that further research will explain the larger errors in alcohol systems and serve as a basis for obtaining better accuracy while maintaining the transferability. Owing to the complicated and subtle behavior of the water molecule and the diverse range of its applications, we have elected not to publish a specific set of parameters for water at this time. Multiple sets of parameters describe pure water equally well, and interested users can readily develop these for themselves by applying the available software. Publication of a standard characterization for water is postponed pending a more detailed study of typical applications and analysis of which parameter set among many satisfies the most applications. Note that the interaction site model of molecular interactions is itself an approximation. That is, the quantum mechanical interaction energies are not likely to follow precisely the sum of independent interaction energies centered on each interaction site. Hence, the entire interaction site formalism must be recognized as merely a characterization of the “effective” potential. As a result, transferable potentials that permit predictions of the vapor pressure to within 5% accuracy may be difficult to supersede. Note that one key to this accuracy is the distinction between isomers at the molecular level by the rigorous molecular dynamics simulation of the repulsive part of the potential. IV. Conclusions The present database of molecular simulations and results for the SPEAD model was broadened, and the well depths for new site types were defined. Although full development of the model will require an intense and prolonged effort, the results presented in this work show that the characterizations of the molecular interactions are transferable and predictions of the vapor pressure and density are superior to what is currently available. Our findings could have an important impact on extensions of molecular modeling from the atomistic scale to the mesoscale. Microsecond time scales are accessible from the atomistic DMD model for a very broad class of computer processors. Because molecular
dynamics simulations by the SPEAD model are at least an order of magnitude faster than conventional simulations of the full potential, the overlap between time scales can be extended, improving the reliability of the mesoscale characterization. Acknowledgment This work was supported in part by National Science Foundation Grants CTS-0075883 and CTS-0226532 and ChemStations Inc., Houston, TX. Literature Cited (1) Cui, J.; Elliott, J. R., Jr. J. Chem. Phys. 2002, 116, 86258631. (2) Cui, J. Step Potential Molecular Models of Pure Components and Mixtures by DMD/TPT, in Chemical Engineering. Ph.D. Dissertation, The University of Akron, Akron, OH, 2001. (3) Elliott, J. R. Fluid Phase Equilib. 2002, 194 (197), 161168. (4) Chapela, G. A.; Scriven, L. E.; Davis, H. T. J. Chem. Phys. 1989, 91 (7), 4307-4313. (5) Elliott, J. R.; Cui, J. AIChE Symp. Ser. 2001, 325, 159162. (6) Cui, J.; Elliott, J. R., Jr. J. Chem. Phys. 2001, 114, 72837290. (7) Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 47144721. (8) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569-2577. (9) Nath, S. K.; Escobedo, F. A.; de Pablo, J. J. J. Chem. Phys. 1998, 108, 9905-9911. (10) Errington, J. R.; Panagiotopoulos, A. Z. J. Phys. Chem. B 1999, 103, 6314-6322. (11) Danner, R. P., Daubert, T. E., Eds. Manual for predicting chemical process design data: data prediction manual/Design Institute for Physical Property Data, American Institute of Chemical Engineers, DIPPR, ed.; American Institute of Chemical Engineers: New York, 1983. (12) Chen, B.; Potoff, J. J.; Siepmann, J. I. J. Phys. Chem. B 2001, 105, 3093-3104. (13) Kiselev, S. B.; Ely, J. F. Ind. Eng. Chem. Res. 1999, 38, 4993-5004.
Received for review August 1, 2003 Revised manuscript received January 8, 2004 Accepted January 15, 2004 IE034036M
