Carbon dioxide: Difference between revisions

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Carbon dioxide

Carbon dioxide (CO₂)

Models

BBV

The BBV (Bock, Bich and Vogel) model ^[1].

EPM

The elementary physical model (EPM) and EPM2 of Harris and Yung ^[2] consists of 12-6 Lennard-Jones sites in conjunction with partial charges centred on each of these sites.

Model	$r_{\mathrm {OC} }$ (Å)	$k_{\theta }$ kJ/mol/rad²	$\sigma _{C-C}$ (Å)	$\epsilon _{C-C}/k_{B}$ (K)	$\sigma _{O-O}$ (Å)	$\epsilon _{O-O}/k_{B}$ (K)	$\sigma _{C-O}$ (Å)	$\epsilon _{C-O}/k_{B}$ (K)	q(O) (e)	q(C) (e)
EPM	1.161	1275	2.785	28.999	3.064	82.997	2.921	49.060	-0.33225	+0.6645
EPM2	1.149	1236	2.757	28.129	3.033	80.507	2.892	47.588	-0.32560	+0.6512

The bond bending potential is given by

\Phi _{bend}(\theta )={\frac {1}{2}}k_{\theta }\left(\theta -\theta _{0}\right)^{2}

where $\theta _{0}=180$ degrees.

GCPCDO

Gaussian charge polarizable carbon dioxide (GCPCDO) model ^[3].

Merker, Engin, Vrabec and Hasse

The Merker, Engin, Vrabec and Hasse model ^[4] consists of three 12-6 Lennard-Jones sites along with a point quadrupole ( $Q=4.0739$ DÅ) placed on the carbon site. The model is given by $r_{\mathrm {OC} }$ = 1.2869 Å, $\sigma _{C}=$ 2.8137 Å $\epsilon _{C}/k_{B}=$ 12.3724 K and $\sigma _{O}=$ 2.9755 Å, $\epsilon _{O}/k_{B}=$ 100.493 K.

Murthy, Singer and McDonald

Murthy, Singer and McDonald proposed four models ^[5], two models (A1 and A2) consisting of two 12-6 Lennard-Jones sites located roughly on the oxygen atoms, plus a point quadrupole located at the molecular centre of mass. Model B differed from models A1 and A2 in the use of the 9-6 Lennard-Jones potential, and model C was a three site model using the Lorentz-Berthelot combining rules for the C-O interactions.

MYVPBMM

The Mognetti et al. model ^[6] ^[7] is a coarse–grained model having either explicit (point) quadrupolar interactions or spherically averaged quadrupolar interactions, in conjunction with a single 12-6 Lennard-Jones site.

Oakley and Wheatley

The Oakley and Wheatley (OW) model ^[8].

SAPT-s

SAPT (symmetry-adapted perturbation theory) ^[9].

SYM

The SYM model ^[10]^[11].

TraPPE

Parameters for CO₂ for use in the TraPPE force field are C having $\epsilon /k_{B}=27.0$ K and $\sigma =2.80$ Å with a partial charge of 0.70 e, and O having $\epsilon /k_{B}=79.0$ K and $\sigma =3.05$ Å with a partial charge of -0.35 e ^[12]. The molecular geometry is rigid, linear, with a C-C bond length set at the experimental value of 1.16 Å. Unlike interactions use the Lorentz-Berthelot combining rules.

Zhang and Duan

Parameters for CO₂ for the Zhang and Duan model ^[13] ^[14] ^[15] are C having $\epsilon /k_{B}=28.845$ K and $\sigma =2.7918$ Å with a partial charge of 0.5888 e, and O having $\epsilon /k_{B}=82.656$ K and $\sigma =3.00$ Å with a partial charge of -0.2944 e. The molecular geometry is rigid, linear, with a C-C bond length set at the experimental value of 1.163 Å. Unlike interactions use the Lorentz-Berthelot combining rules.

Phase diagram

^[16] ^[17] ^[18]

Transport properties

^[19].

References

Related reading

External resources

3D phase diagram of carbon dioxide

[1] S. Bock, E. Bich and E. Vogel "A new intermolecular potential energy surface for carbon dioxide from ab initio calculations", Chemical Physics 257 pp. 147-156 (2000)

[2] Jonathan G. Harris and Kwong H. Yung "Carbon Dioxide's Liquid-Vapor Coexistence Curve And Critical Properties as Predicted by a Simple Molecular Model", Journal of Physical Chemistry 99 pp. 12021-12024 (1995)

[3] Rasmus A. X. Persson "Gaussian charge polarizable interaction potential for carbon dioxide", Journal of Chemical Physics 134 034312 (2011)

[4] Thorsten Merker, Cemal Engin, Jadran Vrabec and Hans Hasse "Molecular model for carbon dioxide optimized to vapor-liquid equilibria", Journal of Chemical Physics 132 234512 (2010)

[5] C. S. Murthy, K. Singer, and I. R. McDonald "Interaction site models for carbon dioxide", Molecular Physics 44 pp. 135-143 (1981)

[6] B. M. Mognetti, L. Yelash, P. Virnau, W. Paul, K. Binder, M. Müller, and L. G. MacDowell "Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: The case of carbon dioxide", Journal of Chemical Physics 128 104501 (2008)

[7] B. M. Mognetti, M. Oettel, P. Virnau, L. Yelash, and K. Binder "Structure and pair correlations of a simple coarse grained model for supercritical carbon dioxide", Molecular Physics 107 pp. 331-341 (2009)

[8] Mark T. Oakley and Richard J. Wheatley "Additive and nonadditive models of vapor-liquid equilibrium in CO2 from first principles", Journal of Chemical Physics 130 034110 (2009)

[9] Robert Bukowski, Joanna Sadlej, Bogumil Jeziorski, Piotr Jankowski, Krzysztof Szalewicz, Stanislaw A. Kucharski, Hayes L. Williams, and Betsy M. Rice "Intermolecular potential of carbon dioxide dimer from symmetry-adapted perturbation theory", Journal of Chemical Physics 110 pp. 3785- (1999)

[10] Kuang Yu, Jesse G. McDaniel, and J. R. Schmidt "Physically Motivated, Robust, ab Initio Force Fields for CO2 and N2", Journal of Physical Chemistry B 115 pp. 10054-10063 (2011)

[11] Kuang Yu and J. R. Schmidt "Many-body effects are essential in a physically motivated CO2 force field", Journal of Chemical Physics 136 034503 (2012)

[12] Jeffrey J. Potoff and J. Ilja Siepmann "Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen", AIChE Journal 47 pp. 1676-1682 (2001)

[13] Zhigang Zhang and Zhenhao Duan "An optimized molecular potential for carbon dioxide", Journal of Chemical Physics 122 214507 (2005)

[14] Thorsten Merker, Jadran Vrabec, and Hans Hasse "Comment on “An optimized potential for carbon dioxide”", Journal of Chemical Physics 129 087101 (2008)

[15] Zhigang Zhang and Zhenhao Duan "Response to "Comment on 'An optimized potential for carbon dioxide' "", Journal of Chemical Physics 129 087102 (2008)

[16] L. Glasser "Equations of state and phase diagrams", Journal of Chemical Education 79 874 (2002)

[17] A. Herráez, R. M. Hanson, and L. Glasser "Interactive 3D phase diagrams using Jmol" Journal of Chemical Education 86: 566 (2009) and website

[18] G. Pérez-Sánchez, D. González-Salgado, M. M. Piñeiro, and C. Vega "Fluid-solid equilibrium of carbon dioxide as obtained from computer simulations of several popular potential models: The role of the quadrupole", Journal of Chemical Physics 138 084506 (2013)

[19] C. G. Aimoli, E. J. Maginn and C. R. A. Abreu "Transport properties of carbon dioxide and methane from molecular dynamics simulations", Journal of Chemical Physics 141 134101 (2014)

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@@ Line 56: / Line 56: @@
 <ref>[http://jchemed.chem.wisc.edu/journal/issues/2009/May/abs566.html  A. Herráez, R. M. Hanson, and L. Glasser "Interactive 3D phase diagrams using Jmol" Journal of Chemical Education '''86''': 566 (2009)] and [http://biomodel.uah.es/Jmol/plots/phase-diagrams/ website]</ref>
 <ref>[http://dx.doi.org/10.1063/1.4792443   G. Pérez-Sánchez, D. González-Salgado, M. M. Piñeiro, and C. Vega "Fluid-solid equilibrium of carbon dioxide as obtained from computer simulations of several popular potential models: The role of the quadrupole", Journal of Chemical Physics '''138''' 084506 (2013)]</ref>
+==Transport properties==
+<ref>[http://dx.doi.org/10.1063/1.4896538  C. G. Aimoli, E. J. Maginn and C. R. A. Abreu "Transport properties of carbon dioxide and methane from molecular dynamics simulations", Journal of Chemical Physics '''141''' 134101 (2014)]</ref>.
 ==References==
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