tsankova_2018
=============

G\. Tsankova, M\. Richter, P\. L\. Stanwix, E\. F\. May and R\. Span, "Accurate High\-Pressure Measurements of Carbon Monoxide's Electrical Properties", ChemPhysChem 19, 784 \(2018\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/tsankova_2018.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1002/cphc\.201701085 <https://doi.org/10.1002/cphc.201701085>`__

**Source kind:** measurement

**Recorded technique:** Relative dielectric permittivity of pure CO from a microwave re\-entrant cavity resonator \(copper\-beryllium; a 2 mm annular gap as the capacitor; the apparatus of Tsankova et al\. 2016\-2017, Refs\. 13, 14\), the fundamental mode only, about 395 MHz \(f00 = 393\.8046 \+\- 0\.0002 MHz in vacuum at 273\.09 K\), S21 measured at 401 frequencies with an HP 8752C network analyser and fitted to a complex Lorentzian \(Eq\. 5\); epsilon\_r from the complex resonance frequencies by Hamelin et al\.'s model \(Eq\. 6\), with the cavity's thermal expansion \(\-16\.89 \+\- 0\.18\)e\-6 /K and pressure distortion \(1\.33 \+\- 0\.19\)e\-6 /MPa calibrated in vacuum and with helium, validated with argon and CO2 \(pp\. 786\-787\)\. Four isotherms, 255\.10, 273\.17, 293\.25 and 313\.28 K, pressures 2 to 8 MPa in 2 MPa steps, up and down; SPRT temperature to \< 20 mK and pressure to 0\.01 % of 13\.8 MPa \(both k = 1\.73\)\. CO of mole fraction 0\.99997 \(Air Liquide N47\), used as received \(p\. 787\)\. Molar densities from Lemmon and Span's equation of state \(J\. Chem\. Eng\. Data 51, 785 \(2006\), in REFPROP 9\.1\), whose density uncertainty is 0\.3 % \(k = 2\) here \(pp\. 787\-788\)\. The molar polarization by Kirkwood's relation, P = \(eps\_r \- 1\)\(2 eps\_r \+ 1\)/\(9 eps\_r rho\) \(Eq\. 1\), and a regression of the Debye virial form \(Eq\. 4\) for alpha\_e, mu\_e and b\_eps over all 27 points \(p\. 789\)\.

**Materials in structured entries:** CO

**Dataset quantities:** polarizability

**Contents:** 1 dataset; 1 formula.

Curation notes
--------------

The library identity is VALIDATED \(DOI 10\.1002/cphc\.201701085\); first page checked \(pdf page 1\: ChemPhysChem 2018, 19, 784\-792; manuscript received 4 October 2017, p\. 792\)\. Page numbers here are journal pages \(pdf page \+ 783\)\. The values used are checked against the PDF's own text \(pdftotext of the library original\) as well as the library's rendering\.

WHAT IS MEASURED\. The static relative permittivity \(395 MHz, far below CO's rotational and vibrational resonances, so both respond as to a static field; 'eps'' is negligible below about 2 GHz', p\. 787\) eps\_r at 27 \(p, T\) points \(Table 2, p\. 788\), relative combined expanded uncertainty \(k = 2\) 52 ppm IN eps\_r \(Table 2 caption; abstract, p\. 784\)\. The '52 ppm' of the abstract is the permittivity's, not the polarizability's\. A dielectric measurement\: electric, without CO's \(diamagnetic\) magnetic term\. CO is polar, so the zero\-density molar polarization is Debye's A\_eps = \(N\_A/3 eps0\)\(alpha\_e \+ mu\_e^2/3kT\) \(Eq\. 3, p\. 785\)\: the distortion polarizability alpha\_e \(electronic PLUS vibrational\: 'the measurements \.\.\. are carried out at low frequencies, where the geometry of the CO molecule can be distorted by the applied electric field\. Thus, the vibrational contribution is already included', p\. 785; 'Our measurements include both', p\. 789\) and the orientation term mu\_e^2/3kT\. The fit separates them through the 1/T dependence over 255\-313 K, with alpha\_e and mu\_e taken independent of temperature and b\_eps one constant \(c\_eps not fitted\: 'only little curvature', rho \<= 3\.81 mol/dm^3, p\. 789\)\. Constants as printed \(p\. 785\)\: N\_A = 6\.0220e23 /mol, eps0 = 8\.8542e\-12 F/m, k\_B = 1\.3806e\-23 J/K \(N\_A/3 eps0 2\.5e\-5 below CODATA's\: negligible\)\.

THE RESULTS \(pp\. 789\-791\)\. alpha\_e = 2\.176e\-40 C^2 m^2 J^\-1 \(= C m^2/V\), 'relative combined expanded uncertainty \(k = 2\) of 1\.01 %' \(p\. 789\); \(2\.176 \+\- 0\.022\)e\-40 \(p\. 791\)\. 2\.176e\-40 C m^2/V = 13\.198 au \(13\.1977; one sigma 0\.0667 au, 0\.51 %\)\. mu\_e = 3\.584e\-31 C m 'approximately 0\.107 D' \(0\.10745 D\), 1\.3 % \(k = 2\) \(p\. 790\), but \(0\.107 \+\- 0\.001\) D on p\. 791 \(0\.93 %\)\: the two uncertainties disagree\. b\_eps = \(1\.015 \+\- 0\.044\) cm^3/mol \(k = 2; abstract and p\. 790\), printed \(1\.014 \+\- 0\.044\) cm^\-3 mol^\-1 on p\. 791 \(the last digit and the unit's sign differ; b\_eps has the unit of 1/rho, cm^3/mol; the Stone et al\. values are also printed in cm^\-3 mol^\-1, pp\. 786, 790\)\. No temperature dependence of b\_eps was resolved \(Stone et al\.'s ab initio 1\.736 at 273 K and 1\.554 at 293 K\)\. The three are recorded in the formula eq4\_CO; alpha\_e is the dataset alpha\_e\_CO\. Comparisons printed\: alpha\_e \+0\.37 % above Maroulis's ab initio 2\.168e\-40 \(electronic only, p\. 789\) and \+0\.28 % above Hohm's \(2013\) electronic 2\.150 \+\- 0\.012 plus Bishop and Cheung's vibrational 0\.020 \+\- 0\.001 \(= 2\.170; p\. 790\); both recompute \(\+0\.369 %, \+0\.276 %\)\. The abstract's 'Literature values from ab initio calculations \.\.\. within 0\.28 %' is the Hohm\-plus\-Bishop comparison, not the ab initio one \(0\.37 %\)\. mu\_e is 2\.2 % and 2\.1 % below the molecular\-beam ground\-state values of Muenter \(0\.10980 D\) and Meerts et al\. \(0\.1097 D\), which the authors attribute to the thermal \(centrifugal\) average of an ensemble at finite temperature \(p\. 790\); recomputed \-2\.14 % and \-2\.05 % with 0\.10745 D\.

CHECKS \(2026\-10\-01; CoolProp 8\.0\.0's CO equation of state, Lemmon and Span 2006, for the densities\)\: see eq4\_CO's check\. In short, a regression of Eq\. \(4\) to Table 2's eps\_r column reproduces the printed alpha\_e, mu\_e and b\_eps to 0\.06 %, 0\.5 % and 0\.8 %, and the printed parameters reproduce the paper's description of Fig\. 6a\. Table 2's P\_meas column is NOT consistent with its eps\_r column\: Eq\. \(1\) with the same densities gives P 0\.004\-0\.021 cm^3/mol above the printed P\_meas, as if eps\_r were lower by a constant 47\.7 \+\- 3\.3 ppm \(mean and standard deviation over the 27 points; the P rounding is 0\.4\-1\.9 ppm in eps\_r\)\. The printed P\_meas reproduce the text's comparison with Maroulis \(Fig\. 4b, '\-\(0\.87 to 1\.63\) %', p\. 788\: \-0\.85 to \-1\.60 % here; P from eps\_r gives \-0\.74 to \-1\.27 %\); a regression to them gives alpha\_e = 2\.172e\-40, mu\_e = 0\.1050 D, b\_eps = 2\.03 cm^3/mol\. So the published parameters come from the eps\_r column \(or from P consistent with it\), and the P column carries an offset the paper does not explain\. The text's Fig\. 6b statement \(P reproduced 'within 0\.78 %' at low and '0\.20 %' at high density, p\. 790\) is reproduced by neither column \(\-0\.41 to \-0\.04 % for the printed P, \-0\.08 to \+0\.17 % for P from eps\_r\)\. The regression's weighting is not stated\: fitted to P computed from eps\_r with relative weights, rather than to eps\_r, the same data give alpha\_e = 2\.181e\-40 and mu\_e = 0\.1052 D\. alpha\_e and mu\_e are strongly anticorrelated \(alpha\_e is a linear extrapolation in 1/T from 3\.19e\-3\-3\.92e\-3 /K to zero\)\.

REPRODUCTIONS OF THIS PAPER\: zhao\_2026's tsankova\_2018\_dp\_CO, 4\.888\(45\) cm^3/mol, is \(alpha\_e \- 0\.020e\-40\) N\_A/\(3 eps0\) = 4\.8880 cm^3/mol \(Bishop and Cheung's vibrational part removed; the 'interpolation to 297 K' changes nothing, alpha\_e being temperature\-independent in this fit\)\. Its uncertainty, 0\.045 cm^3/mol, is not this paper's\: alpha\_e's k = 2 uncertainty is 0\.050 cm^3/mol \(0\.025 at k = 1\); 0\.045 would correspond to 0\.020e\-40\.

Not extracted \(no quantity in the vocabulary\)\: Table 2, eps\_r and the Kirkwood molar polarization at a stated \(p, T\) \(a gas's static permittivity at a state\); mu\_e \(a dipole moment\); b\_eps \(a dielectric virial per unit A\_eps; the vocabulary's refractivity\_virial\_coefficient holds B\_eps = A\_eps b\_eps, which is temperature\-dependent here through A\_eps and not printed\); Table 1 \(the literature's \(T, p\) ranges, no values\); the figures \(no numbers beyond those printed\)\. The total static A\_eps\(T\) with the orientation term is not printed either; from the printed parameters it is 5\.2089, 5\.1907, 5\.1731 and 5\.1578 cm^3/mol at 255\.10, 273\.17, 293\.25 and 313\.28 K \(computed, not data\)\.

**Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

tsankova\_2018/alpha\_e\_CO
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_e_CO",
     "material": "CO",
     "table": "text",
     "quantity": "polarizability",
     "unit": "SI",
     "scale": 1e-40,
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "2 sigma"
     },
     "parameters": {
       "includes": "electronic + vibrational static polarizability (alpha_el + alpha_vib)"
     }
   }

1 inline points in the source record.

pp\. 789, 791 \(and abstract, p\. 784\)\: alpha\_e = \(2\.176 \+\- 0\.022\) x 10^\-40 C^2 m^2 J^\-1 \(C m^2/V\), relative combined expanded uncertainty 1\.01 % \(k = 2\), from a regression of Debye's virial form \(Eq\. 4\) to the static \(395 MHz\) permittivities of 255\-313 K and 2\-8 MPa, with Lemmon and Span's densities\. ELECTRIC\: electronic plus vibrational \(the infrared response is static at 395 MHz\), WITHOUT the orientation term mu\_e^2/3kT \(removed by the 1/T regression, mu\_e = 0\.107 D\) and without a magnetic term\. The value a static electric validator compares with a model's electronic and vibrational terms, not its rotational system \(TC\-751\)\. 13\.198 au\. Temperature\-independent by the fit's assumption over 255\-313 K\. The uncertainty includes the equation of state's 0\.3 % \(k = 2\) in density, common to all points; it is a derived \(regression\) value, anticorrelated with mu\_e \(source notes\)\.

Formulas
--------

tsankova\_2018/eq4\_CO
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq4_CO",
     "material": "CO",
     "equation": "Eqs. (1)-(4), pp. 785-786; the coefficients pp. 789-791",
     "printed": "(eps_r - 1)(2 eps_r + 1)/(9 eps_r) = rho (N_A/3 eps0)(a_e + mu_e^2/(3 k_B T))(1 + b_eps rho + c_eps rho^2); CO: a_e = 2.176 x 10^-40 C^2 m^2 J^-1 (1.01 %, k = 2), mu_e = 3.584 x 10^-31 C m (approximately 0.107 D; 1.3 %, k = 2), b_eps = (1.015 +- 0.044) cm^3 mol^-1 (k = 2), c_eps not fitted",
     "variable": "eps_r: static relative permittivity; rho: molar density (Lemmon and Span 2006, REFPROP 9.1); T: temperature in K (ITS-90); a_e in C^2 m^2 J^-1; mu_e in C m; b_eps in cm^3/mol; N_A = 6.0220e23 /mol, eps0 = 8.8542e-12 F/m, k_B = 1.3806e-23 J/K as printed",
     "state": "none (per molecule); rho the real-gas molar density",
     "density": "real",
     "range": "255.10-313.28 K, 2.0-8.0 MPa, rho <= 3.81 mol/dm^3 (p. 789); used by the authors to compare the literature's permittivities from 77 to 572 K (Fig. 7, p. 791)",
     "coefficients": {
       "a_e": "2.176",
       "mu_e": "3.584",
       "b_eps": "1.015"
     },
     "check": "With CoolProp 8.0.0's Lemmon-Span CO densities at Table 2's (T, p): an unweighted least-squares fit of Eq. (4) (c_eps = 0) to the 27 eps_r values gives a_e = 2.1772e-40, mu_e = 3.5665e-31 C m (0.10692 D), b_eps = 1.007 cm^3/mol (printed 2.176, 3.584, 1.015; the paper's constants or CODATA's make no difference). With the printed coefficients, eps_r - eps_fit is -21.6 to +20.9 ppm, within the 52 ppm (k = 2) and positive at 255.10 and 313.28 K, negative at 273.17 and 293.25 K (one 293.25 K point +16.3 ppm), as p. 790 describes Fig. 6a. Table 2's P_meas column is offset from its eps_r column by the equivalent of -47.7 +- 3.3 ppm in eps_r and gives a_e = 2.172e-40, mu_e = 0.1050 D, b_eps = 2.03 when fitted instead (source notes). Checked 2026-10-01."
   }

The coefficients' uncertainties are k = 2 \(pp\. 789\-790\)\. mu\_e's is 1\.3 % on p\. 790 but \+\-0\.001 D \(0\.93 %\) on p\. 791; b\_eps is 1\.014 on p\. 791 against 1\.015 on pp\. 784 and 790\. a\_e and mu\_e are strongly anticorrelated \(the orientation term is 4\.4\-5\.3 % of A\_eps over 255\-313 K\)\. The printed 0\.107 D is 3\.584e\-31 C m rounded \(0\.10745 D with 1 D = 3\.335641e\-30 C m\)\.

Corrections
-----------

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register </register>` for the checks and decisions.