bose_1972
=========

T\. K\. Bose, J\. S\. Sochanski and R\. H\. Cole, "Dielectric and Pressure Virial Coefficients of Imperfect Gases\. V\. Octopole Moments of CH4 and CF4", J\. Chem\. Phys\. 57, 3592 \(1972\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/bose_1972.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1063/1\.1678813 <https://doi.org/10.1063/1.1678813>`__

**Source kind:** measurement

**Recorded technique:** Static dielectric constants of CH4 \(and CF4\) from three\-terminal parallel\-plate capacitance cells and a decade transformer bridge \(Orcutt and Cole 1967; Sutter and Cole 1970\)\. B\_eps and C\_eps from the cyclic expansion technique \(Sutter and Cole\)\: f = \(eps \- 1\)/\(eps \+ 2\) at densities in the accurately known ratio R = d\_\(i\+3\)/d\_i, Delta f\_i = f\_i \- R^\-1 f\_\(i\+3\) fitted as a polynomial in f\_i \(Eq\. 3\), giving B\_eps/A\_eps^2 and the f\_i^3 coefficient; A\_eps and B\_eps \- A\_eps B\_p from a quadratic fit of f against P/RT at known pressures below 14 atm \(Eqs\. 1\-2\)\. At 6\.6, 49 and 100 degrees C \(Table I\: 279\.8, 322\.5, 373\.4 K\), 1\-100 atm\. Matheson research\-grade CH4\: CO2 \< 10 ppm, O2 6 ppm, N2 19 ppm, C2H6 34 ppm, C3H8 \< 5 ppm \(mass spectrometry\) \(pp\. 2\-3\)\.

**Materials in structured entries:** CH4

**Dataset quantities:** molar\_refractivity, refractivity\_virial\_coefficient

**Contents:** 8 datasets; 0 formulas.

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

Identity checked against the first page \(pdf page 1 is the publisher's cover; journal p\. 3592 is pdf page 2\)\. Page numbers below are pdf pages\.

WHAT THE VALUES ARE\. f = \(eps \- 1\)/\(eps \+ 2\) = A\_eps d \+ B\_eps d^2 \+ C\_eps d^3 \+ \.\.\. \(Eq\. 1, d the molar density\)\: A\_eps is the static \(audio\-frequency\) molar polarization, for non\-polar CH4 the static polarizability, electronic plus the vibrational \('atomic'\) part; B\_eps and C\_eps are the STATIC DIELECTRIC second and third virial coefficients, not the optical refractivity virials\. B\_eps = B\_ind \+ B\_or \(p\. 3\)\: B\_or, the orientation polarization from the dipole induced in one molecule by the octopole moment of the other \(Eq\. 4\), varies as 1/T; from B\_eps against 1/T \(Fig\. 3\) the authors derive B\_ind = 2\.5 cm^6 mol^\-2 for CH4 \('necessarily somewhat crude and uncertain', about one\-third of B\_eps\) and the octopole moment Omega = 3\.0e\-34 esu \(CF4\: 4\.4e\-34\), with Lennard\-Jones 12\-6 parameters eps\_0/k = 137 K, sigma\_0 = 3\.88 Angstrom \(pp\. 3\-4\); 'trusting them to within, say 20 %' \(p\. 5\)\. So the B\_eps here are orientation\-dominated and exceed the optical B\_R\: they are stored as refractivity\_virial\_coefficient \(order 2, and C\_eps order 3\) at infinite wavelength, use = check, never as an optical virial\.

Uncertainty\: 'Derived values of A\_eps, B\_eps, and C\_eps are given in Table I, the error figures being three standard deviations from the least squares fit' \(p\. 3\); stored as '3 sigma'\. Fig\. 3's error bars are also three standard deviations\.

Text \(p\. 3\)\: 'The values of A\_eps from this work which we consider best are 6\.541 \+\- 0\.003 cm^3 mol^\-1 for CH4 and 9\.678 \+\- 0\.003 cm^3 mol^\-1 for CF4, corresponding to polarizabilities 2\.593e\-24 cm^3 for CH4 and 3\.838e\-24 cm^3 for CF4' \(6\.541 = the 322\.5 K value and near the three\-temperature mean 6\.541; 3 A\_eps/\(4 pi N\_A\) = 2\.5928e\-24 cm^3, checked 2026\-09\-26\)\. Earlier values cited by Maryott and Buckley\: 6\.53 \(CH4\); 9\.7, 9\.73, 10\.1 \(CF4\)\. The best CH4 value is entered inline \(A\_eps\_best\_CH4\)\.

Not extracted\: CF4 \(not a curated species\)\: A\_eps 9\.678 \+\- 0\.002, 9\.679 \+\- 0\.004, 9\.690 \+\- 0\.002; B\_eps 11\.35 \+\- 0\.44, 10\.54 \+\- 0\.64, 9\.17 \+\- 0\.75; C\_eps \-836 \+\- 92, \-764 \+\- 218, \-735 \+\- 237 at 279\.8, 322\.5, 373\.4 K \(Table I\); B\_ind\(CF4\) = 3\.5\. Table II, the pressure second virial coefficients \-B\_p \(cm^3 mol^\-1\) from the low\-pressure dielectric data \(errors three standard deviations, p\. 3\) with values interpolated from Dymond and Smith \(1969\)\: CH4 52\.9 \+\- 1\.4 \(lit\. 50\.9\), 35\.8 \+\- 2\.3 \(34\.8\), 21\.8 \+\- 1\.0 \(21\.0\); CF4 104\.6 \+\- 1\.7 \(105\.0\), 74\.0 \+\- 1\.4 \(70\.9\), 43\.0 \+\- 1\.0 \(43\.4\) at the three temperatures\: an equation\-of\-state quantity with no optmat quantity\. The octopole moments and the octopole\-octopole correction \(\_1B\_OmegaOmega = 0\.1 cm^6 mol^\-2 for CH4 at 6\.6 degrees C, p\. 4\) are not optical quantities\.

Reproductions\: achtermann\_1991's B\_eps\_bose\_1972\_279\.8\_CH4, \_322\.5\_CH4 and \_373\.4\_CH4 \(its Table III, Ref\. 45\) reprint this paper's B\_eps digit for digit; hohm\_2013 cites it \(its Ref\. 173\) in the CH4 dielectric mean\.

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

Datasets
--------

bose\_1972/A\_eps\_CH4
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "A_eps_CH4",
     "material": "CH4",
     "file": "CH4/bose_1972__A_eps_CH4.csv",
     "table": "tbl_36d8a70060d0",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "3 sigma"
     },
     "parameters": {
       "includes": "electronic + vibrational static polarizability (row = temperature, K)"
     }
   }

Table I A\_eps \(cm^3 mol^\-1\) of CH4 at 279\.8, 322\.5, 373\.4 K \(rows = temperature, K\)\: the static \(audio\-frequency\) molar polarization, the electronic plus vibrational static polarizability of non\-polar CH4 \(the vibrational part is about 0\.09 cm^3/mol, HITRAN's 0\.24 au\)\. Rises by 0\.006 \(0\.09 %\) from 279\.8 to 373\.4 K, 1\.7 times the combined three\-sigma errors; as the slope A\_tau of schmidt\_2003's Eq\. \(9\) that is 0\.0175 cm^3/mol, the 'A\_tau ~ 17e\-3' Schmidt and Moldover attribute to this paper \(their p\. 22; their own 0\.006 to 0\.011\)\. A check on the static limit \(its use is decided at review\)\.

bose\_1972/A\_eps\_best\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "A_eps_best_CH4",
     "material": "CH4",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "3 sigma"
     },
     "parameters": {
       "includes": "electronic + vibrational static polarizability"
     }
   }

1 inline points in the source record.

p\. 3\: 'The values of A\_eps from this work which we consider best are 6\.541 \+\- 0\.003 cm^3 mol^\-1 for CH4', corresponding to 2\.593e\-24 cm^3\. The authors' choice from Table I \(the 322\.5 K value; the three\-temperature mean is also 6\.541\)\: not independent of A\_eps\_CH4\. No temperature is attached\. Error level as Table I's \(three standard deviations\)\.

bose\_1972/B\_eps\_279\.8\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "B_eps_279.8_CH4",
     "material": "CH4",
     "file": "CH4/bose_1972__B_eps_279.8_CH4.csv",
     "table": "tbl_36d8a70060d0",
     "quantity": "refractivity_virial_coefficient",
     "unit": "cm6/mol2",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "3 sigma"
     },
     "parameters": {
       "order": 2,
       "temperature_k": 279.8
     }
   }

Table I B\_eps = 8\.14 \+\- 0\.29 cm^6 mol^\-2 at 279\.8 K\: the STATIC DIELECTRIC second virial coefficient, B\_ind \+ B\_or with the octopole\-induced orientation term B\_or \(about two\-thirds by the authors' B\_ind = 2\.5\)\. Not the optical refractivity virial B\_R\: a check only \(B\_eps \- B\_R measures B\_or\)\.

bose\_1972/B\_eps\_322\.5\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "B_eps_322.5_CH4",
     "material": "CH4",
     "file": "CH4/bose_1972__B_eps_322.5_CH4.csv",
     "table": "tbl_36d8a70060d0",
     "quantity": "refractivity_virial_coefficient",
     "unit": "cm6/mol2",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "3 sigma"
     },
     "parameters": {
       "order": 2,
       "temperature_k": 322.5
     }
   }

Table I B\_eps = 7\.29 \+\- 0\.32 cm^6 mol^\-2 at 322\.5 K\: static dielectric, as B\_eps\_279\.8\_CH4\.

bose\_1972/B\_eps\_373\.4\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "B_eps_373.4_CH4",
     "material": "CH4",
     "file": "CH4/bose_1972__B_eps_373.4_CH4.csv",
     "table": "tbl_36d8a70060d0",
     "quantity": "refractivity_virial_coefficient",
     "unit": "cm6/mol2",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "3 sigma"
     },
     "parameters": {
       "order": 2,
       "temperature_k": 373.4
     }
   }

Table I B\_eps = 6\.75 \+\- 0\.29 cm^6 mol^\-2 at 373\.4 K\: static dielectric, as B\_eps\_279\.8\_CH4\.

bose\_1972/C\_eps\_279\.8\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "C_eps_279.8_CH4",
     "material": "CH4",
     "file": "CH4/bose_1972__C_eps_279.8_CH4.csv",
     "table": "tbl_36d8a70060d0",
     "quantity": "refractivity_virial_coefficient",
     "unit": "cm9/mol3",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "3 sigma"
     },
     "parameters": {
       "order": 3,
       "temperature_k": 279.8
     }
   }

Table I C\_eps = \-297 \+\- 48 cm^9 mol^\-3 at 279\.8 K \(the header's unit extracts as 'cm9 mol\-8'; the image prints mol^\-3\)\: the static dielectric third virial coefficient, from the f\_i^3 term of the cyclic\-expansion fit \(Eq\. 3\) and the quadratic low\-pressure fit\. Not an optical C\_R\: a check only\.

bose\_1972/C\_eps\_322\.5\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "C_eps_322.5_CH4",
     "material": "CH4",
     "file": "CH4/bose_1972__C_eps_322.5_CH4.csv",
     "table": "tbl_36d8a70060d0",
     "quantity": "refractivity_virial_coefficient",
     "unit": "cm9/mol3",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "3 sigma"
     },
     "parameters": {
       "order": 3,
       "temperature_k": 322.5
     }
   }

Table I C\_eps = \-268 \+\- 50 cm^9 mol^\-3 at 322\.5 K\: static dielectric, as C\_eps\_279\.8\_CH4\.

bose\_1972/C\_eps\_373\.4\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "C_eps_373.4_CH4",
     "material": "CH4",
     "file": "CH4/bose_1972__C_eps_373.4_CH4.csv",
     "table": "tbl_36d8a70060d0",
     "quantity": "refractivity_virial_coefficient",
     "unit": "cm9/mol3",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "3 sigma"
     },
     "parameters": {
       "order": 3,
       "temperature_k": 373.4
     }
   }

Table I C\_eps = \-238 \+\- 48 cm^9 mol^\-3 at 373\.4 K\: static dielectric, as C\_eps\_279\.8\_CH4\.

Formulas
--------

No formulas are recorded.

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.