hohm_1991
=========

U\. Hohm and K\. Kerl, "Interferometric Determination of Mean Polarizabilities and Second Density Virial Coefficients of Methane Between 128 K and 890 K", Ber\. Bunsenges\. Phys\. Chem\. 95, 36 \(1991\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/hohm_1991.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1002/bbpc\.19910950107 <https://doi.org/10.1002/bbpc.19910950107>`__

**Source kind:** measurement

**Recorded technique:** The Michelson twin interferometer of hohm\_1990 \(Meas\. Sci\. Technol\. 1, 329\), its pipe furnace replaced by a liquid\-nitrogen cooling jacket for 128\-298 K \(range Delta T\_I; temperature stable to 0\.2 K over a 90 min measurement\); He\-Ne laser at the vacuum wavelength 632\.99\(10\) nm \(for the dispersion, four He\-Ne lasers at 632\.99, 611\.97, 594\.11 and 543\.51 nm simultaneously, as in hohm\_1990b\)\. CH4 is filled to p\_max \< 0\.3 MPa \(below 2/3 of its vapour pressure\), thermostated 30\-60 min and pumped out isothermally in 4\-11 pressure steps; \(n \- 1\)\_i = Delta N\_i lambda/\(2 L\(T\_i\)\) \(Eq\. 7\) at the ideal\-gas density rho\_0i = p\_i/RT\_i; pressure to about 50 Pa \(dynamic difference transducer\), temperature to 0\.1 K \(NiCr\-Ni thermocouples\)\. The 760\-890 K range \(Delta T\_II\) is the earlier furnace data re\-evaluated \(pp\. 36\-38\)\.

**Materials in structured entries:** CH4

**Dataset quantities:** polarizability

**Contents:** 1 dataset; 2 formulas.

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

Identity checked against the title page \(journal p\. 36 starts on pdf page 1 below the end of the previous article, whose references occupy the top of the page; the last pdf page continues into an unrelated article on sputtering\)\. Page numbers are the journal's \(36\-42\)\: p\. = pdf page \+ 35\. The paper kerl\_1992 cites as its CH4 source \(note d, \[26\]\) and hohm\_1994c as ref\. \[17\]\.

REDUCTION \(pp\. 36\-38\)\. LL\* = \[\(n^2 \- 1\)/\(n^2 \+ 2\)\]/rho\_0 = sum\_\(i=1\)^m A\_i\(lambda, T\) rho\_0^\(i\-1\) \(Eq\. 1\), rho\_0 = p/RT \(R = 8\.31451 J/\(K mol\)\), fitted with m = 3 and weights \(rho\_0i/rho\_0,min\)^2; A\_1 = \(4/3\) pi N\_A alpha\_0\(lambda, T\) \(Eq\. 2, N\_A = 6\.0221367e23\), the polarizability volume of the free molecule \(zero density, so no state\); A\_2/A\_1 = b\_R \- B\(T\) \(Eq\. 3\), with the refractivity virial estimated as b\_R = A\_1/4 \(Eq\. 5; about 1\.6 cm^3/mol at 298 K, against measured 0\.887\(30\) at 323\.15 K \[6\] and 1\.18\(20\) at 298 K \[9\], p\. 37\)\. A\_3 absorbs all residuals and has no physical meaning\. 'As usual standard deviation of measured quantities \(e\.g\. in Tables 1 and 2\) are given in parentheses \(e\.g\. 128\.53\(4\) means 128\.53 \+\- 0\.04\)' \(p\. 36\)\: the sigma column is one standard deviation\.

TABLE 2 \(p\. 39\)\: alpha\_0\(632\.99 nm, T\) and \-B\(T\) at 16 temperatures \(dataset alpha\_T\_CH4\)\. Each Delta T\_I point is one measurement \(the earlier 300\-1000 K data of hohm\_1990 are means of many, p\. 38\)\. The two lowest temperatures \(128\.53, 135\.58 K\) were also evaluated with alpha\_0 fixed at the extrapolation of hohm\_1990's Eq\. \(20\) \(2\.605265 at 128\.53 K, reproduced here to all digits\) and without weights; Table 1 \(p\. 38\) compares, at 128\.53 K, the free fit \(alpha\_0 = 2\.6151\(44\), B = \-67\(77\) cm^3/mol, \|Delta LL\*\| = 2\.7e\-9 m^3/mol\) and the constrained fit \(B = \-245\(20\), 3\.6e\-9\)\. Table 2 prints for 128\.53 K the free\-fit alpha\_0 \(2\.6151\(44\)\) beside the constrained\-fit B \(245\(20\)\)\: the alpha\_0 column is the free fit\. The 769\.02 and 885\.19 K rows are 're\-calculated measurements of B\(T\)' of Hohm's dissertation \[1\] \(p\. 38\)\. Estimated maximum uncertainty \(Eq\. 8, Table 3, p\. 40\)\: \|Delta alpha\_0/alpha\_0\| = 6\.0e\-4 at 296 K and 13\.7e\-4 at 128 K \(\|Delta alpha\_0\| = 1\.5e\-33 and 3\.7e\-33 m^3\), from \|Delta T/T\| 0\.4e\-4 and 3\.1e\-4, \|Delta p/p\| 2\.1e\-4 and 7\.2e\-4, \|Delta\(n \- 1\)/\(n \- 1\)\| = 3\.3e\-4 \(p\. 39\)\.

THE MINIMUM NEAR T\_c\. alpha\_0 shows 'an obvious minimum' near the critical temperature 190\.53 K \(2\.59684 at 188\.14 K beside 2\.61833 at 188\.75 K\), with a large scatter of B\(T\) there \(p\. 39\)\. 'In our opinion, this obvious minimum follows from the mathematical extrapolation to zero density according to Eq\. \(1\), which may not give the required real polarizability of the isolated molecule' \(p\. 40\)\: the authors do not attribute it to the free molecule\. Apart from it, the low\-temperature alpha\_0 are 'in good accordance' with hohm\_1990's high\-temperature formula extrapolated \(Fig\. 2, not digitised\)\: alpha\_0 is nearly independent of T below 300 K\. The mean of the 14 Delta T\_I values is 2\.6064 \(computed\); hohm\_1990's Eq\. \(20\) gives 2\.6053 at 128\.53 K, 2\.6070 at 296\.25 K, 2\.6215 at 769\.02 K \(this paper 2\.6164\(11\), \-0\.19 %\) and 2\.6278 at 885\.19 K \(2\.628435\(62\), \+0\.03 %\) \(computed 2026\-09\-27\)\. At 296\.25 K this paper's 2\.61100\(38\) is 0\.15 % above hohm\_1990's formula \(2\.6070\) and above hohm\_1993's 17\.5929\(17\) au = 2\.6070 angstrom^3 at 294\.47 K and 632\.99 nm \(x 0\.14818474; computed\), which agree with each other\: the one room\-temperature Delta T\_I measurement sits 4 of its standard deviations high\.

B\(T\) \(Table 2, the thermodynamic second virial coefficient; no quantity in the vocabulary, not extracted as data\), \-B/\(cm^3 mol^\-1\) at T/K\: 128\.53\: 245\(20\); 135\.58\: 215\(10\); 168\.77\: 168\(12\); 180\.86\: 121\(20\); 188\.14\: 126\.9\(3\.3\); 188\.75\: 131\.7\(3\.7\); 194\.98\: 100\.6\(4\.6\); 205\.25\: 113\.3\(5\.4\); 206\.19\: 88\.7\(3\.3\); 217\.21\: 105\.2\(7\.2\); 244\.62\: 62\.5\(3\.9\); 260\.82\: 54\.2\(5\.2\); 272\.11\: 51\.0\(7\.8\); 296\.25\: 44\.7\(6\.3\); 769\.02\: \-15\(10\); 885\.19\: \-34\.0\(0\.9\)\. It is B\(T\) = b\_R \- A\_2/A\_1 with the assumed b\_R = A\_1/4, so it is not a refractivity virial\: the measured quantity A\_2/A\_1 = b\_R \- B could be recovered as A\_1/4 \+ \(\-B\) \(a decision left to review\)\. Lennard\-Jones \(12\-6\) parameters from these B\(T\)\: eps/k = 139\.9 K, sigma = 403 pm \(p\. 40\); Table 3's \|Delta B\| 12\.7 and 44\.0 cm^3/mol at 296 and 128 K\. Near T\_c the B\(T\) are 'somewhat falsified' by the unresolved third coefficient \(p\. 40\)\.

DISPERSION \(p\. 39\)\. Measured at several Delta T\_I temperatures with the four lasers \(hohm\_1990b's method\); the individual alpha\_0\(lambda\_i, T\) and the per\-temperature f0, omega\_0 are not printed; 'no clear temperature dependence of these effective molecular parameters', 'the mean standard deviation of the fit \(6\) is better than \|Delta alpha\| = 2e\-34 m^3 or 0\.01 %', and the arithmetic means over Delta T\_I are f0 = 4\.646\(20\), omega\_0 = 2\.1460\(48\)e16 s^\-1 \(formula eq6\_mean\), against f0 = 4\.759, omega\_0 = 2\.1667e16 of Kerl's dispersion curve at 293\.05 K \[13\] \(formula eq6\_kerl\_1982\)\. C6 = 3 f0^2/\(4 E0^3\) = 115\.8\(1\.3\) a\.u\., the mean of the Delta T\_I C6 values \(literature 118 \[13\] with the same estimate, 151 \[20\] Margenau and Kestner\); no quantity\. Figs\. 1\-4 \(LL\* against rho\_0 at 128\.53 K; alpha\_0\(T\); the dispersion curves at 296\.25, 128\.53 and 293\.05 K; B\(T\)\) are not digitised\.

REPRODUCTIONS ELSEWHERE\: kerl\_1992's CH4 Eq\. \(10\) fit is fitted to these data and hohm\_1990's \(its note d; re\-pointed 2026\-09\-27\)\.

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

Datasets
--------

hohm\_1991/alpha\_T\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_T_CH4",
     "material": "CH4",
     "file": "CH4/hohm_1991__alpha_T_CH4.csv",
     "table": "tbl_ca1d21fe5b0e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_range_k": "128.53-885.19"
     }
   }

Table 2 \(p\. 39\)\: alpha\_0\(632\.99 nm, T\) of the free molecule \(10^\-30 m^3\), rows = temperature in K \(128\.53\-885\.19; the temperature's own standard deviation is in the printed column\)\. Standard deviations in the sigma column \(p\. 36\)\. Single measurements in 128\-298 K; a minimum near T\_c = 190\.53 K \(188\.14 and 194\.98 K\) that the authors attribute to the zero\-density extrapolation, not to the molecule \(p\. 40\); the 128\.53 K value is the unconstrained fit \(Table 1\)\. The 769\.02 and 885\.19 K rows are re\-evaluated furnace data \(Hohm's dissertation\)\. use = check\: temperature\-dependent data outside the fits' room\-temperature scope \(decided at review\); the 296\.25 K point is the room\-temperature measurement\.

Formulas
--------

hohm\_1991/eq6\_mean
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq6_mean",
     "material": "CH4",
     "equation": "Eq. (6), p. 37, with the mean constants on p. 39",
     "printed": "alpha_0(omega) = [e^2/(4 pi eps0 m)] f0/(omega_0^2 - omega^2); f0 = 4.646(20), omega_0 = 2.1460(48) x 10^16 s^-1 (arithmetic means over 128-298 K)",
     "variable": "omega = 2 pi c/lambda in s^-1, lambda the vacuum wavelength; alpha_0: polarizability volume of the free molecule in m^3; e^2/(4 pi eps0 m) = 253.2638 m^3 s^-2",
     "range": "543.51-632.99 nm, 128-298 K (the fitted data); the static limit is an extrapolation",
     "coefficients": {
       "f0": "4.646",
       "f0_sigma": "0.020",
       "omega0": "2.1460e16",
       "omega0_sigma": "0.0048e16"
     },
     "check": "At 632.99 nm gives 2.6051 angstrom^3, against Table 2's 128-298 K values 2.5968-2.6183 (mean 2.6064) and 2.61100(38) at 296.25 K (-0.23 %); static limit 2.5550; C6 = 3 f0^2/(4 omega0*^3) with omega0* = 0.519093 au is 115.74, the printed mean 115.8(1.3). Checked 2026-09-27."
   }

The mean of the per\-temperature fits of Eq\. \(6\) to the four wavelengths \(each fit's standard deviation better than 2e\-34 m^3, 0\.01 %\)\. Since the individual fits are not printed and alpha\_0 scatters with temperature by 0\.8 %, this formula gives the shape of the dispersion rather than the absolute level at any one temperature\.

hohm\_1991/eq6\_kerl\_1982
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq6_kerl_1982",
     "material": "CH4",
     "equation": "Eq. (6), p. 37, with the constants of ref. [13] quoted on p. 39",
     "printed": "alpha_0(omega) = [e^2/(4 pi eps0 m)] f0/(omega_0^2 - omega^2); f0 = 4.759, omega_0 = 2.1667 x 10^16 s^-1 (the dispersion curve for T_3 = 293.05 K of Ref. [13])",
     "variable": "as eq6_mean",
     "range": "400-700 nm at 293.05 K (Kerl's data, p. 39)",
     "coefficients": {
       "f0": "4.759",
       "omega0": "2.1667e16"
     },
     "reproduced_from": [
       "K. Kerl, Ber. Bunsenges. Phys. Chem. 86, 812 (1982)"
     ],
     "check": "At 632.99 nm gives 2.6168 angstrom^3 (+0.22 % against eq6_mean); C6 = 117.99 a.u., the printed 118 [13]. Checked 2026-09-27."
   }

Kerl's single\-term fit of 'a lot of data measured at T = 293\.05 K in the full wavelength range between 400 nm and 700 nm by means of a different technique' \(p\. 39\), quoted for comparison \(Fig\. 3\)\. The original is not in the library\.

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.