Precise determination of refractometricparameters for anesthetic agent vapors

J. M. Allison, K. P. Birch, and J. G. Crowder

The absolute refractive indices of the anesthetic agent vapors isoflurane, sevoflurane, enflurane,halothane, and desflurane are determined to a typical uncertainty of 1 part in 107 over the respectivetemperature and pressure ranges of 15-40 0C and 5-45% of their saturated vapor pressures atwavelengths of 632.99, 594.10, and 543.52 nm. The specific refraction, second virial coefficients, anddispersion constants are also derived for each agent, from which an equation for the calculation of agentrefractivity is established that is in agreement with the measured data to within 2 x 10-8.

1. Introduction

For a number of years there has been a growing needto establish a traceable concentration measurementstandard, of suitable accuracy, for the anesthetic gasindustry. This standard can be realized through themeasurement of refractive index, but previously pub-lished datal 2 cover only a limited range of measure-ment conditions and have inadequate uncertaintyand no traceability. The application of these data isalso limited because the relationship between refrac-tivity and the measurement conditions is not knownwith sufficient accuracy. Consequently, there is arequirement for establishing precise refractivity val-ues that are traceable to national standards, and thederivation of the corresponding relationships for theanesthetic agents used in the health-care industry.

Ohmeda (a division of the BOC Group Plc), incollaboration with the National Physical Laboratory(NPL) and the Heriot-Watt University, have under-taken a program of research to develop a high-accuracy measuring system that has been used forthis purpose. This measurement system and itsoperation, described in detail elsewhere,3 are outlinedtogether with results for the anesthetic agents isoflu-rane, sevoflurane, enflurane, halothane, and desflu-

J. M. Allison is with Ohmeda, a division of BOC Group Plc,Station Road, Steeton, West Yorkshire BD20 6RB, United King-dom. K. P. Birch is with the Division of Mechanical and OpticalMetrology, National Physical Laboratory, Teddington, Middlesex TW11OLW, UK J. G. Crowder is with the Department of Physics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK.

Received 26 April 1993; revised manuscript received 19 August1993.

0003-6935/94/132459-06$06.00/0.© 1994 Optical Society of America.

rane over a range of pressures, temperatures, andwavelengths. From the measurement data for eachagent we derive the specific refraction, second virialcoefficients, molecular polarizabilities, and dispersionconstants, from which an equation for the calculationof agent refractivity will be established.

2. Measurement System

Here we describe the main elements of the measure-ment system designed to measure the absolute refrac-tivity of medical gases and vapors over a range oftemperatures, pressures, and wavelengths. The ex-perimental technique used for these measurements isalso described, together with the validation of themeasurement system.

Description of the Measurement System

The measurement system consists of a double-passJamin laser refractometer34 incorporating a dual-compartment gas cell, which is positioned so thateach chamber partially encloses one of the paths inthe interferometer. The cell, which is enclosed by awater jacket, can be evacuated, and a gas sample canbe admitted to the required pressure through amanifold. This arrangement, together with the mea-surement sensor and instrument configuration, isshown in Fig. 1. This configuration permits commu-nication with and receipt of data from the measure-ment sensors through RS232 serial interfaces incorpo-rated in each of the instruments.

The measurement sensors consist of an MKS In-struments type 398 differential manometer and plati-num resistance thermometers, which are automati-cally scanned by an Automatic Systems Laboratories

1 May 1994 / Vol. 33, No. 13 / APPLIED OPTICS 2459

Osc1.osope

Fig. 1. Schematic of measurement system: DVM, digital voltmeter.

Model F26 resistance bridge and Model 148/158scanner. The calibrations of these measurementsensors are traceable to national standards. Theoptical path difference in the refractometer is moni-tored by a bidirectional fringe counting-fractioninginstrument, FT Technologies type FT612AS.

The measurement system uses three separateHe-Ne laser sources that operate at the vacuumwavelengths of 632.99, 594.10, and 543.52 nm.These wavelengths were chosen to cover the disper-sion range of the refractometers currently used in theanesthetic gas industry.

Experimental Technique

One can measure the absolute refractivity of a gas orvapor by evacuating both cell chambers, followed bythe admission of the sample into one of the chambers.The resulting change in optical path length is relatedto refractivity (n - 1) by

NX(n 1) NA + (2.1)21~~~~~~21

where n is the refractive index, N is the inducedfringe change, is the vacuum wavelength of thesource, and I is the length of the cell. Because therefractive index of a vacuum is exactly unity, anyresidual gas pressure in the measurement chamber ofthe cell requires a correction () during the measure-ment process.

The cell and manifold, shown in Fig. 1, are initiallyevacuated to a pressure of less than 0.5 Pa, with allvalves open except V2, V4, and V5. The ball valve V8is switched to connect ports A and B. Once thevacuum gauges indicate that a steady vacuum hasbeen achieved, the differential manometer and fringecounting-fractioning unit are zeroed. One can thenisolate the two chambers by closing valve V3 beforethe sample is admitted into one of the chambers.

We measure the absolute refractivity of a gas byadmitting the gas through valve V5 into the evacu-ated central cell chamber to the required pressure, asindicated by the differential manometer. The gas isthen allowed to reach thermal equilibrium with the

cell before the mean temperature, the gas pressure,and the fringe change (N) are recorded.

We measure the absolute refractivity of a vapor byadmitting the vapor into the evacuated central cham-ber by using valves V6, V7, and V8. The manifold isevacuated up to the three-way valve (V8), which isswitched so that ports A and B are connected. Thesample is admitted in liquid form into the tube aboveport A so that this tube, valve V8, and the tube aboveport B are filled with liquid. Closing the meteringvalve (V7) and switching valve V8 to connect ports Aand C draw the liquid into the vacuum above valveV7. Liquid is then metered through valve V7 intothe evacuated central chamber, where it immediatelyvaporizes, until the required vapor pressure is reached.Valve V6 is then closed to seal the chamber becausethe metering valve does not shut off completely.This procedure ensures that there is no contamina-tion of the vapor from the atmosphere during admis-sion to the gas cell. The sample is again allowed toreach thermal equilibrium before the mean tempera-ture, the vapor pressure, and the fringe change (N)are recorded.

Validation of the Measurement System

To validate the measurement system we determinedthe refractivities of nitrogen and oxygen at atmo-spheric pressure over the temperature range of 15-40 C for comparison with NPL data normalized tothe same pressure and temperature conditions.5The NPL data have also been compared with valuesmeasured by the Swiss Federal Office of Metrology6and shown to be in good agreement within theexperimental uncertainties.

The measurement system uncertainty for nitrogenat atmospheric pressure was calculated to be ±8.6 x10-8 (Ref. 3), whereas that of the NPL data is ±5 x10-8 (Ref. 5), giving a combined value of ±9.9 x 10-8for the comparison. At room temperature (20 C)there is excellent agreement in the comparison, whichvalidates the measurement system to within thecombined uncertainty. However, there is a system-atic offset with temperature in the comparison ofboth gases, which is attributed to a difference be-tween the average measured temperature and thetrue gas temperature. A correction for this offsetwas calculated as a function of temperature with anuncertainty equal to that of the data comparison.After this correction has been applied the measure-ment data for both nitrogen and oxygen are inagreement with the NPL data to within ±2 x 10-8(Ref. 3). This correction has been applied to allsubsequent measurements.

3. Results and Analysis of Experimental Data

The absolute refractivities of the five anestheticagents, measured at a wavelength of 633 nm, areshown in Tables 1-5 over the respective temperatureand pressure ranges of 15-40 °C and 5-45% of theirsaturated vapor pressures (SVP's). This pressurerange was chosen so that condensation does not occur

2460 APPLIED OPTICS / Vol. 33, No. 13 / 1 May 1994

Table 1. Isoflurane Refractivity (n - 1) x 108 at a Wavelength of 633 nm

Pressure(kPa) 15 C 20 C 25 C 30 C 35 C 40 C

2 2899.7 2850.0 2801.9 2755.5 2710.6 2667.14 5807.5 5707.3 5610.6 5517.1 5426.8 5339.46 8723.4 8572.0 8426.0 8284.9 8148.7 8016.98 11647.4 11444.1 11248.1 11058.9 10876.2 10699.6

10 14579.5 14323.6 14077.0 13839.1 13609.4 13387.512 17519.8 17210.6 16912.7 16625.4 16348.2 16080.614 20468.3 20105.1 19755.2 19418.0 19092.8 18779.016 23425.1 23007.0 22604.6 22216.9 21843.2 21482.718 26390.1 25916.5 25460.8 25022.1 24599.3 24191.6

Table 2. Sevoflurane Refractivity (n - 1) x 10 at a Wavelength of 633 nm

Pressure(kPa) 15°C 20 C 25 C 30°C 35°C 40 C

1 1441.7 1417.0 1393.2 1370.1 1347.8 1326.22 2886.3 2836.6 2788.6 2742.3 2697.5 2654.23 4333.7 4258.7 4186.3 4116.5 4049.1 3983.94 5783.9 5683.3 5586.4 5492.8 5402.6 5315.45 7237.0 7110.5 6988.7 6871.2 6758.0 6648.66 8693.0 8540.3 8393.3 8251.7 8115.3 7983.67 10151.8 9972.6 9800.3 9634.3 9474.5 9320.48 11613.5 11407.5 11209.5 11019.0 10835.6 10659.09 13078.1 12845.0 12621.1 12405.8 12198.7 11999.3

Table 3. Enflurane Refractivity (n - 1) x 108 at a Wavelength of 633 nm

Pressure(kPa) 15 C 20 C 25 C 30 C 35 C 40 C

1 1451.4 1426.5 1402.5 1379.3 1356.9 1335.22 2904.9 2854.9 2806.7 2760.1 2715.1 2671.63 4360.6 4285.3 4212.6 4142.5 4074.8 4009.44 5818.4 5717.5 5620.3 5526.5 5435.9 5348.55 7278.4 7151.7 7029.6 6911.9 6798.4 6688.86 8740.6 8587.8 8440.7 8299.0 8162.3 8030.57 10204.9 10025.8 9853.5 9687.6 9527.7 9373.58 11671.5 11465.8 11268.0 11077.7 10894.5 10717.89 13140.2 12907.7 12684.3 12469.4 12262.6 12063.5

Table 4. Halothane Refractivity (n - 1) x 108 at a Wavelength of 633 nm

Pressure(kPa) 15 C 20 C 25 C 30 C 35 C 40 C

1.5 2255.4 2216.8 2179.5 2143.4 2108.6 2074.83.0 4514.6 4437.1 4362.2 4289.8 4219.9 4152.34.5 6777.8 6660.9 6548.2 6439.3 6334.1 6232.46.0 9045.0 8888.4 8737.4 8591.7 8451.1 8315.27.5 11316.1 11119.5 10930.0 10747.2 10570.9 10400.69.0 13591.1 13354.1 13125.8 12905.7 12693.5 12488.6

10.5 15870.1 15592.3 15324.9 15067.3 14818.9 14579.312.0 18153.1 17834.2 17527.4 17231.9 16947.2 16672.713.5 20440.0 20079.7 19733.1 19399.6 19078.4 18768.8

in the gas cell, but these measurements do cover therange of anesthetic agent partial pressures typicallyencountered in clinical practice.

An example of the measurement uncertainties inthe refractivity of halothane at 14 kPa is shown inTable 6, where the total uncertainty is shown to be

+ 11 x 10-8. The principal source of uncertainty canbe seen to be the measurement of pressure, which is+10.8 x 10-8, whereas that for refractivity is only+ 1.5 x 10-8. The total uncertainty is shown in Fig.2 to vary between ± 5 x 10-8 and ± 32 x 10-8 over thepressure range 1-45 kPa.

1 May 1994 / Vol. 33, No. 13 / APPLIED OPTICS 2461

Table 5. Desflurane Refractivity (n-1) x 108 at a Wavelength of 633 nm

Pressure(kPa) 15 C 20 C 25 C 300 C 35 C 40 C

5 5765.4 5666.0 5570.0 5477.2 5387.6 5301.010 11562.5 11360.8 11166.4 10978.7 10797.6 10622.615 17391.5 17084.8 16789.3 16504.6 16230.0 15965.020 23252.7 22838.0 22439.1 22055.0 21685.0 21328.425 29146.3 28620.8 28115.8 27630.1 27162.8 26712.830 35072.7 34433.3 33819.6 33230.2 32663.5 32118.335 41032.0 40275.9 39550.9 38855.2 38187.2 37545.240 47024.7 46148.6 45309.7 44505.5 43734.1 42993.445 53050.8 52051.9 51096.2 50181.2 49304.3 48463.2

The specific refraction and second virial coefficientsof the anesthetic agent vapors can be derived from theexperimental data. Refractive index (n) is related todensity (p) by the Lorentz-Lorenz equation

(n2- 1)(n2 + 2) = pR', (3.1)

where R' is the specific refraction. The vapor den-sity can be derived from the gas equation

PMP ZRT (3.2)

where P is the pressure in pascals, T is the absolutetemperature in kelvins, M is the molar mass, R is theuniversal gas constant, and Z is the compressibilityfactor. Therefore Eq. (3.1) becomes

n 2 -1 PMR'n2 + 2 ZRT (3.3)

The best correlation between (n2 - 1)/(n2 + 2) andpressure at a constant temperature was found to begiven by a second-order polynomial of the form

2- 12 + 2 = aP + bp2 , (3.4)

ideal; therefore when Z = 1,

n2- 1 1 MR'n2 + 2 P RT (3.5)

The specific refraction at a wavelength of 633 nmwas derived from Eq. (3.5) at each of the six tempera-tures for which refractivity was measured; the aver-age value, shown in Table 7, was calculated foreach agent to have a standard deviation of less than0.0002 x 10-4 m3 kg-'. The uncertainty in thespecific refraction data was determined from theaccuracy of the refractivity data to be ±0.0006 x 10-4m3 kg- 1. This uncertainty is equal to the 3a valuefor the specific refraction data, which indicates thatall the significant uncertainties have been taken intoaccount. The results also showed specific refractionto have no measurable dependence over the measure-ment range of temperatures and pressures. Substi-tuting the values for specific refraction into Eq. (3.3)permits Z to be calculated from the experimental dataas a function of pressure for each temperature.

The compressibility factor is also given by the virialequation

B(T)PRT 1 (3.6)

where B(T) is the second virial coefficient. Plottingwhere a and b are constants that were derived fromthe experimental data. The first term (aP) repre-sents the ideal gas behavior of the vapor, whereas thesecond term (bP2 ) represents the deviation from the

,_0

'-4

Table 6. Uncertainty In the Measurement of Halothane Refractivityat 14 kPa

99% ConfidenceInterval in

Physical RefractivityUncertainty Source Uncertainty (n - 1) x 108

Temperature measurement ±0.007 0C ± 1.1Pressure measurement ±5 Pa +10.8Refractivity measurement ±1 x 10-8 + 1.5Total uncertainty + 11.0

0 10 20 30 40 50

Pressure (kPa)

Fig.2. Uncertainty in the measurement of refractivity.

2462 APPLIED OPTICS / Vol. 33, No. 13 / 1 May 1994

40

030 0

0

020 01

0

010

00

C~~~~~~~~

Table 7. Specific Refraction at 633 nm

Specific Refraction (R')Anesthetic Agent (x 10-4 m3 kg-')

Isoflurane 1.2534Sevoflurane 1.1499Enflurane 1.2555Halothane 1.2149Desflurane 1.0930

Substituting Eqs. (3.8) and (3.9) into Eq. (3.7) andexpanding the left-hand side give

(n - 1)(n2+) 4IrPNAa(X)

= 3[RT + B(T)P3' (3.10)

where NA is Avogadro's constant. For gases n is veryclose to unity and (n + 1)/(n2 + 2) is approximatelyconstant; therefore, refractivity can be given by

Z - 1 against P/RT at a constant temperatureproduces a straight line, the gradient of which is B(T).Values derived for B(T) in this way are shown inTable 8, with an uncertainty determined from theaccuracy of the refractivity data to be 120 cm3

mol-1. Data compiled by Dymond and Smith7 give avalue of - 1371 ± 100 cm3 mol-1 for the second virialcoefficient of halothane at 25 C, which is in agree-ment with the derived value to within the measure-ment uncertainties.

From the values derived for specific refraction andthe second virial coefficient, the refractivity of theanesthetic agents can be calculated at a wavelength of633 nm for any pressure and temperature between 5and 45% SVP and 15 and 40 °C, respectively, bysubstituting Eq. (3.6) into Eq. (3.3), which gives

n2- 1n2 + 2

PMR'RT + B(T)P

Other parameters that can be derived are molarrefraction [R], which is related to specific refractionby

47rkPNAa(X)

3[RT + B(T)P]' (3.11)

where

1 n+1

k n2 + 2

A mean value for k for the five anesthetic agents wascalculated to be 1.50008. The use of this single valuefor all the agents contributes a worst-case additionaluncertainty of only 2 x 10-8 in calculating agentrefractivity for the five agents over the respectivetemperature and pressure ranges of 15-40 °C and5-45% SVP.

The refractivities of the anesthetic agents were alsomeasured at wavelengths of 594.10 and 543.52 nm.From these results the agent molecular polarizabili-ties were derived for each wavelength as describedabove; these are shown in Table 9. The uncertaintyin these values was determined from the accuracy ofthe refractivity data to be ± 0.003 x 10-30 m3 .

Away from an absorption band, refractivity can berelated to wavelength by the Cauchy equation

[R] = mR', (3.8)

where m is the molecular weight, and molecularpolarizability, which is given by

ot(k) -3[R] (3.9)4Tr

Molecular polarizability is a function of wavelengthand temperature. However, because specific refrac-tion was found to have no measurable dependence ontemperature, a(X) is assumed to be a function ofwavelength alone.

Table 8. Second Virial Coefficients

Second Virial Coefficient B(T)(cm3 mol-1)

Temperature Iso- Sevo- En- Halo- Des-(IC) flurane flurane flurane thane flurane

15 -1652 -2341 -1767 -1378 -130220 -1559 -2169 -1625 -1297 -123125 -1473 -2020 -1504 -1228 -116630 -1394 -1895 -1403 -1172 -110735 -1320 -1792 -1323 -1128 -105340 -1254 -1715 -1262 -1096 -1005

B' C'n -1 =A' + -+ - (3.12)

where X is the vacuum wavelength and A', B', and C'are constants. Molecular polarizability has beenshown to be approximately proportional to refractiv-ity; therefore, molecular polarizability can be given by

B Ca(x) = A + + -' (3.13)

where A, B, and C are constants. These constantswere derived for each agent by simultaneous equa-tions by using the data shown in Table 9; the resultsare shown in Table 10.

Table 9. Molecular Polarizability

Molecular Polarizability a(X)

Anesthetic (10-30 in)Agent X = 632.99 nm X = 594.10 nm A = 543.52 nm

Isoflurane 9.1666 9.1844 9.2193Sevoflurane 9.1205 9.1366 9.1649Enflurane 9.1827 9.2044 9.2340Halothane 9.5115 9.5370 9.5802Desflurane 7.2810 7.2908 7.3135

1 May 1994 / Vol. 33, No. 13 / APPLIED OPTICS 2463

Table 10. Constants in the Dispersion Equation

Anesthetic A B CAgent (10-30 m3) (10-30 m5 ) (10-30 M7 )

Isoflurane 9.1184 -0.0102 0.0118Sevoflurane 9.0299 0.0263 0.0040Enflurane 8.9374 0.1282 -0.0120Halothane 9.3445 0.0593 0.0031Desflurane 7.3047 -0.0434 0.0136

Substituting Eq. (3.13) into Eq. (3.11) gives

4iTkPNA / B Cn -1 A+- -.3[RT + B(T)P] X2 X4 (3.14)

The constants A, B, C, and k and the second virialcoefficient B(T) have all been derived from the experi-mental data; the refractive index can be calculated forany pressure between 5 and 45% SVP, any tempera-ture between 15 and 40 C, and any wavelengthbetween 544 and 633 nm.

A comparison of values calculated from Eq. (3.14)with the experimental data is shown in Fig. 3 forenflurane. The figure shows the difference betweenthe calculated and measured values as a function ofpressure at a constant temperature at 20 C for threewavelengths. The calculated and measured valuesare in agreement to within 1.3 x 10-8, whichillustrates the high precision of the measurementsand analysis.

As we discussed in Section 1, the previously pub-lished datal 2 cover only a limited range of measure-ment

2

C

-i

Fig. 3.refracti

and no traceability. The application of these data isalso limited because the relationship between refrac-tivity and the measurement conditions is not knownwith sufficient accuracy. Consequently, it is imprac-tical to compare these data with those derived in thispaper.

4. Summary

Through the use of an interference gas refractometer,the refractivities of five anesthetic agent vapors havebeen precisely measured over the respective pressureand temperature ranges of 5-45% SVP and 15-40 Cat wavelengths of 632.99, 594.10, and 543.52 nm, andthe results have been presented. The derivation ofthe second virial coefficients, molecular polarizabili-ties, and dispersion constants for each agent is alsodescribed, from which an equation for the calculationof agent refractivity has been established.

These results provide precise refractivity valuesthat are traceable to national standards for all theinhalation anesthetic gases used in the industry.A comparison has been made with previously pub-lished virial coefficient data that agrees within theexperimental uncertainties. The application of thisdata to concentration measurement by refractom-etry, which will be discussed in detail in a futurepublication, will reduce current uncertainties to lessthan 0.1%. The instrument is currently beingused to investigate interactions between the anes-thetic agent vapors and the medical carrier gases,which may lead to the derivation of correction termswhen Eq. (3.14) is employed in this case.

conditions and have inadequate uncertainty References1. W. Nebe, "Interferometrische Messungen von Halothan-

Konzentrationen," Carl Zeiss J. 10, (1965).2. B. R. Sugg, E. Palayiwa, W. L. Davies, R. Jackson, T. Mc-

0 633 nm Graghan, P. Shadbolt, S. J. Weller, and C. E. W. Hahn, "AnV 594 nm automated interferometer for the analysis of anaesthetic gasA 5 mixtures," Br. J. Anaesth. 61, 484-491 (1988).

3. J. M. Allison, K. P. Birch, and J. G. Crowder, "A measurement

A A v system for the precise determination of the refractive indices ofanaesthetic agent vapours," Meas. Sci. Technol. 4, 571-577(1993).

v u Ei4. M. J. Downs and K. P. Birch, "Bi-directional fringe countingv E v interference refractometer," Precis. Eng. 5, 105-110 (1983).

0 A 5. K. P. Birch, "Precise determination of refractometric param-

A A 0 eters for atmospheric gases," J. Opt. Soc. Am. A 8, 647-651

A (1991).Cy7 , 6. R. Thalmann and W. Hou, "Development of a high accuracy air

1 2 3 4 5 6 7 8 9 1o refractometer," in Proceedings of the Fourth InternationalSymposium on Dimensional Metrology (International Society

Pressure (xPa) for Metrology in Quality Control, Tampere, Finland, 1992).Difference between calculated and measured enflurane 7. J. H. Dymond and E. B. Smith, The Virial Coefficients of Pure

vity. Gases and Mixtures (Oxford U. Press, London, 1980).

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