Optical constants of liquid methane in the infrared* Lary W. Pinkley,t P. P. Sethna, and Dudley Williams Department of Physics, Kansas State University, Manhattan, Kansas 66506 (Received 21 September 1977) The near-normal incidence spectral reflectance R(v) of liquid methane at 98 K has been measured in the infrared in the spectral range 6700-350 cm-'. The resulting values of R(v) have been subjected to Kramers-Kronig phase-shift analysis to provide values of the real n(v) and imaginary k(v) parts of the complex index of refraction N(s) = n(v) + ik(v) in the range 4000-400 cm-'. The results of the present study are presented in graphical form and in tabular form over this range. The strengths S = Sk(v) dv of the absorption bands are compared with the corresponding bands in gaseous methane. Techniques for using the present results to obtain approximate values of the corresponding optical constants of solid methane are discussed. Methane in condensed states is believed to be an impor- tant component of the cloud cover of the outer planets of the solar system. It is important to have a knowledge of the op- tical constants of this material in the infrared for use in the interpretation of proposed studies of these planets from space probes as well as for use in the interpretation of observations being conducted at ground-based observatories. The present work on liquid methane was undertaken as a first step in ac- quiring the needed information. We selected liquid methane for study because the reflection techniques developed in our recent studies' are more readily applied to liquids than to solids. In some of these earlier studies 2 we have shown that valid estimates of the optical properties of solids can be ob- tained from the measured properties of the corresponding liquids; it is therefore to be hoped that our present work will also provide approximate values of the optical constants of solid methane, which is probably more abundant than liquid methane in planetary cloud covers. Methane is a very interesting material from many points of view. The methane molecule CH 4 is a spherically sym- metric molecule that has certain spectroscopic properties that have long been of interest to theorists and experimentalists alike. The spectrum of gaseous methane is characterized by the followingfundamental vibration-rotation bands:3: vi(al) at 2914 cm'1, v 2 (e) at 1526 cm- 1 , v3(f 2 ) at 3020 cm- 1 , and v 4 (f 2 ) at 1306 cm-'. There are numerous much weaker overtone and combination bands in the spectrum of the gas. The study of the finer details of these bands continues to be a topic of major interest to spectroscopists; with every improvement in the resolving power of spectrographs, further information is obtained. 4 The intermolecular forces between methane molecules are very small, as evidenced by the low boiling point 109.1 K and the low melting point 90.7 K for the material; the vapor pressure of methane is high over most of its relatively narrow liquid range. Even solid methane at its melting point has a vapor pressure of 70 Torr. EXPERIMENTAL WORK Our experimental work involved the measurement of spectral reflectance R(v) of methane at near-normal incidence. The liquid methane was obtained by the condensation of UHP 99.97% gaseous methane (Matheson) in a copper coil im- mersed in liquid nitrogen. Samples of the liquid were placed in a shallow glass beaker suspended inside a Dewar vessel containing liquid nitrogen. By adjustment of the height of the beaker above the liquid nitrogen surface, wewere able to control the temperature of the liquid methane. The tem- perature of the liquid methane was monitored by means of a thermocouple; in the course of our study, measurements were made for samples at various temperatures over most of the liquid range. The results we report can be regarded as typical of liquid methane at a nominal temperature of 98 K near the middle of the liquid range. . Samples in the beaker were maintained at a depth of several centimeters; the level of the free surface of the liquid methane was monitored by means of a cathetometer with viewing through an unsilvered portion of the Dewar walls. Because of sample loss due to the high vapor pressure of the liquid, it was necessary at frequent in- tervals to refill the beaker with liquid methane. Probably as a result of the rapid evaporation of the liquid methane, we never encountered problems arising from the condensation of atmospheric water vapor on the cold sample surface. In determining the radiant flux reflected by the free surface of the methane we were faced with a formidable problem as- sociated with the absorption by gaseous methane above the surface of the liquid. This problem was minimized by the use of a system of exhaust pumps used to remove gaseous methane from the optical path and from the air of the laboratory. One of the intakes of the exhaust system was placed inside the Dewar vessel close to the surface of the liquid; others were placed close to the top of the Dewar vessel. The pumping system with its intake openings was arranged to remove the unwanted gaseous methane without producing waves on the surface of the liquid methane sample. The effectiveness of the system in removing methane gas was checked from time to time by a search for absorption associated with the strong Q branches of the gas bands in the air just above the Dewar vessel; an auxilliary horizontal beam of infrared radiation was used in this monitoring process. In arriving at values of R(v) for liquid methane, we first measured the ratio r(v) of the radiant flux reflected from the methane surface to the radiant flux reflected from a water surface when a water sample was placed at the sample position in the reflectometer. The spectral reflectance R(v) of meth- ane was then obtained from the relation R(v) = r(v)RO(v), where Rw (v) is the reflectance of water based on the tables of optical constants of water given in a paper by Downing and Williams, 5 which gives a critical summary of numerous earlier studies of water; in spectral regions where Rw (v) is extremely small it was necessary to use a calibrated mirror in place of 186 J. Opt. Soc. Am., Vol. 68, No. 2, February 1978 0030-3941/78/6802-0186$00.50 C)1978 Optical Society of America 186
Transcript
Optical constants of liquid methane in the infrared*Lary W. Pinkley,t P. P. Sethna, and Dudley Williams
Department of Physics, Kansas State University, Manhattan, Kansas 66506(Received 21 September 1977)
The near-normal incidence spectral reflectance R(v) of liquid methane at 98 K has been measured inthe infrared in the spectral range 6700-350 cm-'. The resulting values of R(v) have been subjected toKramers-Kronig phase-shift analysis to provide values of the real n(v) and imaginary k(v) parts of thecomplex index of refraction N(s) = n(v) + ik(v) in the range 4000-400 cm-'. The results of the presentstudy are presented in graphical form and in tabular form over this range. The strengths S = Sk(v) dvof the absorption bands are compared with the corresponding bands in gaseous methane. Techniquesfor using the present results to obtain approximate values of the corresponding optical constants of solidmethane are discussed.
Methane in condensed states is believed to be an impor-tant component of the cloud cover of the outer planets of thesolar system. It is important to have a knowledge of the op-tical constants of this material in the infrared for use in theinterpretation of proposed studies of these planets from spaceprobes as well as for use in the interpretation of observationsbeing conducted at ground-based observatories. The presentwork on liquid methane was undertaken as a first step in ac-quiring the needed information. We selected liquid methanefor study because the reflection techniques developed in ourrecent studies' are more readily applied to liquids than tosolids. In some of these earlier studies 2 we have shown thatvalid estimates of the optical properties of solids can be ob-tained from the measured properties of the correspondingliquids; it is therefore to be hoped that our present work willalso provide approximate values of the optical constants ofsolid methane, which is probably more abundant than liquidmethane in planetary cloud covers.
Methane is a very interesting material from many pointsof view. The methane molecule CH4 is a spherically sym-metric molecule that has certain spectroscopic properties thathave long been of interest to theorists and experimentalistsalike. The spectrum of gaseous methane is characterized bythe following fundamental vibration-rotation bands:3: vi(al)at 2914 cm'1, v2(e) at 1526 cm-1 , v3(f2) at 3020 cm-1, and v4 (f2)at 1306 cm-'. There are numerous much weaker overtoneand combination bands in the spectrum of the gas.
The study of the finer details of these bands continues tobe a topic of major interest to spectroscopists; with everyimprovement in the resolving power of spectrographs, furtherinformation is obtained.4 The intermolecular forces betweenmethane molecules are very small, as evidenced by the lowboiling point 109.1 K and the low melting point 90.7 K for thematerial; the vapor pressure of methane is high over most ofits relatively narrow liquid range. Even solid methane at itsmelting point has a vapor pressure of 70 Torr.
EXPERIMENTAL WORK
Our experimental work involved the measurement ofspectral reflectance R(v) of methane at near-normal incidence.The liquid methane was obtained by the condensation of UHP99.97% gaseous methane (Matheson) in a copper coil im-mersed in liquid nitrogen. Samples of the liquid were placedin a shallow glass beaker suspended inside a Dewar vessel
containing liquid nitrogen. By adjustment of the height ofthe beaker above the liquid nitrogen surface, we were able tocontrol the temperature of the liquid methane. The tem-perature of the liquid methane was monitored by means of athermocouple; in the course of our study, measurements weremade for samples at various temperatures over most of theliquid range. The results we report can be regarded as typicalof liquid methane at a nominal temperature of 98 K near themiddle of the liquid range. . Samples in the beaker weremaintained at a depth of several centimeters; the level of thefree surface of the liquid methane was monitored by meansof a cathetometer with viewing through an unsilvered portionof the Dewar walls. Because of sample loss due to the highvapor pressure of the liquid, it was necessary at frequent in-tervals to refill the beaker with liquid methane. Probably asa result of the rapid evaporation of the liquid methane, wenever encountered problems arising from the condensationof atmospheric water vapor on the cold sample surface.
In determining the radiant flux reflected by the free surfaceof the methane we were faced with a formidable problem as-sociated with the absorption by gaseous methane above thesurface of the liquid. This problem was minimized by the useof a system of exhaust pumps used to remove gaseous methanefrom the optical path and from the air of the laboratory. Oneof the intakes of the exhaust system was placed inside theDewar vessel close to the surface of the liquid; others wereplaced close to the top of the Dewar vessel. The pumpingsystem with its intake openings was arranged to remove theunwanted gaseous methane without producing waves on thesurface of the liquid methane sample. The effectiveness ofthe system in removing methane gas was checked from timeto time by a search for absorption associated with the strongQ branches of the gas bands in the air just above the Dewarvessel; an auxilliary horizontal beam of infrared radiation wasused in this monitoring process.
In arriving at values of R(v) for liquid methane, we firstmeasured the ratio r(v) of the radiant flux reflected from themethane surface to the radiant flux reflected from a watersurface when a water sample was placed at the sample positionin the reflectometer. The spectral reflectance R(v) of meth-ane was then obtained from the relation R(v) = r(v)RO(v),where Rw (v) is the reflectance of water based on the tables ofoptical constants of water given in a paper by Downing andWilliams,5 which gives a critical summary of numerous earlierstudies of water; in spectral regions where Rw (v) is extremelysmall it was necessary to use a calibrated mirror in place of
186 J. Opt. Soc. Am., Vol. 68, No. 2, February 1978 0030-3941/78/6802-0186$00.50 C) 1978 Optical Society of America 186
0.024
O.' 16 -\R(V
0.008 - -
3600 2800 2000 [200 40
FIG. 1. Spectral reflectance R(Iv) of liquid methane at 98 K as a functionof wave number cm-'.
water as a reference. Reflectance R (i) was determined in thespectral range 6700-350 cm- 1.
k(J)0.080L -
3600 2800 ? C()0 0 40•
FIG. 3. Absorption index k(v) of liquid methane at 98 K as a function ofwave number cm-'.
RESULTS
Figure 1 gives a plot of our values of spectral reflectanceR(v) as a function of frequency expressed in cm-'. Thefractional reflectance over the entire range 4000-400 cm-, israther low. There are two observable dispersion features: thefeature between 3200 and 2800 cm-' in the figure is associatedwith the overlapping fundamental vibration bands v1 and v3:the second somewhat sharper feature between 1400 and 1200cm-' is associated with the overlapping fundamental bandsv2 and V4. Over most of the range we believe that the uncer-tainties in the values of R(v) amount to +2% of the plottedvalues. Incomplete removal of gaseous methane from theoptical path could produce somewhat larger uncertainties inthe vicinity of the two dispersion features.
In order to obtain values of the optical constants from ourmeasured values of R(v) we made use of the values of R(v) overthe entire range of measurement 6700-350 cm-'. We firstmade use of simple Kramers-Kronig phase shift analysis withlinear high-frequency and low-frequency extrapolations toobtain values of n(v) and k(v); the resulting values were thencompared with those obtained by subtractive Kramers-Kroniganalysis, which leads to more reliable values of n(v) and k (v)in the vicinity of the highest and lowest frequencies in therange of actual measurement. We discarded values of theoptical constants in the 6700-4000 cm-l region and in the400-350 cm-' region in order to minimize the influence ofextrapolations on the values of the optical constants plottedin subsequent figures.
The values of nr(v) as a function of wave number are plottedin Fig. 2 for the spectral region between 4000 and 400 cm-'.The general features of the curve in Fig. 2 are similar to the
n(V)C C|
3600 2800 2000 1200 400WAVE NUMBER (cm'1)
FIG. 2. Refractive index n(v) of liquid methane at 98 K as a function ofwave number cm-1.
features in the reflectance curve in Fig. 1. The uncertaintiesin n(v) amount to approximately ±1% of the plotted valuesover most of the spectral range; the uncertainties in the vi-cinity of the two dispersion features may be somewhat largerin view of the possibly larger uncertainties in R(v) in theseregions.
The values of k (v), sometimes called the spectral absorptionindex, are plotted as a function of wave number in Fig. 3 withone major peak at 3000 cm-l and a second peak at 1300 cm-'.Although it is difficult to estimate the uncertainties in k(v)as obtained from the Kramers-Kronig analysis of reflectancedata, we estimate that the uncertainties in the present workamount to +0.001 in spectral regions where k (v) is small andsomewhat less in the vicinity of absorption peaks. Thus inthe range 4000-3100 cm-l our values of k (v) are not signifi-cantly different from zero and have been omitted from the plotin Fig. 3. The uncertainty 5k = ±0.001 should be borne inmind when the low values of k(v) between the major absorp-tion peaks and in the 1200-400 cm-i regions are considered.There is also some reason to believe that the values of k (v) inthe low-frequency tail of the absorption band centered at 3000cm- 1 are somewhat high and may be subject to a correctionbk'(v) of -0.001 in this region.
In Table I we give an abbreviated list of the optical con-stants of liquid methane. In the table we give values of n(v)at widely spaced frequency intervals except in the vicinity ofthe regions of strong absorption; values of n(v) between thelisted frequencies can readily be obtained by using the curvein Fig. 2 as the basis for making interpolations between thevalues tabulated in Table I. Values of k (v) are stated in thetable for frequencies in the vicinities of absorption bands. Asindicated in Fig. 3 values of k (v) in other spectral regions arevery small; they are, in fact, so small that they are negligiblein the computation of particle scattering based on the Mietheory.
DISCUSSION OF RESULTS
We were interested in comparing the intensities of theoverlapping vP and V3 bands at 3000 cm- 1 and the v2 and V4
bands at 1300 cm-1 with the intensities of the correspondingbands in the spectrum of methane gas. Spectroscopists
187 J. Opt. Soc. Am., Vol. 68, No. 2, February 1978 Pinkley et al. 187
TABLE I. Optical constants of liquid methane in the infrared.
usually compare band intensities by comparing the values offSa(v) dv for the bands, where a(v) is the Lambert absorptioncoefficient and is related to k(v) by the relation a(v) =47rvk(v) with v expressed in cm-1 . In a study of gaseous
188 J. Opt. Soc. Am., Vol. 68, No. 2, February 1978
methane Burch and Williams6 have reported values off a (v) dv = 320 cm- 2 for overlapping v, and v3 bands and 185cm- 2 for the V2 and V4 bands for a pressure of 1 atm and atemperature of 273 K; these authors indicate that these valueshave an uncertainty of ±15% and are in fair agreement withearlier studies, to which reference is made. The measuredvalues of S k (v)d v obtained in the present study are 4.4 cm- 1
for the vl and v3 band with a peak at Vp = 3000 cm-' and 5.7cm'1 for the V2 and P4 band with its peak at vp = 1300 cm-1 ;these values also have an estimated uncertainty of approxi-mately 15%. Our present results for X k (v) d1v can be reliablyconverted to X a(v) dv by the relation X a(v)dv = 47rvp fk(v)dv. The ratios of S ax(v) dv for the VI, v3 band to X a (v)dv for the P2, V4 band are 1.73 for the gas and 1.78 for the liquid;in view of the estimated uncertainties, the agreement is nearlyperfect.
A more important comparison involves the absorption permolecule in the two phases. Because k(v) and a(v) are bothproportional to the number N 1 of absorbing molecules per unitvolume, we can compare absorption in the gaseous and liquidsamples by comparing values of f a(v) dv/N1. The results arelisted in Table II in terms of Avogadro's number NA. Theratio of the absorption fa (v) d v per molecule in the gas to theabsorption per molecule in the liquid is 1.19 for the v,, v3 bandand 1.22 for the v2, V4 band. Within the limits of uncertaintystated for the present study and for the Burch-Williams study,we can conclude that the integrated absorption per moleculein the two phases are not significantly different.
This result is in agreement with our earlier results for othermaterials, in which we have compared the intensities of cor-responding bands in the solid and liquid states2 ; in thosestudies we have shown that fk (v) dv for a given band of amolecule or molecular group such as S04-- is directly pro-portional to the number density N1 of the absorbers. Theseresults suggest that the absorption spectrum k(v)-vs-v for solidmethane can be obtained in good approximation from thespectrum of liquid methane and from the known ratio of thedensities of methane in the two phases. Although the detailsin the shape of a given band may be different, the value offk (v) dv of a given band in the solid can be expressed asSk(v) dv for the liquid multiplied by the density ratiop(solid)/p(liquid).
If we agree to ignore differences in characteristic bandshapes between the solid and liquid, we can use subtractiveKramers-Kronig relations along with a knowledge of nD (v) forthe solid at some single frequency to obtain a plot of n (v) -vs-vfor the solid. This plot can be checked in spectral regions
TABLE II. Comparison of absorption of methane in the gas andliquid phasesa b.
Ratio:Band Gas Liquid gas to liquid
f a(v) dy/Ni 4irvpfk(v) dy/NIP1, P3 7.2 X 106 /NA 6.04 X 106 /NA 1.19V2, P4 4.14 X 106/NA 3.39 X 106 /NA 1.22
aNA represents Avogadro's number.bNote that the values of fa(v) dv have an uncertainty of + 15% in both gas and
liquid phases.
Pinkley et al. 188
remote from characteristic absorption bands by the use of theLorentz-Lorenz relation to obtain n(v) for the solid from theknown values of n (P) for the liquid. These methods canprovide tentative approximate values of the optical constantsfor solid methane until it is possible to determine these con-stants from measurements on samples of solid methane.
*Supported in part by NASA.tNow at Lockheed Missiles and Space Co., Huntsville, Ala.'C. W. Robertson and D. Williams, "Optical constants of liquid am-
monia in the infrared," J. Opt. Soc. Am. 63, 188-193 (1973).2H. D. Downing, L. W. Pinkley, P. P. Sethna, and D. Williams, "Op-
tical constants of ammonium sulfate in the infrared," J. Opt. Soc.Am. 67, 186-190 (1977); P. P. Sethna, L. W. Pinkley, and D. Wil-liams, "Optical constants of cupric sulfate in the infrared", J. Opt.Soc. Am. 67, 499-501 (1977).
3G. Herzberg, Molecular Spectra and Molecular Structure (VanNostrand, New York, 1945), p. 307.
4 G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, and C.Amiot, "Ground State of Methane 12CH 4 through Forbidden Linesof the V3 Band," J. Mol. Spctrosc. 57, 246-263 (1975).
5 H. D. Downing and D. Williams, "Optical Constants of Water in theInfrared," J. Geophys. Res. 80, 1656-1661 (1975).
6 D. E. Burch and D. Williams, "Total Absorptance of Carbon Mon-oxide and Methane in the Infrared," Appl. Opt. 1, 587-593(1962).
Light scattering from aggregated noble-metal filmsV. V. Truong* and G. D. Scott
Department of Physics, University of Toronto, Toronto, Ontario, Canada, M5S 1A7(Received 3 June 1977)
The spectral and angular distributions of the scattered light from aggregated noble-metal films havebeen investigated. The films were formed by evaporation on hot glass substrates (300 'C) in order toobtain relatively large and regular size aggregates (200-1000 A). The scattered light from the aggregatedfilms in general exhibited a peak in the spectral region that was studied (0.3-1.0 jum). The experimentalspectral and angular measurements have been compared to results calculated from a theory consideringthe aggregates as spheroidal particles and satisfactory agreement has been obtained. An additionalstructure in the spectral distribution of the scattered light has been found in the case of relatively largesize silver aggregates (> 1000 A).
The optical properties of aggregated metal films havebeen widely studied, but one aspect has often been neglected,i.e., the optical scattering. The intensity of scattered lightfrom thin films was considered to be negligible and the ag-gregated films were approximated by planar films with ef-fective optical constants. 1-3 In some cases, however, as wehave noted for silver films in a previous study, 4 the scatteringincreases with the size of particles forming the film and be-comes more important. A small number of papers- 7 has beenpublished dealing with the scattering of light from aggregatedfilms, but generally these are limited to aggregates of smallsize (- 100 A) and usually the spectral range was only in thevisible and up to X = 0.6,4m. Satisfactory theoretical inter-pretation of the measurements has also been lacking.
In the present work, spectral and angular variations of thescattered light have been measured for a number of aggregatednoble-metal films. The size of particles forming the filmsvaried from less than 100 A to more than 1000 A. The mea-surements have then been compared to the results given bya theory in which the particles are considered as small rota-tional ellipsoids. Satisfactory agreement has been found forfilms having aggregate size up to several hundred angstroms.The present paper adds therefore an interesting aspect to thestudy of the basic physics of aggregates. It describes thepossible relation existing between light scattering and surfacestructure.
1. THEORETICAL CONSIDERATIONS
In order to simplify the picture of the aggregated films, theparticles are assumed to be rotational ellipsoids of identical
size, shape, and orientation. Their cross section in the filmplane is taken to be circular and their size small compared withthe wavelength of the incident light. As shown by a numberof authors2 -4' 8 the rotational ellipsoid has generally an effec-tive polarizability a' given by its components.
1 f-1
11 V[l(e - 1) ± 11 + - yll+
1 E-l4ir [fI(E - 1) + 1] + 'y I
(1)
(2)
where the subscripts 11 and I are defined by the direction ofthe electric field with respect to the film plane, E is the di-electric constant of the metal constituting the particle, f 11 andf l are the depolarization factors of the rotational ellipsoids,-y I and -yI are terms introduced by dipole-dipole interactionsbetween particles.
Let us suppose that the incident field is given by E0 eik-r,then by summing up contributions from all the particles weget the total scattered field5:
N e-i(kR+k-r')ES = E V XV X f (') Eo dv',
i R(3)
where R is the distance from the observation point to a pointinside the scattering particle with position vector r'.
To evaluate the integral in Eq. (3), we may observe that R= r - rj-ro r - Ro.(rj + ro), where Ro is the unit vectorin the direction of observation, rj is the position vector of thejth particle, and ro is the position vector of the source with
189 J. Opt. Soc. Am., Vol. 68, No. 2, February 1978 0030-3941/78/6802-0189$00.50 � 1978 Optical Society of America 189
