Absorption investigation of anthracene vapour

Chemical Physics 53 (1980) 51-62 0 North-Holland Publishing CO~FXI~

ABSORPTION INVESTIGATION

OF ANTHRACENE

VAPOUR *

R.St. DYGDAtA and K. STEFtiSKI ofPhysics, Nicholas Copernicrcs University. ‘Tonrfi. Poland f

Insrirure

Received 28 hforch 1980

.4n optical method for the determination of organic vapour concentrations, based on a statisticA model of the coesistence of the solid and _easphase is presented. A general formula, determining thedependence of the vapour concenrrxion on the cell and its side arm temperatures is obtained. Applying the proposed method, the heat of sublimation of nnthncene, shapes ofabsorption bands of the anthmcene vapour and the oscillator strength of anthracene molecule for the So-,S t electron tmnsition are determined.

I_ Introduction Experimental studies of physical properties of complex organic molecules in the gas phase are largely based on fluorescence and absorption measurements. The accuracy of the determination of the absorption and emission bands of complex organic compounds as functions of temperature, concentration etc. and their molecular parameters like collisional cross section, oscillator strength etc., depend very strongly on the precise determination of the vapour concentration by spectroscopic measurements. In papers published hitherto, this problem was little discussed and the methods of determination of the vapour concentration applied were inaccurate [l--12]. The authors of the previous papers measured vapour pressures of complex organic compounds indirectly, and Frequently different methods of determination of the vapour pressure were used in the case of one corn- ’ pound for different intervals of temperature. The measurements were performed using the Rodebush manometer [4,5,13], the indirect optical [6] or the flux method [7]. Application of such data for the fluorescence or absorption measurements performed

: This work was supported by Resexch Project hlR.I.5. zAddress: lnstytut Fizyki UhIK, 87-100 Torud, III. Grudziadzka 5/7. Poland.

For other cells can be a source oferror in the determined molecular parameters depending on the pressure. Ferguson’s paper [ 141, where inaccurate determination of the concentration has caused a considerable error in the determined oscillator strength for So-S1 electron transition for an anthracene moIecule [ I] can serve as an example. In their previous paper [ 151, the authors proposed a method of determination of the vapour concentration of organic compounds. Basing on the statistical model of the coexistence of the solid and gas phase, a mathematical form of the dependence of the vapour concentration on the temperature of the cell and the temperature of its side arm was derived. In the present paper, the method described in ref. [ 151 is modified. The modification is based on the assumption that the extinction coefficient for the gas phase depends on temperature and concentration. This assumption enables one to determine universal empirical parameters from the formula describing the dependence of the concentration on temperatures of the cell and its side arm. Applying the modified method of determination of the vapour concentration of organic molecules, the heat of sublimation of anthracene, the shape of absorption and emission bands for different temperatures, and concentrations of anthracene vapours and the oscillator strength For the So-S1 electron transition of an anthracene molecule were obtained.

j?

R.St. Dygdata, K. Stefahki

2, Method of determination of vapour concentration of organic compounds in all previous papers, the calculations were performed under assumption that the vapour pressure p depends on the temperature T, in the way which follows from the Clausius-Clapeyron equation [ 161: logp=A

+B/T+ClogT,

(1)

where A, B, Care empirical constants for a given range of temperature. Eq. (1) holds when the whole vapour is in the same temperature. In spectroscopic experiments concerning vapours of organic compounds [ 1,17- 191, fluorescence (or absorption) cells consisting of a proper cell containing vipours under investigation and a side arm being a reservoir of the compound are used. The vapour pressure in the cell depends on the temperature inside and the vapour concentration. It is worth to notice that the vapour concentratian depends on the temperature of the cell as well as on the temperature of the side arm. However, in eq. (1) the dependence on the temperature of the side arm only is taken into ticcount [I]. Neglect of the influence of the cell temperature can cause considerable errors during accurate spectroscopic measurements. The method of determination of the vapour concentration presented below takes into account the influence of both tke temperature of the cell T, and of the side arm T, on it. During spectroscopic investigations of molecular vapours, the compound under investigation is placed in the side arm. We assume that only these molecules, yrhick possess the energy E greater than the subiimalion energy F, can sublimate. Let us write the distri. bution function)(E) of molecules in the gas phase in the form: f(Q = AP(f2-J expC-E/kaT),

(2)

wkere P(K) is the density ofstates, 7’, is the tempemture of the side arm, ke is the Boltzmann constant and A Is a normalization constant. TIE vapour c:oncentrtition in the side arm can be Itlen 1.’ the form:

where No is a c ‘mstant and V denotes volume of the

1 Absorption

of anrhracette

vapour

side arm. From eqs. (2) and (3) it follows [15,20]. that c, = [n(2rn)3’2U’,,/4h3 ] x jE”’

exp(-Efke

7’)dE,

(4)

F

where m denotes the mass of the molecule. It was shown in ref. [ 151 that if the size of the region of intermediate temperatures (between the temperatures of the cell and of the side arm) can be neglected when compared with the size of the cell and the side arm, the vapour concentration in the cell c, can be written as

X

r(; , &h

T, - P),

(5)

where I’(x.y) is incomplete gamma function [21]. The formula (5) can be obtained under assumption that the energy of sublimation F does not depend on temperature. Without this assumption one obtains the dependence of the vapour concentration in the cell on the temperatures of the cell and of the side arm,in the form [15,22]: cc = Q(T;/7’b’2)IY~, %IkuTr -8,

(6)

where U0 is the heat of sublimation reduced to tke temperature 0 K, and 0 and /3are constants. As follows from the Lambert-Beer law, the optical transmissivity of the vapour in the cell depends on its concentration: ln(lo/f) = c,el,

(7)

where/e is the incoming light beam intensity, I is the intensity of the transmitted light. I denotes the length of the cell and e denotes the extinction coefficient. The extinction coefficient E depends in general on the temperature and the concentration of molecules in the cell. Let us assume the following type of dependence: e.h.&)

= eo(h. Tel I- a@, Tckc.

(8)

Parameters E& T,) and oc(h,7’,) can be determined experimentally from the measurements of the extinction coefficients for different concentrations and temperatures. Let us define 00,

Tr, T,) = ln(&/l).

(9)

R.St. Dygdah, K. Stefariski / Absorption of o~~throcenerapour

From eqs. (7)-(9)

one obtains:

53

Comparing eqs. (6) and (10) one obtains:

similar to that of Kelly and Rice 186was used. From the kinetic theory of gases one has that the mass m transported through a capillary with the inner cross section S for the time t is given by [S,23]:

D@, T,, T,) = OI(T,2/T,‘/2)

m = StpJo(2rrk~T/m~)-1’2,

c, =W,

T,, T,)/[+,

X I*(%,b/koTr

Tc) + ol(L TdcclI.

- P)[%(h

Tc) + 4h

TJ

XQ(G%‘2 Y%, (/oh T, - @I.

(II)

Values of Do\, T,, T,) measured for various temperatures T, and fixed temperature Tc can be approximated with eq. (1 I), applying the least-squares method, thus giving the parameters 0 and Uo. When substituted into eq. (6), they make possible the determination of the molecuiar vapour concentration for a wide range of T, and 7’,.

3. Method of determination of the extinction coefficient To measure the extinction coefficient for a given wavelength as a function of the temperature and of the vapour concentration it is necessary to determine both these variables. Such measurements can be easily performed for a constant concentration of molecules by changing the temperature, and when made for different concentrations they enable one to determine the parameters eO(h, Tr j and rr(h, T,) from eq. (8). To perform these measurements, one must directly determine the concentration of the chemical compound vapour. Inserting B mass m of the substance into the cell one obtains unsaturated vapour for a certain temperature Tk. The concentration of this vapour is given by: c, = m/v,

(12)

where V is the volume of the cell. For temperatures of the cell 7’, > Tk one can measure 1,/I as a function of T,, for the constant c,. Therefore one obtains from rhe Lambert-Beer law that: (13) Inaccuracies in the determination of the mass m are the most serious source of error of Q+(T~). To minimize them, the method of evaporation to the cell

(141

where p is the vapour pressure, Jo the probability of a transition of a molecule throug~u he capillary with length 1 (determined by Clausing [24])9 and H/J decotes the mass of a molecule. Filling through the capillary the ce!l for the time t, and then in the same temperature and under the !iame pressure a container for the time t2 > f I onp can easily determine the mass nr, evaporated to the cell from the formula: ml = m2tl/tz,

USI

following directly from eq. (14) having weighted the mass rnz evaporated to the container. The mass m, of the order IO-’ g can be easi!y weighted on an analytical balance. The knowledge of m1 enables one to determine an absolute value of the extinction coefi!cient for a l;iven wavelength, temperature and vapour coqcenlration. Using an absorption spectrophotorneter one obtains absorption bands in relative umts which, compared with the absolute extinction coefficient for the ccrtain wavelength, make possible the determination 01 the absorption band in absolute units.

4. Absorption spectrophotometer An optical system of the spectrophotometer wds designed in such a way that intensities of both the incoming beam f0 and the transmitted beam / ‘were measured with the same photomultiplier. An auto. matic system OFthe spectrophotometer made pos!Jble to perform two types of measurements: (a) measurements of the time dependence uf 111~ extinction coefficient of molecular vapours; (b) meaarremente of the extinction coefficient a:$ a flmction of the wavelength of lhe detection IWIW The automatic system designer! by the authors, constructed of digital integrated circuits, was coupled with such additioilal digital equipments like n qa:trtz clock, voltmeters, printer etc. making a&a whole a system of control and registrstion of the mcasure-

54

RSt- Dygd&, K. Stef&ki/Absorption

ofnnthracene v&w

a shutter, the semi-permeable mirror HM2 and fmally is registered by the RCA lP2S photomultiplier (Pm*) - this is a beam of intensity I. The second beam is directed with mirror M, on the shutter S2 and then on the mirror MI and on the semi-permeable mirror HM2 which directs it on a photomultiplier Pm2 - this is a beam of intensity I,, . The system of shutters S1 and St is controlled by an automatic system SS. The principle of operation of the system is based on the proportionality of a signal from a photomultiplier to one of the beam intensities I or IO. according to the state of both shutters. An SPM2 Zeiss Jena monochromator (MCH*) and EMI 6256 phototiultip!ier

Fig. 1. Scheme of the optical part of the spectrophotometer: hfCH - monochromator, Pm - photomuttiplier, i - lamp, QP - quartz plate. C - absorption ccl, 0 - oven. S - shutter, hl - mirror, Hhl - semipermeable mirror. SS - control snd registration system, R, and Rz - electronic regulators of light intensity and temperature. ments. The scheme of the optical part of the spectrophotometer is shown in fig. I. The lamp L is a source of the detection beam. In investigations under consideration, two different types of lamps were used. A radio frequency mercury lamp similar to that described by Burling et al. [x] was the first one. It has the virtue of having small halfwidths of emitted mercary lines. As the second type, a halogen lamp with a quartz bulb was used to obtain the white light spectrum. An SPM2 Zeiss Jena monochromator (MCH,) separates from the light beam emitted by the lamp L a monochromatic beam of wavelength 1. The part of this beam reflected from a quartz plate Q? is registered by a photomultiplier RCA lP28 @‘ml), whose signal controls the current of the lamp L through an electronic regulator RI, ensuring the stabilization of the fight beam intensity. The second part of the beam, stronger than the reflected one, passes through, and is separated into two beams with a semi-permeable mirror HMI. The beam transmitted by this mirror is absorbed by the vapour of an investigated compound contained in de absorption cell C, then passes through

(Pm3) enables one to per-

form measurements of the emission intensity together with absorption measurements. This part of the optical system is used as an auxiliary during measurements of the extinction coefficient and can be applied during fluorescence measurements. During measurements, the quartz cell is placed in the oven 0, made of an aluminium block and having walls 40 mm thick. The side arm of the cell was placed in an aluminium block round oven with outer diameter 150 mm. Both ovens were mutually ther-

mally insulated. The temperatures of the cell and of the side arm were both measured by Cu-constantan thermocouples. ReguIation of temperatures of both ovens was performed automatically within a range of 0.1 K. In many experimental works [1,15,26] other systems of the spectrophotometer, in which the reference signal I,, and the signal of the detection beam I were measured by two photomultipliers, were used. However in such cases the incompatibility of spectralresponse characteristics of photomultipliers was a source of error in measurements of the intensity ratio, especially when measurements were performed for a wide range of the wavelengths.

5. Experiment and results The methods of determination of the vapour concentration and extinction coefficient were applied to perform spectral investigation of anthracene with an absorption spectrophotometer. The obtained results served as data to determine the heat of sublimation of

anthracene and the parameter 0 from eq. (6). Shapes of absorption and emission spectra of anthracene vapour for different concentrations and temperatures, and the oscillator strength of the So-S, electronic transition were also determined. The measurements were performed for high purity anthracene. The investigated compound was zone rectified [ 18,27-291 in the special device producing high purity monocrystals which were additionally vacuum purified. 5. I. Tite

extinction

as Q function

coefficient

of temperature

for a given

wavelength

and concentration

In this series of measurements cells without a side arm were used. They were filled as described in section 3 and were placed in the oven. At certain temperature the whole anthracene inside a cell evaporates, and the vapour concentration is given by eq. (12). Further increasing of the temperature enables one to determine the extinction coefficient for a constant concentration as a function of temperature. The measurements were performed for the wavelength X = 334.1 nm. This mercury line was chosen, because the absorption band of anthracene has a wide mini-

mum [30] for this wavelength. This fact ensures higher-accuracy of determination of the ratio 10./f than it would be possible in the case of a wav‘elength corresponding to a sharp maximum or a big slope of the absorption curve. The measurements of the dependence of the extinction coefficient on temperature were performed for different concentrations from 10m4 to 1 mol/m’. The results obtained for certain values of the concentration are shown in fig. 2. The dependence of the extinction coefficient on the concentration for some temperatures are shown in fig. 3. It is easy notice that this dependence is not a linear one, but for small concentrations it can be approximated by a linear function as is shown in figs. 4 and 5. The dependence of the extinction coefficient E on the temperature Tc for a given concentration was approximated by a quadratic function: E(C) = A (c)T,2 + B(c) T, -i C(c). A(c), using the least-squares sent the approximate ture, eq. (16). Curves mated. The points in The parameters

3341 I nml

Cc[mol

0

Fig. 2. Dependence of the extinction coefficient on the temperature

for

(16)

B(c), C(c) were determined method. Curves in fig. 2 repredependence of E(C) on temperain fig. 3 are similarly approxifigs. 4 and 5 were taken from

6’1

different concentrations of anthmcene vapour.

R.St. Dygdata. K. Stefatiski / Absorption of anthracene vapow

56

tiig. 3. Dependence

of the extiwtion

coefficient

wives in fig. 3, they were approximated b:r a linear

function from eq. (8) with the least-squares method for ewcry range of the concentration. The obtained values of the parameters eo(h, T,) and ogh, T,) are

10

for some temperatures.

presented in tables 1 and 2 for two different values of the concentration. The determined parameters E&I, TJ and ol(X, Z’,) make possible to obtain parameters 0 and (IO from formula (11).

v 1 -

D

;

I 18 4 I>cpcndcn~o of the

on the concentration

extinction coefficient

on the concentration

(in the range (2-10)

X lo4

Tc IKI 573 523 4?3 423

mol/m’) for some temperatures.

RSt. Dygdata, K. Stefatiski /A hsorption of anthracens vapo:lr

57

h= 334.1Inml

25 t

Fig. 5. Dependence of the extinction

coefficient

on the concentration

Table 1 Values of parameters eo(h, T,.) and a(h. ‘7,) for the concentration ___._.... --_ ----. Parameter

-

(in the range (2-10)

x IV2

mol/m3)

TO
range 2 x lo_4 -2 x 10-3 mol/m3, for :mih,lacene vapour _~.-_ -l_--._--_ .-._ --.---------. ____

Tc (K) 423

413 _.- __-_

~~.

.----

523

--

--. ._-

_

573

--. .-_..

_ __.... __

-.

EO@, T,) m2/moI a(& Tc) ms /mol

2.41 x IO*

2.51 x 102

2.62 X LO2

2.74 X 10’

0.86 x lo4 ---.__.ll_

1.10 x 104

1.22 x 104

1.81 x JO” ----_-_-I__

- ____

-_-

---...

Table 2 Values of parameters eo(h. rc) and U(A, TC) fu Parameter

the concentration ___- __--___-_._

range 2 x 10 9 --2 X 10-l mol/m3, _._ .._-...

Tc (K) 423

473

523

(mz/mol)

2.61 x 102

2.75 X lo2

3.01 x 102

3.28 x 10’

ML Tc) (ms/mo12)

2.75 x IO2

3.62 X IO2

4.75 x 102

6.01 X IO2

_I__I___-____-__

_.

573

_

eo(h Tel

fol anthrarenc

vapou~

--_

RSt. Dygdalir.K_Stefak/Ab&tion

ofanthracene sapour

.5.2. Determination of parameters 0 and U, To determine parameters Q and U,, from eq. (6), a cell tith a side arm was used. The ratio IO/I For the wavelength A = 334.1 run at fixed temperature T, was measured at different reservoir temperatures T,_ The typcial dependences of it on both temperatures are shown in fig 6. Experimental points for every temperature T, were approximated by eq. (11) with the least-squares method. The earlier determined coefficients E,,@, T,) and a(& T,) were used there. The abovementioned approximation gave parameters Ue and 0. It appeared during the data handling that they were very strongly correlated, and therefore eq. (6) was expressed as: cc = O’(T,2/T;‘*)I-(2,

Fig. 6. Typical dependences of the cell Tc and reservoir

U,&T,).

(17)

of D(X, T,. T,) on temperatures r,.

Fig. 7. Absorption

spectra

of anthncene

vapour

for concentration

cc = 4.1 X lo-*

mol/m3.

c

.g L_ 3ocI

Fip. 8. Absorption

Fig 9. Absorption

320 3LO

360

spectm of anthracene vapour for concentration

spectra of anthracene vapour for concentration

t

.._ . hl”.nl

AIL

cc = 4.1 X lo-*

cc = 5.7 X 10-t

380

mol/m3.

mol/m3.

IL%. Dygdda, K. Stefariski /A bsorption of anthracerte vapour

-_L 380

150

Kc

‘20

‘LO

L60

hlnml

f-c. IO.I:mrsston spectra rnormrlized with respect to the height of the first maximum) for the concentration c = 3.4 X 10s2 nr01/m3,

The obtained values of 0’ and Cl, are respectively: cj’ = .;44 t 0.25

state. The oscillator strength is given by

[30]

:

mol m-j Kb3’*,

L’0=(9.78+0.1)X104

Jmol-‘.

5.3. Measurements of absorption ancl emission spectra (ofahracene vapuur TIIC parameters8’ and fJOenable one to determine from eq. (I 7) rhe concentrafion of vapour for wide ranges of bol!t the temperatures of the cell and the side arm. Tnc nbsorption band!: of anthracene in relattvc ui\its were scaled with respect to thus determined concentrations. From an absolute vaiue of the crtinction coefficient determined for the walelengrh X 0 334.1 nm, it was possible to determine abp?rption !?nnds for different temperatures and concentrations WIabsolute units. The typicnl nbsorption spectra of anthracene vdpour are shown in figs. 7-9. Emission spectra (normelhI with respect to the height of tile first maximtm t’orsome tempcraiurcs and the fixed concentratlon rrtc shown in fig. 10. The knowledge of the dcpcndence of the extincriori coefficient on the frequency Yenables one to dzte..nine 111~oscillator strength for the electronic transition from the ground to the first excited singlet

f = 5.63 X IO-”

- e(u/c) d(v/c), s _m

(18)

where u/c is expressed in m-’ and E(V/C)in m* mol-'. For the obtained absorption spectra of anthracene the value off reads: f= 0.091, and does not depend on the vapour concentration or temperature what is in agreement with results of tl:e theory of molecular spectra [30-321.

6. Discussion The performed measurements enabled us to determine p?rhmeters 0’ and Cl0 from eq. (17). The parameter U. is the heat of sublimation reduced to temperature 0 K as shown in ref. [ 151. The obtained value of U, is compared with the values obtained by the other authors in table 3. It follows from this table that the value obtained from spectroscopic measurements is in good agreement with values obtained from other methods. As was mentioned above, in other papers the influ-

R.§r. Dygdaiu, K. Stcfariski / Ahsorption of otrthracmr vopo~

Fig. 11. Shape of absorption spectra obtained by authors of the prcsnt paper i---) wmparcd authurs: Hardtl et al. 1381 (---), Ware e; al. [ 331 (-- . ) and ~orysevltch 1301 (.

ence of the temperature of the cell on the vapour pressure was neglected. This can cause inaccuracies in determination of molecular parameters, especially of the extinction coefficient. The discrepancies between values of the absorption coefficients obtained by other authors and those obtained in the present paper, shown in fig. 11, can be caused by differ-

other

authors

last effect purity

Author Sears, Hopke 141 Klochkov [7 1

Kelley , Rice [ 8 1 Dygdata et al. 1I5 ] present study

U,, (J mol-‘)

in has a richer

the determined the oscillator transition

values

structure.

of different

absorption

strength

degrees

The 0.

band

in absolulo

for the investignlctl

was found.

reported

Its vuluc is cornpdretl

by otl:ei, authors

in table 4. ‘I‘llc

present

vr,lue is in good agreement with the result obkined b), Ware [ 1 j and hksiejcv [33 J. A co1151dcr able discrep,incy

9.78 x IO4

10.01 x 104 9.86 x IO4 (9.81 1- 0.1)

although

can be the result

elcclronic -

IIY ot11?1

of the used anthracene.

From

with

of antbrlccne

+/,ith those obl,lincd

.).

ent methods of determination of the vapour concentration. The shape of the present absorption b;mJ does not difl’er considerably from those obtained by

values, Table 3 Values of the heat of sublimntion

61

between

them

and results

of I;crgu-

son x IO4

(9.78 I 0.1) x IO4

[ 141 is probably caused by uncorrect uelcrmination of the vapour concentration ‘)y the I:jsI iluthor. A good agreement between values of the oscillator strength

for both

the

VkipOUr

anal solulioll

of antllra-

Table 4 Comparison of wlues ofoscillator strength for So-SL electronic transition for the anthrncene molecule Type ofinvestigi~tion

f

Author

“apO”r

0.136 0.093 0.096 0.094

Fergson et al. [ 141 Bnksiejev [ 331 Wue. Cunninghham [ 11 \Vxe. Baldwin [36] Melhnish 1371

vapollr vapour hexnne solution benzene

solution

cene corresponds Platt [35]_

0.102

with results of Pick&t [34] and

References [ 11 W.R. Wxe and P.T. Cunningham, J. Chem. Phys. 43 (1965) 3826. [21 C.A. N&on and C.E. Senseman, Ind. Eng. Chem. 14 (1922) 58. [31 P.S. hlortimerand R.V. Murphy, Ind. Eng. Chem. 15 (1923) 1140. 141 G.W. Sears and E.R. Hopke, J. Am. Chem. Sot. 71 (1949) 1632. 1.51 G.W. Semsand P.R. Hopke, J. Am. Chem. Sot. 71 (1949) 2575. [6] B. Stevens, J. Chem. Sot. 3 (1953) 2973. [7] V.P. Klotchkov. Zh. Fiz. Khim. 32 (1958) 1177 [in RUSSiXl]. [X] J.D. Kelly and F.O. Rice, J. Phys. Chem. 68 (1964) 3794. 191 W.E. Howqrd and E.W. Schlag, Chem. Phys. 17 (1976) 123. [IO] N.A. Borysevich. A.V. Dorokhin and A.A. Kotov, Opt. Spektry. 43 (1977) 655 [in Russian]. [II] G.A. Abakumov, A.V. Dorokhin and AA Kotov, Opt. Spektry. 44 (1978) 486 [in Russian]. [12] S-0. blirunyants and JS. Demchuk, Opt. Spektry. 46 (1979) 267 [in Russianj. [13] H. Rodebush, J. .4m. Chem. Sot. 52 (1939) 3159. [ 141 J. Ferguson, Can. J. Chem. 35 (1957) 1117.

1151 R.S. DVedapd. K. Stefatiski and J. Wolnikowski.

Buli. . .&ad. Polon. sci., Ser. Sci. h¶ath. Asrronom. P&s. 25 (W~?~ 33% j161 A.N. Niesmeyanov, Dxvlenye pnra khimicheskikh elementov (Izd. Akademii Nnuk SSSR, Moscow, 1961) [in Rnssian]. 1171 E.J. Bowen and S. Velkovic. PFOC.Roy. Sot. London 236A (1956) 1. [ li3] A.B. Zah!an, S.Z. \Veisz and R.C. Jarnagin, J. Chem. . Phys. 42 (1965) 4244. [ 191 W.H. van Leeuwen, J. Lnngelaar and J.D. van Voorst. Chem. Phys. Letters 13 (1972) 622. [20] A.S. Dsvydov, Kvzmtovnya mekhnnikn (Fiz. - hIat. Lit., hloscow, 1963) [in Russian]. 1211 hi. Abramowitz and I.A. Segux, Handbook of mathcmatical functions (Dover, New York, 1968). 122) A.Y. Anselm, Vvedenye v teoryu poluprovodnikov (Nauka. hloscow, 1978) [in Russian]. [231 R.D. Present, Kinetic theory of gases (McGraw-Hill, New York, 1958). 1241 P. Clansing, Ann. Physik 12 (1932) 961. [251 D.H. Burling, hl. Czajkowski and L. Krause, J. Opt. Sot. Am. 57 (1967) 1162. 1261 C.T. Ryan and T.K. Custafson, Chem. Phys. Letters44 (1976) 241. 1271 G.S. Beddard, S.J. Formosinho and G. Porter, Chem. Phys. Letters 22 (1973) 235. [28] I. Vogel, Practical organic chemistry, 2nd Ed. (Longmans, London). 1291 T. Deinum, C.J. Werkhoven. J. Lnngelaar, R.P.H. Rettshnick and J.D.W. van Voorst, Chem. Phys. Letters 12 (1971) 189. [3Oj N.A. Borysevich, Vozbuzhdenye sostoynnya slozhnykh molekul v gxzovoy fue (Nauko y Tekhnika, Minsk, 1967) [in Russian]. 1311 W.L. Bogdanov, Opt. Spektry. 43 (1977) 650 [in Russian] _ [321 M.D. Frank-Kamenetskiy and A.V. Luknschin, Usp. Fiz. Nauk I16 (1975) I93 [in Russinn]. [33] N. Bnkseev, Opt. Spektry. 14 (1962) 323 [in Russianl. [34] J. Picket and V. Hoest, J. Chem. Phys. 7 (1939) 439. 1351 J. Platt and L. Jacob, J. Chem. Phys. 16 (1948) 1353. [36] W.R. Ware and B.B. Baldwin, J. Chem. Phys. 43 (1965) 1194. [37] W.H. hlelnish, J. Chem. Phys. 65 (1961) 229. 1381 K.H. Hzrdtl and A. Schnnnan. 2. Noturforsch. Al2 (1957) 715.