Index Headings: Infrared; Emission spectra; Spectral simulation; Space radiator. INTRODUCTION. The liquid droplet radiator concept 1,2 has been devel-.
Evaluation of Space Radiator Performance by Simulation of Infrared Emission KOJI OHTA,* ROBERT T. GRAF, and HATSUO ISHIDAt Department o[ Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106 The total performance of a droplet space radiator has been predicted by simulation of infrared emission spectra. Emission spectra for a droplet are simulated with the use of exact optical theory from the optical constant spectra of a low-molecular-weight silicone, which is a candidate for use as an emission medium of the radiator. Emissive power and total emittance are calculated from the simulated emission spectra for a droplet at different temperatures. It is found that the fourth-power temperature dependence of the emissive power of the blackbody and the temperature dependence of the emissivity inherent to the materials govern the emissive power of the droplet. The progressive decreases in temperature of a droplet and a droplet sheet in space are also simulated. A droplet with a diameter of I/~m is predicted to cool from 500 K to 252 K in two seconds. The effects of the size of a droplet and the number density of the droplets in the sheet on the cooling rate are estimated. A smaller droplet is essential for obtaining effective radiation in the liquid droplet radiator. A dense cloud of the droplet sheet will retard the cooling rate of the droplets because of the reabsorption of the emitted light. Index Headings: Infrared; Emission spectra; Spectral simulation; Space radiator.
INTRODUCTION The liquid droplet radiator concept 1,2 has been developed for practical use as a space radiator because of its weight reduction benefits. In the radiator, droplets of the working fluid are generated into space and reject the waste heat as emissive radiation. At the present time, melted metal at high temperatures or organic liquid with low vapor pressure, like silicone oil, are candidate materials for the working fluid of the radiator. In order to evaluate the total performance of the radiator in space, one must first investigate the radiation characteristics of the working fluid. The purpose of this report is to predict the emission of the working fluid in the form of a droplet from the optical constants of the material in the infrared region. Graybody approximation is a convenient method to deal with the emissive character of materials. It is assumed in this approximation that the emissivity E of the materials is constant with the wavenumber v. In other words, the emissive power of the materials I(v, T) at a temperature T is assumed to be E times that of the blackbody Ib(V, T), irrespective of the wavenumber v: I(v, T) = EIb(V, T)
(1)
where Ib(V, T) is the well-known Planck's equation and is expressed as 3.7404 x lO-Sv3 Ib(v, T) = [erg/(cm.sec)]. (2) [exp(1.4387v/T) - 1] Received 17 July 1987. * Permanent address: Government Industrial Research Institute of Osaka, Midorigaoka, Ikeda, Osaka 563, Japan. t Author to whom correspondenceshould be sent. 114
Volume 42, Number 1, 1988
However, real materials, especially organic materials, usually have a certain spectral distribution of the emission; therefore, the graybody approximation cannot properly describe the emission behavior of the materials. For example, when the material has maximum emissivity at the wavenumber region where the blackbody has the maximum emissive power at a particular temperature, the emission behavior of the material is expected to be close to the blackbody. On the other hand, when the material has little emissivity around the wavenumber where the blackbody has the maximum emissive power, the total emissive power will be much smaller than that of the blackbody. This kind of emission character of the real material cannot be predicted from the graybody approximation. This is the main reason why we must introduce the actual spectral distribution for the prediction of the radiation behavior. In this report, we show a general method for simulating the spectral emittance from an absorption spectrum, and for simulating the emissive power in the form of a droplet and in the form of the droplet sheet of materials, from the simulated emission spectrum. We apply the present method to a silicone oil, DC-705, which is a candidate for the working fluid of a space radiator planned by NASA. SPECTRAL SIMULATION Optical constant spectra of the material for working fluid are necessary for the simulation of the emissive intensity of the materials including spectral distribution. For a free-standing polymer film, several methods have been developed to obtain optical constants, that is, n(v) and k(v) spectra in infrared region2 -5 However, there have been few simple and convenient methods reported for measuring the optical constant spectra of organic liquid materials. Therefore, we have developed a new algorithm to calculate the n(v) and k(v) spectra from an attenuated total reflection (ATR) spectrum. Details of the algorithm will be described elsewhere, along with its application to some polymer materials cast on a prism for ATR measurements. 6 Here we explain the procedure briefly. First, by assuming that the absorbance of the measured ATR spectrum is proportional to the k (v) spectrum, we calculate the proportional coefficient theoretically, and divide the absorbance of the measured ATR spectrum by the coefficient; thus the trial k (v) spectrum is obtained. In this first calculation, n(v) is assumed to be constant over the whole wavenumber region. Next, we obtain the initial n(v) spectrum from the trial k(v) spectrum by using the following Kramers-Kronig relationship:
ooo3-vo2sm/42o~-ou4,2.oo/o © 1988
Society for Applied Spectroscopy
n(.) = n(oo) + _2 C/°° v'k(v') 7r .~ro ~--_ ~2 dr'.
(3)
APPLIED SPECTROSCOPY
Then, we simulate the ATR spectrum from the set of the k(v) and n(v). When the simulated ATR spectrum is different from the measured ATR spectrum, we obtained the new k(~) spectrum from the n(v) spectrum so that the two spectra can reproduce the measured ATR spectrum. And then, we calculate the n(u) spectrum again from the k (v) spectrum using Eq. 3. This process should be iterated until the k(v) and n(v) spectra do not change any more, and also until the simulated ATR spectrum becomes exactly identical to the measured ATR spectrum in the whole wavenumber region. We found that, in some cases of very strongly absorbing materials, this iteration procedure did not give convergence to the reasonable k(r) and n(~) values, depending on the measurement conditions and maximum k(~) value. However, when we use germanium as the material for the internal reflection element, and an incident angle of 45°, this algorithm gives good convergence for most organic materials. Therefore, these measurement conditions were used throughout the present investigation. By using the n(v) and k(~) spectra obtained by the above procedure, we carried out the simulation of emission spectrum on the basis of the exact optical theory. When the system is isothermal, Kirchhofi's law holds, and the directional spectral emittance E(O, ~,) is expressed as the following equation:
E(O, v) = A(O, ~,) = 1 - R(O, ~,) - T(O, ~,)
(4)
where A(O, ~,) is absorptance, R(8, l,) reflectance, and T(0, v) transmittance at the wavenumber ~; the angle 0 is the angle of direction of the emission for E(0, v) and the angle of incidence for A(O, ~), R(0, ~), and T(0, ~). The values R(0, v) and T(O, ~,) are calculated from the k(u) and n(v) spectra with the use of the Fresnel equations. Simple average values of the parallel (p) and perpendicular (s) polarization states should be used for R(O, u) or T(O, z,) values in the emission spectra: ~,R(O, u) = [R,(0, u) + R,(O, u)]/2, (5)
T(O, u) = [Tp(0, v) + T,(O, ~)]/2.
[1 -
Ro(O, u)]{1 - exp[-a(0, u)./]} 1 - Ro(O, u)exp[-a(0, u).l]
(7)
where Ro(O, u) is the reflectivity at the surface of the film and a(O, u) is the absorption coefficient in ease of the emission angle of 0. By averaging the directional emittanee over the whole angle of direction, the hemispherical spectral emittance E(u) is obtained as
E(u) =
~ ,o'0
r/2
E(O, ~,)sin(20) dO.
i
i0
(a}
{b)
Fro. 1. Equivalentthicknessin the calculationof emittanceof a spherical droplet. The directionalemittance from the droplet (a) with the diameter d is equal to the directionalemittancefrom the hypothetical film (b) with the thickness of d × cos2~b.The filledcircles (O) denote origins of the light emission. The directional spectral emissive power I(0, u, T) is given by multiplying Eq. 4 by Planck's equation (2):
I(0, ~,, T) = E(O, u)Ibb', T)/Tr [erg/(cm.sec. steradian)].
(9)
Similarly, by multiplying Eq. 8 by Planck's equation, we calculate the hemispherical spectral emissive power I(~, T) = E(~)Ib(r, T)
[erg/(cm.sec)].
(10)
By integrating Eq. 10 over the whole wavenumber range, we finally obtain the total emissive power I ( T ) , that is, the total amount of the energy flux emitted from the surface of the materials per unit area per unit time: I ( T ) ---
IO,, T) &,
[erg/(cm2-sec)].
(11)
In this ease, the total emittance E(T) at the temperature is defined as
E(T) = I(T)/
Ibb', T) d~
(12)
(6)
In the actual calculation, we used Abeles's matrix method 7 coded with FORTRAN language. When the film is sufficiently thicker than the wavelength of the light, the method considering the interference is not appropriate for the simulation of the emission spectrum. For this case, we used a new algorithm,s developed for those systems with phase incoherency, based on a matrix method similar to Abeles's formula. The explicit formula of the emittance in the case of an incoherent layer of a freestanding film with thickness l is as follows:
E(O, u) =
!
(8)
= I(T)/(aT')
(13)
where a is the Stefan-Boltzmann constant. The above calculation is easily done for a free-standing film by using Eq. 7. With slightly modified equations, a similar calculation is also possible for a droplet. If we assume that the droplet is a perfect sphere, the directional emittance of the light emitted from a point of the sphere surface with the diameter d is the same as the emittance of a film of the thickness d x cos2~b,where ~b is the angle of refraction and obtained from well-known Snell's law: sin 0 = n(v) sin ~b,
(14)
as shown in Fig. 1. We can use Eqs. 8-13 for a droplet as well as for a free-standing film by replacing the thickness I by the equivalent thickness d × cos2~bfor a given angle 0 in the calculation of Eqs. 7 and 8. When the droplet is light-absorbing, the d x {Re[ri(u) cos ~]/n(v)} 2 value should be used instead of d × cos2~b,where ri(u) is the complex refractive index n(u) + ik(~), and ~b is the complex angle of refraction obtained from the same equation (14). The explicit form of the emittance for a droplet is equivalent to the equations by Thomas 9 and APPLIED SPECTROSCOPY
115
Hoffman and Gauvin, 1° which are given for the absorptance of a spherical droplet. In the actual spectral measurements, we limited the integral range in Eq. 11 to the detection range of the detector used, that is, from 700 to 3600 cm-L Once we obtain the total emissive power I(T), we can calculate the temperature change of the droplet. The differential temperature change dT per differential time dt is derived from the following energy balance equation:
- C p p V d T = I ( T ) S dt,
[erg]
(15)
where Cp and p are, respectively, the heat capacity and the density of the material used as the working fluid, while V and S are, respectively, the volume and the surface area of the droplet. Expressing V and S by diameter d gives dT 6I(T) . . . . (16) dt Cppd " In this case, it is assumed that the temperature is constant within the droplet and the temperature is at the degree of absolute zero outside of it. In such cases where the droplet is surrounded by a body with temperature T' (T >> T'), I ( T ) ought to be replaced by I(T) - I(T'). So far, we have dealt with the emission behavior of one droplet of material and did not consider the interaction between different droplets. However, in the real system of the droplet radiator, a large number of the droplets are generated simultaneously and form a sheet of dense clouds. As a result, heat exchange occurs among the droplets through absorption, scattering, and reemission of the emitted light. For this case, we convert the hemispherical spectral emittance E(v) of one droplet to the directional emittance Es(Os, p) of the sheet of the droplets using the following equations:
Es(Os, p) = 1 - exp[-E(~) x rJcos 0s], rs=N
x A x t~,
(17) (18)
where rs is the optical depth of the sheet, N is the number density of the droplets per unit volume, A is the cross section of a droplet and is equal to 7r(d/2) 2, t8 is the thickness of the sheet, and 0~is the angle of the direction from the normal to the plane of the sheet. Relation 17 was depicted in fig. 3 of Ref. i by Mattick and Hertzberg for the case of normal emissivity (0~ = 0°). For the droplet sheet, we can also define the hemispherical spectral emittance Es(v), the directional spectral emissive power I,(Os, v, T), the hemispherical spectral emissive power/~(v, T), the total emissive power I~(T), and the total emittance E~(T) by using the same equations as Eqs. 8--13. In this case, the energy balance equation becomes as follows: dT dt
-
2I,(T) CppNt~ V "
(19)
At the optically thin limit, that is, when the optical depth r, is far smaller than 1, this equation is reduced to Eq. 16. In the graybody approximation, we can solve Eqs. 16 and 19 analytically2 However, in our case I ( T ) or Is(T) is not a simple function of the temperature. Therefore, we must solve Eqs. 16 and 19 numerically to calculate
116
Volume 42, Number 1, 1988
the temperature change. A successive approximation method is adopted here; first, we calculate the finite temperature decrease -AT1 against the finite time interval At at the initial temperature To. We thus obtain the next temperature To - AT~ after At time, after which we calculate the next -AT2 at the temperature To - AT1 by the same procedure. These steps are repeated. The heat capacity and density of the silicone oil used in the calculation of Eqs. 16 and 19 were 1.67 [J/(g-K)] and 1.0 [g/cm3], respectively2 These values are assumed to be constant with temperature all through the present calculation. All the computations were done with a Digital Equipment Corp. VAX/VMS 11-780 computer system. EXPERIMENTAL A trimethylpentaphenyltrisiloxane (DC-705, Dow Corning) sample, which is considered a candidate for the emission medium of the droplet space radiator, was used for this study. A Digilab FTS-20E Fourier transform infrared (FT-IR) spectrometer was used for obtaining infrared spectra. A Wilks Model 9 attenuated total reflection (ATR) attachment and a germanium (Ge) internal reflection element (IRE), with dimensions of 52 x 20 x 2 mm and an endface angle of 45°, were used for ATR measurements. The precise number of reflections between the sample and IRE in ATR measurements should be known for the computations of optical constant spectra. For this purpose, we first put droplets of the liquid sample on the IRE, and then covered them with a polyethylene sheet of defined dimensions. Then the sample liquid was spread over the IRE, and thin liquid film with the same dimensions as the polyethylene sheet was formed between the IRE and the polyethylene sheet, as shown in Fig. 2. Thus, we obtained the number of reflections desired. One reflection corresponds to the length of 4 mm along the direction of the IRE used here. The number of reflections was defined so that the maximum peak of the sample did not exceed one in absorbance units. The optimum number of reflections was four for the silicone oil sample. The liquid film thus made between the IRE and polyethylene sheet was so thick that the polyethylene did not have any interference with the measured spectra. Because of the viscosity of the liquid samples, the liquid did not flow out from the gap between the IRE and sheet, and the sheet did not drop off during the measurements. All the spectra were taken with a high-sensitivity narrow-band MCT detector in the spectral range of 4000 to 650 cm -1, with 400 scans, and at a resolution of 4 cm-L The refractive index of the sample used in the calculation as Moo) was measured with a Bausch-Lomb Abbe refractometer with a white light at room temperature. The value of the refractive index of the DC-705 was 1.579. RESULTS AND DISCUSSION Figure 3 shows the ATR spectrum of the silicone oil sample measured with a Ge prism at the incident angle of 45°. Particular attention was paid to the reproducibility of the measurements, so that we were able to obtain the spectrum with good linearity around zero absorbance. As will be shown later, this linearity is essential
DC-705
2.00
t.8o.
P
/
s
n
for the simulation of an emission spectrum, because a small difference around zero absorbance causes a larger difference in the emission spectrum, especially for a thicker film or larger droplet. Figures 4a and 4b show the spectra of refractive index n (v) and extinction coefficient k (~), respectively, derived from the ATR spectrum (Fig. 3) by our newly developed iterative procedure. In general, it is known that the lower wavenumber side of absorption band becomes larger in ATR spectra, compared with k (~) spectra, because of the anomalous dispersion around the bands. A reasonable k (P) spectrum seems to be obtained through the correction of the distortion or peak shift. Next we simulate the emission spectra from the obtained n(P) and k(P) spectra. Figure 5 shows the simulated normal emittance for a hypothetical free-standing film with thicknesses of (a) 2 ttm, (b) 10 ttm, (c) 100 ttm, and (d) infinity. Since 0 = 0° in this case, the emittance for a free-standing film with the thickness l is equal to that for a droplet with diameter l. When the sample film is thin, the emission spectrum resembles a usual absorption spectrum. From Eq. 7, at the limit of I -~ 0, emittance becomes equal to al, which is just log(e) times the absorbance in the transmission spectrum. On the other hand, the emittance of strong bands for a thick film is saturated to the value of infinite thickness. At the limit of l -- oo, the emittance becomes [1 - R0(0, P)] and the
0.700.60-
0C-705 ATR spectrum IRE: 6e Angle: 45 degrees 4 reflections Non-polarization
t.40.
1.20-
t.00 3600
0.50-
2t50 Wavenumbers (cm"l) 0C-705
700.
k spectrum
0.40-
0.30k 0.20-
O.iOb 0.00 3600
2i50 Wavenumbers (cm-')
700.
Fio. 4. Optical constant spectra of DC-705 calculated ~om the ATR spectrum (Fig. 3). (a) Re,active index. (b) Extinction coefficient spectra.
shape of the spectrum becomes like that of a normal reflection spectrum. Figure 5 also shows that the noise increases as the film becomes thicker. In order to explain the cause of this phenomenon, we introduce the error analytical point of view. 11,12In Eq. 7, Ro is negligible in comparison to [1 e x p ( - a / ) ] for moderate to weak bands. Therefore, emittance can be approximated as E(~, ~) = 1 - exp[-~(~, ~)./].
=, o.5o-
(20)
Then the noise level in emissivity AE can be expressed by the noise level in the absorption coefficient Aa as
0.40< 0.30-
AE = (dE/da)Aa = l x exp[-a(8, ~)./] x Aa.
0.200.t00.00 3600
t.579
t. 60.
zR
G FIG. 2. Experimental setup for ATR measurements. S: sample liquid; P: polyethylene sheet; G: Ge IRE; IR" incident IR light.
0.80-
n-infinity:
n spectrum
2t50 Wavenumbers {CB"l}
700.
FIG. 3. An FT-IR/ATR spectrum of the silicone oil, DC-705, measured with the IRE of Ge, the incident angle of 45°, and 4 reflections.
(21)
This equation expresses that the noise level AE is expanded with the thickness l of the sample, even if Aa is small. In Fig. 6, the expansion ratio (dE/da) is plotted against the thickness l schematically. The ratio has a maximum at l = l/a, and the maximum value is 1/(ae). This means that the noise level AE can be exaggerated more as the absorption coefficient becomes smaller. As APPLIED SPECTROSCOPY
117
DC-705 normal emittance
Expansion ratio of noise level
0.50
0.40-
tie
0.30x
0.20-
O. t0-
"
3600
i--
2t50
0.00
700.
i
I
-
ooo
Wavenumbers {cm-I}
i
1oo
2bo
3'oo
4.bo
5.oo
Thickness x Oo
FIG. 5. Simulated emission spectra of DC-705 for the hypothetical free-standing films with thickness of (a) 2 pm, (b) 10 pm, (c) 100 pm, and (d) infinity (8 = 0°).
mentioned before, this is the reason why we need an absorption spectrum with the small noise in its zero line for the simulation of the emission spectrum. The maximum values are shown in Table I for the case having = 1000 cm -1 and normal emission, where a(0, P) is equal to 41r~k(P). In spite of the presence of such a noise, however, the simulated spectrum reproduces the experimental emission spectrum measured for the same kind of materials? 3 Figure 7 is the hemispherical emittance of a droplet of DC-705 with a diameter of 100 pm, simulated with the use of Eq. 8. The band shape of the spectrum is almost the same as that of the normal direction with the same diameter (Fig. 5c), but the absolute values of the emittance are smaller because the larger angle components with lower emittance contribute to the hemispherical emittance through the sin(20) term in Eq. 8. To calculate the energy value of the emitted light, one must multiply the emittance by Planck's equation (2). Figure 8 shows the normal emissive power of a droplet with 100 pm diameter of 500 K calculated by Eq. 9. The wavenumber region of the maximum of the emittance of the silicone oil agrees with that of the emissive power of the blackbody at this temperature. We can expect the effective performance of the material as an emission medium around this temperature. In Fig. 9, the hemispherical emissive power is shown for the same droplet as used in Fig. 8 at (a) 500 K, (b) 400 K, and (c) 300 K. As the temperature is lowered, the
Fro. 6. The expansion ratio of the noise level dE/da plotted against the thickness L
maximum of the blackbody emission is shifted from the emission bands of the silicone oil toward lower wavenumbers. The area surrounded by the x-axis and each spectral line in Fig. 9 expresses the total emissive power, which means the energy flux emitted from unit surface area per unit time, at each temperature. The total emissive power and total emittance of the silicone oil calculated by Eqs. 11 and 13 are given in Table II, along with the corresponding values of the blackbody. It is assumed that there is no absorption at wavenumbers under 700 cm -1. The silicone oil has an emittance of 0.56 at 500 K, while it is reduced to 0.40 at 300 K, which indicates the temperature dependence of the emittance of the actual material. The temperature changes of a droplet with the diameter of (a) 100 #m, (b) 10 #m, (c) 2 #m, and (d) 1 pm are shown in Fig. 10 for the first two seconds with the initial temperature of 500 K. As the diameter of the droplet decreases, the cooling rate of the droplet in-
1.00
0C-705 hemispherical emittance of a droplet
0.80
0.60 .,..~
o.4oT A B L E I. Maximum of the expansion ratio dE/da of the noise level in emittance to the noise level in absorption coefficient a for given extinction coefficients k at v = 1000 cm 1 and 0 = 0 °.
118
a (cm-') (=4~vk)
dm~ (pm)
d E / d a = ~ (cm)
k 0.001 0.01 0.1 1.0
12.57 125.66 1256.6 12,566.
795.8 79.58 7.958 0.796
0.02927 0.002927 0.0002927 0.0000293
(=l/a)
Volume 42, Number 1, 1988
(=l/(ae))
0.20-
0.00 3600
2150 Wavenumbers
700.
{cm°l}
FIG. 7. Simulated hemispherical emission spectrum of a droplet of DC-705 with a diameter of 100 pm.
"2
DC-705 normal emissive power
800.
TABLE II. Total emissive power of a droplet I(T) of DC-705 with a diameter of 100 pm and of the blackbody Ib(T) and total emittanee E(T) of the droplet at given temperatures.
.4 700.
600.
Temperature (K)
1(73 (105 erg/ (sec.cm~))
Ib(73 (=~T 4) (10 ~ erg/ (sec.cm2))
E(T)
500.
300 400 500
1.84 7.45 19.71
4.59 14.51 35.44
0.401 0.513 0.556
Blackbody~/~~ ~j~J'
400.
0C-705
300. g
200.
/
j,
ioo. m
0.00 3600
2t50 Wavenumbers
Diameter. 0.0t cm Temperature: 500 K 700.
(cB")
FIG. 8. Simulated emissive power of a droplet of DC-705 with a diameter of 100 p m a n d blackbody at 5 0 0 K ( 0 =0°).
creases, as expected from Eq. 16. However, as mentioned before, the emittance E(0, ~) is linearly proportional to the diameter, for droplets with small diameters. Therefore, we can expect the upper limit in the cooling rate to be at the limit of the small diameter. In the first two seconds, the temperatures of droplets with diameters of 100 pm, 10 pm, 2 pm, and 1 pm were calculated to be 409 K, 307 K, 260 K, and 252 K, respectively. Figure 11 shows the effect of the number density of the droplet sheet on the temperature change. In this case, the sheet thickness of 1 cm with the number density N of (a) 10,000/cm 3, (b) 1000/cm 3, and (c) 100/cm 3 corresponds to the optical depth % of the order of 1.0, 0.1, and 0.01, respectively. This figure shows that the denser cloud causes absorption by the droplet of the light emitted from other droplets, and results in the retardation of the cooling rate. As the optical depth decreases, the temperature change becomes identical to the single drop-
2500-
DC-705 hemispherical
let case (Fig. lld). The cooling rate is extremely reduced for lower temperatures. The main reason for this is, of course, the fourth-power temperature dependence of the blackbody, as shown in Eq. 13; the other reason is the temperature dependence of the emittance of the material mentioned above. In the first ten seconds, the temperatures of the sheet of the silicone oil droplet with a diameter of 100 pm were calculated to be 346 K, 309 K, 303 K, and 300 K for the cases of 10,000/cm 3, 1000/cm 3, 100/cm 3, and the optically thin limit (that is, the single droplet), respectively. In these simulations, we did not take into account the contribution from the far-infrared region under 700 cm -1 to the total emittance. However, the main characteristics of the emission behavior of the droplet and the droplet sheet are considered to be well expressed in Figs. 10 and 11. CONCLUSIONS Starting with strict optical constant calculations, we have developed a general method for simulating the total performance of the droplet space radiator. Using this method, we have predicted the temperature changes of one droplet and also the sheet of the droplet with a given optical depth, caused by infrared emission. We added the assumption, in the method used here, that there is no temperature gradient among the droplets and within one droplet. This assumption is reasonable, especially for the cases of a small droplet and a thin droplet sheet. When the droplet is large, or the droplet sheet is sufficiently thick, a temperature gradient is expected to occur
emissive power Temperature
500.
~
2000-
Diameter:
0.01
cm
change of a
droplet
450.
u
400.
t5oo-
t000-
g 350.
b
2 300.
-4
-~ 500.
250. 0.00 3600
3000
2400
tBO0
Wavenumbers
t200 (cm-f)
600.
0.00
FIG. 9. Simulated hemispherical emissive power of a droplet of DC705 with a diameter of 100 pm and blackbody at (a) 500 K, (b) 400 K, and (c) 300 K.
Initial
200. O.O0
temp:
O.40
i
,
O.80 t. 20 Time (sec)
,
,
t. 60
2. O0
FIG. 10. The temperature change of single droplet of DC-705 with diameters of (a) 100 pro, (b) 10 pro, (c) 2 pro, and (d) 1 pro.
APPLIED SPECTROSCOPY
119
500.
Temperature change of a droplet sheet
power of stratified multilayered system with t e m p e r a t u r e gradient along the direction of the depth, s This p r o g r a m can be readily extended to the system of a droplet or a droplet sheet. This m e t h o d will offer a good starting point for the simulation of n o n s t a t i o n a r y states.
i
450.
ACKNOWLEDGMENT The authors gratefully acknowledgethe financial support of National Aeronautics and Space Administration (NASA-Lewis) under Grant NAG 3-705.
,,,, 400. o,1
~- 3 5 0 . I---
Diameter:
300.
250.
0.01 cm
I n i t i a l temp: 500 K
0.00
Coo
4.'00
6.bo
e.~o
lo.o
Time (sec) FIG. 11. The temperature change of a droplet sheet with a thickness of I cm and a number density of (a) 10,000/cms, (b) 1000/cm3, and (c) 100/cm 3, and of (d) a single droplet, of DC-705,with a diameter of 100 #m.
even if there is no t e m p e r a t u r e gradient at the initial stage of the droplet generation. T o predict the emission behavior of such a system, we should consider the time d e p e n d e n c e of the t e m p e r a t u r e gradient. We have alr e a d y developed a new algorithm to obtain the emissive
1. A. T. Mattick and A. Hertzberg, J. Energy 5, 387 (1981). 2. A. F. Presler, C. E. Coles, P. S. Diem-Kirsop, and K. A. White III, AIAA/ASMEThermophysics and Heat Transfer Conference, 86HT-15 (1986). 3. D. L. Allara, A. Baca, and C. A. Pryde, Macromolecules ll, 1215 (1978). 4. G. K. Ribbeg~rd and R. N. Jones, Appl. Spectrosc. 34, 638 (1980). 5. R. T. Graf, J. L. Koenig, and H. Ishida, Appl. Spectrosc. 39, 405 (1985). 6. K. Ohta and H. Ishida, paper submitted to Appl. Spectrosc. 7. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), Chap. 4. 8. K. Ohta and H. Ishida, paper submitted to Appl. Opt. 9. P. H. Thomas, Brit. J. Appl. Phys. 3, 385 (1952). 10. T. W. Hoffman and W. H. Gauvin, Can. J. Chem. Eng. 39, 179 (1961). 11. T. Hirschfeld, Appl. Spectrosc. 30, 550 (1976). 12. K. Ohta and R. Iwamoto, Anal. Chem. 57, 2491 (1985). 13. W. P. Teagan and K. Fitzgerald, NASA CR-174807 (1984).
Demonstration of Reciprocity in the Angular Pattern of Fluorescence Emission Collected from Langmuir-Blodgett Deposited Thin Films P. A. SUCI* and W. M. REICHERT Bioengineering Department, University of Utah, Salt Lake City, Utah 84112
Application of a principle of reciprocity results in an explicit prediction for the angular pattern of fluorescence emission which is detected in the far field from a fluorophore located in a thin film between two dielectric interfaces. With the use of the method of Langmuir-Blodgett deposition, thin films of three different thicknesses were deposited on the fiat surface of a hemicyclindrical quartz prism. Each film was constructed so as to contain a plane of fluorophores located at a specific distance from the prism/film interface. According to the principle of reciprocity, a distinct angular pattern of fluorescence is predicted for each film type. The close correspondence of fluorescence data curves with theoretical curves lends empirical support to the validity of the principle. The prediction made by this principle of reciprocity is relevant to the analysis of observation angle data obtained from variable angle total internal reflection fluorescence spectroscopy (VA-TIRF) and related techniques. Index Headings: Reciprocity; Spectroscopy of Langmuir-Blodgett deposited thin films; Variable angle total internal reflection spectroscopy; Evanescent wave spectroscopy.
Received 7 July 1987. * Author to whom correspondence should be sent. 120
V o l u m e 42, N u m b e r 1, 1988
INTRODUCTION F r o m a biomedical perspective the characterization of thin dielectric films is i m p o r t a n t because of its relevance to protein adsorption studies. In general, optical techniques provide relatively nondestructive m e t h o d s of obtaining information about thin films, and offer the possibility of monitoring dynamic processes. The thickness and refractive index of protein films adsorbed to various surfaces have been d e t e r m i n e d by ellipsometry. 1'2A t t e n u a t ed total reflection techniques measure optical absorption (Fourier t r a n s f o r m spectroscopy) 3 or fluorescence (total internal reflection fluorescence spectroscopy) 4,5 within a film adsorbed to a dielectric substrate. Variable angle total internal reflection fluorescence spectroscopy (VAT I R F ) , e,7 also known as evanescent wave-induced fluorescence (EWIF), 8-1° can provide information a b o u t the density of fluorophores with respect to distance away from the solid s u p p o r t (into the film).
0003-7028/88/42o1-o12752.00/o
© 1988 Society for Applied Spectroscopy
APPLIED SPECTROSCOPY
