Anal. Chem. 1983, 55, 1537-1543
LITERATURE CITED
Table IV,, FTI:R Determination of SiOH and SiH in Known RTV-Silicone Formulations formu-
lation 1
2 3 4 5 6 7 8 9 10 11 12
wt % OH ____ added found 0.69 0.56 0.60 0.80 0.80 0.87 0.70 0.52 0.70 0.70 0.70 0.70
(1) Noll, W. "Chemistry and Technology of Silicones"; Academic Press: New York, 1968. (2) Warrick, E. L.; Pierce, 0. R.; Polmanteer, K. C.; Saam, J. C. Rubber Chem. Techol. 1979, 52, 437. (3) Horn, G. Plaste Kautsch. 1979, 1 1 , 634-637. (4) Owen, J. J. CHEMTECH 1981, 1 1 , 288. (5) Caprino, J. C. Rubber World 1982, 185, 33-34, 39. (6) Mark, J. E.; Andrady, A. L. Rubber Chem. Techno/. 1981, 5 4 , 366-373. (7) Andrady, A. L.; Llorento, M. A.; Sharaf, M. A,; Rahalkar, R. R.; Mark, J. E. J. Appl. Polym. Sci. 1981, 2 6 , 1829-1836. (8) Gottlieb, M.; Macosko, C. W.; BenJamin, G. S.; Meyers, K. 0.; Merrlll, E. W. Macromolecules 1981, 14, 1039-1046. (9) Jones, K; Biddle, K. D.; Das, A. K.; Emblem, H. G. Silic. Ind. 1981, 46,107-111. (10) Whlte, M. l..; Serplello, J. W.; Striny, K. M.; Rosenzweig, W. IEEE Proc. Int. Re/.-Phys. 1981, 430-47. (11) Wong, C. P. ACS Symp. Ser. 1982, 171-183. (12) Rotzsche, H.;Clauss, H.; Hahnewald, H. Plaste Kautsch. 1979, 7 1 , 630-632. (13) Kohler, R. H. Anal. Chem. 1974, 4 6 , 1302. (14) Gilman, H.; Miller, L. S.J. Am. Chem. SOC. 1951, 73, 2367. (15) Kellum, G. E.; Smith, R. C. Anal. Chem. 1967, 39, 1877. (16) Smith, A. 1.. "Analysls of Slllcones"; Wiley: New York, 1974; pp 248-285. (17) Wurst, M.; Churaceck, J. Collect. Czech. Chem. Commun. 1971, 3 , 3497-3506. (18) Dallimore, G. R.; Milllgan, R. J. SAMPE J. 1982, 78, 8-13.
wt % H added found
0.70 0.62 0.63 0.81 0.82 0.89 0.73 0.54 0.68 0.72 0.72 0.72
0.083 0.050 0.11.7 0.050 0.117 0.083 0.083 0.083 0.139 0.028 0.083 0.083
0.089 0.053 0.124 0.053 0.089 0.089 0.089 0.088 0.146 0.029 0.089 0.089
Total SiOH and SiW were determined in the RTV-silicone formulations immediately after their preparation. The results in Table IV show excellent agreement between the amount added and the amount found. However, when these same formulations were analyzed after aging at room temperature, the total SiOH content decreased. This lends further support to the idea that the low results seen for percent DPMS and TPS were because they were not analyzed immediately. Registry No. TPS, 682-01-9; DPMS, '778-25-6; tetraphenyldimethyldisiloxane, 807-28-3.
1537
RECEIVED for review February 7,1983. Accepted May 1,1983. The Bendix Corporation, Kansas City Division, is operated for the U.S.Department of Energy under Contract No. DEAC04-76DP00613.
Pulsed Laser Induced Thermal Diffraction for Absorption Measurements in Small Volumes M. J. Pelletler and J. M. Harrls" Department of Chemistty, UniversiW of Utah, Salt Lake City, Utah 84 112
Absorptlon of radiation from an Interference pattern, formed at the Intersection of two laser beams, can be used to generate a thermal dlffractlon grating In a sample. This grating can be probed with another laser beam, produclng a sensitlve, small volume almrptlon measurement. I n thls work, a pulsed laser forms the gratlng, thus making more effective use of the laser energy than contlnuous wave excltatlon. I n addition, time resolutlon of the dlffractlon signal allows dlscrlmlnatlon agalnst fluorescence and Raman scattering from the sample. The effective volume of the thermal gratlng and the dlffractlon efflclency vs. beam spot slze are studied, and the results are dlscussed relative to small volume absorption measurements. Practlcal mattors affecting the analytlcal appllcatlon of the technlque, suoh as allgnment constralnts and sources of background, are also consldered.
The introduction of lasers into analytical spectroscopic instrumentation has produced, in many cases, significant advances in detection compared to the use of conventional light sources. These improvements arise not simply from the increased optical power of the laser but more often from the unique coherence properties of the beam. For example, the spatial coherence of laser radiation allows the beam to be focused to a diffraction limited spot suitable, for example, for
exciting fluorescence in extremely small volume samples (1-4). The small rate of divergence of laser radiation, another manifestation of the spatial coherence, is responsible for the production and detection of a thermal lens within a sample, which can be used to measure the absorbance of trace-level, nonfluorescent species (5). The temporal coherence of laser radiation, related to the monochromaticity, allows one to detect small optical path differences interferometrically, which has been applied to both thermooptical absorption measurements and refractometry (6). Another thermooptical absorption method, thermal diffraction or real-time holography, has been made possible because of the unique properties of laser radiation. By splitting a laser beam and recombining the two beams within a sample, we can utilize both the spatial and temporal coherence of the beams to generate a regular interference pattern which produces excited states only at the planes of constructive interference. Following nonradiative relaxation of the excited molecules, the resulting periodic temperature distribution can be probed as a transmission grating by diffraction of a another laser beam into a detector. While the generation and detection of thermal gratings or real-time homograms have been studied for many years (7-9), the use of this thermooptical element for calorimetric absorbance measurements has only recently been considered (IO). In this first analytical study of laser-induced thermal diffraction, a
0003-~700/83/0355-1537$0 1.50/0 0 1983 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 55, NO. 9, AUGUST 1983
chopped CW laser was used for excitation. Because of the short relaxation time of the thermal grating, a CW source is limited in the amount of energy it can effectively deposit in the sample. In the present work, a pulsed laser is utilized, the pulse duration of which is much shorter than the thermal time constant. As a result, all of the energy produced by the laser is available for deposit into the grating. This work also considers the effective volume of the thermal grating, the diffraction efficiency vs. beam spot size, and the consequences for small volume absorption measurements. Practical concerns, such as alignment constraints and sources of background signal, are discussed. To deal with the questions concerning diffraction efficiency, a theoretical treatment of the phenomenon is presented.
THEORY A thermal grating is generated by a plane wave interference pattern produced at the waists of two intersecting laser beams. A coordinate system within which to describe the phenomenon can be chosen where the two beams propagate in the X,Z plane a t angles +O and -0 from the Z axis, respectively, and intersect at the origin with a combined angle of 20 between the beams. The intensity of the interference pattern depends on the vector sum of the electric field of the beams = [ E @ )+ E(-O)l[E*(@+ E*(-@] (1) where E(0) and E(-@ are the electric fields of the beams propagating at angles 0 and -0 from the 2 axis, respectively, and the asterisk designates complex conjugate. Using the following transformation to project the beam propagation expression onto the coordinate system described above and assuming 0 is a small angle I(Z,Y,Z)
= X - X02/2 - 0 2 2' = 2 cos 0 + X sin 0 2 - 2 0 2 / 2 + OX X ' = X cos 0 - 2 sin 0
(2)
The electric field of a Gaussian laser beam propagating at an angle 0 from the Z axis is given by (11)
where the confocal distance or Rayleigh range Z R = nw;(X, where the waist of the beam having spot size wo is at the orign, and where X is the wavelength of the laser in the medium. The interference pattern at the beam intersection can be found by substituting eq 3 into eq 1. The terms E(O)E*(O) and E(-O)E*(-O) describe the average intensities of the two beams; these are neglected in the calculation since they do not produce interference. The resulting expression describing the interference intensity is
I(x,Y,Z)= 4EO2exp[-2(X2 COS
+ +
+
02P)/u$] [ ( ~ T O X / X ) ( Z R ~+ / ( Z,"))] Z ~ COS [4aZ/X] (4)
The fact that the interference intensity can be negative is a consequence of ignoring the two noninterfering terms from eq 1. This eliminates the complications of fringe visibility in the diffraction calculations and allows one to consider only the spatially modulated part of the sample excitation. The exponential term in eq 4 describes the overall shape of the interference pattern, which is a three-dimensional Gaussian volume. The two cosine terms determine the fringes in the pattern, of which there are two sets. One set, described by the first cosine term, is parallel to the Y,Z plane and has a fringe spacing near the waist, A, = h / 2 sin 0 or with a small angle approximation, A, = X/20. Away from the waist, the
curvature of the laser beam wavefronts causes the spacing between fringes to increase by a factor (I? + ZRz)/ZRz.The other set of fringes, parallel to the X , Y plane has a spacing Az = X/2 cos 0 or A, = X / 2 when 0 is small. An absorbing sample placed at the beam intersection can convert some fraction of the optical energy into heat through nonradiative relaxation of the excited states. The resulting sinusoidal temperature difference decays exponentially (8) with a time constant which depends on the fringe spacing, A PC,A2
t, = 4n2k
(5)
where p is the density, C, is the specific heat, and k is the thermal conductivity. For pulsed excitation of the sample, where the laser pulse is much shorter than t,, the temperature increase created at the central fringe of the pattern depends on the combined pulse energy of both beams, E, in Joules, and the decadic absorbance per unit length of the sample in cm-', cy, assuming all the energy absorbed is converted to heat 4 ln(10) Epa AT = (6) 4,wo2
Since refractive index varies linearly with temperature for small changes in temperature, An = (dn/dT)AT, the heat deposited into the sample produces a spatial modulation of refractive index proportional to AT and the interference pattern of eq 4. The periodic refractive index structure is equivalent to an optical phase grating or phase hologram. This phase grating can be detected by passing a probe beam through the intersection volume of the excitation beams at an angle which satisfies the Bragg condition for one of the two sets of fringes described above. For this work, the fringes parallel to the Y,Z plane are used due to the larger spacing, A,, which produces a longer time constant, t,, and the longer interaction length
d = uo/sin 0 (7) The fringes in the X , Y plane, although not utilized, could affect the diffraction efficiency of the grating in the Y,Z plane. This is due to the nonlinear nature of the diffraction response (see below) giving rise to cross modulation. Because of the small fringe spacing, A2, and the resulting short time constant, t,, any effect of these fringes decays faster than the time response of the present instrument and could not be observed in this work. The efficiency with which the phase grating can diffract a probe laser beam can be determined from An, the peak refractive index change, using the coupled wave diffraction theory of Kogelnik (12). This theory, which is the simplest and most intuitive of the many methods used to calculate diffraction efficiency, has been recently modified by Moharam, Gaylord, and Magnusson (13) to describe diffraction from three-dimensional, crossed-beam volume gratings. Their result for probing the grating with one of the excitation beams in the limit of weak modulation is given by Anw,
where Xo is the vacuum wavelength of the probe beam. Slightly higher diffraction efficiency is predicted for probing with a beam which is somewhat smaller in spot size than the excitation beams, while use of a longer wavelength probe decreases efficiency (13,14). In this work, the ratios of spot sizes of the probe and excitation beams, wp/w,, ranged from 0.6 to 1.0 while the wavelength ratio was X,/h, = 1.19. These values would reduce the observed efficiency compared to that
ANALYTICAL CHEMISTRY, VOL. 55, NO. 9, AUGUST 1983
Table I. Focussing Optics for Varying Heam Spot Sizes pump beama spot size, lens focal approx distC pm lengths, mm to sample, cm
spot size, wn 1370 200
2300 21 4
e 445
47.5
57
75 140
17 44
50
19
75 50
17 35
20
probe beam lens focal lengths, mm e 75 10 140 75 10 140 75 10 140
1539
approx dist to sample, cm 80 6gd 41 86 7Zd 50 87 70d 50
The HeNe laser output mirror was approxia The Nd:YAG laser output was approximately 1.5 m from the sample. mately 1.0 m from the sample. To be used only as a guide for construction. Optimization should be carried out as Measured from the object end of the microscope objective, nearest to the sample. e None described in the procedure. used. predicted by eq 8 on the average about 14% (14). The relationship between diffraction efficiency and the sample properties is obtained by substituting eq 6 times (dn/dT) into eq 8 to give
The diffracted light intensity, therefore, depends quadratically on the sample absorbance. The sensitivity is expected to increase, as with other thermooptical measurements, for solvents having a large (dn/dT). Unlike CW laser excitation of the grating ( l o ) , the response does not depend on the thermal conductivity of the sample but rather on its heat capacity, due t o the short pulse excitation condition. The approximate volume of the grating given as an ellipsoid bounded by foo from the center of each beam is
V = 8rwO3/(3sin 20)
(10)
The sensitivity to sample concentration, proportional to a, is expected to increase with decreasing coo which also reduces the volume of sample probed by the grating. This trend was tested in this work to the limit where the number of fringes in the grating become fewer than the theory requires. Decreasing the angle at which the excitation beams cross, 20, increases sensitivity due to a larger interaction length and while simultaneously increasing the volume of the grating but only in proportion to the angle. For situations where the entire grating is utilized, the sensitivity of pulsed laser-induced thermal diffraction is therefore optimized when the spot size of'the excitation beams and their angle of intersection are small. The effectiveness of all portions of the grating volume is not equal, however, as the modulation intensity distribution of eq 4 shows. As a result, a better tradeoff between sensitivity and volume might be obtained by using less than the total volume of the grating as defined by eq 9. A study of this concept was carried out as a part of this work.
EXPERIMENTAL SECTION Instrument. An optical diagram of the thermal diffraction instrument is shown in Figure 1. The entire system was constructed on a 4 fi. X 10 ft optical table NRC Model KST-410. The
excitation beam is provided by a Quantronix Model 114R-O/QS SHG Nd:YAG laser system operated at a lamp current of 36.5 A, a Q-switched repetition rate of 100 Hz, and a pulse duration of about 100 ns. The average power was 46 mW at 532 nm, the second harmonic of the laser transition generated by an intracavity, angle tuned SHG crystal. The average power of the laser could be increased by enlarging the diameter of the spatial mode selector, but increases of more than a factor of 2 in average power
--
Figure 1. Optical dlagram of thermal dlffraction instrument: BFO's are beam focuslng optics (See Table I); Ml-M5 are mirrors; BS, BC, and BB are a beam splitter, comblner, and blocker, respectively; S Is the sample cell; F1 and F2 are interference filters; and PMT Is the photomultipller tube. The solid lines indicate the 532-nm excitatlon beams; dashed lines indicate the 633-nm probe beam. The section of the diagram wlthin the dash-dot boundaries is drawn to scale, although the angles between the beams have been exaggerated for clarity.
were accompanied by a noticeable reduction in spatial mode quality. The excitation beam was sent through focusing optics to an interferometer that divided the beam into two equivalent beams and crossed the two beams at their waists in the sample. The angle between the excitation beams, 28, was 3.15' outside the sample. Since the refractive index of the aqueous solvent was 1.33, the angle between the beams in the sample was 2.37'. The beam splitter and beam combiner were two halves of the same plate dielectric beam splitter, Rolyn Optics Model 68.0425. The probe beam was provided by an Aerotech Model PS-5 polarized 5-mW helium neon laser at a wavelength of 632.8 nm. The beam was sent through focusing optics directed into the sample through the beam combiner by mirrors M I and M2 in Figure 1. These two mirrors gave the necessary degrees of alignment freedom for the optimization of the probe beam position, the Bragg angle, and the vertical beam angle. Although the beam polarization at the sample was slightly elliptical, most of the intensity was vertically polarized. The configuration of the focusing optics was changed in order to obtain different beam diameters in the sample. Table I gives the position and focal length of the lenses used in each configuration. The 1 cm focal length lens was a microscope objective from Newport. The other lenses, having focal lengths less than 100 cm, were 25 mm diameter, double convex simple lenses from Rolyn, while those having focal lengths greater than 100 cm were plano-convex. The lenses were all tilted slightly off axis in order to allow the front surface reflections to be removed by spatial filtering. The transmitted probe beam and the pump beam nearest to it were blocked 10 cm after the sample. The other pump beam was filtered out by an argon laser mirror acting as an interference filter. The diffracted probe beam was transmitted by the filter
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ANALYTICAL CHEMISTRY, VOL. 55. NO. 9. AUGUST 1983
with 60% efficiency and reflected from a mirror, M4,W cm away from the sample to a 1.5 an square aperture 85 an from M4. The aperture contained a dielectric interference filter having a peak transmittance of 632.8 nm of 67% and a full width at half maximum of 12 nm. The light transmitted through this filter was detected by a Hamamatsu R372 photomultiplier wired for maximum pulsed response (15). The photomultiplier current was dropped across a 8200-R resistor and the voltage was measured by a Tektronix 5403 oscilloscope and a Nicolet 1110 signal averaging system with a Model 174, 10 MHz plug-in. The samples were held in a 1-cm flow cell. Solutions were pumped through a Millipore Millex-SR 0.5-Fm filter to the sample cell hy a Gilson Mmipuls peristalticpump. Samples were changed by introducing an air bubble into the flow and then pumping 40 mL of the new solution through the system. The pump was then turned off, and after 1min to let the sample settle, data collection could begin. Procedures. The sizes of the beams at the intersection mint were determined by measuring the ratio ofthe amount of intensity transmitted by a pinhole sQVQdtimes larger than the beam spot size and hy a pinhole comparable to or smaller than the spot size ( 1 1 , I f i i . It is necessary tu use the larger pinhole rather than no pinhole at all to measure the full h a m intensity tn avoid scattered light which ran dktort the result. The iocused Q-switched SdYAC. h e r henm was capahle of dsmGng the pinholes a+well as rrearing new onn. To circumvent this problem. the pimp beam spot sizes were measured with the Q-switch turned off. Under these conditions, the laser inrillales continuously, generating a feu milliwntts of532-nm radiation. '1% CW beam had the same unfowxed diameter and far tield divergence as the Q-switched beam, therefore inferring the Q-switehed b n m waist pmition and size from the CW hcam was prahably a g o d approximntion. Since the CU' laser beam contains a aignificant amuunt of energy a t the 1.06 rm fundamental due to the poorer second harmonic generation efficiency, it w8q. newwary U,place a filter immediately hefore the detector to avoid spurious renullo. The si7e of the pinhuleq ured was rhecked by measuring 1 hP diffraction pattern ohserved when illuminated hy the unfucused prohe laser (/7), Ream waist spot sizes were also confirmed by measuring the far-field divergence of the heamp. The optical alignment of the instrument waq a straightforward procedure. The Q-switch of the Nd:YAC. laser was turned off during the initial stages of alignment. The sample cell was replaced hg a pinhule having a radiuq romparable in size to the pump beam radius. The focusing uptics were translated to maximize intensity transmitted through the pinhole for both the pump and the prohe heams. T h i n procedure Iwali7ed the heam waists in the vicinity of the pinhole. Fine tuning of the waiqt Incations along the 1 axis could he done by observing the symmetric intensity profile of the henms visually and making minnr changes in the focusing optics. The two pump beams and the prohe beam were then simultaneouqly aligned through the pinhole and their spot sizes were meniurrd by using the above pruredurc. The heams were adjusted so that the three tmnsmitted spot.?. in thP far field were in the same horizontal plane. In addition, the probe heam wits adjust4 LO the angle calculated tn Pntiafg the 1 3 r w condition. The pinhole was then replaced w i t h a sample cmtaining a solution having an ahsorhnnre of about 0.1. the Q-switch wa5 activated, and a strong thermal diffraction signal was usually observed without further alignment. An alignment optimi7ation could then be carried out based on the mwitiide ofthe observed .iignal. The entire system could be redipnPd and reoptimired in about an hour Idlowing a major change of focusing optics. Chemicals. A cohalt sulfate stock sdution was prepared by dissolving 44.4 g of CoSO,.:H,O with aqueous H,SO, 115 mM) tu make 2 L of a 79 mM wlution. The molar absorptivity at 51 2 nm measured spertrophotnmetrirallg agreed with the NBS value ( 1 R l . = .1.MI( 11.' cni '. At the Nd:YA(> laser wavelength. X = 532 nm. the molar absorptivity was measured to he t = 3.92 M-' mi'. 1 x 4value was uwd LO calculate the absorbance of solutions prepared bv quantitative dilution ufthc stock solvtiun in aqumuq ~
..
~~~~~~~~~
~
~~~~
H,SO,.
RESULTS AND DISCUSSION Alignment Constraints. Since the laser-induced diffraction experiment h a s many more optical constraints than
Flew 2. Fringe pattern for Gaussian l a w beams illustrated by MoEe fringes. A section of the beam from Z = -I,to Z = Z, is iilusbated: (top) beam waists overlapped. small 8; (middle) beam waists overlapped, larger 8; (bottom)beam waists offset by -O.5Zw
other thermooptical absorption methods, the degree of difficulty in aligning and optimizing the instrument will he considered. To observe diffraction from the thermal grating, four conditions must be satisfied. First, the spot sizes of the beam waists of the pump-and-probe lasers must he of comparable size, preferably having the probe beam smaller than the pump to a degree which depends on their relative wavelengths (14).To achieve a particular spot size, one must choose optics depending on the confocal parameters of the laser and the total distance between laser and sample (19). Secondly, the waists of the two excitation beams must be located at point of intersection. When this condition is met, a long region of uniformly spaced fringes is obtained due to the planar phase fronts of the beam near their waists. This is illustrated with a Moiie fringe pattern illustration (20) in Figure 2 (top and middle). When the waists of the beams do not correspond to the center of the intersection, as in Figure 2 (bottom), the spacing of the fringes becomes irregular. These effects would be expected to cause dephasing of the radiation scattered from the grating volume, which would drastically reduce the diffraction efficiency. It is estimated that the heam waists were located in this work to within a fraction (0.2 to 0.4) of the Rayleigh range, Z ,, which ranged from 27 cm to 2 mm in the focused beam studies. The third alignment constraint for observing diffraction is adjusting the angle of the probe beam relative to the thermal grating for the Bragg condition. Since this condition requires that diffraction from all portions of the grating constructively interfere, increasing the interaction length or thickness of the grating, d , decreases the allowable error in Bragg angle. Kogelnik (12) derives a rule of thumb for the angular error within the sample, resulting in a 50% reduction in diffraction efficiency A & p = A/2d = X/400 (11) where Xis again the wavelength of the excitation laser in the sample medium. An experiment measuring the Bragg angle tolerance was carried out for an excitation heam spot size of 214 Fm, wing a 26 mM CoSO, sample. The measured external half power angle was 2.7', corresponding to ABll2 within the sample of 2.0'. This is comparable to the value 2.8' predicted by eq 11. The most severe alignment requirement in the diffraction experiment is that the two excitation beams and probe heam overlap in the sample. Since the angular tolerance depends
ANALYTICAL CHEMISTRY, VOL. 55, NO. 9,AUGUST 1983 NLIMBER so 20 IO 3 7 I
OF FRINQES 4 3
ORATING 102
103
2.5 1
I
VOLUME
(rill
10
2
I
I
I
20
30 I/&
40
50
(rnrn-1)
Flgure 3. Square root of diffracted intensHy vs. inverse spot size. The corresponding grating volume and number of fringes are also indicated. The dashed line represents the ideal proportional response.
on the ratio of the beam spot size at the sample to the distance from the mirrors to the sample, the last mirrors reflecting each beam into the sample are used to accomplish the final beam overlap. The worst case exists for the probe beam where the mirror to sample distance is greatest, about 13 cm. For a 10% error in beam overlap, the minimum probe beam position error would be 2-20 p m for the focused beam studies. This corresponds to an angular tolerance of 3-30”, respectively. As a comparison, the misalignment responsible for a 50% power reduction in a CW argon ion laser was measured to be slightly over 10”. The overlap alignment constraints, therefore, can be met by using standard kinematic optical mounts if the interferometer dimensions are kept small. The need for a vibration-free thiermally stable experimental bed is also apparent. Despite these rather critical alignment constraints imposed on the laser beams which form and probe the grating, the position of the sample was not found to be critical as long as the grating volume was within the sample. The sample cell could be removed and replaced in its holder with no observable effect on the signal. This is not a surprising result, since the angles of the three laser beams are equivalently affected by Snell’s law as they pass through the planar dielectric interface of the sample. Small angular changes in the plane of that interface relative to the beam propagation axes cause the position of the grating in the sample to move but do not affect the overlap or relative angles of the beams. The insensitivity to small changes in the sample orientation would facilitate changing samples without realignment of the instrument. Furthermore, the manipulation of sample to examine the spatial distribution of absorptivity would be possible. Sample Volume Considerations. The greatest analytical potential for thermal diffraction appears to be in measuring weak optical absorption in small sample volumes. The sensitivity of the measurement, in principle, improves with decreasing pump beam spot size, as shown by eq 9, which also reduces the volurrie of the grating. This assumption was tested with the four different pairs of pump-and-probe beam spot sizes, summarized in Table I and the same 26 mM CoS04 sample solution. The square root of the peak diffracted light intensity is plotted as a function of inverse spot size in Figure 3. The diffraction sensitivity increases nearly linearly with (l/wo) for larger spot sizes, although the slope is less than that projected by the largest spot size tested. This slower increase and eventual rollover in the response with smaller spot size could be related to the fringe curvature at the edges of the
1541
grating which depends on the number of fringes (14). Nf = 2 w o / h = (4w0 sin B)/X The degree of fringe curvature in the grating become significant when the length of the grating, d , as given by eq 7, approaches the Rayleigh range, ZR, as shown in eq 4 and illustrated in Figure 2. One can express the ratio of the grating length to Rayleigh range as
d/ZR = X / m 0 sin 6 = (4/7r)N~’l
IO
*
(13)
This shows that the fraction of the Rayleigh range occupied by the grating is -l/Nfi When the number of fringes is small, the resulting fringe curvature causes scattering of radiation from the grating edges which is out of phase with that scattered from the center, which can drastically reduce the overall diffraction efficiency. Since the number of fringes can be increased by using larger intersection angles, which also reduces the fraction of the Rayleigh range covered by the grating, some of the lost sensitivity at the smallest spot sizes as shown in Figure 2 might be recovered by increasing 8. This improvement from increasing 0 would need to be balanced against the loss of sensitivity due to smaller interaction length predicted by eq 9. The fact that substantial increase in concentration sensitivity was observed down to a 57 hm pump beam spot size is still encouraging for small volume measurements, where the grating occupied only 38 nL. This figure for the volume of the grating calculated from eq 10 uses as the boundary f w o on either side of the beam centers where the average intensity is 13.5% of the center intensity. Given the quadratic nature of the diffraction efficiency and the rapid fall-off of a Gaussian intensity distribution, the fraction of the diffracted beam coming from the ends of the grating must be small compared to that from the center. To test the analytical consequences of this expectation, a model for the cell length dependence was developed by using the spatial dependence of the diffraction signal. The expected efficiency was egtimated to be proportional to the square of eq 4, which was multiplied by the intensity profile of the probe laser beam to obtain the spatial dependence of the diffraction signal. Numerical integration of this function in the X,Y plane as a function of 2 yields the expected position dependence of a signal from a thin cell, as shown in Figure 4a. The area under this curve from the center of the grating toward its edges along the 2 axis predicts an interesting cell length dependence, as shown in Figure 4b. Whereas the minimum length of cell specified by the dxoo beam boundary is 2w0/tan 0 = 2w0/0, 90% of the diffraction efficiency could be observed by using a cell having only half of this pathlength, while 50% of the response could be observed from 20% of the pathlength. In addition to the reduced volume which could be achieved without substantial sensitivity loss, the thinner cell reduces the severity of the Bragg condition shown in eq 11. This model was tested by translating a 1-mm cell containing a 79 mM CoS04 sample through the wo = 57 pm and wo = 214 hm gratings. The observed diffracted intensity as a function of position is shown superimposed on the theoretical curve in Figure 4a for wo = 57 pm. The fwhm of the data is 1.6 mm which corresponds to (0.77w0/8),where 8 is the angle outside the sample medium where most of the grating lies. A Fourier transform deconvolution of the finite sample pathlength reduced this width by about 10%. The position dependence of the wo = 214 pm grating was determined by the same procedure to have a fwhm of 5.7 mm, corresponding to (0.74w0/6). These results compare favorably to the prediction by the model, where the fwhm is (0.69w0/8). The slight differences between the observed and predicted position dependence might be due to higher order transverse mode contributions to the excitation beam profile. Some asymmetry
1542
ANALYTICAL CHEMISTRY, VQL. 55, NO. 9, AUGUST 1983
w.
't r
c
V c
e
r
r
n
Sample Position, Zb'/w,
Flgure 5. Time dependent signals from diffractlon experiment: (left) scattering from pump laser (probe laser blocked); (right) diffractlon signal from 0.79 mM CoSO,. The scattering peak was amplified -8X to bring it to full scale.
0 0
0.2 0,4 0,6 OB Half-Lengih of Groting Utilized, ZB/w,
10
Figure 4. Numerical prediction and observed diffraction for partial grating: (a) position dependence for thin section, data polnts indicate observed diffraction from 1 mm pathlengths cell, wo = 57 pm; (B/w,) = 0.48 mm-' is the scale factor where 6 is the angle outside the sample medium; (b) cell length dependence. is also apparent in the sample position dependence which may be evidence for the beam intersection not occurring exactly a t the two waists, giving rise to more fringe curvature on one side of the grating, as shown in Figure 2. Analytical Results. Calibration data were gathered in a 1-3-10 sequence over 2 orders of magnitude in C0S04 concentration using a pump beam spot size, a,,= 57 pm. The plot of square root of diffraction signal vs. the absorbance per unit length of the sample was linear, having a correlation coefficient, r = 0.9996. The signals from pure water and the 15 mM aqueous H2S04solvent were indistinguishable. Dividing the aqueous background signal by the calibration curve slope gives an absorbance per unit length of 6 X cm-l, compared to a value of 2 X cm-l measured by photoacoustic spectroscopy (21). The reproducibility of the solvent blank exhibits a relative standard deviation of 20%, placing it just above the detection limit for the method. While the limit of detection in absorbance per unit pathlength is not spectactular, the corresponding absorbance across the entire grating interaction length given by eq 7 is Amin= 1.5 X lon4 which was achieved in a total probe volume of 38 nL. The aqueous sample medium, chosen for this study because it provided a convenient, stable absorption standard ( I @ , represents the most difficult case for thermooptical methods of detection, due to the small (dnld7') and t,he large specific heat of water compared to other solvents (5,22). By changing the solvent to carbon tetrachloride, for example, one would expect an 18-fold increase in the square root of the diffraction efficiency based on eq 9 and the thermooptical properties of the two solvents (23,24). An experimental comparison of the two solvents confirmed this expectation, yielding a sensitivity improvement of -20 for CC4.
Two sources of signal background and noise affect measurements near the limit of detection, both of which apparently arise from scattering. Raman scattering of the pump laser from the OH stretch of water falls within the pass band of the filter protecting the PMT. An example of this background, which depends only on presence of the excitation laser beams, is shown in Figure 5, along with a typical diffraction signal. By use of the total Raman cross section for the OH stretching transition (25), the expected fraction of scatter collected and detected, the magnitude of the scatter peak is predicted to be about 10 times larger than that observed. The difference between these values is well within the error of estimating collection efficiency and detector response. The conclusion that Raman scattering from the water is sufficiently strong to account for the observed signal appears to be sound. The effect of this background on the measured diffraction signal is minimized by using the differences in the time response of the two wave forms. Since the time constant of the thermal grating, 20 ps, is larger than the duration of the excitation pulse, 0.1 ps, or the detector time response, 4 ps, it is possible to measure the diffracted intensity after the Raman scatter signal has decayed, as shown in Figure 5. This is an important advantage of using a short pulse excitation compared to a pumping wave form which is long relative to the grating time constant, where time resolution of Raman or fluorescence would not be possible. If the latter pumping strategy were necessary because of limitations in available laser equipment, one could use a probe laser of shorter wavelength than the pump to avoid both flourescence and Raman interferences. Equations 8 and 9 predict higher diffraction efficiency for shorter wavelength probe lasers, an added benefit. The predominant noise near the limit of detection in these experiments is due to scattering of probe laser beam by the sample. The observed CW background signal was compared to the pulsed Raman signal in magnitude in an attempt to assign its origin. The Rayleigh scattering cross section for water (26,27),the Raman cross section (25),and the relative energies of the two laser beams were used to predict the expected magnitude of the CW scattering background. Fortunately, in this calculation, the detector sensitivity and collection efficiencies cancel. The observed CW background was 100 times larger than that expected for Rayleigh scattering from the solvent alone. This implies than an additional source of scattering, such as particles passed by the 0.5-pm filter, is present. The sensitivity of the present experiment to particles is not surprising since the optical geometry is identical with a low angle light scattering instrument. Particles as the source
Anal. Chem. 1983, 55, 1543-1547
of this background are hurther supported by the magnitude of the noise. The photomultipher shot noise predicted for the observed background intensity underestimates the observed noise level by 2 orders of magnitude. Filtering particles smaller than 0.5 I.rm from the sample could improve the observed detection limits. The noise in the diffracted intensity, for signals much larger than the background noise, was estimated by recording the amplitudes of 100 transients and calculating their relative standard deviations. For this study, a solution of 26 mM CoS04 in a 1-cm cell was used with a pump beam spot size of 214 pm. Under these conditions, the relative standard deviation of the diffracted intensity was 14%. The average pump power changed by less than 1% over the duration of the measurement, but the pulse-to-pulse energy variation was approximately 6 %. Within the uncertaiinty of the measurements the fluctuation in the signal can be explained by pump laser fluctuations, since the diffraction efficiency depends quadratically on pump energy. CONCLUSIONS
Pulsed laser-induced thermal diffraction appears to hold considerable promise for small volume absorption measurements. The moderate beam alignment constraints are readily met, while the inriensitivityto sample orientation is a practical advantage. The rather slow loss of sensitivity with reduction in sample thickness might prove useful in thin-film measurements. Further experiments a t larger beam intersection angles are necessary to extend the diffraction efficiency increase found for small beam spot sizes. The combination of the above two developments could produce sensitive, absorption measuring capability for subiianoliter detection volumes. LITERATURE CITED (1) Iiershberger, 1. W.; Callls, J. 8.; Christian, GI. D. Anal. Chem. 1979, 5 1 , 1444-1446.
1543
(2) Yeung, E. S.; Sepaniak, M. J. Anal. Chem. 1980, 5 2 , 1465A-1481A. (3) Foiestad, S.; Johnson, L.; Josefsson, €3.; Gab, 8. Anal. Chem. 1982, 5 4 , 925-929. (4) Dovichi, N. J.; Martin, J. C.; Jett, J. H.; Keiler, R. A. Science 1983, 219, 845-647. (5) Harris, J. M.; Dovichi, N. J. Anal. Chem. 1980, 5 2 , 695A-706A. (6) Woodruff, S. D.; Yeung, E. S. Anal. Chem. 1982, 5 4 , 1174-1176. (7) Eichler, H. J.; Enteriein, G.; Munschan, J.; Stahl, H. 2.Angew. Phys. 1971, 3 1 , 1-4. (8) Eichler, H.; SalJe, G.; Stahl, H. J. Appl. Phys. 1973, 4 4 , 5383-538s. (9) Eicher, H. J. Opt. Acta 1977, 2 4 , 631-642. (IO) Pelletler, M. J.; Thorsheim, H. R.; Harris, J. M. Anal. Chem. 1982, 5 4 , 239-242. (1 1) Slegman, A. E. “An Introductlon to Lasers and Masers”; McGraw-Hill: New York, 1971; Chapter 8. (12) Kogeinik, H. BellSyst. Tech. J . 1969, 4 8 , 2909-2947. (13) Moharam, M. G.; Gaylord, T. K.; Magnusson, R. J . Opt. SOC. Am. 1980, 70, 437-442. (14) Siegman, A. E. J. Opt. SOC.Am. 1977, 6 7 , 545-550. (15) Harris, J. M.; Lytle, F. E.; McCaln, T. C. Anal. Chem. 1976, 4 8 , 2095-2099. (16) Sheldon, S. J.; Knight, L. V.; Thorne, J. M. Appl. Opt. 1982, 2 1 , 1663- 1669, (17) Born, M.; Wolf, E. ”Prlnclples of Optics”; Pergamon Press: New York, 1980; p 395. (16) Burke, R. W.; Deardorff, E. R.; Menis, 0. J. Res. Natl. Bur. Stand., Sect. A 1972, 76, 469-482. (19) Kogelnik, H.; Li, T. Proc. IF€€ 1969, 5 4 , 1312-1329. (20) Durst, F.; Stevenson, W. H. Appl. Opt. 1976, 15, 137-144. (21) Tam, A. C.; Patel, C. K. N. Appl. Opt. 1979, 18, 3348-3357. (22) Harrls, T. D. Anal. Chem. 1982, 5 4 , 741A-750A. (23) Abbate, G.; Attanasio, A,; Bernini, U.; Ragozinno, E.; Somma, F. J. PhyS. D : Appl. PhyS. 1978, 9 , 1945-1951 (24) Bolz, R. E., Tuve, G. L., Eds. “Handbook of Tables for Applied Engineering Science”, 2nd ed.; CRC Press: Cleveland, OH, 1973; p 92. (25) Slusher, R. B.; Derr, V. E. Appl. Opt. 1975, 14, 2116-2120. (26) Fabellnskli, I. L. “Molecular Scattering of Light”; Plenum Press: New York, 1968; p 38. (27) Kaye, W.; MoDaniei, J. B. Appl. Opt. 1974, 13, 1934-1940.
RECEIVED for review February 22,1983. Accepted May 10, 1983. This work was supported in part from funds provided by the National Science Foundation through Grant CHE 82-06898.
Identification of Polychlorinated Dibenzo-p-dioxin Isomers by Powder X-ray Diffraction with &I ctron Capture Gas Chromatography P. J. Sloneckev, d. L. Pyle, and 9. S. Gantrell” Department of Ch@mistry,Miami University, Oxford, Ohio 45056
The coupllng of electron capture gas chromatography (EC/ GC) and powder X-ray diffraction (XRD) data is effective In the identificationi of speclfic Isomers of polychlorinated dlbenro-p-dioxins (PCDD’s). Powder XRD data derived from PCDD’s whose single crystal structure determinations have been completed and from PCDD’s derlved from unambiguous syntheses may be used to identlfy PCDD Isomers separated by EC/GC. Excellent correlation was exhlbiied between theoratlcal and experlmental PCDD powder XRD patterns. Powder XRD data obtalned from a diffractometer and a Gandolfl camera were shown to be In good agreement. Preferred orlentation effects sometimes observed in diffractometer analyses did not Interfere with PCDD identlflcatlon of these compounds.
There are 75 possible polychlorinatedl dibenzo-p-dioxins
(PCDD’s), of various degrees of toxicity, having from one to eight chlorine atoms (1-4). They have been detected in incinerator fly ash, herbicide formulations, and chlorophenolic compounds (2, 5-7). Since the identification of the 1,2,3,7,8,9-hexachlorodibenzo-p-dioxin (1968) as a “chick edema factor” (CEF) via X-ray crystallography, many methods for PCDD analysis have been developed (2, 6-9). Single-crystal X-ray structure determinations serve as a bench mark which can be used to identify PCDD compounds from powder X-ray diffraction (XRD), GC, GC/MS, and MS data (IO,11). Powder XRD data derived from those PCDDs for which single-crystal structure determinations have been completed provide useful fingerprint data to check materials suspected of being PCDD’s or mixtures of PCDD’s. In addition, powder XRD data for compounds identified by electron capture gas chromatography (EC/GC) are useful for identifications when PCDD standards are not available for comparison. Further confwmation of PCDD compounds is needed,
0003-2700/83/0355-1543$01.50/00 1983 American Chemical Soclety
