Anal. Chm. 1081, 53, 106-109
106
Time-Resolved Thermal Lens Calorimetry N. J. Dovlchl and J. M. Harrls’ Depsrtmnt of Ctwmisby, Unlvmiiy of Utah,
ssn Lake Ciiy, Utah
84 112
A k h t k approach to meawhg the thermal kns effect k shown to stgntkantly Improve both the dynamlc range and detection l M t s for determlnlng small absorbances. The t M p e n d e n t expanskn of the laser beam k measured as a trartslent and analyzed by a regreash technique whlch averages the short-term make on the dgnal. The rewltlng absorbance detection lhnlto for a l-cm pathlength In CCl, rwlng a 160-mW Ar’ laser are A = 7 X IO-‘. The dynamlc range k expanded, for a thermal lens whose steady-state effectw a d be excesivety aberrant, by ohsewhg t h khetlc response at thnes suffldenily short that the lens ts stlll r e l a tlvely thin.
sponse compared to Beer’s law (2), E = -P(dn/dT)/Xk. The absorbance information contained in the time-dependent intensity, Z&), can be extracted in several ways analogous to kinetic methods of analysis (9). A measurement of the initial, Zb(O), and steady-state, Z,(=), intensities is similar to an equilibrium determination, where in this case the relative change observed is related to absorbance by
+
AZh/Zh(m)= 2.303EA OS(2.303EA)’ (5) This equation can be rearranged by use of the quadratic formula to yield an expression linear in absorbance, which is more convenient for analytical work.
(2AZh/Zh(m) The thermal lens effect, first reported by Gordon et aL (I), has been successfullyapplied to the calorimetric measurement of minute absorbances for tracelevel analytical determinations (2-5). In these studies, the strength of the lens is determined by its effect on the divergence of the same laser beam which heats the sample ( 2 , 4 ) or on the divergence of a second laser beam which probes the heated volume (3,5). In either case, the divergence of the beam before the lens has formed within the sample is compared with the divergence after a steadystate temperatye gradient has developed. In this work, the analytical significance of measuring the time evolution of the thermal lens formation is explored. This mode of thermal lens measurement, first demonstrated for the calorimetric determination of fluorescence quantum yields (61,is similar to kinetic methods of analysis: one obtains quantitative information from the time dependence of a signal rather than from the initial and final amplitudes alone. Absorption of a TEM, laser beam by a thin sample produces a thermal lens whose focal length has a step response, f ( t ) , in the absence of convection, given by (I, 7) (1) f(t) = f ( m ) ( l + t,/2t) where t, is the time constant
t , = 02pC,/4k
( 2)
where w is the spot size (cm) of the laser beam at the sample, p is the sample density in g ~ m -C, ~ ,is the specific heat in J g-’ K-l, and k is the thermal conductivity in W cm-’ K-l. The steady-state focal length of the lens, f(-), is
(3) where P is the laser power (W), (dn/dT) is the variation in refractive index with temperature (usually negative), and A is the sample absorbance. The effect of the thermal lens on the far-field spot size depends on the position of the sample with respect to the beam waist (4,8). The effect maximizes when the sample is located one confocal distance beyond the waist,where the corresponding far-field beam center intensity is given by
+
2.303EA tJ2t
1
+
+
A(
2.303EA 2 1 + t,/2t
)‘I-’
(4)
where E is the enhancement of the linear portion of the re-
+ 1)”’
- 1 = 2.303EA
(6)
This “equilibrium” approach suffers from a low information input rate since only two intensity points are measured over the long delay period required to reach steady state. Since I&) changes more rapidly when t is small (80% of the relative change developes within two time constants, whereas more than nine time constants are required to observe 95% of the steady-state change), one can reduce the delay between the initial and final intensity measurements without significant loas of sensitivity. This approach, equivalent to a fixed-time kinetic method (9),relies on the reproducibility of the time dependence to avoid the need to wait for the steady state to be reached. As long as the solvent composition and sample position are constant, the time evolution of the thermal lens effect is reproducible. A more significant means of increasing the informational degrees of freedom is to gather many points along I&) and determine the absorbance from the time dependence of the signal. A measurement of the initial rate of change of Z&), where the variation is linear, conveniently yields the sample absorbance directly from the slope (6). Zh(t 2, the thermal lens begins to exhibit large aberrations relative
ANALYTICAL CHEMISTAY, VOL. 53, NO. 1, JANUARY 1981
to the simple thin lens model (11, 12). Interference fringes appear in the far-field beam profile due to loss of spherical symmetry in the planes of constant phase. For very strong thermal lenses, convection in the sample can further distort the far-field profile. For situations in which the steady-state thermal lens is distorted and analytically useleas, one may still observe a well-behaved kinetic response at times sufficiently short that the thermal lens is may be approximated as a thin lens. This concept was first applied to determining calorimetric quantum yields (6),where the concentration of the sample was kept large to allow measurement of the absorbance in a conventional manner. In this work, an evaluation of the improvement in analytical precision and dynamic range of thermal lens calorimetry provided by a kinetic measurement is presented.
107
la,
I
EXPERIMENTAL SECTION Instrument. The argon ion laser based, thermal lens calorimeter has been described previously (13). Two modifications have been made to improve the quality of data for times shortly after the shutter is opened. To decrease the background intensity fluctuations caused by the flow of air heated by the illuminated spot on the shutter blade, we placed an additional shutter, made from a simple solenoid, before the faster Uniblitz shutter. The solenoid, which is heated by the laser beam while the sample cook, is energized 10 ms before the shutter is opened. The heated air induced fluctuations are reduced since the delay allows some relaxation to occur and since the solenoid has greater heat capacity than the thin shutter blades. An external comparator circuit, constructed with an LM 311, replaces the software comparator to initiate data collection by resetting the clock which triggers the AID; this allows data gathering to begin immediately upon opening the shutter. D a t a Collection and Manipulation. The program for data collection proceeds as follows. The shutters are closed, and after a software-controlled delay of 0.5 s to allow the decay of the thermal lens formed in the previous experiment, a dark signal transient is captured, and the points are averaged. The shutters are opened, and the signal transient of up to 512 points is captured under DMA control. The shutters are closed; the average dark signal is subtracted from each point of the signal transient, and the process is repeated. For each time channel in the signal transient, the average and standard deviation are accumulated. As a control for spurious results, relative difference between the first and last points in the transient is calculated, and the average and standard deviations are computed. After five experiments are performed, subsequent results which differ from the average by more than five standard deviations are discarded. This procedure eliminates determinant erron arising from an occasional dust particle or bubble in the sample passing through the beam. Typically 100 experiments are averaged. To remove from the data the residual time dependent background signal of the instrument, a transient is collected as above without the sample cell in place; this transient is offset such that its average is zero and then subtracted, point-by-point, from the data. The time-resolved data are fit to eq 4 by using a Marquardt algorithm which combines a linearization of the fitting function with a gradient search when x2 is far from minimized (14). The initial estimate of I(0) is the first data point in the transient. The product, E.A, is first estimated with eq 6 by substituting the last data point for I ( - ) . The time constant is either searched from an initial guess or fixed a t a previously determined value. The uncertainties in the fitted parameters are determined from the diagonal terms of the variance-covariance matrix (14). Reagents. A stock solution of reagent grade iodine in spectrograde carbon tetrachloride is prepared, having a concentration of 2.7 x 10.’ M and an absorbance measured a t 514.5nm of 2.0 x Aliquots of this solution are diluted into CC14to prepare fresh samples for each experiment.
RESULTS AND DISCUSSION T h e improvement in precision of thermal lens calorimetry provided by a time-resolved measurement is illustrated in Figure la. This 512-point transient, gathered on a CC14blank
n
m m 0
I
I
I
O
00
‘
20
6 0
4 0
8 0
IO
0
1 me (mS1
Flgue 1. Thermal lens transient: CCI, blank; best fil of data to eq 4 is also displayed, t , = 65 ms; 512 points are gatheted in each of 100 experments; 64 pohts are pbtted; (a) 500 Hz samplhg rate; @) 5 kHz sampling rate; (c) 50 kHr sampling rate.
with a laser power of 160 mW and a sampling rate of 500 Hz, is characteristic of results near the detection limit of the technique. The short-term fluctuations on the transient, generated within the bandwidth required to resolved Zh(O), would clearly impair a simple two-point determination of AIh/Ih.The best fit of the data to eq 4 averages the noise of the individual points and resulta in values oft, = 65 (f2) ms and EA = 7.8 (f0.4)X The rate of improvement in analytical precision is found by sampling n evenly spaced points over the entire transient, n varying from 4 to 512,and determining the standard deviation of E A from the fit while holding t , constant a t 65 ms. A plot of log ‘TEA vs. log (n 2), where (n - 2) is the number of degrees of freedom, is linear, with a slope of -0.52 f 0.02, indicating little correlation between data points and a statistical noise distribution.
108
ANALYTICAL CMMISTRY. VOL. 53. NO. 1. JANUARY 1981 n
4-
*
I)."*.
Flmn 2.
Analyncal prsc$ion vs.
ITII
data range. Rxed samplng rate of
1 kHr: u p p e r c u v e l ~ t e s ~ e c t r e s ~ l o w n c v w , ! s n a n m M z e d
to 512 data points assuming a ( n - 2)-'12 impownat in predsbn as determined above.
A second advantage provided by a kinetic approach to thermal lens measurements is a reduction in the time required to obtain data. This is illustrated in Figures lb,c where the data rate is increased to 5 and 50 kHz, respectively. Gathering data over a region where the transient changes most significantly, within the first 1.5 time constants as in Figure lb. reaults in a slight improvement in the precision of determining EA = 7.6 ( i O . 1 ) X When the time interval is reduced below tcas in Figure IC,the fit of the data must be constrained to a time constant determined from a longer interval experiment. This requirement arises from the large correlation between t, and EA which exists when t < t., as is evident in eq 7 where they are perfectly correlated. The analytical result from Figure IC,EA = 7.3 (f0.4)x points out the loss in precision which is typical of a short data range. The relationship between analytical precision and data range was studied by using a single 512-point transient gathered a t a 1-kHz sampling rate. When the observed precision is normalized to the anme number of degrees of freedom, a systematic loss in precision is found as the data interval is r e d u d below t., as in Figure 2. This increased uncertainty can be explained by the smaller observed change in the signal a t shorter intervals, while the relative noise on the signal remains constant. This behavior would indicate that an initial slope determination, constrained tot < O.lt, would produce greater analytical uncertainty than a regression analysis over a data range of one or two time constants. Time resolution of the thermal lena also leads to an increase in the dynamic range of response. The behavior of a strong thermal lens, whose steady-state effect on the beam is modified by large aberrations and convection, can still be deaeribed by a simple diffusion model and thin lens expressions a t sufficiently short times, while the focal length is long and convection has not set in. This concept is illustrated in Figure 3, which shows time-resolved photographs of the far-field beam profile. Although the steady-state profile is dominated by large aberrations and convection (note the interference fringes and asymmetry), the early time response shows an expanded beam having little distortion. The fit of the timeresolved beam center intensity is equally well-behaved when restricted to a short data range. This fact allowed the construction of an l a p o i n t linear (r = 0.998) calibration curve over 3.5 orders of magnitude in absorbance, from the solvent blank to the stock I* solution For each point, 100 experiments were averaged; 512 data points were sampled a t a clock rate of 1 kHz for determining detection limits on the solvent blank. For the remainder of the calibration curve, a sampling rate of 50 kHz was chosen for maximum dynamic range. The fit of the data to eq 4 was restricted in the case of large EA to a range where AZh/Ih(t) 5 0.4 to minimize any effecta of aberration; the time constant was fixed throughout a t 65 ms.
H
2.5cm
npUn 3. Thannolved photogapha of tar-Reld beam proffle: (a) beamPofie prohad bya 03,Hank. WNchappodmates wmh 2% me unpertvbed. t = 0. profile: (b) beam pmnle produced at t = 1.5 ms mlng me stock I, solutbn. A l , / l d f ) E 3 (c) beam prom at steady state using Uw stock I, soluHon. Al,/ld-) I 840.
For an observed enhancement a t P = 160 mW of E = 868, the absorbance of the CCI. blank WBB found in this case to be A = 5.0 X lo4, for a 1-em pathlength. The limit of detection defined an twice the standard deviation of the blank signal in units of absorbance was found to be Ah = 7 X 1 0 6 This compares favorably with the limit of detection from a twopoint, A&JIb determination using the same data, which was found to be Ah = 2.2 X lod. The maximum absorbance observable is limited, for a given laser power, by the speed with which the beam may be unblocked and by the sampling rate of the A/D converter. For this particular system, the shutter cthe beam in 125 6 and the diffraction pattern caused by the edge of the shutter leaves the detector field of view within another 200 pa. With the I2 sample of highest absorbance determined, A = 0.02, this allowed 16 points to be fit to eq 4 by use of the fastest clock rate. 50 kHz, allowed by the DMA controller. The sample absorbance represents an increase in dynamic range by a factor 30 over a steady-state, Alh/Ih(-), determination for the particular laser power and resulting enhancement. The relationship between analytical precision and sample absorbance was also studied by using the calibration curve data. For each point on the curve, a constant data range of 64 points from the transient wan fit to eq 4 in order to allow
Anal. Chem. 1981, 53, 109-113
I 0.02
I
l
0.05 01
l
I
l
l
1.0
I
l 10.0
l
I J
500
2303 E A
Flgue 4. Analytkal precision vs. sample absorbance. Resutts are detefmined from a constant 04 point data range.
comparison of results. The relative precision vs. (2.303EA) plot in Figure 4 indicates a contribution from noise sources which are constant and proportional with respect to absorbance. The constant noise, dominant a t small A, may be interpreted as arising from fluctuations in the laser intensity which occur on a time scale shorter than t, This kind of noise leads to minimal correlation between data points and results in the greatly improved precision of the regression analysis approach. The proportional contribution which appears to dominate a t higher sample absorbances arises from drift in the laser power on time scales longer than t, This drift musea the signal to change from experiment to experiment in proportion to the sample absorbance. From the plot of Figure 4, one may postulate the effect on precision of having a larger solvent or background absorbance. Increasing the background by an order of magnitude, for example, would raise the proportional noise contribution by an equal amount, but not enough to make a measurement of the solvent blank proportional noise limited. Therefore, one would expect equiv-
109
dent detection limits as observed with the smaller background. The regression analysis method of thermal lens measurement averages the more significant, short-term noise of the light-regulated laser. With lasers having poorer long-term power stability or samples having very large background a b sorbance, the improvement in precision over a sample AIk/Zk measurement would not be as significant. For t h e situations, a differential thermal lens technique has been developed (13) which is immune to background drift but not to short-term noise. Combining the differential measurement with time resolution might result in an instrument which produces o p timal precision independent of sample background.
LITERATURE CITED (1) Gadon, J. P.; Ldte, R. C. C.; Moore, R. S.; Porto, S. P. S.; whhnery, J. R. J . Appl. /=?IYs. 1065, 36, 3-8. (2) Dovichi, N. J.; Hanls, J. M. Anal. Chem. 1070, 51, 728-731. (3) Imsake, T.; Myaiehl, K.; Ishlbeshl. N. Anel. Chh.Acte 1080. 115,
407-410. (4) Hante, J. M.: Dovlchl, N. J. Anel. chem.1080, 52, 695A-706A. (5) Haushaltec,J. P.; Momis, M. D. A#)/. spectra9c.1080, 31,445-447. (6) Brannon, J. H.; Magde, D. J . Phys. Chem. 1070, 82. 705-709. (7) Cannan, R. 0.; K&y. P. L. Appl. Ws. Lett. 1068. 12, 241-243. (8) Hu, C.; whknecy, J. R. Appl. Opt. 1073. 12. 72-78. (8) Mark, J. 6. Jr.; Rechnltz. G. A.; Wet-dw, R. A. "Khstlcs h Anely%cal chembby";Wsey-Interschce: New Y a k . 1888. (10) MleBng, G. E.; Pardue, H. L. Anel. chem.1070, 50, 1611-1618. (11) whhnery, J. R. Am. Chem. Res. 1074. 7, 225-231. (12) Darw, K. Opt. Cknmm. 1071. 4 , 238-241. (13) Dovichi. N. J.; Hante. J. M. Anel. chem.1080, 52, 2338. (14) Bevlngton, P. R. "Data Reductkn and Erra Analysts fa the Rys(cel sdtmces";W a w H P I : New Y a k , 1869; R w a m 11-5.
RECEIVED for review September 2,1980. Accepted October 22,1980. This material is based upon work supported by the National Science Foundation under Grant CHE79-13177. Fellowship support (N.D.) by the Phillips Petroleum Co.and the American Chemical Society, Division of Analytical Chemistry (sponsored by General Motors), is acknowledged.
Matrix-Assisted Secondary Ion Mass Spectra of Biological Compounds Llllan K. Liu,' Kenneth L. Busch, and R. G. Cooks' Bpartment of Chemistry, Purdue Untverslty, West Lafayette, Indlsna 47907
Secondary Ion mass spectrometry (SIMS) can be used to analyze nonvolatile or thennaty fragle bkmdecules when the^ sample is sputtered from a metal-supported Bmmonlum chloride matrix. Sugars, nucleotides, nudeodd-, and peptldes form Intact protonated 01 catknlred species, and useful fragmentatlons are also obsened. The spectra obtained by this version of the SIMS technique are ShJlarW not #entical wHh those obtained by W, plasma, and laser desorptkn techniques. Ionlzatkn d these large moleales irr SIMS a p parentty occvs by the processes prevbtcdy shown to operate for simpler specks. I n particular, dlrect e)ectkn from the bdld produces the krtact c a t h for tMamlne hydrochloride, whlle catlonlzatkm by sodknn, sllver, and copper is observed for 8 u c ~ # ) 8 .Protonatkn to form (M i- H)' occws for several samples lncludlng arglnlne hydrochkrlde and the trlpeptlde !3lYCYblYCYblYclm.
'On leave from the Department of Chemist National Tsing Hua University, Hsinchu, Taiwan, Republic of ?kina. 0003-2700/81/0353-0108$01.00/0
Ionization of intact molecules of nonvolatile organic samples can be achieved by using several desorption techniques (I), among them the ion-induced sputter process which forms the basis of secondary ion mass spectrometry (SIMS) (2). Such difficult samples have traditionally been analyzed by field desorption (FD) (3) and more recently by laser desorption (LD) ( 4 ) , plasma desorption (PD) (5), and electrohydrodynamic ionization (EHD) (6).Along with SIMS, these techniques circumvent the requirement for sample vaporization. SIMS analysis of compounds such as the amino acids, small peptides, and some drugs and vitamins has already been successful (7,8).We now show that the capabilities of SIMS are enhanced if the organic sample is mixed with ammonium chloride and that protonated or metal-cationized molecular ions can be observed for intact mononucleotides, peptides, sugars,and other nonvolatile and thermally labile compounds. Several of these samplea have not been successfully analyzed by SIMS by use of preparation methods which omit the salt. Other reports of matrix-enhanced ionization have appeared. A urea matrix has been utilized for the analysis of underi0 1880 A W n chemlcel Sodety
