Influence of Heating Rate on Analytical Response in Flameless Atomic Absorption Spectrometry Giancarlo Torsi and Gin0 Tessari lstituto di Chimica Analitica, Universifa di Bari, via G. Amendola, 173, 70726 Bari, ltaly
A graphite rod flameless atomic absorption spectrometer was assembled with high chopping speed, fast response, and good noise rejection. The influence of the input power on the analytical sensitivity was investigated using chromium as a probe for rods of different geometrical dimensions. In satisfactory agreement with the theoretical model, a linear relationship was found between the peak absorption with both the input power and the thermal derivative at the evaporating surface. The possibility of obtaining kinetic information about the evaporation process is discussed. A new detection limit value, 2 X 10-l2 gram for chromium, is also reported.
Two approaches-which imply two different philosophies-are currently investigated in flameless AAS for determining elements in traces. In the first one, pioneered by L'vov ( I , 2) and Massmann ( 3 ) ,a small tube (1-cm diameter X 5 cm long) electrically heated is used as a furnace where the atoms of the analyte are produced for a length of time ranging from 5 to 20 sec. During this time, the beam from the hollow cathode lamp coming in through the middle of the tube is intercepted by the atoms and the absorption is properly recorded. In the other case, a burst of atoms is produced by thermally flashing a good conductor used as support of the sample to be analyzed. These atoms are responsible for a short absorption transient, which with most commercial apparatus lasts for about 0.5 sec (time response of the recorder), This technique became very popular after West and Williams ( 4 ) suggested a graphite filament as support of the sample because of the good thermal and electrical properties of this material. The question which of the two methods is superior is far from being settled since the obvious advantage of the first technique of the long residence of the atoms of the analyte in the optical path is partially offset by: 1) the need of an optical-electronic device to cancel out the large continuous absorption from the carbon material; and 2) a situation in which an equilibrium state is approached, which accounts for the failing of the direct proportionality between the amount of the species under study and the analytical response. Generally these effects can be minimized by increasing the temperature. On the other hand, the full exploitation of the flash technique in principle requires, in order to achieve an instantaneous high level of absorption, the production of a burst of atoms as compact as possible, which, because of the zero vapor pressure, does not need very high temperatures of the support. Over all, the two techniques are probably complementary, but more study is necessary in order to identify the proper area of application. (1) B. V. L'vov, Specfrochirn. Acfa, 17, 761 (1961). (2) B. V. L'vov, "Atomic Absorption Spectrochemical Analysis," English ed., Hilger, London, 1970. (3) H. Massmann, Specfrochirn. Acfa, 23 B, 215 (1968). ( 4 ) T. S.West and X. K . Williams, Anal. Chirn. Acfa, 45, 27 (1969).
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One important aspect which has not been fully investigated is the influence of the input power on the analytical response of the graphite rod atomizer. The only available information concerns plots of peak absorption us. voltage which usually present a parabolic shape. Whereas this shape can be easily understood when the response is limited by the time response of the amplifier-recorder system, it is more difficult to rationalize when fast response systems are used and the heating rates do not appear particularly large (2500 "K/sec). The present paper reports some results for the graphite rod atomizer, about the influence of the heating rate on the analytical response, using chromium as a probe.
GENERAL EXPRESSIONS Before the thermal flash, the atoms of the sample on the rod can be in different physical and chemical states: crystallites of different size; monoatomic layer on the support; atoms inside some crystallites of the matrix or adsorbed onto them; or different chemical compounds with oxygen (oxide and/or substoichiometric oxides), with the support rod (carbides) or with the matrix. In the conditions prevailing during the thermal flash, the tendency of the atoms of the analyte to evaporatewhen they are not lost by evaporation as polyatomic species-does not depend on the free energy content of the gaseous atoms. The reason is that the partial pressure for the investigated species is zero and the gaseous phase behaves as an infinite sink for the evaporating atoms. In this case, the overall process of evaporation is irreversible. By assuming the simplified model of a monoatomic layer distribution which could not be too unrealistic in the case of salt deposition from extremely diluted water solutions, the rate of evaporation can be formally written as dz? -qz = K q z ?
where q (atoms cm-2) is the surface concentration a t 3 = 1, 3 is the fraction of surface coverage, 0 5 3 5 1, t (sec) is the time, and K (sec-l) is the formal rate constant for the evaporation process. Introducing u (cm sec-I), the linear velocity of the evaporating atoms, the concentration nt (atoms cm-3) of atoms in the gaseous phase can be obtained
This quantity, in its turn, is proportional to the instantaneous absorbance provided that: (1) the optical probe is near enough to the evaporating surface to avoid loss of atoms by radial diffusion; and (2) the optical probe is sufficiently small to minimize integration effects in the direction normal to the evaporating surface. In Equation 2, besides the time, temperature-via K-is present. I t is possible to eliminate the time and to simplify this equation by imposing a simple law to the heating rate, as T = To + at, where (Y = dT/dt ("K sec-1) is a constant, obtaining
ANALYTICAL CHEMISTRY, VOL. 45, NO. 11, SEPTEMBER 1973
(3) Assuming for K , the temperature dependence given by the Arrhenius law,
K
=
A exp(-AG*/ RT)
(4)
6 ;exp(-AG*/RT)
(5)
graphite rod, the heat generated per unit time per unit length, i 2 p / s , is balanced for every point x of the rod according t o
ph(T
one has n, = Aq and
-ddt6_ -_ -
ff
exp(-AG*l RT)
where AG* (kJ mole-1) is the free energy of activation for the step which is rate determining for the evaporation process and is assumed independent from 9 and T, A (sec-1) is the preexponential factor and R ( k J mole-I OK-1) is the gas constant. By inspection of Equation 5 , one realizes that the concentration nt, and thus the optical response, must present a peak shape under a linear thermal perturbation since the increase of the exponential factor with temperature is counterbalanced by the decrease of the coverage 0 with the time. From Equations 5 and 6, the maximum coordinates can be obtained by imposing the condition dnt/dT = 0 and assuming v to be constant,
A exp
AG*
AG*
(-E) = RT,2
(7)
and
where T m and (nt), are the coordinates of the maxima and i?,,, the peak coverage. By rearranging Equation 7 21n T , - l n a
AG*
= -
RT m
AR - In *-AG
(9 1
The solution of the differential Equation 6 is beyond the scope of this paper. However it would be possible to meet formally equivalent situations in catalysis studies ( 5 ) . From the last expressions, two points can be stressed: (1) According to the simple model considered, for the same amount of sample on the rod, the shape of the evaporation curves should remain unchanged (6) when the heating rate a is varied and thus also b m should be practically constant. In this case, a proportionality between the peak concentration (nt), and the heating rate a can be found. Therefore, a linear increase of analytical sensitivity should be expected by increasing a , at least up to the point where the model maintains its ability in describing the system. (2) Under favorable circumstances, it is possible to obtain, with this analytical technique, kinetic information.
- To)
(10).
Where p (Q cm) is the resistivity, c (J 8-l "K-l) the specific heat, d (g cm-3) the density, k (J sec-I cm-1 OKp1) the thermal conductivity, and t the total emissivity.of the graphite used; p (cm) is the perimeter of the section s (cm2) of the graphite rod; x (cm) is the distance from the center of the rod. u (J sec-"cm-2 OK-4) is the StefanBoltzmann constant, h (J sec-1 cm-2 "K-l) the heattransfer coefficient for the experimental set up. To is the room temperature. The first term at the right hand side of this expression represents the increase of the heat content with the time; the second, the loss due to conduction toward the ends; the third, the loss due to thermal emission; and the last, the loss by convection. In this expression, the rod was assumed to be thin enough so that the radial distribution of temperature is negligible. Since the sample was deposited on a small region around the center of the rod, only the expression for the growth of the temperature near the center is required and not the spatial distribution of temperatures along the rod. As shown by Jain and Krishnan (7),using a thin rod long enough, a2T/dx2 a t the center should be negligible not only for a steady temperature distribution, but also for a growing one. Thus, if the experimental conditions are presumed to fulfil this assumption the second term in the right hand side of Equation 10 can simply be deleted. The convective term is the most difficult to be treated analytically since in this system, a t some distance away from the heating surface, some turbulence occurs. In this case velocity and temperature a t any point outside the thermal boundary layer are functions of time. The heat-transfer coefficient, which has been introduced following an engineering practice (8), is not quite a satisfactory solution because h is temperature dependent, and a unique h value cannot be assumed for a general solution. However, since this term in the investigated system is found much smaller than that due to emission, no attempt will be made to give a more sophisticated treatment. Thus Equation 10 becomes d T - '2 - E (T4 - To4)- P h ( T - To) (11) d t - ds2 c cds cds When a constant temperature T is considered, a simple proportionality between d T l d t and input power i 2 p l s can be claimed. Since it will be experimentally verified that the temperature of the peak of chromium vaporization remains practically unchanged despite the large variation in heating rate, the simple substitution of the heating rate dT/dt with the input power can be made, a t least in the case of chromium, when Equation 8 is considered. -
EXPERIMENTAL
RELATIONSHIP BETWEEN HEATING RATE AND INPUT POWER The heating rate a is not an easily calculated quantity and it could be useful to describe the system by some more manageable variable as the input power. In order to develop a relationship between these two quantities, one must introduce the energy balance for the system considered. When a constant current i (A) is passing through a
Instrumentation. Several characteristics, which were important for this investigation and not easily found in a commercial apparatus, suggested the opportunity of assembling an atomic spectrometer whose essential lay-out was given by Donega and Burgess (9). The most important features of this instrument were: (1) high chopping frequency in order t o sample efficiently also short transients; ( 2 ) large range of variation of the amplifier-re-
(5) R. J . Cvetanovic and Y . Arnenorniya, Advan. Catal. Relat. Sub., 17,
(7) S. C. Jain and K . S. Krishnan, Proc. Roy. SOC. (London), A 227, 141 (1955). (8) C. 0. Bennett and J. E. Myers, "Momentum, Heat and Mass Transfer," McGraw-Hill Book Co., London, 1962. (9) H. M . DonegaandT. E . Burgess, Ana/. Chem., 42, 1521 (1970).
103 (1967). (6) G. Ehrlich, Advan. Catal. Relat. Sub., 14, 256 (1963)
ANALYTICAL CHEMISTRY, VOL. 45, NO. 11, SEPTEMBER 1973
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cording system band pass in order to get in any situation the greatest possible rejection of noise without distortion of the signal. The beam from the hollow cathode lamp (Fivre) was focused with a lens 1.5 mm above the center of the graphite rod, and modulated by a mechanical chopper (chopping rate continuously changing in the range 400-4000 Hz) driven by a Siemens motor Type 1AD31 with electronic control of the speed. A second lens collected the light coming out of the absorption cell into the entrance slit of the monochromator (Zeiss type MM12 with quartz prisms). The photomultiplier tube (RCA type 6903) was attached to the exit slit of the monochromator, and its signal was amplified and demodulated by a lock-in amplifier (PAR type H R8) which was locked to the chopper via an auxiliary signal produced by a photodiode and a small lamp placed on the opposite side of the wheel of the chopper. An oscilloscope (Tektronix type 502) with a camera or a recorder (Texas Instruments type Servowriter 11) made up the display system. Since the input power during the thermal flash was such as to produce equilibrium temperatures that would have destroyed the graphite rod, a mechanical switch -operated by a synchronous motor-controlled the length of the thermal flash, stopping the current 30-50 msec after the absorption peak. The length of the thermal flash could be continuously changed. In order to monitor with good precision the input power, the current through the graphite rod ( u p to 150 A rms) was displayed on the second channel of the scope. The design of the flameless atomizer has been described already (IO), except that the two supports of the graphite rod were water-cooled. The flameless atomizer was fitted on the top of a variable support which could be moved with two degrees of freedom characterized by the displacement of 1 mm/turn and 0.15 mm/turn for the X and Z directions, respectively, whereas the Y direction was secured by moving the manipulator along the optical rail. A similar support under the housing of the hollow cathode lamp secured the alignment of the optical beam with respect to the monochromator. Different values of resistances were realized by thinning the lower central part of rods of graphite (Ultra Carbon Corp., density 1.9) for the fixed length of 1.3 cm. In order to get a better reproducibility in positioning of the drop a t the center of the rod (and thus a better reproducibility of the absorption peaks), the sample was injected via a 1-p1 microcap (Drummond Corp.) fitted a t the bottom of a device, which secured a reproducible positioning. The procedure for chromium determination has been described already (IO). The only difference introduced was the stopping of argon flow during the thermal flash, because it was found that a better sensitivity and reproducibility was thus obtained. Temperature Measurements. For the temperature measurements the same optical set up-with exclusion of the hollow cathode lamp-was used after the following modifications: (1) the flameless atomizer was rotated go", the rod becoming traverse to the optical direction; (2) the rod was rotated go", so that it presented the curved unfiled surface to the collecting lens; (3) a field stop (D = 1 mm) was placed in correspondence of the center of the rod and normal to the curved surface at 0.5 cm from it. In this way, the optical system sensed only the region of the rod where the sample was usually injected. The wavelength was fixed a t 6500 A (slit opening = 0.2 mm, band pass = 45 A) and the signal from the photomultiplier was fed to the scope through a RC = 1 msec. The remaining conditions were equal to the conditions for the measurements of chromium absorption. In order to calibrate the emission method, the following experiment was devised. A small cavity was made in the upper central part of the rod where the junction of a thermocouple Pt/Pt-Rd (10%) was inserted. With a two channel Servowriter I1 (Texas Instruments), the signals from the thermocouple and the photomultiplier were simultaneously recorded for condition of thermal equilibrium at 1580, 1690, and 1790 "K (5 determinations for each temperature). A diagram of log of photomultiplier signal us. 1/T gave a linear plot whose equation had the theoretical slope of the Wien expression. This plot was used to obtain the temperatures from the measured emissions. Reagents. All chemicals used were of analytical grade purity. Stock solutions were prepared with demineralized water and stored in polyethylene bottles. The chromium solutions were prepared from NazCrOd and were standardized by EDTA titration. The most dilute solutions were freshly prepared before use. The argon used was certified to contain
