2781
Anal. Chem. 1003, 65, 2761-2765
Measurement of Solute Vaporization Rates in an Analytical Flame by Laser-Light Scattering A. G. Childerst and G. M. Hieftje'
Department of Chemistry, Indiana University, Bloomington, Indiana 47405
Laser-light scattering has been used to study the kinetics of alkali chloride particle vaporization in a laminar air-acetylene flame. Vaporization rate constants are determined by a least-squares fit of the vaporization profile to existing vaporization models. For solute particles with radii below 0.25 pm, the particle radius was found to decrease linearly with time,as predicted by smallparticle vaporization theory. Values of smallparticle vaporization rate constants for three alkali chlorides measured by this method are 1.04 mm/s (NaCl), 1.25 mm/s (KCl), and 1.85 mm/s (CsCl). These rates are comparedto those obtained earlier by emission studies and predicted by theory.
addition, this approach does not perturb the flame or plasma in which the measurement is made. In the present study, the vaporization kinetics of three kinds of alkali chloride particles were directly examined by laser-light scattering. Uniform-size droplets, produced by an isolated-dropletgenerator,'were introduced into a laminar ah-acetylene flame. The resulting desolvated solute particles were then sized as a function of their residence time in the flame, to yield a "vaporization profile". The vaporization rate constants were determined by a least-squares fit of the temporally resolved particle-size data to existing models. For alkali chloride particles with radii below 0.25 pm, vaporization was found to proceed linearly with particle radius, in accordancewith a model formulated to describe small-particle vaporization.316
2. THEORY OF SOLUTE PARTICLE
VAPORIZATION 1. INTRODUCTION Flame and plasma atomic spectrometry has found widespread application in the field of elemental analysis. Unfortunately, large systematic errors in the analysis can arise from interelement interferences. In part, these interferences are associated with the processes a sample must undergo in order to produce free atoms or ions. Often, optimization of the observation height in the flame or plasma can reduce interferences to an acceptable level. However, this optimization is usually performed empirically and with little understanding of the mechanismsthat control the interference or its spatial dependence. Clearly, it would be far more satisfactoryand satisfying to understand the underlying cause of each interference and then to eliminate it rationally. Undoubtedly, one of the most critical steps in atom formation is the vaporization of solute particles. In the past, vaporization rates in a flame have been determined by repeatedly introducing uniform-size sample droplets into a laminar flame and measuring the emission of free analyte atoms as a function of the particle residence time.13 From these emission profiles, vaporization rates were determined by assuming that the emission was linearly related to atom or ion concentration. Obviously,gas-phase chemical reactions which change the number of free analyte atoms in the flame can compromise the reliability of this determination. A more direct approach for the measurement of timedependent solute-particle sizes and therefore vaporization rates is to utilize laser-light scattering. A major benefit of laser-light scattering is that this type of direct measurement is independent of gas-phase chemical reactions, molecular dissociation and recombination, and analyte ionization. In
* Author to whom correspondence should be addressed.
t Present address: Magellan, P.O. Box 13341,ResearchTrianglePark, NC 27709. (1) Bleasdell, B. D.; Wittig, E. P.; Hieftje, G. M. Spectrochim. Acta 1981,36B, 205. (2) Pak, Y.; Hieftje, G. M. Spectrochim. Acta 1986,40B, 209. (3) Baatiaans, G. J.; Hieftje, G. M. Anal. Chem. 1974, 46,901.
0005-2700/93/0365-2761$04.00/0
Although the vaporization of solute particles in analytical flames and plasmas has not been well characterized experimentally, tentative models of the vaporization process have been offered in the literature. These descriptions are based on the premise that the vaporization kinetics can be limited either by the rate at which heat is transferred to an aerosol particle or by the rate at which material can diffuse away from the surface of the particle. An overview of the alternatives is presented in ref 5. When the conduction of heat to the particle limits the rate of vaporization, the vaporization is said to be heat-transfercontrolled. In this case, the rate of heat transfer is limited by the thermal conductivity of the gas surrounding the particle. Heat-transfer-controlled vaporization is described by the following equation9-9
where ro is the initial radius of the particle and r ita radius at a time t after vaporization begins; Tgand T,are the temperature of the flame (or plasma) gases and of the surface of the particle, respectively; H, denotes the heat of vaporization of the solute material; M is the molecular weight of the vaporized species; A is the mass counterflow coefficient; X is the lesser thermal conductivity of either the flame gases or the analyte vapor; and p is the density of the molten particle at ita vaporization temperature. The bracketed term in eq 1 can be considered as the heat-transfer-controlled vaporization rate constant for large particles, kV1.1*2pS When mass-transfer controls the rate at which a particle vaporizes, the diffusion coefficient of the analyte vapor, D,, (4) Childers, A. G.; Hieftje, G. M. Appl. Spectrosc. 1986, 40,688. (5) Hieftje, G. M.; Miller, R. M.; Pak, Y.; Wittig, E. Anal. Chem. 1987, 59, 2861. (6) Williams, F. A. J. Chem. Phys. 1960,33, 133. (7) Johnston, P. D. Combust. Flame 1972,18, 373. (8) Borgianni, C.; Capitalli, M.; Cramarossa, F.; Triolo, L.; Molinari, E. Combust. Flame 1969,13,181. (9) Yoshita, T.; Akashi, K. J. Appl. Phys. 1977,48,2252. 0 1993 American Chemlcal Society
2762
ANALYTICAL CHEMISTRY, VOL. 65, NO. 20, OCTOBER 15, 1993
will be important in the description. The mechanism of masstransfer-controlled vaporization proceeds according to the equation:5J@-l2
SIGNAL Oururr
75pm
--AtINTENSTY
In eq 2, P, is the saturation vapor pressure of volatilized analyte material and R is the ideal-gas constant. The term inside the brackets of eq 2 denotes the mass-transfer-controlled vaporization rate constant PV1.5 Unfortunately, the foregoing equations fail to predict accurately the rate of vaporization for particles whose size is on the order of or smaller than the mean-free path of molecules leaving its ~ u r f a c e .On ~ the basis of eq 1and 2, the mass flux per unit area at the particle surface becomes infinitely large as the particle size approaches zer0.~*~9~ As a result, the Knudsen effect becomes important in the vaporization of small particles, and vaporizationbecomessimilar to that which occurs in a vacuum.5J3-l5 When the rate of analyte release from the surface of a particle becomes the limiting process in vaporization, it can be described by the equation:5JlJ6-19
An empirical vaporization coefficient, cy, accounts for vaporization rates lower than those predicted without the coefficient. The bracketed term in eq 3 represents the small-particle vaporization rate, kv2. According to the above equations, both heat- and masstransfer-controlled vaporization of large particles should proceed linearly with the square of particle radius, whereas small-particle vaporization should proceed linearly with particle radius directly. The vaporization kinetics of alkali chloride solute particles has been proposed earlier to change from heat-transfer-controlled to small-particle vaporization.192~5 Assuming the theoretical vaporization models hold, the vaporization mechanism should change from large-particle to small-particle behavior when the rates of mass loss by the particle predicted by the two theories are equal. The particle size at which this change occurs is termed the "critical radius" and denoted rc.19295 3. EXPERIMENTAL SECTION The laser-light scattering instrument developed to measure the size of solute particles vaporizing in an analytical flame is described separately,20but can be appreciated from Figure 1. This instrument is comprised of a laminar air-acetylene flame and a uniform-size droplet-introductionsystem, both of which can be translated relative to the detection zone of the lightscattering instrument. At each observation height in the flame, correspondingto a different point in the vaporization history of the individual particles, the periodic passage of solute particles produces a train of light-scattering pulses that are recorded. In ~~~
~
(10)Langmuir, I. Phys. Rev., Ser. ZZ 1918, 12, 368. (11)Bradley, R. S.;Evans, M. G.; Whytlaw-Gray, R. W. Proc. R. SOC. London l946,186A, 368. (12)Houghton, H.G. Physics 1933, 4, 419. (13)Chen, X.;Pfender, E. Plasma Chem. Plasma Process. 1983, 3, 351. (14)Chen, X.;Pfender, E. Plasma Chem. Plasma Process. 1983,3,97. (15)Chen, X.;Pfender, E. Plasma Chem. Plasma Process. 1982, 2, 293. (16)Wagoner, R. H.;Hirth, J. P. J. Chem. Phys. 1977,67, 3074. (17)Fuchs, N.Phys. 2. Sowjet Union 1934, 6, 225. (18)Monchick, L.;Reiss, H. J. Chem. Phys. 1954, 22, 831. (19)Jacobs, P. W.; Russel-Jones, A. J. Phys. Chem. 1968, 72, 202. (20)Childers, A. G.; Hieftje, G. M. Laser-Light Scattering Instrument for the Measurement of Solute Vaporization Rates in Analytical Flames. Anal. Chem., preceding paper in this issue.
/
Im
particle
L U * TIME
.
Multi -Channel Analysis
4b
PULSE H E I G K
Flgure I. Schematic illustration of data-collection and processing system for the sizing of solute particles vaporizing in an analytical flame. To produce measurable scattering pulses from even submicrometer solute particles, the incident laser beam is focused tightly (left diagram). As a result, and because the paths of particles do not all pass through the same part of the focal spot, a range of scattering amplitudes are generated (upper right). These varying amplitudes are treated by means of pulse-height spectra (PHS), an example of which is shown bottom right. See text and ref 20 for further details.
order to produce scatteringpulses of measurableamplitude, even from submicrometer solute particles, the laser light is brought to a fairly small focal spot (75-pm diameter). As a result, even small variations in the path of solute particles cause a range of scattering pulse heights to be produced (upper right diagram in Figure 1). To treat these varying pulse amplitudes in a statisticallymeaningful manner, pulse-heightspectra (PHS; see example in bottom right of Figure l), a plot of the number of counts versus scattering-pulse height, are compared to PHS collected from standard latex microspheres to determine the height at which the solute particle has decreased to the size of the calibration particles. This PHS comparison was performed by means of quantilequantile (Q-Q) p10ts.~Repeating this process for a number of calibration.-particlesizes produces the vaporization profile. 3.1. Burner and Flame System. The air-acetylene flame was nitrogen-sheathed and supported on an Alkemade-type burner.21*22 The flame was operated with 2.25 L/min acetylene, 15.0 L/min air, and 1.8 L/min nitrogen (as a sheath gas), all of which were prefiltered (Matheson, Model 453, East Rutherford, NJ) and further filtered by a submicrometer membrane filter (Matheson, Model 6184-P4-FF,East Rutherford, NJ) to remove particulates from the flame gases. The flame was stabilized by water cooling the burner head and by positioninga water-cooled metal tube (chimney) around the unobserved upper portion of the The rise velocity of the flame gases was determined to be 10.8 m/s.20 3.2. Droplet-Introduction System. Analyte solutions were 6.81 mg/L Na, 8.37 mg/L K, and 25.2 mg/L Cs, all made from alkali chloride salts (Mallinckrodt, Analytical Reagent Grade, Paris, KY). Uniform-sizedroplets were introduced into the base of the flame at a rate of 8 kHz. The initial radius of the droplets was 25 pm, determined by measuring the volume of solution delivered over a 2-min interval and from the rate of droplet production. At these settings, the onset of emission occurred about 10 cm above the burner head. If it is assumed that the particles are molten and spherical at the onset of emission, then the radii of particles produced by all three salt solutions are identical at 0.60 pm. (21)Hollander, T.Ph.D. Thesis, University of Utrecht, 1964. (22) Clampitt, N.C.; Hieftje, G. M. Anal. Chem. 1974, 46, 382. (23)RUBSO,R. E.; Hieftje, G. M. Anal. Chim. Acta 1981,3, 231. (24)Hieftje, G. M.;Bystroff, R. I. Spectrochim. Acta 1975,30B, 187.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 20, OCTOBER 15, 1993
2769
0.6 0
-b i
f
0.5
-*
0.4
-
1
I
QI
0
0
0.3 -
0.3
Y
0.2
o
/
,
,
,
40
0
,
I
I
I
120
80
nm*
I
I
I
I
200
160
I
0.93.
20 -
I
40
l nm* (pr) 60 I
L
80
J
100
Figure 4. Vaporization profile for a CsCl particle of 0.60-pm initial radius (ro). Line in flgure represents a least-squares fit for particles with radii below 0.25 pm and ylelds a small-particle vaporization rate constant (kv2) of 1.85 f 0.24 "1s. The error In this value Is stated as fl standard deviation, determined from 4 different experimental runs. The correlatlon coefficient for the linear fit of these data was 0.88.
0.6
0.25 pm. Unfortunately, the resolution of the light-scattering instrument is poor for sizes between 0.5 and 0.25 pm because
0.5
of a dip in the scattering response function.20 Therefore, solute particles with radii in this upper range could not be accurately sized; an example of this limited resolution is apparent in Figure 2, where the particle size at 20 ps after the onset of vaporization appears to be larger than those measured earlier in the vaporization history. Nonetheless, there is a reliable and rapid decrease in the 95% channel20 between PHS collected at the onset of vaporization and those collected at the height where 0.25-pm particles were found. This change occurs over a 20-ps period and clearly indicates a sudden decrease in apparent particle size. Several possible explanations exist for this sudden early drop in particle size. First, near or above the critical radius, the rate of radius change per unit time caused by large-particle heat-transfer-controlled vaporization is expected to be much more rapid than the rate of change for small-particlebehavior.6 This greater rate would cause a sudden initial change in particle radius and could therefore account for the sharp break on the left-hand side of Figures 2-4. Second, the formation of hollow, porous, or nonspherical particles at the onset of vaporization would cause faster vaporization. Such particles would have surface areas that are disproportionately large for their solute mass, making them vaporize at a faster rate than predicted from simple theories. Such particle morphologies have been po~tulated3?~8 and observed in particles collected from heated aerosol chambersz-1 and analytical flames.3233 Third, a change in particle shape (e.g., melting) that causes a corresponding reduction in ita surface area could produce the abrupt change in particle size seen in Figures 2-4. Achange in particle shape would appear here as a change in particle size because, for particle sizes in this range, the scattering intensity is dependent on the surface area of the particle. For example, the change from a hollow to a solid particle or from a porous to a molten mass would make it appear as if a drastic change in the particle size had occurred. Lastly, the transition from desolvation to vaporization might not be instantaneous. In this case, the vaporization of the
b
0.4
t
0.3
v II
-
g
L
(PS)
Figure 2. Vaporization profile for an NaCl particle of 0.60-pm initlal radius (ro). Line in figure represents a least-squares fit for particles with radii below 0.25 pm and yields a small-particle vaporization rate of 1.04f 0.12 "1s. The error in this value Is stated constant (kv2) as fl standard deviation determined from 4 different experimental runs. The correlation coefficient for the linear fit of these data was
:
O
240
0.2
0.1
0
20
40
60
80
100
120
140
180
-
3.3. Calibration Pulse-Height Spectra. Calibration PHS were collectedfrom uniform-sizelatex particles (DukeScientific, Series 5000A,Palo Alto, CA). Latex-particle suspensions were made with filtered deionizedwater. Typicaldilution factorswere as follows: 100 OOO for particles below 0.085 pm in radii, 20 OOO for particles between 0.085 and 0.35 Mm, and 4000 for particles above 0.35 pm. All suspensionswere ultrasonicated for 5 min to ensure complete particle dispersion. The suspensionswere nebulized and desolvated with a heating chamber to produce an aerosol of free latex particles.2bm The dry individual particles were passed through the observationzone, and PHS were collected while the flame was off. The velocity of the calibration particles was controlled by regulating the nebulizer gas flow rate and set to that of the vaporizing particles in the flame.20 4. RESULTS AND DISCUSSION 4.1. Vaporization Rate Profiles for Alkali Chloride Particles. Shown in Figures 2-4 are vaporization profiles for NaC1, KC1, and CsC1. In all of the profiles, the particle radius decreasesrapidly from ita initial value to approximately (25) Langer, G.;Pierrard, J. M..J. Colloid Sci. 1963, 18, 95. (26) Fuchs, N.A. J. Aerosol Scr. 1973,4, 406. (27) Raabe, 0.G. Fine Particles; Liu, B. Y. H., Ed.; Academic Press: New York, 1976; p 83.
(28) Alkemade, C. Th.J.; Herrmann, R. Fundamentals of Anulytical Flame Spectroscopy; John Wiley and Sons: New York, 1979; Chapter 4. (29) Holcombe, J. A.; Eklund, R. H.; Grice, K. E. Anal. Chem. 1978, so. - -, -2091. - - .. (30) Skogerboe, R.K.; Freeland, S. J. Appl. Spectrosc. 1985,39,925. (31) Leong, K. H.J. Aerosol Sci. 1981, 12,417. (32) Childers, A. G.;Hieftje, G. M. Appl. Spectrosc. 1986,40, 939. (33) Kelly, R.;Padley, P. J. Nature 1967,216, 258.
2764
ANALYTICAL CHEMISTRY, VOL. 65, NO. 20, OCTOBER 15, 1993 0.6
-f-
0.3
I
+
2
0 2 -
01
+
o
C W
+
DO
m * W
+
no
+ + + oC m(
-
1
W
O 0
+
0 0
+ + O O D D
+ o
Q
* n o
O 0
o
,
,
1
1
1
)
1
1
1
,
D OD ,
n + I
(34)Weast, R. C. Handbook of Chemistry and Physics, 57th ed.; Chemical Rubber Company: Cleveland, Ohio, 1976.
integrated emission intensity from atoms liberated from a vaporizing particle was assumed to be proportional to the total mass of solute vaporized a t a given point in the history of a vaporizing particle. Of course, such rates are dependent on gas-phase chemical reactions and really correspond to overall rates for the conversion of solid solute material into free emitting atoms. Moreover, the accuracy of these earliermeasured rates is compromised by the need to compensate for atomic ionization.2 By comparing these rates to those measured by light scattering, one can determine if the rate of conversion of the analyte vapor to excited atoms is slow compared to the rate of particle vaporization. If the overall rate of atomization and excitation were slow compared to that of vaporization, the slower rate could then be approximated. Clearly, any disparity in rates would be attributable to atomization, because excitation should be very fast in a thermally equilibrated system such as a flame. Shown in Table I are vaporization rates and the corresponding calculated times required for complete vaporization of a 0.60-pm initial particle, for measurements by light scattering and by emission.192 The discrepancy between the rates measured by Bleasdell et al.l and Pak and Hieftje2 can be reconciled by their different experimental procedures. In Bleasdell's study, ionization was not suppressed and had to be mathematically corrected with pseudo-first-order rate equations. Ionization affects atoms mostly in the later stages of vaporization; therefore, this correction procedure was susceptible to large errors in the calculation of small-particle vaporization rata. Pak overcame this problem by suppressing ionization, thereby eliminating the need for its correction and increasing the accuracy of the measured vaporization rate constants. The rates measured here by means of light scattering are between 1.2 and 2.7 times those of Pak2 and 2.2-7.7 times those reported by B1easdell.l This difference suggests that the production of excited atoms from vaporized solute material might not be fast compared to vaporization. This hypothesis is supported by the calculated time required for complete vaporization, tf, of the 0.60-pm particles. The time for complete vaporization in the emission studies was calculated from both large-particle and small-particle vaporization rates. For the present comparison, tf was determined as the time required for the particle radius to decrease to 0.0 pm, based on the least-squares fit of the original particle-size data below 0.25 pm (cf. Figures 2-4). As expected from the disparate vaporization rates, the times determined for complete vaporization by the light-scattering method are 7-32 % of those predicted by Pakzand 6-13 % of those predicted byBleasdell.1 The difference in the k d and tf values can in part be attributed to the cooler flame used in Pak's study (2450 K), caused by the introduction of a large quantity of Cs aerosol, and to the ionization correction in Bleasdell's study. The difference might be caused also by a slow dissociation of molecular speciesin the solute vapor, one of the steps required for the production of excited atoms. Alternatively, an apparently smaller vaporization rate might have been caused in the earlier investigations by self-absorption, which would produce a temporal delay in the observed integrated emission. To verify this hypothesis, studies would have to be performed simultaneously on the same apparatus. This study could be performed by adding an emission channel to the present system; this modification is now underway. Lastly, the differencebetween our results and those reported earlier might be a result of local cooling in the vicinity of a vaporizing particle. This local cooling, induced by the energy demands of vaporization itself, could reduce the emission intensity of atoms liberated from the particle, so the emission-based measurements would be skewed.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 20, OCTOBER 15, l9Q3 2765
Table I. Comparison of Experimental and Theoretical Particle Vaporization Rates a n d Times for Complete Vaporization of a 0.60-pm Solute Particle exptl vaporization rates (ke) and vaporization times (tf) measured by light scattering
exptl vaporization rates ( k a ) and vaporization times (tf) measured by atomic emission
theoretical small-particle vaporization rates5 U ~
~~
0.01
0.02
0.03
0.56
1.1
1.7
260
0.85ob 0.127c 810b~e 41Wr
0.63
1.3
1.9
200 f 13d
0.617* 0.29oc 2700br 17Wr 0.847c 11wr
0.56
1.1
1.7
1.04
0.12
* 1.26 * 0.033 *
1.85 0.24 140 2 9
0 Experimental values obtained by both laser scattering and atomic emission methods are cited. Reference 2. Reference 1. d Time for complete vaporization of a 0.60-pmsolute particle measured directly from ita vaporization profile. e tf is the time for complete vaporization of a 0.60-pmsolute particle, assuming cited values for kvl, k a , and r,.
4.4. Comparison of Measured Vaporization Rates to Theory. Also shown in Table I is a comparison of smallparticle vaporization rates measured by light scattering to those predicted by theory.6 For calculation of the theoretical rate, a vaporization coefficient a! must be assumed. For NaCl vaporizing from a large flat surface at a temperature just below its melting point, the vaporization coefficient was determined to be 0.23.35 However, for materials such as ethanol and water, vaporizing near their boiling points, vaporization Coefficients as low as 0.02-0.03 have been reported.% This large range of coefficients demonstrates the difficulty in calculating the vaporization rate theoretically.
To obtain agreement between the theoretical small-particle vaporization rate constants and those obtained by light scattering, vaporization coefficients of 0.01-0.03 must be assumed. These low vaporization coefficients suggest that the molten solute vaporizes with some difficulty from the surface of a particle. A more detailed treatment of theoretical vaporization rates can be found elsewhere.5
ACKNOWLEDGMENT This work was supported by the National Science Foundation under Grant CHE 90-20631.
RECEIVED for review August 19, 1991. Accepted July 20, (35) Ewing, C. T.;Stem, K. H. J. Phys. Chem. 197S, 79, 2007. (36) Hith, J. P. The Characterization of High-Temperature Vapors; Margrave, J. L., Ed.; Wiley: New York, 1975; Chapter 15.
1993." 0
Abstract published in Advance ACS Abstracts, September 1,1993.
