Hydrogen Flame Ionization for the Detection and Sizing of Organic Aerosols R. WAYNE OHLINE Department of Chemistry, New Mexico Institute o f Mining and Technology, Socorro, Some of the basic properties of the hydrogen flame io'nization detector for the detection and sizing of organic aerosols are described. Calculations indicate that the dletector should b e able to detect organic particles with diameters as small as 1 micron. In addition, the device offers promise in the field of combustion kinetics of very small particles. Equations are derived which correlate pulse shape with particle size and burning rate.
A
the hydrogen flame detector seems to be sensitive to many types of aerosols, efforts have been directed toward understanding the properties of the detector with relatively high molecular weight hydrocarbons. Of interest in defining the capabilities of the detector are this minimum particle size detectable and the resolving time (related to the burn time per particle, or droplet life). For hydrocarbons, it is generally accepted i,hat the responses per unit mass of individual compounds (above about C,) differ only slightly from each other ( 5 , 9). Using the data of Desty, Gleach, and Goldup (4),one obtains the value 6 >( 10-3 coulomb per gram of hydrocarbon for the pure hydrogen flame in air operating a t optimum conditions. The best electrometers-.g., Model 6010 Dynacon, Suclear Chicago Corp., or Victoreen Electrometer Model 457-can detect a charge pulse of something less than lO-l5 coulomb (corresponding to the detection of 0.02 mv. on a capacitance of 50 p Mf.). Assuming a particle density near unity, one calculates that the smallest particle detectable would have a diameter on the order of 1 micron. This picture should not change much as one goes to other types of organic compounds, since the particie mass varies as the cube of the diameter, and the diameter is usually the parameter of interest-that is, the coulombic yield could decrease for a given compound by a factor of 8, and the minimum size detectable would then change only to 2 microns. The burning of single droplets of hydrocarbon fuel has been studied by several workers (6-8). -4s a result it has become apparent that a useful description of the burning rate is obLTHOUGH
tained by assuming that the liquid droplet is surrounded by a spherical diffusion flame. It is also assumed that the droplet surface and flame front are concentric spherical surfaces, and that the radius of the flame sphere is large compared with that of the droplet (the radius of the flame sphere is given, to a first approximation, by the condition that the rates of delivery of fuel and oxidizer to the flame front are in stoichiometric proportion). On the basis of this model, the following relation can be derived :
d 2 = do2
- kt
(1)
where do is the initial droplet diameter, d is the instantaneous diameter, t is the time, and k is a constant depending on the compound and conditions of the oxidation. The validity of Equation 1 is well established for large droplets (on the order of 100-micron diameter), but is only an approximation for the vaporization of droplets of diameter less than 20 microns because of the finite rate of mass transfer through the liquid interface ( 7 ) . This is the case since, in order for Equation 1 t o hold, the rate of mass transfer through the liquid interface per unit area must become infinite as the droplet diameter approaches zero. For droplets of less than 1 micron the increase in vapor pressure caused by surface tension must be taken into consideration ( 7 ) . However, according to Bradley, Evans, and Whytlaw-Gray (2), these deviations are small for evaporating droplets down to 1-micron diameter. In Table I , some typical values of evaporation burning constants are given. The constants appear to be relatively insensitive to compound type and molecwlar weight. In light of these data and those from other sources, it appears that if only an approximate value of k is required, one may assign t o it the value 8 X 10-3 sq. cm. per second. Hence, for particles with diameter of 10 microns, the flame method should be able to resolve something on the order of 10,000 particles per second. PULSE SHAPE
The following treatment assumes that the detector is operated on the saturation plateau-Le., the potential on the
N. M. collecting electrodes is not so great that ion multiplication occurs, nor so small that ions can recombine before collection. I t is also assumed that the mechanism of ion formation is the same as that for the detector operating in the normal (gas chromatographic) mode, and that the rate of production of ions is limited by the rate of volatilization of the droplet. The problem of pulse shape is an important one, since an understanding of the relationships involved leads to predictions of the ultimate resolving time with a given electrometer and to a correlation of pulse height with particle diameter. If Equation 1 represents the situation under study, the rate of delivery of charge Q to the collector probe is
where g is the coulombic yield for the organic compound (coulombs per gram), and p is the particle density. Since the change in charge with respect to time of the measuring capacitor (C, Figure 1) is given by out
it follows t h a t for the electrometer input network shown in Figure 1,
dE dt =
('g) -.-.E
ddo2
- kt -
(4)
do2 t < - = r k where E is the potential across the electrometer input and T is the droplet life. Table I. Selected Values of Evaporation Burning Constants (6) k , sq.
Liquid 100" to 120' C. petroleum ether Kerosine (specific gravity 60"/60° F. = 0.80511 Diesel fuel '(specific gravity 60°/600 F. = 0.8500) Ethyl alcohol Benzene tert-Butylbenzene n-Heptane
cm./sec. 0,0099 0.0096 0 0079 0 0081
0.0097 0 0077 0.0097
VOL. 37, NO. 1 , JANUARY 1965
93
300 V
where
When RC >> r , the capacitor can be considered as not discharging at all during the droplet life. The pulse shape in this case is obtained more conveniently by direct integration of Equation 2. Dividing the result by the capacitance, there results
I
Electrometer
Teflon in sulo lor
vx-55
E For t
c-
H2
t
Filtered air ond particles from atomizer (nebulizer)
Figure 1 .
Schematic diagram of hydrogen flame aerosol detector
=
&!?? 6C
i
do3
-
(do2 - b t ) 3 / 2 ] (8)
> T , the potential change is given by
where E , is the potential on the input network a t the end of the droplet life. Figure 3 shows the results of calculations with the above equations for the following conditions: do = 10 microns p = 0.8 gram per cc., k = 0.008 sq. em. per second, g = 0.006 coulomb per gram, C = 7 5 ppf. JF'ith respect to pulse shape-up through the maximum potential, Equation 5 is an excellent approximation for RC = 7 . 5 X 10-6 second. The pulse shape for RC = 1.2 x 1 0 - ~second closely approximates that obtained by assuming that the capacitor is not discharging. The exponential decays of potential at the end of the droplet life have been omitted for general clarity of presentation. However, these can easily be .visualized when it is recalled that the potential falls to 37% of E , in one time constant. EXPERIMENTAL
For kt
