ANALYTICAL CHEMISTRY
850 Equations 28 are a set of linear equations which express the desired values of F , explicitly in terms of the measured values of c , . The coefficients in the equations depend on the values of 11; (corresponding tu the values oft:) a t which the concentrations c, are measured; more exactly, the coefficients depend on the ratios of the values of Di, as shown by Equation 25. Consequent,ly, if the values of D , are chosen in a geometric sequence, the coefficients of Equations 28 are considerably easier to calculate and the equations themselves are also simplified. I t is usual and desirable. for other reasons also, to choose particle sizes in a geometric sequence when making particle size analyses or reporting particle size distributions. Usually a sequence n-ith common ratio d2 is used. The coefficients in Equations 28 depend also on the value of x = rz/r;-that is, on the dimensions of the centrifuge flask einployed. For the flask described above, s = 3.44 and Equations 28 assume the form (for sizes in a 4 2 sequence):
SO51ENCLATURE
.biy coiisistent units may be employed. a = acceleration of a particle in a centrifugal field, (cni. ' c
D I'
f g m
R T
ru ri
rl s t 1'
v
v' VI
the subsequent terms being negligible. For the first four values of 1 , the equations are slightly altered, as follows:
IJ
z p pf
pa
& w,
w
second)/second. concentration of suspended solids, as a fraction of the concentration of uniform suspension prior to settling, dimeiiaionless = Stokes's law particle diameter of a particle which settles froin a radius r , to a radius F in time t , cm. = F(D) = fraction by weight of particles smailcr than diameter D, in a powder, dimensionless = dF/dD, l/cm. = acceleration due to gravity, (cm./second)/second = effective mass of a ephere immersed in a liquid, grams = Stokes's law drag force, dynes = distance of particle from axis of rotation; also, specifically, distance of sampling point from axis of rotation, cin. = distance of surface of suspension from axis of rotation, cm. = initial distance of particle from axis of rotation (when t = O), cm. = unit vector in direction of radius vector of a particle, em. = ( T / r o ) 2 , dimensionless = time, seconds = w f t , l/second = particle velocity, em. per second = particle velocity relative to liquid medium, cm. per second = velocity of liquid in neighborhood of particle, cm. per second = Stokes's law particle diameter, em. = 9 p / y 2 ( p , - p f ) , l/second = liquid viacosity, poises = liquid density, grams per cc. = particle density, grams per cc. = unit vector orthogonal to rl, cm. = angular velocity of rotation of liquid, radians per second = angular velocity of rotation of particle, radians per second =
I,c>ttersin bold face represent vector quantities. The method of wing these equations to compute size disti ibutions is as follows: The cxperirnental data consist of a series oi i'ractioiiai coiicwtrations, e , measured a t known values of w / and 6, froin which a value of D for each value of c is calculat.ed from Equation 18. The values of c us. D are plotted (usually on logarithmic-normal paper) and a smooth curve is drawn through the points. \-dues of c are read from this curve at any convenient set of values of D in :i fisequence, D,, D2 = d/ZD,, D3 = 2D1, etc. The corresponding values of c are called c1, c2, . . . cn. These values are substitut.ed in Equation 29 t,o give the values of F,, F2, . . . P,. The values of F1, F P , F3, and Fa can be found either by using Equations 29a or by extrapolating the curve of c us. D to get additional points t o use in Equation 29.
LITERATURE CITED
(1) Broarn. ( ' , , .l.P h y s . Chem.. 48, 246--58 (1944). ( 2 ) Codex Book Ca,, Norwood. Mass., Coordinate Paper No. 32376, "Logarithniic-normal." (3) Lol-itt. W.I-.,"Linear Iiitegid Equations," S e w York, D o w r Publications, 1950. (4) Alartiri, 8. I\-.,Symposium on S e i 7 Methods for Particle Size Determination in the Subsirye Range, PP. 66-89, Am. Sac. Testing Materials, M a r r h 4 , 1941. ( 5 ) Rohison. H. E.. arid 3fwi tin, S , TI-.. .J. P/i)ls. ( ' A e w c . . 52, 854-81 (194s). K E C L I ~ . EJanuary D 11, 1951. Presented before the Division of Industrial and Engineering Chemistry, S~'niposiuinon Dispersions in Gnses, at the , M d . , December 17th Annual Chemical Engineering Syiupo=iii~ i Baltimore, 28 and 20. 1950.
Particle-Size Determination in Radioactive Aerosols by Radioautograph J . A . LEAHY Los Alarnos Scientific Laboratory, Los Alamos, N . M .
A
HADIOAUTOGRAPH technique has been used to study particle-size distributions in aerosols of an alpha-emitting compound. The active material \vas collected on filter papcr and placed in contact with nuclear track plates for various exposure times. By counting the number of tracks in the eniulsion for a given exposure time, the size of each emitting particle was calculated from the formula:
where C = number of tracks in cIinulPion from particle of dianivter d microns, t = autograph exposure time, and K = const'ant. Particles as small as 0.2 micron have been accurately determined in aerosols containing as little a s 0.8 ppg. of active material per liter of air. DERIVATIOY OF EQUATION
For a sphere of diameter d microns containing S, atoms of an alpha-emitter whose decay constant is h per minute, collected as
V O L U M E 23, N O . 6, J U N E 1 9 5 1
851
One of the problems encountered i n the study of radioactive aerosols is the low abundance of these particles relative t o atmospheric dust in the sample. Most methods of particle size analysis do not m a k e any- distinction between the radioactive and the inert partiole. Therefore, a new method of discriminating and measuring alpha-emitting radioactive particles was developed. A filter paper sample of an alpha-ray-emjtting aerosol was placed in contact with nuclear traok plates for various exposirre times. By counting the number of tracks in the emulsion for a given expositre time, the size or eaoh
a cornpound having density p and molecuiar weight M, the equa-
emitting particle was calculated from the derived equation d =
(!$)”~
where d = partiole size in microns, C = the number of traoks i n the emulsion emitted from the particle, t = exposure time, and IC is a constant for a given radioactive material. Although the method is not limited to aerosols, i t is particularly useful in healthphysics studies where the permissihle air concentration of alpha-emitting particles in the siie range from 0.1 to 10 microns is extremely low.
01
tion is:
( d N ) = hN,(dl)
,*
=
611
(&)
x
As the diameter is a cube-root function of both exposure time and number of tracks, the method is precise.
10-11
Figure 1. Typioal Group OWX) 24-hour e x p a u r n
Figure 2.
0.9-Micron Partiole (125X)
24-hour exposure
where d N = number of atoms disintegrating in time dt, W = weight of particle, grams, A = Avogadro’s number, V = volume ofparticle, cc., and,f = number of radioactive at.oms per molcrule of compound.
( d N ) = kd3(dt) where k is
B
constant for a given compound
.%ssuming no significant change in the value of N . during exposure, and B 50% geometry for intimate contact brtu.em emulsion and sample, the number of tracks, C, will be:
Figare 3.
Orientation Group (1lOX)
24-hour erpwurs
GENERAL METAOD
The slide or filter paper sample on which the material has been collected is placed in intimate contact with a nuclear t,rack plate (Kodak, Type NTA, 25 microns) and exposed for the desired time in a simple “camera.” After development for 2.5 minutes in Kodak developer D-19, the emulsion is fixed in acid hypo, uashed, and dried. The plate is then scanned microscopically :it a magnification of about 200. Figure 1shows a typical group of clusters u.hieh a n be resolved by decreasing the autogmph exposure time. If a cluster remains too dark t o count on the second exposure, a third shorter exposure is made, eto. By this method of varying exposures, each cluster may be reduced t o a countable number of tracks (approximately 10 to 100). A cluster containing the maximum number of tracks for counting is shown in Figure 2. Far such large clusters, only one quadrant need actually be counted.
852
ANALYTICAL CHEMISTRY
If the concentration of particles on the sample is high enough, i t i B necessary t o count only a small representative area. However, a minimum of 200 particles should be counted per sample. In going from one exposure t o another for a given sample, the eame area can be located by the use of an orientation group such a8 that shown in Figures 3 and 4. The coordinates of this group are determined on the microscope stage and used as the center of the area to be scanned. In using a contaminitted filter paper as the autographer, the group shown was not disturbed, although it was in intimate contact with each emulsion for six exposures. For very short exposurea, seriolls error will result if m y active Figure 6. Large Particle and Agglomerate (1OOX)
particles are transferred to the emulsion. However, there was no evidence of this in any autographs of filter paper deposita. From the number of particles in each size group in the area manned, the numbor of particles on the total filter paper or Elide sample can he computed fmm the ratio of t o t d sample area t o area scanned. This total abundance mtLy then be converted t o a concentration in the air stream from which the samde was taken.
Figure 4.
Orientation Group of Figure 3 (1.OOX) I-hour exposure
DETERMINATION OF SIZCFREQUENCY DlSTRlRUTlON ENTERING AND LEAVING PILOT r u m
This method has been used t o determine the size-frequency distribution of particleicles in the feed to and discharge from an airdecontamination pilot plant. Standard methods of determining particle size were inadequate, because the discharge eoneentratiou of radioactive material was about 0.8 pig. per liter of sir. The filter paper samples which had been used to determine removal efficiencywere used as radioautograph 8ouIces. Figure 5 is a typical distribution of the Pfflunntfrom the plant obtained by this technique.
PARTICLE DIAMETER, p
Figure 5.
Particle Size Distribution on Surface of Filter Paper
C
Figure 7.
Calibration Curve
V O L U M E 23, NO. 6, J U N E 1 9 5 1
.bthe alpha-particle will not paletrate any appreciable thickness of filter paper, the distributions reported are for the surface of each sample of filter paper. In Figure 5 there appears to be a decrease in the count frequency in going from 0.4 to 0.2 micron. This is probably due to penetration of the paper (HollingsworthVose H-70) to a greater depth by the smaller particles. The presence of agglomerzttos may also be detected by this method. Figure 6 shows a track cluster of an agglomerate consisting of radioactive and nonradioactive material. The latter stops the alpha-particles from reaching the emulsion, which results in a very irregular cluster pattern. The particle shown was greater than 5 microns, and is probably duct scale. Only two such particles wwc prescnt in a total of about 1000 particltv observed. For the material used in the% particular tests, the value of K in Equation 1 was 5.04. A calibration curve for the formula:
was constructed to give the particle size as a function o f the number of tracks for a given exposure time (Figure i ) . Cascade impactor samples of the feed to the system taken a t a later date verified the results obtained by radioautograph. Analysis by the method of Hatch and Choate ( 1 ) indicated that 50% of the mass of sample was composed of particles less than 0.9 micron, while 98.6% of the mass was made up of particles lea8 than 5 microns.
853 If there is a very great abundance of large particles, the finer particles will be obscured in the radioautograph unles? the large particles can be removed and studied separately. The isotope being studied (as well as interfering decay products) must be identified. In addition to standard electronic detection devices, the range and track appearance in the emulsion d l help determine the radiation characteristics of the particle. The method is feasible as a research tool on only a few samples, as counting tracks in hundreds of clusters is a tedious and expensive procedure. Projection of the field on a screen is helpful in counting individual tracks. A simpler modification of this method would be to observe the entire cluster for each particle rather than individual tracks. By establishing a standard minimum cluster of about 300 tracks and making several exposures, the particles can be grouped by size range. A photodensitometer could be used to count such large clusters. However, this method is not ap pwcise as counting individual tracks. .b the actual particles are never obuerved, this method does not reveal the true particle shape. An effective diameter for the particle is measured, which is bawd on the mass of each particle. Gamma-emitters must be considered as a separate problem, because they do not produce tracks. By a previous exposuredensity calibration, the size of the particle might, be determined, but this possibility has not been .investigated. LITERATURE CITEII
(1) Ualla Valle, J. hl.. “Mioromeritics.” New York. P i t m a n PublishLIMITATIONS OF RADIOAUTOGRAPH METHOD
ing Co., 1943.
RECEIVEDJanuary 3, 1951. Presented before the Division of Industrial
Obviously, the aerosol being studied must consist of radioactive particulates, as inert material is not detected. However, if inert material is also present, the method gives an analysis for this hazardous material only
and Engineering Chemistry, Symposium on Dispersions in Gases, a t the 17th .4nnual Chemical Engineering Symposium, Baltimore, Md., December 28 and 29, 1950. Based on work performed at Los Alamos Scientific Laboratory of the University of California, under A E C Contract W-7405Eng-36.
Infrared Spectra of Phosphorus Compounds L. W. DAASCH AND D. C. SMITH Naval Research Laboratory, Washington, D. C.
,ipplication of infrared spectroscopy to analytical and structural problems in phosphorus chemistry has been limited by the lack of spectral data on reference compounds, and by the inadequacy of information concerning characteristic frequencies of molecular groups containing phosphorus. This information was sought through study of a large number of phosphorus compounds containing a variety uf moleeular groups of interest. Empirical correlation of sixty reference spectra yielded characteristic
C
ONSIDEXABLE work has been published on the Raman spectra of phosphorus compounds, but infrared data on only a few of the simpler compounds are found in the literature (11, 1 7 ) . A study more extensive than heretofore reported hag therefore been =de of the infrared spectral properties of phosphorus compounds. It has dealt mainly, but not entirely, with organophosphorus compounds. For this type of compound, in particular, very few data have been published.
frequency ranges for a number of groups: P-H, 2350 to 24-40 cm.-’; P-F, 850 to 980 cm.-’; P - C I , 430 to 585 cm.-’; P++ 0-, 1170 to 1310 em.-’; P+-t S-, TOO to 770 cm.-l; P-C (aliphatic), 650 to 750 cm.-’; phenyl-phosphorus group, near 1000 cm.-’ 2550 to 2700 cm.-’; and 1440 cm.-’; P - 0 - H , P-0-C, 1030 to 1090 cm.-’; phosphinic acids, near 1665 cm.-’ The usefulness of these group frequencies for qualitative interpretation of spectra in terms of molecular structure is discussed and illnstrated.
EXPERIMENTAL
and Materials* The Of phosphorus compounds is somewhat complex and at present in a state of flux. Accordingly, a few definitions will simplify discussion of materials and data. Chemical Abstracts has been followed wherever possible in the scheme of nomenclature prwented in Table I.
