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Edited by
... Chemical Instrumentation S. Z.
feature
LEWIN, N e w York University, N e w York 3, N. Y.
These articles, most of which are lo be contrikted by guest authors, are intended lo serue the readers of this JOURNAL by calling attention to new development; i n the theory, design, or auailability of chemical laboratoy instrumenlation, or by presenting useful insights and explanations of topics that are of practical importance lo those who use, or teach the use of, modern instrumentation and instrumental techniques.
VIII.
Instrumentation for Particle Size Analysis. Part Three. 5. Z. Lewin, Deportment
of Chemistry, New York University
The preceding sections have treated the principles of design and application of instrumentation for the determination of the sizes of the particles in a specimen by means of (a) the dispersal and measurement of the individual particles, and ( b ) the distribution of the sample into fractions compoaed of particles falling into more or less well-defined size ranges. A third category of instrumental techniques is available, in the application of which the sample is neither dispersed nor fractionated, but rather a physical or chemical measurement is made that ,yields information related to some kind of average either of the area or volume of the particles, or of that of the voids or inhomogeneities in the sample. Hence, this type of approach may be characterized as based upon the measurement of an inlegml propertu of the sample. Although thia kind of measurement is only capable of yielding information about some averaged (i.e., integrated) size-dependent parameter, it is possible, in some cases, to make the measurement under several different conditions, such that the relative eontribut,iona to the over-all average made by different sired particles changes with the conditions of the experiment. Such data can then often be interpreted t o yield some insights into the distribution of particle sizes in the sample.
Integral Property Techniques A ronsidemhle number of properties is sufficiently sensitive to the dimensions of partirles or of the voids between (or within) them to be potentially useful for particle size analysis. The following list summarizes the properties that have been accorded aerious attention in this respect. 1. Line Broadening of X-Ray Diffraction Pattern. If the particle size of the rrystallites bathed in an x-ray beam is of the order of 0.1 micron and less, the Bragg
reflections (i.e., the intensity maxima governed by the Brsgg law, nA = 2d sin 8, where e is the angle made by the incident heam, of wavelength A, with the set of planes whose interplanar separation is d ) hroaden out. This is due to the fact that whm the uurnber (ef 1 r w t d l h n e s ( o n t r ~ h uting 10 H dilfra~~llnn peak ir ntlt Ilmr, tllr peak 1t.wr its sharpnws, jurt ,LS t h e resolv~ n pp. w e r I i e , sharpncm of rptvtrd llnei, nf a ruled diifr:ivtlc,n prxtinp di~ninisl~r* ari the H ~ P Hillotmn3tcrl 111 d ~ ( w i ~ t dI .t IIM been shown for a monodisperse sample (i.e., one in which all the particles are of the same size) that the line hradening, defined as the width of the line a t half its maximum intensity, is related to the thickness of the crystallites by the formula:
2. Small Angle Scattering of X-Rays. If the intensity of x-radiation scattered hy a sample is measured as a function of angle close to the direction of the undeviated beam, it is observed that the manner in which the intensity falls off with increasing angle is sensitive t o the dimensions of the inhomogeneities present in the sample. This effect is illustrated by the curves shown in Figure 20, which are calculated on the basis of scattering theory. At a given scattering angle, some x-rays reach the detector from particles, and others from voids in the sample. The degree of mutual interference suffered by the various rays coming to a given point at each scattering angle depends upon the relative sizes and numbers of these two types of scattering centers. 3. Scattering of Visible Light. The intensity of the light scattered by particles suspended in a medium of different refractive index is afunction of the angle of viewing, wavelength of the light, and shape and size of the partides. The complex nature ~
Figure 20. Theoretical low angle wanering curves. The ordinates are normalized scattered intensities [Ilhl = total intensity xanered in the diredion h, where h = 4 r @/A; I.(hl = intensity scattered in the direction h by a ringle electron; N = number of particles]. The abscissae ore proportional to the scattering .angle [hR = 4R r e/h, where R is the particle rmdius]. Each curve refers to o different rotia of the pmrticie sire to the size of the interpmrticle spaces [vo = volume of particle, vI overage volume of x m p l e available to each porticie, i.e.. Vo/N, where Va is the t o l d volume of the ~ m n ~ k ;is a constant that is approximately unity]. From Guinier, A., and Fournet, G., "Small-Angle Sconering of X-Rays." John Wiley and Sons, N. Y.. 1955.
of tho interrelationships among these factors is illustrated by the diagram of Figure 21. which shows the variation of intensity with angle for monochromatic light scat-
Figwe 21. Voriotion of rcottered inlensity of light of wavelength A about a sphericml particle of radius r when 2 r r = ah, and refroclive index of the particle is 1.25. The full line. i,, gives the intensity of the vertically polarized component of the icottered light; the dwhed line, in, refers to the horironlally polarized component. From Biumer, H., I. Physik, 32, 124(19251.
tered by s. particle larger than the wavelength of the light. If the particle size is
(Continued on page A4251
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A423
Chemical Instrumentation smaller than the wl~velengthof the light, the scattering pattern is much more uniform, although the intensity in the forward direction remains greater t,han t h a t in the backward or sideward directions. For such particles, the scattering pattern tends t o become independent of the shape of the particles. If the particles are smaller than 0.02 microns in radius, and artre in a dilute suspension in a medium of refractive index n, the turbidit,", T , isexpressed hy the Debye equation:
where I is t.he transmitted intensity, lothe incident intensity, M the molecular weight, c the coneentrat,ion in g/cm$ A the wavelength of the light in air, N the Avogadro number, and dnldc is the refractive index increment of the medium due t o unit increase in concentration of the suspended phase. The particle siaes of monodisperse samples can be determined through measurements of bur bid it,^, sclttt,ered intensity a t selected angles, angular vi~riationin the color of the scattered radiation when white incident light is employed, or relative intensities of t,he vertically and horizontally polarized components in the scattered
..
.
tration and average size. 4. Pressure Drop U n d w S l r e a d n e Flour. If a fluid (gas or liquid) is rnused t o flow through a porous sample, surh as a compacted powder, the pressure drop, Pi PO,across the plug of lengt,h L is given by the expression:
P i-PO - 2 n ~ S ~ ( I - n ) ~ L 9 n1 where n is the viscosity of t,he fluid, u is the velocity of flow, S is the surface area. per unit volume of the powder or porous solid, g is the gravitational constant., and a is the fraction of voids, i.e., n = V,/Vt where V . is the volume of voids in the plug and V cis its total volume. 5. Knudsen. F b w Rate. When the size of the voids in a plug is small in comparison with the mean free path of the molecules of a gas flowing through the plug, the rate of flow is limited only l,y collisions of gas molecules with the solid surfaces, and not by collisions occurring between gas molecules. This is the condition of molecular streaming, or Knudsen flow, and the flow rate is considerably greater than for streamline flow. Measurements of the flow rate under these conditions can therefore be related t o the mean dimensions of the pores and voids in the sample. 6. Gas Adsorption. If the adsorption of a gas on a solid surface is due principally t o van der W a d s forces, as, e.g., in the adsorption of nitrogen on various solids a t liquid nitrogen temper:ttures, the volume adsorbed as a f~lnctionof the pressure, p, can be expressed by the Brunsuer, Emmett. and Teller (B13T) equation:
(Contimed on pogr -4426')
Chemical Instrumentation
where p, is the saturation pressure of the gas, V , is the volume of gas adsorbed when R rnonomole~ulm ia,ver has hren formed, and C is n constant. Figure 22
Relative pressure, p l p , Figure 22. Admrption isotherms as calculated from BET theory for carer in which the exirtence of pores or capilbrier limib the maximum number of molecular layers of odrorbate to the valuer shown. Point B correrpondr to the completion of o monaloyer. The circler show experimental points obtoined for the adsorption of nitrogen on a sample of iron powder. From Blunauer, S., "The Adsorption of Gores and Vapors," Princeton Univerrily Press, 1943.
shows the forms of the cnlrulated adsorption isotherms for several rases in whreh the maximum number of layera of the adsorbed gas varies from 5 to m (the BET equation in the form given above applies specifically only to the latter case). Point B in the figure corresponds to the relative pressure a t which a completed monomolecular layer has been formed. The volume of eas corresoandine: to a
surface area of the sample. When the adsorption is not adequately described by the BET equation, other semi-empirical approaches may he adopted for relating the variation m volume of gas &orbed as a function of the relative pressure to the surfare area of the adsorbingaolid. The rate of adsorption, e . g , -dp/dl in a constant volume system, may be measured in place of the total amount of adsorption. 7. Adsorption of a Solxte from the Liouid Phase. The dsorotion of certain aoitltes on the surfares oi certain solids ~ h o w s a definite saturation value, as shown in Figure 23, and this suggests that under these conditions s. monolayer of adsorbed molecules has been farmed. Determination of the decrease in concentration of t,he solution at the plateau can, on the hasis of this assumption, be utilixd to comput,e the tnt,sl surface ares of the solid phase. (Contintred on page A430)
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Journal OF Chernicol Education
-
Chemical Instrumentation Temperature.
35
25
26
22
OC
20
18
Relative concentration, CK, Figure 23. Adsorption ikothermr of stearic acid in benzene tolutian on several d i d powden. The ordinates ore millimramr of solute adsorbed per grom of solid phase. The abscisoe at the bottom are relotivs concenlrolion, i.e., (he ratio of the concentrotion of the solute to its rdurotion concenlrdion. The obscisroe a l the top show the corresponding quontitier in terms of the temperature of o solution of fixed rompolilion. ~
~~
-
~
~
Equivalent results have bee11 obtained in aome cases with the adsorption of dyes from salut,ion, and this technique has been widely used because of the ease with which the concentration changes that occur can be determined by colorimetry or spectrophotometry. 8. Radioactive Tracer Enhange. I t has heen suggested that if radioactively labeled species in solution can be exchanged for non-radioactive species in the S u r f a r ~ of a solid phase, the decrease in radioactivity of the solution, or the pick-up of activity of the solid, ran be utili~edto yield the tot,al surface area. However, this method is limited to eases in which it can be established that t,he exchange does not penetrate below the surface layer, and that recr,vstallirat.ion or local rell effectsare absent. 9. Ab8-dutP Cd07inaedry. If s solid is allowed to become coated with a layer of an adsorbed liquid which is in equilibrium with the saturated vapor of that liquid, then upon immersing the solid into a reservoir of that same liquid, an amount of heat would he liberated that is equal to the total surfare energy (i.e., surface tension X total area) of the d o r h e d liquid, since the surface of the latter disappears during this process. Since the surface tension of the adsorbed liquid can be presumed to be known, cdarimetric determination of the heat of immersion can be employed t o yield values of the surface area of the solid. This approach is often designated as the Harkins-Jura absolute (HJa) technique. The method is considered t o be absolute since it does not depend upon an assumption as to the area occupied on the surface of the solid by each molecule of adsorbate. 10. Other Techniques. Ot,her parameters that have been shown to he related to surfwe area. or particle sizes are: relationship between magnitude of applied suction and amount of wnt,er removed (Contimam! on pnge A432)
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Journal of Chemical Education
Chemical Instrumentation from s water-saturated packing of the specimen; conductivity uf heat through a packing of the specimen; variation of t,he amount uf heat evolved due t o adsorption of a. gas as a function of the time i t is left in contact with the sample; rate of dissolution of the solid under conditions such that the rate of dissolution is limited by the diffusion of saturated ~olutionaway from the surface of t,he solid; rate of emanation of a vuliltile daughter element from a solid rontainmg x rsdio-
Figure
24.
Opticol
pion
of
the
Wagner
PhotoeledricTurbidimefer.
active parent element,; minimum amount of sn organic adsorbate with which a purous packing must be impregnated t o permit a atpersaturated solution of the impregnant in rantact n,ith one end of the packing t o he seeded by the introduction of seed crystals a t the other end of the packing; trajectories traveled by s ~ r o s o l particles in an electro-statie precipitator; amplitudm of the vibratory motions executed by aerosol particles when subjected t o 8. sonic field of fixed frequency; distance of penetration of suspended partirles into a battery nf standard, narrow channels (called a "diffusion battery"); forces of adhesion hotween particles, as measured by the angle of tilt neceSS;try t o cause B maas of powder t o slide along s.surface. Many of the integral property techniques described in the preceding paragraphs are widely used a t present, and as s consequence rommercisl instrumentation is mailable for the imnlementation of these procedures. The following section desrribes some of this instrumentation t h a t
Figvre 25. Amerimn Instrument the Wogner turbidimeter.
Co. version
of
is specifically designed for particle size analysis; other instruments which are primarily designed for other purposes, but which may be applied t o particle size determinations, such as, e.g., x-ray diffrartron equipment, need not be treated here.
Turbidimeters
(Codinued on page A434)
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Journal of Chemical Education
Chemical Instrumentation cements is the Wagner Photoelectric Turbidimeter, shown in diagram in Figure 24 (available from LsPine Scientific Co.,
Figure 26.
.
snd 27, brings the light t o a. focus a t the ,c, with diaphragm stop placed in the optical path so that a diverging cone of darkness encompasses the light collecting lens of the phutomultiplier (Cirnlinued on page .4440)
,,,,,
Optical plan of the Sinclair-Phoenix Forward-Scattering Smoke Photometer.
Chicago 29, Illinois, $540). I t consists of a. source of light of constant intensity adjusted so that approximately parallel rays of light pass through a. suspension of the substance to be tested and impinge on the surface of a barrier layer photoelectric cell. The transmitted light intensities are measured a t various levels in the sample by adjusting the height of the sample cell, and this is done after specified periods of sedimentation in order t o yield a, particle size distribution. The design of the Wagner turbidimeter made by the American Instrument Co., Silver Spring, Maryland, is shown in Figure 25. The Phoenix Precision Instrument Co., Philadelphia. 40, Pennsylvania, manufactures several instruments based upon the measurement of scattered light. Their Sinclair-Phoenix Forward Scattering Smoke Photometer, shown in Figures 26
"
.o..nnp
r;,t*r
~ i g u r e 27. instrument.
mnrh..m.tir
*. *"""
I.Y
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VilC.
T".
L'".
photograph
C d l ".Id.
of
sin&ir.phoenix
Cdl
Con..
Light %"we
Conden.ing L."IL.
Neu".,
R'-r'
Figure 28.
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Journal of Chemical Education
Spring
d ..i. .'sLmbll
A'h ,om. tic Len'
inrid.", slop,
.ms
L 0.4.
d
IIeLrc
.h....""ltipli..
rubs
Optical plan of the Aminco Absolute Light Scaltering Photometer.
A~lyzer A..rmbl* Position
L."'
a high sensitivity to Chemical h ~ . ~ m e n t ~ t iThis ~ I results I in the insample particles stream; calibration with a dioctyl phthalat,e oil fog of 0.3
,""S"%,O"
"rL,
,.I,,
c.0
Figure 29.
Optical plan of the Model 7 Photo-Nephelometer of Coleman Instruments.
housing. Iienre, the only light reaching the detector is that which is scattered in the forwsrd direction by the specimen.
A440
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lournd o f Chemical Education
micron droplet diameter indicates micrograms per liter ae the minimum detectable concentration of aerosol.
This company also makes a lightscattering photometer designed for the measurement of the types of scattered intensities needed in the determination of the molecular weights of maeramolecules by the Debye technique. The instrument, known as the Brice-Phoenix Light Scattering Photometer, may also be utilized for fluorescence, transmittance, and r e flectance measurements. I t consists asentially of an optical bench, light source, photomultiplier detector, sample campartment, and associated electronics. The American Instrument Co. offers a similar instrument as their Absolute Light Scattering Photometer ($2900). The optical plan of this instrument is shown in Figure 28. The Model 7 Photo-Nephelometer of Coleman Instruments, In& Maywood, Illinois, shown in Figure 29, is designed for orecise andvtical work with turbid soluiions. here are two photocells, viewing the light scattered a t 90' to the incident direction. The summed output is read out hy means of a sensitive gslvanometer. Another instrument is available, viz., the Model 9 Nepho-Calorimeter, which incorporates a third photocell in line with the transmitted beam, so that the device can be employed either for transmittance or scatteringmeasurements. A recording turbidimeter, designed for use in the continuous monitoring of a flowing liquid stream, is made by General Electric Co., Srhenert,ady, Kew Yark. Permeameters Several instruments based upon the (Catinued on paye A442)
Chemical lnstrumentation
Figure 30. The Sub-Sieve Sirer, a n air permeobiiity apparatus made by Firher Scientific Co.
means of the principles involved in low temperature gas adsorption. Their Adsorption Flow Apparatus ($1705) employs a slow, constant flow of nitrogen gas into the sample until a. preselected equilibrium pressure has been attained, a t which point the flow stops and the volume of gas adsorbed is determined. This permits data t o be obtained very rapidly and conveniently. Far more precision, BET data can be obtained by standard volumetric measurements a t several gas
measurement of the air permeability of a. compacted powder or porous solid specimen are in current use. The Sub-Sieve Siser made by Fisher Scientific Co., Pittsburgh 19, Pennsylvania ($465) is illustrated in Figure 30. A regulated flow of dry sir is passed through a weighed sample packed under strirt1.v stsndardiaed conditions into a soeeid cell. and the
pressures. The instrument is shown in Figure 31. A more sophisticated device for facilitating BET gas adsorption measurements is the Kuminco-Orr Surface Area-Pare Volume Analyzer ($6700) from the same company. It incorporates s seven-valve manifold which interconnects three sample holders, a n evacuation system consisting of a cold trap, oil diffusion pump and mechanical pump, a variable volume space, pre88ure indicators, gas inlets, a timer, a thermistor thermometer, and electrical switching controls. Gas chromatographic instrumentation has been aoolied t o the oroblem of determining cpyntities of ahsorbed nitrogen and other gasw in the Model 212 Sorptometer made by Perkin-Elmer Carp., Korwalk, Connecticut ($1750, without recorder). The schematic diagram is shown in Figure 32. A mixture of helium and
t o averwe particle size. A simpler, less precise instrument that is based upon the same principle is the Precisian-Rlaine Fineness Tester (available from most lab om tor,^ supply houses, shout %100). I t caneists of a manometer, teet cell, and stopcock-rubber aspirator bulb assembly for creating the air flow.
Gas Adsorption lnstrumentation The Numee Instruments and Contnds Corp., Apollo, Pennsylvania, manufactures several instruments for the determination of surface areas and pore vohmes by
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Journal of Chemical Education
."Figure 31. Apporotu..
The
Numec
Adsorption
Flow
Figure 32. Flow rchemolic of !he Model 21 2 Perkin-Elmer-Shell Sorptometer.
(Continxed on page ,4444)
Chemical lnstrumenfation nitrogen is passed through the sample, and the thermal emdurtivity is monitored h,v thermal conductivity detectors placed before and after the sample, as in gas chromatography. When t,he sample is immersed in liquid nitrogen and is adsorbing nitrogen from the gas stream, the recorder pen is driven downscale by the imbalanre in the T / C detector signals. When the adsorption ceases, the recorder pen returns to it,a hase line. Hence, the area of the recorded peak is proportional tu the vohlme of nit,rogen removed hy adsorption from t,he gas stream. Similarly, the volume desorbed as the sample is allowed t o warm up is recorded m a peak of opposite direction on the recorder. If t,hese measurements are repeated for diRerent He/X, ratios of the gas stream, the complete adsorption isotherm ran he ohtnined.
Bibliography A s n ~ n a M ,R. M.; FLOTOII., H. E.; A N D C a R ~ s o x ,K. I)., "Particle Size Determination I," Radioactivation," Anal. Cheni., 29, 105S-60 (1957). ALLEX,J. A.; ANT) HAIGB,C. J., "The Permeability Method for the Measurement of Surface Areas of Fine Powders," J . Chew. E d v ~ .31,354-6 , (1954). BAnsu, E. C., "Pzrticle Size hy Spectral Transmission," Znd. Eng. Chent., 18, 365-9 (1!)46). BLOCKER, H. 6 . ; CRAIG,SUSANL.; A N D ORE,C., JR.,"Dynamic Css Adsorption Methods of Surface Area Determination," J . Chon. Phys., 57, 517-20 (1953). BRCNAVER, S.; A N U EMMETT, P. H., "The Use of Low Temperature van der Waals Adsorption Isot,herms in Determining the Surface Area, of Various Adsorhents," J . Am. Chnn. Soc., 59, 2682-9 (1837). BRUXAUER, S.; EMMETT,P. H.; A N D TELLER,E. "The Adsorption of Gases in Mult,imoleeular Layers," J. Am. Chenl. Soe., 60, 309-19 (1938). C*snm, \I1.iM; A N D DEBYE,P., "Determinatim < l f Molecular Weights and Sizes hy Absorption," Phys. Rev., 75, 1370A(19411). DOTE., W. M., "Messwing the Distrihution of Particle Sise in Dispersed Svstems, Ind. Eng. Chrm., Anal. Ed., 18, 32GX (1946). EADTE,F. S.; A N D PAYNE,R. E., "New Instrument for Analyzing Particle-Size Ilistribution," Iron Age, 174, KO.10, 9!l-102(1954). EwINo, W. W.; A N D I,Iu, F. W. J., "Adsorption oi Dyes from Aqueous Solutions on Pigment,s," J . Colloid Sn'., 8, 204-13 (1953). FAIRS,O. L., "1)evelopment.i in the Technique of Partiele-Size Analysis by Microscopic Examinations," J . Roy. d4icroscop.Soe., 71,209-22(1951). GEROLD,V., "Small-Angle Scattering of X-rays and Its Use in Particle-Size Determination," Z. angrw. Phys., 9, 43-55 (19.57). (Continued on page A4461
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Journal of Chemical Education
Chemical instrumentation GREGG,S. J., "Adsorption and Heat-ofWetting Methods of Measuring Surface Area," Sgmposiunz on Particle Site Analysis, 3'rans. Inst. Chem. Engrs. (London), 25, Suppl., 40-6 (Februsrv 4 1947).
GUMPRECHT, R. 0.; A N D SLIEITEYICII, C. M., "Measurements of Pnrtirle Sizes in Polydispersed Systems by Means of Light Transmission Measurements Combined with Differential Settling," J . Phys. Chem., 57.95-7(1953). HAEKIXS,W. I)., "An Adsorption hlethod for the Determination of the Area of n Solid without the Assumption of a hloleeular Ares and the Area Occupied by N2 Mulecules on the Surface nf Solids," J. Chenz. Phrls., 11, 431-2 (1943).
INNES,W. B., ''App&~&tus and Procedure far Rapid Automatic Adsorption, Surface Area, and Pore Volume Measurement," Anal. C h r m , 23,759-63 (1951). JELL~NEK, M. H.; SOLOMON, E.; A N D FANKUCHEN, I., "Measurement and Analysis of Small-Angle I - R a y Scattering," I n d . Eng. C h e w , . 4 n d Ed., 18, 172-5 (194fi). .TOY. , A. S.. ~, "The Determinat,ion of Soecific Surfare hy Gas Adsorption," I'aeiwm, 3 , 254-78 (1 953). ~
~
JURA,G.; A X O POWELL, R. E., "Kinetics of Gss Adsorption as a Methud of Ares. Determination," J. Chem. Phys., 19, 251-2 (1951).
KERKER,M.; A N D LAMER,V. I
