Particle size and particle size distribution of pigments by small-angle X-ray scattering

JOURNAL

OF COLLOID SCIENCE 12, 581-593 (1957)

PARTICLE SIZE AND PARTICLE SIZE DISTRIBUTION OF PIGMENTS BY SMALL-ANGLE X-RAY SCATTERING 1 William J. Marculaifis E. I. duPont de Nemours & Company, Inc., Newark, New Jersey Received July 17, I957; revised September 12, 1957

In this investigation, a standard commercial X-ray diffraction unit is readily adapted to give small-angle X-ray scattering measurements and the technique is applied to pigment systems. The X-ray scattering curves for the dry pigments correlate with the average particle sizes calculated from specific surface measurements by nitrogen adsorption (BET method) and electron micrographs. INTRODUCTION

Small-angle X-ray scattering is a useful tool for determining certain physical structure properties of materials which contain discontinuities in electronic density. It has been found especially useful for determining the average particle size and the particle size distribution of materials such as proteins, high polymers, catalysts, carbons, and colloidal dispersions. Guinier et al. (1) has recently made a comprehensive review of the subject and included a complete bibliography. This investigation involves the simple adaptation of a standard, commercial, X-ray diffraction unit to give small-angle scattering measurements; the measurement of X-ray scattering for pigment systems; and the interpretation of the scattering curves in terms of an average particle size and particle size distribution. DISCUSSION

OF

THEORY

A measure of the scattering of X-rays at small angles by a colloidal system is, in effect, a measure of the distribution of electronic density. By making certain assumptions, this distribution can be interpreted in terms of a radius of gyration for a monodispersed system or a distribution of radii of gyration for a polydispersed system. The radius of gyration is defined as the root mean square of the distances of all the electrons in the particle to its center of electronic gravity and represents an average particle size. For

1The material in this report was presented at the meeting of the American Chemical Societ.),, Colloid D~vision, in Miami Beach, Florida, on April 8, 1957. 581

582

MARCULAITIS

simplicity, reference will be made in this report to an average particle size (radius) instead of radius of gyration. X-ray scattering measurements are theoretically applicable to a wide range of particle sizes but are limited experimentally to an "effective particle size range." Large particles (larger than 1000 A. radius) limit the scattering to inaccessibly small angles, and very small particles (smaller than R = 50 A.) spread out the scattering to large angles but the intensities are weak and difficult to observe. The scattering equation for Np particles of uniform size is: Io = NpI2C~T(k, R)

[11

where I0 is the intensity of scattered radiation at angle 0, Ne is the number of particles, I~ is the Thomson scattering factor for a single electron, N¢ is the number of electrons in the particle, and f(k, R) is the structure factor. In a monodispersed system, assuming spherical particles

f~(k, R) = ( ( k ~ [sin (kR) -- (kR) cos (kR)l) 2 and using Guinier's approximation (1), _ k~/~ ~

f ( k , R) = e ~ ,

where k

-

2~,0 k

O = scattering angle. = wavelength of incident radiation. Substituting and taking the logarithms of both sides, Eq. [1] reduces to:

In

I0 = Jn K

4v~02R~ 3~,~ '

[2]

where K = constant. In the formulae, the small-angle approximation sin 0 = 0 has been made. From the slope of a "log Ie vs. ~ " plot, the particle size can be cMculated. Experimentally, dilute systems are preferred since Eq. [1] assumes that multiple scattering, refraction, and interference are negligible. For polydispersed systems, various methods (2, 3, 7) have been proposed for interpreting experimental scattering curves in terms of a particle size distribution. In this investigation the position and curvature of the "log I~ versus 0v' plot is used as a qualitative measure of the particle size distribution and the method of Jellinek et al. (3) is used to obtain an average particle size.

DISTRIBUTION OF PIGMENTS BY SMALL-ANGLE X-RAY SCATTERING 58~ EXPERIMENTAL ARRANGEMENT

The geometrical arrangement of the North American Phillips Company X-Ray High Angle Diffractometer, adapted to the measurement of X-ray scattering at small angles, is illustrated in Fig. 1. Source--Copper target tube (A). Excitation Potential--lO kv./7 ma. Monochromatic X-Rays--A nickel filter (B) was employed to monochromatize the copper radiation to CuKa. A crystal monochromator was considered but could not be fit into the general arrangement without making serious and difficult changes. The background radiation was reduced by the use of a low excitation potential (10 kg./7 ma.). Definition of X-Ray Beam--The slit system (D, E, G, H) defined the X-ray beam in such a manner that the cross section, divergence, and parasitic scattering were at a minimum. Slits D, E, G, and H have widths of 0.006, 0.006, 0.004, and 0.019 inch, respectively. Attenuation of the X-Ray Beam--The Geiger counter employed in this investigation could not measure intensities in excess of 1500 counts per second because of counter saturation. Therefore, it was occasionally necessary to attenuate the incident beam by the use of additional nickel filters

(c). Sample--The sample was mounted in an X-ray diffraction sample holder (Standard North American Phillips Company powder holder) and placed normal to the incident beam at position F. The thickness of the sample holder (1.3 ram.) regulated the specimen thickness. In most cases a dry powdered sample was used. Radiation Detector--The radiation was detected by a Geiger-Mueller Counter (I) and automatically recorded by a North American Phillips counting rate computer. SMALL-ANGLE X - R A Y SCATI'ERING FOR LATEX

To test the scattering equipment on a material of known particle size, a Dow Polystyrene Latex suspension containing spherical particles (440

EXPERIMENTAL ABCD

ARRANGEMENT EF

CENTIMETERS

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2

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Fi(~. 1. Schematic diagram showing the geometrical arrangement of North American Phillips Company X-Ray Diffraction Apparatus, adapted to the measurement of X-ray scattering at small angles.

584

MARCULAITIS

A. radius) was subjected to scattering measurements. The result of plotting the logarithm of the intensity with respect to the square of the scattering angle is shown in Fig. 2. The solid line is the plot of the experimental data and the dashed line illustrates the deviation of the experimental data from linearity. The portion of the scattering curve near zero angle (below ~ = 0.001 degrees 2) was obtained by extrapolation. The data were determined at 0.01 degree increments. According to the scattering equation for a monodispersed system, the "log I vs scattering angle squared" plot should result in a straight line the slope of which will determine the particle size. The deviation of the experimental data from linearity is recognized as the invalidity of Guinier's ap-

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F~G. 2. Result of measuring the X-ray scattering for a sample of latex. The scale of ordinates gives the logarithm of the scattered intensity and the scale of abscissas, the square of the scattering angle. The dashed line illustrates the deviation of the experimental data from linearity.

DISTRIBUTION OF PIGMENTS BY SMALL-ANGLE X-RAY SCATTERING 585

proximation at large angles. For a particle of given form and radius of gyration, there is a limiting value of the scattering angle, beyond which Guinier's approximation is no longer valid. If the exact form of the structure factor is used instead of Guinier's approximation, the scattering equation is log 10 =

- c~02R 2 '1- flO 4 -t-

....

constant,

-t-

where a and/~ are constants. For such a form, the slope of the curve would be proportional to the particle size only when 0 = 0. Therefore, the slope at the origin is used in calculating the average particle size. The radius of gyration calculated from the slope of the curve at the origin tO001

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FIG. 3. Results of measuring the X-ray scattering for Copper Phthaloeyanine I (Curve A), Copper Phthalocyanine II (Curve B), and Toluidine Red (Curve C). The scale of ordinates gives the logarithm of the scattered intensity and the scale of abscissas, the square of the scattering angle.

586

MARCULAITIS

in Fig. 2 is 680 A. This can be compared with the reported value of 440 A. The larger value was expected, since no correction was made for parasitic scattering and the latex was dispersed in a liquid medium. Further standardization and practical application tests were made on pigment samples which differed in particle size distributions. Average particle sizes of these samples were shown by electron micrographs and calculated from specific surface data (BET method). SMALL-ANGLE X-RAY SCATTERINGFOR PIGMENTARY SAMPLES OF COPPER PHTHALOCYANINE AND TOLUIDINE RED

Scattering measurements were made on pigmentary Copper Phthalocyanine I (Sample A), Copper Phthalocyanine II (Sample B), and Toluidine Red, Color Index No. 69 (Sample C). The average particle sizes (radii) calculated from specific surface measurements by nitrogen adsorption (BET method) are 230 A., 300 A., and 2500 A. for Samples A, B, and C, respectively. The scattering curves for these samples are shown in Fig. 3. In this and subsequent experiments, the data were determined at 0.01 degree increments, the portion of the scattering curve near zero degrees (below 02 = 0.001 degrees~) was obtained by extrapolation, and the curves were normalized to 1000 counts per second at zero scattering angle. Deviation of the scattering data, obtained at 0.01 degree intervals, from the scattering curves shown in the figures was small (maximum observed deviation was 4 %). It is apparent that Sample A contains a distribution of smaller particles than Sample B, and Sample C contains a distribution of much larger particles than Samples A and B (larger slopes indicate larger particles). In this and subsequent experiments measurements were made on dry samples. It is important to realize that the powder samples contain nonuniform particles which are closely packed. The "closeness of packing" or interparticle interference complicates the data and prevents a complete description of the distribution of particle forms and sizes from the scattering curve. SMALL-ANGLEX-RAY SCATTERINGFOR COPPER PHTHALOCYANINESAMPLES SUBJECTED TO DIFFERENT PERIODS OF GRINDING

The following samples of Copper Phtbalocyanine (CPC) were examined: Sample A--CPC unmilled. Sample B - - C P C salt milled (5) for 4 hours. Sample C - - C P C salt milled for 12 hours. Sample D - - C P C salt milled for 16 hours. Sample E - - C P C salt milled for 20 hours. Sample F - - C P C salt milled for 24 hours. Figure 4 shows the scattering curves for Samples A to F. Curves A to F represent Samples A to F, respectively. From this figure it is evident that

D I S T R I B U T I O N OF P I G M E N T S BY S M A L L - A N G L E X - R A Y S C A T T E R I N G I000

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FI(;. 4. Results of measuring the X-ray scattering for a Copper Phthalocyanine umnilled sample (Curve A ), 4 hour salt milled sample (Curve B), 12 hour salt milled sample (Curve C), 16 hour salt milled sample (Curve D), 20 hour salt milled sample (Curve E), and 24 hour salt milled sample (Curve F). The scale of ordinates gives the logarithm of the scattered intensity and the scale of abscissas gives the square of the scattering angle. the unmilled material (Curve A) has a much larger average particle size t h a n the other samples (a lower scattering curve and larger slopes). Curves B to F indicate a smaller " a v e r a g e " particle size for the samples which were nfilled for longer periods of time. Average particle sizes of Samples A to F were calculated from the scattering curves by the method of Jellinek, Solomon, and Fankuchen (3) and are summarized in Table I. The correlation of the average particle size calculated from the scattering curves to t h a t from specific surface measurements is poor for the unmilled sample and the 4 hour grind. I n these samples large particles are present which cannot be accounted for in the scattering

588

MARCULAITIS

curves. Since the samples were examined in the d r y compact form, the values determined from the scattering curves should be considered only qualitatively. Figure 5 shows the electron micrographs of Samples A, B, C, and D. The TABLE I The Average Particle Size of Copper Phthalocyanine Samples Subjected to Different Periods of Salt Milling (5) Average particle size (radius) Sample

Period of milling

From specific surface measurements (A ng drom,)

A B 1) F

Unmilled 4 hours 16 hours 24 hours

3775 525 315 287

From small-angle X-ray scattering measurements (A rig,from,)

386 213 187 160

FIG. 5. Electron micrographs of Copper Phthaloeyanine samples subjected to different periods of grinding. Picture A is the unmilled sample, Picture B is the 4 hour salt milled sample, Picture C is the 16 hour salt milled sample, and Picture D is the 24 hour salt milled sample.

DISTRIBUTION

OF PIGMENTS BY SMALL-ANGLE X-RAY SCATTERING

5~9

decrease in particle size with increased milling is shown by the micrographs. Most of the crystallites in the unmilled sample (Fig. 5A) have a platelike habit. Since two of the dimensions of the plate (length and width) are outside the range of applicability of X-ray scattering, Curve A in Fig. 4 probably represents the smallest dimension (thickness) of the crystallite and not the average particle size. SMALL-ANGLE X-I~AY SCATTERING FOR COPPER PHTHALOCYANINE ( C P C ) ~AMPLES SUBJECTED TO DIFFERENT I-~/[ETHODS OF PARTICLE SIZE IIEDUCTION

The following samples of Copper Phthalocyanine (CPC) were examined: Sample A--"Commercial" CPC.

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FIG. 6. Resu]ts of measuring the X-ray scattering for a Copper Phthalocyanine "Commercial" sample (Curve A), salt milled sample (Curve B), solvent milled sample (Curve C), acid pasted sample (Curve D), and dry milled sample (Curve E). The scale of ordinates gives the logarithm of the scattered intensity, and the scale of abscissas gives the square of the scattering angle.

590

MARCULAITIS

Sample B--CPC ball milled with salt (5). Sample C--CPC ball milled with solvent (4). Sample D--CPC acid pasted (6). Sample E--CPC ball milled (dry). The scattering curves for these samples are shown in Fig. 6. Curves A, B, C, D, and E correspond to Samples A, B, C, D, and E, respectively. It is apparent from the scattering curves that the average particle sizes of Samples A and B are approximately the same. The extended small slope portion of Curve C indicates a smaller average particle size for Sample C than for A and B. Curves D and E indicate larger average particle sizes for Samples D and E. Average particle sizes of Samples A to E were calculated from the scattering curves by the method of Jellinek et al. (3) and are summarized with the values determined from specific surface measurements in Table II. Electron micrographs of Samples A to E are shown in Fig. 7. The electron micrograph of Sample C (Fig. 7C) indicates the presence of smaller particles than in Sample A (Fig. 7A) and a more uniform distribution than Sample B (Fig. 7B). The ultimate particles of Sample B appear to be smaller than those of Sample C, but larger aggregates are also present in Sample B which account for the larger average particle size calculated from specific surface measurements and X-ray scattering. According to Table II, Sample A has approximately the same size as Sample B by X-ray scattering but a much larger average particle size by specific surface measurements. From the electron micrographs of Samples A and B, smaller ultimate particles and larger aggregates can be seen in Sample B. The larger average particle size calculated for Sample A from specific surface measurements may be due to the presence of the surface coating on agglomerates of Sample A which may have made the particles impenetrable to nitrogen (low surface area). X-ray scattering measured the electronic discontinuities within the loosely bound coated agglomerates. The large aggregates in Samples D and E shown in the electron microTABLE II The Average Particle Size of Copper Phthalocyanine Samples Subjected to Different Methods of Treatment Average particle size (radius) Sample

Method of treatment

From specific surface measurements (A ngstroms )

A B C D E

"Commercial" sample Salt milled Solvent milled Acid pasted Dry milled

590 357 306 5,450 20,400

From small-angle X-ray scattering measurements (A ngstroms)

191 198 144 474 613

DISTRIBUTION OF PIGMENTS BY SMALL-ANGLE X-RAY SCATTERING

591

FI(~. 7. Electron micrographs of Copper Phthalocyanine samples subjected to different methods of particle size reduction. Picture A is the "commercial" sample, Picture B is the salt milled sample, Picttzre C is the solvent milled sample, Picture D, the acid pasted sample, and Picture E, the dr F milled s:~mple.

592

MARCULAITIS

graphs D and E in Fig. 7 are responsible for the large average particle sizes calculated from specific surface measurements and small angle X-ray scattering. However, since the dimensions of some of the aggregates are outside the range of applicability of X-ray scattering, they will contribute to the average particle size calculated from specific surface measurements but not to the scattering curves.

Small-Angle X-Ray Scattering for Inks The following Copper Phthalocyanine (CPC) samples were examined: Sample A--CPC 24 hour salt mill grind dispersed in lithographic varnish (1 : 1 ratio). DO

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ill 0

.01 ,02 .05 .04 .05 ,06 SOATTER|NG ANGLE SQUARED (DEGREES) 2

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FIG. 8. Results of measuring the X-ray scattering for a Copper Phthalocyanine 24 hour grind (Curve A) and crude (Curve B) dispersed in lithographic varnish. The scale of ordinates gives the logarithm of the scattered intensity and the scale of abscissas, the square of the scattering angle.

DISTRIBUTION OF PIGMENTS BY SMALL-ANGLE X-RAY SCATTERING 593

Sample B--CPC umnilled sample dispersed in lithographic varnish (1:1 ratio). The scattering curves of Samples A and B are shown in Fig. 8. Curves A and B correspond to Samples A and B. The scattering curves of the CPC material in the dry form were reported in a previous section. The overall smaller slope of Curve .4 indicates the presence of smaller particles in Sample A as compared to Sample B but the scattering by both ink systems is small. The difference in electron density between pigment and varnish dryer is smaller than that between pigment and air. In general, the scattered intensity depends on the square of the difference of the electron density between the particle and surrounding medium. Therefore, X-ray scattering can be applied to pigment dispersions but necessitates the use of a dispersing medium with an electronic density as different as possible from that of the pigment particle. CONCLUSIONS

1. A standard X-Ray Diffractometer can be adapted to give small angle X-ray scattering measurements. 2. Useful particle size and particle size distribution information can be estimated from the scattering data. ACKNOWLEDGMENTS The author gratefully acknowledges the assistance and helpful suggestions of B. H. Perkins, A. R. Hanke, and C. W. Manger. The author also wishes to express his appreciation to A. Micelli for his assistance in carrying out the experiments. ]:~EFERENCES 1. GUIN1ER, A., FOURNET, G., WALKER, C., AND YUDOWITCH,K. L., "Small-Angle Scattering of X-rays." Wiley, New York, 1955. 2. HOSEMANN,R., Ergeb. exakt. Nalurw. 24, 142 (1951). 3. JELLINEK, ]~. H., SOLOMON, E., ANn FANKUCHEN, I., Ind. Eng. Chem. 18, 172 (1946). 4. LANE, F. W., AND STRATTON, i . J. (to E. J[. duPont de Nemours & Co., Inc.), U. S. Patent 2,556,727 (June 12, 1951). 5. LANG,J. W., ANn I)ETRICK, S. R. (to E. I. duPont de Nemours & Co., Inc.), U. S. Patent 2,402,167 (June 18, 1946). 6. LuBs, H. A., "The Chemistry of Synthetic Dyes and Pigments." Reinhold, New York, 1955. 7. SHULL, C. G., AND ROESS, L. C., J. Appl. Phys. 18,295 (1947).