January 15, 1930
INDUSTRIAL A S D ESGIAVEERISGCHE-1fISTRY
63
Experimental Determination of Brightness-Film Thickness Curves of Wet Paints' D. L. Gamble? and A. H. Pfund3 PHYSICAL LABORATORY, JOEINS HOPKINSUNIVERSITY,
ads of determining hiding power have been developed based on either the experidetermination Of the thickness curve Or the use Of Some e m piri c a l or theoretical e q u a t i o n supposedly ex-
BALTIXORE, RID
wedge of paint of increasing thickness and two outer air 17-edgesof corresponding dimensions. The dimensions of the wedge and the design of the plates and clamps were chosen to give minimum distortion of the glass, The lower surface of the pressing the b r i g h t n e s s ' top plate and the upper surthickness relationship. face of the base plate were The purpose Of the work t o be described in this silvered lightly over the paper was primarily to deO u t e r areas f"rming the air Data obtained by this method check quite closely wedges A , C, B , D and an accurate method values obtained with the Pfund cryptometer. for the experimental deterE , G, H , F . This coating mination of brightness-film was made just thick enough thickness curves; and, havto give the desired reflecting obtained reliable curves, to investigate the accuracy with ing power without reducing the transmission too greatly. which existing mathematical equations might be employed The lower face of the base plate was painted with a heavy in representing the brightness-film thickness relationship. coat of black asphalt paint over the central area C, E , F , The chief weakness in existing procedures for the deter- D, so as to afford a black background for the wedge of paint. mination of curves of this type lies in the film-thickness The box A , Figure 2 , has a cover which may be moved in a measurements. The micrometer gage has been employed plane perpendicular t o that of the paper and in a direction for this purpose, and as a result the accuracy of the film- parallel to the paper. The box is stationary. The central thickness measurements is far below that of the brightness portion of the cover consists of a strip of plate glass the determinations. It w-as therefore decided to use an optical width of the wedge described above and extending the length method in determining film-thickness values. The scheme of the box normal to the plane of the paper. The wedge employed necessitates working with the wet paint, but as is placed on this strip of glass and can be moved back and the writers were interested primarily in evaluating pigments forth in a direction normal to the paper. B is an incanthis JTas not a handicap. The brightness-film thickness descent lamp fixed within the box and having a circular curve will shift somewhat in passing from the wet to the dry filament which appears as a straight line when viewed verstate, but there is no reason for not expecting the curve to tically. By means of a short-focus lens, C, a narrow image retain its general form. of the lamp filament, not exceeding 0.5 mm. in width, is focused a t the interface of that portion of the two plates Film-Thickness Measurements forming one of the air wedges. This image is in turn focused It was decided to employ the channeled-spectrum phe- on the slit, F , of a spectrometer by means of a total reflecting nomenon in determining film-thickness values. To ac- prism, D, and a short-focus lens, E. The multiple reflections complish this a glass m-edge, as shown in Figure 1, was de- between the silvered surfaces of the air wedge give rise to signed. The wedge is similar to the Pfund cryptometer. a channeled spectrum. A small helium discharge tube, G, It consists of two plate-glass plates made of 1/4-inch (6-mm.) is placed diagonally in front of the spectrometer slit. In plate glass, 3 by 20 cm. At one end of the base plate are two the spectrometer is observed a field, the lower portion of metal spacers, L and M, so arranged that when the top plate which is filled with the interference fringes of the channeled spectrum, the upper half being filled with the helium reference * Received September 16, 1929. Presented before the Division of lines. The distance between fringes increases with the wave Paint and Varnish Chemistry a t the 78th Meeting of the American Chemical length. By using a flint-glass prism in the spectrometer and Society, Minneapolis, Minn , September 9 t o 13, 1929. making the observations in the red portion of the spectrum, 1 Investigator, Research Division, New Jersey Zinc C o Palmerton, Pa. a Professor of physics, Johns Hopkins Unir ersity. sufficient dispersion is obtained t o permit the counting of u
This paper discusses a method of extreme accuracy for the experimental determination of the brightnessfilm thickness relation, using a Macbeth photometer for measuring the brightness and the channeled spectrum phenomenon in determining film-thickness values. With the data obtained in this manner, an investigation is made of existing mathematical relations used to express the brightness-film thickness relationship. Results show that these equations have definite limitations which make their general assumption decidedly unsafe.
, ~
AKALYTICAL EDITIOlY
64
the number of fringe! lying between the helium lines 5876 and 6678 A. Knowing the number of interference fringes between any two known wave lengths, we may the thickness of the wedge a t the point observed following equation: t =
2p
reference occurring calculate from the
NXiX? cos r (A2 - A,)
where, t = thickness N = number of fringes between wave lengths XI and Xa M = index of refraction of air = 1 r = 0 (approx.) = angle between incident light ray and the normal to upper wedge plate cos I = 1 X i = 5876 A. A2 = 6678 A.
Vol. 2, No. 1
for photometering by sliding back the cover of box A , upon which the wedge rests. While the wedge is still in position for observing the channeled spectrum, a small straight edge is placed across the surface of the top plate of the wedge so that it coincides with the image of the lamp filament giving rise to the spectrum. The wedge is then brought into position for the brightness determination. By shifting the wedge slightly the image of the straight edge is made to coincide with the line of demarcation of the photometer field. The straight edge is then remored and the photometer field adjusted until the line of demarcation just disappears, no attempt being made to match the whole field. In this way we essentially photometer only that narrow strip of the wedge coinciding with the narrow region over which the corresponding thickness measurement is made. All photometer readings were taken-with a green-glass filter transmitting in the region of 5400 A.
.9
5
C
D
d
F
Manipulation
6
H
A wedge of the v e t paint is formed between the glass plates as described above. Measurements are made a t intervals along the wedge until there is no detectable difference in brightness between the wedge film and the infinitely thick layer. Sufficient points are taken to permit accurate plotting of the brightness-film thickness curve. I n order t o investigate the possibility of settling of the pigment, which might affect the results, a paste was placed in the wedge and the brightness-film thickness curve determined. This wedge was then allowed to stand considerably longer than the time required to determine the complete curve. Measurements were again made and the t n o curves thus obtained were found to check very well.
U Figure 1-Glass
Wedge for D e t e r m i n i n g F i l m - T h i c k n e s s Values
Observations are made on corresponding positions of the two air wedges and the average of these two measurements is taken as the thickness of the paint wedge a t that point. Distortion of the wedge was so slight that the measurements on the two air wedges never disagreed more than half a fringe. With the reference lines used, each fringe observed represents an increment of thickness equal to 0.00245 nim. regardless of the magnitude of the thickness measured. The smallest thickness measured was 0.0073 mm. Corresponding to 3 fringes. I n this region one can easily estimate t o fringe, corresponding to an increment of thickness of 0.00061 mm. I n this case the limit of accuracy would be 92 per cent. At a thickness of 0.24 mm. corresponding to 98 fringes and representing an average value for the “hidingthicknesses” of the three pigments measured, the per cent accuracy is 99, assuming that the fringes are too narrow to permit the estimation of a fraction of a fringe. The ordinary micrometer thickness gage can be read only to 0.01 mm. and estimated to about 0.0025 mm. In the case of the thickness gage used with the dry film, the accuracy of the measurements discussed above would be 70 and 99 per cent, respectively. These values do not take into consideration inaccuracies due to irregularities of surface and depression of a m , which are the major sources of error, in the case of the thickness gage. Brightness Measurements
A photometer of the hfacbeth type was employed in making brightness measurements. A new photometer head recently designed by Pfund ( 2 ) was used in this instrument. It is of such design as to permit sharp and complete disappearance of the line of demarcation in the photometer field. The wedge surface is illuminated normally and the photometer placed a t an angle, as illustrated in Figure 2 , to exclude specular reflected light from the surfaces of the glass plates. The instrument was calibrated t o give relative brightness values. After the thickness of the wedge has been determined a t a certain point, the wedge may be brought into position
Figure 2-Apparatus for Brightness-Film Thickness M e a s u r e m e n t s
The data presented in this paper are confined t o mixtures of pigments in straight oil vehicles, where equal proportions of pigment and oil were used. These pastes were prepared by thorough rubbing under a spatula. ResuIts and Discussion
Figure 3 s h o w the brightness-film thickness curves obtained for three white pigments-zinc oxide, lithopone, and zinc sulfide. These curves were determined from pastes, the vehicle of which consisted of 50 per cent medium kettlebodied oil (viscosity, 4 poises) and 50 per cent alkaline refined linseed oil. This particular vehicle was chosen merely to make this investigation conform with other experiments being carried out in the laboratory. Figure 4 shows similar curves for basic carbonate of white lead and a small-particlesize zinc oxide-rubber pigment. These curves viere determined from pastes using pure linseed oil as the vehicle. I n all cases two separate curves were obtained for each pigment and were found t o check almost exactly. The experimental readings are given in Table I. It will be observed that the brightness-film thickness curve is of a type which asymptotically approaches a limiting
ISDCSTRIAL A S D ESGi‘SEERIiYG CHEMISTRY
January 15, 1930
brightness This limiting value is the brightness of a layer of the pigment infinitely thick. Two per cent is generally accepted as the smallest change in brightness that the eye can detect a t moderate intensities. Basing our definition on this fact, we say that complete obscuring of the underlying surface has been obtained when the brightness of the overlying paint surface is within 2 per cent of the brightness of
I
1
I 02
a/
0
theoretical equation for the brightness-thickness relationship of paint films. Bruce found this equation to agree very well with experimental curves obtained by a method described by him ( I ) . This equation is extremely complicated and is of such a form that, even though it might be a true formula for the brightness-thickness relationship, it is of little practical value.
ii
1
iF,/m Thickness In fiflirncfers
1
w
d4
a3
65
Figure 3
Figure 4
an infinitely thick layer of the paint. This point of complete hiding, which is of extreme interest, lies on that portion of the curve where relatively large changes in film thickness are accompanied by extremely small changes in brightness. For this reason it is apparent that considerable accuracy is required in determining the brightness-film thickness curve.
In the same paper Bruce developed, from experimental data, an empirical equation which he found t o agree with the theoretical one quite closely except within the region of very low brightnesses. This equation has the form:
S O . OF
IWTERFEREWCE FRINGES BETWEEN AND
5875 6678
A.
Table I-Experimental D a t a RELATIVE N O . OF BRIGHTNESSINTERFERENCE B.4SED ON
FILM INFINITELY THICK- THICK NESS LAYERAS 1 Mm.
FRINGES
BETWEEN AND
5875 6678 A.
7
6.5 12.5 15 19.5 24.5 29 43.5 59.25 77.5 9s 125
0.00732 0.0109 0.0171 0.0232 0.0305 0.0366 0.0476 0.06 0.0708 0.106 0.144 0.19 0.24 0.305 0.00976 0.0146 0.0171 0,0293 0.0453 0.0537 0.0707 0.1085 0.13 0.172 0.241 0.279
BASEDON
FILM INFINITELY THICK- THICK NESS LAYERAS 1
ZINC SULFIDE
0.284 0.352 0.539 0.659 0.727 0.75 0.802 0.835 0.852 0.90 0.948 0.966 0.974 0.981
LITHOPONE
4 6 7 12 18.25 22 29 44.5 53.25 70.5 98.5 114
BRIGHTWESS
Mm.
ZINC OXIDE
3 4.5
RELATIVE
0.408 0.582 0,627 0.795 0.895 0.912 0.93 0.945 0.95 0.964 0.983 0.993
3 4 5.5 9 12 16 1s 23 32.75 52 66 85.5
0,00732 0.00976 0.0134 0,022 0.0293 0.0391 0.044 0.0562 0.0805 0.126 0.162 0.209
where C = a constant depending upon the material X = film thickness Y = contrast ratio
0.443 0.568 0.67 0.813 0,874 0.903 0.943 0.965 0.967 0.973 0.982 0.993
“Contrast ratio” is defined as the ratio of the brightness of the paint film over a black background t o the brightness of the film over a white surface of a definite brightness. The relative brightness values presented in this paper consist of the ratio of the brightness of the paint film over a black surface t o the brightness of an infinitely thick layer of the paint. We therefore have a special condition of the [‘contrast ratio”-that is, one in which the brightness of the underlying white surface is just equal to the brightness of an infinitely thick layer of the paint. For this reason our data should be directly applicable to the above empirical equation.
BASIC CARBOXATE OF WHITE LEAD
5 8 13
1s
23.25 34 52
0.0122 0.0195 0.0317 0.044 0.0568 0.0832 0.127
0.307 0.462 0.60 0.713 0.784 0.87 0.933
SMALL-PARTICLE-SIZE ZINC OXIDERUBBER PIGMENT
6 8 10 14 18.5 23 37.25 62 95
0.0146 0.0195 0.0244 0.0342 0.0443 0.0562 0.091 0.152 0.231
0.415 0.503 0.555 0.673 0.743 0.788 0.83 0.87 0.90
Although several mathematical equations have been derived supposedly expressing the brightness-film thickness relationship, the most promising are the equations of Bruce (1). By considering a paint film to be made up of a series of finite layers and applying the mathematics worked out by Sir George Stokes expressing the intensity of light reflected and transmitted by a pile of glass plates, Bruce developed a
Table 11-Experimental
a n d C a l c u l a t e d H i d i n g - T h i c k n e s s Values for Three P i g m e n t s DIFFERENCE CAICD. BETWEEN FROM
PIGMENT Zinc oxide Lithopone Zinc sulfide
CRYPTOMETER
Mm. 0.31 0.27 0.178
EXPTL. Mm. 0.305 0.24 0.162
EXFIRICAL
EXPTL.
AWD
CALCD.
EQUATIOW VALUES Mm. 0.232 0.20 0.074
Per cenl 24 17 54
Table I1 gives the hiding thickness for the three pigments zinc oxide, lithopone, and zinc sulfide as determined from the experimental curves and as calculated from the above empirical equation. One set of experimental data is needed to evaluate the constant, C. These data were taken a t the point where the brightness of the film was 95 per cent of the brightness of the infinitely thick layer, a region over which Bruce found the empirical equation to agree very closely with the theoretical one. [‘Hiding thickness” is defined as the thickness of paint film required t o give a brightness just equal t o 98 per cent of the brightness of the infinitely thick
66
A iVAL Y TICBL E DI TI0,V
layer. It will be observed that the experimental and calculated values differ by as much as 54 per cent. Table I1 also includes hiding-thickness values as determined with the Pfund cryptometer. With the exception of the zinc oxide paste, which checks very closely, there exists about a 10 per cent difference between the value obtained from the experimental curve and that given by the crgptometer. This difference is in a direction which would indicate that in the case of the cryptometer the end point is realized a t a point where the wedge film is somewhat more than 98 per cent as bright as the infinitely thick layer. It is not impossible that, under the conditions existing in the cryptometer, the eye is capable of detecting smaller differences in brightness than the generally accepted 2 per cent limit. Brightness-film thickness curves were determined for basic carbonate of white lead and a small-particle-size zinc oxide-rubber pigment (Figure 4). These two pigments are of greatly different particle size and shape and therefore should differ considerably in light-reflecting and -scattering properties. The crossing of these two curves makes apparent the possibility of error that xould arise in assuming the empirical equation in this case. While this may be a rather severe test of the rigidity of the equation, it a t least indicates that the empirical formula has definite limitations. These curves mere not carried to complete hiding thickness because
VOl. 2, s o . 1
of the limitations imposed by the thickness of the spacers used in the wedge a t the time. Conclusions
By employing the channeled-spectrum phenomenon in making thickness measurements, the writers believe they have developed an extremely accurate method for the determination of brightness-film thickness curves. Although only applicable t o wet paints, the method should be of value in investigating the brightness and hiding power characteristics of pigments and in making comparative studies of paints. Although the theoretical and empirical equations discussed seem to express, in a general manner, the brightnessthickness relationship of paint films, the data presented indicate definite limitations. It would not seem safe to employ such equations without a more complete knowledge of these limitations. It is hardly to be expected that a theoretical or empirical formula, developed in the manner these equations have been, should express faithfully the complicated optical system presented by a suspension of pigment in oil. Literature Cited (1) Bruce, Bur. Standards, Tech. Papev 306. (2) Pfund, J . Optccal S O L A . m . , 20 (March, 1929).
Measurement of the Leveling Properties of Paints and Enamels' George S. Haslam and Lester D. Grady, Jr. THE NEW JERSEY
ZINC
COMPANY, PALXERTOX, PA.
This paper shows that the leveling properties of a and simple method for the ONSIDERABLE diffipaint are not entirely expressed by consistency measdetermination of the leveling culty is experienced in properties for plant control. urements. The du Nouy tensiometer is suggested as g r a d i n g t h e leveling an instrument for measuring leveling properties. A Leveling is dependent on qualities of paints and enamcomparison of tensiometer results with results of five that property of a paint that els from a measurement of consistency measuring apparatus shows the value of permits flow after application their consistency characterthe tensiometer in measuring the leveling characterand results in the eradication istics. While it is true that of brush marks and other istics of paints. in general a paint of high irregularities of the surface. Leveling is dependent on forces of flocculation and yield value and low mobility forces of surface tension. The effect of these forces, It is a function of both the has poor leveling, and one flocculation of the pigment which are apparent only at low shearing stresses, of low yield value and and the surface forces of the appears to be measured by the du Nouy tensiometer. h i g h m o b i l i t y h a s good paint which govern flow after leveling, this is not always the cage. I n other words,' it is conceivable that an enamel the high shearing forces of -application have been reof heavy consistency may have better leveling properties moved. This force which produces leveling is not apparthan one of thinner consistency, so that consistency measure- ent during consistency measurements, and its effect is ments would lead to erroneous conclusions if used t o predict masked in these determinations. Since the force which causes leveling is essentially a surleveling qualities. The apparatus developed by Bonney (1) for the measure- face force, the du Xouy tensiometer was used in its measurement of this property gives a good indication of the leveling ment. The results give a numerical value to the leveling properties, provided the consistencies of the paint are the property which follows very closely the grading by a paintsame or nearly so. Large differences in the plastic proper- out test. ties, however, so seriously affect the results as t o render them Experimental Procedure invaluable. The technic developed for the operation of the du Xouy The work of Williamson ( 5 ) requires a very accurate determination of the plastic flow curve and should give a true tensiometer (4) was essentially the same as that used in the evaluation of the leveling properties. However, the present determination of surface tension. The circular rider was paper is an effort to give the average paint producer a rapid brought in contact with the paint surface and completely wet by the paint. The torsional force on the wire was inPresented before t h e Division of Paint 1 Received September 9, 1929. creased slowly a t a constant rate until the ring broke away a n d Varnish Chemistry at the 78th Meeting of t h e American Chemical from the surface, and the angle of rotation necessary to reSociety, Minneapolis, Mino., September 9 to 13, 1929.
C
