SURFACE ROUGHSESS A S D CONTACT -4SGI.E
653
SURF.1CE ROUGHKESS ASD COSTACT AXGT,E J . J. BIKERMAS
Research Laboralories, .llerck and C u m p a n u , Ine., RahwaU, .\-eu: JersPu Received Augirsl 5 , 1949 I. IXTRODUCTION
I t has been reported (1) that contact angles on rough solids are greater than on relatively smooth surfaces and that hyst,eresis of wetting increases with the degree of roughness. However, in almost all publications known to the aut’hor, surface roughness was characterized in qualitative terms only (such as “highly polished,” “ground,” etc.). Parker and Smoluchowski (4) mentioned a quantitative parameter of roughness of their iron plates but’ gave no numerical value for the netting observed. In the present work, contact angles have been measured using solid surfaces the profile of which was determined with a tracer instrument. The system investigated comprised drops of distilled water in air on 18-8 stainless steel plates of different finishes. The chemical composition of all plates and, presumably, of their surfaces is stated to be identical. 11. EXPERIYEh-TAL PROCEDURE
There are six standard sheet finishes of 18-8 stainless steel on the market. Their preparation is described in the booklet entitled “Fabrication of C.S.S. Stainless and Heat-Resisting Steels” (1947) and distributed by the United States Steel Corporation. A summary of this description is given below, together with the “root-mean-square elevations” (h,,,,) of the finishes, determined by means of a tracer instrument.’ The root-mean-square elevations were obtained as follows: A diamond needle, the tip of which has the radius of 13 X cm., was moved along the surface to he explored. In this movement it fell h, em. int’o a depression, rose hp cm. t o reach the summit of the next hill, fell hB cm. into the nextvalley, etc. Theh,,,, definedas+(h: hi hi . . ~)1’2,wascomputedbyan electrical apparatus. A record of the act,ual movement of the needle, i.e., the profile of the surface, on finish S o . 1 has been published ( 3 ) . These profiles and the values of hFmsgiven in table 1 refer to the set of plates (7 x 5 x 0.08 cm.) designated in the following as set I ; it was supplied with a copy of the above hooklet. Set I1 comprised plates (same dimensions) taken from another copy of the booklet. The description of their preparation given in table 1 is valid for both set I and set 11, but the h,,, was not determined for the latter. The plates were washed with soap and hot water, rinsed with distilled water, rubbed with cotton soaked with acetone, rinsed with acetone, rubbed with cotton soaked in carbon tetrachloride, rinsed with carbon tetrachloride, and allowed to dry in air protected from dust.
+ + +
These determinations have been carried out in the laboratories of the Norton Company, Worcester 6, Massachusetts, through the courtesy of Dr. S . S.Kistler. Two lines on each sample were scanned, whence two values of h,,, for each finish.
654
J. J. BIKERMAN
The contact angles formed by water drops on the plates "cleaned" in this manner were determined by a modification of the previous method (2). Drops of the volume v were deposited on the plates and the mean diameters (A) of their bases were at once (before a noticeable evaporation took place) measured in a microscope at a magnification of about 20. The ratio As/v was extrapolated to u = 0, and the contact angle 0 (through water) was calculated from this extrapolated value (A,"/'v) by means of the equation: A 24 sin3 0 -i v ~ ( 2 - 3COS e C O S ~e)
+
A numerical table for the right-hand term of this equation can be found in reference 2. TABLE 1 Values of h,,, for plates of set I FINISH
PREPARAIION
hrrm
~
cm.
..
H o t rolled, annealed, and pickled
3.1 3.1
x x
10-4 10-4
Finish No. 2 D . . , . . , . , , . . . .
Cold rolled, annealed, and pickled
0.8 1.0
x x
10-4 10-4
Finish No. 2 B . , . . . , . . . . . . .
Produced by final light cold rolling
0.25
x x
10-4 10-4
Finish No. 1 ,
,
. . , ... . . . . .
0.40
Finish No. 4 .
,
. . , . . ......
Polished with S o . 120 grit and a lubricant
0.033 X 0.045 X lo-'
Finish No. 6 .
,
. . . . . .. ....
Produced by brushing a KO.4 surface with a rotating brush of tampico fibre loaded with fine abrasive and oil
0.084 X lo-' 0.10 x 10-4
Finish No. 7 .
. . . . . . .. . . .
Polished with S o . 320 grit and a viscous lubricant
0.020
I
x 10-4 0.030 X lo-'
The droplets were deposited either from a microburet (the tip of which was waxed), the volumes being 0.008, 0.004, and 0.002 ml., or from a micrometer syringe, the volumes being 0.008, 0.004, 0.002, and 0.001 ml. In each series eight droplets of each size were measured. Because the spread of the A3/v values rendered extrapolation based on an individual series of droplets inexact, a formula was derived which approximately represented the average dependence of As/u on u for all the observations in this work. It is u
=
4u (1 + 2 8 . 3 ~- 1670~')
u being expressed in milliliters. It follows from this equation that the values of A8/v
found for droplets of 0.008, 0.004,0.002, and 0.001 ml. must be divided by 1.120,
655
SURFACE ROUGHNESS A S D CONTACT .4NGLE
1.087, 1.050, and 1.027, respectively, to obtain AG/v. In this manner, every series of droplets yielded three or four values of A;/,. The mean of these \-alues was used to calculate 0. The precision of these values of 0 is limited chiefly by (a) the deviation of the base of the drops from a perfect circle (see reference 2 and Section IV, below) and ( b ) the poor reproducibility of solid surfaces. In spite of the standardized pretreatment of all plates, the same plate in a duplicate experiment and even the right and the left halves of a plate in one experiment yielded &values differing by 5" or more. The errors due to (a) and ( b ) are believed to be much greater than the error which may be due t o using the empirical equation 2 . TABLE 2 Contact angles (through water) belween air, water drops, and steel plates of iarzoiis degrees of roughness FI\?SE
I 1
Drops from microburet.
/
Z
....
Drops from syringe.. . . . . . . . .
Mean . . . . . . . . . . . . . . . . . . ..~
hO
____________ 1
89"
I
D
1
2
B
1
82O-I76"
93' Si"
65" 57 '
84"
93"
58"
81"
91'
I
60"
6
1
____ 4
70"
i:l 70'
1
1 ~
I
I
7
___ 91" 87
890 89"
Drops from microburet
111. RESULTS
The values obtained for the contact angles e are collected in table 2 . Comparison of the different columns of table 2 shows that surface roughness has no definite effect on 0. The contact angles on finish N o . 1 and finish KO. 7 are identical or nearly identical, although hzmsof the former is more than 100 times that of the latter (in set I). Comparison of the upper and lower parts of table 2 demonstrates that two specimens of supposedly identical finishes may differ more than tlyo specimens of quite different roughness; thus, the difference between the e of t x o specimens of finish 2B was 15'. The two lines marked "microburet" exemplify the reproducibility of contact angles on the same plate subjected to, as far as possible, identical treatment. The greatest difference observed here is 8", Le., again greater than that between the coarsest and the finest finish.
656
J. J. BIKERMAS
There is nosystematic differencebetween droplets from a microburet and those from a micrometer syringe, showing that slight changes in the procedure of deposition have no noticeable effect on wetting. This was confirmed also by special experiments: drops from the microburet mere either first formed at the waxed tip and then transferred onto the plate, or formed on the plate, which was almost in contact with the tip of the microburet, at different rates of flow; no definite effect on 8 mas recognizable. IV. WETTING O F ANISOTROPIC SURFACES
Of the six commercial finishes, S o . 4 is the most anisotropic. Its surface is covered with parallel grooves clearly visible at a magnification as small as 20. The h,,, values given for it above were obtained by moving the diamond needle along the grooves. Water droplets on No. 4 surfaces are elongated in the direction of the grooves. The ratio of the major axis a to the minor axis b of the bases of these droplets usually ITas between 1.15 and 1.20, although also ratios above 1.50 occurred. The roughly elliptical shape of the base undoubtedly causes an error in the above calculation of 8, in which the base is assumed to be circular and A is taken as +(a b ) . Elongated droplets can be formed also on a reasonably isotropic surface, such as 2D or 2B, e.g., by depositing two droplets almost in contact with each other and then causing their coalescence by adding a third droplet. Comparison of these droplets with circular drops on the same surface shows that A of the latter is always less than +(a b ) of the former. Sometimes A is almost equal to b ; in other instances, A = If the last-mentioned equation is assumed, the A : / v values for No. 4 are reduced by about 10 per cent and the &values of table 2 are increased by 3-4'. The uncorrected values are given in table 2 because the correction has no theoretical foundation. Unfortunately, exact calculation of the shape of elongated drops would be extremely tedious. The drops on No. 4 finish (and sometimes also on No. 6 and No. 7 ) had also another peculiarity: the longer sides of their bases were straight along a good part of the contour (see figure 1, in which the direction of the grooves is indicated by an arrow). Apparently, movement of the drop (expansion or contraction) was checked by a microscopic ridge and stopped along its slope.
+
+
V. WETTLVG AND ROUGHNESS
Roughness may be expected to affect wetting differently according to whether (a) the surface is grooved or ridged, ( b ) the drops expand or contract, and (c) the equilibrium contact angle is acute, right, or obtuse. The difference between grooved and ridged surfaces, as these terms are meant here, is that in the former the depressions are connected with each other and enclose elevated islands, while in the latter the ridges enclose disconnected depressions. If the hysteresis of wetting is small, the behavior of a drop on a grooved surface would be determined by the equilibrium contact angle. If this angle is acute, the liquid would spread along the grooves and the observable 8 would be small; an obtuse contact angle would be made even more obtuse, and a right
SURFACE ROUGHSESS AKD COSTACT AKGLE
657
angle would not be affected. On a ridged surface, hysteresis of wetting would determine the behavior. Both spreading and contraction of a drop would be obstructed as long as the equilibrium contact angle is not too small (at 0 = 0 liquid would spread over surfaces of any kind and degree of roughness), i.e., for obtuse, right, and large acute angles. Apparently, there is no experimental proof for this obstruction on the microscopic scale but figure 2 makes its existence highly probable, The main assumption on which figure 2 is based is that the true contact angle, i.e., that between air, liquid, and the actual solid surface (as distinct from its main plane), remains constant during spreading or con-
FIG.
1
FIG.2
FIG.1. Approsinistc shape of drops on the anisotropic surface S o . 4 . The arrow indicates the direction of the grooves. FIG.2. Movement of drop front over a ridge. T h e real contact angle is constant and, in the drawing, is 90”. The position in the bottom of a valley is stable in this instance. Movement either t o the right (contraction) or t o the left (spreading) results in contortion of the drop, which increases the surface energy of the system and may also lift its center of gravity.
traction of a drop. If this assumption is granted, figure 2 s h o w that climbing of the drop front over ridges would involve contortion of the liquid-air interface and, consequently, an increase in the surface energy of the system, which contortion may be associated with lifting of the center of gravity of the drop, Le., an increase also in the gravitational energy. If the drop does not possess this additional energy, its movement mould cease at, a ridge. On a surface which is neither purely “grooved” nor purely “ridged” but a mixture of both, the behavior of a drop is difficult to predict in general terms. It is clear, holyever, that the enhancement of spreading by depressions may be offset by its obstruction due to elevations, thus making the extent of spreading independent of roughness. Although this discussion is of necessity qualitative only, it may be used to account for some of the observations made in this work. The mutual cancella-
658
M. 7%'. GRIEB AKD W. H. CONE
tion of the effects produced by grooves and ridges can be made responsible for 0 being independent of roughness, as shown by finishes No. 1 and No. 7 in table 2. The relatively good wettability of No. 6 finish would indicate its nature as a "grooved" surface. Because the effect of roughness in this work was generally small, accidental impurities often determined the 0 observed (see the last paragraph in the section on experimental procedure). The ratio a : b of droplets deposited with a microsyringe on No. 4 finish was 1.09-1.24 (mean, 1.17) for set I and 1.14-1.25 (mean, 1.19) for set 11, while e was 70" for set I and 89" for set 11.As the ratio a : b was independent of contact angle, ridges, in this instance at least, appear to have greater importance than grooves whose effects for 0 = 70" would be much greater than for 0 = 89". As mentioned in the section on wetting of anisotropic surfaces, the peculiar s m o f drops on KO.4 also seems to be due to ridges. The aut,hor thanks Dr. P. K. Frolich, Vice President for Research and Development, for permission to carry out the work here reported in the laboratories of Merck and Company, Inc., and Dr. S. S. Kistler, Sorton Company, for the roughness data on the samples used. REFERENCES (1) BIKERMAN, J. J.: Surface Chemistry for Industrial Research, p. 332. Academic Press, New York (1918). (2) BIKERMAN, J. J . : Ind. Eng. Chem., Anal. E d . 13, 443 (1941). (3) BIKERMAN, J. J.: J. Applied Phgs. 20, 971 (1949). (4) P A R K E RE, . R . , ASD SMOLTCHOWSKI, R . : Trans. Am. SOC. Xletals 36, 362 (1945).
A DETERMIXATION O F T H E SOLUBILITY OF POTASSIUM ZINC FERROCYANDE hl. W. GRIEB
AND
W. H. CONE
Department of Chemistry, Cniverszty of Idaho, Jioscow, Idaho Received August 6,1943
The use of diphenylbenzidine as an indicator for the titration of zinc with potassium ferrocyanide (1) depends on the ratio of the solubility of zinc ferricyanide to that of potassium zinc ferrocyanide. Because the only available reference ( 5 ) to the solubility of the latter compound was somewhat ambiguous and not in accordance with observations, a determination of its solubility was undertaken. The method employed was a measurement of the oxidation potential of a solution saturated with both zinc ferricyanide and potassium zinc ferrocyanide, which potential is dependent upon the activities of the ferricyanide and ferro-
