EFFECT OF SOME FACTORS ON T H E RING METHOD FOR DETERMINING SURFACE TENSION* BY A. H. NIETZ A N D R. H. L A M B E R T
I n connection with work carried out by one of us1 on orientation a t solid surfaces it became necessary to adopt a convenient and rapid method for determining surface tension. Further, work by Sheppard and Lambert? on flocculation and deflocculation of silver halides gave rise directly to an interest in the ring method. Certain phases of the method were therefore investigated, in particular the dependence of the ring method an contact angle, or degree of wetting of the ring by the liquid to be measured. The effect of certain physical factors such as the size of wire, dimensions of the ring, etc., were briefly reviewed. This present paper is, however, in no sense a comprehensive study of the method, the effects of ring size having been given more exact treatment by MacDougallJ3hark in^,^ JohlinJ5and others. A convenient apparatus for the practical use of the ring method has been described by du Noiiy6 and is manufactured by the Central Scientific Company. This is the instrument used by us. The modified technic of Klopsteg' was employed throughout, as this seems without doubt correct. According to this, the liquid is lowered by a fine micrometer screw and the arm holding the ring is always kept at the zero of torsion of the tensiometer wire. Various tensiometer wires were used, and the wires giving the most convenient readings with the highest accuracy were chosen. Such a wire will give relatively high readings, e . g . , from 150' to 1 7 0 ' ~ when the ring leaves the surface of the liquid. Obviously it is not convenient to change wires always to obtain such high readings. Each wire was calibrated in dynes per degree by means of a small pan and weights substituted for the ring. I n most cases in the following, however, the value used is that of the pull on the ring in degrees, designated as P. The equation often applied t o the tensiometer is
where T is surface tension, F is the force in dynes required to pull out the ring ( F = kP),and 1 is the average perimeter of the ring. It has, of course,
* Communication Xo. 379 from the Kodak Research Laboratories, read a t the Regional Meeting of the American Chemical Society, at Syracuse, N. Y., October 19,1928. 'A. H. Nietz: J. Phys. Chem., 32, 2 5 5 , 620 (1928). Colloid Symposium Monograph, 4, 281-301(1926). 8 Science, 62, 291 (1925). ' Science, 64,333 (1926). Science, 64,93 (1926). E J. Gem Physiol., 1, 521 (1919). ' Science, 60,319 (1924).
1461
T H E RING METHOD FOR DETERMINING SURFACE TENSION
,A
'1 14
100
20
,
Q ,
EFFECT O F SIZE (DIAM.)
FIQ.2
0.0092 WIRE BARE
cu.
I462
A. H. NIETZ AND R. H. LAMBERT
been found that this relation is applicable over only a narrow range of wire and ring sizes, and does not include the effect of contact angle which is present. For the metals copper, silver, and platinum, the latter is negligible. The pull, P , in degrees on the dial of the tensiometer, and therefore the force, F , are straight-line functions of the size of wire, D, constituting the ring, for rings of the same diameter. Some of many such curves obtained are shown in Fig. I . The size of wire, D, is given in inches for the diameter, since wire is usually measured in this manner. For wire of the same size, P is also a straight-line function of the diameter of the ring, as shown in the lower curve of Fig. 2 . MacDougall* has pointed out that for any sort of accuracy in absolute values, the ring should be larger than 1.5 cm. in diameter. Fig. z also includes results with disks of varying diameter. Disks, however, present complex problems in themselves, so that they seem to offer little in t h e application to surface tension measurement. Spheres were also tried though not further investigated, and the relation for pull and size is shown in Fig. 3. This is evidently approximately a straight line, while with disks the function is exponential. The factor to which most attention was paid, however, was the effect of conDlAM (MM) tact angle. Our curiosity was aroused 0 2 4 6 8 1 0 I5 LO in this direction by a table (Table I) published by FergusonQin which the ring CHANGE.IN SIZE OF SPHERES method is definitely classed as being inFIG.3 dependent of contact angle. This is approximately true, as stated, when it is used under certain conditions, but it can be shown that the statement is by no means generally true. Xumerous sets of curves like Fig. I were obtained and from these observations, and interpolations made from them, the data summarized in Fig. 4 were assembled. It is evident at once from this set of curves that the higher the wetting power of the liquid (in this case water) for the material of the ring, the more rapid the change in pull, P , with change of wire size, Conversely, when the degree of wetting is low, as in the lower curve (0 = 120') there is practically no change in pull with wire size. If now we confine ourselves to one wire size, something further can be learned about the effect of contact angle. For this purpose a wire size, D of 0.064 in. was chosen. This will give data corresponding t o a cross-section of 8
LOC.
cit.
9Trans. Faraday SOC., 17, 370 (1921).
THE R I S G METHOD FOR DETERMINING SURFACE TENSION
- 0i
m
d -
0,
e
71
I463
A. H. NIETZ A N D R. H. LAMBERT
e
14
P .I^
RELATION OF P,
e AND
RING W I A M .
FIG.4
140120-
p
A
x
m
e
l 80 oot
60-
e FIG.5 Effect of Contact Angle on Pull of the Tensiometer Ring.
THE RING METHOD FOR DETERMINING SURFACE TENSION
1465
the curves in Fig. 4 taken a t D = 0.064. Actual observations made under these conditions are shown in Fig. 5 , where for a given wire size (0.064 in.) the pull P is plotted against the angle 0 independently determined. The ring was dipped into a small quantity of the molten solid, the coating being as thin as possible. The solids used covered a wide range of organic substances
2.2!
Z.Z(
2.15
2,lO
Ilj ,
-0
-0.2
-0.1
LOG (I+Cp4.0)
0
0.1
, 0.2
0.3
DETERMINING FUNCTION FROM CURE
FIG.6
such as hydrocarbons, alcohols, aldehydes, ketones, acids, etc. There are, of course, several sources of error and factors causing discrepancies involved in this procedure. I n the first place there is a variation in the actual ring size, D, resulting from variation in the thickness of the coating. Further, it was shown in a previous paperlo that conditions during crystallization may have a large effect on surface orientation, so no doubt there are variations in the surface from this cause. I n spite of the very erratic and scattered appearance of these observations they show an almost certain correlation on mathematical treatment. A Bravais-Pearson correlation coefficient was calculated for some 7 5 pairs of observations, this coefficient being so high as to indicate lo
J. Phys. Chem., 32, 268 (1928).
1466
A. H. NIETZ AND R. H. LAMBERT
a practically certain relation between pull and contact angle. For all observations this coefficient was 3.73, and when the most erratic results were excluded, 9.78. Having determined that there is a definite relation between P and 6, we next attempted to set up the form of the function. It was assumed that the term ( I cos 0 ) might enter in the expression and accordingly log P was cos 6 ) . This proved a straight line as shown in Fig. plotted against log ( I 6. Substituting F for k P this gives rise to the expression F = 21T(1 cos e)"
+
+
+
O=O.OOO n=-O.tl P=O.OiO n=-O.l25
D=O.OZO n=-0.033
0 -0.030 n=+O.O58
a0 -
P
0=0.040 n=+0.148
6ot ZO 40
\
t
0
\
40
60
80
100
120
0=0.064 n = +o. 3 9 5
\
0 20
0 = 0 . 0 5 0 n=+O.Z37
140
160
I80
EFFECT OF 8 ON PULL OF TENSIOMETER F - 2 A T (I+ COS. FIG.7
where 1 is the perimeter of the ring, and the other symbols have the meanings previously given. The factor 1 enters as P is in dynes and T in dynes per cm. By further treatment of observed data n is found to be related as follows
D n=k--kl 1 and for the case under examination, where D = 0.064 D 13.1 - = 0 . 2 2 7 . 1 That this expression for the relation between F and 6, F = z1T(1+cos Qn, holds only when D is relatively large is evident a t once from Fig. 7, which n
=
T H E RIXG METHOD FOR DETERMINING SURFACE TENSION
1467
represents a family of curves calculated from the equation. When D is somewhat less than 0.030, n becomes negative, and for negative values of n the curves turn upward beyond about 6 = 105'. This is, of course, absurd, as it is inconceivable that the pull should increase with lower wetting power. From Fig. 7 it is also clear that a t some size of wire in the neighborhood of D = 0 . 0 2 0 the pull will be independent of the contact angle. This may be true and may be the reason why it has been thought that P and 8 are not related. Further, a t about the angle of paraffin, 105 to IIO', Fig. 7 shows a point where the pull is approximately independent of the wire size. The latter was not borne out by the experimental data for paraffin (see Fig.1) and would be extremely difficult to prove or disprove experimentally owing to the physical difficulties involved in coating organic substances evenly to a definite thickness and to uncontrolled factors affecting the nature of the solid surface. We did not succeed, in the limited time given to the problem, in developing a relationship which would hold over a wider range. The equation given did fit the data, however, very nicely for the size of wire used, and the curve put through the observations of Fig. 5 is the result of least-square calculations based on the equation. From Fig. I it is evident that since we have straight lines of the type shown, we must also have the relation
F
=
mD
+ b.
Accordingly, if we are right, this should be compatible with F = alT(l+cos8)", where n = 13.1D/l = 0 . 2 2 7 , which was found to be the case.
summary The ring method for surface tension measurement was investigated as to the effect of dimensions of the ring and as to the effect of contact angle. 2. It was definitely proved that there is a relation between the pull on the ring and the angle of contact between the material of the ring and the liquid. 3 . The form of the function showing this relationship was found to be I.
+
F = 2lT ( I cos e)" though this did not hold over the entire range of wire sizes. 4. The classification of the ring method as being free from the effect of contact angle is definitely in error, being probably partly caused by an accidental choice of rings and materials which showed little if any effect. Rochester, A'. Y . , April 1, 1989.
