Marilyn Kay
and D. W. McClure Portland State Univers~ty Portland, Oregon 97207
II
A Simple, Surface and lntertacial Tension Experiment
M o s t physical chemistry laboratory texts include an experiment dealing with the measurement of the surface tension of a pure liquid. Generally, the technique involves either capillary rise or some form of the du Nouy tensiometer. In our experience, a major criticism of both techniques is the relatively large percentage error encountered, especially when the liquid is an organic compound. This error arises from three principle sources: (a) surface active impurities in the liquids studied, (b) a lack of appreciation for clean glassware and, (c) in the case of the capillary rise apparatus, the fact that the vessel containing the liquid and capillary tube is usually of insufficient diameter. This results in a vaguely defined reference meniscus and a significant capillary rise in the containiugvessel itself. This paper describes a simple capillary rise apparatus which is capable of obviating the last criticism and has the added advantage that the interfacial tension for liquid-liquid interfaces can be easily measured.
as a function of the differential rise is eaily obtained from the usual expression for y,
which assumes a zero contact angle, and a meniscus of negligible volume.2 Here g is the gravitational constant, r the radius of the capillary, h the height from the reference meniscus to the capillary tube meniscus and PI and a are the densities of the two fluids (liquid and air or liquid and liquid). Writing eqn. (1) for each tube, solving for h and calculating the difference in meniscus heights, h2 - h,, we obtain the required expression for the double capillary method
hl and h2 are the meniscus heights measured at their lowest points. This expression applies to both types of measurements to be discussed. Meniscus Correction
Theory
Sugden' in 1921 described a double capillary technique involving the use of two capillaries of different bore. The surface tension was expressed as a function of the differential rise so the reference meniscus in the containingvessel did not enter. The expression for the surface or interfacial tension
' SUGDEN, S., J. Chem. Soc.,
119, 1483 (1921).
'MOORE,W. J., "Physicd Chemktry," (3rd ed.), PrenticeHall, Inc., Englewood Cliffs, N. J., 1962, p. 730. ' ADAMSON, A. W., "Physical Chemistry of Surfaces," (2nd ed.). Interscience (division of John Wilev & Sons. Inc.). New
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The volume of the meniscus is usually assumed negligible relative to the capillary tube volume. In tubes of small bore (r < 0.2 mm) this approximation is adequate except for accurate work where, assuming a hemi-spherical meniscus, a correction term r / 3 is added to h. In larger tubes, such as those used in the liquidliquid interfacial experiment to be described, a considerably more complicated correction must be applied. An iterative correction method applicable to a large range of tubes was originally derived by Sugdenl and more recently discussed by A d a m ~ o n . ~Since Sugden's explanation is less than lucid and Adamson's illustration applies to a single capillary tube, we include for convenience an outline of the correction technique for the differential tube method.
For Mallinckrodt nanograde mhexane measured against water, the following data are obtained hs
-I m
=
2.145 cm
=
0.1003 em
=
0.2997 em
g = 980.6
~(hexane)= 0.6599 a t 20°C p(H10) = 0.9982 at 20'C
An expression for y suitable for any size tube may be written, following Sugden's notation
where
Here, Ap = h - PI, H = h2-hl, and bl and bz are the unknown radii of curvature of the menisci in the two tubes measured a t their minima. Note that if bl = rl and b2 = r2 (small tuhes) then eqn. (2) is recovered. First approximatim. Set
Compute a from eqn. (4). We then obtain the ratios rl/a = 0.1764 and ra/a = 0.5270. From the tables in Sugden's paper or Adamson's book, we find rl/bl, and r2/b2. Then b, = 0.1013 and b2 = 0.3272
We may a t this first stage of approximation calculate y from eqns. (3) and (4) using the new values of bl and b2. This gives y = 52.20 ergs/cmZ, Second Approximation. The same cycle is again carried out using the new values of bl and b2,calculating a, then rl/a and r2/a and finally from the tables, new valu& of bl and bz. ~ a l c n lation of y as before shows no change, so additional iterations are unnecessarv. This meniscus correction can often be 3% or neater.
,------,
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py I
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I I
1
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Schemotic of beaker, tenon block, and capillary tuber.
The apparatus described by Sugden to test hisderived equations, while simple, involved a fair amount of glassblowing. In the figure is shown a simple equivalent set-up involving a long form 180-ml Kimax beaker, a Teflon block of 4 cm diameter and 2-3 cm thickness which acts as a capillary tube holder. The tip of a 100-ml pipet fixed with a propipet' bulb is inserted to a point slightly
above the teflon block. Teflon has the advantage of being inert, easily machined and relatively inexpensive. The holes are dril!ed so that the capillary tuhes fit snugly, and are parallel. Three small support feet are machined into the block since the beaker bottom is never flat and to allow the liquid clear access to the capillary tubes. Experimental Procedure Liquid-Air Tensim. The teflon block and all glassware are cleaned in a. hat mixture of sulfuric and nitric acids (not in chromic acid), rinsed well in distilled water, and air dried. The student must be cautioned not to touch the capillary tubes with his hands, but rather use clean tweezers or polyethylene gloves. The apparatus is then assembled, immersed in a constant temperature bath, and the liquid to be measured added. Since the measurements are most accurate when a descending meniscus is used, it is recommended that between subsequent readings, small amounts of the liquid be drawn up into the pipet via the propipet bulh. The level? in the capillaries are then measured with a cathetometer. The bores of the capillaries depend on the liquids used. In our laboratory, s homologous series of n-alkanes from CsH,, to ClsH8, are used with es;pillaries of approximately 0.4 mm and 1.0 mm i.d. These give differential rises of about 1.6-2.0 cm. Precision bore tubing is used and the student is asked to check its i.d. by weighing a mercury thread whose length is determined by either a traveling microscope or the cathetometer. Liquid-Liquid Tension. The interfacial tension between two Liquid interfaces may be determined with minor technique modification. To minimize equilibration times, it is preferred that the two liquids be mutually very insoluble. The experimental procedure involves fist filling the clean thermostated appartrtttus with distilled water to s level slightly above the capillary tuhes. The less dense liquid is then added carefully, filling the rest of the beaker. Water is then slowly withdrawn via,the pipet until there are two clearly defined menisci in the capillaries. It is essential that the level of the alkane be kept above the ends of the crtpillaries. Additional interfaces can he made by simply withdrawing more wster. Liquid-liquid tensions are very sensitive to small amounts of surface active impurities. N-alkanes purchased in tin cans with stated analyses of 997" gave interfacial tensions against water which were low by 30%. One pass through alumina or Silica Gel reduced the experimental discrepancy to within about 2% of the literature value.' This purification step is considered an essentid part of the experiment. An interesting aspect of the measurements on liquid-liquid systems is that, since the differential rise is inversely proportional to the difference in densities between the two liquids, one can hardly classify the tubes often used as "capillary." For example, in the wster n-alkane system, tubes of approximately 2 mm and 6 mm i.d. gave a differential rise of 2-3 cm. The methods described ace capable of giving results easily within 2% or less if precautions are taken to use reasonably pure compounds and a properly cleaned apparatus. The results may be treated in the usual ways as discussed in physical chemistry laboratory texts. If both liquid-air and liquid-liquid tension measurements are made, Antonow's rule' may be tested.
Acknowledgments
The authors would like to thank the Portland State University Research and Publications Committee for a grant to Miss M. Kay for summer undergraduate research. Available from "Instrumentation Associates Inc.," 17 West 60th St., New York, N. Y. AVEYARD, R.,AND HAYDON, D. A., Tram. Faraday Soc., 61, 2255 (1965). Footnote 3, page 121.
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Volume 47, Number 7 , July 1970
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