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Contact angle in thin liquid film
177
LETTERS TO THE EDITORS f o r m u l a derived b y these authors, which does n o t c o n t a i n Kn, correct. A t finite K n values t h e i o n v e l o c i t y d i s t r i b u t i o n i n t h e v i c i n i t y of t h e particles becomes n o n Maxwellian, a n d t h e f o r m u l a is erroneous. As concerns t h e good a g r e e m e n t b e t w e e n this f o r m u l a a n d t h e e x p e r i m e n t a l results of L i u a n d co-workers at K n values f r o m 1.0 to 1/66, it should be t a k e n i n t o consideration t h a t this a g r e e m e n t was o b t a i n e d o n l y b y a s s u m i n g t h e molecular weight of ions to be 460. Moreover, i n d e r i v i n g this f o r m u l a t h e a u t h o r s neglected t h e mirror forces b e t w e e n ions a n d particles. As these forces t e n d to increase, a n d t h e correction factor c o n t a i n i n g Kn, to diminish, t h e charging rate, these two effects could i n some degree c o u n t e r b a l a n c e each other. N. F u c ~ s
Karpov-Institute of Physical Chemistry, Moscow, U.S.S.R. Received July 1, 1968
Contact Angle in Thin Liquid Film The occurrence of a contact angle in the transition zone between a very thin and a thicker liquid film has been the subject of several recent investigations (1-3). We have developed a simple technique for the measurement of this contact aug]e, based on the Wilhelmy plate technique for measuring the surface tension of a liquid. The plate consists of the thin film to be investigated. The film is formed in a rectangular glass frame (4 cm wide and 2 cm high) made from thin glass rods (diameter 0.05 cm). The frame is suspended from a torsion balance allowing measurement of changes in weight of 0.05 rag. At I cm from the top of the frame a horizontal glass wire (diameter 15 ~) is stretched; this serves to make the volume of the top Plateau border of the film as small as possible, because otherwise it will contribute too much to the measured weight. When the contact angle between the film and the bottom Plateau border is zero, the measured force equals the surface tension multiplied by the horizontal perimeter of the film and the frame. This condition is satisfied for a thick freshly
formed film, which can therefore be used to measure the surface tension of the solution from which the film has been drawn. As the film drains, a "black" film is formed in the upper part. During the subsequent increase in area of this "black" film the sharp horizontal
TABLE
I
CONTACT ANGLES FOR FILMS S T A B I L I Z E D WITI-I 0.05% SODIUM DODECYL SULFATE AND
Cone. NaC1
(molel-i)
VARIOUS
AMOUNTS
Contact
of water thickn. tension solution
angle
0.1
0
0.2
0
0.3 0.35 0.4 0.5 0.6
Equivalent
(degrees) of film (A)
6%0' 8°16~ 9°29' 10°52' 12°17'
110 46 43 42 42 4O 41
OF NaCI
Surface
~5 (Film tension)
(dynes/era) (dynes~era)
32.4 31.5 31.1 30.9 30.4 30.0
32.4 31.3 30.8 30,5 29.8 29.3
boundary between the "black" and the thicker film moves down until it meets the lower Plateau border. At this moment a sudden decrease in the force exerted on the frame is measured, after which the force remains constant. From the decrease in force the contact angle can be calculated in the same way as for a solid Wilhelmy plate. The results obtained for films stabilized with sodium dodecyl sulfate (0.05% ~ 1.74 X i0 -s moles.era73) and various amounts of NaCl are given in Table I. The measurements were carried out at 25.0°C i 0.1°C. The values of the contact angle are mean values of 12 measurements; the standard deviation of the mean is 3 minutes of arc. The only value of the contact angle reported so far in the literature (2) is: 8°50'± 30' for a film stabilized with 0.05% sodium dodecyl sulfate and 0.4 mole/liter NaCI. This value agrees reasonably well with our value of 9°29 , ~: 9' for the same system. The thickness of the equilibrium films was determined by measuring the amount of reflected light. The refleetivities were translated into film thickness, on the assumption that the film consists of water with a refractive index of 1.333. In a film stabilized with the nonionic surfactant octylphenol condensed with an average of I0 moles of ethylene oxide (6 X 10 -4 moles, cm -3) and up to 0.6 mole/liter NaCI, no measurable contact angle could be observed. This means that it is smaller than 15 minutes. Since the rate of formation of the
equilibrium films, stabilized with this surfaetant, is very slow, the accuracy of the measurement is found to be lower than with larger contact angles. The equilibrium thickness of a film with 0.6 mole/ liter NaC1 is 88 A. It is of interest to consider the mechanical equilibrium in the transition region between thin and thick film in somewhat more detail. In the
Journal of ColloidandInterfaceScience,Vol. 29, No. 1, January 1969
178
L E T T E R S TO T H E E D I T O R S
vertical direction, equilibrium is maintained because the film tension at is less than twice the surface tension ~0 of the bulk liquid; in fact as = 2 a0 cos 0. The horizontal components of the surface tension in the transition region--magnitude ¢0 sin ~--must be compensated by the disjoining pressure P~ in the transition region:
-IO00V HtGH VOLTAGE
TRIG
c o s i n e = --
DC
Pd (h) dh ,
hfilm where the film thickness h depends on the vertical coordinate in the transition zone. A rough estimate of the height of the transition zone is obtained by assuming that thedisj oining pressure is mainly determined by van der Waals forces: P~ = - A/6~-h ~. With A = 5 )K 10- ~ erg, the height of the transition zone must be about 10-* cm. REFERENCES 1. DERYAGIN,
B. V., M A R T Y N 0 V ,
G. A., AND
GUTOP, Y. V., Research in Surface Forces 2, 9 (1966).
2. MYSELB, K. J., HUISMAN, H. F., ANn RAZOUK, R. I., J. Phys. Chem. 70, 1339 (1966). 3. PRINOEN, H. M., AND MASON, S. G., J . Colloid Sci. 20, 156 (1965). A. P a I ~ s Unilever Research Laboratory, Vlaardingen, The Netherlands Received July 12, 1968
Birefringence Induced in Gold Sol by Ultrasonic Wave Most molecules and particles, in general, are optically anisotropie because their polarizability is different in various directions. If the molecules or particles are completely randomly distributed in an aggregate, the aggregate behaves as an isotropic medium. Any orientation, whether it exists naturally or is caused by artificial means, leads to anisotropy and thus this medium becomes birefringent. The molecules or particles in the liquid can be orientated by an electric field, a flow, or an ultrasonic field. The last method is not dependent upon the molecules' possessing a permanent dipole moment and thus has an advantage over an electrical method. Also the apparatus is less complicated than the one for the flow and is not so difficult to use. In ultrasonic birefringence there are two Journal of Colloid and Interface ~cience,
VoI.29,
No. 1,
FIG. 1. Block diagram of apparatus for acoustic birefringence measurement. methods. One is based on the dependence of the birefringence oll the intensity of the ultrasonic field and on the frequency of the sound; the other is identical to the electrical method. In the former method the precise measurement of the intensity of the ultrasonic field is attended with serious difficulties. On the other hand, such measurement is not needed in the latter method. Thus, the latter method has an advantage over the former method. A limited ntunber of investigations (1) have been made on birefringenee by means of the former method, but no investigation has been made with the latter method. The apparatus for the study of acoustic birefringenee is shown diagrammatically in Fig. 1. The light source is a 10 v, 50 w tungsten-filament lamp, run from a battery-charging unit. The light beam is made parallel by a lens LI and passed through a heat filter H f and monochromatic filter Mr, Shimazu L-2. This arrangement gives an intense beam, and the intensity is satisfactorily constant. A diaphragm Dm limits the width of beam passing through the polarizer P to a diameter of 5 mm. The beam of linearly polarized light passes through a sample solution in a cell Ce which has a 10 Me X-cut crystal in the bottom, and the beam passes into the part of the detector which is composed of a ~/4 pIate, an analyzer A, a condenser lens L2, and a photomultiplier tube Toshiba M s g s , class B, 9-stage. The vibration directions of the polarizer and ~/4 plate are set 45 ° to the vertical, and the direction of the analyzer is set 90 ° to that of the polarizer. The light beam, therefore, does not pass through the analyzer unless the sample becomes doubly refracting. The birefringence An is approximately related with the stray light intensity I which passed through the oriented particles in liquid by the following equation:
January 1969
I = CG(an)L
[1]
LETTERS TO THE EDITORS f o r m u l a derived b y these authors, which does n o t c o n t a i n Kn, correct. A t finite K n values t h e i o n v e l o c i t y d i s t r i b u t i o n i n t h e v i c i n i t y of t h e particles becomes n o n Maxwellian, a n d t h e f o r m u l a is erroneous. As concerns t h e good a g r e e m e n t b e t w e e n this f o r m u l a a n d t h e e x p e r i m e n t a l results of L i u a n d co-workers at K n values f r o m 1.0 to 1/66, it should be t a k e n i n t o consideration t h a t this a g r e e m e n t was o b t a i n e d o n l y b y a s s u m i n g t h e molecular weight of ions to be 460. Moreover, i n d e r i v i n g this f o r m u l a t h e a u t h o r s neglected t h e mirror forces b e t w e e n ions a n d particles. As these forces t e n d to increase, a n d t h e correction factor c o n t a i n i n g Kn, to diminish, t h e charging rate, these two effects could i n some degree c o u n t e r b a l a n c e each other. N. F u c ~ s
Karpov-Institute of Physical Chemistry, Moscow, U.S.S.R. Received July 1, 1968
Contact Angle in Thin Liquid Film The occurrence of a contact angle in the transition zone between a very thin and a thicker liquid film has been the subject of several recent investigations (1-3). We have developed a simple technique for the measurement of this contact aug]e, based on the Wilhelmy plate technique for measuring the surface tension of a liquid. The plate consists of the thin film to be investigated. The film is formed in a rectangular glass frame (4 cm wide and 2 cm high) made from thin glass rods (diameter 0.05 cm). The frame is suspended from a torsion balance allowing measurement of changes in weight of 0.05 rag. At I cm from the top of the frame a horizontal glass wire (diameter 15 ~) is stretched; this serves to make the volume of the top Plateau border of the film as small as possible, because otherwise it will contribute too much to the measured weight. When the contact angle between the film and the bottom Plateau border is zero, the measured force equals the surface tension multiplied by the horizontal perimeter of the film and the frame. This condition is satisfied for a thick freshly
formed film, which can therefore be used to measure the surface tension of the solution from which the film has been drawn. As the film drains, a "black" film is formed in the upper part. During the subsequent increase in area of this "black" film the sharp horizontal
TABLE
I
CONTACT ANGLES FOR FILMS S T A B I L I Z E D WITI-I 0.05% SODIUM DODECYL SULFATE AND
Cone. NaC1
(molel-i)
VARIOUS
AMOUNTS
Contact
of water thickn. tension solution
angle
0.1
0
0.2
0
0.3 0.35 0.4 0.5 0.6
Equivalent
(degrees) of film (A)
6%0' 8°16~ 9°29' 10°52' 12°17'
110 46 43 42 42 4O 41
OF NaCI
Surface
~5 (Film tension)
(dynes/era) (dynes~era)
32.4 31.5 31.1 30.9 30.4 30.0
32.4 31.3 30.8 30,5 29.8 29.3
boundary between the "black" and the thicker film moves down until it meets the lower Plateau border. At this moment a sudden decrease in the force exerted on the frame is measured, after which the force remains constant. From the decrease in force the contact angle can be calculated in the same way as for a solid Wilhelmy plate. The results obtained for films stabilized with sodium dodecyl sulfate (0.05% ~ 1.74 X i0 -s moles.era73) and various amounts of NaCl are given in Table I. The measurements were carried out at 25.0°C i 0.1°C. The values of the contact angle are mean values of 12 measurements; the standard deviation of the mean is 3 minutes of arc. The only value of the contact angle reported so far in the literature (2) is: 8°50'± 30' for a film stabilized with 0.05% sodium dodecyl sulfate and 0.4 mole/liter NaCI. This value agrees reasonably well with our value of 9°29 , ~: 9' for the same system. The thickness of the equilibrium films was determined by measuring the amount of reflected light. The refleetivities were translated into film thickness, on the assumption that the film consists of water with a refractive index of 1.333. In a film stabilized with the nonionic surfactant octylphenol condensed with an average of I0 moles of ethylene oxide (6 X 10 -4 moles, cm -3) and up to 0.6 mole/liter NaCI, no measurable contact angle could be observed. This means that it is smaller than 15 minutes. Since the rate of formation of the
equilibrium films, stabilized with this surfaetant, is very slow, the accuracy of the measurement is found to be lower than with larger contact angles. The equilibrium thickness of a film with 0.6 mole/ liter NaC1 is 88 A. It is of interest to consider the mechanical equilibrium in the transition region between thin and thick film in somewhat more detail. In the
Journal of ColloidandInterfaceScience,Vol. 29, No. 1, January 1969
178
L E T T E R S TO T H E E D I T O R S
vertical direction, equilibrium is maintained because the film tension at is less than twice the surface tension ~0 of the bulk liquid; in fact as = 2 a0 cos 0. The horizontal components of the surface tension in the transition region--magnitude ¢0 sin ~--must be compensated by the disjoining pressure P~ in the transition region:
-IO00V HtGH VOLTAGE
TRIG
c o s i n e = --
DC
Pd (h) dh ,
hfilm where the film thickness h depends on the vertical coordinate in the transition zone. A rough estimate of the height of the transition zone is obtained by assuming that thedisj oining pressure is mainly determined by van der Waals forces: P~ = - A/6~-h ~. With A = 5 )K 10- ~ erg, the height of the transition zone must be about 10-* cm. REFERENCES 1. DERYAGIN,
B. V., M A R T Y N 0 V ,
G. A., AND
GUTOP, Y. V., Research in Surface Forces 2, 9 (1966).
2. MYSELB, K. J., HUISMAN, H. F., ANn RAZOUK, R. I., J. Phys. Chem. 70, 1339 (1966). 3. PRINOEN, H. M., AND MASON, S. G., J . Colloid Sci. 20, 156 (1965). A. P a I ~ s Unilever Research Laboratory, Vlaardingen, The Netherlands Received July 12, 1968
Birefringence Induced in Gold Sol by Ultrasonic Wave Most molecules and particles, in general, are optically anisotropie because their polarizability is different in various directions. If the molecules or particles are completely randomly distributed in an aggregate, the aggregate behaves as an isotropic medium. Any orientation, whether it exists naturally or is caused by artificial means, leads to anisotropy and thus this medium becomes birefringent. The molecules or particles in the liquid can be orientated by an electric field, a flow, or an ultrasonic field. The last method is not dependent upon the molecules' possessing a permanent dipole moment and thus has an advantage over an electrical method. Also the apparatus is less complicated than the one for the flow and is not so difficult to use. In ultrasonic birefringence there are two Journal of Colloid and Interface ~cience,
VoI.29,
No. 1,
FIG. 1. Block diagram of apparatus for acoustic birefringence measurement. methods. One is based on the dependence of the birefringence oll the intensity of the ultrasonic field and on the frequency of the sound; the other is identical to the electrical method. In the former method the precise measurement of the intensity of the ultrasonic field is attended with serious difficulties. On the other hand, such measurement is not needed in the latter method. Thus, the latter method has an advantage over the former method. A limited ntunber of investigations (1) have been made on birefringenee by means of the former method, but no investigation has been made with the latter method. The apparatus for the study of acoustic birefringenee is shown diagrammatically in Fig. 1. The light source is a 10 v, 50 w tungsten-filament lamp, run from a battery-charging unit. The light beam is made parallel by a lens LI and passed through a heat filter H f and monochromatic filter Mr, Shimazu L-2. This arrangement gives an intense beam, and the intensity is satisfactorily constant. A diaphragm Dm limits the width of beam passing through the polarizer P to a diameter of 5 mm. The beam of linearly polarized light passes through a sample solution in a cell Ce which has a 10 Me X-cut crystal in the bottom, and the beam passes into the part of the detector which is composed of a ~/4 pIate, an analyzer A, a condenser lens L2, and a photomultiplier tube Toshiba M s g s , class B, 9-stage. The vibration directions of the polarizer and ~/4 plate are set 45 ° to the vertical, and the direction of the analyzer is set 90 ° to that of the polarizer. The light beam, therefore, does not pass through the analyzer unless the sample becomes doubly refracting. The birefringence An is approximately related with the stray light intensity I which passed through the oriented particles in liquid by the following equation:
January 1969
I = CG(an)L
[1]