Surface forces and the stability of colloids and disperse systems

S U R F A C E F O R C E S A N D T H E STABILITY O F C O L L O I D S AND D I S P E R S E SYSTEMS I B. V. Derjaguin and T. 1~. Voropayeva

wi~h ~ Part~'ipa~ion of B. N. K a b a n o v 2 and A. S. Titiyevskaya

Laborator~ of Surface Phowmom, Institub~ of Physical Chemistrv of the U.E.~J.R., Acad~rny of 3cigars, Moscow Received April Z~, 1065

ABSTRACT There are discussed two factors controlling the thickness h of a free film of liquid between two bubbles of radius R pressed against one another, the mechanical prop"ertiu of the film and the temperature, The role of the viscosity, ~, is an$1yzed on the buk of the formula h - 2.64 R(~u/~r)tls (¢ surface tension, u the receding velocity of the film perimeter'), which is the simple consequence of the formula for the thickncm of the film left behind the receding wetting perimeter ~(Derjaguin, 1943). A similar formula is also used for the analysis of the role of yield value of the film. The temperature does not change the thickness of the black free filn~ (,~100A.) in contrast to the thicker films governed by electric repulsion. The jumpwise thinning of free films is studied by microfilming. The method of crossed polarized metal wir~ is d~cribed, which 9ermit~ measuremeat of the potential barrier preventing metallic contact in liquid media. The measurements of this barrier in water solutions of electrolytes az a function of potential of the wires are interpreted on the bMie of our theory of colloid stability. The ex~teace of repulsive f0rces (disjoining preuure) at high electrolyte concentratiorm independent of the potential prov~ their nonelectroetatic origin. These measurements were aleo used to calculate Hamaker'e constant of molecular attraction and to determine the potential of zero charge of some metals. INTRODUCTION I t iS common knowledge t h a t the present-day t h e o r y of the stability of colloids is based on the idea of interaction forces arising between the surfaces of the colloid particles or liquid films when they come within close range of one another. There are two papers at the source of ~his theory. One of them is a note b y Kallraann and Wil]st~tter (1) which p u t forth the idea1 Pre~ented to the Unilever Research Symposium on Surface Phenomena in Disperse Systems (1961). s Doctor, Chemical Science.

83

84

B. V. Derjaguin

hypothesis of the basic importance of van der Waals' attraction forces and electrostatic repulsion forces for the stability of sols. The other is Hardy's attempt (2) to detect and study by dfl=ect experiment the repulsion forces arising when solids separated by a liquid interlayer approach each other. Subsequent papers in Other countries, primarily in Holland, developed Kallmann and Willst~tter's idea by theoretical examination of the properties of colloids on the basis of interaction energy versus distancebetween-particle-surfaces diagrams (3). Simultaneously, Hamaker and DeBoer obtained by calculation an expression for the van der Waals' component of interaction. As to experimental investigation of the repulsion forces, it was largely discontinued, and was not taken up again until recently, possibly owing to the fact that Hardy's experiments were soon found to be erroneous. On the other hand, in our Laboratory the theory of interaction of colloid particles was developed in close connection with direct studics of that interaction in model experiments with thin films. (4) The primary impor, tance of this line of study was that it resulted in a more general statement of the equation of state of a thin layer, interrelating its temperature, thickness, and equilibrium disjoining pressure--the fundamental thermodynamical parameter of a thin layer, introduced on the basis of experimental research. Parallel theoretical and experimental investigation of the problem not only ensured a broader approach but also brought tangible results. In 1937 one and the same number of the same Journal carried a paper giving strict experimental proof of the existence of an equilibrium disjoining pressure (5) and another paper which contained a method of calculating that component of the disjoining pressure which is due to the overlapping of ionic atmospheres (6). The latter paper applied that method to calculation of the rate of slow coagulation. Further, the stability criterion of a sol was derived for particles much smaller than the thickness of the ionic atmosphere, compared with which the radius of action of the van der Waals' forces can in this case be considered negligibly small. Subsequently, the theory of stability of lyophobic colloids was developed mainly independently of experimental studies, and its verification was based on an analysis of the results of coagulation threshold determinations. Meanwhile, from the very theory of electrostatic interaction of charged particles in electrol~e solutions there follow both the limits of its application--with respect to concentration--and the difficulty of exact verification in colloid-chemistry experiments, primarily because of the impossibility of exact determination of the surface potential, as well as the conventionality of the methods used in determining the coagulation threshold. True, this second defect can evidently be eliminated by observing the kinetics of coagulation with the aid of the flow ultramicroscope (7) developed originally for measuring the concentration of aerosol par-

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85

tides (8). Less conveniently such observations can be made with Watillon's version of the flow ultramicroscope (9). The necessity of parallel experimental study of surface forces in thin 6l~q became especially evident after the discovery of repulsion forces of another nature, which could not be attributed to the interaction of overlapping diffuse atmospheres. In this communication we shall examine the main results of these studies obtained in recent years. GENERAL THEORY InveStigations of the thicknesses of wetting films formed when an air or gas bubble is pressed against a smooth solid surface have shown unambiguously that after thermodynamic equilibrium has set in the film acquires a uniform thickness h which at any given temperature is a definite function of the capillary pressure Po tending to thin the film, but balanced by the action of surface forces. From the condition of thermodynamic. equilibrium it follows that

p,

OF(h)

=

ah

'

[11

where F (h) is the part of the free energy of the system which depends upon the film thickness ~ a result of the action of the surface forces. W e denote aF(h) ah

by P (h) and term this most important thermodynamic characteristic of the,film its disjoining pressure. In case of a one-component system (10) P(h)

=

•

p

gl

,

[21

where m is the chemical potential of the bulk liquid pha~e, g/is the chemic," ,Jotential of the film, and v is the molar volume. For a film between two identical bubbles, the condition of equilibrium of the film is expressed through the disjoining pressure thus: P= -- P (h).

[3]

INVESTIGATION OF THE DISJOINING PRESSURE OF FREE FILMS' Studies of the disjoining pressure and the equation of state of free filrnA forming between two compressed bubbles were described in a number of previous papers by one of the authors (11). , With the participation of Mrs. A. S. Titijevskaya.

86

B. V. Derjaguin

J!

°T

/

Fie. I. The liquid layer left behind the retreating meniscus The following conclusions were arrived at: An equilibrium positive disjoining pressure can arise only in the presence of dissolved surface-active substances, whether ionogenic or not. At low ionic strength the relationship between the disjoining pressure and the film thickness depends on the forces of iono-electrostatic repulsion. On compression of diffuse ionic atmospheres, owing to gro~vth of the ionic strength, the equilibrium thickness of the film tends to values of the order of 10 .6 cm. which are difficult to account for from the standpoint of ionic atmosphere interaction, even if no allowance is made for the van der Wa~ls' forces favoring thinning of the film) Moreover; for concentrations of the order of 0.1 N and up, the existing methods for calculating this interaction are inapplicable. It is sometimes assumed that the thickness of such black films is determined by their mechanical properties i.e. elevated viscosity or yield value (shearing strength). The impossibility of accounting for the film thickness by the effect of the film viscosity follows from the application of capillary hydrodynamics to calculation of the thickness of the liquid layer remaining behind the retreating meniscus. For the case of the wettable solid substrute (SS) of a film (Fig. 1) one of us derived (13) and confirmed experimentally (14) the formula /

. \2/3

More accurate absolute values of these thicknesses were obtained by A. D. Sheludko, who reduced the influence of the background on these measurements (12). The background might have accounted for about 20 ~. in our measurements. This error does not, however, change the trend of the pressure and temperature dependence of the film thickness.

Selected

Works - 2

87

where.h is the thickness of the remaJniug Rim, ,9 is its viscosity, ¢ is the surface tension, R is the radius of curvature of the meniscus, and u is its rate of retreat. Simple reasoning makes it possible, by doubling the right-hand side of Eq. [4], to obtain the thickness 2h of the free ~]m forming after the retreat of two symmetrically located menisci, e.g., when two bubbles are pressed against one another (Fig. 2), assuming that the presence of a stabilizer makes both surfaces of the film unstretchable (which gives the m~rim,lm film thickness) h ffi 2.642

[5]

The same formula was obtained recently in reference 15. From formula [5] it is evident that a change of u, e.g., by altering the rate of compression of the bubbles, should change h; this change is never observed, however. On the contrary, h is always readily reproducible. Thus, it is not the viscosity that determines this thickness. The dependence of h on the velocity =, which follows from formula [5] at sufficiently low values of the latter, disappears if the film is attributed a plasticity characterized by the yield value 0. As capillary-hydrodynamic calculation shows in this case (16), the thickness of the film forming after slow compression of two bubbles of radius R equals 0= ;r.

h = 3.25

[6]

Hence we get the value of 0 needed to account for the observed values of h; it equals 0.56~hmR -81=.

8 -

[7]

Multiplying 8 by h/2 we find that each surface of the film should display a

f nun

q

I

4

P

J

\ ,,~-- 2 h

F]o. 2, T h e free film formed between two bubbles

B. V. Derjaguin

88

two-dimensional yield value of not less than

[8]

8~= 0.28~ ( R ) 6''

Putting = 30 dynes/cm. 2,

h = 10 -6 cm.,

R

=

i0 -~ era.,

we get 81

=

i0 -~

dyne/cm.

Such a high two-dimensional yield value should affect the measurements of the two-dimensional viscosity at the solution-air interface. But this is not observed for solutions of sodium oleate, OP-10, and others giving free films approx. 10-b cm. thick. Thus, this possibility of attributing the stability of black films to their specific mechariical properties vanishes, and there. fore their stability must be regarded as corresponding to thermodynamic metastable equilibrium whatever the nature of the corresponding forcea Sometimes attempts are made to relate the stability of black films to micelle formation phenomena. However, this relationship cannot~ be re. garded as causal, because black films possess stability below micelle forma. tion concentrations as well. However, a black film may be regarded .as.a sort of analog of a micelle, being a flat miceUe of a special kind with an indefinitely large area. But the euristic value of this standpoint is as yet un. clear. The temperature dependence of the thicknesses of free films (at constant disjoining pressure) is a point of interest. To investigate this problem (17) use was made of the following quartz apparatus (Fig..3). The cell containing the solution is A. The pressure on the bubbles forced out of openings C and D is transmitted through a tee F and is measured by means of syphon gauge E, the tip of which is lowered into an auxiliary

B

FIo. 3. The experimental setup

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89

h,$, 4001 5OO I

1500 20OO

P, d y n./cm 2

Fro.'4. The iso'therms of disjoining pressure for free films with 10-=N water solu. tion of sodium oleate and 10-=hr NaCl added. Curve l--at 23°C. Curve 2--at 50°C. 180 / h,~.

J40 1 I00

~

.o ¢x~oocmz e-e-e-e-.e-e-- 3 A

J

a

ZO 40 60 1", °C

80

FIo. 5. The dependence of the thickness of free films on temperature, l--Water solution of 0.1% of OP-10 with addition of 10-iN NaCl. 2--Water solution 0.i N sodium oleate with addition of 10-=N NaCl. S--Solution 0.05% D B with" addition of 10-aN NaCl.

cell G~ holding the same solution. The main cell has a cover B with a peak window for observation with a microscope furnished with a photometric cap. Tank H with circulating water serves for thermostatic control. Simultaneously, the top. of the apparatus is washed with a stream of air at the same temperature. Some of the results obtained are shown in Figs. 4 and 5. It can be seen that the thickness of free films of solutions of low concentration decreases with rising temperature T, contrary to "black films," which are insensitive to temperature rise in the interval 20 ° to 80 ° . This difference confirms the fact t h a t the repulsion forces in black films are different from those arising by the overlapping of ionic atmospheres. 6 In concluding this phase of the discussion, we show in Fig. 6 some motion photomicrographs illustrating the formation of black films in the process of thinning of free films, and demonstrating clearly that the thickness of the black films is a result of metastable equilibrium and not retardation of thinning under the influence of mechanica! properties. Similar conclusions regarding the nature of the action forces were arrived at by van den Tempel (19) in studying the films of aqueous solutions between two drops of a hydrocarbon phase, by an analogous method. In contrast with these studies, A. D. Sheludko (12, 20) employed a dynamic method.of measuring the disjoining pressure of thin films by 8 The opposite assumption, p u t forth by Overbeek (18), can hardly be reconciled with the entire aggregate of above-described facts. However, we must agree with the desirability of further experimental studies (12).

90

B.V. Oerjaguin v

I

,"

:

"i,+

t-~*t 0

qe~

'

A

i F

,

"

J

~<'3:

.i

t T

-

J

-

J

J v

Fio. 6. Motiotl plmtomicrographs of the process of thinning of free films. (a) 10-iN s~llution of sodium oleate. (b)--O.l% eolutiqm of Ol'-10 + 0.1 N NaCi. (c)0.1% solution of Saponine q- 1 N NaCI.

Selected Works - 2

91

, ,1 " f y

r

f

f

C.,

/

f

,e

/

~.

,

.~ .It

lo'lti. 6 - Conlinucd

their late of thinning under tile action of capillaiT suction• Tile advantage of this method is tile possibility of applying it to the measurement of disjoining pressure in the thickness region corresponding to labile film states, e.g., ill tile region of negative disjoining pt~ssm% con~sponding to the van der Wa~ls' attraction forces outweighing tile repulsion forces. The results obtained by this method depend, however, oil the assumptions tlmt the viscosity of a thin fihn equals its bulk value, that the presence of a stabilizer makes both its sudaces practically unstretchable under the cxl~rimental conditions, and that in the process of thinning the film remains plane-parallel. Under delinite conditioim, for a wide range of solutions these three assumptions may be coimidered valid to a first approximation. But that they at~ not always true has been indicated by investigations of the kinetics of thinning of h~e films of solutions of fatty alcohols in aniline (21) which showed that in this case the lifetime is proportional to the ladius of a disc-

92

B. V.

Derjaguin

shaped film to the first, and. not to the. second, power, as should follow from Reynolds' formula for the rate of thinning of a plane-parallel fihn. Of the results obtained by Sheludko we point out his study of the dependence of the disjoining pressure of the films on the concentration of the electrolyte (22), which coincided exactly with a formula derived by one of us at an ear.lier date (6). Sheludko's method also made it possible to determine the van der Waals' interaction constant for a number of liquids (23); this is of great interest. However, the most interesting fact discovered by Sheludko was that there are a number of solutions for which, despite the absence of diffuse ionic atmospheres, metastable films about 10-6 cm. thick are obtained at definite (rather high) concentrations. An example of these is a 2.5N solution of butyric acid in water (see also reference 12). This is essentially a discovery of a disjoining pressure component of an entirely new nature and with a large radius of action. INVESTIGATION OF THE DISJOINING PRESSURE IN THIN FILMS OF LIQUIDS BETWEEN SOLID SURFACES ~

The disjoining pressure between two solids was first discovered and studied in reference 4. Recently, similar studies were developed by Fuks (25). In the latest papers not only equilibrium disjoining pressures were studied but forces resisting the thinning of the liquid interlayer have also been revealed. These display hysteresis phenomena, indicating their relation to the specific mechanical properties of thin liquid layers. Since in the case of convex bodies the equilibrium interaction forces change in proportion to their curvature radii (26), and the viscous resistance to thinning of the interlayer, in proportion to the squares of their radii. (27, 16), then for slightly convex and especially for flat surfaces, the relative role of the mechanical properties of the liquid layers increases by many times compared to the case of colloid particles. Therefore it is advisable when modeling the interaction of the latter to perform the "model" experiments on bodies of greater curvature. For a number of technical reasons it is most convenient to perform the experiments with crossed filaments or wires. As measurement of the mutual distance is difficul.t in this case, we confined ourselves to measurement of the force barrier Nm preventing contact between metallic filaments immersed in the same liquid m e d i u m / I n the case of an aqueous solution of an electrolyte this barrier is caused by the repulsion forces arising upon overlapping of the ionic atmospheres and capable of outweighing the forces of molecular attraction in the range of medium thicknesses, which are of the, same order as the thickness of the ionic atmospheres (Fig. 7). When the ' This part wa~.prepared in consultation with Prof. B. N. Kabanov, TFor first communication of'this study see reference 28.

93

Selected Works - 2

force barrier N~, is overcome by an ex~rnal force the wires come into contact, which can be judged by t h e jumpwise diss4~pearance of the contact electrical resistance. The following formula may be employed for the transition from crossed wires to microparticles (26): ~(H)

=

N ~,

[9]

where = repulsion force of convex surfaces in electrolyte solution at shortest distance between them H, (H) = energy of interaction per unit area of surfaces of the same nature separated by a plane-parallel layer of the same electrolyte of thickness H, and G = geometric factor depending only on the curvature and orientation of" the surfaces near the zone of closest approach.

N

For the case of two spheres of radius R (the simplest shape of colloidal particles) G = ~R. For two cylinders of radius rl and r2 crossed at an angle of ~, G = 2~ r~/V~,r~/sin ~. Thus, the value ~ (E) can be used to characterize repulsion of the surfaces irrespective of the filament radii, and to calculate the interaction of sphericolloid particles of any radius. The filaments were most often two smooth platinum wires (300 ~ in diameter). Filament 2 was soldered to an elastic torsion hanger 5, and served as the beam of the torsion balance (Fig. 8). The hanger 5 was made of phosphor bronze of rectangular cross section and was firs~ calibrated. For measuring the torsion angle the hanger had a rairror 4 glued t o it.

H

FxG. 7. The force versus distance diagram for croued fiIarnenta in electrolyte Iolution.

94

B.V. Derjaguin

FI~. 8. The experimental setup for investigating the force barriers for the contact of two crossed metallic filaments. Filament 3.was soldered to a bushing which passed through the inlet into cell 6. The bushing of a worm pair was connected through a gear system to a d.-c. motor. By starting.the motor in either direction filament 3 can be very slowly and smoothly moved up to or away from filament 2. To keep the filaments from slipping with respect to one another in the course of their motion, the rotation axes of both filaments were made to coincide. This could be accomplished because the design of the apparatus permitted location of the elastic hanger.carrying filament 2 exactly in the center of the rotating bushing on which filament 3 was fixed. Both filaments having a n angle of encounter of 90 °, were placed in an annular air-tight cell 6. The electrolyte solution was introduced into this cell from tank 7 in which it was first purified, and a~ter use overflowed a weir. By means of a system of connecting, glass tubes both the solution in tank 7 and that in the cell could b e saturated with electrolytic hydrogen. The cell was connected through an electrolytic key to a reference electrode 1. To polarize the filaments auxiliary electrodes 8 and 9 were fused into the cell. Like the main electrodes, these were of platinum wire. All glass parts of the apparatus were of Pyrex glass. The unit was so designed as to allow charging of each filament to any desired potential. Polarization of the filaments was accomplished by means of the circuit shown in Fig. 9, each filament having its own current source and being polarizable to any potential value independent of the other filament. The potentials on the filaments were measured with potentiometer 20 against a calomel electrode when KC1 or ZnCI2 solutions were used and against a mercury-mercurous sulfate electrode, when using H2S0~ or MgSO, solutions. Since determination of the force barrier required establishment of the moment of contact between the filaments, a small difference of potentials (0.01 v.) was set up between them, measured by potentiometer 21. At the

Selected Works - 2

Fie. 9. The electric and optical scheme of the setup moment of contact the potentials on the filaments equaUzed, disturbing the compensation of the system; this caused an automatic device to operate and filament 3 moved away from filament 2. A diagi-am of the device by means of which the direction of rotation of the motor could be reversed at the moment of contact is shown in Fig. 10. A light opaque screen was glued to the pointer of a galvanometer 19 (Fig. 9), which in the zero position blocked the light beam coming from lamp 1 inside the galvanometer. Above the galvanometer scale was a photoconductive cell 2 arranged so that the light beam would fall on it when the galvanometer pointer deviated from the zero position. The photoconductive cell was cut into the circuit of a relay 3, When light fell on the photoconductive cell a relay started another relay, which operated to reverse the rotation of motor 5. Thus, after achievement of contact filament 3 (Fig. 9) automatically began to retreat from filament 2. The torsion angle of the elastic hanger was measured by means of a scanning light relay (Fig. 9), which operated as follows: The light rays from lamp 14 passed through a condenser 13, a grating 1!, consisting of an alternation of dark and light bands of equal width, lens 10, focused on mirror 4 fixed to t h e elastic hanger, were reflected from the mirror, passed back through the same ]ens, and by means of prism 12 were directed onto photo-electric cell 15; as a result, one half of grating 11 was projected on to its other half. Therefore, as the mirror turned, the lines of the first half of grating 11 reflected by mirror 4 shifted with respect to the lines of the other half, decreasing or increasing the illumination of the photocell uniformly over its entire area. At the moment when the dark lines of the tyro halves of the screen fully coincided the illumination of the photocell was a maximtim. On further turning of the mirror the dark lines of one half of the screen began to cover the light spaces of its other half. This decreased the illumination of the photocell, which reached a mini-

95

96

B.V. Derjaguin

A

?

120 V

~;24V

o

_

~

c

.t

FIo. 10. Tho electric circuit mum when the light spaces were fully covered by the dark lines, then it again rose to maximum, etc. The width of the grating bands was selected so that during measurements the maximumangle of rotation of the beam, and therefore, t h e maximum change i n illumination of the photocell, should fall within the interval where an approximately linear relationship is observed between the illumination and the angle of rotation of the mirror. Such linearity is retained over a considerable part of any of the halfperiods, except the region close to the maximum or minimum illumination. The photocell signal amplified by an electronic amplifier 16 was recorded by a recorder 17 the scale of which was first calibrated in force units. Owing to the sensitivity of the unit to jolts its most sensitive part was assembled on a shock-absorbing plate set on a foundation which was dug into the ground and insulated from the floor. Besides, to avoid additional mechanical and other hindrances the unit was remote-controlled.

Preparation of Experiment Before mal~ing measurements all the glass parts of the unit were washed thoroughly with bichromate and then with hi-distilled water. The salt with which the solutions were prepared was recrystallized and calcined. The platinum filaments were cleaned as follows: After immersion for 3 minutes in concentrated sulfuric acid they were placed in-the cell, the subsequent cleaning being carried out electrochemi~ caUy without removing them from the cell. The sequence of all operations is shown in Table I. After this treatment the sulfuric acid solution was forced out by hydrogen and the cell with the filaments was flushed several times with the electroly~e solution and finally filled with it. To purify the solution from surface-aoCive organic impurities and oxygen a platinized platinum screen was placed in the cell and hydrogen was passed through for a long time.

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97

2

TABLE I No. 1 2 3 4 5

Current density

(rain.)

Time

Solution

40-50 2-3 40-50 2-3 40-50

180-240 15 15 15 15

1 N H2SO~ 1 N H2SO, 1 N HsS04 1 N. HsSO4 1 N HsSO4

Polarization (mA p~" ¢m.s) Cathode Anode Cathode Anode Cathode

M easurir~ At the beginning of the experiment the filaments were moved away t o some distance from one another. The zero position of filament 2 (Figs. 8 and 9), fastened to the elastic hanger, was fixed on the scale of the electronic potentiometer 17. After that pro-set potentials were applied to the filaments. Then filament 3 was approached smoothly to filament 2. When filament 3 has come sufficiently close to filament 2 and if a force barrier was present, the latter would begin to move in the same direction as filament 3, twisting the hanger to an angle registered by the potentiometer 17 and proportional to the force of interaction of the filaments. At the moment the force barrier was overcome and the electralyte film was pierced, and therefore the filaments had come into direct contact, the automatic device operated (see Fig. 10), filament 3 moved away from filament 2, and the electronic potentiometer recorded the magnitude of the force barrier between the filaments. Results of Mea,rurements The force barriers were measured for several substances depending o n the potentials on the filaments and the concentration of the soh~tions. 1. Potassium chloride. In dilute solutions (Fig. 11) the force barrier N~ has a minimum value at a potential of 0.2 v. According to published data (29) this same potential corresponds to the point of zero charge of platinum. The force barrier as a function of the potential is depicted as curves symmetrical with respect to the minimum point, at a distance from which they asymptotically approach constant values, which grow as the solution becomes more dilute. At an electrolyte concentration of 0.1 N and high'er the magnitude of the force barrier no longer depends on the potential of the filaments but varies with the concentration of the solution (Fig. 12). A maximum is observed at ~ 1 N solution, and a minimum at ~ 2 N solution, beyond which follows a long rise. ~,. Magnesium sulfate. In dilute solutions of the electrolyte (Fig. 13) the picture is similar to that for potassium chloride solutions, i.e., a minimum at 0.2 v. and symmetry of the curves with respect to that minimum. The dependence of the barrier on the potential, however, disappears n o t ' i n

B. V. Deqaguin

98

U (erg/cm2)

KCl

2 ,I

I

-0.1

0

....

0.1

I

&

1

0.2

0.3

0.4

I ~..

0.5

~o FIe. 11. Energy barrier versus potential for KCI solution U(er /cm 2) KCI

&

00

I

I0

I

2.0 C

,._

3.0

FIO. 12. T h e energy (force) b a r r i e r versus c o n c e n t r a t i o n for K C ] s o l u t i o n MgSO4

U(er /cm 2) ~

o.,

-

..'''~°" 3 x tO- 4 N

-4 10- 2 N

00

J 0.1

~ 0.2

,~. 0..~

, 0.4

~_

£o

Fie. 13. Energy barrier versus potential for MgSO~ solution

0.1 N solution, as w i t h potassium chloride, but in cent[normal solution. At concentrations of 0.01 N and more the magnitude of the force barrier is independent of the filament potential. As the concentration of the solution increases (Fig. 14), the force barrier grows, reaches a maximum at

Selected Works - 2

99

1.5 N solution, drops to a minimum at. 2.5 N solution, and then grows again. $. Sulfuric acid (Fig. !5) and zinc, chloride (Fig. 16). At 0.2 v. the force barrier has a minimum which vanishes in centinormal solution, as in the case of magnesium sulfate. The curve of zinc chloride is not symmetrical with respect to the ordinate axis, which is probably related to the asymmetry of the electrolyte. 4. Butyric acid. As the concentration varies (Fig. 17) the force barrier grows to a maximum at 0.75 N solution, drops to a mln~mum in 1.5 h r solution, again rises to a maximum in 2 . 5 N solution, and then drops again. This behavior of the force barrier is quite analogous to that detected by Sheludko (23) for the thicknesses of the free ~]mR and the lifetime of froths of the same solutions of butyric acid. 6. Carbon tetrachlaride. Before the measurements the carbon tetrachloride was distilled and passed through a colllmn of calcined silica gel. The measurements showed that in this case there is no force barrier, i.e., U(er, /cm2)

MQSO4

0.6 0.5 0.4 0.3 0.2 0.1

°o

,.o

31o

C Fzo. 14. Energy barrier versue concentration for MgSO. solution U(er, /cm2)

H2S04

~

:10-3N

0.3 0.2 0"1

•

;

~"

L

10--2 N

--w

°o.,

01

I

I

0.2 o'.3 0.4 0:5

.

Fzo. 15. Energy barrier vereue potential for sulfuric acid

100

B.V. Derjaguin ZnCl2

U(erg/cm2)

0.7 0 .

5

0.3 0.1

~ 10.2 N

O

0.'

I 0.2

Ol.~

01.4

Fro. 16. Energy barrier versus potential for zinc chloride solution U(ergIcm 2 ) n- Bullery ocid

12 I0 8 6 4

2 0

0

I

I

I

I

1.0

2.0

3.0

4.0

1,

CH

Fro. 17. Energy barrier versus concentration for n-butyric acid contact occurs immediately the filaments come together. As the electrical conductivity of CCI4 is incomparably smaller than that of any aqueous solution, and nevertheless the transitional electrical resistance disappears under a compressing force below the sensitivity of the method, it follows hence that the compression under which the transitional resistance is broken down is required only to overcome the force barrier of the thin interlayer, and is in no way related, say, to the decrease in the contact resistance due to contact (Herzian) deformation of the wires.

Determination of the Zero Charge Point of Gold For this purpose gold filaments were cleaned by cathode polarization and placed in a 10-= N potassium chloride solution. The minimum force barrier value, corresponding to the zero charge point, was observed at 0.05 v. (see Fig. 18) in agreement with reference 30.

Discussion of Results The theory of interaction of hydrophobic convex surfaces in electrolyte solutions (31, 32) leads to the following corollaries: 1. The force barrier (in terms of formula [9] it corresponds to the energy

Selected Works U(ef, /crn2 )

-

2

101

KCL

10- 3 N

0.5 0.05 I

I

-0.I

0.

I

.

0.1

I

l

0.2

0.3

Fxo. •18. Energy barrier versus potential for KCI solution, using gold'filaments barrier for plane-paraUel surfaces of the same nature) should equal zero at the zero charge point. ~. As a function of the potential the force barrier for a symmetrical electrolyte should take the shape of a curve symmetrical with respectto the zero charge point. ~. For an asymmetrical electrolyte no such symmetry should exist. ~. At distances from the zero charge point ofmore than 150 or 200 inv. the force barriers attain constant asymptotic values equal in the cathodic and anodic parts for symmetrical, and unequal for asymmetrical, eleco trolytes. 5. Both force barriers as functions of the potential, and the correspond° hag asymptotic values, should decrease more rapidly with growing concentration, the higher the charge of the counter ion, becoming zero at definite critical values. The results obt~-ined (Figs. 13, 15, 17 and 18) show that these conclusions from the theory are.confirmed at concentrations up to 0.1 N with the reservations that at the zero point or at high concentrations the force barriers do not drop to zero, but to a small, but quite m~a~surable value (that this value is real is shown by the measurement of a true zero for CC1,). However, on further growth of the electrolyte concentration from decinormal upwards (Figs. 14 and. 16), the force barrier not only does not drop, but even grows as a function of the electrolyte concentration, displaying maxima and minima. All this shows that repulsion forces exist which are not taken into account by theory, and the nature of which is yet to be-elucidated. It may be assumed that their appearance is related to the polarity of the solvent. One fact in favor of this assumption is that in a ~olution of carbon tetrachloride, which is a nonpolar liquid, no force barrier exists. •It would obviously be quite a strict verification of theory if we obtained from measurements of force barriers reasonable and consistent values of the Hanaaker constant A.

102

B. V. Derjaguin The theory of interaction in electrolyte solutions of hydrophobic convex surfaces charged to an equal potential ~ = ~ - ~, leads to the following formulas in the case of a symmetrical electrolyte (31). N 2- - r r

-

u

=

A 1 127r H 2 ,

~

[10]

s -

K

H = 2K~ ,

K -2

,

Ill]

[121

where N -- force of interaction of convex surfaces at their shortest distance H, u, 3 - energies respectively of entire interaction and of electrostatic interaction unit area of surfaces of the same nature separated by a plane-parallel layer of the same electrolyte of thickness H, A = H a m a k e r ' s constant of molecular attraction (6), 3' = concentration of electrolyte, moles per cm. 3, n -- n u m b e r of anions or cations in a molecule of the electrolyte, R - universal gas constant, T = absolute temperature, = D e b y e a n thickness of ionic atmosphere, K and E -, elliptic integrals of the first and second kinds with module and limits, _. 1 ul

va r

F¢~

K Sch 2RT

~ 1, = filament radius.

K n o w i n g from experiment the " a s y m p t o t i c " values of N~, and u~ (at large distances from' the zero charge point), equal to N,, and u ~ , and solving the equations du(H) dH u(H)

-

0,

= u.,,

[13]

[14]

we can easily find the only u n k n o w n - - t h e constant of molecular attraction A. F r o m Eq. [10] we find, as the condition of m a x i m u m N and u d3 dH

A 6rH ~'

where the right-hand side expresses the specific force (per square centi-

103

Selected Works - 2

TABLE:-II

KC1 KCI MgSO, 1VIgSO, KC1

7

H X I0'

A X I0m

Metal

10-6. 10-6 3 X I0-' 10-6. I0- e

21.2 29.8 59.7 81.6 86.9

3.56 4.77 2.45 2.33 14.00

Pt Pt Pt Pt Au

meter) of van der Waals' attraction of surfaces separated by a planeparallel layer of electrolyte solution H thick, while the left-hand side (31) dH

.expresses the specific force of electrostatic repulsion of the same surfaces. In the end we obtain the equation

4~RT

i

_

I

--

6fH=

,

denoting equilibrium (unstable) of both forces. Eliminatingthe unknown A from the latter equationand from Eqs. [i0] and [11], we get an equation in terms of _~ 1 [4E0--4 K -

(1--K2)K0] =-

u.~R

47nRT '

[15]

the right-hand part of which contains values determined from experiment, while E0 and Ko are the corn~let~ elliptic integrals of the 1st and 2nd kinds, respectively. Finding from [16] the values of K and g ( ~ ) l and substituting into [19] and [15], .we get thevalues of K and T. Table II shows that Calculated A-values have a reasonable magnitude and for Pt are in satisfactorily mutual agreement. It may be noted that for gold the A-value is much greater. Our thanks are given to Mr. Gutop and Mr. Leonov for their help in some calculations and to Mrs. Vybornova for her help in the experiments. GENERAL CONCLUSIONS

1. There are two approaches to the investigation of surface forces in thin ~]m~: (a) based on microscopical theories of their possible constit u e n t s - v a n der Waals' forces and electrostatic interactions; and (b) based on direct experiments on films leading to a phenomenological treatment of their thermodynamic behavior using the concept of disjoining pressure. It is profitable to use both approaches simultaneously. ~. Pressing together two bubbles one can realize an equilibrium ~lm

104

B. V. Derjaguin

whose thickness is a function of capillary pressure independent of mechanical properties of the film. 3. T h e equilibrium film thickness in the presence of surface-active substances and a high percentage of electrolyte is sensibly independent of t e m p e r a t u r e in contrast to the situation f o r thicker .films and low concentrations of electrolyte solutions. 4. The m e t h o d of crossed polarized metallic filaments permits the direct observation and m e a s u r e m e n t of the force barrier preventing metallic contact in liquid media. 5. The results of barrier-measurements agree in the main with the m o d e r n theory of the stability of colloids. The force barrier at zero charge point and at high electrolyte concentration points to the existence in films of a repulsive force of nonelectrostatic origin. This conclusion is supported by the results for free film.q both by Scheludko and the authors. 6. M e a s u r e m e n t s of the force barrier permit the determination of the zero charge potential of metals. 7. M e a s u r e m e n t s of the force barrier permit the calculation of H a m a k e r ' s constant of molecular attraction for metallic filaments in water. t~EFEREN CES I. KALLMANN, H., AND WILLBT-~TTZR,M., Naturudss. 20, 952 (1932). 2. FI*~oy, W., Phil. Trans. A230, 1 (1931). 3. WI*~AK~.a, H. C., Rec. tray. chim. 55, 1015 (1936); ibid. $8, 3, 727 (1937). 4. Dr.azxQuts, B. V., AND O~vcaov, E. V., Acts Physicochim. U./~.S.S. 5, 1 (1936). 5. D~.aJAOUIN, B. V., AND K u s ~ o v , M. M., Izveatiya Akad. Nauk S.S.S.R. Klas* rnatem, i estesttJ, nauk, serya ¢himilvhesk., No. 5, 1119 (1937) ; Acts Physicochim. U.R.S.S. 10, 25, 153 (1939). 6. DF.~JA(]UIN, B. V., Izvestiya Akad. Nauk S.S.S.R. Klass m a i m . i cute, to. nauk, serya chirnitchesk., No. $, 1153 (1937); Acts Physicochim. U.R.S.S. 10, 333 (1939). 7. Km~azAvc~,.vAiN. M., AND D=.aZAOUXN,B. V., Article in Symposium an Surface Forces, "Issledovanija v oblasti poverchnostn, sil," p. 183; Ed. by Academy of Sciences of S.S.S.R., M. 1961. 8. D ~ z a o u i u , B. V., XUD VLAS~.N~rO,G. J., Doklady Akad. Nauk ~S.S.S.R. 63, 1155 (1948) ; Kolloid. Zhur. 15, 249 (1951) ; J. Colloid Sci. 17, 605 (196.2). 9. WA~.LON, A., ANDGRUUV=.mSZ~.CE,F. VAN,Bull. soc. chim. Belg'ea 63, 115 (1954). Oa'x,~wv.% Ft. H., AND WimuNs, D. I., J. Colloid Sci. 15, 512 (1960). 10. NzaPis, S. V., Doctor's Thesis. Itm'titute ingenerov vodnogo transporta, Lenin. grad, 1955. 11. DZRZAOUIN,B. V., .CUDTITI]C'~VaXAYA,A. S., Kolloid. Zhur. 15,417 (1953); ibid. 22, 398 (1960); Discussions Faraday Soc. No. 18, 32 (1954). 12. Sm~LUDKO,A. D., Koninkl. Ned.Akad. Wetenschap. Proc.,.Ser. B., 65, N1 (1962). 13. D~JAOU~N, B. V., Doklady AN.S.S.S.R. ~9, 11 (1943) ;Acta Phy,icochim. U.R.S.S. 20,349 (1945) ; J Expt. Th, orst. Phys. (U.S.S.R.) 15, 9 (1945). See also LANDAU, L. D., AND L~.VlCH, V. G., Acla Physicochirn. U.R.S.S. 17, 42 (1942). 14. DzazAouxN, B. V., AND T~TXT~.VSX4YA,A. S., Doklady AN. S.S.S.R. 50, 307 (1945). See also D~.aJxou~u, B. V., AND L~.vI, S: M., "Physicochim. teoriia nanesenija tonkich sloev na gibkie podlojki." Ed. by Akad. Nauk S.S:S.R., M. 1957.

Selected Works - 2

15. MYSELS, K., SHINODA, I~., AND FRANKEL, S., "Soap Films," Sect. 5. Pergamon Press,, London, 1959. 16. DZnJAOUZN, B. V., ANXX Lzvx, S. M., "Physicochimitchukaya teorija nanesenija tonkich sloev na gibkie podlojkii" Ed. by Akad. of Sciences S.S.S.R., M. 19,57. 17. Dm~JAOUzN, B. V., AND "IhTXrr.VSXATA, A. S., Kolb~id. Zhur. RR, 398 (1960). 18. Ov~aBzzx, J. TH., J'. Phys. Chem. 84, 1178 (1960). 19. vAw DEN TEMPEL, J. Colloid Sc~. 13, 125 (1958). 20. SmBLWXO, A., Kol~id-Z. 155, 39 (1957); Doklady Akad. Nauk 3.3.8.R. 123, 1074 (1958). 21. DznJAouzN, B. V., ASD TXTIXZVSXAYA, A., Prec. lend Intern. Co,~'. 8urfacz Activily, Vol. i, p. 211 (1957). 22. SHZLUDKO, A., ASD EXZaOVA, D., Dokladl/Akad. Nauk ~q.S.S.R. 127, 149 (19,59); Kolloid-Z. 115, 148 (1959). 23. SHELUDKO,A., AND EXEROVA, D., Kolloid-Z. 188, 24 (1960). 24. SHELUDKO,A., AND EXEROVA,D., Annuaire univ. Sofia, Fac. sci. math~naticue~ et phl/siCues, 54, 205 (1959/1960); Doklady Bolgar. AI~ad. Nauk. 9 [No. 1] (1956) 25. Fuxs, G. I., Paper iv symposium "Issledovanija v oblMti poverchnostn, siP' str. 99, Ed. by Acad. pf Sciences, S.S.S.R.M. 1961. 26. DZR#AOVZN,B. V., Kolloid-Z. 69, 155 (1934). 27. HARDY, W., Prec. Roy. ~oc. (London) A108, 1 (192,5). 28. VOROPA~VA, T. N., DERJAOUIN, B. V., ANn KABANOV, B. N., Doklady Akad. Nauk S.S.S.R. 128, 981 (1959); Kolloid. Zhur. 24, 396 (1962). 29. FRUKXZN, A. N., SCHLY~OZN,'A., AND MEDVZDOVBKI, V., [zvest. Ak.ad. Nau]c S.S.S.R., set. chim., 5, 773 (1936).' GoRoDZ~HXAYA, A. V., AND KARANOV,B. N., Z. Phys. Chem. 4, 529'(1933). BA~ASC~OVA,N. A., Doklady Ak.ad. Nau]~ ~q.~.~.R. 103, 639 (19~). BALASC~OV~,N. A., AND FRtrMxxN, A. N., Doidadlt Akad. Naulc S.S.S.R. 20, 449 (1938). 30. PF0~rZ~.N~U~a, A., AND MASIN0, G., Mstsllkunde 42, 361 (1951). 31. D~zJAOuzN, B. V., ANDLANDAU,L., Acts Physicochim. U.R.8.8. 14, 633 (1941). 32. V~aw~T, E. J., ASD OV~RSZZX,J. Tin, "Theory of The Stability of Lyophobio Colloids." Elsevier, Amsterdam, 1948.

105