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Recent work on surface activity, wetting and dewetting
J O U R N A L OF COLLOID S C I E N C E
11, 623-636 (1956)
RECENT WORK ON SURFACE ACTIVITY, WETTING AND DEWETTING Jean Guastalla Laboratoire de Chimie Physique, Faeult~ des Sciences, Paris Received April 5, 1956
SURFACE ACTIVITY a. Theoretical
Let 7 be the work necessary to increase isothermally and reversibly the free surface area of a pure liquid (i. e., the surface tension). The liquid is placed in a trough. Let us imagine that one of its edges can be displaced; the work necessary to move horizontally this edge of length L over a distance dl in order to increase isothermally and reversibly the free surface area of the liquid an amount d S = L dl, is equal to 7 d S = 7 L dl. This work is done by a mechanical force f which moves the point at which it is applied over a distance d l ; a t equilibrium, f d l = 7 L dl, or 7 = f / L . The pure liquid is then replaced by a very dilute solution of a surfaceactive substance; the work 7ins, which the experimenter would have to do if no adsorption ocurred, is in fact smaller since the experimenter recovers, while working to increase the area of the surface, the adsorption work on the newly created surface, this work being W~as per cm.2 (provided he works isothermally and reversibly). Therefore, the work which the experimenter must supply (per cm. 2) is 7solu, = 7inst - W~d~.The instantaneous tension 7ins~ is practically identical with the surface tension 70 of the pure solvent if the solution is very dilute; the adsorption work W~d~is then represented by the lowering of the surface tension or surface pressure p: 1 7solut
=
70
--
p.
Experimentally, the trough with a movable edge cannot be used for measuring the surface tension 7 because of friction and hydrostatic effects; but the wettable plate method (Wilhelmy, Lord Rayleigh) is an equivalent procedure which is very convenient and direct. A rectangular plate is immersed in a liquid which wets it perfectly and is then partially withdrawn in such a way as to outreach the tangential 1This kind of approach will be particularly useful as applied to wetting, discussed later (1, 2). 623
624
JEAN
GUASTALLA
position of the meniscus; if we then lift the plate a distance dh, the area of the liquid film wetting the plate will be increased by d S = ~ dh ( ~ = the perimeter of the plate), by doing work ~ dh against the surface tension ~. The work is supplied by a mechanical force f which displaces the point where it is applied vertically a distance dh; at equilibrium ~,~ dh = f dh, "y ~-- f / / w ' .
To measure ~, we use a direct-reading balance with an horizontal torsion wire; the movable equipment comprises a galvanometer mirror (R --- 200 cm.) and a rod 2 cm. long, positioned nearly horizontally during measurements, at the end of which the wettable plate is suspended by a silk thread. Displacements of a spot are observed on a scale. The buoyancy on the plate cannot be neglected. It is convenient to include its variations in the calibration of the apparatus (3, 4); the calibration is carried out by means of riders, while the wettable plate suspended from the balance is partially immersed in a liquid having a stable surface tension and the same density as the experimental solution. Then, after the spot is brought to the zero position, the surface of the solution is slowly brought into contact with the lower edge of the plate. As soon as contact is established the plate will be slightly immersed. The surface tension may then be directly calculated from the deviation of the spot along the scale. The plates used are made of rough platinum or rough mica. The accuracy of the measurements may be better than 0.1 dyne/cm. We have also frequently used the Dognon and Abribat tensiometer, where a wettable rough platinum plate is suspended from an electromagnetic balance (5). b. Determination of the Traube Coefficient
The Traube rule states that in an homologous series of surface:active substances there is a constant ratio between the molar concentrations of two consecutive homologs giving rise to the same very small surface tension lowering in aqueous solutions. This law is true only in the limiting case, i. e., at extreme dilutions where adsorption films are supposed to be in the state of a tw0-dimensional ideal gas. According to Langmuir (6) the statistical adsorption equilibrium at great dilutions can be expressed as follows: Alcmoioo = A2~ exp ( - Wo/lcT),
where ~ is the surface density or the number of adsorbed molecules per cm.2, Cmo~o¢the molecular concentration, W0 the immersion work of the hydrocarbon chain, /c the Boltzmann's constant, T the absolute temperature; A1 and A2 are both constants which are available for a given series. If we compare two terms, respectively C~ and C~+1 in an homologous series, it follows that: (~/Cmolo¢)n+1 = (~/Cmolo¢)~" exp (AWo/]cT),
SURFACE ACTIVITY, ~VETTING AND DEWETTING
625
&W0 being the increase in immersion work of the hydrocarbon chain when the chain increases by one CH2 group; n represents the number of carbons in the molecule. The term exp ( A W o / k T ) is called the Traube. coefficient (C,). On a perfect gaseous film, 47 = p = kT~;
~ Cmolec
_
1
p
;
]~T Creolee
therefore the limit of the ratio ~/Cmolo~ at extreme dilutions is obtained by dividing the slope of the tangent at the origin of the adsorption curve by kT (p is plotted against Cmole¢)L. Guastalla has determined the Traube coefficient for the series of saturated acids and for the series of saturated alcohols (at around 22-23°C.) over a chain length range as wide as possible (n between 2 and 12, this range being limited by the insolubility of the higher homologs) (7, 8). The fatty acids were dissolved in 0.01 M hydrochloric acid, since it was necessary to avoid dissociation. A dissociated molecule is much less surface-active than a nondissociated molecule. We know (according to G. Langlois (9)) that if a fatty acid is partially dissociated in solution, it seems that the adsorption layer is in equilibrium only with the undissociated molecules; for instance, if laurie acid is dissolved in 0.00002 M hydrochloric acid, whose pit is close to the pKd of the fatty acid, the adsorption curve p - c is identical to the one obtained by increasing the abscissa of the laurie acid adsorption curve (0.01 M HC1) by a factor of 2. The alcohols were dissolved in pure water, the results being substantially the same with alcohols dissolved in 0.01 M hydrochloric acid. For each of the substances studied an adsorption curve p - c (c = molar concentration) was obtained and the tangent at the origin of the curve was drawn (see, for example, Figs. 1 and 2). The measurements are difficult with the higher members; for example, the pressure of the laurie acid adsorption film i n the gaseous state does not go beyond 0.4 dyne/cm. After O/c)lim has been calculated for each substance of the series, the logarithms of (~/c)~i~ are plotted against n (n = number of carbon atoms in a molecule). If the Traube coefficient is constant it should be possible to draw a straight line through the points. The results for a certain number of acids and alcohols are shown in Fig. 3. The following conclusions may be drawn from the figure. The Traube coefficient is constant over the whole range studied for both acids and alcohols. Its value is the same for the acids and for the alcohols. This value is approximately 2.65, which is rather smaller than the one generally accepted; the immersion work per Ctt~ group (AW0) is about 390 X 10-16 erg. The same conclusions would have been reached if the straight lines corresponding to the acids and alcohols were only parallel; but they are in
626
JEiN
GUASTALLA
dynes/c m
P 20
0
10
C ,mel e/~'I I
0'. 25
0.5 FIG. 1
i dyneS~cm
p
20
10.
C m ole/i 4x10 -5
2 FzG. 2
fact identical, which can be interpreted by assuming that the average length of the chain above the water surface is the same for an acid as for an alcohol having the same number of carbon atoms. Other experiments concerning the Traube rule have been performed with more concentrated solutions, giving real adsorption films (8). The relationship which expresses adsorption equilibrium takes the following form:
Alcmol~= A 2 ~ e x p [
(W°~TW~)]
where, according to J. Guastalla (10), the expulsion energy is
W. = fo !a~ ,; dp,
SURFACE ACTIVITY, WETTING AND DEWETTING
2o!
627
m
19 18 17 16 1.'5, 14
Fie. 3 II 2O 19 16 17
y;/
16 15 number of carbon atoms
14 2
4
6
8
10
12
FIG. 4
(1/6 = z, the molecular area; p~ = p - k T ~ ) . The term W~ is always positive for short-length acids and alcohols; it can be negative over a certain concentration range for long-chain members. For different terms of a homologous series, a comparison is made for the ratios 8/c established for a given value ~ (for example, ~ = (1/40)A. -2) (we then use the isotherms p-¢ calculated from the Gibbs equation). It is possible to determine nearly correctly a Traube coefficient C'T(8) for a given value of 6; this coefficient is higher than the actual Traube coefficient determined at extreme dilutions. The logarithms of ~/c corresponding to ~ = (1/40)A. -2 plotted against n are represented in Fig. 4. A straight
628
JEAN
GUASTALL&
line can be, well enough, drawn through the points; this line cuts the one plotted with the ~/c values extrapolated for extreme dilutions. II. W~TTING a. Theoretical (11, 1, 2)
A very thin rectangular plate made of Plexiglas is suspended from a torsion balance with an horizontal wire. The plate is completely immersed in pure water (which wets it imperfectly). It is then withdrawn vertically and very slowly, while the vertical force to which the plate is subieeted, is measured continuously. First there is a meniscus formed which leans on the upper edge of the plate (as if it were wettable) ; but tangential contact is never obtained. At a certain moment the solid plate frees itself of the liquid and seems to be dry; henceforth the meniscus does not alter in shape and forms a constant angle with the solid. The graph of force vs. height of the plate (after correction for buoyancy) is represented in Fig. 5. The ascending branch of the curve represents the deformation of the meniscus, the plateau corresponding to the constant force measured from the moment at which the plate emerges dry from the meniscus of constant shape. From this moment on, the experimenter does not work any more against surface tension or hydrostatic forces; the work supplied by him is used only for the plate dewetting. Let r be the work of dewetting per cm. 2 (isothermal and reversible). The work of dewetting of the plate over a height dh is r d S = T ~ dh (~being the perimeter of the plate) ; if the mechanical compensation work is f ' dh (force f'), it follows that r ~ dh = f ' dh,
~ = f'/~.
With Plexiglas and pure water, r is positive. With a paraffin-coated plate and pure water, r is negative; it is necessary to supply work to immerse vertically a paraffin-coated plate in pure water. A graph like the one of Fig. 6 is obtained when the vertical force is plotted against the depth of immersion of the lower edge of the plate. Hysteresis. Wetting and dewetting an imperfectly wettable solid cannot
eghdepthdeph \
Fro. 5
FIG. 6
Fro. 7
SURFACE
ACTIVITY~ WETTING
AND
DEWETTING
620
be performed in a strictly reversible manner. If the paraffin-coated plate is partially immersed in pure water and then withdrawn, an hysteresis cycle is obtained on the graph representing the forces (Fig. 7). The area of the cycle represents the work lost. From the two "plateaux" of the forces (immersion and emersion) it is possible to calculate the adhesion tension of immersion r~ (wetting work with opposite sign) and the adhesion tension of emersion r~ (dewetting work). The hysteresis of wetting is well known; it can arise from several causes (roughness of the solid surface, delays either in adsorption or desorption of solute or v a p o r . . . ) . In the case of paraffin and water, the hysteresis is due mainly to the roughness of the paraffin-coated surface. The hysteresis can be greatly decreased by polishing the surface by means of reheating in an oven (12). Wetting by a Solution of an Adsorbable Substance at the Solid-Solution Interface. Let us assume for a moment that there is no hysteresis. The experimenter who would then immerse a paraffin-coated plate in a dilute solution of a substance able to adsorb itself at the paraffin-solution interface would work, if no adsorption occurred, to wet the paraffin surface with a liquid whose properties would be very close to those of pure water (work of wetting~r0). But adsorption takes place, and if the experimenter works reversibly, he recovers the adsorption work at the liquid-solid interface of the solute (W~s per cm.2) when he immerses the plate; he must therefore supply altogether, per cmf, -r~ol~ = - r 0 - W~a~ (he will supply work + r,ol.t when withdrawing the plate if the adsorbed molecules go back into solution). The work W~d, is analogous to a surface pressure, and we shall represent this quantity by p~ (13). It then follows that --Tsolut
~
--T0
--
Pi
~
Tsolut --
pi
;
TO-
If r0 is negative (as, for instance, in the case of the system water-paraffin), it may happen that pc = Wads is greater than (-r0); the work supplied by the experimenter when wetting the plate is therefore reduced to such an extent that the sign is changed; in this case the experimenter obtains positive work when wetting the plate. Harkins and his co-workers (14) have calculated p~, in a certain number of cases, from indirect measurements (determination of the contact angle) ; p~ can be determined much more easily by comparing the force vs. depth graphs established with pure water and with the solution, respectively (Fig. 8). Hysteresis brings in a difficulty. If hysteresis is considerable in the case of pure water, it will be decreased by the presence of the wetting agent. But if the hysteresis is small with pure water (very smooth plates), it will
630
~E~N GU~ST~LLA
be only slightly reduced by the wetting agent, and the values of Pi(o and p~(~) obtained by comparing the immersion and emersion plateaux are nearly identical. Contact Angles. Formerly, the characteristics of wetting were frequently determined by measuring contact angles, these measurements being difficult to carry out. The angles of advance and withdrawal (~a and 0,) are related to 7 and to the two values of T by the relationship r -- 7 cos ~, which is well known and easy to derive from energy considerations. The direct measurement of r by means of the plate is much more convenient than the measurement of 0; moreover, 0 is generally of not much importance. The contact angle is to be considered only as an effect, being the result of 7 competing with T.2 Regarding phenomena like the rise of a liquid in a capillary tube or its penetration in imperfectly wettable pores, the only interesting quantity would be T; for instance, when rising to a height, h, in an imperfectly wettable capillary tube of radius, r, the liquid
\
Fro. 8
stops when the work against the hydrostatic forces, pgh~r2 dh, is equal to the work obtained from the wetting action, 2~rr dh, wherefore h = 2r/pgr, where p is the specific mass of the liquid and g is the acceleration due to gravity.
b. Apparatus and Technique (16, 2) The apparatus which we use for studying wetting (wetting tensiometer, Figs. 9 and 10) permits the simultaneous measurement of surface tension and adhesion tension (the simultaneousness of both measurements being necessary when equilibrium is not instantaneous). The apparatus comprises two torsion balances with horizontal wires which can be displaced a few centimeters, upwards or downwards, independent of each other, in two parallel planes very close to one another. The trough which contains the liquid is fixed. The wettable plate is suspended from one of the balances and the imperfectly wettable plate from the other one. The torsion balance The author would not be in agreement with Harkins on this point (15).
SURFACE ACTIVITY, WETTING AND DEWETTING
631
VI/MIIIIIIIIIIII/MMIIII//I/I///IM///I]/I/IIIIIM/I//I/M///I////I//MI//MI/I//I
M
~-~"~
M4 r
~
H///III/I////J
I
M
2
rllll/ll/lll//l
FIG. 9
..... U ...............
i ......
-7 :FIG. 10 FIGS. 9. and 10. M--vertical mirrors; B--torsion balances; L--lenses; E--scale; /--index; P--light source; C--trough; H--heating. I--
includes small plane mirrors. Light arrives at each of these mirrors in parallel beams after having passed through a convergent lens of long focal length (200 cm.), the light source and a big graduated scale being situated in the focal plane of the lens. The dimensions of the apparatus are reduced because of several reflections on vertical mirrors. In this manner two spots are obtained on a single fixed scale; the position of each spot gives only the torsion angle of the corresponding balance and is not modified by the vertical displacements of the balance if the torsion angle remains constant. Qualitative Experiment. Both the spots are brought to zero (center of the
JEAN GUASTALLA
632
scale). The wettable plate is brought into contact with the surface of pure water; when contact is established, one of the spots rises. Then the second (paraffin-coated) plate is immersed in the water; the plate is pushed upwards and the second spot goes down (T < 0). When a small quantity of a surface-active compound is dissolved in the water, by introducing it on the tip of a rod, the first spot goes down but remains above zero (-y decreases) ; the second spot will then go up and will stabilize above zero (r increases and becomes positive). Wetting Curve; Corrections. Figure 11 represents actual wetting curves (A, paraffin-water; B, paraffin-solution of surfactant); the vertical forces acting on the plate are shown as a function of the displacement downwards of the balance, counted from the contact of the base of the plate with the surface of the liquid. On these rough graphs, the plateaux of the adhesion tension are slightly inclined (buoyancy). In order to correct for this effect in the calculation of the adhesion tension, the two inclined straight lines are extrapolated to the ordinates. If a rigorous treatment is desired, the change of the torsion angle during the experiment should be taken into account; the depth of the lower edge of the plate is a little different from the displacement of the balance-body, counted from the contact of the plate with the liquid. In order to correct for the differences (proportional to the displacements of the spot), a slightly inclined axis instead of the vertical ordinate is taken, the slope of which can be easily determined (broken line, Fig. 11). inclined axis
(dynes) I
ii
+10C
Te: 12,5 ,~ :
//..solution of su,-ractanl" i ~ B . . /.displace r e.n' Of !he
'
Cdyn~sA~o
ba,anoe-
body Cram)
5
~.pure
water
....
'e:-28,S
/
(dynes~m)
I
I I
Polished paraffin-waxed =4,05 cm FIG. II
pla[e
SURFACE ACTIVITY~ WETTING AND DEWETTING c.
6~
Examples of Results Obtained
1. Curves p-c and p~-c; Establishing of a Traube Rule. The wetting of paraffin by solutions of various acids and saturated alcohols has been studied by L. Guastalla at the same time as the surface tension of the same solutions. For the first homologs, the curves p~-c differ rather little from the curves p-c; the differences become more important when the length of the chain increases. Figure 12 shows the curves p~-c and p-c for laurie acid (C12). The ratio of the slopes of the tangents at the origin for both curves is about 20. L. Guastalla has tried to define a kind of Traube coei~icient from the slopes of the tangents to the curves p~-c at the origin, for an homologous series. This coefficient is not constant. For the first members of each series, the coefficient is greater than the one for the free liquid surfaces (for instance, 3.8 for the first acids instead of 2.65). It will tend towards 2.65 for the long-chain members (17). 2. Curves "y-log c and .r-log c for an Industrial Product. It is convenient to plot % ~e, and ~ versus the logarithm of the concentration. The graph (example Fig. 13) indicates the C.M.C. The more the adhesion tension approaches the surface tension, the more efficient is the wetting agent. When the wetting is perfect, the adhesion tension curves rejoin the surface tension curve; this phenomenon is rather exceptional when the solid to be wetted is paraffin. d. Dynamic Wetting
In industry, dynamical wetting has to be considered frequently. The resuits obtained by static measurements are applicable only if the phenomenon is practically reversible.
C]2 ocid ----~ C
FIG. 12
634
JEAN GUA_STtkLLA
dyneS~cm
~75 .
C
50 25 j.
'log c
°25 paraffln
wax
FIG. 13
Rosano (18, 19) has studied the rate of penetration of water and various solutions into small tubes which are paraffin-coated on the inside and into tubes of polyvinyl chloride, under different hydrostatic pressures. For pure liquids and for certain micellar wetting solutions, the progression (or retreat) follows correctly Washburn's law for displacements in wettable tubes, provided 7 is replaced by Te (progression) or by r~ (retreat). For nonmicellar wetting solutions, the rate of progression is generally decreased, since the meniscus zone leaves molecules on the walls of the tube and since the supply of molecules from the solution is not instantaneous (dynamic loss). I n case a network of very small micropores (tissue, porous material) has to be wetted, a definite loss may moreover take place (stop of progression) owing to the great adsorbing surface. In order to study directly the penetration of a wetting solution in a porous material, a rectangular sample of the material may be suspended from a torsion balance, and the increase in weight of the sample may be followed as a function of time, after its lower edge is put in contact with the surface of the liquid. It is necessary to separate from the measured force the effect of the surface tension on the periphery of the sample (test devised by Rosano, Le Peintre and Baudier). III. DEWETTING A wetting agent for paraffin does not necessarily wet any other solid. For instance, the cationic surfactants, which are excellent wetting agents for paraffin, dewet glass or quartz within certain concentration limits. This phenomenon was studied by L. T~n~bre by means of the wetting tensiometer (20, 21). A mica plate having a rough surface was suspended from one of the balances in order to measure the surface tension and a glass plate (micro-
SURFACE ACTIVITY, WETTING AND DEWETTING
635
dyneS~crn so rs
25
°i - 251
log
c
rs
re
(paroffin w~x? FI~. 14
scope cover glass) from the other balance. The wet glass plate is first immersed in the liquid (thermodynamically irreversible dewetting is then observed), and the apparent adhesion tension for glass-solution is measured from an emersion followed by another immersion. As an example, Fig. 14 shows % re, and 7~ paraffin-solution, T~r,,p) and r~(~p,) glass-solution, as a function of the logarithm of the concentrations for solution of lauryl-trimethyl-ammonium bromide. The slope of the rap, curves (glass-solution) has the same sign as the one of the curve of 7, i. e., opposite to the one of the slope for the curve r paraffin-solution. The application of the Gibbs equation (as well as common sense) led to the idea that a film is fixed on the glass plate when it is withdrawn from the solution, the plate being apparently dry, and that this film is restored to the suface of the solution when the glass plate is again immersed. This withdrawal of a film is confirmed by the fact that in the case of nonmicellar solutions of cationic long-chain substances the surface tension increases temporarily while the glass plate is withdrawn and decreases temporarily while it is again immersed. (Tgn~bre has succeeded in determining the rate at which material is deposited on the glass plate.) It is here a question of an additional adsorption, since the glass fixes already a certain number of surfactant molecules when it is immersed in the solution (this fact being confirmed by the rise in the surface tension of the solution after it has been stirred in the presence of glass wool). But, contrary to what may be expected, this additional adsorption is not due to the deposition of a second layer of molecules of surfactant, paraffin ends to paraffin ends, on a first layer already deposited in the bulk of the solution. This additional adsorption would indeed look Iilce an adsorption on the para~n (positive slope for the curve r-log c). But the data rather lead to the assumption that the
636
JEA~
@UASTALLA
polar ends of the molecules of surfaetant are fixed on the glass, during emersion, at the free places between the molecules already adsorbed, in the form of a rather loose network in the bulk of the solution. This method may permit elucidation of the mechanism which lies at the basis of flotation phenomenon. I~EFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
GUASTALLA,J., J. cMm. phys. 49, 250 (1952). GUASTALLA,J., Dr. chim. phys. 51,287 (1954). DERVICl~IAN,D. G., Dr. phys. radium 6, 221 (1935). HA.RKINS,W. D., AND ANDERSON,T. F., Or. Am. Chem. Soe. 59, 2189 (1937). ABmDA.T,M., A.NDDOGNON,A., J. phys. radium 10, 22 S (1939). LA.NGMUIR,I., Dr. Am. Chem. Soe. 39, 1848 (1917). GIIASTALLA.,L., A'NDGUA.STA.IJLA',5., M~m. services ehim. ~tat (Paris) 38, 99 (1953). GUA.srA.LLA.,L., A.NDGUA.S~A.LLA,J., Compt. rend. 240, 425 (1955). LA.NGLOIS,G., M$m. services chim. $tat (Paris) 40, 83 (1955). GTJA.STA.LLA.,J., Compt. rend. 228, 820 (1949). GUA.STA.LLA.,J., A.NDGUA.STA.LLA.,L., Compt. rend. 29.6, 2054 (1948). G~A.STALLAA,L., Compt. rend. 230,824 (1950). G~A.STA.LLA.,J., G~A.STA.LLA.,L., LUzzA.TI,D., ROSA.No, H. L., A.~D SA.aA.GA,L., Compt. rend. 231,220 (1950). FOWKES,F. M., A.NDI{A.RKINS,W. D., Dr. Am. Chem. Soe. 62, 3377 (1940). HA.P:KINS,W. D., A.NDLOESER,E. It., J. Chem. Phys. 18, 556 (1950). GUA.STA.LLA.,J., J. chim. phys. 51, 583 (1954). GuA.STA.~LA.,L., Thesis, unpublished. RosA.No, l=I. L., M~m. services ehim. ~tat (Paris) 36, 309, 437 (1951). RosA.NO, H. L., AANDGVA.S~A.LL~.,J., Compt. rend. 9.30, 628 (1950~ T~N~RE, L., M$m. services ehim. Ztat (Paris) 40, 77 (1955). T ~ N ~ R ~ , L., J. chim. phys. 53, 6 (1956).
11, 623-636 (1956)
RECENT WORK ON SURFACE ACTIVITY, WETTING AND DEWETTING Jean Guastalla Laboratoire de Chimie Physique, Faeult~ des Sciences, Paris Received April 5, 1956
SURFACE ACTIVITY a. Theoretical
Let 7 be the work necessary to increase isothermally and reversibly the free surface area of a pure liquid (i. e., the surface tension). The liquid is placed in a trough. Let us imagine that one of its edges can be displaced; the work necessary to move horizontally this edge of length L over a distance dl in order to increase isothermally and reversibly the free surface area of the liquid an amount d S = L dl, is equal to 7 d S = 7 L dl. This work is done by a mechanical force f which moves the point at which it is applied over a distance d l ; a t equilibrium, f d l = 7 L dl, or 7 = f / L . The pure liquid is then replaced by a very dilute solution of a surfaceactive substance; the work 7ins, which the experimenter would have to do if no adsorption ocurred, is in fact smaller since the experimenter recovers, while working to increase the area of the surface, the adsorption work on the newly created surface, this work being W~as per cm.2 (provided he works isothermally and reversibly). Therefore, the work which the experimenter must supply (per cm. 2) is 7solu, = 7inst - W~d~.The instantaneous tension 7ins~ is practically identical with the surface tension 70 of the pure solvent if the solution is very dilute; the adsorption work W~d~is then represented by the lowering of the surface tension or surface pressure p: 1 7solut
=
70
--
p.
Experimentally, the trough with a movable edge cannot be used for measuring the surface tension 7 because of friction and hydrostatic effects; but the wettable plate method (Wilhelmy, Lord Rayleigh) is an equivalent procedure which is very convenient and direct. A rectangular plate is immersed in a liquid which wets it perfectly and is then partially withdrawn in such a way as to outreach the tangential 1This kind of approach will be particularly useful as applied to wetting, discussed later (1, 2). 623
624
JEAN
GUASTALLA
position of the meniscus; if we then lift the plate a distance dh, the area of the liquid film wetting the plate will be increased by d S = ~ dh ( ~ = the perimeter of the plate), by doing work ~ dh against the surface tension ~. The work is supplied by a mechanical force f which displaces the point where it is applied vertically a distance dh; at equilibrium ~,~ dh = f dh, "y ~-- f / / w ' .
To measure ~, we use a direct-reading balance with an horizontal torsion wire; the movable equipment comprises a galvanometer mirror (R --- 200 cm.) and a rod 2 cm. long, positioned nearly horizontally during measurements, at the end of which the wettable plate is suspended by a silk thread. Displacements of a spot are observed on a scale. The buoyancy on the plate cannot be neglected. It is convenient to include its variations in the calibration of the apparatus (3, 4); the calibration is carried out by means of riders, while the wettable plate suspended from the balance is partially immersed in a liquid having a stable surface tension and the same density as the experimental solution. Then, after the spot is brought to the zero position, the surface of the solution is slowly brought into contact with the lower edge of the plate. As soon as contact is established the plate will be slightly immersed. The surface tension may then be directly calculated from the deviation of the spot along the scale. The plates used are made of rough platinum or rough mica. The accuracy of the measurements may be better than 0.1 dyne/cm. We have also frequently used the Dognon and Abribat tensiometer, where a wettable rough platinum plate is suspended from an electromagnetic balance (5). b. Determination of the Traube Coefficient
The Traube rule states that in an homologous series of surface:active substances there is a constant ratio between the molar concentrations of two consecutive homologs giving rise to the same very small surface tension lowering in aqueous solutions. This law is true only in the limiting case, i. e., at extreme dilutions where adsorption films are supposed to be in the state of a tw0-dimensional ideal gas. According to Langmuir (6) the statistical adsorption equilibrium at great dilutions can be expressed as follows: Alcmoioo = A2~ exp ( - Wo/lcT),
where ~ is the surface density or the number of adsorbed molecules per cm.2, Cmo~o¢the molecular concentration, W0 the immersion work of the hydrocarbon chain, /c the Boltzmann's constant, T the absolute temperature; A1 and A2 are both constants which are available for a given series. If we compare two terms, respectively C~ and C~+1 in an homologous series, it follows that: (~/Cmolo¢)n+1 = (~/Cmolo¢)~" exp (AWo/]cT),
SURFACE ACTIVITY, ~VETTING AND DEWETTING
625
&W0 being the increase in immersion work of the hydrocarbon chain when the chain increases by one CH2 group; n represents the number of carbons in the molecule. The term exp ( A W o / k T ) is called the Traube. coefficient (C,). On a perfect gaseous film, 47 = p = kT~;
~ Cmolec
_
1
p
;
]~T Creolee
therefore the limit of the ratio ~/Cmolo~ at extreme dilutions is obtained by dividing the slope of the tangent at the origin of the adsorption curve by kT (p is plotted against Cmole¢)L. Guastalla has determined the Traube coefficient for the series of saturated acids and for the series of saturated alcohols (at around 22-23°C.) over a chain length range as wide as possible (n between 2 and 12, this range being limited by the insolubility of the higher homologs) (7, 8). The fatty acids were dissolved in 0.01 M hydrochloric acid, since it was necessary to avoid dissociation. A dissociated molecule is much less surface-active than a nondissociated molecule. We know (according to G. Langlois (9)) that if a fatty acid is partially dissociated in solution, it seems that the adsorption layer is in equilibrium only with the undissociated molecules; for instance, if laurie acid is dissolved in 0.00002 M hydrochloric acid, whose pit is close to the pKd of the fatty acid, the adsorption curve p - c is identical to the one obtained by increasing the abscissa of the laurie acid adsorption curve (0.01 M HC1) by a factor of 2. The alcohols were dissolved in pure water, the results being substantially the same with alcohols dissolved in 0.01 M hydrochloric acid. For each of the substances studied an adsorption curve p - c (c = molar concentration) was obtained and the tangent at the origin of the curve was drawn (see, for example, Figs. 1 and 2). The measurements are difficult with the higher members; for example, the pressure of the laurie acid adsorption film i n the gaseous state does not go beyond 0.4 dyne/cm. After O/c)lim has been calculated for each substance of the series, the logarithms of (~/c)~i~ are plotted against n (n = number of carbon atoms in a molecule). If the Traube coefficient is constant it should be possible to draw a straight line through the points. The results for a certain number of acids and alcohols are shown in Fig. 3. The following conclusions may be drawn from the figure. The Traube coefficient is constant over the whole range studied for both acids and alcohols. Its value is the same for the acids and for the alcohols. This value is approximately 2.65, which is rather smaller than the one generally accepted; the immersion work per Ctt~ group (AW0) is about 390 X 10-16 erg. The same conclusions would have been reached if the straight lines corresponding to the acids and alcohols were only parallel; but they are in
626
JEiN
GUASTALLA
dynes/c m
P 20
0
10
C ,mel e/~'I I
0'. 25
0.5 FIG. 1
i dyneS~cm
p
20
10.
C m ole/i 4x10 -5
2 FzG. 2
fact identical, which can be interpreted by assuming that the average length of the chain above the water surface is the same for an acid as for an alcohol having the same number of carbon atoms. Other experiments concerning the Traube rule have been performed with more concentrated solutions, giving real adsorption films (8). The relationship which expresses adsorption equilibrium takes the following form:
Alcmol~= A 2 ~ e x p [
(W°~TW~)]
where, according to J. Guastalla (10), the expulsion energy is
W. = fo !a~ ,; dp,
SURFACE ACTIVITY, WETTING AND DEWETTING
2o!
627
m
19 18 17 16 1.'5, 14
Fie. 3 II 2O 19 16 17
y;/
16 15 number of carbon atoms
14 2
4
6
8
10
12
FIG. 4
(1/6 = z, the molecular area; p~ = p - k T ~ ) . The term W~ is always positive for short-length acids and alcohols; it can be negative over a certain concentration range for long-chain members. For different terms of a homologous series, a comparison is made for the ratios 8/c established for a given value ~ (for example, ~ = (1/40)A. -2) (we then use the isotherms p-¢ calculated from the Gibbs equation). It is possible to determine nearly correctly a Traube coefficient C'T(8) for a given value of 6; this coefficient is higher than the actual Traube coefficient determined at extreme dilutions. The logarithms of ~/c corresponding to ~ = (1/40)A. -2 plotted against n are represented in Fig. 4. A straight
628
JEAN
GUASTALL&
line can be, well enough, drawn through the points; this line cuts the one plotted with the ~/c values extrapolated for extreme dilutions. II. W~TTING a. Theoretical (11, 1, 2)
A very thin rectangular plate made of Plexiglas is suspended from a torsion balance with an horizontal wire. The plate is completely immersed in pure water (which wets it imperfectly). It is then withdrawn vertically and very slowly, while the vertical force to which the plate is subieeted, is measured continuously. First there is a meniscus formed which leans on the upper edge of the plate (as if it were wettable) ; but tangential contact is never obtained. At a certain moment the solid plate frees itself of the liquid and seems to be dry; henceforth the meniscus does not alter in shape and forms a constant angle with the solid. The graph of force vs. height of the plate (after correction for buoyancy) is represented in Fig. 5. The ascending branch of the curve represents the deformation of the meniscus, the plateau corresponding to the constant force measured from the moment at which the plate emerges dry from the meniscus of constant shape. From this moment on, the experimenter does not work any more against surface tension or hydrostatic forces; the work supplied by him is used only for the plate dewetting. Let r be the work of dewetting per cm. 2 (isothermal and reversible). The work of dewetting of the plate over a height dh is r d S = T ~ dh (~being the perimeter of the plate) ; if the mechanical compensation work is f ' dh (force f'), it follows that r ~ dh = f ' dh,
~ = f'/~.
With Plexiglas and pure water, r is positive. With a paraffin-coated plate and pure water, r is negative; it is necessary to supply work to immerse vertically a paraffin-coated plate in pure water. A graph like the one of Fig. 6 is obtained when the vertical force is plotted against the depth of immersion of the lower edge of the plate. Hysteresis. Wetting and dewetting an imperfectly wettable solid cannot
eghdepthdeph \
Fro. 5
FIG. 6
Fro. 7
SURFACE
ACTIVITY~ WETTING
AND
DEWETTING
620
be performed in a strictly reversible manner. If the paraffin-coated plate is partially immersed in pure water and then withdrawn, an hysteresis cycle is obtained on the graph representing the forces (Fig. 7). The area of the cycle represents the work lost. From the two "plateaux" of the forces (immersion and emersion) it is possible to calculate the adhesion tension of immersion r~ (wetting work with opposite sign) and the adhesion tension of emersion r~ (dewetting work). The hysteresis of wetting is well known; it can arise from several causes (roughness of the solid surface, delays either in adsorption or desorption of solute or v a p o r . . . ) . In the case of paraffin and water, the hysteresis is due mainly to the roughness of the paraffin-coated surface. The hysteresis can be greatly decreased by polishing the surface by means of reheating in an oven (12). Wetting by a Solution of an Adsorbable Substance at the Solid-Solution Interface. Let us assume for a moment that there is no hysteresis. The experimenter who would then immerse a paraffin-coated plate in a dilute solution of a substance able to adsorb itself at the paraffin-solution interface would work, if no adsorption occurred, to wet the paraffin surface with a liquid whose properties would be very close to those of pure water (work of wetting~r0). But adsorption takes place, and if the experimenter works reversibly, he recovers the adsorption work at the liquid-solid interface of the solute (W~s per cm.2) when he immerses the plate; he must therefore supply altogether, per cmf, -r~ol~ = - r 0 - W~a~ (he will supply work + r,ol.t when withdrawing the plate if the adsorbed molecules go back into solution). The work W~d, is analogous to a surface pressure, and we shall represent this quantity by p~ (13). It then follows that --Tsolut
~
--T0
--
Pi
~
Tsolut --
pi
;
TO-
If r0 is negative (as, for instance, in the case of the system water-paraffin), it may happen that pc = Wads is greater than (-r0); the work supplied by the experimenter when wetting the plate is therefore reduced to such an extent that the sign is changed; in this case the experimenter obtains positive work when wetting the plate. Harkins and his co-workers (14) have calculated p~, in a certain number of cases, from indirect measurements (determination of the contact angle) ; p~ can be determined much more easily by comparing the force vs. depth graphs established with pure water and with the solution, respectively (Fig. 8). Hysteresis brings in a difficulty. If hysteresis is considerable in the case of pure water, it will be decreased by the presence of the wetting agent. But if the hysteresis is small with pure water (very smooth plates), it will
630
~E~N GU~ST~LLA
be only slightly reduced by the wetting agent, and the values of Pi(o and p~(~) obtained by comparing the immersion and emersion plateaux are nearly identical. Contact Angles. Formerly, the characteristics of wetting were frequently determined by measuring contact angles, these measurements being difficult to carry out. The angles of advance and withdrawal (~a and 0,) are related to 7 and to the two values of T by the relationship r -- 7 cos ~, which is well known and easy to derive from energy considerations. The direct measurement of r by means of the plate is much more convenient than the measurement of 0; moreover, 0 is generally of not much importance. The contact angle is to be considered only as an effect, being the result of 7 competing with T.2 Regarding phenomena like the rise of a liquid in a capillary tube or its penetration in imperfectly wettable pores, the only interesting quantity would be T; for instance, when rising to a height, h, in an imperfectly wettable capillary tube of radius, r, the liquid
\
Fro. 8
stops when the work against the hydrostatic forces, pgh~r2 dh, is equal to the work obtained from the wetting action, 2~rr dh, wherefore h = 2r/pgr, where p is the specific mass of the liquid and g is the acceleration due to gravity.
b. Apparatus and Technique (16, 2) The apparatus which we use for studying wetting (wetting tensiometer, Figs. 9 and 10) permits the simultaneous measurement of surface tension and adhesion tension (the simultaneousness of both measurements being necessary when equilibrium is not instantaneous). The apparatus comprises two torsion balances with horizontal wires which can be displaced a few centimeters, upwards or downwards, independent of each other, in two parallel planes very close to one another. The trough which contains the liquid is fixed. The wettable plate is suspended from one of the balances and the imperfectly wettable plate from the other one. The torsion balance The author would not be in agreement with Harkins on this point (15).
SURFACE ACTIVITY, WETTING AND DEWETTING
631
VI/MIIIIIIIIIIII/MMIIII//I/I///IM///I]/I/IIIIIM/I//I/M///I////I//MI//MI/I//I
M
~-~"~
M4 r
~
H///III/I////J
I
M
2
rllll/ll/lll//l
FIG. 9
..... U ...............
i ......
-7 :FIG. 10 FIGS. 9. and 10. M--vertical mirrors; B--torsion balances; L--lenses; E--scale; /--index; P--light source; C--trough; H--heating. I--
includes small plane mirrors. Light arrives at each of these mirrors in parallel beams after having passed through a convergent lens of long focal length (200 cm.), the light source and a big graduated scale being situated in the focal plane of the lens. The dimensions of the apparatus are reduced because of several reflections on vertical mirrors. In this manner two spots are obtained on a single fixed scale; the position of each spot gives only the torsion angle of the corresponding balance and is not modified by the vertical displacements of the balance if the torsion angle remains constant. Qualitative Experiment. Both the spots are brought to zero (center of the
JEAN GUASTALLA
632
scale). The wettable plate is brought into contact with the surface of pure water; when contact is established, one of the spots rises. Then the second (paraffin-coated) plate is immersed in the water; the plate is pushed upwards and the second spot goes down (T < 0). When a small quantity of a surface-active compound is dissolved in the water, by introducing it on the tip of a rod, the first spot goes down but remains above zero (-y decreases) ; the second spot will then go up and will stabilize above zero (r increases and becomes positive). Wetting Curve; Corrections. Figure 11 represents actual wetting curves (A, paraffin-water; B, paraffin-solution of surfactant); the vertical forces acting on the plate are shown as a function of the displacement downwards of the balance, counted from the contact of the base of the plate with the surface of the liquid. On these rough graphs, the plateaux of the adhesion tension are slightly inclined (buoyancy). In order to correct for this effect in the calculation of the adhesion tension, the two inclined straight lines are extrapolated to the ordinates. If a rigorous treatment is desired, the change of the torsion angle during the experiment should be taken into account; the depth of the lower edge of the plate is a little different from the displacement of the balance-body, counted from the contact of the plate with the liquid. In order to correct for the differences (proportional to the displacements of the spot), a slightly inclined axis instead of the vertical ordinate is taken, the slope of which can be easily determined (broken line, Fig. 11). inclined axis
(dynes) I
ii
+10C
Te: 12,5 ,~ :
//..solution of su,-ractanl" i ~ B . . /.displace r e.n' Of !he
'
Cdyn~sA~o
ba,anoe-
body Cram)
5
~.pure
water
....
'e:-28,S
/
(dynes~m)
I
I I
Polished paraffin-waxed =4,05 cm FIG. II
pla[e
SURFACE ACTIVITY~ WETTING AND DEWETTING c.
6~
Examples of Results Obtained
1. Curves p-c and p~-c; Establishing of a Traube Rule. The wetting of paraffin by solutions of various acids and saturated alcohols has been studied by L. Guastalla at the same time as the surface tension of the same solutions. For the first homologs, the curves p~-c differ rather little from the curves p-c; the differences become more important when the length of the chain increases. Figure 12 shows the curves p~-c and p-c for laurie acid (C12). The ratio of the slopes of the tangents at the origin for both curves is about 20. L. Guastalla has tried to define a kind of Traube coei~icient from the slopes of the tangents to the curves p~-c at the origin, for an homologous series. This coefficient is not constant. For the first members of each series, the coefficient is greater than the one for the free liquid surfaces (for instance, 3.8 for the first acids instead of 2.65). It will tend towards 2.65 for the long-chain members (17). 2. Curves "y-log c and .r-log c for an Industrial Product. It is convenient to plot % ~e, and ~ versus the logarithm of the concentration. The graph (example Fig. 13) indicates the C.M.C. The more the adhesion tension approaches the surface tension, the more efficient is the wetting agent. When the wetting is perfect, the adhesion tension curves rejoin the surface tension curve; this phenomenon is rather exceptional when the solid to be wetted is paraffin. d. Dynamic Wetting
In industry, dynamical wetting has to be considered frequently. The resuits obtained by static measurements are applicable only if the phenomenon is practically reversible.
C]2 ocid ----~ C
FIG. 12
634
JEAN GUA_STtkLLA
dyneS~cm
~75 .
C
50 25 j.
'log c
°25 paraffln
wax
FIG. 13
Rosano (18, 19) has studied the rate of penetration of water and various solutions into small tubes which are paraffin-coated on the inside and into tubes of polyvinyl chloride, under different hydrostatic pressures. For pure liquids and for certain micellar wetting solutions, the progression (or retreat) follows correctly Washburn's law for displacements in wettable tubes, provided 7 is replaced by Te (progression) or by r~ (retreat). For nonmicellar wetting solutions, the rate of progression is generally decreased, since the meniscus zone leaves molecules on the walls of the tube and since the supply of molecules from the solution is not instantaneous (dynamic loss). I n case a network of very small micropores (tissue, porous material) has to be wetted, a definite loss may moreover take place (stop of progression) owing to the great adsorbing surface. In order to study directly the penetration of a wetting solution in a porous material, a rectangular sample of the material may be suspended from a torsion balance, and the increase in weight of the sample may be followed as a function of time, after its lower edge is put in contact with the surface of the liquid. It is necessary to separate from the measured force the effect of the surface tension on the periphery of the sample (test devised by Rosano, Le Peintre and Baudier). III. DEWETTING A wetting agent for paraffin does not necessarily wet any other solid. For instance, the cationic surfactants, which are excellent wetting agents for paraffin, dewet glass or quartz within certain concentration limits. This phenomenon was studied by L. T~n~bre by means of the wetting tensiometer (20, 21). A mica plate having a rough surface was suspended from one of the balances in order to measure the surface tension and a glass plate (micro-
SURFACE ACTIVITY, WETTING AND DEWETTING
635
dyneS~crn so rs
25
°i - 251
log
c
rs
re
(paroffin w~x? FI~. 14
scope cover glass) from the other balance. The wet glass plate is first immersed in the liquid (thermodynamically irreversible dewetting is then observed), and the apparent adhesion tension for glass-solution is measured from an emersion followed by another immersion. As an example, Fig. 14 shows % re, and 7~ paraffin-solution, T~r,,p) and r~(~p,) glass-solution, as a function of the logarithm of the concentrations for solution of lauryl-trimethyl-ammonium bromide. The slope of the rap, curves (glass-solution) has the same sign as the one of the curve of 7, i. e., opposite to the one of the slope for the curve r paraffin-solution. The application of the Gibbs equation (as well as common sense) led to the idea that a film is fixed on the glass plate when it is withdrawn from the solution, the plate being apparently dry, and that this film is restored to the suface of the solution when the glass plate is again immersed. This withdrawal of a film is confirmed by the fact that in the case of nonmicellar solutions of cationic long-chain substances the surface tension increases temporarily while the glass plate is withdrawn and decreases temporarily while it is again immersed. (Tgn~bre has succeeded in determining the rate at which material is deposited on the glass plate.) It is here a question of an additional adsorption, since the glass fixes already a certain number of surfactant molecules when it is immersed in the solution (this fact being confirmed by the rise in the surface tension of the solution after it has been stirred in the presence of glass wool). But, contrary to what may be expected, this additional adsorption is not due to the deposition of a second layer of molecules of surfactant, paraffin ends to paraffin ends, on a first layer already deposited in the bulk of the solution. This additional adsorption would indeed look Iilce an adsorption on the para~n (positive slope for the curve r-log c). But the data rather lead to the assumption that the
636
JEA~
@UASTALLA
polar ends of the molecules of surfaetant are fixed on the glass, during emersion, at the free places between the molecules already adsorbed, in the form of a rather loose network in the bulk of the solution. This method may permit elucidation of the mechanism which lies at the basis of flotation phenomenon. I~EFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
GUASTALLA,J., J. cMm. phys. 49, 250 (1952). GUASTALLA,J., Dr. chim. phys. 51,287 (1954). DERVICl~IAN,D. G., Dr. phys. radium 6, 221 (1935). HA.RKINS,W. D., AND ANDERSON,T. F., Or. Am. Chem. Soe. 59, 2189 (1937). ABmDA.T,M., A.NDDOGNON,A., J. phys. radium 10, 22 S (1939). LA.NGMUIR,I., Dr. Am. Chem. Soe. 39, 1848 (1917). GIIASTALLA.,L., A'NDGUA.STA.IJLA',5., M~m. services ehim. ~tat (Paris) 38, 99 (1953). GUA.srA.LLA.,L., A.NDGUA.S~A.LLA,J., Compt. rend. 240, 425 (1955). LA.NGLOIS,G., M$m. services chim. $tat (Paris) 40, 83 (1955). GTJA.STA.LLA.,J., Compt. rend. 228, 820 (1949). GUA.STA.LLA.,J., A.NDGUA.STA.LLA.,L., Compt. rend. 29.6, 2054 (1948). G~A.STALLAA,L., Compt. rend. 230,824 (1950). G~A.STA.LLA.,J., G~A.STA.LLA.,L., LUzzA.TI,D., ROSA.No, H. L., A.~D SA.aA.GA,L., Compt. rend. 231,220 (1950). FOWKES,F. M., A.NDI{A.RKINS,W. D., Dr. Am. Chem. Soe. 62, 3377 (1940). HA.P:KINS,W. D., A.NDLOESER,E. It., J. Chem. Phys. 18, 556 (1950). GUA.STA.LLA.,J., J. chim. phys. 51, 583 (1954). GuA.STA.~LA.,L., Thesis, unpublished. RosA.No, l=I. L., M~m. services ehim. ~tat (Paris) 36, 309, 437 (1951). RosA.NO, H. L., AANDGVA.S~A.LL~.,J., Compt. rend. 9.30, 628 (1950~ T~N~RE, L., M$m. services ehim. Ztat (Paris) 40, 77 (1955). T ~ N ~ R ~ , L., J. chim. phys. 53, 6 (1956).