98
FREDERICK M. FOWKES
VOl. 57
ltOLE OF SURFACE ACTIVE AGENTS IN WETTING1 BY FREDERICK M. FOWKES Shell Development Company, Emeryville, Calijornia Received July 88, 1068
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A nicclianisni for the wetting of cotton by aqueous solutions of wetting agents is proposed which allows prediction of sinking times of cotton yarn for a variet of wetting agents. The equations require data on the relation between concentration and surface tension of solutions ofthe wetting agent. Penetration of solutions of wetting agents into porous hydrophobic solids proceeds a t a rate determined by the cosine of the contact angle cos 0) of the advancing front on the cotton fibers. As the value of cos e is found to be a linear function of surface tension (y‘\ for alarge variety of surface active agents values of y’ may be identified with values of cos e. An equation derived on this basis (log ts = A f By’)Ban be used td predict sinking times in various wetting tests. Data obtained with Aerosol OT, Aerosol MA and Tergitol 4 illustrate this point. The value of y‘ depends on the concentration of agent in the surface region of the solution. This concentration (c‘) becomes less than the bulk concentration (c) during penetration if the agent is heavily adsorbed on cotton. With solutions of Nonic 218 and Triton X-100, for example, c - c’ is often much larger than c; thus diffusion become the main ratedetermining factors in wetting with these materials. Values of the diffusion constant, D,appear to decrease from 4 X 10-6 cm2/sec. in dilute solutions to 1.5 X cm.2/sec. in concentrated solutions composed mainly of micelles. The relations of sinking time to diffusion and to surface tension may be used additively to predict ratea of wetting for a wide variety of surface active agents.
The wetting of hydrophobic cotton yarn by aqueIt is well-known that the logarithm of siuking ous solutions of surface active agents is used as an time is a linear function of the logarithm of the example of the general problem of penetration of concentration of wetting a ~ e n t . It ~ is now shown liquids into porous phobic solids with the aim of that the logarithm of sinking time is also a linear demonstrating the rate-determining factors in such function of the cosine of the contact angle or of phenomena. surface tension, and that this function is identical First, the relation of surface activity of wetting for many wetting agents. A theoretical basis for agents to rates of wetting was investigated. It is this relation is proposed in this section. shown that the contact angle (e) on cotton of aqueI n this study rates of wetting were determined ous solutions of wetting agents is the factor which for gray unboiled cotton yarn as supplied for the determines rates of wetting, and that the rate of Draves-Clarkson sinking test.* These skeins were wetting is an exponential function of cos 8. For a 54 inch loops of yarn weighing five grams apiece and given test, cos 0 alone determines the sinking time. containing 120 threads. I n a cross section of each Second, the effect of adsorption of wetting agents thread there were 100-200 cotton fibers. The during penetration was studied. It is shown that yarn has a surface of natural waxes and oils which if wetting agents are heavily depleted by adsorption makes it hydrophobic. In this study the oils oiito the cotton during penetration, the replenish- were rinsed out with benzene (at 25’). The hyment of the advancing front by diffusion from the drophobic nature of the waxy surface was demoribulk of solution becomes the factor which deter- strated by the “capillary depression” of water; the mines rates of wetting. Because of this adaorption top 14-20 em. of skeins submerged vertically ill phenomenon, which was demonstrated by heavily water were not penetrated by distilled water. Caladsorbed substances such as Triton X-loo4 and culations based on a model system of capillaries Nonic 218,2the relation of rates of wetting to con- having the same wall perimeter per unit area of tact angle wm demonstrated with solutions of water-air ’ interface (600-800 cm./cm. 2-deterAerosol OTj2Aerosol RIA2 and Tergitol 4 , 2 i n w h i ~ h mined by measurement of hotomicrographs of adsorption and diffusion have negligible effect on cross-sections of cotton thready show that this “capillary depression” may be accounted for with a rates of wetting. Effects of Surface Activity on Rates of Wetting. contact angle (e) of water on this cotton of 107’. -The traditional approach to penetration of Because of this similarity of the surface of waxy porous solids is to approximate the path of flow cotton to other waxes it is proposed to use the conby a parallel bundle of smooth-walled capillaries. tact angles (e) of aqueous solutions on paraffin wax In such a system the rate of penetration is propor- to represent the values of e for solutions of wetting tional to the adhesion tension, y cos e, where y is agents on cotton. Rat,es of penetration of wettjiig solutions i u l o the boundary tension of t,he advancing liquid and 8 i(s c w i i t ’ a c t aiigle on the capillary walls, However, cotton yarn can be measured with a variety of tesls. . Two of these were used in this study; the Dravesi i i tlie case of cottoii threads, the rate of pelietraClarkson sinking test with three-gram hook3 and t . i o i i is not proportional to y cos e, nor is its direction the yarn bundle m e t h ~ d . When ~ this yarn was parallel to the fibers. (1) Presented before the twenty-sixth National Colloid Symposium floated on top of water, as in the yarn-bundle test, which was held under the auspices of the Division of Colloid Chemistry the penetration was observed to occur from the of the American Chetnical Society in Los Angeles, California, June 16sides of threads and yarn in a direction perpendicu18, 1952. lar to the length of the fibers (see Fig. 1). After (2) Aerosol OT, from American Cyanamid Coiiipany, is the sodiuiu salt of di-2-ethylhexyl sulfosuccinate. Aerosol M A ia the dihexyl entry the solution appeared to travel a short derivative. Tergitol4, froin Carbide and Carbon Corp., is the sodium salt of a highly branched alkanol sulfate. Triton X-100, from Rohm and Haan. in a condensate of ethylene oxide with an octyl phenol; tlie polyether chain has about 9 units. Nonic 218, from Sharplcs Chemicals, is a condensate of ethylene oxide with a dodecyl inercaptan; this polyether chain also lias about 9 units.
(3) C. Z. Draves and R. G . Clarkson, Am. Dyestuf R e p t r . , 2.0, 201 (1931). See also Year Boob of .4m.Assoc. Textile Chemixts and Colorists. (4) S. 31. Edelstein and C. Z. Draves, Am. D y e s l u f R e p l r . , 38, 343
(1949).
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ROLEOF SURFACE A.CTIVE AGENTSIN WETTING
Jan., 1953
distance through the threads parallel to the fibers. In slow wetting, penetration occurred at few points and solutions traveled parallel to the fibers for several millimeters, I n rapid wetting, however; penetration occurred a t many more points and parallel travel was negligible. I
I
I
I
Fig. 1,-A, skeins are penetrated by water entering from all sides and in a direction perpendicular to the length of the skein; B, cross section of skein of yarn shows water entering from periphery and moving toward the center; C, within a thread evenly spaced hydrophobic fibers prevent movement of the water meniscus (dashed line), except where fibers marked x intersect the meniscus and permit i t to advance.
The rate of wetting of waxy cotton cloth or yarn (as measured by the various wetting tests) depends on the rate of wetting of the individual threads. The following mechanism for the wetting of threads is visualized. In threads, the close and even spacing of hydrophobic fibers, on contact with the wetting solution, forms a serierr, of highly curved menisci which prevents passage of water or wetting solutjions.6 Indeed, wetting solutions can penetrate the fibers only a t points where imperfectioiis i I i spacing and alignment occur. In Fig. 1C penetration is shown to occur where fibers labeled X lie partly between adjacent fibers of a lower layer. Where these intersect the meniscus between fibers of the lower row, the meniscus moves forward along the length of the newly wet fiber, like a zipper, for some distance. At some other place where the solution is in contact with the thread another such intersection may occur and the meniscus again moves forward. Thus, in steps, the solution moves through the thread perpendic,ularly to the fibers with a rate proportional to the frequency of such intersections. The degree of imperfection may be expressed as shown in Fig. 2.' Here fiber 3 lies above the water meniscus between fibers 1 and 2, and its distance from the meniscus is shown to be d - r cos 8, where d is the distance of fiber 3 from the plane of fibers I and 2, r is the radius of a fiber and 0 the contact angle. When d - r cos 19 has a small enough value, suoli as d', penetration occurs.6 Only a small proportion of the values of d - T cos 8 are as small ( 5 ) A. B. D. Cassie, Disc. Faraday Soc., No. 3, 242 (1948); D. J. Crisp and W. H. Thorpe, i b i d . , No. 3,210 (1948). ~ f i )The value of dB iacresses with cnrvl~fareof the rnenircus which is iwoimrtioiial t o the hydrostittic Iwesswe drop acrow the menkcus. As sinking tiines measure the slowest penetration in a test piece of
cotton. the portion t h a t is rate-determining will have little hydrostatic head and d" will therefore he snlall.
Fig. 2.--Cross section of three fibers in a thread showing how decrease of contact angle (e) brings the water-air interface closer to fiber 3. The curvature of the meniscus is not shown because the radius of curvature of the meniscus (near the top of a skein) is large (on the order of 400p) compared with the diameter of fibers (10-2Op).
as d", so this proportion (y) may be represented by a distribution function such as g = ae-(d' -
T COS
e)/d"
(1)
in which d' represents the average value of d. This s h o w that the proportion of cases where d' - 1' cos e equals or exceeds d" increases as an exponential function of cos e. If the rate of wetting of threads is proportional' to y, then the rate of wetting of cotton test pieces ( l / t s )is also proportioiial to y. Thus a'e-(d' 01'
log t, = -log a'
+ 2,803
,'/,'I
- T aos @/d"
(2)
- 2.303 ( r / d " ) COB 8 (3)
Here the sinking time (&) in a given test is determined by only the contact angle (e). The test constant a' relates the sinking time to the number of threads which must be wetted consecutively before sinking of the skein occurs; when a' is large, sinking is rapid. Equation (3) now relates wetting times to values of contact angle. It appears that contact angles of aqueous solutions on wax rnay be related to thc surface tension. Figure 3 shows that the following relation holds reasonably well for five commercial wetting agents8 COS e = 1.68 - 0.035~ (4 1 Thus equation (3) rnay be chaaged to rclutc siiil
