摘要:

AUTHOR Adam, N. K. 5,96,98, 112, 114, 167, 291, h e y , S. E., 168. Ashpole, D. K., 111, 283, 285. Atkinson, D. I. W., 121, 124. 292. Bailey, G. L. J., 16. Bangham, D. H., 102, 113. Barkas, W. W., 102, 105, 108, 223, 283, 284, 285, 286, 287. Barrer, R. M., 61, 119 Bartell, F. E., 257. Baxter, S., 94, 97, 285, 286. Beakbane, M. E., 273. Beament, J. W. L., 177, 220, 221, 230, Bennet-Clark, T. A,, 134. Bond, R. L., 29, 107, 113. Brinkman, H. C., 126. 231, 238. Carman, P. C., 72. Cassie, A. B. D., 11, 99, 100, 101, 114, Childs, E. C., 78, 129. Crafts, A. S., 153 Crisp, D. J., 98, 166, 210, 232, 282, 291, 239, 283. 292. Dakshinamurti, C., 56. Davies, C. N., 123, 127. Denbigh, K. G., 86, 129. Dodd, C. G., 257. Dresel (?lliss) E. M., 115. Duncan, J. F., 116. Emst, E., 127. Fog& G.E., 162. Foster, A. G., 41, 106, 110. George, N. C., 78. Gregg, S. J., 94, 107. Griffith, M., 29, 115. Griffiths (Miss) &I., 113. INDEX* Hartley, G. S., 128, 223, 283, 286, 291. Henry, P. S. H., 243 Hirst, W., 22, 96, 97, 100, 115. Hurst, H., 193, 221, 224, 230, 232, 235. Hutchison, H. P., 86. Joly, M., 144, 293. Kemball, C., roo, 292. Klinkenberg, A., 124, 224. Lees, A. D., 187, 231 Lewis, F. J., 159. LundegHrdh, H., 139 Maggs, F. A. P., 29, 111, 113, 115. Morris Thomas, A., 114. Neale, S. M., 118. Nieuwenhuis, K. J., 103, 288. Nixon, 1. S., 86. Pal, R., 236, 238. Pearse, J. F., 125. Preston, R. D., 130, 166, 167, 168, 287. Purcell, W. R., 257. Razouk, R. I., 94, 119. Rideal, E. K., I . Robinson, Conmar, 273. Schofield, R. K., 51, 56, 105, 118, 129, Schulman, J.H., 169, 290. Shuttleworth, R. ,- 16, gg. Slifer, Eleanor, H., 182. Starnm, A. J., 264. Swarbrick, T., 238. 167, 284, 288. Talibuddin, O., 51.. Thorpe, W. H., 210,238. Topp, N. E., 273. van den Honert, T. H., 146, 167. 168. Wark, I. W., 111, 286. Wigglesworth, V. B., 172, 220, 238. *The references in heavy type indicate papers submitted for discussion 294AUTHOR Adam, N. K. 5,96,98, 112, 114, 167, 291, h e y , S. E., 168. Ashpole, D. K., 111, 283, 285. Atkinson, D. I. W., 121, 124. 292. Bailey, G. L. J., 16. Bangham, D. H., 102, 113. Barkas, W. W., 102, 105, 108, 223, 283, 284, 285, 286, 287. Barrer, R. M., 61, 119 Bartell, F. E., 257. Baxter, S., 94, 97, 285, 286. Beakbane, M. E., 273. Beament, J. W. L., 177, 220, 221, 230, Bennet-Clark, T. A,, 134.Bond, R. L., 29, 107, 113. Brinkman, H. C., 126. 231, 238. Carman, P. C., 72. Cassie, A. B. D., 11, 99, 100, 101, 114, Childs, E. C., 78, 129. Crafts, A. S., 153 Crisp, D. J., 98, 166, 210, 232, 282, 291, 239, 283. 292. Dakshinamurti, C., 56. Davies, C. N., 123, 127. Denbigh, K. G., 86, 129. Dodd, C. G., 257. Dresel (?lliss) E. M., 115. Duncan, J. F., 116. Emst, E., 127. Fog& G. E., 162. Foster, A. G., 41, 106, 110. George, N. C., 78. Gregg, S. J., 94, 107. Griffith, M., 29, 115. Griffiths (Miss) &I., 113. INDEX* Hartley, G. S., 128, 223, 283, 286, 291. Henry, P. S. H., 243 Hirst, W., 22, 96, 97, 100, 115. Hurst, H., 193, 221, 224, 230, 232, 235. Hutchison, H. P., 86. Joly, M., 144, 293. Kemball, C., roo, 292. Klinkenberg, A., 124, 224. Lees, A. D., 187, 231 Lewis, F. J., 159. LundegHrdh, H., 139 Maggs, F. A. P., 29, 111, 113, 115. Morris Thomas, A., 114. Neale, S. M., 118. Nieuwenhuis, K. J., 103, 288. Nixon, 1. S., 86. Pal, R., 236, 238. Pearse, J. F., 125. Preston, R. D., 130, 166, 167, 168, 287. Purcell, W. R., 257. Razouk, R. I., 94, 119. Rideal, E. K., I . Robinson, Conmar, 273. Schofield, R. K., 51, 56, 105, 118, 129, Schulman, J. H., 169, 290. Shuttleworth, R. ,- 16, gg. Slifer, Eleanor, H., 182. Starnm, A. J., 264. Swarbrick, T., 238. 167, 284, 288. Talibuddin, O., 51.. Thorpe, W. H., 210,238. Topp, N. E., 273. van den Honert, T. H., 146, 167. 168. Wark, I. W., 111, 286. Wigglesworth, V. B., 172, 220, 238. *The references in heavy type indicate papers submitted for discussion 294

ISSN:0366-9033    

DOI:10.1039/DF94803FX001

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

AUTHOR Adam, N. K. 5,96,98, 112, 114, 167, 291, h e y , S. E., 168. Ashpole, D. K., 111, 283, 285. Atkinson, D. I. W., 121, 124. 292. Bailey, G. L. J., 16. Bangham, D. H., 102, 113. Barkas, W. W., 102, 105, 108, 223, 283, 284, 285, 286, 287. Barrer, R. M., 61, 119 Bartell, F. E., 257. Baxter, S., 94, 97, 285, 286. Beakbane, M. E., 273. Beament, J. W. L., 177, 220, 221, 230, Bennet-Clark, T. A,, 134. Bond, R. L., 29, 107, 113. Brinkman, H. C., 126. 231, 238. Carman, P. C., 72. Cassie, A. B. D., 11, 99, 100, 101, 114, Childs, E. C., 78, 129. Crafts, A. S., 153 Crisp, D. J., 98, 166, 210, 232, 282, 291, 239, 283. 292. Dakshinamurti, C., 56. Davies, C. N., 123, 127. Denbigh, K. G., 86, 129. Dodd, C. G., 257. Dresel (?lliss) E. M., 115. Duncan, J. F., 116. Emst, E., 127. Fog& G.E., 162. Foster, A. G., 41, 106, 110. George, N. C., 78. Gregg, S. J., 94, 107. Griffith, M., 29, 115. Griffiths (Miss) &I., 113. INDEX* Hartley, G. S., 128, 223, 283, 286, 291. Henry, P. S. H., 243 Hirst, W., 22, 96, 97, 100, 115. Hurst, H., 193, 221, 224, 230, 232, 235. Hutchison, H. P., 86. Joly, M., 144, 293. Kemball, C., roo, 292. Klinkenberg, A., 124, 224. Lees, A. D., 187, 231 Lewis, F. J., 159. LundegHrdh, H., 139 Maggs, F. A. P., 29, 111, 113, 115. Morris Thomas, A., 114. Neale, S. M., 118. Nieuwenhuis, K. J., 103, 288. Nixon, 1. S., 86. Pal, R., 236, 238. Pearse, J. F., 125. Preston, R. D., 130, 166, 167, 168, 287. Purcell, W. R., 257. Razouk, R. I., 94, 119. Rideal, E. K., I . Robinson, Conmar, 273. Schofield, R. K., 51, 56, 105, 118, 129, Schulman, J.H., 169, 290. Shuttleworth, R. ,- 16, gg. Slifer, Eleanor, H., 182. Starnm, A. J., 264. Swarbrick, T., 238. 167, 284, 288. Talibuddin, O., 51.. Thorpe, W. H., 210,238. Topp, N. E., 273. van den Honert, T. H., 146, 167. 168. Wark, I. W., 111, 286. Wigglesworth, V. B., 172, 220, 238. *The references in heavy type indicate papers submitted for discussion 294AUTHOR Adam, N. K. 5,96,98, 112, 114, 167, 291, h e y , S. E., 168. Ashpole, D. K., 111, 283, 285. Atkinson, D. I. W., 121, 124. 292. Bailey, G. L. J., 16. Bangham, D. H., 102, 113. Barkas, W. W., 102, 105, 108, 223, 283, 284, 285, 286, 287. Barrer, R. M., 61, 119 Bartell, F. E., 257. Baxter, S., 94, 97, 285, 286. Beakbane, M. E., 273. Beament, J. W. L., 177, 220, 221, 230, Bennet-Clark, T. A,, 134.Bond, R. L., 29, 107, 113. Brinkman, H. C., 126. 231, 238. Carman, P. C., 72. Cassie, A. B. D., 11, 99, 100, 101, 114, Childs, E. C., 78, 129. Crafts, A. S., 153 Crisp, D. J., 98, 166, 210, 232, 282, 291, 239, 283. 292. Dakshinamurti, C., 56. Davies, C. N., 123, 127. Denbigh, K. G., 86, 129. Dodd, C. G., 257. Dresel (?lliss) E. M., 115. Duncan, J. F., 116. Emst, E., 127. Fog& G. E., 162. Foster, A. G., 41, 106, 110. George, N. C., 78. Gregg, S. J., 94, 107. Griffith, M., 29, 115. Griffiths (Miss) &I., 113. INDEX* Hartley, G. S., 128, 223, 283, 286, 291. Henry, P. S. H., 243 Hirst, W., 22, 96, 97, 100, 115. Hurst, H., 193, 221, 224, 230, 232, 235. Hutchison, H. P., 86. Joly, M., 144, 293. Kemball, C., roo, 292. Klinkenberg, A., 124, 224. Lees, A. D., 187, 231 Lewis, F. J., 159. LundegHrdh, H., 139 Maggs, F. A. P., 29, 111, 113, 115. Morris Thomas, A., 114. Neale, S. M., 118. Nieuwenhuis, K. J., 103, 288. Nixon, 1. S., 86. Pal, R., 236, 238. Pearse, J. F., 125. Preston, R. D., 130, 166, 167, 168, 287. Purcell, W. R., 257. Razouk, R. I., 94, 119. Rideal, E. K., I . Robinson, Conmar, 273. Schofield, R. K., 51, 56, 105, 118, 129, Schulman, J. H., 169, 290. Shuttleworth, R. ,- 16, gg. Slifer, Eleanor, H., 182. Starnm, A. J., 264. Swarbrick, T., 238. 167, 284, 288. Talibuddin, O., 51.. Thorpe, W. H., 210,238. Topp, N. E., 273. van den Honert, T. H., 146, 167. 168. Wark, I. W., 111, 286. Wigglesworth, V. B., 172, 220, 238. *The references in heavy type indicate papers submitted for discussion 294

ISSN:0366-9033    

DOI:10.1039/DF94803BX003

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

I. FUNDAMENTAL ASPECTS Introductory Paper BY N. K. ADAM PRINCIPLES OF PENETRATION OF LIQUIDS INTO SOLIDS Received 18th February, 1948 Porous solids may range in texture all the way from solids whose sub- stance is impermeable to liquids, but are traversed by capillary tubes of diameter substantially greater than the range of molecular attraction, to solids which have no capillaries or pores in the ordinary sense, but whose substance is capable of dissolving, molecularly, some of the liquid. The theory of penetration into capillaries is well understood, at least when these are of approximately uniform bore. When the bore of the capillaries decreases so far that the molecules on one side begin to attract those on the other, right across the bore, the problem of penetration gradually changes to the problem of solution of a liquid in a solid ; and the theory appears to be very inadequately developed.In all cases, ultimately, the penetration is controlled by the adhesion between molecules ; in the case of penetration into macroscopic capillaries, the relative magnitudes of the adhesion of liquid for solid, and of the self- cohesion of the liquid, together with the diameter of the capillaries, determine the effective pressure driving the liquid into the capillaries. When the bore of the capillaries is so small that there is appreciable adhesion between the opposite walls, the self-cohesion of the solid must also become important. Capillary Penetration The fundamental form& are, as is well known,l easily deduced from the existence of free surface energy at any interface between phases of different composition.This free surface energy arises from the inward attraction of the underlying molecules on those in the surface, and since a surface possessing free energy contracts when free to do so, the free surface energy is also called surface tension. relates the work of adhesion WsL, required to separate unit area of solid and liquid in contact, to the surface tensions ys, y ~ , ysL, of solid, liquid, and solid-liquid interface respectively. Combining with the equation for equilibrium for a liquid resting at a “ contact angle ” on the solid, Young’s equation (1805) results. This gives the fundamental relation between the adhesion of liquid to solid, and the contact angle, showing that there is a bite angle if the adhesion of liquid to solid, W~L, is less than the self-cohesion of the liquid, 2 y ~ ; and zero angle if the adhesion of liquid to solid becomes equal to, or greater than, the cohesion of the liquid.Duprk’s equation, WSL = ys + yL - ysL (1) ys = ysL + yL cos e . (2) wsL = yL(I + cos e) . * (3) cp. Adam, The Physics and Chemistry of Surfaces (1941). pp. 178, 413. and ref. there quoted. 56 PENETRATION OF LIQUIDS INTO SOLIDS When a liquid enters a capillary of small radius, a curved meniscus will be set up unless the contact angle is exactly goo, producing a difference in pressure P , - P , on the two sides of the liquid surface, P, - P , = yL 'I - + -- I) (R, R2, . (4) R,, R , being the principal radii of curvature ; for a capillary of circular section and radius r, this becomes a " penetrating pressure " The contact angle varies, however, with the tendency of the liquid to move along the solid surface, being a maximum when the liquid is advancing over a dry surface.Calling the " advancing " angle, obtained when the meniscus is moving slowly into the capillary, @A, the pressure driving a liquid spontaneously into a capillary of circular section whose walls are parallel to the axis (i.e., uniform section), is - (6) zY cos ea pi = - Y Pi is positive when the meniscus is concave, i.e., when OA < goo. the pressure required to expel the liquid from the capillary is For penetration, the advancing angle 0.4 is the relevant contact angle; where OR is the " recedinq " angle made when the liquid is receding from a previously wetted surface.Since 8.4 > OR, Po > Pi ; a greater pressure is required to expel a liquid from a capillary, than the pressure which drives it in spontaneously. The difference between the advancing and receding contact angles, or " hysteresis " of the contact angle, can be large ; up to 60" on smooth surfaces has been recorded and much larger values on rough surfaces. Hysteresis seems to be larger for water than for organic liquids, but it exists with these also. It does not yet appear fully understood; perhaps there is no single explanation for all cases. Since OA > OR, eqn. (3) shows that the adhesion of liquid for the previously wetted solid exceeds that for the dry solid. Hysteresis has been variously ascribed to films on the dry surface, less easily wetted than the main substance of the solid, and removed by the liquid; to overturning of the surface molecules of the solid, to bring their more hydrophilic parts to the surface, when water touches the surface ; and to the formation of multi-molecular clusters of liquid molecules on the solid surface, after the liquid has receded (Cassie ,).It has long been known that the receding angle tends to decrease as the liquid remains in contact with the solid, probably because the solid soaks up or dissolves, in its surface layers, some of the liquid. states that receding angles are much more variable than advancing angles; on the other hand, Bartell and Wooley3 found that the receding angle with glass or silica, and organic liquids, was easier to reproduce than the advancing angle. The hysteresis in the case of organic liquids and glass may well be due to the receding angle being that obtained when the surface pores in the glass are filled with liquid, the advancing angle depending on the extent to which these pores are dry, or partially filled with liquid.After con- tinued heating in the presence of vapour of the liquid, the advancing angle tends to become equal to the receding. Cassie 2 Cassie, Trans. Faraday SOC., 1948 (this Discussion). 3 Bartell and Wooley, J . Amer. Chem. SOC., 1933, 55, 3518.N. K. ADAM 7 The minimum contact angle obtainable is zero, and for "receding" angles this figure is not uncommon, though it is less often attained with advancing angles. The question, what is the maximum possible advancing angle, on a smooth surface, is an important one for all waterproofing problems.It is probably between 110" and 120'; Ablett made most careful measurements of the contact angle between air, water and parafib wax, finding 113" for the advancing angle, equal by (3) to a work of adhesion of water to dry wax of 44'2 ergslsq. cm., at 20° ( y ~ = 72.8). Long-chain compounds with polar groups at one end of their molecules, such as stearic acid, show angles very nearly as large (Adam and Jessop 5), because the surface consists of hydrocarbon groups, with the polar, water-attracting groups well buried below a layer of hydrocarbon. Baxter and Cassie record an angle of 120° on a proofed wool fibre. Since measurements of the work of adhesion between liquid paraffins and water also give values of the order 40 ergs/sq.cm., a greater work of adhesion being obtained for all other organic liquids, it seems unlikely that, at any rate with organic substances, real contact angles greater than 120° can exist. It is well known, however, that when the surface is rough, i.e. contains minute elevations and depressions, much greater apparent contact angles can be obtained. Coghill and Anderson obtained advancing angles of about 160" with powdered galena thickly sprinkled on a plate, and Adam (1927) found a similar angle for rough surfaces of pigment particles on a plate, coated with stearic acid. Conmar Robinson obtains about 160O for the advancing angle of water on some types of leather. Generally, roughness simply increases the difference between the red contact angle (on a smooth surface of similar attraction for water) and goo; if the real angle is less than goo, some penetration into pits occurs, so that liquid touching the rough surface is in contact with liquid of its own composition, over part of the surface, thus increasing the average work of adhesion over the whole surface; if the real angle is greater than go", air is entrapped in the hollows, over which there is then no adhesion to overlying water so that the average work of adhesion is less than over a smooth surface.Wenzel gives the relation, 8' being the apparent angle on the rough surface, and 0 the ratio between the real area of rough solid accessible to a liquid, and the apparent area, which expresses quantitatively the way in which roughness enhances the difference between the real angle and goo.found, for a (presumably smooth) proofed wool _fibre, OA = 120°, OR = 60" ; for the comparatively rough proofed yarn, Ol.4 = 157". O'R = 20°, figures in excellent agreement with Wenzel's eqn. (8), puttmg 0 = 1-86. Cassie and Baxter lo have investigated the case of fabrics in which cylindrical fibres are spaced in various orderly arrangements, with vacant spaces up to a few times the diameter of the fibres, showing that apparent contact angles up to nearly 160O will be obtained on fabrics with threads appropriately spaced, on which the true angle does not exceed 120'; apparent angles on the cloth, up to about 170", are theoretically possible if the yams are rough surfaces with an apparent angle (advancing) of 150~.Thus by roughness in the yams, combined with accurately maintained cos e' = 0 cos e . * (8) Baxter and Cassie Ablett, Phil. Mag., 1923. 46, 244. Adam and Jessop, J . Chem. SOL, 1925, 1865. II Baxter and Cassje, J . Textile I n s t . , 1945. 36, 167. ' Coghill and Anderson, U.S. Bureau Mines Tech. Paper, 1923, 262, 47. * Conmar Robinson, Trans. Faruday Soc., 1948 (this Discussion). Wenzel, Ind. Eng. Chem., 1936, 28, 988. lo Cassie and Baxter, Trans. Faraday SOC., 1944, 40, 546.8 PENETRATION OF LIQUIDS INTO SOLIDS spacing between them in the cloth, a chemical proofing which would on a smooth surface give an advancing angle of, say, 113" can be made to give an almost perfectly water-repellent surface with advancing angle 160~-170~.The superlative water-repellence of ducks' feathers is due, not to any miraculously water-repellent wax, but to the well-designed structure in which the barbules are kept apart at nearly the theoretically ideal distance. Pores are rarely capillaries of uniform bore. An approximation to the pressure required to force water through the pores of a fabric may be obtained by treating the yarns as " rough " surfaces, and using the apparent advancing angle O'A on the yarn in (6) (Baxter and Cassie, also Bartell et dll). Because cotton yams are rougher than those of Nylon and similar synthetic fibres, the same proofing gives greater resistance to water penetration with cotton cloth than with Nylon cloth of similar weave. The theory of penetration into capillaries of complex shape is difficult.Often aggregates of powders are treated formally as equivalent to capillaries and eqn. (6) and (7) used to deduce the contact angle from the observed pressure Pi produced by the penetrating liquid, or Po, required to expel the liauid. An indemndent deter- FIG. I n mination of the raiius r of the " equivalent capillary " is required ; this may be done by measuring the viscous resistance to flow of a liquid through the thoroughly soaked pow- der (Bartell, 1926, Carman 12). Such methods have their uses, but they may conceal our present ignorance of how the liquid actually finds its way into the nooks and crannies of a solid, where the pores suffer frequent and abrupt changes of size and shape. Simple geometrical considerations given below show that the penetra- tion pressure Pi will decrease, perhaps even become negative, when the meniscus has to find its way past a constriction in a pore.Fig. I a shows a tube of corrugated section, for simplicity taken as a figure of revo- lution about the axis, the walls being inclined at an angle 45" to the vertical axis. If the advancing contact angle is 45" (lower part of figure), Pi will be 2 before passing the constriction where the radius is r, and zero after passing. If 8 > 45" (upper part of figure), Pi becomes negative at the moment of passing, so that unless external pressure is applied, the meniscus will not pass the constriction. Fig. I b shows the more general case (but still a figure of revolu- tion) where the walls are inclined at tpl to the horizontal below the con- striction EF and at v 2 above.Before passing, the radius of curvature of r ; after passing, the radius R is r the meniscus R , is so that the penetration pressure changes from ' 7 sin (eA 4- sin (OA + 93 sin (OA - tp2)' to l1 Bartell, Purcell and Dodd, Trans. Faraduy SOL, 1948 (this Discussion). 18 Carman, Trans. Faraday Soc., 1948 (this Discussion).N. K. ADAM 9 - 2y sin (eA - v2) on passing the constriction. P5 becomes negative if Y OA > tps. This effect of constrictions is analogous to the " edge effect " found by Coghill and Anderson in flotation of solids of angular shape (cp. / I FIG. I b ref. 1, p. 194) ; but the constriction need not be sharp, as the effect depends on the slopes y1 and vz of the walls, not on the abruptness of change of slope. I can attempt only qualitative considerations on the mechanism of pene- tration, when the bore of the capillaries is small enough for the attraction of the walls to extend right across them.Liquid in the pores will every- where be within the range of attraction of the walls. The question whether the surface tension has its normal value in such a capillary has been discussed in connection with capillary condensation,13 but no definite conclusions appear to have been reached. The following considerations indicate that the potential energy of a molecule in the surface of a liquid, in a very narrow tube, will be less than in a free liquid surface. The surface molecule A (Fig. 2) is attracted inwards by the liquid below it in the tube, and this attraction is presumably the same as that from a similar column of free liquid.There is also the downward attraction of the solid walls below the level XY of the surface molecule A, and the upward attraction of the walls above XY, which cancel each other in a vertical direction. Hence the work - X - - - - --y required to bring A from the interior of the liquid to the surface is less than in a free liquid surface, by the attraction which would be exerted down- wards on A, by liquid in the space actually occupied by the walls of the tube below XY. Hence the surface tension is decreased by the attraction of the walls of the tube. In such a very narrow tube it is difficult to speak of a definite contact angle, since the kinetic agitation of the liquid surface must make the surface indefinite in position to one or two molecular diameters, which is the same order of magnitude as the range of molecular attraction and therefore as FIG.2 l3 Brunauer and Emmett, Adsorption of Gases (1943). Vol. I, 126. A*I0 PENETRATION OF LIQUIDS INTO SOLIDS the diameter of the tube (a horizontal line is therefore used in Fig. 2 to suggest the level, though not the probable form, of the surface). Eqn. (5) for the penetrating pressure seems to lose its meaning owing to the indefiniteness of 8. Diffusion of molecules along the walls of extremely narrow tubes, within the range of molecular attraction, probably plays an important part in penetration into pores of this order of magnitude. Barrer brings evidence l4 that the rate of penetration of gases into zeolites, where the pores are of molecular dimensions, is controlled by surface diffusion on the pore walls. Stamm l5 uses a similar conception to describe the movement of water in wood. Penetration into very narrow pores may cause them to widen, and Hirst l6 suggests that this may be one of the causes of hysteresis in adsorp- tion (hysteresis of the contact angle may well be another).If the liquid (or vapour) entering the pore wedges the walls open so that, when full, the walls are beyond each other's range of attraction, the entering liquid must do work in overcoming this attraction between solid walls. This work is not recovered, at least with rigid walls, on removal of the liquid or vapour adsorbed on the solid walls. Charcoal expands when adsorbing gases : Bangham l7 ascribes this to the surface pressure of mobile adsorbed films in the charcoal pores, these films being of the " gaseous " type.There is plenty of other evidence that adsorbed films, if held by van der Waals' forces, are very mobile. When there is appreciable penetration of the liquid, by molecular solution, into the walls of the pores, one may anticipate that a liquid will tend to form a smaller contact angle with the walls than if there were no such " soaking " into the walls ; this will assist penetration along the pores, according to (5). When definite pores are absent, and penetration is wholly by molecular solution, the attraction between solid and liquid molecules must be great enough to separate liquid molecules from each other, and to achieve some degree of separation also of the solid molecules from each other as the liquid molecules penetrate between them. How far the " secretion " of water, or maintenance of a definite gradient of thermodynamic potential (or concentration or pressure), with movement of water against this gradient, will prove to be explicable in terms of the principles applicable to non-living pores, is difficult to predict at present.Several instances of such water secretion are described in this Discussion. ADDENDUM TO PAPER (communicated, 12th April, 1948). By polymerising methyl methacrylate round a Zn former, and dissolving out the Zn with HC1, a tube with zigzag walls similar to that in Fig. I was made ; the minimum radius r was 0.135 cm. The angle v1, and y2 were each about 47"; the advancing contact angle 8, on a flat plate of this material, is of the order 85". The penetrating pressure before passing a constriction, calculated according to the formula in the paper is 802 ; after passing, --.665 dynes/sq. cm. The difference is 1467 dyneslsq. cm., about 15 mm. head of water, assuming the normal surface tension of water. When the walls of the tube were dry, and a reservoir of water communicating with the lower end of the zigzag tube was gradually raised, the meniscus in the tube rose rapidly to the first constriction, then stuck; on raising the reservoir about 10 m., the meniscus passed at once to the next higher l4 Barrer, Trans. Furuduy SOC., 1944, 40, 206. 555 ; 1948 (this Discussion). l5 Stamm, Trans. Faraday Soc., 1948 (this Discussion). lo Hirst, Trans. Faraday Soc., 1948 (this Discussion). l7 Bangham et al., Proc. Roy. SOC. A , 1930, 130, 81 ; 1932, 138, 162; 1934, 147, 152, 175; 1938, 166, 572; J . Chem. SOC., 1931, 1329.N. K. ADAM I1 constriction. The rise continued in this jerky manner, from constriction to constriction, right up the tube. The difference between the experimental value of 10 mm., and the calculated value of 15 mm. may possibly have been due to contamination decreasing the surface tension of the water in the narrow tube.

ISSN:0366-9033    

DOI:10.1039/DF9480300005

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

N. K. ADAM I1 CONTACT ANGLES BY ,4. B. D. CASSIE Received 27th January, 1948 1. Contact Angle and Surface Structure When a drop of liquid is placed on a solid surface it may remain as a drop of finite area, or it may spread indefinitely over the surface. The condition for spreading is that the energy gained in forming unit area of the solid-liquid interface should exceed that required to form unit area of the liquid-air surface; or if ysA is the solid-air interfacial energy, ~ S L is that of the solid-liquid interface, and y u is that of the liquid-air interface, then for spreading : When this inequality is not fuWed, the drop remains finite in size and an equilibrium contact angle exists. The condition for equilibrium requires that, in the absence of gravity effects, the contact angle 8 between the liquid and the solid surfaces is given by : ys.4 - ysL Y W yS.4 - YSL > YLA * (1) (4 cos e = Eqn.(2) shows that the cosine of the contact angle gives the ratio of the energy gained in forming unit area of the solid-liquid interface to that required to form unit area of the liquid-air interface. It should be emphasised that (2) is a geometrical relation, and the unit areas are plane geometrical areas. The surface area of a liquid-air interface is unique and may always be identified with its plane geometrical area, but the surface area of a solid- liquid interface depends very much on the condition of the solid surface. Thus, if a solid surface is roughened so that unit plane geometrical area has an actual surface area u times that of the “ smooth ” surface, the energy gained in forming the solid-liquid interface will be u ( y s ~ - y ~ ~ ) , and the contact angle, 8’, for the rough surface will be given by : The angle 8’ has been termed the “ apparent ” contact angle in contrast with the “ real” angle 8 of eqn.(z), because close inspection of a rough surface would always reveal the “real” contact angle on any element that could be regarded as smooth. It might thus be said that any surface has two advancing and receding contact angles, the apparent angles which are shown on casual inspection of the intersection of the solid and liquid surfaces, and the “ real ” angles seen by a close inspection. The measure- ment of contact angle is, therefore, somewhat arbitrary, for one might Adam, The Physics and Chemistry of Surfaces, 3rd ed.(Oxford, 1941). p. i79. a Wenzel, Ind. Eng. Chem. 1936, 28, 988,12 CONTACT ANGLES pursue this argument to molecular dimensions when the surface would appear rough and heterogeneous. Fortunately, for practical purposes, it is possible to have a reasonable division of surfaces into “ smooth ” and “ rough ” and so attach some meaning to the “ real ” and “ apparent ” contact angles, but unless the smooth surface is a reproducible one, the ‘‘ real ” contact angle will not be reproducible. It is doubtless the difficulty of reproducing a “ smooth ” surface that gives rise to so many different published values for the contact angles of a given liquid and solid. Despite the uncertainty of absolute values of contact angles, eqn.(2) and (3) do give a useful relationship between measurable roughness and contact angle. Thus, a contact angle of more than goo is increased by roughening the surface, and one of less than goo is lessened by roughening. The analysis for a rough surface is readily extended to heterogeneous surfaces. If unit geometrical area of a surface has an actual surface area a, of contact angle O,, and an area a, of contact angle O,, the energy E gained when the liquid spreads over the unit geometrical area is = 0i(yS1.4 - yS,L) + az(YS,A - yS,L) %’’here YS,A, and y s l L are interfacial solid-air and solid-liquid tensions for the a, areas, and y s , ~ and ~ S , L are the interfacial tensions for the a, areas. The contact angle 0” for the composite surface is given by : (4) E YLA cos e” =- = a, cos el + a, cos e, .The most important heterogeneous surface in practice is the porous In this case the solid surface area is a,, and CT, represents air surface. spaces ; Y S , . ~ is then zero, and ys,L becomes YLA, or * (5) cos e” = 0, cos el - 0, . Eqn. (5) has already been given 3 and a number of applications have been di~cussed.~ I t is an equation that can be verified experimentally, and it appears to fit empirical data well to within the limits of The presence of pores, represented by c,, always increases the contact angle O”, and it is possible to have apparent contact angles as large as 150O when the “real ” contact angle is around goo. The equation is particularly useful in discussing natural and artificial porous clothing surfaces, where the aim is to make a , as large as possible consistent with rain drops failing to penetrate the structure. 2.The Problem of Receding Contact Angles The theories of contact angles for rough and heterogeneous surfaces are essentially geometrical, and they can be used for capillary calculations that would otherwise be intractable. Calculation of the pressure required to force water between the yarns in a fabric is an example of the use of eqn. (5). It is a very complex problem when considered in terms of the contact angle of individual fibres, but it is relatively easily solved by use of apparent contact-angle methods4 The calculated pressure in this case agrees to within the limits of error with the measured penetration pressure. It is, of course, only the advancing contact angle that is involved in penetration pressure and , in general, problems that involve only the advancing contact angle appear to give agreement of theory and experiment.The receding contact angle cannot be used with the same confidence, and it is probably true to say that no phenomenon in textiles that involves receding contact angles has been satisfactorily explained. The source of the difficulties Cassie and Baxter, Trans. Faraday SOC., 1944, 40, 546. 4 Baxter and Cassie. J. T e x t . Inst., 1945, 36, T67.A. B. D. CASSIE I3 with receding contact angles is easily traced: it is their instability; the fibre-water receding contact angIe may have one value on first contact with water, but this value decreases rapidly with continued immersion of the fibre in water.The instability of receding contact angles is the real bar to progress in the theory of water repellency, and it may be worth while discussing once again the problem of the difference between the advancing and receding angles. The type of surface that gives finite contact angles is of considerable importance in this respect. The work of adhesion W of the liquid to the smooth solid is given by : and one notes that when 8 is finite, W is less than z y u , or the work of adhesion is always less than that of liquid to liquid. Condensation of the saturated vapour in a form identical with the bulk liquid would not be expected unless W was equal to, or greater than, 2 y u , or unless 8 was zero. But it is well known that vapours are adsorbed on to surfaces that show finite contact angles, and the liquid must show its finite contact angle against the adsorbed layer rather than against the clean solid surface.Bangham and Razouk have discussed contact angles from this point of view, and pointed out that the adsorbed films must be different from the liquid in bulk. The isotherms of the vapour molecules adsorbed on to finite contact- angle surfaces are usually of the sigmoid type, which are now identified with multimolecular adsorption. This adsorption postulates low-energy localised sites, so that at low vapour pressure, molecules are adsorbed exothermically on to the sites; as the vapour pressure increases molecules are supposed to condense on to those already in the low-energy sites, giving rise to multimolecular adsorption, which is in excess of the Langmuir adsorption.The problem of multimolecular adsorption is to account for the excess condensation. If the contact angle is finite, the average work of adhesion must be less than that of liquid to liquid and condensation could not take place at saturation or lower vapour pressures without an increase of entropy compared with that of the liquid in bulk. The increase of entropy comes from the distribution of the adsorbed molecules.6 7 If X molecules of a total number N , are adsorbed singly on to localised sites, their partition function is : w = + cos e) . (6) Qs = (B - X ) ! X ! (7) Where B is the total number of localised sites, Es is the potential energy of an adsorbed molecule relative to one in the bulk liquid, and j s is the partition function for a molecule in a site. The partition function for the (N - X ) condensed or " liquid " molecules is : (8) (N - I) ! QL = (N - X ) ! ( X - I) ! Where EL is the potential energy of a condensed molecule relative to one in the bulk liquid, and j L is its partition function ; j L is usually assumed to be identical with that for a molecule in the bulk liquid.6 Bangham and Razouk, Trans. Faraday SOC., 1947, 33, 1459. Cassie, Trans. Faraday SOC., 1945, 41, 450. 7 Cassie, Trans. Faraday SOC., 1947, a, 615. BAnderson, J . Amer. Chem. SOC., 1946, 68, 688. "Hill, J . Chem. Physics, 1946, 14, 263.I4 CONTACT ANGLES The increase of entropy for the adsorbed molecules comes from the contiprational partition function of the "liquid" molecules.This function represents the number of ways that (N - X ) identical molecules can be divided into X separate compartments with no restrictions as to how many there are in any one compartment. The essential point for the present discussion is that the compartments must be separate : or each compartment must represent a distinct cluster of molecules. If the compartments are not distinct, and they are not distinct in a continuous film, the configurational partition function becomes unity, and the molecules will evaporate when EL is positive, which is the requirement for the existence of a finite contact angle. Hence, any multimolecular layer on a surface which shows finite contact angles must be in the form of distinct clusters of molecules ; it cannot be a continuous film.The surfaces immediately ahead of an advancing contact angle and behind a receding angle are, therefore, heterogeneous : they consist of clusters of liquid separated by areas of liquid-repellent solid surface. The observed contact angle will, therefore, be a composite one of the form 8" given by (4). The contact angle 8, with the clusters will be zero, and that with the solid surface 8 , may have any large value ; there is, in fact, no theoretical objection to 8 , being I ~ o " , or to W of eqn. (6) being zero for the areas of endothermic reaction of the liquid with the surface. If this description of a surface adjacent to a contact angle is correct, the difference between the advancing and receding angles must be due to different values of a, and a2 for an unwetted surface and for one from which a liquid is receding; or the size of the liquid clusters must be different for the two surfaces when exposed to saturation vapour pressure.Now, eqn. (8) does show that such a difference is possible at one vapour pressure, or at one value of QL ; for EL contains the surface energy of the clusters which will depend on their size, and it also contains the entropy term which depends on the number of clusters. If the receding liquid leaves some clusters which cover more than one localised site, the average size of the clusters will be increased, EL will be decreased, and the corresponding increase in QL will be compensated by the reduction in the number of clusters, which reduces the configurational entropy term.The larger clusters will require a greater adsorption of molecules, which corresponds to the well- h o w n adsorption hysteresis effect, and they will give larger values of a, and smaller values of a2. Thus, a liquid advancing on to a " dry " surface may encounter a large number of small discrete clusters which give a small value of al, whilst a receding liquid may leave large clusters with a com- paratively large value of a,; the advancing contact angle will, therefore, be large, and the receding one small. This is, of course, very much a qualitative description of the difference beheen advancing and receding contact angles, and it is essential to deter- mine whether or not the terms in eqn. (8) have the magnitudes necessary for the proposed mechanism. EL can be deduced from the adsorption isotherm, and Anderson* gives values ranging from x75 to 300 cal./mole which are of the order of magnitude one might expect from the surface energies of clusters, each containing a few molecules.EL for water adsorbed by keratin is 550 cal./mole, but this value is complicated by the swelling energy of the keratin.10 The average size of the clusters at saturation vapour pressure can also be deduced from the isotherms,' and they may be shown to range from 2 molecules per cluster for water adsorbed by keratin to 5 per cluster for water adsorbed by Ti0,.8 The clusters are, therefore, (N - I) ! (N - X) ! (X - I) ! 10 Cassie, Symp. SOC. Dyers Col. (Bradford, 1946), p. go.A. B. D. CASSIE 15 quite small and their surface energies should be large as is indicated by Anderson’s data.The configurational entropy contribution to the free energy FM is given by the negative of the logarithm of the appropriate terms in (8) or, neglecting unity in comparison with N and X , by : I If X is -N, so that each cluster contains on the average a molecules, the free energy per mole is given by : a I 1 w=(I-;)log(RT +-log- a a . (10) Eqn. (10) gives FM/N as - 415 cal./mole at 300’ K. for z molecules per cluster, - 335 cal./mole for 4 per cluster, and - 305 for 5 per cluster. These values do not balance the potential energy term EL because of other factors in the partition function expressions (7) and (8), but they are of the same order of magnitude, which is what is required for different sizes of clusters to give the same value of the free energy per mole.Thus, increasing the cluster size from 4 to 5 increases the free energy by 30 cal./mole so far as configurational entropy is concerned, whilst the surface energy might be expected to decrease to ($)2’3 of its original value ; if the original value was 300 cal./mole, the value at 5 molecules per cluster would be 265 cal./mole, or the decrease in free energy due to the increase in cluster size would be 35 cal./mole, which very roughly balances the increase due to the configurational change. It might be thought that this argument could be extended to give one cluster, or a continuous film of adsorbed molecules ; but one notes that the absolute value of the configurational entropy term is generally larger than the energy term, EL ; one cluster would reduce the entropy term to zero, whilst EL can not be reduced to zero, so that a continuous film is not a possible state of the system.One concludes that at saturation vapour pressure, the adsorbed molecules can vary in extent by assuming a number of different configurations which all lead to one value of the free energy per mole, and are, therefore, possible states of the system. If adsorption is obtained by increasing the vapour pressure, one cluster will form at each occupied localised site, and the configuration obtained at saturation vapour pressure will be unique ; correspondingly, the advancing contact angle for a “dry ” surface should be unique. But, when the liquid recedes from the solid surface, it may leave clusters which on the average cover more than one site ; the amount adsorbed will then be greater than that on the surface ahead of the advancing contact angle, and crl will be greater behind the receding angle than ahead of the advancing one, giving a small receding contact angle. There does not seem to be a unique configuration for the receding system, as one value of the free energy per mole can be obtained from a range of configurations ; hence, the receding contact angle will not have a unique value, and this is, in fact, its most troublesome experimental property. My thanks are due to Mr. B. H. Wilsdon, Director of Research, for his interest in this work, and to the Council of the Wool Industries Research Association for permission to publish this account.16 THE SPREADING OF A LIQUID OVER A ROUGH SOLID Summary The relationship of contact angles to surface structure is outlined. The difference between the advancing and receding contact angles is discussed in terms of the modern theory of multimolecular adsorption ; this theory indicates that the advancing angle will be unique, whilst the receding one will generally be less than the advancing angle and need not have a unique value. Wool Idwtries Research Association, Headingley , Leeds, 6.

ISSN:0366-9033    

DOI:10.1039/DF9480300011

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

16 THE SPREADING OF A LIQUID OVER A ROUGH SOLID THE SPREADING OF A LIQUID OVER A ROUGH SOLID BY R. SHUTTLEWORTH* AND G. L. J. BAILEY? Received 23rd February, 1948 The spreading of a liquid over the surface of a solid is a complex phenomenon ; the final position of the liquid at rest depends not only upon the surface energies of the liquid, the solid and the solid-liquid interface, but also upon the roughness of the surface and the manner in which the liquid is placed on the s0lid.l Experimentally, spreading is studied by measuring the variation of the apparent contact angle v, the angle between the general directions of the liquid and solid surfaces. If the solid is rough, this is different from the true contact angle 8, the angle between the liquid and solid surfaces at a particular point in the line of contact.In general, even when the liquid is at rest, the static value of the apparent contact angle Q)E depends upon whether the liquid has reached this position by advancing or receding over the solid, the advancing being always greater than the receding contact angle. The difference in the two values is called hysteresis . Wenze13 was the first to discuss the influence of roughness on apparent contact angle. Hysteresis of the contact angle has previously been attri- buted to the adsorption on the solid, either of the liquid or of a layer of foreign molecule^.^ In this paper the problem of the spreading of a liquid over a rough solid is considered in detail and it is shown that hysteresis of the contact angle will arise merely because of the inevitable roughness of solid surfaces and that it is not necessary to invoke any special mechanism of adsorption to explain it.However, in particular systems it is probable that adsorption contributes to hysteresis, and that the relative importance of the two effects can only be decided by experiment. If gravity is neglected, the final position of the liquid at rest is one of stable or metastable equilibrium in which the total surface energy of the system is a minimum. Because of fluidity it is also necessary that the surface energy of the liquid surface (proportional to the area) be a minimum, subject to the constraints that the liquid volume be constant and that the liquid remain in contact with the solid over a certain (not necessarily plane) 1 Adam, Physics and Chemistry of Surfaces (Oxford, 1941).3 Burdon, Surface Tension and the Spreadixg of Liquids (Cambridge, 1940). a Wenzel, Ind. Eng. Chem., 1936, 28, 98s. 4 Bartell and Wooley, J . Amer. Chem. Soc., 1936, 55, 3515. 6 Langmuir, Science, 1938, 87. 493. * H. H. Wills Physical Laboratory, Bristol University. t British Non-Ferrous Metals Research Association.R. SHUTTLEWORTH AND G. L. J. BAILEY I7 domain. The shape of the surface ABC, Fig. I, which has the minimum area subject to these constraints, is obtained from the consideration that for any small arbitrary change of shape brought about by the elements of area dA being displaced in the directions of their normals by amounts dn, the total change of area is zero for a minimal surface or, J J J(c+k) dA.d.n=o.rI and r 2 are the principal radii of curvature at the point dA and the integration is carried out over all the liquid surface. However, since the total change of volume is zero, Gos . FIG. I . J J J ~ A . d n = o . Hence the minimal surface satisfies the differential equation ' (1) I 1 - +-= const. . Yl r 2 Thus, if the volume of the liquid and the domain over which it is in contact with the solid are specified, its surface is completely defined. Similarly, when the drop is in equilibrium with the solid, any infinitesimal displacement of the line of contact of the three interfaces must produce zero change of energy. When the position of a portion of liquid-gas inter- face is changed from the equilibrium position BC to BD by rotation through an angle do, the decrease of volume being compensated by a corresponding increase over BA, the total change of surface energy is zero.If curvature perpendicular to the plane of the paper is neglected BCdO BC2dt3 1 ( ss - SSL )::; - - s & a -O (AB), = O, SS, SL, SsL being the energies per unit area of the solid, liquid and solid- liquid surfaces respectively. The position of B is arbitrary and therefore BC/AB can tend to zero and the final term be neglected. The equilibrium condition then reduces to ss = ssL + sL cos eE . . * (2) If a volume V of a liquid is p1aced:on a smooth plane solid withiwhich its angle of contact is &, equilibrium occurs when (I) and (2) are satisfied simultaneously. This is a spherical cap whose height It and radius rl are given bv When a liquid is at rest on a rough solid, eqn.(I) and (2) must still be satisfied at all points on its surface and at the line of contact. In general, this necessitates that near the solid the liquid surface be ragged ; but at distances from the line of contact large compared to the wavelength of the solid's roughness, the liquid surface will be smooth and inclined at an angle tpE to the general direction of the solid surface. The value of the contact angle measured on a rough solid is Q)E ; and by an extension of the previous treatment, the value of which gives the absolute minimum of the total surface energy is readily found. In Fig. 2, B represents a line on the liquid surface whose distance from the solid is so large that here the surface is smooth. When q .~ corresponds to minimum total surface energy the change of energy on displacing the surface from BC to BD is zero, the distance CD is supposed small compared to BD but large compared to the dimensions18 THE SPREADING OF A LIQUID OVER A ROUGH SOLID of the roughness. The change in energy of the liquid arises almost entirely from the change of area of the smooth portion of its surface (BD ' - BC ') per unit length. The increase in the solid-liquid interface after this dis- placement is rCD per unit length, where r is the ratio of true to apparent surface area of the solid. By the same argu- ment as is used to derive eqn. (2), SL S S = SSL + - cos Q)E, L@X Y or cos Q)E = Y cos & . (3) This formula was first derived, but in a less rigorous manner, by Wen~el.~ Cassie and Baxter 6 pointed out that when the true angle of contact was greater than goo, the liquid did not penetrate into the concavities of the roughness and that in this case Wenzel's formula must be modified by the inclusion of a further term.When a liquid is placed on a solid surface so as to cover an arbitrary domain, the liquid-gas surface rapidly assumes a shape which satisfies (I). Then in general, 8 the angle between liquid and solid does not satisfy (2) and the liquid spreads or recedes so as to cover a different solid domain, the liquid-gas surface continuing to satisfy the differential eqn. (I), but with different boundary conditions. Movement continues until simultaneously (I) is satisfied over all the surface and (2) over the line of contact at the edge of the solid domain.This will be an equilibrium position of minimum total surface energy, but it need not necessarily be the absolute minimum €or which the apparent contact angle is given by (3). Subsidiary rninima, as well as the absolute minimum, can exist so that positions of metastable as well as stable equilibrium are possible. Two-Dimensional Roughness Although, on solids whose roughness is of such a nature that metastable equilibrium is excluded, (3) gives the general direction of the liquid surface not too near the solid, the shape of the liquid surface in the immediate vicinity of the solid must depend upon the particular form which the rough- ness takes. In order to obtain a detailed picture of the shape of the liquid surface in the immediate vicinity of a rough solid, and to understand the processes of spreading, it is best to consider initially two-dimensional roughness; this has the form of a series of parallel grooves separated by ridges.Spreading over such a surface is anisotropic and will be discussed for directions parallel and perpendicular to the grooves. Ga. n 5 . Sol,d. C D FIG. 2. (a) Spreading Parallel to the Grooves.-A liquid rises or falls in a capillary tube according to whether its angle of contact with the tube is greater or less than goo ; the height of rise or fall is limited only by gravity. A drop of liquid placed on a smooth solid in which there is a groove behaves in a similar manner: if, in equilibrium, the angle of contact is acute, a tongue of liquid will extend from the drop along the groove ; if the angle of contact is obtuse, the reverse will occur and the liquid surface will be dented and not extend so far in the groove as it does on the smooth surface.The exact form of the tongue or dent will depend upon the geometry of the cross-section of the groove, but the deeper and narrower the groove, the more nearly it approximates to a capillary tube and the greater the effect. For small contact angles the liquid will flow to an unlimited length along the groove ; when the angle is large and the groove deep and narrow, the liquid will nowhere touch the bottom. @ Cassie and Baxter, Trans. Faraday SOC., 1944. 40, 546.R. SHUTTLEWORTH AND G. L. J. BAILEY I9 This behaviour is best illustrated by considering the mathematically simple case in which the groove has the form of an isosceles triangle of height h and basal angle (180" - 239).When a large drop rests on such a groove, the surface of the tongue of liquid must have an approximately zero curvature equal to that of the remainder of the drop, and be inclined at the equilibrium angle of contact to the walls of the groove. A solution which satisfies these conditions is that of a plane inclined to the horizontal at an angle Q where cos a = cos OE sec y This is not the complete solution because the plane would not join smoothly with the remainder of the drop : it seems that most of the tongue will have this form, but where the tongue merges into the drop the surfaces will have equal and opposite curvatures in perpendicular directions. The approximate length of the tongue is : h I = - tan a' Because of the definition of y, tan y is always positive so that the sign of 2 depends only upon whether 8E is acute or obtuse.When 8s is acute, the length of the tongue increases as y increases (as the groove becomes sharper) until when it becomes equal to 8 the liquid spreads continuously up the groove to a length determined only by gravity. When the solid is completely covered by identical isosceles grooves, the form of the liquid surface in the grooves and near the solid is that of a plane inclined to the horizontal at an angle a. This is otherwise obvious from (3), for with this type of roughness, r = sec y. When the solid surface contains only occasional grooves connected by plane portions, the presence of tongues makes the liquid surface near the solid ragged.The apparent angle of contact in the grooves a is less than that on the plane portions of the solid, but further from the solid the liquid surface is smooth and has a slope, intermediate between a and 8, given by (3). In general, the section of the groove is not an isosceles triangle, but it can be regarded as being derived from one of angle y-. by a rounding of the comers, y-. is the maximum slope of the side of the groove. Because Y, the roughness ratio, is less than sec y-. this form of groove causes a smaller change in .the apparent contact angle than does the corresponding triangular groove, and the tongues of liquid extend to a smaller distance in the grooves. (b) Spreading Perpendicular to the Grooves.-In this case the line of contact is rectilinear and moves in a direction perpendicular to the length of the grooves.The problem is the spreading of an infinitely long cylinder of liquid, placed on a grooved surface with its axk parallel to the grooves. Initially, the angle 9 between the liquid and the general direction of the solid is ISO", the liquid spreads so as to reduce 9, but for each value of tp the liquid surface remains a cylindrical segment. As spreading progresses, the height of the segment decreases and the radius increases, Fig. 3. The roughness of the solid, i.e., the presence of grooves, causes the true contact angle 8 to be less or greater than the apparent angle y , according to whether the gradient of the solid at the line of contact is the same as, or opposite to, that of the liquid surface (Fig.4, points A and B). The nature of the roughness is specified by the angles y' and y, the inclinations which the positive and negative slopes of the grooves make with the general direction of the solid. The maximum A FIG. 3.20 THE SPREADING OF A LIQUID OVER A ROUGH SOLID angles of slope are y,-. and yfmaX. and the roughness is supposed to be such that these are always less than goo. The true contact angle of the liquid with the negative slope is and with the positive slope 8 = ( p - y , e = + yf. As the liquid spreads, the apparent contact angle, 9, decreases mono- tonically ; 8, the true contact angle, has superimposed upon this same mean FIG. 4. decrease a periodic variation of amplitude v m a .+ V’ma. which occurs each time the line of contact moves over a wavelength of roughness. Spreading ceases when 8 falls to its equilibrium value OE, and this first occurs when The line of contact is then at that portion of a groove where the gradient is a maximum ; and the apparent contact angle is greater than the true contact angle by an amount y m a . This value of y is not the same as that predicted by (3), for although this is a minimum of the total surface energy, it is a subsidiary minimum of metastable equilibrium. If the liquid be spread over the solid by some mechanical means, the apparent contact angle y may be reduced to such an extent that the true contact angle is less than its equilibrium value 8E. The liquid then spon- taneously recedes until 8 increases to t9E.During recession the apparent contact angle increases monotonically whilst the true contact angle has superimposed upon this mean increase a periodic variation of amplitude vmax. + y’ntas. Recession ceases when the true contact angle first reaches its equhbnum value and The line of contact is then at a portion of the groove where the gradient is a maximum, and the apparent contact angle is less than the true by an amount y‘max. This is another position of metastable equilibrium. It is therefore clear why on such a surface the advancing is greater than the receding contact angle, the hysteresis being ymax. + y’max. Other positions of metastable equilibrmm occur for values of Q)E between the extremes of advancing and receding contact angle, but these cannot arise from the spontaneous spreading or recession of the liquid, but only from some form of mechanical spreading.Eqn. (4) and (5) are respectively the boundary conditions for the surfaces of the advancing and receding liquids, for they define the gradient of the surface at the line when it intersects the steepest portion of the groove. When the advancing apparent contact angle is obtuse or the receding apparent contact angle acute, (4) and (5) are not always applicable ; for there is the possibility that the planes defined by them could not form part of the liquid surface because they intersect the next ridge, as at C , Fig. 4. When this is so, the first positions of equilibrium will not be given by (4) and (5), but the advance or recession of the liquid will continue beyond this with the corresponding decrease or increase of the apparent contact angle.The final position of the liquid at rest will be the first metastable equilibrium Q)E = OE + vmax. (4) vE = eE - v ~ ~ . (5)R. SHUTTLEWORTH AND G. L. J. BAILEY 21 position for which the predicted boundary conditions are such that the liquid surface clears the top of the next ridge. This will be for the advancing liquid when and for the receding liquid when Q)E = OE + YE, FE = OE - Y‘E, where yIE and are the gradients of the groove at the place where the liquid surface meets the solid, they are less than the maximum gradients. In order that a large hysteresis exist between the advancing and the receding apparent contact angles, it is not sufficient merely to increase the maximum gradient of the groove ; it is also necessary that the sides have a large gradient at a place whose distance from the top is small compared to the groove width.When the grooves are narrow at their points of greatest gradient, YE + y ’ ~ will be small and there will be only small hysteresis. Three -Dimensional Roughness The roughness on the surface of a real solid will not be in the form of grooves but will probably be isotropic with the same properties in all directions. Two limiting forms of such surface texture occur: a plane covered by an array of hills standing on equal square bases, and the corresponding female surface of a plane covered by an array of square hollows. Spreading on the latter kind of surface would be of the same nature as spreading perpendicular to the grooves in the two-dimensional case; the angle of contact would be greater or less according to whether the liquid was advancing or receding.This hysteresis is greatest when the ridges between the hollows are steep and the widths of the hollows large compared to their depth. Spreading on the male form of surface, in which valleys exist between the hills, is analogous to two-dimensional spreading parallel to the grooves ; positions of metastable equilibrium do not arise, the apparent contact angle is given by (3) and is greater or less than the true contact angle accord- ing to whether the latter is obtuse or acute. Spreading will occur in the valleys between the hills so as to form projecting tongues of liquid, and if the angle of contact is sufficiently small it will proceed until they are full.The occurrence of spreading in the valleys excludes the possibility of metastable equilibrium, in which the line of contact lies on the slope of a ridge; but before the general line of contact can advance so as to reduce the apparent contact angle the valley in front must first fill with liquid. This viscous flow of the liquid in the narrow valleys will determine the rate at which spreading occurs. Experiment shows that advancing and receding angles of contact may vary by so much as 60°, but that sometimes the liquid will slowly assume an equilibrium value which is the same for spreading and recession. Little is known of the texture of solid surfaces, but experiments on contact resistance indicate that even the smoothest solid surfaces have projections higher than 100 A. and these would be sufficient to explain the observed effects. Summary A liquid placed on an ideally smooth solid spreads until the total surface energy is an absolute minimum and the contact angle is uniquely defined. When the solid is rough, the value of the apparent contact angle a t the absolute minimum of surface energy is different and is given by Wenzel’s expression. In equilibrium, the liquid22 MOBILE INSOLUBLE ADSORBED FILMS surface near a rough solid must be ragged in order that it intersect the solid a t the true contact angle. On solids, whose roughness is formed by isolated pits, subsidiary minima of total surface energy exist and hysteresis of contact angle arises because the liquid comes to rest a t a different minimum after spreading and recession. The inevitable roughness of solids is sufficient to explain hysteresis. H. H . Wills Physical Laboratory, University of Bristol.

ISSN:0366-9033    

DOI:10.1039/DF9480300016

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

22 MOBILE INSOLUBLE ADSORBED FILMS THE MECHANICAL INTERACTION BETWEEN MOBILE INSOLUBLE ADSORBED FILMS, CAPILLARY CONDENSED LIQUID AND FINE-STRUCTURED SOLIDS BY W. HIRST Received 19th March, 1947 Provided that the adsorption isotherm of a vapour on a homogeneous fine-structured solid is reversible, the free energy lowering per unit mass of the solid is given to a high degree of approximation by the integrated form of the Gibbs-Duhem equati0n.l n 0 where GAO is the Gibbs free energy per gram of pure adsorbent, GA is the Gibbs free energy per gram of adsorbent when in equili- brium with the vapour at pressure # and fugacity f, mA, m B are the masses of adsorbent and adsorbate respectively, and M is the molecular weight of the adsorbate. The free energy lowering derived in this way is very nearly correct no matter what the method of interaction between solid and vapour may be.In particular, if the solid is rigid and incapable of dissolving the vapour. the free energy lowering is completely accounted for by the lowering of its surface free energy and 5 1 2 d log, f = FC* where F is the (Helmholtz) 0 free energy lowering per unit surface, and C is the surface area per gram. Should the solid swell on adsorption of a vapour, the free energy lowering of the solid may not now be equated to the surface free energy lowering only, since some energy will be stored in the solid as work of expansion. Accordingly, where W is the work of expansion. It should be noted that C may no longer be constant. The magnitude of W will depend on the physical properties of the solid, notably on its mechanical properties, and on the mechanism whereby swelling occurs.It is to be expected, for example, that more work would be expended in stretching the actual substance of the solid than in merely separating its structural units. The adsorption isotherm alone however does not provide the evidence whereby a separate evaluation of FC and W may be made, nor does it, by itself, enable the mechanism of swelling to be determined. * This equation is exact. 'Bangham, Nature, 194.1. 154, 837. G.40 - GA = FC - WW. HIRST 23 There are additional uncertainties of interpretation when, as often happens with swelling adsorbents, the isotherms exhibit hysteresis, for the question arises how to determine the decrease in free energy of the system when the isotherm does not conform to the thermodynamic condition of reversibility implied in eqn.(I). It is possible by considering the properties of suitable models to suggest how to obtain approximate solutions for such problems as these in the case that the adsorbed films are mobile and insoluble. Although this qualification necessarily limits the generality of the conclusions, mobile films are of common occurrence.2 The reason why it is possible to progress with such problems when the surface films are mobile is because a mobile film exerts a spreading pressure Q, numerically equal to F. It is the action of the spreading force of the film on the underlying solid which causes the swelling so that observation of the changes in dimensions and the changes in mechani- cal properties which accompany adsorption provides additional evidence which may facilitate the interpretation of the adsorption isotherms.A few examples as illustrations of one method of approach are given below. The earlier are concerned with the interaction between deformable solids and surface films and the later examples consider the additional effects arising from capillary condensation. The Cause of Swelling by Adsorption of an Insoluble Mobile Film .- There are two recognised ways 6 whereby a mobile insoluble film may cause a non-rigid adsorbent to swell. They correspond to the two cases mentioned earlier of swelling of the actual solid substance and swelling by separation of the constituent units. If any system free from external restraint is in equilibrium, the net force acting across any imaginary surface dividing the system into two parts is zero.Then, if the system in equilibrium consists of a solid on which is adsorbed a mobile film, which exerts a spreading force, it follows that the solid must be in tension. Therefore, during the process of adsorption, the solid expanded. The second swelling mechanism corresponds to the earlier stages of a process of peptisation. If the fine-structured solid contains crevices too narrow to accommodate on either face an adsorbed film of the thickness natural to an external surface, the spreading force-squeezing the adsorbed phase into the crevices-will tend to force the walls apart. Capillary Condensation.-When capillary condensation occurs, the surface becomes covered with liquid. The spreading pressure at the adsorbent- adsorbate interface then becomes, by the equation of Young and Dupre,8 * where Q,A = spreading pressure when the surface is covered by liquid, vsv = spreading pressure when the surface is covered by vapour, ylV = surface tension of the liquid and qsl = ySv + nv cos e 8 = contact angle.Beyond the range of the surface field the liquid is under a tension, the 'Bangham and Fakhoury, J . Chem. Soc., 1931, 1324; Bangham, Fakhoury and Gregg, J. Chem. SOC., 1942, 696. 'Harluns and Jura, J. Anter. Chem. SOC., 1944. 66, 1356. 6Hill, J . Chem. Physics, 1946, 14, 441. Bangham and Fakhoury, Proc. Roy. SOC. A , 1931, 130, 81 ; Bangham, Ultra-Fine Structure of Coals and Cokes (B.C.U.R.A., 1g44), p. 27.?Orowan, Nature, 1944. 154. 341. * Bangham and Razouk, Trans. Faraday SOC.. 1937. 33, 1459. Mohamed, Proc. Roy. SOC. A , 1934, 147, 152. * Here p is a positive and y is a positive quantity so that, for €I< F. qd is greater than pm.24 MOBILE INSOLUBLE ADSORBED FILMS magnitude of which, for a definite temperature, depends on the vapour pressure. Therefore when liquid condenses in a porous solid two new forces act, one parallel to the surface (due to the quantity y cos 0.) and the other due to the hydrostatic tension in the liquid acting normally to the surface. For simplicity of calculation in those of the following examples which deal with capillary condensation, it will be supposed that the range of the surface field is negligible as compared with the distance of separation of the surfaces between which liquid condenses, and that, beyond this range, the liquid is under uniform tension.(A) Adsorption without Capillary Condensation I. Swelling by Stretching the Structural Units.-To show more clearly how to obtain the fraction of the free energy change of the solid which is stored as work of expansion, the model offering the simplest mathematical treatment is chosen. Consider a cylindrical cavity of original length I , and radius yo with elastic walls (Fig. I a). The elasticity is supposed to be anisotropic so that the walls may stretch longitudinally but not radially. A small opening in one end of the cylinder allows the inner surface to adsorb vapour from the outside space. On adsorption of a vapour the spreading force of the film acting on the ends of the cavity will extend the walls to a length Z at which the elastic restoring force of the walls equals the spreading force of the adsorbedam.At equilibrium, for a solid obeying Hooke's law, (I - l o ) I 0 V i = k - where k is a constant related to the elastic properties of the material. Then, for an expansion AZ = (t?,+At?) * (2nr0 - dz) The surface energy The free energy Hence the work of Using eqn. (I), work of expansion per unit mass of adsorbent lowering = 9 (lo+ Ai) . ( 2 7 ~ 0 ) ( l o + dl) lowering of the system = V (lo+ AZ 2Z0 + A1 21, + AZ M J . (27cr0){ (I, + AZ) - (4AZ)) {Free energy lowering of the system} expansion = ~ - AZ RT? mI, = - . - dlogef 0 This quantity may be evaluated experimentally. Similar calculations may be made for more complicated models, eg., for three-dimensional swelling of a cylindrical cavity, for the swelling of an assembly of spherical particles, etc.The consideration of other models will lead to a change in the proportionality factor which in the example above is AZlaL, + Al. 11. The Widening of Crevices.-Structures such as those in Fig. I d and e may conveniently be represented by the model of Fig. I g and h, in which the resistance of the material at the head of a crevice to the spreading * I t should be noted that the quantity y cos 8 may depend on the vapour pressure at which condensation occurs.W. HIRST 25 force which is tending to force the walls apart is represented as an elastic restraint controlling the distance of separation of rigid surfaces.Then, if the area of the rigid surface is A and of the elastic material A 2, relations such as those developed in the preceding example will apply to the area A t only. It is unlikely that in any practical case the structure would be suffi- ciently well represented by the model for the ratio A J A , to have much significance, and the equations for the model are not developed. a b d e 9 h k 1 V N . PRESMC n t v*p. PI)ESSW)L P FIG I . Its important qualitative features are : (I) the expansion is proportional to the spreading pressure tp, (2) the work of expansion is smaller than in I by a factor depending on the ratio AJA,. There is no limit to this ratio and the work of expanding the solid may be negligible. 111. Rigid Surfaces held together by Surface Forces with some Elastic Restraint.-If there are regions within a swelling solid where the surfaces are sufficiently close together for surface forces to contribute appreciably to the cohesion of the solid, the adsorption isotherm may be expected to show hysteresis.This is because surface forces decrease as an inverse power of the distance of separation so that a spreading force which26 MOBILE INSOLUBLE ADSORBED FILMS just suffices to cause the surfaces to move apart will be more than sufficient to keep them apart. A simple representation of such a system is shown in Fig. I k, I , m. An elastic restraint is incorporated to prevent infinite separation of the surfaces and it will be supposed that the solid may deform elastically around the cohering regions before these spring apart.The characteristic features of the model would then be : (I) in the early stages of adsorption, the expansion being controlled by elastic restraints would be proportional to the spreading pressure ; (2) when the surfaces separate, the expansion and adsorption suddenly increase for constant spreading pressure ; (3) after separation, the swelling being again limited by the elastic restraint is roughly proportional to the spreading pressure ; (4) during desorption, the shrinkage is initially roughly proportional to the decrease in spreading pressure ; (5) when the combined action of the surface forces and elastic restraint overcome the expanding action of the film there is a sudden collapse of the separated surfaces ; and (6) in the final stage the shrinkage is proportional to the reduction in spreading pressure.The behaviour of such a system is shown diagrammatically in Fig. I n and p . It is also to be expected that the system would be more compressible after the originally cohering regions have been forced apart. Since, along the path AB, Fig. 19, the expanding force exceeds the resis- tance to expansion and, along CD, the force of contraction exceeds the resistance of the film, neither the application of eqn. (I) to the adsorption isotherm nor to the desorption isotherm gives the free energy lowering of the system when exposed to saturated vapour. The former path would lead to a value too small and the latter to too large a value. There need be no relation between the area of the hysteresis loop observed experimentally and the mechanical work stored in the solid along the path AB, for it might happen that the sudden swelling enabled adsorbed vapour molecules to reach parts of the internal surface which they could not previously approach. The primary meaning of the hysteresis loop is that there is a barrier preventing the adsorption from continuing until the porous solid possesses the minimum free energy consistent with the vapour pressure.I t will be noted that in the important practical case for which the work of expansion is a small part of the free energy change due to adsorption, the application of the integrated Gibbs-Duhem equation to the desorption isotherm gives an approximate value for the surface free energy lowering of the system.(B) Capillary Condensation IV. Condensation in a Cylindrical Cavity with Thin Walls of Iso- tropic Material.-((a) The author has shown elsewhere that when capillary condensation takes place in a cylindrical cavity with thin isotropic walls, the tube shrinks radially. The new radius r is given by 7 1 r l - 7 --.- y cos 0 v Y 1 - 7 0 2 7 - Y I where Y,, is the original radius in vacuo, and r l is the radius when the capillary is expanded by the film pressure v. As a result of the radial Hirst. Nature, 1947, 159, 267.W. HIRST 27 shrinkage, when the vapour pressure is lowered slightly, liquid will remain in the tube, i.e., the adsorption isotherm exhibits hysteresis. (b) The decrease in the longitudinal expansive force is so that the length of the cavity will decrease, remain constant, or increase according as r l q is greater than, equal to, or less than ry cos 6. Since rl is necessarily greater than r and since at saturation pressure tp for many adsorbent-adsorbate systems is several times as large as y cos 8, it is to be expected that on capillary condensation at higher vapour pressures a longitudinal contraction would occur.On raising the vapour pressure further, the tension in the condensed liquid relaxes and it is under no tension when in equilibrium with the saturated vapour. The swelling pressure at the solid-liquid interface is then equal to the sum of the pressure in a surface film when exposed to saturated vapour and the quantity y cos 8.* It is, therefore, the same as it would have been had the porous solid been completely immersed in liquid and there would be no change in dimensions if this were done.It will be noted that as a consequence of condensation the radial expansion (and probably the longitudinal expansion also) would increase more rapidly with pressure than it would if condensation did not occur. V. Condensation between Plane Parallel Rigid Surfaces held by Restraints. If A is the free area of the rigid plates (Fig. I h ) , d is their distance of separation, L is the periphery of the plates, 2 is the total periphery of the restraints, and n is the cross-section of the restraints. On condensation, the force tending to cause contraction 2y cos 0 . A - a + y c o s 6 . L and the force opposing contraction = Z(q + y cos 6) + a (some function of the mechanical properties of the restraints).If the mechanical properties of the restraining material are known, the dimensional changes accompanying condensation can be calculated. The important distinction between this and IV is that the ratio of the magnitudes of the force of contraction to the opposing force may have any value and a sufficiently slight restraint would be completely overcome on condensation of liquid and the system collapse. It will be noted that should the actual structure of the system be similar to that depicted in Fig. I d, the contact areas such as are marked C in Fig. I d and f may increase after condensation and the mechanical compressibility of the system decrease. The isotherm would exhibit hysteresis for the same reason as in IV a. * Note, as before, that this quantity may not be constant but depend on the vapour pressure.28 MOBILE INSOLUBLE ADSORBED FILMS Conclusions The usefulness of these examples is most simply illustrated by the following conclusions which may be drawn from them.I. If it is possible to estimate the work of expanding a solid from independent measurements of its mechanical properties, calculations such as those in I may determine whether swelling is due to an extension of the actual substance of the solid or represents a separation of the constituent units (I and 11). 2. The interplay between the spreading force of the adsorbed film and the elastic restraints of the solid system may control the magnitude of the swelling even though the work of expansion is negligible (11).3. If the isotherm exhibits hysteresis due to the mechanism of I11 and the work of expansion is small, the desmption isotherm may be used to obtain an approximate figure for the free energy lowering of the system. 4. If the hysteresis in an isotherm is due to the mechanism of 111, measurements of the length and deformability of the system over the region of hysteresis would show that on desorption the system would be larger, and more deformable than on adsorption. 5. If liquid condenses in capillaries of uniform size in a solid, the latter should shrink radially (IV). In practice, the capillaries in a solid would probably cover a range of sizes and the effect due to capillaries within a given narrow range of diameters might be masked by the relatively rapid expansion of other capillaries after condensation.6. On capillary condensation in a system such as shown in Fig. I d its deform- ability might decrease. But, again, this effect would probably not be observed in practice for reasons analogous to those given in 5 above. 7. If there is capillary condensation and the system be in equilibrium with the saturated vapour, no change in length would be observed on plunging the system into liquid (IV c). Conversely, should a change in length be observed, capillary condensation has not occurred. This argument was first advanced by Bangham.lO 8. If condensation occurs between parallel plates whose distance of separation is controlled by only weak constraints, the system may collapse. In conclusion, it is desirable to mention that the two mechanisms described above which would lead to hysteresis in the isotherms of vapours on swelling fine-structured solids are not the only causes of hysteresis but are additional to a number of other causes, notably hysteresis due to phase transitions in the adsorbed films,s which have been discussed by other authors. The dominant point brought out by consideration of the models is that although swelling com- plicates the adsorption phenomena, a study of it and of the mechanical properties of the swelling solid may provide the evidence necessary to solve the additional problems presented. This work is part of a fundamental investigation of the influence of moisture films on the strength and breakage of coals and of the influence of sorption swelling on the movement of assemblies of fuel particles. Summary The adsorption isotherms on swelling solids are more difficult to interpret than those on rigid materials. However, if the adsorbate is insoluble and forms mobile-surface films, the swelling is caused by the spreading force of the film acting on the underlying solid. Observation of the changes in dimensions and mechanical properties which accompany adsorption therefore provides evidence to help in interpreting the adsorption isotherms. Suggestions are offered as to how this may be done for a number of simple models. B.C. U.R.A . , 13, Grosvenor Gardens, s. w.1 10 Bangham and Razouk, Proc. Roy. SOC. A , 1938, 166, 572.

ISSN:0366-9033    

DOI:10.1039/DF9480300022

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

SOME PROPERTIES OF WATER ADSORBED IN THE CAPILLARY STRUCTURE OF COAL BY R. L. BOND M. GRIFFITH AND F. A. P. MAGGS 1 Zsigmondy 2. anorg. Chem. 1911 71 356. a Brunauer Emmett and Teller J . Amer. Chem. Sot. 1938 60 309. Received 27th February 1948 The examination of the properties of adsorbed water is of importance since water is present to a considerable extent in many naturally occurring materials used in industry; for instance a quantity of water of the order of millions of tons is mined annually in association with coal in this country. Much interest lies then in the attributes of the adsorbed phase and since it is often implicit in publications dealing with the gas-solid interface that water adsorbed on porous solids simulates the behaviour of bulk water this paper describes a few critical experiments designed to emphasise any differences that may exist between the two phases.The numerous applications of the theory of capillary condensation have a common basis in the assumption that vapours adsorbed on any fine- structured solid will be in equilibrium with a vapour pressure uniquely determined by the curvature of the meniscus formed in the micro-capillaries even if these are of molecular dimensions ; hysteresis is ascribed to a change in the angle of contact between this meniscus and the solid (or film-covered solid).* Whilst identity between bulk liquid and the adsorbed film formed at saturation is not explicitly postulated by Brunauer Emmett and Teller a in their multilayer theory it is difficult to resist the conclusion that infinite adsorption of bulk liquid on plane surfaces is implied.Again hark in^,^ in his calorimetric method of estimating surface areas assumes that an adsorbed film of water on anatase at saturation vapour pressure possesses a surface energy identical with that of the free liquid. In contrast with these assumptions we may recall Foster’s observation that no sign of condensation of water on silica gel-a system regarded as a classical example of capillary condensation-could be detected very close to saturation even though the isotherm took a sharp upward turn at high relative pressures. Similarly Bangham observed that drops of liquid placed on the surface of mica subjected to a jet of the supersaturated vapours refused t o spread.He also measured a free-energy change not equal to but less than the surface tension of the liquid on immersing in liquid methanol and ethanol rods of charcoal previously saturated from the vapour phase. Bangham2* concluded that a difference of phase exists between the adsorbed film and bulk liquid. (See also Frumkin and CasseL8) Indeed Greg and Maggs find that many apparent examples of capillary condensation are more fittingly attributed to changes of phase within the adsorbed film. 8 Harkins and Jura J . Amer. Chem. Soc. 1944 66 1362. Hirst Nature 1947 159 267. 6 Lambert and Foster Proc. Roy. Soc. A 1932 EM. 246. Bangham and Sawexis Trans. Furaday SOC. 1938 34 554. * From a different standpoint Hirst 4 has shown that hysteresis is a possible con- sequence of the effect of changed pore dimensions brought about by liquid condensation.29 WATER IN CAPILLARY STRUCTURE OF COAL coal 30 The pore structure of coal is particularly favourable to the occurrence of capillary condensation ; density measurements made by Franklin lo have shown that the pores contain constrictions of molecular dimensions the size of the constrictions decreasing with increasing maturity of the coals. We shall show however that although the observations particularly at satura- tion vapour pressure point to the occurrence of liquid condensation certain aspects of the behaviour of the adsorbed and the bulk water stand in very sharp contrast. That these divergencies in behaviour represent a real phase difference is amply demonstrated by the qualitative experiments to be described ; a quantitative examination of the phenomena is in hand.Experimental Samples.-The coals used in this work were stored in nitrogen as an slack ; a sample of each coal was withdrawn ground to pass 72 B.S.S. and kept in sealed bottles until required. For experiments using - 240 B.S.S. coal samples were taken from these bottles and ground by hand. The analyses of the coals (- 72 B.s.s.) are given in Table I. We shall have occasion whilst discussing the results to refer to the porosity and surface area of the coals. By porosity is meant the volume of the pores which is accessible to helium in a lump of coal ; the porosity values quoted here are those given by Franklin,lo whose coal samples were taken from the same batch as those used in the present work.Values for the inner surface area of coals are calculated directly from the heat of wetting of the coal in methanol.ll In all the tables coals are arranged in order of decreasing rank. Description (Seyler's Classification) c. Anthracite Group Ax D. CarbonaCeoUS P. Meta-bituminous . . R. Para-bituminous . . Meta-lignitous K. Meta-lignitous - . A. Porosity and the Volume of Water Adsorbed at Saturation.- Samples of the coals ground to pass 240 B.s.s. contained in tared weighing bottles were thoroughly evacuated; dry air was then admitted and the stoppered bottles were immediately weighed. After further evacuation the coals were exposed to saturated water vapour until adsorption ceased the * Cassel J .Chem. Physics 1945. 13 249. 7 Frumkin Gogoritzkaja Kabanov and Nekrassov PhysiR. 2. Sowjet. 1932 I 255. Gregg and Maggs Trans. Faraday Soc. 1948 H 123. 10 Franklin Ph.D. Thesis (Cambridge. 1946). 11 Maggs Proc. Conf. Ultrafine Structure of Coals and Cokes (B.C.U.R.A.) 1944 p. 95; Bond and Maggs Coal Rssrarch (in press). fFn TABLE I ANALYSES OF COALS USED I Proximate ~nalysis (airdried basis) - vola- % % Ultimate Analysis d.m.f. (Pam's basis) % gen % % d. g.-1 Heat of Vetting in Oxy- Nitro 4ethanoP gm tile datte 1.m.f. - % - - - Fixed :arbor 2'9 1-7 1.2 90.6 8.5 94'2 4'9 15.2 81.6 4'4 1.5 91'7 2.4 4-1 4-6 4'8 1.7 89-4 4'8 24.0 35'2 70'9 59'8 83-1 12.9 1.9 2'0 17.6 82.6 5-1 9'9 5-3 10'1 54'9 37-9 Samples were ground to pass 240 B.S.S.R. L. BOND M. GRIFFITH AND F. A. P. MAGGS adsorbed water being measured by reweighing. The results are recorded in column 3 of Table 11. (Good agreement with these values was also given by exposing the Same coals to saturated water vapour in a desiccator evacuated on a filter-pump although somewhat longer times of exposure were required.) 3= ~ TABLE I1 ADSORPTION OF WATER AT SATURATION VAPOUR PRESSURE ON COALS Saturation Adsorption - Coal C D F Porosity 10-8 cc./cc. 10'1 2'2 3'2 H 7'7 12-3 K A comparison of the saturation adsorption-expressed in ~ m . ~ water adsorbed per ~ m . ~ of dry coal-with the porosity of the coal reveals that with some of the coals more water is adsorbed than would be required merely to fdl the pores.Some light is thrown on this by the following experiment (suggested by previous work with methanoll2). A prism of coal K was evacuated weighed and its size measured with a dial gauge; re-evacuation was followed by the adsorption of saturated water vapour ; the swelling and the quantity of water adsorbed were measured with the results shown in Table 111. (V S and P represent the volume of wate . adsorbed the volume swelling and the porosity respectively and are expressed in yo by volume.) Three experiments were made on the same 15.7 prism. 9'9 10'2 10-2 g./g. 5'9 1'7 3'6 10'0 12'1 2'0 9'5 The volume adsorbed is equal quantitatively to the sum of the volume swelling and the porosity and there is thus prima facie evidence that the pore volume of the swollen coal is completely filled with adsorbed water at saturation.* TABLE I11 SWELLING OF COAL 13.1 IS IN ' WATER 2'4 VAPOUR I1 2'1 I 2-6 13'6 12 Maggs Trans. Faraday SOC. 1946 #. I1 *In the experiments with methanol a surface compression was measured as a reduction in the total volume of the system ; this effect appears to be small in the present case. 3.9 2'2 4'7 I 3-0 Saturation Adsorption 10-1 cc./cc. I1 WATER IN CAPILLARY STRUCTURE OF COAL TO PUMPS FIG. 1.-Volumetric adsorption apparatus. 32 King and Wilkins l3 have assumed the volume of water adsorbed at satura- tion vapour pressure to be equal to the porosity of the coal.Of the liquids most suitable both on account of the negligible adsorption compression * of small molecular volume able to penetrate the coal structure water is the and the relatively small swelling (coal K swells about 16 g and 2 O /o b .y volume in methanol benzene and water respectively). With low-rank bituminous coals however neglect of the adsorption swelling is liable to introduce errors up to 3 yo in the porosity ; with lignites the error is probably con- siderable (a volume swelling of 25 yo has been observed by us on immersing a lignite in water). B. Adsorption Isotherms-Since coals are often exposed to air of various humidities the form of the adsorption isotherm is of importance practically; at the same time the deductions to be drawn from such data add considerably to our knowledge of the nature of the adsorbed water.APPARATUS.-A conventional volumetric apparatus was slightly modified (Fig. I) to facilitate measurement of the adsorption up to saturation vapour pressure. The manometer (A) was of 20 mm. tubing to avoid meniscus errors. Distilled water (bulb B) was further purified by fractional distillation under vacuum in the apparatus. The burette (C) (ca. 620 cc. capacity) and the sample bulb (D) were situated in a water-bath kept at 24.56 & o.02~ c. In general a measured quantity of water vapour was frozen into appendix E from the burette cut-off F was raised and on lowering cut-off G and warming the appendix adsorption took place.The vapour pressure in the burette was never allowed to rise above 0.8 saturation vapour pressure so that deviations from the gas laws were minimised. For pressures greater than this and approaching saturation v.P. equilibrium was established between the coal and liquid water in the appendix H the quantity not adsorbed being King and Wilkins Proc. Conf. Uitrafine Structure of Coak and Cokes (B.C.U.R.A.) 1944 P. 46. * Adsorbed methanol for instance occupies 17 yo less volume than does free liquid methanol .Is R. L. BOND M. GRIFFITH AND F. A. P. MAGGS 33 measured in the burette; this appendix was immersed in the water-bath. The coals were prepared by grinding through 240 B.S.S. as this has been found to lead to speedier adsorption than with coarser m a t e d .A blank experiment was performed to test the behaviour of the apparatus especially in view of an observation by Norrish14 of marked adsorption of water on the glass apparatus. The magnitude of the experimental error (whether due to adsorp- tion on the glass errors of measurement or deviation of water vapour from the gas laws) is shown to be small by the result of the blank experiment (curve (a) Fig. 2). The isotherms are given graphically in Fig. 2. The saturation values obtained in Section A have been included in Fig. 2 and the adsorption Abscissz Relative pressure. C FIG. ;?.-Adsorption isotherms of water on five coals at 2 5 O c. Ordinates Percentage weight adsorbed. branches extend to these.The isotherms given by coals H and K are similar to those found for systems where bulk condensation is said to occur ; more- over the decrease in hysteresis as the coals increase in rank could be readily related to the concomitant reduction in the size of the pores. If we suppose for the moment that the adsorbed film does not differ from bulk water several properties of the adsorbate may be readily measured. Whilst values of the vapour pressure and freezing point for instance may be susceptible to the influence of the pore diameter measurement of the dielectric constant and of the volume change on freezing would provide critical data for testing the initial postulate. Such measurements are described in sections C and D. C. Freezing Point of Adsorbed Water.-A characteristic property which could be used for identlfving bulk water is the sharp volume change which occurs on freezing.The volume of water adsorbed by certain l4 Norrish and Russell Nature 1947 160 57. B WATER IN CAPILLARY STRUCTURE OF COAL FIG. 3.-Dilatometric experiments. Curve I . Dibutyl phthalate dry. 2. Dibutyl phthaiate satur- ated with water. 3. Dry coal (- 72 B.s.s.) + dry dibutyl phthalate. 4. Dry coal (f pieces) + dry dibutyl phthalate. 5. Saturated dibutyl phtha- late + 1.5 cm.3 water. 6. Coal (- 72 B.s.s.) satur- + 0.5 cm.s excess water ated with water vapour and saturated dibutyl phthalate. 7. Coal (- 72 B.s.s.) satur- ated with water vapour + saturated dibutyl phtha- late.Ordinates Scale readings of menisci (in cm.). Abscissze Temperature O c. 34 bituminous coals (e.g. coal K) is sufficiently great to cause a volume change at the freezing point which could be readily detected dilatometrically if it occurs and is of the same magnitude as that of bulk water. From saturated vapour 12 % by weight of water was adsorbed at 21' c. by a sample of coal K ground to pass 72 B.S.S. This saturated coal sample was put into a thin-walled glass cylinder to which a calibrated capillary tube was attached ; the system was then completely filled with water-saturated dibutyl phthalate.* The temperature of this system was decreased steadily from that of the room to about - 70' c. and changes in volume of the coal and adsorbed water were detected by the movement of the meniscus in the capillary tube.To correct for extraneous volume changes due to components of the system other than adsorbed water control dilatometers were used making a total of seven filled as follows (4) Dry coal (r) + dry dibutyl phthalate. (I) Dry dibutyl phthalate. (2) Dibutyl phthalate saturated with water. (3) Dry coal (-72 B.s.s.) + dry dibutyl phthalate. (5) Dibutyl phthalate + 1-5 ~ m . ~ liquid water. (6) Coal (-72 B.s.s.) saturated with water vapour + dibutyl phthalate saturated with water + 0.5 ~ m . ~ liquid water. (7) Coal (-72 B.s.s.) saturated with water vapour + dibutyl phthalate saturated with water. The readings of the meniscus levels in the capillary tubes are plotted against temperature in Fig.3 ; the ordinate units are arbitrary. The blank experiments of bulbs (I) and (2) show that no correction need be applied for unusual volume changes in the dilatometric liquid. The experiment with bulb (5) (containing water and dibutyl phthalate) shows that the presence of the oil-water interface will not prevent freezing ; that is the experimental conditions were suitable for the detection of bulk water. * It was anticipated that the very large molecules of this liquid would be unlikely to penetrate the pore constrictions of the fine structure of the coal and displace the adsorbed water molecules. Dibutyl phthalate has the further advantage of being deformable even a t - 70° c. and was therefore suitable for use as a dilatometric fluid in this series of experiments.R. L. BOND M. GRIFFITH AND F. A. P. MAGGS The volume change of the bulk water is marked (bulb 5) ; its occurrence at about - 8" c. appears to be due to supercooling.* The quantity of water adsorbed in the coal was similar to that in the bulb (5) ; freezing of the adsorbed water could therefore be readily detected. It is clear from curve 7 in Fig. 3 that a phase change of this nature does rcot occw between + 20° c. and - 70° c. for adsorbed water. Whilst precautions were taken to keep the coal saturated with water (eg. the dibutyl phthalate was water-saturated before the experi- ment) the theory of capillary condensa- 35 tion assumes that the pores will contain bulk liquid over a range of relative pressure particularly in the steeply rising final part of the isotherm15; therefore failure to detect a freezing point cannot be ascribed to this cause.In the case where water in excess of that required for saturation of the coal was present (bulb 6) a volume change FIG. +-Thermal expansion apparatus- corresponding to that caused by the freezing of the excess water alone was observed; even the ice thus formed failed to crystallise the adsorbed water. Such an experiment provides a simple method of determining the quantity of ordinary water present in coal. SGme degree of supercool&g is ekily attained and it might be thought that in small pores where disturbances (such as convection currents) are minimised considerable supercooling would be possible.It has been shown however that the presence of coal is sufficient to crysta.Uk supercooled bulk liquid (footnote p. 35 also curve 6 Fig. 3). It seems most improbable that the absence of freezing of the adsorbed water at so low a temperature as - 70" c. can be attributed to ordinary supercooling. Some supporting experiments have been made in which the coefficient of thermal expansion of cod K (in the was measured between + 20" c. and form of rods of compressed powder) - 20" c. using the apparatus shown in Fig. 4. Measurements were made on rods of the compressed coal powder both dry and with adsorbed water. Blank experiments using silica rods of negligiblethermal expan>ion were used to correct for length changes of the apparatus.The results are shown in Fig. 5 where the percentage change in FIG. 5.-Thermal expansion of coal K containing adsorbed water. Curve I . Dry coal. l6 Cohan J . A w . Chem. SOC. 1938 60 433. * Water cooled in glass tubing remained liquid at - 10.5~ c. ; no special precautions were needed to achieve this. Vibration or tapping did not induce crystallisation but a thin.glass rod or a speck of coal (either dry or wet) immersed in the supercooled water caused freezing. 2. Coal + 3.7 % adsorbed 3. Coal water. + 14.2 % adsorbed water. Ordinates Percentagecontraction. Abscissae Temperature O c. 10 10 -1,o -2,o WATER IN CAPILLARY STRUCTURE OF COAL FIG. 6.-Dielectric constant of coal K containing adsorbed water. Curve I .Air. 2 . Dry coal. 3. Coal saturated with water vapour. Ordinates Apparent dielectric constant. Abscissae Temperature O c . 36 length is plotted against the temperature. Again the results gave no indication of freezing of the water in this temperature range. It was observed however that the coefficient of thermal expansion was changed from 4 2 to 5.0 x I O - ~ O c.-l by the adsorption of water at saturation V.P. D. Dielectric Constant.-In another method employed for investi- gating the behaviour of adsorbed water advantage was taken of the fact that at an appropriate frequency a marked change in dielectric constant occurs when water freezes. The temperature dependence of the capacitance of a condenser containing saturated coal was measured at a frequency of 15 kc./sec.using a high-frequency bridge of the Schering type fitted with a Wagner earth; balance points were located with a Muirhead amplifier detector. A substitution method was employed the capacitance under investigation being in parallel with an N.P.L.-calibrated variable air condenser. Three sets of data were obtained with the same parallel plate condenser supported in a bath which could be held at any required temperature between + 20° and - 70° c. Determinations were made of the capacitance of the condenser with the following materials forming its dielectric (I) a+ (2) dry coal K ground to pass 72 B.s.s. and (3) the same coal saturated with water vapour at 25" c. The possibility of very slow heat transfer was investigated and rejected and readings were taken only after both temperature and capacitance readings had remained steady for 30 min.An apparent dielectric constant E' was measured which represents the dielectric constant of the coal powder plus voidage; such comparative values are adequate for the detection of the liquid-solid phase change. The variation of E' with tempera- ture for the three systems is given in Fig. 6. Curve (I) shows that corrections for the variation of the capacitance of the empty condenser with temperature are negligible. The effect of the adsorbed water on E' for coal is very marked and is greater than would be anticipated for the addition of 12 yo bulk water.* The dispersion curve for the system coal plus adsorbed water shows no break which might denote freezing (such as those found for claysI6).On the other hand the occurrence of partial freezing at successively lower temperatures is not precluded. 16 Alexander and Shaw J . Physic. Chem. 1937 41 955. * From Wiener's law (random distribution of spheres) or from work of Sillars J. I m t . Elect. Eng. 1937 80 378. R. L. BOND M. GRIFFITH AND F. A. P. MAGS 37 E. Wetting and Free-Energy Changes at Coal Surfaces-The measurement of the free-energy changes which take place on immersing coal saturated from the vapour phase in water provides a reliable method for the detection of phase differences. Whilst the free-energy decrement during adsorption from the vapour may be easily evaluated from the adsorp- tion isotherm that which occurs on immersion is less readily evaluated.For charcoal rods however Banghaml7 has shown that the adsorption expansion is directly proportional to the free-energy change and this observation provides a method for overcoming the difficulty in dealing with immersion. (a) ENERGY CHANGE ON ADSORPTION FROM THE VAPouR.-The free-energy decrements (Fa) at saturation vapour pressure have been evaluated from the isotherms of Fig. 2 by the relation developed by Bangham 1 8 MC s d(log,+) ; s being the adsorption at the interface of extent C F RT F = - 0 at the vaDour pressure p,. By taking values for C from the heats of' wetting in methanol Fa has been estimated for -the five coals ; the results of these calculations are given in Table IV. TABLE IV ENERGY CHANGES OCCURRING DURING ADSORPTION OF WATER VAPOUR F,Z (from desorption) :from adsorption) (from desorption) erg.cm.-' roo erg. g.-l erg. cm.-p 69 6.1 2'2 52 4'0 Coal C D F H 7' 89 '5'9 F,X (from adsorption) 107 erg. g.-l 6-1 2'2 3'4 13'2 12-8 K '7'3 l7 Bangham and Razouk PYOC. Roy. Soc. A. 1938 166 572. 73 A feature of these results lies in the contrast with the values obtained for organic liquids on coals the value of Fs for a saturated methanol film being about zoo erg. cm.-2. The surface pressure of a film of adsorbed water is evidently insufficient to displace adsorbed films of organic vapours from coal surfaces. (b) ADSORPTION SWELLING.-The relation between the swelling and the energy change at various points of the isotherm has been tested in the following manner A rod of coal K formed by pressing the powder (-72 B.s.s.) at 3 ton in.-2 was placed in a metal extensometer attached to a glass vacuum system by a copper-glass seal.The extensometer consisted of a dial gauge graduated in IO* cm. which was enclosed in a close-fitting metal jacket provided with a plate-glass window. Since it was found that the metal of the extensometer also adsorbed water vapour it was necessary to measure the adsorption on a further rod of compressed powder contained in a glass jacket attached to the system through a ground-glass joint. This jacket (which was fitted with a tap) could be detached and weighed at l*Bangham and Fakhoury Proc. Roy.Soc. A 1931 130 81; Bangham and Fakhoury J . Chm. Sot. 1931 1324. WATER IN CAPILLARY STRUCTURE OF COAL FIG. 7.-Adsorption expansion of coal. Curve I . Variation with weight adsorbed. 2. Variation with free-energy decrement. Ordinates Percentage linear expansion. Abscissae Upper Free energy decrement 107 erg g.-l Lower Percentage weight of water adsorbed. 38 appropriate intervals. The whole apparatus was kept in an air thermostat held at 25' C. Thorough out-gassing of both coal and water preceded the experiment. The free-energy change at various adsorptions was estimated from the isotherm K of Fig. 2. In Fig. 7 the results of this experiment are expressed as the variation of the percentage linear expansion with both the weight of water adsorbed and the free-energy change occurring on adsorption.Whilst in the former case the curve is not linear proportionality is shown between the swelling and the energy change (curve 2 Fig. 7). By using the value of the gradient of the latter curve it is possible to estimate free-energy changes from the accompanying expansion. (C) THE FREE-ENERGY RELATION BETWEEN SATURATION -4ND IMMERSION.- The free energies of saturation and immersion of plane surfaces are related in the following manner FL = FS + y cos 8 where y is the surface tension of the liquid and 8 is the angle of contact between the liquid and the vapour-saturated solid. Thus the saturated solid will expand on immersion if etZ 7c and will The final expansion was 1-28 yo. The angle of contact 2 2 n 2 contract if 8>-.Identity between the liquid and adsorbed phases is of Fourse shown by 8 = 0 when a marked increase in length will occur. The rod of compressed coal used in the experiment of the previous section was mounted in the dial-gauge extensometer and after thorough evacuation was exposed to saturated water vapour at 2 5 O c. for 3 days. A linear expan- sion of 1-23 yo was recorded. Boiled distilled water was then admitted through a tap. calculated from these results is 4" under 5. In view of the closeness of this result to the critical angle of F further experiments were devised which are based on the following considerations. The significance of a finite angle of contact (as Bangham 24 has emphasised) is that it demonstrates the degree of incongruity between the surface of the bulk liquid and the adsorbed film on the solid and one of the simplest ways in which the presence of a finite angle of contact can be shown for solids of density greater than that of the liquid is by flotation experiments.A zero angle of contact for instance leads to the inability of the solid to float at all whilst for a powder which floats the value of 8 must be finite. The ability of the solid to float is dependent on the shape of the solid as well R. L. BOND M. GRIFFITH AND F. A. P. MAGGS above the surface only if O>-" according to the following relation 39 as the angle of contact ; a solid having vertical sides however will float in which g = acceleration due to gravity ; P = the periphery of the solid at the liquid meniscus; V =volume of solid and V i = the volume immersed.For systems where ps>p~ the solid will float above the surface To PVUPS 2 periphery to volume. The densities of the coals measured by helium dis- placement lie between 1-5 and 1-3 g . cm.-3 and the lump densities of the dry coals fall in the range 1-37 to 1.15 g . ~ m . - ~ . Calculation shows that the largest cube of coal which would just float (i.e. taking 8 = n) is a centimetre cube. (d) FLOTATION EXPERIMENTS-S~P~~S of all five coals (ground to pass 72 B.s.s.) were sprinkled on clean water surfaces ; none of the coals showed any tendency to sink even after 20 weeks. To obviate any effects which might be attributed to adsorbed gases the simple apparatus sketched in Fig.8 was used. Coal powders were well evacuated at 80" c. allowed to reach equilibrium with saturated water vapour at room temperature and then tipped on to the water sur- face. Apart from a few particles (<I yo) which sank immediately the saturated coal remained floating on the surface for the following ten weeks after which observations were discontinued. Adequate confirmation of the flotation experiments was obtained when flat plates of coal weighing up to 60 g . were easily floated by placing the coal OR a freshly floated filter-paper which sank leaving the coal afloat. A further experiment was made in which the piece of coal was placed on thoroughly degassed ice. After several hours' pumping (with the water frozen) the ice was allowed to melt ; the coal floated and had not sunk after 6 days.* t for flotation FIG.&-Apparatus It was found impossible to fulfil the conditions of the flotation equation for whatever the size or shape of the l&p the unwetted upper surface of the coal lay below the plane of the water surface ; in all cases the water meniscus curved downwards to meet the periphery of the upper surface of the lumps. &!vPs - 2 vipL) + pr cos e = 0 ; only when O>z the depth of immersion being dependent on the ratio of 2 experiments. It is concluded from these experiments that the angle of contact between water and coal K is finite and is a little under 9. Preliminary quantitative experiments have been made by measuring the minimum load required to sink a number of pieces of coal; whilst the influence of the extent of the periphery is predominant it is apparent that the evaluation of 8 will involve the shape of the meniscus and the surface tension of the liquid.For instance the action of wetting agents-which cause the coal lumps to sink-may depend on the reduction of 8 or the lowering of the surface tension or-more probably-on both. Work is in hand to elucidate these points. * On pumping a piece of coal floating on water bubbles of gas steadily escaped from the coal which remained froding until a large bubble from the water burst so swamping the coal. WATER IN CAPILLARY STRUCTURE OF COAL 40 Nature of the Adsorbed Film of Water. Interpretation of the results reported in Sections A and B along the lines of the B.E.T.multilayer theory or of the capillary condensation theory would lead to the conclusion that the water adsorbed by coal at saturation vapour pressure has the properties of three-dimensional liquid water. The critical experiments of the subsequent sections however make this simple conclusion untenable. The proportionality between the adsorption expansion and the surface pressure of the water film at room temperature (Section E) leaves little doubt that the water-coal system behaves in the same manner as the charcoal- alcohol systems investigated by Bangham,17 where the adsorbed films were shown to behave as a two-dimensional phase. It is at once apparent that the increase in the coefficient of thermal expansion of coal compacts brought about by adsorbed water is due to the kinetic mobility of the adsorbed molecules.By regarding the two-dimensional film of water as a distinct phase the absence of a normal melting-point is understandable.* It is not clear how- ever whether a gradual transition to a solid phase takes place when the temperature is steadily lowered. Hardy,20 for instance found that the water in plant cells froze in stages the proportion of ice formed being dependent on the lowering of the temperature. On the other hand Fosterz1 could find no evidence of the freezing of water adsorbed on silica gel even at - 65" c. ; Rau 22 was able to supercool water droplets to - 72O c. but as Bangham has pointed out there is some evidence to suggest that the water surface of drops at this temperature was remarkably akin to the adsorbed phase.From the several lines of approach described in this paper it is con- cluded that it is incorrect to treat adsorbed water as though it were bulk water. The authors are glad to acknowledge the help and suggestions of Dr. D. H. Bangham Director of Research Laboratories British Coal Utilisation Research Association in planning this work ; they are grateful to the Council of the Association for permission to publish these results. Summary. The relation between liquid water and adsorbed water is discussed in the light of current theories and whereas capillary condensed water might be expected to possess the properties of the bulk phase measurements of the dielectric constant and volume changes on cooling coal saturated with water vapour show no evidence of a sharp freezing point.The significance of the angle of contact between liquid water and saturated coal is discussed ; measurements of the freeenergy decrement on wetting saturated coal suggest that the angle of contact is about goo but the value must in fact be less from the flotation experiments. It is concluded that a phase difference exists between water adsorbed on coal and bulk water. British Coal Utilisation Research Association 13 Grosvenor Gardens London. 19 Bndgeman Physics of High Pressure (London 1931). 20 Hardy Collected Scienti$c Papers (Camb. Univ. Press 1936). 21 Batchelor and Foster Trans. Furuday SOC. 1944 -40 300.22 Rau Schrift. Deut. Akad. Luftfuhrtforsch 1944 8 (u) 65 ; see also Frank Nature 19q6D 157 267' 2JBangham. Nafure 1946 157 733. 24 Bangham J. Chem. Physics 1946 14 352. * According to Bridgeman,lg liquid water cannot exist below ca. - 20' c. even under pressure ; further the pressures developed by the volume change on ice formation are too small to depress the freezing point sufficiently even in an undeformable container. SOME PROPERTIES OF WATER ADSORBED IN THE CAPILLARY STRUCTURE OF COAL BY R. L. BOND M. GRIFFITH AND F. A. P. MAGGS Received 27th February 1948 The examination of the properties of adsorbed water is of importance since water is present to a considerable extent in many naturally occurring materials used in industry; for instance a quantity of water of the order of millions of tons is mined annually in association with coal in this country.Much interest lies then in the attributes of the adsorbed phase and since it is often implicit in publications dealing with the gas-solid interface that water adsorbed on porous solids simulates the behaviour of bulk water, this paper describes a few critical experiments designed to emphasise any differences that may exist between the two phases. The numerous applications of the theory of capillary condensation have a common basis in the assumption that vapours adsorbed on any fine-structured solid will be in equilibrium with a vapour pressure uniquely determined by the curvature of the meniscus formed in the micro-capillaries, even if these are of molecular dimensions ; hysteresis is ascribed to a change in the angle of contact between this meniscus and the solid (or film-covered solid).* Whilst identity between bulk liquid and the adsorbed film formed at saturation is not explicitly postulated by Brunauer Emmett and Teller a in their multilayer theory it is difficult to resist the conclusion that infinite adsorption of bulk liquid on plane surfaces is implied.Again hark in^,^ in his calorimetric method of estimating surface areas assumes that an adsorbed film of water on anatase at saturation vapour pressure possesses a surface energy identical with that of the free liquid. observation that no sign of condensation of water on silica gel-a system regarded as a classical example of capillary condensation-could be detected very close to saturation even though the isotherm took a sharp upward turn at high relative pressures.Similarly Bangham observed that drops of liquid placed on the surface of mica subjected to a jet of the supersaturated vapours refused t o spread. He also measured a free-energy change not equal to but less than the surface tension of the liquid on immersing in liquid methanol and ethanol rods of charcoal previously saturated from the vapour phase. Bangham2* concluded that a difference of phase exists between the adsorbed film and bulk liquid. (See also Frumkin and CasseL8) Indeed Greg and Maggs find that many apparent examples of capillary condensation are more fittingly attributed to changes of phase within the adsorbed film. In contrast with these assumptions we may recall Foster’s 1 Zsigmondy 2.anorg. Chem. 1911 71 356. a Brunauer Emmett and Teller J . Amer. Chem. Sot. 1938 60 309. 8 Harkins and Jura J . Amer. Chem. Soc. 1944 66 1362. 6 Lambert and Foster Proc. Roy. Soc. A 1932 EM. 246. Hirst Nature 1947 159 267. Bangham and Sawexis Trans. Furaday SOC. 1938 34 554. * From a different standpoint Hirst 4 has shown that hysteresis is a possible con-sequence of the effect of changed pore dimensions brought about by liquid condensation. 2 30 Oxy-gm % % 1-7 2.4 4-1 9'9 10'1 WATER IN CAPILLARY STRUCTURE OF COAL Nitro gen -1.2 1.5 1.7 1.9 2'0 The pore structure of coal is particularly favourable to the occurrence of capillary condensation ; density measurements made by Franklin lo have shown that the pores contain constrictions of molecular dimensions the size of the constrictions decreasing with increasing maturity of the coals.We shall show however that although the observations particularly at satura-tion vapour pressure point to the occurrence of liquid condensation certain aspects of the behaviour of the adsorbed and the bulk water stand in very sharp contrast. That these divergencies in behaviour represent a real phase difference is amply demonstrated by the qualitative experiments to be described ; a quantitative examination of the phenomena is in hand. % -94'2 91'7 89-4 83-1 82.6 Experimental Samples.-The coals used in this work were stored in nitrogen as an slack ; a sample of each coal was withdrawn ground to pass 72 B.S.S.and kept in sealed bottles until required. For experiments using - 240 B.S.S. coal samples were taken from these bottles and ground by hand. The analyses of the coals (- 72 B.s.s.) are given in Table I. We shall have occasion whilst discussing the results to refer to the porosity and surface area of the coals. By porosity is meant the volume of the pores which is accessible to helium in a lump of coal ; the porosity values quoted here are those given by Franklin,lo whose coal samples were taken from the same batch as those used in the present work. Values for the inner surface area of coals are calculated directly from the heat of wetting of the coal in methanol.ll In all the tables coals are arranged in order of decreasing rank.TABLE I ANALYSES OF COALS USED fFn % 2'9 4'4 4'8 5-1 5-3 coal Description (Seyler's Classification) c. Anthracite Group Ax D. CarbonaCeoUS P. Meta-bituminous . . R. Para-bituminous . . Meta-lignitous K. Meta-lignitous - . I Proximate ~nalysis (airdried basis) Fixed :arbor % -90.6 81.6 70'9 59'8 54'9 -vola-tile datte 1.m.f. % -4'9 15.2 24.0 35'2 37-9 Ultimate Analysis d.m.f. (Pam's basis) Heat of Vetting in 4ethanoP d. g.-1 8.5 4-6 4'8 12.9 17.6 Samples were ground to pass 240 B.S.S. A. Porosity and the Volume of Water Adsorbed at Saturation.-Samples of the coals ground to pass 240 B.s.s. contained in tared weighing bottles were thoroughly evacuated; dry air was then admitted and the stoppered bottles were immediately weighed.After further evacuation the coals were exposed to saturated water vapour until adsorption ceased the 7 Frumkin Gogoritzkaja Kabanov and Nekrassov PhysiR. 2. Sowjet. 1932 I 255. * Cassel J . Chem. Physics 1945. 13 249. Gregg and Maggs Trans. Faraday Soc. 1948 H 123. 10 Franklin Ph.D. Thesis (Cambridge. 1946). 11 Maggs Proc. Conf. Ultrafine Structure of Coals and Cokes (B.C.U.R.A.) 1944 p. 95; Bond and Maggs Coal Rssrarch (in press) R. L. BOND M. GRIFFITH AND F. A. P. MAGGS 3= adsorbed water being measured by reweighing. The results are recorded in column 3 of Table 11. (Good agreement with these values was also given by exposing the Same coals to saturated water vapour in a desiccator evacuated on a filter-pump although somewhat longer times of exposure were required.) TABLE I1 ADSORPTION OF WATER AT SATURATION VAPOUR PRESSURE ON COALS 9'9 10'2 9'5 ~ Coal -C D F H K 13.1 ' 2'4 I1 2'0 I1 I 2-6 2'1 I1 13'6 : Porosity 10-8 cc./cc.10'1 2'2 3'2 7'7 12-3 Saturation Adsorption 10-2 g./g. 5'9 1'7 3'6 10'0 12'1 Saturation Adsorption 10-1 cc./cc. 3.9 2'2 4'7 I 3-0 15.7 A comparison of the saturation adsorption-expressed in ~ m . ~ water adsorbed per ~ m . ~ of dry coal-with the porosity of the coal reveals that with some of the coals more water is adsorbed than would be required merely to fdl the pores. Some light is thrown on this by the following experiment (suggested by previous work with methanoll2).A prism of coal K was evacuated weighed and its size measured with a dial gauge; re-evacuation was followed by the adsorption of saturated water vapour ; the swelling and the quantity of water adsorbed were measured with the results shown in Table 111. (V S and P represent the volume of wate . adsorbed the volume swelling and the porosity respectively and are expressed in yo by volume.) Three experiments were made on the same prism. TABLE I11 SWELLING OF COAL IS IN WATER VAPOUR The volume adsorbed is equal quantitatively to the sum of the volume swelling and the porosity and there is thus prima facie evidence that the pore volume of the swollen coal is completely filled with adsorbed water at saturation. * 12 Maggs Trans. Faraday SOC. 1946 #. *In the experiments with methanol a surface compression was measured as a reduction in the total volume of the system ; this effect appears to be small in the present case 32 WATER IN CAPILLARY STRUCTURE OF COAL King and Wilkins l3 have assumed the volume of water adsorbed at satura-tion vapour pressure to be equal to the porosity of the coal.Of the liquids of small molecular volume able to penetrate the coal structure water is the most suitable both on account of the negligible adsorption compression * and the relatively small swelling (coal K swells about 16 g and 2 O /o b .y volume in methanol benzene and water respectively). With low-rank bituminous coals however neglect of the adsorption swelling is liable to introduce errors up to 3 yo in the porosity ; with lignites the error is probably con-siderable (a volume swelling of 25 yo has been observed by us on immersing a lignite in water).Adsorption Isotherms-Since coals are often exposed to air of various humidities the form of the adsorption isotherm is of importance practically; at the same time the deductions to be drawn from such data add considerably to our knowledge of the nature of the adsorbed water. APPARATUS.-A conventional volumetric apparatus was slightly modified (Fig. I) to facilitate measurement of the adsorption up to saturation vapour B. TO PUMPS FIG. 1.-Volumetric adsorption apparatus. pressure. The manometer (A) was of 20 mm. tubing to avoid meniscus errors. Distilled water (bulb B) was further purified by fractional distillation under vacuum in the apparatus.The burette (C) (ca. 620 cc. capacity) and the sample bulb (D) were situated in a water-bath kept at 24.56 & o.02~ c. In general a measured quantity of water vapour was frozen into appendix E from the burette cut-off F was raised and on lowering cut-off G and warming the appendix adsorption took place. The vapour pressure in the burette was never allowed to rise above 0.8 saturation vapour pressure so that deviations from the gas laws were minimised. For pressures greater than this and approaching saturation v.P. equilibrium was established between the coal and liquid water in the appendix H the quantity not adsorbed being King and Wilkins Proc. Conf. Uitrafine Structure of Coak and Cokes (B.C.U.R.A.), * Adsorbed methanol for instance occupies 17 yo less volume than does free liquid 1944 P.46. methanol .I R. L. BOND M. GRIFFITH AND F. A. P. MAGGS 33 measured in the burette; this appendix was immersed in the water-bath. The coals were prepared by grinding through 240 B.S.S. as this has been found to lead to speedier adsorption than with coarser m a t e d . A blank experiment was performed to test the behaviour of the apparatus especially in view of an observation by Norrish14 of marked adsorption of water on the glass apparatus. The magnitude of the experimental error (whether due to adsorp-tion on the glass errors of measurement or deviation of water vapour from the gas laws) is shown to be small by the result of the blank experiment (curve (a) Fig. 2). The saturation values obtained in Section A have been included in Fig.2 and the adsorption The isotherms are given graphically in Fig. 2. C FIG. ;?.-Adsorption isotherms of water on five coals at 2 5 O c. Ordinates Percentage weight adsorbed. Abscissz Relative pressure. branches extend to these. The isotherms given by coals H and K are similar to those found for systems where bulk condensation is said to occur ; more-over the decrease in hysteresis as the coals increase in rank could be readily related to the concomitant reduction in the size of the pores. If we suppose for the moment that the adsorbed film does not differ from bulk water several properties of the adsorbate may be readily measured. Whilst values of the vapour pressure and freezing point for instance may be susceptible to the influence of the pore diameter measurement of the dielectric constant and of the volume change on freezing would provide critical data for testing the initial postulate.Such measurements are described in sections C and D. C. Freezing Point of Adsorbed Water.-A characteristic property which could be used for identlfving bulk water is the sharp volume change which occurs on freezing. The volume of water adsorbed by certain l4 Norrish and Russell Nature 1947 160 57. 34 WATER IN CAPILLARY STRUCTURE OF COAL bituminous coals (e.g. coal K) is sufficiently great to cause a volume change at the freezing point which could be readily detected dilatometrically if it occurs and is of the same magnitude as that of bulk water. From saturated vapour 12 % by weight of water was adsorbed at 21' c.by a sample of coal K ground to pass 72 B.S.S. This saturated coal sample was put into a thin-walled glass cylinder to which a calibrated capillary tube was attached ; the system was then completely filled with water-saturated dibutyl phthalate.* The temperature of this system was decreased steadily from that of the room to about - 70' c. and changes in volume of the coal and adsorbed water were detected by the movement of the meniscus in the capillary tube. To correct for extraneous volume changes due to components of the system other than adsorbed water control dilatometers were used making a total of seven filled as follows : (I) Dry dibutyl phthalate. (2) Dibutyl phthalate saturated with water. (3) Dry coal (-72 B.s.s.) + dry dibutyl phthalate.(4) Dry coal (r) + dry dibutyl phthalate. (5) Dibutyl phthalate + 1-5 ~ m . ~ liquid water. (6) Coal (-72 B.s.s.) saturated with water vapour + dibutyl phthalate (7) Coal (-72 B.s.s.) saturated with water vapour + dibutyl phthalate The readings of the meniscus levels in the capillary tubes are plotted against temperature in Fig. 3 ; the ordinate units are arbitrary. saturated with water + 0.5 ~ m . ~ liquid water. saturated with water. FIG. 3.-Dilatometric experiments. Curve I . Dibutyl phthalate, 2. Dibutyl phthaiate satur-ated with water. 3. Dry coal (- 72 B.s.s.) + dry dibutyl phthalate. 4. Dry coal (f pieces) + dry dibutyl phthalate. 5. Saturated dibutyl phtha-late + 1.5 cm.3 water. 6. Coal (- 72 B.s.s.) satur-ated with water vapour + 0.5 cm.s excess water and saturated dibutyl phthalate.7. Coal (- 72 B.s.s.) satur-ated with water vapour + saturated dibutyl phtha-late. Ordinates Scale readings of Abscissze Temperature O c. dry. menisci (in cm.). The blank experiments of bulbs (I) and (2) show that no correction need be applied for unusual volume changes in the dilatometric liquid. The experiment with bulb (5) (containing water and dibutyl phthalate) shows that the presence of the oil-water interface will not prevent freezing ; that is the experimental conditions were suitable for the detection of bulk water. * It was anticipated that the very large molecules of this liquid would be unlikely to penetrate the pore constrictions of the fine structure of the coal and displace the adsorbed water molecules.Dibutyl phthalate has the further advantage of being deformable even a t - 70° c. and was therefore suitable for use as a dilatometric fluid in this series of experiments R. L. BOND M. GRIFFITH AND F. A. P. MAGGS 35 The volume change of the bulk water is marked (bulb 5) ; its occurrence at about - 8" c. appears to be due to supercooling.* The quantity of water adsorbed in the coal was similar to that in the bulb (5) ; freezing of the adsorbed water could therefore be readily detected. It is clear from curve 7 in Fig. 3 that a phase change of this nature does rcot occw between + 20° c. and - 70° c. for adsorbed water. Whilst precautions were taken to keep the coal saturated with water (eg. the dibutyl phthalate was water-saturated before the experi-ment) the theory of capillary condensa-tion assumes that the pores will contain bulk liquid over a range of relative pressure particularly in the steeply rising final part of the isotherm15; therefore failure to detect a freezing point cannot be ascribed to this cause.In the case where water in excess of that required for saturation of the coal was present (bulb 6) a volume change FIG. +-Thermal expansion apparatus-corresponding to that caused by the freezing of the excess water alone was observed; even the ice thus formed failed to crystallise the adsorbed water. Such an experiment provides a simple method of determining the quantity of ordinary water present in coal. SGme degree of supercool&g is ekily attained and it might be thought that in small pores where disturbances (such as convection currents) are minimised, considerable supercooling would be possible.It has been shown however, that the presence of coal is sufficient to crysta.Uk supercooled bulk liquid (footnote p. 35 also curve 6 Fig. 3). It seems most improbable that the absence of freezing of the adsorbed water at so low a temperature as - 70" c. can be attributed to ordinary supercooling. Some supporting experiments have been made in which the coefficient of thermal expansion of cod K (in the form of rods of compressed powder) was measured between + 20" c. and - 20" c. using the apparatus shown in Fig. 4. Measurements were made on rods of the compressed coal powder, both dry and with adsorbed water.Blank experiments using silica rods of 10 10 -1,o -2,o FIG. 5.-Thermal expansion of coal K 2. Coal + 3.7 % adsorbed 3. Coal + 14.2 % adsorbed Ordinates Percentagecontraction. Abscissae Temperature O c. containing adsorbed water. Curve I . Dry coal. water. water. negligiblethermal expan>ion were used to correct for length changes of the apparatus. The results are shown in Fig. 5 where the percentage change in l6 Cohan J . A w . Chem. SOC. 1938 60 433. * Water cooled in glass tubing remained liquid at - 10.5~ c. ; no special precautions were needed to achieve this. Vibration or tapping did not induce crystallisation but a thin.glass rod or a speck of coal (either dry or wet) immersed in the supercooled water caused freezing 36 WATER IN CAPILLARY STRUCTURE OF COAL length is plotted against the temperature.Again the results gave no indication of freezing of the water in this temperature range. It was observed, however that the coefficient of thermal expansion was changed from 4 2 to 5.0 x I O - ~ O c.-l by the adsorption of water at saturation V.P. D. Dielectric Constant.-In another method employed for investi-gating the behaviour of adsorbed water advantage was taken of the fact that at an appropriate frequency a marked change in dielectric constant occurs when water freezes. The temperature dependence of the capacitance of a condenser containing saturated coal was measured at a frequency of 15 kc./sec. using a high-frequency bridge of the Schering type fitted with a Wagner earth; balance points were located with a Muirhead amplifier detector.A substitution method was employed the capacitance under investigation being in parallel with an N.P.L.-calibrated variable air condenser. Three sets of data were obtained with the same parallel plate condenser, supported in a bath which could be held at any required temperature between + 20° and - 70° c. Determinations were made of the capacitance of the condenser with the following materials forming its dielectric (I) a+ (2) dry coal K ground to pass 72 B.s.s. and (3) the same coal saturated with water vapour at 25" c. The possibility of very slow heat transfer was investigated and rejected and readings were taken only after both temperature and capacitance readings had remained steady for 30 min.An apparent dielectric FIG. 6.-Dielectric constant of coal K containing adsorbed water. Curve I . Air. 2 . Dry coal. 3. Coal saturated with water vapour. Ordinates Apparent dielectric constant. Abscissae Temperature O c . constant E' was measured which represents the dielectric constant of the coal powder plus voidage; such comparative values are adequate for the detection of the liquid-solid phase change. The variation of E' with tempera-ture for the three systems is given in Fig. 6. Curve (I) shows that corrections for the variation of the capacitance of the empty condenser with temperature are negligible. The effect of the adsorbed water on E' for coal is very marked and is greater than would be anticipated for the addition of 12 yo bulk water.* The dispersion curve for the system coal plus adsorbed water shows no break which might denote freezing (such as those found for claysI6).On the other hand the occurrence of partial freezing at successively lower temperatures is not precluded. 16 Alexander and Shaw J . Physic. Chem. 1937 41 955. * From Wiener's law (random distribution of spheres) or from work of Sillars J. I m t . Elect. Eng. 1937 80 378 R. L. BOND M. GRIFFITH AND F. A. P. MAGS 37 E. Wetting and Free-Energy Changes at Coal Surfaces-The measurement of the free-energy changes which take place on immersing coal saturated from the vapour phase in water provides a reliable method for the detection of phase differences. Whilst the free-energy decrement during adsorption from the vapour may be easily evaluated from the adsorp-tion isotherm that which occurs on immersion is less readily evaluated.For charcoal rods however Banghaml7 has shown that the adsorption expansion is directly proportional to the free-energy change and this observation provides a method for overcoming the difficulty in dealing with immersion. decrements (Fa) at saturation vapour pressure have been evaluated from the isotherms of Fig. 2 by the relation developed by Bangham 1 8 : (a) ENERGY CHANGE ON ADSORPTION FROM THE VAPouR.-The free-energy RT F = - MC s d(log,+) ; s being the adsorption at the interface of extent C, 0 at the vaDour pressure p,. By taking values for C from the heats of' wetting in methanol Fa has been estimated for -the five coals ; the results of these calculations are given in Table IV.TABLE IV ENERGY CHANGES OCCURRING DURING ADSORPTION OF WATER VAPOUR Coal C D F H K F,X (from adsorption) 107 erg. g.-l 6-1 2'2 3'4 13'2 12-8 F,Z (from desorption) roo erg. g.-l 6.1 2'2 4'0 '5'9 '7'3 :from adsorption) erg. cm.-p 69 52 7' 89 73 F, (from desorption) erg. cm.-' A feature of these results lies in the contrast with the values obtained for organic liquids on coals the value of Fs for a saturated methanol film being about zoo erg. cm.-2. The surface pressure of a film of adsorbed water is evidently insufficient to displace adsorbed films of organic vapours from coal surfaces. (b) ADSORPTION SWELLING.-The relation between the swelling and the energy change at various points of the isotherm has been tested in the following manner A rod of coal K formed by pressing the powder (-72 B.s.s.) at 3 ton in.-2 was placed in a metal extensometer attached to a glass vacuum system by a copper-glass seal.The extensometer consisted of a dial gauge graduated in IO* cm. which was enclosed in a close-fitting metal jacket provided with a plate-glass window. Since it was found that the metal of the extensometer also adsorbed water vapour it was necessary to measure the adsorption on a further rod of compressed powder contained in a glass jacket attached to the system through a ground-glass joint. This jacket (which was fitted with a tap) could be detached and weighed at l7 Bangham and Razouk PYOC. Roy. Soc. A. 1938 166 572. l*Bangham and Fakhoury Proc.Roy. Soc. A 1931 130 81; Bangham and Fakhoury J . Chm. Sot. 1931 1324 38 WATER IN CAPILLARY STRUCTURE OF COAL appropriate intervals. The whole apparatus was kept in an air thermostat held at 25' C. Thorough out-gassing of both coal and water preceded the experiment. The free-energy change at various adsorptions was estimated from the isotherm K of Fig. 2. In Fig. 7 the results of this experiment are expressed as the variation of the percentage linear expansion with both the weight of water adsorbed and the free-energy change occurring on adsorption. Whilst in the former case the curve is not linear proportionality is shown between the swelling FIG. 7.-Adsorption expansion of coal. Curve I . Variation with weight adsorbed. decrement. Ordinates Percentage linear expansion.Abscissae Upper Free energy decrement 107 erg g.-l Lower Percentage weight of water adsorbed. 2. Variation with free-energy and the energy change (curve 2 Fig. 7). By using the value of the gradient of the latter curve it is possible to estimate free-energy changes from the accompanying expansion. The free energies of saturation and immersion of plane surfaces are related in the following manner FL = FS + y cos 8 where y is the surface tension of the liquid and 8 is the angle of contact between the liquid and the vapour-saturated solid. Thus the saturated solid will expand on immersion if etZ and will contract if 8>-. Identity between the liquid and adsorbed phases is of Fourse shown by 8 = 0 when a marked increase in length will occur.The rod of compressed coal used in the experiment of the previous section was mounted in the dial-gauge extensometer and after thorough evacuation, was exposed to saturated water vapour at 2 5 O c. for 3 days. A linear expan-sion of 1-23 yo was recorded. Boiled distilled water was then admitted through a tap. The angle of contact calculated from these results is 4" under 5. In view of the closeness of this (C) THE FREE-ENERGY RELATION BETWEEN SATURATION -4ND IMMERSION.-7c n 2 The final expansion was 1-28 yo. 2 result to the critical angle of F further experiments were devised which are based on the following considerations. The significance of a finite angle of contact (as Bangham 24 has emphasised) is that it demonstrates the degree of incongruity between the surface of the bulk liquid and the adsorbed film on the solid and one of the simplest ways in which the presence of a finite angle of contact can be shown for solids of density greater than that of the liquid is by flotation experiments.A zero angle of contact for instance leads to the inability of the solid to float at all whilst for a powder which floats the value of 8 must be finite. The ability of the solid to float is dependent on the shape of the solid as well R. L. BOND M. GRIFFITH AND F. A. P. MAGGS 39 as the angle of contact ; a solid having vertical sides however will float above the surface only if O>-" according to the following relation : 2 &!vPs - vipL) + pr cos e = 0 ; in which g = acceleration due to gravity ; P = the periphery of the solid at the liquid meniscus; V =volume of solid and V i = the volume immersed.For systems where ps>p~ the solid will float above the surface only when O>z the depth of immersion being dependent on the ratio of periphery to volume. The densities of the coals measured by helium dis-placement lie between 1-5 and 1-3 g . cm.-3 and the lump densities of the dry coals fall in the range 1-37 to 1.15 g . ~ m . - ~ . Calculation shows that the largest cube of coal which would just float (i.e. taking 8 = n) is a centimetre cube. (d) FLOTATION EXPERIMENTS-S~P~~S of all five coals (ground to pass 72 B.s.s.) were sprinkled on clean water surfaces ; none of the coals showed any tendency to sink even after 20 weeks. To obviate any effects which might be attributed to adsorbed gases the simple apparatus sketched in Fig.8 was used. Coal powders were well evacuated at 80" c. allowed to reach 2, To PVUPS t equilibrium with saturated water vapour at room temperature and then tipped on to the water sur-face. Apart from a few particles (<I yo) which sank immediately the saturated coal remained floating on the surface for the following ten weeks after which observations were discontinued. Adequate confirmation of the flotation experiments was obtained when flat plates of coal weighing up to 60 g . were easily floated by placing the coal OR a freshly floated filter-paper which sank leaving the coal afloat. A further experiment was made in which the piece of coal was placed on thoroughly degassed ice.After several hours' pumping (with the water frozen) the ice was allowed to melt ; the coal floated and had not sunk after 6 days.* It was found impossible to fulfil the conditions of the flotation equation for whatever the size or FIG. &-Apparatus for flotation experiments. shape of the l&p the unwetted upper surface of the coal lay below the plane of the water surface ; in all cases the water meniscus curved downwards to meet the periphery of the upper surface of the lumps. It is concluded from these experiments that the angle of contact between water and coal K is finite and is a little under 9. Preliminary quantitative experiments have been made by measuring the minimum load required to sink a number of pieces of coal; whilst the influence of the extent of the periphery is predominant it is apparent that the evaluation of 8 will involve the shape of the meniscus and the surface tension of the liquid.For instance the action of wetting agents-which cause the coal lumps to sink-may depend on the reduction of 8 or the lowering of the surface tension or-more probably-on both. Work is in hand to elucidate these points. 2 * On pumping a piece of coal floating on water bubbles of gas steadily escaped from the coal which remained froding until a large bubble from the water burst so swamping the coal 40 WATER IN CAPILLARY STRUCTURE OF COAL Nature of the Adsorbed Film of Water. Interpretation of the results reported in Sections A and B along the lines of the B.E.T. multilayer theory or of the capillary condensation theory would lead to the conclusion that the water adsorbed by coal at saturation vapour pressure has the properties of three-dimensional liquid water.The critical experiments of the subsequent sections however make this simple conclusion untenable. The proportionality between the adsorption expansion and the surface pressure of the water film at room temperature (Section E) leaves little doubt that the water-coal system behaves in the same manner as the charcoal-alcohol systems investigated by Bangham,17 where the adsorbed films were shown to behave as a two-dimensional phase. It is at once apparent that the increase in the coefficient of thermal expansion of coal compacts brought about by adsorbed water is due to the kinetic mobility of the adsorbed molecules.By regarding the two-dimensional film of water as a distinct phase the absence of a normal melting-point is understandable.* It is not clear how-ever whether a gradual transition to a solid phase takes place when the temperature is steadily lowered. Hardy,20 for instance found that the water in plant cells froze in stages the proportion of ice formed being dependent on the lowering of the temperature. On the other hand Fosterz1 could find no evidence of the freezing of water adsorbed on silica gel even at - 65" c. ; Rau 22 was able to supercool water droplets to - 72O c. but as Bangham has pointed out there is some evidence to suggest that the water surface of drops at this temperature was remarkably akin to the adsorbed phase. From the several lines of approach described in this paper it is con-cluded that it is incorrect to treat adsorbed water as though it were bulk water. The authors are glad to acknowledge the help and suggestions of Dr. D. H. Bangham Director of Research Laboratories British Coal Utilisation Research Association in planning this work ; they are grateful to the Council of the Association for permission to publish these results. Summary. The relation between liquid water and adsorbed water is discussed in the light of current theories and whereas capillary condensed water might be expected to possess the properties of the bulk phase measurements of the dielectric constant and volume changes on cooling coal saturated with water vapour show no evidence of a sharp freezing point. The significance of the angle of contact between liquid water and saturated coal is discussed ; measurements of the freeenergy decrement on wetting saturated coal suggest that the angle of contact is about goo but the value must in fact be less from the flotation experiments. It is concluded that a phase difference exists between water adsorbed on coal and bulk water. British Coal Utilisation Research Association, 13 Grosvenor Gardens London. 19 Bndgeman Physics of High Pressure (London 1931). 20 Hardy Collected Scienti$c Papers (Camb. Univ. Press 1936). 21 Batchelor and Foster Trans. Furuday SOC. 1944 -40 300. 22 Rau Schrift. Deut. Akad. Luftfuhrtforsch 1944 8 (u) 65 ; see also Frank Nature, 2JBangham. Nafure 1946 157 733. 24 Bangham J. Chem. Physics 1946 14 352. * According to Bridgeman,lg liquid water cannot exist below ca. - 20' c. even under pressure ; further the pressures developed by the volume change on ice formation are too small to depress the freezing point sufficiently even in an undeformable container. 19q6D 157 267

ISSN:0366-9033    

DOI:10.1039/DF9480300029

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

PORE SIZE AND PORE DISTRIBUTION BY A. GRAHAM FOSTER Received 17th Febrwry, 1948 In discussing the problem of estimating capillary radii of porous solids, I shall deal here only with those methods based on experimentally determined sorption isothermals, which may be classified as follows. (a) Methods based on the Capillary Thy.-The Kelvin equation when applicable gives the pore radius directly. The conditions under which the equation may be applied and the question of its validity will be discussed. (b) Methods based on Langmuir, B.E.T. or Harkins-Jura theories in which the surface area of the solid is calculated from the sorption isothermals. I have shown1 that an approximate estimate of the surface area can be made from the capillary radius using the relation S/V = z/r for the surface/ volume ratio of a cylinder.Conversely, knowing S and V one can make a rough estimate of r, assuming that the pores are cylinders of uniform diameter. The chief application of the method would appear to be to systems where capillary condensation is absent and the Kelvin equation inapplicable. (c) Approximate estimates derived by considering the shape of sorption iso- thermals, e.g., if sorption practically ceases after the formation of a mono- layer, we may infer that the pore radius is of the order 1-2 molecular diameters. Following Brunauer,2 I have discussed recently 3 how the shape of the isothermal alters as the number of adsorbed layers increases. I. Application of the Kelvin Equation (a) Radius -volume Curves .-In 1932, a modified version of Zsigmondy’s capillary theory was pr~posed,~ in which it was postulated (a) that con- densation did not occur until after the formation of an adsorbed layer approximately two molecules thick, and (b) that over the range of the hysteresis area, desorption equilibria were determined by .the Kelvin equation, assuming complete wetting, i.e., where p d is the desorption pressure, Po the saturation pressure, V the molar volume and y the surface tension of the absorbed liquid at temperature T ; r is the radius of curvature of the meniscus in the capillary over which the pressure p d prevails and is usually identified with the radius of the capillary space in which condensation occurs.According to the capillary theory, one would expect that (after converting pressures to radii and concentrations to volumes), pressure-concentration isothermals for dzferent liquids would be reduced to the same radius-volume, or r-v, curve, the latter being determined by the structure of the adsorbent.This simple view ignores two factors : (a) the density of the adsorbed liquid may differ from that of the bulk liquid and thus lead to incorrect values of v ; and (b) since condensation follows layer adsorption, the value of I calculated from the Kelvin equation is less than the true pore radius yo by an amount A equal to the thickness of the adsorbed layer. B* Foster, Proc. Roy. SOC. A , 1934, 147, 128. Adsorption of Gases and Vapours (Oxford, 1944). Foster, Trans. Faraday SOC., 1932, 28, 645. Ch. VI. a Foster, J. Chem. SOC., 1945, 769. 4142 PORE SIZE AND PORE DISTRIBUTION Although it was shown that isothermals for the same liquid at diferent temperatures reduced to identical r-v curves, yet it was not found possible to reduce isothermals of diflment liquids to the same Y-v curve.The r-v curves for benzene and alcohol on ferric oxide were, however, identical in shape and could be made to coincide by displacement parallel to the axes. Lack of suitable experimental data has hitherto restricted further work on these lines, but an analysis has now been made of the isothermals of fifteen different liquids determined on ferric oxide by Broad and F ~ s t e r . ~ In the absence of detailed information about orientation of adsorbed molecules, we cannot determine accurately the thickness of the adsorbed layer but can only make an approximate estimate.This has been done by calculating molecular diameters (a) from the normal density (d) of the liquid by means of the well-known relation 0 = 1-33 X IO-' ( y 3 . which assumes hexagonal close-packing and is similar to the relation used by Brunauer 2 for surface areas. If the Kelvin equation gives the radius r of the space left after completion of the adsorbed layer, assumed to be of thickness 20, then the true pore radius yo will be given by ro = r + 20, and for a given adsorbent, should be constant and independent of the nature of the adsorbed substance. FIG. I. I. 0 EtOH + Dioxan. 11. 0 Morpholine A Triethylamine. III. 0 n-hexane x CHCl, A Benzene. IV. 0 EtOH A Dioxan + EtAc ~ B u t y l Acetate 0 Pxylene. Fig. I shows the data of Broad and Foster plotted as ro - v curves.Curve I is drawn through the points from the isothermals of ethyl alcohol and dioxan, which clearly coincide. The points on curve I1 are for tri- ethylamine and morpholine, whilst the actual line represents curve I shifted to correspond with the displacement of the Y scale. It is evident that within the limits of experimental error, the ro - v curves for all four liquids coincide. In curve 111, data for rt-hexane, benzene and chloroform are shown reduced to the same radius-volume curve, again with the yo scale shifted so as to avoid confusion with curves I and 11. The latter can be brought very nearly into coincidence with curve I11 by vertical displacement corresponding to the shift of the ro scale. This means that isothermals for seven different liquids have been brought into virtual coincidence when Broad and Foster, J . Chem.SOC., 1945, 446.A. GRAHAM FOSTER 43 plotted as r,, - v curves. Unfortunately, the data for the remaining substances investigated do not show such good agreement. Toluene and cyclohexane give a common curve, which lies 1.2 A. above curve I, whilst points for carbon tetrachloride lie about 0.5 A. above the latter; Y,,-ZI curves for H20 and D20 coincide exactly but lie 2 A. below curve I, whilst .n-octane lies 3 A. above. It was suggested by Broad and Foster that better agreement in this latter case would be obtained by assuming that the long-chain molecule lies flat in the adsorbed layer. Curve IV, which shows data for five different liquids reduced very nearly to the same radius-volume curve, is based on unpublished work by Batchelor and Foster on an ‘‘ aged ” sample of the ferric oxide gel used for the other experiments.It seems fair to conclude that if a more exact allowance for the thickness of the adsorbed layer could be made, radius-volume curves would, in general, coincide. (b) The Validity of the Kelvin Equation.-It is generally thought that this equation mist break down when r approaches molecular dimensions, since both y and V may then depart from their normal values, and a mathematical analysis of this question is urgently required. For the present, we can merely apply the equation in its usual form and seek independent confirmation of the correctness, or otherwise, of the calculated radii.It is obvious from the results just described that the equation remains valid for comparative purposes when the calculated radii are of the order 20 A., whilst the Y-ZI curves of Broad and Foster6 for H20 and D20 on silica gel, which coincide completely, show calculated values as low as 8 A. Crowther and Pun measured the V.P. of water in soils and also made indirect measurements in which moist soil was shaken with benzene and the F.P. depression observed. Assuming that the V.P. in the latter systems was determined by the water-benzene interfacial tension in accordance with the Kelvin equation, good agreement between the two methods was found even when the calculated radii were below 10 A. Here again, we have no proof of the correctness of the calculated values but merely a demonstration of the apparent validity of the equation for comparative purposes.The term 2/r which appears in eqn. (I) represents the surface/volume ratio of a cylinder and arises because when dn moles of liquid condense in a pore of radius r, the volume dv covers up free surface (of the adsorbed layer on the walls) ds = 2 dv/r. Thus we should not interpret r too literally as a simple “radius.” If the cross-section of the pores is not circular, the factor 2/r must be replaced by the corresponding value of dsldv. We must also not attach too much importance to the approximate agreement between these Y values and those calculated from the relation Y = 2 (total volume adsorbed/g.) + (total surface arealg.) because this merely proves that &/dv = s/v, and the numerical factor 2 may be incorrect in both cases.However, if the pores are uniform in shape we might expect, by comparing the values of Y obtained by these two methods, to obtain some information on the manner in which the equation breaks down, since the second method involves no assumption about v or y. There are unfortunately few data available which give consistent values for surface areas in systems where capillary condensation also occurs. Emmett and de Witt * found hysteresis loops in the sorption of nitrogen, oxygen and argon on porous glass. Their radii calculated from 2s/v, which they denote by YV, average about 31 A. whilst the values derived from Broad and Foster, J . Chem. SOC., 1945, 372. Crowther and Puri, Proc. Roy. SOC. A , 1924, 106, 232.sEmmett and de Witt, J . Amer. Chem. SOC., 1943. 65, 1253.44 PORE SIZE AND PORE DISTRIBUTION the Kelvin equation YK average 22 A,, so that addition of 8 A., representug two adsorbed layers, would give excellent agreement. Emmett and Cines extended this work and quote figures for N,,A and butane on several porous glasses which show good agreement between rv and ( r ~ + 4) A. for one adsorbed layer, but the agreement would still be reasonably good for (YK + 8) A., assuming two layers. The data of Broad and Foster do not give consistent values for the surface area of ferric oxide gel when values of a2, calculated from the density of the liquid, are used for the surface area per molecule. The figures for ethyl alcohol give rv = 37 A. compared with ( r ~ + 20) = 31 A.(c) Pore Distribution.--A point on a radius-volume curve represents the volume v required to fill all the pores having radii between o and Y. The slope dv/dr indicates the volume dv required to fill those pores having radii between r and r + dr, hence a graph of dv/dr against r shows the extent to which pores of given radius contribute to the total volume. It has already been pointed out * that this curve corresponds roughly to a FJG. 2. I . Benzene-Fe,O,(B). III. H,O-SiO,(B). 11. Dioxan + Alcohol-Fe,O,. IV. H,O-Al,OS. Gaussian distribution. Some typical volume-distribution curves are shown in Fig. 2 ; some are obviously not quite symmetrical, but none are very markedly skew, and all show a clearly defined maximum corresponding to the point of idexion in the radius-volume curve and indicating the mean value of the capillary radius. In general, the smaller the mean radius the sharper the maximum, e.g., silica gel B with a radius of 10 A.shows a much sharper peak than ferric oxide B where the mean radius is go A. Higuti lo observed a similar effect with a mixed gel of titania and ferric oxide. Raising the temperature of activation increased the pore radius and lowered the height of the distribution curve whilst at the same time the total volume was diminished. The ferric oxide gel investigated by Lambert and Foster showed the same behaviour after treatment with water.* It will be observed that some curves do not extend far to the left of the maximum. This is Emmett and Cines, J . Physic. Chem., 1947. 51, 1248.10 Higuti, B i d . Inst. Phys. Chem. Res., Tokyo, 1939, 18, 65 jA. GRAHAM FOSTER 45 because condensation gives way to layer adsorption as the pressure falls, and we are then unable to apply the Kelvin equation. So far as capillary effects are concerned the axis should be shifted to correspond with the point at which hysteresis begins, and volumes reckoned from the start of the condensation process and not from the beginning of layer adsorption. dnldr dvldr dnldr dvldr dn/dr I const. I1 a - b r I11 a/* IV aira VI af@ VII e- V a / A IX ed+)' Curve (a) for a = 2 I h = r ] KEY TO FIG. 3 dvldr ~ ar-2 (+ve values only) ar a ajr'ln alr rat?- a+ - by3 Curve (b) (Numerical constants omitted.) The statement that the dv/dr curves show the pores to be distributed according to the normal law of probability is not strictly true.It is really the number of pores of different radii rather than their volume which we46 PORE SIZE AND PORE DISTRIBUTION would expect to be distributed in this manner. The actual pores are most likely to be highly irregular spaces and cavities between coagulated particles of solid, the sizes of which are distributed around a mean. The Kelvin equation, as we have shown, interprets this complex structure in terms of a simpler structure of uniform non-intersecting cylinders of varying radii. If we assume these to have unit length, then the volume of any group of n cylinders of radius r is obviously n r k . If then, there are drt, such cylinders having radii between r and r + dr, their volume will be dr = nr2dn.If we take the normal error function to denote the distribution of radii about the mean value a we shall have with a maximum at r = a d%/dr2 = o when r2h2 - rh2a - I = o giving which reduces to rmax= a only when h)>a. If the dvldr values for the curves in Fig. 2 are divided by r2, no difference can be detected in the radii at which the maxima occur so we may infer that this condition is fulfilled for these systems. dn = k exp { - h2(r - a)2}dr . (3) :. dv = nr2dn = knr2 exp { - h2(r - a)2}dr . (4) rmax= &{a + (a2 + 4/h2)+} a v p r H,O-S1O, System, FIG. 4. It is of interest to consider simpler distributions than that of eqn. (3). In Fig. 3 I have sketched roughly the curves of dn/dr, dv/dr and v against r for a number of simple cases. It appears that the v-r curve will be concave to the v axis unless dn/dr falls ofi at least as the - 512 power of r (V).Case I1 is the simplest to give a curve resembling any actual v-r curve. A simple exponential decay dn/dr = a c r also gives this type of curve (VII), which is also found even when one branch of the normal probability curve is missing, i.e., in the case a = 0, which makes r = o the most probable radius (VIII). The normal error function with a = 2 and h = I is shown in (IXa). It is difficult to say how far any of these distributions are likely to be realised in practice. All curves so far described show reasonable agreement with Case IX. A new sample of silica gel which has just been examined * gives the remarkable water isothermal shown in Fig. 4. The pressure is proportional to concentration between the limits 8-16 mm.(i.e., 150-450 mg./g.) covering practically the entire hysteresis area. The v-r curve has no inflexion over the range of capillary condensation and consequently the dvldr curve shows no maximum. I do not think this abnormal behaviour can be attributed to the disturbing effect of layer adsorption or to the smallness of the pore radii, since other silica gels show normal distributions * Miss M. J. Brown (unpublished work). The displacement of r,, from a is clearly shown in curve b.A. GRAHAM FOSTER 47 x (= @/Po) = exp ( -b/rL down to 8 A. If the Kelvin equation is written in the form and the linear range of the isothermal as x = x o + av, where v is reckoned from the beginning of capillary condensation, the curve will be represented by the relation, and or dn/& e-b1*/~4, a combination of exponential and inverse fourth-power decay.In theory dv/dr will have a maximum at Y = b/2 which corresponds to x = e-2= 0.135, which is too low a relative pressure for condensation to occur (Y = 4 A.). Finally, since we have shown that the maxima of der/dr and dn/dr do not in general coincide, we must consider whether we are justified in using the relation s/v = Z/Y for an assembly of non-uniform pores. For the surface and volume of a small number dn of pores between r and r + dr we shall have ds = zmdn and dv = m2dn exp ( - b/r) = x o + av dv/dr = b/ar2 exp ( - b / ~ ) , m whence s = znk [Y exp ( - h2(r - J m and v = nk 1 r2 exp ( - h2(r - a)2) dr i; Evaluation of these integrals shows that there is no simple solution except when ah is large, when of course we get the expected result s/v = z/a, where a is the " mean " radius Since we have already shown that the maxima of the dn and the dv curves coincide for the systems illustrated in Fig.2, we may assume that the simple relation is also valid for these systems. Obviously, however, we must use this relation with care especially when the distribution curve is flat or unknown. 11. Determination of Surface Areas and Emmett.'* Methods based on actual sorption measurements from the gas phase fall into two classes (i) based on the Langmuir equation and hence on measure ments carried out whilst the monolayer is actually being formed, and (ii) based on the multilayer theory, where the amount v, required to complete the monolayer is obtained by extrapolation from the region of multi-layer adsorption.In endeavouring to calcdate the surface area by these methods the common difficulty is to choose a suitable value for the area occupied by a single adsorbed molecule. In the absence of definite information about molecular orientation it is customary to use the value of a2 calculated by eqn. (2). Comprehensive reviews have been given by Brunauer (a) Langmuir Method.-The linear plot enables the saturation value z to be determined easily. A number of low- pressure isotherms which obey this relation have been described recently13 l1 Ref.% Ch. IX. lZ.Advunces in Colloid Science (New York, 1g4z), Vol I. FFoster, J. CAem. SOC., 1945, 360.48 PORE SIZE AND PORE DISTRIBUTION and I have indicated how a correction for multilayer adsorption can be applied in favourable cases.14 (b) B.E.T.Method.-The fundamental equation of the B.E.T. theory is where v is the actual amount adsorbed at pressure$, and v, the amount required to complete the monolayer. The equation is derived by summation over an infinite number of layers and, in practice, a linear relation is not found over a very wide range. I have discussed elsewhere some of the simple limiting cases which might reasonably be expected.15 Examination of the now extensive adsorption data for non-porous solids fails to reveal any systems which show particularly good agreement with the limiting case v/vm = Po/($,,-$) which arises when the heat of sorption in the first layer is large and c large.(c) “ Point A ” and “ Point B ” Methods.-These were derived before the development of the multilayer theory and apply only to iso- thermals with a linear middle portion which begins at “ point B ” and extrapolates to zero pressure at “ point A.” I have already shown l4 that when low-pressure data are available the ‘‘ point A ” values agree well with those obtained from the Langmuir equation, and also that there is some theoretical basis for the “ point A4,” but not for the “ point B ” method. (d) Harkins-Jura “ Absolute ” Method.-If a non-porous solid covered with an adsorbed film in the presence of saturated vapour is immersed in bulk liquid heat H is evolved given by C = 4.185 x 107H/h, where C is the surface area and k the total surface energy y - Tdy/dT.C may thus be determined calorimetrically without assumptions about surface areas of molecules. The area of a sample of anatase (TiOJ found by this method l 6 agreed closely with the value found by the 9.E.T. method taking 02 = 16.2 A . ~ for N,. The method is also applicable to porous solids since the heat change accompanying capillary condensation is a similar effect. The data of Lambert and Clark l7 for benzene or ferric oxide show an integral heat of sorption over the hysteresis area of 2-30 cal., which with h = 66 erg./cm.a gives C = 1.4 x ~o~crn./g. Direct application of the Kelvin equation gives r = 16 A,, whence C = 2v/r, where v is the volume range of the hysteresis loop = 0.115 ~ m . ~ , giving C = 1-44 x rob. This is, of course, the surface of the adsorbed layer which is less than the true surface of the solid in the ratio r/ (r + A ) , where A is the thickness of the layer.(e) Harkins- J u r a “ Relative ” Method.-According to these workers,l* condensed films in monolayers follow the empirical relation where n, is the surface pressure (formerly denoted by F) and a, (formerly A ) the area available per molecule in the surface layer, defined by where M/q is the adsorption in molelg. and C the specific surface. may be substituted into the Gibbs’ equation n = b - aa,,, (7) a,= MZINq . (8) Eqn. (7) l4 Foster, J . Chent. SOC., 1945, 773. l5 Foster, J . Chena. Soc., 1945, 769. l8 Harkins and Jura, J . Amer. Chem. Soc., 1944, 66, 1362. l7 Lambert and Clark, Proc. Roy. Soc. A , 1929, 122, 497.18Harkins and Jura, J . Amer. Chem. SOC., 1946, 68, 1941.A. GRAHAM FOSTER 49 dn = (RT/MC)q. d log, p . - (9) d log, 9 = {a(Ma2/NRT}dqlq3 . * (10) giving which on integration gives the Harkins- Jura isotherm, where A = a(Ma2/2NRT, or C = kA+, where k2 = 2NRT/aM2, and is assumed to be characteristic of a given adsorbate at a given temperature, independent of the nature of the adsorbent ; k can be evaluated from a single experiment by the absolute method on a non-porous solid and this value used for other adsorbents, porous or non-porous, at the same temperature.ls log, p = B - A/q2 . (11) TABLE I Molecule H20 .. .. .. NH3 co, N, .. .. .. .. CHC1,F . . .. .. n-C,H ,OH .. .. n-C4H,o v .. .. X-C~H,, .. .. .. A .. .. .. .. .. .. .. .. .. .. .. .. C2Ha ..Kr .. .. .. .. I-Butene .. .. .. I 10.8 13'7 13-8 I 4-2 I 5-2 15.2 I 6.2 26.4 30'5 31'3 32.0 45'0 Area per Molecule (A.,) Column I.-Calculation from ean. (2). ,, 2.-Harkins and Jura.<* CaIculation for best fit of B.E.T. Method with H. J. method. ,, 3.-Living~ton.~~ (SO,, TiO,, BaSO,. Graphite.) ,, 4.-Davis, de Witt and Emmett.e3 (Metal foil, glass spheres. Al,O,, 50,. ZnO, W.) ,, 5.-Emmett and Cines.# (Porous glass.) (TiO,, ZrSiO,, BaSO,, SO,.) Livingston 2o and Emmett have both considered the compatibility of the B.E.T. theory with the Harkins-Jura relation and conclude that, if a given set of data follow the B.E.T. equation, the H.J. method will not give a linear plot unless the B.E.T. constant c is at least 50. The value of 02 needed to make the two methods agree increases with c, e.g., from 13.6 to 246 A .~ for N, as c changes from 50 to 1000. On the one hand, Harkins and Jural* criticise the B.E.T. assumption of constant molecular area for a given adsorbate and on the other, Emmett a criticises the assumption that k , which depends on a in eqn. (7), is independent of the adsorbent. In spite of the apparent agreement between the two methods obtained by Harkins and Jura,lS we must remember that both theories are empirical, the H.J. theory because it uses an empirical relation (7) to integrate the Gibbs' equation and the B.E.T. because its fundamental assumption is untrue, viz., that the net heat of sorption is zero for all layers after the first. Harkins and Jural* having determined C by the absolute method used the B.E.T.l'Harkins and Jura, J . Amer. Chem. SOC., 1944, 66, 1366. ao Livingston, J . Chem. Physics, 1947. e3 Davis, de Witt and Emmett, J . Physic. Chem., 1947. 51, 1232. Emmett, J. Amer Chem. SOC., 1946, 68. 1784. Livingston, J. Amer. Chem. Soc., 1944, 66, 569.50 PORE SIZE AND PORE DISTRIBUTION method to determine the monolayer adsorption and then calculated 02 per molecule of N,. For 86 different solids, they quote 16 different values, grouped mainly round three peaks at 14-05, 15-25 and 16-05 A . ~ . The smallest area 13.6 lies close to that calculated from the density of solid N, and the largest 16.8 lies close to that calculated from the density of liquid N 2. In Table I, I have collected the available data for " observed " surface areas per molecule.The fact that the product (z/M) a2 is not constant when the values of column I (calculated from eqn. (2)) are used is surprising since both Goldmann and Polanyi 24 on charcoals and Broad and Foster 25 on silica gel B found excellent agreement. On silica gel A, the latter workers found that the product decreased with increasing molecular diameter, and that z/M gave a linear plot against 118 which no longer passed through the origin. This was attributed to the presence of tapering capillaries about 10 A. wide at their open ends. None of the results quoted in Table I appears to be capable of interpretation in a similar manner and we are thus left in a most unsatisfactory position. The problem is probably related to that arising in the discussion of volume-radius curves, i.e., if the area of the monolayer cannot be estimated from the " normal " cross- sectional area u2, we cannot expect a itself to represent accurately the " thickness '' of the adsorbed layer, since both are calculated from eqn.(2). At present, I can only suggest some such explanation as that proposed by Herington and who pointed out that if a hexagonal molecule had to be attached to fixed points in the lattice of the solid at all its corners, the surface would never be completely covered and even at saturation as much as 35 % might be bare. It is difficult, however, to see how such an explanation could apply to small and simple molecules like N, and A. 111. The Shape of Sorption Isothermals When condensation occurs and can be recognised as such, eg., by the appearance of a hysteresis loop, we can apply the Kelvin equation to deter- mine the pore radius.The smallest calculated radii at which condensation appears are of the order 10 A. Thus, water on silica gel shows hysteresis from 11 A. down to about 8 A. whilst other liquids show mean radii of about 15 A. on silica and titania gels. Taking 5 A. as an average molecular diameter, a calculated radius of 15 A. corresponds to a true pore radius about five times the molecular diameter, if the adsorbed layer is two mole- cules thick. It follows that our remaining problem-how to estimate pore size when condensation does not occur-is concerned with the behaviour of systems in which r/a < 5. We can recognise the cases where r/a = I or 2 by the fact that unirnolecular adsorption then accounts for virtually the entire sorption process, and are thus left with r/a varying from 3-5 as the cases to be identified. I have already shown l5 that when n is put equal to 2 or 3 the B.E.T.theory predicts linear isothermals. The effect of the curvature of the surface of the adsorbent, which is ignored by this theory, has been considered by Broad and Foster who showed that isothermals for n = 4 - 6 at curved surfaces would assume roughly the same shape as those for which n = 2 - 3 at a plane surface. We can thus regard the linear isothermals found for alcohols on silica gel as representing the intermediate case where n lies between 2 - 6. (The converse argument that n = z - 6 necessarily gives a linear isothermal does not apply since the magnitude of the heat of sorption is also involved.) Z 4 Goldmann and Polanyi, 2.physik. Chem., 1928, 132, 356. 25 Broad and Foster, J . Chem. SOC., 1945, 366. t 6 Herington and Rideal, Trans. Faradny SOC., 1944, 40, 505.A. GRAHAM FOSTER 51 A further check can be made by using the relation r = 2v/s, but a simpler method is to calculate the ratio of the monolayer to the total sorption (z/q8). The percentage of total volume of a cylinder represented by the first layer has the following values : n 1 2 3 4 5 6 7 8 9 1 0 4 Q 8 (%> 100 75 55 44 36 30 26 23 21 I9 Thus, when we find z/qs = 51 for ethyl alcohol on silica gel B, we suspect n to lie between 3 and 4 which would give 7 = 15 - 20 A. On the same gel, water shows a large hysteresis loop with mean radius 10 A. corresponding to a true radius of 16 - 17 A. if two layers are present. Summary The determination of capillary radii of porous solids by application of the Kelvin equation, from estimates of surface area and indirect methods, is discussed. It is shown that radius-volume curves for different substances on a given adsorbent can be made to coincide when allowance is made for the thickness of the adsorbed layer. Volume-distribution curves, showing how f a r pores of given radius contribute to the total pore-volume, are described for SiO e, Fe ,O,and A1 20, gels, and the effect of different distribution of pore radii on the shape of the isothermal is discussed. It is suggested that the difficulty of estimating molecular surface areas encountered in applying the B.E.T. and other adsorption methods to the determination of surface areas is related to the difficulty in estimating the thickness of the adsorbed layer which is encountered in applying the capillary theory. Chemistry De$artmeltt, Royal Holloway College, (University of London), EnglefieU Green, Surrey.

ISSN:0366-9033    

DOI:10.1039/DF9480300041

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

A. GRAHAM FOSTER MEASUREMENT OF INTERNAL SURFACE BY NEGATIVE ADSORPTION BY R. K. SCHOFIELE AND 0. TALIBUDDIN Received 1st March, 1948 The purpose of this paper is to show how measurements of the small increase in concentration that occurs when a salt solution is shaken up with a sample of dry fibre may be used, in certain circumstances, to calculate both the internal surface and the volume of pore space inside the fibres. The theoretical background is provided by Gouy’s theory of the ionic distribu- tion in the difEuse component of the electric double-layer, which the first- named authorZ has extended to obtain an expression for the negative adsorption of the ions electrostatically repelled from the phase boundary. With mathematical help from Dr. M. H. Quenouille he obtained, for the case when all the attracted ions have valency Y and all the repelled ions have valency Y/$, the expression as a good approximation, provided the first term is several times the second.J . Physique, 1910, 9, 457. Nature, 1947, 160, 408.52 MEASUREMENT OF INTERNAL SURFACE Here 92 is the electrolyte concentration in m.equ./cc., and r is the total charge in the diffuse layer expressed in m.equ./cm.2. r- is the part of r due to the deficit of repelled ions. 6 stands TABLE I Valency Ratio P Factor Q 3-1416 (n) 2-91 2-88 2-83 2.76 2-65 2'4495 (V''6) 2'0000 I -69 1-4641 (dG-2) 1-16 0.96 for 87c;F2/.5RTJ so that vp has the value 1.06~ . 1015 cm./m.equ. for water at 20' c. q depends on the valency ratio, 9, in the manner shown in Table I, where the entries to four decimal places have been directly calculated, and the rest obtained from them by a graphical method.Eqn. (I) has been worked out for the case of a plane interface and an infinite depth of liquid in which the ions are in ideal solution, and caution must be exercised in applying it to a natural fibre in a real salt solution. Still assuming ideal solution, an examination of the case, where two parallel and opposed interfaces are separated by a finite distance 2X, shows that when v p r X is less than about 10, r / approximately. Eqn. (2) is, in effect, Donnsn's equation for the membrane eqizilit>rium in the form ( z / x ) = (_y/x)-P - (?J/x). Hence, if $T.X is too small, (I) is not valid at any value of n. If, however, vprX exceeds about 30, eqn. (I) can be applied for values of q/&@ between about 15/(vpT) and X/z (values computed for p = I).The approximation is closer the wider this gap. Whatever the value of v p r X , the equation (3) r- - == X - bnlh . n holds approximately wh.en bnllp is a small fraction of X , b being a constant depending on p , vp, r and X . The extrapolation, used below to obtain the volume of the pore space, is based on this approximation. The main effect of departures from ideal solution as in eqn. (3) of specific adsorption of the attracted ions and of hydration effects close to the interface is to increase or decrease the part of r - / n that is independent of n. Thus the dope of the graph of r - / n against ~ / l / < should be close to q,/fifi within the range of n appropriate to eqn.(I), but these disturhances will prevent us from obtaining r from the intercept. KO precise treatment of the effects of curvature of the interface has been attempted. It is clearly desirable that the principal curvatures should everywhere be small compared with dvp. Even when this is not true in detail, some compensation may arise between portions of the interface having opposite curvatures. The area obtained be!ow for the internal surface of jute fibres must be regarded as the equivalent area of a plane in te dace . Experimental One sample of retted " white " jute and two of retted " red " jute, kindly given by the Indian Jute Mills Association, which we will distinguish by the letters A, B and C, were milled, and then steeped in N./IOO Na,CO, solution in order t o hydrolyse ester linkages.They were then washed with water until small test samples, when shaken up with N. KC1 solution, showed a PH value a littleR. K. SCHOFIELD AND 0. TALIBUDDIN 53 below 7.* The samples were then divided into parts which were washed with Li, Na, K and Ca chlorides respectively, and then with water, until they were free of chloride. These sub-samples were &-dried at room temperature, and stored in desiccators over CaC1,. The $H values determined in N. KC1 were all close to 6. 10 g. portions of the calcium-treated jutes were leached with KCl solutions, and the exchangeable calcium released was determined. In this way the number, E, of milliequivalents of negatively charged groups (mainly - COO- groups) attached to 100 g.of dry fibre was found for each sample, the loss of water on drying at 1 0 5 O c. having been determined on separate portions. Experiments were made on sample C using Li, Na, K and Ca chlorides at concentrations from ~ . / 1 2 8 to N. The strongest solutions were not used in experiments with samples A and B, since it is doubtful whether a theory that postulates ideal solution can usefully be applied to solutions more concentrated than N./IO. The experiments on sample A were made with Na and Ca chlorides, and on sample B with KCl also. In each experiment, a 10 g. portion of the sub-sample containing the appro- priate cation was weighed into a dry flask. After adding 200 cc. of the test solution, the flask was tightly stoppered, shaken several times, left standing overnight and again shaken well next morning.A convenient volume of the resulting solution was then delivered into a second dry flask, and weighed, and its chloride content was determined by the Volhard method. A parallel determination was also made of the chloride in a similar weighed volume of the original solution. The small increase, An, in the concentration could usually be estimated t o about 3 yo, the determinations for the strongest solutions being least exact. For each experiment the percentage moisture, m, in the fibre (dry basis) was determined by drying a separate 5 g. portion in an oven at 105O C . In order to find out how much of the observed effect must be ascribed to agencies other than the negative charges, parallel experiments were made with solutions containing ~ ./ 2 0 HCl. As these solutions have PH 1 - 3 , most of the carboxyl groups were in the uncharged -COO- condition. The weakest of these solutions contained only ~ . / 2 0 HC1 except for the small number of metallic ions released from the fibre. The next contained the salt in addition at N./ZO, making the total chloride concentration N./IO. Only with sample C were these experiments taken up to normal chloride. A base-free sub-sample was prepared from sample C by washing it first with HCl and then with water until it was free of chloride. This, when dry, produced concentration changes in ~ . / 2 0 HCl that increased with the time of storage, indicating an instability of structure. Results It is convenient to distinguish by the suffixes 6 and 1-3 the results obtained at PH 6 and PH 1.3 respectively, and to define v I by the equation (4) with a similar equation for v1.*. A set of values for sample C in NaCl solutions is set out in Table 11.It will be seen that vl.) rises with fall in n to a maximum value which is practically attained at N./IO. Although it is impossible to obtain PH 1-3 in solutions weaker than ~ . / 2 0 it is reasonable to consider that 11 cc. per 100 g . is the part of v I not due t o the negative charges at all concentrations below N.!20. This 11 cc. presumably represents water inside the fibre substance from which chloride ions are completely excluded owing to their size. It corresponds to the 12-5 cc. of water which has been observed by Sookne and Hams to be taken from acid solutions by cotton.The cause of the fall in vl., with rise in n above N./IO cannot be given with certainty. It may indicate a positive adsorption of chloride occumng when the electrical potential in the solution in contact with the internal surface of the Text. Res., 1940. 10, 405. * For the basis of this technique, see Saric and Schofield, PYOC. Roy. Soc. A , 1946, 185.431.54 MEASUREMENT OF INTERNAL SURFACE vl. 3 (PH 1.3) CC./IOO g. fibre is only slightly less than that in the bulk of the solution. This effect would diminish rapidly with reduction in salt concentration because the concentration of chloride ions against the surface is further reduced by the mounting difference in electrical potential. TABLE 11-NEGATIVE ADSORPTION OF CHLORIDE BY JUTE (Sanzple C in NaCl) Difference V B cc./100g.~ I Chloride c o x . n 1'0 0.5 0'2 0.1 0.05 0-025 0.0125 0.00625 0'0 (*2 6) CC./IOO g. 15.1 23'7 32'7 40'3 34'2 59'4 72-2 79'4 (86.0) I I Q dYpn A . 7'3 8-8 10.9 10'2 11.0 (11.0) (11.0) (11.0) (11.0) 7'8 14-9 22-5 29-4 43'2 61.2 68-4 48-4 (75.0) 6.1 8.6 13'7 27'3 38-6 77'2 1 I 00 I The quantity of greatest interest is the difference VE between v I and vl.$, for this is the direct consequence of the presence at PH 6 of E m.equ. of negative charges per 100 g. A plot of VE against n (cp.eqn. (3)) shows that VE is tending to the limit, V , when n is very small. This is evidently the volume of the water-filled pore space which is freely accessible to chloride ions when the internal surface is uncharged, but from which chloride ions tend to be excluded when it is negatively charged.I' for sample C is 75 cc. per roo g. y. . YE- v. I 20 40 c FIG. I In order to show how eqn. (I) can be used to obtain the internal surface the experi- mental values of VE for sample C in Li, Na, and K chlorides are plotted in Fig. I against q/m There is a distinct tendency for the points for LiCl to be above, and those for ICC1 to be below, the points for NaCl; but there is no indication of any difference in slope at the higher concen- trations or in V. Only one curve has therefore been drawn. The equivalent plane area, A , obtained from the slope of the straight portion is 1.5 x I O ~ c n 2 per IOO g., or 150 m.2 per g. Dividing E by A we get 1-47 x 10-7 m.equ./cm.* for r, so that 15/$r = 11 A. Dividing V-by A 'we get 50 A.f6r x so that XI2 = 25 A. Hence we were justified in using the slope between these limits to obtain A . As a further check, values for VE were calculated by means of Donnan's equation, and these were used to construct the broken curve. This falls well above the experimental points where they have been used to obtain the internal area. Thus the conditions that must be fulfilled when (I) is used to obtain the equivalent plane area are satisfied in the case of sample C. The value thus obtained for A is roughly a thousand times the external surface of the fibres.R. K. SCHOFIELD AND 0. TALIBUDDIN White Jute Red Jute Sample A Sample B I 6.0 v CC./Ioo g. . 68 A m.a/g. . (200) 130 r m.equ./cm.$ . (0-33. 10-7) x A. 55 Red Jute Sample C 22'0 75 150 50 1-47.I o - ~ The results for sample B (the other sample of " red " jute) are shrdar to those for sample C, but those for sample A (the '' white " jute) plotted in Fig. 2 are strikingly different. When the Donnan curve was constructed The results obtained with CaCl, were not entirely concordant. For this salt q/& is 1-03 compared with 2 for the alkali chlorides, and the results obtained with samples B and C generally reflect this difference. Three experiments with sample A gave points that all lie below the Donnan curve. If these results can be confirmed and extended] they may enable us to make a rough estimate of the surface area. Discussion The value of r obtained for sample C, if interpreted as a uniform surface distribution of negatively charged groups, gives an average distance of about 1 2 ~ .between neighbouxing groups, while the value of X indicates that, on an average, the surfaces are separated by about IOOA. It is, therefore, quite reasonable to picture these groups as giving rise to an ionic distribution of the Gouy type.56 IONIC DIFFUSION AND ELECTRICAL CONDUCTIVITY On general grounds it is likely that, in sample A also, the negative groups are distributed over an internal surface. The close fit of the points in Fig. z to the Donnan curve indicates that v#lrX = v&?W/A2 cannot much exceed 10, so A cannot be much less than 200 m.2/g. This value gives 0.33 x 10-7 m.equ./cm.2 for r and 27 A. for X . In this case, the negative groups would be spaced at about 25 A. on the internal surfaces which would on an average be separated by about 5 0 ~ .In this case it is not to be expected that the Gouy treatment would be applicable. Since it appears that the negative groups are distributed nearly uniformly through the volzcme of the pore space, we would expect Donnan’s equation to hold as Procter found it to do in the case of swollen gelatine. On the other hand, the Congo Red studied by Donnan and Harris5 did not obey Donnan’s equation very closely, presumably because the -SO3- groups are not uniformly dispersed in the solution but clustered on the surfaces of micelles. Summary An extension of Gouy’s treatment gives the equation for the negative adsorption T- of the repglled idns in the diffuse part of the electric double-layer. The conditions under which this equation can be applied and the errors that may arise in non-ideal conditions are set out.Measurements have been made at PH 6 and #JH 1-3 of the small increase in concentra- tion occurring when samples of jute are shaken up in chloride solutions, the concentra- tion, n, ranging from N. to ~ . / 1 2 8 . of water taken by IOO g. of dry jute is close to 11 cc. for concentrations below N./IO. This water is presumably taken into the fibre substance where chloride ions cannot enter. At PH 6 the volume vI is greater than tr1.8. The difference, vg, must be due to the influence of the negatively charged groups. Their amount, E, was determined for each of the three samples of jute by cation exchange. The limit, V , of VB as n--M is the volume of the pore space which ranges from 50 to 75 cc. per IOO g. In the case of two samples of “ red ” jute all the conditions for the application of eqn. ( I ) were fulfilled over a sufficient range of concentration for the equivalent plane area,A, of the internal surface to be obtained from the slope of the graph of VE against q / d v p n . In the case of a sample of ‘‘ white” jute the conditions are not fulfilled, and the results follow Donnan’s equation for the membrane equilibrium. In the “ red ” jute the average separation of negative (mainly -COO-) g~oups on the internal surface is about 1 2 A . and the average width of the pore space about roo A. In the “ white ” jute the groups are a t least 25 A. apart on the surface and the average width of the pore space does not exceed SOA. At 1.3, the volume It is roughly a thousand times the external surface of the fibres. Rothamsted Experimntnl Station , Harpeidefl, Herts. J . Chem. SOC., 1914, 105, 313. J . Chem. SOC., 1911, gg, 1554.

ISSN:0366-9033    

DOI:10.1039/DF9480300051

出版商:RSC    

年代:1948

数据来源: RSC

摘要:

56 IONIC DIFFUSION AND ELECTRICAL CONDUCTIVITY IONIC DIFFUSION AND ELECTRICAL CONDUCTIVITY IN SANDS AND CLAYS BY R. K. SCHOFIELD AND C. DAKSHINAMURTI Received 26th February, 1948 It has often been suggested, but never proved, that water in fine pores suffers a modification of its properties through the operation of long-range forces. It appeared possible that a quantitative study of the migration of ions through media having pores of widely different sizes might provide new evidence. In any case, since ions diffuse through soil to plant roots,R. K. SCHOFIELD AND C. DAKSHINAMURTI 57 a study of ionic diffusion in porous media more or less resembling soil appeared very desirable. As none of the methods hitherto used appeared suitable, a new technique has been developed. In order to simplify the underlying theory, all our diffusion experiments have been carried out under conditions of constant total ionic concentration. Thus, when N./IO KBr and N./IO KNO, come into contact there is an inter-diffusion in which the sum of the nitrate and bromide concentrations remains practically unaltered.This is because the nitrate ion has nearly the same mobility as the bromide ion. Were their mobilities exactly equal, the diffusion process would be governed by a single diffusion constant for any given total concentration and temperature. In the more general case represented by the inter-diffusion of N./IO KBr and N./IO NH,NO,, there are two diffusion constants, one for the anions and another for the cations. Theoretical Imagine that two still solutions, A and B, containing ions of equal mobilities, but chemically distinguishable, and of the same concentration, Co, are brought into contact at a p h e surface.The ions of solution A will at once start to diffuse into solution B, and vice versa. From considera- tions of symmetry it is evident that, in the plane where contact was made, the ionic concentrations will immediately fall to, and remain at, Cg = &Co. Following the treatment of Einstein1 the amount, q, of ions that diffuse across area A of this plane in time z is related to the diffusion coefficient, D, and the root mean square displacement of an individual ion, dx by the equation, For diffusion into a solution of depth 1.5 dx, q is only 0.2 ya less than for diffusion into a solution of infinite depth. If one of the two solutions was held in a system of parallel channels occupy- ing only a fraction, f, of the total cross-section, ions initially at concentra- tion Co in these channels would maintain a concentration C g at the boundary such that C J 3 - - ' Iif co (4 In this case if q, A , f and Co are measured, D is obtained by combining eqn.(I) and (2). If one of the solutions is held in a porous bed, Cg can be determined by (I), if q, A and z are measured and D is known. An effective value of f can then be obtained by using (2). Experimental Tubes of about 0.5 mm. bore and external diam. 2.0 mm. were cut to a length of 4-5 cm. and ground at both ends. They were tightly packed in the lower part of a flat-bottomed cylindrical vessel so that the ground ends were level. The space inside and between the tubes was filled with N./IO KBr solution, and the excess KBr solution on top of the ground surface was removed.The volume of the liquid that filled the capillaries was obtained by weighing, and the fractional area, f, was calculated. In the first two experiments N./IO KNO, solution, and in the subsequent experiments N./IO NH,NO, solution, was placed above the tubes to a height of 4-5 cm. The solution was delivered slowly through a capillary tube, bent up at the end, which was held against the wall of the Einstein, Ann. Physik, 1905, 17, 549.58 IONIC DIFFUSION AND -ELECTRICAL CONDUCTIVITY vessel and raised as the filling proceeded so as to cause as little mixing as possible. Even if there is slight mixing, its effect on the total amount of the ionic diffusion will be insignificant since it amounts to shifting the time of starting the experi- ment by a few minutes only, the amount diffused being proportional to the square root of the time of diffusion.During the diffusion, the upper end of the vessel was closed with a ground-glass plate smeared with grease to prevent evaporation. The experiments were conducted in a constant temperature room at about 2 0 . 5 ~ c. The choice of the electrolytes used in the experiments was based on two considerations. (I) The density of the KBr solution which filled the lower part of the vessel is greater than that of either the KNO or NH,NO I solution of the same concentration. This ensures that the mixing is not due to the density differences.(2) It is known from conductivity data that the mobility of the NO,- ion is only a little less than that of the B r ion, and the agreement between the mobilities of the K+ and NH,+ ions is even closer. The amount of bromide found in the upper solution will thus give very nearly the diffusion coefficient of the B r ion in N./IO KBr or N./IO NH,Br solutions. At the same time, the ammonium found in the lower solution should give even more closely the coefficient for the NH,+ ion in N./IO NH,NO, or N./IO NH,Br. After a measured time the upper liquid was removed with a pipette fitted with a hypodermic needle. The amount of solution left in the lower part was checked by re-weighing, and the appropriate correction was applied in calculating the amount diffused.The solution that was removed would contain the K+ and B r ions that diffused upwards and would be depleted by the K+ and NO s- ions, or NH,+ and NO s- ions, that diffused downwards. The quantity of bromide and ammonium was estimated volumetrically. The accuracy of the diffusion measurements depends mostly on the accuracy of the estimation of these ions in small quantities. The quantities of bromide could be determined to within I yo error. For ease of manipulation the loss of ammonium from the upper solution was determined by difference. The results obtained in this way are less accurate than was expected. The results for ammonium ions are, nevertheless, given in the Tables to show the order of magnitude of the values obtained. This correction, however, was usually less than I yo.Results The values of the diffusion coefficients for bromide and ammonium ions are recorded in Table I. TABLE I. DIFFUSION COEFFICIENTS FOR BR- AND NH,+ Temperature c. 21'0 f 0'1 21-0 f 0'1 20-5 f 0-1 20.5 f 0-1 31'0 f 0'1 21'0 f 0'1 15'5 & 0.25 15'5 f 0-25 15'5 f 0'2.5 A cm.B ~ 6-16 4'45 3'79 4-16 3'79 3'94 4-14 4'48 3'79 f 0.297 0.292 0.303 0.283 0.309 0.285 0.284 0.303 0.313 7 days 2'0 1-684 1.670 1.760 1.740 1'573 1.750 1-729 1.674 PIC0 for xomide cc . 3-08 I .696 1.846 1.817 1.687 1.691 1.872 1-571 3'00 DBI- :m. Z/day 1-87 I -85 1-74 1-81 1-86 1-86 1-53 1-47 1-43 ammon- cm.a/ day ium cc. I I- I - - - - - I - The results for 15.5" c. were obtained during a period when the electric current was not available for operating the thermostat, and are consequently less accurate than those at 21.0~ c., or 2 0 .5 ~ c. The same technique was used to study the ionic diffusion in glistening dew, in mixtures of glistening dew and glass beads, in sand and in clays. In theseR. K. SCHOFIELD AND C. DAKSHINAMURTI 0.289 0.179 0.273 0.808 0.790 0.462 59 0.327 - 0-291 0-970 - - experiments, the diffusion coefficients were taken from Table I, and the fractional areas were calculated. The ‘‘ glistening dew ” consists of glass spheres mostly of 70 I.M.M. in size, while the sand was about zoo I.M.M. in size. By miXing beads of 3.0 mm. d i m . with the glistening dew, a porosity as low as 0.23 was obtained. In addition t o the inert materials of more-or-less uniform size, three different clays- kaolin, Rothamsted subsoil clay and bentonitewere studied.The kaolin, marked “Osmo No. I purified by electrosmosis,” was supplied by Messrs. Fullers’ Earth Union Limited. The Rothamsted subsoil clay is the clay fraction treated for the removal of iron oxide. The bentonite used was the finest fraction obtained in a supercentrifuge, with a particle size of the order of 50 millimicrons. In order to check the values off obtained from ionic diffusion, measurements were made of the electrical conductivities of the same systems using N./IO KBr as electrolyte. A conductivity cell with parallel rectangular electrodes, coated with platinum black, was used. Except with kaolin it was possible to obtain the porosities within the ranges used in the diffusion experiments. The kaolin suspension, however, was too thick to flow into the conductivity cell. It contains 8 yo mica.TABLE 11. FRACTIONAL AREAS CALCULATED FROM DIFFUSION AND CONDUCTIVITY MEASUREMENTS IN INERT MATERIALS AND CLAYS Material ~~ ~ Ghteningdew . Glistening dew and glass beads . Sand . Bentonite . Rothamsted subsoil clay . Kaolin . DifEusion Measurements No. of experi- ments made Porosity P 0.366 0-236 0.352 0.996 0.909 0.716 Conductivity Measurements Porosity P f d 0’290 - 0-269 0.836 0.790 - The results obtained from the diffusion and conductivity measurements are given in Table 11. Although several difiusion measurements were made with each system studied, only one representative observation is recorded for each. The fractional areas were calculated from the diffusion measurements of both the Br- and NH4+ ions.The ratio between the conductivity of the porous system and the free electrolyte is taken as the fractional area, fcond. Discussion For a bed of coarse particles there is no doubt that the ratioflp is simply an indication of the twists and constrictions in the water channels. The ratios obtained from Table I1 for the kaolin and subsoil clay are also readily interpreted in this way. The 0.91 yo suspension of bentonite in N./IO KBr is a thixotropic gel, and has a conductivity 16 yo less than that of the salt solution. The particles, although they occupy only 0.4 yo of the total volume, consist of plates only 10 A. thick. Their thickness was established by measuring negative adsorption of chloride, which showed the total area of a gram of particles to be close to 800 sq.m. The weak rigidity of the gel and the hindrance to ionic migration could both be due to the existence of a network in which the particles tend to adhere by their edges.60 IONIC DIFFUSION AND ELECTRICAL CONDUCTIVITY Normality of Per cent. Weight i Electrolyte of Bentonite 0'1 0.9 I 0.05 1-14 0.0333 0.76 0.025 0.57 0.0167 the electrophoresis of particles and the oppo- 0.836 site migration of the 0.924 corresponding excess of 0.974 cations more than off- sets the obstruction 1.028 1-026 Relative Conductivity the chargedR. K. SCHOFIELD AND C. DAKSHINAMURTI 61 In the clay systems there are more cations than anions owing to the negative charges on the particles. Taking this into consideration, the electrical conductivities are found to be concordant with the diffusion measurements. The conductivity of N./IO KBr solution is reduced 16 yo by adding 0.91 yo of a very h e bentonite which, under these conditions, forms a thixotropic gel, whereas the conductivity of ~ . / 4 0 KBr is increased 3 % by adding 0.57 yo of the same bentonite which in this case forms a deflocculated suspension devoid of rigidity. These bentonite particles are plates 10 A. thick. These results strongly support the view that the bentonite particles in a thixotropic gel form a kind of network in which the edges of neighbouring particles are drawn towards each other. Rodtcamsted Experimental Station, Har#enden, Herts.

ISSN:0366-9033    

DOI:10.1039/DF9480300056

出版商:RSC    

年代:1948

数据来源: RSC