T H E FREEZING OF WATER I N CAPILLARY SYSTEMS: A CRITICAL DISCUSSION BY E. A. FISHER
A considerable amount of work has been done a t various times on the freezing of water in such capillary systems as inorganic hydrogels, soils, etc. This work has been mainly along two lines (a) the actual depression of the freezing point as related to the moisture content and nature of the system and (b) dilatometric determinations of the amounts of water that will freeze at various temperatures. Both lines of investigation have been applied by G. T. Bouyoucos and his eo-workers1 to soil-water systems with such remarkable results that to accept them at their face value would necessitate an entirely new conception of the moisture relations of the soil and the forms in which water exists in the soil and other similar capillary systems. Thus it was found by Bouyoucos that the lowering of the freezing point of a soil increased in approximately geometrical progression as the moisture content decreased in arithmetical progression and this seemed to indicate that, conbrary to general belief, the concentration of the soil solution in any particular soil sample is not inversely proportional to the moisture content of the sample. The difficulty was explained away by assuming that a considerable proportion of the water of the soil was either physically adsorbed or loosely chemically combined or present in solid solution so that this portion of the water was not free to function as a solvent but was removed from its active liquid phase. A similar conclusion had been reached, apparently quite independently, by Foote and Saxton2 in a dilatometric study of the freezing of water in sand, lampblack and the hydrogels of alumina, ferric oxide, and silica. These workers found that considerable quantities.of water, in some cases up to 50 or 60 percent of the dry weight of gel, apparently failed to freeze in the hydrogels while no such phenomenon was observed with sand or lampblack. Bouyoucos and his co-workers obtained similar results in their dilatometric studies on soils. They found in 73 cases examined that the amount of water that failed to freeze at 78°C was nothing in the case of quartz sand but varied with soils from 1 . 2 % (calculated on a dry weight basis) with a coarse sand to 14.6% with a California silty clay loam. They also give the following 1 G. T. Bouyoucos and others: Mich. Agr. Coll. Expt. Sta. Tech. Bull. 24 (19x5); 27 (1916); 31 (1916); 36 (1917); 37 (1917); 42, (1918); J. Agri. Res. 8, 195 (1917); 15, 331 (1918); 20, 267 (1920); 20, 587 (1921); Soils Sei. 11, 33, 255, (1921). * J. Am. Chem. SOC. 38, 588 (1916); 39, 627, 1103 (1917).
FREEZING O F WATER IN CAPILLARY SYSTEMS
36 I
for other materials: peat 6%, silica 32%,, animal charcoal 19.0%~burned clay 2.8% and lampblack 2 . 0 % ~ ~ These conclusions have not been generally accepted by workers in soil science and some critical work has been done. Foote and Saxton found with silica gels that the amount of water that would not freezeat - 78°C varied from ~ 9 . 6 7to~ 44.6yC, Lenher2 submitted samples of silica gel to pressure so as to squeeze out some of the water and found a water content of 12.3 to 12.9% after exposure for some time to a pressure of 2 7 2 , 7 0 0 kgs. per sq. in. In these expcriments more than half the ‘combined’ water of Foote and Saxtori was squeezed out by mechanical pressure. While these results are not theoretically inconsistent3 with Foote and Saxton’s conccption of ‘combined’ water the amount of such water squeezed out by the pressure applied appears surprisingly large. Keen* submitted the freezing point depression data of Bouyoucos to mathematical analysis and concluded that in any given soil sample the water rendered unfree is not a constant amount but must vary with the total moisture content a conclusion that was contradicted by later experimental work of Bo~youcos.~ F. W. Parker6 showed that, although the presence of colloidal particles had been shown by many investigators to have an extremely small or even negligible effect on the freezing point of a liquid, very different,results obtained if the amount of water is reduced until it’ is entirely in 6he film or capillary condition. Thus ferric oxide, alumina, soil, or silica would cause a depression of the freezing point of water, benzene, or nitrobenzene when the liquid exists in the film or capillary condition in the solid mat>erial. This had been shown to be the case by Bouyoucos himself’ with quartz and water but he attributed it to the solubility of something in the sand itself. Parker pointed out that if part of the water is rendered unfree by a soil then aqueoiis solutions of alcohol, glycerin or sugar should be rendered more concentrated when added to a dry It was demonstrated that such was not the case and that thc freezing point depression due to capillarity and that due to the presence of solutes are in all cases a d d i t , i ~ e .Parker’s ~ work appears to be satisfactory as This may be experimental error since Foote and Saxton (loc. cit). found in one case wit,h lampblack that 101.787~of the water froze a t -78°C. The error with sand was + I . 85%. * J. Am. Chem. SOC.43, 391 (1921). a Nernst : “Theoretical Chemistry”, 766 (1923); Rooseboom: “Die heterogenen Gleichgewichte,” Erstes Heft, p. 213. J. Agri. Sri. 9, 400 (1919). Soil Sci. 11, 255 (1921). J. Am. Chem. SOC.43, 1 0 1 1 (1921). Bull. 24 and 31 loc. cit. . This would be so even if the solutes were appreciably adsorbed by the dry soil. The amount of ‘combined’ water may he as much as 40 or jO percent of the total water present. I t is unlikely that a non-electrolyte would be adsorbed to a degree that would obliterate the effect on conrentratjon.of t,he removal of such large amounts of solvent. Sugar is known to be adsorbed but is so only to a slight extent,. Soil Sci. 13, 43 (1922).
362
E. A. FISHER
a qualitative basis for clearing up the apparent anomalies of the freezing point depressions but leaves the dilatometric results untouched. It is the object of the present note to indicate a few criticisms that may affect the validity of the conclusions drawn from the experimental results. The work of BOU~OUCOS, Foote and Saxton, and of Parker establishes the fact that the freezing point of water in capillary systems is lower than that of water in bulk.1 Thus in Fig. 12 are plotted the volumes of contraction and expansion upon cooling to zo'Candrewarmingof quartz sand. AB represents the contraction on cooling the sand water from jo t,o .'1At - I O freezing commenced, the whole of the water froze a t this temperature and RC measures the increase in volume consequent on the freezing. From this measured expansion the amount of water frozen can be calculated and in the case of quartz sand corresponds to the known water content. C D measures the contraction on cooling the sand ice from -I' to -20'. CD is almost exactly parallel to AB. On raising the temperature the process is quantitatively a3 reversed except that melting did not take -5' -lo" -15' place until 0' was reached. FIG.I In Fig. z are given the data for a clay soil. Again AB represents the contraction of soil water from 5' to .'1DC measures the expansion due to the freezing of some water at -.'1 Along CD from -I' to -4' the curve represents the result of expansion due to the freezing of capillary water and of the contraction of soil ice water due to decreasing temperature. From - 4' to - 78' the curve is straight within the limits of experimental error and is nearly parallel to AB. DE should be coincident with CD up to -4'. The slight divergence is probably due to some little water in the very finest capillaries not freezing until below -4' although the amount in this particular case is insufficient to produce a definite curvature.
+
+
+
+
+
A possible source of error in determinations of freezing point depressions of liquids in capillary systems mag be pointed out here as no reference seems to have been made t o it in the literature of the subject. If IOO gms. of soil containing 1.0 percent of water is supercooled to -4°C and then solidification is induced, 80 calories of (latent) heat are liberated. Of these about 4 Cal. are used up in raising the temperature of the ice from -4' to approximately oo, leaving 67 cals. to raise the 99 gms. dry soil through the same tem erature range. Assuming the specific heat of soil to be about 0.20 [H. E. Patten: U. Dept. Agri., Bur. Soils, Bull. 50, (1909): Bouyoucos: Mich. Agri. Coll. Expt. Sta., Tech. Bull. 17 (1913)], 79 cals. will be needed for the latter purpose. Hence measurements of F. P. D. in such systems arc accurate only if the water content is greater than a certain critical amount, e.g. in the above example about I . o percent. 2 Figs. I and 2 are reproduced from Bouyoucos: Bull. 36 loc. cit,.
k).
FREEZING O F WATER IN CAPILLARY SYSTEMS
363
It has been suggested that some or all the apparent depression of the freezing point may be due to supercooling and Bouyoucos has shown that capillary water may be supercooled to -4.2' without freezing if agitation is carefully avoided. Water in bulk can be supercooled to - 6 O without freezing but in all cases supercooling is negligible if agitation is employed. Supercooling - can however be definitely ruled out here since, on warming the frozen mass, ice begins to melt at -4'. A solid cannot be superheated above its melting point and the fact that curvature in DE begins a t -4' shows that some ice must be melting a t that temperature. With some samples of silica gel Foote and Saxton showed that curvature began on rewarming even below -30'. There can be no doubt therefore as to the experimental facts of capillary water having a lower F.P. than water in bulk. Such a lowering of F.P. must also follow theoretically from tjhe lowering of vapor pressure of water due to capillarity since only theliquid phase is so affected'. That is, the vapor pressure-temperature curve for capillary water is below that of water in bulk while the curve for the ice phase FIG. 2 is unaffected. Hence the point of intersection of the ice and water v.p. curve, i.e. the F.P. must be lower in capillary than in non-capillary systems. In such systems as those considered here the 'capillary-adsorbed' water, as it is called by BOU~OUCOS, is held in two ways: some little of it is held as an adsorbed film round the particles of material, but by far the greater portion is present as annular water wedges between the grains. These two kinds of water, although regarded as one kind by BOU~OUCOS, Parker and others, exist probably under very different mechanical conditions. The adsorbed film is held on the surface of the particles by cohesive forces of great magnitude and it has been calculated, from certain experimental data, that such films may be under pressures of the order of magnitude of 10000 to 20000 atmospheres with corresponding increase in density.2 The water wedges however, owing to the concavity of their menisci and when the diameters of the menisci are less than 3p, are probably under negative pressure or tensionsthat increase very rapidly with decreasing diameters. Thus3 the tension is connected with vapor pressure by the relationship Po -Po Q=RTp.log,o P1 See ref. I , p. 362. A . M. Williams: Proc. Roy. SOC. 98 A, 223 (1920);Harkins and Ewing: J. Am. Chem. SOC.43, 1787 (1921). a F. J. W.Whipple: Proc. Phys. SOC. Lond. 34, I (1922).
354
E. A . FiSHER
in which Q = tension, R = gas constant, T = absolute temperature, po = vapor pressure of water in bulk i.e. over a plane surface, pl = the vapor pressure of water over the meniscus, PO=atmospheric pressure all measured in C. G. S. units, and p = density of water. The tube radius, r, can be calculated from the relationship
i n which u
=
surface tension, whence 2(T g= -p,
r
Thus when the diameter of the meniscus has becn lowered to 2.4 pp (corresponding for example in the case of a Rothamsted clay subsoil with 55.4 percent clay fraction, to a water con tent of 7.5 percent’ the tension may be as high as I I 7 0 atmospheres. Assuming that the compressibility and extensibility curves for water are continuous? and extrapolating to a pressure of - I 1 7 3 atmospheres the volume of the water would be over 7 percent greater than its volume in bulk.3 The expansion on freezing nccordirrg to Foote and Saxton’s figures is 9.32 percent, or according to Bunsen’s data 9.07 percent. The actual expansion therefore due to the freezing of such water in this particular case would be not 9 percent but 2 percent. Since the amounts of water frozen is calculated from the magnitude of the expansion 78 percent of the water in the example cited would be returned as ‘unfree’ i.e. as unfrozen at 78OC. The validity of the conclusions drawn from dilatometric work depends, as Foote and Saxton themselves point out, on the density of capillary water being thc same as that of water in bulk and their work on lampblack certainly appeared to show that this assumption was correct for lampblack. It was therefore assumed to hold also for hydrogel. This conclusion however may bequestioned. The curve for lampblack4 (Fig. 3) differed in some important respects from those for hydrogels and soils. Both C D and D’F (Fig. 3 ) were straight but were not coincident over any part of their course. D’F was practically parallel E. A. Fisher: Proc. Roy. Soc. 103 A . 139 (1923).
* This was shown to be the case by A. M. Worthington:
Phil. Trans. 183 A , 355 ( 1 8 9 s ) for pressure ranges of -17 and +12 atmospheres for alcohols. 3 It is not desired to lay any particular stress on these values of 7 percent and 1170 atmospheres. The former is the result of a particularly large extrapolation and the latter rests on the applicability of considerations of surface tension to pores of extremely small dimensions. Both may be unsound in such extreme cases but, as in the application of the gas laws to the concentrated solutions, the orders of magnitude may be right even though the actual values are probably far from correct. In any casc the relations between vapor pressures and tensions of capillary columns do not depend on surface tension considerations and are more reliable. The existence of such tensions in capillary liquid columns has been used by Whipple (loc. cit) as an explanation of the action of a hair hygrometer and by the present writer [(J.-Agri. Sci. 14 (1924)] to explain residual shrinkage in soils and clays. J. Am. Chem. Soc. 39, 627 (1917).
FREEZING O F WATER IN CAPILLARY SYSTEMS
365
to AB as in other cases but no curvature was exhibited by any part of the curve. The divergence of C D and D’F seems to indicate that some capillary water was being frozen along CD: it is certainly difficult to attribute any other significance to this divergence. At the same time it is equally difficult to see why progressive freezing of apparently such considerable quantities of water should not be accompanied by curvature between C and D, especially just below C. Such curvature invariably occurs with soils and hydrogels. It corresponds to the fact that for different decrement8sof temperature the amount of water freezing per given decrement diminishes at a rapidly increasing rate, and this simply means (a very obvious conclusion in the case of granular media in which the capillaries are in the nature of water wedges) that on any probablc distribution of capillaries as regards size a group of large capillaries will contain a larger total amount of water than a group of smaller ones. Thus if there are present a series FIQ.3 of pores of circular cross section of radii r l > r2> . r,,, the water in which would freeze a t -t1’, -to2,. . . -tan, and the numbers of each were nl, n2. . . 11,. Then the volume of each group would be m1r211,7rn2r212,. . . 7rnnr2nln in which l,, 12,. . . .1, are the lengths of the pores. The freezing cuive CD would be straight (assuming constancy of density for the water) only in the very improbable contingency of anlr1211,being equal to 7rn2r2712, being equal to 7rn,,r2,1n. In all cases (except lampblack), where the cuivatuie telow C is slight, CD and DF lie relatively close to each other. Such is the case with alumina for example which has little capillary water but much ‘combined’ water. Lampblack on the other hand seems to have much capillary water but no ‘combined’ water. Moreover, in spite of the large amount of capillaiy water below - 6’ indicated by the cooling curve, no ice melted on waiming to -6’ which was the highest temperature of re-warming attained in Foote and Saxton’s experiments: the warming curve indicates the absence of capillary water up to -6’. It was unfortunate that re-warming was not continued t o 0’. Lampblack certainly appears anomalous in some respects and the argument based on its behavior that the density of water in soils and hydrogels is that of water in bulk is not convincing. The above explanation of the so-called ‘combined’ or unfree water of hydrogels and soils is consistent with many of the experimental data. Thus any process, such as prolonged digestion with water, that would reduce the size of the capillaries would reduce the amounts of both of apparent capillary water (Le. the water that freezes below oo C) and of ‘combined’ water (that apparently will not freeze a t all). The former would be affected relatively to
366
E. A. FISHER
a much greater extent than the latter because in the latter case although the smaller capillaries would mean less water, the greater tensions due to reduction in size of the smallest capillaries would result in greater extension of the water resulting again in a smaller expansion on freezing. The amount of water returned as combined would be relatively increased thus reducing the absolute amount. Table I, slightly modified from Foote and Saxton’s paper, illustrates this.
TABLE I Apparent Capillary and Apparent Combined Water in Silica Gel Material
Untreated Digested with water 24 hrs. Digested with water 7 days
Apparent Cap. Water
% of dry Wt. of SiOz
App. Combined Water yoof dry Wt. of SiOl
57
44.3
44
39.1
29
29 .o
Again the effect of repeated freezing and thawing, on the amounts of capillary and ‘combined’ water might be expected to differ with different materials as was actually found to be the case by Bouyoucos. With granular material like sands and sandy loams comparatively poor in colloidal matter little effect would be expected. With clay soils rich in colloidal matter repeated freezing would tend to flocculate the colloids, causing some slight approximation to silts:’ one would expect in this case a reduction in the amount of ‘combined’ water. With silica gel in which the water is present not as annular water wedges as is the case with silts but in thick-walled actual capillary pores little effect would be expected. These expectations are quite borne out by the data given in Table 11. Lampblack again appears to be anomalous. Such an explanation is also consistent with the fact that the amount of water that apparently fails t o freeze is quite independent of the total moisture content. In any given annulus as the temperature is lowered the water would presumably freeze from the surface, i.e. the meniscus, inwards. A fresh meniscus, smaller in diameter, would be formed and the unfrozen wedge would be lower in vapour pressure and freezing point and, if the above considerations arc valid, under greater tension and therefore of slightly greater relative volume. Provided the lowering of temperature be brought about gradually, as is generally the case, so that equilibrium can be established at each temperature the amount of so-called ‘combined’ water should obviously be independent of the total moisture content. If the system could be very rapidly cooled to a lowtemperature,say - 7 8 O , so that the mass froze rapidlythereby affording insufficient time for the progressive adjustments in vapour pressure and tension to occur, it is not unlikely that the amount of ‘combined’ water would be found to be dependent on the total moisture content. This however does not appear to have been invcstigated. Cf. S. U. Piclcering: Proc. Roy. Roc. 94 4, 315 (1918).
FREEZING O F WATER I N CAPILLARY SYSTEMS
367
TABLE I1 Effects of Repeated Freezing and Thawing on the Amount of Water that failed to freeze a t - 78OC (Bouyoucos) 'Material
.Times frozen
Water that failed to freeze
Material
Times frozen
Water that failed to freeze
I
2.40
2
I .80
3
I .80
I
I .60
2
I .60
I
I .20 I .oo
ccs.
ccs.
Quartz sand
Fine sandy loam
Loam
Heavy brown silt 1 oam
I
0.00
2
0.00
I
0.80
2
0.80
3
0.80
I
I .60
2
I .60
3
I
I
2.40
2
I.75,
3
1.75
Heavy dark brown silt loam I 3
I
2
Clay
2
3
Wisconsin superior Clay
Silica
Muck
.60
2
Peat
3
I .oo
I
3.60 2 .go 2 .go
2
3
Lampblack
I
0.90
2.45
2
0.46
1.85
3 4
0.10 0.IO
.go I .go I .90
Summary The dilatometric studies of Bouyoucos and his co-workers on soils and of Foote aqd Saxton on inorganic hydrogels appeared to indicate that much of the water in such systems failed to freeze even at temperatures as low as 78OC and it was concluded that such water cannot be present as free liquid water but must be physically adsorbed or chemically combined or in solid solution. I n the above note these conclusions are criticised. It is pointed out that water present in very fine capillary tubes or pores must be under considerable tension and hence possibly the density of such water is not necessarily the same as that of water in bulk. The conclusions of the workers cited rest on the assumption that the density of water in such capillary systems is the same as that of water in bulk. Until this point is cleared up by further experimental work it is difficult to accept these conclusions based as they are solely on dilatometric studies. The writer is glad to record his indebtedness to Professor J. W. McRain, F.R.S., for helpful criticism in the preparation of this paper. Department of Teztile Iiidustries L e e h Unic>ersity
