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(12) MCBAIKAND FERGUSON:J. Phys. Chem. 31, 564 (1927). (13) RIDEAL:Trans. Faraday SOC.32,4 (1936). (14) SKIELS:J. Phys. Chem. 33, 1175 (1929). (15) URQOHART:J. Textile Inst. T20, 125 (1920). (16) V A N BEMMELEN, J. M.: D i e Adsorption. Theodor Steinkopff, Dresden (1910). (17) VERNOX:Trans. Faraday SOC.27, 241 (1931). (18) ZSIGMONDY: Z. anorg. Chem. 71, 356 (1911).
HYSTERESIS IK SORPTIOX. I1 SCANNING OF
THE
HYSTERESIS LOOP. TITANIA GEL-WATERSYSTEM
KITTUR SUBBA RBO Department of Chemistry, Central College, University of Mysore, Bangalore, I n d i a Received Sovember 16, 1939
The permanence of hysteresis in the sorption of water on titania gel has been shown in the previous communication (5). The exact cause of the phenomenon of hysteresis has, however, been a matter of controversy. The explanation based on the cavity concept (3) has been gaining greater recognition during recent times. With a view to elucidating the exact cause of the phenomenon, the permanent hysteresis loop obtained in the sorption of water on titania gel has been scanned by traversing the loop from the various intermediate points on the sorption and the desorption curves enclosing the hysteresis loop. The results are found to give a convincing proof of the cavity concept. SORPTION AND DESORPTION ISOTHERMS AND THE LANGMUIR EQUATION
The applicability of the Langmuir equation
for monomolecular adsorption to the fifteenth sorption and desorption
isotherms was tried. The p
/
and p curve (figure l),instead of being
a straight line, shows a clear inversion a t a point corresponding to the relative humidity of 0.52. SORPTION AND DESORPTION ISOTHERMS AND THE WILLIAMS-HENRY EQUATION
The Williams-Henry equation
z/m log - = kl
P
+hm 5
HYSTERESIS I N SORPTION.
507
I1
the most exacting equation for monomolecular adsorption, was next XlOO
-curve (figure 2) shows applied. I n this case also the __ and log xlOO'm
m
P
a definite inversion point corresponding to an adsorption of 6.5 per cent of water.
R
FIG. 1. Sorption and desorption of water on titania gel. Langniuir equation. 0, desorption.,
0 , sorption;
FIG.2. Sorption and desorption of water on titania gel. tion. 0 , sorption; 0 , desorption.
. Williams-Henry
equa-
In the foregoing graphs the two inversion points are found to focus on the same point on the sorption and desorption isotherms. The inversion point indicates a change in the nature of the process. The gel holds 6.5 per cent of water by monomolecular adsorption and the remaining 20 per cent by capillary condensation. The capillary radius corresponding
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KITTUR SUBBA RAO
to this transition point is 16 A. (2). It is clear that in titania gel the two processes,-monomolecular adsorption and capillary condensation,-are distinct. One such clear case of monomolecular adsorption being followed by capillary condensation is found in the sorption of water on copper oxide (2). SCANNING OF THE HYSTERESIS LOOP
Starting from any intermediate point on the sorption curve enclosing the hysteresis loop,-if desorption is tried, the loop is crossed and the main desorption curve is reached (figure 3). From any intermediate point on
5
0
IS
20
IS
30
P p c r r u - e tn rnm
FIQ.3. Scanning the hysteresis loop in the sorption of water on titania gel the desorption curve, however,-if sorption is tried, the main sorption curve is not reached but a separate curve is traced in juxtaposition to the main sorption curve, until the peak of the hysteresis loop is reached (figure 4). The various intermediate points on the sorption and the desorption curves were reached from the zero and the saturation pressures, respectively. These significant observations are satisfactorily explainable only on the basis of the cavity concept. It has already been stressed ( 5 ) that cavities with constricted ends are alone responsible for the hysteresis effect, whereas with a system of purely V-shaped pores, the sorption and desorp tion curves should be coincident. At any point along the main sorption
HYSTERESIS IN SORPTION.
509
I1
curve, there are always some cavities completely filled with water, some partially filled, and some yet unfilled. If a t this stage desorption is tried, the partially filled cavities are progressively emptied in the same way as the V-shaped pores. The cavities which are completely filled, however, entrap the water and retain it until a minimum pressure is reached at which water condensed at the necks of these cavities will just be in equilibrium with the water vapor. Below this minimum pressure the cavities are completely emptied. Owing to this entrapping of water, the hysteresis loop is crossed and the main desorption curve is reached.
0L
5
15
' O
"
20
rnesSuPe '1
25
30
mm
FIG.4. Scanning of the hysteresis loop in the sorption of water on titania gel
At any intermediate point along the main desorption curve enclosing the hysteresis loop, there are some cavities completely filled and some completely emptied, there being no possibility of a cavity being partially emptied. The larger fraction of these completely filled cavities were filled a t very near the saturation pressure. If a t this intermediate point sorption is tried, a separate curve is traced until the peak of the hysteresis loop is reached. One obvious corollary follows from the above discussion. Judging from the nature of the results on the scanning of the hysteresis loop, it is clear that an intermediate point on the main desorption curve can be reached in two ways,-by starting either from the peak of the hysteresis loop or from an intermediate point on the main sorption curve. If sorption is
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KITTUR SUBBA R.40
tried after reaching the point in these two ways, separately, the courses followed should not be coincident, but the curve traced according to the latter method must be displaced towards the pressure axis. The experimental results (figure 5 ) are in conforniity with this corollary. Point B on the main desorption curve was reached starting from a point A on the main m p t i o n curve. On trying sorption at this point B, the main sorption curve is reached. Whereas if sorption were tried from the same point B reached from C at saturation pressure, the main sorption curve would not be reached, but a separate curve would be traced until the peak of
3
20
Pr‘:rru*o /n m m .
25
30
5
FIG.5. Scanning of the hysteresis loop in the sorption of water on titania gel
the hysteresis loop is reached (figure 4). This experiment was tried with the hysteresis loop, after it had suffered a complete “drift.” I n the sorption of water on charcoal a study of the crossing of the hysteresis loop, starting from the sorption and desorption curves, has been made (1). The results show that, starting from a point on the sorption curve, the desorption curve is reached, and that, starting from a point on the desorption curve, the sorption curve is reached, the latter observation being different from what has been recorded in the present paper. I n accordance with the cavity idea, this indicates the absence, in the particular sample of charcoal, of wide cavities having extremely narrow constrictions. It follows from the cavity concept that on trying desorption a t any intermediate point on the main sorption curve enclosing the hysteresis
HYSTERESIS I N SORPTIOh-.
I1
51 1
loop, the loop m u d alnays be crossed and the main desorption curve reached. But on trying sorption from any intermediate point on the deqorption curve, the curve may either follow a separate course in juxtaposition to the main sorption curve or just graze it until the peak of the hystereiis loop iq reached. Whether a preqsure less than that 11 hich corresponds to the neck of the cavity is alnayq necessary for emptying a cavity, or any pressure intermediate lietween those corresponding to the neck and the body of the cavity i i qufficient, is a question which is definitely dccided by the results on the icaiining of the hysteresis loop. The hysteresis loop itself can be cau-ed in (,ither of these ways. But the results on the scanning of the loop obtaiiird by trying sorption a t the various intermediate points on the desorption cuive (figure 4) indicate that a cavity is emptied only when the piewure iq reduced heloiv what is required for water condensed a t the neck of the cavity to be in equilibrium with the water vapor. CHAR.%CTERISTICS O F THE HYSTERE5IS LOOP
The hrsterebiq loop stretches up to the saturation point on one side and to a relative humidity of 0.35 on the other, with a tapering of the loop. The rapid rise of the latter part of the sorption curve indicates the existen2e of capacdty in the gel, in the region of pore radius ranging from about 30 A. to 160 A. This capacity is due partly to J--shaped pores and partly to cavitieq vith constricted ends, the latter alone being responsible for the permanent h3steresis loop. I n any porous adsorbent. it is probable that there are always theqe t a o types of capillaries. It follows, then, that the hysteresis effect must alnays he exhibited and that it is the rule rather than the exception. But instances of systems not exhibiting hysteresis are numerous in the literature. K h y hysteresis is not exhibited in a large number of cases is a question yet to be explained. One of the causes (4). however, for the disa'ppearance or the absence of the hysteresis loop has been found to be the elasticity of the cavity wall I t is of interest to note that, to reach a point on the main sorption curve, it is necessary to start from the tail-end of the hysteresis loop. Beyond this point on the sorption curve, an attempt to go back t o the original point results in the crossing of the hysteresis loop, until the main desorption curve is reached. If, after reaching the desorption curve, sorption is tried, it may be just possible to reach the original point on the main sorption curve. If this is not possible, it is necessary t o start from the tail-end of the loop in order to reach the original point again. A point on the main desorption curve, however, can he reached either from the peak of the hysteresis loop or 'from points on a portion of the sorption curve. If, however, the point on the desorption curve cannot be reached from a point on the sorption curve, it is necessary to approach
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KITTUR SUBBA RAO
it from the peak-end. I n encircling the hysteresis loop, it is unnecessary to go beyond a relative humidity of 0.35, at which the tail-end of the hysteresis loop terminates. Below this point, down to zero pressure, the sorption and desorption curves merge into one, and this part of the isotherm can be traced to and fro any number of times by successive sorptions and desorptions. In accordance with the cavity concept, it is obvious that the true equilibrium curve is really the sorption curve, because along the desorption curve, the cavities with constricted ends retain the liquid in a metastable equilibrium. SUMMARY
Application of the Langmuir and the Williams-Henry equations for monomolecular adsorption to the sorption and desorption isotherms of water on titania gel a t 3OoC. shows a clear transition from monomolecular adsorption to capillary condensation. The hysteresis loop has been scanned by traversing it from various intermediate points on the sorption and the desorption curves enclosing the hysteresis loop. The scanning of the loop has revealed certain characteristics which focus on the concept of cavities with constricted ends as a general cause of hysteresis. The results on the scanning of the loop indicate that a cavity completely filled with water is emptied only when it is exposed to a relative humidity less than what is required for water condensed a t the neck of the cavity to be in equilibrium with the water vapor. I n accordance with the cavity concept, the true equilibrium curve is the sorption curve, because along the desorption curve the cavities retain the liquid in a metastable equilibrium. The author is grateful to Prof. B. Sanjiva Fta6 for the keen interest evinced in the course of this work. REFEREKCES (1) ALLMAND, HAND,AND MANNINQ: J. Phys. Chem. 33, 1694 (1929). (2) MCBAIK:The Sorption of Gases and Vapours by Solids, p. 439. George Routledge and Sons, Ltd., London (1932). (3) MCBAIN:J. Am. Chem. SOC.67, 699 (1935). (4) RAO,K.S.: Current Sci. 8, 258 (1939). (5) RAO,K.S.: J. Phys. Chem. 46, 500 (1941); Paper I.
