the adsorption of iodine by potassium...

Adsorption of Iodine by Potassium Iodide. 217

at the end-points. Roughly speaking, it means that if equation (1) possesses one solution behaving in the required manner near = and another solution behaving in the required manner near x — b, then it is possible so to choose X that these solutions join up and become identical. The theorems themselves are of mainly mathematical interest, and will be published elsewhere.

This theory covers the important cases occurring in wave mechanics, and in particular it shows that Wilson’s equation must possess eigen-solutions of the usual kind. These solutions seem to have evaded his search when he compares his general asymptotic forms of solution, on p. 625 of his paper, with a particular case (p. 624) in which certain coefficients do not vanish. This is sufficient to show that the corresponding coefficients in the general form do not vanish identically. But it does not follow that they cannot vanish, as required by the boundary conditions, for particular values (eigen-values) of the parameters, and in fact our work has shown that they must actually vanish in this way.

The Adsorption of Iodine by Potassium Iodide.B y B r ia n W h ip p , Hutchinson Research Student, St. John’s College,

Cambridge.

(Laboratory of Colloid Science, Cambridge.)

(Communicated by E. K. Rideal, F.R.S.—Received February 16, 1933.)

Opinion has been divided for some years as to whether the adsorption of a vapour on a solid surface is confined to a monomolecular layer until the vapour pressure reaches the saturation value, or whether multimolecular layers are formed.

Experimental work has generally failed to provide an unequivocal answer to this point, often because the true area of the surface of the adsorbent could not be estimated. I t is now recognized that the true area of a surface may be many times the apparent area, and the ratio of these will depend on the previous treatment of the surface. The position has been complicated further by the difficulty of determining the amount of adsorption on a small area of a plane surface when the adsorption is so small as to be undetectable without sensitive apparatus ; consequently, the bulk of the experimental work has been carried

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218 B. Whipp.

out on finely divided adsorbents, of large surface. This breaking up of the adsorbent, whether accomplished by chemical or mechanical means, is bound to have an unpredictable effect on the ratio of the true to apparent area of the surface, as distinct from the purely geometrical multiplication. The use of porous or finely divided adsorbents may also introduce the additional complication of capillary condensation of vapours in the spaces between the particles. I t is clear, as was first emphasized by Langmuir in 1918, that the investigation of adsorption on plane surfaces, using more delicate technique, is the first step towards a solution of the problem. Langmuir* measured the adsorption of gases on large plane surfaces of mica, glass and platinum at low temperatures and pressures. He showed that the adsorption reached a maximum, which corresponded to slightly less than one complete monomolecular layer, and that the extent of adsorption was related to the pressure by an equation of the form

x — —} where a and b are constants involving the condensation coefficient,1 + ap

the time of life of adsorbed molecules in the surface, and the number of “ adsorbing centres.”

Some evidence for the existence of a single layer only of molecules of a vapour is to be found in the work of Frazer, Patrick and Smithf and of LathamJ who showed that a freshly blown, “ fire-polished ” glass bulb adsorbed vapours to the extent of not more than one molecular layer at saturation pressure, but that after etching the glass with water or chromic acid, much larger quantities were taken up.

The determination of the adsorption of gases on crystals is important, not only because the crystals have approximately plane surfaces possessing a known number of adsorbing ions, but because, in simple cases at least, the attractive forces can be calculated. Thus Lennard-Jones and Dent§ found that the forces on an argon atom outside a potassium chloride crystal should become negligible at distances from the surface greater than the diameter of one atom.

A series of studies of the amounts of iodine adsorbed on condensed films of the halides of alkaline earth, has been made by de Boer.|| Some of his earlier results were explained by an hypothesis which suggested as many as

* ‘ J. Amer. Chem. Soc.,’ yoJ. 40, p. 1368 (1918). t ‘ J. Phys. Chem.,’ vol. 31, p. 897 (1927).t ‘ J. Amer. Chem. Soc.,’ vol. 50, p. 2987 (1928); cf. also Carver, vol. 45, p. 63

(1923) and Curry, ‘ J. Phys. Chem.,’ vol. 35, p. 859 (1931).§ ‘ Trans. Faraday Soc.,’ vol. 24, p. 100 (1928).|| ‘ Z. phys. Chem.,’ B, vol. 13, p. 134 (1931).




ten layers of adsorbed molecules but bis later work* has yielded results which can only be explained on the theory of a monomolecular layer.

The balance of evidence now available favours the theory of a monomolecular layer.f I t should, however, be observed, (1) that uncertainties in determinations of the area may easily amount to 100 per cent., so that it is generally impossible to find more than the order of the number of layers adsorbed, and(2) that very few experiments throw light on the adsorption equilibria at saturation pressures.

There has, in fact, been no expression deduced which fits the experimental facts of adsorption of vapours over the complete range of pressure. Indeed, the results have generally been so unsatisfactory that the question of the existence of a definite adsorption maximum at saturation pressure has hardly been considered.

In the following paper sensitive adsorption measurements are described and definite evidence is presented for the existence of a bimolecular layer of iodine on potassium iodide crystals at saturation pressure, and an isotherm is suggested which fits the experimental results over the whole range of pressure. This expression contains only the two constants of Langmuir involving the extent of the adsorbing surface and the rates of evaporation of the molecules in the adsorbed phase.

Experimental.

The adsorbent was contained in the adsorption bulb A, fig. 1. This was connected by a tap to a bulb B of known volume, acting as a charger, and to a Pirani pressure gauge P. Iodine was admitted by the tap T4 to the charger, which was connected by the tap T2 to a mercury condensation pump, McLeod gauge, a bulb of known volume C, mercury manometer M, and liquid air trap L. The charger was divided into two parts by the tap T3 so that large or small charges of iodine could conveniently be admitted to the adsorbent.

The volumes of the various parts of the apparatus between the taps were found by admitting dry air into them from the standard calibrating bulb C. The pressures before and after expansion were read on the manometer M.

In an experiment, the apparatus was evacuated and the adsorbent baked out. The charger was filled with iodine vapour at a known pressure, and, after expanding this charge into the adsorption bulb, the pressure was read

* ‘ Z. phys. Chem.,’ B, vol. 14, p. 457 (1931); B, vol. 15, p. 300 (1932); B, vol. 17, p. 16J (1932).

t But, cf. Schlliter, * Z. phys. Chem.,’ A, vol. 153, p. 68 (1931).



220 B. Whipp.

on the Pirani gauge. The amount of adsorption was calculated from the difference between the calculated and observed pressures. Several expansions could be made and data for a complete isotherm obtained from one experiment.

The iodine was purified by three distillations from aqueous potassium iodide, which freed it from chlorine, bromine, iodine chloride and cyanogen iodide (the two latter being soluble in water). I t was separated from the aqueous distillate, dried in a desiccator, placed in the tube i3 and sealed to the apparatus. After being evacuated at 0° C. for about two hours on the condensation pump to free it from traces of water-vapour and gases, it was distilled vacuo into i 2 and finally into iv The tubes and were then sealed off at S.

McLEOD

KOH

Fio. 1.

The Pirani gauge consisted of a platinum filament in a single loop about 10 cm. long, mounted on springy platinum-iridium supports, which kept it taut. I t was made of ribbon about 80 p wide and 8 p thick. In all experiments the filament was kept at a constant temperature by varying the current through it, so that its resistance, as indicated by a Wheatstone bridge arrangement, remained constant.* Pressures over the range 1 — 50 X 10 3 mm. could be read with sufficient accuracy.

The Pirani gauge was immersed in a constant temperature bath at 20° C.,

* Campbell, 4 Proc. Phys. Soc.,’ vol. 33, p. 287 (1921).




and calibrated by maintaining various constant temperature mixtures round the iodine in ix and reading a voltmeter connected across the bridge when balanced. Eutectic mixtures were tried as constant temperature baths, but it was found more convenient to surround the iodine with a large unsilvered Dewar vessel full of HCl/ice freezing mixture. Although the temperature so obtained was not perfectly constant, it rose only slowly on account of the large heat capacity of the freezing mixture, and equilibrium vapour pressures were easily reached for each temperature of the bath. The temperature of the bath was read on a mercury thermometer, standardized at the National Physical Laboratory, and the pressure of the iodine corresponding to any temperature of the bath was obtained by interpolation from the data given in the International Critical Tables.

It was found that Shell Apiezon L grease was a good tap lubricant. For a short time after greasing the taps, the grease evolved a gas when in contact with iodine (probably HI), but if the taps were well turned over a period of a few days while in contact with iodine vapour, the evolution ceased. A small absorption of iodine in the grease remained, but this could be made negligible (compared with the adsorption on the crystals) by using a large quantity of adsorbent and a large charging bulb.

By using a sensitive dead-beat pointer galvanometer across the Wheatstone bridge, and by controlling the heating current in the filament of the Pirani gauge by dial resistance boxes, the bridge may be balanced rapidly, and pressure readings taken within 1 and 1 | minutes of an expansion. Data for a complete isotherm could be obtained in about 12 to 15 minutes.

The disadvantage of using a large amount of adsorbent is tha t the time of baking out must be increased, and as it was found that the salt volatilized too quickly if a high temperature was employed, it was never baked at above 200° C. To obtain reproducible results the salt had to be kept at this temperature for about 20 hours in a high vacuum between experiments.

Results.

The temperature of the adsorbent was always 0° C.A series of experiments was carried out with an empty adsorption vessel.

No instantaneous adsorption of iodine by the glass was noted and the data show that for iodine vapour deviations from Boyle’s law are less than the experimental error, even up to saturation pressure.

The results of a typical experiment are shown in Table I.



222 B. Whipp.

Blank Experiment.

(Pressures are in mm. X 10 “3. Saturation pressure is 30 X 10"3 mm.)

Table I.

Charge number. Observed pressure after expansion.

Calculated pressure (assuming gas laws).

! 12-(5 12-62 20-0 19-93 24-4 24-24 27-0 26-85

i28-0 28-3

The maximum error is 1 per cent. This represents the combined errors in the calibration of the apparatus and the readings of the Pirani gauge.

The Isotherms.

A series of experiments was carried out on the one sample of potassium iodide. This consisted of about 115 gm. of selected crystals of about 2 mm. edge (B.D.H. Analytical Reagent), and had an approximate area (estimated from the size of the crystals) of 1700 cm.2. The volume of the dead space in the adsorption bulb was found by expanding into it dry air free from carbon dioxide from the charging system, and reading pressures on the manometer M. Adsorption of air by the crystals was negligible.

When the amount adsorbed was plotted against the pressure, it was found :—

(1) That the lower pressure portion of the isotherm fitted the Langmuirequation x — abpj(l -f- a/p) reasonably accurately.

(2) That at higher pressures the adsorption increased almost linearly and tangentially to the original curve until saturation pressure was reached.

(3) That the isotherms showed a definite maximum at the saturation pressure, when the amount of iodine adsorbed was, in all cases, roughly double that obtained by extrapolating to saturation pressure the Langmuir equation as determined from the initial portion of the isotherm.

(4) That the total number of molecules adsorbed at saturation was approximately twice the number of ions of one kind in the surface of the crystals used.




(5) Apart from one or two irregularities, the amount adsorbed at saturation gradually decreased throughout the course of the exeriments.

Some of the results are shown in Table II. Of the two Langmuir constants, a is proportional to the time of life of an adsorbed molecule in the surface, and b to the number of adsorbing centres. The adsorption is recorded as the difference between the observed and calculated pressures. These latter units may be reduced to gram moles at any time by multiplying by

410 X 10 -« 22-4 X 760

= 2-40 X 10~8,

410 c.c. being the free volume of the adsorbing bulb and charger.The Langmuir constants in this table have been called provisional ”

because they have been obtained from the first portion of the isotherms, that is, below’ a pressure of 4 X 10-3 mm. In general (except in experiments which were not continued to higher pressures testing the application of the Langmuir equation to the initial portion) there was only one point on the isotherm below this pressure. The provisional constants were only used to calculate the ratio of the maximum adsorption calculated from the Langmuir equation to the total adsorption at saturation pressure. I t will be seen tha t the mean ratio is 0-50(4) with a mean deviation from the mean of 10 per cent.

Table II.

Experiment.

Provisional Langmuir constants. Saturation

adsorptionRatio

Langmuir

b. a .moles X 2*40 X 10“8. maximum /tot al.

5 58-5 0-375 96 0-566 31-5 0-20 55 0-509 41-7 0-65 80 0-47

10 35-4 0-438 80 0-40(3)12 39-2 0-403 70 0-51(2)13 34-8 0-375 57-5 0-55(5)16 24-8 0-274 40-5 0-54(8)17 20-4 0-356 37 0-50(5)19 23-4 0-312 41 0-41(5)23 33-6

i0-300 52-5 0-57(0)

Now as the Langmuir equation represents the formation of a single layer, ratios of about 0-5 must indicate the formation of a bi-molecular layer on the surface at saturation pressure. At low pressures the amount of iodine in the



224 B. Whipp.

second layer will be negligible, but, with increasing pressure, the amount adsorbed will increase relative to that adsorbed in the first layer, until, at saturation, the two amounts are equal.

This prediction is confirmed by calculations on the area of the crystals covered. The distance apart of ions in the lattice of potassium iodide is3 *53 A. There are thus 4*04 X 1014 ions of each kind present per square centimetre of surface. Now in the (1, 1, 1) plane of an iodine crystal there are4 • 35 X 1014 iodine molecules per cm.2* so that it is reasonable to assume that the iodine molecules will only be adsorbed on ions of one kind. If they were adsorbed on both kinds of ions, impossibly close packing would result.

The simple geometrical area of the crystals has been estimated by ordinary mensuration as approximately 1700 cm.2 on the assumption that they are 2 mm. cubes. I t is pointless to attempt to estimate the area of the surface with greater accuracy. Thus the total number of adsorbing ions is

1700 X 4-04 X 1014 — 6-9 X 1017.

The amount of iodine adsorbed at saturation decreases throughout the experiments. This shows that the baking or the treatment with iodine is decreasing the effective area of the adsorbent. If the maximum amount of adsorption recorded is divided by two and expressed as a number of molecules, we obtain 6 * 8 X 1017 for the first layer.

It happens that the agreement is even better than would have sufficed or been expected for the proof of the theory.

The Kinetics of Adsorption.

The most logical interpretation of the facts is to assume the existence of a strongly adsorbed layer of molecules attracting to itself a second layer by the action of much weaker fields. The forces binding the molecules adsorbed in the second layer will be much less than those binding the molecules in the first, so that the rate of evaporation of the former molecules will be higher than that of the latter.

The number of adsorbing centres for the second layer must be the same as for the first because the amounts adsorbed in the two layers are equal at saturation pressure.

If it be assumed that iodine is adsorbed in the second layer according to simple Langmuir kinetics represented by the equation x = a'bp/(l + a'p),

* Langmuir, 4 J. Amer. Chem. Soe.,’ vol. 54, p. 2812 (1932).




where b is proportional to the amount of the surface covered by the first layer, while a' is to a, of the original Langmuir equation, as the rate of evaporation of molecules in the first layer is to that of those in the second—and is so small that direct proportionality is given up to saturation pressure—then the final gradient of the adsorption curve, as calculated from the equation, is ten times too small. I t is thus clear that the second layer cannot be built up by a mechanism similar to tha t obtaining for the first layer, and that some other process is involved.

The Mechanism of Formation of the Second Layer.

In this section an attem pt is made to derive an equation which shall fit the experimental results.

Let v be the rate of evaporation from unit area of first layer when completely formed (assuming no second layer present to impede evaporation), and let v' be the corresponding quantity for the second layer. Let 0 and 0' be the fractions of total surface covered with the first and second layers respectively.

Let jjt be the number of gram moles striking 1 cm.2 of surface per second, then

(i. = , , (1.0)V 2tuMRT

where p is the pressure and M the molecular weight of the gas.The rate of condensation of molecules on the first layer is ap (1 — 0) where

a is the condensation coefficient. The rate of evaporation is given by v (0 — 0') on the assumption that evaporation from the first layer cannot take place when this is covered by a second layer. Hence, for equilibrium of the first layer,

a (A (1 — 0)' = v ( 0 — 0'). (1.1)

Similarly for the second layer the rate of evaporation is v'0'. If we assume that condensation occurs in the second layer whenever a molecule from the gas phase strikes the first layer, whether or no the first layer is already covered by a second layer, the rate of condensation will be a'jjiO, where a' is the condensation coefficient for the second layer. This implies that the molecules m the second layer are so loosely held that they are pushed aside laterally by the impact of fresh molecules from the gas phase, until the first layer is completely covered.

VOL. cxli.— a. Q



226 B. Whipp.

Condensation into the second layer is thus similar to condensation of iodine vapour on to a solid surface of iodine and involves the assumption of a low critical energy increment for lateral mobility.

Equating the rates of condensation and evaporation for the second layer,

a'fxO = v'0\ (1.2) *

Substituting the value of 0 from (1.2) in (1.1)

Now

(1.3)

(1.4)

where p is the pressure in the gas phase.The only properties of the surface upon which a and a' are dependent are

the condensation coefficients, the number of adsorbing ions per unit area and the time of life of adsorbed molecules in the surface so that they may be considered as the respective mean lives of the molecules adsorbed in the first and second layers.

Hence

or

Similarly,

I 1 - 3 = O 'I V 1}(1.5)

0, _ a ap 2 (1.6)1 + p{a — a') *

0 = ap/{ 1 + p ( a — a')}. (1.7)

If xtbe the amount of iodine adsorbed in the first layer and x2 that adsorbedin the second, then

and x2 N'0', N ’

where N' is the number of adsorbing spaces and N is the Avogadro number. Therefore from (1.6) and (1.7)

- f # ____ (1.8)

andXl 1 -\- p{a a') *

a a'bp2Xs> -

1 + p (a — a) ’(1.9)

where 6 (= N'/N) is the Langmuir constant representing the number of adsorbing centres.




Thus, X, the total adsorption (= -f- is given by

X = (1 +1 4

(2.0)

At the saturation pressure xx = x 2. Equating and x2 and writing p Q for the saturation pressure, we find

a'p0 = 1. (2.1)

Thus a'which is proportional to the mean life of molecules in the second layer is not an arbitrary constant, but is simply related to the saturation vapour pressure.

Substituting the value of a' from (2.1) in (2.0), we obtain finally,

X = (fbp_(1 4~ ) /»2 2) 1 + ap

as the adsorption isotherm.At the saturation pressure X = 26 as would be expected.If we consider the kinetics of evaporation and condensation of molecules

of iodine vapour on a solid iodine surface, we find that for equilibrium,

a p. = v

where a" is the condensation coefficient and v" is the rate of evaporation for a solid iodine surface.

Thus assuming the same value of the condensation coefficients a', a",

a"p0 == 1,

where a" represents the mean life of the molecules in the surface layer of a solid iodine crystal. Thus (by (2.1)) the rate of evaporation of molecules in the second layer is the same as that of molecules on a pure iodine surface, provided the coefficients a', a" are equal.

In Table II I are the values of X calculated from the isotherm (2.2) together with the amounts actually observed (interpolated at the pressures for which X has been calculated). In each space in the table the calculated amount is placed above the observed amount. Underlined figures show where the theoretical value was equated to the experimental value for the purpose of calculating the constants a and 6. At the bottom of the table the values of the constants for the several isotherms have been tabulated.



228 B. Whipp

Table III.

Isotherm. 1. 2. 4. 6. 16. 17.

Pressure—2 x 10~3 mm........... 21-4 22-7 27-9 8-4 8-5 8-1

21-2 22-7 29-7 8-8 9-0 8-2

4 x 10-8 mm........... 32-1 30-9 38-7 14-0 13-0 12-532 0 30-9 38-7 14-0 13-0 12-5

6 X 10~3 mm........... 39-3 36-2 45-7 18-25 __ __39-8 36-5 45-2 18-0 — —

8 X 10~3 mm........... 44-9 40-5 51-0 21-7 18-7 18-245-2 40-2 50-4 21-2 18-5 18-0

10 X 10-3 mm........... 49-7 43-8 55-7 — — _50-0 44-3 55-5 — — —

12 X 10-3 mm........... 54 0 47-0 60-0 27-6 22-7 22-454-0 47-0 60-0 26-5 22-3 22-1

14 x 10~3 mm........... 58-2 50-0 64-2 _ __ _57-8 49-7 64-4 — — —

16 X 10-3 mm........... 62-2 52-9 68-2 32-6 26-2 25-761 0 51 0 69-7 32-0 25-5 25-1

20 X 10“3 mm...........—

——

37-537-5

— —

22 x 10~3 mm........... — -- - — — 31-0 —— — — 31-0 —

25 X 10~3 mm........... __ __ __ 42-8 33-4 32-8— — — 45-5 35-0 32-5

28 X 10~3 mm........... — — — 46-0 — 35-0— — — 50-0 — 35-0

30 X 10-3 mm........... _ - _ 48-4 37-4 37-0— — — 52-5 40-6 37-3

Langmuir constants— »(a ).............................. 0-400 0-665 0-590 0-259 0-346 0-325(b) .............................. 43-6 36-3 46-7 22-7 18-65 18-45

The amounts adsorbed are in units of moles X 2-40 X 10“5, the calculated values being inserted above the observed values.

In isotherm 1, fig. 3, the data are shown up to about two-thirds saturation pressure whilst in fig. 2 the complete analysis of isotherm 17 is shown up to actual saturation, xx and x2 being the amounts adsorbed in the first and second layers respectively (calculated from equations (1.8) and (1.9)). In each case the experimental data (not interpolated) have been plotted as points, and the



Adsorption of Iodine by Potassium . 229

5 JO

P ressu re mm.xio Fig. 2.

P n e s s u r e inmm.x to~^ Fig. 3.



230 B. Whipp.

values calculated from equations (2.2), (1.8) and (1.9) as tlie smooth curves. I t will be seen that there is good agreement between the experimental and theoretical values.

The value of a' deduced from equation (2.1) is about ten times smaller than that of a, and so at low pressures its effect is negligible and the isotherm reduces to a simple Langmuir expression.

In his original work of 1918, Langmuir ( cit.) found the constants a and b of his simple equation to vary irregularly throughout the course of the experiments and the same effect has been observed in the present work. This is in all probability owing to an alteration in the surface of the adsorbent caused by the long process of baking-out.

When taking the data for isotherms 6 and 16 at pressures near to saturation, the iodine pressure in the apparatus fell slowly after each expansion. This was shown to be caused by absorption of iodine by the grease, owing to the spreading of the grease from the taps during a period of hot weather. In isotherm 17 the pressures were read as soon as possible after each expansion and the curve is seen to fit the theoretical expression up to saturation pressure.

Discussion.

Langmuir* has shown from the data given by Harris, Mack and Blakef that adsorbed films of iodine are not likely to contain more than 4*35 X 1014 molecules of iodine per cm.2 (the number per cm.2 in the (1, 1, 1) face of an iodine crystal) after the first layer because repulsive forces will become operative at greater densities of packing. On these grounds he criticized the earlier theory of de Boer (loc. cit.), which demanded vertical rows of iodine atoms above each anion of salt, giving a layer density of 7*75 X 1014 molecules/cm.2. Langmuir considered the arrangement of molecules in the adsorbed film to be generally quite irregular after the first layer.

The potassium iodide crystal appears to be peculiarly suited to act as a foundation of stable layers of iodine molecules because the number of ions of one kind per cm.2 is 4-04 X 1014. Iodine molecules being adsorbed on ions of one kind, and the distance between K ions and I ions being 3*52 A., it follows that the smallest distance apart of the adsorbed molecules is a/2 X (3 • 52)2 A. and the next smallest 2 X 3*52 A.

These distances are approximately the same as those found by Harris, Mack and Blake (loc. cit.) for two of the sides of the unit cell of iodine. I t may

* ‘ J. Amer. Chem. Soc.,’ vol. 54, p. 2812 (1932). t ‘ J. Amer. Chem. Soc.,’ vol. 50, p.1583 (1932).



Adsorption of Iodine by Potassium . 231

therefore be expected that the forces between the iodine molecules in a bi- molecular layer adsorbed on potassium iodide are of the same order as the homo-polar forces between the molecules in a pure iodine crystal, and thus the bi-molecular layer attains equilibrium with the vapour at the saturation pressure of pure iodine. Optical examination of the adsorbed films designed to show (a) the thickness of the layer as in the experiments of Frazer,* and ( ) the polarization of the iodine by measurement of its absorption spectra, as in the work of Chilton and Rabinowitschf would be of interest in this connection.

Chilton and Rabinowitsch show that the absorption spectra of iodine adsorbed on calcium fluoride (as measured by de Boer) and on chasabite are similar to that of solid iodine. The adsorbed films in this work were of a yellowish-brown colour so that it would seem from the colours of the films observed by Chilton and Rabinowitsch that the molecules are polarized to the same extent as those in solid iodine.

We have assumed that there is lateral diffusion in the second adsorbed layer and if this layer is similar to the surface layer of an iodine crystal, as we have indicated, we should anticipate the phenomenon of surface diffusion in the latter case. This prediction is of interest in connection with the respective theories of crystal growth of Kossel and Stranski on the one hand, and of Volmer on the other.

According to Kosselt the limiting factor in the growth of crystals is the slow rate at which a lattice plane is built up. Kossel and Stranski§ imagine that the molecules are regularly orientated on the surface and leave out of account the possibility of lateral mobility. Volmer|| on the other hand concludes that the condensation of isolated molecules and small aggregates is always a much more rapid process than that deduced by Kossel and Stranski, and regards the surface as covered by a two-dimensional mobile layer ; the velocity of crystallization being governed by the rate at which lattice nuclei rea formed by lateral diffusion. A nucleus of given size is only in equilibrium with the two-dimensional mobile layer at a definite degree of supersaturation, the degree of supersaturation necessary increasing as the size of the nucleus becomes smaller, so that as the degree of supersaturation is reduced, the rate of growth of the nucleus will fall, reaching zero before the equilibrium (saturation) pressure is * * * §

* ‘ Phys. Rev.,’ vol. 34, p. 644 (1929).t ‘ Z. phys. Chem.,’ B, vol. 19, p. 110 (1932).J ‘ Nachr. Ges. Wiss. Gottingen,’ p. 135 (1927).§ ‘ Z. phys. Chem.,’ A, vol. 136, p. 259 (1928).|| * Z. phys. Chem.,’ A, vol. 156, p. 1 (1931).



232 Adsorption of Iodine by Potassium Iodide.

reached. This region of zero growth of a crystal in its still supersaturated vapour has been observed directly by Volmer ( cit.) for iodine, thus supporting the existence of the mobile surface layer.

The fact that the second adsorbed layer when full contains the same number of molecules as the first seems to indicate that, for iodine on potassium iodide at least, lateral mobility is subject to certain constraints by the hetero-polar substrate.

It may be noted that the existence of K I3 as a separate phase was disproved. Experiments were carried out in which the pressure of iodine above a bi- molecular layer of adsorbed iodine was slowly reduced by absorption of the iodine vapour in tap grease. These were continued until only a fraction of a single layer remained adsorbed, but in no experiment did the pressure show any stationary value below that of saturation. In a review of the evidence in favour of the existence of potassium tri-iodide as a solid phase, Bancroft, Scherer and Gould* show that it is extremely unlikely that solid K I3 has been prepared, although this does not exclude the possibility of its existence in solution.

My great thanks are due to Professor E. K. Rideal, F.R.S., for suggesting this work and for his valuable encouragement and criticism, and to Dr. 0. H. Wansbrough-Jones for much helpful advice.

I also wish to express my thanks to the Goldsmiths’ Company and to the Department of Scientific and Industrial Research for grants which enabled the investigation to be carried out.

Summary.

Adsorbed films of iodine on potassium iodide crystals are found to be two molecules thick at the saturation pressure. A kinetic explanation of the process is advanced on the assumption of a loosely bound second layer, and a two-constant isotherm is deduced which represents the adsorption up to saturation pressure. Evidence is presented showing that the surface molecules in the bi-molecular film have properties similar to those in the surface of a crystal of pure iodine and the bearing of this on Volmer’s theory of crystal growth is considered. Potassium tri-iodide is not formed as a separate phase.

* ‘ J. phys. Chem.,’ vol. 35, p. 764 (1931).



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