Wetting transitions at triple points; A study based upon the analysis of stepwise adsorption isotherms

Surface Science 147 (1984) 48-64 North-Holland. Amsterdam

48

WETTING TRANSITIONS AT TRIPLE POINTS; A STUDY BASED UPON THE ANALYSIS OF STEPWISE ADSORPTION ISOTHERMS Isabella DPC/SCM, Received

C. BASSIGNANA

* and Y. LARHER

Centre d%tudes Nuclkaires de Saclay, F- 91 I91 21 June 1984; accepted

for publication

** Gif SW Yuefte Cedex, France

24 July 1984

This adsorption isotherm study finds that ethylene adsorption on PbI, is limited to only a few layers at T< T,, (the triple point temperature of bulk ethylene) but that almost unlimited adsorption can take place as r,, is approached. This behaviour is qualitatively identical to the behaviour of the ethylene/graphite system previously reported. In both cases wetting by ethylene is incomplete below r,, since the adlayers formed have an orientational order which is in compatible with that which is found in the bulk solid ethylene. However, C,H, shows a strong tendency to wetting somewhat below its bulk triple point temperature because it can form a liquid or at least an orientationally disordered solid film of limited thickness. The similarities and differences between these two systems are discussed. In addition, we discuss in general systems for which wetting is temperature dependent, The first part of this paper is devoted to outlining in detail how stepwise adsorption isotherms on powdered samples can be used to give information about wetting of the exposed basal face. The merits and limitations of this method are discussed in the context of the ethylene/PbI, example.

Information on wetting from stepwise adsorption isotherms As the pressure of an adsorbate is increased isothermally (T = constant) towards its bulk saturation value, ph( T),the mole quantity N,( T,p) adsorbed on a single crystal face can behave in two distinct ways: (i) it can tend asymptotically to infinity (Nt( pb) = cc) or (ii) it can remain finite (N,( P,,) < CO), in which case the adsorption isotherm crosses the pi, axis at a finite non-zero angle. These two classes represent two distinct types of wetting behaviour: the first corresponding to complete or perfect wetting of the crystal surface by the condensed 3D phase and the second to incomplete wetting or puddling of the adsorbate on the surface [l-3]. Given this correspondence, the measure of adsorption isotherms in the vicinity of P,, on a single crystal face can be used to give interesting informa* Present address: Institute fur Physikalische Chemie 11, D-8000 Munchen 2, Fed. Rep. of Germany. ** Author to whom inquiries should be addressed.

der Universitat

0039-6028/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

Munchen,

Sophienstrasse

I. C. Bassignana, Y. Larher / Wetting transirions at triple points

49

tion about the wetting of this face by the bulk phase of the adsorbate be it liquid or solid *. Can we extend this statement to adsorption measures made on a powder sample? This is an important question and, from a practical standpoint, since adsorption measurements of adgases over powdered samples are not only easier to make but are also more accurate than those over single crystals, there is a considerable interest in pursuing it. At first sight the answer is no, because the quantity measured in an adsorption experiment is the total sum of the amount of matter adsorbed on the various crystal faces as well as that condensed in the interparticle spaces. Moreover, the latter part, which corresponds to capillary condensation, can become very important as p tends to pb. As a result one has no access to the amount adsorbed on a particular crystal face. It would thus seem that adsorption results for powders are largely useless in the context of the wetting problem. This quite realistic view was expressed by Adamson in 1968 [2]. However, there are now examples for which such a statement turns out to be too pessimistic, namely for cases in which stepwise adsorption isotherms are observed (see, for instance, ref. [5]). Such isotherms show quasi-vertical steps of almost equal height, indicating the deposition of successive monolayers on a particular crystal face. In the case of adsorption on graphite or on lamellar halides it is the basal face. On this face a first order 2D (two-dimensional) condensation is associated with the deposition of each layer, thus the discontinuities in the isotherms. The vertical steps occur at a pressure p,,( T), where n refers to the nth layer. Accordingly, one can in principle count the maximum number of layers deposited on the basal face, n,,, at a given temperature by counting the number of steps on the adsorption isotherm. This is a convenient way to have some information on the wetting of this face. Since perfect wetting corresponds to n,,, = co, it cannot, strictly speaking, be rigorously proved from an adsorption isotherm, but it can be conjectured: in this paper we will present examples in which an important increase of n,,, with temperature can safely be interpreted as a transition to perfect wetting. The problem is to get a good estimate of n,,, in the incomplete wetting regime. of Only a lower bound for nmax can be estimated from a direct observation an adsorption isotherm since, as the number of layers increases, p,, approaches pb and the experimental inaccuracy limits the number of detectable layers. A second more serious difficulty arises from the fact that the steps on the isotherms are never strictly vertical due to imperfections of the substrate and finite size effects [6]. In addition, capillary condensation becomes very important asp +pb and the steps are generally erased in the vicinity of pb. Even with the best substrates no steps have ever been observed at pressures above * Wetting as defined by the Young-Duprk equation [4] imposes no restrictions on the phase of the wetting substance, so that, contrary to intuition, it is possible to have even wetting of one solid by another.

50

I. C. Bassignana, Y. Larher / Wetting transitions clt triple points

0.95 p,,. Also, hysteresis is another difficulty associated with capillary condensation. Although direct counting of layers from an isotherm is ruled out, in many cases it is still possible to indirectly determine the maximum number of adlayers at a given temperature from the In p versus T-' phase diagram. At Tn. the temperature at which the logp, versus T-' curve intersects the log p,, versus T-' curve, n max changes from n to n - 1. At this point the difference log p, - logp, defining the stability of the n-layer film with respect to the dense phase of the bulk adsorbate changes sign. Of course the logp, versus T-' curve has to be extrapolated since, as stated above, p, cannot be measured directly in the vicinity of ph. However, when log p, is extrapolated over a sufficiently small temperature range, the procedure should be safe. In addition, the extrapolation is facilitated by the good linearity of the curves logp, and log pt, versus T-' over large temperature intervals. The procedure outlined here was first used in 1973 by Larher and Haranger [7] for Kr adsorbed on the basal face of CaI,. These authors were able to show that, while increasing the temperature, the maximum number of adlayers increases from 1 to 2 at 70.5 K. A few other examples of an increase with temperature of the maximum number of adlayers have been observed since then: for instance, for NO adsorbed on CaI, this number increases from 0 to 1 at 83.5 K [8,9]; CO, on graphite behaves similarly at 104 K [lo]. In all these cases, the change in the incomplete wetting regime is observed in a temperature range where the bulk phase of the adsorbate is a solid. In these cases it has been proposed that no wetting occurs because the substrate tends to impose on the first adlayer a solid-like order which is incompatible with the order present in the bulk crystal of the adsorbate. As a result, that part of the cohesion energy of the film which stems from the attraction between the adparticles is diminished. And since the part due to the attraction by the substrate decreases as the film thickness increases, it is understandable that the film can become unstable with respect to the bulk 3D crystals [5]. This is a simplified explanation which ignores entropy effects that also play an important part [5,7.10]. Nevertheless, it conveys the basic idea. The kind of order involved can be positional (e.g. Kr on CaI, [5,7]) or orientational (e.g. (NO), on CaI, [8,9] or CO, on graphite [lo]). Of course at the triple point temperature of the bulk adsorbate, 7;, *, wetting can become complete for these systems, because a liquid is disordered (more precisely has only short range order) and consequently a factor such as the positional or orientational order is expected to play a less important part. Unfortunately, for the systems mentioned above, our procedure is not ade* We will use the expression “triple point” exclusively to designate coexistence of a gas, a liquid and a solid for a one-component system. Since other kinds of triple points (gas + two solids) are only exceptionally met within this article no confusion can arise from this convention.

I.C.

Bassignana,

Y. Larher /

Wetting transitions at triple points

51

quate to detect a wetting transition at T’,, because at this temperature the steps are no longer vertical since the critical temperature in the n th layer, Tjc”‘, is lower than T,,: for CO,, T,, = 216.6 K and for CO,/graphite, T$‘,”= 127.5 K; for N,O, T31= 182.04 K and for N,O/graphite, Tj’,‘)= 118.5 K; for Kr on CaI,, T$:) is not known but is also expected to be somewhat lower than T,,. If one wants to use the procedure described above to investigate possible changes in the wetting regime at Tjt, then one has to look at systems for which T,, < T$‘,). The aim of this paper is precisely to discuss such systems of which a first example, ethylene on graphite, was extensively studied in 1977 by Menaucourt, Thorny and Duval [11,12]. In essence, these authors came to the conclusion that C,H, only wets graphite at T > T,,. They correctly state that the incomplete wetting is due to a structural effect. Since the ethylene molecules are orientationally ordered in the bulk crystal phase at TXt [13,14], one is led to believe that the inability of solid ethylene to wet graphite is somehow related to this type of order, just as for NO [8,9] or CO, [lo]. One then conjectures that adsorbates which wet a given substrate above Tjt will show a transition to an incomplete wetting regime below T,, if at T < T,, the bulk crystal phase is already orientationally ordered. If this is true, the behaviour of the C,H,-graphite system should have some generality. This view is supported indeed by a number of experimental results: those of Regnier et al. [15,16] for the adsorption of C,H, on graphite and also the preliminary results of Menaucourt [ll] for C,H, adsorbed on BN or CdBr,. In this paper we present detailed adsorption isotherms for a similar system, namely C,H, on the lamellar halide PbI,. Like CdBr,, PbI, is a lamellar halide. For these layer-like compounds, samples mostly limited by their basal face are easily prepared [17]. In the discussion of the data, the comparison with those of Menaucourt et al. [12] for C,H, on graphite will be emphasized and we will try to make more precise the conditions under which one can expect a wetting transition to occur at the triple point of the bulk adsorbate.

2. Experimental results 2. I. Experimental The adsorption isotherms were measured volumetrically with an experimental set-up similar to that previously described [18]. The gases used in the vapour pressure thermometer were either CH, or Xe. To determine the temperature we utilized the data of Armstrong et al. [19] in the first case and those of Leming and Pollack [20] in the second. The ethylene adgas (Pdt de 1’Air Liquide, N40, purity 99,99%) was used without further purification. The PbI, substrate was prepared by sublimation in a stream of dry nitrogen [17].

I.C.

52

Bassignana,

Y. Lmher /

Wetting transrtrons at triple points

Its specific surface area, determined by measuring an adsorption isotherm for Xe, was 5.4 m2 g-‘. The sharp vertical risers in the adsorption isotherms (figs. 1, 3 and 4) attest to the very high purity of the gas, the excellent homogeneity of the substrate and also to the absence of a temperature gradient over the volume occupied by the substrate. The graphite sample was exfoliated graphite kindly provided by A. Thorny. 2.2. General aspect

of the multilayer adsorption of C, H4 on Phi,

Fig. 1 shows adsorption isotherms of C,H, on PbI, at three different temperatures: 104.2, 95.9 and 88.0 K, and gives qualitative evidence for the increase of the maximum number of adlayers with increasing temperature. The isotherms show 4 adlayers at 104.2 K, 2 at 95.9 K and only 1 at 88.0 K. These values will be confirmed by the logp versus T-’ phase diagram which will be discussed below. Comparison of these isotherms with those for C,H, on graphite (fig. 1 of ref. [12]) shows that qualitatively the two systems are very similar. Quantitatively there are small differences in the T,‘s and 7”:)‘s but these can be attributed to differences between the two substrates and are also discussed in detail below. In comparing the two systems, the one fact which it was not possible to reconcile was that the adsorption isotherms of ethylene on graphite show a maximum of only three overlayers at T > T,, , while our measurements on PbI z show a maximum of four. As will be clarified in the discussion, we would 10.0

5: 8.5 B

1L z 6.0 .t: z 3 u

x

T=

*

T =

95.9 K

T =

88.0 K

r

104.2K

4.0

7J 8 3!? 2.0

Fig. 1. Adsorption isotherms for ethylene on Pbl, at three different temperatures.

I.&. Bassignana,

Y. Lurher /

Wetting transitians at @ipIe points

53

expect a larger rather than a smaller number of overlayers on the graphite surface. We were prompted to look more carefully at C,H, adsorption on graphite near pb at T > T3t, and we did indeed find a fourth layer (fig. 2). We did not attempt to get evidence for a fifth layer. 2.3. Log p uersus T -

’ phase

diagram

To determine the disappearance temperatures T, we need the logp, and log p, versus T-’ curves. For the vapour pressure of C,H,, we will utilize the measurement of Menaucourt [21]. To obtain the logp, versus T-' curve we have determined sets of adsorption isotherms independently for the first three layers. We present only those for the 1st (fig. 3) and the 2nd (fig. 4), those for the 3rd being analogous to the latter. The log,,p versus T-’ phase diagram is represented in fig. 5. The coefficients for the R lnp versus T-r regression lines are given in table 1. The interest of including the factor R, the gas constant, is to give these coefficients a simple physical meaning: the slopes are related to the molar enthalpy differences h, - u,, or h, - ub; the ordinates to the origin, to the molar entropy equations differences spO- S, or sgO- sb. This results from the following

180

I I

ethylene

/

graphite

3” 8 4’ layers T =104,26K

1.9%

2al

2.02 Log,,P

Fig. 2. Adsorption layer.

isotherm

204

206

208

3.00

IPal for ethylene

on graphite

in the domain

of formation

of the fourth

I.C. Bassignana. Y. Lmher / Wetting tramdons at trip/e pornts

54

Table 1 Entropy and Hdmholtz

free energy of ethylene

h, - u, 1st Layer 2nd Layer 3rd Layer

multilayers

so*-

on Phi,

and pure ethylene

S” (cal mol -’ K”‘)

hn-h,

Sal- SP

(Cal mol-‘)

(cal mol-‘f

(cal mol-’

- 4607.1 - 3869.9 - 3761.9

46.28 45.45 45.36

845.6 108.4 0.4

- 0.60 - 0.23 -0.32

104iTi122 88
-4716

54.89

_

_

T < 103.95

- 3763

45.69

_

T > 103.95

Temperature range(K)

K-‘)

Bulk ethylene g/s coexistence (ref. [Ill])

Bulk ethylene g//coexistence (ref. [21])

[18,22]: RInp,=

-(hg-~,,)T-‘+(~gO-~,,),

RdlnpJdT-‘=

(1) (2)

-(&.-u,,), __ ethylene

/ pb],

---

1” layer

19

1.7

2.1

I

23

LogloP [Pal Fig. 3. Adsorption

isotherms

for ethylene

on Pbl,

in the domain

of formation

of the first layer.

I. C.

Bassignana,

/ Weiiing

Y. tarher

transitions

at triple

1.8

2.2

poinis

55

3.4 ethylene

1 Pbl,

2”d Iayer

2.9

-8 E ZY.. ,x ‘2

2.4

2 1 ff 5: 2

1.9

1.4 -0.2

0.2

0.6

1.4

1.0

Log,P

2.6

30

lPa1

Fig. 4. Adsorption isotherms for ethylene cm PbI, in the domain of formation of the second layer. Note that at T= 88.0 K the second layer has disappeared.

1

08

09

II

IO IO2

Fig. 5. Phase diagram. The boidface the solid lines with experimental ethylene/graphite [11,12].

12

f T CK1

lines show bulk ethylene gas-liquid and gas-solid points show ethylene/PbI, and the dashed

coexistence, lines show

I.C. Bassignana,

56

Table 2 2D critical

and disappearance

Temperature (W

CC T;T Ti’, T, r, T4

Y. L.arher / Weltrng transitions at triple pornts

temperatures

for ethylene

multilayers

Ethylene/Pbl, (present work)

Ethylene/graphite (refs. [11,12])

122.5 * 1 119 *1 118 +1 89.6 100.2 103 a)

118+1 119*1 _ 19.9 98.3 702 a)

on Pbl,

and on graphite

Ethylene/graphite (refs. [38,49])

75

a) These values are each determined from a single isotherm. b, This value of T4 was reported by Sutton et al. [38] in a preliminary report of their X-ray data. Unfortunately these authors do not comment on the existence of a fourth layer and in their more recent high resolution study they report only three layers [49].

RTlogp,

= -(h,

R dlogp,/dT-’

- ZQJT= -(hg-

+ sgo - Sb, u,).

(3) (4)

where the indexes g, b and n correspond respectively to bulk gas, bulk condensed phase and n th layer. The index b is replaced by /(liquid) or s (solid) when the nature of the bulk phase is specified. The index 0 indicates the entropy at unit pressure l(Pa); for an ideal gas h, = h,,. These equations define the quantities u, and s, which can be considered as representing the molar energy and entropy of the nth adlayer. Subtracting eq. (3) from eq. (1) one can also write: f,-f,=RTlog(p,/p,)=(u,-u,)-T(s,,-s,),

(5)

in which f= u - Ts is the molar Helmholtz free energy. Table 2 contains the disappearance temperatures T, derived from these regressions, as well as the values of Tjc"', the critical temperature for the s are determined from the isotherms in the usual way various layers. The T$(,"' [6,23]. These together with the values of u,, and s, give interesting information on the adlayers. For comparison this table also includes the values of T:,"' for the layers of C,H, adsorbed on graphite. Reexamination of the graphite data somewhat different from theirs. [11,12] led us to propose a value of Tj',"

3. Discussion Above, we discussed how the transition from complete to incomplete wetting of a substrate by C,H, can be attributed to the dramatic decrease at T3,of the orientational order present in the bulk C,H, crystal. However, the experimental results, which show an increase in the maximum number of

adlayers as T approaches Tjt,suggest a strong tendency to complete wetting below T3talso. The analysis to be carried out later will even suggest that the adfilm can be made arbitrarily thick on condition that the difference Txt- T is made sufficiently small. How is this possible? Briefly stated, our argument is as follows: the 2D layers of ethylene can remain liquid at temperatures where the bulk phase is already solid, i.e. below the triple point temperature T3,. Unlike the bulk solid, the liquid adfilm can wet the substrate because it lacks strong orientational order. Our guess that the film remains liquid-like below 7;, is based for the most part on a comparison of our thermodynamic results with those previously obtained by others and especially with those of Gilquin and Larher [24,25] on the adsorption of 0, on graphite and lamellar halides. We were especially interested in comparing our work to Gilquin’s since, unlike previous studies of the adsorption of Ar, Kr, Xe or CH, on the same substrates [5-7,18,23,26-331, these measurements were made above the triple point temperature of the adsorbate. And this is one reason for conjecturing that the adlayers are liquid-like. This is not always true for n = 1 since the first layer is in direct contact with the substrate. This view is indeed strongly supported by the behaviour of Tiz'and s, for n 2 2. In the case of Ar, Kr, Xe or CH, these parameters varied a lot, because of a strong influence of the surface corrugation upon the structure of the crystalline adlayers. But, on the other hand, for 0, they are constant within experimental accuracy because the surface corrugation has little influence on a liquid adlayer. Moreover, the value taken by Tjt' agrees with the value already observed for the 2D gas-liquid transition in monolayers of Ar, Kr, Xe or CH,, adsorbed on graphite or on lamellar halides [24,31,33]. Txcbeing the critical temperature of the bulk adsorbate, for all these systems one finds T,,/T,, = 0.39 + 0.01. We will not discuss in detail the meaning of s,. We just remind the reader that the quantities unr s, and f, defined in section 2 represent, under certain conditions (see refs. [18,22]) molar quantities of the nth layer. This is no longer true when an important change in the (n - 1)th layer is associated with the 2D condensation in the n th one, but this is not too restricting when the successive adlayers are liquid-like. Indeed in the case of O,, Gilquin and Larher [24,25] found that from the 2nd layer onwards s, is constant and equal, within experimental accuracy, to the molar entropy of bulk liquid oxygen. We interpret this result as indicating that the structure of the successive adlayers (with perhaps the exception of the first one), are not significantly perturbed by the structure of the underlying surface. This means that in the difference f, -fe, the only contribution different from zero is the excess potential energy due to the substrate. Since this quantity decreases as the inverse cube of the distance from the substrate [34], one can write: f, -ft=

RTlog(p,,/p,)- A@/n3,

58

I. C. Bassignana,

Y. Lmher

/ Wetting transitions at triple points

which is rather well obeyed for 0, as soon as n 2 2. When eq. (6) is obeyed, m the film thickness can grow to infinity. This is what we expect since the derivation neglects any perturbation of the film by the substrate. Then we should also have s, = sp. When s, has already attained its asymptotic value at n = 2, then n,,, can grow to infinity. In practice, when s2 = sJ = So, one can safely state that n,,, = co, which means perfect wetting. Given these results, what can we say about the layers of C,H, adsorbed on Phi,? We note first that T;:’ and T;:j are equal and take the same value as on graphite. The ratio TjJn’/T3, = 118/282.4 = 0.42 (see ref. 1351 for T;,) is shghtiy different from the constant 0.39 cited above, but we know from previous studies that for the 2D gas-liquid transition of markedly unspherical molecules, this ratio can show indeed somewhat different values. For example, for adsorption on graphite T,,/T,, for C,H, is 0.42 [15,16] for CO, it is 0.42 [lo] and for N,O it is 0.38 [lo]. We note also that our values of T$“’ (n > 2) are equal to T:,” for the 2D condensation of C,H, on graphite. This point is important since we know that this condensation corresponds to a gas-liquid equilib~um. This is demonstrated by recent NMR [36] and diffraction studies [37,38] on this particular system, showing that a triple point temperature exists at 67 K much below T$i’. In conclusion, the values of TiL (n 2 2) for the adsorption of C,H, on PbI, as well as on graphite tend to show that the adlayers are liquid-like at least from the 2nd onwards. We can say nothing by about the 1st adlayer of C2H4 on PbI,, which can be strongly influenced the structure of the surface. For Oz whose adsorption has been studied on various lamellar halides [24,25] this is indeed the case. The guess that the adlayers are liquid-like is also strongly supported by the accuracy. From values of the entropies, since s z = s3 = se within experimental our previous discussion this means that above TX,, C,H, wets PbI,. Two other facts support this: firstly the observation of a 4th step at 104.2 K; secondtly the fact that eq. (6) is reasonably well obeyed. Indeed ( ff- fi)/( jr- f,) = 3.65 to be compared with the theoretical estimate 27/8 = 3.37. Recall that for 0, or C, H, on graphite this quantity was respectively 3.44 [24] and 3.42 [11,12]. Since p//p4 is close to unity and since we have only one isotherm for the 4th layer (fig. l), our estimate of (f!- fs)/( f(- f,) is probably not very good. But using its theoretical values 64/27 = 2.37 and the experimental estimate of pB/pc= 0.847, we calculate p4/pe= 0.93. The agreement with our experimental value, p4/pp= 0.95 should be considered as satisfying, particularly since p4 and p/ have been measured under two different sets of experimental conditions. (For p/we have taken the values of Menaucourt ]21].) Using eq. (6) we estimate a value of 0.97 for the relative pressure of the 5th step of C,H, on PbI 2. The 5th step is experimentally inaccessible because of capillary condensation. This argument suggests perfect wetting with n.,,, = 00 above T3,. Such a conclusion would be entirely correct for solid adlayers studied below the roughening temperature of the bulk adsorbate, for instance Ar on CdCl z below

I.C. Bassignana,

Y. L.arher /

Wetting transitions at trtpfe points

59

69 K [5,393. But this is very improbable in the case of liquid adlayers. Indeed computer simulations 140-421 show that a Lennard-Jones liquid in the vicinity of a solid surface is stratified up to only 5 or so layers. Beyond this, the liquid adfilm will grow continuously, i.e. with no layering. When the adlayers stay liquid-like below T;,, s, remains equal to sL and we can still write a simplified version of eq. (5): f,, -f,

= RTlog(

Up,)

= AQi/n3 + 7;,.rr - T%,

(7)

where sr = s,- S, is the fusion entropy of bulk ethylene. As the temperature decreases from above to below T3,, s, - sb changes abruptly from 0 to sr. At the same time u,, - ut, changes discontinuously by T3pf, going from a negative to a positive value for n & 2. That is, the nth layer becomes energetically unstable compared to the condensed phase of the bulk adsorbate, It can still exist over a small temperature range below T3, because of its high entropy (s, > s,). Note that below T3( the situation is the~odynamically similar to that described in the first section for solid overlayers [5,7-lo]. The physical picture for liquid overlayers, however, is simpler: the n th layer is a 2D liquid unperturbed by the surface. For solid overlayers the n th layer is a solid whose large entropy stems from a perturbation due to the surface of the substrate. The disappearance temperatures for the ethylene adlayers on PbI, and on graphite are given in table 2. This table also includes estimates for T4. The values are calculated in each case using one experimentally determined value of p4 together with the assumption that sq = sp. As we saw above this assumption is good in this limit and so these values of T4 are probably not far from the true values. At the disappearance temperature, f, -fb = 0, so we can easily derive an approximate expression for 7, from eq. (7): lr, = TSr f A@,‘n3st = T,, - IA@j,‘n3s,.

(8)

Here we see that T, is a function of two independent factors, Ad, and sr. A@ is a measure of the adsorbate-substrate potential; the greater the /A@/, the lower the disappearance temperature. And indeed we see (table 2) that all the T,,‘s for the ethylene-graphite system are lower than for the ethylene-Pbl, system. This result is not surprising since previous studies have shown that graphite is a much more strongly attracting substrate than any of the lamellar halides [l&32]. For this reason also, for any given adsorbate, we always expect an equal or greater number of adlayers on graphite than on any of the iamellar halides. Whereas A@ is particular to the adsorbate-substrate system under study, sr (the melting entropy of the bulk adsorbate) is a property exclusively of the adgas. Eq. (8) shows that the larger sr, the higher T,; in other words, the higher the melting entropy, the lesser the tendency to wetting below Tjt. One-component crystals can be either of two types (see ref. [43]): (i) those

60

I.C. Bassignana,

Y. Larher / Wetting transitions at triple poinrs

which have only positional order frozen in at T3, and the crystal remains orientationally disordered in a certain range of temperatures below T3,,i.e. plastic crystals, and (ii) those for which both types of order are frozen in at 7;,. sr is much larger in the 2nd case and consequently wetting by oriented crystals should be much more difficult than by plastic ones. Our analysis of the log p versus T- ’ phase diagram thus brings a strong support to the view we expressed in section 1 that the orientational order within solids can be an obstacle to wetting. This is especially true of C,H, since here sr is very large: sr = 7.70 cal molt ’ K-’ [44]. On the other hand, plastic crystals should be able to wet substrates more easily than oriented crystals. And indeed there is no indication that the multilayer adsorption on graphite of CF, [45,46], N, [47] or 0, [48] in their plastic ranges is limited. This discussion assumes of course that there is no phase transition in the adfilm close to ph. Such a transition would be reflected in a break of the In p versus T- ’ curve and so make the extrapolation procedure outlined in section 1 more problematic. Our isotherm results as well as those of Menaucourt et al. [11,12] escape this criticism. However, we cannot exclude the possibility that in both cases the values of T,, can be slightly overestimated because of a break in the log p, versus T- ' curves within the small temperature interval over which they have been extrapolated. In the case of the C,H,-graphite system, an independent measure of T, by Sutton et al. [38] by X-ray diffraction suggests that the thermodynamic estimates of T,, are good (see table 2 for a comparison). Both methods give the same values for T3.The agreement for T2 seems not so good. Sutton et al. propose 75 K for T, as compared to 79 K reported by Menaucourt. However, when one looks at the phase diagram derived from the diffraction study (fig. 3 of ref. [49]) a spurious variation of T2between 75 and 79 K appears, so that in fact the agreement is within experimental accuracy. The X-ray study suggests that the 2nd layer becomes solid-like above 7;,, so that we should be able to see a break in the logp, versus Tp' curve. This break is probably too small to be detected in the isotherm work and does not significantly affect the estimate of T2.The fact that this break is not detectable indicates that the transition entropy is low and suggests that this solid adlayer remains orientationally disordered. This conjecture seems plausible since an NMR study [36] has shown that the first layer stays orientationally mobile to at least 13 K below its triple point, i.e. down to 55 K. In section 1 we stated that wetting would be hindered if the substrate imposed on the first adlayers an order incompatible with the order within the bulk crystal. The X-ray studies mentioned above [38,49] as well as the neutron diffraction investigations of Satija et al. [37] on the same system support this view. They show that the .first layer of ethylene adsorbed on graphite has a structure which is not found in its bulk crystal. The structure taken by the adfilm can be very important in determining wetting. Let us look in more detail at a specific example, CF, on graphite. The

I. C. Bassignana,

Y. Larher /

Wetting transitions at triple points

61

plastic phase of CF,, called /3, is stable from Tap = 76.2 K up to its melting temperature T,, = 89.5 K and its fusion entropy sr = 1.87 cal mol-’ K-’ is quite low [50]. According to eq. (8) for CF,, the T,‘s should be farther from T,, than for C,H,. DollC et al. [45,46] have shown that for CF,, T3 < Tab. Since the entropy of the a/I transition for bulk CF, is large (4.64 cal mall’ K-‘) it is tempting to suggest that the wetting temperature T, = Tap. However, a recent LEED-RHEED study [51,52] shows that for CF, on graphite, T, = 37 K. This is much below Tap, showing that CF, even in its oriented phase can wet the surface. A conjecture favourable for the wetting of a smooth surface by the crystal phase of an adsorbate is the existence within this phase of a dense crystallographic plane in which the molecules have an orientational order favourable to interaction with the substrate. Such a situation exists neither for C,H, nor for adsorbates having the Pa3 crystal structure, e.g. CO,, N,O as well as N,, CO at low temperatures. For CF,, the situation seems a priori more favourable since (Y-CF~ can be seen as a superposition of close-packed (001) planes [53]. CF, is almost spherical and the perturbation of the orientational order of this plane by the substrate is probably weak. Consequently (Y-CF~ can ‘wet graphite down to 37 K. From eq. (8) we know that a high adsorption energy can also favour wetting, but this type of argument cannot be used to compare the behaviour of a-CF, to that of C,H, since both adsorbates have comparable adsorption energies on graphite. The existence of a large range of temperatures over which the oriented (Y-CF~ wets graphite warns us against generalizing the wetting behaviour of C,H, to all adsorbates whose bulk liquid phase freezes towards an oriented solid with a large entropy change. Such adsorbates can continue to wet the substrate below their triple point if their crystal possesses a dense crystallographic plane showing a good “orientational compatibility” with the surface of the substrate. This idea is a generalization of the concept of positional incompatibility already introduced by one of us to explain the incomplete wetting of a number of lamellar halides by rare gases [5]. In both cases the structural perturbations due to the surface are responsible for incomplete wetting. The importance of such effects was noted by Adamson as early as 1968 [2]. The value of the wetting temperature is a compromise between these perturbations which tend to impede wetting and the strength of the attraction of the substrate which tends to favour it. Orientational order may in some instances also be very important in determining incomplete wetting by liquids. Liquid water has important short range orientational order [54] because the hydrogen bonds between molecules are strongly directional. This property may to a great extent be responsible for the non-wetting of graphite by water, which was observed as early as 1951 [55]. It may also contribute significantly in the case of the NH,-graphite system 1561. Recently

some

theoretical

studies

have

also looked

into

the problem

of

I.C. Bassignana,

62

Y. Larher

/ Wetting transitions

at trrple points

wetting (see, for instance, refs. [57,58]). These studies emphasize the importance of the relative strength of the adsorbate-adsorbate (u) to the adsorbate-substrate (u) interaction potential. Unfortunately this approach does not take into account structural effects. Substrates with different u will necessarily be composed of atoms of different physical size. As we saw above, the size of the space between atoms or “corrugation” of the substrate can be an important factor in determining wetting, especially in the case of solid adlayers. in addition, these theories also do not take account of the properties of the bulk adgas such as 7;,. Pandit and Fischer [59] have also considered the effect of the bulk triple point on wetting. These authors can generate a ten or so different phase diagrams but none corresponds to that observed for C,H,. One of their diagrams (their fig. 4a) is quite close to it; however, for this case the authors assume a stratification of the wetting phase on an infinite thickness, which is not realistic for a liquid. We have been looking at systems for which the amount of gas adsorbed at saturation increases as the temperature is raised. This types of behaviour. which at first seems puzzling, was observed and explained as early as 1957 by Everett and co-workers [60,61]. Unfortunately these authors used non-uniform substrates so that the increase with temperature of the amount of gas adsorbed at saturation was continuous. With uniform substrates the phenomenon is much more striking since the increase is discontinuous. The main advantage of observing discontinuities (1st order phase transitions) is that they permit a much deeper discussion. And the analysis carried out in this paper centres around a discussion of the physical parameters associated with these transitions. Before closing, we would like to comment on the method which is often used to obtain information on wetting from adsorption isotherms, i.e. looking at the angle at which the adsorption isotherm intersects the pi, axis. In section 1 we have criticized this method. However, since it is often used, we want to make two other comments on it. First, a technical difficulty can be encountered, regardless of the sample, powdered or monocrystalline. A cold point in the adsorption cell can artificially interrupt the adsorption isotherm at a pressure somewhat below R,, and incorrectly suggests an incomplete wetting regime. Second, capillary condensation is dependent on the temperature in the incomplete wetting regime. The lowering of the vapour pressure in a capillary of diameter r is given by [62]: RTlog(

p/p,)

= -2au(cos

0)/r.

where u, u and 0 are respectively the interfacial tension, the molar volume and the contact angle. Perfect wetting is at 0 = 0, but capillary condensation can occur as long cos 8 > 0, i.e. 0 < 7r/2. When three adlayers are already adsorbed on a substrate, (for instance above 98.3 K or 100.2 K for the ethylene-graphite

I. C. &ssignanu, Y. h-her

/ Wetfrng transitions at triple points

63

and ethylene-PbI, systems respectively), 8 should be close to zero, at any rate definitely lower than s/2. Above these temperatures the capillary condensation can be very important and incorrectly suggests perfect wetting. But at lower temperatures, 0 can become higher than 77/2, so that interparticle condensation cancels out and the isotherms intersect the p,, axis at a non-zero angle. One can conclude that incomplete wetting takes place here. As a result, though this method cannot give an absolute value of T.., it can at least give a lower bound. The data of Delachaume et al. [63] on the C,H,/BN system illustrate this point.

References [l] B.V. Derjaguin and Z.M. Zorin, in: Proc. 2nd Intern. Congr. on Surface Activity, Ed. J.H. Shulman (Butterworths, London, 1957) p. 145. [2] A.W. Adamson, J. Colioid Interface Sci. 27 (1968) 180. [3] J.G. Dash, J. Physique 38 (1977) C4-201. [4] J.S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Clarendon, Oxford, 1982). [5] Y. Larher and F. Millet, J. Physique 38 (1977) C4-189. [6] Y Larher, Mol. Phys. 38 (1979) 789. [7] Y. Larher and Haranger, Surface Sci. 39 (1973) 100. [S] A. Enault, Thesis, Nancy (1975): CEA Note 1841, January 1976. [9] A. Enault and Larher, Surface Sci. 62 (1977) 233. [lo] A. TerIain and Y. Larher, Surface Sci. 125 (1983) 304. [ll] J. Menaucourt, Thesis, Nancy (1977). 1121 J. Menaucourt, A. Thorny and X. Duval, J. Physique 38 (1977) C4-195. [13] W. Press and J. Eckert, J. Chem. Phys. 65 (1976) 4362. 1141 G.J.H. van Nes and A. Vos, Acta Cryst. B35 (1979) 2953. [15] J. Regnier, Thesis, Nancy (1976). [16] J. Regnier, J. Menaucourt, A. Thorny et X. Duval, J. Chim. Physique 68 (1971) 796. [17] Y. Larher, J. Chim. Physique 68 (1971) 796. [18] Y. Larher, Thesis, Orsay (1970); CEA Report 4089, December 1970. 1191 G.T. Armstrong, F.G. Brickwedde and R.B. Scott, Nat]. Bur. Std. 55 (1955) 1. [ZO] C.W. Leming and G.L. Pollack, Pbys. Rev. B2 (1970) 3323. (211 J. Menaucourt, J. Chim. Physique 79 (1982) 531. (221 Y. Larher, J. Chim. Physique 65 (1968) 974. [23] Y. Nardon and Y. Larher, Surface Sci. 42 (1974) 299. [24] B. Gilquin, Thesis, Nancy (1979); CEA Note 2091, August 1979. 1251 B. Gilquin and Y. Larher, Surface Sci. 75 (1978) 703. [26] A. Thorny, Thesis, Nancy (1968). [27] Y. Nardon, Thesis, Nancy (1972); CEA Note 1574, February 1973. [28] F. Millet. Thesis Nancy (1976); CEA Note 1865, March 1976. (291 C. Tessier, Thesis, Nancy (1983); CEA Report 5250. March 1984. [30] A. Thorny and X. Duval. J. Chim. Physique 67 (1970) 286. [31J A. Thorny and X. Duval, J. Chim. Physique 67 (1970) 1101. [32] Y. Larher, J. Colloid Interface Sci. 37 (1972) 836. 1331 F. Millot, Y. Larher and C. Tessier, J. Chem. Phys. 76 (1982) 3327. [34] W.A. Steele, The Interaction of Gases with Solid Surfaces. (Pergamon, Oxford, 1974). 1351 A.P. Kudchadker, G.H. Alani and B. Zwolinski, Chem. Rev. 68 (1968) 659.

64

I.C. Bassignana,

Y. Lmher

/ Wetting transitions at triple points

[36] J.Z. Lareze and R.T. Rollefson, Surface Sci. 127 (1983) L172. [37] SK. Satija, L. Passel, J. Eckert, W. Ellenson and H. Patterson, Phys. Rev. Letters 51 (1983) 411. [38] M. Sutton, S.G. Mochrie and R.J. Birgeneau, Phys. Rev. Letters 51 (1983) 407. [39] Y. Larher, in: Proc. 4ieme Conf. Intern. de Thermodynamique Chimique, Montpellier. 1975, Vol. 7, p. 5. [40] G.A. Chapella, G. Saville, S.M. Thompson and J.S. Rowlinson. J. Chem. Phys. Faraday Trans. II, 73 (1978) 1133. [41] I.K. Snook and W. van Megen, J. Chem. Phys. 70 (1979) 3099. 1421 S. Toxvaerd, Faraday Symp. Chem. Sot. 16 (1981) 159. [43] N.G. Parsonage and L.A.K. Staveley, Disorder in Crystals (Clarendon. Oxford, 1978). [44] C.J. Egan and J.D. Kemp, J. Am. Chem. Sot. 59 (1937) 1264. 1451 P. Dolle, Thesis, 3rd cycle, Nancy (1979). 1461 P. Doll&, M. Matecki and A. Thorny, Surface Sci. 91 (1980) 271. [47] R.D. Diehl and S.C. Fain, J. Chem. Phys. 77 (1982) 5065. [48] D.d. Awschalom, G.N. Lewis and S. Gregory, Phys. Rev. Letters 51 (1983) 586. [49] D.H.J. Mochrie, M. Sutton, R.J. Birgeneau, D.E. Moncton and P.M. Horn, preprint. [50] A. Euchen and E. Schriider, 2. Physik. Chem. B41 (1938) 307. [51] J. Suzanne, J.L. Seguin, M. Bienfait and E. Lerner, Phys. Rev. Letters 52 (1984) 637. [52] J.M. Gay, M. Bienfait and J. Suzanne, J. Physique, to be published. [53] D.N. Bol’shutkin, V.M. Gasan, A.J. Prokhvatilov and A.I. Erenburg, Acta Cryst. B28 (1972) 3542. [54] I.P. Gibson and J.C. Dore, Mol. Phys. 48 (1983) 1019. [55] C. Pierce, R.N. Smith, J.W. Wiley and H. Cordes, J. Am. Chem. Sot. 73 (1951) 4551. [56] G. Bomchil, N. Harris, M. Leslie, J. Tabony and J. White, J. Chem. Sot. Faraday Trans. 1. 75 (1979) 1535. [57] R. Pandit, M. Schick and M. Wortis, Phys. Rev. B26 (1982) 5112. [SS] P. Tarazona and R. Evans, Mol. Phys. 48 (1983) 799. [59] R. Pandit and R.B. Fischer, Phys. Rev. Letters 51 (1983) 1772. [60] G.H. Amberg, D.H. Everett, L.H. Ruiter and F.W. Smith, in: Proc. 2nd Intern. Congr. on Surface Activity, Ed. J.H. Shulman (Butterworths, London, 1957) p. 3. [61] D.H. Everett, Faraday Symp. Chem. Sot. 16 (1981) 254. [62] D.H. Everett, in: Solid-Gas Interface, Ed. E.A. Flood (Dekker, New York, 1967) p. 1055. [63] J.C. Delachaume, M. Coulon and L. Bonnetain, Surface Sci. 133 (1983) 365.