Langmuir 1989,5, 240-245
240
Thermodynamic Characterization of the Adsorption of NO at the (100) Face of NiO Microcrystals Edoardo Garrone,*it Bice Fubini,' Estrella Escalona Platero,+*Sand Adriano Zecchinat Istituto di Chimica Fisica, Uniuersitci di Torino, Via P. Giuria 7, 10125 Torino, Italy, and Istituto di Chimica Generale ed Inorganica, Facoltci di Farmacia, Uniuersitd di Torino, Via P. Giuria 9, 10125 Torino, Italy Received June 24, 1987. I n Final Form: April 20, 1988 Previous work (Escalona Platero, E.; Fubini, B.; Zecchina, A. Surf.Sci. 1987,179,404) has shown that at 303 K (i) nitric oxide adsorbs linearly and reversibly onto the Ni2+square lattice at the (100)face of structure is probably formed, and (ii) at high pressures the filling NiO, up to a coverage 0.5, where a ~(2x2) of the second half of the available sites begins, which takes place by the tilting of NO admolecules. In the present work, experimental volumetric and calorimetricisotherms are used to calculate the molar enthalpy and molar entropy of the adsorbed phase. The decrease in molar enthalpy of the adsorbed phase with coverage up to 0 = 0.5 is interpreted as due to a repulsive interaction among next nearest neighbors transmitted through the solid. The quasi-chemicalapproach accounts satisfactorily for the behavior of the molar enthalpy of the adsorbed phase but not for the molar entropy. The standard entropy of the Its dependence upon the molar heat of adsorption is adsorbed phase is calculated at 0 = 0 and 0 = 'Iz. discussed.
Introduction The statistical description of a surface immobile layer requires knowledge of the geometrical distribution of the sites of adsorption. Monocrystals, exposing well-defined surfaces, i.e., showing a regular array of well defined sites, provide, in principle, excellent experimental probes for theoretical models. However, their extremely low surface area renders difficult the direct measurement of the involved thermodynamic quantities (e.g., the energy of adsorption), in particular as a function of coverage. One way to circumvent these difficulties relies on the use of sintered powders in microcrystal form with welldefined crystal planes. In a previous investigation,' it has been shown that NiO samples can be prepared as stoichiometrically and morphologicallydefied powders, whose specific surface area may be varied by sintering from ~ 1 5 0 to -1 m2 g-l. Along the sintering process the shape of microcrystals approaches that of ideal cubelets, as shown by TEM. Accordingly, the reactivity of low coordinative situations (like corners, edges, and defects) becomes less evident, and eventually the reactivity of the (100)faces alone may be studied. As far as NO is concerned,' it was established that (i) NO adsorbs reversibly on (100)faces a t ambient temperature and (ii) NO adsorbs irreversibly on low coordinative situations, with the prevalent formation of nitrito species. In a subsequent paper? the reversible chemisorption at the (100)faces was studied by IR spectroscopy and microcalorimetry. The following were concluded. (i) NO is adsorbed on Ni2+ions with formation of linear nitrosylic species. (ii) A t moderate pressures (some 15 Torr) the coverage is around 0.5 (the same result has also been found for the low-temperature chemisorption of C 0 3 ) . (iii) A t 8 = 0.5, NO adsorbed molecules probably form a 42x2) square lattice (Scheme I) and interact both vibrationally (by dipole-dipole coupling) and chemically, through electronic effects transmitted by the solid. This latter effect is revealed, inter alia, by a decrease in the heat of adsorption. (iv) The filling of the remaining half of the Istituto di Chimica Fisica.
* Istituto di Chimica Generale ed Inorganica.
*Present address: Departamento de Quimica Inorganica, Facultad de Quimica, Universidad de Oviedo, 33071 Oviedo, Spain.
0743-7463/89/2405-0240$01.50/0
surface lattice sites begins only when the formation of the 4 2 x 2 ) lattice is nearly complete. This much weaker process requires substantial NO pressures, so that it is far from being complete at room temperature and is accomplished by the tilting of the surrounding NO admolecules from their perpendicular position (Scheme 11). (v) There is an overall agreement with a model proposed long ago by Wan$ for an assembly of particles adsorbed on a square lattice showing repulsive interactions between nearest neighbors (hereafter NN); this model is based on the quasi-chemical (hereafter QC) approach. In the present paper, we analyze these data in some greater detail, show that the occurrence of NN pairs is (1) Escalona Platero, E.; Coluccia, S.; Zecchina, A. Langmuir 1985,1, 407. (2) Escalona Platero, E.; Fubini, B.; Zecchina, A. Surf. Sci. 1987,179, 404. (3) Escalona Platero, E.; Coluccia, S.; Zecchina,A. Surf. Sci. 1986,171,
465. (4) Wang, J. S. Proc. R . SOC.1937, A161, 127.
0 1989 American Chemical Society
Thermodynamic Characterization of N O Adsorption
Langmuir, Vol. 5, No. I, 1989 241 1.1
. D
uu-
I
-
5
,
15
IO
20
p/1arr
25
Figure 2. Calorimetric isotherm (integral heat vs pressure). Figure 1. Volumetric isotherm (adsorbed amounts vs pressure).
Symbols as in Figure 1.
Different symbols refer to different subsequent runs. Open symbols, adsorption; solid symbols, desorption. negligible and that the decline in the energy of adsorption in the range 0 < 0 < 0.5 arises from the repulsion among next nearest neighbors (hereafter NNN), and also compute the adsorption entropy for the NO/NiO (100)system. The reader is referred to Scheme I for a clear definition of NN and NNN pairs.
Experimental Section The NiO sample was prepared as described in ref 1 and 2. Sintered samples show a specific surface area too small to be determined confidently through the standard BET methods. The number of Ni2+exposed by such samples was thus measured by determining the adsorbed amount at which 0 = 0.5. Completion of the 42x2) structure is monitored by a steep decrease in the differential heat of adsorption (see below),which takes place at 12.0 bmol of NO per gram of NiO it is inferred that the sample used for the microcalorimetric measurements,exposed 1.56 x 1019 Ni2+ions/g of the solid, Le., had a specific surface area of 1.34 m2 g-l, in agreement with much rougher Kr BET estimates. Calorimetric measurements have been carried out by means of a Tian-Calvet microcalorimeter connected to a volumetric apparatus6allowing the simultaneous determination of uptakes and heats released both in adsorption and desorption. The pressure was monitored by a transducer gauge (Baratron MKS); the microcalorimetric cells were kept at 303 K. The NiO sample, previously outgassed at 1073K, was contacted with 40 Torr NO for several hours to allow the completion of the irreversible adsorption that takes place, to a very small extent, also on sintered samples with a heat of reaction above 115 kJ Evacuation at 303 K was carried out in the calorimeter and monitored by a slow endothermic heat effect; reversible desorption was considered completed when no drift from the instrumental base line could be detected. Stepwise adsorption of NO was then studied, followed by stepwise desorption. Several adsorption/desorption cycles have been performed, both to improve the quality of the results and to check the thermodynamic reversibility of the process through the coincidence of adsorption and desorption "calorimetric" isotherms. In accord with the nonactivated nature of the adsorption under study, the thermograms (heat evolution diagrams) were those typical of instantaneous processes, showing an exponential decay of the heat flow. We note in passing that the absence of slow processes also rules out the occurrence of any ratecontrollii diffusion. Results Adsorption and Calorimetric Isotherms. The volumetric isotherm up to 28 Torr is reported in Figure 1. The low-coverage region is illustrated in the inset. For coverages lower than 0.1, a proportionality is seen between (5) Fubini, B. Rev. Gen. Therm. 1979, 18, 297. Gravelle, P.C.Proc. 5th Int. Congr. Catal. Hightower, H., Ed.;North Holland Amsterdam, 1973. Gravelle, P.C.Adu. Catal. 1972,22, 191. Gravelle, P. C. Catal. Rev.-Sci. Eng. 1977, 16, 37.
-"t -75-
-Is0
2
4
6
8
lb
12
14 n./pmol
d"
Figure 3. (a) Molar heat of adsorption as a function of adsorbed
amounts. Solid curve, experiment (smoothed data); broken w e , QC model (see text); vertical arrow, extent of the molar energy of repulsion among admolecules at 8 = l / % (b) Differential heat of adsorption as a function of adsorbed amounts.
equilibrium pressures and uptakes (Henry's law) 0 = hp, where h = 5.5 Torr-'. The isotherm as a whole does not fit the Langmuir formula. It is noteworthy that the last portion of it (from 0 = 0.32, i.e., for pressures higher than 0.6 Torr) satisfactorily fits the Temkin isotherm (0 = kl k2 In p ) , which implies a linear fall of the differential heat of adsorption with coverage. The calorimetric isotherm is reported in Figure 2. From the above data, molar and differential heats of adsorption have been calculated after computer smoothing of the experimental curves. These are reported as a function of coverage in Figure 3. The molar heat of adsorption, qht = (Qht/ns) shows a constant value of -83.2 kJ mol-' up to 0 = 0.12 and then declines down to -73.5 kJ mol-l. At 6 = 0.5 the molar heat of adsorption is -74.8 kJ mol-'. The broken curve in Figure 3a is calculated according to Wang's model (see,below). The molar enthalpy of adsorption A& = Ha - H , is readily calculated, being AJ€ = qht RT.6 Enthalpic data thus show clearly the nonideality of the process. The differential heat (q" = aQht/dnJ (Figure 3b) shows a plateau (0 < 0.12) followed by an almost linear decrease
+
+
(6) Garrone, E.; Rouquerol, F.; Fubini, B.; della Gatta, G. J . Chem. Phys. 1979, 76, 528.
242 Langmuir, Vol. 5, No. 1, 1989
Garrone et al. cides with that for an ideal chemisorption,as expect& the actual value of the standard entropy of the adsorbed phase is calculated below. At a coverage around 0.13, the experimental points depart from the ideal curve and decline thereafter rather slowly. An ill-defined minimum is also seen at 0 = 0.20, whose amount is however just larger than the experimental uncertainty. The meaning of the upper curve is given below.
,
\ \ \ \
1
0
4
1'2
8
1
n, / ( ~ r n ag? ~
Figure 4. Molar entropy of the adsorbed phase aa a function of adsorbed amounts. Solid curve, experiment (smoothed data); broken curve, ideal (Henry)adlayer; dot-dash curve, QC model (see text). with coverage, in agreement with the observation that the Tempkin isotherm holds in this region. Above 0 = 0.5, where tilted NO species are formed, the heat of adsorption decreases dramatically. Entropy of Adsorption. In preceding papers?' it was shown that the molar entropy of adsorption may be computed in a reversible process from the integral heats of adsorption Qint, adsorbed amounts ns, and equilibrium pressures p through the formula
Ss(nn)- Sg(p) = Qint/Tns+ R / n s j n ' n s d In p / p e 0
(1)
where Snand Sg are the molar entropy of the adsorbed phase and gaseous phase, respectively, and the other symbols have their usual meaning. Assuming the gas phase to be ideal, eq 1transforms into Sa(ns)= S@g- R In p / p e
+ qint/T+ R / n s J n ' n s d In p / p e
(2)
The first term on the right-hand-side of eq 1is the molar entropy of gaseous NO in the reference state. This, at 298 K and 1atm, is 210.7 J mol-l K-l.s At 303 K and 1 Torr the reference state adopted here is evaluated to be 266.3 J mol-' K-l, of which 206.6 J mol-' K-' is due to translations. The third term is simply proportional to the molar heat of adsorption, plotted in Figure 3a. The second and fourth terms only regard the adsorption isotherm, reported in Figure 1. The integral is evaluated numerically; it is readily seen that, in the region 0 = 0, as long as Henry's law holds, the integral reduces to R. The calculated values of the entropy of the adsorbed phase are plotted in Figure 4 as a function of adsorbed amounts. It is seen that at low coverages the curve coin(7) Garrone, E.; Ghiotti, G.; Giamello, E.; Fubini, B. Faraday Trans. 1 1981, 77, 2613. ( 8 ) Natl. Bur. Stand. (US.) Circ. 1952, 500.
J. Chern. Soc.,
Discussion The Ni2+cations at the (100)face of NiO constitute a square lattice of sites, onto which NO adsorbs. Repulsive interaction takes place among admolecules, as shown by the decrease of the molar and differential heat of adsorption (Figure 3). Repulsion may arise either from direct electronic overlap between admolecules, from dipole-dipole repulsion, or from the alteration of the electronic properties of the Ni2+site caused by adsorption on neighboring sites. In the following, evidence will be given about which kind of repulsion is operative. Because of the difference in the two mechanisms of adsorption, we consider separately the region 0 < 0 < ' I 2 and 0 > Although IR evidenceSshows that the formation of tilted species starts slightly before the completion of the 4 2 x 2 ) structure, we will neglect this feature and clear cut the two phenomena, encouraged in doing so by the very low coverage of tilted species below 8 = 0.6, a~ suggested by the low intensity of the related IR bands. Whereas the adsorption phenomena in the region 8 > ' I 2 are too complex to be described by simple models, in the the thermodynamic properties of the region 0 < 0 < 'Iz adsorbed phase can be studied by means of simple classical models, envisaging pairwise NN apd NNN interactions. 0 < 0 < lI2. The treatment of an assembly of interacting molecules adsorbed on a square lattice is a classical topic of statistical me~hanics.~It is well-known that, even in the simplest case of NN repulsion only, the related Ising problem cannot be solved exactly except for 0 = lI2, for which a solution has been given by Onsager.lo Coverages less than l I 2 may be treated either by approximate analytical methods (Bragg-Williams (hereafter BW) and QC approach4) or by Monte Carlo simulations.l1J2 These latter show that order-disorder transitions occur between a "lattice-gas" or "lattice-fluid" and an ordered 4 2 x 2 ) structure. The situation is much more complex if N" interaction is also considered; other order-disorder transitions occur,12 giving rise to complex phase diagrams for the adsorbed phase. For these reasons, we will discuss separately the situation at 0 = 0 (where all interactions among adsorbates are and the intermediate region. negligible), 0 = 1. Henry &@on (0 = 0). For 0 < 0.1, the molar heat of adsorption is constant at -83.2 kJ mol-', and Henry's law is followed. Under these circumstances, the molar entropy of adsorption coincides with that of a dilute ideal system, as is seen in Figure 4. This can be written as Sa(@ = Sale(O)- R In 0, where Sa@(0)is the standard molar entropy of the adsorbed phase at infinite dilution. This can be calculated from 2, which becomes Sa@(0)- R In 0 = Sg@- R In p / p e + qint/T + R from which Save(0) = R In h + q h t / T + R + Sg@ (3)
'12,
(9) Hill, T. L. Statistical Mechanics; New York, 1956; Chapter VII. (10) Onsager, L. Phys. Reo. 1941,65, 117. (11) Doyen, G.; Ertl, G.; Plancher, M. J. Chem. Phys. 1975,62,2957. ( 1 2 ) Binder, V.; Landau, D. P. Surf. Sci. 1976, 61, 577.
Thermodynamic Characterization of NO Adsorption
Langmuir, Vol. 5, No. 1, 1989 243
4
Figure 5. Configurational energy at 8 = 'Iz due to NN interactions as a function of the interaction parameter VI.Solid curve, exact solution; broken curve, QC model; dot-dash curve, BW model. Horizontal straight line, experimental value.
h being the constant in Henry's law. By insertion of the appropriate values into eq 3, we reckon Se~e(0) to be 14.3 J mol-' K-'. 2. 0 = 'I2. The molar energy of interaction among is computed from Figure 3a data to adsorbates at 0 = 'Iz be +8.4 kJ mol-' (3.3 in R T units) as the difference between -83.2 (initial molar heat) and -74.8 kJ mol-' (molar heat of adsorption a t 8 = 'I2). The question arises whether this repulsion energy has to be ascribed to NN and/or NNN interactions. In the following we will show that it entirely arises from repulsion from NNN adsorbed only, as the number of NN pairs is likely to be very small. Let us suppose for the moment that only nearest neighbors repel each other with an energy V,. In this case we take advantage of the fact that an exact formulagJO exists for the interaction (or configurational) energy at 0 = 'I2. Econ?I2/RT= -2KF(K) K = -V,/RT F(K) = 2 coth 2K[1 (2/7r)(2 tanh2 2K - l)Kl(kl)] (4) where K1 = Jg/2 1/(1- k,2 sin2 d a is the complete elliptic integral of the first kind and kl = 2 sinh !2K/cosh2 2K. The configurational energy at 0 = ' I 2in R T units is reported in Figure 5 as a function of Vl/RT. The quasi-chemical approach4yields for the configurational molar energy at any coverage 8 Econf = 2Vl[l - 2 ( 1 - o ) / ( l + P)1 (5)
+
+
P = [l - 400 - O ) ( l - 7)]'12; 7 = exp(-Vl/RT) which becomes at 0 =
'I2 = 2V171/2/1
+
(6) For comparison, this function is also reported in Figure 5. In both cases, because of the higher Vl, the lower the number of NN pairs, and a maximum is seen in the curves. This does not hold for the BW approximation, where the number of pairs of NN does not depend upon Vl. For further comparison, the configurational molar energy of interaction at 8 = ' I 2in this approximation (which simply equals Vl), is reported in Figure 5. As expected, the QC approach yields results lying between the BW and the exact method. This latter shows that the molar energy of repulsion at 8 = ' I 2cannot exceed =0.8RT, so that the measured value Q
~
/
~
has to be ascribed mainly to interaction between NNN admolecules. To have an estimate of V,, we observe that the Ni-Ni distance at the (100)face is 2.95 A,which is less than twice the van der Waals radius of NO. Repulsion between two parallel NN admoleculesshould rise primarily from direct electronic repulsion. In the 1iterature,l3J4it has been shown that CO on metals, when closely packed in a parallel array, exhibits an NN repulsion greater than predicted on the basis of the repulsive part of the Lennard-Jones (or similar) potential. Owing to the similarity of bonding between CO on metals and NO on NiO, it is feasible to extend this observation to our case and use the repulsion energy between two NO molecules as calculated from the LJ potential as a lower estimate of V,. Data concerning parameters entering the LJ potential q(r) = 4 ~ [ ( u / r ) ' ~( ~ / r ) ~ ] for NO are found in ref 15. From t = 131 K and u = 3.17 A, we compute that Vl is at least 3.8RT and probably considerably more. Figure 5 shows that negligible NN interaction takes place under these circumstances. This definitely means that a 42x2) structure is formed without any NN pair, whose molar energy of interaction at 0 = ' I 2is simply 1/2zV2,z = 4 being the coordination number of a site in the square lattice and V2 the repulsion between two NNN molecules. The result is V2 = 4.1 kJ mol-'. The distance between two NNN sites being 4.18 A, the direct electronic repulsion can be evaluated, by the same procedure as above, to be of the order of 0.15 kJ mol-', i.e., much less than what was observed. Another possible repulsion is that between the parallel dipoles of adsorbed NO. As for two NO molecules 4.18 8, apart, we reckon that the repulsion energy is 0.02 kJ mol-'. All this means that repulsion mostly arises because of other reasons. There is evidence that these are electronic effects transmitted by the solid. Because NO is an electron donor, adsorption from a NNN site to an occupied one is less facile, the involved Ni cation being richer in electronic charge. In spectroscopic terms, this fact is monitored by the presence of a substantial static shift lowering the NO stretching frequency, counterbalanced by the dynamic (dipolar) shift; a thorough discussion is given in ref 2. From Figure 4, it is seen that the molar entropy at 0 = ' I 2is 36.3 J mol-' K-l. The residual configurational entropy at 0 = ' I 2is R In 2, because two equivalent ~ ( 2 x 2 ) sublattices are possible. The standard entropy of the c(2x2) phase is thus 30.5 J mol-' K-'. This value is substantially higher than what is found for 0 = 0. An interpretation of this fact is given below. It has to be noted that, although the definition of the standard state is obviously different at 0 = 0 and 0 = 'I2,the two standard entropies are strictly comparable, as they only concern the internal degrees of freedom of NO. 3. Intermediate Region (0.1 < 8 < 0.5). Because formation of NN pairs does not occur, for the mere reason that NN repulsion is too strong, treatments envisaging the presence of both NN and NNN pairs like the Monte Carlo one given by Binder and Landau12or the analytical one given by Honig16are not appropriate. Instead, adsorption in this coverage region may be regarded as due to "large" admolecules actually inhibiting further adsorption on the four adjacent sites and weakly interacting with each other. The Monte Carlo treatment of such a system is in progress. (13) Tracy, J. C.; Palmer, P. W. J. Chern. Phys. 1969,51, 4852. (14) Ertl, G.; Koch, J. 2. Naturforsch. 1970, 25a, 1906. (15) Hirachfelder,0.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids;New York, 1954; p 1111. (16) Honig, J. M.Adu. Chern. 1961, 31, 239.
244 Langmuir, Vol. 5, No. 1, 1989
Garrone et al.
i
i 1
CO/ZrlO
If
50'
In order to apply approximate analytical methods, we consider here a rough description of the surface layer, which is obtained by considering the adsorption process as occurring only on the 42x2) lattice. Here, NN sites are the NNN sites of the original 1 X 1 lattice, whose interaction energy has been determined above to be 4.1 kJ mol-'. We may thus apply for the filling of the vacant sites of the 42x2) lattice the QC treatment given by Wang," paying obvious attention to the fact that the coverage on the 42x2) lattice extends up to unity. The molar energy of adsorption, computed by means of eq 5, is reported in Figure 3 as a function of coverage (broken curve). The agreement with the experiment is satisfactory. The question arises as to how large the approximation is involved in the QC approach. Again, this can be estimated only at 8 = l/z, for which the exact solution exists. From the plots in Figure 5, it is seen that at Vz = 4.1 kJ mol-' (1.62 in RT units) the QC value for the interaction energy is some 20% higher than value predicted by the Onsager formula; i.e., the approximation is still not exceedingly large and of the order of magnitude of the discrepancy between experimental and calculated values of the molar heat of adsorption (Figure 3a). The molar entropy of the QC model is not given exactly by Wang" or textbooks on statistical mechanics." The latter furnish, however, the excess (or configurational) energy (eq 5) and the free energy of the system. From these, one obtains for the molar entropy
+ sexQc + (1 - 8 ) In (1- e)] SsxQc = - R / ~ ( z / ~ ) ( V ~ / R T+AB + C) SQC" = Sida
Side
= -R/8[8 In 8
A = 28(l - 8 ) / ( l + 0) B = 8 In [ ( p - 1 + 28)(1 - e ) ] / [ ( p+ 1 - 28)e] C = In ( p + 1 - 28)/[(1 + p)(1 - e)]
P has been defined in eq 5. The calculated molar entropy of the adsorbed phase, according to the QC model, is reported in Figure 4. The disagreement with the experimental values is clear. Probable reasons for this are as follows. (i) Neglecting a substantial fraction of the possible sites affects the configurational entropy much more than the configurational (excess) energy. (ii) The standard entropy of the surface phase varies markedly along coverage (compare the values at 8 i= 0 and 8 = '/2). (iii) Order-disorder phenomena are known to take place in the system"J2 which are not taken into account by the QC treatment. In particular, if we apply the results by Binder and Landau12to our model of the adsorption as occurring only on the 42x2) lattice, with NN repulsion of 3.8 kJ mole1, (17) Fowler,R. H.; Guggenheim, E. A. Statistical Thermodynamics; Cambridge, 1960;p 41.
-100
/
0
-x) A.H/(kJrnol-')
Figure 6. Correlation between standard entropy of the adsorbed phase and standard enthalpy of adsorption.
an order-disorder transition is predicted at 8 = 0.35 from a lattice gas to a (2x2) structure (Scheme 111). It is thus tempting to ascribe the sudden change (ill-defined minimum) occurring at 8 = 2 X 0.20 in the molar entropy (Figure 4) to such a phenomenon. B > 0.5 Region. The characterization of the adsorption process in this region is poor. We were actually unable to study the whole of the process because high NO pressures are required. Under these circumstances, the volumetric evalution of uptakes becomes unaccurate. Measurements at low temperature are necessary to study this coverage region with accuracy. However, it is evident that the adsorption of NO on the residual half of Ni2+sites is characterized by definitely low adsorption enthalpies. The differential heat of adsorption (Figure 3) falls dramatically and reaches -60 kJ mol-', which we reckon to be representative for the enthalpy of such a process. Such a low value is largely due to the destabilization of the NO admolecules neighboring the newly adsorbed one (Scheme 11). Similarly, no definite inference can be drawn as far as the molar entropy is concerned (Figure 4). We just point out that, according to Scheme 11, the tilted NO molecules probably prevent the adsorption of further NO molecules onto the sites toward which tilting has occurred. Thus, the adsorption of one NO molecule on an empty site of the ~ ( 2 x 2lattice ) is equivalent to the adsorption of a large adparticle, occupying the nine sites of the lattice; the differential entropy for the latter kind of process has been calculated by Monte Carlo methods.18 Correlation between Standard Entropy of the Adsorbed Phase and Standard Heat of Adsorption. We have already pointed out that, in the two well-defined cases dealt with in the present paper (8 i= 0 and 8 = '/J, the higher the absolute value of the standard enthalpy of adsorption, the lower the standard entropy. To substantiate this observation, we may make use of similar data, previously published,' concerning CO adsorption in molecular form by a process close to that of NO bonding. This is done in Figure 6; the CO data correlate quite well with the present NO data. The straight line in Figure 6 is based on too few points to have a firm physical meaning. It seems, however, to indicate that -95 kJ mol-' is a limiting (18)Baker, B. G.J. Chem.Phys. 1966,45, 2694.
Langmuir 1989,5, 245-249 value for the enthalpy of adsorption of both CO and NO. A plausible explanation of the correlation observed is as follows. The standard entropy of adsorption is ascribable to the stretch of the cation-carbon (or cation-nitrogen) bond and to two bending modes of CO (or NO). The frequencies involved are usually (see, e.g., ref 19) assumed to parallel the strength of adsorption AaH. As a matter of fact, the Ni-N (or similar) motion can be represented by a Morse function, whose depth is the adsorption energy: hence the relationship between the cation-carbon (or nitrogen) stretching frequency and the strength of adsorption. As to the bending vibrations (deformations), there is little direct evidence. In a set of systems, however, not too far from that under study (namely H-bonded complexes of the type FH-B, where B is a base molecule), the libration modes of HF have been observed to parallel the strength of adsorption.20 The entropy associated with a harmonic vibration is a decreasing function of the frequency of vibrati~n.'~In conclusion, the greater the strength of adsorption, the smaller the entropy associated with the residual vibrations of the adsorbed molecules, as observed. (19) Tompkins, F. C. Chemisorption of Gases on Metals; London, 1978; p 131. (20) Andrews, L. J. J. Phys. Chem. 1984, 88, 2940.
245
Conclusions Whereas the region 0 > 0.5 requires ad hoc measurementa for a satisfactory thermodynamic characterization, the data concerning the region 0 < 0 I 0.5 allow a number of conclusions to be drawn on the basis of simple pairwise models. The repulsion between NN admoleculesis too strong to allow the formation of NN pairs: this is in line with the experimental finding that adsorption on adjacent sites takes place (nearly) after the completion of the 42x2) structure and implies tilting of the surrounding admolecules. The decline in the molar enthalpy of adsorption is thus ascribable to NNN repulsions, the extent of which may be evaluated from the value at 0 = 0.5. Considering the adsorption as only occurring on the 42x2) lattice, one can apply the Wang model (QC approach). The decline in the heat of adsorption is satisfactorily accounted for, in sharp contrast with the entropy of adsorption. The standard entropy of adsorption increases, passing from 0 = 0 to 0 = 0.5; this is in line with an already reported correlation between standard entropy and molar enthalpy of adsorption. Registry No. NiO, 1313-99-1; NO, 10102-43-9.
Salt Effects in Free Nonionic Films Boomgaard, Th. van den and J. Lyklema* Wageningen Agricultural University, Department of Physical and Colloid Chemistry, P.O.Box 8038, 6700 EK Wageningen, The Netherlands Received June 17, 1988. In Final Form: October 14, 1988 The thickness has been measured of macroscopic aqueous films, stabilized by nonionic surfactants consisting of a hydrophobic part and a poly(ethy1ene oxide) moiety. Special attention has been paid to the influence of electrolytes. In the fiis, the surfactants behave like coiled polymers. Addition of electrolytes increases the rate of drainage. As a function of the electrolyte concentration, the equilibrium thickness passes through a maximum. These maxima are similar to those for the Huggins constant for the corresponding micelles. The interaction between electrolytes and nonionic surfactants continues to be topical, and there are several reasons for this interest. The widespread use of poly(oxyethylene) as a polymer and as the hydrophilic moiety in the most important class of nonionic surfactants is one of these reasons. Salt effects are particularly relevant when the chemicals named act as stabilizers for colloids. More to the basic side, the mode of interaction of ions with the oxyethylene group, and perhaps with other parts of the molecule, poses a number of interesting problems. The purpose of the present paper is to contribute to the insight into this matter by studying the influence of some electrolytes on the thickness of free aqueous films, stabilized by nonionics. More particularly, the surfactant Synperonic NPE-1800 will be emphasized. Although this substance is a commercial product and not homodisperse, its solution' and adsorption properties2have been studied in some detail,3 Present address: Department of Chemical Engineering, University of Twente, The Netherlands.
Table I. Surfactants Used systematic name C'8hP(13)E(26) C9PhP(13)E(60) C9PhP(13)E(85)
C9PhP(13)E(26) C 9 P W 10)
CBPhE( 15) C9PhE,ZO)
commercial code NPE-1800 NPE-A NPE-B NPE-C NP-10 NP-15 NP-20
M, x 10-3 2.15 0.02 3.15 f 0.02 4.73 f 0.03 9.33 0.07 0.66 0.01 0.88 f 0.01 1.10 f 0.01
* * *
so they are well characterized. Comparison of the film results with those of the previus work is helpful to clarify and analyze trends. With regard to the electrolyte concentration, a large range of concentrations will be studied. One of the main motivations is that the Huggins constant of NPE-1800 micelles passes through a maximum as (l).Boomgaard, Th. van den; Zourab, Sh. M.; Lyklema, J. Progr. Colloid Polym. Sei. 1983, 68, 25. (2) Boomgaard, Th. van den; Tadros, Th. F.; Lyklema, J. J. Colloid Interface Sd. 1987, 116,8. (3) Boomgaard, A. van den, Ph.D. Thesis, Wageningen Agricultural University, 1985.
0743-7463/89/2405-0245$01.50/00 1989 American Chemical Society
