Langmuir 2005, 21, 10481-10486
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Adsorption Structures on MetalssA Thermodynamic Description Andrzej Stokłosa,* Stefan S. Kurek, and Barbara J. Laskowska Cracow University of Technology, Institute of Chemical Engineering and Processing, ul. Warszawska 24, 31-155 Krako´ w, Poland Received May 27, 2005. In Final Form: August 17, 2005
Thermodynamic conditions of the adsorption of gaseous molecules on metals are discussed in this work. The equilibria of the formation of surface arrays comprising several atoms, the formation of ordered structures, and the dissolution of gas atoms in the metal have been reviewed. It was found that the heat and the free energy of chemisorption is affected by the change in the number and energy of bonds between metal atoms and the adsorbate in the structures being formed. It was pointed out that the change in the interactions between the surface metal atoms before and after the adsorption must be followed by an energetic effect that would affect the chemisorption energy.
Introduction The development of modern surface research techniques in the last half-century widely discussed in a number of textbooks and monographs1-3 allowed the composition and the symmetry of many chemisorbed species formed on the surface of single crystals to be determined.2,3 Desorption studies, particularly those made with the application of modern techniques, revealed the existence of many structures, often of very different heats of adsorption, hence, the binding energy. They are often interpreted assuming the occurrence of different structures of adsorbed species of close lying energies. The initial results showed that the equilibrium constant of chemisorption and the heat of chemisorption depend on the surface coverage, which is incorporated in the Freundlich (θ ) kp1/m) and Temkin (θ ) A ln Kp) equations.1 They both predict a dependence of the energy of chemisorption on the surface coverage, the Freundlich model, an exponential, and the Temkin, a linear one, contrary to the Langmuir adsorption equation that was derived with the assumption of a constant energy of adsorption, independent of the surface coverage. Frumkin-type adsorption, often encountered in electrochemical systems, is based on the Langmuir equation modified by taking into account lateral interactions between adsorbed species similarly to the Temkin equation and thus characterized also by a linear dependence of the energy on the surface coverage. The application of statistical thermodynamics for the description of adsorption isotherms allowed the character of the used equations to be rationalized. The obtained equations fit well the experimental data.4-7 Nonetheless, relatively * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Tompkins, F. C. Chemisorption of Gases on Metals; Academic Press: London, 1978. (2) Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; John Wiley: New York, 1994. (3) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surface; John Wiley: New York, 1997. (4) Ward, C. A.; Findlay, R. D. J. Chem. Phys. 1982, 76, 5599, 5615, 5624. (5) Nagai, K. Surf. Sci. 1988, 203, L659; 1991, 244, L147. (6) Kreuzer, H. J.; Pagne, S. H. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surface; Rudzin´ski, W., Steele, W. A., Zgrablich, G., Eds.; Elsevier: Amsterdam, 1997.
simple models of the adsorption phase (with a stationary, mobile layer etc.) differ from the reality. Because the determination of the pressure of nitrogen, oxygen, or hydrogen, when studying simultaneously the chemisorption structures, is difficult, there is a lack of the description of “phase systems”, which determine the conditions of their existence. Despite the presence of much information on the composition and the structure of adsorption forms, there is no thermodynamic description of these states known yet, for the description based on the Langmuir theory or the accepted description by Hill8 is not satisfactory. This work presents a thermodynamic description of various probable adsorption states on the metal surface and discusses equilibria between them for the example of simple systems, in which dissociative chemisorption occurs. Surface Arrays At low coverages, it is assumed that there is no interaction between the adsorbate atoms. Generally, with increasing coverage, the repulsive interaction is considered to appear. The formation of ordered structures, likewise the formation of a crystalline structure, results from an optimization of interactions not only between the adsorbate atoms but also between the adsorbent atoms. If the surface phase is treated as a surface solution, then, consequently, the formation of surface arrays should be considered, in which interaction between several adsorbate atoms X and surface metal atoms would occur. Hence, at particular ranges of coverage, some defined types of surface arrays, consisting of several atoms, should dominate. For instance, let us consider processes of the dissociative adsorption of molecules X2 and the formation of arrays formed on the (100) surface of a regular crystal, MaXb. The simplest surface array would consist of an atom X placed in a surface void, interacting with four metal atoms. Such a structure is generally accepted as a chemisorption form of atoms X. The process of the formation of such a (7) Panczyk, T.; Rudzin´ski, W. J. Phys. Chem. B 2004, 108, 2898. (8) Hill, L. Adv. Catal. 1952, 4, 211.
10.1021/la051402t CCC: $30.25 © 2005 American Chemical Society Published on Web 09/30/2005
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surface array is described by the equation
4M(surf) + 1/2X2 ) M4X(surf) ∆G1° ) -RT ln[M4X(surf)]/[M(surf)]4pX21/2 (1) If two atoms X interact, a surface array M7X2 would be formed, and the equation describing the equilibria between the discussed surface arrays would assume the following form:
∆G2° ) -RT ln[M7X2(surf)]4/[M4X(surf)]7pX21/2 (2) More complex structures can also be formed, the interaction of, for instance, four atoms, would yield the surface array M9X4
9M7X2(surf) + 5X2 ) 7M9X4(surf) ∆G3° ) -RT ln[M9X4(surf)]7/[M7X2(surf)]9pX25 (3) At a low surface coverage, it can be assumed that statistically distributed surface arrays M4X exist. An increase in the pressure will cause an increase in the concentration of these surface arrays, but, as can be seen from eqs 2 and 3, the increase in the concentration of more complex compounds would occur. In these surface arrays, the number of metal atoms per one X atom decreases, but since we assume that these surface arrays do not interact among themselves, we have to exclude a significant number of metal atoms that do not interact with atom X (atoms in the nearest neighborhood of the surface arrays, the second coordination sphere). Thus, it can be seen that at a low increase in the surface coverage, the number of unoccupied metal atoms (including their nearest neighborhood), or the number of potential adsorption centers, which consist of several atoms (M4, M7, and M9), rapidly decreases. A complete description of adsorption states consisting of several types of defect surface arrays being in equilibrium is possible, but would be quite complex. The problem is how to define the activity of individual surface arrays and the “concentration” of unoccupied metallic centers. Gibbs Energy of Chemisorption. The description of a chemisorption system as a two-dimensional binary solution can be verified by the analysis of experimental data by means of eqs 1-3. In such cases in defined ranges of pX2, the successive types of the surface arrays will dominate one after the other. Since the surface arrays have different structures, their standard Gibbs energies of formation will also be different. Let us discuss the formation of a surface array of the general formula MaXb, which would be the dominating surface array under certain given conditions
(4)
The above equation shows that on the surface formed by a large number of metal atoms, as a result of the reaction, comes to the generation of a bond between a metal atoms and b X atoms. The equilibrium state of such a system is defined by the equality of chemical potentials of its components
aµMsurf + (b/2)µX2 ) µMaXb
aµ°M + aRT ln aM + (b/2)µ°X2 + (b/2)RT ln pX2 ) µ°MaXb + RT ln aMaXb (6) A rearrangement yields (assuming that aM corresponds to 1 - θ, and aMaXb to θ/a)
7M4X(surf) + 1/2X2 ) 4M7X2(surf)
aMsurf + b/2X2 ) MaXb(surf)
concentration of adsorbed atoms will cause a decrease in the number of available adsorption sites, the chemical potential of atoms that do not interact and atoms bonded to atoms X will be a function of their activities (aM and aMaXb)
(5)
As can be seen, it will depend on the chemical potential of molecules X2 in the gas phase. Since the increase in the
-(µ°MaXb - aµ°M - (b/2)µ°X2) ) -∆G°ch ) RT ln(aMaXb/aaM pXb/22 ) ) RT ln(θ/(a(1 - θ)a)pXb/22 ) (7) If the standard chemical potential of the species MaXb is taken as a sum of the standard chemical potentials of the components, eq 7 will take the form
aµ°M′ + bµ°X′ - aµ°M - (b/2)µ°X2 ) ∆G°ch
(8)
where µ°M′ and µ°X′ denote chemical potential of the interacting atoms of metal M and atoms X, respectively. If, as a result of adsorption, the chemical potentials of metal atoms do not change (µ°M′ = µ°M), then the adsorption state will depend only on the chemical potential of atoms X on the surface, and in such a case, eq 7 assumes the form of the classical Langmuir equation.8 Chemisorption brings a change in the interaction of metal atoms with their neighbors; therefore, the value of the standard Gibbs energy of chemisorption (∆G°ch) would be affected by the value of ∆µ°M′, which defines the difference between the chemical potential of the metal before and after the chemisorption of the atom X. The above fact requires a certain definition of the chemisorption bond. If the energy of the bonding M-Xsurf is defined as the energy of the interaction of a metal atom with atom X, then it will be equal to the heat of the process
MXsurf ) M/surf + X(g) ∆G°(surf) bond MX
(9)
(surf) , which at 0 K will be equal the energy of bonding EbondMX (surf) and at higher temperatures will be equal ∆G°bondMX. In turn, the atom M/surf returning to the preadsorption state releases the energy
M/surf ) Msurf
∆G°M* ) µ°M - µ°M′ ) ∆µ°M′
(10)
which will be equal to the difference between the chemical potentials of metal atoms before and after adsorption. The energy of a chemisorptive bond determined from the heat of adsorption is therefore lower by the difference between the chemical potentials of metal atoms before and after the adsorption. As the surface coverage increases, the relative concentration of individual surface arrays with different values of ∆G°ch varies. The resultant value of ∆G°ch, will vary depending on the surface coverage (the heat of adsorption will vary). Statistically distributed surface arrays form an unordered structure, which with increasing surface coverage will be transformed into an ordered structure. Ordered Structures The formation of an ordered structure can be described with an equation analogous to eq 4, but there is a fundamental difference between these two states. In the
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case of an unordered state (“a surface solution”) there is no interaction between atoms X (or we assume it to be negligible). Atoms X are distributed on the surface in such a way that these interactions do not occur. The occurrence of an ordered structure is a result of the optimization of the interaction energy, both between metal atoms following the approach of an atom X as well as the optimization of the interaction between the latter. In many chemisorption structures, it comes to a change in the position, hence, in the symmetry of the surface metal atoms, which is linked to a significant change in the interaction energy between metal atoms.1-3 A number of ordered structures can be sequentially formed with the increase in the pressure of X2, similarly as following the increase in the pressure of the oxidant, the successive oxides of the same metal (M2O, MO, M3O4 etc.) are formed. Figure 1 presents an example of one of the simpler ordered structure sequences being formed on the (100) face of a regular crystal, in which the atoms are placed in surface voids between the metal atoms. In the first structure, M16X, the distance between atoms is nearly equal to four lattice parameters and in the M4X structure to two lattice parameters, at only half potentially available occupied sites. In the M2X structure, every second void is occupied, and in the MX structure, all the voids are occupied. It is worth noting that in the case of M16X, the coverage is equal 0.0625, whereas for M4X it is raised to 0.25 and between the M4X units there are no free metal atoms; hence, it can hardly be treated as an ideal binary solution. The formation of the structures presented in Figure 1 can be described by the following equations:
32M(surf) + X2 ) 2M16X(surf) ∆G°11 ) RT ln pX2
(11)
2
/3M16X(surf) + X2 ) 8/3M4X(surf) ∆G°12 ) RT ln pX2 (12)
2M4X(surf) + X2 ) 4M2X(surf) ∆G°13 ) RT ln pX2 (13) 2M2X(surf) + X2 ) 4MX(surf) ∆G°14 ) RT ln pX2
(14)
As can be seen, each structure is characterized by limiting pressures, pX2, the lower one, above which the structure is formed, and the upper one, above which it is converted into a phase, in which the ratio of X/M is higher. In real systems, particularly on low symmetry planes and at higher coverages, a number of types of various ordered structures will occur, depending on the plane and the metal type. Analogous sequences of ordered structures to those presented in Figure 1, but also of many other types, will be formed on each plane of any (hkl) indices. In many systems, the ordering of X atoms along surface rows of metal atoms was found (e.g., the structures of adsorbed hydrogen in (100) plane of nickel: c(2 × 6)H, (2 × 1)H, in which case peaks on desorption curves were ascribed to individual structures9 etc.). The individual structures will have different energy of interaction between atoms. At the maximum coverage, structures with atom order, composition and binding energy close to those that occur in monolayers of the metal oxidation product should be formed. The maximum equilibrium pressure for chemisorption should not be therefore higher than the metal/ oxidation product equilibrium pressure. These pressures (9) Weinberg, W. H. In Workshop on Interface Phenomena, Springer Series in Surface Science; Grunze, M., Kreuzer, H. J., Eds.; SpringerVerlag: Berlin, 1987; Vol. 8.
Figure 1. Sequence of structures being formed on the (100) plane of the regular lattice: (a) M16X structure, (b) M4X, (c) M2X, and (d) MX.
for systems like, e.g., M-O, are very low. Higher equilibrium pressures occur in the case of metal-hydrogen systems. Similarly to binary compounds that generally show deviation from stoichiometry,9-12 in the case of surface compounds, a significant deviation from the composition of a given structure may be expected, particularly at pressures close to the pressure above which its transition occurs. In the case of compounds exhibiting significant deviation from stoichiometry (e.g., CeO2-x, NbO2-x, etc.13), the change in the composition in the range of the existence of a given phase is described by the change in the chemical potential of the oxidizer, which is defined as the change in the standard Gibbs energy of the oxidizer and is proportional to the deviation from stoichiometry (δ)13
µ′′X - µ′X2 ) ∆G°X2 ) RT ln pX2 ∝ nRT ln δ
(15)
where n is a coefficient depending on the type of point defects that dominate in the given range of the oxidizer pressure. In a number of oxide systems, the formation of so-called homologue-compounds, MnO2n-m, etc., was found (Ti-O, V-O, Nb-O, Mo-O, etc.12). They are formed by the elimination or by ordering of the point defects.14 Therefore, it seems that in the case of two-dimensional surface “compounds” the structures being formed should be all the more considered as nonstoichiometric compounds or a series of compounds of the homologue type. The composition and sequence of surface “compounds” will depend on the symmetry of atoms in a given plane (they will be different for different planes). The possibility of the formation of metastable structures, or of low degree (10) Kro¨ger, F. A. The Chemistry of Imperfect Crystal; NorthHolland: Amsterdam, 1974. (11) Kofstad, P. Nonstoichiometry, Diffusion and electrical Conductivity in Binary Metal Oxides; John Wiley: New York, 1972. (12) Rao, C. N. R.; Raveau, B. Transition Metal Oxides; VCH: Weinheim,, 1995. (13) Sørensen, O. T. In Nonstoichiometric Oxides; Sørensen, O. T., Ed.; Academic Press: New York, 1981. (14) Anderson, J. S. In Defects in Oxides NBS Special Publ., No 364, 1972.
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of order that occur in “amorphous” states, is also plausible. At the surface of polycrystalline samples, a quasicontinuous change in the composition of the surface “phase” can practically be considered. The above concept is essentially applied generally, since it follows from the studies of chemisorptive phases that ordered adsorbed atom areas exist predominantly on the surface. In a number of studies, the formation of “islands” of various sizes was found. These islands can be treated formally as growing structures. The coexistence of two different structures being in equilibrium or their conversion in an nonequilibrium state was also observed.15 The assumption of the above concept beyond the range of small surface coverages allows adsorption states to be described by equations of type (11-14) and the composition variations within the phase/structure can be expressed by equations of type (15). The sequence of equations of type (11-14) defines the range of existence of individual phases/ structures on the given plane (hkl) at a given temperature. Hence for adsorption states, systems should exist for which a dependence of log pX2 versus 1/T could be determined, analogous to those we use for oxides and sulfides etc. (Richardson-Jeffe systems). The above problems in solids are discussed more extensively in the work.16 The existence of a limiting pressure pX2 for a given structure depends on ∆G°i for the type (11-14) reactions. The standard Gibbs energy for the structures described by equations (11-14) is a difference between the Gibbs energy of the bonding of a surface metal atom with an adsorbed atom X that form that structure (∆G°bondM16X), and the energy of dissociation of molecules X2 (∆G°disX2) and the Gibbs energy of the change in interactions between the metal atoms before and after the adsorption (the change in the chemical potential of the metal), expressed by the term ∆G°M*
∆G°1 ) -(2 ∆G°band.M16X - ∆G°disX2 - 32∆G°M*)
(16)
The values of ∆G°i for subsequent structures, in turn, are associated with the change in the energy of bonds in these structures, which results from the increase in the number of atoms X, the Gibbs energy of the dissociation of X2 molecules, and the change in the chemical potential of surface metal atoms in these structures
∆G°2 ) -(8/3∆G°band.M4X - 2/3∆G°bondM16X - ∆G°dis.X2 32/3∆G°M*) (17) where ∆G°bondM4X denotes the standard Gibbs energy of the bond in the structure M4X and ∆G°bondM16X denotes the standard Gibbs energy of the structure that underwent the transition. The structure M16X at the moment of the transition would consist of more atoms X per 16 metal atoms. This structure would differ from the initially formed structure by the value of δ that could be called the deviation from the “stoichiometric” composition, M16X1+δ. Together with the change in the bonding energy in individual structures, mainly with the change in the number of bonds M-X (the number of interacting atoms), the value of the term ∆G°M* will change, which results from the change in interactions between metal atoms in these structures. The changes in interactions between atoms and the changes (15) Ertl, G. In Chemistry and Physics of Solid Surface VIII; Vanselow, R., Howe, R., Eds.; Springer-Verlag: Berlin, 1990. (16) Stokłosa, A.; Wzorek, B. High. Temp. Mater. Process. 2004, 23, 103, 113.
Figure 2. Dependence of cohesion (bonding) enthalpy of Ma/bO (MaOb ≡ Ma/bO) of various metals (per one oxygen atom) depending on the composition. The values were calculated with eq 18 from thermodynamic data.18
in their positions lead to its reconstruction and must be followed by the mentioned energetic effects. The exoergic effects, associated with the change in the number and the energy of bonds, are accompanied by the endoergic effects of the weakening of the bonds between the surface metal atoms and the metal atoms in their neighborhood (the first and the second coordination spheres). In effect, the negative values of ∆G°i of the formation of subsequent structures are less and negative, which results in the quite significant lowering of the measured isosteric heat of adsorption with increasing surface coverage. This fact cannot be rationalized by the change in the activity of the “reactants” in the Langmuir equation. The approximately linear change in the heat of adsorption with increasing surface coverage in the Temkin equation does not contradict the above concept. In the case of polycrystalline samples, the formation of a great number of twodimensional surface compounds, little different energetically, on many planes of different (hkl) indices, with increasing X2 pressure, must be followed (in the first approximation) by the mentioned linear or logarithmic (as in Freundlich equation) change in the heat of adsorption. Lowering of the heat of adsorption as a result of the formation of ordered structures was found by Ertl and co-workers17 for the adsorption of CO on palladium. Despite the fact that many ordered structures have been described,2 the corresponding heats of adsorption have not been determined. To confirm the hypothesis outlined in the previous paragraph, Figure 2 presents the change in the cohesion enthalpy (atomization enthalpy) for a number of oxides of the same metal. They are calculated per one oxygen atom depending on the composition (metal “deficit”) expressed in moles per mole oxygen atoms. This value is close to the surface coverage we use for expressing (17) Conrad, H.; Ertl, G.; Koch, J.; Latta, E. E. Surf. Sci. 1974, 43, 462.
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the extension of adsorption. The atomization enthalpy was based on thermodynamic data18 at 298 K and calculated with the following equation:
∆H°coh.MnO ) ∆fH°MnO - 1/2∆H°dis.O2 - n∆H°subM
(18)
where ∆H°coh.MnO, ∆fH°MnO, ∆H°disO2, and ∆H°subM denote cohesion (bonding) enthalpies in a given oxide (MaOb ≡ Ma/bOdMnO), the formation enthalpy of the oxide, oxygen dissociation, and the enthalpy of sublimation of the metal, respectively.18 As can be seen from Figure 2, the values of the enthalpy of cohesion as a function of the composition of the oxide are approximately fitted by a curve not very different from a straight line for the presented systems. The Gibbs energies of the formation of MnO2n-m phases lie practically on a straight line for the systems Ti-O and V-O. It should be emphasized that also in the oxides, the space filling, the symmetry, and hence the coordination number, consequently the number of bonds between the metal and oxygen, change significantly. Notwithstanding the significant differences in the properties of the oxides, the values of the cohesion enthalpies against the composition yield a function not much different from linear. It can be expected that likewise, in the case of chemisorptive structures, the changes in their “resultant” bonding energies would exhibit a similar character, which is confirmed by the change in the isosteric heat of adsorption. Solubility of Atoms X in Metal, Formation of Interstitial Phases The attainment of an equilibrium state at the metal surface, particularly at higher temperatures, suggests a possibility of the dissolution of the gas in the metal and the attainment of appropriate equilibrium states in the bulk of the metal, or, more often, a metastable equilibrium in the subsurface layer (principally at lower temperatures). This process is called gas incorporation. The simultaneous occurring of hydrogen chemisorption and the dissolution in palladium were indicated in the studies of Godowski et al.19 and other authors.20,21 In a number of works, it was postulated that nitrogen or carbon atoms, formed as a result of carbon oxides dissociation or the decomposition of organic compounds upon catalytic processes, enter the subsurface layer of metals. The dissolution of hydrogen or the formation of hydrides on Pd, Ti, Zr, etc. was also observed.20-22 In such cases, it is postulated that a so-called sublayer is formed upon slow diffusion or electrochemical evolution of X atoms, particularly at low temperatures. In such systems, we deal with the relatively low solubility of gas atoms.23 Advantageous steric conditions (the size of crystallographic voids and radii of diffusing atoms) promote the dissolution of atoms X in the metal. If metallic clusters are small (e.g., on a carrier) and the temperature is elevated, then we can expect that the equilibrium between the surface (18) Pankratz, L. B. Thermodynamic Properties of Elements and Oxides, United States Bureau of Mines, Bulletin 672, Washington 1982. (19) Godowski, E.; Stalen, R. H.; Felter, T. E. J. Vac. Sci. Technol. 1987, A5, 1103. (20) Schlapbach, L. In Hydrogen in Intermetallic Compounds II; Schlapbach, L., Ed.; Springer-Verlag: Berlin, 1992; Topics in Applied Physics, Vol. 67. (21) Lewis, F. A.; Aladjem, A.; Eds. Hydrogen Metal Systems I and II, (Solid State Phenomena; Scitec Publ., Balaban Publ.: 2000; Vols. 49, 50, and 73-75. (22) Conway, B. E.; Tilak, B. V. Electrochim. Acta 2002, 47, 3571. (23) Smithells Materials Reference Book; Gale, W. F., Totemeier, T. C., Eds.; Elsevier: Amsterdam, 2004.
and the metallic phase would be attained
MX(surf) ) M(Xsol)
∆G°MX/X(sol)
(19)
where M(Xsol) denotes atom X dissolved in the metal and X(surf) is a chemisorbed atom on the surface. The sum of the chemisorption and reaction 19 describes the equilibrium state between the dissolved atoms X and the pressure pX2. The standard Gibbs energy of dissolution of X atoms is therefore equal to the sum of the Gibbs energy of adsorption and the dissolution of X atoms. The surface process in such a case becomes more complicated, due to the differences in the rates of the chemisorption and dissolution processes, the equilibrium state is attained in the subsurface layer and the dissolution occurs at the rate characteristic of the given system and the T, p conditions. Hence, atoms X are consumed continuously. The following equation describes the formation of an interstitial phase and the equilibrium state of such a system
n/mM + X2 ) 2/mMnXm
∆G°MmXn ) RT ln pX2 (20)
As can be seen, a pressure higher than the defined equilibrium pressure is needed for the interstitial phase to be formed. Hence, at pressures higher than the equilibrium pressure, the thickness of the interstitial phase will grow and the rate of this process will depend on the rate of diffusion of X atoms in the product MnXm, which will occur at the activity gradient of X at the phase boundaries M/MnXm′ and MnXm′′/pX2 (MnXm′ and MnXm′′ indicate a plausible existence of two different structures at these two boundaries). In effect, the surface process at the given pressure of X2 will be associated with quite a fast chemisorption process and a slow process of a continuous growing of the layer of MnXm, which depends on the difference between the equilibrium pressure and the pressure at the surface. The interstitial layers would grow at pressures higher than those defined for the maximum surface coverage. The measured energetic effect of the adsorption/sorption process will generally vary during the experiment. Summary The thermodynamic analysis of chemisorption carried out allows the following conclusions to be drawn: 1. The coexistence of defined forms of adsorbed atoms, with rising surface coverage, depends on the equilibria being attained, the equilibria between the chemically adsorbed atoms and surface “arrays” comprising several metal and X atoms. The formation of a given ordered structure occurs after a defined pressure of X2 molecules has been exceeded. The limiting ordered structure is a monolayer phase of a structure close to the structure and composition of a compound being formed as a result of the oxidation of the given metal. The maximum pressure of X2 molecules in such cases cannot exceed the equilibrium pressure of the system metal/solid oxidation product. 2. If the chemisorption is accompanied by dissolution of gas atoms in the metal or its subsurface layer and/or the formation of interstitial phases, then, in such a case, the equilibrium pressure of gaseous molecules X2 may be higher than the pressure corresponding to the maximum adsorption. 3. The changes in the relative concentrations of individual surface arrays with increasing pressure of X2 cause
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a continuous variation in the heat of chemisorption, and, precisely, the standard Gibbs energy of adsorption. The appearance of an ordered “phase” causes a sudden, jump change in the heat of adsorption. With rising surface coverage, the standard Gibbs energy values of the formation of individual structures will form a monotonically rising, approximately linear curve. 4. The standard Gibbs energy of the dissociative chemisorption, depends on the bonding energy of the
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chemisorptive bonding being formed and on the Gibbs energy of the dissociation of X2 molecules, and on the change in the chemical potential of the surface atoms before and after the chemisorption. Acknowledgment. The authors thank Prof. Jerzy Haber and Prof. Barbara Grzybowska-SÄ wierkosz for helpful discussions. LA051402T
