2.3 Influence of water at interfaces
2.3.1 Physisorption and chemisorption
The formation of water layers on ceramic oxide surfaces depends on the temperature, as well as on the surface properties. Heating results in desorption, while cooling results in adsorp-tion of water from the humid atmosphere. In case the adsorbent is bound to the surface via Van-der-Waals interaction, this type of bonding is referred to as physisorption (acronym for
“physical adsorption”). The physisorption enthalpy typically is in the range of the conden-sation enthalpy of the adsorbent, as the forces involved in the physisorption process are the same than those responsible for the condensation of vapor. Deviations can occur depending on the substrate chemistry and surface structure. An adsorbent that impinges on the surface can transfer the physisorption energy stepwise to the substrate, transforming the energy into heat which is dissipated by the substrate lattice. The adsorbent molecule typically remains intact during this process which is called accommodation.106 Typical adsorption enthalpies are in the range of 20−90 kJ/mol.107
In contrast to physisorption the so called chemisorption on cooling the substrate already happens at rather high temperatures (roughly about300°C), as the chemisorption enthalpy is typically in the order of 100−200 kJ/mol. In this case the adsorbent forms a chemical (typically covalent) bond to the substrate. Thus, the chemisorption enthalpy is of the same order of magnitude as the respective chemical reaction. The adsorbing molecule (adsorp-tive) can be destroyed during this process. The discrimination between physisorption and chemisorption only by means of the enthalpies is rather imprecise. In order to describe the nature of the adsorption process spectroscopic methods can be used.106,107
The gas in the atmosphere is in a dynamic equilibrium with the adsorbent on the surface.
Therefore, the surface coverage Θ depends on the partial pressure of the adsorptive in the gas phase. This dependence is described by so called adsorption isotherms. These isotherms are models for the adsorption behavior taking the temperature, the partial pressure, and approximations concerning the interaction of the gas molecules and the substrate character-istics into account.
One of the first models describing the adsorption process was developed by Irving Langmuir in 1916.108Langmuir studied chemical reactions at low pressures and electron emission when he became interested in the phenomenon of adsorption and developed a theory that had been verified by a large number of experiments since then.109 Directly influenced from Bragg’s work on crystal structures, Langmuir derived that chemically unsaturated atoms at the sur-face of a solid exist.110 Gas atoms impinging the surface, condense driven by the force to saturate these surface atoms. The kinetics of this process is described by the rate constant of adsorption k
ad. Once condensed, the molecules or atoms subsequently evaporate from the surface, described by the rate constant of desorption kdes.
Langmuir described the dependence of the surface coverage Θ of an adsorbed gasA on the pressure above the surface at a given temperature108:
A(g)+ Msurf AMsurf. (21) HereMis a vacant surface site. Given that the coverage of the surface is proportional to the partial pressurepofAand to the number of vacant sites, which can be written asN(1− Θ), with N being the number of all binding sites available on the uncovered surface, the change of coverage during adsorption with time is given by:
dΘ dt =k
adp N(1− Θ) (22)
The desorption is described by:
dΘ dt =−k
desN Θ (23)
Given that K =
kad
kdes
when an equilibrium is reached. The Langmuir isotherm can be derived from (22) and (23).
Θ = K p
1 +K p withK = kad
kdes
=K
0exp
∆adH RT
(24) Figure 2.8 shows Langmuir isotherm plots for different values of K. The coverage increases with increasing pressure. As K is temperature dependent, fitting Langmuir isotherms mea-sured at different temperatures by variation of K, the isosteric adsorption enthalpy can be determined from the van’t-Hoff-equation. Langmuir made three assumptions deriving his model. The first is that adsorption only leads to one single monolayer of adsorptive on the adsorbent. Further a ideally flat and homogeneous surface is assumed. All binding sites are equal. The final assumption of the Langmuir model is that the occupation of a neighboring binding site does not influence the ability for adsorption of an adsorptive molecule. Despite
Figure 2.8: Langmuir isotherms for different values of K. The largerK becomes, due to an decrease in temperature, or a higher enthalpy of adsorption, the lower the partial pressure p at which the coverageΘ gets unity, as described by equation (24).
these assumptions, the Langmuir isotherm typically describes chemisorption processes very well. A typical example for a adsorption process that can be described with the Langmuir isotherm is thus the adsorption of chemically active gases on metal surfaces.
For adsorption of water on metal oxide surfaces one typically observes adsorption of more than one monolayer. For these cases where the heat of adsorption becomes a function of the coverage and multilayer adsorption occurs, other isotherms were derived for the modeling of these processes. The so called BET isotherm, named after Brunauer, Emmett and Teller, who published this in 1938, is basically a generalization of the Langmuir isotherm to multi molecular adsorption.111 Assuming that at equilibrium the rate of condensation at a given pressure pon an bare surface areas0 must remain constant, the condensation rate and the evaporation rate are equal, which is basically described by the Langmuir equation as well.
kad,1ps
0 =k
des,1s
1exp
−∆adH
1/RT (25)
The heat of adsorption of the first layer with the surface areas0 is given by∆adH
1. kad,1 and kdes,1 are the rate constants of adsorption and desorption of the first layer and independent of the coverage in this layer.
The next layer s1 is also assumed to stay constant under given equilibrium conditions.
Four different processes need to be taken into account. Condensation on the bare sur-face (k
ad,1ps
0), condensation of a second on the first layer (k
ad,2ps
1), and evaporation from the second (kdes,2s2e−∆adH2), as well as first (kdes,1s1e−∆adH1) layer. One obtains:
kad,2ps
1+k
des,1s
1e−∆adH1/RT =k
des,2s
2e−∆adH2/RT +k
ad,1ps
0 (26)
Comparing (25) with (26) one obtains that the rate of condensation on the top of the first layer is equal to the evaporation rate from the second layer.
a2ps
1 =b
2s
2e−∆adH2/RT. (27)
This holds true for all consecutive layers i
aipsi−1 =bisie−∆adHi/RT. (28) Brunauer, Emmett and Teller assume in their model, that the enthalpy of adsorption ∆adHi for i >1is equal for all layers, except the first one, and equal to the heat of liquification of the adsorptive:
∆adHi = ∆liqH =−∆vH. (29) They also assumed that the adsorption and desorption rate constants for the second and higher layers have a constant ratio g
kad,i
kdes,i =g . (30)
With Θ =
V Vm
, where V is the total volume of gas adsorbed and V
m the volume of gas adsorbed, when the adsorbent is covered with one layer of adsorptive molecules, Brunauer, Emmett and Teller derived their isotherm equation by summation over all layers i and the surface areas si,
Θ = V Vm =
∞
P
i=0
isi
∞
P
i=0
si
. (31)
By introducing some abbreviations like
c= kad,1g
kdes,1
e
∆ad
H
1
−∆ cond
H
RT
(32) with ∆condH being the condensation enthalpy of the liquid phase of the adsorbate and solving the summations, they obtained
ΘBET = v vm =
cpp
sat
(1− pp
sat)
1−(1− c)
p psat
(33)
Figure 2.9:BET isotherm for different values ofcwith a) linear and b) logarithmic scaling of the ordinate.
The curve progression can be decomposed into two regions, one below and the other above a coverage of Θ = 1. The larger c becomes, due to an decrease in temperature, or a higher difference between the enthalpy of adsorption of the first layer and the liquification enthalpy, the lower the partial pressure pat which the coverageΘgets unity, and the tighter the curvature in both regions.
for the BET-equation. This equation results in a S-shaped isotherm. For c >1the isotherm has two regions, as shown in figure 2.9. In the low pressure region the isotherm is concave towards the pressure axis and reduces to a special form of the Langmuir isotherm, thus describing the adsorption of a fist molecular layer. As the pressure p approaches p
sat, the coverage Θ becomes large and the curve becomes convex with increasing pressure. For p = psat the BET-equation has a pole, thus becomes infinite. When the coefficient c becomes large (c 1) , the BET isotherm can be expressed in the following simplified formalism.
ΘBET= 1 1− pp
sat
. (34)
This expression often is sufficient for describing nonreactive gases on polar surfaces for example, wherec ≈100. The heat of adsorption of the very first monolayer is large compared to the condensation enthalpy, and adsorption of the second layer occurs as soon as the first layer is filled. For c 1andp 1the BET becomes the Langmuir isotherm. Conversely, if∆adH
1 is smaller or equal to∆condH,c becomes small and multilayer adsorption already occurs while the first layer is still incomplete.
Using the Clausius-Clapeyron equation the isosteric heat of adsorption∆qst (differential heat of adsorption) can be determined. The strength of the adsorbate bond determines under which pressure and temperature combination the same coverage is found. Measuring the adsorption of a gas at various temperatures over a certain pressure range of interest thus
gives the isosteric heat of adsorption:
1 p
∂P
∂T
Θ
=
∆qst
RT2 (35)
The BET-model is based on the following assumptions. (i) The adsorption takes place on fixed sites. (ii) The sites are energetically identical. (iii) No lateral interaction is allowed between the adsorbed molecules. The inclusion of lateral adsorbate-adsorbate interaction leads to the formation of islands.112
With the theoretical background described in this section, in the following two sections the state of knowledge about the influence of water on electrical conductivity of ceria based materials is presented. As the driving forces of chemisorption and physisorption are different, the literature is divided into such works, investigating a temperature regime at elevated temperatures (T?150
◦C) where chemisorption is most likely the relevant process, and those studies with a focus on a lower temperature regime, where physisorption is most likely to occur. Nevertheless, it is emphasized that the transition between the two regime is diffuse.
2.3.2 Literature on the influence of humidity on the conductivity of ceria