Supplemental Material
Table A – Most important isotherms for pure gas systems and temperature dependence of their parameters. ( θ is fractional occupancy, qsat is the concentration
of adsorbate at saturation, Qst is the isosteric heat of adsorption, H ads is the enthalpy of adsorption, and bo is b at reference temperature To ).
Isotherm
T-dependence of parameters
Langmuir
θ
bP
q
 L
qsat 1 bL P
(A1)
 Q T

bL  bL,o exp  st  o  1

T
T

 o
Linear
q  qsatbL P  KP
(A3)
 Q T

K  Ko exp  st  o  1

 To  T
Nitta
Freundlich
θ
 n uθ 
nNbN P 
exp  N 
n
1  θ 
 kT 
N
q  bF P1 / n F
Freundlich
θ
(A5)
(A7)
bLF P 
q

1/ n
qsat 1  bLF P 
 Q T

bN  bN,o exp  st  o  1

 To  T
  T
bF  bF, o exp 
A0




 Q T

bLF  bLF,o exp  st  o  1

T
T


 o
1 / nLF
LF
(A4)
Notes
bL , Langmuir constant
In the low pressure region it reduces to the Henry law,
and for sufficiently high pressures reaches the saturation
capacity characteristic of the monolayer coverage.
K , Henry’s constant
At low occupancies (low pressure and/high temperature)
bL P  1 and the Langmuir equation reduces to this
linear relation.
n N , number of sites occupied
1 nF  T A0
Langmuir-
(A2)
Parameters
(A10)
(A6)
(A8)
(A9)
(A11)
1/ nLF  1/ nLF,o  LF 1  To / T  (A12)
qs at  qs at,o exp  LF 1  T / To 
(A13)
by an adsorbed molecule
u , adsorbate-adsorbate
interaction parameter
bN ,adsorption affinity constant
When adsorbate-adsorbate interactions are not as strong
as adsorbate-adsorbent ones, u  0 .
In this case, Nitta isotherm reduces to the Langmuir
equation if nN  1 .
nF and bF , Freundlich
equation parameters
A0 , distribution parameter
 , parameter of the Clapeyron
equation
The parameter nF is generally greater than unity; the
larger is this value, the more nonlinear is the isotherm.
bLF , adsorption affinity
constant
nLF , surface heterogeneity
nLF is usually greater than unity, and the larger is its
value the more heterogeneous the system is.
parameter
 LF , constant parameter
1
Dual-site
Langmuir
q  qsat,A
Dual-site
Langmuir-
q  q sa t, A
bL, A P
 qsat,B
1  bL, A P
b P 
1  b
P
1 / nLF, A
LF,A
1 / nLF, A
bL, B P
(A14)
1  bL, B P
 q sa t, B
LF,A
b P 
1  b P 
1 / nLF, B
LF,B
(A15)
1 / nLF, B
LF,B
A and B, referring to
adsorption sites A and B
Dual-site Langmuir parameters have the same
temperature dependence as those of the single-site
Langmuir model.
A and B, referring to
adsorption sites A and B
Dual-site Langmuir-Freundlich parameters have the
same temperature dependence as those of the single-site
Langmuir-Freundlich model.
Freundlich
q s at  qs at,A  qs at,B
q s at  qs at,A  qs at,B
When
Toth
bT P
q
θ

t
q sat
1  bT P 


1/ t
(A16)
t  to  T 1  To / T 
(A17)
bT and t , Toth isotherm
parameters
t  1 , it reduces to the Langmuir equation.
Similarly to the Langmuir-Freundlich parameter, t
characterizes the system heterogeneity. The temperature
dependence of bT and qsat may be equivalent to those
of the Langmuir-Freundlich isotherm.
2