Membrane Gas Separation

p, atm
P
CO2
Figure 3.3 Peremeability coeffi cients P (CO 
2
 ) (in Barrer) as a function of upstream 
pressure in the cell of mass spectrometric unit (downstream pressure is zero, T = 22
o
 C)

---

50
Membrane Gas Separation
10 – 20 atm [26] . In the case of PTMSN, as is seen from Figure 3.3 , p
min
is approximately 
0.5 atm. The reason for a strong tendency to plasticization of PTMSN by carbon dioxide 
is not completely clear. For its explanation, the whole shape of the sorption isotherm in 
a wide range of pressure should be compared, which is not yet available for PTMSN. The 
differences of solubility coeffi cients at infi nite dilution (initial slopes of the sorption 
isotherms) are suffi ciently large to explain such strong plasticization effects.
3.3.3
Sorption and Diffusion 
Sorption thermodynamics were studied using the IGC method for a number of solutes 
(n - alkanes C 
3
– C 
16
, cyclohexane, methylcyclohexane) in the range 50 – 250 ° C. For all the 
solutes, the linear dependencies of log S versus 1/ T enabled an estimation of the enthalpies 
of sorption  
Δ
 H
s
. It was shown that when the size of the solutes (e.g. their critical volume 
V
c
) increases the negative enthalpies of sorption also increase. This dependence can be 
presented by the equation:
Δ
H
aV
b
s
c
=
+
(3.4)
where a =
−
0.071
±
0.002 and b =
−
16.9
±
0.9, correlation factor R
2
= 0.993. Using this 
correlation, enthalpies of sorption of light gases and, via Equation ( 3.3 ), the activation 
energies of diffusion of light gases were also estimated. The found E
D
(kJ/mol) values 
are as follows: O 
2
= 23.5; N 
2
= 27.9; CO 
2
= 16.2; CH 
4
= 24.6. These values are not as 
small as those observed in PTMSP [20] , however, they are relatively low as compared to 
the diffusion activation energies in conventional glassy polymers. So judging by this 
parameter too, PTMSN can be considered as intermediate between ultra - permeable poly-
mers like PTMSP and conventional glassy polymers. 
The IGC method also resulted in the determination of the solubility coeffi cients S in 
PTMSN. The S values were also determined as the ratio P / D for light gases. The combined 
results are presented in Figure 3.4 in the form of correlation of S versus squared critical 
temperature of solutes. The data for PTMSN obtained by the two methods are compared 
with the results of the investigation of PTMSP, the polymer having extremely high solu-
bility coeffi cients.
It was shown that PTMSN is characterized by unusually great solubility coeffi cients. 
It is seen from Figure 3.4 that PTMSN has only marginally smaller S values as compared 
with PTMSP. A similar conclusion in comparison of these two polymers can be made 
based on comparison the S values obtained as the ratio S = P / D (see Table 3.7 ). It can be 
assumed that rigid chains of PTMSN, as evidenced by its very high glass transition 
temperature and the presence of bulky Si(CH 
3
) 
3
groups attached directly to the main 
chains, are the reasons for great sorption parameters. Table 3.7 also indicates that higher 
permeability of PTMSP is caused obviously by signifi cantly larger values of its diffusion 
coeffi cients. The values of D and E
D
in PTMSN imply that the structure of free volume 
in this polymers is not as opened as it is in PTMSP.