Micromeritics TriStar II 3020 - Sphere Pore Geometry (Cheng;Yang

TriStar II 3020 Appendix C
302-42828-01 - Dec 2012 C-21
Sphere Pore Geometry (Cheng/Yang)
P
Po
-------


ln
6 N
1

*
12
N
2

*
22
+L
3
10
32
J A
4
/J cm
4

RT L d
0
–
3
----------------------------------------------------------------------------------------------------------
=
d
0
L
-----


6
1
12
------
T
1
1
8
---
T
2
+


–
d
0
L
-----


12
1
90
------
T
3
1
80
------
+ T
4


+
When you use the Cheng/Yang
11
method, the following equation is solved for each value of P. The
value of L is determined when the solved-for relative pressure is within 0.1% of the collected absolute
pressure.
where
R
= gas constant (8.31441 x 10
7
ergs/mole K)
T = analysis bath temperature (K), from an entered or calculated value on the Po
and Temperature Options dialog
d
0
=
where:
D
A
= molecular diameter (Å) from the Horvath-Kawazoe Physical Properties
dialog
D
S
= diameter of sample atom (Å) from the Horvath-Kawazoe Physical dialog
L = pore width (nucleus to nucleus) (Å)
P = equilibrium pressure (mmHg)
Po = saturation pressure (mmHg)
N
1
=4 L
2
N
S
, where N
S
= number of sample atoms/cm
2
at monolayer
N
2
= 4 (L - d
0
)
2
N
A
, where N
s
= number of gas molecules/cm
2
e*
12
=, where
*
22
=, where
T
1
=
T
2
=
D
A
D
S
A+
2
-----------------------------
A
S
4d
S
6
-------------
A
S
6 MC
2

S

A


S

S
------

A

A
------
+
-----------------------------------------------
=
A
A
4D
A
6
---------------
A
A
3 MC
2

A

A

2
-----------------------------------------------
=
1
1 S–
3
-------------------
1
1 S+
3
-------------------
–
1
1 S+
2
-------------------
1
1 S–
2
-------------------
–