Page 255 - Gas Adsorption Equilibria

5. Oscillometry 241

2.2.1 The Motion of the Pendulum in Vacuum

The equation of motion of the rotational pendulum loaded with sorbent
material is [5.1, 5.2]:

Here is the angular displacement or amplitude of the pendulum, the
dot (•) indicating the time derivative. The moment of inertia consists of
two parts

with

being the moment of inertia of the empty disk of mass and being the
moment of inertia of the sorbent material within the ring slit. Assuming
this material to be homogenously distributed within the slit – in case of pellets
their characteristic dimensions should be at least one order of magnitude
smaller than the width or height (d) of the slit – this moment of
inertia can be written as

The retarding moment of the torsional wire included in the equation of
motion (5.1) can be calculated from the wire’s length its diameter
the elasticity modulus (E) and the Poisson number by the relations [5.2,
5.3]