Page 69 - Advances in Textile Biotechnology

48 Advances in textile biotechnology

−3

• specific weight of pectinase, ρ E = 1300 kg m and
−1
• pectinase concentration in the solution, C E = 5 g l , i.e. a frequently used
concentration
The surface area of the capillary A cap can be calculated by:

A cap = π d L cap [2.32]
cap
and the volume of the capillary by:

1
2
V cap = π d L cap [2.33]
cap
4
By using the values for the capillary length and capillary diameter as
−16
−10
2
3
given above, A cap = 6.3 × 10 m and V cap = 3.1 × 10 m . If the enzyme is
assumed to be a sphere, then its diameter can be calculated using:
6 M E
d E = 3 [2.34]
N AV ρπ
E
−1
23
where N AV is the Avogadro number (= 6 × 10 mol ). From the values given
above, the enzyme diameter is d E = 50 Å. This value is in accordance with
values given in the literature. These enzymes adsorb at the surface of the
capillary and it is suggested here that they adsorb in a simple rectangular
array, which means that the maximum number of enzymes adsorbed at the
surface n max is given by:
A
n max = [2.35]
2
d E
2
in which A is the surface area in m .
16
2
Thus, n max = 4 × 10 molecules per m . The maximum surface concentra-
tion of enzymes, Γ E,max can be calculated by:
* E,max = n max [2.36]
N AV
−2
−8
For this case we calculated Γ E,max = 6.7 × 10 mol m . Therefore, the capillary
−17
−10
2
surface area of 6.3 × 10 m can contain at maximum 4.2 × 10 mol pec-
−1
tinase. With an enzyme concentration C E of 5 g l in the capillary liquid and
−16
3
a capillary liquid volume of 3.1 × 10 m , the number of moles of pectinase
−17
in the liquid is calculated as 3.1 × 10 . This example shows that the avail-
ability of pectinase in the capillary liquid is of the same order of
magnitude as the number of moles of pectinase that can be adsorbed at
the capillary wall. However, for enzymes, there is always an adsorption–
desorption equilibrium. From the calculations made here, it is clear that the
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