production of selected secondary metabolites in transformed ...

CuSO4, Cu(ClO4)2 and Cu2P2O7 of the same Cu 2+ concentration (0.1 mol.dm –3 ) as a stock
solution for diffusion experiments of the same time duration (24 hours). Finally, the solution
pH – dependency and solution ionic strength dependency of the diffusion process was
checked by diluting CuCl2 salt using the differently concentrated hydrochloric acid and
sodium chloride, respectively. For all of these experiments the same Cu 2+ concentration
(0.1 mol.dm –3 ) as well as the time duration (24 hours) was used and the same experimental
technique (see above) was adopted.
RESULTS AND DISCUSSION
The value of calculated effective diffusion coefficient of copper(II) ions in humic gel was
7.96×10 -10 m 2 .s –1 . This value is in good agreement with the one pre–determined by another
experimental method (see [3]) and was used for all following calculations. As can be seen on
Fig. 3 and Fig. 4, total diffusion flux of Cu 2+ through solution–gel phase interface linearly
increases with the initial concentration of copper(II) in solution and with the square root of
time duration of diffusion experiment. The later dependency is however much more
complicated; the nonzero intercept of the regression line indicates that the linearity is just
illusory and in fact the dependency is curved. Klučáková et al. in [5] stated the equation for
the total diffusion flux across the solution–gel interface:
ε c D τ
0
g
m = (1)
1+
ε D / π
g D
in which m stands for the total diffusion flux, c0 is initial concentration of the ion in solution,
τ is the time duration of the diffusion, ε is ratio of ion concentration in the gel and in the
solution in final equilibrium (at the “end of diffusion”), Dg and D is diffusion coefficient of
cupric ions in humic gel and in solution, respectively. Following this equation the value of ε
was calculated from total diffusion flux corresponding to c0 and τ values. It was found that for
the same duration of diffusion experiment this value is constant for different initial
concentrations of the solution but it varies for different duration of experiment (Fig. 5). This
fact could be explained by the apparatus construction (small solution volumes – gel weight
ratio) or by the time–consuming formation of some stable structural or chemical complexes
between gel and ions. This affects the mobility of ions (retention of ions can lead up to their
immobilization in gel) and their equilibrium in gel and solution. This fact could explain
mentioned deformation of total flux time dependency as well.
The knowledge of the ε value allows
the calculation of theoretical
y = 6.454E-03x
concentration profiles of the copper (II)
R
ions in the humic gel (used
mathematical apparatus is presented in
detail in reference [5]) for individual
experiment conditions (initial
concentration, time duration). The
example on Fig. 6 shows very good
agreement between calculated and
measured concentration profiles.
2 50
40
= 1.000E+00
30
20
10
0
0 2000 4000 6000 8000
total flux [mol.m -2 ]
c0 [mol.m -3 ]
Fig. 3 The total diffusion flux dependency on
the initial concentration of Cu 2+ in the
solution (diffusion duration 24 hours)
Sborník soutěže Studentské tvůrčí činnosti Student 2006 a doktorské soutěže O cenu děkana 2005 a 2006
Sekce DSP 2006, strana 225