chemia - Studia

APPLICATION OF NUMERICAL METHODS IN THE TECHNOLOGY OF HYDROXYAPATITE
From the kinetic data, the values of the rate constant and activation
energy at pH 8.5, 9.1, 9.7, 10.2, 11.3, 12 were calculated. Based on the values
obtained for activation energy, it has been established that the transformation
of amorphous calcium phosphate into hydroxyapatite can be described by a
combined macrokinetic mechanism: transfer-mass conversion. The mathematical
model of the process was established and the constant values from the
mathematical model equation were determined [11.12]. Simulations were
made based on the proposed model and the results show a good agreement
with the experimental data values, which confirms the validity of the model.
Starting from these results, in the present work a method that can be used
to determine quickly and easily the values for degree of conversion (η ) in
different experimental conditions is presented. A comparison between the
numerical results and analytical results indicates that predictions obtained with
the new technique are closer to the analytical solutions.
RESULTS AND DISCUSSION
The interpolation of experimental data in order to obtain spline
interpolation function was performed with Mathcad 15. The experimental
data presented in a previous communication [11.12] were used in the present
0 0
0 0
study. Thus, for two temperatures T1 = 20 C and T2 = 50 C , the spline S (t)
was determined, which is a function of one variable and approximates
function η experimentally determined. Figures 1 and 2 show the spline function
at various pH values:
a ( τ )
b ( τ )
1
c ( τ )
d ( τ )
e ( τ )
f ( τ )
A 〈 2〉
( )
k
( B 〈 2〉
)
k
( C 〈 2〉
)
k
( D 〈 2〉
)
j
( E 〈 2〉
)
j
F 〈 2〉
0.5
( )
i
τ τ
0
1 × 10 4
2 × 10 4
3 × 10 4
, , τ , τ , τ , τ , A 1〉
, B 1〉
, C 1〉
, D 1〉
, E 1〉
, F 1〉
( )
k
( )
k
( )
k
( )
j
( )
j
( )
i
Figure 1. Graphic representation of the degree of transformation of amorphous
phase in hydroxyapatite using spline function at 20 0 C and 6 pH values.
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