ESTUDO DA DIFUSÃO MOLECULAR ATRAVÉS DE
FILTROS DE MICROFIBRA USANDO A
ESPECTROMETRIA FTIR-PAS
Ossamu Nakamura (Instituto de Física da UFBA - ossamu@ufba.br)
Roger D. Lowe, Richard D. Snook (DIAS / UMIST - UK)
Abstract
In this work the diffusion of the angina therapeutic agent, nitroglycerin,
through a skin mimetic is described. The mimetic is a polyethylene glycol
loaded microfibre filter to which a transdermal drug patch is attached. The
diffusion process is monitored using dynamic scanning FTIR -Photoacoustic
in which the IR beam illuminates the filter with the transdermal patch
underside. Thus the nitroglycerin diffuses up through the filter. Using the
different thermal diffusion lengths, as determined by the wavelength
dependent modulation frequency of the FTIR spectrometer, the diffusion
process is monitored. A convenient model is developed to provide a
measurement of the ratio of the thermal diffusivity coefficient to the diffusion
coefficient of the nitroglycerin through the polyethylene glycol loaded filter.
1
Experimental
The
measurements
were
made
using
a Bio-Rad FTS
6000
spectrometer with a MTEC photoacoustic cell (model 300). The spectra were
obtained in the rapid scan mode at a mirror velocity of 0.08 cm/s. In order to
improve the signal to noise ratio, 20 scan were averaged for each
measurement in the range 400 cm-1 to 4000 cm-1 with a resolution of 8 cm-1.
Nitro-Dur (Schering Plough Ltd.)
Inc ident IR
light
nitroglycerin transdermal patches with
the dose rate of 0.4 mg/h were used.
The filter used were GF/F glass
microfibre filter with nominal particle
W in d o w
G as
retention of 0.7 m (Whatman Int.
Ltd.).
These
were
saturated
M i cr o p h o n e
in
polyethylene glycol 400 in order to aid
F ilt e r
the diffusion process, and so that they
more closely mimic the behaviour of
skin.
D r u g co ntain g layer
B a c k ing la y e r
Results and Discussion
Prior to the experiments, a spectrum was obtained from the stick side of the
Nitro - Dur patch, so that the absorption peaks of nitroglycerin could be
located. The main peaks appear at 752 cm-1 (due to NO2 deformation - out
of plane), 852 cm-1 (due to NO2 - stretching), 1276 cm-1 (due to NO2
symmetric stretching), and a double peak at 1665 cm-1 and 1738 cm-1 (due
to NO2 asymmetric stretching). A second measurement was made of the
2
filter that had been saturated with polyethylene glycol 400, for the purpose of
providing a reference or blank spectrum for the ensuing investigation. Both
spectra were obtained with the photoacoustic cell purged with helium for 10
4000
3500
3000
1500
1000
-1
752 cm
852 cm
-1
1276 cm
-1
-1
2500
2000
-1
Wavenumber (cm )
1665 cm
-1
1738 cm
Signal Amplitude (a.u.)
Filter+glycol
Patch
Air
2361 cm
-1
minutes and normalised with carbon black.
500
Figure1
It was important to know the location of the absorption peaks due to the
air because some of the following experiments were to be performed without
first purging the photoacoustic cell. An ambient air spectrum was obtained by
first recording a spectrum of the filter and the polyethylene glycol 400 with the
cell purged with helium, and then afterwards a second measurement was
made under air without changing any other experimental parameters. By
dividing the second spectrum by the first the air spectrum was obtained. The
3
major feature of this spectrum to note is the peak at 2361 cm-1 due the
presence of CO2.
A series of experiments were then performed to investigate the rate of
diffusion of nitroglycerin from the patch and through the filter and some
spectra normalised against carbon black are shown in figure 2. The air
correct results are shown in figure 3 where the peaks due to the diffusion of
4000
3500
3000
2500
2000
-1
Wavenumber (cm )
1500
1000
500
Figure 2
4000
2209 cm
-1
2237 cm
-1
7'
19'
35'
60'
140'
225'
Concentration (a.u.)
Signal Amplitude (a.u.)
7'
19'
35'
60'
140'
225'
2361 cm
-1
the nitroglycerin through the filter can now be seen clearly
3500
3000
2500
2000
1500
1000
500
-1
Wavenumber (cm )
Figure 3
Apart from the peaks which belong to nitroglycerin and CO2 (2361 cm-1),
figure 3 shows the appearance of bands at 2209 cm-1 and 2237 cm-1. These
peaks do not appear in the spectrum of either the patch or the filter and PEG
400 and only begin to show during the course of an experimental run. The
spectra in figure 3 were obtained with the photoacoustic cell closed all the
time, from the first to the last. However, if the cell is opened between each
measurement, these bands no longer appear (see figure 4).
It suggested therefore that some or all of these peaks are due to a
volatile substance which are released from the sample during an
experimental run due the IR heating.
4
The identity of this substance has
not been elucidated but these bands
2'
21'
35'
60'
214'
do not fall into spectrally significant
region and did not interfere with the
results
from the analysis which
follows. Figure 5 shows the increase
in intensity of the peaks which
correspond
3500
3000
2500
2000
-1
Wavenumber (cm )
1500
1000
500
appearance
of
nitroglycerin in the filter.
1276 cm
752 cm
-1
852 cm
-1
7'
19'
35'
60'
140'
225'
-1
1643 cm
-1
-1
Figure 4
1659 cm
4000
the
1800
1700
1600
1500
1400
1300
1200
1100
1000
900
800
700
600
-1
Wavenumber (cm )
Figure 5
Numerical Analysis
Figure 6 shows the time evolution of the intensity of the peaks which
correspond the increasing of the concentration of nitroglycerin in the filter.
The absence of peaks in the first minutes of the experiment indicates that the
nitroglycerin has not yet reached the layer corresponding to the first thermal
diffusion length of the filter.
5
-1
1643 cm
-1
1276 cm
-1
852 cm
-1
752 cm
-1
Concentration (a.u.)
1658 cm
0
20
40
60
80
100
120
140
Time (min)
160
180
200
220
Figure 6
The above spectra were obtained using the FTIR spectrometer
operating in the dynamic mode so that the modulation frequency f of the
incident light depends upon the wavelength f  2
mirror velocity, and k 
1

v

 2  k  v where v is the
is the wavenumber. Using v = 0.08 cm/s, the
modulation frequencies are 120 Hz, 136 Hz, 204 Hz and 263 Hz for the
nitroglycerin peaks at wavenumber 752 cm-1, 852 cm-1, 1276 cm-1 and 1643
cm-1, respectively. For all these frequencies the sample can be said thermally
thick. Given this condition, the photoacoustic signal is generated within a
layer of thickness, between the top surface of the filter and to a depth into the
filter dependent upon the wavelength at which the peaks occur. Using the
Rosencwaig Gersho1 model for a two-layer sample, in a case where the first
layer is thermally thick, it can be shown that the signal amplitude is (for l <
) proportional to the optical absorption coefficient 1 of the layer directly
6
exposed to the light. If the signal is proportional to 1, it means that the
nitroglycerin peaks recorded in these spectra can be interpreted as being the
variation of the optical absorption coefficient with time. This coefficient can
then be related to the change with time of the concentration of the active
substance within the filter.
Using a simplified model it is possible to approximately predict
molecular diffusion across a non homogeneous and porous medium. The
c(x,t)
 2c(x,t)
D
diffusion equation is
where c(x,t) is the space time
t
x 2
dependent concentration and D is the diffusion coefficient. The space
average concentration for a region of thickness d is2, 3:
N
c ( t)  c o 
8c o
2

n0
 D 2 (2n  1)t 
1
exp


(2n  1) 2
4d 2


where
co
shows
the
is
the
initial
concentration.
Figure
7
plot
of
this
expression where N = 0, 1 and 1000. It
Concentration (a.u.)
can be seen that only for times less than
2 minutes is there a significant difference
n=0
n=1
n = 1000
between the curves, Thus, for the results
of this work it will be sufficient to take
0
5
10
15
20
25
30
Time (min)
35
40
45
50
only the first 2 terms of the expression.
Figure 7
Therefore this equation can be simplified, and an approximated value
for the average concentration can now be derived using the equation:
D 2
1


c ( t )  c o  c1 exp( a o t )  exp( 9a o t ) where a 0 
4d2
9


7
This equation can be fitted to the data shown in figure 6 and values of
ao and the characteristic diffusion time  o  1 / a o can be obtained. These
values are shown in table 1. A fitted curve for the peak at 1643 cm-1 is shown
in figure 8.
ao(min-1)
o(min)
752
0.02133
46.8
852
0.02701
37.0
1276
0.02832
35.3
1643
0.03414
Table 1
29.3
Concentration (a.u.)
Peak
k ( cm-1 )
0
20
40
60
80
100
120
Time (min)
140
160
180
200
220
Figure 8
The characteristic time differs from one peak to another because it
depends upon the thickness of the layer from which the signal is generated,
and consequently on the frequency of modulation or the wave number. For
the purpose of calculation a layer thickness d = 2 can be defined. Using the
fact that the thermal diffusion length is  

 f
f  2  k  v , the value of ao become equal to: a o 
and using the expression
D
k  v , so o is inversely
8
proportional to the wave number.
0,022
From this equation an important
0,020
-1
a0 (min )
relationship can be deduced. From the
0,018
angular coefficient b of the curve ao =
0,016
ao(k) we can obtain the ratio D/1,
0,014
0,012
600
which is obtained using the least
700
800
900
1000
1100 1200 1300 1400
-1
Wavenumber (cm )
1500
1600
1700
1800
square method to obtain a best fit line
Figure 9
to ao = ao(k).
8
This angular coefficient is given by: b 
 D
   v . The value of the
8  1 
scan velocity is v = 0.08 cm/s and using the average value of b for all sets of
experiments we find
D
1
 1.48  0.59 x10 6 . For a typical value of 1, of say
PEG 400 at 2.98 x 10-3 cm2/s would yield a diffusion coefficient for
nitroglycerin of 4.4 x 10-9 cm2/s for the PEG 400 impregnated filter. A typical
value for diffusion through skin would be of same order, so our skin mimetic
system would seem appropriate.
It is important to stress that an approximate value of D/1 is obtained
because the diffusion of nitroglycerin into the mimetic in a dynamic process
where the parameters of thermal diffusivity and optical absorption coefficient
are changing with time. However these parameters vary little during the
measuring time of 20 seconds for 20 scans which is at least 100 times less
than the characteristic diffusion time. Similarly a static theoretic model has
been used although again the concentration is not expect to vary generally in
a layer within the measurement time.
References
1. Rosencwaig, A. and Gersho, A., J. Appl. Phys., 47, (1976), 64.
2. Cranck, J., The Mathematics of Diffusion, 2nd Ed., Clarendon Press,
Oxford, (1975), 18
3. Skelland, A. H. P., Diffusional Mass Transfer, John Wiley & Sons, London
(1974), 34.
9