NEURONAL NETWORK USED FOR INVESTIGATION OF WATER
IN POLYMER GELS
*T. RUSU *, *C. IOJOIU and **V. BULACOVSCHI
* P. Poni Institute of Macromolecular Chemistry, Ghica Voda Street,
41A, Iasi 6600 Romania, teia@tuiasi.ro
** Gh. Asachi Technical University, Iasi, 6600, vbulacov@ch.tuiasi.ro
Abstract
The paper deals with the synthesis and characterization of some copolymer
networks build up from sequences of polydimethyilsiloxane (PDMS) and
poly(methacrylic acid) (PMAA). The water diffusion properties of the networks
are also investigated by using a neuronal network (NN) algorithm. The
proposed algorithm is an empirical one, which simultaneously retrieves several
physical parameters over the copolymer network properties as a relation
between the molecular ratios of copolymer sequences. Comparison with other
NN algorithms is presented.
1. Introduction
Modern chemistry has made important efforts to develop and to test theoretical
concepts for providing new macromolecular compounds with the structure
related to imposed properties for new areas of applications. Hybrid materials
with different molecular architectures have attracted an increased interest in
recent years.
This paper focuses on copolymers containing hydrophilic and
hydrophobic sequences that confer them special transport properties. The
molecular ratio between the two sequences has an important role for the
properties of such copolymers like shape-selective separation and water (small
size particles) delivery.
It is known from literature that hydrogels reveal phase transitions
making swelling-deflation changes in response to environmental modifications,
e.g. solvent composition [1, 2], ionic strength [3], temperature [2-5], electronic
field [6] and light [7]. Such stimuli-responsive polymers have been investigated
with application to artificial muscles [8], immobilization of enzymes [9],
concentration of dilute solutions [10, 11] and chemical valves [12].
Using stimuli-responsive amphoteric gels there have been attempts for
temporal control of water release. Thus, a swollen gel in ethanol immersed in
water undergoes immediately spontaneous translation and rotational motions
with two-thirds of its volume immersed in water. In the course of its motion the
gel gradually sinks and finally settles at the bottom of the vessel due to
contraction and cease of motion [13]. The speed, duration and mode of gel
motions are associated with its size, shape and chemical nature. Such polymer
gels, exhibiting motion in water, have potential applications as soft-touch
manipulators, target drug-delivery devices, micro-agitators, and micro
generators. Their study is under way.
Networks prepared by reacting functionalized polydimethylsiloxanes
(PDMA) with different cross-linking agents are considered ideal models for
studying network formation and properties [14]. PDMS is highly hydrophobic,
very flexible and shows little variation of its properties with temperature. Since
its mechanical properties are poor, for their improvement one should synthesize
cross-linked copolymers based on PDMS [15].
This paper deals with the synthesis and characterization of amphoteric
networks (gels) based on PDMS–co–PMAA sequences. The water-diffusion
properties of the obtained gels are investigated by using some neuronal network
algorithms.
2. Experimental
The polymer gels were obtained by radical copolymerization of
polydimethylsiloxane macro-initiators with methacrylic acid in presence of
ethyleneglycol dimethacrylate as cross-linking agent [16].
The synthesis of the azoester macroinitiators (AzoPDMS), with
different molecular weights of siloxane sequences and different contents of azo
groups, was realized according to Scheme 1, and the experimental data are
summarized in Table 1.
The synthesis of PDMS-poly(methacrylic acid) (PMAA) hydrophobic–
hydrophilic gels was realised according to Scheme 2 [17], their characteristics
being summarized in Table 2.
CH3
CH3
CH3
Si
O
R O OC (CH 2)2 C N N C (CH 2)2 COO R Si O
CH3
CN
CN
+
+
MAA
EGDMA
PDMS - co - PMAA
HO - PDMS
H2N - PDMS
CH3
CH3
ClOC
C2H4 C
N=N
C
CN
CH3
[O
CH3
CH3
CH3
C3H6 ( Si O )mSi C 3H6 OOC C2H4 C N = N
CH3
CH3
CN
(AzoE-PDMS)
CH3
[ HN
C2H4 COCl
CN
C
C2H4 CO] q
CN
CH3
CH3
CH3
C3H6 ( Si O ) Si C 3H6 NHOC
n
CH3
CH3
C2H4 C
CN
(AzoA-PDMS)
N=N
C
C2H4 CO ]
p
CN
Scheme 1
TABLE 1. Characteristic data for Azo-PDMS
Sample
Cod
NH2
(mol/kg)
Mn
(GPC)
Mw/Mn
(GPC)
Sample
cod
N2
(%)
NH2 - DS
NH2 –
PDMS1
NH2 –
PDMS1
8.06
0.92
1360
1.6
16.982
6.174
0.13
2000
1.4
Azo - DS
Azo –
PDMS1
Azo –
PDMS2
Azo
groups
(mol/kg)
2.021
0.734
3.879
0.395
CH3
CH3
CH3
Si
O
R O OC (CH2)2 C N N C (CH2)2 COO R Si O
CH3
CN
CN
+
+
MAA
EGDMA
PDMS - co - PMAA
Scheme 2
TABLE 2. Characteristic data for PDMS–co-PMAA obtained by radical
polymerization of MMA in presence of AzoPDMS
Initial mixture*
Sample
Network
MnPDMS
SiO/MAA
Yield,
SiO/MAA**
Aspect
(from
Molar
%
Molar ratio
AEPS)
ratio
5040
0.5
I.1
85.9
0.42
Gel
6620
0.5
I.2
87.6
0.44
Gel
14060
0.5
I.3
86.9
0.43
Gel
5040
2.0
II.1
89.4
1.63
Gel
6620
2.0
II.2
87.1
1.74
Dense gel
14060
2.0
II.3
90.4
1.81
Dense gel
* Polymerization in sealed ampoules; 80C; 20 hours; solvent, toluene (total
concentration 25%); EGDMA, 1% molar against MAA
** Determined from elemental analysis (Si content)
3. Characterization data
3.1. MACRO-INITIATOR CHARACTERIZATION
The characterisation of macro-initiators was made by IR (SPECORD M80 IR)
and NMR (Bruker AC 200). The IR spectra revealed the following absorptions:
1265 cm-1 - Si-CH3; 800, 1110, 1020 cm-1 - Si-O-Si; 1789 cm-1 -> 1738 cm-1
CACV inclusion in the PDMS sequence.
In the 1NMR spectra (CDCl3) (Fig. 1) one finds: 0.01ppm (6H, CH3-Si,
s), 0.43-0.47 ppm (2H, -CH2-Si, m;  isomer), 0.81-0.88 ppm (3H, CH3-CH, d;
 isomer), 1.00-1.08 ppm (1H, CH3-CH, q;  isomer), 1.40–1.47 ppm (2H, -
CH2 -CH2 -CH2 -, m;  isomer), 2.73-2.85 ppm (2H, CH2-NH2, m).
For the AzoA-PDMS: 0.01ppm (6nH, CH3Si, s), 0.43-0.47 ppm (2H, -CH2Si,
m;  isomer), 0.80-0.88 ppm (3H, CH3-CH, d;  isomer), 1.00-1.08 ppm (1H,
CH3-CH, q;  isomer), 1.20 ppm (3H, CH3-C(CN), s), 1.40–1.47 ppm (2H, CH2 -CH2 -CH2 -, m;  isomer), 1.60-1.66 ppm (2H, CH2-C(CN), m), 2.262.43 ppm (2H, -CH2-CO, m), 3.11-3.19 ppm (2H, CH2-NHCO, m).
Figure 1. 1H-RMN spectra for AzoA-PDMS
3.2. CHARACTERIZATION
NETWORKS
DATA
FOR
THE
PDMS–co–PMAA
The chemical structure and the thermal behavior of the cross-linked copolymers
were established by IR spectroscopy and differential scanning calorimetry
(DSC) (Perkin Elmer DSC-7 device), respectively (Fig. 2). Scanning Electron
Microscopy (SEM) (Phillips XL 300 microscope) analysed the microstructure
of the resulting networks (Fig. 3).
Figure 2. Typical IR and DSC curves
Figure 3. The SEM image of the network
4. Water diffusion tests
The synthesized copolymers were submitted to the water delivery test. Equal
amounts of samples from each of the six copolymers were llowed to achieve the
swelling equilibrium by keeping them in an excess of water for three days.
Then, the excess of water was removed by filtration and the swollen samples
were submitted to control dryness thermosetting at 100C and weighed at every
two hours [18]. The results are presented in Figure 4 and Table 2. The content
of residual water was followed as a function of time and molar ratio of the two
polymeric blocks.
Residual water
(%)
Time (h)
Figure 4. Residual water from the macromolecular network vs. time and
molecular ratio.
The water delivery tests were subsequently used in conceiving a Multilayer
Perceptron Neuronal Network. A comparison of this algorithm with other
global diffusion speed retrieval algorithms for amphoteric copolymers polymers
is presented. We also examined different diffusion conditions related to
different forms of polymer-soil moisture presenting various cross-sections of
evaporation speed retrieval error analysis.
5. Neural network method
A generic neuron
Multilayer Perceptron NN employing feed forward, fully connected topology
Neural networks (NNs) are well suited for a very broad class of non-linear
approximations and mappings. Neural networks consist of layers of uniform
processing elements, nodes, units, or neurons. The neurons and layers are
connected according to a specific architecture or topology. The number of input
neurons, n, in the input layer is equal to the dimension of the input vector X.
The number of output neurons, m, in the output layer is equal to the dimension
of the output vector Y. A Multilayer Perception NN always has at least one
hidden layer with k generic neurons. The neuron is a non-linear element because
its output zj is a non-linear function of its inputs X. So, problem which can be
mathematically reduced to a non-linear mapping can be solved using the NN
represented. NNs are robust with respect to random noise and sensitive to
systematic, regular signals.
From a mathematical point of view, the multi-parameter retrieval algorithm
corresponds to a continuous mapping [19]. It maps a vector of ECs, T, onto a
vector of retrieved physical parameters, g. NNs are well suited for performing a
wide variety of continuous mappings. The architecture of the NN that we used
is the OMBNN3 algorithm (Scheme 3). The NN which represents this algorithm
has n = 4 inputs, m = 3 outputs, and one hidden layer with k = 12 neurons.
This NN can be also written explicitly as:
k
n
j 1
j 1
g q  bq  aq tanh{  wqj [tanh(   jiTi  B j )]   q },.....q  1,..., m
(1)
where the matrix ji and the vector j represent weights and biases in the
neurons of the hidden layer; qj and the q represent weights and biases in the
neurons of the output layer; the aq and bq are scaling parameters.
Scheme 3
However, as shown in Scheme 3, even such an approximate separation of
signals allows the reducing of the random and systematic errors in diffusion
speed and to reduce the dependence of the diffusion speed bias on V and L.
For comparison were selected three alghoritms:
- the original global operational (cal/val) algorithm developed by Goodberlet
[20] (GSW);
- the current operational algorithm (GSWP) which is the same as the GSW
algorithm but corrected for water vapor by Petty [21];
- a physically-based (PB) retrieval algorithm developed by Wentz [22].
Table 3 shows that the NN algorithm provides significant improvement in
retrieval accuracy at high diffusion speeds. Error budgets (m/s) for different
diffusion speed algorithms and separately for higher diffusion speeds are also
considered.
TABLE 3.
Algorithm
Bias
GSW
GSWP
PB
OMBNN3
-0.2 (-0.5)
-0.1 (-0.3)
0.1 (-0.1)
-0.1 (-0.2)
Algorithm
RMSE
1.4 (1.8)
1.3 (1.6)
1.3 (1.8)
1.0 (1.3)
Total RMSE
1.8 (2.1)
1.7 (1.9)
1.7 (2.1)
1.5 (1.7)
W>15 m/s
RMSE
(2.7)
(2.6)
(2.6)
(2.3)
6. Results and Discussion
The OMBNN3 algorithm has the ability to retrieve not only diffusion speed but
also three other parameters: columnar water vapor V and columnar liquid water
L as shown in Figure 5.
Figure 6 presents diffusion speed related to molecular ratio of PDMS/PMAA
and the number of matches for the OMBNN3 algorithm.
Figure 5. Water diffusion speed retrieved by four different algorithms as
functions of columnar water vapor (Solid line - OMBNN3, dotted line - GSWP,
dashed line - GSW, and dash-dotted line the Wentz algorithm).
Figure 6. Water diffusion speed related to molecular ratio of PDMS/PMAA
7. Conclusion.
One of the challenges of modern chemistry deals with the design of
macromolecules with imposed properties. With this idea in mind we have
used/tested an empirical neural network (NN) algorithm, which simultaneously
retrieves several physical parameters over some polymer network properties
from evaporation conditions (EC), primary emphasizing on water diffusion
speed in a copolymer gel. This NN-based algorithm, which retrieves diffusion
speed, columnar water vapor, and columnar liquid water, has been developed
recently.
Conditional simulation is one of the most rational approaches for modeling
unsaturated flow and transport. The presented NN algorithm is a multiparameter one that includes some inputs, one hidden layer, and corresponding
outputs. The combined analytical-numerical multilayer Perceptron NN and
OMBNN3 approach was developed for the analysis of flow and diffusion
transport processes in porous media. The OMBNN3 and the multi-layer
Perceptron algorithms, both employing the simultaneous multi-parameter
retrieval approach, reduce the bias, and the dependence of the bias, on both
water vapor and columnar liquid water concentrations. The OMBNN3
algorithm demonstrates the best performances. The random errors for the
OMBNN3 algorithm are significantly smaller and less dependent on the other
related medium parameters than those for the other algorithms.
A comparison of this algorithm with other algorithms is also presented. The
simulation parameters can be used for optimization of the molecular ratio of the
polymer sequences to build up networks with imposed diffusion properties
according to the desired areas of application.
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