# Electron Beam Synthesis and Characterization of Acrylamide/Acrylic Acid Hydrogels Using Trimethylolpropane Trimethacrylate as Cross-Linker

Authors: Gabriela Craciun; Elena Manaila; Maria Daniela Stelescu
Journal: Journal of Chemistry
 (2016)

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## Abstract

The purpose of the paper is to present the synthesis and characterization of hydrogels prepared by free-radical copolymerization of acrylamide and acrylic acid in aqueous solutions using potassium persulfate as initiator and trimethylolpropane trimethacrylate as cross-linker, via the radiation technique. The samples were subjected to electron beam treatment in the dose range of 2 to 4 kGy and the influence of the absorbed dose and amount of cross-linker on the swelling properties, diffusion coefficient, and network parameters of hydrogels was investigated. A possible reaction mechanism for acrylamide/acrylic acid/trimethylolpropane trimethacrylate hydrogels was also suggested. The structure and morphology of hydrogels were characterized by Fourier Transform Infrared Spectroscopy and Scanning Electron Microscopy.


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## Body

## 1. Introduction

Hydrogels are three-dimensionally cross-linked hydrophilic polymers capable of swelling and retaining huge volume in the swollen state, even under pressure. These macromolecule networks can absorb water, many hundreds of times more than their dried weight. Due to their unique characteristics like hydrophilicity, swelling in aqueous media, nonsoluble nature in aqueous fluids, and ionic aspects, they are applied in biomedicine, bioengineering, pharmaceutical, food industry, or agriculture [1–3]. Because of their excellent response to changing of the environment conditions such as temperature, pH, and solvent composition, hydrogel particles distributed in soil are capable of absorbing water and then slowly releasing it from the polymeric matrix [1, 4]. Hydrogels are broadly classified into two categories: permanent or chemical gel and reversible or physical gel. Permanent or chemical gel is a covalently cross-linked network obtained by replacing hydrogen bond with a stronger and stable covalent bond [5, 6]. They reach an equilibrium swelling state which depends on the polymer-water interaction parameter and the cross-link density [5, 7]. In the reversible or physical gel, the networks are held together by molecular entanglements and/or secondary forces including ionic, hydrogen bonding or hydrophobic interactions. In the physically cross-linked gels, dissolution is prevented by physical interactions which exist between different polymer chains [5, 7].The various techniques adopted for hydrogels preparation are the physical and chemical cross-linking, the grafting polymerization, and the radiation cross-linking [5, 8–10]. The initiation of chemical reactions by using radiation is increasingly used for novel hydrogels obtaining. The radiation technique is more preferable than the chemical one, because of the advantage offered by the gentle control of cross-linking level by variation of the absorbed dose. It is a simple additive-free process which is happening at any temperature; the reactions such as polymerization, cross-linking, and grafting can be easily controlled and the treatment can be limited to a specific area [11]. The processing of materials by irradiation with accelerated electrons removes many drawbacks of the conventional technologies, because ionizing radiation initiates polymerization without thermal input from the outside, due to free radicals that are formed at the interaction with the monomers and especially with the solvent (water in this case). So, a good solution to produce polymeric materials is to use ionizing radiation and especially electron beams, which direct their energy in the entire volume of the monomeric solutions to be irradiated.The purpose of this study is to present the synthesis and characterization of some hydrogels prepared by free-radical copolymerization of acrylamide and acrylic acid in aqueous solutions using potassium persulfate as initiator and trimethylolpropane trimethacrylate as cross-linker. The free-radical copolymerization was realized by electron beam irradiation in the dose range of 2 to 4 kGy in atmospheric conditions and at room temperature. The cross-linker was used in conjunction with the radical cure systems in order to improve physical properties of the final product. A possible reaction mechanism is proposed. The obtained hydrogels were investigated through swelling and diffusion experiments and also using the infrared spectroscopy in order to evaluate the chemical structure of the obtained networks. The surface appearance was also observed using the technique of Scanning Electron Microscopy.


## 2. Experimental

### 2.1. Materials

The materials used for the obtaining of hydrogels are shown in Table1: acrylamide (AMD) and acrylic acid (AA) as comonomers, potassium persulfate (PP) as initiator, and trimethylolpropane trimethacrylate (TMPT) as cross-linker. All reagents were obtained from LACHEMA, Germany, and were used directly, without purification.Table 1
Thematerials used for the preparation of the hydrogels.
Materials
Chemicalcharacteristics
Chemical structure
Acrylamide (AMD)
(i) Molecular weight: 71.08 g/mol(ii) Density: 1.13 g/cm3 (iii) Melting point: 84.5°C(iv) Solubility in water: 2.04 kg/L at 25°C
Acrylic acid (AA)
(i) Molecular weight: 72.06 g/mol(ii) Density: 1.051 g/cm3 (iii) Melting point: 14°C(iv) Boiling point: 141°C(v) Solubility in water: miscible
Potassium persulfate (PP)
(i) Molecular weight: 270.322 g/mol(ii) Density: 2.477 g/cm3 (iii) Melting point: 14°C(iv) Boiling point: 141°C(v) Solubility in water: 1.75 g/100 mL at 0°C
K2S2O8
Trimethylolpropane trimethacrylate (TMPT)
(i) Molecular weight: 338.4 g/mol(ii) Boiling point: >200°C(iii) Density: 1.06 g/cm3 (iv) 75 ± 3% active ingredientOther chemicals used in this study for physical and chemical characterization of the hydrogels were of analytical grade.


### 2.2. Experimental Installation and Sample Preparation

The experiments were carried out using the electron linear accelerator called ALIN 10 from the National Institute for Laser, Plasma and Radiation Physics. The ALIN 10 linear accelerator is a travelling-wave type, operating at a wavelength of 10 cm and having 164 W maximum output power. The accelerating structure is a disk-loaded tube, which operates in theπ/2 mode. The optimum values of the electron beam, peak current I
E
B and EB energy E
E
B to produce maximum output power P
E
B for a fixed pulse duration τ
E
B and repetition frequency f
E
B, are as follows: E
E
B
=
6.23 MeV, I
E
B
=
75 mA, and P
E
B
=
164 W (f
E
B
=
100 Hz, τ
E
B
=
3.5 μs). The EB effects are related to the absorbed dose (D) and absorbed dose rate (D
∗). The absorbed dose is the major parameter in the electron beam (EB) irradiation [12]. The performances of polymerization and copolymerization processes are provided by the strict control of this parameter [12]. In our experiments the electron beam dose rate was fixed at 2 kGy/min, in order to accumulate doses between 2 and 4 kGy. The absorbed dose was determined using the conventional Fricke dosimeter. The thickness of 2.5 cm of the irradiated samples was established in accordance with the samples densities (of about 1 g cm−3 in our case) and EB energy. For irradiation, two types of aqueous solutions were prepared (Table 2). The solutions were placed in polyvinylchloride (PVC) containers of 3 cm diameter and irradiated in atmospheric conditions and at room temperature of 25°C with 2 kGy, 3 kGy, and 4 kGy. After irradiation, the obtained hydrogels were cut into pieces of 3
±
4 mm length, dried in air for 3 days and in a laboratory oven at 50°C for 12 hours to constant weight, and then stored in desiccators. The dried hydrogels were used to determine the parameters of swelling, diffusion, and network.Table 2
The hydrogels synthesis details.
Samples codes
Amount of chemicals (mol/L)
Irradiation dose (kGy)
AMD
AA
PP
TMPT
H1-1, H1-2, H1-3
5
0.5
3.70× 10−3
2.95× 10−3
2, 3, 4
H2-1, H2-2, H2-3
5
0.5
3.70× 10−3
5.90× 10−3
2, 3, 4


### 2.3. Sample Characterization

#### 2.3.1. Fourier Transform Infrared (FTIR) Spectroscopy Analysis

In order to obtain spectral information regarding the chemical structure of hydrogels, a FTIR spectrophotometer, JASCO FT/IR 4200, was used by ATR measurement method. Samples spectra are the average of 30 scans realized in absorption, in the range of 4000–600 cm−1, with a resolution of 4 cm−1.


#### 2.3.2. Experiments of Swelling and Diffusion

The swelling of dried hydrogels was carried out by immersion in doubly distilled water at25
±
0.1°C in a water bath, in order to determine the parameters of swelling and diffusion. The amount of absorbed water was determined by weighing the samples, after wiping with filter paper, at various time intervals. The swollen hydrogels were weighed using an electronic balance (HR 200, 0.1 mg resolution).


#### 2.3.3. Scanning Electron Microscopy (SEM)

The morphology of the lyophilized hydrogels was determined using a scanning electron microscope (FEI/Phillips, USA). Small pieces of swelled gels were freeze-dried in order to avoid the collapse of porous structure. Freeze-drying was carried out in vacuum at −80°C for 40 h using the Christ Alfa 2–4 (Martin Christ, Germany) lyophilizer. For scanning, the lyophilized samples have been cut in order to expose the inner surface. Samples were placed on an aluminum mount, sputtered with gold palladium, and then scanned at an accelerating voltage up to 30 kV.


## 2.1. Materials

The materials used for the obtaining of hydrogels are shown in Table1: acrylamide (AMD) and acrylic acid (AA) as comonomers, potassium persulfate (PP) as initiator, and trimethylolpropane trimethacrylate (TMPT) as cross-linker. All reagents were obtained from LACHEMA, Germany, and were used directly, without purification.Table 1
Thematerials used for the preparation of the hydrogels.
Materials
Chemicalcharacteristics
Chemical structure
Acrylamide (AMD)
(i) Molecular weight: 71.08 g/mol(ii) Density: 1.13 g/cm3 (iii) Melting point: 84.5°C(iv) Solubility in water: 2.04 kg/L at 25°C
Acrylic acid (AA)
(i) Molecular weight: 72.06 g/mol(ii) Density: 1.051 g/cm3 (iii) Melting point: 14°C(iv) Boiling point: 141°C(v) Solubility in water: miscible
Potassium persulfate (PP)
(i) Molecular weight: 270.322 g/mol(ii) Density: 2.477 g/cm3 (iii) Melting point: 14°C(iv) Boiling point: 141°C(v) Solubility in water: 1.75 g/100 mL at 0°C
K2S2O8
Trimethylolpropane trimethacrylate (TMPT)
(i) Molecular weight: 338.4 g/mol(ii) Boiling point: >200°C(iii) Density: 1.06 g/cm3 (iv) 75 ± 3% active ingredientOther chemicals used in this study for physical and chemical characterization of the hydrogels were of analytical grade.


## 2.2. Experimental Installation and Sample Preparation

The experiments were carried out using the electron linear accelerator called ALIN 10 from the National Institute for Laser, Plasma and Radiation Physics. The ALIN 10 linear accelerator is a travelling-wave type, operating at a wavelength of 10 cm and having 164 W maximum output power. The accelerating structure is a disk-loaded tube, which operates in theπ/2 mode. The optimum values of the electron beam, peak current I
E
B and EB energy E
E
B to produce maximum output power P
E
B for a fixed pulse duration τ
E
B and repetition frequency f
E
B, are as follows: E
E
B
=
6.23 MeV, I
E
B
=
75 mA, and P
E
B
=
164 W (f
E
B
=
100 Hz, τ
E
B
=
3.5 μs). The EB effects are related to the absorbed dose (D) and absorbed dose rate (D
∗). The absorbed dose is the major parameter in the electron beam (EB) irradiation [12]. The performances of polymerization and copolymerization processes are provided by the strict control of this parameter [12]. In our experiments the electron beam dose rate was fixed at 2 kGy/min, in order to accumulate doses between 2 and 4 kGy. The absorbed dose was determined using the conventional Fricke dosimeter. The thickness of 2.5 cm of the irradiated samples was established in accordance with the samples densities (of about 1 g cm−3 in our case) and EB energy. For irradiation, two types of aqueous solutions were prepared (Table 2). The solutions were placed in polyvinylchloride (PVC) containers of 3 cm diameter and irradiated in atmospheric conditions and at room temperature of 25°C with 2 kGy, 3 kGy, and 4 kGy. After irradiation, the obtained hydrogels were cut into pieces of 3
±
4 mm length, dried in air for 3 days and in a laboratory oven at 50°C for 12 hours to constant weight, and then stored in desiccators. The dried hydrogels were used to determine the parameters of swelling, diffusion, and network.Table 2
The hydrogels synthesis details.
Samples codes
Amount of chemicals (mol/L)
Irradiation dose (kGy)
AMD
AA
PP
TMPT
H1-1, H1-2, H1-3
5
0.5
3.70× 10−3
2.95× 10−3
2, 3, 4
H2-1, H2-2, H2-3
5
0.5
3.70× 10−3
5.90× 10−3
2, 3, 4


## 2.3. Sample Characterization

### 2.3.1. Fourier Transform Infrared (FTIR) Spectroscopy Analysis

In order to obtain spectral information regarding the chemical structure of hydrogels, a FTIR spectrophotometer, JASCO FT/IR 4200, was used by ATR measurement method. Samples spectra are the average of 30 scans realized in absorption, in the range of 4000–600 cm−1, with a resolution of 4 cm−1.


### 2.3.2. Experiments of Swelling and Diffusion

The swelling of dried hydrogels was carried out by immersion in doubly distilled water at25
±
0.1°C in a water bath, in order to determine the parameters of swelling and diffusion. The amount of absorbed water was determined by weighing the samples, after wiping with filter paper, at various time intervals. The swollen hydrogels were weighed using an electronic balance (HR 200, 0.1 mg resolution).


### 2.3.3. Scanning Electron Microscopy (SEM)

The morphology of the lyophilized hydrogels was determined using a scanning electron microscope (FEI/Phillips, USA). Small pieces of swelled gels were freeze-dried in order to avoid the collapse of porous structure. Freeze-drying was carried out in vacuum at −80°C for 40 h using the Christ Alfa 2–4 (Martin Christ, Germany) lyophilizer. For scanning, the lyophilized samples have been cut in order to expose the inner surface. Samples were placed on an aluminum mount, sputtered with gold palladium, and then scanned at an accelerating voltage up to 30 kV.


## 2.3.1. Fourier Transform Infrared (FTIR) Spectroscopy Analysis

In order to obtain spectral information regarding the chemical structure of hydrogels, a FTIR spectrophotometer, JASCO FT/IR 4200, was used by ATR measurement method. Samples spectra are the average of 30 scans realized in absorption, in the range of 4000–600 cm−1, with a resolution of 4 cm−1.


## 2.3.2. Experiments of Swelling and Diffusion

The swelling of dried hydrogels was carried out by immersion in doubly distilled water at25
±
0.1°C in a water bath, in order to determine the parameters of swelling and diffusion. The amount of absorbed water was determined by weighing the samples, after wiping with filter paper, at various time intervals. The swollen hydrogels were weighed using an electronic balance (HR 200, 0.1 mg resolution).


## 2.3.3. Scanning Electron Microscopy (SEM)

The morphology of the lyophilized hydrogels was determined using a scanning electron microscope (FEI/Phillips, USA). Small pieces of swelled gels were freeze-dried in order to avoid the collapse of porous structure. Freeze-drying was carried out in vacuum at −80°C for 40 h using the Christ Alfa 2–4 (Martin Christ, Germany) lyophilizer. For scanning, the lyophilized samples have been cut in order to expose the inner surface. Samples were placed on an aluminum mount, sputtered with gold palladium, and then scanned at an accelerating voltage up to 30 kV.


## 3. Results and Discussion

### 3.1. Synthesis and Reaction Mechanism Aspects

In our study, the EB radiation technique was used in order to prepare AMD/AA hydrogels in the presence of TMPT as cross-linker. The initiating of chemical reactions by irradiation is usually done using ionizing radiations with energies ranging from 0.5 to 10 MeV. Radio-induced polymerization is quite similar to classic polymerization through addition of free radicals. The initial phase of polymerization involves, in both types of polymerizations, classic and induced by ionizing radiations, the introducing of a certain amount of energy in the system, the initiating energy. In the case of radio-induced polymerization, the initiating energy is introduced by ionizing radiation and involves the radical formation. The advantage of radio-induced copolymerization is that the radicals can be formed by decomposition of all components of the system: solvent (in this case, water), initiator, and monomers [12–14]. A possible reaction mechanism for obtaining free radicals by electron beam irradiation from a system formed of water, potassium persulphate, and monomers (acrylamide and acrylic acid) is given in Scheme 1.Scheme 1
The scheme of possible reaction mechanism for obtaining free radicals by electron beam irradiation from a system formed of water, potassium persulphate, and monomers (acrylamide and acrylic acid).The main function of the ionizing radiation is to achieve the first step of the polymerization process: the initiation phase leading to free radical formation and to some specific side effects. The next polymerization phases, propagation, completion, and the chain transfer process, occur almost identically as in classic polymerization processes. Based on our results and literature studies [2, 15], a possible reaction mechanism for the copolymerization of acrylamide and acrylic acid by electron beam irradiation is proposed in Scheme 2.Scheme 2
The scheme of a possible reaction mechanism for obtaining hydrogels based on acrylamide and acrylic acid in the presence of free radicals formed by water radiolysis or initiator decomposition.The cross-linkers are usually used in conjunction with the radical cure systems in order to promote cross-linking reactions and to improve the physical properties. They are typically polyfunctional monomers and are effective in modification of materials not only by cross-linking but also by grafting and radical addition. The addition of an appropriate polyfunctional monomer in the polymer matrix may lead to the obtaining of a desired cross-linking density even at lower absorbed doses. By increasing the cross-link density, the network performance can be improved also. There are two important classes in which the polyfunctional monomers can be grouped, according to their influence on cure kinetics or to their physical properties. The polyfunctional monomers of type I are highly reactive and very effective for the increasing of both rate and state of cure (acrylate, methacrylate, or maleimide functionality). The polyfunctional monomers of type II are based on allyl reactive sites and increase the state of cure only. In order to obtain hydrogels with improved network characteristics and good physicochemical properties we used TMPT (a polyfunctional monomer of Type I) as cross-linker.It is suggested that the polymerization reaction of AMD/AA in presence of TMPT can be depicted as a two-step process: in the first step, a rapid initial polymerization of the polyfunctional monomer occurs and in the second step the reaction between the polymerized polyfunctional monomer and the AMD/AA chains takes place in order to form a cross-linked AMD/AA-TMPT network [16, 17]. Scheme 3 presents a possible reaction mechanism between AMD/AA chains in the presence of TMPT which occurs in EB cross-linking.Scheme 3
The scheme of a possible reaction mechanism between AMD/AA and TMPT in EB cross-linking.


### 3.2. Spectral Characterization

The infrared spectroscopy was carried out in order to investigate the chemical structure of the obtained hydrogels and the results presented in Figures1 and 2 were obtained in absorbance in the range of 4000–650 cm−1.Figure 1
FTIR spectra for hydrogels having 2.95 × 10−3 mol/L TMPT, in the range of (a) 750–2000 cm−1 and (b) 2000–4000 cm−1.
(a)
(b)Figure 2
FTIR spectra for hydrogels having 5.90× 10−3 mol/L TMPT, in the range of (a) 750–2000 cm−1 and (b) 2000–4000 cm−1.
(a)
(b)The broad bands in the range of 3345 to 3330 cm−1 are attributed to the symmetric and asymmetric –NH stretching vibrations of AMD and the broad bands in the region of 3200–3190 cm−1 are characteristic for the absorptions of –OH groups of AA. The methylene group vibrations are used to monitor the extent of polymerization. The absorbance in the range of 2937–2933 cm−1 is assigned to the asymmetrical stretching vibrations of  –CH2 from AMD or AA [18, 19]. The bands in the range of 1774–1785 cm−1 correspond to the carbonyl stretching vibration of C=O connected to the carboxyl group but in the range of 1647–1657 cm−1 can be attributed to the C=O group connected to the amide group [18]. The characteristic band which appeared in the range of 1600–1620 cm−1 is due to the amide II bands. Amide II results from the N–H bending vibration and from the C–N stretching vibration. Symmetric stretching of COO− is found at 1450–1410 cm−1 in poly(acrylamide-co-acrylic acid) spectra [18]. On the other hand, the bands at 1443 cm−1 and 1353 cm−1 are attributed to the CH2 bending and –CH bending vibrations, respectively. For the polyacrylamide, the –CN stretching appears at 1350–1345 cm−1 and –C–O stretching at 1125–1116 cm−1. The C–O–C asymmetric stretching and C–O stretching from AA are confirmed with the absorptions around 1190–1180 cm−1 and 1065–1025 cm−1, respectively [20].


### 3.3. Swelling and Diffusion Experiments

#### 3.3.1. The Measurement of Gel Fraction

Normally, the hydrogel content of a given material is estimated by measuring its insoluble part in dried sample after immersion in water. In order to determine the gel fraction and the soluble fraction in the obtained hydrogels, dried samples of 0.05 g were immersed in double distilled water in order to swell for 72 h [4]. After filtration, the extracted gel was dewatered by nonsolvent ethanol, dried in air and then to constant weight in a laboratory oven for 5 h at 50°C, and finally reweighed. The gel fraction and soluble fraction were determined as follows [21]:(1)
Sol_fraction
%
=
W
0
-
W
1
W
0
×
100
,
Gel_fraction
%
=
100
-
Sol_fraction
,where W
0 is the initial weight of the dried sample and W
1 is the weight of sample after extraction from the water and drying.Figure3 shows the effect of the absorbed dose and amount of TMPT on the gel fraction and soluble fraction of hydrogels. It was found that the gel fraction depends on the concentration of TMPT, increases with radiation dose increasing, and attains a maximum at the radiation dose of 4 kGy.Figure 3
The effect of the absorbed dose and amount of PP and TMPT on gel fraction and soluble fraction of hydrogels.


#### 3.3.2. Swelling Measurements

On the cross-linked AMD/AA/TMPT hydrogels, the dynamic swelling experiments were performed in distilled water, at room temperature (25
±
0.1°C), and the mass increasing was pursued as a function of time. A fundamental relationship exists between the swelling of a polymer in a solvent and the nature of polymer and solvent. The swelling S, expressed in percentages, was calculated from the following relation [15, 22]:(2)
S
%
=
M
t
-
M
0
M
0
×
100
,where M
t is the mass of the swollen gel at time t and M
0 is the initial mass of the dried gel (at time t
=
0).The water intake of initially dried hydrogels was pursued for a long period of time. The hydrogels swelling isotherms, as a function of the absorbed dose and the amount of cross-linker, are shown in Figure4.Figure 4
The effect of the absorbed dose and amount of TMPT on the hydrogels swelling.It can be seen that the swelling increases with the increase of the TMPT amount at the same absorbed dose, until a certain point when it becomes constant. It can be noticed that, for the sample which contains a higher amount of TMPT (5.90 × 10−3 mol/L) even at the highest irradiation dose (4 kGy), the swelling is around 3900%, compared with the sample irradiated at the same dose, but with a lower content of TMPT (2.95 × 10−3 mol/L), for which the swelling is almost 3500%. Also, the swelling is strictly dependent on the absorbed dose. The swelling decreases with the increasing of absorbed dose, since the degree of cross-linking increases and the water entering is restricted.


#### 3.3.3. Equilibrium Water Content

Another parameter used for the assessment of hydrogels swelling is the percentage of equilibrium water content (EWC%) and it can be calculated from the following equation [22, 23]: (3)
EWC
=
M
S
-
M
0
M
S
×
100
,where M
S is the mass of the swollen gel at equilibrium and M
0 is the mass of the dried gel at time t
=
0.The results are presented in Figure5 and it can be noticed that all samples show values of EWC% over 95%, even for high irradiation doses. Also, the EWC% values of hydrogels which contain high amounts of TMPT are larger compared to those that contain small amounts at the same absorbed dose. This result can be explained by the fact that TMPT is a hexafunctional cross-linker and its use in large amounts may form several bonds between chains [22].Figure 5
The effect of the absorbed dose and amount of TMPT on the equilibrium water content of hydrogels.


#### 3.3.4. Swelling Kinetics

In order to examine the controlling mechanism of the swelling processes, several kinetic models are used to test experimental data. A simple kinetic analysis is the first-order equation in the form [15](4)
d
S
d
t
=
k
1
,
S
S
max.
-
S
,where  k
1
,
S is the rate constant of first-order swelling and S
max. is the degree of swelling at equilibrium.After the definite integration by applying the initial condition (S
=
0 at t
=
0 and S
=
S at t
=
t) equation becomes(5)
ln
⁡
W
=
k
1
,
S
t
,
W
=
S
m
a
x
.
S
max.
-
S
.A second-order equation based on swelling equilibrium degree is expressed in the form [15](6)
d
S
d
t
=
k
2
,
S
S
max.
-
S
2
,where k
2
,
S is the rate constant of second-order swelling.After integration and applying the initial condition (S
=
0 at t
=
0 and S
=
S at t
=
t), equation becomes(7)
t
S
=
A
+
B
t
,where A is the reciprocal of the initial swelling rate and B is the inverse of the degree swelling at equilibrium:(8)
A
=
r
0
=
1
k
2
,
S
×
S
max.
2
,
B
=
1
S
max.
.Also, by fitting the experimental data using the first-order equation and the second-order equation (Figure6), the swelling kinetic parameters including the rate constant of first- and second-order swelling (k
1
,
S and k
2
,
S), the theoretical degree swelling at equilibrium (S
max.), and the initial swelling rate (r
0) can be calculated from the slope and intercept of lines (Figure 6). The results are listed in Tables 3 and 4.Table 3
The variation of first-orderk
1
,
S/min−1 and second-order k
2
,
S/g gel (g water min)−1 swelling rate constants with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
k
1
,
S  × 103
2.95× 10−3
3.14
2.59
2.65
5.90× 10−3
2.81
2.08
2.61
k
2
,
S  × 107
2.95× 10−3
6.28
4.65
5.83
5.90× 10−3
2.15
2.65
5.46Table 4
The variation of initial swelling rater
0/g water (g gel min−1) and equilibrium swelling degrees (theoretical) S
max
⁡
./g water (g gel)−1 with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
r
0  × 102
2.95× 10−3
3.42
6.29
9.21
5.90× 10−3
3.63
6.44
7.76
S
max.
2.95× 10−3
6820
5843
4315
5.90× 10−3
11321
7651
4859Figure 6
The first-order (a) and the second-order (b) swelling kinetics of hydrogels.
(a)
(b)From Table3 it is observed that the swelling rate constant decreases with the increase in the amount of TMPT, indicating that the diffusion rate decreases at higher TMPT concentrations. This suggests that the water diffusion at higher TMPT concentrations is hindered due to steric obstacles caused by association which leads to denser gel structure [24].It can be noticed that the initial swelling rate constant (r
0) of the hydrogels has rapidly increased with the increasing of absorbed dose for both TMPT concentrations. For samples which contain a higher amount of cross-linker, the initial swelling rate constant is small at the highest absorbed dose, compared with the samples that have a lower content of cross-linker at the same absorbed dose (4 kGy). TMPT has a high degree of functionality, fast undergoes addition reactions, and increases the cross-linking degree of the hydrogels. The swelling properties of hydrogels containing cross-linkers are changed because of the structure of cross-linker. When the cross-linkers are added to the hydrogel systems, it is known that they will cause changes in the swelling ratio of hydrogels, because the molecules of cross-linkers are placed between the chains of monomers [25]. The maximum equilibrium swelling ratios theoretically calculated are in a good agreement with the equilibrium swelling ratios experimentally obtained. As it is shown in Figure 6, the second-order swelling equation seems to fit better than the first-order equation.


#### 3.3.5. Determination of Swelling Power

Because of the hydrogels applications in biomedicine, pharmaceutical, environmental, and agricultural engineering, the analysis of the mechanisms of water diffusion has gained considerable attention lately. When a glassy hydrogel is brought in contact with water, water diffuses into the hydrogel and the hydrogel swells. Diffusion involves migration of water into preexisting or dynamically formed spaces between the chains of hydrogel. The swelling of hydrogels involves a larger scale segmental motion, resulting ultimately in an increased distance of separation between hydrogel chains. By the exploiting of the swelling experiment, the diffusion of water into hydrogel can be determined. By applying the following equation to the 60% of swelling curves, the nature of the diffusion of water into hydrogels can be evaluated [25]:(9)
F
swp
=
M
t
-
M
0
M
0
=
k
t
n
,
ln
⁡
F
swp
=
n
ln
⁡
t
+
ln
⁡
k
,where M
t and M
0 are the mass of the swollen and dry sample at time t, k is the swelling constant, and n is the swelling exponent which is indicative of the transport mechanism.The abovementioned equation is valid for the first 60% from the fractional uptake. For the hydrogels obtained in this study,ln
⁡
F versus ln
⁡
t values are plotted and are shown in Figure 7. The swelling constant and swelling exponent are calculated from the slopes and intercepts of the lines, respectively, and are listed in Table 5. According to the relative rates of diffusion (R
d
i
f
f) and relaxation (R
r
e
l
a
x), there are three cases of diffusion [26–28]: Case I: n
=
0.45
–
0.5 indicates a Fickian diffusion mechanism, in which the rate of diffusion is much smaller than the rate of relaxation (R
d
i
f
f
≪
R
r
e
l
a
x) and the system is controlled by diffusion; Case II: n
=
1.0, where the diffusion process is much faster than the relaxation process (R
d
i
f
f
≫
R
r
e
l
a
x) and the system is controlled by relaxation; Case III: 0.5
<
n
<
1.0 indicates non-Fickian (anomalous) diffusion mechanism, which describes those cases where the diffusion and relaxation rates are comparable (R
d
i
f
f
≈
R
r
e
l
a
x). Occasionally, when n
>
1, the situation is regarded as Super Case II kinetics [26, 29, 30].Table 5
The variation ofn and k with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
n
2.95× 10−3
0.86
0.89
0.85
5.90× 10−3
0.82
0.70
0.88
k
2.95× 10−3
0.281
0.164
0.137
5.90× 10−3
0.444
0.507
0.142Figure 7
The plots ofln
⁡
F versus ln
⁡
t for hydrogels.From Table5 it is observed that the values of swelling coefficient vary between 0.7 and 0.89. Due to these results, we can say that the diffusion of water into the hydrogels obtained in this study shows a non-Fickian character.The study of water diffusion phenomena in hydrogels clarifies the polymer behavior. The swelling-time curves of hydrogels in water are used to calculate the diffusion coefficients. One of the methods for calculating the diffusion coefficient (D) isthe short time approximation method. This method is valid only for the first 60% of the swelling [15]. The diffusion coefficients have been calculated using the following relation:(10)
F
=
4
D
π
×
r
2
1
/
2
t
1
/
2
,where D is in cm2 sec−1, t is in sec, and r is the radius of cylindrical polymer sample (cm).For the hydrogels obtained in this study, the graphs ofF versus t
1
/
2 are showed in Figure 8. The diffusion coefficients were calculated from the slopes of the lines and the results are listed in Table 6.Table 6
The variation of the diffusional coefficient (D × 10−4/cm2 sec−1) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
2.95× 10−3
2.43
2.15
1.63
5.90× 10−3
16.17
5.49
4.08Figure 8
Plots ofF versus t
1
/
2 for hydrogels.From Table6 the increasing trend for diffusional coefficients with the increase of TMPT amount and their decreasing trend with the decrease of absorbed dose are observed. From Figure 5 it is observed that the equilibrium water content shows the same variation trend. This can be explained as follows: the increasing of the number of cross-links inside the network per volume unit leads to the decreasing of the free spaces for water molecules, so the water uptake decreases.


#### 3.3.6. Network Studies

One of the most important structural parameters for the characterization of the cross-linked polymers isM
c, the average molar mass between cross-links, which is directly related to the cross-link density. The swelling equilibrium is widely used to determine M
c. According to the theory of Flory and Rehner for a perfect network, M
c is calculated using the following relation [15]:(11)
M
c
=
-
V
1
d
p
ν
S
1
/
3
-
ν
S
/
2
ln
⁡
1
-
ν
S
+
ν
S
+
χ
ν
S
2
,where V
1 is the molar volume of the solvent (in this case water: 18 cm3 mol−1), d
p is the polymer density (1.106 g cm−3), ν
S is the volume fraction of the polymer in the swollen gel (cm3) and is equal to 1
/
S, and χ is the Flory-Huggins interaction parameter between the solvent and polymer.The value ofχ is calculated as follows [31–33]:(12)
χ
=
0.431
-
0.311
ν
S
-
0.036
ν
S
2
.The cross-link density, q, is defined as being the mole fraction of the cross-linked units:(13)
q
=
M
0
M
c
,where M
0 is the molecular weight of the repeating units from polymer and is calculated using the following relation [31, 33]:(14)
M
0
=
m
AMD
×
M
AMD
+
m
AA
×
M
AA
+
m
TMPT
×
M
TMPT
m
AMD
+
m
AA
+
m
TMPT
,where m
AMD,  m
AA, and m
TMPT are the masses of acrylamide, acrylic acid, and cross-linker (TMPT) expressed in grams and M
AMD,   M
AA, and M
TMPT are the molar masses of acrylamide, acrylic acid, and TMPT expressed in g mol−1.Another parameter used for cross-link density characterization isυ
e which represents the number of elastically effective chains totally included in a network per volume unit and it is calculated with the following relation:(15)
υ
e
=
d
p
N
A
q
M
0
,where N
A is the Avogadro number.The values of parametersM
c, q, and υ
e were calculated as above and are listed in Table 7.Table 7
The variation of the number-average molar mass between cross-links (M
c/g mol−1), cross-link density (q), and number of elastically effective chains (υ
e) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
M
c  × 10−3
2.95 × 10−3
589 817
407 327
239 736
5.90 × 10−3
1 187 695
584 394
296 537
q  × 107
2.95 × 10−3
1.218
1.764
2.997
5.90 × 10−3
0.610
1.241
2.445
υ
e  × 1014
2.95 × 10−3
1.875
2.715
4.613
5.90 × 10−3
0.931
1.892
3.729From Table7 it is observed that the number-average molar mass between cross-links of hydrogels has increased with the increasing of the amount of cross-linker (TMPT) but has decreased with the increasing of absorbed dose. The values of the cross-link density and number of elastically effective chains are inversed due to the value of number-average molar mass between cross-links. The increasing of the amount of cross-linker decreases the cross-linking density and increases the swelling (Figure 5), because the hydrogels obtained are not stiff. Increasing the cross-linker concentration increases M
c between the two main backbones. A large value of M
c indicates long chains between the two backbones. The obtained results show that the M
c values are affected by the absorbed dose. The increasing of absorbed dose leads to the decreasing of M
c, since the hydrogel becomes more and more dense. However, AMD includes several hydrophilic fragments and thus the hydrogels show a high degree of swelling.Other important parameters used for the assessment of networks are gel pore size or mesh size (ξ) and porosity (P%). Using the calculated values of number-average molecular mass between cross-links, M
c, the mesh size was determined with the following equation [34]:(16)
ξ
=
ν
S
-
1
/
3
2
C
n
M
c
M
r
,where ν
S is the volume fraction of the polymer in the swollen gel, l is the length of the C–C bond along the polymer backbone (0.154 nm), C
n is the Flory characteristic ratio of the polymer, and M
r is the molecular mass of the repeated unit.The characteristic ratioC
n, for poly(AMD-co-AA) hydrogels, was taken as the weighted average of C
n values for poly(AMD) and poly(AA) chains, according to their molar ratio in the hydrogel (C
n was taken as 8.8 and 6.7 for poly(AMD) and poly(AA), resp.).The porosityP (%) of the obtained hydrogels was determined using the following equation [15]:(17)
P
%
=
V
d
1
-
V
d
×
100
,where V
d is the volume ratio of water at equilibrium. The values of the mesh size ξ (nm) and porosity (P) are shown in Table 8.Table 8
The variation of mesh size (ξ) and porosity (P) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
ξ
/nm
2.95× 10−3
161.46
124.81
86.37
5.90× 10−3
262.94
160.43
100.11
P (%)
2.95× 10−3
98.34
97.93
97.15
5.90× 10−3
98.91
98.33
97.49As it is presented in Table8, the mesh size and porosity have increased with the increasing of the amount of cross-linker (TMPT) and have decreased with increasing of the absorbed dose. The mesh size is related to the space available for transport of a solute or of a solvent in a network. The increasing of the mesh size and porosity results in the increasing of water content in the hydrogel. More than that, from the results it is observed that the degree of cross-linking had a significant influence on the mesh size. Hydrogels having higher degree of cross-linking have a relatively shorter distance between two cross-linking points and as a result, the mesh sizes and porosity of these hydrogels are lower.


### 3.4. SEM Analysis

The surface appearance and the structure of copolymers were observed using the technique of Scanning Electron Microscopy. The scanning electron micrographs of hydrogels obtained by electron beam irradiation at 2 kGy, 3 kGy, and 4 kGy, respectively, are shown in Figures9–11.Figure 9
Scanning electron micrographs of hydrogels obtained by electron beam irradiation at 2 kGy: (a) 2.95 × 10−3 mol/L TMPT; (b) 5.90 × 10−3 mol/L TMPT.
(a)
(b)Figure 10
Scanning electron micrographs of hydrogels obtained by electron beam irradiation at 3 kGy: (a) 2.95 × 10−3 mol/L TMPT; (b) 5.90 × 10−3 mol/L TMPT.
(a)
(b)Figure 11
Scanning electron micrographs of hydrogels obtained by electron beam irradiation at 4 kGy: (a) 2.95 × 10−3 mol/L TMPT; (b) 5.90 × 10−3 mol/L TMPT.
(a)
(b)The cross-link density and composition affect the microstructure of hydrogels which in turn influences the swelling characteristics. From the results presented in Table7 it is observed that the cross-link density of hydrogels has decreased with the increasing of the amount of cross-linker (TMPT) but has increased with the increasing of absorbed dose. On the other hand, the mesh size and porosity have increased with the increasing of the amount of cross-linker (TMPT) and have decreased with increasing of the absorbed dose (Table 8). As it can be seen from Figures 9(a) and 9(b), the hydrogels having a high amount of TMPT (5.90 × 10−3 mol/L) and irradiated at 2 kGy have presented a more open and porous channel structure than the hydrogels having a lower content of TMPT (2.95 × 10−3 mol/L) and irradiated at the same irradiation dose. These pores facilitate the transport of water [35–37]. The results are in concordance with the observations from swelling studies. With the increasing of the absorbed dose, the morphology of the hydrogels is changing. The SEM micrographs of the hydrogels obtained at 3 kGy (Figure 10) show a semiporous structure with thick struts between pores (a) and a porous structure with a broad network (b). As it can be seen from Figures 11(a) and 11(b), the SEM micrographs of hydrogels obtained at 4 kGy present an irregular surface with semiporous structure, with macro- and micropores within the hydrogels.


## 3.1. Synthesis and Reaction Mechanism Aspects

In our study, the EB radiation technique was used in order to prepare AMD/AA hydrogels in the presence of TMPT as cross-linker. The initiating of chemical reactions by irradiation is usually done using ionizing radiations with energies ranging from 0.5 to 10 MeV. Radio-induced polymerization is quite similar to classic polymerization through addition of free radicals. The initial phase of polymerization involves, in both types of polymerizations, classic and induced by ionizing radiations, the introducing of a certain amount of energy in the system, the initiating energy. In the case of radio-induced polymerization, the initiating energy is introduced by ionizing radiation and involves the radical formation. The advantage of radio-induced copolymerization is that the radicals can be formed by decomposition of all components of the system: solvent (in this case, water), initiator, and monomers [12–14]. A possible reaction mechanism for obtaining free radicals by electron beam irradiation from a system formed of water, potassium persulphate, and monomers (acrylamide and acrylic acid) is given in Scheme 1.Scheme 1
The scheme of possible reaction mechanism for obtaining free radicals by electron beam irradiation from a system formed of water, potassium persulphate, and monomers (acrylamide and acrylic acid).The main function of the ionizing radiation is to achieve the first step of the polymerization process: the initiation phase leading to free radical formation and to some specific side effects. The next polymerization phases, propagation, completion, and the chain transfer process, occur almost identically as in classic polymerization processes. Based on our results and literature studies [2, 15], a possible reaction mechanism for the copolymerization of acrylamide and acrylic acid by electron beam irradiation is proposed in Scheme 2.Scheme 2
The scheme of a possible reaction mechanism for obtaining hydrogels based on acrylamide and acrylic acid in the presence of free radicals formed by water radiolysis or initiator decomposition.The cross-linkers are usually used in conjunction with the radical cure systems in order to promote cross-linking reactions and to improve the physical properties. They are typically polyfunctional monomers and are effective in modification of materials not only by cross-linking but also by grafting and radical addition. The addition of an appropriate polyfunctional monomer in the polymer matrix may lead to the obtaining of a desired cross-linking density even at lower absorbed doses. By increasing the cross-link density, the network performance can be improved also. There are two important classes in which the polyfunctional monomers can be grouped, according to their influence on cure kinetics or to their physical properties. The polyfunctional monomers of type I are highly reactive and very effective for the increasing of both rate and state of cure (acrylate, methacrylate, or maleimide functionality). The polyfunctional monomers of type II are based on allyl reactive sites and increase the state of cure only. In order to obtain hydrogels with improved network characteristics and good physicochemical properties we used TMPT (a polyfunctional monomer of Type I) as cross-linker.It is suggested that the polymerization reaction of AMD/AA in presence of TMPT can be depicted as a two-step process: in the first step, a rapid initial polymerization of the polyfunctional monomer occurs and in the second step the reaction between the polymerized polyfunctional monomer and the AMD/AA chains takes place in order to form a cross-linked AMD/AA-TMPT network [16, 17]. Scheme 3 presents a possible reaction mechanism between AMD/AA chains in the presence of TMPT which occurs in EB cross-linking.Scheme 3
The scheme of a possible reaction mechanism between AMD/AA and TMPT in EB cross-linking.


## 3.2. Spectral Characterization

The infrared spectroscopy was carried out in order to investigate the chemical structure of the obtained hydrogels and the results presented in Figures1 and 2 were obtained in absorbance in the range of 4000–650 cm−1.Figure 1
FTIR spectra for hydrogels having 2.95 × 10−3 mol/L TMPT, in the range of (a) 750–2000 cm−1 and (b) 2000–4000 cm−1.
(a)
(b)Figure 2
FTIR spectra for hydrogels having 5.90× 10−3 mol/L TMPT, in the range of (a) 750–2000 cm−1 and (b) 2000–4000 cm−1.
(a)
(b)The broad bands in the range of 3345 to 3330 cm−1 are attributed to the symmetric and asymmetric –NH stretching vibrations of AMD and the broad bands in the region of 3200–3190 cm−1 are characteristic for the absorptions of –OH groups of AA. The methylene group vibrations are used to monitor the extent of polymerization. The absorbance in the range of 2937–2933 cm−1 is assigned to the asymmetrical stretching vibrations of  –CH2 from AMD or AA [18, 19]. The bands in the range of 1774–1785 cm−1 correspond to the carbonyl stretching vibration of C=O connected to the carboxyl group but in the range of 1647–1657 cm−1 can be attributed to the C=O group connected to the amide group [18]. The characteristic band which appeared in the range of 1600–1620 cm−1 is due to the amide II bands. Amide II results from the N–H bending vibration and from the C–N stretching vibration. Symmetric stretching of COO− is found at 1450–1410 cm−1 in poly(acrylamide-co-acrylic acid) spectra [18]. On the other hand, the bands at 1443 cm−1 and 1353 cm−1 are attributed to the CH2 bending and –CH bending vibrations, respectively. For the polyacrylamide, the –CN stretching appears at 1350–1345 cm−1 and –C–O stretching at 1125–1116 cm−1. The C–O–C asymmetric stretching and C–O stretching from AA are confirmed with the absorptions around 1190–1180 cm−1 and 1065–1025 cm−1, respectively [20].


## 3.3. Swelling and Diffusion Experiments

### 3.3.1. The Measurement of Gel Fraction

Normally, the hydrogel content of a given material is estimated by measuring its insoluble part in dried sample after immersion in water. In order to determine the gel fraction and the soluble fraction in the obtained hydrogels, dried samples of 0.05 g were immersed in double distilled water in order to swell for 72 h [4]. After filtration, the extracted gel was dewatered by nonsolvent ethanol, dried in air and then to constant weight in a laboratory oven for 5 h at 50°C, and finally reweighed. The gel fraction and soluble fraction were determined as follows [21]:(1)
Sol_fraction
%
=
W
0
-
W
1
W
0
×
100
,
Gel_fraction
%
=
100
-
Sol_fraction
,where W
0 is the initial weight of the dried sample and W
1 is the weight of sample after extraction from the water and drying.Figure3 shows the effect of the absorbed dose and amount of TMPT on the gel fraction and soluble fraction of hydrogels. It was found that the gel fraction depends on the concentration of TMPT, increases with radiation dose increasing, and attains a maximum at the radiation dose of 4 kGy.Figure 3
The effect of the absorbed dose and amount of PP and TMPT on gel fraction and soluble fraction of hydrogels.


### 3.3.2. Swelling Measurements

On the cross-linked AMD/AA/TMPT hydrogels, the dynamic swelling experiments were performed in distilled water, at room temperature (25
±
0.1°C), and the mass increasing was pursued as a function of time. A fundamental relationship exists between the swelling of a polymer in a solvent and the nature of polymer and solvent. The swelling S, expressed in percentages, was calculated from the following relation [15, 22]:(2)
S
%
=
M
t
-
M
0
M
0
×
100
,where M
t is the mass of the swollen gel at time t and M
0 is the initial mass of the dried gel (at time t
=
0).The water intake of initially dried hydrogels was pursued for a long period of time. The hydrogels swelling isotherms, as a function of the absorbed dose and the amount of cross-linker, are shown in Figure4.Figure 4
The effect of the absorbed dose and amount of TMPT on the hydrogels swelling.It can be seen that the swelling increases with the increase of the TMPT amount at the same absorbed dose, until a certain point when it becomes constant. It can be noticed that, for the sample which contains a higher amount of TMPT (5.90 × 10−3 mol/L) even at the highest irradiation dose (4 kGy), the swelling is around 3900%, compared with the sample irradiated at the same dose, but with a lower content of TMPT (2.95 × 10−3 mol/L), for which the swelling is almost 3500%. Also, the swelling is strictly dependent on the absorbed dose. The swelling decreases with the increasing of absorbed dose, since the degree of cross-linking increases and the water entering is restricted.


### 3.3.3. Equilibrium Water Content

Another parameter used for the assessment of hydrogels swelling is the percentage of equilibrium water content (EWC%) and it can be calculated from the following equation [22, 23]: (3)
EWC
=
M
S
-
M
0
M
S
×
100
,where M
S is the mass of the swollen gel at equilibrium and M
0 is the mass of the dried gel at time t
=
0.The results are presented in Figure5 and it can be noticed that all samples show values of EWC% over 95%, even for high irradiation doses. Also, the EWC% values of hydrogels which contain high amounts of TMPT are larger compared to those that contain small amounts at the same absorbed dose. This result can be explained by the fact that TMPT is a hexafunctional cross-linker and its use in large amounts may form several bonds between chains [22].Figure 5
The effect of the absorbed dose and amount of TMPT on the equilibrium water content of hydrogels.


### 3.3.4. Swelling Kinetics

In order to examine the controlling mechanism of the swelling processes, several kinetic models are used to test experimental data. A simple kinetic analysis is the first-order equation in the form [15](4)
d
S
d
t
=
k
1
,
S
S
max.
-
S
,where  k
1
,
S is the rate constant of first-order swelling and S
max. is the degree of swelling at equilibrium.After the definite integration by applying the initial condition (S
=
0 at t
=
0 and S
=
S at t
=
t) equation becomes(5)
ln
⁡
W
=
k
1
,
S
t
,
W
=
S
m
a
x
.
S
max.
-
S
.A second-order equation based on swelling equilibrium degree is expressed in the form [15](6)
d
S
d
t
=
k
2
,
S
S
max.
-
S
2
,where k
2
,
S is the rate constant of second-order swelling.After integration and applying the initial condition (S
=
0 at t
=
0 and S
=
S at t
=
t), equation becomes(7)
t
S
=
A
+
B
t
,where A is the reciprocal of the initial swelling rate and B is the inverse of the degree swelling at equilibrium:(8)
A
=
r
0
=
1
k
2
,
S
×
S
max.
2
,
B
=
1
S
max.
.Also, by fitting the experimental data using the first-order equation and the second-order equation (Figure6), the swelling kinetic parameters including the rate constant of first- and second-order swelling (k
1
,
S and k
2
,
S), the theoretical degree swelling at equilibrium (S
max.), and the initial swelling rate (r
0) can be calculated from the slope and intercept of lines (Figure 6). The results are listed in Tables 3 and 4.Table 3
The variation of first-orderk
1
,
S/min−1 and second-order k
2
,
S/g gel (g water min)−1 swelling rate constants with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
k
1
,
S  × 103
2.95× 10−3
3.14
2.59
2.65
5.90× 10−3
2.81
2.08
2.61
k
2
,
S  × 107
2.95× 10−3
6.28
4.65
5.83
5.90× 10−3
2.15
2.65
5.46Table 4
The variation of initial swelling rater
0/g water (g gel min−1) and equilibrium swelling degrees (theoretical) S
max
⁡
./g water (g gel)−1 with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
r
0  × 102
2.95× 10−3
3.42
6.29
9.21
5.90× 10−3
3.63
6.44
7.76
S
max.
2.95× 10−3
6820
5843
4315
5.90× 10−3
11321
7651
4859Figure 6
The first-order (a) and the second-order (b) swelling kinetics of hydrogels.
(a)
(b)From Table3 it is observed that the swelling rate constant decreases with the increase in the amount of TMPT, indicating that the diffusion rate decreases at higher TMPT concentrations. This suggests that the water diffusion at higher TMPT concentrations is hindered due to steric obstacles caused by association which leads to denser gel structure [24].It can be noticed that the initial swelling rate constant (r
0) of the hydrogels has rapidly increased with the increasing of absorbed dose for both TMPT concentrations. For samples which contain a higher amount of cross-linker, the initial swelling rate constant is small at the highest absorbed dose, compared with the samples that have a lower content of cross-linker at the same absorbed dose (4 kGy). TMPT has a high degree of functionality, fast undergoes addition reactions, and increases the cross-linking degree of the hydrogels. The swelling properties of hydrogels containing cross-linkers are changed because of the structure of cross-linker. When the cross-linkers are added to the hydrogel systems, it is known that they will cause changes in the swelling ratio of hydrogels, because the molecules of cross-linkers are placed between the chains of monomers [25]. The maximum equilibrium swelling ratios theoretically calculated are in a good agreement with the equilibrium swelling ratios experimentally obtained. As it is shown in Figure 6, the second-order swelling equation seems to fit better than the first-order equation.


### 3.3.5. Determination of Swelling Power

Because of the hydrogels applications in biomedicine, pharmaceutical, environmental, and agricultural engineering, the analysis of the mechanisms of water diffusion has gained considerable attention lately. When a glassy hydrogel is brought in contact with water, water diffuses into the hydrogel and the hydrogel swells. Diffusion involves migration of water into preexisting or dynamically formed spaces between the chains of hydrogel. The swelling of hydrogels involves a larger scale segmental motion, resulting ultimately in an increased distance of separation between hydrogel chains. By the exploiting of the swelling experiment, the diffusion of water into hydrogel can be determined. By applying the following equation to the 60% of swelling curves, the nature of the diffusion of water into hydrogels can be evaluated [25]:(9)
F
swp
=
M
t
-
M
0
M
0
=
k
t
n
,
ln
⁡
F
swp
=
n
ln
⁡
t
+
ln
⁡
k
,where M
t and M
0 are the mass of the swollen and dry sample at time t, k is the swelling constant, and n is the swelling exponent which is indicative of the transport mechanism.The abovementioned equation is valid for the first 60% from the fractional uptake. For the hydrogels obtained in this study,ln
⁡
F versus ln
⁡
t values are plotted and are shown in Figure 7. The swelling constant and swelling exponent are calculated from the slopes and intercepts of the lines, respectively, and are listed in Table 5. According to the relative rates of diffusion (R
d
i
f
f) and relaxation (R
r
e
l
a
x), there are three cases of diffusion [26–28]: Case I: n
=
0.45
–
0.5 indicates a Fickian diffusion mechanism, in which the rate of diffusion is much smaller than the rate of relaxation (R
d
i
f
f
≪
R
r
e
l
a
x) and the system is controlled by diffusion; Case II: n
=
1.0, where the diffusion process is much faster than the relaxation process (R
d
i
f
f
≫
R
r
e
l
a
x) and the system is controlled by relaxation; Case III: 0.5
<
n
<
1.0 indicates non-Fickian (anomalous) diffusion mechanism, which describes those cases where the diffusion and relaxation rates are comparable (R
d
i
f
f
≈
R
r
e
l
a
x). Occasionally, when n
>
1, the situation is regarded as Super Case II kinetics [26, 29, 30].Table 5
The variation ofn and k with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
n
2.95× 10−3
0.86
0.89
0.85
5.90× 10−3
0.82
0.70
0.88
k
2.95× 10−3
0.281
0.164
0.137
5.90× 10−3
0.444
0.507
0.142Figure 7
The plots ofln
⁡
F versus ln
⁡
t for hydrogels.From Table5 it is observed that the values of swelling coefficient vary between 0.7 and 0.89. Due to these results, we can say that the diffusion of water into the hydrogels obtained in this study shows a non-Fickian character.The study of water diffusion phenomena in hydrogels clarifies the polymer behavior. The swelling-time curves of hydrogels in water are used to calculate the diffusion coefficients. One of the methods for calculating the diffusion coefficient (D) isthe short time approximation method. This method is valid only for the first 60% of the swelling [15]. The diffusion coefficients have been calculated using the following relation:(10)
F
=
4
D
π
×
r
2
1
/
2
t
1
/
2
,where D is in cm2 sec−1, t is in sec, and r is the radius of cylindrical polymer sample (cm).For the hydrogels obtained in this study, the graphs ofF versus t
1
/
2 are showed in Figure 8. The diffusion coefficients were calculated from the slopes of the lines and the results are listed in Table 6.Table 6
The variation of the diffusional coefficient (D × 10−4/cm2 sec−1) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
2.95× 10−3
2.43
2.15
1.63
5.90× 10−3
16.17
5.49
4.08Figure 8
Plots ofF versus t
1
/
2 for hydrogels.From Table6 the increasing trend for diffusional coefficients with the increase of TMPT amount and their decreasing trend with the decrease of absorbed dose are observed. From Figure 5 it is observed that the equilibrium water content shows the same variation trend. This can be explained as follows: the increasing of the number of cross-links inside the network per volume unit leads to the decreasing of the free spaces for water molecules, so the water uptake decreases.


### 3.3.6. Network Studies

One of the most important structural parameters for the characterization of the cross-linked polymers isM
c, the average molar mass between cross-links, which is directly related to the cross-link density. The swelling equilibrium is widely used to determine M
c. According to the theory of Flory and Rehner for a perfect network, M
c is calculated using the following relation [15]:(11)
M
c
=
-
V
1
d
p
ν
S
1
/
3
-
ν
S
/
2
ln
⁡
1
-
ν
S
+
ν
S
+
χ
ν
S
2
,where V
1 is the molar volume of the solvent (in this case water: 18 cm3 mol−1), d
p is the polymer density (1.106 g cm−3), ν
S is the volume fraction of the polymer in the swollen gel (cm3) and is equal to 1
/
S, and χ is the Flory-Huggins interaction parameter between the solvent and polymer.The value ofχ is calculated as follows [31–33]:(12)
χ
=
0.431
-
0.311
ν
S
-
0.036
ν
S
2
.The cross-link density, q, is defined as being the mole fraction of the cross-linked units:(13)
q
=
M
0
M
c
,where M
0 is the molecular weight of the repeating units from polymer and is calculated using the following relation [31, 33]:(14)
M
0
=
m
AMD
×
M
AMD
+
m
AA
×
M
AA
+
m
TMPT
×
M
TMPT
m
AMD
+
m
AA
+
m
TMPT
,where m
AMD,  m
AA, and m
TMPT are the masses of acrylamide, acrylic acid, and cross-linker (TMPT) expressed in grams and M
AMD,   M
AA, and M
TMPT are the molar masses of acrylamide, acrylic acid, and TMPT expressed in g mol−1.Another parameter used for cross-link density characterization isυ
e which represents the number of elastically effective chains totally included in a network per volume unit and it is calculated with the following relation:(15)
υ
e
=
d
p
N
A
q
M
0
,where N
A is the Avogadro number.The values of parametersM
c, q, and υ
e were calculated as above and are listed in Table 7.Table 7
The variation of the number-average molar mass between cross-links (M
c/g mol−1), cross-link density (q), and number of elastically effective chains (υ
e) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
M
c  × 10−3
2.95 × 10−3
589 817
407 327
239 736
5.90 × 10−3
1 187 695
584 394
296 537
q  × 107
2.95 × 10−3
1.218
1.764
2.997
5.90 × 10−3
0.610
1.241
2.445
υ
e  × 1014
2.95 × 10−3
1.875
2.715
4.613
5.90 × 10−3
0.931
1.892
3.729From Table7 it is observed that the number-average molar mass between cross-links of hydrogels has increased with the increasing of the amount of cross-linker (TMPT) but has decreased with the increasing of absorbed dose. The values of the cross-link density and number of elastically effective chains are inversed due to the value of number-average molar mass between cross-links. The increasing of the amount of cross-linker decreases the cross-linking density and increases the swelling (Figure 5), because the hydrogels obtained are not stiff. Increasing the cross-linker concentration increases M
c between the two main backbones. A large value of M
c indicates long chains between the two backbones. The obtained results show that the M
c values are affected by the absorbed dose. The increasing of absorbed dose leads to the decreasing of M
c, since the hydrogel becomes more and more dense. However, AMD includes several hydrophilic fragments and thus the hydrogels show a high degree of swelling.Other important parameters used for the assessment of networks are gel pore size or mesh size (ξ) and porosity (P%). Using the calculated values of number-average molecular mass between cross-links, M
c, the mesh size was determined with the following equation [34]:(16)
ξ
=
ν
S
-
1
/
3
2
C
n
M
c
M
r
,where ν
S is the volume fraction of the polymer in the swollen gel, l is the length of the C–C bond along the polymer backbone (0.154 nm), C
n is the Flory characteristic ratio of the polymer, and M
r is the molecular mass of the repeated unit.The characteristic ratioC
n, for poly(AMD-co-AA) hydrogels, was taken as the weighted average of C
n values for poly(AMD) and poly(AA) chains, according to their molar ratio in the hydrogel (C
n was taken as 8.8 and 6.7 for poly(AMD) and poly(AA), resp.).The porosityP (%) of the obtained hydrogels was determined using the following equation [15]:(17)
P
%
=
V
d
1
-
V
d
×
100
,where V
d is the volume ratio of water at equilibrium. The values of the mesh size ξ (nm) and porosity (P) are shown in Table 8.Table 8
The variation of mesh size (ξ) and porosity (P) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
ξ
/nm
2.95× 10−3
161.46
124.81
86.37
5.90× 10−3
262.94
160.43
100.11
P (%)
2.95× 10−3
98.34
97.93
97.15
5.90× 10−3
98.91
98.33
97.49As it is presented in Table8, the mesh size and porosity have increased with the increasing of the amount of cross-linker (TMPT) and have decreased with increasing of the absorbed dose. The mesh size is related to the space available for transport of a solute or of a solvent in a network. The increasing of the mesh size and porosity results in the increasing of water content in the hydrogel. More than that, from the results it is observed that the degree of cross-linking had a significant influence on the mesh size. Hydrogels having higher degree of cross-linking have a relatively shorter distance between two cross-linking points and as a result, the mesh sizes and porosity of these hydrogels are lower.


## 3.3.1. The Measurement of Gel Fraction

Normally, the hydrogel content of a given material is estimated by measuring its insoluble part in dried sample after immersion in water. In order to determine the gel fraction and the soluble fraction in the obtained hydrogels, dried samples of 0.05 g were immersed in double distilled water in order to swell for 72 h [4]. After filtration, the extracted gel was dewatered by nonsolvent ethanol, dried in air and then to constant weight in a laboratory oven for 5 h at 50°C, and finally reweighed. The gel fraction and soluble fraction were determined as follows [21]:(1)
Sol_fraction
%
=
W
0
-
W
1
W
0
×
100
,
Gel_fraction
%
=
100
-
Sol_fraction
,where W
0 is the initial weight of the dried sample and W
1 is the weight of sample after extraction from the water and drying.Figure3 shows the effect of the absorbed dose and amount of TMPT on the gel fraction and soluble fraction of hydrogels. It was found that the gel fraction depends on the concentration of TMPT, increases with radiation dose increasing, and attains a maximum at the radiation dose of 4 kGy.Figure 3
The effect of the absorbed dose and amount of PP and TMPT on gel fraction and soluble fraction of hydrogels.


## 3.3.2. Swelling Measurements

On the cross-linked AMD/AA/TMPT hydrogels, the dynamic swelling experiments were performed in distilled water, at room temperature (25
±
0.1°C), and the mass increasing was pursued as a function of time. A fundamental relationship exists between the swelling of a polymer in a solvent and the nature of polymer and solvent. The swelling S, expressed in percentages, was calculated from the following relation [15, 22]:(2)
S
%
=
M
t
-
M
0
M
0
×
100
,where M
t is the mass of the swollen gel at time t and M
0 is the initial mass of the dried gel (at time t
=
0).The water intake of initially dried hydrogels was pursued for a long period of time. The hydrogels swelling isotherms, as a function of the absorbed dose and the amount of cross-linker, are shown in Figure4.Figure 4
The effect of the absorbed dose and amount of TMPT on the hydrogels swelling.It can be seen that the swelling increases with the increase of the TMPT amount at the same absorbed dose, until a certain point when it becomes constant. It can be noticed that, for the sample which contains a higher amount of TMPT (5.90 × 10−3 mol/L) even at the highest irradiation dose (4 kGy), the swelling is around 3900%, compared with the sample irradiated at the same dose, but with a lower content of TMPT (2.95 × 10−3 mol/L), for which the swelling is almost 3500%. Also, the swelling is strictly dependent on the absorbed dose. The swelling decreases with the increasing of absorbed dose, since the degree of cross-linking increases and the water entering is restricted.


## 3.3.3. Equilibrium Water Content

Another parameter used for the assessment of hydrogels swelling is the percentage of equilibrium water content (EWC%) and it can be calculated from the following equation [22, 23]: (3)
EWC
=
M
S
-
M
0
M
S
×
100
,where M
S is the mass of the swollen gel at equilibrium and M
0 is the mass of the dried gel at time t
=
0.The results are presented in Figure5 and it can be noticed that all samples show values of EWC% over 95%, even for high irradiation doses. Also, the EWC% values of hydrogels which contain high amounts of TMPT are larger compared to those that contain small amounts at the same absorbed dose. This result can be explained by the fact that TMPT is a hexafunctional cross-linker and its use in large amounts may form several bonds between chains [22].Figure 5
The effect of the absorbed dose and amount of TMPT on the equilibrium water content of hydrogels.


## 3.3.4. Swelling Kinetics

In order to examine the controlling mechanism of the swelling processes, several kinetic models are used to test experimental data. A simple kinetic analysis is the first-order equation in the form [15](4)
d
S
d
t
=
k
1
,
S
S
max.
-
S
,where  k
1
,
S is the rate constant of first-order swelling and S
max. is the degree of swelling at equilibrium.After the definite integration by applying the initial condition (S
=
0 at t
=
0 and S
=
S at t
=
t) equation becomes(5)
ln
⁡
W
=
k
1
,
S
t
,
W
=
S
m
a
x
.
S
max.
-
S
.A second-order equation based on swelling equilibrium degree is expressed in the form [15](6)
d
S
d
t
=
k
2
,
S
S
max.
-
S
2
,where k
2
,
S is the rate constant of second-order swelling.After integration and applying the initial condition (S
=
0 at t
=
0 and S
=
S at t
=
t), equation becomes(7)
t
S
=
A
+
B
t
,where A is the reciprocal of the initial swelling rate and B is the inverse of the degree swelling at equilibrium:(8)
A
=
r
0
=
1
k
2
,
S
×
S
max.
2
,
B
=
1
S
max.
.Also, by fitting the experimental data using the first-order equation and the second-order equation (Figure6), the swelling kinetic parameters including the rate constant of first- and second-order swelling (k
1
,
S and k
2
,
S), the theoretical degree swelling at equilibrium (S
max.), and the initial swelling rate (r
0) can be calculated from the slope and intercept of lines (Figure 6). The results are listed in Tables 3 and 4.Table 3
The variation of first-orderk
1
,
S/min−1 and second-order k
2
,
S/g gel (g water min)−1 swelling rate constants with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
k
1
,
S  × 103
2.95× 10−3
3.14
2.59
2.65
5.90× 10−3
2.81
2.08
2.61
k
2
,
S  × 107
2.95× 10−3
6.28
4.65
5.83
5.90× 10−3
2.15
2.65
5.46Table 4
The variation of initial swelling rater
0/g water (g gel min−1) and equilibrium swelling degrees (theoretical) S
max
⁡
./g water (g gel)−1 with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
r
0  × 102
2.95× 10−3
3.42
6.29
9.21
5.90× 10−3
3.63
6.44
7.76
S
max.
2.95× 10−3
6820
5843
4315
5.90× 10−3
11321
7651
4859Figure 6
The first-order (a) and the second-order (b) swelling kinetics of hydrogels.
(a)
(b)From Table3 it is observed that the swelling rate constant decreases with the increase in the amount of TMPT, indicating that the diffusion rate decreases at higher TMPT concentrations. This suggests that the water diffusion at higher TMPT concentrations is hindered due to steric obstacles caused by association which leads to denser gel structure [24].It can be noticed that the initial swelling rate constant (r
0) of the hydrogels has rapidly increased with the increasing of absorbed dose for both TMPT concentrations. For samples which contain a higher amount of cross-linker, the initial swelling rate constant is small at the highest absorbed dose, compared with the samples that have a lower content of cross-linker at the same absorbed dose (4 kGy). TMPT has a high degree of functionality, fast undergoes addition reactions, and increases the cross-linking degree of the hydrogels. The swelling properties of hydrogels containing cross-linkers are changed because of the structure of cross-linker. When the cross-linkers are added to the hydrogel systems, it is known that they will cause changes in the swelling ratio of hydrogels, because the molecules of cross-linkers are placed between the chains of monomers [25]. The maximum equilibrium swelling ratios theoretically calculated are in a good agreement with the equilibrium swelling ratios experimentally obtained. As it is shown in Figure 6, the second-order swelling equation seems to fit better than the first-order equation.


## 3.3.5. Determination of Swelling Power

Because of the hydrogels applications in biomedicine, pharmaceutical, environmental, and agricultural engineering, the analysis of the mechanisms of water diffusion has gained considerable attention lately. When a glassy hydrogel is brought in contact with water, water diffuses into the hydrogel and the hydrogel swells. Diffusion involves migration of water into preexisting or dynamically formed spaces between the chains of hydrogel. The swelling of hydrogels involves a larger scale segmental motion, resulting ultimately in an increased distance of separation between hydrogel chains. By the exploiting of the swelling experiment, the diffusion of water into hydrogel can be determined. By applying the following equation to the 60% of swelling curves, the nature of the diffusion of water into hydrogels can be evaluated [25]:(9)
F
swp
=
M
t
-
M
0
M
0
=
k
t
n
,
ln
⁡
F
swp
=
n
ln
⁡
t
+
ln
⁡
k
,where M
t and M
0 are the mass of the swollen and dry sample at time t, k is the swelling constant, and n is the swelling exponent which is indicative of the transport mechanism.The abovementioned equation is valid for the first 60% from the fractional uptake. For the hydrogels obtained in this study,ln
⁡
F versus ln
⁡
t values are plotted and are shown in Figure 7. The swelling constant and swelling exponent are calculated from the slopes and intercepts of the lines, respectively, and are listed in Table 5. According to the relative rates of diffusion (R
d
i
f
f) and relaxation (R
r
e
l
a
x), there are three cases of diffusion [26–28]: Case I: n
=
0.45
–
0.5 indicates a Fickian diffusion mechanism, in which the rate of diffusion is much smaller than the rate of relaxation (R
d
i
f
f
≪
R
r
e
l
a
x) and the system is controlled by diffusion; Case II: n
=
1.0, where the diffusion process is much faster than the relaxation process (R
d
i
f
f
≫
R
r
e
l
a
x) and the system is controlled by relaxation; Case III: 0.5
<
n
<
1.0 indicates non-Fickian (anomalous) diffusion mechanism, which describes those cases where the diffusion and relaxation rates are comparable (R
d
i
f
f
≈
R
r
e
l
a
x). Occasionally, when n
>
1, the situation is regarded as Super Case II kinetics [26, 29, 30].Table 5
The variation ofn and k with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
n
2.95× 10−3
0.86
0.89
0.85
5.90× 10−3
0.82
0.70
0.88
k
2.95× 10−3
0.281
0.164
0.137
5.90× 10−3
0.444
0.507
0.142Figure 7
The plots ofln
⁡
F versus ln
⁡
t for hydrogels.From Table5 it is observed that the values of swelling coefficient vary between 0.7 and 0.89. Due to these results, we can say that the diffusion of water into the hydrogels obtained in this study shows a non-Fickian character.The study of water diffusion phenomena in hydrogels clarifies the polymer behavior. The swelling-time curves of hydrogels in water are used to calculate the diffusion coefficients. One of the methods for calculating the diffusion coefficient (D) isthe short time approximation method. This method is valid only for the first 60% of the swelling [15]. The diffusion coefficients have been calculated using the following relation:(10)
F
=
4
D
π
×
r
2
1
/
2
t
1
/
2
,where D is in cm2 sec−1, t is in sec, and r is the radius of cylindrical polymer sample (cm).For the hydrogels obtained in this study, the graphs ofF versus t
1
/
2 are showed in Figure 8. The diffusion coefficients were calculated from the slopes of the lines and the results are listed in Table 6.Table 6
The variation of the diffusional coefficient (D × 10−4/cm2 sec−1) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
2.95× 10−3
2.43
2.15
1.63
5.90× 10−3
16.17
5.49
4.08Figure 8
Plots ofF versus t
1
/
2 for hydrogels.From Table6 the increasing trend for diffusional coefficients with the increase of TMPT amount and their decreasing trend with the decrease of absorbed dose are observed. From Figure 5 it is observed that the equilibrium water content shows the same variation trend. This can be explained as follows: the increasing of the number of cross-links inside the network per volume unit leads to the decreasing of the free spaces for water molecules, so the water uptake decreases.


## 3.3.6. Network Studies

One of the most important structural parameters for the characterization of the cross-linked polymers isM
c, the average molar mass between cross-links, which is directly related to the cross-link density. The swelling equilibrium is widely used to determine M
c. According to the theory of Flory and Rehner for a perfect network, M
c is calculated using the following relation [15]:(11)
M
c
=
-
V
1
d
p
ν
S
1
/
3
-
ν
S
/
2
ln
⁡
1
-
ν
S
+
ν
S
+
χ
ν
S
2
,where V
1 is the molar volume of the solvent (in this case water: 18 cm3 mol−1), d
p is the polymer density (1.106 g cm−3), ν
S is the volume fraction of the polymer in the swollen gel (cm3) and is equal to 1
/
S, and χ is the Flory-Huggins interaction parameter between the solvent and polymer.The value ofχ is calculated as follows [31–33]:(12)
χ
=
0.431
-
0.311
ν
S
-
0.036
ν
S
2
.The cross-link density, q, is defined as being the mole fraction of the cross-linked units:(13)
q
=
M
0
M
c
,where M
0 is the molecular weight of the repeating units from polymer and is calculated using the following relation [31, 33]:(14)
M
0
=
m
AMD
×
M
AMD
+
m
AA
×
M
AA
+
m
TMPT
×
M
TMPT
m
AMD
+
m
AA
+
m
TMPT
,where m
AMD,  m
AA, and m
TMPT are the masses of acrylamide, acrylic acid, and cross-linker (TMPT) expressed in grams and M
AMD,   M
AA, and M
TMPT are the molar masses of acrylamide, acrylic acid, and TMPT expressed in g mol−1.Another parameter used for cross-link density characterization isυ
e which represents the number of elastically effective chains totally included in a network per volume unit and it is calculated with the following relation:(15)
υ
e
=
d
p
N
A
q
M
0
,where N
A is the Avogadro number.The values of parametersM
c, q, and υ
e were calculated as above and are listed in Table 7.Table 7
The variation of the number-average molar mass between cross-links (M
c/g mol−1), cross-link density (q), and number of elastically effective chains (υ
e) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
M
c  × 10−3
2.95 × 10−3
589 817
407 327
239 736
5.90 × 10−3
1 187 695
584 394
296 537
q  × 107
2.95 × 10−3
1.218
1.764
2.997
5.90 × 10−3
0.610
1.241
2.445
υ
e  × 1014
2.95 × 10−3
1.875
2.715
4.613
5.90 × 10−3
0.931
1.892
3.729From Table7 it is observed that the number-average molar mass between cross-links of hydrogels has increased with the increasing of the amount of cross-linker (TMPT) but has decreased with the increasing of absorbed dose. The values of the cross-link density and number of elastically effective chains are inversed due to the value of number-average molar mass between cross-links. The increasing of the amount of cross-linker decreases the cross-linking density and increases the swelling (Figure 5), because the hydrogels obtained are not stiff. Increasing the cross-linker concentration increases M
c between the two main backbones. A large value of M
c indicates long chains between the two backbones. The obtained results show that the M
c values are affected by the absorbed dose. The increasing of absorbed dose leads to the decreasing of M
c, since the hydrogel becomes more and more dense. However, AMD includes several hydrophilic fragments and thus the hydrogels show a high degree of swelling.Other important parameters used for the assessment of networks are gel pore size or mesh size (ξ) and porosity (P%). Using the calculated values of number-average molecular mass between cross-links, M
c, the mesh size was determined with the following equation [34]:(16)
ξ
=
ν
S
-
1
/
3
2
C
n
M
c
M
r
,where ν
S is the volume fraction of the polymer in the swollen gel, l is the length of the C–C bond along the polymer backbone (0.154 nm), C
n is the Flory characteristic ratio of the polymer, and M
r is the molecular mass of the repeated unit.The characteristic ratioC
n, for poly(AMD-co-AA) hydrogels, was taken as the weighted average of C
n values for poly(AMD) and poly(AA) chains, according to their molar ratio in the hydrogel (C
n was taken as 8.8 and 6.7 for poly(AMD) and poly(AA), resp.).The porosityP (%) of the obtained hydrogels was determined using the following equation [15]:(17)
P
%
=
V
d
1
-
V
d
×
100
,where V
d is the volume ratio of water at equilibrium. The values of the mesh size ξ (nm) and porosity (P) are shown in Table 8.Table 8
The variation of mesh size (ξ) and porosity (P) with the amount of TMPT and absorbed dose.
TMPT (mol/L)
Absorbed dose (kGy)
2
3
4
ξ
/nm
2.95× 10−3
161.46
124.81
86.37
5.90× 10−3
262.94
160.43
100.11
P (%)
2.95× 10−3
98.34
97.93
97.15
5.90× 10−3
98.91
98.33
97.49As it is presented in Table8, the mesh size and porosity have increased with the increasing of the amount of cross-linker (TMPT) and have decreased with increasing of the absorbed dose. The mesh size is related to the space available for transport of a solute or of a solvent in a network. The increasing of the mesh size and porosity results in the increasing of water content in the hydrogel. More than that, from the results it is observed that the degree of cross-linking had a significant influence on the mesh size. Hydrogels having higher degree of cross-linking have a relatively shorter distance between two cross-linking points and as a result, the mesh sizes and porosity of these hydrogels are lower.


## 3.4. SEM Analysis

The surface appearance and the structure of copolymers were observed using the technique of Scanning Electron Microscopy. The scanning electron micrographs of hydrogels obtained by electron beam irradiation at 2 kGy, 3 kGy, and 4 kGy, respectively, are shown in Figures9–11.Figure 9
Scanning electron micrographs of hydrogels obtained by electron beam irradiation at 2 kGy: (a) 2.95 × 10−3 mol/L TMPT; (b) 5.90 × 10−3 mol/L TMPT.
(a)
(b)Figure 10
Scanning electron micrographs of hydrogels obtained by electron beam irradiation at 3 kGy: (a) 2.95 × 10−3 mol/L TMPT; (b) 5.90 × 10−3 mol/L TMPT.
(a)
(b)Figure 11
Scanning electron micrographs of hydrogels obtained by electron beam irradiation at 4 kGy: (a) 2.95 × 10−3 mol/L TMPT; (b) 5.90 × 10−3 mol/L TMPT.
(a)
(b)The cross-link density and composition affect the microstructure of hydrogels which in turn influences the swelling characteristics. From the results presented in Table7 it is observed that the cross-link density of hydrogels has decreased with the increasing of the amount of cross-linker (TMPT) but has increased with the increasing of absorbed dose. On the other hand, the mesh size and porosity have increased with the increasing of the amount of cross-linker (TMPT) and have decreased with increasing of the absorbed dose (Table 8). As it can be seen from Figures 9(a) and 9(b), the hydrogels having a high amount of TMPT (5.90 × 10−3 mol/L) and irradiated at 2 kGy have presented a more open and porous channel structure than the hydrogels having a lower content of TMPT (2.95 × 10−3 mol/L) and irradiated at the same irradiation dose. These pores facilitate the transport of water [35–37]. The results are in concordance with the observations from swelling studies. With the increasing of the absorbed dose, the morphology of the hydrogels is changing. The SEM micrographs of the hydrogels obtained at 3 kGy (Figure 10) show a semiporous structure with thick struts between pores (a) and a porous structure with a broad network (b). As it can be seen from Figures 11(a) and 11(b), the SEM micrographs of hydrogels obtained at 4 kGy present an irregular surface with semiporous structure, with macro- and micropores within the hydrogels.


## 4. Conclusions

In this paper the synthesis and characterization of some hydrogels prepared by free-radical copolymerization of acrylamide and acrylic acid in aqueous solutions using potassium persulfate as initiator and trimethylolpropane trimethacrylate as cross-linker are presented. The hydrogels were obtained by electron beam irradiation in the dose range of 2 to 4 kGy in atmospheric conditions and at room temperature. The cross-linker was used in conjunction with the radical cure systems in order to improve physical properties of the final product. A possible reaction mechanism was proposed. Therefore, the reaction in presence of TMPT was described as a two-step process: the first step consists of the rapid initial polymerization of the polyfunctional monomer and in the second step the reaction between the polymerized polyfunctional monomer and the chains of AMD/AA takes place in order to form a cross-linked AMD/AA-TMPT network. The infrared spectroscopy was carried out in order to investigate the chemical structure of the obtained hydrogels. So, the symmetric and asymmetric –NH stretching vibrations of AMD and the absorptions of –OH groups of AA were highlighted. For monitoring the extension of polymerization, the methylene group vibrations were used. The asymmetrical stretching vibrations of –CH2 from AMD or AA were highlighted also. Were also found the bands which correspond to the carbonyl stretching vibration of C=O connected to the carboxyl group and amide group. From polyacrylamide, the –CN stretching and –C–O stretching have been found. The C–O–C asymmetric stretching and C–O stretching from AA were confirmed.The obtained hydrogels were investigated through swelling and diffusion experiments. Thus, gel fraction and swelling measurements, evaluations of the equilibrium water content and kinetics of swelling, determination of swelling power, and finally network studies were performed. It was found that the gel fraction depends on the concentration of TMPT, increases with the radiation dose increasing, and attains a maximum at the radiation dose of 4 kGy. The swelling is strictly dependent on the absorbed dose. It presents an increasing with the increasing of the amount of TMPT at the same absorbed dose and a decreasing with the increasing of absorbed dose, since the degree of cross-linking is increased and the water entering is restricted. Swelling of the hydrogels having 2.95 × 10−3 mol/L cross-linker has increased up to 2000%, while swelling of the hydrogels having 5.9 × 10−3 mol/L cross-linker has increased up to 3000%. The percentage of the equilibrium water content for the hydrogels which contain a high amount of TMPT was found higher compared to those which contain smaller amounts obtained at the same absorbed dose. The maximum equilibrium swelling ratios theoretically calculated are in a good agreement with the equilibrium swelling ratios experimentally obtained.Diffusion coefficients of hydrogels were calculated by the short time approximation and were found as being 1.43 × 10−4–1.64 × 10−4/cm2 sec−1 and 16.17 × 10−4–3.21 × 10−4/cm2 sec−1 for a cross-linker concentration of 2.95 × 10−3 mol/L and of 5.9 × 10−3 mol/L, respectively. They have the same variation trend as the equilibrium water content. They increase with the increasing of TMPT amount and decrease with the decreasing of absorbed dose. The number-average molar mass between cross-links of hydrogels increased with the increasing of the amount of cross-linker (TMPT) but decreased with the increasing of absorbed dose. Also, the mesh size and porosity have increased with the increasing of the amount of cross-linker (TMPT) and have decreased with increasing of the absorbed dose. Hydrogels having higher degree of cross-linking have a relatively shorter distance between two cross-linking points and for this reason, the mesh sizes and porosity of these hydrogels have decreased.The surface appearance and the structure of copolymers were observed also using the technique of Scanning Electron Microscopy. The hydrogels having a high amount of TMPT (5.90 × 10−3 mol/L) and irradiated at 2 kGy have presented a more open and porous channel structure than the hydrogels having a lower content of TMPT (2.95 × 10−3 mol/L) and irradiated at the same irradiation dose. The results are in concordance with the observations from swelling studies. With the increasing of the absorbed dose, the morphology of the hydrogels is changing. The SEM micrographs of the hydrogels obtained at 3 kGy show a semiporous structure with thick struts between pores and a porous structure with a broad network. The SEM micrographs of hydrogels obtained at 4 kGy present an irregular surface with semiporous structure.



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*Source: 1470965-2016-04-05.xml*