Polyacrylamide (PAA) has a very high molecular mass and high electrical load, which makes it suitable for many applications, especially condensing and sludge dehydration processes as well as coagulants in various industrial processes. In the effluent, due to the concentration of polyacrylonitrile polymer, the pH is between 4.5 and 7.5, which provides hydrolysis of polyacrylonitrile. Therefore, before the proximity of polyacrylonitrile (PAN), according to the following mechanism, at first, the cyanide group is converted CONH2 (Poly acrylamide) and then hydrolyzed to the carboxylate group [poly acrylic carboxylate (PAC)] [28].
The reaction of PAN to PAA with PAA interface is as follows that the difference between thermodynamic functions (Eth) compared to PAN and PAC in accordance with the following equation is calculated:
(1)
|
ΔEth = Eth (PAA)-Eth (PAN)
|
(2)
|
ΔEth = Eth (PAC)-Eth (PAA)
|
The calculated thermodynamic functions for structures of PAN, PAA and PAC (Table 2) are: total Energy (Etotal), Zero-point vibrational energy (ZPE), reaction formation (Ho), Gibes free energy (Go), dipole moment (μ), heat capacity (Cv) and entropy (So). The results show that dipole moment (D) for PAC has decreased than to PAN, but carboxylate groups are more hydrophilic than cyanide groups and as a result the level of hydrolyzed polymers become more hydrophilic. The reason for this can be related to the hydrogen bonding of carboxylate groups with water molecules on the surface of the polymer. Zero-point vibrational energy for the PAA intermediate has the highest value, which is related to the functional group CONH2, by converting it to the carboxylate group, the value of ZEP reaches 1530.62kJ.mol-1. The data in Table 2 shows energy calculations of highest occupied molecular orbital (EHOMO), lowest unoccupied molecular orbital (ELUMO and gap energy (Eg=ELUMO-EHOMO).
The highest value of EHOMO belongs to PAA and the lowest value of ELUMO belongs to PAC, which indicates the progress of the reaction towards the hydrolysis of PAN. The chemical activity of the compounds shown in Table 2 is described by: the chemical or electronegative potential (χ) which is a measure of the hardness and softness of the molecular structure (χ=-(ELUMO+EHOMO)/2), the chemical hardness (η) is η=(ELUMO-EHOMO)/2, chemical softness (σ) is calculated with σ=1-η, and the electrophoresis (ω) is ω=χ2/(2η).
Table 2. Calculated thermodynamic functions and chemical activities for the hydrolysis of PAN to PAC.
S
J.K-1.mol-1
|
Cv
J.K-1.mol-1
|
Go
kJ.mol-1
|
Ho
kJ.mol-1
|
ZEP
kJ.mol-1
|
μ
D
|
Etotal
kJ.mol-1
|
|
111.43
|
56.39
|
-445.789
|
-412.567
|
120.68
|
11.17
|
-217.63
|
PAN
|
113.87
|
65.41
|
-436.724
|
-402.773
|
175.10
|
9.73
|
-79.51
|
PAA
|
120.59
|
69.77
|
-469.584
|
-433.629
|
153.06
|
4.29
|
-276.14
|
PAC
|
ω
eV
|
σ
eV
|
η
eV
|
χ
eV
|
Eg
eV
|
LUMO
eV
|
HOMO
eV
|
|
10.62
|
-5.54
|
6.54
|
11.79
|
0.65
|
-12.44
|
0.65
|
PAN
|
7.39
|
-4.29
|
5.29
|
8.85
|
0.87
|
-9.72
|
0.87
|
PAA
|
11.14
|
-4.20
|
5.20
|
10.77
|
-0.18
|
-10.59
|
-0.18
|
PAC
|
According of equations 1 and 2 are calculated chemical activity data and the difference in the thermodynamic functions of the two polyacrylonitrile hydrolysis reactions (Table 3). The data show, that polyacrylonitrile (PAC) has a softer chemical structure and is more electrophilic. It can easily interact with TiO2 nanoparticles and reduces polyacrylamide in the environment.
Table 3. Thermodynamic parameters of two reactions of polyacrylonitrile hydrolysis.
ΔS
J.K-1.mol-1
|
ΔGo
kJ.mol-1
|
ΔHo
kJ.mol-1
|
|
2.44
|
9.07
|
9.79
|
PAN→PAA
|
6.72
|
-32.86
|
-30.86
|
PAA→PAC
|
Therefore, the results show that the presence of carboxylate groups creates a better bond between polyacrylonitrile polymer and titanium dioxide nanoparticles, because one of these new methods of increasing the hydrophilicity of the membrane surface is adding nanoparticles to the polymer structure. Due to their very small size, the nanoparticles are placed in the empty spaces between polymer chains in the structure. Also, since polyacrylonitrile is hydrolyzed and has carboxylate groups. They provide the possibility of stabilizing nanoparticles on their surface. The presence of these groups causes the formation of strong dative bonds and as a result stabilizes titanium dioxide nanoparticles on the used polymer. Titanium dioxide has two important allotropic forms; rutile and anatase. The rutile form has a higher density and higher refractive index than anatase. In this study, the rutile form (Figure 3) is used.
First, the rutile structure of titanium dioxide nanoparticles is simulated, and then, using the previous calculation method and basis. The structure is optimized and prepared for composite with hydrolyzed polyacrylonitrile (PAC). The polymers used in the entire study, have been considered as octamers so can be investigated all aspects and mechanisms of their interactions.
-Modification of PAC using titanium dioxide nanoparticles
Titanium dioxide nanoparticles were simulated in the form of rutile crystals. In this study, hydrolyzed polyacrylonitriles (PAC) are approached from four sides to rutile titanium dioxide nanoparticles and interaction is created between them. Figure 4 shows the optimized structure of this modified polymeric nanoabsorbent (rTiO2@PAC).
The hydrolyzed polymer structure of polyacrylonitrile with titanium dioxide nanofiller (rTiO2@PAC) was simulated in four stages and subjected to thermodynamic and electrical calculations. Figure 5 shows the steps of addition. At first, when PAC approaches rutile titanium dioxide nanoparticles, all the structural and thermodynamic properties show a significant change because are changing the symmetry and geometric structure of the compounds. Table 4 shows the thermodynamic properties of the addition stages of hydrolyzed polyacrylonitrile, which, by adding titanium dioxide nanoparticles, its thermodynamic properties such as dipole moment increased, which indicates changes in the symmetry and overall structure of the composition. When PAC is added in the second stage, due to the creation of more structural symmetry, the dipole moment decreases and reaches 8.63D, and finally, with the addition of four PAC polymer structures, the dipole moment reaches its lowest value, 7.71D.
By examining Gibbs free energy and enthalpy, the lowest value belongs to the fourth stage, which shows the tendency of titanium dioxide nanoparticles to interact with PAC polymer, according to the laboratory data of increasing titanium dioxide nanoparticles to PAC polymer [27] and matching Well between the results, it shows the correctness of the calculation data. The reduction of entropy and heat capacity in the second and fourth stages shows the stability of the structure and order created in the modified polymer. The structural parameters of Table 4 show that with the addition of titanium dioxide nanoparticles, the gap energy is reduced, which indicates the reduction of the distance between the energy levels of the HOMO and LUMO orbitals. Therefore, the softness of the chemical structure increases (σIV=-3.44eV) and its hardness decreases (μ=4.44eV), which causes the absorption of environmental pollutants and its reduction to other products, and the retention and blockage between pores decreases. This is the result of compliance. It is good with experimental data [27].
Table 4. Thermodynamic parameters of polyacrylonitrile membrane modification steps with rutile titanium dioxide nanoparticles.
S
J.K-1.mol-1
|
Cv
J.K-1.mol-1
|
Go
kJ.mol-1
|
Ho
kJ.mol-1
|
ZEP
kJ.mol-1
|
μ
D
|
Etotal
kJ.mol-1
|
|
1137.34
|
719.39
|
-101.73
|
-101.28
|
215.29
|
9.97
|
285.55
|
I
|
1080.13
|
715.21
|
-106.57
|
-106.48
|
209.74
|
8.63
|
282.99
|
II
|
1512.14
|
765.88
|
-126.71
|
-112.73
|
319.42
|
9.56
|
293.75
|
III
|
1092.67
|
686.29
|
-227.68
|
-265.45
|
356.95
|
7.71
|
377.56
|
IV
|
ω
eV
|
σ
eV
|
η
eV
|
χ
eV
|
Eg
eV
|
LUMO
eV
|
HOMO
eV
|
|
0.46
|
-3.76
|
4.76
|
2.11
|
9.52
|
-6.87
|
2.65
|
I
|
0.68
|
-3.53
|
4.54
|
2.49
|
9.07
|
-7.02
|
2.05
|
II
|
0.42
|
-3.71
|
4.71
|
2.00
|
9.41
|
-6.71
|
2.70
|
III
|
0.44
|
-3.44
|
4.44
|
1.99
|
8.88
|
-6.43
|
2.45
|
IV
|
After simulating the modifications done on the nanopolymer and its composite with rTiO2, the steps of approaching polyacrylamide and turning it into other materials by the modified nanoabsorbent ((C24H32O16)4Ti9O6) such as:
(C24H32O16)4Ti9O6 + C24H40N8O8 → (C24H32O16)4Ti9O6--- C24H40N8O8
(C24H32O16)4Ti9O6--- C24H40N8O8 → (C24H32O16)4Ti9O6 + 4N2 + 10C2H4 + 4CO2
This absorption and conversion of polyacrylamide is in 5 stages, which are: presence in the environment, proximity to the nano-absorbent, orientation, electron exchange and conversion to the product. In steps 1 to 3, as mentioned, polyacrylamide (C24H40N8O8) approaches the rTiO2@PAC nanocomposite and is placed in a suitable position for electron exchange with nanoparticles inside the membrane, which after the exchange and interaction in the fourth step, poly Acrylamide turns into ethylene, carbon dioxide and nitrogen compounds. Simulation steps and optimized geometric structures (Figure 6) and its thermodynamic and structural properties are calculated using B3LYP/6-31*G++ calculation method.
Table 5 shows the thermodynamic parameters of reduction and removal of polyacrylamide from the water environment. All the calculations have been done in aqueous environment and with the approach of polyacrylamide from stage I to III, there are no significant changes in many thermodynamic parameters, while the dipole moment has increased, which indicates structural changes in the complex created between created pollutant and nanoabsorbent. In the fourth stage, these changes are more noticeable, which indicates the interaction between them. The thermodynamic parameters in the A-V stage show significant changes, which indicate the reduction in polyacrylamide and its conversion to other compounds. These transformations have heat of formation and negative free energy, which indicates the spontaneity and exothermic nature of the reaction. By comparing the experimental data [27], after placing the rTiO2@PAC nanocomposite in an aqueous environment containing polyacrylamide and analyzing the output solution, its structural reduction has been observed.
Table 5. Thermodynamic parameters of polyacrylamide reduction by modified rTiO2@PAC membrane.
S
J.K-1.mol-1
|
Cv
J.K-1.mol-1
|
Go
kJ.mol-1
|
Ho
kJ.mol-1
|
ZEP
kJ.mol-1
|
μ
D
|
Etotal
kJ.mol-1
|
|
2763.14
|
874.33
|
-267.69
|
-265.78
|
360.85
|
4.52
|
391.23
|
A-I
|
2778.75
|
876.54
|
-264.12
|
-262.53
|
367.45
|
4.78
|
389.01
|
A-II
|
2781.39
|
878.97
|
-264.03
|
-261.86
|
367.95
|
4.79
|
370.78
|
A-III
|
2779.75
|
881.56
|
-263.59
|
-261.06
|
371.25
|
5.13
|
399.96
|
A-IV
|
2811.76
|
957.47
|
-278.63
|
-271.16
|
353.78
|
3.43
|
301.35
|
A-V
|
ω
eV
|
σ
eV
|
η
eV
|
χ
eV
|
Eg
eV
|
LUMO
eV
|
HOMO
eV
|
|
-0.92
|
7.15
|
-6.15
|
3.36
|
-12.31
|
-9.51
|
2.79
|
A-I
|
-0.93
|
7.23
|
-6.22
|
3.41
|
-12.45
|
-9.63
|
2.82
|
A-II
|
-0.95
|
7.38
|
-6.38
|
3.49
|
-12.77
|
-9.87
|
2.90
|
A-III
|
-0.96
|
5.44
|
-4.45
|
2.91
|
-8.89
|
-7.36
|
1.53
|
A-IV
|
-0.90
|
4.60
|
-3.61
|
2.54
|
-7.19
|
-6.14
|
1.05
|
A-V
|
Table 5 shows the structural changes of this interaction, which has a softer structure as the contaminant approaches, and the transfer of electrons from the contaminant to the membrane takes place, and in the A-V stage, the structure becomes harder. The increase of titanium nanoparticles changes the structure of polyacrylonitrile and increases the voids on the surface of the modified nanocomposite and tends to absorb cationic compounds. These nanoparticles cause significant changes in the structural properties of the membrane due to their photocatalytic properties. Polyacrylamide is a water-soluble polymer that becomes cationic as soon as it is placed in the water environment, and due to the presence of titanium dioxide nanoparticles. It is modified towards a nanocomposite, and by converting it into other products, the problems of membrane blockage, and so on have been solved, which can increase the lifespan of nanocomposite.
In this research, after simulating the modified membrane with titanium dioxide nanoparticles and the mechanism of reducing this secondary pollutant in five stages, according to the following equation, the absorption energy of all its stages can be investigated:
In this equation, Em-X is the total energy of the nanocomposite along with the pollutant (polyacrylamide), Em is the total energy of the nanocomposite, EX is the total energy of the pollutant or compounds around the nanocomposite rTiO2@PAC. The absorption energy of the mechanism of the simulated steps according to equation (3) can be seen in Figure 7.
It is worth noting that when the pollutant approaches the modified membrane and the interaction between them causes an increase in energy. And in the fifth stage, a strong increase in the absorption energy is seen, which indicates the release of materials created from the conversion of polyacrylamide. The comparison between the calculated and experimental data shows that nanopolymer modified with titanium dioxide nanoparticles reduces the secondary pollutant of polyacrylamide, and by using these nanoparticles, the performance of nanocomposite can be increased and due to the photocatalytic properties of titanium nanoparticles. The nanocomposite can be recovered by using ultraviolet light or raising the temperature. In general, by adding and modifying the surface by Radman titanium dioxide nanoparticles and polyacrylonitrile polymer, the performance increased, which can be used to reduce the pollution of coal washing factories.