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       Due to the abundant sodium resource, sodium-ion batteries (NIBs) represent a promising alternative solution for electrochemical energy storage. Currently, the main obstacle in the development of NIB technology is the lack of electrode materials that can reversibly store/release sodium ions for a long time. Therefore, the aim of this study is to theoretically investigate the effect of glycerol addition on polyvinyl alcohol (PVA) and sodium alginate (NaAlg) blends as NIB electrode materials. This study focuses on the electronic, thermal, and quantitative structure-activity relationship (QSAR) descriptors of polymer electrolytes based on PVA, sodium alginate, and glycerol blends. These properties are investigated using semi-empirical methods and density functional theory (DFT). Since the structural analysis revealed the details of the interactions between PVA/alginate and glycerol, the band gap energy (Eg) was investigated. The results show that the addition of glycerol results in a decrease in the Eg value to 0.2814 eV. The molecular electrostatic potential surface (MESP) shows the distribution of electron-rich and electron-poor regions and molecular charges in the whole electrolyte system. The thermal parameters studied include enthalpy (H), entropy (ΔS), heat capacity (Cp), Gibbs free energy (G) and heat of formation. In addition, several quantitative structure-activity relationship (QSAR) descriptors such as total dipole moment (TDM), total energy (E), ionization potential (IP), Log P and polarizability were investigated in this study. The results showed that H, ΔS, Cp, G and TDM increased with increasing temperature and glycerol content. Meanwhile, the heat of formation, IP and E decreased, which improved the reactivity and polarizability. In addition, by adding glycerol, the cell voltage increased to 2.488 V. DFT and PM6 calculations based on cost-effective PVA/Na Alg glycerol-based electrolytes show that they can partially replace lithium-ion batteries due to their multifunctionality, but further improvements and research are needed.
       Although lithium-ion batteries (LIBs) are widely used, their application faces many limitations due to their short cycle life, high cost, and safety concerns. Sodium-ion batteries (SIBs) may become a viable alternative to LIBs due to their wide availability, low cost, and non-toxicity of the sodium element. Sodium-ion batteries (SIBs) are becoming an increasingly important energy storage system for electrochemical devices1. Sodium-ion batteries rely heavily on electrolytes to facilitate ion transport and generate electrical current2,3. Liquid electrolytes are mainly composed of metal salts and organic solvents. Practical applications require careful consideration of the safety of liquid electrolytes, especially when the battery is subjected to thermal or electrical stress4.
       Sodium-ion batteries (SIBs) are expected to replace lithium-ion batteries in the near future due to their abundant ocean reserves, non-toxicity, and low material cost. The synthesis of nanomaterials has accelerated the development of data storage, electronic, and optical devices. A large body of literature has demonstrated the application of various nanostructures (e.g., metal oxides, graphene, nanotubes, and fullerenes) in sodium-ion batteries. Research has focused on the development of anode materials, including polymers, for sodium-ion batteries due to their versatility and environmental friendliness. Research interest in the field of rechargeable polymer batteries will undoubtedly increase. Novel polymer electrode materials with unique structures and properties are likely to pave the way for environmentally friendly energy storage technologies. Although various polymer electrode materials have been explored for use in sodium-ion batteries, this field is still in its early stages of development. For sodium-ion batteries, more polymer materials with different structural configurations need to be explored. Based on our current knowledge of the storage mechanism of sodium ions in polymer electrode materials, it can be hypothesized that carbonyl groups, free radicals, and heteroatoms in the conjugated system can serve as active sites for interaction with sodium ions. Therefore, it is critical to develop new polymers with a high density of these active sites. Gel polymer electrolyte (GPE) is an alternative technology that improves battery reliability, ion conductivity, no leakage, high flexibility, and good performance12.
       Polymer matrices include materials such as PVA and polyethylene oxide (PEO)13. Gel permeable polymer (GPE) immobilizes the liquid electrolyte in the polymer matrix, which reduces the risk of leakage compared to commercial separators14. PVA is a synthetic biodegradable polymer. It has a high permittivity, is inexpensive and non-toxic. The material is known for its film-forming properties, chemical stability and adhesion. It also possesses functional (OH) groups and a high cross-linking potential density15,16,17. Polymer blending, plasticizer addition, composite addition and in situ polymerization techniques have been used to improve the conductivity of PVA-based polymer electrolytes to reduce matrix crystallinity and increase chain flexibility18,19,20.
       Blending is an important method for developing polymeric materials for industrial applications. Polymer blends are often used to: (1) improve the processing properties of natural polymers in industrial applications; (2) improve the chemical, physical, and mechanical properties of biodegradable materials; and (3) adapt to the rapidly changing demand for new materials in the food packaging industry. Unlike copolymerization, polymer blending is a low-cost process that uses simple physical processes rather than complex chemical processes to achieve the desired properties21. To form homopolymers, different polymers can interact through dipole-dipole forces, hydrogen bonds, or charge-transfer complexes22,23. Blends made from natural and synthetic polymers can combine good biocompatibility with excellent mechanical properties, creating a superior material at a low production cost24,25. Therefore, there has been great interest in creating biorelevant polymeric materials by blending synthetic and natural polymers. PVA can be combined with sodium alginate (NaAlg), cellulose, chitosan and starch26.
       Sodium alginate is a natural polymer and anionic polysaccharide extracted from marine brown algae. Sodium alginate consists of β-(1-4)-linked D-mannuronic acid (M) and α-(1-4)-linked L-guluronic acid (G) organized into homopolymeric forms (poly-M and poly-G) and heteropolymeric blocks (MG or GM)27. The content and relative ratio of M and G blocks have a significant effect on the chemical and physical properties of alginate28,29. Sodium alginate is widely used and studied due to its biodegradability, biocompatibility, low cost, good film-forming properties, and non-toxicity. However, a large number of free hydroxyl (OH) and carboxylate (COO) groups in the alginate chain makes alginate highly hydrophilic. However, alginate has poor mechanical properties due to its brittleness and rigidity. Therefore, alginate can be combined with other synthetic materials to improve water sensitivity and mechanical properties30,31.
       Before designing new electrode materials, DFT calculations are often used to evaluate the fabrication feasibility of new materials. In addition, scientists use molecular modeling to confirm and predict experimental results, save time, reduce chemical waste, and predict interaction behavior32. Molecular modeling has become a powerful and important branch of science in many fields, including materials science, nanomaterials, computational chemistry, and drug discovery33,34. Using modeling programs, scientists can directly obtain molecular data, including energy (heat of formation, ionization potential, activation energy, etc.) and geometry (bond angles, bond lengths, and torsion angles)35. In addition, electronic properties (charge, HOMO and LUMO band gap energy, electron affinity), spectral properties (characteristic vibrational modes and intensities such as FTIR spectra), and bulk properties (volume, diffusion, viscosity, modulus, etc.)36 can be calculated.
       LiNiPO4 shows potential advantages in competing with lithium-ion battery positive electrode materials due to its high energy density (working voltage of about 5.1 V). To fully exploit the advantage of LiNiPO4 in the high-voltage region, the working voltage needs to be lowered because the currently developed high-voltage electrolyte can only remain relatively stable at voltages below 4.8 V. Zhang et al. investigated the doping of all 3d, 4d, and 5d transition metals in the Ni site of LiNiPO4, selected the doping patterns with excellent electrochemical performance, and adjusted the working voltage of LiNiPO4 while maintaining the relative stability of its electrochemical performance. The lowest working voltages they obtained were 4.21, 3.76, and 3.5037 for Ti, Nb, and Ta-doped LiNiPO4, respectively.
       Therefore, the aim of this study is to theoretically investigate the effect of glycerol as a plasticizer on the electronic properties, QSAR descriptors and thermal properties of PVA/NaAlg system using quantum mechanical calculations for its application in rechargeable ion-ion batteries. The molecular interactions between PVA/NaAlg model and glycerol were analyzed using Bader’s quantum atomic theory of molecules (QTAIM).
       A molecule model representing the interaction of PVA with NaAlg and then with glycerol was optimized using DFT. The model was calculated using Gaussian 0938 software at the Spectroscopy Department, National Research Center, Cairo, Egypt. The models were optimized using DFT at the B3LYP/6-311G(d, p) level39,40,41,42. To verify the interaction between the studied models, frequency studies performed at the same level of theory demonstrate the stability of the optimized geometry. The absence of negative frequencies among all the evaluated frequencies highlights the inferred structure in the true positive minima on the potential energy surface. Physical parameters such as TDM, HOMO/LUMO band gap energy and MESP were calculated at the same quantum mechanical level of theory. In addition, some thermal parameters such as the final heat of formation, free energy, entropy, enthalpy and heat capacity were calculated using the formulas given in Table 1. The studied models were subjected to the quantum theory of atoms in molecules (QTAIM) analysis in order to identify the interactions occurring on the surface of the studied structures. These calculations were performed using the “output=wfn” command in the Gaussian 09 software code and then visualized using the Avogadro software code43.
       Where E is the internal energy, P is the pressure, V is the volume, Q is the heat exchange between the system and its environment, T is the temperature, ΔH is the enthalpy change, ΔG is the free energy change, ΔS is the entropy change, a and b are the vibrational parameters, q is the atomic charge, and C is the atomic electron density44,45. Finally, the same structures were optimized and the QSAR parameters were calculated at PM6 level using the SCIGRESS software code46 at the Spectroscopy Department of the National Research Center in Cairo, Egypt.
       In our previous work47, we evaluated the most probable model describing the interaction of three PVA units with two NaAlg units, with glycerol acting as a plasticizer. As mentioned above, there are two possibilities for the interaction of PVA and NaAlg. The two models, designated 3PVA-2Na Alg (based on carbon number 10) and Term 1Na Alg-3PVA-Mid 1Na Alg, have the smallest energy gap value48 compared to the other structures considered. Therefore, the effect of Gly addition on the most probable model of the PVA/Na Alg blend polymer was investigated using the latter two structures: 3PVA-(C10)2Na Alg (referred to as 3PVA-2Na Alg for simplicity) and Term 1 Na Alg − 3PVA-Mid 1 Na Alg. According to the literature, PVA, NaAlg and glycerol can form only weak hydrogen bonds between hydroxyl functional groups. Since both the PVA trimer and the NaAlg and glycerol dimer contain several OH groups, the contact can be realized through one of the OH groups. Figure 1 shows the interaction between the model glycerol molecule and the model molecule 3PVA-2Na Alg, and Figure 2 shows the constructed model of the interaction between the model molecule Term 1Na Alg-3PVA-Mid 1Na Alg and different concentrations of glycerol.
       Optimized structures: (a) Gly and 3PVA − 2Na Alg interact with (b) 1 Gly, (c) 2 Gly, (d) 3 Gly, (e) 4 Gly, and (f) 5 Gly.
       Optimized structures of Term 1Na Alg- 3PVA –Mid 1Na Alg interacting with (a) 1 Gly, (b) 2 Gly, (c) 3 Gly, (d) 4 Gly, (e) 5 Gly, and (f) 6 Gly.
       The electron band gap energy is an important parameter to consider when studying the reactivity of any electrode material. Because it describes the behavior of electrons when the material is subjected to external changes. Therefore, it is necessary to estimate the electron band gap energies of HOMO/LUMO for all the structures studied. Table 2 shows the changes in HOMO/LUMO energies of 3PVA-(C10)2Na Alg and Term 1Na Alg − 3PVA- Mid 1Na Alg due to the addition of glycerol. According to ref47, the Eg value of 3PVA-(C10)2Na Alg is 0.2908 eV, while the Eg value of the structure reflecting the probability of the second interaction (i.e., Term 1Na Alg − 3PVA- Mid 1Na Alg) is 0.5706 eV.
       However, it was found that the addition of glycerol resulted in a slight change in the Eg value of 3PVA-(C10)2Na Alg. When 3PVA-(C10)2NaAlg interacted with 1, 2, 3, 4 and 5 glycerol units, its Eg values ​​became 0.302, 0.299, 0.308, 0.289 and 0.281 eV, respectively. However, there is a valuable insight that after adding 3 glycerol units, the Eg value became smaller than that of 3PVA-(C10)2Na Alg. The model representing the interaction of 3PVA-(C10)2Na Alg with five glycerol units is the most probable interaction model. This means that as the number of glycerol units increases, the probability of interaction also increases.
       Meanwhile, for the second probability of interaction, the HOMO/LUMO energies of the model molecules representing Term 1Na Alg − 3PVA –Mid 1Na Alg- 1Gly, Term 1Na Alg − 3PVA –Mid 1Na Alg- 2Gly, Term 1Na Alg − 3PVA –Mid 1Na Alg- 3Gly, Term 1Na Alg − 3PVA –Mid 1Na Alg- 4Gly, Term 1Na Alg − 3PVA –Mid 1Na Alg- 5Gly and Term 1Na Alg − 3PVA –Mid 1Na Alg- 6Gly become 1.343, 1.34 7, 0.976, 0.607, 0.348 and 0.496 eV, respectively. Table 2 shows the calculated HOMO/LUMO band gap energies for all structures. Moreover, the same behavior of the interaction probabilities of the first group is repeated here.
       The band theory in solid state physics states that as the band gap of an electrode material decreases, the electronic conductivity of the material increases. Doping is a common method to decrease the band gap of sodium-ion cathode materials. Jiang et al. used Cu doping to improve the electronic conductivity of β-NaMnO2 layered materials. Using DFT calculations, they found that doping decreased the band gap of the material from 0.7 eV to 0.3 eV. This indicates that Cu doping improves the electronic conductivity of β-NaMnO2 material.
       MESP is defined as the interaction energy between the molecular charge distribution and a single positive charge. MESP is considered an effective tool for understanding and interpreting chemical properties and reactivity. MESP can be used to understand the mechanisms of interactions between polymeric materials. MESP describes the charge distribution within the compound under study. In addition, MESP provides information about the active sites in the materials under study32. Figure 3 shows the MESP plots of 3PVA-(C10) 2Na Alg, 3PVA-(C10) 2Na Alg − 1Gly, 3PVA-(C10) 2Na Alg − 2Gly, 3PVA-(C10) 2Na Alg − 3Gly, 3PVA-(C10) 2Na Alg − 4Gly, and 3PVA-(C10) 2Na Alg − 5Gly predicted at the B3LYP/6-311G(d, p) level of theory.
       MESP contours calculated with B3LYP/6-311 g(d, p) for (a) Gly and 3PVA − 2Na Alg interacting with (b) 1 Gly, (c) 2 Gly, (d) 3 Gly, (e) 4 Gly, and (f) 5 Gly.
       Meanwhile, Fig. 4 shows the calculated results of MESP for Term 1Na Alg- 3PVA – Mid 1Na Alg, Term 1Na Alg-3PVA – Mid 1Na Alg- 1Gly, Term 1Na Alg-3PVA – Mid 1Na Alg − 2Gly, Term 1Na Alg-3PVA – Mid 1Na Alg − 3gly, Term 1Na Alg-3PVA – Mid 1Na Alg − 4Gly, Term 1Na Alg- 3PVA – Mid 1Na Alg- 5gly and Term 1Na Alg-3PVA – Mid 1Na Alg − 6Gly, respectively. The calculated MESP is represented as a contour behavior. The contour lines are represented by different colors. Each color represents a different electronegativity value. The red color indicates the highly electronegative or reactive sites. Meanwhile, the yellow color represents the neutral sites 49, 50, 51 in the structure. The MESP results showed that the reactivity of 3PVA-(C10)2Na Alg increased with the increase of red color around the studied models. Meanwhile, the red color intensity in the MESP map of the Term 1Na Alg-3PVA – Mid 1Na Alg model molecule decreases due to the interaction with different glycerol content. The change in the red color distribution around the proposed structure reflects the reactivity, while the increase in intensity confirms the increase in electronegativity of the 3PVA-(C10)2Na Alg model molecule due to the increase of glycerol content.
       B3LYP/6-311 g(d, p) calculated MESP Term of 1Na Alg-3PVA-Mid 1Na Alg interacting with (a) 1 Gly, (b) 2 Gly, (c) 3 Gly, (d) 4 Gly, (e) 5 Gly, and (f) 6 Gly.
       All the proposed structures have their thermal parameters such as enthalpy, entropy, heat capacity, free energy and heat of formation calculated at different temperatures in the range from 200 K to 500 K. To describe the behavior of physical systems, in addition to studying their electronic behavior, it is also necessary to study their thermal behavior as a function of temperature due to their interaction with each other, which can be calculated using the equations given in Table 1. The study of these thermal parameters is considered an important indicator of the responsiveness and stability of such physical systems at different temperatures.
       As for the enthalpy of the PVA trimer, it first reacts with the NaAlg dimer, then through the OH group attached to carbon atom #10, and finally with glycerol. Enthalpy is a measure of the energy in a thermodynamic system. Enthalpy is equal to the total heat in a system, which is equivalent to the internal energy of the system plus the product of its volume and pressure. In other words, enthalpy shows how much heat and work is added to or removed from a substance52.
       Figure 5 shows the enthalpy changes during the reaction of 3PVA-(C10)2Na Alg with different glycerol concentrations. The abbreviations A0, A1, A2, A3, A4, and A5 represent the model molecules 3PVA-(C10)2Na Alg, 3PVA-(C10)2Na Alg − 1 Gly, 3PVA-(C10)2Na Alg − 2Gly, 3PVA-(C10)2Na Alg − 3Gly, 3PVA-(C10)2Na Alg − 4Gly, and 3PVA-(C10)2Na Alg − 5Gly, respectively. Figure 5a shows that the enthalpy increases with increasing temperature and glycerol content. The enthalpy of the structure representing 3PVA-(C10)2NaAlg − 5Gly (i.e., A5) at 200 K is 27.966 cal/mol, while the enthalpy of the structure representing 3PVA- 2NaAlg at 200 K is 13.490 cal/mol. Finally, since the enthalpy is positive, this reaction is endothermic.
       Entropy is defined as a measure of the unavailable energy in a closed thermodynamic system and is often considered as a measure of the disorder of the system. Figure 5b shows the change in entropy of 3PVA-(C10)2NaAlg with temperature and how it interacts with different glycerol units. The graph shows that the entropy changes linearly as the temperature increases from 200 K to 500 K. Figure 5b clearly shows that the entropy of the 3PVA-(C10)2Na Alg model tends to 200 cal/K/mol at 200 K because the 3PVA-(C10)2Na Alg model exhibits less lattice disorder. As the temperature increases, the 3PVA-(C10)2Na Alg model becomes disordered and explains the increase in entropy with increasing temperature. Moreover, it is obvious that the structure of 3PVA-C10 2Na Alg- 5 Gly has the highest entropy value.
       The same behavior is observed in Figure 5c, which shows the change in heat capacity with temperature. Heat capacity is the amount of heat required to change the temperature of a given amount of substance by 1 °C47. Figure 5c shows the changes in heat capacity of the model molecule 3PVA-(C10)2NaAlg due to interactions with 1, 2, 3, 4, and 5 glycerol units. The figure shows that the heat capacity of the model 3PVA-(C10)2NaAlg increases linearly with temperature. The observed increase in heat capacity with increasing temperature is attributed to phonon thermal vibrations. In addition, there is evidence that increasing the glycerol content leads to an increase in the heat capacity of the model 3PVA-(C10)2NaAlg. Furthermore, the structure shows that 3PVA-(C10)2NaAlg−5Gly has the highest heat capacity value compared to other structures.
       Other parameters such as free energy and final heat of formation were calculated for the studied structures and are shown in Figure 5d and e, respectively. The final heat of formation is the heat released or absorbed during the formation of a pure substance from its constituent elements under constant pressure. Free energy can be defined as a property similar to energy, i.e., its value depends on the amount of substance in each thermodynamic state. The free energy and heat of formation of 3PVA-(C10)2NaAlg−5Gly were the lowest and were -1318.338 and -1628.154 kcal/mol, respectively. In contrast, the structure representing 3PVA-(C10)2NaAlg has the highest free energy and heat of formation values ​​of -690.340 and -830.673 kcal/mol, respectively, compared to other structures. As shown in Figure 5, various thermal properties are changed due to the interaction with glycerol. The Gibbs free energy is negative, indicating that the proposed structure is stable.
       PM6 calculated the thermal parameters of pure 3PVA- (C10) 2Na Alg (model A0), 3PVA- (C10) 2Na Alg − 1 Gly (model A1), 3PVA- (C10) 2Na Alg − 2 Gly (model A2), 3PVA- (C10) 2Na Alg − 3 Gly (model A3), 3PVA- (C10) 2Na Alg − 4 Gly (model A4), and 3PVA- (C10) 2Na Alg − 5 Gly (model A5), where (a) is the enthalpy, (b) entropy, (c) heat capacity, (d) free energy, and (e) heat of formation.
       On the other hand, the second interaction mode between PVA trimer and dimeric NaAlg occurs in the terminal and middle OH groups in the PVA trimer structure. As in the first group, the thermal parameters were calculated using the same level of theory. Figure 6a-e shows the variations of enthalpy, entropy, heat capacity, free energy and, ultimately, heat of formation. Figures 6a-c show that the enthalpy, entropy and heat capacity of Term 1 NaAlg-3PVA-Mid 1 NaAlg exhibit the same behavior as the first group when interacting with 1, 2, 3, 4, 5 and 6 glycerol units. Moreover, their values ​​gradually increase with increasing temperature. In addition, in the proposed Term 1 Na Alg − 3PVA-Mid 1 Na Alg model, the enthalpy, entropy and heat capacity values ​​increased with the increase of glycerol content. The abbreviations B0, B1, B2, B3, B4, B5 and B6 represent the following structures respectively: Term 1 Na Alg − 3PVA- Mid 1 Na Alg, Term 1 Na Alg- 3PVA- Mid 1 Na Alg − 1 Gly, Term 1 Na Alg- 3PVA- Mid 1 Na Alg − 2gly, Term 1 Na Alg- 3PVA- Mid 1 Na Alg − 3gly, Term 1 Na Alg- 3PVA- Mid 1 Na Alg − 4 Gly, Term 1 Na Alg- 3PVA- Mid 1 Na Alg − 5 Gly and Term 1 Na Alg- 3PVA- Mid 1 Na Alg − 6 Gly. As shown in Fig. 6a–c, it is obvious that the values ​​of enthalpy, entropy and heat capacity increase as the number of glycerol units increases from 1 to 6.
       PM6 calculated the thermal parameters of pure Term 1 Na Alg- 3PVA- Mid 1 Na Alg (model B0), Term 1 Na Alg- 3PVA- Mid 1 Na Alg – 1 Gly (model B1), Term 1 Na Alg- 3PVA- Mid 1 Na Alg – 2 Gly (model B2), Term 1 Na Alg- 3PVA- Mid 1 Na Alg – 3 Gly (model B3), Term 1 Na Alg- 3PVA- Mid 1 Na Alg – 4 Gly (model B4), Term 1 Na Alg- 3PVA- Mid 1 Na Alg – 5 Gly (model B5), and Term 1 Na Alg- 3PVA- Mid 1 Na Alg – 6 Gly (model B6), including (a) enthalpy, (b) entropy, (c) heat capacity, (d) free energy, and (e) heat of formation.
       In addition, the structure representing Term 1 Na Alg- 3PVA- Mid 1 Na Alg- 6 Gly has the highest values ​​of enthalpy, entropy and heat capacity compared with other structures. Among them, their values ​​increased from 16.703 cal/mol, 257.990 cal/mol/K and 131.323 kcal/mol in Term 1 Na Alg − 3PVA- Mid 1 Na Alg to 33.223 cal/mol, 420.038 cal/mol/K and 275.923 kcal/mol in Term 1 Na Alg − 3PVA- Mid 1 Na Alg − 6 Gly, respectively.
       However, Figures 6d and e show the temperature dependence of the free energy and the final heat of formation (HF). HF can be defined as the enthalpy change that occurs when one mole of a substance is formed from its elements under natural and standard conditions. It is evident from the figure that the free energy and the final heat of formation of all the studied structures show a linear dependence on temperature, i.e., they gradually and linearly increase with increasing temperature. In addition, the figure also confirmed that the structure representing Term 1 Na Alg − 3PVA- Mid 1 Na Alg − 6 Gly has the lowest free energy and the lowest HF. Both parameters decreased from -758.337 to -899.741 K cal/mol in the term 1 Na Alg − 3PVA- Mid 1 Na Alg − 6 Gly to -1,476.591 and -1,828.523 K cal/mol. It is evident from the results that HF ​​decreases with the increase of glycerol units. This means that due to the increase of functional groups, the reactivity also increases and hence less energy is required to carry out the reaction. This confirms that plasticized PVA/NaAlg can be used in batteries due to its high reactivity.
       In general, temperature effects are divided into two types: low-temperature effects and high-temperature effects. The effects of low temperatures are mainly felt in countries located at high latitudes, such as Greenland, Canada, and Russia. In winter, the outside air temperature in these places is well below zero degrees Celsius. The lifespan and performance of lithium-ion batteries can be affected by low temperatures, especially those used in plug-in hybrid electric vehicles, pure electric vehicles, and hybrid electric vehicles. Space travel is another cold environment that requires lithium-ion batteries. For example, the temperature on Mars can drop to -120 degrees Celsius, which poses a significant obstacle to the use of lithium-ion batteries in spacecraft. Low operating temperatures can lead to a decrease in the charge transfer rate and chemical reaction activity of lithium-ion batteries, resulting in a decrease in the diffusion rate of lithium ions inside the electrode and ionic conductivity in the electrolyte. This degradation results in reduced energy capacity and power, and sometimes even reduced performance53.
       The high temperature effect occurs in a wider range of application environments, including both high and low temperature environments, while the low temperature effect is mainly limited to low temperature application environments. The low temperature effect is primarily determined by the ambient temperature, while the high temperature effect is usually more accurately attributed to the high temperatures inside the lithium-ion battery during operation.
       Lithium-ion batteries generate heat under high current conditions (including fast charging and fast discharging), which causes the internal temperature to rise. Exposure to high temperatures can also cause battery performance degradation, including loss of capacity and power. Typically, the loss of lithium and the recovery of active materials at high temperatures lead to capacity loss, and the power loss is due to an increase in internal resistance. If the temperature gets out of control, thermal runaway occurs, which in some cases can lead to spontaneous combustion or even explosion.
       QSAR calculations are a computational or mathematical modeling method used to identify relationships between biological activity and structural properties of compounds. All designed molecules were optimized and some QSAR properties were calculated at the PM6 level. Table 3 lists some of the calculated QSAR descriptors. Examples of such descriptors are charge, TDM, total energy (E), ionization potential (IP), Log P, and polarizability (see Table 1 for formulas to determine IP and Log P).
       The calculation results show that the total charge of all the studied structures is zero since they are in the ground state. For the first interaction probability, the TDM of glycerol was 2.788 Debye and 6.840 Debye for 3PVA-(C10) 2Na Alg, while the TDM values ​​were increased to 17.990 Debye, 8.848 Debye, 5.874 Debye, 7.568 Debye and 12.779 Debye when 3PVA-(C10) 2Na Alg interacted with 1, 2, 3, 4 and 5 units of glycerol, respectively. The higher the TDM value, the higher its reactivity with the environment.
       The total energy (E) was also calculated, and the E values ​​of glycerol and 3PVA-(C10)2 NaAlg were found to be -141.833 eV and -200092.503 eV, respectively. Meanwhile, the structures representing 3PVA-(C10)2 NaAlg interact with 1, 2, 3, 4 and 5 glycerol units; E becomes -996.837, -1108.440, -1238.740, -1372.075 and -1548.031 eV, respectively. Increasing the glycerol content leads to a decrease in the total energy and hence to an increase in the reactivity. Based on the total energy calculation, it was concluded that the model molecule, which is 3PVA-2Na Alg-5 Gly, is more reactive than the other model molecules. This phenomenon is related to their structure. 3PVA-(C10)2NaAlg contains only two -COONa groups, while the other structures contain two -COONa groups but carry several OH groups, which means that their reactivity towards the environment is increased.
       In addition, the ionization energies (IE) of all the structures are considered in this study. Ionization energy is an important parameter for measuring the reactivity of the studied model. The energy required to move an electron from one point of a molecule to infinity is called ionization energy. It represents the degree of ionization (i.e. reactivity) of the molecule. The higher the ionization energy, the lower the reactivity. The IE results of 3PVA-(C10)2NaAlg interacting with 1, 2, 3, 4 and 5 glycerol units were -9.256, -9.393, -9.393, -9.248 and -9.323 eV, respectively, while the IEs of glycerol and 3PVA-(C10)2NaAlg were -5.157 and -9.341 eV, respectively. Since the addition of glycerol resulted in a decrease in the IP value, the molecular reactivity increased, which enhances the applicability of the PVA/NaAlg/glycerol model molecule in electrochemical devices.
       The fifth descriptor in Table 3 is Log P, which is the logarithm of the partition coefficient and is used to describe whether the structure being studied is hydrophilic or hydrophobic. A negative Log P value indicates a hydrophilic molecule, meaning that it dissolves readily in water and dissolves poorly in organic solvents. A positive value indicates the opposite process.
       Based on the obtained results, it can be concluded that all the structures are hydrophilic, since their Log P values ​​(3PVA-(C10)2Na Alg − 1Gly, 3PVA-(C10)2Na Alg − 2Gly, 3PVA-(C10)2Na Alg − 3Gly, 3PVA-(C10)2Na Alg − 4Gly and 3PVA-(C10)2Na Alg − 5Gly) are -3.537, -5.261, -6.342, -7.423 and -8.504, respectively, while the Log P value of glycerol is only -1.081 and 3PVA-(C10)2Na Alg is only -3.100. This means that the properties of the structure being studied will change as water molecules are incorporated into its structure.
       Finally, the polarizabilities of all structures are also calculated at the PM6 level using a semi-empirical method. It was previously noted that the polarizability of most materials depends on various factors. The most important factor is the volume of the structure under study. For all structures involving the first type of interaction between 3PVA and 2NaAlg (the interaction occurs through carbon atom number 10), the polarizability is improved by the addition of glycerol. The polarizability increases from 29.690 Å to 35.076, 40.665, 45.177, 50.239 and 54.638 Å due to interactions with 1, 2, 3, 4 and 5 glycerol units. Thus, it was found that the model molecule with the highest polarizability is 3PVA-(C10)2NaAlg−5Gly, while the model molecule with the lowest polarizability is 3PVA-(C10)2NaAlg, which is 29.690 Å.
       Evaluation of QSAR descriptors revealed that the structure representing 3PVA-(C10)2NaAlg − 5Gly is the most reactive for the first proposed interaction.
       For the second interaction mode between the PVA trimer and the NaAlg dimer, the results show that their charges are similar to those proposed in the previous section for the first interaction. All structures have zero electronic charge, which means that they are all in the ground state.
       As shown in Table 4, the TDM values ​​(calculated at PM6 level) of Term 1 Na Alg − 3PVA-Mid 1 Na Alg increased from 11.581 Debye to 15.756, 19.720, 21.756, 22.732, 15.507, and 15.756 when Term 1 Na Alg − 3PVA-Mid 1 Na Alg reacted with 1, 2, 3, 4, 5, and 6 units of glycerol. However, the total energy decreases with the increase of the number of glycerol units, and when Term 1 Na Alg − 3PVA- Mid 1 Na Alg interacts with a certain number of glycerol units (1 to 6), the total energy is − 996.985, − 1129.013, − 1267.211, − 1321.775, − 1418.964, and − 1637.432 eV, respectively.
       For the second interaction probability, IP, Log P and polarizability are also calculated at the PM6 level of theory. Therefore, they considered three most powerful descriptors of molecular reactivity. For the structures representing End 1 Na Alg-3PVA-Mid 1 Na Alg interacting with 1, 2, 3, 4, 5 and 6 glycerol units, IP increases from −9.385 eV to −8.946, −8.848, −8.430, −9.537, −7.997 and −8.900 eV. However, the calculated Log P value was lower due to the plasticization of End 1 Na Alg-3PVA-Mid 1 Na Alg with glycerol. As the glycerol content increases from 1 to 6, its values ​​become -5.334, -6.415, -7.496, -9.096, -9.861 and -10.53 instead of -3.643. Finally, the polarizability data showed that increasing the glycerol content resulted in the increase of the polarizability of Term 1 Na Alg- 3PVA- Mid 1 Na Alg. The polarizability of the model molecule Term 1 Na Alg- 3PVA- Mid 1 Na Alg increased from 31.703 Å to 63.198 Å after interaction with 6 glycerol units. It is important to note that increasing the number of glycerol units in the second interaction probability is carried out to confirm that despite the large number of atoms and complex structure, the performance is still improved with the increase of glycerol content. Thus, it can be said that the available PVA/Na Alg/glycerin model can partially replace lithium-ion batteries, but more research and development is needed.
       Characterizing the binding capacity of a surface to an adsorbate and evaluating the unique interactions between the systems requires knowledge of the type of bond existing between any two atoms, the complexity of intermolecular and intramolecular interactions, and the electron density distribution of the surface and the adsorbent. The electron density at the bond critical point (BCP) between the interacting atoms is critical for assessing the bond strength in QTAIM analysis. The higher the electron charge density, the more stable the covalent interaction and, in general, the higher the electron density at these critical points. Moreover, if both the total electron energy density (H(r)) and the Laplace charge density (∇2ρ(r)) are less than 0, this indicates the presence of covalent (general) interactions. On the other hand, when ∇2ρ(r) and H(r) are greater than 0.54, it indicates the presence of non-covalent (closed shell) interactions such as weak hydrogen bonds, van der Waals forces and electrostatic interactions. QTAIM analysis revealed the nature of non-covalent interactions in the studied structures as shown in Figures 7 and 8. Based on the analysis, the model molecules representing 3PVA − 2Na Alg and Term 1 Na Alg − 3PVA –Mid 1 Na Alg showed higher stability than the molecules interacting with different glycine units. This is because a number of non-covalent interactions that are more prevalent in the alginate structure such as electrostatic interactions and hydrogen bonds enable alginate to stabilize the composites. Furthermore, our results demonstrate the importance of non-covalent interactions between the 3PVA − 2Na Alg and Term 1 Na Alg − 3PVA –Mid 1 Na Alg model molecules and glycine, indicating that glycine plays an important role in modifying the overall electronic environment of the composites.
       QTAIM analysis of the model molecule 3PVA − 2NaAlg interacting with (a) 0 Gly, (b) 1 Gly, (c) 2 Gly, (d) 3 Gly, (e) 4 Gly, and (f) 5Gly.