Hydrogels are regarded as polymers with three-dimensional (3D) networks produced as a result of chemical or physical crosslinking of hydrophilic polymers. Recently, these new classes of polymers have been widely engaged in biomedical sectors such as scaffolds for tissue engineering, systems for drug delivery, and electrolytes for energy storage devices [[1], [2], [3]]. The use of hydrogels from polymeric materials as electrolytic materials is a new research area, and polymers are also considered excellent raw materials for such applications due to their inherent properties such as high-water retention capacity, good temperature range, excellent mechanical properties, higher electrochemical window, low cost, and lightweight [[4], [5], [6], [7], [8], [9], [10], [11]]. Hence, there are many reports on the use of some polymers, such as polyacrylamide, polyethylene oxide, polyacrylic acid, polymethylmethacrylate, polyvinylidene fluoride, and polyvinyl alcohol, etc., for the development of electrolytic hydrogels, etc. [[12], [13], [14], [15], [16]]. Out of these polymers, polyvinyl alcohol (PVOH) is a better option due to its low price, biodegradability, harmless nature, high thermal stability, chemical resistance, high flexibility, and good film-forming properties [17]. Despite the limitation of low ionic conductivities and mechanical properties noticed in PVOH hydrogels, which leads to deterioration and deactivation [18], additives such as ionic liquids, solvents with high ionic conductivity such as aqueous potassium hydroxide, nanoparticles, fibers, crystals, plasticizers, cross-linking agents, etc. have been established to improve the properties of polyvinyl alcohol hydrogel [19,20]. Pointedly, nano-cellulose particles, fibers, and crystals have been extensively employed to improve the mechanical properties of PVOH hydrogel [[21], [22], [23], [24], [25], [26]].

Several experiments have been conducted on the use of polyvinyl alcohol/cellulose/nano-cellulose composite hydrogel electrolytes, but not much attention has been given to the interactions of the hydrogel with the cellulose-based additive at the atomic level. A notable merit of molecular-based simulations is the provision of informed guidelines for experimental studies, reduced time, and lower cost of computations [27,28]. Molecular dynamics (MD) has remained a unique theoretical means to study material geometries, structures, and properties at the atomic scale. It is an indispensable tool in the prediction of the dynamic behavior and properties of several polymeric systems [29]. Wei et al. investigated the atomic properties and relationship of nano silica in polyvinyl/polyacrylamide composites by molecular dynamics. The comparative study revealed that the chains of polyacrylamide easily adsorbed on the surface of silica particles compared to polyvinyl alcohol molecular chains; also, the mechanical properties of the polymer blend, such as stiffness, improved due to the presence of the nano particles. A higher content of the nano silica resulted in a decrease in the polymer molecular chains [20,30]. Dou et al. (2022) reported the mechanism of ion conduction in a nano-structured bio-inspired solid-state electrolyte. The fast ion migration resulted in an electrolyte with higher ionic conductivity and a battery with higher power densities and extensive flexibility [31]. In this light, Haung and his group conducted molecular dynamics simulations to gain insight into the morphologies of PVA and sodium polyacrylate (PANa) hydrogels and to discover the fundamental molecular mechanisms that underpin the superb water retention abilities of PaNa hydrogel. They observed an excellent dispersed morphology of the PANa chains compared to the chains of PVA. A higher interaction energy, specifically strong electrostatic forces, between the molecules of PANa and water compared to the interaction forces between PVA, and water molecules was noticed. This accounted for the high water - holding capacity of the PANa - based electrolyte. The dendrite–free semi-solid electrolyte interface formed was a result of the intermolecular interactions between the negative ionic groups present in PANa molecular chains and the charged zinc ions, leading to a faster diffusion of ionic species through the electrodes [32]. Li et al. (2016) studied ionic transport in polymer-based electrolyte hydrogels via MD simulations and other theoretical models. Increased binding energies of the ions and the polymer backbone led to faster ion transport in the diluted hydrogels than in the heavier gels. Weak-field ionic transport also improved with increased electrolyte concentration [33]. In addition, Zou et al. (2021) employed computer-based simulations and experimental studies to investigate the capability of carbon (iv) oxide CO2-functionalized polyvinyl alcohol (PVA) in the presence of tetramethylguanidine (TMG) via the PVA ionization process in reducing CO2 poisoning in zinc-air batteries as well as account for the high ionic conductivities of PVA-TMG hydrogels. The CO2 functionalized PVA-TMG hydrogel reduced CO2 poisoning and decreased dendrite formation. A noticeable improvement in hydroxyl ion diffusion through the ionized PVA-TMG hydrogels was due to the higher water retention of PVA and the strong interaction between potassium ions and OCO2. The solvent-accessible surface area (SASA), the binding energies, and the dissociation energy simulation parameters were utilized to deeply understand the performance of both hydrogels. SASA of PVA-TMG hydrogel was greater than that of the pristine PVA, whose SASA reduced with increased simulation time. The binding and dissociation energies between the ionized PVA-TMG and water were higher than the interaction energies between the pristine PVA and water molecules. Hence, the CO2-ionized PVA-TMG hydrogel maintained a longer cycle life when subjected to a CO2-filled environment of about 22.7 % and remained stable over a longer period (12 times) more than the plain PVA [34]. Similarly, Hu and others, by employing a multi-scale modeling technique, established a relationship between the mechanical properties and electrochemical properties of a PVA-based gel electrolyte. The electrochemical approach caused mechanical strain in the gel electrolyte, while changes in mechanical behavior tuned the ionic behavior of the gel electrolyte [35]. Recently, Lyu et al. simulated the mechanism of hydrogen bonding between PVA polymer chains in dimethylsulfoxide/water (DMSO/H2O) mixed solvents through molecular dynamics. The radial distribution function analysis showed a significant reduction in the average distance between the hydroxyl groups in PVA chains. An increase in the content of DMSO reduced PVA chain solvation, which led to the formation of intermolecular hydrogen bonds in PVA polymer chains [36].

Therefore, the aim of this study was to study the electronic properties and effect of water and temperature on the energetic and mechanical properties of polyvinyl alcohol and cellulose–based hydrogels via DFT calculations and molecular dynamics. To achieve our goal, the hydrogel was produced using polyvinyl alcohol and cellulose at the molecular level using the density functional theory approach. Quantum chemical calculations were used to investigate the quantum chemical descriptors and electronic properties of polyvinyl alcohol, while molecular dynamics simulations (MDS) were used to investigate the interactions between polyvinyl alcohol, water, and cellulose in the formation of hydrogel. Also, the dependence of water and temperature on the binding energy, cohesive energy density, and mechanical properties of the hydrogel composite were assessed using MDS.