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  Preparation of Polyaniline-Based Nanocomposites for Photocatalytic Degradation of Pollutants and Hydrogen Production

  (2026-08-27) Hait, Pritam; Basu, Soumen; Mehta, Rajeev

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  Chapter 1: Nanotechnology allows us to work with materials that are extremely small—about one-billionth of a meter. At this tiny scale, materials behave differently and can show special abilities. One important use of such materials is in photocatalysis, a process where sunlight helps break down harmful chemicals in water or produce clean fuel like hydrogen. This thesis focuses on creating new photocatalyst materials made by combining polyaniline (a conducting polymer) with different metal-based nanoparticles. Polyaniline can absorb visible light and help move electrical charges more efficiently, making the overall material work better under visible light. The goal of this research is twofold: i) To remove harmful dyes and pollutants from wastewater using sunlight, and ii) To generate hydrogen gas, a clean and renewable fuel, using the same sunlight-driven process. The materials developed in this work are tested using different scientific tools to understand their structure, how they absorb light, and how well they perform. The results show that these newly designed nanocomposites can clean polluted water more effectively and also produce hydrogen in a more efficient and eco-friendly way. In simple terms, this research aims to turn sunlight into a powerful tool—for cleaner water and cleaner energy. Chapter 2: Recently, polyaniline-based photocatalysts have gained great attention due to their narrow band gap (E = 1.77 eV), which enables them to absorb a significant amount of visible light (~ 43%) in the solar spectrum. In this study, we have synthesized a ternary nanocomposite (PANI/BiOCl/GO) through an oxidative polymerization approach, incorporating polyaniline (PANI), graphene oxide (GO), and bismuth oxychloride (BiOCl). Different weight percentages of composites (GO/BiOCl: 0.5%, 1%, 2.5%, and PANI: 99.5%, 99%, 97.5%) were prepared and named as 0.5PBG, 1PBG, and 2.5PBG, respectively. The ternary nanocomposite's successful development, crystallinity, purity, porosity, and optical properties were evaluated through several spectroscopic and surface analysis techniques, including UV-Vis-DRS, PL, XRD, XPS, BET, and EDS analysis. FESEM and HRTEM images unveiled the porous characteristics of PANI, the morphology of exfoliated GO layers, and the nanoplate-like structure of BiOCl. The ternary nanocomposite was finally tested for its ability to degrade an organic dye, rhodamine-b (Rhb), and in the process also generate solar-light-driven green hydrogen by water half-splitting. The composite achieved about 90% detoxification (assigned from GC-TCD by analyzing the evolved CO2 gas after degradation) and 96% color removal of Rhb dye within 120 minutes. The degradation of Rhb by 1PBG displayed a first-order reaction, featuring a rate constant 7.25 times higher than that observed for pure PANI, 3.8 times higher than for pure GO, and 3.9 times higher than for pure BiOCl. Thus, the ternary composites achieve a good amount of synergy. Significantly, this reaction rate constant is 4.7 times greater than the rate observed with commercially used TiO2-P25 photocatalyst. Various reaction parameters including solution pH, different illumination areas, catalyst dosage, and the study of scavengers were investigated to understand their effects on the degradation reaction. The photocatalyst's reusability effectiveness was evaluated over 6 cycles, and its stability was subsequently confirmed through XRD and ICP-OES analysis. The LC-MS study revealed the identification of various intermediates and end products following the degradation reaction. The nanocomposite also produced 1000 ppm of hydrogen gas with an apparent quantum efficiency (AQE) of 17.97% when CH3OH was used as a sacrificial agent, 500 ppm (AQE of 9.69%) in the acidic conditions, and 600 ppm (AQE of 11.63%) in the basic conditions. In a broader perspective, this endeavor paves the way for exploring fresh opportunities in the utilization of this ternary nanocomposite. Its potential extends beyond accelerating dye degradation to encompass diverse solar-driven applications as well. Chapter 3: Polyaniline-based photocatalysts have attracted attention due to their favourable bandgap (2.7 eV) and significant visible light absorption (~43%). In this study, a novel ternary nanocomposite, PANI/GO/MoO3, synthesized via oxidative in-situ polymerization, combining polyaniline (PANI), graphene oxide (GO), and molybdenum trioxide (MoO3) was presented with different wt./wt. %. Comprehensive characterization using XRD, BET, EDS, XPS, PL, and UV-Vis-DRS revealed crystallinity, porosity, and superior optical properties, respectively. FESEM image confirmed the porous morphology of PANI, exfoliated GO layers, and MoO3 nanorods (60-80 nm). Among the composites, 2.5PGMO (GO-MoO3: 2.5 wt.% and PANI: 97.5 wt.%) exhibited the highest electron lifetime (0.612 ms), significantly outperforming individual components like PANI (0.0495 ms), GO (0.023 ms), and MoO3 (0.022 ms). Photocatalytic activity was validated through both methyl orange (MO) degradation and solar-driven hydrogen production via water splitting. The 2.5PGMO composite achieved 98% MO removal and 70% detoxification within 120 minutes, with a reaction rate surpassing traditional photocatalysts. Optimal conditions, such as pH, catalyst dosage, and scavenger presence, enhanced performance. The composite shows 85% degradation of the pollutant over five cycles and stability of the nanocomposite was confirmed by XRD and ICP-OES. In solar hydrogen production, it delivered an apparent quantum efficiency (AQE) of 30.76% using CH3OH as a sacrificial agent, with nearly 28% AQE across varying pH conditions. This study underscores the PANI/GO/MoO3 nanocomposite as a promising multifunctional photocatalyst for simultaneous environmental remediation and sustainable hydrogen production, paving the way for advanced solar-driven technologies. Chapter 4: This study focused on creating a ternary nanocomposite (PANI/GO/MoS2) using an oxidative polymerization technique. The composite incorporated polyaniline (PANI), graphene oxide (GO), and molybdenum disulfide (MoS2) in different weight ratios. Comprehensive characterizations were performed using UV-Vis-DRS, PL, XRD, XPS, BET, and EDS to evaluate the material's crystallinity, purity, porosity, and optical properties. FESEM imaging revealed the porous nature of PANI, the exfoliated structure of GO, and the nanosphere morphology of MoS2 (35-55 nm in diameter). This composite was tested for its effectiveness in degrading methyl orange (MO) dye and generating green hydrogen via visible-light-driven water splitting. Within 120 minutes, it achieved around 81.23% detoxification and 99% removal of MO dye. The degradation process adhered to first-order kinetics with a rate constant 7.1 times higher than pure PANI, 22 times higher than GO, 6.35 times higher than MoS2, and 9.26 times greater than the commercial TiO2-P25 photocatalyst, indicating strong synergy among the components. The study also examined the impact of various reaction parameters like pH, illumination area, catalyst dosage, and scavengers on the degradation process. Reusability of the photocatalyst was assessed over six cycles, maintaining 80% stability, as confirmed by XRD analysis. GC-MS identified the intermediates and final degradation products. The nanocomposite achieved hydrogen production with an apparent quantum efficiency (AQE) of 26% using CH3OH as a sacrificial agent, and AQEs of 22%, 19%, and 15% under acidic, basic, and neutral conditions, respectively. This research highlights the potential of ternary nanocomposites for diverse applications beyond dye degradation, including various solar-driven technologies. Chapter 5: In this study, a binary nanocomposite comprising polyaniline (PANI) and nickel–aluminium layered double hydroxide (Ni-Al LDH) was synthesized via an oxidative polymerization method, with varying LDH loadings (2, 5, and 7 wt%). Comprehensive physicochemical characterization including UV-Vis DRS, photoluminescence (PL), XRD, XPS, BET, and EDS was employed to investigate the optical, structural, compositional, and textural attributes of the materials. From FESEM the porous morphology of PANI and the hierarchical, flower-like morphology of LDH were observed. The photocatalytic performance of the composite was evaluated for Congo red (CR) dye degradation and photocatalytic hydrogen evolution under visible light irradiation. After 120 minutes, the system achieved 98% dye removal and approximately 50% mineralization, as confirmed by total organic carbon analysis. Kinetic studies indicated pseudo-first-order behaviour, with the rate constant exceeding those of pristine PANI, LDH, and TiO2-P25 by factors of 6, 8, and 9, respectively, evidencing a pronounced synergistic interaction. Operational parameters such as pH, catalyst loading, illumination area, and the presence of scavengers significantly influenced activity. The composite maintained ~70% catalytic efficiency over six consecutive cycles. HRMS enabled identification of intermediate and final degradation products. Under methanol-assisted conditions, the composite exhibited a hydrogen evolution AQE of 20%, with AQEs of 18%, 21%, and 16% in acidic, basic, and neutral media, respectively. These results underscore the composite's bifunctionality for environmental remediation and solar-driven energy conversion.

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  Buckling and Vibration Characteristics of Functionally Graded Sandwich Structures with Conventional and Auxetic Core: Analytical and Finite Element Study

  (2026-08-26) Singh, Rajbir; Bhardwaj, Gagandeep; Grover, Neeraj

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  Functionally graded sandwich plates (FGSPs) have emerged as an importance class of structural components in modern engineering fields such as in aerospace, mechanical, and marine structures due to their superior stiffness-to-weight ratio, improved thermal resistance, and enhanced structural stability. The present thesis presents a comprehensive analytical and numerical investigation of the buckling and vibration behaviour of FGSPs based on the Inverse Trigonometric Shear Deformation Theory (ITSDT). The governing equations are formulated using the principle of virtual work in combination with linear structural kinematics and generalized Hooke’s law. An analytical employing ITSDT is developed to obtain-closed form solutions for plates with simply supported boundary conditions (SSSS). In addition, a finite element (FE) formulation is established to analyze the structural response of plates subjected to more complex boundary conditions such as clamped-clamped-clamped-clamped (CCCC) and clamped simply supported-clamped-simply supported (CSCS). In order to evaluate the influence of different material arrangements within the sandwich structure, three configurations of FGSPs - Type-A, Type-B, and Type-C, are considered. In the Type-A configuration, the core layer is made of ceramic material while the face sheets consist of functionally graded materials whose properties vary according to a power-law distribution. For Type-B plates, the core is composed of functionally graded, whereas the top and bottom face sheets are made of ceramic and metallic materials, respectively. In the Type-C configuration, the core is modeled as an auxetic honeycomb structure characterized by a negative Poisson’s ratio, while the face sheets are composed of functionally graded materials. The equivalent elastic properties of the auxetic honeycomb core are evaluated using analytical expressions based on the geometric parameters of the honeycomb unit cell. A detailed parametric study is carried out to investigate the influence of several important parameters on the structural behaviour of FGSPs. These parameters include the span-to-thickness ratio (a/h), aspect ratio (a/b), power-law index (p), auxetic cell angle (θ), core thickness configurations of the sandwich layers, and different boundary conditions. The structural performance is evaluated in terms of the dimensionless fundamental natural frequency and the dimensionless critical buckling load. For the buckling analysis, both uniaxial and biaxial in-plane compressive loading conditions are considered in order to study their influence on the stability characteristics of the plates. The results obtained from the analytical solutions and finite element simulations show excellent agreement with previously reported results in the literature, confirming the accuracy and reliability of the proposed ITSDT-based formulation and the developed numerical model. The parametric investigation indicates that the power-law index significantly affects the structural response of FGSPs. The dimensionless fundamental frequency and the critical buckling load decrease with an increase in the power-law index. The span-to-thickness ratio also has a strong influence on the vibrational behaviour of the plates. It is observed that the dimensionless fundamental frequency increases as the span-to-thickness ratio increases, primarily due to the reduction in transverse shear deformation effects and the predominance of bending behaviour in relatively thinner plates. Similarly, the aspect ratio influences the stability characteristics of the plates, with the dimensionless critical buckling load decreasing as the aspect ratio increases. Furthermore, the nature of the applied in-plane compressive loading plays an important role in the buckling response, as the critical buckling load under uniaxial compression is found to be considerably higher than that under biaxial compression for plates with simply supported boundary conditions. The study further demonstrates that the thickness of the core layer has a significant influence on the vibrational response of FG sandwich plates. An increase in the core thickness enhances the bending rigidity of the sandwich structure, which results in higher natural frequencies. Moreover, boundary conditions considerably affect both the vibration and buckling responses of the plates. Structures with clamped boundary conditions exhibit higher natural frequencies and greater buckling resistance compared with plates having simply supported boundary edges. The thickness distribution scheme of the sandwich layer also plays a crucial role in determining the structural performance, where configurations with thicker core regions generally lead to improved stiffness and higher natural frequencies. For Type-C plates, the inclusion of an auxetic honeycomb core introduces distinctive mechanical characteristics due to its negative Poisson’s ratio behaviour. The results indicate that the auxetic core enhances the stiffness and stability of the sandwich plates while also providing additional flexibility in structural design through the variations in geometric parameters such as the cell angle. Overall, this work establishes a robust analytical and numerical framework for the investigation of vibration and buckling behaviour of functionally graded sandwich plates. The outcomes of this study provide valuable insights into the influence of material gradation, geometric configuration, boundary conditions, and auxetic core characteristics on the structural performance of sandwich plates, thereby contributing to the optimal design and development of advanced lightweight structural systems for modern engineering applications.

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  Horseman

  (1994) Ghosh , Santanu

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  Grapher

  (1994) Guleria , Sanjeev Kumar

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  A Study of Numerical Methods for Nonlinear Problems and Their Applications

  (2026-08-24) Rani, Litika; Kansal, Munish

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  Computational methods have been effectively used to tackle real-world problems like global positioning systems, fluid flow, control systems, chemical reactions, computational economics, and biological and physical phenomena with the advent of modern high-speed digital electronic computers. These applications demonstrate the growing dependence on computational approaches in solving complex practical problems. Because of its practical aspect, many look for solutions that are “good enough,” but defining what “good enough” means is more difficult. Determining the required accuracy therefore becomes a central topic in computational problem solving. The methodology and techniques for addressing scientific and engineering challenges have experienced significant transformations. The increasing complexity of the nonlinear problems under study largely drives these changes. This complexity arises from the complex structures analyzed in the mathematical modeling of various real-world instances. As a result, exact analytical solutions are often difficult or impossible to obtain. Simultaneously, approximate numerical solutions to problems are often sufficient. In many cases, such approximations provide results that are both accurate and computationally efficient. An approximation of the solution is necessary, precise to a specified number of decimal places or within a defined tolerance. Various numerical techniques for solving a specific problem generate a sequence of approximations that converge to the desired solution. The quality of these approximations must be evaluated in relation to the problem’s requirements. But “good enough” depends on the application area. The primary objectives include finding the best possible approximate solutions for scalar or systems of nonlinear equations, along with higher-degree polynomials, transcendental functions, extensive multidimensional systems, and both ordinary and partial differential equations. Secondly, it addresses the calculation of the matrix sign function, which is subsequently utilized to compute solutions for nonlinear matrix equations. This function plays an important role in extending numerical techniques to matrix-based problems. The matrix sign function is an axiomatic study of the intuitive concepts that govern the matrix function of non-singular square matrices, which are fundamental concepts in matrix theory. Therefore, performing these computations requires strong theoretical knowledge. The present study requires the knowledge of not only the original problem but also the derivation, error analysis, and performance limits of the numerical methods used to solve it. This research develops new optimized iterative methods for solving nonlinear scalar, vectorial, and matrix equations, aiming for high convergence orders with minimal computational cost and adhering to theoretical rigor to avoid common numerical pitfalls. This emphasis is particularly important when numerical methods are applied to practical problems. As a fact, some algorithms do not work for real-world problems. Although numerical techniques have improved greatly, some limitations still exist. Comprehensive numerical experiments consistently validate the theoretical developments. This computational experience is useful, as it connects exact arithmetic theory with finite-precision computation. At the same time, studying dynamical behavior through basins of attraction proves that the proposed schemes are better, efficient, and useful in real-world computing instances. To present these results in a systematic manner, the thesis is organized as follows: Chapter 1 provides an introduction and developments in the theory related to nonlinear scalar, vector, and matrix equations. We present a thorough literature review of algorithms for nonlinear problems. The applications of these algorithms for computing the matrix sign function are studied as well. Furthermore, we review basic mathematical concepts that drive the study of nonlinear solvers and the existence of the matrix sign function. Chapter 2 deals with developing a higher-order optimal family of Chebyshev–Halley type methods to solve a univariate nonlinear equation with multiple roots. The proposed scheme considers weight functions that are selected adequately to optimize the convergence order and demands only four functional evaluations at each iteration. An extensive convergence analysis is also provided that demonstrates the establishment of eighth-order convergence for the developed scheme. As a result, the efficiency index of the proposed scheme is optimal according to the Kung-Traub conjecture. Finally, the theoretical findings are verified through numerical experiments that include real-life and nonlinear academic problems. In addition, the dynamical study of iterative schemes reflects a comprehensive overview of their stability, convergence properties, and graphical aspects by drawing attraction basins in the complex plane. Chapter 3 aims to develop and analyze a new derivative-free class of higher-order iterative methods for locating multiple roots numerically. The scheme is generated by using King’s type it erative method. By employing the Traub-Steffensen technique, a derivative-free family is proposed, which requires three functional evaluations to achieve optimal fourth-order convergence. Moreover, it can be observed that the theoretical convergence results of the family are symmetrical for different multiplicities of roots. Finally, a wide variety of nonlinear problems are included to confirm the applicability and effectiveness of the proposed methods. Chapter 4 deals with the development of multi-step vectorial iterative schemes for solving non linear systems, achieving fourth and sixth-order convergence. The proposed methods are designed to minimize computational costs by employing a single inverse operator and reducing the number of functional evaluations per iteration. Furthermore, the proposed three-step scheme is generalized into a (q +1)-step family, increasing the convergence order to 2q +2. While standard local convergence analysis based on Taylor series expansion is common, but it has limitations, as it requires the use of higher-order derivatives. To overcome this limitation, the theoretical analysis in a Banach space setting is conducted that relies solely on first-order derivatives. The existence of a unique solution is guaranteed within a specific domain, whose radius of convergence is formally obtained using Lipschitz constants. Furthermore, the theoretical results are tested on several numerical examples to check the performance and stability of the proposed methods in comparison to existing counterparts. In chapter 5, some new iterative families that utilizes a derivative-free approach, requiring two frozen divided differences and one matrix inversion per iteration are proposed. Additionally, a general multi-point family using a fifth-order scheme as a predictor is derived. The proposed families are analyzed both theoretically and numerically, and experimentation is conducted using a range of numerical problems to confirm the theoretical results on convergence order and computational efficiency. The dynamical properties of each iterative method are studied by means of basins of attraction. In chapter 6, a novel matrix iteration for numerically computing the matrix sign function is proposed. An extensive convergence analysis is carried out in the matrix case to achieve fourth order convergence. The basins of attraction are illustrated to demonstrate the global convergence behavior of the proposed method. Analytically, it is shown that the presented scheme is asymptotically stable. Furthermore, theoretical developments are numerically verified by discussing the clustering of eigenvalues around ±1. Moreover, a class of numerical examples for matrices of various dimensions is assessed to exhibit the efficacy of the proposed method. In chapter 7, the primary objective is to develop two novel iterative schemes for computing the sign of a matrix that has no pure imaginary eigenvalues. Detailed convergence analysis and asymptotic stability of the proposed methods are discussed. It is shown that the new schemes converge globally by drawing attraction basins. In addition, the obtained results are extended to compute non-trivial solutions of the Yang-Baxter-like equation, provided the given matrix has no eigenvalues on the imaginary axis. To illustrate the effectiveness of theoretical developments, a class of numerical examples for matrices of various dimensions, including eigenvalue clustering, is worked out. Chapter 8 discusses the summary and future aspects of the presented work.

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