Hydrogen peroxide (H 2 O 2 ) is a mild but versatile oxidizing agent with extensive applications in bleaching, wastewater purification, medical treatment, and chemical synthesis. The state-of-art H 2 O 2 production via anthraquinone oxidation is hardly considered a cost-efficient and environment-friendly process because it requires high energy input and generates hazardous organic wastes. Photocatalytic H 2 O 2 production is a green, sustainable, and inexpensive process which only needs water and gaseous dioxygen as the raw materials and sunlight as the power source. Inorganic metal oxide semiconductors are good candidates for photocatalytic H 2 O 2 production due to their abundance in nature, biocompatibility, exceptional stability, and low cost. Progress has been made to enhance the photocatalytic activity toward H 2 O 2 production, however, H 2 O 2 photosynthesis is still in the laboratory research phase since the productivity is far from satisfaction. To inspire innovative ideas for boosting the H 2 O 2 yield in photocatalysis, the most well-studied metal oxide photocatalysts are selected and the modification strategies to improve their activity are listed. The mechanisms for H 2 O 2 production over modified photocatalysts are discussed to highlight the facilitating role of the modification methods. Besides, methods for the quantification of H 2 O 2 and associated radical intermediates are provided to guide future studies in this field.

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A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

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