In this study, several simple equations are suggested to investigate the effects of size and density on the number, surface area, stiffening efficiency, and specific surface area of nanoparticles in polymer nanocomposites. In addition, the roles of nanoparticle size and interphase thickness in the interfacial/interphase properties and tensile strength of nanocomposites are explained by various equations. The aggregates/agglomerates of nanoparticles are also assumed as large particles in nanocomposites, and their influences on the nanoparticle characteristics, interface/interphase properties, and tensile strength are discussed. The small size advantageously affects the number, surface area, stiffening efficiency, and specific surface area of nanoparticles. Only 2 g of isolated and well-dispersed nanoparticles with radius of 10 nm (R = 10 nm) and density of 2 g/cm3 produce the significant interfacial area of 250 m2 with polymer matrix. Moreover, only a thick interphase cannot produce high interfacial/interphase parameters and significant mechanical properties in nanocomposites because the filler size and aggregates/agglomerates also control these terms. It is found that a thick interphase (t = 25 nm) surrounding the big nanoparticles (R = 50 nm) only improves the B interphase parameter to about 4, while B = 13 is obtained by the smallest nanoparticles and the thickest interphase.

Breast cancer (BC) is the most common cancer in women, which is also the second most public cancer worldwide. When detected early, BC can be treated more easily and prevented from spreading beyond the breast. In recent years, various BC biosensor strategies have been studied, including optical, electrical, electrochemical, and mechanical biosensors. In particular, the high sensitivity and short detection time of electrochemical biosensors make them suitable for the recognition of BC biomarkers. Moreover, the sensitivity of the electrochemical biosensor can be increased by incorporating nanomaterials. In this respect, the outstanding mechanical and electrical performances of graphene have led to an increasingly intense study of graphene-based materials for BC electrochemical biosensors. Hence, the present review examines the latest advances in graphene-based electrochemical biosensors for BC biosensing. For each biosensor, the detection limit (LOD), linear range (LR), and diagnosis technique are analyzed. This is followed by a discussion of the prospects and current challenges, along with potential strategies for enhancing the performance of electrochemical biosensors.