The shear viscosity of a polymer melt is a measure of its resistance to deformation under shear stress. The effect of molecular weight and temperature on the shear viscosity of a polymer melt can be understood through the following relationships:1. Molecular weight: As the molecular weight of a polymer increases, the shear viscosity of the polymer melt also increases. This is because higher molecular weight polymers have longer chains, which leads to more entanglements and interactions between the chains. These entanglements and interactions make it more difficult for the polymer chains to slide past one another, resulting in a higher resistance to deformation and thus, higher shear viscosity.2. Temperature: As the temperature of a polymer melt increases, the shear viscosity generally decreases. This is because the increased thermal energy allows the polymer chains to move more freely, overcoming the entanglements and interactions that contribute to the resistance to deformation. As a result, the polymer melt becomes less viscous at higher temperatures.The relationship between molecular weight, temperature, and shear viscosity can change depending on the type of polymer structure:1. Linear polymers: For linear polymers, the shear viscosity increases with molecular weight according to a power-law relationship ~Mâ, where is the shear viscosity, M is the molecular weight, and a is a constant . The effect of temperature on linear polymers follows the Arrhenius equation, which states that the shear viscosity decreases exponentially with increasing temperature.2. Branched polymers: Branched polymers have a more complex relationship between molecular weight and shear viscosity due to the presence of side chains. The shear viscosity still increases with molecular weight, but the rate of increase may be different compared to linear polymers. The effect of temperature on branched polymers is similar to that of linear polymers, with the shear viscosity decreasing as temperature increases.3. Cross-linked polymers: Cross-linked polymers have covalent bonds between the polymer chains, which significantly affect their shear viscosity. The shear viscosity of cross-linked polymers is less sensitive to molecular weight and temperature changes compared to linear and branched polymers. This is because the cross-links restrict the movement of the polymer chains, making it more difficult for them to slide past one another even with increased molecular weight or temperature.In summary, the shear viscosity of a polymer melt is influenced by its molecular weight and temperature, with the relationship between these factors varying depending on the type of polymer structure linear, branched, or cross-linked .