The effect of molecular weight on the melt viscosity of polystyrene at varying shear rates can be understood by examining the relationship between molecular weight, viscosity, and shear rate.1. Molecular weight: As the molecular weight of polystyrene increases, the size and complexity of the polymer chains also increase. This leads to more entanglements and interactions between the chains, which in turn increases the melt viscosity of the polymer.2. Shear rate: Shear rate is the rate at which a material is deformed under shear stress. At low shear rates, the polymer chains have enough time to disentangle and rearrange themselves, resulting in a lower viscosity. However, at high shear rates, the chains do not have enough time to disentangle, and the viscosity increases.The relationship between molecular weight, melt viscosity, and shear rate can be described by the following general trends:1. At low shear rates:- For a given shear rate, as the molecular weight of polystyrene increases, the melt viscosity also increases.- For a given molecular weight, as the shear rate decreases, the melt viscosity increases.2. At high shear rates:- For a given shear rate, as the molecular weight of polystyrene increases, the melt viscosity also increases, but the effect is less pronounced than at low shear rates.- For a given molecular weight, as the shear rate increases, the melt viscosity decreases.In summary, the melt viscosity of polystyrene is influenced by both its molecular weight and the shear rate. At low shear rates, the effect of molecular weight on viscosity is more pronounced, while at high shear rates, the effect of shear rate becomes more dominant.