The effect of molecular weight on the viscosity of polymer melts is a well-studied phenomenon in polymer science. In general, the viscosity of a polymer melt increases with increasing molecular weight. This is because higher molecular weight polymers have longer chains, which leads to increased entanglements and interactions between the chains, resulting in higher resistance to flow i.e., higher viscosity .Experimental evidence for the effect of molecular weight on the viscosity of polymer melts can be found in numerous studies. One of the most famous relationships between molecular weight and viscosity is the Mark-Houwink equation: = K * Mâwhere is the intrinsic viscosity, M is the molecular weight, and K and a are constants that depend on the specific polymer and solvent system. The exponent a typically ranges from 0.5 to 0.8 for most polymers, indicating that viscosity increases with increasing molecular weight.In a classic study by Ferry 1961 , the viscosity of polystyrene melts was measured as a function of molecular weight. The results showed that the viscosity increased with increasing molecular weight, following a power-law relationship consistent with the Mark-Houwink equation.Comparing these experimental results with existing theories, we can look at the Rouse and reptation models. The Rouse model, developed in the 1950s, is a simple theoretical model that describes the motion of polymer chains in a melt or solution. According to the Rouse model, the zero-shear viscosity 0 of a polymer melt is proportional to the molecular weight M as follows:0 MHowever, the Rouse model does not account for chain entanglements, which become increasingly important as molecular weight increases. To address this limitation, the reptation model was developed by de Gennes in the 1970s. The reptation model considers the motion of polymer chains as they "snake" or "reptate" through a network of entanglements with other chains. According to the reptation model, the zero-shear viscosity is proportional to the molecular weight raised to the power of 3.4:0 M^3.4This prediction is in better agreement with experimental data for high molecular weight polymers, where chain entanglements play a significant role in determining viscosity.In summary, the viscosity of polymer melts increases with increasing molecular weight, as demonstrated by experimental evidence and supported by theoretical models such as the Mark-Houwink equation, the Rouse model, and the reptation model. The reptation model, which accounts for chain entanglements, provides a more accurate description of the relationship between molecular weight and viscosity for high molecular weight polymers.