The relationship between molecular weight and viscosity in polymer melts can be described by the Mark-Houwink-Sakurada MHS equation, which is a semi-empirical relationship that correlates the intrinsic viscosity of a polymer solution to its molecular weight. The MHS equation is given by:[] = K * M_v âwhere:[] is the intrinsic viscosity of the polymer solution,M_v is the viscosity-average molecular weight of the polymer,K and a are constants that depend on the specific polymer-solvent system and temperature.In polymer melts, the viscosity is related to the intrinsic viscosity [] by the following equation: = [] * Cwhere C is the concentration of the polymer in the melt.From these equations, it can be inferred that the viscosity of a polymer melt increases with increasing molecular weight. The exponent 'a' in the MHS equation determines the extent of this relationship. For most polymers, the value of 'a' ranges from 0.5 to 0.8, indicating that the viscosity increases more than linearly with molecular weight.In summary, the relationship between molecular weight and viscosity in polymer melts is that the viscosity increases with increasing molecular weight, and this increase is more than linear. The exact relationship depends on the specific polymer-solvent system and temperature.