Most of the literature on adsorption of methylene blue a cationic dye support Langmuir and Freundlich whereas my fitting with Langmuir isotherm gave a negative value for intercept while that of nf value is less than 1.
If you are working with a ion exchange system, the selection of the working pH is a critical issue. You must know the isoelectric point of both methylene blue and the cation exchanger used to ensure that MB is in the cationic form (i.e., positively charged) and the adsorbent in the anionic form (i.e., negatively charged). Otherwise, the attraction between both parts may be weak or even you can get electrostatic repulsion.
Check again the optimal conditions of adsorption, and repeat the experimental studies. The value of qmax cannot be negative.
Anifat Bankole, The type of adsorbent and adsorbate determine the shape of the equilibrium curve. The shape is also influenced by pH, Co, ca, T, rpm and various side effects. Whether it is possible to fit a given function to the equilibrium curve is determined by its shape. You probably got a line shape close to a power function with an exponent greater than one, and you are trying to approximate it with the Langmuir isotherm, which mathematically is a hyperbolic function asymptotically converging to qm.