How many models do we have to fit the impedance data? I want to know all models. Please can anyone help me on this topic. Suggesting websites and pdf's is appreciated.
Such answer depends on the complexity of data. While there are simple and straight forward answers to simple impedance data (e.g: straight line, 45 degree line, etc), there are countless different fittings that can be used to fit your data as they get more complex. Not all of these fittings will be correct, however, as the equivalent circuit fitting should resemble a valid physiochemical properties/setup from the actual sample/system that is being investigated.
James MacDonald's Impedance Spectroscopy (http://goo.gl/BeA1TQ) would be a good book to refer. A review paper from Annual Review also offers some great overall insights on impedance spectroscopy (http://goo.gl/7bSNhj)
You can check the book cover Bioimpedance and Bioelectricity Basics by Grimnes and Martinsen http://www.sciencedirect.com/science/book/9780123740045. But the most important issue is not what model to use to fit better your EIS data. You need to realize what you are after, do you want to have model that describes a given structure, thus the different elements might represent some specific structure, or you just one to find a way to characterize your samples for classification purpose, etc. Once you know your purpose then you can decide if you need a behavioral or explanatory model