Say if instance I have a 100 ml solution with micelles formed using some surfactant. Now if I pour that 100 ml solution into 500 ml of water, will those micelles break up into free surfactant again?
Also, is there a way to calculate the binding energy of a micelles and see if the new solution with micelles (immediately after mixing) within the 500 ml of water will overpower that binding energy, to force the micelles to break up?
Diluting a detergent solution at the CMC will result in a transition from a micellized into a disaggregated state. The definition of the CMC is that it is the concentration of onset of micellization. Below this concentration micelles do not exist.
For the diluted solution, surfactant in micelles will have a higher free energy than free detergent. In general, if you can determine (or compute, say) the free energy of the detergent in the free state versus in the micelle then you can make a prediction as to which state is preferred. Such a computation might not be simple, depending on the degree of detail with which you seek to describe the interactions in the micelles versus the freely solubilized surfactant.
