Question

As length of hydrophobic part of micelle increases, cmc

Answer 1

the explanation is based on on the competition of two processes concerning the temperature change of water structure that stipulates the hydrophobic hydration of hydrocarbon chain of surfactant (the longer chain the lower CMC) and hydration properties of hydrophilic groups that begin to play more important role usually in the interval about 20-50 degrees when the water structure became less and facilitate the hydrophilic hydration of polar group of surfactant molecule. So, point of temperature minimum should depend from surfactant nature and HLB may be.

Answer 2

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Within any class of surface active agent, the CMC decreases with increase in chain length of the hydrophobic portion (alkyl group). As a general rule, the CMC decreases by a factor of 2 for ionics (without added salt) and by a factor of 3 for nonionics on adding one methylene group to the alkyl chain.