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[Display omitted] The previously observed effects of nonpolar additives on the scission energy and rheological properties of surfactant wormlike micelles can be explained in terms of the spatial distribution of the additive within the micelles. The dependence of the scission energy with the molecular organization of the system can be analyzed with a molecular theory capable of describing the thermodynamics and structure of the micelles. A new theoretical method to determine the scission energy of surfactant wormlike micelles is introduced. This methodology is based on a molecular theory that explicitly considers molecular details of all components of the micelles, and their inter- and intramolecular interactions without the use of fitting and/or empirical macroscopic parameters. The predicted effects of the concentration, molecular structure and hydrophobicity of the additive on the scission energy of cetyltrimethylammonium bromide (CTAB) wormlike micelles are found to be in qualitative agreement with previous experimental observations. In particular, our theory captures the decrease of micellar length with increasing content of highly hydrophobic additives and the non-monotonic dependence of the viscosity with additive hydrophobicity. The latter effect arises because highly and mildly hydrophobic additives affect the scission energy of wormlike micelles via markedly different molecular mechanisms. [ABSTRACT FROM AUTHOR]