More significantly they found that addition of relatively short-chain alcohol and other co-surfactant additives is sufficient to lower the bending constant by an order of magnitude. Based on these findings, we believe that there exist two different situations for the compressed amphiphilic monolayers, depending on the experimental conditions (see Figure ). For the first case (Figure ), it is the large and insoluble surfactants of same type that compose of the monolayer. In this case, the stiffness κ of the compressed monolayer for bulk nanobubbles is rather large (κ >>1 𝑘 𝑇 ). With eq 3, the minimization of 𝐹 with respective to bubble radius at constant total area A (or equivalently, the fixed number of surfactant molecules at the nanobubble interface) leads to a relation between the optimal bubble radius 𝑅 and the spontaneous radius of curvature 𝑅 ,