1d. (10pts) The "packing parameter" (P) is a good predictor of what type of self-assembled structures will be favored for amphiphiles of different size and shape. P=V, where is the length of an amphiphile, V is the volume per amphiphile and is the surface area per amphiphile headgroup. For spherical micelles, the optimum ratio of these amphiphile dimensions is : V=31 - whereas, for amphiphiles that form bilayers, this ratio is closer to 1 . For a cylindrical nanofiber with an aggregation number N, a nanofiber length L and radius , show that the ratio of its volume V, to its surface area A is: AV2 (For a very long nanofiber where L>>, you can ignore the surface area of the 2 ends of the nanofiber) Show that if amphiphiles are close-packed in a nanofiber, the packing parameter P=1/2 (Close packing roughly means that the volume of the nanofiber is equal to the volume per amphiphile multiplied by the aggregation number (i.e. V=Nv ) and that the surface area of the nanofiber is equal to the aggregation number multiplied by the surface area occupied by each amphiphile headgroup (i.e. A=N )