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88  Liquid-gas  and liquid-liquid  interfaces

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        Figure  4.14  Micellar  structures,  (a)  Spherical  (anionic) micelle.  This  is  the  usual
        shape  at  surfactant concentrations  below  about  40  per  cent,  (b)  Spherical  vesicle
        bilayer structure (see also Figure 4.28), which is representative of the living cell, (c) and
        (d)  Hexagonal  and  lamellar  phases  formed  from  cylindrical and  laminar micelles,
        respectively.  These,  and  other  structures,  exist  in  highly  concentrated  surfactant
        solutions
           micelle,  m,  and  the  number  of  carbon  atoms  per  hydrocarbon
           chain, n, are  approximately  related  as follows:


               n     12     14     16     18
               m     33     46     60    78

           Laminar  and  cylindrical  models,  in  contrast,  provide  no  satis-
           factory  mechanism  by  which  the  size  of  the  micelles  might  be
           limited.
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