Surfactant packing parameter Thermodynamics of micellization

packing parameter , micelle shape

the shape of surfactant molecule can described surfactant packing parameter,




n

s




{\displaystyle n_{\text{s}}}

(israelachvili, 1976). packing parameter takes account volume of hydrophobic chain (




v

c




{\displaystyle v_{c}}

), equilibrium area per molecule @ aggregate interface (




a

e




{\displaystyle a_{e}}

), , length of hydrophobic chain (




l

c




{\displaystyle l_{c}}

):

n

s


=



v

c




a

e


∗

l

c







{\displaystyle n_{\text{s}}={\frac {v_{c}}{a_{e}*l_{c}}}}

it should noted packing parameter specific surfactant not constant. dependent on various conditions affect each volume of hydrophobic chain, cross sectional area of hydrophilic head group, , length of hydrophobic chain. things can affect these include, not limited to, properties of solvent, solvent temperature, , ionic strength of solvent.

cone, wedge, , cylinder shaped surfactants

the shape of micelle directly dependent on packing parameter of surfactant. surfactants packing parameter of




n

s




{\displaystyle n_{\text{s}}}

≤ 1/3 appear have cone-like shape pack form spherical micelles when in aqueous environment (top in figure). surfactants packing parameter of 1/3 <




n

s




{\displaystyle n_{\text{s}}}

≤ 1/2 appear have wedge-like shape , aggregate in aqueous environment form cylindrical micelles (bottom in figure). surfactants packing parameter of




n

s




{\displaystyle n_{\text{s}}}

> 1/2 appear have cylindrical shape , pack bilayer in aqueous environment (middle in figure).