TY - JOUR
T1 - Translational and rotational contributions to the size of micelles in dilute surfactant solutions
AU - McMullen, William E.
AU - Gelbart, William M.
AU - Ben-Shaul, Avinoam
PY - 1984
Y1 - 1984
N2 - Equilibrium theories of micellar self-assembly in dilute surfactant solutions are now well established. The fundamental thermodynamic quantity is μs, the chemical potential of an aggregate comprised of s surfactants: μs = μs° + kT ln (Xs/s), where Xs is the mole fraction of surfactant molecules incorporated into s-micelles. The distribution of aggregate sizes ({Xs}) follows from the equilibrium condition s′μs = sμs′ (all s and s′), as soon as the s dependence of μs° is specified. But previous theories have implicitly interpreted the standard chemical potential μs° as the reversible work required to insert an s-micelle into aqueous solution at a particular point and with a particular orientation. In the present work we outline a simple but systematic derivation of μs. We show that the above μs° must be augmented by the translational and rotational contributions familiar from a statistical-thermodynamic treatment of the ideal (molecular) gas partition functions. Including these "new" terms in the micellar exchange equilibrium leads to new forms for the size distributions and relative stabilities of rodlike and disklike aggregates in dilute solution. The results of numerical calculations are presented for commonly accepted values of the micellar self-assembly parameters. Inclusion of translational and rotational degrees of freedom is shown in general to favor smaller aggregates, making finite disks still more likely than previously believed.
AB - Equilibrium theories of micellar self-assembly in dilute surfactant solutions are now well established. The fundamental thermodynamic quantity is μs, the chemical potential of an aggregate comprised of s surfactants: μs = μs° + kT ln (Xs/s), where Xs is the mole fraction of surfactant molecules incorporated into s-micelles. The distribution of aggregate sizes ({Xs}) follows from the equilibrium condition s′μs = sμs′ (all s and s′), as soon as the s dependence of μs° is specified. But previous theories have implicitly interpreted the standard chemical potential μs° as the reversible work required to insert an s-micelle into aqueous solution at a particular point and with a particular orientation. In the present work we outline a simple but systematic derivation of μs. We show that the above μs° must be augmented by the translational and rotational contributions familiar from a statistical-thermodynamic treatment of the ideal (molecular) gas partition functions. Including these "new" terms in the micellar exchange equilibrium leads to new forms for the size distributions and relative stabilities of rodlike and disklike aggregates in dilute solution. The results of numerical calculations are presented for commonly accepted values of the micellar self-assembly parameters. Inclusion of translational and rotational degrees of freedom is shown in general to favor smaller aggregates, making finite disks still more likely than previously believed.
UR - http://www.scopus.com/inward/record.url?scp=0000230168&partnerID=8YFLogxK
U2 - 10.1021/j150670a029
DO - 10.1021/j150670a029
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AN - SCOPUS:0000230168
SN - 0022-3654
VL - 88
SP - 6649
EP - 6654
JO - Journal of Physical Chemistry
JF - Journal of Physical Chemistry
IS - 26
ER -