An Improved Form for the Electrostatic Interactions of Polyelectrolytes in Solution and its Implications for the Analysis of QELSS Experiments on Sodium Dodecyl Sulfate and Cetyl Trimethyl Ammonium Bromide Solutions

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Institution: | Worcester Polytechnic Institute |
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Advisor(s): | George D. J. Phillies |

Degree: | Ph.D., Physics |

Year: | 1997 |

Volume: | 155 pages |

ISBN-10: | 1581120087 |

ISBN-13: | 9781581120080 |

The electrostatic interaction between two charged spheres in the presence of a screening electrolyte is calculated at the level of the linearized Debye-Hückel
theory. The calculation is performed analytically as a multipole expansion
by applying two-center spherical harmonic expansions and symbolic manipulation
methods. I focus on charge-charge and charge-induced dipole interactions,
calculated for two spheres of possibly unequal size. The former interaction
is given to good approximation by the familiar Debye-Hückel form ~
q_{1}q_{2}exp[-k(R-2a)]/[(epsilon*r(1+ka)^2]. The new
results are the charge-induced dipole interactions. Physically, these terms
arise from two sources: (i) surface polarization charge at the surface
of each sphere, and (ii) exclusion of the counterion cloud of each sphere
from the volume occupied by the other sphere. With parameters appropriate
for micelles, the charge-induced dipole interactions dominate the charge-charge
interaction at small separations.

Quasi-elastic light scattering measurements of the diffusion of sodium
dodecyl sulfate (SDS) and cetyl trimethyl ammonium bromide (CTAB) micelles
in aqueous solutions, and the diffusion of mesoscopic optical probes through
the same solutions, were carried out at 35°C and multiple solvent ionic
strengths. Assuming a spherical micelle, I deduced the micelle radius,
aggregation number, charge, and hydration from nonlinear least-squares
fits to both probe and mutual diffusion data. For SDS micelles the charge
that I find is lower than reported in the literature [Hayter, J. B.; Penfold,
J. *Colloid & Polymer Science* **1983**, 261, 1022; Triolo,
R.; Caponetti, E.; Graziano, V. *J. Phys. Chem.* **1985**, 89,
5743.] because I used an improved functional form of the micellar electrostatic
interaction. I find a smaller aggregation number and a larger micellar
hydration than literature values. My analysis of CTAB data implies extensive
micellar growth, and failure of the spherical micelle assumption.