### Abstract

The Langmuir-Hinselwood (L-H) equation is the simplest kinetic equation which is consistent with Langmuir's equilibrium isotherm. This kinetic equation cannot describe well the dynamic surface tension data for octanol, sodium dodecyl sulfate (SDS), and other surfactants. A new kinetic equation for the rate of adsorption from the subsurface (dl/dt = k^{a}_{L}c(θ,t)(1-θ) exp(-Bθ)-k^{d}_{L} Γ exp(-Bθ). where θ is the fractional surface coverage Γ/Γ_{m}, c(θ,t) is the subsurface concentration, and k^{a}_{L}, k^{d}_{L}, and B are constants) includes modification of the kinetics but not of the equilibrium isotherm. The new equation describes better the capture efficiency of the interfacial monolayer for additional surfactant, and can describe activation barriers for adsorption and desorption, or cooperative adsorption caused by primarily attractive interactions between the monolayer and the dissolved surfactant. This equation was used in a new model of mixed kinetics for one-dimensional diffusion/adsorption/desorption. For octanol and heptanol, the initial adsorption rate is controlled by intrinsic adsorption/desorption kinetics (slow adsorption/desorption). With increasing surface coverage, dynamic adsorption gets closer to the diffusion-controlled limit (fast adsorption/desorption relative to diffusion). This indicates attractive and cooperative interactions of alcohol molecules in the monolayer. For sodium di-2-ethylhexylsulfosuccinate (DESS or AOT) and SDS, adsorption is much slower than predicted by diffusion-controlled models. The modified L-H equation in a mixed-kinetics model can fit the data well. The capture efficiency factor, k^{a}_{L} exp(-bθ), increases with increasing SDS concentration c_{SDS} or NaCl concentration c_{s}, indicating that adsorption is strongly affected by electrostatic barriers. For c_{s} = 0 and c_{SDS} = 1.7 to 5.9 mM (for θ_{c}<0.4), the estimated surface electrical potential is in the range 150-230 mV, and is consistent with classical double-layer theory. For θ_{c} > 0.4 and a high salt concentration, the parameter B may involve substantial steric or other interactions.

Original language | English |
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Pages (from-to) | 189-201 |

Number of pages | 13 |

Journal | Colloids and Surfaces |

Volume | 69 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 1992 Dec 11 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

*Colloids and Surfaces*,

*69*(2-3), 189-201. https://doi.org/10.1016/0166-6622(92)80230-Y