Surface tension of binary mixtures of benzene + propionic acid and butanoic acid between 298.15 K and 318.15 K: Measurement and modeling

Tahery, Reza; Hernández, Ariel

doi:10.1016/j.jct.2022.106723

Cited by 6 publications

(14 citation statements)

References 43 publications

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“…The number of molecular layers less than 1 has been reported in the literature (such as ∼0.27 to 0.52 for benzene−propionic acid and benzene−butanoic acid). 16 For the binary mixtures with N 2 ≥ 1, the active molecules can be arranged in the surface layer with their long axis perpendicular to the surface, while when N 2 < 1, their most likely arrangement is parallel or inclined to the surface. The difference in the arrangement states is due to the difference in the dissimilarity between the molecules of two components.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

“…The simple mixing rule was modified by Laaksonen and Kulmala and then by Piñeiro et al to take into account the size difference and interaction between components. The combination of the extended Langmuir model and the modified Eberhart mixing rule was widely used to describe the surface tension or composition isotherms. ,,, However, we noticed that the model fitting is generally good for the L I - and L II -type isotherms but not for the S-type ones . In fact, most of the existing models cannot reasonably describe the S-type isotherms.…”

Section: Introductionmentioning

confidence: 94%

“…where β � K ϕ (note that β is commonly used to represent the adsorption equilibrium constant in the extended Langmuir model 6,16,25,28 ).…”

Section: Langmuirmentioning

confidence: 99%

“…The λ values were generally estimated by coupling eq 18 with the extended Langmuir model (eq 15) in previous reports. 6,16,25,28 Combination between Models. The general adsorption model (eqs 10 or 14) and the extended Langmuir model (eq 15) can be separately coupled with the modified Eberhart model (eqs 17 or 18) to describe the change of the surface tension and composition with the bulk composition.…”

Section: Langmuirmentioning

confidence: 99%

“…14,28,44 Thus, the so-obtained τ value here may be regarded as an average or apparent value, similar to the case of the Shereshefsky model. 16,22 ■ EXPERIMENTAL SECTION Chemicals. All chemicals were of analytical grade and used as received.…”

Section: Langmuirmentioning

confidence: 99%

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General Adsorption Model to Describe Sigmoidal Surface Tension Isotherms of Binary Liquid Mixtures

et al. 2022

Langmuir

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Surface tension (σ) isotherms of liquid mixtures can be divided into Langmuir-type (L-type, including LI- and LII-type) and sigmoid-type (S-type, including SI- and SII-type). Many models have been developed to describe the σ-isotherms. However, the existing models can well describe the L-type isotherms, but not the S-type ones. In the current work, a thermodynamic model, called the general adsorption model, was developed based on the assumption of surface aggregation occurring in the surface layers, to relate the surface composition with the bulk one. By coupling the general adsorption model with the modified Eberhart model, a two-parameter equation was developed to relate the σ with the bulk composition. Its rationality was examined using the σ data of 10 binary mixtures. The results indicate that the new model can accurately describe the S- and L-type isotherms of binary liquid mixtures, showing a good universality. One advantage of the model is that its two parameters, i.e., the adsorption equilibrium constant (K) and the average aggregation number (n), can be estimated by linear fitting experimental σ data, thereby obtaining unique values. This model suggests that the S- and LII-type isotherms arise from the surface aggregation (n ≠ 1). In addition, the standard molar Gibbs free energy of surface adsorption (ΔG̃ad 0) and the apparent surface layer thickness (τ) were analyzed for 10 binary mixtures. The ΔG̃ad 0 data suggest that the order of adsorption tendency is LI-type ≫ SI-type ≈ SII-type > LII-type, and the strong adsorption usually corresponds to large τ. This work provides a feasible model for describing the S-type isotherms and a better understanding of the surface properties of liquid mixtures.

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Section: ■ Results and Discussionmentioning

confidence: 99%