New insight into surface tension inverted curvature for liquid-liquid and solid-liquid binary mixtures: The special case of hexamethylenetetramine in water

Bermúdez-Salguero, Carolina; Penagos, Julio Alberto Clavijo; Romero, Carmen M.; Gracia-Fadrique, Jesús

doi:10.1016/j.colsurfa.2014.02.014

Cited by 3 publications

(8 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It can be seen that, relatively speaking, Δ G ̃ ad, x 0 and Δ G ̃ ad,ϕ 0 for the L I -type systems exhibit large negative values (about −4.54 kJ mol –1 for water–EtOH and −10.15 kJ mol –1 for water–BuOH), while those for the L II -type and S-type exhibit small negative and even positive values (from about −2.14 to 1.23 kJ mol –1 ). Note that positive Δ G ̃ ad 0 values have also been reported in the literature . These results indicate that the L I -type isotherms correspond to the strong adsorption, while the L II -type and S-type to the weak adsorption, which are reasonable.…”

Section: Resultssupporting

confidence: 84%

“…Some thermodynamic and empirical models were analyzed for their predicted limiting slopes, including those proposed by Szyszkowski, , Frumkin, Belton and Evans, Eberhart, Shereshefsky, Connors and Wright, Lamperski, Brocos et al, Azizian and Moghadam, and Bermúdez-Salguero et al It was found that most of the existing models cannot describe the S-type isotherms (see Section S1). The extended Langmuir model coupled with the modified Eberhart mixing rule can describe the S-type isotherms, but the agreement between the model prediction and the experimental data is not good for some binary liquid mixtures .…”

Section: Theoretical Basismentioning

confidence: 99%

“…Various shapes of σ-isotherms were observed for binary liquid mixtures. 6,18,19 Three main types can be defined 18 based on the surface tension deviation (Δσ) of real systems from their hypothetical ideal state, Δσ = σ − ∑σ i 0 c i,b , where σ i 0 is the surface tension of pure component i. As shown in Scheme 1A, the first one exhibits negative deviation (Δσ < 0) over the entire composition range, which may be called "Langmuir-I type" (L I -type) isotherms, owing to the fact that they may be described using the existing (classical or modified) Langmuir models.…”

Section: ■ Introductionmentioning

confidence: 99%

“…6,11,16 The second one exhibits positive deviation (Δσ > 0) over the entire composition range, with an opposite curvature to that of the L I -type isotherms, which may be called "Langmuir-II type" (L II -type), owing to the fact that they may also be described using the existing Langmuir models. 6,11,19 The last type of isotherms show sigmoidal shape: a negative deviation followed by a positive one, or an opposite tendency. The sigmoid-type (S-type) isotherms may be divided into two subcategories: one with the negative deviation followed by a positive one, called "S I -type", and the other with an opposite tendency, called "S II -type".…”

Section: ■ Introductionmentioning

confidence: 99%

“…Many models for correlating the surface tension and composition with the bulk composition have been developed based on Gibbs thermodynamics, − ,− statistical mechanics, ,− and empirical or semiempirical induction. ,− The Gibbs adsorption equation, the Langmuir isotherm, and the Butler equation are the three basic models of surface thermodynamics, although each model contains some simplifying assumptions. − ,,,− In fact, the Gibbs and Langmuir equations can be derived from the Butler equation. , The Gibbs equation cannot visually describe the surface tension or composition isotherms because it only provides information on the surface excess concentration obtained from the change of surface tension with the bulk concentration. , Theoretically, the Butler equation can lead to various shapes of σ-isotherms except for the S I -type, as revealed by Santos and Reis . However, it is difficult to directly use the Butler equation to describe the isotherms.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

et al. 2022

Langmuir

View full text Add to dashboard Cite

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.

show abstract

Section: Resultssupporting

confidence: 84%