Shape and curvature of surface tension isotherms for liquid mixtures

Santos, M. Soledade C.S.; Reis, João Carlos R.

doi:10.1016/j.colsurfa.2017.01.013

Cited by 10 publications

(20 citation statements)

References 45 publications

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“…Surface tension of solutions and surface adsorption of their components are key subjects of colloid chemistry − and nano-thermodynamics. − The combination of the two Butler equations offers a useful tool, allowing the estimation of both equilibrium surface composition and equilibrium surface tension of solution. − However, the Butler equations are used less frequently than they could/should be. One of the reasons is their awkward derivation, in which the partial surface tensions of the components are introduced without being properly defined.…”

Section: Introductionmentioning

confidence: 99%

Improved Derivation of the Butler Equations for Surface Tension of Solutions

Kaptay

2019

Langmuir

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The Butler equation was published in 1932 to describe the equilibrium surface composition and equilibrium surface tension of solutions. Unfortunately, it used the so-called “partial surface tension of a component”, which was not properly defined by Butler, leading to a reluctant acceptance of this equation. Although the present author defined the partial surface tension recently in this journal, it is considered an advantage to derive the same key equations of Butler without the need to employ the concept of partial surface tension. This derivation is offered in the present paper, starting from the two fundamental equations of Gibbs. No assumptions are made on the thickness and structure of the surface region, it is only supposed that the surface region has an average composition with a negligible concentration gradient. In this way, the Butler equations are obtained, which have more general validity compared to the original Butler equations derived by supposing a surface monolayer.

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Section: Introductionmentioning

confidence: 99%

Improved Derivation of the Butler Equations for Surface Tension of Solutions

Kaptay

2019

Langmuir

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“…Summing up, even though imperfect, the Butler equation has the advantage of providing an explicit and mathematically simple expression for the surface tension of liquid mixtures. This feature has allowed various surface phenomena to be successfully modeled ,,,− while employing the Butler equation. It has been, herein, demonstrated that it can continue to be confidently applied because of the small, largely inconsequent numerical errors involved.…”

Section: Discussionmentioning

confidence: 99%

Examination of the Butler Equation for the Surface Tension of Liquid Mixtures

Santos

Reis

2021

ACS Omega

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The classical Butler equation used to describe surface tension and the surface composition of liquid mixtures is revisited. A straightforward derivation is presented, separating basic chemical thermodynamics and assumptions proper to Butler’s model. This model is shown to conceal an approximation not recognized by other researchers. The shortcoming identified consists of not allowing surface standard values to vary with surface tension by virtue of the changing composition. A more rigorous equation is derived and shown to yield the Butler equation in case of incompressible surface phases. It is concluded that the Butler equation slightly overestimates ideal surface tensions. Butler’s surface-phase concentrations of the surface-active component are also slightly overestimated in the surface-active component dilute range, being just underestimated at higher concentrations. Despite this, Butler’s model stands as a very good standard due to its versatility.

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“…Each of the above four isotherms provides distinctive information on a particular system. 6,18 The π r is an important dimensionless parameter, which varies between zero and unity. 18 Especially in the modified Eberhart model, it may equal the surface content of component 2.…”

Section: Langmuirmentioning

confidence: 99%

“…6,18 The π r is an important dimensionless parameter, which varies between zero and unity. 18 Especially in the modified Eberhart model, it may equal the surface content of component 2. 25,37 Therefore, we will describe the shapes of isotherms according to the change of π r with bulk compositions.…”

Section: Langmuirmentioning

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%

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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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Shape and curvature of surface tension isotherms for liquid mixtures

Cited by 10 publications

References 45 publications

Improved Derivation of the Butler Equations for Surface Tension of Solutions

Improved Derivation of the Butler Equations for Surface Tension of Solutions

Examination of the Butler Equation for the Surface Tension of Liquid Mixtures

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

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