# Thermodynamic Characterization of Rhamnolipid, Triton X-165 and Ethanol as well as Their Mixture Behaviour at the Water-Air Interface

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Dissuasion

#### 2.1. Some Physicochemical Properties of Water, RL, ET and TX165

^{2}. This value is close to that of the contact area determined by Groszek [31] based on the water vapour adsorption on the quartz surface, which is equal to 10 Å

^{2}. This means that 1 × 16.6

^{−}

^{6}mole of water is needed to cover the given surface by its monolayer. The value of the water molecule contactable area equal to 10 Å

^{2}is very often used for the thermodynamic consideration of the surfactants adsorption at the water-air interface [26,32]. This adsorption decreases the water surface tension. According to van Oss et al. [33,34,35] water is the bipolar liquid and its surface tension results from the Lifshitz-van der Waals and Lewis acid-base intermolecular interactions. The Lewis acid-base interactions lead to the hydrogen bonds formation between the water molecules. Thus, the water surface tension can be divided into the Lifshitz-van der Waals component (LW) and the acid-base (AB) one, which results from the electron-acceptor and electron-donor parameters. As a result of the surfactants adsorption at the water-air interface, the surface tension of water is reduced, especially its AB component [26,32].

^{3}and to the value obtained from the ET density, which is equal to 97.3 Å

^{3}. As follows from the calculations the ethanol molecule can be put in a regular cube with the edge equal to 4.6 Å [30]. Thus, the contact area of the ET molecule with other one does not depend on its orientation and is about 21 Å

^{2}[30]. This point out that one ET molecule can replace two water molecules in the interface monolayer.

^{2}and 35.7 Å

^{2}, respectively. At the parallel orientation of RL molecule towards the air phase the contactable area of its tail is equal to 87.3 Å

^{2}and that of the head to 72.1 Å

^{2}[26]. In the case of TX165 at the parallel orientation of its molecule at the interface, the contactable area of the tail is equal to 52.12 Å

^{2}and that of the head to 101.4 Å

^{2}. Taking into account the contactable area of water and ET it can be stated that in the bulk phase one molecule of ET can be surrounded by 12 molecules of water. The tail of the TX165 can be surrounded by about 20 water molecules, and the head can be bound by strong hydrogen bonds with about 40 molecules and weak ones also with 40 water molecules. In the case of RL its tail can be surrounded by about 30 molecules of water and the head by 28 ones.

^{3}are also changed as a function of its concentration. Depending on the ET concentration it is treated in the practice as the co-surfactant and/or co-solvent [1,42]. This fact causes that the aqueous solution of ET must be treated thermodynamically in a different way from the aqueous solutions of typical surfactants.

^{3}most surfactants are present in the bulk phase in the monomeric form which decides about their concentration in the bulk phase [1]. In this range of surfactants concentration it be can assumed that with a small error ${X}^{b}=\frac{C}{\omega}$ ($C$ is the concentration of surfactants and $\omega $ is the number of the water moles in 1 dm

^{3}) and ${f}^{*}\cong 1$. Indeed, in the considered concentration range of the surface active agent ET fulfills such conditions if its chemical potential is defined asymmetrically. In such case it can written:

^{3}, the $\mathrm{\Gamma}$ values calculated using $C$ and ${X}^{b}$ do not differ much. However, the difference increases as the increasing ET concentration. It was concluded by them that the most reliable values of the Gibbs surface excess concentration of ET at the solution-air interface can be obtained from the following equation [26,32]:

^{3}, it is possible to calculate the surface area occupied by the water and ET molecules covering the surface by monolayer. Next, it is possible to determine the two dimensional concentration of ET in the monolayer (${\mathrm{\Gamma}}^{s}$) corresponding to its concentration in the bulk phase based on the equation:

^{3}the values of $\frac{C}{{X}^{S}}$ can be constant. Unfortunately, in this range of ET $C$ it is difficult to measure reliable values of the surface tension. It should be mentioned that above $C$ = 1 mol/dm

^{3}the changes of $\frac{C}{{X}^{S}}$ and $\frac{{a}^{0}}{{X}^{S}}$ a as a function of $C$ are almost linear. From these dependences one can deduce that ${f}^{0}$ is not equal to unity and increases with the increasing $C$. It is interesting that the ET concentration in the surface region determined from the Frumkin equation (Equation (14)) in the range of C in the bulk phase from zero to the value corresponding to the maximal Gibbs surface excess concentration at the solution-air interface fulfils the linear form of the Langmuir equation [1]:

_{3}O

^{+}ions are joined with the oxyethylene group [44,45]. For this reason the hydrophilic long part of TX165 molecule cannot be oriented perpendicularly towards the water-air interface at the perpendicular orientation of tail. This way of orientation increases the area occupied by one TX165 molecule at the interface. This is also another way of TX165 molecule orientation. The tail is oriented parallel to the water-air interface and the head perpendicularly. This way of TX165 molecule orientation also increase its contactable area. However, the two ways of TX165 molecules orientation give almost the same values of $\frac{C}{{X}^{S}}$ which are close to that of $a$ determined from Equation (20) as well as from the Szyszkowski equation (Table S1). The same dependences as for TX165 take place in the case of RL (Figure S2) (Table S1). However, the maximal fraction of the surface occupied by the RL molecules is close to its perpendicular orientation. Indeed, the values of $\u2206{G}_{ads}^{0}$ calculated from Equation (19) using the values of constant $a$ determined from the linear form of the Langmuir equation, Szyszkowski equation and calculated from $\frac{C}{{X}^{S}}$ are similar for a given surfactant.

#### 2.2. Surface Behaviour of ET + RL + TX165 Mixtures

^{3}. These concentrations in the bulk phase were close to the ET concentration corresponding to its unsaturated monolayer at the solution-air interface $\left({C}_{\mathrm{E}\mathrm{T}}^{unsat}\right)$ the maximum Gibbs surface excess concentration $\left({C}_{\mathrm{E}\mathrm{T}}^{max}\right)$, critical aggregation concentration (CAC) and to that higher than CAC, respectively.

^{−8}mol/dm

^{3}), 0.5 (9.92 × 10

^{−7}mol/dm

^{3}), 5 (9.92 × 10

^{−6}mol/dm

^{3}) and 20 mg/dm

^{3}(3.96 × 10

^{−5}mol/dm

^{3}). The RL concentrations in the bulk phase equal to 0.01, 0.5 and 5 mg/dm

^{3}corresponded to the unsaturated monolayer at the water-air interface $\left({C}_{\mathrm{R}\mathrm{L}}^{unsat}\right)$, the first concentration at which the saturated RL layer was formed $\left({C}_{\mathrm{R}\mathrm{L}}^{f,sat}\right)$ and to that smaller than CMC but larger than ${C}_{\mathrm{R}\mathrm{L}}^{f,sat}$, respectively. The RL concentration equal 20 mg/dm

^{3}is close to its CMC [47,48].

_{3}O

^{+}, the head of the TX165 molecule can become ionic. In this case weak repulsive intermolecular interactions can occur.

^{3}similar to the surface tension of an individual ET aqueous solution does not prove that there is no adsorption of RL and TX165 at the solution-air interface. As mentioned above the surface tension of RL and TX165 tails is close to that of ET. Therefore, it is difficult to determine directly the lack of adsorption of RL and TX165 at the high concentration of ET based only on the surface tension. Our previous studies [26,32] proved that the composition of the adsorption monolayer at the first approximation, can be predicted from the surface tension isotherms of aqueous solutions of the individual mixture components. Thus, it is possible to explain the presence in the adsorption monolayer of not only ET molecules but also RL as well as TX165 at the ET concentration at which the surface tension of the mixture solution is close to that of the ET itself.

## 3. Materials and Methods

#### 3.1. Materials

^{3}and the variable concentration of TX165 from 0 to 4 × 10

^{−}

^{3}mol/dm

^{3}. The series of the aqueous solutions of RL + ET +TX165 mixture included the constant concentration of the ET + RL sum and the variable concentration of TX165 as mentioned above. The constant sum concentration of ET + RL was prepared from all possible combinations of ET at the concentrations equal 1.07, 3.74, 6.69 and 10.27 mol/dm

^{3}and RL at the concentrations equal 0.01 (1.98 × 10

^{−}

^{8}mol/dm

^{3}), 0.5 (9.92 × 10

^{−}

^{7}mol/dm

^{3}), 5 (9.92 × 10

^{−}

^{7}mol/dm

^{3}) and 20 mg/dm

^{3}(3.96 × 10

^{−}

^{5}mol/dm

^{3}), respectively.

#### 3.2. Methods

## 4. Conclusions

## Supplementary Materials

^{3}, 0.5 mg/dm

^{3}, 5 mg/dm

^{3}and 20 mg/dm

^{3}vs. the logarithm of TX165 concentration ($\mathrm{l}\mathrm{o}\mathrm{g}{C}_{TX165}$) as well as plot of the surface tension of the aqueous solution of the RL + ET mixture (b) at the constant ET concentration equal to 1.07 mol/dm

^{3}, 3.74 mol/dm

^{3}, 6.69 mol/dm

^{3}and 10.27 mol/dm

^{3}vs. the logarithm of the RL concentration (${\mathrm{l}\mathrm{o}\mathrm{g}C}_{RL}$). Figure S4. A plot of the Frumkin concentration at the solution-air interface ($\mathsf{\Gamma}$) of RL, ET and their sum at the constant ET concentration equal to 1.07 mol/dm

^{3}(a), 3.74 mol/dm

^{3}(b), 6.69 mol/dm

^{3}(c) and 10.27 mol/dm

^{3}(d) vs. the logarithm of the RL concentration ($\mathrm{l}\mathrm{o}\mathrm{g}{C}_{RL}$). Figure S5. A plot of the Gibbs concentration ($\mathsf{\Gamma}$) of TX165 as well as the Frumkin concentration ($\mathsf{\Gamma}$) of TX165, RL and their sum at the constant RL concentration equal to 0.01 mg/dm

^{3}(a), 0.5 mg/dm

^{3}(b), 5 mg/dm

^{3}(c) and 20 mg/dm

^{3}(d) vs. the logarithm of the TX165 concentration (${C}_{TX165}$). Figure S6. A plot of the Gibbs concentration ($\mathsf{\Gamma}$) of TX165 as well as the Frumkin concentration ($\mathsf{\Gamma}$) of TX165, ET and their sum at the constant ET concentration equal 1.07 mol/dm

^{3}(a), 3.74 mol/dm

^{3}(b), 6.69 mol/dm

^{3}(c) and 10.27 mol/dm

^{3}(d) vs. the logarithm of the TX165 concentration (${C}_{TX165}$). Figure S7. A plot of the Gibbs concentration ($\mathsf{\Gamma}$) of TX165 as well as the Frumkin concentration ($\mathsf{\Gamma}$) of TX165, RL, ET and their sum vs. the logarithm of the TX165 concentration (${C}_{TX165}$) at the constant RL concentration equal to 0.01 mg/dm

^{3}and constant ET concentration equal to 1.07 mol/dm

^{3}(a), 3.74 mol/dm

^{3}(b), 6.69 mol/dm

^{3}(c) and 10.27 mol/dm

^{3}(d). Figure S8. A plot of the Gibbs concentration ($\mathsf{\Gamma}$) of TX165 as well as the Frumkin concentration ($\mathsf{\Gamma}$) of TX165, RL, ET and their sum vs. the logarithm of the TX165 concentration (${C}_{TX165}$) at the constant RL concentration equal to 0.5 mg/dm

^{3}and constant ET concentration equal to 1.07 mol/dm

^{3}(a), 3.74 mol/dm

^{3}(b), 6.69 mol/dm

^{3}(c) and 10.27 mol/dm

^{3}(d). Figure S9. A plot of the Gibbs concentration ($\mathsf{\Gamma}$) of TX165 as well as the Frumkin concentration ($\mathsf{\Gamma}$) of TX165, RL, ET and their sum vs. the logarithm of the TX165 concentration (${C}_{TX165}$) at the constant RL concentration equal to 5 mg/dm

^{3}and constant ET concentration equal to 1.07 mol/dm

^{3}(a), 3.74 mol/dm

^{3}(b), 6.69 mol/dm

^{3}(c) and 10.27 mol/dm

^{3}(d). Figure S10. A plot of the Gibbs concentration ($\mathsf{\Gamma}$) of TX165 as well as the Frumkin concentration ($\mathsf{\Gamma}$) of TX165, RL, ET and their sum vs. the logarithm of the TX165 concentration (${C}_{TX165}$) at the constant RL concentration equal to 20 mg/dm

^{3}and constant ET concentration equal to 1.07 mol/dm

^{3}(a), 3.74 mol/dm

^{3}(b), 6.69 mol/dm

^{3}(c) and 10.27 mol/dm

^{3}(d). Figure S11. A plot of $\frac{C}{{X}^{S}}$ and $a$ for TX165 (a), RL (b) and ET (c) vs. the logarithm of the TX165 concentration (${C}_{TX165}$). Figure S12. A plot of $\frac{C}{{X}^{S}}$ and $a$ for TX165 (a), RL (b) and ET (c) vs. the logarithm of theTX165 concentration (${C}_{TX165}$). Figure S13. A plot of the standard Gibbs free energy of adsorption ($\u2206{G}_{ads}^{0}$) calculated from Equation (19) for TX165 (a), RL (b) and ET (c) vs. the logarithm of the TX165 concentration (${C}_{TX165}$). Figure S14. A plot of the standard Gibbs free energy of adsorption ($\u2206{G}_{ads}^{0}$) calculated from Equation (19) for TX165 (a), RL (b) and ET (c) vs. the logarithm of the TX165 concentration (${C}_{TX165}$).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

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**Figure 1.**A plot of the ET Guggenheim-Adam excess concentration at the water-air interface (${\mathrm{\Gamma}}^{GA}$) (curve 1—correspond to the values calculated from Equation (8)) as well a plot of the ET total concentration (${\mathrm{\Gamma}}^{tot}$) (curves 2–4 correspond to the values calculated from Equations (10), (12) and (14), respectively) vs. its concentration (${\mathrm{C}}_{\mathrm{E}\mathrm{T}}$) (

**a**) and a plot of the RL (

**b**) and TX165 (

**c**) Gibbs surface excess concentration ($\mathrm{\Gamma}$) (curve 1 correspond to the values calculated from Equation (6)) as well as its total concentration $({\mathrm{\Gamma}}^{tot}$) (curves 2 and 3 correspond the values calculated from Equations (12) and (14) vs. the logarithm of the surfactant concentration $\left(\mathrm{l}\mathrm{o}\mathrm{g}C\right)$.

**Figure 2.**A plot of the surface tension $\left({\gamma}_{LV}\right)$ of the aqueous solution of the TX165 + ET mixture at the constant ET concentration equal to 1.07 mol/dm

^{3}(points 1, curves 1′ and 1″), 3.74 mol/dm

^{3}(points 2, curves 2′ and 2″), 6.69 mol/dm

^{3}(points 3, curve 3′) and 10.27 mol/dm

^{3}(points 4, curve 4′) vs. the logarithm of the TX165 concentration $\left({C}_{\mathrm{T}\mathrm{X}165}\right)$. Points 1–4 correspond to the measured values, curves 1′–4′ and curves 1″, 2″ correspond to the values calculated from Equations (1) and (2), respectively.

**Figure 3.**A plot of the surface tension $\left({\gamma}_{LV}\right)$ of the aqueous solution of the RL + ET + TX165 mixture at the constant RL concentration equal to 0.01 mg/dm

^{3}and ET concentration equal to 1.07 mol/dm

^{3}(points 1, curves 1′ and 1″), 3.74 mol/dm

^{3}(points 2, curves 2′ and 2″), 6.69 mol/dm

^{3}(points 3, curve 3′) and 10.27 mol/dm

^{3}(points 4, curve 4′) vs. the logarithm of the TX165 concentration $\left({C}_{\mathrm{T}\mathrm{X}165}\right)$. Points 1–4 correspond to the measured values, curves 1′–4′ and curves 1″, 2″ correspond to the values calculated from Equations (1) and (2), respectively.

**Figure 4.**A plot of the surface tension $\left({\gamma}_{LV}\right)$ of the aqueous solution of the RL + ET + TX165 mixture at the constant RL concentration equal to 0.5 mg/dm

^{3}and ET concentration equal to 1.07 mol/dm

^{3}(points 1, curves 1′ and 1″), 3.74 mol/dm

^{3}(points 2, curves 2′ and 2″), 6.69 mol/dm

^{3}(points 3, curve 3′) and 10.27 mol/dm

^{3}(points 4, curve 4′) vs. the logarithm of the TX165 concentration $\left({C}_{\mathrm{T}\mathrm{X}165}\right)$. Points 1–4 correspond to the measured values, curves 1′–4′ and curves 1″, 2″ correspond to the values calculated from Equations (1) and (2), respectively.

**Figure 5.**A plot of the surface tension $\left({\gamma}_{LV}\right)$ of the aqueous solution of the RL + ET + TX165 mixture at the constant RL concentration equal to 5 mg/dm

^{3}and ET concentration equal to 1.07 mol/dm

^{3}(points 1, curves 1′ and 1″), 3.74 mol/dm

^{3}(points 2, curves 2′ and 2″), 6.69 mol/dm

^{3}(points 3, curve 3′) and 10.27 mol/dm

^{3}(points 4, curve 4′) vs. the logarithm of the TX165 concentration $\left({C}_{\mathrm{T}\mathrm{X}165}\right)$. Points 1–4 correspond to the measured values, curves 1′–4′ and curves 1″, 2″ correspond to the values calculated from Equations (1) and (2), respectively.

**Figure 6.**A plot of the surface tension $\left({\gamma}_{LV}\right)$ of the aqueous solution of the RL + ET + TX165 mixture at the constant RL concentration equal to 20 mg/dm

^{3}and ET concentration equal to 1.07 mol/dm

^{3}(points 1and curve 1′), 3.74 mol/dm

^{3}(points 2and curve 2′), 6.69 mol/dm

^{3}(points 3 curve 3′) and 10.27 mol/dm

^{3}(points 4, curve 4′) vs. the logarithm of the TX165 concentration $\left({C}_{\mathrm{T}\mathrm{X}165}\right)$. Points 1–4 correspond to the measured values, curves 1′–4′ correspond to the values calculated from Equation (1).

**Table 1.**Components and parameters of the ET, TX165 and RL surface tension (${\gamma}_{LV}$) at 293 K, the maximal concentration at the water-air interface (${\mathrm{\Gamma}}^{max}$), limiting concentration at the water-air interface (${\mathrm{\Gamma}}^{0}$) and limiting area occupied by one water, TX165, ET and RL molecule (${A}_{0}$).

Substance | ${\mathit{\gamma}}_{\mathit{L}\mathit{V}}^{\mathit{L}\mathit{W}}$ [mN/m] | ${\mathit{\gamma}}_{\mathit{L}\mathit{V}}^{+}$ [mN/m] | ${\mathit{\gamma}}_{\mathit{L}\mathit{V}}^{-}$ [mN/m] | ${\mathit{\gamma}}_{\mathit{L}\mathit{V}}^{\mathit{A}\mathit{B}}$ [mN/m] | ${\mathit{\gamma}}_{\mathit{L}\mathit{V}}$ [mN/m] | ${\mathit{A}}_{0}$ [Å ^{2}]
| ${\mathbf{\Gamma}}^{\mathit{m}\mathit{a}\mathit{x}}$ [×10 ^{−}^{6} mol/m^{2}]
| ${\mathbf{\Gamma}}^{0}$ [×10 ^{−}^{6} mol/m^{2}]
| Ref. |
---|---|---|---|---|---|---|---|---|---|

Water from ${\gamma}_{WH}$ | 21.80 | 25.60 | 25.50 | 51.00 | 72.80 | 10.00 | 16.60 | 16.60 | [39] |

Water from θ | 26.85 | 22.975 | 22.975 | 45.95 | 72.80 | - | - | - | [40] |

ET | 21.40 | 0.09 | 9.00 | 1.80 | 24.20 | 21.00 | 7.91 | 7.91 | [30] |

TX165 tail | 22.00 | - | - | - | 22.00 | 35.70 | 2.12 | 4.65 | [26] |

TX165 head | 27.70 | 0.33 | 50.20 | 8.14 | 35.84 | - | - | - | [26] |

RL tail | 21.80 | - | - | - | 21.80 | 69.09 | 2.01 | 2.403 | [26] |

RL head | 35.38 | 0.04 | 56.74 | 3.01 | 38.39 | - | - | - | [26] |

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**MDPI and ACS Style**

Zdziennicka, A.; González-Martín, M.L.; Rekiel, E.; Szymczyk, K.; Zdziennicki, W.; Jańczuk, B.
Thermodynamic Characterization of Rhamnolipid, Triton X-165 and Ethanol as well as Their Mixture Behaviour at the Water-Air Interface. *Molecules* **2023**, *28*, 4987.
https://doi.org/10.3390/molecules28134987

**AMA Style**

Zdziennicka A, González-Martín ML, Rekiel E, Szymczyk K, Zdziennicki W, Jańczuk B.
Thermodynamic Characterization of Rhamnolipid, Triton X-165 and Ethanol as well as Their Mixture Behaviour at the Water-Air Interface. *Molecules*. 2023; 28(13):4987.
https://doi.org/10.3390/molecules28134987

**Chicago/Turabian Style**

Zdziennicka, Anna, Maria Luisa González-Martín, Edyta Rekiel, Katarzyna Szymczyk, Wojciech Zdziennicki, and Bronisław Jańczuk.
2023. "Thermodynamic Characterization of Rhamnolipid, Triton X-165 and Ethanol as well as Their Mixture Behaviour at the Water-Air Interface" *Molecules* 28, no. 13: 4987.
https://doi.org/10.3390/molecules28134987