Colloids and Surfaces B: Biointerfaces 119 (2014) 22–29

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Thermodynamic properties of rhamnolipid micellization and adsorption ´ ´ DIANA Manko, ANNA Zdziennicka ∗ , BRONISŁAW Janczuk Department of Interfacial Phenomena, Faculty of Chemistry, Maria Curie-Skłodowska University, Maria Curie-Skłodowska Sq. 3, 20-031 Lublin, Poland

a r t i c l e

i n f o

Article history: Received 15 February 2014 Received in revised form 4 April 2014 Accepted 23 April 2014 Available online 4 May 2014 Keywords: Biosurfactant Rhamnolipid Micellization Adsorption Standard free energy of micellization and adsorption

a b s t r a c t Measurements: of the surface tension, density, viscosity and conductivity of aqueous solutions of rhamnolipid at natural and controlled pH were made at 293 K. On the basis of the obtained results the critical micelle concentration of rhamnolipid and its Gibbs surface excess concentration at the water–air interface were determined. The maximal surface excess concentration was considered in the light of the size of rhamnolipid molecule. Next the Gibbs standard free energy of rhamnolipid adsorption at this interface was determined on the basis of the different approaches to this energy. The standard free energy of adsorption was also deduced on the basis of the surface tension of n-hexane and water-n-hexane interface tension. Standard free energy obtained in this way was close to those determined by using the Langmuir, Szyszkowski, Aronson and Rosen, Gu and Zhu as well as modified Gamboa and Olea equations. The standard free energy of rhamnolipid adsorption at the water–air interface was compared to its standard free energy of micellization which was determined from the Philips equation taking into account the degree of rhamnolipid dissociation in the micelles. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Surfactants are amphihilic molecules which have two different parts: hydrophobic chain (tail) and hydrophilic group (head) [1]. These compounds influence the surface and interface tension through the formation of the aggregates co-called micelles and adsorption on different interfaces. Surfactants can be divided into two main groups: synthetic surfactants and biosurfactants. Synthetic surfactants are produced by organic chemical reactions and biosurfactants are produced by a number of microorganisms, including bacteria, yeast and fungi [2]. Biosurfactants have very interesting properties such as: good biodegradability, low toxicity or effectiveness at extreme temperature, pH and salinity. Because of their properties biosurfactants can be treated as potential substitutes of chemical compounds obtained by classical synthesis [3–6]. Among biosurfactants rhamnolipids have very interesting properties from theoretical and practical points of view. Rhamnolipids which are mainly produced by Pseudomonas aeruginosa during cultivation on glucose, glycerol or triglycerides

∗ Corresponding author. Tel.: +48 81 537 56 70; fax: +48 81 533 3348. E-mail address: [email protected] (A. Zdziennicka). http://dx.doi.org/10.1016/j.colsurfb.2014.04.020 0927-7765/© 2014 Elsevier B.V. All rights reserved.

[7–13] represent of glycolipid. There are many types of rhamnolipids; however, they possess similar chemical structures [14]. Generally rhamnolipids contain a hydrophilic head formed by one or two rhamnose molecules and a hydrophobic group composed of one or two fatty acid chains [14–16]. The form of rhamnolipids produced by bacteria and the proportion between them depend on their strain, the carbon source and the culture conditions [2,17]. Rhamnolipids have various applications such as pharmaceuticals [18,19], cosmetic products, food items, detergents [20] and bioremediation enhancers [21,22]. Additionally, rhamnolipids possess anti-proliferative activity against a human breast cancer cells [16,23] and anti-microbial against bacteria and phytopathogenic fungi species [11,24]. Though there are the many studies dealing with the adsorption and volumetric properties of rhamnolipids, the problem of their surface activity and tendency to form micelles in aqueous solutions is not quite clear. In the literature it is even possible to find different values of efficiency and effectiveness of rhamnolipid adsorption as well as of critical micelle concentration [25–27]. On the one hand, it can result from the fact that rhamnolipids produced by Pseudomonas sp. can be a mixture of various 4–28 homologues where monorhamnolipid is a dominant form [14]. One the other hand, the studies dealing with the adsorption and aggregation properties of

D. Ma´ nko et al. / Colloids and Surfaces B: Biointerfaces 119 (2014) 22–29

rhamnolipid are based mainly on the measurements of the surface tension. Moreover, the data connected with these properties are different and incoherent in many cases [25–27]. We must also remember that in practical application of rhamnolipid the knowledge of its tendency to adsorb at the water–air interface and to aggregate in the bulk phase should be very helpful. These tendencies can be expressed and predicted by the thermodynamic parameters of the rhamnolipid adsorption and micellization process. In the literature it is difficult to find a complex analysis of these processes based on the data obtained from the measurements of different physicochemical properties of aqueous solutions of rhamnolipid. Thus, the purpose of our studies was to determine the critical micelle concentration of the studied rhamnolipid and its surface excess concentration at the water–air interface and standard free energy of adsorption and micellization by using different approaches to these processes. This purpose was achieved by measurements of the surface tension, density, dynamic viscosity and conductivity of aqueous solutions of rhamnolipid at natural pH in a wide range of its concentration as well as their theoretical consideration. 2. Materials and methods 2.1. Materials R-95 Rhamnolipid obtained from SIGMA-ALDRICH (95%) was used without further purification. The aqueous solutions of rhamnolipid were prepared using doubly distilled and deionized water (Destamat Bi18E) which had an internal specific resistance of 18.2 M. The purity of water was additionally controlled by the surface tension measurements before preparing the solutions. The concentration of rhamnolipid was changed in the range from 2 × 10−4 to 40 mg/dm3 . 2.2. Measurements The equilibrium surface tension (LV ) of the aqueous solutions of rhamnolipid was measured by the Krüss K9 tensiometer according to the platinum ring detachment method (du Nouy’s measurements, the tensiomemethod). Before the surface tension  ter was calibrated using water LV = 72.8 mN/m and methanol





LV = 22.5 mN/m according to the procedure of Huh and Mason [28]. The ring was cleaned with distilled water and heated to red colour with a Bunsen burner before each measurement. In all cases more than 10 successive measurements were carried out. The standard deviation depending on the surfactant concentration was in the range from ±0.1 to ±0.25 mN/m. The measurement temperature was controlled by a jacketed vessel joined to a thermostatic water bath with the accuracy ±0.1 K. The uncertainty of the surface tension measurements was equal from 0.3 to 0.7% depending on the range of surfactant concentration. All the experiments were done at 293 K within ±0.1 K. The density of the aqueous solutions of rhamnolipid was measured with a U-tube densitometer (DMA 5000 Anton Paar) at the constant temperature 293 K. The precision of the density and temperature measurements given by the manufacturer is ±0.000001 g/m3 and ±0.001 K. Uncertainty was calculated to be equal to 0.01%. All the viscosity measurements of the aqueous solutions of rhamnolipid were performed with the Anton Paar viscosimeter (AMVn) at 293 K ±0.01 K with the precision of 0.0001 mPa s and uncertainty 0.3%. The densitometer and viscosimeter were calibrated regularly with distilled and deionized water. The specific conductivity () measurements of the aqueous solutions of rhamnolipid were made by the conductometer, Mettler Toledo, joined with the thermostat LAUDA RE 415S with the

23

Fig. 1. A plot of the surface tension (LV ) of the aqueous solutions of rhamnolipid vs. the logarithm of concentration (C). Curves 1 and 2 correspond to the molar concentration of representative monorhamnolipid and dirhamnolipid, respectively.

temperature precision equal to ±0.1 K. The relative uncertainty of the conductivity measurements did not exceed ±0.5%. All these physicochemical properties were determined at natural pH of aqueous solutions of rhamnolipid. 3. Results and discussion According to the studies of many authors [9,17,22,29–32] rhamnolipids produced by Pseudomonas aeruginosa, grown with different carbon sources can be mixtures of 4–28 different homologues. Among them the mono- and dirhamnolipids are present [8,10,11,33,34]. Therefore, for determination of the molar concentration of the rhamnolipid studied (C) by us the molecular weight of mono- (504) and dirhamnolipid (650) was taken into account. Therefore, for the calculations of all quantities as well as expression of some quantities as a function of molar concentration of rhamnolipid double values of this concentration were used. 3.1. Surface excess concentration of rhamnolipid at water–air interface The shape of the isotherm of surface tension (LV ) of aqueous solutions of rhamnolipid (Fig. 1) depends on the density and orientation of biosurfactant molecules in the adsorption monolayer at the water–air interface. The density of surfactants in this layer can be determined, among other things, by using the Gibbs adsorption equation. For the ionic surfactant of the type AB electrolyte (AB ↔ A+ + B− ) if f ≈ 1 (f is the surfactant activity coefficient) and X ≈ C/ω (where X is the mole fraction of the surface active agent, C is the molar concentration of the surface active agent and ω is the number of molecules of water in 1 dm3 ) the Gibbs adsorption equation assumes the following form [1,35,36]:  =−

C 2RT

 d  LV

dC

=−

1 2RT

 d  LV d ln C

=−

1 4.606RT

 d  LV d log C

(1) where  is the Gibbs surface excess concentration of the ionic surfactant of the type AB electrolyte. It appeared that the changes of the surface tension of the aqueous solutions of rhamnolipid as a function of its concentration (C) (Fig. 1) can be described by the first order exponential function. Thus, it was possible to calculate LV /dC and then  from Eq. (1). However, the maximal Gibbs surface excess concentration of

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Fig. 2. A plot of the Gibbs surface excess concentration ( ) of rhamnolipid vs. the logarithm of concentration (C). Curves 1 and 2 correspond to the molar concentration of representative monorhamnolipid and dirhamnolipid, respectively.

Fig. 3. A plot of the density () of the aqueous solutions of rhamnolipid vs. the concentration (C). Curves 1 and 2 correspond to the molar concentration of representative monorhamnolipid and dirhamnolipid, respectively.

rhamnolipid was determined from the relationship between the surface tension of solutions and log C in this concentration range. It appeared that the isotherm of rhamnolipid surface excess concentration (Fig. 2) has a shape typical of classical surfactants [37]. It is difficult to compare the shape of the  isotherm to those in the literature because it is difficult to find such data. However, the value of the maximal surface excess concentration of rhamnolipid obtained by us equal to 2.01 × 10−6 mol/m2 (Fig. 2) is close to that obtained by Chen et al. [25]. It should be noted that in the literature it is possible to find different values of the maximal rhamnolipid surface excess concentration [26,27]. It is a question whether the maximal Gibbs surface excess concentration of rhamnolipid at the water–air interface is reasonable taking into account the size of rhamnolipid molecule. The value of 2.01 × 10−6 mol/m2 (Fig. 2) corresponds to the area occupied by a molecule of rhamnolipid at the water–air interface which is equal to 82.6 A˚ 2 . If we assume that the Gibbs plane at the solution–air interface is chosen in such a way that the hydrophilic part of rhamnolipid molecule is in the liquid phase and the hydrophobic one in the air, the hydrophilic group is oriented parallel to the interface and the hydrophobic one perpendicular to the interface, respectively, then the minimal length of a molecule calculated on the basis of the length of bonds between particular atoms and the contact angle between bonds [38], at the first approximation, is equal to 15.31 A˚ and the width ˚ respectively. In the calculations it was assumed that the 4.512 A, average minimal distance between molecules is equal to 1.58 A˚ [39] and that the heterocyclic ring is oriented perpendicular to the O CH CH2 CO CH CH2 COOH group. Expressing, at the first approximation, the minimal area occupied by a rhamnolipid molecule by the rectangle [40], it was found equal to 69.08 A˚ 2 . This area corresponds to 2.403 × 10−6 mol/m2 of the Gibbs surface excess concentration and can be treated as the limiting area for a representative monorhamnolipid molecule in the surface layer at the water–air interface (Ao ). This value is higher than the maximal surface excess concentration calculated from Eq. (1). On the other hand, it is more probable that the average minimal distance between the rhamnolipid molecule can be higher than 2 A˚ [40] and the minimal area occupied by the representative monorhamnolipid corresponds to the saturated adsorbed monolayer should  be higher than 77.55 A˚ 2  = 2.14 × 10−6 mol/m2 . Taking this fact into account, it seems that the minimal area occupied by one molecule of rhamnolipid determined by us (82.6 A˚ 2 ) is reasonable and that the studied rhamnolipid contains mainly the representative monorhamnolipid. It is interesting that the most literature data

dealing with the maximal surface excess concentration of rhamnolipid at the water–air interface are close to this value [25,27]. If we assume that the ratio of the calculated limiting area to the minimal area obtained from the Gibbs equation is equal to the fraction surface occupied by rhamnolipid at the solution–air interface, then it is possible, at the first approximation, to establish the minimal surface tension of the aqueous solutions of rhamnolipid. The decrease of the water surface tension depends on the surface tension of the compounds from which the hydrophobic part of surfactant was formed. The representative monorhamnolipid can be treated as possessing the hexyl group as a hydrophobic one. The surface tension of n-hexane at 293 K is equal to 18.49 mN/m [41] and that of water to 72.8 mN/m. Taking into account the values of surface tension and mole fraction of the area occupied by rhamnolipid at the surface–air interface, we obtained the minimal surface tension of the representative monorhamnolipid as equal to 27.38 mN/m [42]. This value is close to the measured minimal values of the rhamnolipid surface tension which is equal to 27.89 mN/m and which is in the accordance with the literature data [15]. 3.2. Critical micelle concentration Another specific property of surfactants is the tendency to form aggregates in the bulk phase at a concentration called the critical micelle concentration (CMC). It should be stressed that the CMC values determined for rhamnolipid by various researchers were obtained mainly from the changes of the surface tension of solutions as a function of their concentration. However, there is a lack of confirmation of this data of CMC by the measurements of other physicochemical properties. Therefore, apart from the surface tension, the changes of density, viscosity and conductivity as a function of rhamnolipid concentration for its CMC determination were taken into account (Figs. 3–5). From Figs. 1 and 3–5 it appeared that the inflection point was observed on the surface tension, density, viscosity and conductivity isotherms and the CMC of rhamnolipid obtained on the basis of these isotherms is equal to 26.24; 24.06; 25.72 and 25.43 mg/dm3 , respectively. The CMC values obtained by us are in the range of rhamnolipid CMC determined by other authors (1–200 mg/dm3 ) [10,11,16,24,43,44]. The wide range of the CMC rhamnolipid which can be find in the literature [10,11,16,24,43,44] probably results from the fact that rhamnolipid is a mixture of various 4–28 homologues where monorhamnolipid is a dominant form [9]. It should be also noticed that the discrepancy in the CMC values can suggest

D. Ma´ nko et al. / Colloids and Surfaces B: Biointerfaces 119 (2014) 22–29

25

Fig. (ϕV ) (curves 1,1 and 1 ) and the partial molar volumes  6. A plot of the apparent V¯ M (curves 2 and 2 ) of rhamnolipid vs. the logarithm concentration (C). Curves 1, Fig. 4. A plot of the viscosity () of the aqueous solutions of rhamnolipid vs. the concentration (C). Curves 1 and 2 correspond to the molar concentration of representative monorhamnolipid and dirhamnolipid, respectively.

that CMC should be treated rather as a range of concentration in which aggregates can be formed but not as one pinpoint or that each method of CMC determination is sensitive to different sizes of aggregates. 3.3. Apparent and partial molar volume of rhamnolipid The micelle formation is correlated with the changes of solution structure and it should be reflected in the apparent (ϕV ) and partial   V M molar volumes of surfactant. The apparent molar volume was determined from the following equation [45]:

V =

MS 1000 (0 − ) + 0 CS 0

(2)

where MS is the molecular weight of surfactant, CS is its concentration mol/cm3 and 0 and  are the density of a “pure” solvent and the solution, respectively. In our calculations according to the rhamnolipid form [26] there was taken into account the molecular weight equal to 650 and

1 and 2 correspond to the molar concentration of representative monorhamnolipid and 1 and 2 dirhamnolipid, respectively.

504 g/mol for di- and monorhamnolipids, respectively, as two main and representative forms of this biosurfactant. The partial molar volume V¯ M was calculated from equation [46]:



V¯ M

MS = 



1−

100 − Cp 





d dCp

(3)

where Cp is the percentage weight of the solute. It appeared that the  data fit a polynomial of Cp given by  = a + bCP + dCP2

(4)

where a, b and d are the constants. It proved that both apparent and partial molar volumes of rhamnolipid changed very slightly as a function of rhamnolipid concentration (Fig. 6). However, on the V − C curves a very small infection point can be found. It is interesting that this point corresponds to the rhamnolipd CMC. On the contrary, the dependence between V M and the rhamnolipid concentration is linear (Fig. 6). Unfortunately, the values of apparent and partial molar volumes of rhamnolipid obtained by us are difficult to compare with the literature data because of the lack of this type data. 3.4. Standard free energy of micellization and adsorption at the water–air interface The presence of surfactant in water causes the increase of the surface free energy which can be minimalized by the adsorption and micellization process of surfactants. It is reflected in the values of the standard Gibbs free energy of adsorption and micellization. 3.4.1. Standard free energy of rhamnolipid micellization For the ionic surfactants of the type AB (1:1) the Gibbs  electrolyte  ◦ standard free energy of micellization Gmic can be calculated, among other things, from the Philips equation [47] which has the following form: ◦

Gmic =

Fig. 5. A plot of the conductivity () of the aqueous solutions of rhamnolipid vs. the concentration (C). Curves 1 and 2 correspond to the molar concentration of representative monorhamnolipid and dirhamnolipid, respectively.



2−

p n



RT ln

CMC ω

(5)

where n is the number of surfactant ions forming a micelle, p is the number of counterions bound to the micelle and p/n is equal to (1 − ˛) where ˛ is the degree of the surfactant dissociation in the micelle. Because the rhamnolipids are typical anionic surfactants due to the presence of the carboxylic group in their molecule, it was possible to determine the degree of H+ bonding to the micelle (p/n)

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D. Ma´ nko et al. / Colloids and Surfaces B: Biointerfaces 119 (2014) 22–29

that in this concentration range, there are no interactions between rhamnolipid molecules in the monolayer at the water–air interface ◦ and Gads determined for this range of rhamnolipid concentration can be treated as a standard free energy of rhamnolipid adsorp◦ tion. The Gads values determined in this way are equal to −85.04 or −86.28 kJ/mol depending on the molecular weight taken into account for the determination of rhamnolipid concentration (for mono- or dirhamnolipid). It is known that it is difficult to obtain good quality values of the surface tension of aqueous solutions of surfactant at their low concentration. Therefore, it is sometimes ◦ more reasonable to determine Gads on the basis of the surface tension values corresponding to the saturated monolayer at the water–air interface by using the Rosen and Aronson equation which for the ionic surfactants of type AB electrolyte can be expressed in the following form [1,51]:



◦

Fig. 7. A plot of the standard Gibbs free energy of rhamnolipid adsorption Gads



calculated from Eq. (6) vs. the logarithm of concentration (C). Curves 1 and 2 correspond to the molar concentration of representative monorhamnolipid and dirhamnolipid, respectively.

from the conductivity changes as a function of its concentration [1,48]. This degree was calculated on the basis of the slope of linear part of the  − C curve after and before CMC and is equal to 0.11. Taking into account the obtained by us values of p/n and rham◦ nolipid CMC, the values of Gmic were determined from Eq. (5). They are in the range from −61.66 to −60.17 kJ/mol. Thus, independently of the method of CMC determination and the molecular ◦ weight of di- and monorhamolipids the obtained values of Gmic are close to each other. ◦ It should be stressed that Gmic of rhamnolipid is considerably lower than for the classical anionic surfactants and even nonionic one [49]. It means that rhamnolipid tendency to form micelle is very high. 3.4.2. Standard free energy of rhamnolipid adsorption at the water–air interface In the literature there are many approaches  ◦ for  determination of the standard free energy of adsorption Gads . The most commonly used is the Langmuir equation modified by de Boer which has the form [50]: Ao C Ao exp = exp A − Ao A − Ao ω



◦

− Gads RT



(6)

where A is the area occupied per molecule at the water–air interface and Ao is the “excluded area”, i.e. the area of the interface unavailable to one molecule due to the presence of another. Assuming that this excluded area is equal to the limiting area occupied by one molecule of the representative monorhamnolipid at the water–air interface determined by us, from the size of this ◦ rhamnolipid we calculated Gads from Eq. (6) taking into account ◦ 2RT instead RT. Of course, the Gads values corresponding to the range of rhamnolipid concentration (0–0.02 mg/dm3 ) in which the unsaturated monolayer at the water–air interface is formed are stable (Figs. 1 and 7) and then rapidly decrease to the concentration of rhamnolipid equal to 5 mg/dm3 . This value is lower than that of rhamnolipid CMC obtained by us but it is in the range of the literature data [44]. Above this concentration the increase of ◦

Gads is observed. It is known that the Langmuir equation can ◦ be applied for Gads determination by using the area occupied per rhamnolipid molecules in the unsaturated monolayer in which there are no mutual interactions between the adsorbed molecules. ◦ The stable values of Gads calculated from Eq. (6) corresponding to the concentration in the range from 0 to 0.02 mg/dm3 suggest

◦

Gads = 2RT ln

C − ω1 w

(7)

where C and  correspond to the saturated monolayer of surfactants  ◦  ( is the difference between the surface tension of solvent LV and solution (LV )), ω1 is the area occupied by one mole of the surfactant at the water–air interface. ◦ The values of Gads calculated from Eq. (7) are equal to −83.64 and −84.88 kJ/mol depending on the rhamnolipid molecular weight taken into account for its concentration determination (for monoor dirhamnolipid). From the analysis of the Gibbs surface excess concentration of surfactant at the water–air interface, it results that the monolayer for most surfactants is saturated already at the concentration of surfactant in the bulk phase corresponding to that at which the reduction of water surface tension by 20 mN/m is obtained [1]. As results from Fig. 1 the studied rhamnolipid fulfilled this con◦ dition. In such case it is possible to calculate Gads on the basis of the rhamnolipid concentration corresponding to the surface tension of aqueous solutions of rhamnolipid equal to 52.8 mN/m ( = 20 mN/m) by using the modified Gamboa and Olea equation which for the ionic surfactants type AB electrolyte (1:1) has the following form [52,53]: ◦

Gads = −4.606RT (pC20 + K1 )

(8)

where K1 is the constant. The constant K1 was calculated on the basis of the limiting area of rhamnolipid molecule at the water–air interface equal to 69.08 A˚ 2 ◦ (K1 = 2.49). The value of Gads calculated from Eq. (8) is equal to −88.22 kJ/mol. As mentioned above, Eq. (6) is fulfilled for the low concentration of surfactant and Eq. (7) for the concentration corresponding to the saturated monolayer at the water–air interface, however, the o determination Szyszkowski equation gives the possibility of Gads on the basis of surface tension of aqueous solution of rhamnolipid in the range from 0 to CMC because the constant b in this equation is correlated with the standard Gibbs free energy of adsorption and for rhamnolipid fulfills the following expression [49]:

b = ωexp

o

Gads

2RT

(9)

o calculated in this way is equal to The value of Gads −84.4 kJ/mol. In our previous study [37] we found that the Gu and Zhu isotherm adsorption equation [54–56] derived for the solid– solution interface can be satisfactorily applied for the solution–air interface.

D. Ma´ nko et al. / Colloids and Surfaces B: Biointerfaces 119 (2014) 22–29

The general equation of the Gu and Zhu adsorption isotherm has the form [55]:



 =

 ∞ k1 C 1/na + k2 C na −1



1 + k1 C 1 + k2 C na −1





(10)

where k1 and k2 are the equilibrium constants of the surface monolayer and micelle formation, respectively (there is the equilibrium between the adsorbed and free species in the bulk phase), and na is the aggregation number of the surface micelles. If na > 1 and k2 C2  1 from Eq. (10) we obtain [55]:  =

 ∞ KC na 1 + KC na

(11)

where K = k1 k2 . Eq. (11) can be transformed to the logarithmic form:



log

 ∞ −



= log K + na log C

(12)

◦

Gads 2RT

(13)

It appeared that using  ∞ equal to 2.403 × 10−6 mol/m2 the plot of log / ( ∞ −  ) is linear in the low range of rhamnolipid concentration whose slope is equal to 1.01. ◦ Thus, it was possible to calculate of Gads from Eq. (13) and it is equal to −86.04 and −87.3 kJ/mol depending on the rhamnolipd molecular weight taken into account in its concentration determination (for mono- or dirhamnolipid). ◦ Comparing the Gads values obtained from the Langmuir [1,50], Szyszkowski [1] and Gu and Zhu equations [54–56] it can be stated that there is good agreement between them and these values are close to those determined from the Rosen and Aronson [1,41], and modified Gamboa and Olea equations [52]. This agreement indicates that the limiting area occupied by the representative monorhamnolipid at the water–air interface calculated on the basis of the size and proper orientation of the hydrophilic group at the water–air interface is quite reasonable because this value was used ◦ for the calculation of Gads in Eqs. (6), (8) and (9). The additional ◦ confirmation of our statement are the Gads values determined from the following equation [1,57]: ◦

◦

head (the state when the surfactant molecules are oriented by the hydrophilic groups toward the air). The surface free energy of the hydrocarbon tail results from the Lifshitz-van der Waals intermolecular interactions, and that of the hydrophilic head from the Lifshitz-van der Waals, Lewis acid–base and electrostatic interactions. If it is assumed that after adsorption at the aqueous solution of the surfactant–air interface, the hydrophobic tail or its part is in the air phase and the hydrophilic head or head with a part of tail is in the solution phase, the transfer of surfactant molecules from the bulk aqueous phase to the surface monolayer is associated with changes of the interfacial free energy of the water-tail (WT ) to the surface free energy of tail (T ) and the interfacial free energy water-head (WH ) from WH to WH1 because of the dehydration of the head during the adsorption process [40]. Thus, the standard free energy of adsorption at the aqueous solution of surfactant–air interface should fulfill the condition [40]: ◦

If a plot of log / ( ∞ −  ) is a straight line, then the K and na constants can be determined from Eq. (12). In the case when na = 1, then K = 1/a where a is the constant in the Langmuir equation which at 293 K for anionic surfactants type AB electrolyte (1:1) fulfills the condition [1]: a = 55.4exp

27

Gads = Gmic −

CMC  max

(14) ◦

where CMC is the surface pressure in CMC and CMC = LV − CMC ( CMC is the surface tension at CMC and  LV CMC is the surface LV excess concentration at CMC). o are in the range from −82.83 to The calculated values of Gads −82.45 and from −83.94 to −82.69 kJ/mol depending on the rhamnolipid molecular weight taken into account for determination (for mono- or dhirhamnolipid) of its concentration in mol/dm3 . The adsorption process of the surfactant at the interface is connected with work of the hydrophilic (head) and hydrophobic (tail) parts of its molecules transfer from the bulk phase to the interface. However, the contribution of this work to the standard free energy of surfactant adsorption is different. Therefore, these two works should be taken into account considering the adsorption of a given surfactant at the water–air interface [1]. According to van Oss and Constanzo [39], the surface free energy of a surfactant can be divided into the surface free energies of the hydrocarbon tail (the state when the surfactant molecules are oriented by the hydrophobic groups toward the air phase) and

Gads = AT N (T − WT ) + AH N (WH1 − WH )

(15)

where AT is the contactable area of the surfactant tail or its part, AH is the contactable area of the surfactant head or head with a part of tail. If during the transport of the surfactant molecule from the bulk phase of solution to the surface monolayer its head does not dehydrate then Eq. (15) can be expressed in the form [40]: ◦

Gads = AT N (T − WT )

(16)

It was shown earlier [34] that the contactable area of n-alkane molecule (A) can be calculated from the simple expression: A = 4 (l + d) (w + d) + 2(w + d)

2

(17)

In the case of the hydrocarbon surfactant having the alkyl group as a hydrophobic one the contactable area of such group is found by the following expression: AT = 4(l + d/2)(w + d) + (w + d)

2

(18)

If it is assumed that the representative monorhamnolipid has two hexyl groups as a hydrophobic one (tail) and after adsorption in the aqueous solution of surfactant–air interface, this group is in the air phase and the hydrophilic group (head) in the solution phase the transfer of rhamnolipid molecules from the bulk aqueous phase to the surface monolayer is associated with the change the interfacial free energy of water-n-hexane to the surface free energy of n-hexane. Taking into account that the l + d/2 is equal to 10.82 A˚ and w + d = 4.6 A˚ the contactable area of the hexyl group was calculated and it was equal to 220.25 A˚ 2 . Because we assumed that the representative monorhamnolipid has two hexyl groups therefore the total contactable area was equal to 440.5 A˚ 2 . Knowing that the surface free energy of n-hexane is equal to 18.49 mJ/m2 [41] at 293 K and the water-n-hexane interfacial free energy 51.1 mJ/m2 [41], the o from Eq. (16) is equal to −86.52 kJ/mol. calculated value of Gads Of course, for our calculation we assumed that the hexyl groups are oriented perpendicular to the solution–air interface. This value is in good accordance with that obtained from the Langmuir equation. ◦ The obtained values of Gads for rhamnolipid determined on the basis of all equations used in our calculations are almost twice as low as the standard free energy of adsorption of nonionic Tritons and lower than that of the classical anionic and cationic synthetic surfactants [43]. It is not clear that the standard free energy of rhamnolipid adsorption being the measure of its efficiency to adsrob at the water–air interface is twice as low as that of Tritons. It is connected with application of 2RT instead of RT in all equations ◦ ◦ used for Gads calculation. However, the obtained Gads value by using Eq. (16) is close to those obtained from the other equations in ◦ which 2RT was applied. On the other hand, Gads calculated from

28

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the Langmuir equation deals with the dilute solution of surfactant for which the unsaturated monolayer is formed at the water–air interface. For such case the parallel orientation of the hydrophobic group at the water–air interface is more probable than the perpendicular one. Taking this into account and the fact that even two groups of CH2 can be present in the water phase [49], the cal◦ culated value of Gads from Eq. (16) is equal to −47.78 kJ/mol. This value is close to that obtained from the Aronson and Rosen equation [1,51] if RT instead of 2RT is used in this equation and somewhat lower than that determined from the Langmuir equation [44] under the same assumption. The values calculated in such way are only ◦ slightly lower than Gads for Tritons [49].

[12]

[13]

[14]

[15]

[16]

4. Conclusions From the measurements and thermodynamic considerations it results that: The area occupied by rhamnolipid in the saturated monolayer at the water–air interface is equal to 82.6 A˚ 2 . This area is somewhat higher than the “excluded area” of monorhamnolipid (which is equal to 69.08 A˚ 2 ) determined on the basis of the cross sectional area of the hydrophilic and hydrophobic groups being in the monolayer at the water–air interface oriented perpendicularly to this interface. The tendency of rhamnolipid to adsorb at the water–air interface and form the micelles is higher than for the classical synthetic surfactants because the standard Gibbs free energy of adsorption and micellization of rhamnolipid determined by using different models is considerably lower than those of the synthetic ones. It is possible to predict the standard Gibbs free energy of adsorption on the basis of the surface tension of n-hexane and the n-hexane-water interface tension. The rhamnolipid molar volume changes only slightly during the micelles formation and CMC determined by surface tension, density, viscosity and specific conductivity is considerably lower even than such nonionic surfactant as Triton TX-100. The dissociation of the rhamnolipid molecules in the micelles is only slightly lower than in the monomeric form.

[17] [18] [19]

[20]

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