Application of an extended DLVO theory for the calculation of the interactions between emulsified oil droplets in alcohol solutions

Colloids and Surfaces B: Biointerfaces 14 (1999) 19 – 26 www.elsevier.nl/locate/colsurfb

Application of an extended DLVO theory for the calculation of the interactions between emulsified oil droplets in alcohol solutions Agnieszka Wia˛cek, Emil Chibowski * Department of Interfacial Phenomena, Faculty of Chemistry, Maria Curie-Skl*odowska Uni6ersity, 20 031 Lublin, Poland

Abstract The stability of diluted emulsions (0.1% v/v) of n-dodecane in 1 M methanol, ethanol or propanol was studied. The effective diameter and zeta potential were determined by dynamic light scattering. The parameters were measured 5, 30, 60, 120 min and after 1 day after preparation of the emulsions by mechanical mixing at 10 000 r.p.m. for 3 min. Calculations of the free energy interactions between dodecane droplets were conducted applying van Oss et al.’s extended DLVO theory, in which acid–base interactions involving electron donor and electron acceptor parameters are also accounted for. For this purpose the interfacial tensions of oil – alcohol solutions were taken from the literature. The acid–base interactions were evaluated considering two variants. In the first we assumed a close-packed monolayer of alcohol molecules on the droplet surface, interacting by hydrogen bonds with water as well with alcohol molecules. In the second variant, it was considered that in these electrolyte-free systems (pH close to neutral) the measured zeta potentials were due to the oriented alcohol dipoles on the droplet surface. This would mean that the slipping plane is very close to the droplet surface. Both variants lead to the same conclusion that in these system the dominant role is played by attractive acid–base interactions, which is much bigger than the equally attractive apolar Lifshitz–van der Waals interaction. Repulsive electrostatic interactions play only a minor role. © 1999 Elsevier Science B.V. All rights reserved. Keywords: n-Tetradecane–water emulsion; Alcohol; Zeta potentials; Effective diameters; Stability; Extended DLVO

1. Introduction Problems of emulsion properties and stability are still attractive for fundamental studies as well as for practical purposes [1]. This is because of the wide applications of emulsion systems in many industries; dairy, pharmacy, cosmetics, medicine, road construction, etc. [2]. It may be noticed that * Corresponding author.

the application of emulsifiers–stabilizers of natural origin is of great interest [3]. From the viewpoint of fundamental studies, emulsion systems are interesting as model systems for studying the stability of dispersed systems in general. First of all, submicron droplets can be considered as hard non-conducting spheres. Such systems are good model systems for studying oil droplet–dispersing liquid–oil droplet free energies of interactions, for which it is relatively easy to determine the elec-

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A. Wia˛cek, E. Chibowski / Colloids and Surfaces B: Biointerfaces 14 (1999) 19–26

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trokinetic (zeta) potential and the interfacial tension. At present it is well known that the classical DLVO stability theory can be applied only to a limited number of dispersed systems for the purpose of evaluating in order to evaluate the balance of interacting forces between two particles across the liquid phase [4 – 6]. According to Derjaguin and Churajev [7] it cannot be applied to either very hydrophilic or to very hydrophobic surfaces, on which the contact angle of water is less than 15° (hydration forces) or greater than 64° (hydrophobic forces). Van Oss et al. [8–11] were among the first to offer a quantitative expression for the calculation of hydration forces due to hydrogen bonding, or more generally electron donor– electron acceptor (Lewis acid–base) interactions between two similar or dissimilar surfaces interacting across a liquid phase, DG131 or DG132, respectively. Van Oss and Giese [12] define hydrophilicity – hydrophobicity of a solid surface by interfacial free energy of interaction DG131. If its value is positive the surface is hydrophilic, and the surface is hydrophobic if DG131 B0. In general, one more term should be added [8 – 11] to the total interaction energy between two particles according to: LW AB EL DG TOT 131 = DG 131 +DG 131 +DG 131

(1)

where DG is the Lifshitz – van der Waals interaction energy (mainly due to London dispersion forces), DG AB 131 is the acid – base – electron donor and electron acceptor interaction energy, and DG EL 131 is the electrostatic interaction energy, which for moieties of the same material is repulsive. On the other hand, the Lifshitz – van der Waals interaction is always attractive for the two moieties. However, the acid – base interaction may be attractive or repulsive depending on the magnitude of the electron donor, g − , and electron acceptor, g + , parameters of the interacting phases 1–3–1. The purpose of this paper is the determination of the interaction energy between two emulsion droplets of n-dodecane in aqueous solution of alcohol (methanol, ethanol and propanol) using AB the extended DLVO theory. The DG LW 131 and DG 131 interactions were evaluated based on interfacial tension measurements [13] and DG EL 131 interactions LW 131

were calculated using the measured zeta potentials of the droplets. The nano-size droplets were considered as hard spheres. 2. Experimental The emulsions of n-dodecane (Reachim, pure, equilibrated with Al2O3) were prepared in 1 M aqueous solution of methanol (POCh, Gliwice, Poland), ethanol (Polmos, Poland) or propanol (Fluka) by dissolving 0.1 ml of the alkane in a suitable volume of the alcohol. Then water was added to obtain the above final concentration of the alcohol in 100 ml of the emulsion. In the case of ethanol, its 96% aqueous solution was used in which the alkane was dissolved, and methanol and propanol were water free. Because of decreased solubility of the alkane in the alcohol after addition of water, the emulsion formed spontaneously and then was further homogenized mechanically for 5 min in a homogenizer at 10 000 r.p.m. Next, the multimodal size distribution and effective diameters, as well zeta potentials were determined in the same experiment (the same sample of the emulsion) with the help of a ZetaPlus instrument (Brookhaven Instr. Co., USA), which applies dynamic light scattering to both the size and zeta potential determinations. The parameters were determined 5, 15, 30, 60 and 120 min after preparation of the emulsion. 3. Calculations of the interfacial free energy interaction To calculate the total free energy of interaction, DG TOT 131 , particular terms of Eq. (1) have to be calculated separately. In the case of two identical spherical surfaces interacting through water, the equations are much simplified.

3.1. Calculation of Lifshitz–6an der Waals free energies of interaction For two identical surfaces, which is the case here, at the minimum equilibrium distance d0 the attractive Lifshitz–van der Waals interaction, 2 DG LW 131 , in mJ/m , between two flat surfaces is [8]:

A. Wia˛cek, E. Chibowski / Colloids and Surfaces B: Biointerfaces 14 (1999) 19–26 LW DG LW 131 = − 2g 13

(2)

Where g LW 13 is the apolar interfacial tension component between n-dodecane droplet and the alcohol solution. The interfacial tensions of dodecane–alcohol (methanol, ethanol or propanol) were taken from the literature. They were determined by Jan˜czuk et al. [11], who used the ring and sessile drop methods. For two spheres having a radius R, and if R  d, the proper equation for DG LW 131 as a function of d is following [8,10]: DG LW 131 = − A131R/12d

(3)

where A131 is the Hamaker constant, and do is equal to 0.15890.008 nm [8]. There is a relationship between the Hamaker constant and DG LW 131,d 0: 2 − DG LW 131,d 0 = A/12pd 0

(4)

Knowing the droplet diameter, Lifshitz–van der Waals interactions can be calculated both for the equilibrium distance d0 and a far away distance d, in the non-retarded mode.

3.2. Calculation of acid– base free energies of interaction For two identical flat surfaces separated by water, at the equilibrium distance d0 the free energy of acid – base interaction (here due to hydrogen bonding) can be expressed [10] as: + − 1/2 − 1/2 − 1/2 +(g + −(g + DG AB 131 = − 4[(g 1 g 1 ) 3 g3 ) 1 g3 ) + 1/2 − (g − ] 1 g3 )

(5)

where the subscripts 1 and 3 at the surface tensions, g, mean dodecane and the alcohol solution, respectively, and the sign ‘+ ’ is for the electronacceptor and ‘− ’ for the electron-donor interactions. To calculate DG AB 131 at a distance d the ‘decay length’ l has to be known. Its value is still debatable and can vary between 0.2 nm (for nonhydrogen bonded water molecules) [14] to as high as 13 nm [15]. Nevertheless, a reasonable value for l seems to be about 1 nm [9]. The decrease of acid–base interaction with distance d for two spheres of radius R can be calculated from Eq. (6) according to [9]:

AB DG AB 131 = plRDG 131,d 0exp[(d0 − d)/l]

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(6)

Note that in Eq. (6) DG AB 131,d 0 pertains to the two parallel-plane interaction. As it results from Eq. (5), to calculate the energy of acid–base interaction at a distance d one has to know the surface free energy components: the electron donor g − i and electron acceptor g + parameters for the doi decane droplet and for the alcohol solution. In the case of a ‘bare surface’ of a dodecane droplet in water, only the second term on the right hand side in Eq. (5) would have a non-zero value. However, in the case of an emulsion prepared in 1.0 M solution of methanol, ethanol or propanol, on the droplet surface there are adsorbed molecules of the alcohol, therefore in Eq. (5) all terms on right hand side are non-zero. Now, the problem is how to determine the g − and g + parameters both for i i the alcohol solution and the droplet surface. As for the solution the problem seems to be less ambiguous. Jan˜czuk et al. [13], who used interfacial tension and contact angle measurements on paraffin wax, indicated that the polar surface tension components of methanol, ethanol and 2 propanol (g AB i ), equal 6.49, 3.32, and 2.97 mJ/m , respectively. Applying van Oss et al.’s [8] approach, the polar interactions of alcohol are due to hydrogen bonding and they are expressed by the geometric mean of electron donor and elec− 1/2 tron acceptor interactions; g AB = 2(g + . All l gl ) though the parameters are not known, two times the geometric mean of them is equal to the values given above. In fact, the same procedure can be applied to any aqueous alcohol solution, for − which g AB is known. Because g + l l and g l parameters are interrelated it is possible to calculate the true value of the acid− base interaction free energy, DG AB 131, even though the individual parameters are not known. For simplicity, it is reasonable − to assume that g + l = g l . As for the n-dodecane droplet with the adsorbed alcohol molecules, two variants can be considered. In the first one, there is a closely packed layer of alcohol molecules on the droplet surface, because the oil phase was dissolved in the alcohol before adding the water. In the second variant, the amount of the alcohol molecules (dipoles) on the droplet surface is derived from the measured zeta potential. This

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A. Wia˛cek, E. Chibowski / Colloids and Surfaces B: Biointerfaces 14 (1999) 19–26

would imply that the zeta potential of the droplet is totally due to the oriented alcohol dipoles in this electrolyte-free system and that the shear plane is located very close to the dipole polar heads.

3.2.1. Variant 1 To calculate the acid – base component assuming the close-packed alcohol molecules on the droplet surface, first the area s occupied by one alcohol molecule (cross-section) should be determined. A value of s =0.21 nm2 is a reasonable one, and as a first approximation the same for the three alcohol studied can be assumed [16]. Hence, there are n=4.76 ×1018 molecules/m2. Then, the acid–base free energy per single alcohol molecule can be calculated, which equals: g AB A /n (J/molec). The droplet diameter, being known, the surface area of the droplet can be calculated and one then also knows the number of the alcohol molecules n/m2 and the acid – base component of the dode2 cane droplet g AB D(A) (in mJ/m ). 3.2.2. Variant 2 The dipole moment of the aliphatic alcohols is practically solely due to the OH group and is the same for the three alcohol studied. It is mOH = 1.6 D = 0.533× 10 − 29 Cm. Because the – O–H distance d= 0.96 A, =0.96 × 10 − 10 m, the dipole charge qdip =mOH/d = 0.555 ×10 − 19 C. For a sphere the total electric charge Qe at the slipping plane can be calculated from the zeta potential [17]: Qe =(4po0) DR (1 + kR)w

(7)

where o0 is the electric permittivity of the free space, D is the dielectric constant of the solution, R is the droplet radius, k is the Debye parameter and w is the zeta potential. Given the droplet charge Qe, the surface area of a droplet and the dipole charge, one can calculate the number of alcohol dipoles per unit surface, n= dipoles/m2. Then, knowing g AB A(dip) of the individual dipole (for calculations see variant 1 above), it is possible to calculate g AB of the droplet surface in mJ/m2. A Next, following the same procedure as in variant 1 the acid–base interaction between two droplets through the water phase DGAB 131 can be calculated.

3.3. Calculation of electrostatic free energy interaction To calculate of electrostatic repulsion energy one has to know the value of the electric potential at the surface, C0, which is difficult to measure. The potential which can be determined experimentally is the electrokinetic potential, w, and for low values ( : 25 mV) for a sphere of radius R the relationship holds: c0 = w (1+x/R) ekx

(8)

Where x is the distance from the surface and k is the Debye parameter. However, instead of the surface potential C0 the zeta potential w is usually used for the calculation of the repulsive interaction. Because for these emulsions we consider their surface charge as resulting from the oriented dipoles of the alcohols, the use of zeta potential for the calculations is justified. An approximated equation for the interaction energy and w ranging between 25 and 50 mV reads [18]: 2 DG EL 131 = 0.5 DRw ln[1+ exp(− kd)]

(9)

where D is the dielectric constant of the medium, R is the droplet radius, d is the distance between the droplets and k is the Debye–Hu¨ckel parameter.

4. Results and discussion The effective diameters and zeta potentials of the emulsions are shown in Fig. 1 a and b, respectively depending on the time since the emulsion preparation. The effective diameter is the hydrodynamic diameter including the electrical double layer thickness. It is the diameter that a sphere would have in order to diffuse at the same rate as the particle being measured. The effective diameter can also be called ‘equivalent sphere diameter’. In the case of spherical emulsion droplets the effective diameter is a good approximation of true one. As can be seen from Fig. 1a the emulsions in 1 M ethanol were stable during 2 h, and in 1 M propanol they were stable during one day. However, in 1 M methanol the diameter fluctuated and after 2 h it increased from 700 nm

A. Wia˛cek, E. Chibowski / Colloids and Surfaces B: Biointerfaces 14 (1999) 19–26

(5 min old emulsion) to ca. 2900 nm. This means that coalescence of the droplets had occurred during that time. This instability of the effective diameter of the droplets in methanol was accompanied by a decrease in negative zeta potential (Fig. 1b), from−40 mV to close to zero in 2 h. More stable zeta potentials were found in 1 M

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ethanol and propanol. Although it was not possible to determine the effective diameters in methanol and ethanol after one day, the zeta potentials in these emulsions are shown in Fig. 1b. The zeta potentials were only about 11–12 mV. Based on the results from Fig. 1a and b, the free energies interaction were calculated in the

Fig. 1. Effective diameters and zeta potentials of n-dodecane droplets in emulsions prepared in 1 M methanol, ethanol or propanol for different times after preparation of the emulsion.

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Table 1 Parameters describing interfacial properties of n-dodecane emulsion (0.1% v/v) in 1 M alcohol Parameter

Dispersing phase Propanol

Ethanol

Methanol 5 min

pH Zeta potential (mV) Effective diameter Def (nm) 1/k (nm) kd Xmax (nm) sd (droplet) (mC/cm2) DG LW 131 (kT) DG EL 131 (kT) V.1. DG AB 131 (kT) V.2. DG AB 131 (kT) DG LW 131 /R (kT/nm) DG EL 131/R (kT/nm) V.1. DG AB 131/R (kT/nm)

30 min

1h

2h

6.8 −46.2 431

7.0 −47.1 659

6.3 −60.8 748

6.3 −35.0 1737

6.3 −23.8 979

6.3 −1.3 2862

7686 0.28 3883 −0.019 −9.6 338 −5159 −1696 −0.04 1.63 −23.9

1002 0.33 5937 −0.013 −10.3 538 −16975 −7800 −0.03 1.57 −51.5

4322 0.86 6730 −0.021 −12.0 1016 −23021 −8576 −0.03 2.71 −61.5

4322 2.01 15633 −0.008 −27.9 781 −53963 −19932 −0.03 0.90 −62.1

4322 1.13 8803 −0.007 −15.7 74 −30442 −11231 −0.03 0.15 −62.2

4322 3.31 26138 −0.0003 −46.0 186 −87890 −32837 −0.03 0.13 −61.4

manner discussed above. In Table 1 the measured parameters and calculated values of the free energies of interaction DG131 at the minimum equilibrium distance d0 are listed. Because for emulsions in ethanol and propanol solutions the effective diameter and zeta potentials did not vary much during 2 h, they were averaged and then EL used for calculating DGAB 131 and DG131. For the emulsion in methanol solution the interaction energies were calculated for the times studied, i.e. 5, 30, 60 and 120 min. The acid – base, DGAB 131, interactions were calculated for both variants and given in Table 1. From the results it can be seen that at the equilibrium distance d0 the acid–base interactions are dominant in the system studied, independently on the way they were calculated. The results based on the zeta potentials (variant 2) are smaller than those calculated assuming a close-packed layer of the alcohol molecules on the droplet surface. Nevertheless they still are dominant, showing that the emulsions will tend to coalesce (negative DGAB 131), if the droplets approach each other close enough. However, the distances between the droplets are great (surface-to-surface) and therefore the emulsion in propanol and ethanol solutions are stable even for one day (Fig.

1). This is not the case for the emulsion in 1 M methanol, where, although the distance between the droplets is greatest (because of large droplets produced from the same total volume of dodecane), the emulsion is not stable. In general, the larger droplet the less stable the emulsion is. Here, this may be a result of extremely strong acid–base interaction (Table 1). It should be noticed, however, that the dynamic light scattering technique (applied here) does not allow the determination of droplet concentrations. Therefore, some of them may have coalesced and floated up, while the rest of the droplets remained practically of the same size. Nevertheless, the results from Table 1 clearly show, as could be expected, that the most stable emulsions are the ones prepared in n-propanol solutions. Here the droplet size and the attractive energy are the smallest. Because the droplet sizes were different in each alcohol solution, they were normalized [5,19] to the droplet radius R, in order to be able to compare the interaction energies. The interactions thus recalculated are also listed in Table 1. Actually the same relationships hold as discussed above. The smallest attractive interactions, apolar Lifshitz–van der Waals and polar acid–base, appear in n-propanol solution, while

A. Wia˛cek, E. Chibowski / Colloids and Surfaces B: Biointerfaces 14 (1999) 19–26

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Fig. 2. Changes in the total free energies of interaction as a function of distance expressed in multiples of the equilibrium distance d0 = 0.158 nm.

the electrostatic repulsions are small in all three alcohols. It is interesting to note that in methanol AB solutions the normalized DGLW 131 and DG131 interactions are practically constant during 2 h, despite the fact that the droplet size changes markedly during this time. More information can be obtained from the changes in the interaction energies with distance between the droplets. Results of these calculations are presented in Fig. 2, for propanol, ethanol and methanol (5 min old emulsion), respectively. It appeared that at a distance 50d0 the total interaction energy is positive, 149, 283 and 214 kT, for propanol, ethanol and methanol, respectively. The same is true for 100 d0. However, for the emulsion in 1 M methanol after 1 h, the total interaction energy is only 38.6 kT (not presented in Fig. 2). These results explain why these diluted emulsions are stable. To coalesce the droplets have to approach each other through the distances at which the repulsion exists. Therefore, this energy barrier probably keeps them apart. To conclude, one may say that this extended DLVO approach gives a realistic picture of the mechanism of the emulsion stability.

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