Microstructure of ionic liquid (EAN)-rich and oil-rich microemulsions studied by SANS

Abstract

In a previous study we investigated the phase behavior of microemulsions consisting of the ionic liquid ethylammonium nitrate (EAN), an n-alkane and a nonionic alkyl polyglycolether (C_iE_j). We found the same general trends as for the aqueous counterparts, i.e. a transition from an oil-in-EAN microemulsion via a bicontinuous microemulsion to an EAN-in-oil microemulsion with increasing temperature. However, unlike what happens in the corresponding aqueous systems, in EAN-in-oil microemulsions only a very small amount of EAN was detected by NMR-measurements. This is why we investigated the phase behavior and microstructure of EAN-rich n-dodecane-in-EAN microemulsions and oil-rich EAN-in-n-octane microemulsions. We found that the ionic liquid emulsification failure boundary has an extraordinarily small slope, which suggests that the amphiphilic film loses its ability to solubilize EAN with an increase in temperature by only a few degrees. The analysis of the small angle neutron scattering (SANS) curves unambiguously shows that this behavior is due to the fact that the EAN molecules form a substructure with a characteristic length scale of Λ ≈ 8 Å inside the EAN-in-oil droplets. In more detail, the analysis of the SANS data with the GIFT method revealed a transition from spherical to cylindrical structures approaching the respective critical endpoint temperatures. By using the respective form factors and combining them with a Gaussian spatial intensity distribution to account for the EAN sub-structure we were able to describe the scattering curves nearly quantitatively.

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1 Introduction

The correlations between phase behavior, interfacial tension, microstructure and composition of microemulsions composed of water, hydrocarbons and nonionic alkyl polyglycolether surfactants (C_iE_j) are well understood.^1–6 The influence of molecular properties such as the size of the head group or the length of the hydrocarbon chain^3,5 as well as the addition of additives like electrolytes,³ alcohols^7,8 and block co-polymers^9,10 on the phase behavior have been studied extensively, too.

In the past ten years several groups have used ionic liquids (ILs) to formulate microemulsions. Since ionic liquids exhibit unique solvent properties,^11–13 these systems are interesting, for example, as reaction media.^12,14 Generally speaking, the solvophobicity¹⁵ of an IL strongly depends on its molecular structure. Several examples of microemulsions with an IL as either the polar^16–20 or the nonpolar^21–23 component have been reported. Ethylammonium nitrate (EAN), which was in fact the first ionic liquid to be reported in the literature,²⁴ was used as a replacement for water in microemulsions stabilized by both ionic^16,17 and nonionic¹⁹ surfactants. Due to their high boiling temperature, microemulsions containing EAN (or other polar ionic liquids) can be utilized in high temperature applications.¹⁶ The microstructure of EAN-in-oil microemulsions stabilized by an ionic surfactant was studied with small angle neutron scattering (SANS) over a broad temperature range. It was found that spherical droplets are formed with radii in the range of 2 nm to 3 nm, depending on the volume of solubilized EAN while no pronounced temperature dependency was observed.¹⁷ Atkin and Warr observed a correlation peak in a small angle X-ray scattering (SAXS) curve for a microemulsion composed of equal mass fractions of EAN and n-dodecane, stabilized by the surfactant triethylene glycolmonododecylether (C₁₂E₃) and fitted this curve with the Teubner–Strey model.¹⁹ For microemulsions and lamellar phases with propylammonium nitrate (PAN) instead of EAN as well as for micelles of C_iE_j surfactants in EAN, SANS spectra have also been recorded.^25,26

We published a systematic study on the interfacial tension, microstructure and composition of a microemulsion consisting of EAN, an n-alkane and the nonionic surfactant C₁₂E₃²⁷ to complement the data published by Atkin and Warr on the very same system.¹⁹ We were able to show that with increasing temperature the system undergoes a phase inversion with (a) the characteristic minimum of the interfacial tension at the phase inversion temperature and (b) the characteristic change of the self-diffusion coefficients of the solvents which is known from water–n-alkane–C_iE_j microemulsions.^5,28,29 Unlike what happens in the corresponding aqueous systems, in EAN-in-oil microemulsions only a very small amount of EAN could be detected by NMR-measurements. We speculated that this behavior can be connected to the fact that EAN itself forms a substructure with a domain size of about 1 nm.³⁰

In order to understand the different behavior of EAN-in-oil microemulsions compared to water-in-oil microemulsions and in order to clarify whether the EAN nanostructure is responsible for the difference, we studied the phase behavior and microstructure of both EAN-rich and oil-rich microemulsions. To study the properties of EAN-rich microemulsions we chose the system EAN–n-dodecane–C₁₂E₃, while the system EAN–n-octane–C₁₂E₃ was chosen to study oil-rich microemulsions. We have chosen two different oils in order to work at similar temperatures, namely between 30–37 °C. If we worked with one system only, we would have to deal with temperature differences of about 20 °C. In this case, a quantitative comparison of the data would have been difficult, since temperature has an enormous effect on the monomeric solubility of C₁₂E₃ in both n-alkanes and EAN. We measured the phase behavior of both EAN-rich and n-octane-rich microemulsions and studied the evolution of the microstructure along the respective emulsification failure boundary^31,32 with SANS.

2 Experimental

2.1 Materials

Ethylammonium nitrate (EAN, purity > 97%) was purchased from Iolitec (Heilbronn, Germany) and used without further purification. The nonionic surfactant triethylene glycolmonododecylether (C₁₂E₃, purity > 95%) was purchased from TCI (Zwijndrecht, Belgium). Deuterated n-octane (D18, 98%) and n-dodecane (D26, 98%) were provided by Cambridge Isotope Laboratories (Andover, USA). The oils n-dodecane (H26, purity ≥ 99%) and n-octane (H18, purity ≥ 99%) were purchased from Sigma-Aldrich (Steinheim, Germany).

2.2 Phase behavior

Samples of ∼1 ml total volume were prepared in sealed glass tubes. The masses of EAN (m_A), oil (m_B), and surfactant (m_C) were determined with an accuracy of ±0.001 g. For the determination of the phase diagram, a magnetic stirring bar was added and the glass tubes were placed in a thermostated water bath. For a given composition, the number and type of phases were determined visually as a function of temperature with an accuracy of ±0.05 K.

The phase behavior of IL-rich and oil-rich microemulsions is characterized performing vertical sections (so called funnel cuts) through the phase prism.^31,32 For EAN-rich microemulsions the phase boundaries were determined as a function of temperature T and mass fraction

of n-dodecane (B) in the overall mixture, while the mass fractionof C₁₂E₃ (C) in the mixture of EAN (A) and C₁₂E₃ (C) is kept constant. The phase boundaries of the oil (n-octane)-rich microemulsions were recorded as function of temperature and mass fractionof EAN keeping the mass fractionof C₁₂E₃ (C) in the mixture of n-octane (B) and C₁₂E₃ (C) constant.

2.3 SANS-measurements

The scattering curves were recorded with the D11 spectrometer of the Institut Laue Langevin (ILL), Grenoble, France. Sample to detector distances of 1.75 m and 10.00 m with a collimation length of 8.0 m and 10.5 m, respectively, were chosen for the experiments. The wavelength of the neutrons was set to λ = 6 Å so that the scattering vector q = 4π sin(θ/2)/λ ranged from 0.015 to 0.350 Å⁻¹ (θ is the scattering angle). The wavelength distribution of the spectrometer is Δλ/λ = 0.09 as specified by the ILL. All samples were prepared following the procedure for the investigation of the phase behavior. With a view to adjusting film contrast conditions (equal scattering length density of EAN and oil) the protonated oils were partially replaced by deuterated oils. The mass m_B of deuterated and protonated oil were chosen such that the total volume fraction of oil was equal to the volume fraction of the non-deuterated sample. Prior to the SANS experiments the phase-transition temperatures, i.e. the oil (oefb) and the IL emulsification failure boundary (iefb), were measured, which revealed that the partial deuteration of the oil causes only a slight shift of the phase boundaries (see Fig. 1). After that the samples were filled into a Hellma-quartz QS glass cell (1 mm path length) which is then transferred to the homebuilt cell holder ensuring that the sample stays homogeneous. The SANS measurements were then performed at temperatures slightly above the oefb (EAN–n-dodecane–C₁₂E₃) and slightly below the iefb (EAN–n-octane–C₁₂E₃), respectively, with an accuracy of ±0.05 K. The data were recorded using a two dimensional ³He-gas detector with 128 × 128 detector elements of 1 cm². The intensity was radially averaged in order to obtain a one-dimensional scattering curve and the incoherent scattering of H₂O was used as secondary calibration standard in order to normalize the scattering intensity. All measured scattering intensities were corrected for the background and the dead time of the detector was taken into account.

Fig. 1 T–w_B section (left) and T–w_A section (right) through the phase prism of the systems EAN–n-dodecane–C₁₂E₃ and EAN–n-octane–C₁₂E₃ at γ_a = 0.08 and γ_b = 0.16, respectively. Note the strong difference of the slope of the efb on the EAN-rich (left) and the oil-rich (right) side of the phase prism. The rather weak increase of the efb with temperature on the oil-rich (right) side of the phase prism indicates that the surfactant C₁₂E₃ loses its ability to solubilize EAN within a few degrees. 2̲ = oil-in-EAN microemulsion coexisting with oil excess phase, 2̄ = EAN-in-oil microemulsion coexisting with EAN excess phase, 1 = one-phase region, 3 = microemulsion coexisting with EAN and oil excess phase. The squares correspond to the composition and temperature of the SANS samples (mixture of protonated and deuterated oils).

2.4 Scattering theory

Scattering curves contain valuable information about the microstructure of a sample. An approach aimed at extracting this information from experimental data is to calculate theoretical scattering curves using a structural model that describes the scattering of a sample of a given microstructure. By fitting the theoretical curve to the experimental data one can then obtain parameters such as the size, and the polydispersity of the structure.

For a sample consisting of an ensemble of scattering particles, the scattering intensity I(q) can be modeled using the decoupling approximation.³³ Following this approach, the total scattering intensity can be factorized into inter- and intra-particle scattering contributions according to

I(q) = nP(q)S(q). (5)

Here P(q) and S(q) are the form and structure factor, respectively, while n is the particle number density³⁴ taking into account the volume v_C per C₁₂E₃ molecule v_C = 568 ų and the area a_c per C₁₂E₃ molecule at the EAN/n-alkane interface set to a_c = 64 Ų.³⁵ In order to describe the recorded scattering data the form factors of polydisperse spherical and cylindrical core–shell particles were used in combination with a diffuse scattering length density distribution recently suggested by Foster.³⁶ The polydispersity is taken into account using a Gaussian distribution of the radius, the cross sectional radius and the cylinder length. For details see the ESI.†

With increasing concentration of the microemulsion droplets, inter-particle interactions contribute to the scattering intensity, which can be accounted for by using an appropriate structure factor. For spherical microemulsion droplets it was found that the averaged Percus Yevick structure factor S_PY(q) for polydisperse hard spheres^37,38 can be used to describe the influence of the inter-droplet interactions. However, in the system under discussion these inter-droplet interactions seem to be significantly weaker than the hard-sphere interaction considered by the Percus Yevick structure factor (Fig. 2, inlet).

Fig. 2 SANS curves of (left) EAN-rich microemulsions (EAN–n-dodecane–C₁₂E₃) at γ_a = 0.08 and different n-dodecane mass fractions w_B and of (right) oil-rich microemulsions (EAN–n-octane–C₁₂E₃) at γ_b = 0.16 and different EAN mass fractions w_A. The samples were prepared almost in film contrast using a mixture of protonated and deuterated oils. All measurements were performed at temperatures near the oefb and iefb, respectively. The inlet shows the individual scattering contributions by means of the sample with the lowest n-dodecane mass fraction w_B = 0.052: form factor for polydisperse spherical droplets P_sphere using a diffuse scattering length density distribution suggested by Foster³⁶ (dotted line), averaged Percus Yevick structure factor S_PY for polydisperse hard spheres³⁸ (using a much smaller droplet volume fraction, short dashed line) and Gaussian spatial intensity distribution I_gauss^47,48 describing the contribution of the EAN substructure (dashed-dotted line). Note, that neglecting the inter-particle interactions the scattering data are almost quantitative described apart from small but systematic deviations at low and intermediate q.

Another approach aimed at gaining structural information from the experimental scattering data is to make use of the Generalized Inverse Fourier Transformation (GIFT). Here, the scattering data are transformed into real space, yielding the pair distance distribution function (PDDF) p(r).^39,40 This method does not depend on a priori information about the shape of the investigated particle. However, an appropriate structure factor has to be applied in the decoupling approximation (see eqn (5)) and hence is not model-free. In order to extract the PDDF from the experimental scattering curves the GIFT software developed by Bergmann, Fritz and Glatter^41,42 was used.

3 Results and discussion

3.1 Phase behavior

Recently, we published phase diagrams of the systems EAN–n-octane–C₁₂E₃ and EAN–n-dodecane–C₁₂E₃ containing equal mass fractions of EAN and n-alkane. The phase diagrams were measured as a function of the temperature and the surfactant mass fraction.²⁷ We found that the phase boundaries of both systems have the same fish-like shape as those known from microemulsions composed of water–n-alkane–C_iE_j.² Furthermore, the shift of the phase inversion temperature (PIT) to lower temperatures when n-dodecane (T̃ = 40 °C) is replaced with n-octane (T̃ = 23 °C) is similar in both aqueous and EAN-containing microemulsion systems.² However, we found by NMR-measurements that only a very small amount of EAN is solubilized in EAN-in-oil microemulsions, whereas a reasonable amount of oil could be detected in oil-in-EAN microemulsions.

In order to clarify whether this behavior is related to the fact that EAN itself forms a nanostructure with a domain size of about 1 nm,³⁰ we investigated the phase behavior and the microstructure of both EAN-rich and oil-rich microemulsions. The system EAN–n-dodecane–C₁₂E₃ was chosen to study EAN-rich microemulsions, while the system EAN–n-octane–C₁₂E₃ was chosen to study oil-rich microemulsions. In the former case, the phase behavior was studied as a function of the temperature and the n-dodecane mass fraction (w_B), keeping the fraction of C₁₂E₃ in the EAN/C₁₂E₃ mixture constant at γ_a = 0.08. In the second case, the phase behavior was studied as a function of the temperature and the EAN mass fraction (w_A), keeping the fraction of C₁₂E₃ in the n-octane/C₁₂E₃-mixture constant at γ_b = 0.16. As already mentioned, we decided to work with two different oils in order to work at very similar temperatures, namely between 30–37 °C, which, in turn, allows us to neglect the temperature dependent monomeric solubility of C₁₂E₃ in both EAN and oil.

On the left hand side of Fig. 1 the T–w_B phase diagram of the system EAN–n-dodecane–C₁₂E₃ is shown. As can be seen, the phase behavior of the EAN-rich microemulsion is analogous to that of oil-in-water (o/w)-microemulsions.³ The funnel shaped one-phase region is limited by the (lower, 2̲ → 1) oil emulsification failure boundary (oefb) and the (upper, 1 → 2̄) near critical boundary (ncb). The slope of the oefb is rather steep, i.e. the amount of solubilized oil and thus the size of the microemulsion droplets increases moderately with increasing temperature similar to what is known for oil-in-water microemulsions.⁴³ Starting from the cloud temperature of the binary EAN/C₁₂E₃-system at γ_a = 0.08 and T = 88.2 °C the ncb decreases with increasing w_B and eventually runs through a narrow minimum. The existence of such a narrow minimum⁴⁴ is an indication that C₁₂E₃ is neither a weak nor a strong surfactant on the EAN-rich side, which is in agreement with its rather low efficiency.²⁷ The intersection of oefb and ncb determines the maximum amount of n-dodecane that can be solubilized in the EAN–C₁₂E₃ mixture. At higher values of w_B the three-phase region exists. The phase diagram of the oil-rich microemulsion system EAN–n-octane–C₁₂E₃ is shown on the right hand side of Fig. 1. While the general trend of the phase boundaries is analogous to the aqueous counterparts stabilized by rather weak surfactants, the slope of the (upper, 1 → 2̄) IL emulsification failure boundary (iefb) is extraordinarily small. Thus, the surfactant C₁₂E₃ loses its ability to solubilize EAN within a few degrees. This unusual feature might be caused by the EAN nanostructure (correlation length of 1 nm³⁰) which might be altered under the confinement, i.e. within the EAN-in-oil droplets. Moreover, the slope of the (lower, 2̲ → 1) ncb is rather steep, which is an indication that C₁₂E₃ is a rather weak surfactant⁴⁴ on the oil-rich side of EAN-in-oil microemulsions.

3.2 SANS

In order to elucidate the significantly different behavior of EAN-in-oil microemulsions compared to the well-known water-in-oil microemulsions as well as to clarify whether the EAN nanostructure is responsible for this behavior, we studied the microstructure of both EAN- and oil-rich microemulsions with SANS. In order to measure in film contrast, the scattering length density of the respective oils were adjusted to match the scattering length density of EAN (ρ(EAN) = 3.6 × 10⁻⁶ Å⁻²) by adding deuterated oils. Accordingly, the oils were prepared with volume fractions of ϕ_d-C8 = 0.58 and ϕ_d-C12 = 0.56 of the corresponding deuterated oils in the mixture of protonated and deuterated oil. Note that the monomeric solubility of the surfactant in the solvents (EAN and oil) was not taken into account. As can be seen in Fig. 1, the partial deuteration of the oils causes only a slight shift of the phase boundaries, which is in agreement with SANS studies on water–n-decane–C_iE_j microemulsions.⁴⁵ In these systems a shift of the phase boundaries by +0.3 K was found if one replaces protonated by deuterated n-alkanes. The composition of the samples as well as the measuring temperatures and the fit parameters used to describe the scattering curves are compiled in Table 1. The scattering curves of EAN-rich (EAN–n-dodecane–C₁₂E₃, γ_a = 0.08) and oil-rich (EAN–n-octane–C₁₂E₃, γ_b = 0.16) microemulsions recorded at different weight fractions of n-dodecane (w_B) and EAN (w_A) close to the respective emulsification failure boundary are shown in Fig. 2, left and right. The incoherent scattering contribution I_incoh was subtracted from the scattering curves.

Table 1 Parameters used to describe the scattering curves with the form factor of polydisperse droplets^35,46 or cylinders³⁶ taking into account the scattering contribution of EAN via a Gaussian spatial intensity distribution.^47,48 The volume of the C₁₂E₃ molecule and the area of the surfactant head group was set to v_C = 568 ų and a_c = 64 Ų,³⁵ respectively. The sample composition is given by the mass fractions w_B, w_A, γ_a and γ_b. R₀ corresponds to the mean cross section radius, L₀ to the length of the cylinder and σ_R and σ_L are the corresponding polydispersities. The parameters d and χ describe the thickness of the shell and the sharpness of the scattering length density profile. Δρ_core and Δρ_film are the scattering length density differences and F the fudge factor accounting for inaccuracies in absolute intensity and scattering length densities. The parameters of the additional Gaussian scattering contribution, i.e. the characteristic length scale Λ of the EAN substructure and the prefactor I_0,gauss are also given

EAN–n-dodecane–C12E3				EAN–n-octane–C12E3
w B	0.052	0.060	0.063	w A	0.044	0.081	0.115
γ a	0.08	0.08	0.08	γ b	0.16	0.16	0.16
T/°C	31.2	34.1	36.5	T/°C	32.8	31.5	29.5
R 0/Å	25	29	23	R 0/Å	25	21	28.5
σ R	0.4R0	0.4R0	0.4R0	σ R	0.4R0	0.4R0	0.4R0
d/Å	4	4	4	d/Å	8	9	8
L 0/Å	—	—	90	L 0/Å	—	100	135
σ L	—	—	0.4L0	σ L	—	0.4L0	0.4L0
χ/Å	2	2	2	χ/Å	6	6	6
ϕ C,i	0.080	0.078	0.078	ϕ C,i	0.070	0.068	0.062
F	1.0	0.9	1.1	F	0.8	1.2	1.1
Δρcore/10^−6 Å^2	0.93	1.10	1.43	Δρcore/10^−6 Å^2	1.19	1.61	1.80
Δρfilm/10^−6 Å^2	1.79	1.79	1.79	Δρfilm/10^−6 Å^2	3.58	3.58	3.58
Λ/Å	14	13	13	Λ/Å	8.0	8.0	8.0
I 0,gauss/cm^−1	0.28	0.20	0.20	I 0,gauss/cm^−1	0.28	0.28	0.28

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The shape of the scattering curves of both the EAN-rich (left) and the oil-rich (right) microemulsions is somehow unexpected. Under film contrast conditions a more or less pronounced minimum of the scattering intensity at q ≈ π/R₀ is expected to be observed. The lack of this minimum is an indication for a comparatively large polydispersity as well as for the fact that the scattering intensity contains contributions from both bulk and film contrast. Furthermore, additional scattering contributions, which might be caused by the EAN substructure known to be of the size of about 1 nm,³⁰ can be observed at large values of the scattering vector q. Note that this contribution is particularly pronounced for the oil-rich microemulsions. However, the trends observed at low q values correspond to those known from aqueous microemulsions.^34,46 Thus, approaching the respective critical endpoint temperatures one observes an increasing forward scattering intensity which points towards an increasing elongation of the structures.⁴⁹

Form/structure factor analysis. The analysis of the scattering data is exemplary discussed by means of the n-dodecane-in-EAN microemulsion with the lowest mass fraction w_B = 0.052 of n-dodecane (Fig. 2, inlet). We combined the form factor for polydisperse spherical droplets (dotted line) and the averaged Percus Yevick structure factor³⁸ for polydisperse hard spheres (short dashed line) in order to describe the scattering data (for details see the ESI†). Thereby, we had to reduce the droplet volume fraction by two thirds (from ϕ_dr = ϕ_C,i + ϕ_B = 0.14 to ϕ_dr = 0.05) to obtain a reasonable description (solid line) of the scattering data, which indicates that the inter-droplet interactions are much softer than the hard sphere interactions assumed in the model. In order to describe the additional scattering contribution at large values of q we used a Gaussian spatial intensity distribution (dashed-dotted line)where Λ is the characteristic length scale of the substructure. This approach is analogous to the one used to describe the scattering caused by polymer chains in polymer gels.^47,48

Thus, the total scattering intensity I of this sample (solid line) was modeled by

I = S_PY(FnP_sphere + I_gauss), (7)

where the fudge factor F (given in Table 1) accounts for inaccuracies in scattering length densities. Note that one should add up the scattering amplitudes of the microemulsion droplets and the EAN substructure and then calculate the square of this sum to obtain the total scattering intensity. This would give rise to an additional cross-term in eqn (7), which was admittedly neglected for the sake of simplicity. As can be seen, the recorded scattering are data almost quantitatively described. However, systematic deviations can be observed especially at intermediate values of q, which might be caused by the fact that we neglected the cross-term of the scattering amplitudes from microemulsion droplets and the EAN substructure. Note that the contribution of the cross-term is largest around q ≈ 0.09 Å⁻¹, i.e. at the position where both scattering contributions have a similar intensity. Furthermore, the agreement between the used form-/structure factor model and the experimental data could not be improved considerably by taking into account the finite resolution of the instrument.

As both the model analysis of the EAN-rich microemulsion with the smallest weight fraction of n-dodecane (Fig. 2, inlet) and the GIFT-analysis (see below) show only a small influence of the structure factor, we neglected the inter-particle interactions and used only the combination of form factor and Gaussian spatial intensity distribution to describe the scattering data (long dashed line). To be more precise, the scattering data of the samples with w_B = 0.060 and w_B = 0.063 were fitted using the form factors for polydisperse spherical and cylindrical droplets, respectively. Note that for the latter a Gaussian distribution of the cross section radius and the length of the cylindrical droplets was assumed.

In the same way the scattering data of the EAN-in-n-octane microemulsions were analyzed using the form factor for polydisperse spherical droplets (eqn (S6), ESI†) for the sample with an EAN mass fraction of w_A = 0.044, while the form factor for cylindrical droplets (eqn (S8), ESI†) was used for the samples with w_A = 0.081 and w_A = 0.115. Taking into account the scattering contribution of the EAN substructure and neglecting contributions of the inter-particle structure factor also the scattering data of the n-octane-rich microemulsions are described almost quantitatively. Note, that the systematic deviations around q ≈ 0.09 Å⁻¹ are again most probably caused by the fact that we neglected the cross-term of the scattering amplitudes from microemulsion droplets and the EAN substructure.

The fit parameters used to describe the scattering curves are compiled in Table 1. Interestingly, the values obtained for the characteristic length scale of the EAN substructure Λ = 13.0 Å nm (n-dodecane-in-EAN microemulsions) and Λ = 8 Å nm (EAN-in-n-octane microemulsions) are of the same order of magnitude as the domain size of 10.1 Å found by Hayes et al. in pure EAN.³⁰ The observation, that the length scale of the EAN substructure is smaller in EAN-in-n-octane microemulsions, might be caused by two effects, namely a confinement of the EAN in the core of the EAN-in-n-octane droplets and an interaction of the EAN molecules with the surfactant head groups.

Fig. 3 illustrates the scattering length density profiles (top) calculated from the radial distribution function (eqn (S5), ESI†) with the parameters obtained from the fitting of the experimental scattering data and the schematic representations of the interfacial layer (bottom).

Fig. 3 (top) Scattering length density profiles obtained from the analysis of the scattering curves. (left) EAN–n-dodecane–C₁₂E₃ microemulsions (oil-in-EAN); (right) EAN–n-octane–C₁₂E₃ microemulsions (EAN-in-oil). (bottom) Schematic drawing of the interfacial layer. The diffuse nature of the profiles is a consequence of the penetration of the oil molecules into the hydrophobic surfactant chains, while the EAN molecules solvate the surfactant head group. Both effects lead to a substantial core contrast Δρ_core and a significant reduction of the film contrast Δρ_film.

The scattering length density profiles of the n-dodecane-in-EAN microemulsions (left, top) clearly show that the profile of all samples is quite diffuse. It possesses a relative large core contrast Δρ_core = ρ_bulk − ρ_core although we aimed for Δρ_core = 0. Furthermore, the maximum of the scattering length density profile is by more than a factor of two smaller than the value Δρ_film = 3.6 × 10⁻⁶ A² obtained for full film contrast. Both results, namely the large core contrast and the comparably small film contrast, are a consequence of the strong penetration of the oil molecules in the alkyl chains of the surfactant and of the solvation of the surfactant head groups by EAN molecules (depicted in Fig. 3 left, bottom). The latter effect was also reported by Araos and Warr,²⁶ who studied micelles of C₁₂E₅ in EAN. Interestingly, as a consequence of the smaller cross sectional radius the scattering length densities of core and film are almost identical in the case of the cylindrical droplets (w_B = 0.063) which leads to an almost pure bulk contrast.

The scattering length density profiles of the inverse EAN-in-n-octane microemulsions (right, top) are even more diffuse. Here, too, the core contrast Δρ_core differs clearly from Δρ_core = 0, which suggests that the comparably small droplets have no “pure” EAN core, but rather an extended EAN solvation shell around the surfactant head groups. Due to the larger compactness of the EAN solvation shell, which might come from the inverse structure of the microemulsion droplets, the maximum of the scattering length density profile is located at a somewhat larger value of Δρ. Compared to the n-dodecane-in-EAN microemulsions, the decrease of the scattering length density is also less steep, indicating that the penetration of the shorter n-octane molecules in the alkyl chains of the surfactant is more pronounced for the inverse droplet microemulsions.

GIFT-analysis. In an alternative approach the scattering data were analysed using the GIFT (Generalized Indirect Fourier Transformation) method, which was successfully applied for the analysis of scattering curves of microemulsions with either spherical or cylindrical geometry.⁵⁰ GIFT transforms the experimental scattering curves into real space, yielding the pair distance distribution function (PDDF) p(r)^39,51 without in-depth knowledge about the shape of the investigated microstructure. However, the structure factor S(q) has to be chosen in advance and is calculated by separating its scattering contribution from the form factor by means of factorization (see eqn (5)). Hence, the GIFT analysis is not fully model-free either.

As for the model fits we first used an averaged Percus Yevick structure factor for polydisperse hard spheres.^37,38 However, for all samples the influence of the structure factor on the scattering is surprisingly low, as found in the model fits. The resulting normalized p(r) functions are shown in Fig. 4. The PDDFs of the EAN-rich samples with w_B = 0.052 and w_B = 0.060 (left) as well as the PDDF of the oil-rich sample with w_A = 0.044 (right) have a nearly symmetrical shape, which suggests that the microemulsion droplets are almost spherical.^50,52 The PDDFs of the other samples are asymmetric, indicating the existence of elongated droplets.⁵¹

Fig. 4 Pair distance distribution functions p(r) of (left) EAN-rich EAN–n-dodecane–C₁₂E₃ microemulsions for γ_b = 0.08 at different n-dodecane mass fractions w_B and (right) oil-rich EAN–n-octane–C₁₂E₃ microemulsions for γ_a = 0.16 at different EAN mass fractions w_A obtained by the GIFT analysis.^41,42

For the n-dodecane-in-EAN microemulsions (Fig. 4, left), the maximum of the PDDF shifts from 46 Å at w_B = 0.052 (T = 31.2 °C) to 62 Å at w_B = 0.060 (T = 34.1 °C) and 50 Å at w_B = 0.063 (T = 36.5 °C). The shift of the maximum to smaller values of r from 62 Å to 50 Å, also found in other microemulsion systems,⁵³ is connected to the elongation of the initially spherical droplets. The maximum length scale of the PDDF, which corresponds either to the diameter of spherical droplets or to the length of cylindrical droplets, grows with increasing mass fraction of n-dodecane and with increasing temperature, respectively. The PDDF of the sample at w_B = 0.063 (36.5 °C) shows an additional maximum at larger distances, which may be caused by the interaction of cylinders.⁵⁴ Note that near the intersection of oefb and ncb, i.e. the lower critical end point temperature T_l, the formation of networks might start as it is known to occur in the corresponding water-rich microemulsions.⁵⁵ For the oil-rich EAN-in-n-octane microemulsions the maximum of the PDDF shifts from a value of 52 Å at w_A = 0.044 (T = 32.8 °C) to 64 Å at w_A = 0.081 (T = 31.5 °C) and 80 Å at w_A = 0.115 (T = 29.5 °C). Approaching the upper critical end point temperature (temperature T_u where iefb and ncb meet) by decreasing the temperature, one observes an extension of the PDDFs towards larger distances which unambiguously indicates the elongation of the droplets.

Comparing the length of the cylinders obtained from the model analysis with the maximum length scale observed in the PDDFs, it becomes obvious that the latter value is much larger. This result is not surprising as the length L₀ obtained from the form factor analysis corresponds to the mean length of the polydisperse cylindrical droplets, while the maximum length scale observed in the PDDF corresponds to the length of the longest cylinders present in the sample. Additionally, we assumed a Gaussian distribution for the length of the cylindrical droplets, while according to some studies⁵⁶ an exponential distribution of the cylinder length is more probable in microemulsion systems.

Comparison of droplet radii obtained from GIFT-analysis, form factor analysis, and composition. A comparison of the position of the maximum R_PDDF,max of the respective PDDF curves with the radii R₀ obtained from the form factor analysis (Table 1) reveals that the latter are much smaller. However, in order to extract the droplet radius from a PDDF curve one has to be aware of the fact that not only the shape but also the internal structure determines the shape of the PDDF and the position of the maximum. Glatter showed³⁹ that full spheres provide symmetric PDDFs, where the position of the maximum indicates the radius of the droplet. However, for inhomogeneous spheres, as in the study at hand, the shape of the PDDF becomes increasingly asymmetric if the ratio droplet radius to film thickness is increased. Accordingly, the maximum of the PDDF is shifted to the right. Thus, for inhomogeneous spheres the position of the maximum does not correspond to the radius of the sphere. In order to account for the inhomogeneity, we used the data of Glatter to extract the radius R_GIFT from the PDDFs according to

For details see the ESI.† Furthermore, due to the diffuse nature of the scattering length profile the radius R₀ obtained from the form factor analysis underestimates the radius of the droplets. In order to account for this phenomenon, we defined the radius R_FFA as the distance r where the scattering length density differs by 5% from the scattering length density ρ_bulk of the bulk, i.e.

Δρ(R_FFA) = 0.95ρ_bulk. (9)

Another way to determine the radius of spherical microemulsion droplets is based on purely geometrical considerations. Accordingly, the radius R_comp is given by the composition of the sample as

where v_C = 568 ų and a_C = 64 Ų are the volume and area occupied by a C₁₂E₃ molecule at the interface, p = σ/R₀ = 0.4 is the polydispersity index, ϕ is the volume fraction of the component solubilized in the droplet and ϕ_C,i the volume fraction of surfactant at the interface.³² To obtain ϕ_C,i, the amount of surfactant solubilized monomerically in EAN and oil has to be subtracted from the total volume fraction ϕ_C of surfactant. The monomeric solubility of C₁₂E₃ in EAN was found to be γ_mon,a ≈ 0.01 ± 0.01.²⁷ The monomeric solubilities of C₁₂E₃ in the respective oils (γ_mon,b ≈ 0.07 ± 0.01) at the phase inversion temperature were estimated from γ₀ and [small gamma, Greek, tilde] which are the surfactant mass fractions at the “fish-head” and “fish-tail” in the T—γ diagram, respectively.⁵ According to Kahlweit et al. the monomeric solubility of nonionic surfactants in oil increases with temperature.⁴³ Thus, a monomeric solubility γ_mon,b ≈ 0.095 ± 0.01 of C₁₂E₃ in n-octane was used for the EAN-in-n-octane microemulsions.

Having determined the radius of the microemulsion droplets for different samples along both the oefb and the iefb, we will discuss the evolution of the characteristic domain size ξ (note that ξ = R for droplet microemulsions along the respective efb) with the temperature in the following. For microemulsions of the type water–n-alkane–C_iE_j it has been shown that the domain size runs through a distinct maximum at the phase inversion temperature T̃, where the microstructure is known to be bicontinuous.⁴ In order to prove whether or not this trend is also found for microemulsions containing EAN, the radii obtained by the analysis of the SANS curves and from the composition are plotted as a function of the temperature T–T̃ in Fig. 5 and compiled in Table 2. The relative temperature T–T̃ is used to compare the temperature dependence of the domain size of different systems. Since the system EAN–n-octane–C₁₂E₃ exhibits a very similar behavior as the system water–n-octane–C₈E₃ with respect to efficiency, and interfacial tension,^27,35 the temperature dependence of the domain size of the latter system (stars) is included in Fig. 5.

Fig. 5 Characteristic domain size ξ plotted as a function of the relative temperature T–T̃ for the systems EAN–n-dodecane–C₁₂E₃ and EAN–n-octane–C₁₂E₃. Shown are the radii obtained from GIFT (R_GIFT, triangles), form factor and Teubner–Strey³⁴ analysis (R_FFA, squares), and composition (R_comp, circles). The temperature variation of the domain size in the system water–n-octane–C₈E₃ is shown for comparison (stars).³² The drawn line describes the temperature variation of the principal curvatures of the amphiphilic film.^3,32

Table 2 Droplet radii obtained from GIFT-analysis (R_GIFT), form factor analysis (R_FFA), and composition (R_comp). Note that the droplets of the samples studied at w_B = 0.063, w_A = 0.081, w_A = 0.115 have a cylindrical structure. Thus, the given values correspond to the cross sectional radius of the cylinder

EAN–n-dodecane–C12E3				EAN–n-octane–C12E3
w B	0.052	0.060	0.063	w A	0.044	0.081	0.115
T/°C	31.2	34.1	36.5	T/°C	32.8	31.5	29.5
R FFA/Å	34	38	31	R FFA/Å	52	47	54
R GIFT/Å	28	38	31	R GIFT/Å	34	43	52
R comp/Å	40	43	45	R comp/Å	34	47	54

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As can be seen, both systems, the EAN and the aqueous microemulsion, show the same general trend. The maximum domain size ξ_max = 128 Å found for the bicontinuous EAN microemulsion³⁵ is slightly larger than the maximum domain size of the ternary system water–n-octane–C₈E₃ where ξ_max = 103 Å.³² This result is in line with the finding that, although the two surfactants have a similar efficiency, the monomeric solubility of C₁₂E₃ in EAN and n-octane is much larger than the monomeric solubility of C₈E₃ in water and n-octane, which results in a smaller internal interface and thus in a larger domain size. All in all, the droplet radii R_GIFT, R_FFA and R_comp obtained from the GIFT and form factor analysis of the SANS data as well as from the composition are in almost quantitative agreement (within ±6 Å, except the samples at w_B = 0.063 and w_A = 0.044) despite the approximations made.

Examining the data more thoroughly, one finds that in the case of aqueous microemulsions the droplets on the water-rich side are slighly larger than on the oil-rich side. This small but systematic difference indicates that in aqueous microemulsions nonionic surfactants act less strongly on the oil-rich side compared to the water-rich side, which can partly be ascribed to the higher temperature. For the EAN microemulsions the droplets on the EAN-rich side seem to be smaller than on the oil-rich side. This apparently different behavior of aqueous and EAN microemulsions is, however, caused by the fact that different EAN-microemulsion systems are studied on the EAN-rich and oil-rich side as explained above. As C₁₂E₃ solubilizes n-octane more efficiently than n-dodecane,²⁷ the n-dodecane-in-EAN droplets are smaller than the EAN-in-n-octane droplets.

Finally, the evolution of the domain size with increasing temperature is discussed in more detail. We recall that the microstructure of the samples studied close to the respective critical endpoint temperatures corresponds to cylindrical structures. Thus, the domain size corresponds to the cross sectional radius of cylinders and not to the radius of droplets. Consequently, a slight jump in the ξ(T–T̃)-curve is found in the temperature regimes where the microstructure changes its geometry. A comparison of the slope of the data points on the EAN- and oil-rich side reveals that the increase of the droplet radius observed with increasing temperature for n-dodecane-in-EAN microemulsions is much less pronounced than the decrease found for EAN-in-n-octane microemulsions. This result is in perfect agreement with the different slopes of the oefb and the iefb in the phase diagrams (Fig. 1). While the oefb is rather steep, i.e. the amount of solubilized oil increases moderately with increasing temperature, the iefb has an extraordinarily small slope, which suggests that the amphiphilic film loses its ability to solubilize EAN with an increase in temperature by only a few degrees. Using SANS we were able to prove that this quite extraordinary behavior is a consequence of the fact that the EAN molecules form a substructure with a characteristic length scale of Λ = 8 Å inside the EAN-in-oil droplets. Furthermore, these results also explain NMR-data published in previous studies^27,34 where hardly or even no EAN could be detected on the oil-rich side at temperatures above the phase inversion temperature.

4 Conclusions

In aqueous microemulsion systems the spontaneous curvature depends nearly linearly on temperature and changes its sign at the phase inversion temperature (PIT).^4,29,32 As a consequence, the temperature dependence of the phase behavior, interfacial tension and microstructure is symmetrical with respect to the PIT.^4,29,32 Although the same general features are found in ternary EAN–n-alkane–surfactant systems,^15,23 only a very small amount of EAN is solubilized in oil-rich microemulsions. In order to elucidate whether the asymmetric behavior of EAN microemulsions with respect to the PIT can be ascribed to the presence of an EAN substructure in the EAN droplets, we studied the properties of both oil-in-EAN and EAN-in-oil microemulsions.

Studying the phase behavior, we found that the oil emulsification failure boundary (oefb) is rather steep, while the slope of the IL emulsification failure boundary (iefb) is extraordinarily small. The different slopes suggest that the surfactant C₁₂E₃ is able to continuously solubilize more and more oil when the PIT is approached, while it loses its ability to solubilize EAN within a few degrees once the PIT is exceeded.

In order to study whether the variation of the spontaneous curvature with temperature in EAN microemulsions is linear or not, we investigated the evolution of the nanostructure along the respective efbs by SANS. The pair distance distribution functions (PDDF) obtained from the GIFT analysis show a transition from spherical to cylindrical structures approaching the respective critical endpoint temperatures. Thereby, the influence of the structure factor on the scattering is surprisingly low, indicating that inter-droplet interactions are much less pronounced than hard sphere interactions. Applying the respective form factors for polydisperse spherical and cylindrical droplets, a Gaussian spatial intensity distribution had to be used to describe the additional scattering contribution at large q. Assigning this contribution to the EAN substructure, we found, that its length scale Λ is comparable to the domain size of 10.1 Å found by Hayes et al. in pure EAN.³⁰ The fact, that the length scale is smaller in EAN-in-oil microemulsions (Λ = 8 Å) than in oil-in-EAN microemulsions (Λ = 13.0 Å) is attributed to the confinement of the EAN molecules in the core of the EAN-in-oil droplets and their interaction with the surfactant head groups.

Finally, the evolution of the domain size with increasing temperature prove our hypothesis of a non-linear variation of the spontaneous curvature in EAN microemulsions. Related to the urge of the EAN molecules to form their own substructure, the radius of the EAN-swollen droplets decreases strongly within a narrow temperature range of only 3 K, while the radius of oil-swollen droplets varies in a less pronounced way over a wider temperature range if the phase inversion is approached.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We would like to thank the German Research Foundation (DFG) for funding (project STU287/3-1). We also thank Diana Zauser, Stefan Lülsdorf, Dr Yvonne Pütz and Dr Lena Grassberger for valuable help with the SANS measurements. Furthermore, we would like to acknowledge the Institut Laue Langevin (ILL) in Grenoble (France) in providing the facilities for the SANS measurements and the valuable support of the local contacts Dr Ralf Schweins and Dr Peter Lindner of the D11 spectrometer.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8cp06228e

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