A methodology for measuring the characteristic curvature of technical-grade ethoxylated nonionic surfactants: the effects of concentration and dilution

Amir Ghayour

doi:10.1515/tsd-2022-2464

Article Publicly Available

A methodology for measuring the characteristic curvature of technical-grade ethoxylated nonionic surfactants: the effects of concentration and dilution

Amir Ghayour
Amir Ghayour received his B.Sc. in chemical engineering from Shiraz University (Iran) in 2013, and his M.A.Sc. in chemical engineering from the University of Toronto in 2019. He is currently a Formulation and Application Technology Lead at Syngenta in Canada. He has expertise in surfactant and polar oil characterization for agrochemical applications. He is interested in formulation engineering, colloids, emulsions, and interfacial science.

Published/Copyright: December 15, 2022

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From the journal Tenside Surfactants Detergents Volume 60 Issue 1

Abstract

Characterization of the behaviour of commercially available non-ionic surfactants has received considerable attention due to their efficacy in a variety of applications. The main challenge in the application of these types of surfactants is that the hydrophilicity of the surfactant varies with concentration and dilution due to the polydispersity of the ethylene oxide groups. The hydrophilicity of a surfactant can be quantified by the characteristic curvature (Cc) parameter of the hydrophilic–lipophilic difference (HLD) framework. In this work, a model based on natural logarithmic regression was developed to calculate the Cc value of commercial surfactants as a function of surfactant concentration by a fast and simple phase scan. The slope of the Cc curve and the measured Cc at a reference concentration were used to develop the model. The Cc values determined with the model agreed with the measured values from the phase scans. Furthermore, the linear mixing rule proved to be reliable for mixtures of polydisperse ethoxylated surfactants. Finally, the impact of the water-to-oil ratio on the Cc was evaluated and the implications were discussed.

Keywords: characteristic curvature; dilution; ethoxylated nonionic surfactants; HLD; microemulsions

1 Introduction

Nonionic surfactants are one of the most widely used classes of surfactants in a range of industries. The annual global consumption of surfactants is estimated at 20 Mtons [1]. Nonionic ethoxylated surfactants are widely used in detergents, surface cleaners, cosmetics, and personal care products [2], [3], [4], [5], [6]. They are also commonly used for enhanced oil recovery, agrochemical, and food processing applications [7], [8], [9], [10], [11]. Furthermore, nonionic surfactants are insensitive to pH, can form microemulsions without cosurfactants, and have lower critical micelle concentration (CMC) than ionic surfactants, making them suitable carriers for drug delivery systems [12]. Furthermore, these surfactants are mostly 100% active, more resistant to multivalent cations than ionic surfactants, and come in various structures [13].

Technical-grade nonionic surfactants, also called commercial surfactants, are more commonly applied in industrial applications than in their pure form because of their low cost of production and often provide better performance [14]. Technical-grade surfactants are polydisperse in the number of ethylene oxide (EO) groups and exhibit a Poisson distribution; only the average EO is reported for any specific commercial surfactant, e.g., nomenclature C_iE_j [15, 16]. To demonstrate the polydispersity of commercial surfactants, Lukowicz et al. [17] conducted GC-MS on a C₈E₄ commercial surfactant. They found that 4 EO oligomers make up only 14.8 wt% of the total surfactant, while higher and lower EO groups have lower concentrations. The polydispersity of commercial surfactants produces a lower surface tension below CMC and a deep minimum around the CMC compared to pure monodispersed surfactants due to the presence of hydrophobic compounds [18]. There is often a residual amount of unreacted alcohol in commercial nonionic surfactants, competing with the ethoxylated surfactants for interfacial adsorption or adsorb in the palisade layer, impacting the curvature of the system [19, 20].

Nonionic surfactants are essential in the agrochemical industry and are applied as co-formulants in pesticide formulations and tank-mix adjuvants [21, 22]. Adjuvants are primarily alcohol ethoxylates that increase the biological activity of agrochemical active ingredients by increasing spray retention, penetration, and uptake of agrochemicals in plant cuticles [23, 24]. As a result of the complicated behavior of surfactants, formulation development is heavily reliant on the experience of a formulator and the time-consuming process of trial and error to design and optimize formulations. Therefore, the opportunity to apply new methodologies and surfactant theories to save time and resources has become appealing in a wide range of industries.

Surfactant theories are gaining popularity in industry because they provide a theoretical view of surfactants’ behavior and are increasingly accurate in describing experimental observations [8, 25, 26]. One of the theories that have become widely adopted is the Hydrophilic-Lipophilic Difference (HLD) framework due to its robust methodologies and the extensions, such as Net and Average Curvatures (NAC), that allow it to be applied to real-world conditions [27], [28], [29], [30]. Unlike the HLB, the HLD considers the formulation conditions of the whole system and includes the contribution of all variables [10, 31, 32]. The HLD of nonionic surfactant systems is represented by the following equation [33]:

(1) H L D = b ⋅ S − k ⋅ E A C N + C c + c T ( T − 25 ° C )

where the constant b is dependent on the type of electrolyte, e.g., b = 0.13 for NaCl. The term S is the concentration of salt in the system, usually measured in grams of salt per 100 mL of solution. Most conventional surfactants have k values of 0.15–0.17. However, for some extended anionic or cationic surfactants, this experimentally derived constant could be as low as 0.05 or as high as 0.7 [34, 35]. The EACN represents the hydrophobicity of the oil phase. The term c T is the temperature coefficient. Ethoxylated nonionic surfactants have a positive c T (∼+0.06), meaning that the system becomes more lipophilic as temperature increases. The term Cc represents the characteristic curvature of the nonionic surfactant. It corresponds to the normalized net-curvature of the surfactant at reference conditions [36]. A negative Cc value represents a more hydrophilic surfactant, while a positive value represents a more hydrophobic one. At HLD = 0, also known as the phase inversion point (PIP), the net-curvature of the system is zero. Therefore, the surfactant has an equal affinity to oil and water, thus, forming a bicontinuous phase at concentrations above the critical microemulsion concentration (CµC) [29]. The HLD = 0 is often referred to as the optimum point because the system undergoes minimum interfacial tension [37, 38].

Interestingly, the HLD equation is independent of the concentration of the surfactant. This feature allows the calculation of the HLD of pure surfactant systems based only on three factors: the nature of the oil phase, the aqueous phase, and temperature. However, for commercial surfactants with polydisperse EO groups, the concentration of the surfactant will affect the Cc, and therefore, the concentration must be considered. This paper will introduce a methodology to measure the Cc while considering the concentration and dilution effects.

Characterizing the behavior of commercial surfactants has been the topic of many scientific investigations in efforts to optimize surfactant-oil-water (SOW) systems [8, 36, 39], [40], [41]. Salager et al. [42] provided a method to characterize an unknown surfactant by mixing an equal weight of a reference and test surfactants having different hydrophilic moieties to perform HLD scans. They reported numerous σ values (similar to Cc) for nonionic and ionic surfactants. Acosta [30] calculated the Cc of linear alcohol ethoxylates based on the group contribution correlation of the constituents and created a model for predicting the Cc of pure alkyl ethoxylates. The model is presented as

(2) C c = 0.28 ⋅ S A C N + 2.4 − E O N

where SACN is the number of carbons in the surfactant’s tail and EON is the number of ethylene oxide groups in the surfactant’s head.

Zarate-Muñoz et al. [16] developed a simple methodology to measure the Cc of commercial nonionic surfactants within minutes. They measured the optimum salinities of commercial surfactants at 10% concentration via the emulsion stability technique and checked the results with interfacial tension data and solubilization curves. The emulsion stability method produced accurate results within minutes. Mixed surfactant scans were conducted to determine the Cc of commercial nonionic surfactants, which produced linear correlations for most surfactant mixtures. The method was used to determine the optimum salinity of surfactant mixtures and required simple, readily available equipment.

The main challenge of determining the Cc of technical-grade surfactants is their dependence on concentration. Changing the concentration of technical-grade surfactants can significantly impact hydrophilicity and thus change the Cc. Consequently, the polydispersity of these surfactants makes group contribution correlations ineffective. The main objective of this work is to introduce a practical methodology to measure the characteristic curvature of technical grade ethoxylated surfactants as a function of concentration and develop a simple procedure to calculate the Cc. Then the linear mixing rule of ethoxylated surfactants is assessed by mixing two commercial ethoxylated surfactants at different molar ratios to observe their Cc mixture. Finally, the effect of the water-to-oil ratio (WOR) on the Cc of surfactants is evaluated.

2 Experimental procedure

2.1 Materials

The following technical-grade nonionic surfactants made by BASF were used in this study: LUTENSOL XL 70 (C₁₀E₇, 100% active), LUTENSOL TDA 6 (C₁₃E₆, 100% active), LUTENSOL TO 5 (C₁₃E₅, 100% active), LUTENSOL XP 40 (C₁₀E₄, 100% active). ColaWet MA-80 (sodium dihexyl sulfosuccinate, SDHS, 85% active) was kindly donated by Colonial Chemical. Solvents used were hexane, heptane, decane, hexadecane (Thermo Fisher Scientific, purity ≥ 99%), sodium chloride (Fisher BioReagents, purity ≥ 99%), and deionized water.

2.2 Microemulsion phase behavior scans

Salinity phase scans were conducted to measure the optimum salinity of surfactant-oil-water (SOW) systems. 2 mL of the aqueous phase and 2 mL of the oil phase were added to a 2-dram vial. Heptane was used as the oil phase for Cc measurements, and additionally, hexane, decane, and hexadecane were used to measure the k coefficients. Varying concentrations of active surfactant were added to the system starting from 2% to 30% surfactant of half the total volume. For concentration-effect studies, the water-to-oil ratio (WOR) was equal to 1. For WOR effect studies, the WOR (volume ratios) ranges from 0.5 to 4 at constant surfactant concentration relative to the oil phase. The operating temperature was (25 ± 1) °C. The vials were vigorously shaken twice a day for three days and left to reach equilibrium for two weeks.

2.3 Optimum salinity (S*) and Winsor Type I-III and III-II transition points

The salinity at which the system reaches HLD = 0 is called the optimum salinity (S*). The excess oil and water volumes and the microemulsion middle phase were measured at equilibrium conditions to determine the HLD = 0. ImageJ software was used to analyze the pictures taken of the vials. The optimum salinities were fitted via HLD-NAC algorithms [29, 30]. Figure 1 represents the HLD-NAC model for a salinity phase scan.

Figure 1:

Salinity phase scan for a 3% C₁₃E₆-heptane-water system at 25 °C. The volumes of the phases are determined by fitting the optimum salinity and the characteristic length using the HLD-NAC model. The blue and red lines represent the fitted lower and upper microemulsion phase borders, respectively.

Furthermore, the HLD transition points from Winsor Type I to III and from Type III to II were obtained for each concentration using the HLD-NAC model. Subsequently, the HLD values were converted to temperature using the temperature coefficient c T .

3 Results and discussion

3.1 Fish phase diagram

A fish diagram reveals many properties of a surfactant system, including critical microemulsion concentration (CµC), Winsor Type I, II, III, IV microemulsion regions, and the X point, which corresponds to the complete solubilization of oil and aqueous phases with a minimum amount of surfactant [43, 44]. The phase inversion temperature (PIT) (the temperature at which HLD = 0) at the X point can be used to characterize oils and surfactants [44]. While pure nonionic surfactants produce horizontal fish diagrams, technical-grade surfactants exhibit slanted diagrams [45, 46]. Kunieda et al. [47] demonstrated the dependence of the PIT of commercial nonylphenol ethoxylated surfactants (NPE) with varying ethoxylation degrees on surfactant concentration by plotting their fish diagrams. The PIT plots show that as the ethoxylation degree of NPEs increases, they become less sensitive to concentration.

In the case of technical-grade ethoxylates, the low EO oligomers will disproportionately partition in the excess oil phase causing extreme distortions in the fish diagram, more noticeable at low concentrations [48]. In addition to the polydispersity of the ethoxylated fractions, the unreacted alcohols will further distort the fish diagram [49, 50]. Figure 2 presents the fish diagrams of technical-grade C₁₃E₆ surfactant in heptane and NaCl brine.

$Figure 2: The fish diagrams of technical-grade C13E6 in a heptane-water system at WOR = 1. (a) The parameters are fitted using the HLD-NAC and presented as HLD values. The liquid crystalline phases (LC) are experimentally observed using cross-polarized lights. (b) The HLD values are converted to temperature using the k, EACN, Cc, and c T ${c}_{\mathrm{T}}$ values for the commercial surfactant.$

Figure 2:

The fish diagrams of technical-grade C₁₃E₆ in a heptane-water system at WOR = 1. (a) The parameters are fitted using the HLD-NAC and presented as HLD values. The liquid crystalline phases (LC) are experimentally observed using cross-polarized lights. (b) The HLD values are converted to temperature using the k, EACN, Cc, and c T values for the commercial surfactant.

The fish diagram, as a function of the HLD, is fitted using HLD-NAC algorithms. The X point, i.e., the start of the Type IV microemulsion, occurs at a concentration between 10% and 11%. Type IV microemulsions may exhibit the formation of liquid crystal phases, indicating a low or zero curvature [51]. Figure 2a demonstrates the formation of these crystalline phases. These include fully lamellar liquid crystals and phases with co-existing microemulsion and liquid crystal phases. Figure 2b demonstrates the slanted fish diagram of a commercial surfactant. The temperature fish diagram is modeled via the HLD by incorporating the temperature coefficient ( c T ) of the C₁₃E₆ surfactant. The highly distorted body reveals the polydisperse nature of the surfactant. The head of the fish (the left part of the diagram) becomes increasingly vertical as the concentration decreases. This phenomenon corresponds to the excess partitioning of low ethoxylated surfactants in the excess oil phase, resulting in a more hydrophilic surfactant behavior at the interface [45].

3.2 Characteristic curvature as a function of concentration

Polydisperse alkyl ethoxylates are known to exhibit varying hydrophilicity at different concentrations. Acosta and Natali [50] demonstrated that the Cc of commercial ethoxylated surfactants as a function of concentration are fitted using a logarithmic function. Accordingly, the characteristic curvature of the commercial nonionic C₁₃E₆ surfactant is measured at different concentrations and presented in Figure 3. A gradual increase in hydrophobicity is observed as the concentration increases. This increase in hydrophobicity follows a natural logarithmic regression with an R-squared value of 0.998.

Figure 3:

Cc curve versus surfactant concentration for C₁₃E₆-heptane-water system, WOR = 1. A natural logarithmic trendline is used to fit the data.

Additionally, the Cc values of two other commercial nonionic surfactants were measured and presented in Figure 4. A natural logarithmic function can accurately fit the Cc values versus concentration for commercial nonionic surfactants. Table 1 summarizes the Cc equations of these surfactants.

Figure 4:

The Cc curves versus surfactant concentration for C₁₃E₅, C₁₃E₆, and C₁₀E₇ technical grade surfactants in heptane-water systems.

Table 1:

The characteristic curvature functions of commercial ethoxylated surfactants with 5, 6, and 7 ethylene oxide groups and their respective R-squared from experimental Cc values.

Surfactant	Cc function	R ²
C₁₀E₇	0.74·ln(x) − 3.91	0.990
C₁₃E₆	1.13·ln(x) − 3.29	0.998
C₁₃E₅	1.36·ln(x) − 3.34	0.999

To interpret the change in Cc as a function of concentration, it is necessary to understand the partitioning of surfactants in the microemulsion middle phase and the excess oil and water phases. Graciaa et al. [52] demonstrated that the average EON in the excess oil phase decreases with increasing surfactant concentration. Moreover, in a Type III system, the concentration of surfactant in the excess aqueous phase is not higher than the CMC value and can therefore be considered negligible [53]. Therefore, most surfactant fractions will be partitioned to the middle and excess oil phases. At low surfactant concentrations, the low mole ethoxylates, i.e., hydrophobic fractions, will disproportionately partitioned to the excess oil phase, thus making the interfacial-active surfactants in the middle phase more hydrophilic [32, 53]. Consequently, the Cc is more negative at low concentrations. As the surfactant concentration increases, the amount of low mole ethoxylates in the excess oil phase remains roughly constant since the excess oil phase is saturated with the hydrophobic fractions. Consequently, the relative amount of EO in the oil phase to the total added surfactant will decrease. This will cause the total surfactants in the middle phase to become more hydrophobic, thus increasing the Cc.

The partitioning of the different fractions of surfactants can explain the change in Cc in the type III region, but a valid question is, why does the surfactant become more lipophilic in the Type IV region where excess oil and aqueous phases do not exist? The answer could be explained by the behavior of the unreacted alcohols (polar oils). According to Ghayour and Acosta [20], polar oils will segregate between the surfactants’ hydrophobic tail near the oil-water interface, making the system more hydrophobic by increasing the total Cc and decreasing the EACN of the system (increase in HLD). Therefore, even in the absence of excess phases, the polar oils segregating at the oil-water interface in the bicontinuous phase make the system more hydrophobic. Therefore, the excess partitioning phenomenon of oligomers along with the polar oil behavior, can fully explain the surfactant concentration effect in Winsor Type III and IV regions.

3.3 Model development

The previous section demonstrates that the Cc of a commercial ethoxylated nonionic surfactant follows a natural logarithmic trend as a function of concentration:

(3) C c = a ⋅ ln ( x ) + d

where x is the concentration of the surfactant, and constants a and d are unique for each surfactant.

The rate of change of the Cc function at any concentration indicates the partitioning of the different fractions of the surfactant. The derivative of this function (Cc versus x) will result in the slope of the Cc curve along the x-axis.

(4) d C c d x = a x

At low concentrations, a x is a large value, indicating a higher partitioning of low ethoxylated oligomers in the oil phase. In effect, the oligomers with higher EO will participate at the interface, thus decreasing the effective Cc of the surfactant. Conversely, at high concentrations, a x is a small value, indicating lower partitioning of the low EO oligomers in the oil phase relative to the total amount of surfactant added to the system. Therefore, the surfactants participating at the oil-water interface have an overall lower EO, resulting in a more positive Cc.

Applying Eq. (3) to the nonionic HLD equation, Eq. (1), at optimum salinity yields

(5) H L D ∗ = b ⋅ S ∗ − k ⋅ E A C N + [ a ⋅ ln ( x ) + d ] + c T ( T − 25 ° C ) = 0

The differentiation of Eq. (5) as a function of concentration (x) and solving for “a” yields

(6) a = − b ⋅ x r e f . d S ∗ d x

Here, b is the salinity constant in the HLD equation. This equation implies that “a” can be calculated at a reference concentration by measuring the change in optimum salinity resulting from an infinitesimal change in surfactant concentration. For practical reasons, however, d S ∗ d x should be considered as Δ S ∗ Δ x where Δ x is a minor change in concentration having a measurable Δ S ∗ . The term x r e f is equal to ( x 1 + x 2 ) / 2 , i.e., the average of the two experimental surfactant concentrations. To demonstrate this technique, x 1 and x 2 can be 10% and 11%, respectively, and therefore, x r e f is equal to 10.5% and Δ x = 1.

The term “a” can be measured based on the analysis above, and the surfactant’s Cc can be calculated using Eq. (3). The term “d” in Eq. (3) is replaced by the Cc at the reference concentration ( C c r e f ) approximated to be the average of the Cc values at x 1 and x 2 concentrations. Therefore, the value of Cc at any concentration of x is equal to

(7) C c x = C c r e f − a ⋅ ln ( x r e f ) + a ⋅ ln ( x )

which can be rearranged to give the following equation.

(8) C c x = C c r e f + a ⋅ ln ( x x r e f )

Here, the term C c x is the Cc of the commercial nonionic surfactant at the desired concentration x, “a” is the slope of the Cc versus x curve (Eq. (6)), and x r e f and C c r e f are the reference concentration and the Cc at that concentration, respectively. Since “a” is constant for each surfactant, the C c x can be calculated at either lower or higher concentrations than the C c r e f as one slides along the x-axis.

3.4 Model analysis and application

The model was applied to three technical grade surfactant systems to evaluate its accuracy. Figure 5 demonstrates the method for calculating the “a” parameter using the optimum salinity curve of the surfactant. The change in S^* is induced by a change in concentration at x r e f which is used to calculate “a” values using Eq. (6). These experimental conditions and the “Measured a” using the model are reported in Table 2. The “Fitted a” values are extracted from Table 1, which were determined by fitting the experimental phase scans at multiple concentrations with natural logarithmic trendlines.

$Figure 5: Change in optimum salinity (S*) as a function of surfactant concentration for C13E6-heptane-water system. The slope of the curve at x r e f ${x}_{\mathrm{r}\mathrm{e}\mathrm{f}}$ is used to calculate “a” using Eq. (6).$

Figure 5:

Change in optimum salinity (S*) as a function of surfactant concentration for C₁₃E₆-heptane-water system. The slope of the curve at x r e f is used to calculate “a” using Eq. (6).

Table 2:

Measured and fitted “a” values for commercial surfactants with different degrees of ethoxylation.

Surfactant	x _ref	Cc_ref	ΔS*	Measured a	Model a	Standard deviation
C₁₀E₇	10.5	−2.25	0.44	0.60	0.74	0.045
C₁₃E₆	10.5	−0.57	0.85	1.16	1.13	0.024
C₁₃E₅	5.5	−1.03	1.98	1.42	1.36	0.023

The values from Table 2 are used to calculate the Cc curves using Eq. (8). Figure 6 presents the experimental Cc values and the modeled Cc curves for the three surfactants.

Figure 6:

The Cc versus concentration of technical-grade C₁₀E₇, C₁₃E₆, C₁₃E₅ surfactants. Dotted lines are predicted via the model, and the markers are experimental values.

The standard deviation of the modeled Cc values from the experimental ones is calculated and reported in Table 2. The error in Cc is not greater than 0.18 units at any concentration for the tested surfactants. These results fall within the acceptable range of Cc values reported having an error of ±0.2 units [16]. Moreover, the standard deviation for the entire Cc curve is less than 0.05 for any surfactant, suggesting that the proposed model and the procedure for determining Cc values are reliable.

The Cc model is a practical method to calculate the characteristic curvature of commercial nonionic surfactants in a fast-paced industry environment. One significant advantage of the method is that the C c r e f can be chosen at the concentration that the SOW system creates microemulsions that are easily detectable at room temperature. Commercial nonionic surfactants could have highly negative or positive Cc values, and adding to the complexity, is the excess partitioning of low ethoxylated surfactants, e.g., EON ≤ 4. In practice, the combination of the above factors makes it difficult and time-consuming, often requiring trial and error, to find the PIP of the system at multiple concentrations to fit a curve. Furthermore, depending on how large the slope of the Cc curve is, it may be required to go to extreme high or low temperatures, even changing the reference oil (EACN) to induce the transition necessary to reach the PIP. Therefore, the conventional method of determining the Cc curve may require multiple scans at different temperatures to determine the c T and multiple scans with different EACN oils to determine the k before the Cc values can be accurately measured. By applying the proposed methodology, one will only need to find the PIP at a reasonable concentration, and once the system has reached equilibrium (after two weeks), top-up all the tubes with a known amount of surfactant (for example, one drop) and observe the new PIP. Then, the Cc curve can be calculated by inputting the experimental values in Eqs. (6) and (8), saving time and resources.

3.5 Revisiting the group contribution model

Understanding the selective partitioning of commercial surfactants is crucial for determining the Cc of surfactants. The total amount of surfactant and the water-to-oil (WOR) ratio are two factors that affect the partitioning of commercial surfactants [54, 55]. Upon adding a commercial surfactant or a surfactant blend to an oil-water system at optimum conditions, the oligomers distribute differently in the oil phase and at the interface [28, 56]. At low surfactant concentrations, where the slope of the Cc curve is large, the partitioning of the low ethoxylated fractions of the commercial surfactant is higher in the oil phase. Generally, oligomers with less than 3 EO and 50% of oligomers with 4 EO will partition into the oil phase [53]. With the low mole ethoxylates partitioning in the oil phase, high mole ethoxylates will remain at the interface and create a more hydrophilic surfactant. Therefore, the Cc of the surfactant will be more negative (more hydrophilic), as seen in previous sections. According to Graciaa et al. [52, 53], as the surfactant concentration increases, the partitioning of low EO in the oil phase will decrease, making the surfactant more hydrophobic, indicated by a small slope in the Cc curve. In other words, the ratio of the number of low EO surfactants in the oil phase will continuously decrease compared to the total amount of EO at the interface. Therefore, as the surfactant concentration increases, the bulk of the added surfactant resides in the middle phase. Consequently, at a specific surfactant concentration, the composition of the interfacial-active surfactants should approach that of the pure surfactant, i.e., the EON reported in the nomenclature C_iE_j.

We hypothesize that at a sufficiently high surfactant concentration, the Cc of the commercial surfactant will be identical to that of its reported pure form. The group contribution model of pure ethoxylated surfactants proposed by Acosta [30] is used to determine the equivalent concentration at which the commercial surfactant will have an identical Cc to its pure form.

Table 3 presents the Cc values obtained using the group contribution model of pure nonionic surfactants (independent of concentration), Eq. (2), and the Cc values obtained from Eq. (8) at concentrations in which the two Cc values are equal (equivalent surfactant concentration). The group contribution model was developed based on pure-grade linear alcohol ethoxylates with 2 ≤ EON ≤ 6 [30, 57, 58].

Table 3:

The Cc values calculated by the group contribution model and the model proposed in this paper. The “a” parameter and the equivalent surfactant concentration for each surfactant are reported.

Surfactant	Cc group contribution	Cc derivative model	a	Equivalent surfactant concentration (%)
C₁₃E₆	0.04	0.03	1.13	20
C₁₃E₅	1.04	1.05	1.35	30
C₁₀E₄	0.36	0.34	1.67	35

A trend is observed between “a”, EON, and the equivalent surfactant concentration. A surfactant with a small “a” has a small slope in the Cc curve which indicates the effect of the partitioning of the low mole ethoxylates will diminish quicker. In contrast, a large “a” indicates that the surfactant has higher partitioning throughout the scan. Thus, the effects of partitioning will diminish slower. This phenomenon results in surfactants having a lower “a” reach their equivalent pure Cc at lower concentrations. Moreover, as the nominal EON of surfactants decreases, the increase in “a” indicates that the slope of the Cc curve is more prominent for low mole ethoxylates.

By combining the group contribution correlation with the model proposed in this paper and assuming “a” based on the surfactant EO number, the Cc curve of a commercial surfactant can be roughly predicted and used as a starting point for experimental Cc measurements.

3.6 Linear mixing rule of commercial ethoxylated surfactants

Commercial products often comprise mixtures of surfactants due to superior performance [13, 17, 33, 59]. A linear mixing rule is used to determine the Cc of the surfactant mixture based on the molar fraction ( X i ) of each component [33, 60].

(9) C c m i x = X 1 ( C c 1 ) + X 2 ( C c 2 )

Here, C c i is the Cc of the ethoxylated surfactant at the total surfactant concentration, not the individual surfactant concentration. The accuracy of a linear mixing rule for non-linear phenomena such as concentration and temperature effects is a topic of interest. With regards to the effect of temperature on the Cc, Salager et al. [28] suggest that the temperature coefficient ( c T ) itself varies slightly with temperature. Thus, the linear HLD equation should be considered “local approximations” when conducting temperature scans. Considering that a commercial ethoxylated surfactant comprises dozens of different oligomers and hundreds of different conformations that are impacted by temperature in complex ways, it is reasonable to assume that the predictive capabilities of the HLD have shortcomings in extreme conditions. Dado et al. [26] observed non-linear behavior when conducting temperature scans to determine the Cc values of nonionic surfactants using a pure C₁₀E₄ surfactant. The non-linearity was attributed to the variable temperature coefficient, the dual oil-like and surfactant-like nature of polar fractions, and the low EO oligomers of the surfactants.

To investigate the validity of the linear mixing rule at a constant temperature, the commercial C₁₀E₇ and C₁₀E₄ surfactants are mixed at 50/50 mol% and 70/30 mol%, respectively, while the k_mix (EACN coefficient) values are assumed to follow a mole-based linear mixing rule. The Cc results are presented in Figure 7. To assess the accuracy of the linear mixing rule, the calculated and experimental Cc values at 1% concentration are compared, i.e., the constants of the natural logarithm trendlines: 5.41, 4.50, 4.20, and 3.89. For both the 50/50 and 70/30 ratios, the error is less than 3.5%. Considering all the natural sources of error, e.g., mixing of surfactants and reading values by the operator and differences in commercial surfactant batches, we conclude that the linear mixing rule is an accurate and practical method at constant temperatures. The main takeaway from Figure 7 is that for mixtures of ethoxylated surfactants with similar chemistry, the C c i must be the Cc of that individual surfactant at the combined surfactant concentration.

Figure 7:

The Cc curves of commercial C₁₀E₇, C₁₀E₄, and two mixtures at 50/50 mol% and 70/30 mol%. The markers at 1% surfactant concentration are not derived experimentally but are added for visual representation based on the trendline equation.

3.7 The effect of water to oil ratio on the characteristic curvature of commercial surfactants

In numerous real-world applications, surfactant mixtures are diluted in water to achieve results [61], [62], [63]. Salager et al. [56] demonstrated the impact of dilution on the hydrophilicity of surfactants. As the water-to-oil ratio (WOR) increases, the more hydrophilic fractions of the surfactant partition into the water phase. Thus the fractions participating at the interface are more lipophilic. Shinoda et al. [64] determined the phase inversion temperature of a 5% nonionic surfactant (NPE9.7) system and demonstrated that the PIT decreases with increasing WOR. This implies that the surfactant becomes more lipophilic upon dilution. Figure 8 is a re-creation of the data from [30, 64]. This demonstrates the significant impact of WOR on the Cc of ethoxylated surfactants. There is a striking similarity between the effect of WOR in Figure 8 and the effect of surfactant concentration in Figure 4. This is not surprising since the effect of dilution is predominantly a concentration-dependent phenomenon in its nature.

Figure 8:

The change in Cc of commercial NPE9.7 surfactant as a function of WOR (weight ratios) at 5% constant surfactant concentration. Data points obtained from [30, 64].

The surfactant fraction that participates at the oil-water interface becomes increasing lipophilic with the increase in WOR as the surfactant concentration remains constant in the SOW system. However, to mitigate this problem, Acosta and Natali [50] introduced the idea that the oil-equivalent concentration is the most relevant parameter for surfactant characterization.

Figure 9 demonstrates the Cc of C₁₃E₆ as a function of WOR (bottom x-axis) and surfactant concentration in the SOW system (top x-axis). The trendline for the concentration-effect is y = 1.13 · ln(x) − 3.29 while that of WOR is y = 0.08·ln(x) − 0.39. This suggests that by considering the oil-equivalent concentration of a surfactant, the hydrophilicity (Cc) will remain mostly constant upon dilution. This has considerable advantages for designing water-free products, such as emulsifiable concentrate (EC) formulations in the agrochemical industry. It is important to mention that dilution due to changing the water to oil ratio is not necessarily the same phenomenon as spontaneous emulsification, where the surfactant-rich oil phase is poured into the aqueous phase to create emulsions (or nano/microemulsions) spontaneously.

Figure 9:

The Cc curves of C₁₃E₆ as a function of surfactant concentration in the oil phase (blue circles) and change in WOR at a constant 15% concentration in the oil phase (orange squares).

To put in perspective the concentration and dilution behavior of nonionic ethoxylated surfactants, the Cc of the anionic surfactant, sodium dihexyl sulfosuccinate (SDHS), was measured at different concentrations and WORs. The concentration equation of SDHS at WOR = 1 was measured to be Cc = −0.026 · ln(x) − 0.92 and presented in the top x-axis in Figure 10. The negative slope indicates that, contrary to ethoxylated nonionic surfactants, anionic surfactants become more hydrophilic as concentration increases. However, the magnitude of this effect is negligible compared to alkyl ethoxylates. In addition, the bottom x-axis in Figure 10 represents the effect of WOR on the Cc of SDHS at 30% concentration. The results reveal Cc = 0.0962·ln(WOR) − 1.053 while considering the equivalent salinity resulting from the anionic surfactant’s dissolution in water. These findings are aligned with the literature on the dilution behavior of anionic and nonionic surfactants [56]. Overall, the HLD framework can act as a tool for understanding surfactants’ concentration and dilution behavior, including alcohol ethoxylates and anionics. This provides a mathematical approach based on scientific theory to select and replace adjuvants and move towards a biobased surfactant space in the agrochemical industry.

Figure 10:

The Cc values of SDHS as a function of surfactant concentration in the oil phase (blue triangles) and change in WOR at a constant 30% concentration in the oil phase (orange squares).

4 Conclusions

In this work, a practical methodology to calculate the characteristic curvature (Cc) of technical grade alcohol ethoxylate surfactants is presented. The Cc of alcohol ethoxylates as a function of concentration follows a natural logarithmic function, which means they become increasingly lipophilic with increasing concentration. The slope of the Cc function corresponds to the change in the partitioning of the oligomers in the excess oil phase and the microemulsion middle phase. A model for calculating the Cc curve of nonionic surfactants was proposed by performing a simple phase scan. The slope of the Cc curve was determined by performing a phase scan at a reference concentration. Subsequently, the slope and the curve at a reference concentration are used to calculate the Cc curve. In addition, the Cc values obtained with this model are compared with those predicted with a group contribution model for pure alkyl ethoxylates. The concentration at which the Cc of the commercial surfactant is equivalent to that of the pure form is determined. This gives a valuable insight into the partitioning behavior of commercial surfactants.

The linear mixing rule was used to determine the Cc of two mixtures of ethoxylated surfactants and proved to be an accurate method with a deviation of less than 3.5% from the experimental results. The Cc values of mixtures of surfactants with similar chemistry demonstrate that the combined surfactant concentration must be considered when the Cc value of a surfactant is included in the linear mixing rule. Finally, the effect of WOR on a commercial C₁₃E₆ surfactant was quantified as Cc = 0.08·ln(WOR) − 0.39, showing that WOR has a negligible effect on the change in Cc. Based on concentration and dilution experiments, the relevance of oil-equivalent concentrations of surfactants was confirmed.

Corresponding author: Amir Ghayour, Syngenta, Honeywood Research Facility, Plattsville, Ontario, N0J 1S0, Canada, E-mail: amir.ghayour@syngenta.com

About the author

Amir Ghayour

Amir Ghayour received his B.Sc. in chemical engineering from Shiraz University (Iran) in 2013, and his M.A.Sc. in chemical engineering from the University of Toronto in 2019. He is currently a Formulation and Application Technology Lead at Syngenta in Canada. He has expertise in surfactant and polar oil characterization for agrochemical applications. He is interested in formulation engineering, colloids, emulsions, and interfacial science.

Acknowledgments

The author is grateful for the support of colleagues and the management at Syngenta and BASF.

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2022-06-09

Revised: 2022-09-12

Accepted: 2022-09-14

Published Online: 2022-12-15

Published in Print: 2023-01-27

Articles in the same Issue

https://doi.org/10.1515/tsd-2022-2464

Keywords for this article

characteristic curvature; dilution; ethoxylated nonionic surfactants; HLD; microemulsions