# On the Characteristic Curvature of Alkyl-Polypropylene Oxide Sulfate Extended Surfactants

## Authors

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- Accepted:

DOI: 10.1007/s11743-011-1303-2

- Cite this article as:
- Hammond, C.E. & Acosta, E.J. J Surfact Deterg (2012) 15: 157. doi:10.1007/s11743-011-1303-2

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## Abstract

The hydrophobicity of alkyl-polypropylene oxide sulfate surfactants was evaluated via their characteristic curvature (Cc) using the hydrophilic-lipophilic difference (HLD) framework. A close examination of the relationship between the molecular structure of the surfactants considered (structure of the alkyl group and the number of propylene oxide groups in each surfactant) and their Cc led to a group contribution model that, for the first time, takes into consideration the geometry of the alkyl tail group. Based on this group contribution model, branching at the C2 (beta-carbon) position of the alkyl group produces the largest increase in characteristic curvature. This observation is consistent with the notion that the Cc is associated with the packing factor for anionic surfactants. Branching at the C2 position tends to produce cylindrical or inverse cone shape packing, typical of more hydrophobic (positive Cc) surfactants. This study also confirms previous observations that, different from conventional anionic surfactants, the phase behavior of alkyl polypropylene oxide sulfates is less sensitive to electrolyte concentration and that these formulations turn hydrophobic with increasing temperature, akin to the behavior of nonionic surfactants.

### Keywords

MicroemulsionCharacteristic curvaturePhase behaviorHLDOptimal salinitySolubilizationInterfacial tension## Introduction

Branched alcohol-polypropylene oxide (PPO) sulfates, are known to be effective at emulsifying heavy oils and can be used to improve the recovery of oil from otherwise under producing wells [1–9]. These surfactants, along with other surfactants containing intermediate PPO groups in between the alkyl group and the hydrophilic head group, are typically identified as “extended” surfactants. The term extended surfactants refers to the fact that the propylene oxide group introduces a gradual transition between the lipophilic alkyl group and the hydrophilic group, thus “extending” the reach of these groups into the oil and aqueous phases [10]. Extended surfactant chemistries are diverse and include alkyl-PPO—polyethylene oxide (PEO)-sulfate, carboxylates and carbohydrate head groups [11–18].

In order to take advantage of the improved solubilization capacity of extended surfactants, it is necessary to find the appropriate match between the molecular structure of the surfactant and the set of required formulation conditions. These formulation conditions involve the oil of interest, the temperature of the system, the background electrolyte (including electrolyte type and concentration) and the presence of oil-soluble or water-soluble co-solvents or co-surfactants. To this end, the groups of Sabatini and Salager published two systematic studies that characterized the hydrophilic-lipophilic nature of selected extended surfactants using the hydrophilic-lipophilic difference (HLD) framework [19, 20]. While these studies confirmed that the HLD framework can be used to characterize extended surfactants, the limited set of extended surfactants considered prevent a detailed comparison between molecular structure and surfactant hydrophilic-lipophilic nature. The purpose of this study is to close that gap and introduce elements of group contribution theory to estimate the hydrophilic-lipophilic nature of extended surfactants based on their molecular structure.

The HLD is not the only framework to characterize the hydrophilic-lipophilic nature of surfactants. One of the earliest approaches was Bancroft’s rule. Bancroft’s rule states that the phase (oil or water) in which the surfactant is soluble is the continuous phase of the resulting emulsion [21, 22]. Therefore, by identifying the type of emulsion formed with a given oil, this could be used as the basis to categorize the hydrophobicity of the surfactant. Griffin’s hydrophilic lipophilic balance (HLB) built on the ideas of Bancroft and established an arbitrary scale of surfactant and oil hydrophobicity based on the stability of oil and water emulsions [23]. The initial HLB emulsification experiments that led to the HLB scale were performed at room temperature (RT), using water with low electrolyte concentration. The arbitrary 1–40 scale is still in use by formulators as a rule of thumb for guiding the formulation of emulsions. For example, surfactants with HLB values between 3 and 6 (hydrophobic surfactants) are considered good water-in-oil emulsifiers, and HLB values between 10 and 15 are considered oil-in-water emulsifiers. There are several problems with HLB. One of them is the fact that the HLB scale is not based on equilibrium conditions (thus it is difficult to draw thermodynamic relationships), and the second problem is that the scale does not consider the formulation conditions. Perhaps the reason that the HLB method remains a popular choice among formulators is the fact that Davies introduced a group contribution method that can be used to estimate the value of the HLB based on the molecular structure of the surfactant [24].

Shinoda used phase diagrams, extending Winsor’s microemulsion work [25] and developed the Phase Inversion Temperature (PIT) concept [26] for non-ionic alcohol ethoxylate surfactants. The cloud point of alcohol ethoxylates is an offset of the PIT [27]. The PIT is analogous to the optimum salinity and the formation of the Winsor III phase consisting of three phases; oil, bicontinuous (microemulsion) and water. In other cases, the PIT is reported as an interval where the microemulsion changes from oil-in-water (Winsor I) to water-in oil (Winsor II). One advantage of the PIT over HLB is that PIT is based on equilibrium (microemulsion) phase behavior and not emulsion stability. The PIT is an empowering concept, as this parameter can be used to predict some elements of the phase behavior of emulsions and microemulsions [28, 29]. Davis compared all these methods and the empirical formulation correlations of Bourrel and Salager that led to the HLD concept [30–32]. These semi-empirical correlations have been refined into what is now referred to as the hydrophilic-lipophilic deviation (HLD) concept [33–35].

Another method of characterizing the hydrophobicity of a surfactant is determining its packing parameter which is equal to the volume of the hydrophobe (*V*) divided by the product of the effective area of the surfactant (*a*) at the interface times the length of the surfactant tail (*L*), or *V*/(*a* * *L*) [36]. This method is particularly suitable in understanding liquid crystal phase behavior, but it does not consider the changes in area of the surfactant or the solvated volume of the hydrophobe with changes in formulation conditions. Kunz et al. [37] compared the packing parameter, HLD and PIT concept, and found a correlation among the three frameworks. One added benefit of the HLD framework is that it can be combined with the net-average curvature (NAC) model to predict the solubilization capacity, phase volume, phase transition, interfacial tension and viscosity of microemulsion systems [38–40].

The NAC model was originally introduced as a statistical description of the curvature of microemulsion assemblies (oil-swollen micelles, water-swollen reverse micelles, and bicontinuous systems) [38]. Later, via neutron scattering studies, it was determined that the average curvature term represents the surface area to volume ratio of the microemulsion assemblies [41], and that the net curvature represents the area-averaged curvature of the microemulsion assembly [40]. In the NAC model, the net curvature scales to the ratio between the HLD of the formulation divided by the length of the surfactant tail [38].

*S*(g/100 mL) is the electrolyte concentration,

*b*is a constant (for NaCl is 0.13 and 0.1 for CaCl

_{2}),

*k*is a constant characteristic of the type of hydrophilic group of the surfactant and the type of electrolyte (0.1–0.2 in most cases), EACN is the equivalent alkane carbon number for the oil (e.g. EACN of hexane = 6),

*Φ*(

*A*) and

*f*(

*A*) represent the influence of cosurfactant or cosolvent,

*c*

_{t}and

*α*

_{t}are temperature coefficients and

*T*(°C) is the temperature of the system. The curvature interpretation of the HLD equation led to the re-interpretation of the original sigma (surfactant) parameter in the HLD equation as the characteristic curvature parameters for nonionic (Cc

_{n}) and ionic surfactants (Cc

_{i}) [34]. The characteristic curvature represents the net curvature, normalized by the surfactant tail length, of a microemulsion assembly produced by the surfactant under a set of reference conditions, namely

*S*= 1 g NaCl/100 mL, EACN = 0 (e.g., benzene), at 25 °C, and no alcohol or cosurfactant. The characteristic curvature for ionic surfactant has been found to correlate with the packing factor for those surfactants, and the curvature for nonionics correlates with the HLB for those surfactants.

In addition to the curvature interpretation, a second interpretation of the HLD is that it depicts the change in free energy associated with transferring a surfactant molecule from the oil phase to the aqueous phase normalized by the thermal energy (*R* × *T*) [33]. In both cases, negative values of HLD mean the formulation will tend to produce oil-in-water microemulsions. Near zero values of HLD will produce systems bicontinuous in oil and water. Optimal formulations are bicontinuous and contain the same volumes of oil and water. Here the net curvature is zero and HLD = 0 [31–33, 38]. The values of Cc_{n} or Cc_{i} (or σ in earlier forms of the HLD and surfactant affinity difference–SAD-equation) represent the relative hydrophilic-lipophilic nature of the surfactant when it adsorbs at the oil–water interface. Positive values of Cc (e.g. Aerosol-OT Cc_{i} = +2.5) are characteristic of lipophilic surfactants that tend to form water-in-oil microemulsions. Negative values of Cc (e.g. sodium dodecyl sulfate Cc_{i} = −2.5) are characteristic of hydrophilic surfactants. It is important, however, clarify that the qualifications of hydrophilicity and lipophilicity, in this work, correspond to the tendency of the surfactant to form micelles or reverse micelles, respectively. There are other ways to qualify the relative hydrophilicity of a surfactant such as its critical micelle concentration, Krafft temperature, etc.

There have been some elements of group contribution methods to calculate the values of Cc. For example, for ethoxylated alcohols Cc_{n} = α-EON, where α is a function of the length and structure of the alkyl group and EON is the number of ethylene oxide groups of the surfactant [42, 43]. Similarly, there are group contribution equations to estimate Cc_{i} (σ) [34, 42]. Unfortunately, just like the HLB group contribution of Davies, the equations for Cc_{i} do not consider the geometry of the alkyl group. In this article this gap is addressed using alkyl-polypropylene oxide sulfate (extended) surfactants.

## Materials and Methods

### Materials

Nanopure, 18 micro-Ohm/cm, deionized (DI) water was used for all dilutions and to rinse the lab. glassware. The aqueous solution of sodium chloride (26 wt.%) was purchased from Fluka and used as received. Dodecane (>99+%), and tetradecane (>99+%) were purchased from Sigma–Aldrich (St. Louis, MO) and used as received.

^{®}Alcohol) is produced by hydroformylation of an olefin. Br-Oxo (ISALCHEM

^{®}Alcohol) indicates the alcohol is the branched isomeric fraction separated from Oxo alcohol (LIAL

^{®}Alcohol). L-Oxo (ALCHEM

^{®}Alcohol is the linear fraction separated from Oxo alcohol (LIAL

^{®}Alcohol). FT-Oxo (SAFOL

^{®}Alcohol) is alcohol derived from the oxo process from a Fischer–Tropsch olefin feed. TDA (MARLIPAL

^{®}O13 Alcohol) is produced from an Oxo process with a butylene trimer. Ziegler (ALFOL

^{®}Alcohol) is linear alcohol made from oligomerization of ethylene.

Alcohol and alcohol propoxylate data

Base alcohol | Abbreviation | Alc. MW | Calc. Alkyl C# | Est. Ave. C length | C2–Br per –OH | Mid-Br per –OH | PON (NMR) |
---|---|---|---|---|---|---|---|

ISALCHEM | Br-Oxo 123 | 194.34 | 12.51 | 10.09 | 0.906 | – | 3.96 |

MARLIPAL | TDA | 201.41 | 12.90 | 10.49 | 0.560 | 1.88 | 4.01 |

LIAL | Oxo 123 | 194.58 | 12.55 | 11.03 | 0.569 | – | 3.89 |

SAFOL | FT-Oxo 23 | 192.41 | 12.40 | 11.79 | 0.050 | 0.50 | 4.08 |

ALFOL | Ziegler 12 | 186.34 | 12.00 | 11.94 | 0.030 | – | 3.91 |

ALCHEM | L-Oxo 123 | 194.88 | 12.61 | 12.46 | 0.034 | – | 3.78 |

The fourth column in Table 1 represents the number of carbons in the base alcohol from the hydroxyl number value. The fifth column represents the estimated length (in number of carbons) of the alkyl group compiled from composite data from several techniques and represents a best guess value. The sixth column represents the best guess value of the number of carbons next to the alcohol group (also known as C_{2} or β-carbons). The seventh column indicates the number of branched carbons that are not located in the C2 position. The last column represents the average number of propylene oxide groups in the alcohol propoxylate as determined by proton NMR taking into the account the methyl branching in the starting alcohol.

_{3}to hydroxyl (–OH). The resulting acid was neutralized with NaOH. No addition treatments were conducted. The compositional data for the alcohols was based on “typical” data. Table 2 summarizes the activity of the samples provided as well as the free oil and free salt composition and molecular weight.

Alcohol propoxylate sodium sulfate data

Alcohol–4P Na sulfate | Active % | Oil % | Na | MW |
---|---|---|---|---|

Br-Oxo 123 | 27.7 | 0.80 | 0.1 | 534 |

TDA | 29.2 | 0.80 | 0.09 | 537 |

Oxo 123 | 28.1 | 0.48 | 0.1 | 527 |

FT-Oxo 23 | 27.5 | 1.93 | 0.09 | 532 |

Ziegler 12 | 29.1 | 0.37 | 0.13 | 516 |

L-Oxo123 | 27.3 | 0.47 | 0.11 | 519 |

### Methods

Standard solutions of surfactants were prepared and brought to pH > 10 using two drops 50% NaOH. The pH 10 condition was used to simulate conditions compatible with enhanced oil recovery applications. Pipettes with flame-sealed tips were used. The standard solutions, surfactant, saline, DI water and oil were metered into pipettes. Surfactants were dosed at a concentration of ~1.5 wt.% in the aqueous phase. The total volume of the aqueous phase (including the surfactant) was 2.5 mL. The total volume of the oil phase (dodecane or tetradecane) in each vial was 2.5 mL.

## Results and Discussion

*S**) as described above. The method of using solubilization curves to determine

*S** provides a reasonable interpolation between experimental points (vials) that are close to the optimal salinity.

*S**)] as a function of temperature for microemulsions formulated with the extended surfactants of Table 2 and dodecane. Figure 4 presents the same information for microemulsions prepared with tetradecane. In both Figures the term ln(

*S**) increases linearly with temperature. To understand this trend it is important to keep in mind the HLD equation for ionic surfactants (Eq. 2). At optimal formulation conditions HLD = 0, and therefore:

For each surfactant Cc_{i} is constant, and the values of EACN are constant in each Figure (Fig. 3 EACN = 12; Fig. 4 EACN = 14). As predicted by Eq. 3 the relationship between ln(*S**) and temperature (*T*) is linear, and the slope of the linear trend line represents the value of α_{t} for each surfactant. The values of the slopes are similar which is consistent with the tendency to assume that the value of α_{t} is constant and the same for a given surfactant family [42]. The single value of α_{t} obtained for the C12–4PO–SO_{4}Na family is *α*_{t} = −0.0059 ± 0.0012 (standard deviation).

Another important observation regarding Figs. 3 and 4 is that, for a given temperature, the value of ln(*S**) is highly dependent on the surfactant. This is also predicted by Eq. 3, and according to that equation, other variables being equal, larger values of ln(*S**) correspond to more negative values of Cc_{i} (i.e. more hydrophilic surfactants). This is an interesting fact because all the surfactants considered have, nominally, the same C12–4PO–SO_{4}Na structure and the main difference among them is the geometrical configuration of the alkyl group.

*S**) for a given surfactant at a given temperature obtained with dodecane (Fig. 3) and the value of ln(

*S**) obtained with tetradecane (Fig. 4), one confirms the prediction of Eq. 3 that higher EACN values produce larger ln(

*S**) values. Furthermore, one can use these values of ln(

*S**) for a given surfactant and temperature to estimate

*k*:

*k*calculated using this equation are presented in Fig. 5 for each surfactant and temperature. As shown in Fig. 5, the value of

*k*ranges from 0.04 to 0.06 and slightly decreases with increasing temperature. In the HLD correlation (Eq. 2) the value of

*k*is independent of temperature, but it depends on the type of surfactant used [42, 43]. Figure 5 shows that there are no clear differences in the

*k*values among the surfactants evaluated, suggesting that for this family of C12–4PO–SO

_{4}Na surfactants it is appropriate to assume that they can be represented by a single

*k*value (

*k*= 0.049 ± 0.009 [standard deviation]) estimated from all the values presented in Fig. 5.

In general, little data has been published on the values of α_{t} and *k* for extended surfactants. Velasquez et al. [19] have reported *α*_{t} values for extended surfactants ranging from −0.008 to −0.012 °C^{−1}. Those values are slightly larger than the average “*α*_{t}” = −0.0059 °C^{−1} reported here.

Witthayapanyanon et al. reported a value of *k* = 0.053 for Br-Oxo 145-8PO–SO_{4}Na [3], which is in good agreement with the average *k* value of 0.049 determined in this study. Witthayapanyanon et al. also reported a slightly higher *k* = 0.087 for C12–8PO–SO_{4}Na [3]. It is uncertain if *k* is affected by the number of PO groups in the propoxylate. There are reports that *k* values are influenced by the number of PO groups [10] and other reports that suggest that there is no influence [19]. Velasquez et al. [19] reported higher *k* values, in the order of 0.12. Similar values have been reported by Phan et al. [44] for Br-Oxo 145-8P Na Sulfate. Witthayapanyanon et al. [20] also reported *k* = 0.069 for a C12–14PO–2EO–SO_{4}Na surfactant. For the rest of this work the average values of α_{t} and *k* reported earlier will be used in determining the Cc_{i} values for extended surfactants.

*S**), EACN,

*T*, and the calculated values of

*α*

_{t}and

*k*, the Cc

_{i}for each surfactant can be calculated using Eq. 3. These calculated values of Cc

_{i}are summarized in Fig. 6 as a function of temperature for systems formulated with dodecane (Fig. 6a) and systems formulated with tetradecane (Fig. 6b). The values of Cc

_{i}should not be a function of the oil or temperature [34, 42, 43]. Indeed, the values of Cc

_{i}are characteristic for each surfactant and vary very little with temperature or the EACN of the oil.

_{i}values with the molecular structure of the alkyl group, a group contribution model was introduced, similar to that proposed by Salager et al. [42, 43] but specifying the number of carbons that are linked to the linear chain (C

_{L}), to the mid-chain carbons (C

_{MB}) and the carbons attached to the β position (C

_{β}) as indicated in Table 1. Therefore:

_{4}Na group. Given that there are six values of Cc

_{i}and only four constants, the systems of equations is over-constrained and requires an optimization routine to find the best fit of constants that will give produce the lowest possible error. To this end, the error function was defined: ΣCc

_{i}−C1 × C

_{L}+ C2 × C

_{MB}+ C3 × C

_{β}+ C4. The values of the constants that produce the minimal value of the of the error function were obtained using the Solver package of Microsoft Excel 2007. An additional set of constrains were introduced to guide to solution, namely C1 > 0, C2 > 0, C3 > 0 and C4 < 0 as C1 through C3 represent “lipophilic” contributions to Cc

_{i}and C4 represents the hydrophilic contribution. The values of these constants are summarized in Table 3.

Group contribution factors for Cc_{i}

Cc | Group |
---|---|

0.100 | C in alkyl chain length |

0.071 | Mid-chain branch |

0.690 | C2 branch |

−3.181 | 4PO + SO |

0.158 | –PO– group |

−3.813 | –SO |

_{4}Na surfactants and tetradecane as the oil phase. The optimal electrolyte concentration (expressed as ln(

*S**)), and the calculated values of of α

_{T}and

*k*reported above were introduced in Eq. 3 to calculate the values of Cc

_{i}for these surfactants. Figure 7 presents the Cc

_{i}values as function of the number of propylene oxide groups in the molecule. According to Fig. 7, each additional PO group increases the value of Cc

_{i}by 0.158 units. Using this fact, Table 3 also includes the PO and sulfate contributions to C4 and to the overall Cc

_{i}calculation.

Care must be taken in working with large number of moles of PO due to the potential of byproduct formation [45]. Any allyl PPG or PPG made in the reaction will effect the hydroxyl number and NMR analysis giving an inaccurate account of the systems composition. It is also noted that the EO addition to a secondary alcohol (alcohol–POx) does not give the same ethoxymer distribution as EO added to a primary alcohol.

_{i}values calculated from experimental values and the values calculated using the group contribution factors presented in Table 3. Overall, the difference between the experimental and group contribution values is small (less than 3% in most cases). However, this small difference is expected because the experimental values were used to fit the contribution factors. Unfortunately, it is difficult to compare to other Cc

_{i}values in the literature because the molecular structure of the alkyl group of the surfactants used is not clear. It is however, known that the Cc

_{i}for sodium dodecyl sulfate ranges from −2.3 to −2.5 [34]. Using the group contributions of Table 3, a value of Cc

_{i}of −2.61 is estimated, which is close to the reported value.

Calculated characteristic curvature (Cc_{i}) based on PO content and group contributions using the NMR PO content compared to the experimentally derived values

Alcohol–4P Na sulfate | NMR PON | Cc | Cc |
---|---|---|---|

Br-Oxo 123 | 3.96 | −1.53 | −1.55 |

TDA | 4.01 | −1.61 | −1.61 |

Oxo 123 | 3.89 | −1.70 | −1.75 |

FT-Oxo 23 | 4.08 | −1.92 | −1.93 |

Ziegler 12 | 3.91 | −1.98 | −1.96 |

L-Oxo123 | 3.78 | −1.93 | −1.95 |

Salager and collaborators introduced methods of estimating σ values (i.e. Cc_{i} values) using group contribution theory, that for sodium alkyl sulfate surfactants become: Cc_{i} = 2.25 *k* × C_{alkyl} −55 *k* [42, 43]. In that correlation, *k* is the same constant that precedes EACN in Eq. 3 and C_{alkyl} is the number of carbons in the alkyl group of the surfactant, regardless of their position in the chain. Considering the value of *k* = 0.049, then the contribution of each carbon in the alkyl group is 0.11, which is close to the value reported for the linear carbon contribution in Table 3. The hydrophilic contribution of the sulfate group to the Cc_{i} (−55 *k* = −2.7) in the correlation of Salager and collaborators is smaller than that reported in Table 3. However, the values are close enough to further support the use of group contribution theory to estimate the values of Cc_{i}.

The biggest contrast between the group contribution factors of Salager and collaborators and those presented in Table 3 is the introduction of a different contributing factor for the number of carbons in the C2 branching position. The contribution of these carbons is approximately 0.7, which means that the addition of one carbon in the C2 position is equivalent to adding 7 carbons in the linear chain (each contributing 0.1 units to Cc_{i}). To our knowledge there has been no previous study reporting this effect, however it helps explain the big contrast between the hydrophilic nature of sodium dihexyl sulfosuccinate (Cc_{i} = −0.9) and the hydrophobicity of sodium bis(2-ethylhexyl) sulfosuccinate (Cc_{i} = +2.5) [34]. In this case, the only difference between these two surfactants is the presence of four carbons in the C2-branching position, and they are responsible for the significant shift in +3.4 units of Cc_{i}, which means a contribution of +0.85 units per carbon in the C2-branching position. This magnitude is close to the value of 0.7 observed in this work for the C12–4PO–SO_{4}Na surfactants.

_{i}could be linked to the relation between Cc

_{i}and the packing factor of the surfactant [34]. When the geometry of the molecule favors the inverse cone shape, the surfactant tends to form reverse micelles, corresponding to a positive contribution to Cc

_{i}. The presence of the C2-branching, as illustrated in Fig. 8, tends to produce this reverse cone shape that leads to more hydrophobic surfactants. It might also be expected that mid-chain branching, albeit having a lesser effect, should contribute more than linear carbons to the Cc

_{i}value. However, due to the increased level of disorder in the alkyl chain away from the headgroup [46], one could predict that the packing of these mid-branching groups is equivalent to that of a linear alkyl group with a certain degree of coiling in the disordered chain as is depicted in Fig. 8. This interpretation is consistent with the fact that the contribution to Cc

_{i}of linear and mid-branching carbons in Table 3 is approximately the same.

## Summary and Significance

The primary reason that the HLB has been the parameter of choice to characterize the hydrophilic-lipophilic nature of surfactant is that it can be readily calculated from the molecular structure. The introduction of the HLD framework has introduced a more quantitative method to characterize the hydrophobicity of the formulation, and the hydrophobicity of the surfactant itself via the characteristic curvature. In this work we introduced a group contribution model to calculate the Cc_{i} of extended surfactants that is consistent with literature data and with an earlier group contribution model introduced for other types of surfactants. However, in that previous model there was no consideration for the geometry of the alkyl group. In this work we determined that C2 branching (i.e. branching at the β-carbon) substantially improves the hydrophobicity of the surfactants, thus producing substantial positive shifts in Cc_{i} values.

Using group contribution methods, a formulator can determine the best surfactant for a given set of formulation conditions for surfactant–oil–water systems. Using Eq. 3, for example, and the conditions of the formulation (EACN of the oil of interest, and the electrolyte concentration and the temperature of the system) it is possible to define the required Cc_{i}. Using the group contribution method one can “design” the surfactant of interest (number of PO groups, number of carbons in the alkyl group, and number of carbons in the C2 position), or alternatively, the formulator can test if off-the-shelve surfactants with known molecular structure approach the desired Cc_{i}. The Cc_{i} and the HLD framework in combination with the net-average curvature (NAC) model can also be used to predict some of the properties of the formulation such as interfacial tension, solubilization, phase transitions, drop size and viscosity.

## Acknowledgments

The authors thank Geoff Russell for sulfating the materials, Nomihla Valashiya-Mdleleni for assistance with the phase boundary studies and Herbert Perkins and Nunzio Andriollo for analytical data.