# How to Use the Normalized Hydrophilic-Lipophilic Deviation (HLDN) Concept for the Formulation of Equilibrated and Emulsified Surfactant-Oil-Water Systems for Cosmetics and Pharmaceutical Products

^{*}

## Abstract

**:**

_{N}) equation with a surfactant contribution parameter (SCP), to handle more exactly the effects of formulation variables on the phase behavior and the micro/macroemulsion properties.

## 1. Introduction

_{3}methyl or a simple -OH hydroxyl added somewhere in the molecule) could make it behave very differently.

## 2. The Phenomena and Involved Variables in Equilibrated and Emulsified Surfactant-Oil-Water Systems

#### 2.1. Principal Phenomena

- Phase behavior in one solvent fluid, i.e., the complete or partial solubility, in particular the concept of cloud point for nonionic surfactants in water that indicates the importance of temperature in the case of polyethoxylated species.
- Surfactant molecules’ self-association in a solvent fluid, e.g., the formation of micelles or other aggregates, either in aqueous or oily phases.
- The association structure of surfactants with two immiscible fluids, e.g., oil and water, as in an adsorbed single interface layer, or more complex arrangements like microemulsions, liquid crystals, vesicles, liposomes, etc.

#### 2.2. Particularly Important Properties in Some Applications

- Phase behavior, i.e., the occurrence of 1, 2 or 3 phases in a surfactant-oil-water (SOW) ternary or in a quaternary system when a second surfactant or a so-called cosurfactant, such as an alcohol, is added.
- The surface or interfacial tension at the fluid/fluid limit (e.g., air/water or oil/water) that varies with the nature of the ingredients, and their contents.
- Adsorption of amphiphilic substances, i.e., their location at interface, and its consequences as far as the wettability is concerned.
- Interfacial effects concerning dispersions with a high surface area, particularly the stability of emulsions, foams, and solid particle suspensions.

## 3. One-Dimensional Scan with Typical Formulation Variables

_{HH}and A

_{LL}in Figure 2. As could be seen in a detailed analysis [45] and in a very complete review book [32], this addition could become very complex to analyze, and it is not necessary for the purpose of the present review. Consequently, it is believed that the simplified original R relation or its R’ alternative are sufficient to easily discuss the basic formulation issues in the following text. What will be used further on is an essentially similar generalized formulation criterion, the so-called hydrophilic-lipophilic deviation (HLD), which is no more than the difference between the numerator and denominator of R, i.e.,

^{2}, thus faster than Aco when ACN increases. Consequently, the R numerator (Aco − Aoo) will increase or decrease depending on the ACN value. It is in general found that if ACN is large enough (as with liquid alkanes, i.e., if ACN > 5) the negative term Aoo will dominate Aco, and thus R and HLD will decrease [32].

_{opt}= 11) takes place when the minimum concentration of surfactant Cs* happens.

_{om}and γ

_{wm}, where m is the microemulsion middle phase. Optimum formulation, SP*, which happens at the crossing of these two SP curves in Figure 3, indicates the equal solubilization of oil and water in the microemulsion middle phase.

^{2}= 0.30 ± 0.05 mN/m.

_{10}γ

_{min}where γ

_{min}is the minimum interfacial tension in a scan, has been recently introduced and is precisely related to the different variables for a very simple system [60].

_{N}term with N for “new” or “normalized” surfactant parameter to match with the HLD

_{N}generalized expression proposed later to eliminate some confusion.

## 4. Multidimensional Scans and Optimum Formulation Events

_{i}= K

_{ij}dV

_{j}

_{i}and a K

_{ij}before dV

_{j}, as in Equation (4), the relation can be written in a more general way for any ij pair of two formulation variables V

_{i}and V

_{j}with two coefficients, i.e., with one coefficient characteristic of each variable as in Equation (5). It is worth noting that Equations (5) and (6) can be multiplied by any coefficient, without any change. In other words, one of the two coefficients can be arbitrarily taken as unity or as any other appropriate value.

_{i}dV

_{i}= K

_{j}dV

_{j}or K

_{i}dV

_{i}− K

_{j}dV

_{j}= 0

_{i}are constant coefficients in Equation (6):

_{i}dV

_{i}

_{i}V

_{i}+ CST

_{i}− V

_{i-ref}) with the corresponding modification of selection of the CST to make HLD = 0 when the variable values for an experimental optimum formulation are entered.

_{i}(V

_{i}− V

_{i-ref}) + CST

_{i-ref}. Some of them are obvious for most people as 0 °C or 25 °C for the temperature reference, or S = 0 (no salt) for nonionic systems. However, S = 1 wt% NaCl or another fixed value is required for ionic systems, since the surfactant is a salt (thus S = 0 is not possible to reach in practice), and also because there is a logarithmical salinity scale. For the oil, ACN

_{ref}= 8 (octane), would result in a reasonable reference, while ACN

_{ref}= 0, which is often used because it eliminates a term, is not a very significant selection, since it would mean that the reference alkane would be without any carbon atom, an unreal case. The use of ACN = 0 for benzene is not always an accurate assumption.

_{i}coefficients in Equations (7a) and (7b) can be used to divide the equation HLD = 0, so that the coefficient before a selected variable V

_{i}would become unity.

_{Lns}

_{LnS}= LnS − K

_{ACN}ACN + σ = 0

_{A}C

_{A}, with C

_{A}being the concentration in vol % and K

_{A}a negative coefficient whose absolute value increases with the alcohol lipophilicity. As a consequence, for butanol, pentanol, hexanol, etc., the alcohol term is positive. Then both surfactant and cosurfactant term, i.e., σ and −f(A), are positive and increase when they are more lipophilic. The f(A) variation is practically linear with concentration up to a variation of about one unit of LnS, i.e., up to 0.5% of pentanol and 0.3% of hexanol. Above it, part of the alcohol leaves the interface and goes to the oil phase and segregates close to interface, hence producing a decrease in K

_{A}. The sec-butanol has practically no effect (K

_{A}~ 0) and the n-butanol has a small negative effect (K

_{A}= −0.3 to −0.5) that varies with the surfactant and oil phase.

_{T}~ 0.010 ± 0.005 °C

^{−1}for anionics and about the double for cationics. The pressure effect reported only some time ago [90] has in most cases a very small K

_{p}coefficient value in HLD; it is thus generally negligible at ambient conditions.

_{LnS}= Ln(S/S

_{ref}) − K

_{ACN}(ACN-ACN

_{ref}) + σ − K

_{A}C

_{A}− K

_{T}(T-T

_{ref}) − K

_{p}(P-Pr

_{ef}) = 0

_{ref}= 1). Obviously, a log

_{10}S term or LnS with salinity expressed in mol/L of NaCl would give an appropriate similar relationship but with a different numerical value for σ. Additionally, it is now clear that σ also included the integration constant CST and the references for the other variables in Equation (8b), not only T

_{ref}and P

_{ref}, but also S

_{ref}(usually 1), ACN

_{ref}and C

_{Aref}(normally 0) and eventually σ

_{ref}(which is not really known and is arbitrarily taken as 0 to avoid a semantic confusion).

_{A}. Such a selection of the surfactant parameter σ is clearly confusing. This is why it has to be rectified.

_{ACN}coefficient in Equation (8a), as well as the other K’s in Equation (8b), was found to depend on the nature of the surfactant head group.

_{EON}= K

_{S}S − K

_{ACN}ACN − K

_{A}C

_{A}+ K

_{T}(T-T

_{ref}) − K

_{p}(P-P

_{ref}) + α − EON = 0

_{GN}= K

_{S}S − K

_{ACN}ACN − K

_{A}C

_{A}+ K

_{T}(T-T

_{ref}) − K

_{p}(P-P

_{ref}) + α − GN = 0

_{ACN}is still the coefficient of ACN but with a different meaning in Equations (8c) and (8d), i.e., ∂EON/∂ACN (respectively ∂GN/∂ACN) and a specific value of about 0.14–0.16 (respectively 0.10) for ethoxylated alcohols and alkylphenols (polyglycerol alcohols respectively).

_{ACN}has a completely different meaning in Equations (9a), (9b) and (9c) including a different sign for ionics and nonionics. It is therefore erroneous to say that it is the same, even if the absolute value more or less coincides for alkyl sulfonates (+0.16) and ethoxylated alcohols (about −0.15) as well as with carboxylates (+0.10) and polyglycerols nonionics (−0.10).

_{ACN-LnS}

_{ACN-EON}

_{ACN-GN}

_{PO}PON with a coefficient of 0.15. This means that the hydrophobicity added by a PO group in the tail is equivalent to adding half a -CH

_{2}- methylene group. In other words, the polypropylene intermediate group, that contains three carbon atoms, brings a hydrophobicity equivalent to only adding half a carbon in an alkyl group in the tail. This is why the size of an extended surfactant with the same parameter is considerably larger, with no problem of precipitation. It is also the reason why the extended surfactants provide a good solubilization, particularly with polar oils (like natural triglycerides), and why they are good candidates for cosmetics and pharmaceuticals [76,85,92,95,96,97,98,99,100,101,102,103,104,105,106,107].

_{EON}= 0 (8c) expression, β is the term that includes the nonionic surfactant contribution (β = α − EON) as well as the integration constant and the references. It was first introduced as a combination of two variables describing the surfactant structure. The EON is the (average) number of ethylene oxide groups in the surfactant head, that is the usually scanned in nonionic systems, so a K = −1 coefficient was taken for EON and thus K = 1 coefficient for β in Equation (8c). The term α indicates the contribution of the tail that is typically described as a linear alkyl group, increasing by about 0.33 units when a carbon atom is added in the tail. However, it also includes the integration constant [68].

_{LnS}or K

_{S}coefficient. Furthermore, it is not justified to put a unit coefficient in HLD equation in front of LnS or EON, which are completely different variables, as indicated in Equations (9a), (9b) and (9c). It is the same for the cases of scanning the intermediate propoxylation number, PON, for extended surfactants or for the glycerol number, GN, in alkyl acid ester surfactant. As for the negative (−1) coefficient in front of ACN (instead of +1) in equations 8a-b-c-d, it is arbitrary. What is justified is to have the same coefficient in front of ACN in all the cases of HLD equations, thus providing the same scale for all the effects.

_{N}with a (−1) coefficient in front of ACN (i.e., equivalent to HLD

_{ACN}in the previous notation) would make it possible to handle a combination of two or more equations when the surfactants are mixed, particularly when they are ionic and nonionic species.

_{ACN}, thus becoming the “normalized” HLD

_{N}, in which the surfactant contributing parameter SCP is also taken with a (+1) coefficient by definition.

_{ACN}or β/K

_{ACN}for appropriate reasons [69], although these were not specifically justified. At that time, it was not stated either that this parameter was not really a critical value for the surfactant effect because it also included the integration constant and the references. To avoid any confusion, the old HLD relations should be divided by the corresponding experimental coefficient K

_{ACN}as in formula (10) to produce the generalized HLD

_{N}relationship (11) valid in all the cases, where the coefficients indicated as lowercase k’s have to be introduced according to the experimental data, and to the proper selected references.

_{N}= SCP − (ACN − ACN

_{ref}) + [LnS (or b S) − K

_{A}C

_{A}± K

_{T}(T-T

_{ref}) − K

_{p}(P-P

_{ref})]/K

_{ACN}= 0

_{ACN}

_{N}= SCP − (ACN − ACN

_{ref}) + k

_{LnS}LnS (or k

_{S}S) − k

_{A}C

_{A}± k

_{T}(T-T

_{ref}) − k

_{p}(P-P

_{ref}) = 0

_{ref}= 25 °C and P

_{ref}= 1 bar, while the salinity references are S = 0 for nonionics, or S = 1 for ionic amphiphiles (as well as S = 1 for a mixture of ionic and nonionic surfactants), and in most cases without alcohol (C

_{A}= 0). In the current Equation (11), the oil reference could be taken as ACN

_{ref}= 0, so that, with the previously selected references, the HLD

_{N}= 0 equation can be simply be written as the very simple expression SCP = (P)ACN.

_{N}equations

_{N}= 13.3 + 2.25 SAT − 6.67 EON − ACN + 0.33 (T-25) = 0

_{2}-) groups in its tail (2.25 × 3 = 6.75) or by removing 6.6 methylene groups (6.6) in the n-alkane.

^{.}by Acosta et al. [108], with no more explanation than a better feeling.

**C**haracteristi

**C**. This term is also wrong to use the word characteristic because it does not only depend on the surfactant, but also on the selected references for the other variables, and on the CST. Consequently, it is not a characteristic, as salinity is for brine, ACN for an n-alkane oil, and the temperature and pressure for the system conditions. Actually, the HLB defined by Griffin as one-fifth of the weight percentage of its head part could be a more logical surfactant characteristic, because it only depends on the surfactant. However, it is known to be inaccurate because it does not take into account the nature of the hydrophilic part, a fact that is critical for the surfactant behavior. Additionally, the use of curvature to characterize a surfactant could result in conceptual mistakes, when it is textually said that Cc < 0 or > 0 means that the surfactant is hydrophilic or lipophilic [82,99,110].

_{N}< 0 or vice versa.

_{S}is 0.13 ± 0.03 for wt% NaCl, but it is 0.10 for CaCl

_{2}and 0.09 for KCl), the Equation (11) becomes, with K

_{S}= 0.13:

_{EON}= β + 0.13 S − 0.15 ACN + 0.05 (T − 25) = 0

_{N}normalized according to ACN is:

_{N}= HLD

_{ACN}= 6.67 β + 0.87 S − ACN + 0.33 (T − 25) = 0

_{N}= 0, which could be written as

_{N}= PACN − ACN + 0.87 S + 0.33 (T − 25) = 0

_{N}= 0 plane in the three variables space (V1 = ACN, V2 = S and V3 = T-25) intercepts the ACN axis, i.e., S = 0 and T-25 = 0, at a V1* = value which is the surfactant preferred ACN with the three selected references, i.e., its PACN. If this value cannot correspond to a real alkane, it is thus an extrapolated value called EACN or a virtual equivalent that could be called EPACN too, a slightly simpler name than the historical EPACNUS.

_{ACN}.

_{ref}= 0. The characteristic parameter is then deduced from a reference in which there is no alcohol and at 1% NaCl salinity.

_{N}= SCP − (ACN − ACN

_{ref}) + k

_{LnS}Ln (S/1) − k

_{A}(C

_{A}-0) − k

_{T}(T − T

_{ref}) − k

_{p}(P − P

_{ref}) = 0

_{ACN}= 0.15. The HLD

_{N}expression is thus essentially the same with a positive sign for the temperature effect and a different salinity reference, which is S = 0. This is due to the fact that the logical reference with nonionics is no salt since it eliminates a variable, as is the case in many studies [111].

_{N}= SCP − (ACN − ACN

_{ref}) + k

_{S}(S-0) − k

_{A}(C

_{A}-0) + k

_{T}(T − T

_{ref}) − k

_{p}(P-P

_{ref}) = 0

_{0}+ 2.25 SAT

_{ACN}~ 0.15–0.16), approximately 0.5 additional carbon atoms in the tail (equal to a molecular weight increase of approximately six units) rises PACN by ±1 unit as noted in Equation (16).

_{N}for all surfactants allow to make the following comparisons that give an idea on what is more or less significant in changing the system formulation.

_{N}will approximately increase one unit, at everything else constant.

_{N}indicates that this increase in PACN by one unit can be compensated to keep the optimum with an alcohol ethoxylate system by an increase of one unit in the oil ACN, a decrease of ~0.5 carbon atom in the n-alkyl tail of the surfactant (SAT), a reduction of salinity by 1.2 wt% NaCl or a reduction of temperature by 3 °C.

_{A}C

_{A}with C

_{A}concentration in wt%, is positive but very small (K

_{A}~ +0.5) for ethanol and propanol, and it is almost zero for sec-butanol which is often used up to 3 wt% so as to avoid precipitation with anionic surfactants of high molecular weight as petroleum sulfonates. However, there is a significant negative effect on HLD

_{N}for lipophilic alcohols such as n-butanol, pentanols, hexanols, etc. The linearity effect is satisfied up to 2% for n-pentanol (k

_{A}= −7.5 + 0.5) and iso-pentanol (k

_{A}= −6.0 ± 0.5), and up to 0.5% for n-hexanol (k

_{A}= −15 ± 2) with a deviation (decrease in the slope k

_{A}) at higher concentration in which the alcohol start partitioning in the oil phase as a lipophilic linker, i.e., a polar oil segregated close to interface [113,114,115]. For n-butanol the data is not accurate and seems to vary with the surfactants from k

_{A}= −1.5 to –3.0. For ethoxylated nonionic surfactants, the alcohol cosurfactants have a similar effect but the k

_{A}have different values, about half those found for the ionic surfactant case, i.e., for 1-pentanol and isopentanol (k

_{A}= −4 and − 3) and for n-hexanol (k

_{A}= −8 ± 1).

_{0}(σ

_{0}/K or β

_{0}/K) is the value corresponding to PACN when the SAT is extrapolated to 0, i.e., when the tail is removed. It was found to depend on the head group, and on the selected references, usually 0 or 1%wt NaCl, 25 °C, no alcohol, and zero ACN

_{ref}virtual oil. Some values of PACN

_{0}found in the following list (including the first published data [68,116]) in the literature mostly correspond to relatively pure surfactants. However, the indicated values are only approximations (±3–4 units), in general at Cs = 1–2 wt% and WOR = 1 [73,78,100,108,117].

_{0}for ionic surfactants and, for nonionics, it appears as a specified number of EO groups, 5 EO or 10 EO, inside the PACN

_{0}value. In nonionic surfactants with no specification of head group, the EON (ethylene oxide number) or GN (glycerol group number) appears in the PACN

_{0}column. In all cases, the surfactant PACN may be calculated from Equation (16) that indicates how to add the contribution of the alkyl tail. No data is indicated for extended surfactants, firstly because the reported K values are not consistent in the published data (from 0.06 to 0.11) on different species, and secondly because it seems to be also altered by the intermediate PON size and also by the presence of some 1–3 EON groups before an ionic head. Additionally, these products are mixtures and their PACN is likely to significantly depend on their concentration. It is thus recommended to make a specific measurement in each case of extended surfactant.

_{N}.

_{0}, which is the same as adding four more carbon atoms in a linear tail, with the benzene attached in the second carbon.

_{N}equation to describe the formulation.

_{N}and the emulsion properties, the third way to describe the phase behavior in the Figure 4 prism is examined. This last cut at constant surfactant concentration (Cs) is important in practice because it exhibits the easier correspondence of formulation with emulsion properties, i.e., on its type, stability, drop size and viscosity, as will be examined below.

## 5. Relation of HLD Values with Micro-, Mini-, and Macroemulsion Properties

_{N}interval from −5 to +5, the emulsions are very unstable, unless they are gels with lamellar crystals or with a very high polymer content. This is extremely important in practice since it implies that a small change in temperature, e.g., from 20 °C to 35 °C, is enough to break an O/W nonionic macro- or nanoemulsion when it is placed on the skin. On the contrary, the same increase in temperature can stabilize the same type of emulsion made with a proper ionic surfactant because of the opposite change in stability versus HLD.

_{N}= 0, i.e., in the 10–20 unit range on both sides, there is a stable zone for the two types of emulsions. Of course, this stability zone could be high or very high depending on stabilization phenomena, which have been extensively discussed in the literature. Figure 15 clearly shows that the generalized optimum formulation effect at HLD ~ 0 overcomes all stabilization effects [140,141].

_{N}units from the optimum on both sides, the stability decreases, sometimes slowly, sometimes quickly. This means that if a high stability is required for an O/W (respectively W/O) emulsion, the HLD

_{N}should be adjusted for a negative (respectively positive) value in the 10–20 unit range, using up to six variables, i.e., with a lot of flexibility. It can be seen from Figure 15 that, depending on the case, the stable zone can be larger or narrower, and higher or lower. What is the best for each application depends on the process in particular, since a small change, for instance 10 °C in temperature, can produce the emulsion inversion or a displacement in the stability properties, as well as other characteristics like the drop size or the viscosity, as will be quickly discussed below.

_{N}~ 0 with the WIII phase behavior in the WOR central part, i.e., when there is no more than 70–75% of one of the phases. In this range, the HLD is the unique criterion to attain O/W or W/O types so-called A+ and A- “normal” emulsions in which the continuous phase is the one containing most of the surfactant. In the extreme WOR zones, called B and C, the normal emulsions occur when the HLD matches the occurrence of the continuous phase with most of the surfactant, i.e., B+ (respectively C-), which may be considered as the continuity of the A+ (respectively A-) zone with a high dilution, i.e., a large excess of the external phase.

_{N}~ ±10 both types of emulsions are stable, as clearly seen in Figure 15. Moreover, if the stability tends to decrease when the HLD

_{N}gets further away from optimum, it is a slow variation in general and a large change is required for the stability to significantly decrease. Consequently, there is a stability zone which is generally large, e.g., from 10 to 30 units of HLD

_{N}on each side.

_{N}= 0 where the interfacial tension is minimum, and thus where oil drops made by some mixing tend to elongate and break up easily, and to become smaller. However, it is also close to HLD

_{N}= 0 where the emulsion stability is very poor and where coalescence takes place quickly thus increasing the size of the drops. This minimum drop size then comes from the competition between two opposite effects and it may be slightly changed by the stirring process or the phase viscosity ratio.

_{N}, with a proper formulation variable. Such a determination is often more effective than other frequently used techniques such as an extra strong mixing or a temperature increase to reduce the viscosity. It is important to bear in mind that the viscosity tends to increase with the internal phase ratio of the emulsion (% vol of internal phase).

_{N}= 0. It is worth noting that there is a competitive situation between the actual stability and the viscosity [156,158], since being too close to HLD

_{N}= 0 could increase the viscosity because of smaller drops, but also be less stable.

_{N}= 0, and, it should be noted, not on the other side of the optimum line as many people have suggested to produce an inversion [165] which does not help unless it is necessary to avoid the problem of a too high viscosity ratio between the drop and external phase (like η

_{int}> 5 η

_{ext}) in the Weber ratio plot [166,167,168].

## 6. Additional Advantages and Complications with Complex Systems and Mixtures of Ingredients

_{N}correlation actually includes the contribution of the head and tail of a unique surfactant, the ACN of an n-alkane oil, and the NaCl salinity of the aqueous phase of a low complexity system, as well as the temperature and pressure. To these six variables, the type and concentration of a cosurfactant like a n-alcohol can be added through the f(A) (=k

_{A}C

_{A}) term, thus resulting to the contribution of eight variables in a single one, i.e., an extraordinary simplification.

^{+}Cl

^{−}, and a large variety of amphiphiles including natural ingredients and their modifications.

#### 6.1. Equivalent Oil Alkane Carbon Number (EACN)

_{N}equation is written twice, i.e., as follows with the original normalized expression:

_{1}= (1/K) LnS

_{1}+ CST and ACN

_{2}= (1/K) LnS

_{2}+ CST

_{1}= 7) has an optimum salinity S

_{1}and the one with a second oil (ACN

_{2}) has an optimum salinity S

_{2}, then:

_{2}= 7 + (1/K) [Ln(S

_{2}) − Ln(S

_{1})]

_{2}, which is called the equivalent ACN (EACN) can be calculated [67]. A lot of data have been reported with various second scans in conditions of detection of the optimum which could be more or less accurate, in particular if the WIII zone is particularly large [170,171,172,173,174,175,176].

_{i}is the fraction (molar in theory but often simply volumetric) of the “i” species in the mixture.

_{MIX}= ∑ X

_{i}EACN

_{i}

#### 6.2. Equivalent Salinity

_{N}expression.

_{N}equation and the equivalence is easy to handle.

#### 6.3. Equivalent SCP in Surfactant Mixtures

_{N}~ −6 or −8 to produce an O/W small-drop nanoemulsion cream.

_{MIX}= X

_{1}LnS

_{1}+ X

_{2}LnS

_{2}or LnS

_{MIX}= ∑ X

_{i}LnS

_{i}

_{MIX}= X

_{1}EON

_{1}+ X

_{2}EON

_{2}or EON

_{MIX}= ∑ X

_{i}EON

_{i}

_{MIX}= ∑ X

_{i}HLD

_{i}only if the K coefficient is the same for all the surfactants used, which is not always true in particular in a mixture of ionics with different Ks in front of ACN, and for ionic/nonionic mixtures where the definitions of K are different. To avoid this problem, it is absolutely necessary to use the normalized HLD

_{N}for such mixtures, and thus the surfactant contribution parameter SCP with the same coefficient as the real or virtual scan variable, i.e., SCP = N

_{MIN}, σ/K, β/K, Cc/K, PIT/K in the first generation of equations. With the normalized ACN real or virtual scan, SCP = PACN according to the HLD

_{NMIX}= ∑ X

_{i}HLD

_{Ni}

_{N}equation where the ACN coefficient is unity, at the same water salinity, oil ACN, temperature, pressure and same alcohol, is

_{MIX}= ∑ X

_{i}PACN

_{i}

_{N}parameter to define the surfactant contribution with the corresponding integration constant (SCP) is plotted versus the mixture composition. In many cases and because of some inaccuracy either on the SCP of each surfactant or in the exact content of each species in the mixture, some small deviation is observed, as can be seen in the case illustrated in Figure 19b.

#### 6.4. Problems in Surfactant Mixtures with Interactions and Partitioning of Species

_{NMIX}= ∑ X

_{i}HLD

_{Ni}+ interaction term

_{N}equation either for anionic or nonionic systems.

_{MIX}= X

_{1}HLD

_{1}+ X

_{2}HLD

_{2}is also wrong, not only because the Gex/RT interaction is missing, but also because in general the HLD

_{1}and HLD

_{2}equations do not have the same scales because of different Ks. In other words, it is like calculating an average between a temperature of 20 °C and another one of 60 °F, which is not 40° in some intermediate degree scale.

_{NMIX}= X

_{1}HLD

_{N1}+ X

_{2}HLD

_{N2}

_{N}expressions with different salinity terms, it can be said that the mixing of an anionic and nonionic surfactants definitively reduces the LnS*, i.e., it turns the mixture more lipophilic in the central region because of a specific interaction between their head groups. The salinity scan is nevertheless the easiest to carry out in this case, probably more than theoretical advantageous but unavailable in practice ACN scan. Some solution has to be found to translate a simple experiment in an equivalent simple data.

_{N}for both equations, it is found that the ΔPACN produced by reducing the Cs from 0.01% to 0.001% is −3.8 for the nonionic which becomes more hydrophilic and +1.9 for the anionic, which becomes more lipophilic. If the proper calculation is carried out to find out what is the mixture that would produce a compensation of the two effects to avoid the change in PACN with the change in Cs, it is found that it is 35% of the nonionic.

_{N}but it is useless to make some theoretical predictions, and it is much simpler to carry out a few appropriate experiments.

_{1}S

_{2}OW tridimensional diagram explains the effect of Cs and WOR resulting in a variation of interfacial partitioning. It actually shows that the HLD = 0 plane is slanted inside the 3D pyramid [142,198].

_{N}and, as a consequence, the phase behavior and the emulsion properties. Even if this means that things are extremely complex, it also means that some expertise about the effects of the spontaneously formulation changes would make it possible to successfully solve problems.

## 7. Conclusions

_{N}formula with three or four variables must be handled numerically, avoiding the purely empirical trial and error methods that would cost time and money.

_{N}formulation is necessary to assimilate the basic practical know-how presented here. Then, and after several years of learning more and of improving practice, the next levels of expertise would allow the researcher to solve problems after conducting a few experiments only, a striking result when it is known that over a dozen of variables must quite frequently be tested.

_{N}.

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Different types of solubilization in a surfactant-oil-water (SOW) system according to the aspect type and Winsor R ratio: Type I when R < 1, Type III when R = 1 and Type II when R > 1.

**Figure 2.**Interactions of the surfactant molecule adsorbed at the oil–water limit with neighboring water and oil molecules found in swollen micelles (Type I) or inverse micelles (Type II), as well as in middle phase lamellae or other complex bicontinuous structure (Type III).

**Figure 3.**Optimum formulation has been shown in the very first trials [26] to correspond to the minimum interfacial tension and to a unit partition coefficient between oil and water excess phases (right plot), as well as the occurrence of a maximum solubilization, with equal solubilization parameters (SP) in the microemulsion middle phase (left plot).

**Figure 4.**The three-dimensional way to handle the description of a SOW system as a function of the generalized formulation hydrophilic-lipophilic deviation (HLD), as well as constant surfactant concentration (Cs) and water-to-oil ratio (WOR). There are three types of 2D cuts at constant formulation, constant WOR = 1, and constant concentration of surfactant Cs.

**Figure 5.**Top: Phase behavior at constant formulation cut for three cases of salinity (Winsor’s diagrams). Bottom: Solubilization as C

_{S}surfactant concentration to attain a single-phase microemulsion at constant WOR = 1 cut (vertical fish diagram). In both cases the formulation scan is carried out by a change in salinity.

**Figure 6.**Detection of optimum formulation by different criteria maximizing the performance index PERFIND (minimum interfacial tension γ*, maximum solubilization parameter SP* and minimum surfactant spending C*s) to attain a single-phase microemulsion at the tail of the fish diagram.

**Figure 7.**Different occurrences taking place at the optimum value (V*) of a single variable scan, whichever the formulation variable V.

**Figure 8.**Effects of two formulation variables (water salinity and oil alkane carbon number (ACN)) on interfacial tension with a minimum at optimum (

**left**) and on the best solubilization in a fish diagram as the surfactant concentration Cs* minimum to attain a single-phase region (

**right**).

**Figure 9.**Solubilization as SP parameters (essentially indicating the performance index PERFIND) vs two formulation variables, i.e., water salinity (as S or ln S) versus oil ACN.

**Figure 10.**Aspects of a typical (LnS vs ACN) bidimensional scan and other similar cases involving two formulation variables (EON: surfactant ethylene oxide number, GN: surfactant glycerol number, SAT: surfactant alkyl tail carbon number, C

_{A}: alcohol concentration, f(A) = K

_{A}C

_{A}: alcohol effect).

**Figure 11.**Variation of optimum formulation in the EON−T subspace with commercial mixtures of ethoxylated nonylphenols with EON = 4 and EON = 9 with a wide distribution.

**Figure 12.**Tridimensional (ACN, T, S) formulation scan with the optimum formulation plane (HLD = 0) is intercepting the ACN axis at the value of the fourth variable (the preferred alkane carbon number—PACN).

**Figure 14.**Phase behavior in the formulation-WOR cut of the 3D prism shown in Figure 4.

**Figure 16.**Classical formulation-composition diagram (HLD-WOR) showing the inversion line and emulsion types.

**Figure 17.**Classical formulation-composition diagram (HLD-WOR) showing the basic properties (stability, drop size and viscosity) as described a long time ago [155].

**Figure 18.**LnS vs ACN and oil mixtures. LnS* is experimentally determined with pure benzene and placed on the extrapolated LnS*-ACN dashed line for the C12 sulfate. Xs are the volume fractions in the oil mixtures.

**Figure 19.**Variation of the surfactant contributing parameter SCP for different kinds of binary surfactant mixtures discussed in the text. (

**a**) no interaction = linear mixture, (

**b**) small interaction ± linear mixture (

**c**) anionic-nonionic = less hydrophilic interaction and (

**d**) catanionic (precipitate) with ± zero charge.

**Figure 20.**Salinity scan for mixtures of anionic and nonionic surfactants at very low concentration.

**Figure 21.**Variation of optimum salinity versus surfactant concentration for ionic and nonionic systems.

**Table 1.**Surfactant head contribution parameter PACN

_{0}expressed in ACN units as in Equation (16).

Na n-alkyl carboxylate | PACN_{0} = −50 |

Na n-alkyl sulfate | PACN_{0} = −57 |

Na alkane sulfonate | PACN_{0} = −48 |

Na iso-alkyl benzene sulfonate | PACN_{0} = −30 |

Na alkyl orthoxylene sulfonate | PACN_{0} = −25 |

Extended surfactants | no consistent data |

Cl n-alkyl ammonium at pH = 3 | PACN_{0} = −32 |

Cl n-alkyl trimethyl ammonium | PACN_{0} = −46 |

Cl n-alkyl pyridinium | PACN_{0} = −47 |

iso-alkyl phenol ethoxylate | PACN_{0} = + 23 − 6.67 EON |

iso-alkyl phenol + 5 EO | PACN_{0} = −10 |

n-alcohol ethoxylate | PACN_{0} = + 13 − 6.67 EON |

n-alcohol + 5 EO | PACN_{0} = −20 |

n-alcohol + 10 EO | PACN_{0} = −55 |

iso-alcohol ethoxylate | PACN_{0} = −2 − 6.67 EON |

iso-alcohol + 5 EO | PACN_{0} = −35 |

iso-alcohol + 10 EO | PACN_{0} = −68 |

n-alkyl carboxylic acid polyglycerol ester | PACN_{0} = + 34.5 − 10 GN |

**Table 2.**Equivalent oil alkane carbon number (EACN) values for oils with branching, cycles, double and triple bonds.

Oil | EACN | Oil | EACN |
---|---|---|---|

Myrcane | 9.5 | p-menthane | 6 |

Cyclohexane | 2.5 | Cyclohexene | −1 |

Ethylcyclohexane | 4.5 | Isopropylcyclohexane | 5.5 |

Benzene | 0 or less | p-cymene | −0.5 |

Limonene | 1.6 | terpinolene | 0.3 |

Octyl benzene | 4 | decyl benzene | 6 |

p-xylene | −2 | 1-decene | 5.5 |

1-octene | 4 | 1-octyne | −2 |

1-dodecene | 8 | 1-dodecyne | 2 |

Squalane (branched C30) | 24 | Dibutyl ether | 3.4 |

Ethyl myristate | 5 | Ethyl oleate | 7 |

Hexyl octanoate | 6.2 | Hexyl dodecanoate | 9.3 |

Hexyl methacrylate | 0 | Isopropylmyristate | 7.5 |

Miglyol 840–diglyc. C11 | 9 | Miglyol 812 triglyc. C11 | 14 |

Soya oil triglyceride C18 | 18 | Trilaurin | 16 |

Triolein | 21 | Tristearin | 24 |

Glycerol trioctanato | 12.3 | Glycerol tridecanoate | 14 |

1-Chlorodecane | 3.5 | 1–10 Dichloro decane | 6 |

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## Share and Cite

**MDPI and ACS Style**

Salager, J.-L.; Antón, R.; Bullón, J.; Forgiarini, A.; Marquez, R.
How to Use the Normalized Hydrophilic-Lipophilic Deviation (HLDN) Concept for the Formulation of Equilibrated and Emulsified Surfactant-Oil-Water Systems for Cosmetics and Pharmaceutical Products. *Cosmetics* **2020**, *7*, 57.
https://doi.org/10.3390/cosmetics7030057

**AMA Style**

Salager J-L, Antón R, Bullón J, Forgiarini A, Marquez R.
How to Use the Normalized Hydrophilic-Lipophilic Deviation (HLDN) Concept for the Formulation of Equilibrated and Emulsified Surfactant-Oil-Water Systems for Cosmetics and Pharmaceutical Products. *Cosmetics*. 2020; 7(3):57.
https://doi.org/10.3390/cosmetics7030057

**Chicago/Turabian Style**

Salager, Jean-Louis, Raquel Antón, Johnny Bullón, Ana Forgiarini, and Ronald Marquez.
2020. "How to Use the Normalized Hydrophilic-Lipophilic Deviation (HLDN) Concept for the Formulation of Equilibrated and Emulsified Surfactant-Oil-Water Systems for Cosmetics and Pharmaceutical Products" *Cosmetics* 7, no. 3: 57.
https://doi.org/10.3390/cosmetics7030057