Hydrophilic-Lipophilic Balance, Solubility Parameter, and Oil-Water Partition Coefficient as Universal Parameters of Nonionic Surfactants

HANS S C H O l l

Received February 23, 1995, from the School of Pharmacy, Temple Universiv, Philadeiphia, PA 19140. publication June 27, 1995@.

Accepted for

Abstract 0 The following three parameters describing the balance between the hydrophilicity of the polar moieties and the lipophilicity of the hydrocarbon moieties of nonionic surfactants are tabulated and examined: hydrophilic-lipophilic balance (HLB), oil-water partition coef- ficient (Kwo), and a solubility parameter (60) modified to take into account hydrogen bonding between water and the ether and hydroxyl groups of the surfactants. The purpose of the study is to ascertain whether these parameters are universal properties applicable to different categories of nonionic surfactants. Included were the following five nonionic surfactant categories or homologous series, comprising a total of 51 surfactants for which KWO values are available: octoxynols, nonoxynols, polyoxyethylated linear alcohols and dodecylamines, and sorbitan monoesters. The HLB of each homologous surfactant series gave a nearly linear correlation with log KWO. However, the five lines were spread far apart rather than falling on a single master curve. Therefore, the HLB is not a universal property, because it is based exclusively on the weight-percent of polyoxyethylene or polyol in the surfactant molecule while disregarding its molecular weight, the chemical nature of its hydrophilic and lipophilic moieties, and the structural features of the latter. These characteristics are taken into account when computing 60. The correlation between the 51 experimental log KWO values and their calculated 60 is linear, with a regression coefficient of 0.902. Moreover, it is possible to estimate the Kwo value of a nonionic surfactant (which is difficult to determine experimentally) from its 60 value (which is readily calculated) within a 95% confidence limit. Our conclusion, subject to continuing reappraisal as additional KWO values become available, is that 60 is a universal property applicable to all categories of nonionic surfactants.

Introduction In view of the large and growing number of commercially

available nonionic surfactants and their expanding uses, a reliable and readily obtainable property or parameter for their classification, characterization, and selection is much needed. Surfactants are amphipathic and their properties and uses depend largely on the balance between the hydrophilic propensity of their polar moieties and the lipophilic propensity of their hydrocarbon tails. Among the parameters used to quantify this balance for nonionic surfactants are the hydro- philic-lipophilic balance (HLB), the oil-water partition coef- ficient (Kwo), and the solubility parameter The present study evaluates and compares these three parameters.

Since the relation between HLB and oil-water partition coefficients of nonionic surfactants was examined? numerous additional values of the latter have been published. Therefore, the first purpose of the present study is to re-examine the relation between these two properties by including all new partition data.

Surfactants usually operate in contact with water. There- fore, we have developed a realistic solubility parameter for nonionic surfactants that includes a hydrogen-bonding com-

~

@ Abstract published in Advance ACS Abstracts, August 1, 1995.

ponent and compared its values for different homologous surfactant series with the HLB value^.^ Our second purpose is to examine the relation between these two properties for the additional nonionic surfactants for which partition coef- ficients have become available.

Our third and main purpose is to compare the solubility parameters and the oil-water partition coefficients for all nonionic surfactants for which the latter have been measured and to examine the possibility that either or both constitute universal parameters applicable to all different categories of nonionic surfactants.

Hydrophilic-Lipophilic Balance Griffin's HLB system classifies nonionic surfactants accord-

ing to their water or oil solubility and end use. It is employed to select emulsifiers for specific oil^^-^ and suspending agents for specific solid^.^ Initially, Griffin assigned numerical HLB values to nonionic surfactants by means of emulsification experiment^.^ Because this procedure was laborious, he subsequently developed the following equation for calculating the HLB rather than determining it experimentally:

E + P 5 HLB =-

E and P represent the weight-percent of polyoxyethylene and polyols (such as glycerin, sorbitan, or glucose) in the surfactant molecule, respecti~ely.~.~

Numerous attempts to find a universal correlation between the HLB and a given physicochemical property that is applicable to all categories of nonionic surfactants were unsuccessful.* Simple, usually monotonic and often linear relations exist between the HLB and each of the following solution properties within the homologous series of a single surfactant category, such as nonoxynols: spreading coef- f i ~ i e n t , ~ heat of hydration,1° critical micelle concentration (cmc),'l cloud point,12 oil-water partition coefficient,2 and solubility parameter.3 However, homologous series of other surfactant categories, such as sorbitan monoesters or poly- oxyethylated aliphatic alcohols, exhibit different relations between the HLB and such a property. When any of the surfactant properties listed above is plotted against the HLB, the various categories of nonionic surfactants produce diver- gent curves rather than a single master curve. Thus, the HLB is not a universal parameter.12

The reasons why the HLB falls short of a universal parameter are implicit in eq 1, which defines it as 20% of the weight-percent of polyoxyethylene or polyol in the surfactant molecule. This definition lumps together polyethylene glycol and polyol derivatives and also disregards the nature of the lipophilic moiety and the molecular weight of the surfactant. Polyoxyethylated surfactants based on linear and branched paraffins, cycloparaffins, olefins, alkylbenzenes, and alkyl- naphthalenes of comparable HLB values have different polarities, different solubilities, and hence different physico- chemical properties and end uses. Even within a given

0 1995, American Chemical Society and American Pharmaceutical Association

0022-3549/953184- 1215$09.00/0 Journal of Pharmaceutical Sciences / 121 5 Vol. 84, No. 10, October 1995

surfactant category and a t constant HLB, the molecular weight has a pronounced effect on such surfactant properties as surface activity, cmc, and cloud point.12 Thus, the HLB is an oversimplified concept that is useful only as a first approximation.

Solubility Parameter While the solubility parameter is widely used for studying

solutions of small nonelectrolyte molecules13 as well as solvents and plasticizers for polymers,14 it has rarely been applied to nonionic surfactants.3

The original definition of 6, namely, the square root of the energy of vaporization per unit volume of liquid to an ideal gas, referred to nonpolar solvents and solutes forming regular solutions, where dispersion forces accounted for all intermo- lecular attractions. The concept was subsequently extended to polar systems by adding the contributions of dipole-dipole interactions and hydrogen b ~ n d i n g . ’ ~ , ~ ~

Solubility Parameter Based on Dispersion Forces-For molecules that are so large and nonvolatile that they decom- pose during measurements of vapor pressures and heats of vaporization (e.g., polymers and typical water-soluble nonionic surfactants), a solubility parameter based on dispersion forces, 6 ~ , can be estimated as the sum of the molar attraction constants F for all functional groups:’*

where M , is the molecular weight of the surfactant. The surfactant densities d at 20-25 “C were either taken

from the literature (including handbooks and suppliers’ catalogs, bulletins, and data sheets), measured at 25 “C, or estimated as the volume-weighted average of the densities of polyethylene glycols and the phenol or amine to which ethylene oxide had been added. Whenever such calculated densities could be checked against experimental values, the agreement was within fl%.

The F values used were those of Table 2 of ref 3. The sole addition was F for the nitrogen atom of tertiary amines, 61 (cal cm3)1’2/mol.’5 According to eq 2, the units of 6 are therefore (ca l /~m3)~/~ .

Below are the structural formulas of the homologous surfactant series from which the P values were computed. The nonyl group in nonoxynols (I) is a propylene trirner:l6

I

The density of liquid nonoxynols a t 25 “C can be correlated with either p or the HLB by two approximately equivalent linear regression equations:

l o g p = -10.78 + 11.15d (n = 26, r = 0.980) (3)

and

d = 0.9495 + 0.008068HLB (n = 26, r = 0.979) (4)

Both equations apply top < 15 and HLB < 15.0. More highly poIyoxyethylated nonoxynols are solid a t 25 “C; in that case, d in eq 2 is the density of melts supercooled to 25 “C.

The octyl group in octoxynols (11) is an isobutylene dimer:I6

CH3 I

The density was calculated with eq 5 of ref 3. Polyoxyethylated dodecylamine~’~ (111) are not symmetri-

cal: a b because ethylene oxide adds faster to the first amine hydrogen atom of 1-dodecylamine (primary amine) than to the second (secondary amine).l8Jg

The structure of sorbitan monoesters (IV) is

I I I I HO-HC,CH,CH -OH HO-HC-CH-OH

I OH

Iv

where R is the acyl radical C,H2,+1CO-. Sorbitan is a mixture of 5- and 6-membered rings; the two ring structures have the same F value.

Contribution of Hydrogen Bonding to the Solubility Parameter-The solubility parameters of various homologous series of nonionic surfactants based solely on dispersion forces, calculated from measured heats of vaporization or by means of eq 2, were either independent of the HLB or decreased slightly as the HLB increased.3 This unrealistic pattern was due to the fact. that the accepted F value for the ether oxygenI4 is not much larger than that of the hydrogen atom (70 versus 60 f 10). The effective F value for the ether group in the presence of water is considerably larger because of hydra- tion: each ether oxygen forms direct hydrogen bonds with two water molecules.20

Therefore, the contribution of hydrogen bonding to the solubility parameter, &, must be taken into account. (The contribution of dipole forces, on the other hand, is negligible).3

& = JT 5000md

The factor m represents the number of functional groups in a surfactant molecule capable of forming hydrogen bonds either as proton acceptors or donors. It comprises all hydroxyl, ether (including acetal but excluding ester), and amine groups. For instance, the addition of a + b ethylene oxide molecules to the primary amine in I11 introduces (a - 1) + ( b - 1) ether groups and two hydroxyl groups. The total number of hydrogen-bonding groups, including the amine nitrogen, is m = a - 1 + b - 1 + 2 + 1 = a + b + 1. For sorbitanmonoesters (N), m = 4 includes three hydroxyl and one ether group.

Overall Solubility Parameter-The two solubility pa- rameters that account for the contributions from dispersion forces and hydrogen bonds are combined3 according t0l32 l4

1216 / Journal of Pharmaceutical Sciences Vol. 84, No. 10, October 1995

to yield the overall solubility parameter do. Equation 6 was corroborated by correlating the 60 of nonionic surfactants with polarity parameters determined by gas chromatography.21

The upper limit for the 60 value of all polyoxyethylated surfactants (at HLB = 20) is that of pure polyethylene glycol. For polyethylene glycol 3350 (Carbowax 4000), = 9.28 and 60 = 14.96.13 For high molecular weight polyethylene oxide polymers, the calculation below is based on a single repeat unit, -CH&HzO--, with molecular weight M, = 44.05 and CF = 336:

336d - 6 -----8.77 and D- M,

336d 2 5000d - 14.40 JE- The density value, d = 1.15 g/mL, was extrapolated for a melt supercooled to room temperature.

These two calculated 6 values, based on eq 6, are in excellent agreement with the experimental 6 values deter- mined for polyethylene oxide, namely, 8.9 as the lower limit in poorly hydrogen-bonding solvents (60 = d~ only) and 14.5 as the upper limit in strongly hydrogen-bonding solvents like water (60 from eq 6).22 These considerations validate eq 6.

Oil-Water Partition Coefficients Measurements of oil-water partition coefficients of nonionic

surfactants are beset by the following two experimental difficulties: Lengthy contact times between the two liquid phases are required to reach equilibrium distribution because agitation promotes emulsification. Workmg below the cmc requires analyzing very low surfactant concentrations. How- ever, such partition coefficients are very useful. For instance, in emulsification, they control not only whether the emulsions will be of the water-in-oil (W/O) or oil-in-water ( O N ) type and their phase inversion but also their relative stability. There- fore, any method for estimating partition coefficients instead of measuring them would be advantageous.

The oil-water partition or distribution coefficient is defined as

n

L'W Go=c 0 (7)

where C are the molar equilibrium concentrations of the surfactant in water (subscript W) and in oil (subscript 0).

For thermodynamic calculations, concentrations are usually expressed in mole fractions, x, rather than as molarities, M. The relation between the corresponding partition coefficients is

(8)

where t represents the molar volumes of the two solvents. Because water has a lower molecular weight and molar volume than oils, K& usually exceeds Kwo by an order of magnitude. All partition coefficient data listed below refer to molar concentrations. For simplicity, the superscript M in Go is omitted.

In order to be used in this study, values of partition coefficients had to be independent of concentration: only KWO values determined in a concentration range where the parti- tion or distribution isotherms (plots of CO versus CW) are straight lines passing through the origin were employed.

Table 1-Oil-Water Partition Coefficients and Other Properties of Nonoxynols

p" HLB 60,~ (callcm3)'" log Go Solvent Temp, "C Ref

5.0 10.00 12.14 -1.7905 Heptane 20 31,32 6c 10.91 12.32 -2.682 Cyclohexane 25 25,27 7.3 11.87 12.51 -0.643 Hexane 25 29

20 29 EC 12.31 12.60 -1.845 Cyclohexane 25 25,27 8.5 12.59 12.64 -0.362 Hexane 20 28,29

10.0 13.33 12.795 0.000 Heptane 20 31,32 15.0 15.00 13.12 1.602 Heptane 20 31,32

a Number of oxyethylene units per molecule. * Calculated with eq 6. Homo- geneous surfactants; all others are normally distributed.

When C and KWO values cover several decades, partition isotherms are plotted on a log-log scale. In that case, linear plots with 45" slopes are required to yield usable KWO values.

Moreover, usable KWO values are only obtained below the cmc because partition isotherms change slope in the vicinity of the cmc. In the case of homogeneous or monodisperse polyoxyethylated surfactants that are primarily water-soluble, the isotherms frequently begin to run parallel to the CW axis at the cmc. This indicates that CO remains constant as the overall surfactant concentration is increased further while CW increases and that all additional surfactant molecules in the aqueous phase associate into micelles. Since the concentra- tion of nonassociated surfactant molecules in the aqueous phase remains practically constant and equal to the cmc, no additional partitioning of surfactant into the oil phase takes place. If the homogeneous surfactants are primarily oil- soluble, the situation is rever~ed .~~-~O

The partition isotherms of normally distributed or polydis- perse polyoxyethylated surfactants also undergo well-defined breaks at the cmc, but the changes in slope are not as pronounced as those of homogeneous surfactants: On log- log plots, the slopes change from 45" to approximately 20- 30" at the cmc rather than to 2 e 1 - 0 . ~ ~ ~ ~ ~ Premicellar associa- tion such as dimerization in either phase also results in variable and hence unusable KWO values.30

In the strictest sense, the partition coefficient in eq 7 should be the ratio of surfactant activities rather than concentrations. Nonionic surfactants have very low cmc values and their partition coefficients are determined at concentrations below the cmc. In such dilute solutions, the activity coefficients are close to unity and the activities close to concentrations, which justifies the use of concentrations in eq 7. Beginning at the cmc, the activity coefficients decrease abruptly.

Normally distributed polyoxyethylated surfactants undergo some fractionation during partitioning measurements: The species having the lowest degree of ethoxylation dissolve preferentially in the oil phase while those having the highest degree of ethoxylation dissolve preferentially in the aqueous phase. At low degrees of ethoxylation, the KWO of homoge- neous surfactants are lower than those of normally distributed surfactants with the same average degree of ethoxylation. "he situation is reversed at high degrees of e t h o x y l a t i ~ n . ~ ~ ~ ~ ~ ~ ~ ~ However, for primarily water-soluble surfactants, the Kwo of normally distributed and homogeneous species of comparable (average) degrees of ethoxylation differed only by factors smaller than 2.5. For comparison, the addition of one ethylene oxide unit increased the KWO value by a factor of = 2.8.24

Only partition coefficients in oils that are immiscible with water are included in Tables 1-3. Therefore, partition data in octanol and benzene were not used. On a mole fraction basis, the solubility limit of water in benzene at 25 "C is xg = 0.0029 while that of benzene in water is xo = 0.00035. The 6 value of anhydrous benzene is 1.7 units larger than that of heptane, but the 6 value of benzene saturated with water

-0.540 Hexane

Journal of Pharmaceutical Sciences / 1217 Vol. 84, No. 14 October 1995

Table 2-lsooctane-Water Partition Coefficients at 25 "C and Other Properties of Octoxynols

p' HLB ao,b ( c a l l ~ m ~ ) ' ' ~ log $0 Ref

1C 2c 2.00 2.98 3c 4c 4c 4.07 5c 5c 5.0 5.01 6c 6c 6.03 7c 7.05 7.5 EC EC 8.03 9C 9.06 9.7 9.93

1 o c 12.3 16.0 20 40

3.52 5.985 5.985 7.78 7.81 9.21 9.21 9.30

10.33 10.33 10.33 10.34 11.23 11.23 11.26 11.98 12.02 12.31 12.61 12.61 12.63 13.15 13.18 13.49 13.59 13.62 14.48 15.47 16.205 17.90

10.89 11.43 11.43 11.78 1 1.79 12.05 12.05 12.07 12.265 12.265 12.265 12.27 12.43 12.43 12.435 12.58 12.58 12.64 12.69 12.69 12.695 12.795 12.80 12.86 12.875 12.89 13.055 13.25 13.40 13.74

-3.735 -3.144 -2.383 -1.845 -2.504 -2.007 -2.176 -1.323 -1.609 -1.777 -0.921 -0.889 -1.228 -1.322 -0.595 -0.740 -0.348 -0.367 -0.298 4.301 -0.0851

0.152 0.190 0.00432 0.276 0.585 0.329 1.496 1.362 1.674

24 24 24 24 24 24 27 24 24 27 23 24 24 27 24 24 24 23 24 27 24 24 24 23 24 24 23 24 23 24

a Number of oxyethylene units per molecule. Calculated with eq 6. Homo- geneous surfactants; all others are normally distributed.

exceeds that of heptane by a larger amount because heptane is immiscible with water. For this reason, the heptane-water partition coefficients of octoxynols exceeded their benzene- water partition coefficients by factors of 50-2500, the factor being larger for the more highly polyoxyethylated surfac- tants.31J2

The water-immiscible oils employed in Tables 1-3 (with their 60 = 6~ valued5 in parentheses) are isooctane or 2,2,4- trimethylpentane (6.86), n-hexane (7.271, n-heptane (7.501, n-dodecane (7.921, and cyclohexane (8.19). They have ap- proximately the same polarity since their 6 values cover a range of only 1.3 units. Commingling the KWO values obtained with these four saturated hydrocarbon oils in Tables 1-3 to determine the subsequent correlations is also justified by the following observation: When the solutes were normal primary C4 to C7 alcohols and the oils n-octane (7.541, n-dodecane (7.921, and n-hexadecane (8.3), changing the 6 of the oil by 0.8 unit caused only 1.4-1.6-fold changes in the oil-water partition coefficient^.^^

The partition coefficients of Tables 1-3 were obtained between 20 and 25 "C. Commingling such values is permis- sible because KWO varies only slightly with temperature throughout this 5 "C range.24,29 It is also necessary because the temperatures in some partition measurements were only controlled within &1 or even f 2 "C. Furthermore, comparable conclusions were obtained when only KWO determined at 25 "C were used in the computations below.

Relation between Hydrophilic-Lipophilic Balance and Oil-Water Partition Coefficient

The relation between HLB and log KWO for the five categories of nonionic surfactants shown in Figure 1 yields

l 8 t 0 ' .p t J t Po.

"i 12 m L

-4.0 - 2-0 0 2.0 log K,,

Figure 1-Relation between the hydrophilic-lipophilic balance and the logarithm of the oil-water partition coefficient for the five categories of nonionic surfactants. Key: (0) homogeneous octoxynols; (0) normally distributed octoxynols; (W) homogeneous nonoxynols; (U) normally distributed nonoxynols; (A) homogeneous polyoxyethylated alcohols; (v) fractionated polyoxyethylated dodecylamines; (X) sorbitan monoesters.

the following conclusions. Within each homologous series, the relation is linear; all correlation coefficients are 30.97.

The effect of polydispersity on such a relation is surprisingly small: For the 16 normally distributed octoxynols, the linear least-squares regression equation is

HLB = 12.84 + 2.68 log Kw, ( r = 0.987) (9)

For the 14 homogeneous octoxynols, it is

HLB = 13.42 + 2.24 log Kwo ( r = 0.968) (10)

When the data for the 30 octoxynols are combined, the linear correlation coefficient is not reduced significantly:

HLB = 13.10 + 2.29 logKwo (r = 0.969) (11)

Thus, a broadened molecular weight distribution of the polyoxyethylene moiety affects the relation between the HLB and the partition coefficient far less than a change in the chemical characteristics of the hydrocarbon moiety.2 The exception are the points for the two homogeneous nonoxynols, which lie distinctly above the straight line for the six normally distributed nonoxynols. The linear correlation coefficient for the latter is 0.985, but inclusion of the two homogeneous nonoxynols lowers it to 0.866.

The lines representing the homologous series of different surfactant categories are spread far apart, despite the fact that the scale of the abscissa is logarithmic. The lines have different slopes. Their intercepts on the HLB axis a t a fixed log KWO value differ significantly. For instance, a t log KWO = -2.0, the HLB ranges from 5.5 to 12, covering one-third of the 20 units of the full HLB scale. For log KWO = 0, the HLB values range from 7 to 13.5.

1218 /Journal of Pharmaceutical Sciences Vol. 84, No. 10, October 7995

Table 3-Oil-Water Partition Coefficients and Other Properties of Polyoxyethylated Normal Alcohols, Polyoxyethylated RDodecylamines, and Sorbitan Monoesters

Surfactant HLB do,a (~allcm~)”~ log Go Solvent Temperature, “C Ref

Polyoxyl3 butyl etherb Polyoxyl4 butyl etherb Polyoxyl 3 pentyl etherb Polyoxyl4 pentyl etherb Polyoxyl4 dodecylamineC Polyoxyl 5 dodecylamineC Polyoxyl6 dodecylamineC Polyoxyl7 dodecylamineC Polyoxyl 8 dodecylamineC Polyoxyl9 dodecylamineC Sorbitan monooleate Sorbitan monostearate Sorbitan monopalmitate

12.81 14.08 12.00 13.33 9.75

10.86 11.76 12.49 13.1 1 13.63 4.3e 4.7e 6.7e

13.06 13.24 12.76 13.13 11.92 12.15 12.34 12.49 12.62 12.73 11.59 1 1.99 12.22

1.646 2.126 1.074 1.542

-1.42 -0.77 -0.31

0.1 1 0.53 1.02

-3.432 -3.208 -0.503

Dodecane Dodecane Dodecane Dodecane Heptaned Heptaned Heptaned Heptaned He p t a n e Heptaned f f f

25.00 i 0.05 25.00 + 0.05 25.00 i 0.05 25.00 i 0.05 2 0 + 2 2 0 1 2 20?2 20 li: 2 20 + 2 20+2

34 34 34 34 17 17 17 17 17 17 2,35 2,35 2,35

aCalculated with eq 6. bHomogeneous surfactants. CSingle, homogeneous fractions in the chromatogram. dThe aqueous phase was 0.1 N NaOH to prevent ionization of the tertiary amine groups. For all other surfactants, it was water. eExperimental v a l ~ e . ~ - ~ The other values were calculated with eq 1. ’Not specified; possibly petroleum ether.

2 0 ’s 1.0 -

B O -

,o -1.0-

Y 0

-2.0 -

-3.0

11.0 12.0 13-0 14.0

8, Figure 2-Relation between ihe logarithm of the oil-water partition coefficient and the overall solubility parameter for the five categories of nonionic surfactants. Key: same as in Figure 1.

Because the points representing the different surfactant categories fall on divergent lines rather than on a single master curve, the HLB is not a universal property of nonionic surfactants.

Relation between Overall Solubility Parameter and Oil-Water Partition Coefficient

The data are collected in Tables 1-3 and plotted in Figure 2. The straight lines pertaining to the homologous series of different surfactant categories are very close together, espe- cially when considering that the scale of the ordinate is logarithmic and covers six decades.

For statistical comparisons, the lines are represented by equations of the type

log K,, = a + bd, (12)

However, the intercepts a are fictitious because the lowest

Value of 60 is not zero but 60. The mean 6~ value is 9.66 i 0.22 for the three sorbitan monoesters. The SD values of the other 48 surfactants are even more similar to each other, with a mean of 8.73 f 0.10.

The statistical analysis of the data of Figure 2 was carried out in the three different ways detailed below.

Pairwise Comparisons of Regression Lines by t Tests-A computerized analysis of ccjvariance program, SPSS Version 4.1 on IBM mainframe computer with the CMS operating system, was used to compare pairs of regression lines by t tests. The sorbitan monoesters were excluded because that category contains only three surfactants. The slopes pertaining to the remaining four surfactant categories were compared in pairs. There are six combinations of four slopes taken two at a time. Of the six pairs that were compared, the only pair whose difference was statistically significant was the slope of the 30 octoxynols ( b = 2.116) and the slope of the eight nonoxynols ( b = 3.868). Likewise, the difference between the slopes of the regression lines of the 16 normally distributed octoxynols ( b = 1.8886) and the six normally distributed nonoxynols (b = 3.3327) was statistically significant.

Next, the regression line of the homogeneous octoxynols is compared with that of the normally distributed octoxynols. The regression line for the 14 homogeneous octoxynols has an extrapolated intercept a = -27.60, a slope b = 2.139, and a regression coefficient r = 0.963. The corresponding values for the 16 normally distributed octoxynols are a = -24.07, b = 1.889, and r = 0.987. Comparison of the two extrapolated intercepts, the two slopes, and the two regression coeficients by means of t tests (applicable to small samples) as well as by Z tests (for larger samples)36 indicates that their differences are not statistically significant even at the 10% probability level. Hence, there is insufficient basis to believe that the two lines are not coincident.

This conclusion reinforces the observation made above that fractionation of normally distributed surfactants during oil- water partitioning was not extensive enough to affect their partition coefficients in a major way.

Simultaneous Comparison of All Regression Lines by the F Test-The regression lines for the five categories of surfactants were compared by means of the F test, conducted with the above MANOVA program as well as by the step-by- step procedure with a hand-held c a l c ~ l a t o r . ~ ~ The F test was repeated for seven surfactant categories obtained by separat- ing homogeneous from normally distributed octoxynols and nonoxynols, and for four surfactant categories obtained by

Journat of Pharmaceutical Sciences / 1219 Vol. 84, No. 10, October 1995

30-

2 0 -

1-0 -

0 0- x’

0 -1.0- ET

-2.0 -

-3-0-

11.0 120 13.0 14.0

so Figure 3-Relation between the logarithm of the oil-water partition coefficient and the overall solubility parameter for the pooled population of 51 nonionic sur- factants: Regression line and 95% confidence belt. Key: same as in Figure 1.

pooling the sorbitan monoesters with the polyoxyethylated dodecylamines.

In every case, the differences in the slopes b (as well as the differences in the extrapolated intercepts a ) were significant a t probability levels 4%. This agrees with the previous observation that one of the six pairs of slopes examined exhibited a statistically significant difference.

95% Confidence Band-The preceding two methods deal with the individual regression lines of the five surfactant categories. The third method pools the log KWO - 60 values for all 51 surfactants. The equation of the overall regression line is

log K,, = -30.92 + 2.4296, ( r = 0.902) (13)

This regression line and the 95% confidence belt or band for individual log KWO values3s are plotted in Figure 3. The upper and lower curve seem to be parallel straight lines rather than the customary branches of a hyperbola38 because of the compressed scale of the ordinate and the expanded scale of the abscissa. This indicates that the hazard of predicting log KWO values from 60 according to eq 13 is hardly any larger a t the extremes than in the middle of the experimental range. The two curves flare out beyond that range.

Of the 51 data points, one lies clearly outside the 95% confidence belt while two others lie just barely outside. This is in keeping with the expectation that about 5% of the sample points fall outside a 95% confidence belt.38

The results of the third method indicate that the pooled data can be represented by a single straight regression line and a 95% confidence belt. This does not contradict the result of the second method, according to which all five regression lines pertaining to the five surfactant categories are unlikely to be coincident.

Conclusions-The observation that log KWO and 60 of all nonionic surfactants tested, regardless of category, have a common monotonic relation (eq 13) leads to the following two conclusions. First, the oil-water partition coefficients of most nonionic surfactants can be predicted from their overall solubility parameters with satisfactory dependendability. This

is advantageous because both properties are difficult to measure experimentally, but the latter can be estimated readily from the chemical structure of the surfactant.

Second, because these two i n d e ~ e n d e n t ~ ~ parameters that characterize the balance between the hydrophilic and hydro- phobic propensities of the various categories of nonionic surfactants are connected by a single, comprehensive relation applicable to all surfactants tested (eq 13), they can be regarded as universal properties of nonionic surfactants. This conclusion and eq 13 will be re-evaluated as new nonionic surfactants and/or new oil-water partition coefficients become available.

1.

2. 3. 4. 5. 6.

7.

8. 9.

10. 11. 12. 13.

14.

15. 16.

17.

18. 19. 20. 21.

22.

23.

24.

25.

26. 27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

References and Notes Moroi, Y. In Micelles-Theoretical and Applied Aspects, Ple- num: New York, 1992; Chapter 2. Schott, H. J . Pharm. Sci. 1971,60,648-649. Schott, H. J . Pharm. Sci. 1984, 73, 790-792. Griffin, W . C. J . SOC. Cosmetic Chern. 1949, 1, 311-326. Griffin, W. C. J . SOC. Cosmetic Chem. 1954, 5, 1-8. Shinoda, K.; Kunieda, H. In Encyclopedia of Emulsion Technol- ogy; Becher, P., Ed.; Marcel Dekker: New York, 1983; Vol. I, Chapter 5. Patton, T. C. In Paint Flow and Pigment Dispersion, 2nd ed.; Wiley-Interscience: New York, 1979; pp 285-290. Becher, P. J . Dispersion Sci. TechnoE. 1984, 5, 81-96. Ross, S.; Chen, E. S.; Becher, P.; Ranauto, H. J. J . Phys. Chern.

Racz, I.; Orban, E. J . Colloid Sci. 1965,20, 99-103. Schott, H. J . Pharm. Sci. 1969,58, 1131-1133. Schott, H. J . Pharm. Sci. 1969,58, 1443-1449. Shinoda. K. In Princides of Solution and Solubilitv: Marcel

1959, 63,1681-1683.

.,, .- ~~~~~ ~

Dekker: NewYork, 1978; Chapter 4. Van Krevelen, D. W. In Properties of Polymers: Their Estimation and Correlation with Chemical Structure. 2nd ed.: Elsevier: Amsterdam, 1976; Chapter 7. Hoy, K. L,. J . Paint Technol. 1970,42, 76-118. Enyeart, C. R. In Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1967; Chapter 3. James, A. D.; Wates, J. M.; Wyn-Jones, E. J . Colloid Interface Sci. 1993,160, 158-165. Shachat. N.: Greenwald. H. L. In ref 16. D 23.

I I

Reck, R.’A. ’In ref 16, p’191. Schott. H. J . Pharm. Sci. 1980. 69. 369-378. Szymanowski, J.; Sobzynska, A.; Voekel, A. J. Pharm. Sci. 1988,

Brandrup, J.; Immergut, E. H. In Polymer Handbook, 3rd ed.; Wilev: New York. 1989: D VIU550.

77, 893-897.

Greinwald, H. L.;’Kice, E. B.; Kenly, M.; Kelly, J . Anal. Chem.

Crook. E. H.: Fordvce. D. B.: Trebbi. G. F. J . Colloid Interface 1961,33, 465-468.

Sci. 1965, Zd, 1911204. ’

Harusawa, F.; Saito, T.; Nakajima, H.; Fukushima, S. J . Colloid Interface Sci. 1980, 74, 435-440. Harusawa, F.; Tanaka, M. J . Phys. Chem. 1981,85,882-885. Harusawa, F.; Nakajima, H.; Tanaka, M. J. SOC. Cosmetic Chem. 1982, 33, 115-129. Warr, G. G.; Grieser, F.; Healy, T. W. J . Phys. Chem. 1983,87, 4520-4524. Allan, G. C.; Aston, J . R.; Grieser, F.; Healy, T. W. J . Colloid Interface Sci. 1989, 128, 258-274. Marland, J. S.; Mulley, B. A. J . Pharm. Pharmacol. 1972, 24, 729-734. Petrov, A. A.; Pozdnyshev, G. N. Kolloidnyi Zh. 1966,28,858- 865. Kruglyakov, P. M.; Koretskii, A. F. Doklady h a d . Nauk. SSSR 1971,197, 1106-1109. Aveyard,, R.; Mitchell, R. W. Trans. Faraday Soc. 1969, 65, 2645-2653. Manabe, M.; Koda, M.; Shirahama, K. Bull. Chem. SOC. Jpn.

Davies, ?J. T. Proc. 2nd Int. Congress Surface Activity 1957, 1, 1975,48,3553-3556.

426-438. Kleinbaum, D. G.; Kupper, L. L. In Applied Regression Analysis and Other Multivariate Methods; Duxbury Press: N. Scituate, MA, 1978; Chapter 8. Snedecor, G. W.; Cochran, W. G. In Statistical Methods, 6th ed.; Iowa State University Press: Ames, IA, 1972; Chapter 4. Reference 37, Chapter 6.

1220 / Journal of Pharmaceutical Sciences Vol. 84, No. lo, October 1995

39. The partition coefficient of a solute between two immiscible solvents was derived theoretically from the solubility parameters of the three components: Srebrenik, S.; Cohen, S. J. Phys. Chem. 1976, 80, 996-999. However, their derivation assumed the absence of “complexes” such as are formed by association through hydrogen bonding, i.e., their pertinent solubility pa- rameters were d~ rather than do values. Thus, the derivation is not applicable when water is present, let alone water plus polyoxyethylated or polyhydroxylated compounds. In that case, the pertinent parameters are Kwo and do; they are independent of each other because solvent-solute complexation occurs only in the aqueous phase and enhances only the solubility in water but not in the oil ohase.

40. Davies, J. T.; Rideal, E. K. In Interfacial Phenomena; Academic Press: New York, 1961; Chapter 8.

41. Schott, H. J . Pharm. Sci. 1990, 79, 87-88. 42. Vold. R. D.: Vold. M. J. In Colloid and Interface Chemistrv:

Addison-Wesley Puhlishing: Reading, MA, 1983; pp 397-39i: 43. Komarova, A. B.; Dubyaga, E. G.; Tarakanov, 0. G. Metody Anal.

Iskhodnogo Syr:ya Penopoliuretanoo 1976, 87-89.

Acknowledgments It is a pleasure to acknowledge helpful discussions and assistance

with the computer analysis by Mrs. Roslyn Gorin, Manager of Statistical Applications, Temple University. This work was presented at the 142nd annual meeting of the APhA, March 18-22, 1995, Orlando, FL.

Appendix Free Energy of Transfer of Oxyethylene Groups from

Oil to Water-The work or change in standard free energy for transferring a mole of oxyethylene units from oil to water is calculated by the equation

where the superscripts p and p-1 refer to the number of oxyethylene units; R is the gas constant, 1.987 cal/mol K, and T is the absolute temperature, 298 K.

Most points on a plot of log KWO versus p fall on a straight line. However, the slope begins to decrease a t p = 15 (possibly because longer polyoxyethylene moieties assume more of a random coil conformation, double back, and interact more extensively with themselves). For a precise estimate by means of eq 14, points with KWO > 35 andor p > 13 are excluded. In that case, the regression line, with n = 40 and r = 0.856, has a slope, d log Kwddp, of 0.370. According to eq 14, this corresponds to a change in the standard free energy of transfer from oil to water of -500 cal/mol per -CH&HzO- unit (or a work of transfer of 500 cal/mol). As expected, the free energy change is negative, indicating that the transfer of the hydrophilic groups from oil to water occurs spontane- ously. This value agrees with -487 f 38 cal/mol found for normally distributed polyoxyethylated alkylphenols31 and with -600 found for homogeneous polyoxyethylated alkylphenols2* and polyoxyethylated normal alcohols.34

Examination of the Davies HLB System-An alternate method for computing the HLB due to Da~ies,~~.*O although supposedly based on Griffin’s scale, has been shown by algebraic analysis to lead to completely different HLB values for nonionic surfactants than those of Griffin.41 Griffin validated his HLB scale and eq 1 experimentally by conduct- ing extensive emulsification experiment^.^ Any alternate method for computing the HLB that supplies values for nonionic emulsifiers a t variance with those of Griffin must, therefore, be considered erroneous.

Whether Davies’ HLB scale, despite its unrealistic values, is a t least self-consistent is examined below. Davies treated the HLB as an additive and constitutive property. He computed group numbers for the various functional groups

6

4

I.;/”;, , , , 2 - 4.0 -2.0 0 2.0

log Kw, Figure 4-Relation between Davies’ hydrophilic-lipophilic balance logarithm of the oil-water partition coefficient for four categories of surfactants. Key: same as in Figure 1; heavy line represents eq 16.

and the nonionic

in the surfactant molecules based largely on Griffin’s reported HLB values. Davies’ HLB (HLBn) is calculated a@,*”

HLBD = x(hydrophi1ic group numbers) - 0.475e + 7 (15)

where e is the number of carbon atoms in the hydrocarbon moiety of the surfactant molecule, regardless of whether the carbon is in the form of -CH3, -CH2--, >CH--, or =CH-. Hydrophilic group numbers are positive and lipophilic group numbers negative. The ether oxygen has a group number of 1.3 but the oxyethylene repeat unit, -CH2CH20--, was assigned the group number of 0.33 rather than 1.3 - (2K0.4753 = 0.35.

Davies’ theoretical considerations, combining the kinetics of emulsion coalescence with the free energy change of transferring a surfactant molecule from water to oil, resulted in the following e q u a t i ~ n : ~ ~ . * ~ ~ * ~

HLB, = 7 + 0.829 log K,, (1 6)

This equation is widely assumed to be universally applicable to all nonionic surfactants. It has even been used to estimate the HLBD of nonionic surfactants when not all group numbers were available, e.g., for polyoxyethylated silicones.43

Equation 16 is examined below by plotting the HLBn values of nonionic surfactants, calculated with eq 15 and published values of group number^,^^,^^ against the logarithm of their experimental oil-water partition coefficients from Tables 1-3. Figure 4 compares the line according to eq 16 (drawn as a heavy line) with the actual lines for four of the five surfactant categories. Since Davies did not list a group number for the un-ionized tertiary amine group, the polyoxyethylated dode- cylamines were omitted.

The extrapolated log KWO value for HLBD = 0 is -8.444 according to eq 16. The actual intercepts range from -21.26 to -4.930. The slope of the line according to eq 16 is 0.829, while the actual slopes range from 0.318 t o 1.012.

Eq 16 embodies the theoretical basis for Davies’ HLB system.42 Since the lines and the regression equations of the four categories of nonionic surfactants examined differ exten-

Journal of Pharmaceutical Sciences / 1221 Vol. 84, No. 70, October 1995

sively from each other and from Davies’ line and equation, the Davies system is not self-consistent. Equation 16 and, hence, the underlying theory are invalid.

The factual disparity between Griffin’s and Davies’ HLB systems has already been d o c ~ m e n t e d . ~ ~ As a further ex- ample, polyoxyl8 lauryl ether and its sesquimer, polyoxyl 12 oleyl ether, have nearly identical HLB values of 13.1 and 13.3 according to eq 1, but HLBD values of 5.8 and 4.3, respectively, according to eq 15. According to Griffn4-6 as well as D a v i e ~ , ~ ~ . ~ ~ nonionic surfactants with HLB >/ 13 are water-

soluble and promote OMr emulsions while those with HLB < 6 form unstable dispersions in water and promote W/O emulsions. The two surfactants mentioned above form clear solutions in water at room temperature over a wide range of concentrations and act as O/W emulsifiers, as predicted by Griffin’s HLB system but opposite to the prediction of the Davies system. In view of its theoretical and factual short- comings, the latter should be abandoned.

559500722

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