Emulsions - Surfactant Science and Technology - page 309

Hildebrand solubility parameter or cohesive energy density ( d ). The concept is that
the solubility and surface activity of a given surfactant structure can be quanti-
tatively related to the ''critical'' HLB number for the emulsification of a given
oil phase in aqueous solution by its solubility parameter or cohesive energy density
in water. The efficiency of a surfactant at emulsifying and stabilizing an oil phase
will be a function of the relative degrees of interaction of the various portions of
the surfactant molecule with the oil and aqueous phases. The original concepts
of HLB were, as seen above, based on a simple ratio of hydrophilic to hydropho-
bic groups in the molecule. With the introduction of Hildebrand solubility
parameters, usually denoted as d , as a quantitative way to calculate the solubility
of materials, especially polymers, in various solvents, an attempt was made to relate
the HLBs of a number of surfactants to their calculated d . Their results fitted the
relationship

243

d ¼

HLB þ

12 : 3 ð 9 : 12 Þ

54

where d , in SI units, is in (megapascals) 1/2 (MPa 1/2 ). More complicated treatments
used three-dimensional Hansen parameters to relate the emulsifying tendencies of
surfactants with oils in terms of the ratios of the cohesive energies of the oil and the
hydrophobic portion of the surfactant molecule and that of the water with the
hydrophilic portion. In that concept, the best result can be expected when the var-
ious components of the cohesive energy density of the three phases—oil, water, and
surfactant—are matched. The dispersion (d), polar (p), and hydrogen bonding (h)
portions of the three-dimensional solubility parameters are, to a first approximation,
related by

d 2 ¼ d d þ d p þ d h ð 9 : 13 Þ

so that division of Eq. (9.13) by d 2 will lead to

1 ¼ f d þ f p þ f h ð 9 : 14 Þ

where f is that fraction of the total solubility parameter attributable to each type of
interaction. Using that relationship, it is possible to construct a triangular diagram
that can relate the d values of each component and serve as a useful predictive tool
for emulsion formulation. Unfortunately, the utility of such an approach is some-
what limited by the scarcity of experimental data for most surfactant structures
and the complications introduced by the complex and sometimes varied composi-
tions of many industrial surfactants.
When all of the component solubility parameters of the oil and the surfactant are
matched, a relationship between HLB and chemical composition of the form

20M h
M l þ

HLB ¼ ð 9 : 15 Þ

M h