Chapter 6
Modeling Polydispersity in Multicomponent Nonideal Mixed Surfactant Systems Paul M . Holland
Downloaded by UNIV OF ARIZONA on August 10, 2012 | http://pubs.acs.org Publication Date: September 8, 1992 | doi: 10.1021/bk-1992-0501.ch006
General Research Corporation, Santa Barbara, CA 93111
A method for treating polydispersity in nonideal mixed surfactant systems is presented. This simplifies the more general regular solution approach for treating multicomponent nonideal mixtures for the special case of homologous groups of surfactant components which behave ideally within the group, and nonideally with other components in the mixture. This results in a tractable approach for treating nonideal surfactant mixtures with many components, a situation which often arises when polydisperse commercial surfactants are used in nonideal mixtures. Application of this method is used to demonstrate the effects of polydispersity on the properties of nonideal surfactant mixtures and predicted trends are shown to be consistent with experimental results. Polydisperse surfactant mixtures are used in nearly all practical applications of surfactants. This polydispersity usually arises from the presence of different isomers and the various chain length surfactant molecules that are produced when synthesizing typical commercial surfactants. Each of the different single-specie surfactants in the polydisperse mixture may exhibit different properties such as critical micelle concentration (CMC), limiting surface tension, etc. Because of this, measurement of the gross properties of a polydisperse surfactant mixture may not be adequate to properly describe the behavior of the system. In addition to the unavoidable polydispersity that arises from impurities in starting materials and the natural variability of reaction products during synthesis, mixtures of different types of surfactants are often deliberately formulated. These formulations can be used to improve surfactant system performance by exploiting synergism based on nonideal interactions between different surfactant types (2,2). As a result, mixed surfactant systems used in practical applications can often be highly complex when considered at the level of single-specie components. This situation highlights the need for a tractable approach to polydispersity in nonideal mixed surfactant systems. A number of studies on ideal and nonideal mixtures with polydisperse surfactants are reported in the literature (3-8). These include experimental mixed CMC (4-6) and 0097-6156/92/0501-0114S06.00/0 © 1992 American Chemical Society
In Mixed Surfactant Systems; Holland, P., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.
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Modeling Polydispersity in Surfactant Systems
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ultrafiltration (5,6) measurements on "binary" nonideal surfactant mixtures where one of the "surfactants" is a polydisperse mixture. These studies show CMCs to be well described using a "binary" nonideal model with a single interaction parameter (4-6) whereas micellar compositions and monomer concentrations (5,6) show deviations similar to those observed in ideal mixtures of polydisperse nonionic surfactants (3).
Downloaded by UNIV OF ARIZONA on August 10, 2012 | http://pubs.acs.org Publication Date: September 8, 1992 | doi: 10.1021/bk-1992-0501.ch006
Multicomponent Nonideal Surfactant Mixtures A generalized approach has been previously developed for treating multicomponent nonideal mixed surfactant systems and successfully demonstrated in modeling ternary mixed systems (9-11). Key results of this pseudophase separation model will be summarized here to provide a starting point for examining the effects of polydispersity (see also Chapter 2, this volume). The CMC of a system of any number of components is given by the generalized expression -7-
"
(1)
Cmu
ffi
where C ^ is the mixed CMC, a the mole fraction of component i in the total surfactant mixture, f the activity coefficient, and C* the CMC of pure component / (see Legend of Symbols). This allows the mixed CMC to be readily calculated from the composition of the system if the activity coefficients and CMCs of the singlespecie components are known. For monomer concentrations and micellar mole fractions, the generalized expression t
applies, where m = J2 t
c m
( 3 )
i»l
It is straight forward to solve this for any number of single-specie components given the activity coefficients. This allows the individual monomer concentrations to be obtained by
C + /,C, - M and the mole fractions in the micelle to be obtained from a,C *i
=
