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Theoretical aspects of micellisation in surfactant mixtures
Current Opinion in Colloid & Interface Science 6 Ž2001. 350᎐356
Theoretical aspects of micellisation in surfactant mixtures John D. HinesU Unile¨ er Research Laboratory, Oli¨ ier ¨ an Noortlaan 120, 3133 AT Vlaardingen, The Netherlands
Abstract Mixtures of surfactants in aqueous solution provide a complex and rich challenge to theoretical description. Micellisation and micelle growth are areas of central importance and are the focus of this review. Recently, many novel experimental techniques have been developed and used to obtain data that would previously have been very difficult or impossible to find. This has in turn fuelled theoretical work so it is not surprising to find that this period has seen many challenges made to established approaches and new ones developed. Regular solution theory continues to be widely applied, however, several experimentalists have independently called attention to its limitations. Molecular thermodynamic approaches have been developed to increasing levels of complexity and broader ranges of application, in many cases, superseding the regular solution approach in the arsenal of experimenters. Significant advances have been made both in the breadth and in the depth of the molecular thermodynamic models available, now including adsorption in addition to the micellar case. True molecular approaches to micellisation in practical systems are still some way off, but recent work using lattice models brings this closer. 䊚 2001 Elsevier Science Ltd. All rights reserved. Keywords: Surfactant; Micelle; Mixture; Non-ideal; Regular; Solution; Molecular; Thermodynamic; Theory; Adsorption
1. Introduction The study of mixing in surfactant systems has for some time now been an area of particular activity both in academic and industrial research. Within this field, which in principle deals with interactions of mixed systems in the bulk solution and at interfaces as well as with other components Že.g. polymers., study of micellisation is most popular. This is understandable given the relative ease with which data for the critical micelle concentration Žcmc. and micelle size and kinetics can be obtained and also given the importance often placed on these values Žparticularly the cmc. in defining other aspects of solution behaviour.
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Tel.: q31-10-460-5497; fax: q31-10-460-5192. E-mail address: [email protected] ŽJ.D. Hines..
It is fair to say that the majority of activity has been confined to experimental study and documentation of behaviour in situations that are for the most part poorly understood at a theoretical level. One simple model ᎏ the regular solution treatment ŽRST. as proposed initially by Rubingh w1x ᎏ is ubiquitous in this area and has proved, surprisingly perhaps, extremely useful in characterising and differentiating between systems and the type and extent of interactions that they contain. Surprising not because this model is fundamentally flawed, but rather because it is so simple that to successfully describe self-aggregation behaviour in a system containing more than one type of complex amphiphilic molecule might seem unlikely. Unfortunately, this very success has resulted in many cases, of far too much importance and theoretical credence being placed on certain aspects of the model, e.g. the suggestion that excess entropy of micellisation must be zero, such that genuine and
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J.D. Hines r Current Opinion in Colloid & Interface Science 6 (2001) 350᎐356
substantive progress towards deeper understanding has sometimes been slow. Within the last decade and particularly the last few years, two distinct trends away from this approach have emerged. Crudely divided, the first of these can be characterised as experimental work which has shown deficiencies in the simple model, either by accessing new areas of information Žby utilising newly developed measurement techniques . or by making better more accurate measurements of the cmc on ever more complex mixtures. To some extent driven by this and to some extent independently, the second trend has been towards the development of more rigorous and refined theoretical descriptions. The purpose of this review is principally, to update on the latter trend, but to do so in the absence of the context provided by the former would be relatively valueless. Reviews of overlapping subjects have already been presented in this and other journals by Blankschtein w2x and also by Kronberg w3x both in 1997 and by Khan and Marques w4x in 1999. While some overlap with these is inevitable, as much attention as possible has been focussed on most recent developments.
2. Context: experiment and application As well as being of enormous interest for purely academic reasons, investigation of mixed surfactants has been fuelled for several years by a continuing desire on the part of industry to better understand and, hence make better use of such systems. This desire stems from the understanding at a relatively general level that in many cases, the physical proper-
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ties of such systems can lie outside the boundaries defined by each component and the realisation that proper manipulation of such properties can greatly enhance the performance of many commercial products. Due to the cost of such formulations, this science has been most widely applied in markets such as personal cleaning products, hair care and laundry. Of the physical properties examined in detail, the cmc has been most popular, however, in more recent times, growth in new experimental methodologies has been accompanied by an increase in the amount and quality of data on micelle size w5᎐9x and shape w10᎐12x, micellar dynamics w13᎐16x and ᎏ importantly for mixtures ᎏ micelle composition w17᎐20x. These new data have in turn provided the fuel for improved theoretical understanding. The regular solution approach presented by Rubingh w1x and then used widely Žsee e.g. w21x for a reasonably recent list of contributions . owes much of its success to its simplicity. A single adjustable parameter Žoften referred to as  . is applied to the ideal binary mixing model of Lange and Beck w22x to account for non-ideal interactions. Many binary mixtures have been treated in this way and Holland w23x has extended the treatment to the general multi-component case. The parameter , although it has no physical significance, has been used to describe details of interactions w21x and has proved useful in determining crude classes of ‘types’ of interaction that can occur. Prediction of mixed cmc andror micelle composition using the RST approach requires that the cmc of both pure components Žin the binary case. and one mixture be measured.  can then be calculated and
Fig. 1. Dependence of calculated cmc vs. composition on the data used. Diamonds are measured points and curves are calculated on the basis of each. Surfactants are SDS and C 12 B at 298 K. RST calculations using data measured from surface tension curves and presented in ref. w26 䢇 䢇 x.
J.D. Hines r Current Opinion in Colloid & Interface Science 6 (2001) 350᎐356
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used to generate the desired values for the whole composition range. This is of course exactly the sort of information that industrial researchers in particular are looking for. Within the last 3᎐4 years, however, there have been several independent studies published to show that, for many important cases, the cmc is not at all well described by this simple model w24 ,25,26 ,27,28 x. An example of this data is shown in Fig. 1, taken from the 1998 work of Hines et al. w26 x on a relatively strongly interacting mixture of anionic Žsodium dodecyl sulfate ᎏ SDS. and zwitterionic Ž n-dodecyl-N, N-dimethyl amino betaine ᎏ C 12 B. surfactants. It is clearly evident that each experimental measurement produces a different value of  and hence a different set of predictions. Prediction error is as high as 100%. This and other careful work by Eads and Robosky w24 x and Huang and Somasundaran w28 x have shown that such error is not inherent in the experiment, but is evidential of a fundamental shortcoming in the single parameter model. The accuracy and, in some cases, validity of the single parameter model have also been brought into question by new data arising from novel techniques. In particular, Penfold et al. w29 ,30 ,31x, Staples et al. w32x and Hines et al. w25᎐27x have utilised neutron reflectivity and scattering to directly interrogate the composition of micelles and adsorbed layers on a number of substrates. In addition, pulsed-field-gradient NMR measurements made by Eads and Robosky w24 x and ultrafiltration data gathered by Huang and Somasundaran w28 x have led to the same conclusion ᎏ that the predicted compositions obtained from the single parameter model are prone, even more than the cmc, to large errors and inaccuracies. Aside from cmc and composition, many additional important physical properties of mixed micelles have been identified and can now be accurately measured. In particular, the size and shape of aggregates has been measured both by light and neutron scattering w5᎐12x. It has been shown w7᎐10,33,34x that in mixed systems these properties, along with the composition, are not monodisperse but rather follow often wide and heavily skewed distributions. This along with the recognition that such asymmetry can have profound impact on macroscopic properties Žsuch as those of commercial significance. has also contributed to the desire to find better, more rigorous and complete theoretical descriptions. 䢇䢇
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3. Theoretical approaches Within the context that these new experimental directions have provided, several key advances in theory have taken place in recent years. Not surprisingly,
in many cases, the same driving forces are present and in more than one instance, the same set of workers. In keeping with the structure already applied, it is useful to consider these advances in groups by their genealogy, or to put it another way, by first considering the starting point in each case. Perhaps the best place to begin such an analysis is with those approaches arising directly out of the original RST approach w1x previously described and applied so widely. In many cases, the same workers who have been instrumental in drawing attention to the weaknesses and limitations of the standard approach have also attempted to improve upon it. Most notably, Huang and Somasundaran w28 x and Eads and Robosky w24 x have described almost the same enhancements entirely independently. In both cases, experimental evidence has shown that the micelle composition in certain strongly interacting systems is not well described by RST. Both sets of workers have observed that the non-ideality parameter calculated varies with composition Žand concentration . in a way, which is not allowed by the model. This is because the single parameter relates excess free energy to the micelle composition in a way that forces the former to follow a symmetrical path with respect to the latter. In addressing the limitations of RST, they both use this as the weak link and invoke a new, second parameter to separately treat asymmetry in both the cmc and the micelle composition. In many ways, it is not surprising that two independent investigations should both arrive at the same conclusions ᎏ the use of a single parameter and the restrictions that it imposes are both the weak and strong points of RST. As experimentation exposes the limitations in this, so improvements will be made. Both Huang and Somasundaran w28 x and Eads and Robosky w24 x phrase the second adjustable parameter in terms of a contribution by asymmetry in the components of the mixture. In one case w28 x, the phrase ‘packing parameter’ is used while in the other w24 x van Laar expressions are identified as containing the necessary dependence not only on the cmc of each component but also on its physical size Žand hence packing.. Again, this route is probably the most obvious one to take and has many merits. It is clear though that from the data presented that the story is not complete. In their paper w24 x, Eads and Robosky concede that in some cases apparent asymmetry is observed when both surfactants present are of very similar size and shape Žhence the contribution from the second van Laar parameter would be expected to be small.. It is clear that these approaches are asking the right questions but perhaps are still too heavily influenced by the single parameter model. Hines et al. w26 x have also used multi-parameter approaches to 䢇䢇
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J.D. Hines r Current Opinion in Colloid & Interface Science 6 (2001) 350᎐356
model their experimental data. In this case, however, no physical significance is inferred ᎏ rather the data is fitted to yield essentially accurate descriptions of the important free energy terms ᎏexcess enthalpy and entropy. While not in itself predictive, this work is perhaps a more honest assessment of the application of classical thermodynamic models to mixed micellisation and certainly the information obtained has been of enormous value in building more rigorous theories. Finally along this theme, the 1996 paper of Georgiev is worth mentioning w35 x, even though it has already appeared in a review of this type. This work is notable for its individuality ᎏ Georgiev takes the Markov chain approach to polymerisation and applies it directly to the formation and growth of micelles. In principle a very interesting and credible idea. Indeed this is one of the few truly different classical approaches seen in recent times. Unfortunately, the model has not been significantly used since in its current form it does not add substantially to the information available from standard RST and requires substantially more data to generate the necessary parameters. In his paper, Georgiev again brings this standard model to bear as a reference point for his new parameters. It would be interesting to see what progress could be made by removing this unnecessary and restrictive link. Another important branch of mixing theory that has seen substantial growth in recent times is the molecular thermodynamic ŽMT. approach due in the most part to earlier work by Nagarajan and Ruckenstein w36,37x and Blankschtein and various co-workers w38᎐41x. This approach is based in essence on the much earlier work of Israelachvili, Mitchell and Ninham w42,43x who identified regimes of packing within various micellar shapes. By calculating the variation in magnitude of important energetic considerations as a function of changing micellar shape Žand hence molecular packing., essentially ab initio calculation of the cmc as well as a variety of other key properties can be made. The MT approach holds the important advantages over the classical model that it is not restricted to parameterisation of activity coefficients ᎏ within these energy contributions no artificial symmetry is implied ᎏ and that as a molecular theory, genuine prediction without experimentation is possible. In addition, this is a much more practical approach in many ways than pure simulation, based as it is on only a relatively small number of considerations. The last 3᎐4 years has seen arguably more activity in this particular area than in any other covered by this review. Perhaps a key reason for this is the increasing appreciation among many workers not intimately connected with one model or other of the 䢇
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practical limitations of RST. The former has certainly been, and continues to be, of enormous value in many practical situations, but the MT approach offers much more flexibility and depth. Examples of this relatively recent level of application can be found in the 1998 paper of Meagher et al. w44x, which discusses experimentally observed enthalpy of micellisation measurements in the light of the MT approach, and also in the 1999 work of Lopez-Fontan et al. w45x which compares experimental data on the influence of chain length on micellar composition with a variety of available models. It is fair to say that up until most recent times, excellent experimental work such as this would almost certainly have drawn solely upon RST for theoretical comparison. The recent work of Reif and Somasundaran w46 x has applied the inherent flexibility of the MT approach to some of the issues raised by restrictions in RST. Specifically, they describe how asymmetry in excess free energy can lead to significant differences between actual activity coefficients and those produced by either RST or the simplest version of the MT model. The remaining challenge of course is to improve on this state. Extension of the MT approach itself has continued and indeed gathered pace in recent times. Much of this activity has, as previously, come from the group of Blankschtein who, along with various co-workers, has in the past 3᎐4 years tackled several outstanding issues. The issue of growth of mixed micelles, not well addressed by RST or other classical models, can be included naturally within a MT framework. This issue has been addressed with some success in both all non-ionic w47,48 x and ionicrnon-ionic w49x systems, at least for relatively regular patterns. Perhaps more critically, a much more rigorous consideration of electrostatic forces in charged mixed micelles has been developed w50 ,51x, such that not only can essentially arbitrary mixtures of ionic and non-ionic surfactants be treated, but also zwitterionic components can be included within precisely the same framework. The same group has also shown how the MT approach can be extended from the binary to the general multicomponent case w52 ,53x, albeit with some reference to earlier RST work w23x and, not least, they have done a great deal to popularise this model by describing user-friendly software tools w53᎐55x and by reporting on commercial w53x as well as new academic applications. Also using the MT approach, the 2000 work of Braibanti et al. w56x has examined in much greater detail than before the nature of the hydrophobic contribution to the total free energy of micellisation. Combined with parameterisation of experimental data, they produce a molecular thermodynamic model of this process that explicitly includes the relationship of 䢇䢇
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J.D. Hines r Current Opinion in Colloid & Interface Science 6 (2001) 350᎐356
the number of molecules of water restructured by the presence of hydrophobic entities. Although micellisation per se is considered, specific issues relating to mixtures are not. This is an important step though along the road to a more complete and flexible solution. Finally, in this area, and not specifically covering micellisation, several authors have tackled independently the issues of extension of the MT model to interfaces and other situations. Mulqueen and Blankschtein w57x and Hines w58x have formulated interfacial models based very closely on the micellar case. These of course have the advantage of containing an inherent transparency between the two processes in bulk and at interfaces. It is clear that many of the same fundamental driving forces are at work and these approaches accurately mirror that. Although not quite as closely related, and dealing with the very specific case of redox-induced changes in adsorption, the work of Aydogan et al. w59x also represents a broadening of the MT approach to deal with interfacial issues. The recent work of Li et al. w60x, in which a molecular thermodynamic approach to treat microemulsion containing systems is described, can be viewed as a similar and consistent extension to the approach, retaining as it does the clear and fundamental building blocks. Looking more broadly at molecular based theories of micellisation, one notes a considerable amount of work in recent times focussed on the problem in general, but much less concerned with mixing in detail. Lattice models have been used with some success to describe aggregation behaviour in the context of Monte Carlo simulations, but these still suffer from the difficulties of translation of important properties from real systems. Bhattacharya and Mahanti w61x have addressed this issue to some extent by reference back to the MT approach, with which they show good agreement. In the related field of polymer-surfactant interactions, work has tended to focus much more on molecular approaches and use of simulation. Here, of course, the micelle itself has often been treated as a sphere or regular shape with a certain, applied charge density. Some cross-over between the two levels of detail has been applied by Konop and Colby w62 x who, coming more from the polymer side of the issue, address in some detail, the nature of the charged surface of a micelle in terms of counter-ion condensation, initially of small independent species then later of polyions. Although again not specifically considering mixing, this treatment also contains some useful insights to that problem and should be considered and assimilated as the area moves forward. 䢇䢇
4. Summary and conclusions This review has described some of the recent advances and major forward steps in theoretical evaluation of micellisation in mixed surfactant systems. It has tried to do this within a very clear and explicit context that is defined largely by experimentation and by observation of deficiencies in current working models. That is a very important point and suggests, in the humble opinion of the author that this area is in very good scientific health. The constant challenge to theory of new and more probing experiment, and the subsequent refining of that theory, is what drives true understanding. Within that context, we have seen in recent times a growing appreciation in the wider experimental community that existing theory may have reached its limits. Newer and more rigorous approaches that have been available for some time have now become themselves the subject of much more interest and, consequently, critique. In a number of areas, particularly in mixed systems, this increased overlap of experiment and theory has led directly to important insights and new theoretical approaches. For the future, it is important that this interaction continues. There are of course a number of issues still not completely resolved. Of these, two can be identified as critical. The nature of energetics of mixing in micelles and at surfaces should be more generally described. The role of the solvent is clearly important but it is only very recently that this has been made explicit in theory. Many of the apparent restrictions on practical application of theory stem from the assumptions made at this level, so these should certainly be addressed. The second area is the application of increasingly complex models and theories to predict more and different information, some of which may be very difficult to access experimentally. An example using MT theory might be the size and shape of micelles as well as the cmc. More properties should be explored and their importance to practical problems examined. References and recommended reading 䢇 䢇䢇
of special interest of outstanding interest
w1x Rubingh DN. In: Mittal KL, editor. Solution chemistry of surfactants. New York: Plenum, 1979. w2x Blankschtein D, Shiloach A, Zoeller N. Thermodynamic theories of micellar and vesicular systems. Curr Opinion Coll Interface Sci 1997;2:294᎐300. w3x Kronberg B. Surfactant mixtures. Curr Opinion Coll Interface Sci 1997;2:456᎐463. w4x Khan A, Marques EF. Synergism and polymorphism in mixed surfactant systems. Curr Opinion Coll Interface Sci 2000;4:402᎐410.
J.D. Hines r Current Opinion in Colloid & Interface Science 6 (2001) 350᎐356 w5x Lichtenberg D, Opatowski E, Kozlov MM. Phase boundaries in mixtures of membrane-forming amphiphiles and micelleforming amphiphiles. BBA-Biomembranes 2000;1508:1᎐19. w6x Lesieur P, Kiselev MA, Barsukov LI, Lombardo D. Temperature-induced micelle to vesicle transition: kinetic effects in the DMPCrNaC system. J Appl Crystallogr 2000;33:623᎐627. w7x Bergstrom M, Pedersen JS. A small-angle neutron scattering ŽSANS. study of tablet-shaped and ribbon-like micelles formed from mixtures of an anionic and a cationic surfactant. J Phys Chem B 2000;103:8502᎐8513. w8x Griffiths PC, Whatton ML et al. Small-angle neutron scattering and fluorescence studies of mixed surfactants with dodecyl tails. J Colloid Interface Sci 2000;215:114᎐123. w9x Li F, Li GZ, Chen JB. Synergism in mixed zwitterionic-anionic surfactant solutions and the aggregation numbers of the mixed micelles. Coll Surf A 1998;145:167᎐174. w10x Bergstrom M. Thermodynamics of anisotropic surfactant micelles. I. The influence of curvature free energy on the micellar size and shape. J Chem Phys 2000;113:5559᎐5568. w11x Chen L, Shen HW, Eisenberg A. Kinetics and mechanism of the rod-to-vesicle transition of block copolymer aggregates in dilute solution. J Phys Chem B 1999;103:9488᎐9497. w12x Asakawa T, Sunagawa H, Miyagishi S. Diffusion coefficients of micelles composed of fluorocarbon surfactants with cyclic voltammetry. Langmuir 1998;14:7091᎐7094. w13x Telgmann T, Kaatze U. Monomer exchange and concentration fluctuations in polyŽethylene glycol. monoalkyl etherrwater mixtures. Dependence upon non-ionic surfactant composition. J Phys Chem A 2000;104:4846᎐4856. w14x Kaatze U, Hushcha TO, Eggers F. Ultrasonic broadband spectrometry of liquids: a research tool in pure and applied chemistry and chemical physics. J Solut Chem 2000;29: 299᎐368. w15x Costantino L, D’Errico G, Roscigno P, Vitagliano V. Effect of urea and alkylureas on micelle formation by a non-ionic surfactant with short hydrophobic tail at 25⬚C. J Phys Chem B 2000;104:7326᎐7333. w16x O’Connor AJ, Hatton TA, Bose A. Dynamics of micellevesicle transitions in aqueous anionicrcationic surfactant mixtures. Langmuir 2000;13:6931᎐6940. w17x Merta J, Garamus VM, Kuklin AI, Willumeit R, Stenius P. Determination of the structure of complexes formed by a cationic polymer and mixed anionic surfactants by small-angle neutron scattering. Langmuir 2000;16:10061᎐10068. w18x Griffiths PC, Roe JA, Jenkins RL et al. Micellization of sodium dodecyl sulfate with a series of non-ionic n-alkyl malono-bis-N-methylglucamides in the presence and absence of gelatin. Langmuir 2000;16:9983᎐9990. w19x Blandamer MJ, Briggs B, Cullis PM, Engberts JBFN. Titration microcalorimetry of mixed alkyltrimethylammonium bromide surfactant aqueous solutions. Phys Chem Chem Phys 2000;2:5146᎐5153. w20x Ruiz CC, Aguiar J. Interaction, stability, and microenvironmental properties of mixed micelles of Triton X100 and n-alkyltrimethylammonium bromides: influence of alkyl chain length. Langmuir 2000;16:7946᎐7953. w21x Rosen MJ. Surfacants and interfacial phenomena. 2nd edition New York: John Wiley and Sons, 1989. w22x Lange H, Beck KH. Koll Z-Z Polym 1973;251:424. w23x Holland PM, Rubingh DN. Non-ideal multicomponent mixed micelle model. J Phys Chem-US 1983;87:1984᎐1990. w24x Eads CD, Robosky LC. NMR studies of binary surfactant 䢇䢇 mixture thermodynamics: molecular size model for asymmetric activity coefficients. Langmuir 1999;15:2661᎐2668. Takes careful experimental data and identifies inconsistencies with calculated micelle compositions using RST. Extended thermody-
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namic analysis introducing second parameter of interaction yields more accurate predictions. w25x Hines JD, Thomas RK, Garrett PR, Rennie GK, Penfold J. A study of the interactions in a ternary surfactant system in micelles and adsorbed layers. J Phys Chem B 1998;102: 9708᎐9713. w26x Hines JD, Thomas RK, Garrett PR, Rennie GK, Penfold J. 䢇䢇 Investigation of mixing in binary surfactant solutions by surface tension and neutron reflection: strongly interacting anionicrzwitterionic mixtures. J Phys Chem B 1998;102: 8834᎐8846. A very thorough experimental analysis of a strongly interacting binary system using traditional as well as more modern approaches ŽNR.. Detailed thermodynamic analysis including scope for further parameterisation is made but explicitly without forced interpretation of parameters. Conclusions made as to nature and origin of excess free energy of mixing. w27x Hines JD, Thomas RK, Garrett PR, Rennie GK, Penfold J. Investigation of mixing in binary surfactant solutions by surface tension and neutron reflection: anionicrnon-ionic and zwitterionicrnon-ionic mixtures. J Phys Chem B 1997;101: 9215᎐9223. w28x Huang L, Somasundaran P. Theoretical model and phase 䢇䢇 behaviour for binary surfactant mixtures. Langmuir 1997;13:6683᎐6688. Novel approach made to experimental investigation of binary mixtures. Micelle compositions observed do not agree with predictions of RST. Further analysis confined to traditional thermodynamics, but introduces concept of second ‘packing’ parameter. w29x Lu JR, Thomas RK, Penfold J. Surfactant layers at the 䢇䢇 airrwater interface: structure and composition. Adv Colloid Interface Sci 2000;84:143᎐304. Summary and review of much work done using neutron reflectively to probe mixed surfactant layers. Significant new information has been obtained in this way to push theory into new and important directions. w30x Penfold J, Staples E, Thompson L et al. Structure and com䢇 position of mixed surfactant micelles of sodium dodecyl sulfate and hexaethylene glycol monododecyl ether and of hexadecyltrimethylammonium bromide and hexaethylene glycol monododecyl ether. J Phys Chem B 1999;103:5204᎐5211. Experimental analysis using neutron reflectivity and scattering that again highlights inconsistencies and limitations of prevailing models. w31x Penfold J, Staples E, Tucker I et al. The composition of mixed surfactants and cationic polymerrsurfactant mixtures adsorbed at the air-water interface. Coll Surf A 1997;128: 107᎐117. w32x Staples E, Tucker I, Penfold J, Warren N, Thomas RK. The structure and composition of surfactant-polymer mixtures of sodium dodecyl sulfate, hexaethylene glycol monododecyl ether and poly-Ždimethyldialyl ammonium chloride. adsorbed at the air-water interface. J Phys-Condens Mat 2000;12: 6023᎐6038. w33x Aswal VK, Goyal PS. Mixed micelles of alkyltrimethylammonium halides: a small-angle neutron-scattering study. Physica B 1998;245:73᎐80. w34x de la Maza A, Coderch L, Lopez O, Parra JL. Transmission electron microscopy and light scattering studies on the interaction of a non-ionicranionic surfactant mixture with phosphatidylcholine liposomes. Micro Res Tech 1998;40:63᎐71. w35x Geogiev GS. Markov chain model of mixed surfactant sys䢇 tems 1. New expression for the non-ideal interaction parameter. Colloid Polym Sci 1996;274:49᎐58. Innovative and individual work proposing novel model for mixed micellisation. Has been under-utilised since publication.
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w36x Nagarajan R, Ruckenstein E. Theory of surfactant self-assembly: a predictive molecular thermodynamic approach. Langmuir 1991;7:2934᎐2969. w37x Nagarajan R. Molecular theory for mixed micelles. Langmuir 1985;1:331᎐341. w38x Naor A, Puvvada S, Blankschtein D. An analytical expression for the free-energy of micellisation. J Phys Chem-US 1992;96:7830᎐7832. w39x Puvvada S, Blankschtein D. Thermodynamic description of micellization, phase-behaviour, and phase-separation of aqueous-solutions of surfactant mixtures. J Phys Chem US 1992;96:5567᎐5579. w40x Puvvada S, Blankschtein D. Theoretical and experimental investigations of micellar properties of aqueous-solutions containing binary-mixtures of non-ionic surfactants. J Phys Chem-US 1992;96:5579᎐5592. w41x Sarmoria C, Puvvada S, Blankschtein D. Prediction of critical micelle concentrations of non--ideal binary surfactant mixtures. Langmuir 1992;8:2690᎐2697. w42x Israelachvili JN, Mitchell DJ, Ninham BW. Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers. J.Chem.Soc. Faraday Trans. II 1976;72:1525᎐1568. w43x Israelachvili JN, Mitchell DJ, Ninham BW. Theory of self-assembly of lipid bilayers and vesicles. Biochim Biophys Acta 1977;470:185᎐201. w44x Meagher RJ, Hatton TA, Bose A. Enthalpy measurements in aqueous SDSrDTAB solutions using isothermal titration microcalorimetry. Langmuir 1998;14:4081᎐4087. w45x Lopez-Fontan JL, Suarez MJ, Mosquera V, Sarmiento F. Mixed micelles of n-alkyltrimethylammonium bromides: influence of alkyl chain length. Phys Chem Chem Phys 1999;15:3583᎐3587. w46x Rief I, Somasundaran P. Asymmetric excess free energies and 䢇䢇 variable interaction parameters in mixed micellization. Langmuir 1999;15:3411᎐3417. Following on from the work of Huang and Somasundaran w28 䢇 䢇 x and also of Hines et al. w26 䢇 䢇 x, this work considers for the first time explicitly the issue of potentially asymmetric free energies in the context of the molecular thermodynamic framework. w47x Thomas HG, Lomakin A, Blankschtein D, Benedek GB. Growth of mixed non-ionic micelles. Langmuir 1997; 13:209᎐218. w48x Zoeller N, Lue L, Blankschtein D. Statistical-thermodynamic 䢇䢇 framework to model non-ionic micellar solutions. Langmuir 1997;13:5258᎐5275. Important extension and significant re-formulation of the existing molecular thermodynamic model based on a considerably more rigorous statistical thermodynamic treatment of micellisation in non-ionic surfactant systems. w49x Shiloach A, Blankschtein D. Measurement and prediction of ionicrnon-ionic mixed micelle formation and growth. Langmuir 1998;14:7166᎐7182. w50x Shiloach A, Blankschtein D. Prediction of critical micelle 䢇䢇 concentrations and synergism of binary surfactant mixtures containing zwitterionic surfactants. Langmuir 1997;13: 3968᎐3981. Important extension of the molecular thermodynamic approach in
which the formalism used to calculate electrostatic free energy contributions in significantly re-written and dealt with in much more detail and rigour. This allows among other things an integrated approach to be taken for ionic and zwitterionic surfactants but is in general a much more complete appraisal of the situation. w51x Shiloach A, Blankschtein D. Predicting micellar solution properties of binary surfactant mixtures. Langmuir 1998;14: 1618᎐1636. w52x Shiloach A, Blankschtein D. Prediction of critical micelle 䢇 concentrations of non-ideal ternary surfactant mixtures. Langmuir 1998;14:4105᎐4114. First work to eplicitly combine the existing work in RST due to Holland and Rubingh w23x with the molecular thermodynamic approach to allow simple treatment of mixtures of more than two surfactants. w53x Coret J, Shiloach A, Berger P, Blankschtein D. Critical micelle concentrations of ternary surfactant mixtures: theoretical prediction with user-friendly computer programs and experimental design analysis. J Surf Det 1999;2:51᎐58. w54x Zoeller NJ, Shiloach A, Blankschtein D. Predicting surfactant solution behaviour. CHEMTECH 1996;26:24᎐31. w55x Blankschtein D, Shiloach A, Zoeller N. User-friendly computer programs to predict surfactant solution behaviour. J Soc Cos Chem 1997;48:71᎐72. w56x Braibanti A, Fisicaro E, Compari C. Hydrophobic effect solubility of non-polar substances in water, protein denaturation and micelle formation. J Therm Anal Calorimetry 2000;61:461᎐481. w57x Mulqueen M, Blankschtein D. Prediction of equilibrium surface tension and surface adsorption of aqueous surfactant mixtures containing zwitterionic surfactants. Langmuir 2000;16:7640᎐7654. w58x Hines JD. A molecular thermodynamic approach to the prediction of adsorbed layer properties of single and mixed surfactant systems. Langmuir 2000;16:7575᎐7588. w59x Aydogan N, Gallardo BS, Abbott NL. A molecular-thermodynamic model for Gibbs monolayers formed from redox-active surfactants at the surfaces of aqueous solutions: redox-induced changes in surface tension. Langmuir 1999;15:722᎐730. w60x Li XS, Lu JF, Li YG, Liu JC. A new molecular thermodynamic model for osmotic pressures in micelle and oil water microemulsion systems with non-ionic and ionic surfactants. Ind Eng Chem Res 1999;38:2817᎐2823. w61x Bhattacharya A, Mahanti SD. Energy and size fluctuations of amphiphilic aggregates in a lattice model. J Phys Condens Matter 2000;12:6141᎐6160. w62x Konop AJ, Colby RH. Role of condensed counterions in the 䢇䢇 thermodynamics of surfactant micelle formation with and without oppositely charged polyelectrolytes. Langmuir 1999;15:58᎐65. Important work that makes explicit the considerations involved in treating the energetics of counter-ion condensation as part of the process of micellisation. Mainly focuses on the use of such considerations in treating surfactant-polymer complex formation, but contains many important insights that can progress the state-of-theart in predicting surfactant mixture behaviour.
Theoretical aspects of micellisation in surfactant mixtures John D. HinesU Unile¨ er Research Laboratory, Oli¨ ier ¨ an Noortlaan 120, 3133 AT Vlaardingen, The Netherlands
Abstract Mixtures of surfactants in aqueous solution provide a complex and rich challenge to theoretical description. Micellisation and micelle growth are areas of central importance and are the focus of this review. Recently, many novel experimental techniques have been developed and used to obtain data that would previously have been very difficult or impossible to find. This has in turn fuelled theoretical work so it is not surprising to find that this period has seen many challenges made to established approaches and new ones developed. Regular solution theory continues to be widely applied, however, several experimentalists have independently called attention to its limitations. Molecular thermodynamic approaches have been developed to increasing levels of complexity and broader ranges of application, in many cases, superseding the regular solution approach in the arsenal of experimenters. Significant advances have been made both in the breadth and in the depth of the molecular thermodynamic models available, now including adsorption in addition to the micellar case. True molecular approaches to micellisation in practical systems are still some way off, but recent work using lattice models brings this closer. 䊚 2001 Elsevier Science Ltd. All rights reserved. Keywords: Surfactant; Micelle; Mixture; Non-ideal; Regular; Solution; Molecular; Thermodynamic; Theory; Adsorption
1. Introduction The study of mixing in surfactant systems has for some time now been an area of particular activity both in academic and industrial research. Within this field, which in principle deals with interactions of mixed systems in the bulk solution and at interfaces as well as with other components Že.g. polymers., study of micellisation is most popular. This is understandable given the relative ease with which data for the critical micelle concentration Žcmc. and micelle size and kinetics can be obtained and also given the importance often placed on these values Žparticularly the cmc. in defining other aspects of solution behaviour.
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Tel.: q31-10-460-5497; fax: q31-10-460-5192. E-mail address: [email protected] ŽJ.D. Hines..
It is fair to say that the majority of activity has been confined to experimental study and documentation of behaviour in situations that are for the most part poorly understood at a theoretical level. One simple model ᎏ the regular solution treatment ŽRST. as proposed initially by Rubingh w1x ᎏ is ubiquitous in this area and has proved, surprisingly perhaps, extremely useful in characterising and differentiating between systems and the type and extent of interactions that they contain. Surprising not because this model is fundamentally flawed, but rather because it is so simple that to successfully describe self-aggregation behaviour in a system containing more than one type of complex amphiphilic molecule might seem unlikely. Unfortunately, this very success has resulted in many cases, of far too much importance and theoretical credence being placed on certain aspects of the model, e.g. the suggestion that excess entropy of micellisation must be zero, such that genuine and
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substantive progress towards deeper understanding has sometimes been slow. Within the last decade and particularly the last few years, two distinct trends away from this approach have emerged. Crudely divided, the first of these can be characterised as experimental work which has shown deficiencies in the simple model, either by accessing new areas of information Žby utilising newly developed measurement techniques . or by making better more accurate measurements of the cmc on ever more complex mixtures. To some extent driven by this and to some extent independently, the second trend has been towards the development of more rigorous and refined theoretical descriptions. The purpose of this review is principally, to update on the latter trend, but to do so in the absence of the context provided by the former would be relatively valueless. Reviews of overlapping subjects have already been presented in this and other journals by Blankschtein w2x and also by Kronberg w3x both in 1997 and by Khan and Marques w4x in 1999. While some overlap with these is inevitable, as much attention as possible has been focussed on most recent developments.
2. Context: experiment and application As well as being of enormous interest for purely academic reasons, investigation of mixed surfactants has been fuelled for several years by a continuing desire on the part of industry to better understand and, hence make better use of such systems. This desire stems from the understanding at a relatively general level that in many cases, the physical proper-
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ties of such systems can lie outside the boundaries defined by each component and the realisation that proper manipulation of such properties can greatly enhance the performance of many commercial products. Due to the cost of such formulations, this science has been most widely applied in markets such as personal cleaning products, hair care and laundry. Of the physical properties examined in detail, the cmc has been most popular, however, in more recent times, growth in new experimental methodologies has been accompanied by an increase in the amount and quality of data on micelle size w5᎐9x and shape w10᎐12x, micellar dynamics w13᎐16x and ᎏ importantly for mixtures ᎏ micelle composition w17᎐20x. These new data have in turn provided the fuel for improved theoretical understanding. The regular solution approach presented by Rubingh w1x and then used widely Žsee e.g. w21x for a reasonably recent list of contributions . owes much of its success to its simplicity. A single adjustable parameter Žoften referred to as  . is applied to the ideal binary mixing model of Lange and Beck w22x to account for non-ideal interactions. Many binary mixtures have been treated in this way and Holland w23x has extended the treatment to the general multi-component case. The parameter , although it has no physical significance, has been used to describe details of interactions w21x and has proved useful in determining crude classes of ‘types’ of interaction that can occur. Prediction of mixed cmc andror micelle composition using the RST approach requires that the cmc of both pure components Žin the binary case. and one mixture be measured.  can then be calculated and
Fig. 1. Dependence of calculated cmc vs. composition on the data used. Diamonds are measured points and curves are calculated on the basis of each. Surfactants are SDS and C 12 B at 298 K. RST calculations using data measured from surface tension curves and presented in ref. w26 䢇 䢇 x.
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used to generate the desired values for the whole composition range. This is of course exactly the sort of information that industrial researchers in particular are looking for. Within the last 3᎐4 years, however, there have been several independent studies published to show that, for many important cases, the cmc is not at all well described by this simple model w24 ,25,26 ,27,28 x. An example of this data is shown in Fig. 1, taken from the 1998 work of Hines et al. w26 x on a relatively strongly interacting mixture of anionic Žsodium dodecyl sulfate ᎏ SDS. and zwitterionic Ž n-dodecyl-N, N-dimethyl amino betaine ᎏ C 12 B. surfactants. It is clearly evident that each experimental measurement produces a different value of  and hence a different set of predictions. Prediction error is as high as 100%. This and other careful work by Eads and Robosky w24 x and Huang and Somasundaran w28 x have shown that such error is not inherent in the experiment, but is evidential of a fundamental shortcoming in the single parameter model. The accuracy and, in some cases, validity of the single parameter model have also been brought into question by new data arising from novel techniques. In particular, Penfold et al. w29 ,30 ,31x, Staples et al. w32x and Hines et al. w25᎐27x have utilised neutron reflectivity and scattering to directly interrogate the composition of micelles and adsorbed layers on a number of substrates. In addition, pulsed-field-gradient NMR measurements made by Eads and Robosky w24 x and ultrafiltration data gathered by Huang and Somasundaran w28 x have led to the same conclusion ᎏ that the predicted compositions obtained from the single parameter model are prone, even more than the cmc, to large errors and inaccuracies. Aside from cmc and composition, many additional important physical properties of mixed micelles have been identified and can now be accurately measured. In particular, the size and shape of aggregates has been measured both by light and neutron scattering w5᎐12x. It has been shown w7᎐10,33,34x that in mixed systems these properties, along with the composition, are not monodisperse but rather follow often wide and heavily skewed distributions. This along with the recognition that such asymmetry can have profound impact on macroscopic properties Žsuch as those of commercial significance. has also contributed to the desire to find better, more rigorous and complete theoretical descriptions. 䢇䢇
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3. Theoretical approaches Within the context that these new experimental directions have provided, several key advances in theory have taken place in recent years. Not surprisingly,
in many cases, the same driving forces are present and in more than one instance, the same set of workers. In keeping with the structure already applied, it is useful to consider these advances in groups by their genealogy, or to put it another way, by first considering the starting point in each case. Perhaps the best place to begin such an analysis is with those approaches arising directly out of the original RST approach w1x previously described and applied so widely. In many cases, the same workers who have been instrumental in drawing attention to the weaknesses and limitations of the standard approach have also attempted to improve upon it. Most notably, Huang and Somasundaran w28 x and Eads and Robosky w24 x have described almost the same enhancements entirely independently. In both cases, experimental evidence has shown that the micelle composition in certain strongly interacting systems is not well described by RST. Both sets of workers have observed that the non-ideality parameter calculated varies with composition Žand concentration . in a way, which is not allowed by the model. This is because the single parameter relates excess free energy to the micelle composition in a way that forces the former to follow a symmetrical path with respect to the latter. In addressing the limitations of RST, they both use this as the weak link and invoke a new, second parameter to separately treat asymmetry in both the cmc and the micelle composition. In many ways, it is not surprising that two independent investigations should both arrive at the same conclusions ᎏ the use of a single parameter and the restrictions that it imposes are both the weak and strong points of RST. As experimentation exposes the limitations in this, so improvements will be made. Both Huang and Somasundaran w28 x and Eads and Robosky w24 x phrase the second adjustable parameter in terms of a contribution by asymmetry in the components of the mixture. In one case w28 x, the phrase ‘packing parameter’ is used while in the other w24 x van Laar expressions are identified as containing the necessary dependence not only on the cmc of each component but also on its physical size Žand hence packing.. Again, this route is probably the most obvious one to take and has many merits. It is clear though that from the data presented that the story is not complete. In their paper w24 x, Eads and Robosky concede that in some cases apparent asymmetry is observed when both surfactants present are of very similar size and shape Žhence the contribution from the second van Laar parameter would be expected to be small.. It is clear that these approaches are asking the right questions but perhaps are still too heavily influenced by the single parameter model. Hines et al. w26 x have also used multi-parameter approaches to 䢇䢇
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model their experimental data. In this case, however, no physical significance is inferred ᎏ rather the data is fitted to yield essentially accurate descriptions of the important free energy terms ᎏexcess enthalpy and entropy. While not in itself predictive, this work is perhaps a more honest assessment of the application of classical thermodynamic models to mixed micellisation and certainly the information obtained has been of enormous value in building more rigorous theories. Finally along this theme, the 1996 paper of Georgiev is worth mentioning w35 x, even though it has already appeared in a review of this type. This work is notable for its individuality ᎏ Georgiev takes the Markov chain approach to polymerisation and applies it directly to the formation and growth of micelles. In principle a very interesting and credible idea. Indeed this is one of the few truly different classical approaches seen in recent times. Unfortunately, the model has not been significantly used since in its current form it does not add substantially to the information available from standard RST and requires substantially more data to generate the necessary parameters. In his paper, Georgiev again brings this standard model to bear as a reference point for his new parameters. It would be interesting to see what progress could be made by removing this unnecessary and restrictive link. Another important branch of mixing theory that has seen substantial growth in recent times is the molecular thermodynamic ŽMT. approach due in the most part to earlier work by Nagarajan and Ruckenstein w36,37x and Blankschtein and various co-workers w38᎐41x. This approach is based in essence on the much earlier work of Israelachvili, Mitchell and Ninham w42,43x who identified regimes of packing within various micellar shapes. By calculating the variation in magnitude of important energetic considerations as a function of changing micellar shape Žand hence molecular packing., essentially ab initio calculation of the cmc as well as a variety of other key properties can be made. The MT approach holds the important advantages over the classical model that it is not restricted to parameterisation of activity coefficients ᎏ within these energy contributions no artificial symmetry is implied ᎏ and that as a molecular theory, genuine prediction without experimentation is possible. In addition, this is a much more practical approach in many ways than pure simulation, based as it is on only a relatively small number of considerations. The last 3᎐4 years has seen arguably more activity in this particular area than in any other covered by this review. Perhaps a key reason for this is the increasing appreciation among many workers not intimately connected with one model or other of the 䢇
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practical limitations of RST. The former has certainly been, and continues to be, of enormous value in many practical situations, but the MT approach offers much more flexibility and depth. Examples of this relatively recent level of application can be found in the 1998 paper of Meagher et al. w44x, which discusses experimentally observed enthalpy of micellisation measurements in the light of the MT approach, and also in the 1999 work of Lopez-Fontan et al. w45x which compares experimental data on the influence of chain length on micellar composition with a variety of available models. It is fair to say that up until most recent times, excellent experimental work such as this would almost certainly have drawn solely upon RST for theoretical comparison. The recent work of Reif and Somasundaran w46 x has applied the inherent flexibility of the MT approach to some of the issues raised by restrictions in RST. Specifically, they describe how asymmetry in excess free energy can lead to significant differences between actual activity coefficients and those produced by either RST or the simplest version of the MT model. The remaining challenge of course is to improve on this state. Extension of the MT approach itself has continued and indeed gathered pace in recent times. Much of this activity has, as previously, come from the group of Blankschtein who, along with various co-workers, has in the past 3᎐4 years tackled several outstanding issues. The issue of growth of mixed micelles, not well addressed by RST or other classical models, can be included naturally within a MT framework. This issue has been addressed with some success in both all non-ionic w47,48 x and ionicrnon-ionic w49x systems, at least for relatively regular patterns. Perhaps more critically, a much more rigorous consideration of electrostatic forces in charged mixed micelles has been developed w50 ,51x, such that not only can essentially arbitrary mixtures of ionic and non-ionic surfactants be treated, but also zwitterionic components can be included within precisely the same framework. The same group has also shown how the MT approach can be extended from the binary to the general multicomponent case w52 ,53x, albeit with some reference to earlier RST work w23x and, not least, they have done a great deal to popularise this model by describing user-friendly software tools w53᎐55x and by reporting on commercial w53x as well as new academic applications. Also using the MT approach, the 2000 work of Braibanti et al. w56x has examined in much greater detail than before the nature of the hydrophobic contribution to the total free energy of micellisation. Combined with parameterisation of experimental data, they produce a molecular thermodynamic model of this process that explicitly includes the relationship of 䢇䢇
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the number of molecules of water restructured by the presence of hydrophobic entities. Although micellisation per se is considered, specific issues relating to mixtures are not. This is an important step though along the road to a more complete and flexible solution. Finally, in this area, and not specifically covering micellisation, several authors have tackled independently the issues of extension of the MT model to interfaces and other situations. Mulqueen and Blankschtein w57x and Hines w58x have formulated interfacial models based very closely on the micellar case. These of course have the advantage of containing an inherent transparency between the two processes in bulk and at interfaces. It is clear that many of the same fundamental driving forces are at work and these approaches accurately mirror that. Although not quite as closely related, and dealing with the very specific case of redox-induced changes in adsorption, the work of Aydogan et al. w59x also represents a broadening of the MT approach to deal with interfacial issues. The recent work of Li et al. w60x, in which a molecular thermodynamic approach to treat microemulsion containing systems is described, can be viewed as a similar and consistent extension to the approach, retaining as it does the clear and fundamental building blocks. Looking more broadly at molecular based theories of micellisation, one notes a considerable amount of work in recent times focussed on the problem in general, but much less concerned with mixing in detail. Lattice models have been used with some success to describe aggregation behaviour in the context of Monte Carlo simulations, but these still suffer from the difficulties of translation of important properties from real systems. Bhattacharya and Mahanti w61x have addressed this issue to some extent by reference back to the MT approach, with which they show good agreement. In the related field of polymer-surfactant interactions, work has tended to focus much more on molecular approaches and use of simulation. Here, of course, the micelle itself has often been treated as a sphere or regular shape with a certain, applied charge density. Some cross-over between the two levels of detail has been applied by Konop and Colby w62 x who, coming more from the polymer side of the issue, address in some detail, the nature of the charged surface of a micelle in terms of counter-ion condensation, initially of small independent species then later of polyions. Although again not specifically considering mixing, this treatment also contains some useful insights to that problem and should be considered and assimilated as the area moves forward. 䢇䢇
4. Summary and conclusions This review has described some of the recent advances and major forward steps in theoretical evaluation of micellisation in mixed surfactant systems. It has tried to do this within a very clear and explicit context that is defined largely by experimentation and by observation of deficiencies in current working models. That is a very important point and suggests, in the humble opinion of the author that this area is in very good scientific health. The constant challenge to theory of new and more probing experiment, and the subsequent refining of that theory, is what drives true understanding. Within that context, we have seen in recent times a growing appreciation in the wider experimental community that existing theory may have reached its limits. Newer and more rigorous approaches that have been available for some time have now become themselves the subject of much more interest and, consequently, critique. In a number of areas, particularly in mixed systems, this increased overlap of experiment and theory has led directly to important insights and new theoretical approaches. For the future, it is important that this interaction continues. There are of course a number of issues still not completely resolved. Of these, two can be identified as critical. The nature of energetics of mixing in micelles and at surfaces should be more generally described. The role of the solvent is clearly important but it is only very recently that this has been made explicit in theory. Many of the apparent restrictions on practical application of theory stem from the assumptions made at this level, so these should certainly be addressed. The second area is the application of increasingly complex models and theories to predict more and different information, some of which may be very difficult to access experimentally. An example using MT theory might be the size and shape of micelles as well as the cmc. More properties should be explored and their importance to practical problems examined. References and recommended reading 䢇 䢇䢇
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w1x Rubingh DN. In: Mittal KL, editor. Solution chemistry of surfactants. New York: Plenum, 1979. w2x Blankschtein D, Shiloach A, Zoeller N. Thermodynamic theories of micellar and vesicular systems. Curr Opinion Coll Interface Sci 1997;2:294᎐300. w3x Kronberg B. Surfactant mixtures. Curr Opinion Coll Interface Sci 1997;2:456᎐463. w4x Khan A, Marques EF. Synergism and polymorphism in mixed surfactant systems. Curr Opinion Coll Interface Sci 2000;4:402᎐410.
J.D. Hines r Current Opinion in Colloid & Interface Science 6 (2001) 350᎐356 w5x Lichtenberg D, Opatowski E, Kozlov MM. Phase boundaries in mixtures of membrane-forming amphiphiles and micelleforming amphiphiles. BBA-Biomembranes 2000;1508:1᎐19. w6x Lesieur P, Kiselev MA, Barsukov LI, Lombardo D. Temperature-induced micelle to vesicle transition: kinetic effects in the DMPCrNaC system. J Appl Crystallogr 2000;33:623᎐627. w7x Bergstrom M, Pedersen JS. A small-angle neutron scattering ŽSANS. study of tablet-shaped and ribbon-like micelles formed from mixtures of an anionic and a cationic surfactant. J Phys Chem B 2000;103:8502᎐8513. w8x Griffiths PC, Whatton ML et al. Small-angle neutron scattering and fluorescence studies of mixed surfactants with dodecyl tails. J Colloid Interface Sci 2000;215:114᎐123. w9x Li F, Li GZ, Chen JB. Synergism in mixed zwitterionic-anionic surfactant solutions and the aggregation numbers of the mixed micelles. Coll Surf A 1998;145:167᎐174. w10x Bergstrom M. Thermodynamics of anisotropic surfactant micelles. I. The influence of curvature free energy on the micellar size and shape. J Chem Phys 2000;113:5559᎐5568. w11x Chen L, Shen HW, Eisenberg A. Kinetics and mechanism of the rod-to-vesicle transition of block copolymer aggregates in dilute solution. J Phys Chem B 1999;103:9488᎐9497. w12x Asakawa T, Sunagawa H, Miyagishi S. Diffusion coefficients of micelles composed of fluorocarbon surfactants with cyclic voltammetry. Langmuir 1998;14:7091᎐7094. w13x Telgmann T, Kaatze U. Monomer exchange and concentration fluctuations in polyŽethylene glycol. monoalkyl etherrwater mixtures. Dependence upon non-ionic surfactant composition. J Phys Chem A 2000;104:4846᎐4856. w14x Kaatze U, Hushcha TO, Eggers F. Ultrasonic broadband spectrometry of liquids: a research tool in pure and applied chemistry and chemical physics. J Solut Chem 2000;29: 299᎐368. w15x Costantino L, D’Errico G, Roscigno P, Vitagliano V. Effect of urea and alkylureas on micelle formation by a non-ionic surfactant with short hydrophobic tail at 25⬚C. J Phys Chem B 2000;104:7326᎐7333. w16x O’Connor AJ, Hatton TA, Bose A. Dynamics of micellevesicle transitions in aqueous anionicrcationic surfactant mixtures. Langmuir 2000;13:6931᎐6940. w17x Merta J, Garamus VM, Kuklin AI, Willumeit R, Stenius P. Determination of the structure of complexes formed by a cationic polymer and mixed anionic surfactants by small-angle neutron scattering. Langmuir 2000;16:10061᎐10068. w18x Griffiths PC, Roe JA, Jenkins RL et al. Micellization of sodium dodecyl sulfate with a series of non-ionic n-alkyl malono-bis-N-methylglucamides in the presence and absence of gelatin. Langmuir 2000;16:9983᎐9990. w19x Blandamer MJ, Briggs B, Cullis PM, Engberts JBFN. Titration microcalorimetry of mixed alkyltrimethylammonium bromide surfactant aqueous solutions. Phys Chem Chem Phys 2000;2:5146᎐5153. w20x Ruiz CC, Aguiar J. Interaction, stability, and microenvironmental properties of mixed micelles of Triton X100 and n-alkyltrimethylammonium bromides: influence of alkyl chain length. Langmuir 2000;16:7946᎐7953. w21x Rosen MJ. Surfacants and interfacial phenomena. 2nd edition New York: John Wiley and Sons, 1989. w22x Lange H, Beck KH. Koll Z-Z Polym 1973;251:424. w23x Holland PM, Rubingh DN. Non-ideal multicomponent mixed micelle model. J Phys Chem-US 1983;87:1984᎐1990. w24x Eads CD, Robosky LC. NMR studies of binary surfactant 䢇䢇 mixture thermodynamics: molecular size model for asymmetric activity coefficients. Langmuir 1999;15:2661᎐2668. Takes careful experimental data and identifies inconsistencies with calculated micelle compositions using RST. Extended thermody-
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namic analysis introducing second parameter of interaction yields more accurate predictions. w25x Hines JD, Thomas RK, Garrett PR, Rennie GK, Penfold J. A study of the interactions in a ternary surfactant system in micelles and adsorbed layers. J Phys Chem B 1998;102: 9708᎐9713. w26x Hines JD, Thomas RK, Garrett PR, Rennie GK, Penfold J. 䢇䢇 Investigation of mixing in binary surfactant solutions by surface tension and neutron reflection: strongly interacting anionicrzwitterionic mixtures. J Phys Chem B 1998;102: 8834᎐8846. A very thorough experimental analysis of a strongly interacting binary system using traditional as well as more modern approaches ŽNR.. Detailed thermodynamic analysis including scope for further parameterisation is made but explicitly without forced interpretation of parameters. Conclusions made as to nature and origin of excess free energy of mixing. w27x Hines JD, Thomas RK, Garrett PR, Rennie GK, Penfold J. Investigation of mixing in binary surfactant solutions by surface tension and neutron reflection: anionicrnon-ionic and zwitterionicrnon-ionic mixtures. J Phys Chem B 1997;101: 9215᎐9223. w28x Huang L, Somasundaran P. Theoretical model and phase 䢇䢇 behaviour for binary surfactant mixtures. Langmuir 1997;13:6683᎐6688. Novel approach made to experimental investigation of binary mixtures. Micelle compositions observed do not agree with predictions of RST. Further analysis confined to traditional thermodynamics, but introduces concept of second ‘packing’ parameter. w29x Lu JR, Thomas RK, Penfold J. Surfactant layers at the 䢇䢇 airrwater interface: structure and composition. Adv Colloid Interface Sci 2000;84:143᎐304. Summary and review of much work done using neutron reflectively to probe mixed surfactant layers. Significant new information has been obtained in this way to push theory into new and important directions. w30x Penfold J, Staples E, Thompson L et al. Structure and com䢇 position of mixed surfactant micelles of sodium dodecyl sulfate and hexaethylene glycol monododecyl ether and of hexadecyltrimethylammonium bromide and hexaethylene glycol monododecyl ether. J Phys Chem B 1999;103:5204᎐5211. Experimental analysis using neutron reflectivity and scattering that again highlights inconsistencies and limitations of prevailing models. w31x Penfold J, Staples E, Tucker I et al. The composition of mixed surfactants and cationic polymerrsurfactant mixtures adsorbed at the air-water interface. Coll Surf A 1997;128: 107᎐117. w32x Staples E, Tucker I, Penfold J, Warren N, Thomas RK. The structure and composition of surfactant-polymer mixtures of sodium dodecyl sulfate, hexaethylene glycol monododecyl ether and poly-Ždimethyldialyl ammonium chloride. adsorbed at the air-water interface. J Phys-Condens Mat 2000;12: 6023᎐6038. w33x Aswal VK, Goyal PS. Mixed micelles of alkyltrimethylammonium halides: a small-angle neutron-scattering study. Physica B 1998;245:73᎐80. w34x de la Maza A, Coderch L, Lopez O, Parra JL. Transmission electron microscopy and light scattering studies on the interaction of a non-ionicranionic surfactant mixture with phosphatidylcholine liposomes. Micro Res Tech 1998;40:63᎐71. w35x Geogiev GS. Markov chain model of mixed surfactant sys䢇 tems 1. New expression for the non-ideal interaction parameter. Colloid Polym Sci 1996;274:49᎐58. Innovative and individual work proposing novel model for mixed micellisation. Has been under-utilised since publication.
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w36x Nagarajan R, Ruckenstein E. Theory of surfactant self-assembly: a predictive molecular thermodynamic approach. Langmuir 1991;7:2934᎐2969. w37x Nagarajan R. Molecular theory for mixed micelles. Langmuir 1985;1:331᎐341. w38x Naor A, Puvvada S, Blankschtein D. An analytical expression for the free-energy of micellisation. J Phys Chem-US 1992;96:7830᎐7832. w39x Puvvada S, Blankschtein D. Thermodynamic description of micellization, phase-behaviour, and phase-separation of aqueous-solutions of surfactant mixtures. J Phys Chem US 1992;96:5567᎐5579. w40x Puvvada S, Blankschtein D. Theoretical and experimental investigations of micellar properties of aqueous-solutions containing binary-mixtures of non-ionic surfactants. J Phys Chem-US 1992;96:5579᎐5592. w41x Sarmoria C, Puvvada S, Blankschtein D. Prediction of critical micelle concentrations of non--ideal binary surfactant mixtures. Langmuir 1992;8:2690᎐2697. w42x Israelachvili JN, Mitchell DJ, Ninham BW. Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers. J.Chem.Soc. Faraday Trans. II 1976;72:1525᎐1568. w43x Israelachvili JN, Mitchell DJ, Ninham BW. Theory of self-assembly of lipid bilayers and vesicles. Biochim Biophys Acta 1977;470:185᎐201. w44x Meagher RJ, Hatton TA, Bose A. Enthalpy measurements in aqueous SDSrDTAB solutions using isothermal titration microcalorimetry. Langmuir 1998;14:4081᎐4087. w45x Lopez-Fontan JL, Suarez MJ, Mosquera V, Sarmiento F. Mixed micelles of n-alkyltrimethylammonium bromides: influence of alkyl chain length. Phys Chem Chem Phys 1999;15:3583᎐3587. w46x Rief I, Somasundaran P. Asymmetric excess free energies and 䢇䢇 variable interaction parameters in mixed micellization. Langmuir 1999;15:3411᎐3417. Following on from the work of Huang and Somasundaran w28 䢇 䢇 x and also of Hines et al. w26 䢇 䢇 x, this work considers for the first time explicitly the issue of potentially asymmetric free energies in the context of the molecular thermodynamic framework. w47x Thomas HG, Lomakin A, Blankschtein D, Benedek GB. Growth of mixed non-ionic micelles. Langmuir 1997; 13:209᎐218. w48x Zoeller N, Lue L, Blankschtein D. Statistical-thermodynamic 䢇䢇 framework to model non-ionic micellar solutions. Langmuir 1997;13:5258᎐5275. Important extension and significant re-formulation of the existing molecular thermodynamic model based on a considerably more rigorous statistical thermodynamic treatment of micellisation in non-ionic surfactant systems. w49x Shiloach A, Blankschtein D. Measurement and prediction of ionicrnon-ionic mixed micelle formation and growth. Langmuir 1998;14:7166᎐7182. w50x Shiloach A, Blankschtein D. Prediction of critical micelle 䢇䢇 concentrations and synergism of binary surfactant mixtures containing zwitterionic surfactants. Langmuir 1997;13: 3968᎐3981. Important extension of the molecular thermodynamic approach in
which the formalism used to calculate electrostatic free energy contributions in significantly re-written and dealt with in much more detail and rigour. This allows among other things an integrated approach to be taken for ionic and zwitterionic surfactants but is in general a much more complete appraisal of the situation. w51x Shiloach A, Blankschtein D. Predicting micellar solution properties of binary surfactant mixtures. Langmuir 1998;14: 1618᎐1636. w52x Shiloach A, Blankschtein D. Prediction of critical micelle 䢇 concentrations of non-ideal ternary surfactant mixtures. Langmuir 1998;14:4105᎐4114. First work to eplicitly combine the existing work in RST due to Holland and Rubingh w23x with the molecular thermodynamic approach to allow simple treatment of mixtures of more than two surfactants. w53x Coret J, Shiloach A, Berger P, Blankschtein D. Critical micelle concentrations of ternary surfactant mixtures: theoretical prediction with user-friendly computer programs and experimental design analysis. J Surf Det 1999;2:51᎐58. w54x Zoeller NJ, Shiloach A, Blankschtein D. Predicting surfactant solution behaviour. CHEMTECH 1996;26:24᎐31. w55x Blankschtein D, Shiloach A, Zoeller N. User-friendly computer programs to predict surfactant solution behaviour. J Soc Cos Chem 1997;48:71᎐72. w56x Braibanti A, Fisicaro E, Compari C. Hydrophobic effect solubility of non-polar substances in water, protein denaturation and micelle formation. J Therm Anal Calorimetry 2000;61:461᎐481. w57x Mulqueen M, Blankschtein D. Prediction of equilibrium surface tension and surface adsorption of aqueous surfactant mixtures containing zwitterionic surfactants. Langmuir 2000;16:7640᎐7654. w58x Hines JD. A molecular thermodynamic approach to the prediction of adsorbed layer properties of single and mixed surfactant systems. Langmuir 2000;16:7575᎐7588. w59x Aydogan N, Gallardo BS, Abbott NL. A molecular-thermodynamic model for Gibbs monolayers formed from redox-active surfactants at the surfaces of aqueous solutions: redox-induced changes in surface tension. Langmuir 1999;15:722᎐730. w60x Li XS, Lu JF, Li YG, Liu JC. A new molecular thermodynamic model for osmotic pressures in micelle and oil water microemulsion systems with non-ionic and ionic surfactants. Ind Eng Chem Res 1999;38:2817᎐2823. w61x Bhattacharya A, Mahanti SD. Energy and size fluctuations of amphiphilic aggregates in a lattice model. J Phys Condens Matter 2000;12:6141᎐6160. w62x Konop AJ, Colby RH. Role of condensed counterions in the 䢇䢇 thermodynamics of surfactant micelle formation with and without oppositely charged polyelectrolytes. Langmuir 1999;15:58᎐65. Important work that makes explicit the considerations involved in treating the energetics of counter-ion condensation as part of the process of micellisation. Mainly focuses on the use of such considerations in treating surfactant-polymer complex formation, but contains many important insights that can progress the state-of-theart in predicting surfactant mixture behaviour.