Nonlinear Dynamics in Polymeric Systems - ACS Publications

Chapter 18

Nonlinear Dynamics in Surfactant Systems

Downloaded by UNIV OF GUELPH LIBRARY on September 12, 2012 | http://pubs.acs.org Publication Date: November 18, 2003 | doi: 10.1021/bk-2004-0869.ch018

Mark Buchanan Department of Complex Systems, Vrije Universiteit, Amsterdam, The Netherlands

Interface instabilities, known as myelins, are an example of exotic nonequilibrium behavior present during dissolution in a number of surfactant systems. Although much is known about equilibrium phase behavior much still remains to be understood about nonequilibrium processes present in surfactant dissolution. In this chapter nucleation and growth, self and collective diffusion processes and nonlinear dynamics and instabilities observed in various polymeric systems are reviewed. These processes play an important role in our understanding of myelin instabilities. Kinetic maps and the concept of the free energy landscape provide a useful approach to rationalize some of the more complex behavior sometimes observed.

© 2004 American Chemical Society

In Nonlinear Dynamics in Polymeric Systems; Pojman, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.


227 Although much work has been done to study equilibrium behavior in surfactant systems many nonequilibrium dynamic behavior are still far from well understood. When neat or concentrated surfactant is contacted with solvent complicated diffusion process occurs due to the presence of mesophase at the interface. Initially, at the interface, the formation, type and structure of the mesophase will influence the subsequent dynamics. In some cases the interface can become unstable during dissolution and rather striking instabilities form. To obtain a good understanding of such complicated nonlinear processes has relied on a systematic study of the equilibrium phase behavior in such systems. This has given us a firm basis on which to study the nonequilibrium behavior. In this chapter I will review problems related to dissolution kinetics and nonlinear process that occur in surfactant systems. First we discuss the role of phase kinetics in surfactant dissolution. Then the diffusive processes are discussed where it is important to appreciate the difference between self and collective diffusion. Finally, interface instabilities will be discussed which includes some of the most recent and significant observations. These studies are extremely interesting in the context of industrial problems such as detergency.

Kinetics of phase formation The dissolution of a mesophase is, in most cases, diffusions limited. This means the composition at the interface between phases corresponds to the equilibrium composition. This is indeed the main assumption behind the linear penetration scan which involves observing surfactant contacted with an aqueous phase in a capillary tube or between a glass slide and coverslip (2-9). Using polarization microscopy the structural arrangement of the intermediate mesophases can be identified (10). A quantitative approach to verify that the phase boundaries coincide with the equilibrium phase boundaries can be performed using refractive index measurements (11). It is true provided concentration gradients are not too large and the evolution is linear. Interferometry can also be used to follow the whole concentration profile as it evolves through time (72). Generally mesophases form rapidly which leads to a diffusion-limited growth. Times of order seconds or less have been reported in T-jump experiments where a homogeneous sample is subjected to a temperature change and the time for the mesophase to form is measured (13). However, in some penetration scan experiments times much longer than a second have been observed. Time resolved X-ray and neutron scattering have also been used to elucidate the kinetic behavior in many surfactant systems (14, 15). For the case of dissolution kinetics transitions between micelle and vesicle structures have been studied during homogeneous dilution of the solvent (16). Transient structures such as disks have been observed during such a transition.


228 The molecular assembly of a typical mesophase involves molecules having to diffuse distances of about λ ~ lOnm to make new structures. Given the self diffusion coefficient is of order D ~ 10" mV then we would expect structures to form λ / D ~ μ8 - ms where as timescales of order seconds are observed* The accepted and most likely explanation is the need to nucleate the new phase. The delay of one phase out of another can be explained by nucleation and growth in simple systems. When there is competition to nucleate several mesophases then it becomes too complicated to think in these simple terms. So for more complicated systems it is easier if we think in terms of the free energy u

1


2

landscape.

At this point it is useful mention work on colloid / non-adsorbing polymer mixtures (17-19). This simple system provides us with a case study where the nonequilibrium behavior can be successfully explained by kinetic maps determined from the free energy landscape.

Such a theory has also been useful is describing behavior of samples in the three-phase region (lamellar, sponge and micellar phases) (20). After applying a temperature change the phase boundaries change position. As the sample relaxes, most of the sponge phase is replaced by lamellar phase and the sample is observed as it equilibrates. All directly observable behavior can be explained in terms of a quasi-equilibrium free energy landscape by first identifying the fast and slow components. In this case, bilayer concentration equilibrates rapidly whereas the bilayers reorganize slowly.

Diffusion processes During surfactant dissolution the two diffusion processes can be identified. On the molecular scale a molecule undergoes self diffusion where the diffusion coefficient is determined from its mean squared displacement. Various NMR techniques have been used to study quantitatively self diffusion processes (2i24). It is important to note that each component in the system will have a self diffusion coefficient. Diffusion coefficients for a number of mesophase systems have been collected where values of order 10" - 10" mV were reported (25). The self diffusion coefficients of the solvent are typically reduced no more than an order of magnitude in the presence of mesophases which essentially act as obstacles to the solvent (25, 26). Collective diffusion is the response of a given species to a concentration gradient. In the dissolution process collective diffusion plays the most important role. In the case of a two-component system there will be only one collective 12

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1



229 diffusion coefficient as a surfactant concentration gradient inevitably implies a solvent concentration gradient the opposite way. Dynamic light scattering (DLS) is an effective technique to measure the collective diffusion coefficients by measuring the time correlation of the concentration fluctuations. These experiments allow us to can determine the collective modes of the system that couple to concentration fluctuations. In binary systems this connection is quite useful since there is only one independent concentration variable. Then one can obtain the collective diffusion coefficient theoretically from the dynamic structure factor in the long wavelength limit. It is not always the case that self diffusion and collective diffusion coefficients are related. In the case of water transport in a lamellar phase the collective modes of motion, including the modes that correspond to concentration fluctuations have been identified (27). Since the water movement between bilayers can be considered as Poiseuille flow where the driving force is a pressure gradient in the water which is related to the mean interlayer spacing and hence to the surfactant concentration. For the case of a dilute lamellar phase this connection can be used to calculate the collective diffusion coefficient. This can be related to microscopic quantities such as solvent viscosity and the bilayer interaction energy such as electrostatics, van der Waals (27, 28), or undulation forces (29). Furthermore, in nonionic surfactant hexagonal phases collective diffusion coefficients have been found to be more than an order of magnitude larger than the self diffusion coefficient (30). In all of the above cases the samples are considered well oriented but in reality the phase would be constructed from randomly oriented domains which complicates further this senario.

Dissolution kinetics In most penetration scans performed in surfactant dissolution experiments the phases are homogeneous and the interface between them is sharp. However, in some cases the interface becomes unstable and dramatic instabilities can be observed. There are many examples of instabilities that are well understood that maybe rationalized in terms of kinetic maps or dissolution paths, or dynamic instabilities involving fluid flow (e.g. Marangoni effects) or other Laplacian growth instabilities", such as Mullins-Sekerka instabilities (31). However, myelins (Figure 1) are an example of an instability that remains poorly understood. 4t



230

Figure 1. (a) Myelin interface in Cl2E3/water system; (b) At later times (several minutes) coil structures can be observed. Scale bar is 20/M.

Myelin formation is perhaps one of the most intriguing instabilities in nature. These instabilities appear during the swelling and dissolution of a surfactant lamellar phase and are primarily observed in surfactant systems that have a large miscibility gap between the lamellar phase and the solvent. In this case surfactant molecules can remain organized in bilayer structures up to high dilutions due to their low preferred curvature. (In contrast myelins are not observed in surfactant systems that have higher preferred curvature which posses a very small miscibility gap.) Within myelin the surfactants are organized in bilayer structures where the bilayers stack in a multi-tubular fashion. These multi-lamellar tubules and are approximately ten microns in width (Figure 1). The myelin phenomenon started to appear in old articles published on solubility and detergency of soap solutions. Stevenson reported myelinic like structures during the removal of oil from clothes fibers (32). A few years later Harker also referred to myelin instabilities in similar experiments (33). In the late 1950s Lawrence reported qualitatively that myelins with different structures were dependent on the surfactant and composition (34, 35). The first quantitative results were not produced until the 1980s when Sakurai and coworkers obtaining growth rates for the myelins in the egg-yolk lecithin/water system (36, 37). Using freeze fracture electron microscopy they have confirmed that the bilayers in the myelins have a multi-tubular organization (38, 39). They have also reported that myelins can have a variety of structures depending on the length of time they have been growing (40). The lamellar formation and structure and the influence of counterions have been studied using both microscopy and freeze fracture techniques (41, 42). More advanced techniques have been used to study dynamics of myelins in penetration scans by using tracer particles to follow fluid flow (9). As well as


231 quantification of the swelling process by determination of an effective diffusion coefficient many qualitative features have been observed. Penetration scans where swelling and growth dynamics is observed up to longer timescales show a change in the growth exponent. At later times there is a transition from a diffusive to subdiffusive regime where the growth exponent changes from t to about t (Figure 2). Such a transition is likely to be due to some complicated internal reorganization of the bilayers (43).


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Figure 2. Temporal evolution of myelin growth in lecithin (Egg PC) system over long times reveals a diffusive regime at early times followed by a subdiffusive regime. Figure courtesy of J. Leng.

Another intriguing feature of myelin growth is there ability to form helical structures (Figure lb). These have been observed in a variety of systems (9, 40, 44, 45). One argument for there formation is based on the influence of spontaneous curvature of the membranes in the myelin figures (45). By spraying polymer onto the surface of the myelin figure the spontaneous curvature can be changed and coiling is observed. A recent theoretical study has also shown that spontaneous curvature and a decrease in the bilayer spacing can also lead to coiling instability (46). Myelins have also been observed to collapse when an intermediate sponge phase is present between the lamellar phase and the micellar phase (47). After the formation of the myelins sponge phase is observed to from at the surface (Figure 3). The delayed formation of the sponge phase in this case is consistent


232


with the kinetic-pathway theory; initially the swelling of bilayers occurs and at later timescales bilayers can reorganize forming sponge phase. In this case is the fast and slow components can be identified to the bilayer concentration and reorganization respectively.

Figure 3. Deflated myelin in CaE / W penetration scan at T=60 °C where an intermediate sponge phase is present. After some time patches of sponge phase form at the myelin surface. Bar is 20μηι. 5

Despite most of the myelin studies having focused on growth and late timescale behavior the mechanism for their formation is still unknown. Penetration scans using onion phase (lamellar phase is presheared into multilamellar vesicles or onions) have shown that myelin formation can be suppressed (48). This implies that there formation is sensitive to bilayer organization in the lamellar phase. Dissolution of these onion phases also have interesting and exotic behavior (48, 49). Instabilities that manifest themselves in surfactant and polymeric systems have been considered in an attempted to elucidate the myelin instability. In polymer-like micelles (or wormlike micelles) instabilities have been observed in the directional growth of hexagonal phases in a temperature gradient (30). These instabilities are an example of the Mullins and Sekerka type (31). In the case of polymer gels, instabilities appear during growth, which resemble a raspberry like texture at the surface. This instability is due to the elastic properties of the gel which is a network of chemically bonded polymers. As the gel swells at the surface it remains anchored to the rest of the unswollen gel and the surface buckles (50).


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However, myelin instabilities have evaded elucidation by the above mensioned instabilities. The well known finger-like instabilities which involves material diffusing onto the tip do not apply in this case as myelin growth as growth occurs as a result of backflow. Furthermore, myelins cannot be described by elastic instabilities such as polymer gels since there is no strong anchoring between layers in the lamellar phase. Myelins still remain unclassified in terms of our current understanding of instabilities in a variety of systems.

Conclusions Our progress in understanding dissolution kinetics has been advanced from surfactant systems whose equilibrium phase behavior is well understood. Since phase formation is relatively fast, the kinetics are often simple and the dynamics are often controlled by collective diffusion. In cases where this breaks down and more complex behavior is observed free energy landscapes have provided us with important new insights. However, formation of instabilities such as myelins still remain a mystery and cannot be classified with well founded surfactant and polymeric instability theories. At present no theoretical explanation for their formation exists despite having been observed 150 years earlier by R. Virchow (51).

Acknowledgement I would like to thank P. Warren, J. Leng, M . E. Gates, S. U. Egelhaaf and P. R. Garrett for useful discussions.

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