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Synopsis
Systems of cylindrical micelles formed through the aggregation of surfactant
molecules exhibit rich rheological behavior. These elongated structures
are currently used industrially as viscosity-enhancement agents, since
high zero-shear viscosities can be achieved at relatively low concentrations.
Other potential applications as drag-reducing additives and model rheological
fluids have been proposed, thus motivating numerous structural, rheological,
and theoretical studies [Candau and Oda (2001)]. Despite this, relatively
little attention is given to fundamentally understanding how the structure
of the micelles dictates macroscopic behavior. Up until now, it was not
clear how micellar flexibility, length, and interactions control the rheology.
In this work, a combination of characterization, structural, and rheological
techniques are used to quantify the coupling between rheology and structure
in systems of cetyltrimethylammonium
p-toluenesulfonate (CTAT).
As a result of this work, we show that using additives to intelligently
control the structure of the micellar system, the subsequent rheology
is precisely tuned to achieve customized flow-modifiers or model fluids.
We also identify universal behavior in the shear-induced structure (SIS),
a structural transition that has been linked to drag-reducing capabilities.
Most importantly, this work quantifies the coupling between micellar microstructure
and macroscopic flow behavior, thereby cultivating future areas of research
and novel applications of cylindrical micellar systems.
Discussion of Results
Coupling between micellar microstructure and rheology
 The
ultimate goal of this work is to quantify the coupling between the structure
of the micellar system and its flow behavior. In describing the structure
of a system of cylindrical micelles, there are key aspects that need to
be considered; these include micellar size, flexibility, intramicellar
(surface) charge, intermicellar (electrostatic) interactions, and entanglements.
Though the breaking and reforming dynamics of micellar systems cause polydispersity
in length [Cates (1987)], micellar size can be quantified by the average
contour length (L) and cross-sectional radius(rcs). The persistence
length (lp)
or Kuhn statistical length (b) describe local rigidity and can be used
to assess micellar flexibility. In ionic surfactant systems, some of the
associated counterions remain in the bulk solution (unbound). As a result,
the micelle possesses a net surface charge. This surface charge can be
altered if other counterions, which bind to the micelle, are added to
the system. Alternatively, added ions that remain close to the surface
of the micelle screen electrostatic repulsions between neighboring surfactant
molecules, changing the effective micellar surface charge. Because of
free coions and counterions in solution, the Debye screening length (k-1)
characterizes the extent of intermicellar electrostatic interactions.
With increasing concentration, micelles grow in length and number, and
steric interactions or entanglements become important to the dynamics
of the system. Therefore, quantifying the entanglement density or the
number of entanglements per micelle is a useful means of describing the
structure of these semidilute systems.
 The
results of this work quantify the coupling between the structural parameters
described above and macroscopic flow behavior. For example, decreasing
micellar length decreases ho and increases (ratec)
and increases (ratec) in dilute systems of CTAT: The comicellization
of the copolymers with CTAT leads to the formation of shorter micelles,
which have greater critical shear rate for the onset of the SIS (ratec).
Low concentrations of HPC also have similar effects on micellar structure
and rheology through binding interactions. However, higher concentrations
of HPC may induce intermicellar networks or bridging, which lead to increases
in zero-shear viscosity (ho) and inhibit micellar mobility,
causing no SIS formation. The changes in micellar radius with these polymers
as detected in SANS are consistent with the binding of these polymers
to the micelles, yet we do not have direct evidence that these polymers
decrease length. Recall that the correlation peak in SANS makes decoupling
micellar length from flexibility impossible. However, the order of magnitude
decreases in tR, accompanied
by dramatic decreases in h*(w->0), of
semidilute systems of CTAT upon adding these polymers illustrate this
convincingly (see below).
The importance of
electrostatic interactions to the structure and rheology of dilute systems
of CTAT micelles is established [Truong and Walker (2002)]. Low concentrations
of NaCl are used to screen the intermicellar electrostatic repulsions,
enhancing steric interactions between micelles and causing increases in
ho. At high NaCl composition, the
micelles are effectively "uncharged", i.e. the distribution
of ions around the micelle is such that no significant intermicellar electrostatic
interactions are detected in static scattering measurements. Adding increasing
amounts of NaCl to these systems mainly increases the flexibility of the
micelles. As in dilute polymer systems, this increase in flexibility (L/b)
at fixed length decreases ho [Doi and Edwards (1986)]. These
systems also exhibit shear-thinning behavior, where the critical shear
rates increase with increasing flexibility. This is consistent with recent
studies of dilute polyelectrolyte systems that are screened with added
salt [Andrews et al. (1998)].
Clearly, the coupling between micellar microstructure and macroscopic
flow behavior has been established by this work. From this, the effects
of various additives on the structure and rheology of both dilute and
semidilute micellar systems can be predicted. Conversely, the structure
of a mixed system can be deduced from the rheology.
Controlling rheological behavior with additives
Widespread use of cylindrical micellar systems as drag-reducing additives
or model rheological fluids can only be made possible if such rheological
behavior can be controlled. The onset of the shear-induced structure (ratec)
and ho can be tuned with added polymer
[Truong and Walker (2000)]: With PEO, the ho of the SIS forming system can
be tailored, with little effect to ratec. HPC allows for dramatic
increases to ratec. The copolymers also increase ratec
but without increasing ho. Increases in ratec
with the addition of HPC and Pluronic occur through binding or comicellization
interactions, which cause variations in micellar size. At low concentrations,
ho and ratec can be manipulated
with these polymers in ways not possible in the pure CTAT system. That
is, changing temperature or surfactant concentration does not mimic these
effects. However, such polymer-CTAT interactions lead to dramatic changes
to the micellar structure at high polymer concentration, thereby suppressing
the SIS formation entirely. Using these three polymers, we have identified
that the amphiphilic nature of the polymers (not size nor flexibility)
dominates whether or not binding occurs and, consequently, manipulation
of the SIS formation.
 The effects
of the above polymers on dilute CTAT systems are shown to be analogous
to the case of semidilute micellar systems [Truong and Walker (2002)].
Instead of ho and ratec, the relative
parameters are low-frequency dynamic viscosity h*(w->0) and
terminal relaxation time tR. By changing micellar length at fixed micellar
concentration, the addition of polymers can be used to attain linear viscoelastic
behavior not achievable in the pure CTAT system: h*(w->0) can
be enhanced with PEO without affecting micellar length. Low concentrations
of the binding polymers (HPC and Pluronic copolymers) decreases both h*(w->0) and
tR by decreasing micellar length. Lowering CTAT concentration has similar
effects on h*(w->0), yet
the viscoelastic behavior is lost because of decreased entanglements in
the more dilute system. As in the dilute CTAT systems, high concentrations
of binding polymers can suppress the micellar rheology in semidilute systems,
causing weakly elastic fluids.
Shear-induced structure
Another goal of this work is to identify the key aspects of the micellar
microstructure, which cause the formation of the SIS. Previously, electrostatic
interactions have been established as a requirement for this structural
transition [Rehage et al. (1986), Hoffmann et al. (1991), Berret et al.
(2001)]. Our work with dilute CTAT/NaCl systems indicates that the micellar
systems that form SIS are rigid in conformation. In addition, there is
a clear distinction in the role of micellar flexibility and charge on
the onset of the SIS formation and the sheared structure [Truong and Walker
(2000)]: Various polymers that bind or comicellize with CTAT decrease
micellar length, lowering ratec. At rest, qxo, a parameter
that is defined in SANS experiments and is sensitive to micellar charge
and flexibility, varies greatly with added polymer. Once the SIS begins
to form, there is a universal behavior in the evolution of the SIS with
respect to qxo. That is, qxo(Af) does not vary for mixed systems at Af
> 0.2, showing that there is a commonality in micellar flexibilty and
charge in the SIS, which is independent of the polymer composition of
the system.
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Works cited
Andrews, N. C., A. J. McHugh, and J. D. Schieber, "Polyelectrolytes
in shear and extensional flows: Conformation and rheology," Journal
of Polym. Sci.: Part B: Polym. Phys., p. 1401-1417 (1998).
Berret, J. F., R. Gamez-Corrales, Y. Serero, F. Molino, and P. Lindner,
"Shear-induced micellar growth in dilute surfactant solutions,"
Europhys. Lett. 54, p. 605-611 (2001).
Candau, S. J. and R. Oda, "Linear viscoelasticity of salt-free wormlike
micellar solutions," Colloids Surf., A 183-185, p. 5-14 (2001).
Cates, M. E., "Reptation of living polymers: Dynamics of entangled
polymers in the presence of reversible chain-scission reactions,"
Macromolecules 20, p. 2289-2296 (1987).
Doi, M. and S. F. Edwards, "The theory of polymer dynamics",
International series of monographs on physics, 73: New York, Oxford Press
(1986).
Hoffmann, H., S. Hofmann, A. Rauscher, and J. Kalus, "Shear-induced
transitions in micellar solutions," Prog. Coll. Polym. Sci. 84, p.
24-35 (1991).
Rehage, H., I. Wunderlich, and H. Hoffmann, "Shear-induced phase
transitions in dilute aqueous surfactant solutions," Prog. Coll.
Polym. Sci. 72, p. 51-59 (1986).
Publications
Truong, M. T. and L. M. Walker, "Tuning the linear viscoelastic behavior
of wormlike micelles through binding of nonionic additives," in preparation.
Truong, M. T. and L. M. Walker, "Quantifying the importance of micellar
microstructure and electrostatic interactions on the shear-induced structural
transition of cylindrical micelles," Langmuir 18, p. 2024-2031 (2002).
Truong, M. T. and L. M. Walker, "Controlling the shear-induced structural
transition of rodlike micelles using nonionic polymer," Langmuir
16, p. 7991-7998 (2000).
"Rheology and structural transitions in wormlike micellar systems
controlled by added nonionic polymer," M. T. Truong and L. M. Walker,
Proceedings of the XIIIth International Congress on Rheology: Cambridge,
UK, 3, 310-312 (2000).
Awards
Society of Rheology
Poster Award (October 2001):
"Model behavior of mixed systems of nonionic polymer and
living polyelectrolyte," M. T. Truong and L. M. Walker.
CMU ChEGSA Symposium
Award (October 2001):
"Rheological significance of flexibility in wormlike micellar systems
through analogy to 'living' polyelectrolytes," M. T. Truong and L.
M. Walker.
CMU ChEGSA Symposium
Award (October 1999):
"The effects of nonionic polymer on the shear-thickening of rodlike
micelles," M. T. Truong and L. M. Walker.
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