Polymerization of wormlike micelles induced by hydrotropic salt

Article abstract of DOI:10.1021/ma047646m

Addition of the hydrotropic salt sodium tosylate (TSNa) to solutions of a polymerizable cationic surfactant, methacryloyloxyundecyltrimethylammonium bromide (MUTB), leads to a transition from spherical to wormlike micelles about 40 nm in length. The wormlike micelles were successfully polymerized to yield stable, single-phase solutions of polymerized micelles. The polymerized wormlike micelles were several hundred nanometers long, although their cross-sectional radius remained unchanged (～2 nm). The spherical to wormlike micelle transition, and the wormlike micelles polymerized at different molar ratios of TSNa to MUTB, were characterized using quasi-elastic and static light scattering, small-angle neutron scattering, NMR, and cryogenic transmission electron microscopy.

Full text of DOI:10.1021/ma047646m

2482
Macromolecules 2005, 38, 2482-2491
Polymerization of Wormlike Micelles Induced by Hydrotropic Salt
Shiyong Liu,† Yamaira I. Gonza´lez,‡ Dganit Danino,§ and Eric W. Kaler*,‡
Department of Polymer Science and Engineering, University of Science and Technology of China,
Hefei, 230026, Anhui Province, P.R. China; Department of Chemical Engineering, University of
Delaware, Newark, Delaware 19716; and Department of Biotechnology and Food Engineering,
Technion-Israel Institute of Technology, Haifa, Israel 32000
Received November 15, 2004; Revised Manuscript Received January 5, 2005
ABSTRACT: Addition of the hydrotropic salt sodium tosylate (TSNa) to solutions of a polymerizable
cationic surfactant, methacryloyloxyundecyltrimethylammonium bromide (MUTB), leads to a transition
from spherical to wormlike micelles about 40 nm in length. The wormlike micelles were successfully
polymerized to yield stable, single-phase solutions of polymerized micelles. The polymerized wormlike
micelles were several hundred nanometers long, although their cross-sectional radius remained unchanged
(∼2 nm). The spherical to wormlike micelle transition, and the wormlike micelles polymerized at different
molar ratios of TSNa to MUTB, were characterized using quasi-elastic and static light scattering, small-
angle neutron scattering, NMR, and cryogenic transmission electron microscopy.
Introduction
The counterions in these micelles contain a polymeriz-
able vinyl group that binds to the hydrophilic am-
monium headgroups of the wormlike micelles. Upon
polymerization, the shell of linked counterions retains
the cross-sectional structure of the micelles, although
there is a reduction in the overall length of the polym-
erized micelles, possibly due to confinement of the
polymerized counterions to the micellar surface.
Single-tailed surfactants generally form globular mi-
celles in aqueous solution above their critical micelle
concentration. These micelles can transform into worm-
like micelles with addition of inorganic (e.g., Cl- and
Br-)1-4 or organic counterions (e.g., salicylate,5,6 tosy-
late,7 chlorobenzoate,8 or hydroxynaphthalene carboxy-
late9). Likewise, micelle elongation can result from
increasing the surfactant concentration10 or addition of
oppositely charged surfactants11,12 or uncharged com-
pounds such as aromatic hydrocarbons.13 Of special
interest are the salts of organic counterions, called
hydrotropes. Hydrotropes are amphiphilic molecules
that become weakly surface active at high concentra-
tions. Unlike surfactants, hydrotropes have a short tail
that hinders their self-assembly into micelles.14 On the
other hand, hydrotropes bind more strongly to the
surfactant headgroups in the micelles than inorganic
counterions, so that micellar growth can occur at much
lower surfactant and counterion concentrations.
Wormlike micelles display rich rheological behavior,
often at low total surfactant concentrations (∼10-3 mol/
L).15-17 The entangled micellar solutions are similar to
polymeric solutions, and their behavior can be best
described by “living polymer” models.18,19 However, the
equilibrium and dynamics of these microstructures are
determined by a delicate balance of intermolecular
forces that can be easily disrupted. External changes
such as temperature, dilution, variation of salt concen-
tration, or the addition of oils or polymers can lead to
the disruption of the wormlike microstructure.19,20
Polymerization is one route to stabilize surfactant
self-assembled microstructures. Vesicles,21 spherical
micelles,22-26 lamellae,27 and hexagonal arrays of cyl-
inders28 have been polymerized, but reports of polymer-
izing wormlike micelles are rare.29-31 Kline et al.
reported the polymerization of rodlike micelles from
cetyltrimethylammonium 4-vinylbenzoate (CTVB).29,31
Becerra et al.30 reported an alternate approach to
templating wormlike micelles by polymerizing styrene
solubilized inside the core of micelles of the cationic
surfactant cetyltrimethylammonium tosylate. This ap-
proach does not stabilize the wormlike micelle micro-
structure. Instead, the polymer product partially adopts
the morphology of the micelle core, and the result is a
mixture of empty micelles and rigid solid rods, whose
length depends on the styrene-to-surfactant molar ratio.
In this paper, the structural fixation of stable worm-
like micelles formed in mixtures of a polymerizable
surfactant with an oppositely charged hydrotropic salt
is investigated. Solutions of spheroidal micelles were
prepared from the cationic surfactant, methacryloyloxy-
undecyltrimethylammonium bromide (MUTB), whose
polymerizable methacrylate group is located in the
hydrophobic tail. Micellar growth was induced by added
sodium tosylate (TSNa), and the resulting wormlike
micelles were then polymerized to fix their microstruc-
ture. The initial wormlike micelles and the polymerized
micelles were characterized using quasi-elastic and
static light scattering (QLS and SLS, respectively),
NMR, small-angle neutron scattering (SANS), and
cryogenic transmission electron microscopy (cryo-TEM).
The wormlike micelles can be successfully polymerized
to yield single-phase stable solutions of polymerized
micelles whose structure and properties are insensitive
to dilution. The cross-sectional radius of the wormlike
assemblies (∼2 nm) does not change upon polymeriza-
tion, but their length increases considerably.
Materials and Methods
† University of Science and Technology of China.
‡ University of Delaware.
Materials. Methacryloyl chloride was distilled under re-
duced pressure and stored at 4 °C. 11-Bromoundecanol,
trimethylamine (anhydrous), sodium tosylate, anhydrous tet-
rahydrofuran (THF), and ethyl ether were purchased from
§ Technion-Israel Institute of Technology.
* To whom correspondence should be addressed: e-mail
kaler@che.udel.edu; Tel (302) 831-3553; Fax (302) 831-6751.
10.1021/ma047646m CCC: $30.25 © 2005 American Chemical Society
Published on Web 02/26/2005

Macromolecules, Vol. 38, No. 6, 2005
Polymerization of Wormlike Micelles 2483
distances were used to give a range in scattering vector of
0.004-0.5 Å-1. The data were corrected for detector efficiency,
background, and empty cell scattering and placed on an
absolute scale using NIST procedures. For data analysis, the
ideal model scattering curves were smeared to take into
account the instrument resolution.35 The quality of the fit is
assessed from the reduced ø2 error values between model and
data.
SANS Modeling. The approximate cross-sectional radius (rcs)
of the micelles was obtained by analyzing the scattering data
at q values beyond any interaction peaks in the scattering plots
using the Guinier approximation for the form factor36
Figure 1. Chemical structures of the cationic surfactant
methacryloyloxyundecyltrimethylammonium bromide (MUTB)
and the hydrotropic salt sodium tosylate (TSNa).
qI(q) ∼ exp(-q2Rg,cs2/2)
(1)
Aldrich. The initiator 2,2′-azobis(2-methylpropionamide) di-
hydrochloride (V50, Wako Pure Chemical Industries, Ltd.) was
recrystallized from methanol.
where Rg,cs is the cross-sectional radius of gyration of the
cylindrical micelles and is related to the micellar cross-
sectional radius by
Preparation of MUTB. The synthesis of MUTB has been
reported elsewhere.32 Briefly, 11-bromoundecanol (20 g, 0.08
mol) and 320 mL of anhydrous THF were mixed in a flask at
0 °C under N2, followed by the addition of 10.8 mL (0.11 mol)
of methacryloyl chloride. The reaction system was bubbled
with N2 at room temperature for 2 h and left under stirring
overnight. The unreacted methacryloyl chloride and solvent
were removed under reduced pressure. The yellowish residue
was dissolved in ethyl ether and washed with saturated
sodium hydrogen carbonate solution until the aqueous layer
was basic. After evaporation of the ether, a viscous yellowish
liquid of 11-bromoundecyl methacrylate was obtained with a
yield of 91%. MUTB with a yield of 75% was obtained by
reacting 11-bromoundecyl methacrylate with trimethylamine
gas in diethyl ether at 0 °C, following the procedure described
by Michas et al.33 The chemical structures of the synthesized
MUTB and of TSNa are shown in Figure 1. Their structures
and purity were verified by 1H NMR. The spectra of these
species are discussed below.
Polymerization of Wormlike Micelles. Samples for po-
lymerization were prepared with water or D2O and depleted
of oxygen by bubbling with nitrogen for about 30 min. After
dissolution at room temperature of the desired MUTB and
TSNa amounts, the solution mixtures were heated to 60 °C.
The water-soluble initiator V50, predissolved in degassed
water or D2O, was injected (the molar ratio of MUTB to V50
was fixed at 100), and the polymerization was carried out at
60 °C for 2 h.
x
rcs
)
2Rg,cs
(2)
More accurately, models of rigid or semiflexible cylinders
were used to fit the neutron scattering spectra measured for
both the original and polymerized wormlike micelles. For
monodisperse rigid circular cylinders and in the absence of
intermicellar interactions, the scattered intensity as a function
of the scattering vector is given by37
dΣ
dΩ
I(q) )
(q) ) N(Fcyl - Fsolv)2(πrc,s2L)2 ×
2
L
2
sin q cos R
(
)
J1(qrc,s sin R)
qrc,s sin R
π/2
2
sin R dR (3)
∫
0
L
2
[
]
q
cos R
Here, J1(x) is the first-order Bessel function, R is the angle
between the cylinder axis and the scattering vector q, Fcyl and
solv are the scattering length densities of the micelle and the
F
solvent, respectively, N is the number density of micelles, rcs
is the cross-sectional radius, and L is the length of the micelles.
The semiflexible model used Pedersen and Schurtenberger’s
calculation38 of the form factor for a wormlike chain with
excluded-volume interactions. This model allows the estima-
tion of rcs as well as the contour length (Lc) and the persistence
length (lp) of the micelles, which are an indication of micellar
flexibility. All other intermicellar interactions were neglected.
For both models, rcs was initially set to the value calculated
from the Guinier plot in order to find the adjustable param-
eters of L or Lc and lp. Later, rcs was also varied until a
minimum for the value of ø2 for the model fit to each SANS
spectrum was found. The scattering length density (SLD) for
each component was calculated by summing the scattering
amplitudes of each group or atom in the molecule and dividing
the total by the sum of the respective volumes. For MUTB and
QLS and SLS. QLS and SLS measurements were made
using a Brookhaven BI-200SM goniometer and a BI9000AT
digital correlator. Samples at 25 °C were irradiated with 488
nm light produced from a Lexel 2 W argon ion laser. QLS
measurements were made at five different angles ranging from
50° to 130°. The intensity correlation data were analyzed by
the method of cumulants to provide the average decay rate,
Γ
) q2Da, where Da is the apparent diffusivity coefficient,
2 2
and the normalized variance, ν ) [( Γ2 - Γ )/ Γ ], which is
a measure of the width of the distribution of the decay rates.34
Here, q is the magnitude of the scattering vector given by q )
(4πn/λ) sin(θ/2), n being the refractive index of the solvent, λ
the wavelength of light, and θ the scattering angle. Stock
solutions of each pure surfactant were filtered through 0.22
µm Millipore Acrodisc-12 filters prior to preparing samples.
In SLS, the angular dependence of the excess absolute time-
averaged scattered light intensity, known as the Rayleigh ratio
Rvv(q), of a series of diluted polymerized micellar solutions
(concentrations ranging from 5.3 × 10-5 to 4.5 × 10-4 g/mL)
led to the apparent weight-average molar mass (Mw)app and
TSNa, the calculated SLD are 2.1 × 10-7 and 1.6 × 10-6 Å-2
,
respectively. The scattering length density of D2O is 6.3 × 10-6
Å-2
.
1H NMR. 1H NMR measurements were performed at 25 °C
on a Bruker AC250 NMR spectrometer (resonance frequency
1
of 250 MHz for H).
Cryo-TEM. Prior to specimen preparation, the micellar
solutions were equilibrated at 25 °C in the controlled environ-
ment vitrification system (CEVS)39 for 20 min. Vitrified
specimens were prepared on either a Quantifoil 3.5R bare grid
or a 400 mesh copper grid coated with a perforated Formvar
film (Ted Pella). Briefly, a small drop (∼5 µL) was applied to
the grid and blotted with a filter paper to form a thin liquid
film of solution. The blotted sample was immediately plunged
into liquid ethane at its freezing point (-196 °C) and stored
under liquid nitrogen. The vitrified specimens were examined
in a Philips CM120 transmission electron microscope, operated
at 120 kV, using an Oxford 3500 cryo-holder maintained at
below -178 °C. Images were recorded digitally on a Gatan 791
MultiScan cooled charge-coupled device (CCD) camera with
2
1/2
the root-mean-square z-average radius of gyration Rg
z
(written as Rg ). The dn/dc value (0.17 mL/g) of the polymer-
ized micelles was measured at 25 °C using an interferometric
refractometer (λ ) 488 nm) for a range of concentrations.
SANS. SANS measurements were made at the National
Institute of Standards and Technology (NIST) in Gaithersburg,
MD. An average neutron wavelength of 6 Å with a spread of
11% was used. Samples were held at 25 °C in quartz “banjo”
cells with 2 mm path lengths. Three sample-to-detector

2484 Liu et al.
Macromolecules, Vol. 38, No. 6, 2005
Figure 3. Apparent diffusion coefficient, Da, before and after
Figure 2. Average decay rates of the intensity correlation
function as a function of q2 for solutions at 50 mM MUTB and
different molar ratio of TSNa, xTSNa. The slopes of the lines
yield the apparent diffusivity coefficients, Da.
polymerization for solutions at 50 mM MUTB as a function of
the molar ratio of TSNa, xTSNa
.
butions. Da can be related to the infinite dilution
diffusion coefficient D0 by
the Digital Micrograph software package, at low dose condi-
tions to minimize electron beam radiation damage. Brightness
and contrast enhancement were done using the Adobe Pho-
toshop 7.0 ME package.
Da ) D0[1 + kD(c - cac)]
(4)
where kD is the diffusion “virial” coefficient and c is the
surfactant concentration. D0 is related to the length of
the rod and its axial ratio p ) L/d via
Results and Discussion
Formation of Wormlike Micelles and Micellar
Growth. MUTB surfactant in water has a critical
micelle concentration of 15 mM at 25 °C.32 Homoge-
neous solutions are obtained when MUTB (e80 mM) is
mixed with TSNa up to molar ratios xTSNa ) [TSNa]/
[MUTB] of 3.0. The counterion binding between tosylate
and MUTB headgroups is not as strong as the interac-
tions between p-toluidine hydrochloride (PTHC) and
sodium dodecyl sulfate (SDS).40 Upon addition of PTHC
to SDS, a 1:1 complex forms in the mixed solution, and
there is a region of precipitate at [PTHC]/[SDS] molar
ratios > 1.0. When TSNa is added to MUTB solutions,
a slightly bluish tinge appears at xTSNa g 1.5, indicating
an apparent micellar growth (a transition from spherical
to wormlike micelles). At xTSNa ) 2.0, the critical
aggregation concentration (cac) drops to 2.0 mM MUTB,
as measured by surface tension. This reduction in cac
is a well-known effect of adding a hydrotropic counterion
salt to a surfactant solution.41
QLS. The elongation of the micelles upon addition of
TSNa to 50 mM MUTB solutions was characterized by
QLS. For all compositions, the average decay rate Γ
varies linearly with q2 (Figure 2), and the curves pass
the origin. This indicates that the apparent diffusivity
of the micelles, Da, depends mostly on their translational
motion, which holds true for scattering vector values
qL < 3. Only at larger qL values is the rotational motion
of the rods expected to increasingly contribute to the
apparent diffusivity. Therefore, with q ) 3.1 × 105 cm-1
(the largest scattering vector considered), qL < 3 implies
that the micelles should be smaller than about 100 nm.
The slope of the lines in Figure 2 yields Da, and Da
decreases with increasing xTSNa (open circles, Figure 3).
For a dilute suspension of rigid rods, this reduction in
Da implies an elongation of the rods.42 Likewise, for
hydrotrope-surfactant mixtures, a reduction in Da can
be interpreted as a transition from spherical to wormlike
micelles of increasing length,40 albeit the microstructure
of the aggregates needs to be corroborated using comple-
menting techniques as shown in the next sections.
kBT
D0 )
(ln p + ú)
(5)
3πηL
where kB is the Boltzmann constant, T is the absolute
temperature, and η is the solvent viscosity. ú is a
function of the axial ratio p and was estimated using
the Tirado et al.43 expression of the shape factor, which
is valid for axial ratios in the range of 2-30. Likewise,
kD can be expressed as44
kD ) 2MB2 - kf - vj
(6)
where M is the micelle molecular weight, B2 is the
osmotic second virial coefficient, which accounts for
excluded-volume interactions, kf is the hydrodynamic
virial coefficient, which accounts for friction due to direct
physical hindrance and/or hydrodynamic interactions,
and vj is the specific volume of the micelles. This analysis
neglects any micelle flexibility, which is a valid assump-
tion here since the micelles are only a few times longer
than their persistence length (see SANS results below).
The above expressions are solved iteratively for L
assuming that the cross-sectional radius of the micelles
is preserved. The micellar core radius was set at 2.05
nm, which is approximately the length of the hydrocar-
bon chain of MUTB.45 Addition of TSNa clearly causes
micellar growth up to L ∼ 40 nm at xTSNa ) 3.0 (Figure
4). For comparison, the equivalent sphere hydrodynamic
diameter at each molar ratio is also shown.
NMR Studies: Counterion Adsorption. NMR is
a powerful technique for investigating how the hydro-
trope is associated with the micelle. The electrostatic
and hydrophobic interactions between the hydrotrope
counterions and the surfactant forming the micelles
influence the orientation of the hydrotrope within the
micelle interface. NMR measurements have shown that
salicylate ions are strongly adsorbed to cetyltrimethyl-
ammonium bromide (CTAB) micelles in a configuration
that allows the carboxylic and hydroxyl groups to
protrude from the micelles.15 Insertion of the hydrotrope
is reflected by an upfield shift of the hydrotrope aro-
To determine the length of the micelles, Da was
corrected for hydrodynamic and thermodynamic contri-

Macromolecules, Vol. 38, No. 6, 2005
Polymerization of Wormlike Micelles 2485
micellar surface. The trimethylammonium signal also
shifts upfield, further confirming that the hydrophobic
portion of the tosylate intercalates between the surfac-
tant headgroups. When the concentration of TSNa is
doubled (Figure 5D), the extent of the shift for the m-
and p-proton resonances is smaller compared to the
extent of the shift seen for the 50 mM TSNa case. The
less prominent upfield shift is probably due to the
contribution of free (unbound) tosylate ions to the total
signal.
Shikata et al.48 observed a similar trend for solutions
of CTAB with sodium salicylate (SS) hydrotrope. They
found that when the SS concentration is low relative to
the CTAB concentration, the aromatic salicylate signals
move upfield relative to the position of the lines in a
pure SS solution. However, these lines move back
toward a lower magnetic field when the SS concentra-
tion is larger than the CTAB concentration and eventu-
ally approach the position of the lines in a SS solution.
The measurements indicate the formation of a 1:1
complex of hydrotrope counterion and surfactant, for
molar ratios of SS to CTAB greater than 1. Comparison
Figure 4. Average length of the unpolymerized wormlike
micelles (L) and the average equivalent sphere hydrodynamic
diameter (Dh) as a function of the molar ratio of TSNa, xTSNa
;
[MUTB] ) 50 mM.
1
of the H NMR spectrum of MUTB and the mixtures
shows that addition of TSNa to MUTB solutions broad-
ens the resonance lines associated with hydrogen atoms
in the surfactant tail below 2 ppm (Figure 5C,D). This
indicates that the oil core of the wormlike micelles is
less fluid (more closely packed) than that of the spheri-
cal micelles.
Cryo-TEM. Typical cryo-TEM images of the as-
semblies existing in solution before polymerization at
50 mM MUTB and xTSNA ) 2 are presented in Figure 6.
In thick regions (as in Figure 6A) the structures overlap,
and it is difficult to identify individual micelles and
determine their shape and length. However, in thin
vitrified regions (∼100 nm in thickness, Figure 6B),
coexistence of small globular micelles of about 5 nm in
diameter (black arrows), short and flexible wormlike
micelles (black arrowheads), and a few closed micellar
loops of several nanometers in diameter (white arrows)
are clearly seen, indicating that before polymerization
small globular micellar assemblies and wormlike mi-
celles, smaller than 50 nm in length, are the dominant
structures in solution.
Figure 5. 1H NMR spectra of (A) spherical MUTB micelles,
(B) TSNa salt, (C, D) MUTB/TSNa mixtures of wormlike
micelles, and (E) polymerized wormlike micelles. The MUTB
concentration in the mixtures is 50 mM.
matic proton lines as well as an upfield shift of the
surfactant headgroup proton resonances. A similar
trend is observed in mixtures of other hydrotropes with
surfactants.40,41
1H NMR spectra of TSNa, MUTB, and their mixtures
are shown in Figure 5A-D. The peak assignments of
the MUTB main lines (Figure 5A) were made by
comparison to spectra of cetyltrimethylammonium
tosylate and similar quaternary ammonium amphiphilic
methacrylates.46,47 Within the surfactant tail, the vinyl
and methacryl methyl group lines appear at δ ) 5.6-
6.0 and 1.9 ppm, respectively, and are important for
monitoring the completion of the polymerization reac-
tion. On the other hand, the trimethylammonium head-
group displays a large peak at 3.1 ppm due to the
protons of the three methyl groups attached to the
nitrogen atom. The TSNa spectrum (Figure 5B) shows
the two ortho protons as a downfield doublet at δ ) 7.7
ppm because of coupling with the meta protons. Like-
wise, the two m-protons appear as a doublet at δ ) 7.3
ppm, while the signal for the three methyl protons at
the p-position shows further upfield at δ ) 2.4 ppm.
Upon mixing 50 mM TSNa with 50 mM MUTB
(Figure 5C), the m-protons as well as the p-CH3 reso-
nances shift upfield from their original positions, while
the positions of the o-proton resonances remain es-
sentially unchanged. This indicates that the tosylate ion
strongly binds to the micelles, with its m- and p-
positions inserted into the micellar interior and the
o-protons and the sulfonate atoms protruding from the
Characterization of the Polymerized Wormlike
Micelles. Polymerization of the wormlike micelles at
different [TSNa]/[MUTB] ratios (0.7, 2.0, 2.5, and 3.0)
was carried out for 2 h, at which time 1H NMR showed
that the reaction was complete. During polymerization,
the solution mixture remained as one phase. A deepen-
ing of the bluish tinge and increasing viscosity were
observed, both of which indicate qualitatively apparent
micellar growth. The polymerized wormlike micellar
solutions were stable for more than 7 months.
1
1. 1H NMR Results. In the H NMR spectrum of
wormlike micelles before polymerization (Figure 5C,D),
the signals at δ ) 1.9 ppm (-CH3 on the methacrylate
group of MUTB surfactant) and δ ) 5.6-6.0 ppm (-CH2
on the double bond) can be clearly observed. After
polymerization for 2 h, all the signals characteristic of
the unsaturated double bonds have disappeared (Figure
5E), indicating complete polymerization of the double
bonds of the surfactant monomers. Another interesting
feature of the polymerized wormlike micelles is that the
signals due to the surfactant tail at <2 ppm, and the
signal of the -CH2 protons next to the ester group (4.1
ppm), are barely noticeable, which suggests the core is

2486 Liu et al.
Macromolecules, Vol. 38, No. 6, 2005
Images of the diluted sample show several regions of
mostly entangled, flexible, and probably branched mi-
celles, coexisting with several stretched, micrometer-
long cylindrical structures (black arrows, Figure 7B).
These micron scale structures were not imaged in the
unpolymerized samples, and they are clearly polymer-
ized micelles. Closed rings (white arrows), several tens
of nanometers in diameter, are also often seen. The
smaller rings are similar to those found before polym-
erization, but the larger rings were not detected before,
and they most likely formed upon polymerization. From
these micrographs it is evident that the polymerized
micelles have the same diameter as the unpolymerized
micelles. Also, in Figure 7B-E the vitrified areas
between the wormlike micelles are devoid of small
structures. The absence of globular and short micelles,
which existed before polymerization, strongly suggests
that all the small assemblies were polymerized or linked
to large wormlike micelles. Finally, the folded micelles
seen particularly in Figure 7B,E indicate that branched
micelles can also form upon polymerization.
3. QLS and SLS Results. QLS and SLS were also
used to characterize the polymerized wormlike micelles.
Figure 3 compares the diffusivity coefficients of worm-
like micelles before and after polymerization at different
xTSNa. The diffusivities of the polymerized micelles were
calculated following the approach discussed earlier,
namely from the slope of Γ as a function of q2. Da
decreased dramatically after polymerization, especially
at higher xTSNa ratios, indicating an increase in micellar
length. The estimated lengths of polymerized micelles
at different xTSNa ratios are shown in Figure 8. The
average length of the wormlike micelles polymerized at
xTSNa ) 2.0 is 246 nm. Comparison with the calculated
length of 34 nm for the micelles before polymerization
(at xTSNa ) 2.0) indicates there is a 7-fold increase in
the micellar length. Such long micelles after polymer-
ization are not expected to be entirely rigid rods as
corroborated by SANS results below. Thus, the calcu-
lated length of the polymerized micelles underestimates
the true length of the micelles. During polymerization,
surfactant monomers can add continuously to the
propagating radical located in the core of the wormlike
micelles to form much longer wormlike micelles with
fixed structures.
The polymerized structures are insensitive to dilution,
and Da remains almost constant upon dilution from 50
mM MUTB to 0.5 mM MUTB (Figure 9), indicating
successful “locking-in” of the wormlike micellar struc-
ture. The structure of unpolymerized wormlike as-
semblies typically changes with dilution, and mixed
micelles disassociate into unimers at concentrations
below the critical aggregation concentration (2.0 mM,
at xTSNa ) 2.0). The successful capture of a stable
wormlike micellar structure was also confirmed by the
similar Da value measured after dialysis of the polym-
erized wormlike micelle solutions against deionized
water.
Figure 6. Cryo-TEM micrographs of the unpolymerized
samples at xTSNa ) 2.0 and [MUTB] ) 50 mM. The observed
microstructures depend on the region of the vitrified film that
is imaged. (A) Thick regions: wormlike micelles of different
lengths. (B) Thin regions: small globular micelles (black
arrows), flexible wormlike micelles (black arrowheads), and a
few closed micellar loops of several nanometers in diameter
(white arrows).
“locked” so that the mobility of the surfactant tail is
greatly restricted after polymerization. This is expected
given that polymerization has covalently linked the
hydrophobic tails, and such line broadening is charac-
teristic of polymerized surfactant monomers containing
a reactive group on the tail.49 The fluidity of the
hydrophobic tail enclosed in the core decreases as the
micelles evolve from spheres, to wormlike structures,
to polymerized wormlike micelles.
2. Cryo-TEM Results. Samples at 25 °C from the
viscous polymer solution containing 50 mM MUTB and
xTSNa ) 2.0, and from the same sample diluted three
times, that is, therefore, of much lower viscosity, were
examined by cryo-TEM. In Figure 7A, the micelles
appear to be cylindrical in shape and longer than those
found before polymerization. However, because of the
high concentration, the structures overlap. To see the
individual assemblies, the sample was diluted by 3.
Since the structure of the wormlike micelle does not
change with dilution, SLS can be used to measure the
molar mass and the radius of gyration of the polymer-
ized wormlike micelles. A Zimm plot analysis (Figure
10) yields a weight-average micelle molar mass of about
5.0 × 106 g mol-1. This value corresponds to ap-
proximately 11 000 MUTB surfactant molecules in each
polymerized micelle, assuming that all the surfactant
molecules have participated in the formation of the

Macromolecules, Vol. 38, No. 6, 2005
Polymerization of Wormlike Micelles 2487
Figure 7. Micrographs of the polymerized micelles (xTSNa ) 2.0 and [MUTB] ) 50 mM). (A) Under no dilution, long overlapping
structures are observed. (B-E) After three times dilution, individual assemblies are evident such as numerous flexible micelles,
some stretched, micrometer-long cylindrical micelles (black arrows), and large closed loops (white arrows).
polymerized wormlike micelles and assuming the for-
mation of a 1:1 complex between MUTB surfactant
headgroups and the tosylate counterions. The z-average
hydrodynamic radius of gyration ( Rg ) of the polymer-
ized wormlike micelles is 108 nm, and the equivalent
sphere hydrodynamic radius ( Rh ) for the same sample
is 29 nm; thus, Rg / Rh ) 3.7. This ratio, which depends
on the particle shape and density profile of the scatter-
ing objects, is about 1.5 for monodisperse random coils,50
while for elongated micelles it varies in the range of
1.3-4.0.51 Here, the high value of Rg / Rh is consistent
with an extended wormlike microstructure.
4. SANS Results. SANS was used to characterize the
unpolymerized (open squares) and polymerized (open
triangles) wormlike micelles in D2O at 50 mM MUTB
and xTSNa ) 2.0 (Figure 11). The spectra for the

2488 Liu et al.
Macromolecules, Vol. 38, No. 6, 2005
Figure 11. SANS spectra for the (0) unpolymerized and (4)
polymerized wormlike micelles in D2O. A semiflexible cylinder
model with three adjustable parameters is used to fit both
spectra (solid lines; Table 1). The spectrum of the polymerized
wormlike micelles is shifted upward by a factor of 10 for clarity.
Figure 8. Average length of the polymerized wormlike
micelles (L) and the average equivalent sphere hydrodynamic
diameter (Dh) as a function of the molar ratio of TSNa, xTSNa
;
[MUTB] ) 50 mM.
Figure 12. Cross-sectional Guinier plots for unpolymerized
micelles, polymerized wormlike micelles, and polymerized
wormlike micelles after 18 times dilution.
Figure 9. Apparent diffusion coefficient, Da, and scattering
intensity upon dilution for wormlike micelles polymerized at
50 mM MUTB and xTSNa ) 2.0.
before polymerization, suggesting that the cross-sec-
tional radius of the micelles is preserved during polym-
erization. After polymerization, an increase of the
scattering in the low-q region is observed, which indi-
cates an increase in length of the wormlike micelles.
These results qualitatively confirm that the cross-
sectional structure of the wormlike micelles has been
preserved during polymerization and that the length of
the micelles increases.
The cross-sectional radius of the micelles is first
obtained by analyzing the intermediate-q portions of the
scattering curves using the Guinier approximation for
the form factor. Guinier plots are shown in Figure 12
for the original (open squares) and polymerized micelles
(open circles). From the fitted linear portions of the
curves, the unpolymerized and polymerized micelles
have a micellar radius of 1.9 and 2.0 nm, respectively.
These are in good agreement with the calculated length
of a fully extended MUTB molecule of 2.05 nm (which
was used in the light scattering calculations above).
The scattering data before polymerization can be best
fit using a semiflexible cylinder model, giving a cross-
sectional radius rcs of 1.7 nm, a contour length Lc of 41.3
( 0.9 nm, and a persistence length lp of 12.2 ( 0.7 nm.
The results are summarized in Table 1. Note that the
length of the wormlike micelles obtained from QLS (34
nm, Figure 4) is in agreement with the contour length
from SANS fitting. Fitting the scattering data of the
polymerized micelles to a semiflexible cylinder model
yields rcs ) 1.8 nm, Lc ) 127 ( 5 nm, and lp ) 24 ( 1
nm (Table 1). Thus, SANS results show that polymer-
ization increases the length of the wormlike micelles
from about 40 to 130 nm.
Figure 10. Zimm plot of polymerized micelles (polymerized
at 50 mM MUTB and a molar ratio, xTSNa ) 2.0). A series of
dilute polymerized solutions (concentrations ranging from 5.3
× 10-5 to 4.5 × 10-4 g/mL) were used for the static light
scattering measurements.
unpolymerized and polymerized micelles display a q-1
dependence at intermediate q values, which is a signa-
ture of scattering from cylindrical objects. The spectra
are thus qualitatively consistent with the presence of
wormlike micelles in solution before and after polym-
erization. Because of the screening effect of TSNa salt,
the neutron scattering profiles do not show an interac-
tion peak at lower q values such as often arises in
spectra from micellar solutions of alkyltrimethylammo-
nium surfactants.
The spectrum of the polymerized micelles overlaps at
intermediate and high q values with that of the micelles

Macromolecules, Vol. 38, No. 6, 2005
Polymerization of Wormlike Micelles 2489
Table 1. Results of Fitting the Semiflexible Cylindrical Model to SANS Spectra of the Initial Wormlike Micelles, the
Polymerized Wormlike Micelles, and Polymerized Micelles after Dilutiona
sample description
rcs (nm) (Guinier)
rcs (nm) (fitting)
Lc (nm)
lp (nm)
[MUTB] ) 50 mM, unpolymerized
1.9
2.0
2.1
2.1
1.7
1.8
2.0
2.1
41.3 ( 0.9
127 ( 5
187
12.2 ( 0.7
24 ( 1
23
[MUTB] ) 50 mM, polymerized
[MUTB] ) 50 mM, polymerized and diluted 18 times
[MUTB] ) 25 mM, polymerized and diluted 18 times
227
25
a In all entries, [TSNa]/[MUTB] ) 2.0.
also observed for a second sample originally polymerized
at 25 mM of MUTB and xTSNa ) 2.0 and also diluted by
18 times so that [MUTB] ) 1.4 mM. In this case, the
best fit (Table 1) gives a radius and persistence length
similar to that of the sample polymerized at [MUTB] )
50 mM. This suggests that the radius and rigidity of
the polymerized micelles might not depend on the initial
amount of monomer. Modeling of any of these data using
the rigid cylinder model gave poor quality fits at low q
values. Similarly, a model-independent analysis using
the indirect Fourier transform method could not provide
information on the length of the micelles because the
estimated lengths are larger than π/qmin, which is the
maximum length scale that can be probed using this
approach.52,53
Mechanism. Several groups have observed micellar
growth during polymerization of spherical micelles.
Cochin et al. proposed a mechanism for micellar polym-
erization that completely excludes a topological polym-
erization of spherical micelles.25 Their mechanism con-
siders the dynamic nature of the micelles and the degree
of reactivity of the polymerizable group, and a similar
approach can account for the growth of the micelles. The
interplay of the variables presented below favors mi-
cellar growth for the case of mixtures with a low cac,
whose surfactants contain a polymerizable group of high
reactivity such as methacrylate, located within the tail.
Other scenarios require a different treatment as re-
viewed elsewhere.25
Figure 13. SANS spectra for the (O) original polymerized
wormlike micelles (no dilution) and (0) the same polymerized
micelles after 18 times dilution. The solid line represents the
best fit to the experimental data using a semiflexible model
with excluded volume interactions (Table 1). The dotted line
is the scattering profile of the diluted sample times a factor of
18 and overlaps the experimental data of the undiluted
micellar solution.
The dynamic nature of the micelle is best described
in terms of the micelle lifetime and the time for the
association of surfactant monomers into the micelles.
During polymerization the mean lifetime of the initial
micelles is given by54
-1
σ2
N
Figure 14. Holtzer plot of polymerized wormlike micelles
polymerized at different MUTB concentrations and then
diluted 18 times. The upturn at low q values indicates a
semiflexible wormlike microstructure.
tm ) Nτ2a 1 +
a
(8)
[
]
where N is the average aggregation number of the
micelles, a ) (c - cac)/cac is a solubility term given by
the concentration of surfactant (c) and the cac of the
mixture, σ is the standard deviation of the aggregation
number distribution, and τ2 is the relaxation time
associated with the formation-breakdown of the mi-
celles. σ2/N is typically close to 155 and far from the cac,
a . 1, so that eq 8 reduces to
Neutron scattering measurements of this polymerized
sample after 18 times dilution ([MUTB] ) 2.8 mM) are
displayed in Figure 13. The results from the Guinier
analysis and from the best fit using the semiflexible
model are summarized in Table 1. When the scattered
intensity of this dilute sample is multiplied by 18, the
scattering profile of the nondiluted sample is recovered
(Figure 13). Since the scattered intensity of the diluted
and nondiluted samples scales linearly with dilution,
the structure factor of the assemblies is one. This result
confirms it is appropriate to neglect intermicellar
interactions other than the excluded-volume interac-
tions, as is done in the analysis above.
Evidence of the flexibility of the micelles is obtained
from a Holtzer plot (Figure 14), which is constructed to
highlight the deviation of the scattering data from that
of ideal, rigid cylinders. In this plot, the upturn in the
low-q region indicates the micelles are best described
by a semiflexible cylinder model. A similar upturn is
tm ) Nτ2
(9)
which is applicable here, since the cac ) 2 mM for
solutions made at xTSNa ) 2.0.
The relaxation time τ2, as determined by various
methods, can vary over a broad range (1-500 ms)
depending on concentration, temperature, or surfactant
chain length.55 A good approximation for cationic sur-
factants with chain length between 14 and 16 carbon
atoms and T > 40 °C is τ2 in the range of 1-20 ms.25 N
is easily calculated from the micelle and surfactant
dimensions, and for the 34 nm long unpolymerized

2490 Liu et al.
Macromolecules, Vol. 38, No. 6, 2005
micelles N ≈ 1100 (MW ∼5 × 105). Therefore, from eq
9, tm ≈ 1-20 s. This time is considerably longer than
typical spherical micelle lifetimes of 10-2-10-1 s.25
In addition, the aggregation number of the micelles
fluctuates around N due to the diffusion of surfactant
monomers in to and out of the micelle. This flow of
surfactant is important since unreacted monomer can
migrate from one micelle to another during the course
of the reaction. The time scale for association of a
monomer species, ta, is given by (k+cac)-1, where the
Acknowledgment. We acknowledge the support of
the National Science Foundation CTS-9814399. The
National Institute of Standards and Technology, Gaith-
ersburg, MD, provided neutron scattering facilities used
in this work. P. A. Hassan, G. M. Santonicola, and S.
R. Kline provided insightful comments about scattering
data analysis. The cryo-TEM studies were performed
at the “Cryo-TEM Hannah and George Krumholz Labo-
ratory for Advanced Microscopy” at the Technion, part
of the “Technion Project on Complex Fluids”.
association rate constant is k+ ≈ 109 (M s)-1 55
.
Thus, ta
≈ 5 × 10-7 s, so that monomers are continuously
entering micelles and can potentially be incorporated
into the growing chain of an initiated micelle.
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