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Small angle neutron scattering investigation of rodlike micelles aligned by shear flow
451
Advances in Colloid and interface Science, 34 (1991) 451-476
Elsevier Science Publishers B.V., Amsterdam
SMALL
ANGLE
MICELLES
NEUTRON
ALIGNED
J PENFOLD+,
SCATTERING
INVESTIGATION
OF
RODLIKE
BY SHEAR FLOW
E STAPLES* and P G CUM~lNS*
+ Neutron Science Division, Rutherford * Unilever Research,
Appleton
Port Sunlight Laboratory,
Laboratory,
Chilton, Didcot, Oxon
Quarry Road East, Bebington,
Wirral
CONTENTS
Abstract.............................................................. 451 1. Intrcduction.......~....................~.............................45 2 2.lT-leoq................................................................ 454 analysis procedures...=.................45 6
3. Eqerimsnt al.details and data
4. H~~~~~~o~l~f~ion ......................................... 463 5. Nonionic micefles................................................... ..466 6. Mixed nonionic-cationicmicelles...................................... 470 7. Interactions, shear induced struc~s
and viscoslastic @ases........47 2
8. .%mnazy............................................................... 474 References.................................. ..-.......................47 5
ABSTRACT
The application of small angle neutron scattering (SANS) to the study of anisotropically shaped micelles, aligned by shear flow, is discussed. A typical shear flow apparatus and the theoretical basis of the data analysis are briefly presented. Some studies on dilute rodlike micelles are used to illustrate the analysis procedure, and to introduce complications due to hindered rotation, flexibility, polydispersity, turbulence and shear induced structures. Particular attention has been focused on the role of hindered rotation. More recent experimental results on the evolution of micelle size with temperature for nonionic surfactants, and the nature of mixed nonionic-cationic micelles, will be discussed in more detail. Recent experiments on viscoelastic and interacting micellar phases will be briefly described.
OOOl-8686/91/$09.100 1991-E1sevierSciencePublishersB.V.
452
1. INTRODUCTION
In recent years, SANS has been applied to the study of a range of dilute isotropic micellar systems [l], following the initial work of Hayter and Penfold [2,3] to include the nature of intermicellar were ambiguous
interactions.
Early studies on anisotopically
due to lack of momentum
the orientational
averaging
of the isotropic
More recently considerable
progress
shaped micelles [4]
transfer, Q, range, and insensitivity
due to
solution.
has been made in the study of anisotropically
shaped micelles by SANS, where shear flow alignment
[5,6] has been used to remove
much of the intensitivity
measurements.
The technique measurements
of the orientationally
is now well established,
and a number
of groups
have reported
on dilute rodlike micelles [7], mixed surfactant phase [8], shear induced
structures
[9], concentrated
dependent
studies [I l] have been made.
of the same techniques
(interacting)
and viscoelastic
systems
[5, lo],
and time
In a related area there has been extensive use
[12] to study shear phenomena
may be used as model macrofluids on laboratory
averaged
in colloidal suspensions,
in which non-Newtonian
time scales; but this is beyond
behaviour
which
can beobserved
the scope of this review and will not be
discussed.
In the 1950s optical flow birefringence anisotropic
micelles, colloids and polymers,
upon that pioneering
A suspended
elongated
to the local streamlines. diffusion coefficient,
[13,14] to study
and the recent neutron studies draw heavily
particle subjected to a viscous shear gradient G will precess angular velocity being a function of the orientation
Simultaneously,
Brownian motion, characterised
Dr, will tend to randomise
of these two competing
the orientations.
effects can be characterised
relative
by a rotational
The relative importance
by the parameter,
I- = G/Dr; full
and to understand
the scattering
can only occur when r as1.
In practice, pattern
developed
optical work.
in the flow, the instantaneous
alignment
was extensively
perfect alignment
from a partially
aligned
is never achieved, system
an estimate
of the orientational
distribution
p@,+;T) (where 8,+ are the normal polar angles, see Figure 1) must be made.
Hayter
453
and Penfold [5] have developed for the SANS scattered
an analytic form of this distribution
geometry
which is a refinement
function appropriate
of the original optical form of
Peterlin and Stuart [I 51 and Jerrard [16]. Hoffman et al [I I], in parallel, have in contrast developed important
a numerical
solution
of the basic Langevin
or Fokker-Plank
aspect of their work is that not only can they predict equilibrium
but they can calculate the time dependence
of the orientational
equation;
an
distributions,
distribution
function.
-z detector
7/
12
/
I
shear aradient
1
incic bea,
Figure 1. Cartesian and angular coordinates referred to the centre of a cylindrical micelle at origin. The relationship to the spectrometer geometry is shown schematically. The momentum transfer, Q, lies in the X-Z plane.
From a range of dilute rod-like dilute
phases
behave
However, in particular A range of phenomena
micelles studies, the general impression
remarkably
like rigid monodisperse
circumstances
rods
under
is that the shear
effects due to subtle flexibility are observed
due to intermicellar
interactions
have been observed
[5,9,19]
and evidence for shear induced structures in some systems have been reported
Effects due to polydispersity,
turbulence
in particular the effect of hindered
[7]. [17]. [9].
and hindered rotation will be discussed, and
rotation will be considered
in more detail.
454
Finally, the main emphasis micelle
size
with
monoheadecylether, (cetyltrimethyl
on recent experimental
temperature
for
the
results will be on the evolution
nonionic
C&Es, and the nature of mixed
ammonium
bromide,
&TAB)
of
surfactant
hexaethyleneglycol
nonionic
(C,aEs) and cationic
micelles.
2. THEORY
The scattering anisotropic
from
monodisperse
dilute (non-interacting)
isotropic
solution
of
micelles is given by
I(Q) = < (F(Q)l*>o
where F(Q) is the form factor for a micelle at a given orientation transfer Q and < > o denotes
For uniform cylinders
relative to the momentum
an average over all such orientations.
of length 21 and diameter
2a :
F(Q) = (FQ,~) = 2~s Vjs (01 cosy) J1 (QasiwMQasW
(2)
where y is the angle between Q and the cylinder axis, V is the volume, p0 the scattering amplitude
relative to that of the solvent, J,(x) is the first order Bessel function of the first
kind, and j,(x)
= sinx/x.
coated cylinders
Evaluation
is straightforward
The intensity function
of F(Q) for other models
averaging.
expression,
[I 91.
Further, for interacting micelles it is difficult to write an equivalent
since the correlation
of orientation
If all the micelles have the same orientation,
where S,(Q) interactions calculation
and
in (1) is not very sensitive to the micelle model due to the
orientational
l(Q) = F*(Q)
such as ellipsoids
with position is generally
not calculable.
then
S,(Q)
is the structure factor for a fluid of aligned micelles.
(S,(Q)
= 1 .O) the scattered
In the absence of
intensity displays the micelle geometry.
The
of structure factors for rodlike systems is now receiving much attention [20].
455
A convenient
method for aligning dilute rodlike micelles is shear flow, and we have
already seen that the degree of alignment the competing
is associated
effects of G and Dr (characterised
with the relative importance
by the parameter
of
T = G/Dr), and
where for dilute rods with I > a Dr is given as [5] :
Dr = 3kaT (s -t) / (87~~~1~) (s > 2) where s = log(2l/a),
Predominantly
scattered
t = 1.57 - 7 (0.28 - I/s)~ and n is the solvent viscosity.
couette flow [21,22] has been used to provide the shear alignment,
and the scattering be achieved,
(4)
geometry
is shown in Figure 1. In general perfect alignment
and an orientation
distribution
must be employed
will not
such that the resultant
intensity will be given by
where cos y+
= sir@cos$cos+
f
cos&in$
We will refer to the Qll and QJ_ directions
For the CL direction + dependence
projected
that used in the original dependence
probability
depends
only on 6, with the
out. This highlights the difference between this geometry optical
Hayter and Penfold [5] to improve
p(H.f$:l-) =
constant.
when $ = 0 and v/2 respectively.
(Jr=n/2) the scattering
on Q (the extinction
have developed
and A is an experimental
studies
[13-161 where 0 is integrated
angle) is measured.
This sensitivity to 6 has allowed
upon previous estimated
an analytic form of p(&+,T)
and
out and the
[I 51 of p(6,+,T), and they
where
(1 - cos2$0)(1 + sin28cos2$0)3/2 4n[ 1 - sin2 8 cm 2& cos 2(@- $o)12
and 241) = arctan(S/T)
(6)
456
In contrast,
Hoffman et al (11) have developed
Fokker-Plank
numerical
solutions to the Langevin or
equation
where f is the orientation
distribution
function,
o(O) = i/4 p sin 2+sin26
(6a)
o(+) = -i/2
(6b)
(1 - p cos2+)sin6
p = [L2 - (2a)2]/[L2 + (2a)2]
(6~)
and L = 21.
This has been particularly evolution
important
of the rod distribution
3. EXPERIMENTAL
DETAILS AND DATA ANALYSIS PROCEDURES
The data presented angle scattering
for their “stop flow” studies [l 11where the time
function has been studied.
in this review have been predominantly
diffractometers
[23], and on the LOQ [24] spectrometer
Various shear cell geometries, plates
cylinders,
detail elsewhere Couette
cylinders
[21,22],
disc [6], have been used to produce
either
for in the case of rotating
if d c
a constant gradient across the gap is achieved, the characteristic
Grenoble
0.d’.
which include rotating concentric
[5], or a rotating
Poiseuille or Couette flow. Couette flow is more preferable, concentric
on the small
on the ISIS pulsed neutron source, in various
different Cl ranges between the extreme values of 0.002 and
flow between
measured
Dl 1 and D17 at the lnstitut Laue Langevin,
parabolic
form.
[21,22] and therefore
cell designed
by Cummins
Couette shear cell is constructed rotor which is stationary,
whereas Poiseuille flow will always have
A number of these devices have been described
in
we will briefly present the main features of the
et al [21] specifically
for surfactant
studies.
The
of quartz, with an outer rotor which rotates and an inner
see Figure 2.
457
Figure 2. Schematical
This geometry
view of shear cell constructed
inhibits the production
by Cummins
et al.
of Taylor vortices and establishes a constant shear
gradient across the gap. An important feature is the rotating seal which presents solvent loss, sample rejection and foaming.
The shear gradient is related to the rotation speed
and gap width, and for the 0.5 mm gap in the cell gives a maximum
shear gradient of
2.5 x IO4 s-l (G = 5.28N, where N is the rotor speed in rpm).
Figure 3 shows the intensity contours for scattering from 0.03M &TAB
in 0.4M KBr
at shear gradient of 5000 s-l (Figure 3a) and at a shear gradient of 7500 s“ (Figure 3b); shown in Figures 3c and 3d is the calculated for a rigid monodisperse
contours
(using equations
rod of length 21 = 2700A and diameter 2a =
MA. These
are typical of the range of dilute rodlike micelles that have been studied. patterns,
such as those
dimensions.
in Figure
3, contain
detailed
2, 4, 5 and 6)
information
about
However, it is difficult in practice to extract accurate quantitative
from such plots.
curves
The scattering
In order to make a simple and more precise quantitative
the rod
information analysis of
such data, it is convenient directions,
Qfl and CL
earlier) in a consistent
to consider
By comparing
the intensity the absolutely
scattered
in the two orthogonal
scaled data with theory [5] (see
way for a range of G, it is possible to extract a rod diameter
and a length 21 [5,7]. Figure 4 shows a typical fit for 0.04M dodecyldimethyl chloride
2a
ammonium
(DDACI) in 4.OM NaCl at a shear gradient of 7000 s-l (the data are consistent
with a rod length of 2500A and a diameter of #A).
At higher Q values the sensitivity of
the data to rod length results from the shear dependence
of the anisotropy,
low Q and high G the Q(I data are most sensitive to the rod length. determined
principally
by the form of short dimension
whereas at
The QL intensity is
of the rod.
Figure 3. (a) Experimental intensity contours for scattering for 0.03M C1sTAB/0.4M KBr/D20 at 313K and G = 5000 s-l, (b) as (a) except at G = 7500 s“, (c), (d) theoretical intensity contours for (a)(b) with 21 = 27OOA and 2a = 47A.
In Figure 3 is was shown that there was excellent intensity
contours
situation,
and in Figure 5 we show an example
observed.
for 0.03M C,sTAB/O.4M
agreement
KBr with theory. where deviation
in the shape of the
This is not afways the from theory is clearly
For the 0.04M DDACI in 4M NaCl (Figure 5a) there is now more intensity in
the off-symmetry
directions.
This redistribution
of intensity has been attributed
to the
459
presence
of subtle rod flexibility
[7], and in Figure 5b is shown a calculated
contour which attempts to take the flexibility into account.
theory, Cummins et al [7] have simulated the effects of the redistribution to rod flexibility by assuming of angles
about
that the micellar orientations
are distributed
of the equivalent
over a cone The
simulated intensity contour for DDACI (Figure 5b), which is now in good agreement
with
data, is calculated
direction
of intensity due rigid rod.
the observed
the mean orientational
intensity
In the absence of a rigorous
for a cone angle of 20’.
There has been much recent
interest on the flexible nature of rodlike micelles [25]. Much of the recent light scattering experimental theories
data on such systems have been interpreted
of “living polymers”
using the recently developed
[26], based on the well established
highly flexible chains. The general observation
polymer
theories for
from the neutron scattering studies is that
under shear the range of systems studied do not show any marked degree of flexibility.
I(O)
(in
orbitrory
units)
Figure 4. Measured scattered intensities taken along the QI (0) and GII (0) directions for 0.04M DDACV4M NaCI/DsO at T= 298Kfor G = 7000 s-l: the solid lines are calculated curves for 21= 2500A and 2a = MA.
460
(b)
Figure 5. (a) measured intensity contours for 0.04M DDAW4M NaCI/D,O at T= 298K and G =7000 s-l, (b) calculated intensity contours for 21=2500A, 2a = 44A and for flexible rods with a core angle of 20”.
It is possible that the imposition Flexibility has been observed DDACI, C&Es at temperatures C,sTAB/CxEy observations, surfactant
[18].
of a shear gradient
alters the flexibility of the rods.
in some systems under shear, and these are notably the approaching
The main factors
principally the headgroup
the cloud point [27,28], and mixtures
affecting
rod flexibility
environment
chain length (this will be discussed
of polydispersity;
by theory.
are then, from these
and of secondary
importance
the
later in the context of C,sEs micelles).
At higher G ( > 1O4s-l) there is a region where the anisotropy at a slower rate than suggested
of
of the data increases
Such an effect can be interpreted
that is, the reduced anisotropy
in terms
results from the weaker orientational
coupling of the shorter rods. However, there is additionally
the possibility
of turbulence
461
being a contributing randomising turbulence
factor; turbulent
will start at G - lo4 s-l).
enough additional
randomisation
(this has been observed
By introducing distribution pattern
diffusion.
(For viscosities
At sufficiently high G, turbulence
that the degree of anisotropy
a further
of ca 10m2Pas will contribute
should start to decrease
in some extreme cases).
a polydispersity,
of rod lengths,
is significantly
differences
flow will have the effect of contributing
term in addition to the rotational
altered
in orientational
based
on an arbitrarily
chosen
it can be clearly shown [7] that the anisotropic for a substantial
probability
polydispersity,
reflecting
log-normal scattering the large
for different lengths (see Figure 6).
Figure 6. Theoretical intensity contour at G = ~OOOAfor 21= 2500A and 2a = MA, with a polydispersity of u = 0.5.
However, the absence of any well defined minimum QI
intensity
polydispersity
plots for most of the dilute systems is present.
These two observations
systems investigated
the polydispersity
from a polydisperse
system
from the QI form factor in the
studied
clearly indicate that some
suggest that for the majority of dilute
has a variance, u, c 0.2. The analysis of data
using a monodisperse
model
will produce
systematic
462
deviations,
which can be rationalised
Figure 7). Recent theoretical substantially
by introducing
treatments
[29] suggest that the application
alter the micelle size distribution;
experimental
observations
-0
an effective shear gradient
these predictions
(see
of shear can
are not consistent with
over the range of dilute rodlike micelles [7,28] studied.
2
4
6
8
10
12
14
16
18
20
x103
Appliedsheor(s-‘1
Figure 7. Effective shear gradient polydispersities: (a) monodisperse,
as a function of true shear gradient (b) u = 0.2 and (c) u = 0.3.
There has been much discussion breaking [5,7,27,28]
[26,30].
The overriding
tobacco mosaicvirus,
deformation
of micellar
and will be discussed evidence
have observed
rods, and
with that from well defined rodlike systems such as
for limited and modest growth with increasing
later in the context of hindered rotation. for such processes
has been reported
for the specific systems hexadecyl
and tetra decyltrimethyl
shear induced
and
systems
TMV [7]. However, recent data on r&Es has a low concentrations
have shown some evidence
(C&,DAB)
growth,
for a wide range
is that under shear the micelles behave like rigid monodisperse
that the data is mostly consistent
convincing
about shear induced evidence
for a range of
structures
(see later).
ammonium Cummins
The strongest
shear [31], and most
by Hoffman et al [9], who
octyl dimethyl ammonium salicylate (ITMA-sal)
bromide
the formation
et al [7] have investigated
of
a range of
463
micellar systems with quite different critical micellar concentrations micelle lifetimes and monomer-micelle
exchange
important,
counteracted
then they must be furtitously
rates.
(cmcs), and hence
If break-up
processes
are
by collision and self assembly
processes.
The discussion
to date has focused
However,
a number
interacting
systems,
of interesting
predominantly
observations
on non-interacting
[5,11,18)
and these will be discussed
systems.
have now been made
in
in more detail in a later section.
4. HINDERED ROTATIONAL DIFFUSION
Many of the dilute rodlike micelles investigated higher degrees of anisotropy
than expected
low Q implies an increase in the “effective”
Effective rod length
by Cummins et al [7] at low G show
theoretically.
The enhanced
anisotropy
at
rod length (see Figure 8).
fin i)
6ooo I 5000 0 4000 \\ “o<--.N
3000
o*Izl
; a-*
1000
-6.0
0
-======a
-
0
I
0
t
I
I
I
10
2 $4heorgrodie~t
(x1O381I
Figure 8. Effective rod length as a function of shear gradient for (a) (0) 0.03M CTAB/0.4M KBr/D20, (b) (*) 0.04M DDACl14M NaCI/DsO and (c) (+) TMV/DaO.
464
Although
in terms of interactions
the entangled
or concentrated
density and L is the rod length. will hinder rotational
region, i.e. C > 1/L3, where C is the micelle number However,
as alignment
is induced
it is predicted
have a concentration is truly dilute.
in the system, the
until at high degrees of alignment the dilute rotational diffusion
will be recovered.
With the exception
of DDACI (see Figure 8), and some
systems of very short rods (21 < 1500A) [7], this phenomena Therefore,
are dilute, they are in
In such regimes in the isotropic solution, entanglements
diffusion.
hindering will be reduced, coefficient
all the systems investigated
is generally
that for a given micellar system this hindered
dependence,
and should disappear
This trend has been shown for sodium
observed.
rotation should
when the rod concentration dodecyl
sulphate,
SDS (see
Figure 9).
Effectwe
1000
rod length
(ini)
I
t-
I 8
I 6
I 4
I 2
0
I 10
Sheargradient,G(xlO3eC-‘)
Figure 9. Effective rod length as a function of shear gradient for SDS/l .3M NaCI/DsO for (0) O.lM, (+) O.O7M, (A) 0.05M and (x) 0.025M.
However, length.
there is in addition
a significant
A more clearer confirmation
C,sEs where the concentration and at the lowest concentration
concentration
dependence
is shown in Figure 10 for the nonionic
dependence
on the rod surfactant
of the rod length is much less pronounced,
(0.001 M) there is clearly no hindered
rotation.
At this
465
lowest concentration
of C&Es there is some evidence
However, it is a small effect and may also be attributed
6000
5000
+\ I
3000
micellar
‘+
\
+~p-----.
o-o-
I 20
I
0
I
I
l+ o----------o
I
4-o 5hmr
prodmf
I 60
I
I 80
, G (x 1O’rc“)
Figure IO. Effective rod length as a function of shear gradient O.O2M, (+) 0.002M and (0) O.OOlM.
for C1sEs/D20 for (0)
The DDACI data remains an exception to a well defined pattern of hindered The system,
growth.
in flexibility.
.
\
4000
of modest to changes
however,
showed
the most marked
flexibility,
rotation.
and it may be that the
conditions for hindering are more complex than the overlap condition,
and are inherently
linked with the flexibility of the rods.
From the data presented rotation and rigidity correlate
in Figures 8 and 10, there is further evidence that hindered in the series
TMV z C,sEs z CTAB > DDACI and that monomer C&Es i
exchange
rates follow the same pattern
CTAB < DDACI.
Hence monomer
exchange
and flexibility may indicate the same behaviour.
466 In the presence
of hindered
rotation, the orientational
under shear will no longer be exactly described we assume possible
that the form of the resulting
to extract the shear dependence
Figure I I), and the form of dependence et al [32].
Hoffman
diffusional
coefficient
experiment,
and coworkers from
probability
distribution
of the rotational
of individual
evolution
is similar, then it is
diffusion coefficient
diffusion
in a “stop
coefficient
cetylpyridinium
salicylate
of the flow”
Dr(t) (with a
relaxed time - 300 ms) which they attributed to the influence of inter-particle between the charged
(see
by Odel
the time dependence
of the anisotropy
a time dependent
rods
[5]. However, if
is similar to that reported for polymers [I I] have followed
the time
and have extracted
probability
by the dilute theories
interactions
(CPS) micelles.
1000 -
600
n
600
n
n
n I
400
n
200
m
0
I 2
I 4
I Sheo~grodicn?,
Figure 11. Shear gradient dependence CTAEV0.4M KBr/DsO at T= 313K.
5. NONIONIC
I
I 6(reCl’?
I 12
of the rotational
I 14
diffusion coefficient for 0.03M
MICELLES
Many studies [33,34], using a range of techniques,
have addressed
the integrity of the micelle unit as the cloud point is approached. systems
5 XW’
whose micelles
the question of
The consensus,
have low axial ratios, is that the micellar weight variation
for is
10
-I-
+
3
468
insignificant.
As the cloud point is approached
In the Q range investigated for such aggregation. perturbation
micelle associated
is expected
to occur.
(0.06-0.1 A-‘) there is no evidence in the scattering patterns
This implies that aggregation
to the orientation
processes are only causing a minor
process, and that the rod lengths in Figure 12 reflect the
true micelle geometry.
In micellar systems, the micelle geometry the surfactant area per headgroup. sut-factant micelles, modifications
can be rationalised
In the presence of electrolyte, to EO/EO interactions
area per molecule and hence the micelle geometry. thiocyanate, effectively
increased
consistent
with the ethylene
or decreased.
“Salting
of
can occur which will modify the
The addition of “salting in” (sodium
NaSCN) and “salting out” (NaCI) electrolyte
of the phase diagram
by considerations
for the C,E, nonionic
have an effect on all regions
oxide
in” electrolyte
(EO) chain length is of particular
being interest
because it allowed the evolution of micellar size to be followed over a wider temperature range [28], as a result of the cloud point being raised (0.5M NaSCN increases the cloud point of 1% C,sEs in DsO from 38 to 51 “C).
Throughout
that temperature
SANS from the shear aligned system was shown to be consistent
range, the
with long rigid rods
(see Figure 13).
10 0 0
0.005
0 020
0.010
Momentum
transfer,
0.030
0.040
0 (ii-‘1
Figure 13. Scattered intensity I(Q) (in arbitrary units) versus momentum transfer Q for 1% C1sEe/D20 at 31 “C at G = 5000 s-l; (*) Q perpendicular and (0) Q parallel. The solid lines are calculated curves for 21= 3400A and 2a = 6OA.
469
With increasing and
temperature
eventually
temperature
decreased
(towards the cloud curve), the rod length initially increase (see Figure
of 12°C. This evolution
14), reaching
a maximum
in rod length is accompanied
at a reduced
by an increase in the
rod flexibility (see Figure 15)
1
Figure 14. Effective rod length as a function of reduced C1,Es/D20/0.5M NaSCN at G = 5000 s-l. The increase in rod length is attributed area per molecule, are associated
whereas the subsequent
with modifications
temperature
to the dehydration
(T,-T) for 1%
derived reduction
in the
decrease in length and changes inflexibility
to the intramicelle
EO-EO interaction.
Figure 15. Intensity contour plots for 1% C1sEs/0.5M NaSCN/DsO at G = 9000 s-’ and (a) T=34”C and (b) T=42”C.
470
6. MIXED CATIONIC-NONIONIC
The addition
of a charged surfactant to the nonionic surfactant micelles is expected
to modify the intra headgroup should further complicate measurements
MICELLES
interaction,
have investigated
nonionic-cationic
the interacting
for other interacting cationiclnonionic
70
-
60
-
interaction
micelles
of the mixed
systems
intermicellar
in the scattering
interactions
occurs, reminiscent
[5], and distinct differences
(see
of that seen
are observed
at different
concentrations.
I
-
anisotropic
by the effect of the pronounced
Figure 16), a well defined maximum
00
of intermicellar
Penfold et al [18] in a series of recent
surfactants C,sEs and C,sTAB. The SANS from these mixed systems
is now dominated
90
and the presence
the micelle geometry.
I
I
I
I
1
I
I
I
I
I
I
+++
+
+ 4
lo-
“brn
$$k 1
I 0.01
OO
@@a0 I
I
I O-02
I
I
0.03
Momentum
transfer,
@@s@mm@QI
I O-04
0
,
I 0.05
I 0.06
( b-‘1
Figure 16. Scattering cross section (in cm-‘) in the Q parallel (0) and Q perpendicular (0) directions versus momentum transfer, Q, for 3% C&Es/ 0.3% C1sTAB/D20 at T=40”C and G=9000 s-l.
At low Ct6TAB concentrations micelles
present
in the system
shearing
the system
(-e 1% mol ratio), in the absence of shear, the long show no evidence
an interaction
of intermicellar
peak is observed.
interactions.
The position
On
of the peak is
471
consistent
with a rod length
- 4000A, which compares
favourably
with the estimate
(- 3700A) based on the coupling of an isolated rod with the shear field.
At much higher C,sTAB concentrations prevents the formation invariance
(- 20% mol ratio) the headgroup
of a long rod species.
of the interaction
dominated
At &TAB
concentrations
with shear, indicating deduced
intermediate
A strong interaction
the Cl parallel direction
dependence
EO-EO attraction.
between these two extremes the situation is
peak is observed
spacing is inconsistent
in the presence
in excess of several thousand temperature
reflecting the increased
and its position in Q is invariant
some local order in the unaligned
from the interparticle
interaction
is reflected in the
curves with shear. The axial ratio of the short
rods increases with increasing temperature,
more complex.
The small anisotropy
solution.
A mean rod length
with the absence
of intensity in
of shear, which indicates that the rod length is
angstroms.
of the anisotropy
In this intermediate
concentration
range, the
at a fixed shear shows distinct trends (see
Figure 17). lntenslty
intensity
mox~mum (in orbltroryunits)
maximum (in orbitrory
units1
4007
300 t
200
100 IL
OL 30
40
Temperature
O-O-$ 50 ( *C)
I
30
0
-
Temperature
50
I 61
(OC)
Figure 17. Intensity maximum in the Q perpendicular (0) and Q parallel (0) directions for (a) 3% C1sE6/5% mol ratio C,sTAB/DsO and G = 7000 S-l and (b) 3% r&Es/l 0% mol ratio C,sTAB/DsO and G = 1000 s-l.
472
At 5% mol ratio the anisotropy whereas
at a given shear decreases with increasing temperature,
at 10% mol ratio the anisotropy
trends are similar to those observed
grows with increasing
temperature.
for the C&E, alone, and so indicate the same EO/EO dominated even in the presence
of marked
These
for the evolution of micelle length with temperature intermicellar
interactions
structural evolution
and charged
intramicellar
interactions.
7. INTERACTIONS,
SHEAR INDUCED STRUCTURES AND VlSCOE!-ASTlC
Hoffman et al [9] have reported the observation specific micellar systems. birefringence
of shear induced structures in some
They have used neutron scattering results [9] to confirm flow
results [36] from tetradecylmethyl
ammonium
salicylate, which suggests
a shear induced phase of rodlike micelles above a threshold analysed
their anisotropic
micelle.
Small
aggregates
rodlike
PHASES
scattering micelles
value of shear. They have
patterns to reveal the existence
which are weakly
aligned,
of two types of
and very large rodlike
which are strongly aligned, and which are only present above a threshold
value of G. The two micelle species are in equilibrium
with each other and Hoffman et
al have been able to determine
to the side of the large oriented
the shift of equilibrium
micelles with shear.
In a different system, N-hexadecyloctyl et al have also observed
the formation
shear, G. Both phases are strongly short rodlike micelles contrast,
shows
indication
interacting,
however
which are only weakly aligned.
strong
of a hexagonal
concentrations
dimethyl ammonium
alignment type
bromide
[9], Hoffman
of shear induced structures about a threshold
of long
order
highly
the initial phase consists of
The shear induced interacting
in this phase.
rods;
The change
there
phase, by is some
in the relative
of the two species with shear has been determined.
Penfold et al [31] have shown some clear evidence for subtle micelle growth for C&Es at low concentrations
(see Figure IO) for a system rod dilute non-interacting
rods.
In
a range of other simple rodlike systems [7,27,28] they have seen no evidence for shear induced structures.
We have already discussed briefly, in other contexts, the contribution interactions.
They have a pronounced
of intermicellar
effect on the shape of the scattering patterns, and
473
on the shear dependence
of the anisotropy.
dilute theories for such cases. been pronounced
contributions
strong interactions,
the scattering
suppression
of the scattering
It is no longer applicable
In many of the systems investigated from intermicellar
interactions.
intensity has a well defined maximum the intensity maximum
in the QA_direction (I to the flow) when the rods are substantially the dilute theories
In most cases, for and a marked
at low Q due to the form of the structure factor S(Q). This
is not always true, and for weaker interactions the rod length deduced
to apply simple
[5,9,31] there have
from the shear dependence
are applicable,
may only appear
aligned
In such cases
of the anisotropy,
are in good agreement
simple analysis of the position of the intensity maximum
and assuming
with those derived from a
(Qmax) using
- 2nr = d = l/N” Q max where N is the micelle member
This agreement
may be fortuitous:
the intensity maximum from equation alignment
density and d is an intermicellar
is apparent
as in cases where there is a strong interaction and
even in the isotropic solution, a micelle size derived
[9] is usually not consistent with the Qll intensity for a saturation of the rod
(i.e. in general, it predicts too short a rod length) [31].
For many of the systems with stronger striking feature, in that the position
interactions
Penfold [5] for the systems SDSltetradecyl was associated assumption
with the formation
It was then assumed
(Q,,)
This was initially observed dimethyl
propane
of local small ordered
that the domains
by Hayter and
sulphonate, domains
is invariant TDPS, and
in the isotropic
aligned with increasing
shear.
This
was originally refuted by Kalus et al fl O]; however, it has now been observed
for a range of systems with strong inter-micellar be coincidental. simulations
[5,9,31] there is an even more
in Q_L of the intensity maximum
with shear and hence degree of alignment.
solution.
spacing
In fact, recent unpublished
interactions
work by Klein et al [20] has shown in
that local order in such systems is expected.
shear invariance
So far, there
in Q,,,
is due to the presence
has been
little work
structure factors for such systems,
[20,21]
f5,9,31], and is unlikely to
Indeed, we assume that this
of local order.
to caicuiate
orientational
and there have been no attempts
dependent
to confront the
414
recent theories TTMA-Sal
[21] with experimental
and CsC,,,DAB,
data.
Hoffman et al (9,lO) have, however,
on the assumption
for
that local order exists in the isotropic
solution used to zero shear scattering to extract on S(Q). From the further assumptions that this S(Q) is then isotropic and independent the form
of the
hexadecylpyridium
anisotropic salicylate
scattering
theoretical
factors
at higher
shear
values.
[lo] they have included an angular dependent
Data is now being measured structure
of shear, they have been able to predict
observed
in anisotropic
For
to g(r).
that can provide the possibility of the determination systems,
and provide
an impetus
of
to forthcoming
developments.
8. SUMMARY
The combination anisotropic
of shear flow alignment
micellar solutions
their interpretation
and SANS for the study of the structure of
has been discussed.
have been presented,
in avariety
of problems.
interacting
systems has been discussed.
Recent experimental
results and
and have been shown to provide new insights
The current progress with more complex multicomponents
and
REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.
B Cabane, R Duplessix and T Zemb in Surfactants in Solution, Vol 1 pg 373 Plenum Press (1984) J B Hayter and J Penfold, J Colt Polym Sci (1983) 261 1022 J B Hayter and J Penfold, J Chem Sot Faraday Trans 1 (1981) 77 1951 D J Cebula and R H Ottewill, Coil and Polymer Sci (1982) 260 1118 J B Hayter and J Penfold, J Phys Chem (1984) 68 4589 H Thurn, J Kalus and H Hoffman, J Chem Phys 80 (1984) 3440 P G Cummins, E Staples, J B Hayter and J Penfold, J Chem Sot Faraday Trans 1 (1987) 83 2773 E J Staples, P G Cummins, F Leng and J Penfold, Chem Phys Lett 149 (1988) 191 J Kalus, H Hoffman, S H Chen and P Lindner, J Phys Chem (1989) 93 4267 and J Kalus, H Hoffman and K Ibel, Coil & Polymer Sci 267 818 (1989) J Kalus and H Hoffman, J Chem Phys (1987) 87 714 L Herbst, H Hoffman, J Kalus, H Thurn, K lbel and R P May, Chem Phys 103 (1986) 437 and J Kalus, S H Chen, H Hoffman, G Neubauer, P Lindner and H Thurn, J Appl Cryst 21 (1988) 777 N A Clark and B J Ackerson, Phys Rev Lett (1980) 44 1005 H A Scheraga and J K Backus, J Am Chem Sot (1951) 73 5108 H A Scheraga and R Cerf, Chem Rev (1952) 51 185 A Peterlin and H Stuart in “Hand und Jahrbuck der Chemischen Physik”: Akad Verlag Becker und Erler Kom-Ges: Leipzig (1943) Band 8 ~~44-51 H G Jerrard, Chem Rev (1959) 89 345 P G Cummins, E Staples and J Penfold - unpublished results J Penfold, E Staples and P G Cummins, Proceedings of ACS Meeting, Washington (1990) J B Hayter - to be published R Klein - private communication, and J KG Dhont and R Klein, Prog in Coll & Polymer Sci 73 (1987) 90 P G Cummins, R Staples, B Millen and J Penfold, Meas Sci Technol 1 (1990) 179 P Lindner and R C Oberthur, Rev Phys Appl (1984) 19 759 Neutron beam facilities at the high flux reactor available for users (Institut Laue Langevin, Grenoble, 198 5) Neutron scattering instruments at the ISIS Facility: User Guide (Rutherford Appleton Laboratory RAL-90-041 (1990) S J Candau, E Hirsch and R Zana, Physics of complex and supra molecular fluids, eds S A Safran and N A Clark (Wiley, NY) (1987) M E Cates, J Phys 49 (1988) 1593 P G Cummins, J B Hayter, J Penfold and E Staples, Chem Phys Let-t 138 (1987) 436 P G Cummins, E Staples, J Penfold and R K Heenan, Langmuir (1989) 5 1195 S Q Wang, W M Gelbart, A Ben-Shaul, J Phys Chem 94 (1990) 2219 S A Safran, P A Pinans, M E Cates and F C MacKintosh, J Phys (1990) 51 1410 J Penfold, P G Cummins and E Staples - to be published J A Odel, A Keller and E D T Atkins, Macromolecules (1985) 18 1443 M Corti, C Miner0 and V Degiorgio (1984) J Phys Chem 88 309
476
34. L J Magid, R Triolo and J S Johnson (1984) J Phys Chem 88 5730 35. K Rendall, G J T Tiddy, M Lal and L G Baxendall, Proc 6th Int Conf on Surfactants, New Delhi, India (1986) 36. I Wunderlich, H Hoffman and H Rehage, Rheol Acta (1987) 26 532
Advances in Colloid and interface Science, 34 (1991) 451-476
Elsevier Science Publishers B.V., Amsterdam
SMALL
ANGLE
MICELLES
NEUTRON
ALIGNED
J PENFOLD+,
SCATTERING
INVESTIGATION
OF
RODLIKE
BY SHEAR FLOW
E STAPLES* and P G CUM~lNS*
+ Neutron Science Division, Rutherford * Unilever Research,
Appleton
Port Sunlight Laboratory,
Laboratory,
Chilton, Didcot, Oxon
Quarry Road East, Bebington,
Wirral
CONTENTS
Abstract.............................................................. 451 1. Intrcduction.......~....................~.............................45 2 2.lT-leoq................................................................ 454 analysis procedures...=.................45 6
3. Eqerimsnt al.details and data
4. H~~~~~~o~l~f~ion ......................................... 463 5. Nonionic micefles................................................... ..466 6. Mixed nonionic-cationicmicelles...................................... 470 7. Interactions, shear induced struc~s
and viscoslastic @ases........47 2
8. .%mnazy............................................................... 474 References.................................. ..-.......................47 5
ABSTRACT
The application of small angle neutron scattering (SANS) to the study of anisotropically shaped micelles, aligned by shear flow, is discussed. A typical shear flow apparatus and the theoretical basis of the data analysis are briefly presented. Some studies on dilute rodlike micelles are used to illustrate the analysis procedure, and to introduce complications due to hindered rotation, flexibility, polydispersity, turbulence and shear induced structures. Particular attention has been focused on the role of hindered rotation. More recent experimental results on the evolution of micelle size with temperature for nonionic surfactants, and the nature of mixed nonionic-cationic micelles, will be discussed in more detail. Recent experiments on viscoelastic and interacting micellar phases will be briefly described.
OOOl-8686/91/$09.100 1991-E1sevierSciencePublishersB.V.
452
1. INTRODUCTION
In recent years, SANS has been applied to the study of a range of dilute isotropic micellar systems [l], following the initial work of Hayter and Penfold [2,3] to include the nature of intermicellar were ambiguous
interactions.
Early studies on anisotopically
due to lack of momentum
the orientational
averaging
of the isotropic
More recently considerable
progress
shaped micelles [4]
transfer, Q, range, and insensitivity
due to
solution.
has been made in the study of anisotropically
shaped micelles by SANS, where shear flow alignment
[5,6] has been used to remove
much of the intensitivity
measurements.
The technique measurements
of the orientationally
is now well established,
and a number
of groups
have reported
on dilute rodlike micelles [7], mixed surfactant phase [8], shear induced
structures
[9], concentrated
dependent
studies [I l] have been made.
of the same techniques
(interacting)
and viscoelastic
systems
[5, lo],
and time
In a related area there has been extensive use
[12] to study shear phenomena
may be used as model macrofluids on laboratory
averaged
in colloidal suspensions,
in which non-Newtonian
time scales; but this is beyond
behaviour
which
can beobserved
the scope of this review and will not be
discussed.
In the 1950s optical flow birefringence anisotropic
micelles, colloids and polymers,
upon that pioneering
A suspended
elongated
to the local streamlines. diffusion coefficient,
[13,14] to study
and the recent neutron studies draw heavily
particle subjected to a viscous shear gradient G will precess angular velocity being a function of the orientation
Simultaneously,
Brownian motion, characterised
Dr, will tend to randomise
of these two competing
the orientations.
effects can be characterised
relative
by a rotational
The relative importance
by the parameter,
I- = G/Dr; full
and to understand
the scattering
can only occur when r as1.
In practice, pattern
developed
optical work.
in the flow, the instantaneous
alignment
was extensively
perfect alignment
from a partially
aligned
is never achieved, system
an estimate
of the orientational
distribution
p@,+;T) (where 8,+ are the normal polar angles, see Figure 1) must be made.
Hayter
453
and Penfold [5] have developed for the SANS scattered
an analytic form of this distribution
geometry
which is a refinement
function appropriate
of the original optical form of
Peterlin and Stuart [I 51 and Jerrard [16]. Hoffman et al [I I], in parallel, have in contrast developed important
a numerical
solution
of the basic Langevin
or Fokker-Plank
aspect of their work is that not only can they predict equilibrium
but they can calculate the time dependence
of the orientational
equation;
an
distributions,
distribution
function.
-z detector
7/
12
/
I
shear aradient
1
incic bea,
Figure 1. Cartesian and angular coordinates referred to the centre of a cylindrical micelle at origin. The relationship to the spectrometer geometry is shown schematically. The momentum transfer, Q, lies in the X-Z plane.
From a range of dilute rod-like dilute
phases
behave
However, in particular A range of phenomena
micelles studies, the general impression
remarkably
like rigid monodisperse
circumstances
rods
under
is that the shear
effects due to subtle flexibility are observed
due to intermicellar
interactions
have been observed
[5,9,19]
and evidence for shear induced structures in some systems have been reported
Effects due to polydispersity,
turbulence
in particular the effect of hindered
[7]. [17]. [9].
and hindered rotation will be discussed, and
rotation will be considered
in more detail.
454
Finally, the main emphasis micelle
size
with
monoheadecylether, (cetyltrimethyl
on recent experimental
temperature
for
the
results will be on the evolution
nonionic
C&Es, and the nature of mixed
ammonium
bromide,
&TAB)
of
surfactant
hexaethyleneglycol
nonionic
(C,aEs) and cationic
micelles.
2. THEORY
The scattering anisotropic
from
monodisperse
dilute (non-interacting)
isotropic
solution
of
micelles is given by
I(Q) = < (F(Q)l*>o
where F(Q) is the form factor for a micelle at a given orientation transfer Q and < > o denotes
For uniform cylinders
relative to the momentum
an average over all such orientations.
of length 21 and diameter
2a :
F(Q) = (FQ,~) = 2~s Vjs (01 cosy) J1 (QasiwMQasW
(2)
where y is the angle between Q and the cylinder axis, V is the volume, p0 the scattering amplitude
relative to that of the solvent, J,(x) is the first order Bessel function of the first
kind, and j,(x)
= sinx/x.
coated cylinders
Evaluation
is straightforward
The intensity function
of F(Q) for other models
averaging.
expression,
[I 91.
Further, for interacting micelles it is difficult to write an equivalent
since the correlation
of orientation
If all the micelles have the same orientation,
where S,(Q) interactions calculation
and
in (1) is not very sensitive to the micelle model due to the
orientational
l(Q) = F*(Q)
such as ellipsoids
with position is generally
not calculable.
then
S,(Q)
is the structure factor for a fluid of aligned micelles.
(S,(Q)
= 1 .O) the scattered
In the absence of
intensity displays the micelle geometry.
The
of structure factors for rodlike systems is now receiving much attention [20].
455
A convenient
method for aligning dilute rodlike micelles is shear flow, and we have
already seen that the degree of alignment the competing
is associated
effects of G and Dr (characterised
with the relative importance
by the parameter
of
T = G/Dr), and
where for dilute rods with I > a Dr is given as [5] :
Dr = 3kaT (s -t) / (87~~~1~) (s > 2) where s = log(2l/a),
Predominantly
scattered
t = 1.57 - 7 (0.28 - I/s)~ and n is the solvent viscosity.
couette flow [21,22] has been used to provide the shear alignment,
and the scattering be achieved,
(4)
geometry
is shown in Figure 1. In general perfect alignment
and an orientation
distribution
must be employed
will not
such that the resultant
intensity will be given by
where cos y+
= sir@cos$cos+
f
cos&in$
We will refer to the Qll and QJ_ directions
For the CL direction + dependence
projected
that used in the original dependence
probability
depends
only on 6, with the
out. This highlights the difference between this geometry optical
Hayter and Penfold [5] to improve
p(H.f$:l-) =
constant.
when $ = 0 and v/2 respectively.
(Jr=n/2) the scattering
on Q (the extinction
have developed
and A is an experimental
studies
[13-161 where 0 is integrated
angle) is measured.
This sensitivity to 6 has allowed
upon previous estimated
an analytic form of p(&+,T)
and
out and the
[I 51 of p(6,+,T), and they
where
(1 - cos2$0)(1 + sin28cos2$0)3/2 4n[ 1 - sin2 8 cm 2& cos 2(@- $o)12
and 241) = arctan(S/T)
(6)
456
In contrast,
Hoffman et al (11) have developed
Fokker-Plank
numerical
solutions to the Langevin or
equation
where f is the orientation
distribution
function,
o(O) = i/4 p sin 2+sin26
(6a)
o(+) = -i/2
(6b)
(1 - p cos2+)sin6
p = [L2 - (2a)2]/[L2 + (2a)2]
(6~)
and L = 21.
This has been particularly evolution
important
of the rod distribution
3. EXPERIMENTAL
DETAILS AND DATA ANALYSIS PROCEDURES
The data presented angle scattering
for their “stop flow” studies [l 11where the time
function has been studied.
in this review have been predominantly
diffractometers
[23], and on the LOQ [24] spectrometer
Various shear cell geometries, plates
cylinders,
detail elsewhere Couette
cylinders
[21,22],
disc [6], have been used to produce
either
for in the case of rotating
if d c
a constant gradient across the gap is achieved, the characteristic
Grenoble
0.d’.
which include rotating concentric
[5], or a rotating
Poiseuille or Couette flow. Couette flow is more preferable, concentric
on the small
on the ISIS pulsed neutron source, in various
different Cl ranges between the extreme values of 0.002 and
flow between
measured
Dl 1 and D17 at the lnstitut Laue Langevin,
parabolic
form.
[21,22] and therefore
cell designed
by Cummins
Couette shear cell is constructed rotor which is stationary,
whereas Poiseuille flow will always have
A number of these devices have been described
in
we will briefly present the main features of the
et al [21] specifically
for surfactant
studies.
The
of quartz, with an outer rotor which rotates and an inner
see Figure 2.
457
Figure 2. Schematical
This geometry
view of shear cell constructed
inhibits the production
by Cummins
et al.
of Taylor vortices and establishes a constant shear
gradient across the gap. An important feature is the rotating seal which presents solvent loss, sample rejection and foaming.
The shear gradient is related to the rotation speed
and gap width, and for the 0.5 mm gap in the cell gives a maximum
shear gradient of
2.5 x IO4 s-l (G = 5.28N, where N is the rotor speed in rpm).
Figure 3 shows the intensity contours for scattering from 0.03M &TAB
in 0.4M KBr
at shear gradient of 5000 s-l (Figure 3a) and at a shear gradient of 7500 s“ (Figure 3b); shown in Figures 3c and 3d is the calculated for a rigid monodisperse
contours
(using equations
rod of length 21 = 2700A and diameter 2a =
MA. These
are typical of the range of dilute rodlike micelles that have been studied. patterns,
such as those
dimensions.
in Figure
3, contain
detailed
2, 4, 5 and 6)
information
about
However, it is difficult in practice to extract accurate quantitative
from such plots.
curves
The scattering
In order to make a simple and more precise quantitative
the rod
information analysis of
such data, it is convenient directions,
Qfl and CL
earlier) in a consistent
to consider
By comparing
the intensity the absolutely
scattered
in the two orthogonal
scaled data with theory [5] (see
way for a range of G, it is possible to extract a rod diameter
and a length 21 [5,7]. Figure 4 shows a typical fit for 0.04M dodecyldimethyl chloride
2a
ammonium
(DDACI) in 4.OM NaCl at a shear gradient of 7000 s-l (the data are consistent
with a rod length of 2500A and a diameter of #A).
At higher Q values the sensitivity of
the data to rod length results from the shear dependence
of the anisotropy,
low Q and high G the Q(I data are most sensitive to the rod length. determined
principally
by the form of short dimension
whereas at
The QL intensity is
of the rod.
Figure 3. (a) Experimental intensity contours for scattering for 0.03M C1sTAB/0.4M KBr/D20 at 313K and G = 5000 s-l, (b) as (a) except at G = 7500 s“, (c), (d) theoretical intensity contours for (a)(b) with 21 = 27OOA and 2a = 47A.
In Figure 3 is was shown that there was excellent intensity
contours
situation,
and in Figure 5 we show an example
observed.
for 0.03M C,sTAB/O.4M
agreement
KBr with theory. where deviation
in the shape of the
This is not afways the from theory is clearly
For the 0.04M DDACI in 4M NaCl (Figure 5a) there is now more intensity in
the off-symmetry
directions.
This redistribution
of intensity has been attributed
to the
459
presence
of subtle rod flexibility
[7], and in Figure 5b is shown a calculated
contour which attempts to take the flexibility into account.
theory, Cummins et al [7] have simulated the effects of the redistribution to rod flexibility by assuming of angles
about
that the micellar orientations
are distributed
of the equivalent
over a cone The
simulated intensity contour for DDACI (Figure 5b), which is now in good agreement
with
data, is calculated
direction
of intensity due rigid rod.
the observed
the mean orientational
intensity
In the absence of a rigorous
for a cone angle of 20’.
There has been much recent
interest on the flexible nature of rodlike micelles [25]. Much of the recent light scattering experimental theories
data on such systems have been interpreted
of “living polymers”
using the recently developed
[26], based on the well established
highly flexible chains. The general observation
polymer
theories for
from the neutron scattering studies is that
under shear the range of systems studied do not show any marked degree of flexibility.
I(O)
(in
orbitrory
units)
Figure 4. Measured scattered intensities taken along the QI (0) and GII (0) directions for 0.04M DDACV4M NaCI/DsO at T= 298Kfor G = 7000 s-l: the solid lines are calculated curves for 21= 2500A and 2a = MA.
460
(b)
Figure 5. (a) measured intensity contours for 0.04M DDAW4M NaCI/D,O at T= 298K and G =7000 s-l, (b) calculated intensity contours for 21=2500A, 2a = 44A and for flexible rods with a core angle of 20”.
It is possible that the imposition Flexibility has been observed DDACI, C&Es at temperatures C,sTAB/CxEy observations, surfactant
[18].
of a shear gradient
alters the flexibility of the rods.
in some systems under shear, and these are notably the approaching
The main factors
principally the headgroup
the cloud point [27,28], and mixtures
affecting
rod flexibility
environment
chain length (this will be discussed
of polydispersity;
by theory.
are then, from these
and of secondary
importance
the
later in the context of C,sEs micelles).
At higher G ( > 1O4s-l) there is a region where the anisotropy at a slower rate than suggested
of
of the data increases
Such an effect can be interpreted
that is, the reduced anisotropy
in terms
results from the weaker orientational
coupling of the shorter rods. However, there is additionally
the possibility
of turbulence
461
being a contributing randomising turbulence
factor; turbulent
will start at G - lo4 s-l).
enough additional
randomisation
(this has been observed
By introducing distribution pattern
diffusion.
(For viscosities
At sufficiently high G, turbulence
that the degree of anisotropy
a further
of ca 10m2Pas will contribute
should start to decrease
in some extreme cases).
a polydispersity,
of rod lengths,
is significantly
differences
flow will have the effect of contributing
term in addition to the rotational
altered
in orientational
based
on an arbitrarily
chosen
it can be clearly shown [7] that the anisotropic for a substantial
probability
polydispersity,
reflecting
log-normal scattering the large
for different lengths (see Figure 6).
Figure 6. Theoretical intensity contour at G = ~OOOAfor 21= 2500A and 2a = MA, with a polydispersity of u = 0.5.
However, the absence of any well defined minimum QI
intensity
polydispersity
plots for most of the dilute systems is present.
These two observations
systems investigated
the polydispersity
from a polydisperse
system
from the QI form factor in the
studied
clearly indicate that some
suggest that for the majority of dilute
has a variance, u, c 0.2. The analysis of data
using a monodisperse
model
will produce
systematic
462
deviations,
which can be rationalised
Figure 7). Recent theoretical substantially
by introducing
treatments
[29] suggest that the application
alter the micelle size distribution;
experimental
observations
-0
an effective shear gradient
these predictions
(see
of shear can
are not consistent with
over the range of dilute rodlike micelles [7,28] studied.
2
4
6
8
10
12
14
16
18
20
x103
Appliedsheor(s-‘1
Figure 7. Effective shear gradient polydispersities: (a) monodisperse,
as a function of true shear gradient (b) u = 0.2 and (c) u = 0.3.
There has been much discussion breaking [5,7,27,28]
[26,30].
The overriding
tobacco mosaicvirus,
deformation
of micellar
and will be discussed evidence
have observed
rods, and
with that from well defined rodlike systems such as
for limited and modest growth with increasing
later in the context of hindered rotation. for such processes
has been reported
for the specific systems hexadecyl
and tetra decyltrimethyl
shear induced
and
systems
TMV [7]. However, recent data on r&Es has a low concentrations
have shown some evidence
(C&,DAB)
growth,
for a wide range
is that under shear the micelles behave like rigid monodisperse
that the data is mostly consistent
convincing
about shear induced evidence
for a range of
structures
(see later).
ammonium Cummins
The strongest
shear [31], and most
by Hoffman et al [9], who
octyl dimethyl ammonium salicylate (ITMA-sal)
bromide
the formation
et al [7] have investigated
of
a range of
463
micellar systems with quite different critical micellar concentrations micelle lifetimes and monomer-micelle
exchange
important,
counteracted
then they must be furtitously
rates.
(cmcs), and hence
If break-up
processes
are
by collision and self assembly
processes.
The discussion
to date has focused
However,
a number
interacting
systems,
of interesting
predominantly
observations
on non-interacting
[5,11,18)
and these will be discussed
systems.
have now been made
in
in more detail in a later section.
4. HINDERED ROTATIONAL DIFFUSION
Many of the dilute rodlike micelles investigated higher degrees of anisotropy
than expected
low Q implies an increase in the “effective”
Effective rod length
by Cummins et al [7] at low G show
theoretically.
The enhanced
anisotropy
at
rod length (see Figure 8).
fin i)
6ooo I 5000 0 4000 \\ “o<--.N
3000
o*Izl
; a-*
1000
-6.0
0
-======a
-
0
I
0
t
I
I
I
10
2 $4heorgrodie~t
(x1O381I
Figure 8. Effective rod length as a function of shear gradient for (a) (0) 0.03M CTAB/0.4M KBr/D20, (b) (*) 0.04M DDACl14M NaCI/DsO and (c) (+) TMV/DaO.
464
Although
in terms of interactions
the entangled
or concentrated
density and L is the rod length. will hinder rotational
region, i.e. C > 1/L3, where C is the micelle number However,
as alignment
is induced
it is predicted
have a concentration is truly dilute.
in the system, the
until at high degrees of alignment the dilute rotational diffusion
will be recovered.
With the exception
of DDACI (see Figure 8), and some
systems of very short rods (21 < 1500A) [7], this phenomena Therefore,
are dilute, they are in
In such regimes in the isotropic solution, entanglements
diffusion.
hindering will be reduced, coefficient
all the systems investigated
is generally
that for a given micellar system this hindered
dependence,
and should disappear
This trend has been shown for sodium
observed.
rotation should
when the rod concentration dodecyl
sulphate,
SDS (see
Figure 9).
Effectwe
1000
rod length
(ini)
I
t-
I 8
I 6
I 4
I 2
0
I 10
Sheargradient,G(xlO3eC-‘)
Figure 9. Effective rod length as a function of shear gradient for SDS/l .3M NaCI/DsO for (0) O.lM, (+) O.O7M, (A) 0.05M and (x) 0.025M.
However, length.
there is in addition
a significant
A more clearer confirmation
C,sEs where the concentration and at the lowest concentration
concentration
dependence
is shown in Figure 10 for the nonionic
dependence
on the rod surfactant
of the rod length is much less pronounced,
(0.001 M) there is clearly no hindered
rotation.
At this
465
lowest concentration
of C&Es there is some evidence
However, it is a small effect and may also be attributed
6000
5000
+\ I
3000
micellar
‘+
\
+~p-----.
o-o-
I 20
I
0
I
I
l+ o----------o
I
4-o 5hmr
prodmf
I 60
I
I 80
, G (x 1O’rc“)
Figure IO. Effective rod length as a function of shear gradient O.O2M, (+) 0.002M and (0) O.OOlM.
for C1sEs/D20 for (0)
The DDACI data remains an exception to a well defined pattern of hindered The system,
growth.
in flexibility.
.
\
4000
of modest to changes
however,
showed
the most marked
flexibility,
rotation.
and it may be that the
conditions for hindering are more complex than the overlap condition,
and are inherently
linked with the flexibility of the rods.
From the data presented rotation and rigidity correlate
in Figures 8 and 10, there is further evidence that hindered in the series
TMV z C,sEs z CTAB > DDACI and that monomer C&Es i
exchange
rates follow the same pattern
CTAB < DDACI.
Hence monomer
exchange
and flexibility may indicate the same behaviour.
466 In the presence
of hindered
rotation, the orientational
under shear will no longer be exactly described we assume possible
that the form of the resulting
to extract the shear dependence
Figure I I), and the form of dependence et al [32].
Hoffman
diffusional
coefficient
experiment,
and coworkers from
probability
distribution
of the rotational
of individual
evolution
is similar, then it is
diffusion coefficient
diffusion
in a “stop
coefficient
cetylpyridinium
salicylate
of the flow”
Dr(t) (with a
relaxed time - 300 ms) which they attributed to the influence of inter-particle between the charged
(see
by Odel
the time dependence
of the anisotropy
a time dependent
rods
[5]. However, if
is similar to that reported for polymers [I I] have followed
the time
and have extracted
probability
by the dilute theories
interactions
(CPS) micelles.
1000 -
600
n
600
n
n
n I
400
n
200
m
0
I 2
I 4
I Sheo~grodicn?,
Figure 11. Shear gradient dependence CTAEV0.4M KBr/DsO at T= 313K.
5. NONIONIC
I
I 6(reCl’?
I 12
of the rotational
I 14
diffusion coefficient for 0.03M
MICELLES
Many studies [33,34], using a range of techniques,
have addressed
the integrity of the micelle unit as the cloud point is approached. systems
5 XW’
whose micelles
the question of
The consensus,
have low axial ratios, is that the micellar weight variation
for is
10
-I-
+
3
468
insignificant.
As the cloud point is approached
In the Q range investigated for such aggregation. perturbation
micelle associated
is expected
to occur.
(0.06-0.1 A-‘) there is no evidence in the scattering patterns
This implies that aggregation
to the orientation
processes are only causing a minor
process, and that the rod lengths in Figure 12 reflect the
true micelle geometry.
In micellar systems, the micelle geometry the surfactant area per headgroup. sut-factant micelles, modifications
can be rationalised
In the presence of electrolyte, to EO/EO interactions
area per molecule and hence the micelle geometry. thiocyanate, effectively
increased
consistent
with the ethylene
or decreased.
“Salting
of
can occur which will modify the
The addition of “salting in” (sodium
NaSCN) and “salting out” (NaCI) electrolyte
of the phase diagram
by considerations
for the C,E, nonionic
have an effect on all regions
oxide
in” electrolyte
(EO) chain length is of particular
being interest
because it allowed the evolution of micellar size to be followed over a wider temperature range [28], as a result of the cloud point being raised (0.5M NaSCN increases the cloud point of 1% C,sEs in DsO from 38 to 51 “C).
Throughout
that temperature
SANS from the shear aligned system was shown to be consistent
range, the
with long rigid rods
(see Figure 13).
10 0 0
0.005
0 020
0.010
Momentum
transfer,
0.030
0.040
0 (ii-‘1
Figure 13. Scattered intensity I(Q) (in arbitrary units) versus momentum transfer Q for 1% C1sEe/D20 at 31 “C at G = 5000 s-l; (*) Q perpendicular and (0) Q parallel. The solid lines are calculated curves for 21= 3400A and 2a = 6OA.
469
With increasing and
temperature
eventually
temperature
decreased
(towards the cloud curve), the rod length initially increase (see Figure
of 12°C. This evolution
14), reaching
a maximum
in rod length is accompanied
at a reduced
by an increase in the
rod flexibility (see Figure 15)
1
Figure 14. Effective rod length as a function of reduced C1,Es/D20/0.5M NaSCN at G = 5000 s-l. The increase in rod length is attributed area per molecule, are associated
whereas the subsequent
with modifications
temperature
to the dehydration
(T,-T) for 1%
derived reduction
in the
decrease in length and changes inflexibility
to the intramicelle
EO-EO interaction.
Figure 15. Intensity contour plots for 1% C1sEs/0.5M NaSCN/DsO at G = 9000 s-’ and (a) T=34”C and (b) T=42”C.
470
6. MIXED CATIONIC-NONIONIC
The addition
of a charged surfactant to the nonionic surfactant micelles is expected
to modify the intra headgroup should further complicate measurements
MICELLES
interaction,
have investigated
nonionic-cationic
the interacting
for other interacting cationiclnonionic
70
-
60
-
interaction
micelles
of the mixed
systems
intermicellar
in the scattering
interactions
occurs, reminiscent
[5], and distinct differences
(see
of that seen
are observed
at different
concentrations.
I
-
anisotropic
by the effect of the pronounced
Figure 16), a well defined maximum
00
of intermicellar
Penfold et al [18] in a series of recent
surfactants C,sEs and C,sTAB. The SANS from these mixed systems
is now dominated
90
and the presence
the micelle geometry.
I
I
I
I
1
I
I
I
I
I
I
+++
+
+ 4
lo-
“brn
$$k 1
I 0.01
OO
@@a0 I
I
I O-02
I
I
0.03
Momentum
transfer,
@@s@mm@QI
I O-04
0
,
I 0.05
I 0.06
( b-‘1
Figure 16. Scattering cross section (in cm-‘) in the Q parallel (0) and Q perpendicular (0) directions versus momentum transfer, Q, for 3% C&Es/ 0.3% C1sTAB/D20 at T=40”C and G=9000 s-l.
At low Ct6TAB concentrations micelles
present
in the system
shearing
the system
(-e 1% mol ratio), in the absence of shear, the long show no evidence
an interaction
of intermicellar
peak is observed.
interactions.
The position
On
of the peak is
471
consistent
with a rod length
- 4000A, which compares
favourably
with the estimate
(- 3700A) based on the coupling of an isolated rod with the shear field.
At much higher C,sTAB concentrations prevents the formation invariance
(- 20% mol ratio) the headgroup
of a long rod species.
of the interaction
dominated
At &TAB
concentrations
with shear, indicating deduced
intermediate
A strong interaction
the Cl parallel direction
dependence
EO-EO attraction.
between these two extremes the situation is
peak is observed
spacing is inconsistent
in the presence
in excess of several thousand temperature
reflecting the increased
and its position in Q is invariant
some local order in the unaligned
from the interparticle
interaction
is reflected in the
curves with shear. The axial ratio of the short
rods increases with increasing temperature,
more complex.
The small anisotropy
solution.
A mean rod length
with the absence
of intensity in
of shear, which indicates that the rod length is
angstroms.
of the anisotropy
In this intermediate
concentration
range, the
at a fixed shear shows distinct trends (see
Figure 17). lntenslty
intensity
mox~mum (in orbltroryunits)
maximum (in orbitrory
units1
4007
300 t
200
100 IL
OL 30
40
Temperature
O-O-$ 50 ( *C)
I
30
0
-
Temperature
50
I 61
(OC)
Figure 17. Intensity maximum in the Q perpendicular (0) and Q parallel (0) directions for (a) 3% C1sE6/5% mol ratio C,sTAB/DsO and G = 7000 S-l and (b) 3% r&Es/l 0% mol ratio C,sTAB/DsO and G = 1000 s-l.
472
At 5% mol ratio the anisotropy whereas
at a given shear decreases with increasing temperature,
at 10% mol ratio the anisotropy
trends are similar to those observed
grows with increasing
temperature.
for the C&E, alone, and so indicate the same EO/EO dominated even in the presence
of marked
These
for the evolution of micelle length with temperature intermicellar
interactions
structural evolution
and charged
intramicellar
interactions.
7. INTERACTIONS,
SHEAR INDUCED STRUCTURES AND VlSCOE!-ASTlC
Hoffman et al [9] have reported the observation specific micellar systems. birefringence
of shear induced structures in some
They have used neutron scattering results [9] to confirm flow
results [36] from tetradecylmethyl
ammonium
salicylate, which suggests
a shear induced phase of rodlike micelles above a threshold analysed
their anisotropic
micelle.
Small
aggregates
rodlike
PHASES
scattering micelles
value of shear. They have
patterns to reveal the existence
which are weakly
aligned,
of two types of
and very large rodlike
which are strongly aligned, and which are only present above a threshold
value of G. The two micelle species are in equilibrium
with each other and Hoffman et
al have been able to determine
to the side of the large oriented
the shift of equilibrium
micelles with shear.
In a different system, N-hexadecyloctyl et al have also observed
the formation
shear, G. Both phases are strongly short rodlike micelles contrast,
shows
indication
interacting,
however
which are only weakly aligned.
strong
of a hexagonal
concentrations
dimethyl ammonium
alignment type
bromide
[9], Hoffman
of shear induced structures about a threshold
of long
order
highly
the initial phase consists of
The shear induced interacting
in this phase.
rods;
The change
there
phase, by is some
in the relative
of the two species with shear has been determined.
Penfold et al [31] have shown some clear evidence for subtle micelle growth for C&Es at low concentrations
(see Figure IO) for a system rod dilute non-interacting
rods.
In
a range of other simple rodlike systems [7,27,28] they have seen no evidence for shear induced structures.
We have already discussed briefly, in other contexts, the contribution interactions.
They have a pronounced
of intermicellar
effect on the shape of the scattering patterns, and
473
on the shear dependence
of the anisotropy.
dilute theories for such cases. been pronounced
contributions
strong interactions,
the scattering
suppression
of the scattering
It is no longer applicable
In many of the systems investigated from intermicellar
interactions.
intensity has a well defined maximum the intensity maximum
in the QA_direction (I to the flow) when the rods are substantially the dilute theories
In most cases, for and a marked
at low Q due to the form of the structure factor S(Q). This
is not always true, and for weaker interactions the rod length deduced
to apply simple
[5,9,31] there have
from the shear dependence
are applicable,
may only appear
aligned
In such cases
of the anisotropy,
are in good agreement
simple analysis of the position of the intensity maximum
and assuming
with those derived from a
(Qmax) using
- 2nr = d = l/N” Q max where N is the micelle member
This agreement
may be fortuitous:
the intensity maximum from equation alignment
density and d is an intermicellar
is apparent
as in cases where there is a strong interaction and
even in the isotropic solution, a micelle size derived
[9] is usually not consistent with the Qll intensity for a saturation of the rod
(i.e. in general, it predicts too short a rod length) [31].
For many of the systems with stronger striking feature, in that the position
interactions
Penfold [5] for the systems SDSltetradecyl was associated assumption
with the formation
It was then assumed
(Q,,)
This was initially observed dimethyl
propane
of local small ordered
that the domains
by Hayter and
sulphonate, domains
is invariant TDPS, and
in the isotropic
aligned with increasing
shear.
This
was originally refuted by Kalus et al fl O]; however, it has now been observed
for a range of systems with strong inter-micellar be coincidental. simulations
[5,9,31] there is an even more
in Q_L of the intensity maximum
with shear and hence degree of alignment.
solution.
spacing
In fact, recent unpublished
interactions
work by Klein et al [20] has shown in
that local order in such systems is expected.
shear invariance
So far, there
in Q,,,
is due to the presence
has been
little work
structure factors for such systems,
[20,21]
f5,9,31], and is unlikely to
Indeed, we assume that this
of local order.
to caicuiate
orientational
and there have been no attempts
dependent
to confront the
414
recent theories TTMA-Sal
[21] with experimental
and CsC,,,DAB,
data.
Hoffman et al (9,lO) have, however,
on the assumption
for
that local order exists in the isotropic
solution used to zero shear scattering to extract on S(Q). From the further assumptions that this S(Q) is then isotropic and independent the form
of the
hexadecylpyridium
anisotropic salicylate
scattering
theoretical
factors
at higher
shear
values.
[lo] they have included an angular dependent
Data is now being measured structure
of shear, they have been able to predict
observed
in anisotropic
For
to g(r).
that can provide the possibility of the determination systems,
and provide
an impetus
of
to forthcoming
developments.
8. SUMMARY
The combination anisotropic
of shear flow alignment
micellar solutions
their interpretation
and SANS for the study of the structure of
has been discussed.
have been presented,
in avariety
of problems.
interacting
systems has been discussed.
Recent experimental
results and
and have been shown to provide new insights
The current progress with more complex multicomponents
and
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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
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