Progr Colloid Polym Sci (2004) 129: 9–15
DOI 10.1007/b100297
 Springer-Verlag 2004

Tadashi Kato
Koji Minewaki
Kyoko Miyazaki
Youhei Kawabata
Toshiyuki Shikata
Shigeyuki Komura
Masatoshi Fujii

T. Kato (&) Æ K. Minewaki Æ K. Miyazaki
Y. Kawabata Æ S. Komura Æ M. Fujii
Department of Chemistry,
Tokyo Metropolitan University, Hachioji,
Tokyo 192-0397, Japane-mail: kato-tadashi@c.metro-u.ac.jp
T. Shikata
Department of Macromolecular Science,
Osaka University, Toyonaka,
Osaka 560-0043, Japan

Effects of shear flow on structuresof lamellar phase in a nonionicsurfactant /water system

Abstract Eﬀects of shear ﬂow on the
structure of a lamellar phase in
C16E7 (hepta(oxyethylene glycol)-nhexadecylether)/water system (40–55 wt% of C16E7) at 70 C are
studied by using small-angle neutron
scattering (SANS), small-angle lightscattering (SALS), and shear stressshear rate relationships. The repeat
distance takes a deep minimum(referred to as d*) at the shear rate
0.1–1 s)1. As the concentration of
C16E7 decreases, the repeat distanceat rest increases whereas d* remains
almost constant and nearly equal to
the thickness of bilayers obtained
from the line shape analysis of small
angle X-ray scattering at rest. These
results suggest that the water layer isIntroduction
Structures of surfactant self-assemblies are often aﬀectedby shear ﬂow because their characteristic relaxation time
_ >1(s) is usually long enough to satisfy the condition cs
for the typical shear rate c_ ¼ 102  103 s1 [1]. In thepast 10 years, eﬀects of shear ﬂow on the structure of thesurfactant lamellar phase have been studied extensively
by using microscopy, NMR, and various kinds ofscattering techniques. After the pioneering work of Rouxand coworkers [2–5] who found the transformation fromthe lamellar phase to the multilamellar vesicles (onions),
various types of shear eﬀects have been reported: change
in orientation of membranes [6–8], sponge-to-lamellartransformation [9, 10], multilamellar-to-unilamellar vesicle transformation [11–13], reduction in the spacing[14–19], collapse of membranes [20], formation ofmultilamellar cylinders as intermediate structures

excluded by shear ﬂow and that thelamellar phase segregates into
surfactant-rich and water-richregions. Although macroscopic
phase separation does not occur,
SALS intensity takes a maximum atthe shear rate giving d*, which isconsistent with the SANS results.
Mechanism for the decrease in therepeat distance is discussed in relation to the change in the size of thelamellar domains.

Keywords Shear ﬂow Æ Lamellar
phase Æ Nonionic surfactant Æ Small
angle scattering Æ SANS Æ SALS

between lamellar and onions [21–24], and formation of
Ribbon phase [25]. These eﬀects have been found for the
shear rate of 15 · 103 s)1. In our previous studies, on
the other hand, attention has been paid to the behaviors
at relatively low shear rates, 10)350 s)1. At these shear
rates, we have measured small-angle neutron scattering(SANS) on the lamellar phase of a nonionic surfactant
C16H33(OC2H4)7OH (C16E7)/D2O system [15–17, 26].
This system was chosen because phase behaviors andstructures of the micellar and lamellar phases had beenstudied extensively by us [27–30]. We have found that therepeat distance (d) decreases signiﬁcantly (down to about
40% of the initial d value in the extreme case) anddiscontinuously by shear ﬂow [26]. In the present study,
to conﬁrm these ﬁndings, we have measured small angle
light scattering (SALS) and the shear stress as a functionof shear rate, in addition to further analyses of the SANS
data.

10

Experimental
Materials
C16E7 was purchased from Nikko Chemicals, Inc. in crystalline
form (>98%) and used without further puriﬁcation. Deuterium
oxide purchased from ISOTEC, Inc. (99.9%) was used after being
degassed by bubbling of nitrogen to avoid oxidation of theethylene oxide group of surfactants. Samples containing thedesired amount of surfactant and water (10 g) were sealed in an
Erlenmeyer ﬂask. For homogenization, we annealed samples for
3 h at about 55 C with occasional shaking and then held them atroom temperature for 21 h. This treatment was repeated forabout one week.
All the measurements were made at 70 C because the existence
region of the lamellar phase extends to the lower concentration
above about 67 C [27].

Shear SANS
Measurements of SANS were carried out at the instrument SANSU of Institute for Solid State Physics of University of Tokyo in
Tokai with a Couette-type shear cell. The cell consists of two
concentric cylinders, an inner aluminum stator and an outer quartz
rotor. The stator diameter and the gap are 48 and 1 mm,
respectively. Details of the cell have been reported before [31].
The diameter of the neutron beam is 5 mm and the scatteredneutrons are detected by a two dimensional position-sensitive
detector having 65 · 65 cm2 (128 · 128 pixels) area. The sampleto-detector distance is 1 m for all runs. Thus the momentum
transfer is 0.3<q<2.5 nm)1 (q=(4p/k) sinh, where 2h is thescattering angle and k=0.7 nm is the neutron wavelength).
Two scattering conﬁgurations were used; one is the so-calledradial conﬁguration where the beam is directed through the centerof the cell (along the velocity gradient direction), and the other is thetangential conﬁguration where the beam is directed through the endof the cell (along the ﬂow direction). The two-dimensional (2-D)
SANS pattern in the ﬂow-vorticity plane is obtained in the radialconﬁguration, while that in the velocity gradient-vorticity plane is
obtained in the tangential conﬁguration. For the lamellar structure,
there are three principal orientations, perpendicular, transverse,
and parallel orientations, with the layer normal along the vorticity,
ﬂow, and velocity gradient directions, respectively. Therefore, theperpendicular and transverse orientations can be detected by using
the radial conﬁguration whereas the perpendicular and parallelorientations can be detected by using tangential conﬁguration. Itshould be noted that in the tangential conﬁguration the intensity forthe vorticity direction is much lower than that for the velocity
gradient direction even for an isotropic sample due to the path
diﬀerences of the scattered neutron beam. So only the radialconﬁguration is used for detecting the perpendicular orientation.
After we transferred the sample into the outer rotor, we put inthe stator as slowly as possible at the temperature where isotropic
phases exist, that is, 45 C for the 48 wt % sample (bicontinuous
cubic (V1) phase) and 50 C for the 40 wt% sample (micellar (L1)phase). Then the sample was heated to 70 C and held for about
20 min before the ﬁrst collection of SANS data at rest. At eachshear rate, SANS data were collected every 10 min ﬁrst for either
the radial or the tangential conﬁguration for 1–3 h to detect thechange in the structure as a function of time. After that, thescattering conﬁguration was changed from the radial (tangential) to
the tangential (radial) conﬁguration and data collection was madein the last 20 min for each shear rate. Although a vapor seal isincorporated in our cell, it is diﬃcult to keep the concentration of
the sample over 8–9 h at 70 C. Hence, two independent runs werenecessary to cover the desired range of the shear rate.

Fig. 1 Schematic representation of the shear SALS apparatus

Shear stress and shear SALS
A Rheometer (Nihon Rheology Kiki, NRM-2000) was modiﬁed
for SALS measurements under shear ﬂow. Figure 1 shows
schematic representation of the apparatus. The light source is a
He-Ne laser (NEC GLG5360, 5 mW at 632.8 nm). The sample cellis the same as that for SANS measurements except for that bothstator and rotor are made of quartz. The temperature of the cell is
controlled to ±0.1 C by Peltier elements and a heater in an air
bath. The intensity of scattered light is detected by a CCD camera
system (Hamamatsu Photonics C4880-80-22A). Details of theapparatus will be reported elsewhere [32]. In the present study,measurements have been performed in unpolarized conﬁguration;neither polarizer nor analyzer has been inserted in the optical path.
For the 55 wt% sample, shear stress has been measured with acone-and-plate rheometer (Rheometrics, ARES). Cone angle andradius are 25 mm and 0.04 rad, respectively.

Results and discussion
Decrease in repeat distance
Figure 2 shows evolution of 1-D (one dimensional)
SANS patterns in the velocity gradient direction of thetangential conﬁguration (corresponding to the parallelorientation) obtained by integrating the scattering intensity over a segment of width D/=±10 (/: azimuthal
angle) with increasing shear rate (at 48 wt%). These data
were collected 1–3 h after the changing shear rate (see theexperimental section) and so in almost stationary states
except for the patterns (C) and (D) which were obtained
10 and 20 min after the changing the shear rate from 0.3
to 1 s)1, respectively.
In Fig. 3, the repeat distance (d) obtained from theﬁrst reﬂection at 48 wt% is plotted against the shear rate.
In the range 0–0.1 s)1, the repeat distance depends on theshear rate only slightly. When the shear rate increases
from 0.3 to 1 s)1, the repeat distance decreases suddenly
to 5.2 nm. With the further increase in the shear rate, dincreases again through a minimum (referred to as d*,hereafter). Figure 3 demonstrates that the shear ratedependence of d is almost the same for all the principal
orientations of lamellae.
It can be seen from Fig. 2 that two separated peaks
are observed 10 min after the changing shear rate from
0.3 to 1 s)1 (C). After 20 min, the peak at the lower angle
disappears whereas the peak at the higher angle increases(D). The position of this peak remains unchanged even11

Fig. 3 Shear rate dependence of the repeat distance for the vorticity(open circles), transverse (open squares), and parallel (open triangles)orientations [26]. The diﬀerent symbol sizes correspond to diﬀerent
runs (see the experimental section). Inserted images are 2-D SALS
patterns for the shear rate 0.3, 1, and 3 s)1 from left to rightExclusion of water layers

Fig. 2a,b Evolution of 1-D SANS patterns with increasing shear ratein the velocity gradient direction of the tangential conﬁguration(corresponding to the parallel orientation) at 48 wt% obtained byintegrating scattering intensity over a segment of width D/=±10
where / is the azimuthal angle [26]. The scattering intensities are
represented in: a normal; b log scales. The patterns A, B, E, and F are
obtained in the stationary state for the shear rate 0, 0.3, 1, and 3 s)1,
respectively. The patterns C and D are obtained 10 and 20 min after
the changing shear rate from 0.3 to 1 s)1, respectively

after 1 h, although the peak height decreases (E). These
results indicate that the decrease in the repeat distance at
1 s)1occurs discontinuously, suggesting some sort oftransition. Similar shear rate dependence of the repeat
distance has been observed for other concentrations
except for the diﬀerence in the speciﬁc shear rate (c_  )giving d*. At 40 and 55 wt%, c_  is 0.1–0.3 s)1 which isslightly lower than that at 48 wt%. At present, however,
it is diﬃcult to discuss the concentration dependence ofc_  because it depends on shear history [16].
Figure 4 shows concentration dependence of therepeat distance at rest (d0) and d* (see the open symbols).
As the concentration of C16E7 decreases from 55 to
40 wt%, d0 increases from 6.5 nm to 8.5 nm whereas d* isalmost independent of concentration. At 40 wt%, therepeat distance decreases from 8.5 nm to 5.2–5.6 nm andso the amount of the reduction is fairly large compared toother two concentrations.

In a dilute lamellar phase formed by nonionic surfactant,the repulsive interactions between membranes are dominated by undulation ﬂuctuations of membranes [33, 34].
In this case, the volume fraction of membrane (/s) can be
expressed in terms of the repeat distance d as
d¼

2dAs
/s A ?

ð1Þ

where d is the half-thickness of membranes, As is the total
membrane area, and A^ is the membrane area projectedon the plane orthogonal to the mean membrane normal.
It has been shown from theoretical arguments that theshear ﬂow suppresses undulation ﬂuctuations of bilayers[35–39]. This leads to a reduction in the ratio As/A^ andtherefore in the repeat distance. In fact, the reduction of dby shear ﬂow has been found experimentally [14, 18, 19].
In these studies, however, the ratio (d0–d)/d0 (d0 and d are
the repeat distance at rest and under shear, respectively)
is only a few %. In the present study, on the other hand,(d0–d*)/d0 is about 40, 30, and 25% at 40, 48, and55 wt%, respectively. Such a large amount of reductionin the repeat distance has not been reported so far.
When the repeat distance decreases without a changeof /s, Eq. (1) gives an expression of (d0–d)/d0 in terms ofthe membrane area asd0  dAs =A?
¼1
d0
As0 =A?

ð2Þ

12

Fig. 4 Concentration dependence of the repeat distance at rest (opensymbols, upper) and the minimum value under shear d* (open symbols,
lower), d*, for the vorticity (open circles), transverse (open squares),and parallel (open triangles) orientations [26]. The crosses and closed
triangles indicate the repeat distance and the total thickness of thebilayers, respectively, obtained from small-angle X-ray scattering at
rest [27]Fig. 5a,b Shear rate dependences of: a the peak height; b the line
width of the ﬁrst reﬂection for the vorticity (open circles), transverse(open squares), and parallel (open triangles) orientations. The diﬀerent
symbol sizes correspond to diﬀerent runs. In part (a), the left ordinate
indicates the peak height for the vorticity and transverse orientations
whereas the right ordinate for the parallel orientation. The units ofthese axes are arbitrary. The intensity for the parallel orientation
cannot be compared with those for the vorticity and the transverse
orientations

where As and As0 are the total membrane areas undershear and at rest, respectively. Because the relation
1<As/A^<As0/A^ holds, (d0–d)/d0 cannot exceed (1–A^/
As0) even if As/A^=1. In our previous study [27], we havestudied the structure of the lamellar phase at rest formedin the same system (C16E7–D2O) using small-angle X-ray
scattering (SAXS). It has been found that d is inversely
proportional to /s above 70 C, which indicates that A^/
As0 is close to unity. This, together with the foregoing
relation (d0–d)/d0<(1–A^/As0), indicates that (d0–d)/d0
should be much smaller than unity. Thus, (d0–d*)/d0
cannot be as large as in the present study without thechange in the concentration.
In our previous study [27], we have also obtained thehalf-thickness of the hydrophobic layer dhc and thethickness of the hydrophilic layer deo from the line shapeanalysis of SAXS. Figure 4 includes the total membranethickness at rest (closed triangles) obtained from thesedata (2d=2dhc+2deo) together with d0 (closed circles).
Interestingly, d* is nearly equal to 2d. It should be notedthat the thickness may decrease slightly by shear ﬂow[17]. Nevertheless, this result strongly suggests that thewater layer in the lamellar phase is excluded by shear
ﬂow, leading to segregation into water-rich and surfactant-rich regions. During the shear SANS measurements,
however, we could not observe any turbidity of thesample to the naked eye. So we may infer that the
segregated regions do not reach macroscopic size.
Figure 3 also includes 2-D SALS patterns at diﬀerent
shear rates at 48 wt%. The light scattering intensity
increases substantially as the shear rate increases from
0.3 to 1 s)1. As the shear rate increases further, thescattering intensity decreases but still larger than that at
0.3 s)1. When the surfactant-rich and water-rich regions
coexist, the diﬀerence in the concentration between theseregions should increase with the decrease in the repeat
distance in the lamellar (surfactant-rich) region. Because
the light scattering intensity is proportional to themagnitude of concentration ﬂuctuations, the light13

scattering intensity is expected to take a maximum atc_ ¼ c_  . Thus, the SALS results are consistent with the
SANS results.
Bruinsma and Rabin [36] predicted that such a shearinduced segregation occurs above a critical shear rate
given byðkB T ÞkB T¼
gj3=2 d 3
gðj=kB T Þ3=2 d 3

ðq  q0 Þ2

ð4Þ
2r2
where q0 is the location of the ﬁrst diﬀraction peak. If theresolution function and the scattering function are also
Gaussian, r can be expressed as r2=rr2+rs2 where rr
and rs are the widths of the resolution function and thescattering function, respectively. Figure 5b shows shear
rate dependence of rs obtained from r and rr where rr is
calculated from the following equation [40]: 2 2 2 2 
2pdb
2p DD q20 Dk 2
2
þ
þ
ð5Þ
rr ¼
k 16L2
k 6L2 6 kIðqÞ / exp½

5=2

c_ c ﬃ

As can be seen from Fig. 2, the reduction of the peakheight accompanies broadening of the line width. So wehave obtained the line width from the least-square ﬁttingof the 1-D SANS pattern for the parallel orientation toGaussian distribution function given by

ð3Þ

where kB is the Boltzmann constant, T the absolutetemperature, g the viscosity of solvent, j the bending
constant of a surfactant layer, and d the interlayer
spacing. For g10)2 poise=10)3 Pa s, d  10 nm, andj  kBT, c_ c is calculated to be 4 · 106 s)1 which is morethan six orders of magnitude higher than c_  in the present
study. A ﬁt to the observed c_  (1 s)1) requires
replacement of d by 1 lm or replacement of g by
104 poise=103 Pa s. Ramaswamy [37] has also shownthat the lamellar phase loses its stability and segregates
above the critical shear rate given by the similar equationas Eq. (3). It should be noted that these theories assume
direct suppression of undulation ﬂuctuations of membranes by shear ﬂow. In this case, the reduction of dshould be observed only in the limited orientation. In thepresent study, however, the shear rate dependences of d
are almost the same for all the principal directions as canbe seen from Fig. 3.
Shear ﬂow and lamellar domains
As described in the previous section, the present resultscannot be explained by the existing theories. To ﬁnd someclue as to how the shear ﬂow aﬀects the repeat distance,
we compare the shear rate dependence of the repeat
distance with other properties. Figure 5a shows the shear
rate dependence of the peak heights for the three principal
orientations obtained from the 1-D SANS pattern. Notethat the peak heights for the vorticity and the transverse
orientations are obtained from the radial conﬁguration
whereas the peak height for the parallel orientation is
obtained from the tangential conﬁguration. So the peakheight for the parallel orientation cannot be comparedwith those for the perpendicular and transverse orientations. Figures 3 and 5a demonstrate that the peak heightdecreases signiﬁcantly as the shear rate increases up to
0.1 s)1 where the jumping of the repeat distance does not
yet occur. It has been known that the shear ﬂow aﬀects theorientation of lamellae [6–8]. If there is alignment, there
should be an increase in the peak height in one direction(corresponding to that particular lamellar orientation) on
the cost of the two others. In our experiments, however,
the reduction of the peak height is observed for all theprincipal orientations, which cannot be explained by
the change in the orientation of lamellae alone.

where k and db are the wave length and the diameter ofthe neutron beam, L is the sample-to-detector length, DD
is the full width at half-maximum of the spatial
resolution of the detector, and Dk is the width of thewave-length distribution. It can be seen from Fig. 5b thatthe line width rs increases with increasing shear rate up to
0.3 or 1 s)1 and, then, decreases. It has been known thatbroadening of the diﬀraction line is observed when thegrain size (or domain size for the liquid crystal phase)decreases less than the critical value [41]. So the results in
Fig. 5b may suggest that the lamellar domains aresubstantially shrunk by shear ﬂow for the shear rate of10)2 to 1 s)1.
When we discuss the undulation ﬂuctuations ofmembranes in the lamellar phase, it is tacitly assumed
that the size of the lamellar domains (Ld) is muchlarger than the so-called ‘‘patch’’ or ‘‘collision’’ length(Lp) which dominates the repeat distance [42]. If thelamellar domains shrink so greatly as the condition
Ld>>Lp no longer holds, however, the mean amplitude of undulation ﬂuctuations decreases signiﬁcantly
and so the lamellar spacing cannot be maintained. Thiscan explain why the reduction of d occurs for the shear
rate as low as 0.1 to 1 s)1; the time scale of the
ﬂuctuation of the lamellar domain is expected to bemuch slower than of the undulation ﬂuctuations ofmembranes. It should be noted, however, that rs is
aﬀected by not only the domain size but also theﬂuctuations of the repeat distance due to the undulation mode and/or the peristatic mode [43]. So we needanalyses of the whole scattering curve taking into
account these ﬂuctuations as well as the domain size.
Finally, shear stress-shear rate relationships are shownin Fig. 6. For the 55 wt% sample, the shear stress slightly
decreases with increasing shear rate between 2 · 10)2 and
5 · 10)1 s)1. At 48 wt%, such behaviors may be seen in
the shear rate range less than 2 · 10)2 s)1. Note that these14stress are necessary. Work along this line is in progress andwill be reported elsewhere.

Conclusions
The present results may be summarized as follows:

Fig. 6 Shear stress-shear rate relationships at 48 wt% (closed circles)
and 55 wt% (open circles) obtained within 10 min after changing
shear rate and that for the stationary state at 48 wt% (triangles)

results have been obtained within 10 min after changing
the shear rate. The shear stress for the stationary state at
48 wt% show only monotonous increase (see the triangles). The result for the 55 wt% sample reminds us thetheoretical prediction by Olmsted [44, 45] for phaseseparation at common stress or common strain rate (shearrate) for the shear thinning transition. However, such
shear thinning behaviors can also be explained by theshrink of the lamellar domain. For further quantitative
discussion, more systematic measurements of the shear

1. As the shear rate increases, the repeat distance (d)decreases discontinuously (down to 40% of d atrest in the extreme case) at 0.1 · 1 s)1 and takes aminimum.
2. The shear rate dependences of d are almost the samefor the three principal orientations of lamellae.
3. The minimum value of d (d*) is almost independent of
the concentration and nearly equal to the total
thickness of bilayers at rest obtained from SAXS.
4. These results 1–3 suggest the shear-induced segregation into surfactant-rich and water-rich regions.
5. Although macroscopic phase separation does notoccur, SALS intensity takes a maximum around theshear rate giving d*, which is consistent with the
SANS results.
6. The forgoing results cannot be explained by theexisting theories. The shear rate dependences of thepeak height and line width of the ﬁrst reﬂection
suggest that the shrink of the lamellar domain iscorrelated with the decrease in the repeat distance.
Acknowledgment This research was partially supported by Ministry of Education, Science, Sports and Culture, Grant-in-Aid for
Scientiﬁc Research (B), 11440207, 1999, and 15340140, 2003.

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