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Structure of giant micelles: a small angle neutron scattering study
J. Appell, J. Marignan
To cite this version:
J. Appell, J. Marignan. Structure of giant micelles: a small angle neutron scattering study. Journal de Physique II, EDP Sciences, 1991, 1 (12), pp.1447-1454. �10.1051/jp2:1991161�. �jpa-00247602�
Classification Physics Abstracts
61.30 64.70 82.70
Structure of giant micelles : a small angle neutron scattering study
J. Appell and J. Marignan
Groupe de Dynamique des Phases Condenskes (associated to the C.N.R.S. UA 233), Universitk des Sciences et Techniques du Languedoc, 34095 Montpellier Cedex 5, France
(Received lst July 1991, accepted18 September 1991)
Abstract. The local structure of elongated micelles of cetylpyridinium chlorate in brine is determined using small angle neutron scattering (scattering vectors range from 2 x10~~ to
5 x10~' A-~). They are found to be long flexible cylinders. The radius of the circular cross section is 20 ± A and the persistence length characterizing the flexibility is 170 ± 50 A. Both
are
found to be independent of the nature or of the conientration of the counterion.
1, Introduction,
In dilute solutions of water or brine, surfactant molecules associate reversibly forming aggregates of different morphologies and thus a variety of phases. Among these, isotropic
solutions of micelles have been largely studied; at low concentrations the micelles are
generally globular [I] but they have been found to grow in certain systems when increasing the surfactant concentration and/or the salt content (ionic surfactant) [2-6] or the temperature (non-ionic surfactant) [7, 8]. This is traced back to the specificity of the surfactant and to the
modification of the balance of intermolecular forces which modifies the preferred local structure [9]. When this unidimensional growth is highly favored the micelles become very
long rod-like aggregates which, on a length scale larger than the persistence length (system dependent), are flexible. The properties of such micellar solutions have been found to parallel those of flexible polymers up to a certain point [10-12]. But the dynamical and rheological properties of these solutions are found to differ from those of classical polymer solutions : the reversible association of the surfactant molecules introduces major differences a_large size distribution and possibly other mechanisms for the relaxation of stresses, Cates and Candau [13] have reviewed the recent experimental and theoretical results on these «wornllike
surfactant micelles ».
This prompted us recently to reinvestigate, using light scattering, the cetylpyridinium
chlorate (CPCIO~) in concentrated (sodium chlorate) brine. We found evidence that the
micelles grew to such an extent that at all concentrations above the critical micellar concentration the solutions had structural properties analoguous to that of polymers in the
1448 JOURNAL DE PHYSIQUE II bt 12
semi dilute range [12]. In these studies we have assumed that the CPCI03 micelles have the
same local structure and the same flexibility than the cetylpyridinium bromide micelles we had previously studied [14]. The aim of the present study is to verify this assumption.
Furthertnore the fact that the CPCIO~ micelles are very long and form a transient network of
entangled micelles at low concentration I.e. with a large correlation length favors, as we shall
see below, the manifestation of the flexibility in the scattering pattem. In order to reach our
goal we undertook a small angle neutron scattering study on the largest possible q-range (from 2x10~~ to 4x10~~l~~). The scattering pattems are then analyzed using the
procedures developed for the structural studies of colloidal or micellar aggregates [15-18].
The results obtained confirnl that on the local scale the micelles are identical regardless of the nature of the counterion or the concentration of the added electrolyte : they are cylindrical with a circular or almost circular cross section and the micellar thread is higl~ly flexible.
2. Experimental procedures.
2.I SAMPLE PREPARATION. Cetylpyridinium chlorate (CPCiO~) is obtained by recristalli-
zation from a solution of cetyl pyridinium cl~loride (CPCI) in a concentrated sodium cl~lorate brine and then purified according to standard procedures as described in [12]. Deuterated brine is prepared by dissolution of sodium cl~lorate in D~O (99.8 §b D). The samples are prepared by weight.
2.2 SMALL ANGLE NEUTRON SCATTERING : DATA iCQUISITION AND TREATMENT. The
small angle neutron scattering experiments are performed at the cameras Dl I and D16 of the Institut Laue Langevin in Grenoble. The samples are contained in quartz cells (Hellma) with
a path of 2 mm. Experiments are performed at T
=
35 °C (the Krafit temperature for this system is = 32 °C). Intensities relative to the incoherent scattering of H~O in a cell with a path of I mm are obtained from the measured intensities after substraction of the solvent and empty cell contributions. The data are then put on an absolute scale following the standard
procedures [19, 20].
At Dll, experiments are performed with low spatial resolution. The wave length
= 10 h
and the scattering vectors (q) range from 2 x 10~ l~ to 1.5
x 10~~ l~ ~. These data
were
completed on the low q -side by light scattering measurement (3x10~~A~~ to 3x
10~~ l~
~) described previously [12]. We showed there, that already at 0.25 §b CPCIO~ (the concentration used here) the solutions are in the semi dilute regime (I.e. a transient network of entangled micelles) with a correlation length (f
= 1150 ± 501
see below).
At D16, the experiments are performed with high spatial resolution ; the wavelength 4.52h and the scattering vectors range from 7 x 10~~ h~' to 5 x10~~ h~' The sample=
contains lo §b CPCIO~.
The interpretation of our results is made assuming that the local structure of the elongated
micelles does not depend on the concentration of surfactant and that only their overall length will increase with increasing concentration. This assumption is consistent with our previous study on solutions of giant micelles where we showed the striking analogy between these solutions and those of polymer solutions in the semi dilute regime [12]. Furthernlore the agreement found between the values for the radius of the locally cylindrical micelle deduced, within this assumption, from experiment on high aid low concentration micellar solutions is in favor of this assumption.
3. Results and dhcussion.
The overall scattering pattern is displayed in figure I. It is worth noting that the intensity
spans more than 6 orders of magnitude in the investigated q-range and that the scattering
~s
~
~s
£
MW I
Ia4
la~
q(1"~)
Fig. I. Log/Log display of the scattering pattern. The lowest q-range (up to 3 x 10~~A~') is from
a
light scattering measurement and the intermediate q-range is from SANS both on a sample 0.25 fb
CPCI03 in lM NaCl03 brine. The highest q-range (from 7 x 10~~ to 4
x 10~ A~
~) is from SANS on a
sample lo fb CPCI03 in lM NaCl03 brine [21].
patterns from light scattering, and from the two SANS experiments overlap perfectly (within
a scaling factor) [2 Ii. The oscillation due to the local fortn factor of the micelles is noticeable
even in this representation. We will examine in turn the different q-regions of this scattering pattern which will allow for the determination of the dimensions characterizing the flexible
rod-like micelles.
From this pattern we have computed the Porod invariant of the micellar solution (0.0025 g/g CPCIO~ in IMNaCIO~ brine). We assume here that the q~~ dependence of
I(q) observed in the highest investigated q-range is valid up to infinite q :
Q
= l~ q~I(q) dq = [2.I ± o-I x 10~°cm~~ (I)
o
This compares reasonably with the computed scattering power Q
=
2.55 x10~°cm~~
assuming one contrast factor : the contrast between the hydrogen atoms of the paraffinic core
of the micelles (with an assumed density p
=
0.85 g/cm~) and the deuterium atoms of the brine [18].
3. I THE CORRELATION LENGTH. In a previous study [14] we showed that even at these low
concentrations the solutions had structural properties analoguous to that of a polymer
solution in the semi dilute range: the solutions contains very long micelles which are
entangled. The relevant length measured in the very lowest q-range is then the correlation
length f. In this range the intensity varies as :
1(q)
= 1(0)
~
(2) 1+ (qf
and fis derived from the plot shown in figure 2 : f = 150 ± 50 h. This correlation length is irrelevant for the local structure of the elongated micelles but its value is however important.
In particular, as we will see later, it puts a lower limit to the q-range where the observation of the flexible micellar coil is possible.
1450 JOURNAL DE PHYSIQUE II bt 12
o
3 4 5
q ~(10 "~l"2)
Fig. 2. In the lowest q-range the scattering pattern reflects the finite correlation length a measure of the micellar entanglement. This is best displayed in the plot I/I(q) versus q~ which is linear for the
lowest q-values according to (2).
3.2 THE LOCAL STRUCTURE OF THE ELONGATED MICELLES.
3.2.I The large q range
= the Porod region. From the measured Porod limit:
lim q~I (q
= [5.5 ± 0.5 x 10~~ cm~ ~ we can deduce a first value for the radius of the micelle
q - o
assuming it is locally cylindrical with a circular cross section. We use the well known
relationship for the ratio of surface (S~ to volume (V) :
(
=
~
=
"
rim q41(q)
r Q
~ _ ~
and the above value for Q and we obtain an estimate of r : r~ = 23 ± 41.
At the highest scattering vectors oscillations are superimposed on the q~~ decrease characteristic of a sharp interface. This is already perceptible in figure I as mentioned above.
These oscillations correspond to the form factor of the scattering aggregates they are best
displayed on a q~I(q) versus q plot as shown in figure 3. We tried to match these oscillations to those corresponding to the form factors of different local structures and only succeded with the form factor for a locally cylindrical aggregate. The best computed curve is shown in
figure 3 it is obtained assuming a circular cross section (f
=
20 ± 0.51) and
a very narrow
Gaussian distribution of radii ( (r f)~
= 2 1) in order to account for the damping of the
oscillations. In fact the position of the two first oscillations is very sensitive to the choice of f but not to the width of the Gaussian distribution. But the damping of the oscillation is not well accounted for by introducing solely a distribution of radii and no better agreement was obtained by assuming only a slight ellipticity of the cross section most probably both factors
play a role but it is impossible to ascertain their respective weight here.
3.2.2 The intermediate q-range. In this rangg we sense the rod-like structure of the
scattering micelles. More precisely for a random distribution of rods with a finite cross section
we expect qI (q) to vary as [16, 17] :
q I (q)
= 7rcM~(b~ v~ po)~ exp
~~~~~
(3)
2
~
g
#
"
w
#
~+#
#
q(10 "~i "~)
Fig. 3. Form factor oscillations in the Porod region the dots are experimental results on the sample with lo fb CPCI03 in lM NaCl03 brine, the solid line is the best curve obtained assuming a distribution of circular cross sections for the elongated micelles f
=
20 ± 0.5 A and (f r)~
=
2A.
(b~-v~po) is the contrast between the particle and the solvent in (cm/g), c the
concentration in g/cm3 and M~ the mass par unit length of the scattering rods (= the
paraffinic core).
Relation (3) is expected to hold in the range qr~ < I and qi~ ml with r~ the radius of
gyration of the cross section of the rod and i~ the persistence length (the length below which the linear object can be considered as straight). In figure I it can be seen that the intensity
varies as q~~ in the range 1.5 x 10~~ l~~
< q < I.I x 10~~ l~~.
In this range the plot of Ln(qI(q)) versus q~ is shown in figure 4 it is linear in perfect
agreement with our assumption of a locally rod-like micelle. We obtain r~ =
15.51 and M~
= 9.6 x10~~~g/cm from which we derive the radius of gyration r~
=
/r~
= 22±
41 and
a geometrical radius r~ =
[3M~/4p]l~/31= 21±41 (with
p the density of the
paraffinic core).
q~(10"~i'~)
Fig. 4. Ln (qI (q) as a function of q~ in the intermediate q-range for the sample 0.25 fb CPCIO~ in lM NaCl03 brine. The plot is linear between qr~ =
0.2 to 1.7, r~
= 15.5 ± 2A is deduced from (3).
1452 JOURNAL DE PHYSIQUE II bt 12
The local §tructure of the micellar aggregates as reflected in the high and intermediate q range is indeed foi~nd to be that of a rod with a circular cross section. If we compare the values
obtained for the radius of the cross section we find an excellent agreement within
experimental errors. The most precise determination is that obtained from the oscillations reflecting the form factor so that we adopt the value r
= 20 ± 11
as the best experimental
value. It is identical to the value measured previously for the CPBr elongated micelles [14]
and to the values determined in the intermediate q-range for a solution with 0.0025 g/g CPCIO~ in 4M NaCIO~ brine. We can thus state that the nature of the counterion and the concentration of added electrolyte have no detectable influence on the radius of the paraffinic
core of the micelle as seems indeed reasonable.
3.3 THE FLEXIBILITY oF THE ELONGATED MICELLES. At still smaller q's the flexibility of the micelles, if any, must show up in the scattering pattern. If the micelles were very long rigid cylinders the scattered intensity would behave as q~ (cf. relation (3)) until the leveling out
reflecting the finite correlation length f. A careful inspection of figure I shows that between the q~~ behavior and the leveling out there is a region where the intensity falls off more
rapidly with q. This appears in a clearer fashion in figure 5 where we have plotted
qI(q)exp[(qr~)~/2] versus q. In this representation the curve is expected (cf. (3)) to be horizontal in the q-range where rigid rods are « seen and at smaller q's it is expected to fall
rapidly to 0 indicating the finite value of f. In figure 4 we note, when q decreases, a sharp
increase of the curve from the horizontal line starting at an onset value qr= I.I x
10~~ l~~. If
we assume the micelles to be flexible then, below this value of q, one probes
«free» parts of the micellar threads undergoing a random walk: q is such that
qf~< I and (3) is no longer valid but q must still be greater than f~~ and this restricts considerably the range where this random walk can be observed. The scattered intensity is
expected to decrease as q~ ~ with v =
2 for a Gaussian coil and v
= 1.66 for a coil in a good
solvent undergoing a self avoiding random walk [22, 23]. In figure 6 the Log/Log plot of
intensity versus q illustrate this point : the intensity tends to follow the law expected for a coil
M
~~
Cfi
~f
qf 4
q(10'~l~~)
Fig. 5.-Plot of qI(q)lexp[- (qr~)~/2] versus q to show olT the flexibility of the micelles.
qr marks the crossover between the pattem due to an infinite rigid thread (horizontal line) and the pattern due to a flexible thread undergoing a self avoiding random walk (= a rapid rise in this
representation). Crosses: 0.25fb CPCI03 in lMNaCl03 brine and circles: 0.25fb CPCIO~ in 4M NaCl03 brine.
.2.5 qf -1.5 Log q( l'~)]
Fig. 6. Log/Log disfilay in the low q-range region showing off the trend (see text) to a power law behavior of the scattered intensity with q characteristic of the self avoiding random walk of the micellar thread. The straight line correspond to the theoretical law with a slope
=
-1.66.
in a good solvent which is represented there by the straight line. It is worth noting that the
,region of q, where « free parts of the micelle are probed, is larger here than for CPBr micelles [14] where the rise in a plot similar to that of figure 5 was much smaller the
interpretation was, there, somewhat far fetched but is well confirmed by the present results.
As already mentioned above we have measured the scattering pattem of the solution 0.0025 CPCIO~ in a 4M NaCIO~ brine and found no influence of the salt concentration on the local structure of the micelles. To test its possible influence on the flexibility of the micelles. The
curves for the solutions in 4M or lM brine are displayed in figure 5. One can remark that the
curve for the solution in 4M brine rises steeper than that for the solution in lM brine although
qr is identical. It is probably related to the proximity of the phase separation existing in these
highly salted solutions [10] in H~O brine the phase separation occurs around 55 °C and is not
perceptible at 35 °C but in deuterated brine we found it to take place around 40 °C so that modifications associated to this phase separation can already play a role at 35 °C. This will be discussed in details in a forthcoming paper.
The important point is that the onset value qr is identical for both solutions. A value identical within experimental errors has also been found for CPBr micelles [14]. This onset value is related to the persistence length characteristic of the micellar flexibility:
i~ =
1.9/qr [24]. The value obtained for i~ =
170 ± 50 l~ is in reasonable agreement with
our previous estimates [4, 5].
The micelles of CPCIO~ are indeed found to be cylindrical and highly flexible and their local structure is identical to that of CPBr micelles and essentially insensitive to the
concentration of added electrolyte.
Acknowledglnents.
We gratefully acknowledge the assistance of E. Pebay-Peroula (ILL Grenoble) and R. May (ILL Grenoble) for their help and advices for the neutron experiments. We thank
P.Bassereau for her collaboration in the neutron experiments and G. Porte for many
stimulating discussions.
