Determination of critical micelle concentration by hyper-Rayleigh scattering

Article abstract of DOI:10.1021/ja029070r

The critical micelle concentration (CMC) of several surfactants that contain an NLO chromophore, either at the hydrocarbon tail, or at the hydrophilic headgroup, or even as a counterion, was determined by hyper-Rayleigh scattering (HRS). In all cases, the HRS signal exhibited a similar variation with surfactant concentration, wherein the CMC is inferred from a rather unprecedented drop in the signal intensity. This drop is attributed to the formation of small pre-micellar aggregates, whose concentrations become negligible above CMC. In addition, a probe molecule, which upon protonation yielded a species with significantly enhanced HRS intensity, was developed and its utility for the determination of the CMC of simple fatty acids was demonstrated.

Full text of DOI:10.1021/ja029070r

Published on Web 01/18/2003
Determination of Critical Micelle Concentration by
Hyper-Rayleigh Scattering
Suhrit Ghosh, Anu Krishnan, Puspendu K. Das, and S. Ramakrishnan*
Contribution from the Department of Inorganic and Physical Chemistry,
Indian Institute of Science, Bangalore 560012, India
Received October 24, 2002 ; E-mail: raman@ipc.iisc.ernet.in
Abstract: The critical micelle concentration (CMC) of several surfactants that contain an NLO chromophore,
either at the hydrocarbon tail, or at the hydrophilic headgroup, or even as a counterion, was determined by
hyper-Rayleigh scattering (HRS). In all cases, the HRS signal exhibited a similar variation with surfactant
concentration, wherein the CMC is inferred from a rather unprecedented drop in the signal intensity. This
drop is attributed to the formation of small pre-micellar aggregates, whose concentrations become negligible
above CMC. In addition, a probe molecule, which upon protonation yielded a species with significantly
enhanced HRS intensity, was developed and its utility for the determination of the CMC of simple fatty
acids was demonstrated.
value.4 On the other hand, linking them to the periphery of a
dendrimer was shown to cause an effective lowering of â.5 In
Introduction
Critical micelle concentration (CMC) of surfactants is readily
determined by a variety of simple techniques, wherein an
appropriate property such as osmotic pressure, ionic conduc-
tance, scattered light intensity etc., is monitored as a function
of concentration. A break in the plot of the chosen property
versus concentration often signifies the formation of micellar
aggregates.1 Most of these measurements rely on the change in
the property due to the formation of large aggregates of the
amphiphile molecules (typically, about 50-100 molecules)
above CMC. Any further addition of amphiphiles to the solution,
it is expected, will not alter the concentration of free surfactants
in solution but will only lead to an increase in the number of
such micellar aggregates. Because the aggregates and free
species contribute to different extents toward the measured
property, an abrupt change of slope occurs at the CMC. Both
the size and the shape of these surfactant aggregates are known
to depend on a variety of factors such as the surfactant and salt
concentrations, temperature, etc. However, only a few methods,
such as dynamic light scattering and SAXS, have been utilized
directly to probe such size and shape changes.
the former case, there is a cumulative addition of the individual
chromophoric dipoles leading to a large net dipole along the
helical axis, which in turn results in a large coherent second
harmonic response. Although in the latter, it is due to the near
spherical symmetry attained by the higher generation dendrimers
causing just the opposite effect on the â value. More recently,
significant enhancement in â has been realized in dendritic
wedges in which the NLO chromophores are incorporated
between the branching junctions.6 Other examples in which the
spatial fixation of the relative orientation of the chromophores
has been exploited to modulate the net â value, include those
in which the chromophores are linked to a calixarene skeleton7
or other rigid molecular frameworks.8 The formation of su-
pramolecular H-bonded assemblies in solution has also been
studied using HRS.9
HRS is forbidden in a centrosymmetric structure, and for a
perfect spherically symmetric arrangement of NLO chro-
mophores, it is expected, that â would be zero in the electric
dipole approximation. However, any deviation from the perfectly
spherical arrangement of molecular dipoles would lead to second
(4) Kauranen, M.; Verbiest, T.; Boutton, C.; Teerenstra, M. N.; Clays, K.;
Scouten, A. J.; Nolte, R. J. M.; Persoons, A. Science. 1995, 270, 966.
(5) Put, E. J. H.; Clays, K.; Persoons, A.; Biemans, H. A. M.; Luijkx, C. P.
M.; Meijer, E. W. Chem. Phys. Lett. 1996, 260, 136.
Hyper-Rayleigh scattering2 (HRS) has been shown to be an
effective tool to examine spatially correlated NLO chro-
mophores, which can lead to either a reduction or enhancement
of their hyperpolarizability, â.3 Rigidly tethering the NLO
chromophores onto a helical polymer backbone, such that the
chromophores make a fixed angle (*90°) with respect to the
helical axis has been shown to dramatically enhance the â
(6) Yokoyama, S.; Nakahma, T.; Otomo, A.; Mashiko, S. J. Am. Chem. Soc.
2000, 122, 3174.
(7) Kelderman, E.; Derhaeg, L.; Heesink, G. J. T.; Verboom, W.; Engbersen,
J. F. J.; Hulst, N. F. V.; Persoons, A.; Reinhoudt, D. N. Angew. Chem.,
Int. Ed. Engl. 1992, 31, 1075. Kenis, P. J. A.; Noordman, O. F. J.;
Houbrechts, S.; Hummel, G. J. V.; Harkema, S.; Veggel, F. C. J. M. V.;
Clays, K.; Engbersen, J. F. J.; Persoons, A.; Hulst, N. F. V.; Reinhoudt, D.
N. J. Am. Chem. Soc. 1998, 120, 7875.
(8) Deussen, H. J.; Hendrickx, E.; Boutton, C.; Krog, D.; Clays, K.; Bechgaard,
K.; Persoons, A.; Bjornholm, T. J. Am. Chem. Soc. 1996, 118, 6841.
Hendrickx, E.; Boutton, C.; Clays, K.; Persoons, A.; Van Es, S.; Biemans,
T.; Meijer, B. Chem. Phys. Lett. 1997, 270, 241. Mukhopadhyay, P.;
Bharadwaj, P. K.; Savita, G.; Krishnan, A.; Das, P. K Chem. Commun.
2000, 1815.
(1) Evans, D. F.; Wennerstrom, H. The Colloidal Domain, 2nd ed.; Wiley-
VCH: New York, 1999.
(2) Clays, K.; Persoons, A. Phys. ReV. Lett., 1991, 66, 2980. Clays, K.;
Persoons, A. ReV. Sci. Instrum. 1992, 63, 3285.
(3) Clays, K.; Hendrickx, E.; Verbiest, T.; Persoons, A. AdV. Mater. 1998, 10,
643.
(9) Ray, P. C.; Das, P. K. Chem. Phys. Lett. 1997, 281, 243.
9
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J. AM. CHEM. SOC. 2003, 125, 1602-1606
10.1021/ja029070r CCC: $25.00 © 2003 American Chemical Society

Determination of CMC by HRS
A R T I C L E S
Scheme 1
harmonic scattering. Thus, detection of second harmonic scat-
tered light could serve as a sensitive probe of structural
organization. The application of this technique to micelle
formation can add valuable insight into the structural properties
of micelles. With this hypothesis, we decided to examine
whether the formation of micellar aggregates is detectable by
HRS in solution. Several surfactants that incorporate a NLO
chromophore were designed, synthesized and their aggregation
properties studied by HRS.
of a molecule the external reference method12 is used. In this
method, the second harmonic signal from the sample and from
a known reference compound (for example, para-nitroaniline)
in the same solvent is monitored, and I2ω is plotted versus
concentration, which under normal circumstances yield straight
lines. From the known â of the reference compound, the â value
of the unknown is determined from the ratio of the slopes of
the two straight lines. In other words, a steeper straight line for
the unknown compared to that of the reference implies a higher
value of â of the former. In the I2ω vs concentration plot,
therefore, the slope of the line is a qualitative measure of the
first hyperpolarizability of the solute.
Results
The structures of different surfactants examined in this study
are shown in Scheme 1.
In the present study, we directly monitor I2ω as a function of
concentration - the slopes prior to and after micellization would
reflect the â values of the free surfactants and that when
incorporated in micellar aggregates, respectively. A plot of I2ω
versus concentration of surfactant A is shown in Figure 1a. It
is apparent that the variation of the HRS intensity does not
follow the simple linear variation one might expect for nonas-
sociating chromophores. The CMC of A was determined
independently from ionic conductance measurements and was
found to be 5.8 mM, which is close to the concentration at which
one sees a sudden drop in the HRS intensity. It is possible that
the micellization of surfactant A, which causes a clustering of
the chromophores in the hydrophobic core of the micelle, could
lead to a variation of the local dielectric thereby leading to some
variation in the HRS signal. To preclude such effects, a second
surfactant B, in which the chromophores, upon micellization,
would be located at the hydrophilic periphery of the micellar
aggregate, was examined.
From Figure 1b, it is clear that the variation in the HRS
intensity of B occurs in much the same way as seen in the case
of surfactant A.13 The CMC values of the different surfactants
determined by ionic conductance measurements are compared
with those determined by HRS in Table 1. It is clear that the
first break in the curvesthe point where the HRS intensity
begins to fall, occurs at the CMC. Interestingly, in both cases,
the fall in the HRS intensity at CMC is followed by an increase
at some higher concentration.
Compound A, is an anionic amphiphile in which the p-nitro-
phenoxy-chromophore (a Donor-Acceptor NLO chromophore)
is incorporated at the end of the hydrocarbon tail, while in B
the NLO chromophore forms a part of the hydrophilic head-
group. Surfactant A was synthesized by coupling p-nitrophenol
with 11-bromoundecenylic acid, ethyl ester followed by hy-
drolysis, while B was prepared by reacting lauroyl chloride with
4-aminopyridine followed by quarternization with methyl iodide.
The model chromophore C was made similarly from 4-ami-
nopyridine, using acetyl chloride instead of lauroyl chloride.
Surfactant D, on the other hand, was synthesized by ion-
exchange of the bromide counterion in cetyl trimethylammonium
bromide (CTAB) with the appropriate benzoate.10 The structures
of all the surfactants were confirmed by their 1H NMR spectra.
Hyper-Rayleigh Scattering. Hyper-Rayleigh scattering (HRS)
experiment is based on a two-photon scattering process, in which
the intensity of the second harmonic scattered light (I2ω),
generated by focusing an intense laser beam (Iω) on to an
isotropic solution, is measured.11 The intensity of the incoher-
ently scattered second harmonic light depends on the different
components of the molecular first hyperpolarizability tensor â.
The intensity of the second harmonic signal in an HRS
experiment is generally given as
I
2ω ) gN â2 I2
ω
where N is the number density,
indicates orientational
To further confirm that aggregation was the reason for the
observed variation, a model chromophore C, which is similar
to surfactant B but does not possess the long hydrocarbon tail,
was examined. The variation of the HRS intensity (Figure 1c)
in this case was seen to follow the expected linear behavior
with concentration, as in the case of nonaggregating chro-
mophores. This confirms that the first deviation from linearity
in the HRS plot is indeed reflective of the onset of micellization.
averaging, and the factor ‘g’ clubs the scattering geometry and
instrumental factors. For a system in which solute molecules
are dissolved in a solvent
I2ω/Iω2 ) G[Nsol â2 sol + Nsolv â2
]
solv
Generally, for the measurement of first hyperpolarizability (â)
(10) The synthesis and polymerization studies of this chromophore will be
published elsewhere. Geeta Kheter Paul and S. Ramakrishnan. To be
published.
(11) Hendrickx, E.; Clays, K.; Persoons, A. Acc. Chem. Res. 1998, 31, 675.
Clays, K.; Persoons, A.; Maeyer, De Leo Hyper-Rayleigh Scattering in
Solution. In Modern Nonlinear Optics, Part 3; Evans, Myron, Keilich,
Stanislaw, Eds.; Advances in Chemical Physics Series, Vol. LXXXV, John
Wiley & Sons Inc.: New York, 1994.
(12) Kodaira, T.; Watanabe, A.; Ito, O.; Matsuda, M.; Clays, K.; Persoons, A.
J. Chem. Soc., Faraday Trans., 1997, 93, 3039.
(13) The variation in the UV-vis spectra of the surfactant B as a function of
concentration, spanning the range above and below CMC, followed the
expected Beer-Lambert’s law confirming the absence of any specific
ground-state interactions between the chromophores above CMC.
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A R T I C L E S
Ghosh et al.
Figure 2. Variation of HRS signal intensity as a function of acid
composition.
Table 1. CMC Values Determined by HRS and Ionic
Conductance Measurements
CMCby
conductance
CMCbyHRS
measurement
surfactant
A
B
D
5.8 × 10-3
6.4 × 10-4
3.4 × 10-4
5.7 × 10-3
6.2 × 10-4
3.9 × 10-4
Scheme 2
An NLO Probe for CMC Determination. In an effort to
further extend this HRS approach for CMC determination, we
designed a probe molecule E (Scheme 2) that can detect the
micellization of long-chain fatty acids. The probe is designed
such that it can be protonated in the presence of an acid to yield
a salt F that would have a significantly higher â value. In E,
the protonation of the pyridine ring makes it a strong electron
withdrawing group resulting in an enhancement of its â.
Figure 2 shows the variation in the HRS signal when the
probe molecule is titrated with an acid - both HCl and acetic
acid show a saturation in the intensity at an acid:probe ratio of
ca. 1:1. A 3-5-fold enhancement in the signal intensity is
noticed upon protonation. The absolute value of the signal is
higher in the case of HCl, probably reflecting the higher
concentration of the protonated form. To test the feasibility of
using E as a probe for CMC studies, it was taken along with
nonanoic acid in three different acid:probe mole ratios - 1.7:
1, 2.4:1, and 3:1. Maintaining these mole ratios, the HRS signal
intensity was measured as a function of dilution, and these are
plotted in Figure 3. It is clear that the general behavior is similar
to the earlier observations, and the CMC of the fatty acid-salt
is in the range: 1.8-3.9 mM. At a low acid-to-probe ratio, the
CMC is apparently slightly higher but the difference is minimal
beyond a ratio of 2.4:1. This is again a reflection of the acid-
base equilibrium constant, which approaches a limiting value
at high acid concentrations.
Figure 1. Variation of HRS signal intensity as a function of concentration
for molecules A, B, C, and D.
Chromophore as the Counterion. Another surfactant D,10
wherein the NLO chromophore (4-acryloyloxy benzoate) is the
counterion, was also examined using HRS. Figure 1d, shows
that such a surfactant too exhibits a similar trend showing a
fall in HRS intensity at CMC. Thus, it is evident that even the
clustering of the NLO chromophores in a nearly spherically
symmetric fashion around the aggregated hydrophobic tails of
the surfactant causes a drop in the HRS intensity.
Discussion
The most widely accepted rationalization of the micellization
process is one where the concentration of the free surfactant
remains nearly constant after the onset of micellizations
implying that any further addition of surfactant leads only to
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Determination of CMC by HRS
A R T I C L E S
Figure 4. Variation of HRS signal intensity as a function of CTAB
concentration at constant p-nitrophenol concentration. The arrow indicates
the CMC of this mixture.
Figure 3. Variation of HRS signal intensity as a function of concentration
at different acid:probe ratios.
the generation of more micellar aggregates.1 This implies that
the free surfactant concentration [S]free at any point above CMC
is equal to CMC that is
Figure 5. Comparative variation of Rayleigh scattering and HRS signal
intensity as a function of concentration of surfactant A.
the CMC of CTAB.14 The CMC of CTAB in the presence of
PNP was independently measured by conductance method and
was found to be 0.84 mM. In yet another experiment, both the
linear Rayleigh (Iω) and the hyper-Rayleigh (I2ω) scattering
intensities were monitored sequentially from the same sample
as a function of dilution. This was done by the use of a series
of neutral density filters for measurement of the linear Rayleigh
scattering. Figure 5 shows one such representative measurement
carried out for surfactant A. The expected increase in the
Rayleigh scattering intensity after CMC is seen, which is
distinctly different when compared to the unusual drop in the
HRS intensity. It is, however, apparent that the CMC as detected
by the linear Rayleigh scattering is slightly higher than that seen
by HRS. It is known that CMC values do vary a little depending
on the method employed for its determination.1 These control
experiments confirm that this unexpected variation of the HRS
signal is indeed a direct consequence of the near spherically
symmetric assembly of the chromophoric units upon micelli-
zation.
[S]free ) CMC
This being the case, the slope of the variation of any given
property (whose intrinsic value per molecule is lower for the
micelle than the free species) as a function of concentration
may be expected to decrease after micellization. Even if the
micelles do not contribute at all toward the measured property,
one might at best expect the value to plateau beyond CMC.
However, our observations show a lowering of the HRS
intensity upon micellization, up to a concentration of about 2
times the CMC, before it begins to increase again. This is a
rather unprecedented observation, and therefore, we carried out
a few control experiments to preclude trivial effects due to
simple scattering, etc. In the first control experiment, the HRS
signal of a simple chromophore, p-nitrophenol (PNP), was
monitored in the presence of increasing concentrations of a
standard surfactantscetyl trimethylammonium bromide, CTAB.
It is important to note that the primary source of the HRS signal
in this experiment is the PNP, which is assumed to be
isotropically distributed in the medium, while the micellization
of the relatively “HRS-silent” CTAB creates an increasingly
scattering medium. The fact that no variation in the SH signal
intensity is seen as one traverses through the CMC of CTAB
(see Figure 4) clearly demonstrates that trivial scattering effects
do not contribute to the drop in the HRS intensity. If linear
Rayleigh scattering due to the formation of micellar aggregates
were to affect the HRS signal from the chromophore, then we
should see a decrease in the HRS intensity from PNP, above
One plausible explanation for this observation is the formation
of smaller pre-micellar aggregates (such as dimers or trimers)
in which the chromophoric dipoles could effectively add up
leading to a higher effective â value (per chromophore).15 Above
CMC, however, the concentration of such smaller aggregates
(14) As pointed out by one of the reviewers, the PNP could be partitioned into
the hydrophobic interior of the CTAB micelles, once formed, and this could
result in a change in the HRS signal. We exclude this factor, as its
contribution, if any, appears to be minimal as seen from the almost invariant
HRS intensity as one traverses through the CMC of CTAB.
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A R T I C L E S
Ghosh et al.
may become negligible due to their inclusion into the micelles,
thus causing the actual concentration of free surfactants to go
down. Under such circumstances one would see a drop in the
HRS signal at CMC, which reflects the loss of the smaller
aggregates that possess a higher effective â value (per chro-
mophore) compared to the micelles. But as the concentration
of micellar aggregates increase the contribution due to these
larger aggregates begin to dominate and the HRS signal
increases again. The fact that the HRS signal continues to
increase at higher concentrations is a clear indication that the
contribution from micellar aggregates is nonzero, although the
relative slopes before and after, suggest that the effective â value
(per chromophore) of the micellar aggregates is indeed lower.
through a set of condensing optics and broadband as well as
narrow band filters, on a UV-vis photomultiplier tube (PMT)
and averaged in a digital storage oscilloscope. Each data point
was averaged over 400 shots. The input power was monitored
using a power meter. All data were collected at laser powers
e12mJ/pulse which is below the threshold for stimulated
Raman, self-focusing/self-defocusing, Brillouin scattering and
dielectric breakdown.
CMC Determination using HRS. A typical procedure is
provided here. 113 mg of the cationic surfactant B, was
dissolved in 100-mL double distilled water to make a 2.7 mM
solution. 20-mL of this stock solution was taken for the HRS
measurement, and it was diluted in steps by replacing a fixed
volume (typically, 2-3 mL) of the solution with the same
volume of distilled water, using a micropipet, till the final
concentration was well below the CMC (as determined by
conductivity measurement). At each concentration, the I2ω value
was measured and was plotted against the concentration to
determine the CMC. A similar dilution procedure was followed
for the ionic conductivity measurements also. In the case of
nonanoic acid, an aqueous suspension of a weighed amount of
the acid was taken along with the probe molecule E (in the
appropriate acid:probe ratio) and sonicated to generate a
homogeneous solution of the resulting salt. This solution was
diluted in steps with distilled water as described above. At each
concentration, the I2ω was measured and was plotted against
the concentration to determine the CMC.
Conclusions
In summary, we have shown that the CMC of surfactants
that incorporate a NLO chromophore, either at their tail end, or
at their headgroup or even as a counterion, can be readily
determined by HRS. The CMC is detected by a rather
unprecedented drop in the HRS signal, which we believe could
be due to the formation of smaller pre-micellar aggregates whose
effective â value is higher than that of the micellar aggregates.
It is postulated that the concentration of these pre-micellar
aggregates becomes negligible beyond CMC, thus explaining
the observed decrease in HRS intensity. At higher concentra-
tions, the contribution from the increasing numbers of micelles
dominates causing the HRS intensity to increase again (a simple
concentration effect). One advantage of the HRS technique is
that the CMC is inferred by a change in the sign of the slope
(which appears as a peak) as opposed to, a simple change of
slope (sometimes a very small one) typically seen in most of
the standard approaches. This makes the detection of CMC using
HRS more precise. Furthermore, the sensitivity of this approach
to the shape of the micellar aggregate provides an added
advantagesfor instance, formation of elongated or cylindrical
micelles at higher concentrations may be detected.
An NLO chromophoric probe, whose â value increases
severalfold upon protonation, has also been developed. This
probe was utilized to measure the CMC of a simple long chain
fatty acid, which formed a salt with the probe. An interesting
feature of this probe is that it can be utilized to study the
formation of well-defined secondary structures in macromol-
ecules that have pendant acid functionality. Formation of various
types of structures, such as a helix, may be readily detected by
HRS using such probes. They could also be used to investigate
solvent and temperature-induced conformational transitions in
suitable designed polymer systems. Studies along these lines
are currently underway and will be reported in the future.
Control Experiment using PNP and CTAB. A 4.83 mM
solution of CTAB was prepared using a 10 mM aqueous solution
of p-nitrophenol. 12 mL of this solution was taken for HRS
measurement, and it was diluted in steps by replacing a fixed
volume (typically, 1-3 mL) of the solution with the same
volume of a 10 mM solution of p-nitrophenol (using a
micropipet) till the final concentration was well below the CMC
of the CTAB-p-nitrophenol mixture (as determined by conduc-
tivity measurement). This ensured that the concentration of the
p-nitrophenol remained unchanged after each dilution step. The
I
2ω value was measured after each dilution, and plotted against
the concentration of CTAB.
HRS Measurements using Mixtures of the Probe and an
Acid. Typically, 500 µL of the probe solution (74.6 mM in
MeOH) was taken along with varying volumes (250-1600 µL)
of the aqueous HCl solution (43 mM) and the total volume was
made up to 12 mL with water, for the HRS measurement. In
this way, the I2ω values were measured maintaining a fixed
concentration of the probe, whereas the acid:probe ratio was
varied. A similar procedure was followed using acetic acid also.
Plots of I2ω versus acid:probe ratio are shown in Figure 2.
Acknowledgment. S.R. would like to thank Department of
Science and Technology for financial support and P.K.D. thanks
the Department of Biotechnology for partial funding of this
project. We also thank Ms. Geeta Kheter Paul for providing a
sample of surfactant D.
Experimental Section
HRS Measurements. The apparatus used for the HRS
measurements has been described in detail elsewhere.9 In brief,
the fundamental (1064 nm) of a Q-switched Nd:YAG laser was
focused by a planoconvex lens (f.l. 22 cm) to a spot 5 cm away
after passing through a glass cell containing the sample solution.
The scattered light in the perpendicular direction was collected,
Supporting Information Available: Experimental details for
the synthesis of the various surfactants, the model compound,
and the probe molecule, along with their 1H-NMR spectral data.
This material is available free of charge via the Internet at
http://pubs.acs.org.
(15) It is not essential that the effective â value (per molecule) of the smaller
aggregates be higher than that of the free species. But for this kind of
behavior to be seen, this value should certainly be higher than that of the
â -value (per molecule) of the micellar aggregates.
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