Journal of Colloid and Interface Science 499 (2017) 202–208
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Journal of Colloid and Interface Science
journal homepage: www.elsevier.com/locate/jcis
Regular Article
Study on the applicability of dynamic light scattering (DLS) to
microemulsions including supercritical carbon dioxide-swollen micelles
Shane Patrick Cadogan a,b,1, Christian Joachim Hahn c, Michael Heinrich Rausch a,b, Andreas Paul Fröba a,b,⇑
a
Professur für Advanced Optical Technologies – Thermophysical Properties, Department of Chemical and Biological Engineering (CBI), Friedrich-Alexander-Universität
Erlangen-Nürnberg, Paul-Gordan-Strabe 6, 91052 Erlangen, Germany
b
Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität Erlangen-Nürnberg, Paul-Gordan-Strabe 6, 91052 Erlangen, Germany
c
Covestro Deutschland AG, 51365 Leverkusen, Germany
g r a p h i c a l a b s t r a c t
a r t i c l e
i n f o
Article history:
Received 31 January 2017
Revised 28 March 2017
Accepted 28 March 2017
Available online 30 March 2017
Keywords:
Droplet size
Dynamic light scattering (DLS)
Microemulsion
Nonionic surfactant
Polyester polyol
Principle of Supercritical Microemulsion
Expansion (POSME)
Supercritical carbon dioxide
a b s t r a c t
The applicability of dynamic light scattering (DLS) for the characterization of the size of supercritical carbon
dioxide (sc-CO2)-swollen micelles in a polyester polyol-based multicomponent microemulsion with nonionic surfactant has been thoroughly proved for the first time in this work. Systematic experiments confirming that a hydrodynamic mode is observable in either a homodyne or a heterodyne detection
scheme as well as the evaluation of the influence of the laser power applied to the slightly colored
microemulsion have ensured an accurate implementation of this technique for a technically relevant system. The correlation times associated with the translational diffusion coefficient of the swollen micelles in a
continuous liquid phase were measured for temperatures from (298.15 to 338.15) K at pressures of (90 and
100) bar. While there was no significant effect of pressure, it was found that the translational diffusion coefficient increases with increasing temperature as expected. We postulate this is primarily related to the
effect of decreasing viscosity of the continuous phase. An estimation of the hydrodynamic diameter of
the sc-CO2-swollen micelles is in good agreement with values for similar systems reported in the literature.
For the derivation of absolute sizes for corresponding systems, also dynamic viscosity and refractive index
data will be determined simultaneously in a currently developed closed experimental loop.
Ó 2017 Elsevier Inc. All rights reserved.
⇑ Corresponding author at: Professur für Advanced Optical Technologies – Thermophysical Properties, Department of Chemical and Biological Engineering (CBI) and
Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Paul-Gordan-Strabe 6, D-91052 Erlangen,
Germany.
E-mail addresses: christian.hahn@covestro.com (C.J. Hahn), michael.rausch@fau.de (M.H. Rausch), andreas.p.froeba@fau.de (A.P. Fröba).
1
Unfortunately, the author deceased before completing the article.
http://dx.doi.org/10.1016/j.jcis.2017.03.111
0021-9797/Ó 2017 Elsevier Inc. All rights reserved.
S.P. Cadogan et al. / Journal of Colloid and Interface Science 499 (2017) 202–208
Nomenclature
Symbols
bi
D
g(2)(s)
kB
n
p
q
r
T
k0
g
H
experimental constants
diffusion coefficient, m2 s–1
normalized intensity correlation function
Boltzmann constant, J K–1
refractive index
pressure, Pa
modulus of scattering vector, m1
hydrodynamic radius, m
absolute temperature, K
wavelength in vacuo, m
dynamic viscosity, Pa s
scattering angle, rad
1. Introduction
The Principle of Supercritical Microemulsion Expansion
(POSME) process is an interesting example of a technical application of microemulsion science [1,2]. This process involves the formation of a micellar solution in a hydrophilic solvent (e.g. a polyol)
in the presence of a blowing agent such as carbon dioxide (CO2)
and a suitable surfactant. The conditions are then adjusted so that
the critical pressure and temperature of the blowing agent are
exceeded. After a microemulsion has formed in which the micelles
are swollen with supercritical blowing agent, the mixture is
decompressed, and in the presence of a suitable reactant (e.g. isocyanates), solidified to form a solid foam with gas swollen pores in
the size scale of micrometers [1]. The size of micelles swollen with
supercritical blowing agent in the microemulsion stage is one of
the key governing parameters of the final size distribution of the
pores, which in turn governs the insulation properties of the polyurethane foam produced. The main thrust of the work carried out
to date on POSME has been on the formulation and phase behavior
of these systems, where CO2 is a top candidate among possible
blowing agents for future developments [1–7]. For the speedy
development and rapid screening of the optimal conditions under
which this process should be performed, but also for other processes involving microemulsions formed under supercritical conditions, it is necessary to have an inexpensive yet reliable technique
for the determination of the size and size distribution of the pools
or droplets of the supercritical component in the microemulsion.
In general, the characterization of the size, size distribution, and
shape of the dispersed phase in microemulsions is of great importance in their application in technical processes [8–11]. Small angle
neutron and small angle X-ray scattering are two commonly
implemented methods to study such properties [12–15]; however,
such techniques are relatively expensive and require specialist
equipment. Transmission electron microscopy applied to shockfrozen samples is another used technique [16–18], and despite
exposing the system under investigation to a large, albeit brief,
thermal gradient to freeze the microemulsion, yields both the size
and shape of the dispersed phase along with information regarding
which type of phase is present. A comparison of these techniques
can be found in several publications in addition to a technique
based on nuclear magnetic resonance (NMR) [19–21].
Dynamic light scattering (DLS) is a rapid and robust method for
the determination of the translational particle diffusion coefficient
and the size or size distribution of a distinct species dispersed in a
continuous phase in a contact-free, routine manner [22–24].
Assuming the diffusing species to be spherical, non-interacting
s
sC
203
time, s
correlation time, s
Abbreviations
carbon dioxide
CO2
DLS
dynamic light scattering
DPSS
diode-pumped solid state
FO
fiber optics
NMR
nuclear magnetic resonance
PMT
photomultiplier tube
POSME principle of supercritical microemulsion expansion
sc-CO2 supercritical carbon dioxide
bodies, the Stokes-Einstein relation can be employed to calculate
the hydrodynamic size of the dispersed species [24,25]. DLS has
indeed been applied for the characterization of the hydrodynamic
radii of water swollen micelles [14,26–30] and oil swollen micelles
[31]. In most of these studies as well as in many analytical laboratories, commercial DLS devices are used as off-the-shelf solutions
for the characterization of the sizes of, for example, polymers, proteins, and particles [10,32–37]. The direct application of such
equipment to systems for which it has not been proven that the
experimental boundary conditions and the implemented data evaluation routines yield correct results requires a critical assessment.
In context with microemulsions and also emulsions existing at
temperatures and pressures related to or close to the supercritical
state of one of the components, only a few studies applying DLS for
micelle size characterization can be found in the literature [38–42].
All of them were performed at fixed scattering angles without adding well-defined reference light and lack experimental proof that
the evaluated light scattering signals are related to a true hydrodynamic mode. The applied data evaluation strategies always assume
a homodyne detection scheme where a possible superposition
with, e.g., stray light from cell windows is neglected without verification. This is particularly critical when scattering angles distinctly different from 90° are applied [38–40]. Reported
validation measurements based on a comparison of the DLS results
for solid particle dispersions obtained in newly designed pressure
cells with those from a standard measurement cell do not automatically imply that the results received for microemulsions in a
next step are reliable [41,42]. Furthermore, lacking comments on
the effect of the applied laser power and possible effects of light
absorption inducing at least local changes of the thermodynamic
state in colored samples [41] raise some doubts on the reliability
of the reported results.
The present contribution represents, to the best of our knowledge, the first comprehensive study critically evaluating the capability of DLS for providing information on the size of micelles in
microemulsions at temperatures and pressures related to the
supercritical state of one component. To prove the applicability
to technically relevant systems, supercritical CO2 (sc-CO2)swollen micelles in a microemulsion based on a polyester polyol,
an industrial grade nonionic surfactant, and several other components were investigated at conditions relevant to the POSME process. The accessible information related to the size of the
micelles is given in terms of the reciprocal of the mean lifetime
of microscopic fluctuations in the droplet number density, which
is directly proportional to the translational diffusion coefficient of
the droplets. Based on estimated viscosity and refractive index
204
S.P. Cadogan et al. / Journal of Colloid and Interface Science 499 (2017) 202–208
data for the probed mixtures, a realistic value for the micelle size
could be approximated.
3. Experimental
3.1. DLS assembly
2. Method
In DLS experiments from the bulk of fluids in macroscopic thermodynamic equilibrium, the dynamics of microscopic fluctuations
in pressure, temperature, and concentration are analyzed [22]. In
light scattering experiments, these fluctuations are reflected by
the temporal modulation of the scattered light intensity. For fluid
mixtures consisting of a continuous phase and dispersed particles,
droplets, clusters, or macromolecules, the light scattering process
caused by these inhomogeneities is dominant in comparison to
that associated with fluctuations on the molecular level. The temporal analysis of the scattered light intensity governed by the inhomogeneities gives access to the dynamics of the fluctuations in the
number density of the scatterers [44], i.e. particles, droplets, or
macromolecules. In a DLS experiment, the dynamics of fluctuations
are analyzed by the calculation of the correlation function of the
scattered light intensity.
In the case of monodisperse and freely diffusing droplets, the
general normalized intensity correlation function can be described
by
g ð2Þ ðsÞ ¼ b0 þ b1 expð2s=sC Þ þ b2 expðs=sC Þ :
|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}
homodyne term
ð1Þ
heterodyne term
In Eq. (1), the correlation time sC represents the mean lifetime of
!
droplet number density fluctuations at a defined wave vector q ,
while b0, b1, and b2 are experimental constants. The correlation time
sC can be related to the translational particle or droplet diffusion
coefficient D via
1
sC ¼ ðDq2 Þ ;
ð2Þ
where q is the modulus of the scattering vector,
q¼
4pn
sinðH=2Þ:
k0
ð3Þ
In Eq. (3), n is the refractive index of the sample fluid, H is the scattering angle formed between the directions of the light transmitted
through and scattered from the fluid, and k0 is the wavelength of
the incident light in vacuo.
From the Stokes-Einstein equation
D¼
kB T
6p g r
ð4Þ
and the measured translational droplet diffusion coefficient D, in
principle the hydrodynamic radius r of the droplets can be calculated if the dynamic viscosity of the mixture g is known. In Eq.
(4), kB and T are the Boltzmann constant and the absolute temperature, and it is assumed that the diffusing droplets do not interfere.
The latter prerequisite holds at sufficiently small number densities
of the droplets, which is also necessary for the validity of Eq. (1).
For a light scattering experiment, it must be ensured that either
b1 = 0 or b2 = 0, cf. Eq. (1), by adjusting the ratio of the intensity of
the scattered light to that of light added from other coherent
sources, e.g., from a reference laser beam. In a homodyne detection
scheme (b2 = 0), in principle only light scattered from the droplets
is analyzed, whereas in the case of heterodyne conditions (b1 = 0),
the detected signals are dominated by coherent reference light
superimposed on the scattered light. In the experiments described
in the following section, either homodyne or heterodyne conditions have to be strictly adhered to.
The optical configuration of the DLS set-up is illustrated in
Fig. 1. A diode-pumped solid state (DPSS) laser (Cobolt Samba,
k0 = 532.1 nm, maximum output power 1000 mW) was used as
the light source. The laser beam was guided to the cell by mirrors
M1 to M5. A half-wave plate (B1) and a polarization beam splitter
(C1) were used to control the intensity and polarity of the incident
light, which was focused into the sample by a lens (E, f = 500 mm).
For measurements performed in a heterodyne detection scheme,
coherent reference light was siphoned off from the incident laser
beam via a beam splitter (A), guided with the mirrors M6 and
M7, and superimposed on the scattered light. An interference filter
(D) as well as a half-wave plate (B2) combined with a polarization
beam splitter (C2) were used to control the intensity of this reference light. The scattered light was detected by two photomultiplier
tubes (PMTs). For experiments in which the scattered light propagated through free space, the aperture required for defining the
scattering angle was placed immediately after the cell. For measurements with a single-mode fiber optic (FO) cable, the latter
was attached to the PMTs and to the aperture. The signals from
the PMTs were fed to a digital single-tau correlator and the calculated pseudo-cross correlation function was analyzed using associated software. The reported expanded uncertainties (k = 2) for the
obtained correlation times correspond with the respective double
standard deviation related to the fitting procedure.
Unless indicated otherwise, all measurements were performed
without the addition of reference light and with a scattering angle
H of (90 ± 0.2)° (k = 2), adjusted by back-reflection from the sample cell windows.
3.2. Material and sample preparation
A sample mixture supplied by Covestro Deutschland AG, Germany, and related to the POSME process was used as a basis for
producing microemulsions. This mixture contains 54.3 wt% of
polyester polyols, 10.2 wt% of glycerol, 10.2 wt% of tris(2-chloroiso
propyl)phosphate as a flame retardant, 0.2 wt% of a catalyst, and
25.1 wt% of nonionic polyoxyethylene-modified polydimethylsiloxane (tradename XIAMETERÒ OFX-5211 from Dow Corning,
USA) as a surfactant. Liquid CO2 was purchased from Linde GmbH,
Germany, and had a purity of 99.995 vol%.
Without further treatment, but taking care not to introduce any
particulate matter, approximately 18 mL of the sample mixture
was added to a 40 mL high-pressure cell, which is described in
detail in Ref. [43]. The cell was then pressurized with CO2 to
approximately 80 bar, corresponding to a CO2 mass fraction of
about 0.12 in the final mixture. To mix the contents, the cell was
manually agitated, where a glass bead layer (glass bead diameter
2.8 mm) with a depth of about 1 cm served to enhance mixing. It
should be mentioned that manual agitation was no longer performed after the first mixing procedure. Thus, extended equilibration times of more than 8 h were allowed before performing the
DLS measurements after changing temperature and/or pressure.
Heating wires were attached to the outer cell wall, which was
subsequently surrounded by insulation material. The temperature
of the system was measured and controlled through an in-house
developed program applying two calibrated Pt-100 X resistance
thermometers with an absolute uncertainty (k = 2) of 20 mK. The
temperature stability during the measurements was smaller than
5 mK. The pressure of the cell was monitored with a bourdon pressure gauge connected to the cell, where the uncertainty (k = 2) of
the reported pressure values was estimated to be 2 bar. The
S.P. Cadogan et al. / Journal of Colloid and Interface Science 499 (2017) 202–208
205
Fig. 1. The optical arrangement used in the current study: M1-M7, mirrors; A, beam splitter; B, half-wave plate; C, polarization beam splitter; D, interference filter; E,
biconvex lens (f = 500 mm); PMTs, photomultiplier tubes; DPSS laser (k0 = 532.1 nm). The continuous line and the long dashed line show the incident light and the reference
light, respectively. The dotted line denotes the detected scattered light.
pressure was controlled via a volumetric screw pump connected to
the CO2 vessel. It should be mentioned that increasing or decreasing the pressure of the sample volume was performed by adding or
removing CO2, i.e. the mixture was subjected to small concentration changes whenever the pressure was changed.
Measurements analyzing the temperature dependence from
(298 to 338) K were performed at pressures of (90 and 100) bar.
A colorless excess phase was always observed in the upper part
of the cell during the experiments. The DLS measurements focused
on the lower, slightly colored microemulsion phase, where sc-CO2rich droplets were present in the polyol-rich bulk fluid. The formation of the microemulsion can be explained by the characteristics
of the nonionic surfactant. It is based on a trisiloxane where the
siloxane backbone is very hydrophobic and the polyethylene glycol
tail is very hydrophilic. Hydrophobic CO2 is partially dissolved in
the polyol, where further CO2 is solubilized by the hydrophobic
backbone of the surfactant. As the hydrophilic polyethylene glycol
tail of the surfactant dissolves very well in the polyester polyol and
the glycerol, a microemulsion can be formed.
4. Results and discussion
4.1. Method validation
To confirm any correlation functions obtained were solely due
to the presence of sc-CO2-containing droplets in a microemulsion
and not caused by particulate contaminants in the provided
polyol-based mixtures or micelles of the surfactant formed without CO2, correlation functions were recorded prior to the addition
of CO2. As indicated in Fig. S1 in the supporting information, no signals related to hydrodynamic diffusion modes were found. Thus,
the single exponentials found in the time domain of interest for
all measurements in the microemulsion phase after adding scCO2 could be related to the presence of droplets. In these cases,
most of the standard deviations of the correlation times obtained
from the correlation functions were smaller than 1%, which indicates a narrow droplet size distribution. The absence of further
exponentials in the correlation functions further proves the
Fig. 2. The inverse of the correlation time, s1
C , plotted against the modulus of the
scattering vector squared, q2. The line denotes a linear regression of the data. Error
bars indicate the expanded uncertainty (k = 2) of the inverse fitted correlation
times.
assumption of approximately monodisperse droplet size. Moreover, possible multiple scattering processes could be excluded
because no additional signals in the short-time range could be
found. Furthermore, the laser beam did not show any significant
diameter expansion when crossing the microemulsion phase.
To prove that the light scattering signals evaluated were related
to the translational droplet diffusion mode, the adherence to the
corresponding working equation, Eq. (2), was verified. For this,
the reciprocal of the determined correlation times sC was plotted
as a function of the squared moduli of the respective scattering
vectors. The modulus of the scattering vector q was varied by
adjusting scattering angles between (84 and 96)° using the rotating
stage indicated in Fig. 1. Fig. 2 shows the results obtained at
T = 314 K and p = 80 bar assuming a constant refractive index, n,
of 1.42. This value corresponds to the refractive index of the
polyol-based sample mixture without added CO2 at T = 303 K as
measured with an Abbe refractometer (Adago NAR-2T). The refractive index of polyols is only a weak function of temperature, which
is not expected to contribute significantly to the results obtained.
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S.P. Cadogan et al. / Journal of Colloid and Interface Science 499 (2017) 202–208
The linear behavior shown in Fig. 2 confirms that a hydrodynamic mode is the origin of the obtained exponentials in the correlation functions. According to Eq. (2), the value of the translational
particle diffusion coefficient D is equal to the slope of the line in
Fig. 2, and was found to be 5.4 1012 m2 s1.
Spurious light from undesired but inevitable sources in the laboratory may prevent obtaining correlation functions related to a
purely homodyne detection scheme, in particular when the scattered light is guided to the PMTs in a free space arrangement. Confirmation that the recorded correlation functions were purely
homodyne was obtained by comparison with the results from a
heterodyne detection scheme in which the scattered light is superimposed with coherent reference light. Such proof is given if the
correlation times evaluated according to Eq. (1) for experiments
at a given state point with and without added reference light agree.
Corresponding experiments were conducted at T = 300 K and
p = 91 bar, where the obtained correlation functions are depicted
in Fig. 3.
The correlation times and thus the mean lifetimes of the droplet
number density fluctuations determined from the recorded correlation functions, sC, were found to be (408.54 ± 2.61) ls in the
homodyne regime and (411.14 ± 3.28) ls in the heterodyne
regime. This agreement within the stated uncertainties demonstrates that the measurements performed without adding defined
reference light adhered to homodyne conditions where b1 >> b2,
cf. Eq. (1). It is worth mentioning that this state could only be
reached by a thorough optical isolation of the signal beam path
from the ambience in the laboratory, where no other light sources
than the laser and some LCDs from the setup instrumentation were
present. To avoid any doubt about the investigated regime, it is recommended to ensure heterodyne conditions by adding coherent
reference light with sufficiently high intensity in any kind of DLS
experiment. Although this also allows for the analysis of smaller
inhomogeneities, it is not common practice when commercial
solutions are applied. Users of such instruments, however, should
be aware that purely homodyne measurements are not selfevident without taking respective measures.
Instead of a free-space experiment in which the scattered light
propagates through air to the detectors, optical fibers can also be
used to guide the scattered light from the sample cell to the PMTs.
For homodyne type experiments, this reduces the effect of spurious
light superimposing the scattered light and is realized in most
commercially available DLS instruments. A comparison of the
results observed in a free-space configuration and with a fiber
optic is shown in Fig. 4. Due to the reduction of the aperture size
associated with the small diameter of the fiber, the intensity of
the scattered light detected by the PMTs was lower for the corresponding measurements, which is the reason for the larger scatter
Fig. 4. Comparison between measurements performed using free space (closed
circles) and fiber optics (open circles) to guide the scattered light to the PMTs. The
results are given with a confidence level of 95% (k = 2).
of the correlation data. Nevertheless, the obtained correlation
times further confirm measurements performed without a fiber
optic and without the addition of reference light correspond to true
homodyne measurements. It should be noted, however, that the
presence of additional signals from a heterodyne contribution
has to be considered towards smaller values of the scattering angle
also when fiber optics are used. Thus, the evaluation of the experimental data becomes more complex. To allow for an accurate
analysis of the obtained correlation functions, one has to design
the experiment to be either homodyne or heterodyne.
As the polyol based sample was translucent yet slightly colored,
the possibility of thermal lensing and local heating due to absorption of energy from the incident green laser light [24] was investigated. This was accomplished by varying the incident laser power
and comparison of the resulting correlation times sC. The power of
the incident laser beam was measured with an optical power
meter (Newport 842-PE) directly in front of the cell body. As
shown in Fig. 5, a relevant effect of the incident laser power on
the measured decay time of the droplet number density fluctuations could only be observed for the highest applied incident laser
power. Here, the slightly but significantly smaller correlation time
may indicate first effects of laser light absorption. Thus, all further
experiments were performed with an incident laser power of about
50 mW. Further reduction leads to a decreasing scattered light
intensity, resulting in higher uncertainties for the determined correlation times. This is indicated in Fig. 5 by the large error bar for
the data point obtained with the lowest incident laser power.
4.2. Droplet diffusion coefficient and estimated droplet size
The effect of temperature and pressure on the translational particle diffusion coefficient of droplets in the microemulsion is
Fig. 3. Comparison between measurements performed in the homodyne (open
circles, left axis) and heterodyne (open squares, right axis) regime. The correlation
times given are supplied with a confidence level of 95% (k = 2).
Fig. 5. Correlation time sC plotted against the power of the incident laser light Pi.
The expanded uncertainties (k = 2) are also shown.
S.P. Cadogan et al. / Journal of Colloid and Interface Science 499 (2017) 202–208
Fig. 6. Inverse of the correlation time, s1
C , plotted against temperature T. Error bars,
which are only given if they are larger than the symbols, correspond to the
expanded uncertainty (k = 2).
shown in Fig. 6. Here, the reciprocal of the correlation time of the
droplet number density fluctuations is given as a function of temperature. This kind of data representation was chosen because s1
C
is directly proportional to the droplet diffusion coefficient. The latter, however, cannot be calculated exactly as the refractive indices
of the microemulsions could not be measured within this work.
As expected, the correlation times decrease with increasing
temperature, indicating that the diffusivity of the sc-CO2-swollen
micelles increases with increasing temperature. This is probably
related to decreasing dynamic viscosity with increasing temperature. Further analysis of the temperature dependence, however,
is not reasonable because also the composition of the sample cell
volume changes somewhat between the different temperatures
due to the regulation of the pressure by adding or releasing CO2.
Furthermore, lacking information on the temperature dependence
of the dynamic viscosity of the microemulsion hinders a reliable
discussion if the changes in the diffusivity go along with changes
in the droplet size. Within the investigated conditions, no clear
trend can be found regarding the pressure dependence.
Assuming a microemulsion viscosity of 5 mPa s at T = 318 K and
p = 100 bar, which in our opinion is a reasonable value given that it
has been shown that the absorption of CO2 can drastically reduce
the viscosity of polyols [45], we estimate from our measurement
results a hydrodynamic sc-CO2-swollen micelle diameter of
17 nm for this specific example. This is in good agreement with literature data for typical droplet diameters in microemulsions
involving supercritical fluids in general [38–41,46] and sc-CO2swollen micelles in particular [2,4,6] ranging from (3 up to 30) nm.
5. Conclusions
This work has thoroughly proved for the first time that DLS is a
suitable method for the droplet size characterization of technically
relevant microemulsions where micelles are swollen with a fluid in
its supercritical state and the continuous phase is a multicomponent mixture. While other studies performed for similar systems
[38–42] simply assume that the evaluated signals are related to a
hydrodynamic mode, the evaluated scattering angle dependency
of the correlation times determined from the recorded correlation
functions demonstrates that the obtained results can be attributed
to the translational diffusion of sc-CO2-swollen micelles. Also the
validity of a purely homodyne detection scheme was confirmed.
This is not self-evident, especially for scattering angles smaller
than 90° which were used in some similar investigations [38–40]
without testing possible effects from heterodyne contributions
due to spurious light. If such precautions are not taken, it is possible that the results obtained are erroneous by up to a factor of 2.
207
While the effect of varying laser power on the obtained results
for the slightly colored samples was evaluated and taken into
account within the present work, publications which do not
include comments on the effects of potential laser heating for,
e.g., dyed microemulsion phases [41] raise some doubts regarding
the reported results. Local heating of the sample may cause an
overestimation of the translational diffusion coefficient at a given
temperature and hence an underestimation of the corresponding
hydrodynamic radius of the investigated species. All in all, the present contribution shows that an improvident use of commercial
DLS solutions may result in erroneous results, whereas a careful
test of the capabilities of the method can pave the way to valuable
information related to the droplet size of swollen micelles in
sophisticated microemulsion systems. For the system investigated
here, it was found that the translational diffusion coefficient of the
sc-CO2-swollen micelles does not vary significantly at a given temperature for the studied pressures. Its expected increase with
increasing temperature at constant pressure can be related to the
decreasing viscosity of the continuous phase. An estimated hydrodynamic diameter of the micelles is in good agreement with values
reported for similar systems in the literature [2,4,6,38–41,46]. On
the basis of the present investigations, our current efforts aim at
the precise determination of the absolute size and size distribution
of sc-CO2 swollen micelles in POSME-related microemulsions. For
this, we focus on the development of a closed experimental loop
that allows for the simultaneous measurement of the droplet diffusion coefficient, the refractive index, and the dynamic viscosity for
well-defined state points.
Acknowledgements
This work was supported by and published with the permission
of Covestro Deutschland AG. Their support is gratefully appreciated. Furthermore, this work was financially supported by the German Research Foundation (Deutsche Forschungsgemeinschaft,
DFG) by funding the Erlangen Graduate School in Advanced Optical
Technologies (SAOT) within the German Excellence Initiative.
Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.jcis.2017.03.111.
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