Measuring Size, Size Distribution, and Polydispersity of Water-in-Oil

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Measuring Size, Size-Distribution and Polydispersity of Waterin-Oil Microemulsion Droplets using Fluorescence Correlation Spectroscopy: Comparison to Dynamic Light Scattering Mohammad Firoz Khan, Moirangthem Kiran Singh, and Sobhan Sen J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b09920 • Publication Date (Web): 19 Jan 2016 Downloaded from http://pubs.acs.org on January 24, 2016

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Measuring Size, Size-Distribution and Polydispersity of Waterin-Oil Microemulsion Droplets using Fluorescence Correlation Spectroscopy: Comparison to Dynamic Light Scattering Mohammad Firoz Khan, Moirangthem Kiran Singh, and Sobhan Sen* Spectroscopy Laboratory, School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India ABSTRACT: Water-in-oil microemulsion droplets (MEDs) are thermodynamically stable supramolecular structures formed in mixture of water and oil, stabilized by surfactant layer. Here we use fluorescence correlation spectroscopy (FCS) to measure the diffusion, and the size, size-distribution and polydispersity of MEDs prepared in ternary mixtures of water/oil/sodium bis(2ethylhexyl) sulfosuccinate (AOT) in heptane, isooctane and nonane at (near) single droplet level. We compare FCS data directly to dynamic light scattering (DLS) data, which shows that the optical matching point (OMP) conditions of MEDs in different oils (where excess optical polarizability of droplets vanish) severely influence DLS data, while FCS extracts the accurate size, sizedistribution and polydispersity of AOT-MEDs in all three oils. This suggests that extreme precaution must be taken in acquiring and explaining DLS data of MEDs in solution. FCS data show nearly identical W0-dependent (peak) size variations of AOT-MEDs in all three oils, though a subtle increase in (average) polydispersity of droplets is observed with increase in carbon chain-length of oils. Establishing the accuracy of FCS data for AOT-MEDs, we further apply FCS to measure the size parameters of MEDs prepared in quaternary mixture of water/oil/cetyl trimethylammonium bromide (CTAB)/1-butanol in hexane, heptane and isooctane. Unlike AOT-MEDs, FCS data show substantial effect of added co-surfactant (1-butanol) and external oil on size, size-distribution and polydispersity of quaternary CTAB-MEDs. Analysis of size-distributions reveals large variation of polydispersity which possibly indicates the existence of larger shape-heterogeneity, together with size-heterogeneity, of CTAB-MEDs compared to AOTMEDs in solution.

INTRODUCTION Water-in-oil microemulsion droplets/reverse micelles are thermodynamically stable nanometer-sized supramolecular assemblies that are formed in a mixture of water and oil, stabilized by a surfactant layer which decreases the interfacial tension between the two immiscible liquids.1-3 These nanostructures embed water inside their polar core, stabilized by the polar head-groups of surfactants (and co-surfactants), while the aliphatic tails of surfactants penetrate into continuous oilphase (Figure 1).1-3 Over the years, microemulsion droplets (MEDs) have found wide variety of applications ranging from stabilization of proteins,4 DNA,5,6 polymers,7 ionic liquids,8,9 etc. in their polar core – to their extensive use as nanoreactors10 for nanoparticle synthesis,11-16 purification/extraction of biomolecules,17 drug delivery,18 and in textile,19 cosmetic20 and food21 industry. Because of the unique character of embedded liquids inside core of MEDs a variety of experimental4,7,9,22-25 and simulation26-28 studies have been performed to understand the structure and dynamics of these confined liquids. Nevertheless, efficient use of MEDs requires detailed characterization of their various size parameters. Several techniques have been utilized to characterize structure, size, sizedistribution and polydispersity of MEDs in solution, which include NMR,29-37 small-angle neutron30,38-40 and X-ray scattering30,41 (SANS, SAXS), viscosity42 and conductivity measurements,35,43 dynamic light scattering,35,44-50 and fluorescencebased time-resolved50,51 and correlation spectroscopy,52-54 as

well as molecular dynamics (MD) simulation.26-28,32,55 Even though these studies found that size of MEDs can be characterized by parameter W0 (= [polar phase]/[surfactant]), the structural simplicity of these nano-droplets has been questioned time-and-again primarily because of their inherent size and shape heterogeneity which strongly depend on the constituent molecules.32,55 Despite having large sum of data on shape and size of MEDs, question remains how the shape, size, sizedistribution and polydispersity of MEDs vary when they are prepared in different ternary and quaternary systems-of-

Figure 1. Structure of microemulsion droplet: In the picture, rw is radius of water-core,  is thickness of surfactant layer, Rh is hydrodynamic radius. p, s, and np are dielectric constants of polar phase, surfactant layer and non-polar phase, respectively.

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Among different techniques, contrast variation dynamic light scattering (DLS) experiment is routinely used to measure size, size-distribution and polydispersity of MEDs in solution, primarily because of easy availability of the technique and its ease of use.35,44-50 However, it turns out that the constituent phases of MEDs, i.e., polar liquid inside core, surfactant layer, and continuous non-polar oil-phase have different dielectric constants of p, s and np, respectively, which follow a relationship: p < np < s (see Figure 1).45-49,54 Because of this, at a particular W0 (size), the excess optical polarizability of droplets become zero according to equation 1.45 4

3

(1)

This happens because with increase in size of polar-core (rw), the first term in right hand side of equation-1 becomes more negative while the second term becomes more positive. This leads to a situation where the two terms cancel at a particular W0 (i.e., rw).45 This condition is called optical matching point (OMP) where the excess polarizability of nano-droplets (relative to bulk non-polar phase) becomes zero.45-49 Consequently, the intensity of scattered light from these droplets reaches zero which makes the droplets invisible in light scattering experiments.45-49 In actual experiment however, the scattered intensity reaches to a minimum value (not to zero) because of inherent polydispersity of droplet-sizes.45-49 The (average) excess polarizability is directly proportional to the refractive index change (∆n) of droplets, relative to pure non-polar solvent. Hence, as ∆n changes with W0, the scattered intensity from droplets dips near OMP which can introduce inaccuracy in the measured size (and size-distribution) of MEDs as obtained from photon correlation spectroscopy.45-49 In fact, because of inherent size-polydispersity, the apparent effect of OMP on the measured size can spread over broad W0 range.45-49 Based on these facts, it is possible that changing the non-polar phase with oils and/or surfactants of different refractive indices can actually change the OMP condition. These issues complicate the size measurements of MEDs in light scattering experiments,45-49 which can even provide misleading results.44,48 Moreover, MEDs have low scattering cross-section which makes the (low) scattered signal from these droplets difficult to detect. Consequently, the obtained size-distribution may get biased toward larger size because larger droplets scatter more than the smaller ones. Not only that, light scattering technique is very sensitive to the unwanted scattered signal from dust particles present in solution.56 Unlike light scattering techniques, fluorescence correlation spectroscopy (FCS) measures the molecular diffusion by correlating fluorescence fluctuations originating from a single (or few) diffusing fluorescent-molecule (or molecular aggregate) in-and-out of a tiny observation volume (~1 fL) created inside the sample-solution using a laser, a high numerical aperture objective-lens and a confocal pinhole placed at the imageplane.57-59 The uniqueness of FCS in measuring diffusion, and subsequently the size and size-distribution of particles, lies with the fact that it captures the diffusion-time of individual particle in extremely dilute condition (down to single molecule level), and provides accurate size information of particles in solution.60-62 Moreover, if the fluorescence fluctuations originate from chemical reactions of the observing molecules then one can also extract the kinetic information of such reaction

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from FCS data.13,67 Because of these advantages, FCS is extensively used to study diffusion and molecular interactions in biomolecular systems.67-74 However, conventional FCS also suffers from several disadvantages when compared to DLS: In FCS it is difficult to measure particle-sizes larger than ~1/10th of the size of observation volume.60-62 This difficulty does not arise in DLS measurement. Moreover, choosing suitable fluorescent probes and labeling them to other non-fluorescent (macro)-molecules for measuring molecular diffusion pose further challenge. DLS, on the other hand, does not require any fluorescent tag. It has been also pointed out that for measuring diffusion time using conventional FCS, one has to have the precise size and shape information of observation volume, so called the molecular detection function (MDF), which controls the positiondependent excitation and collection of fluorescence from a molecule inside the observation volume.63,64 In fact, a small variation in shape/size of observation volume can lead to erroneous fluorescence autocorrelation function. Improved FCS method such as 2-focus FCS has been introduced to overcome such problem.65 Nevertheless, using a stable (conventional) FCS setup it is possible to characterize the size parameters of nanoscale supramolecular MED-systems whose size (Rh) ranges between ~1 – 15 nm. In fact, only recently our group reported a detailed procedure for using FCS to measure accurate size, size-distribution and polydispersity of AOT-MEDs (in isooctane) at (near) single droplet level, which easily bypasses the OMP problem associated with MEDs in light scattering experiments.54 In this paper, we present an extensive characterization of size, size-distribution and polydispersity of water-in-oil MEDs prepared in variety of ternary and quaternary systems-ofmolecules using FCS – so as to obtain a comprehensive understanding of their size parameters in solution. We directly compare the size and size-distributions of MEDs measured using FCS and DLS, prepared in ternary mixtures of water/sodium bis(2-ethylhexyl) sulfosuccinate (AOT) in three different oils – heptane, isooctane and nonane. We show that OMP conditions in different oils significantly influence DLS data while FCS extracts the accurate size and size-distribution of AOTMEDs in all three oils. Having established the accuracy of FCS data for ternary AOT-MEDs, we further apply FCS to measure the diffusion and size parameters of MEDs prepared in quaternary mixture of water/cetyl trimethylammonium bromide (CTAB)/1-butanol in three different oils – hexane, heptane and isooctane. In this set, we also vary concentration of 1-butanol, keeping the CTAB concentration constant, in order to observe the effect of co-surfactant on size parameters of quaternary CTAB-MEDs. FCS data reveal that W0dependent peak-size variations of ternary AOT-MEDs are nearly identical in all three oils except only a subtle increase in size-polydispersity with increase in carbon-chain lengths of external oil. On contrary, substantial effect of co-surfactant (1butanol) and external oils on various size parameters of quaternary CTAB-MEDs is observed. Unlike in AOT-MED systems, the W0-dependent peak-sizes decrease with increase in carbon-chain of external oils. Analysis of size-distributions of MEDs in particular oil reveals large variation of polydispersity of quaternary CTAB-MEDs, which strongly depend on the amount of co-surfactant present and W0 value. On the other hand, polydispersity of AOT-MEDs remains nearly constant with W0 change. These observations possibly indicate that a


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variety of spherical/non-spherical CTAB-MED structures are formed in solution having larger size/shape heterogeneity compared to AOT-MEDs whose shapes remain (nearly) spherical.

EXPERIMENTAL SECTION Materials: Surfactants AOT (≥99%, SigmaUltra) and CTAB (≥98%) were from Sigma-Aldrich and Spectrochem, respectively. 1-butanol, n-Hexane, n-heptane and isooctane were from Spectrochem (UV grade), and nonane was from Acros Organics. Fluorescent dyes, sulforhodamine-B (SRhB) and rhodamine-6G (Rh6G) were from Sigma, and were used without further purification. AOT was purified using activated charcoal in diethyl ether: The mixture was stirred for hours and filtered through 0.2 m filter, and then solvent was evaporated. This method removes fluorescent impurities of AOT efficiently.54 Purification of CTAB was performed by recrystallization in a mixture of 10:1 isooctane/ethanol. All solvents (except 1-butanol) were distilled and dried before using them for sample preparation. Sample Preparation: Before sample preparation, AOT was dried at 100C for ~4 hours. From dried AOT we prepared 15 mM stock solution in different oils (heptane, isooctane, nonane) and different stock concentrations of SRhB in water. Then we prepared MEDs of W0 = 2 to 50 or 60 by adding requisite amount of water with SRhB – so that the final (overall) concentration of SRhB was ~1 nM. These solutions were then put in a vortex-mixture until they were clear. As SRhB is negatively charged molecule it solubilizes within water-core and insoluble in non-polar oils. It is expected that SRhB preferentially says in water-rich region inside polar core of droplets. SRhB concentration was chosen in such a way that on an average we observe only 1 – 2 dye-embedded droplet(s) inside the FCS observation volume. This was checked directly by monitoring the amplitude of fluorescence correlation function G() at  = 1 µs. For DLS measurements, the AOT-MED samples were prepared in the same fashion keeping AOT concentration at 100 mM (without adding dye). Quaternary water-in-oil CTAB-MEDs were prepared in three different oils (hexane, heptane and isooctane) with cosurfactant (1-butanol) of various concentrations. We took CTAB stock concentration of 50 mM and added different 1butanol amounts such that 1-butanol/CTAB ratios (P0) were 10, 15, 20, 25, 30 and 35. We then prepared CTAB-MEDs of W0 (= [water]/[CTAB]) from 2 to 50 by adding requisite amount of water (mixed with SRhB) such that the final (overall) concentration of SRhB was ~1 nM. FCS Setup: We used FCS setup home-built on Olympus (IX71) inverted confocal microscope using 60 waterimmersion objective with correction-collar (NA 1.2, UPlanSApo, Olympus).13,54,67 Samples were excited with 532 nm CW DPSS laser (25 mW, CNI Lasers). The laser beam was expanded to dia. of ~11 mm using a pair of lenses such that it overfills the back aperture of objective. This was done to achieve the highest spatial resolution in FCS setup. The laser power at sample position was controlled by ND filters and was kept at < 75 µW – so as to avoid saturation and minimize the triplet conversion of dye-molecule. The fluorescence bursts from SRhB (embedded inside MEDs) were collected with the

same objective, and was passed through a dichroic (No. XF2016, Omega Optical Inc., USA) and an emission filter (No. 607AF75, Omega Optical Inc., USA) to block the scattered excitation. The fluorescence signal was then focused through a tube lens onto a multi-mode fiber patch-cord (M67L01 - Ø25 µm, 0.10 NA, Thorlabs) placed at the imageplane, which acted as the confocal pinhole. Fluorescence signal was then fed onto a single photon avalanche photodiode (SPCM-AQRH-13-FC, Perkin Elmer). The autocorrelation of fluorescence bursts were obtained by hardware-correlation using FLEX correlator card (FLEX990EM-12D, Correlator.com, USA). Autocorrelation curves were collected in a routine written in LabView. The correlation curves were then analyzed in IGOR-Pro software (WaveMetrics, USA). For FCS measurements all samples were kept inside a home-made closed-cell prepared on a glass cover-slip (No. 1) that ensured the stability of samples during experiments. At least 4-5 independent measurements (each of 100 s acquisition) were performed for fresh MED solutions, and average of these data is presented as final correlation curves. All measurements were carried out at 25 C. FCS Theory: In FCS experiment, one detects fluorescence fluctuations from dyes diffusing through an observation volume and calculates the normalized autocorrelation function G() of the fluctuations as57-59 G ( ) 

F t F t    F t 

(2)

2

where F(t) (= F(t) - F(t)) is the fluctuation of fluorescence from the temporal average , and  is the time shift. For 3-D Gaussian-shaped observation volume with radial (r) and axial length (l ), G() can be expressed as57-59

1 G    N

  1   D 

  

1

  r 2   1       l    D 

    

1

2

(3)

where N is average number of particles in the observation volume, and D is the average time a particle takes to cross the volume, which can be related to diffusion constant (D) as57-59 (4) We standardized our FCS setup using rhodamine-6G (Rh6G) in water using its known diffusion coefficient of 4.14 × 10-6 cm2 sec-1.75 Rh6G in water showed characteristic diffusion time of ~35 (2) s in the present FCS setup. From these values, the radial length (r) and the effective volume (Veff) were measured to be 235 nm and 0.56 fL, respectively. The size, i.e., hydrodynamic radius (Rh), of droplets was obtained through Stokes-Einstein relation (equation 5).54 (5) where kB is the Boltzmann’s constant, T is temperature (25C in the present case), and η is the viscosity of bulk solvent. To extract various size parameters of AOT-MEDs, the viscosities of bulk solvents were used in equation-5. However, in quaternary CTAB systems it was reported previously that the co-surfactant (1-butanol) actually partition between surfactantlayer and bulk oil-phase by fractions of ~0.31 and ~0.69, re-



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spectively.32,76 Therefore, the bulk viscosities of non-polar oils, mixed with 69% butanol, were calculated using theoretical procedure.77 These viscosities were then used in equation-5 to calculate the size-distributions of CTAB-MEDs. DLS Setup: A commercial DLS setup (Malvern Zeta Sizer ZS 90) fitted with a 633 nm CW laser and a PMT-detector was used for size measurements of AOT-MEDs. All MED solutions were filtered prior to measurements. Solutions were loaded in a quartz cuvette of 10 mm path length and (scattered) photon correlations were obtained directly in instrument software. For each sample 20 sets of data were accumulated for 50 s each. The correlation data were analyzed using CONTIN algorithm78 in-built within the data acquisition software to obtain the size-distributions. The refractive indices and viscosities of bulk non-polar solvents were used in the analysis. Final size-distributions were obtained by averaging all 20 sets of data for respective samples. All measurements were carried out at 25 C.

RESULTS AND DISCUSSION FCS Data for AOT-MEDs: We measured fluorescence autocorrelation curves of dye-embedded AOT-MEDs of different W0 values, prepared in ternary mixtures of water, AOT and

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heptane or isooctane or nonane (Figure 2). Note that the (negative) charge of dye (SRhB) does not affect the measured correlation data. This was confirmed by measuring control correlation curves of MEDs using a positively charged dye (rhodamine-6G) and comparing the same with previous data which show identical feature (see Figure S1 in Supporting Information). Also, the smooth feature of correlation curves (devoid of any steps) in Figure 2 confirms that the fluorescence correlations originate from only diffusion of dye-embedded MEDs in-and-out of the tiny observation volume. However, measuring correct fluorescence correlation curves of MEDs using FCS is not trivial primarily because of the existence of refractive index mismatch among MEDs of different W0 values44-49,52-54 as well as between MED-solution and objective immersion-liquid (water in this case).54 Hence, one has to follow a systematic procedure to solve these problems – so as to obtain the correct correlation curves in FCS.66 Although FCS had been used earlier by groups of Eicke52 and Robinson to measure MED sizes,53 only recently our group has shown how one can solve the refractive mismatch problem by adjusting the correction-collar of objective lens.54 It was also shown that optimum depth of focal-point inside MED-solution is required to nullify the optical aberration.54 In the present study, we find that the optimum objective-collar position ranges within ~0.17–0.20 depending on W0 value while optimum depth of focal-point stays at ~30 µm inside the sample-solution from

Figure 2. Fluorescence correlation curves measured for SRhB-loaded AOT-MEDs of different W0 in n-heptane, isooctane and nonane (panels in left). Size-distributions (in hydrodynamic radii - Rh) of AOT-MEDs for different W0 extracted from fitting analysis of correlation curves using Gaussian distribution model (GDM) (panels in right). The peak-Rh shifts to larger value and width of distributions get larger with increase in W0. See also Table 1 for the values of peak-Rh and widths.


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the cover-glass for AOT-MEDs. Correction-collar dependence of correlation data was observed by measuring the correlations at different collar positions (see Figure S2 in Supporting Information). Nevertheless, in every experiment the correctioncollar was varied systematically to find the optimum position where D was minimized and amplitude of correlation was maximized. These conditions validate the aberration-corrected (smallest) confocal volume inside MED solution. As expected, the minimum D was obtained at a collar position ~0.21 for low W0, while this position got shifted systematically towards ~0.17 as W0 increased, similar as observed earlier.54 Figure 2 shows the final correlation curves obtained for AOT-MEDs of W0 = 2 to 50 or 60, prepared in three different oils. The gradual shift of correlation curves toward higher time with increasing W0 indicates slower diffusion of MEDs of higher W0. Importantly, from Figure 2 we find that total shift and spread of curves over time-axis remain similar for AOT-MEDs in all three oils. This provides the first indication that for a particular W0 diffusion dynamics of AOT-MEDs remain similar in three oils. Gaussian Distribution Model Analysis: One objective of the present study is to check how the external non-polar solvents influence (peak) size, size-distribution and polydispersity of ternary and quaternary MEDs in solution. For this purpose we used a 3D Gaussian distribution model (GDM) to analyze FCS data, instead of discrete 3D diffusion model.54 This is also because the discrete 3D-diffusion model could not fit the FCS data properly so as to extract the inherent sizeheterogeneity of MEDs in solution. To check this issue, we first fitted fluorescence correlation curves with equation-3, assuming no size-heterogeneity of AOT-MEDs in solution. The discrete fits for MEDs prepared in heptane, isooctane and nonane are shown in Figure 3, along with the residuals-of-fits which are poor. Actually, MEDs in solution have high sizeheterogeneous; hence, smaller number of discrete diffusion component does not provide the accurate size information of MEDs. Earlier DLS studies revealed Gaussian-type sizedistribution for AOT-MEDs that spread over broad range.7 In fact DLS measurements performed here also show similar size distributions (see below). As we proposed earlier,54 assuming m-numbers of particles (dye-embedded-MEDs) diffusing in-and-out of the observation volume with times Di, equation-3 can be modified to ∑

1

1

/

(6)

where ’s are the relative amplitudes of fluorescent particles/aggregates, which relate to average number of particles within observation volume and their brightness. In the present experimental condition (i.e., ~1 nm dye and 15 mM AOT), the number of dyes relative to available number of MEDs in solution is calculated to be very low: Using known aggregation numbers of AOT-MEDs in isooctane, the dye/MED ratios are found to be 1 : 4.9 × 106 (for W0 = 2; aggregation no. 33)88 and 1 : 1000 (for W0 = 50; aggregation no. 1380).29 It should also be noted here that in solution MEDs are always in dynamic equilibrium – randomly coalescing and de-coalescing several times (in tens-of-microsecond) within the time taken by MEDs to diffuse through observation volume.13,89 This allows the (dye) molecules embedded inside the polar core of MEDs to exchange with others within their diffusion time.13 Because MED-sizes are highly heterogeneous in solution,

Figure 3. Representative fits to fluorescence correlation data: Comparison of single-component fit and GDM analysis as well as their respective residuals-of-fits for AOT-MEDs in n-heptane (upper panel), isooctane (middle panel) and nonane (lower panel). Blue line – single component fit; red line – GDM analysis. Fits to other correlation curves are similar. See text for details.

Ddistribution should be considered in logarithmic timescale.54 Such D distributions can be obtained assuming a Gaussian distribution in on logarithmic time-scale as54


,

(7)


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Table 1. Peak-Rh and full width at half maxima (FWHM) of size-distributions of AOT-MEDs obtained from FCS and DLS measurements. Polydispersity calculated from FCS data for MDD of W0 > 20 are also presented. n-Heptane W0

FCS

*

2

Peak Rh (nm) 2.00

FWHM (nm) 1.34

4

2.31

6

2.66

DLS#



FWHM (nm)

--

Peak Rh (nm) --

1.61

--

2.5

1.5

1.94

--

2.7

1.6

--

8

3.01

2.29

--

3.2

1.8

10

3.31

2.59

--

3.8

2.2

15

4.15

3.31

--

4.1

2.0

20

4.85

3.80

---

4.8

2.8

25

5.94

4.88

0.036

6.1

3.6

30

6.99

5.95

0.033

5.7

2.8

35

8.01

7.31

0.032

5.9

2.1

40

9.30

8.75

0.030

9.7

3.4

45

10.44

10.17

0.029

10.5

4.6

50

12.11

12.89

0.030

12.3

3.9

55

13.42

15.34

0.032

--

--

60

14.36

18.45

0.034

--

--

Isooctane 2

1.99

1.53

--

--

--

4

2.30

1.83

--

2.2

1.4

6

2.71

2.17

--

2.8

1.8

8

2.94

2.41

--

3.1

1.9

10

3.32

2.67

--

3.4

2.0

15

4.06

3.28

--

4.1

2.5

20

4.90

3.87

--

4.8

2.6

25

5.77

5.00

0.042

4.9

3.6

30

7.06

6.64

0.039

5.3

8.2

35

8.08

8.49

0.042

7.2

9.7

40

9.25

10.97

0.039

8.8

13.0

45

10.30

12.08

0.041

11.1

13.5

50

12.44

12.55

0.032

--

--

2

1.98

1.47

--

--

--

2.36

1.81

--

2.0

1.2

6

2.60

2.21

--

2.6

1.4

8

2.97

2.85

--

2.8

1.7

10

3.18

2.99

--

3.0

2.0

15

4.28

3.91

--

4.0

2.7

20

5.03

4.88

--

3.9

4.4

25

6.16

6.10

0.049

4.2

3.0

30

7.35

7.38

0.043

5.6

5.0

35

7.97

8.48

0.044

7.8

7.6

40

9.37

10.35

0.040

10.1

14.0

45

10.58

11.91

0.038

--

--

50

12.10

13.65

0.035

--

--

* Error  0.05 nm (obtained from repeated measurements).  0.10 nm (obtained from CONTIN analysis).

#

with relative amplitudes of components as Ai, peak diffusion time as p, and b is related to width of distribution. We fitted FCS data of dye-labeled-MEDs using equation-6: A total of 150 fixed Di time-components, logarithmically spaced within 10 – 106 s, were used in the GDM analysis. (Note that to discard the (small) triplet contribution (T  1.5 s) we analyzed the correlation data using pure diffusive GDM starting at 10 µs. This we checked by comparing the fits to correlation data using only 3D diffusion-model and the 3D-diffusion coupled to triplet relaxation, which clearly showed that one must exclude data upto ~10 s to get rid of the triplet contribution – see Figure S3 in Supporting Information.) In the least-square fitting analysis, Ai’s and b were varied to get the best distribution of which could model the experimental correlation data correctly. Assuming spherical shapes79 the distributions of hydrodynamic radii (Rh) of AOT-MEDs were then calculated using equations-5 from versus D distributions obtained from GDM analysis, and the results are plotted in Figure 2. In Figure 3 we compare the residuals of GDM fits with that of single-component fits. It is readily seen that the residuals of GDM analyses are significantly improved. Previously our group had shown that the GDM improves the residuals over single-component fit because of the inherent sizeheterogeneity of MEDs in solution.54 This was confirmed by analyzing correlation data of a pure-dye diffusing in pure solvents of different viscosities and of a dye-protein complex in water where no size-heterogeneity is expected.54 For these systems it was found that GDM analysis do not improve the residual compared to single-component fit.54 Thus, we conclude that the obtained size-distributions of MEDs from GDM analysis are real and not instrumental artifact. From size-distributions, the peak-sizes of AOT-MEDs of different W0 values are obtained and tabulated in Table 1 along with their full width at half maxima (FWHM) of sizedistributions in three different oils. From these sizedistributions we calculated the polydispersity () as45,54

where

Nonane 4

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Error

〈

〉

〈

〉

〈

〉

1

(8) (9)

In equation-9, f(Rh) is the size-distribution (in logarithmic scale) obtained from GDM analysis. We see from Table 1 (and Figure 2) that the FWHM of the distributions become larger for W0 > 20. Previously we and other groups have shown that the variation of AOT-MED size (peak-Rh) with W0 follow linear relationship till around W0 = 20.54,82 However, beyond this W0 the size variation deviates from linearity which arises mainly from size-heterogeneity of MEDs in solution.45,54 Previously, we had shown that one can extract the sizepolydispersity by fitting non-linear part of size-variation with W0 using Coated Droplet Model as well as by analyzing independent size-distribution.54 Here, we calculated the polydispersity () from individual size-distribution using equation-8 for W0 > 20 (Table 1). It can be seen that the polydispersity values obtained are small which remain nearly constant with W0 variation in particular oil. However, careful scrutiny of data shows that there is a subtle increase in the (average) polydispersity with increase in carbon chain lengths of oils: The (average) polydispersity values are found to be 0.032 (in heptane), 0.039 (in isooctane) and 0.042 (in nonane). In fact, re-


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cent microsecond MD simulation study55 obtained sizepolydispersity of AOT-MEDs in isooctane very similar to that obtained here as well as in our previous study.54 Thus, FCS not only provides accurate size information, but also the sizedistribution and polydispersity MEDs in solution. DLS Data for AOT-MEDs: In order to observe the optical matching point (OMP) problem, we performed DLS measurements on AOT-MEDs prepared in the three non-polar solvents. As noted above, the OMP depends on refractive index (dielectric constant) of bulk non-polar phase. The refractive indices of heptane, isooctane and nonane are 1.3876, 1.3914 and 1.4050, respectively, which suggest that the OMPs of MED solutions will change in different non-polar solvent. Table 1 includes the peak hydrodynamic radii and FWHM of size-distributions of AOT-MEDs in three solvents, measured using DLS, while Figure 4 directly compares the peak-size variation of AOT-MEDs with W0 as obtained from FCS and DLS measurements. It can be clearly seen that near OMP the sizes obtained from DLS measurements are deviated substantially from the (correct) sizes of MEDs as obtained from FCS measurements. More importantly, as predicted by equation-1, it is nicely seen that the position of OMP sifts toward lower W0 with increasing refractive index of bulk non-polar phase (see Figure 4). This is expected because the refractive index of water is smaller than bulk non-polar phase; hence, decrease in size of water-core (rw) makes the excess polarizability zero at lower W0 according to equation-1. The deviation of DLS-data from FCS-data arises from the fact that – near OMP the scattered signal becomes negligible from most of the droplets, and thereby the effect of multiple scattering from smaller and bigger droplets becomes dominant which eventually makes the photon correlations faster than expected.81 This leads to the apparent lower-size of droplets than expected (see Figure 4). However, it can be seen that the sizes of MEDs obtained from FCS and DLS measurements are similar (within error limits) outside the OMP region. These observations clearly suggest that DLS can not provide the accurate size and sizedistribution of MEDs near OMP, which FCS can. The similarity of MED-sizes obtained from present FCS and DLS data (outside OMP region) as well as from previous NMR,29 IR88 and simulation27,55 studies also confirms that the embeddeddye inside MEDs do not affect the overall MED sizes. To show the erroneous result of DLS measurements near OMP, we compare few size-distributions of AOT-MEDs obtained from DLS and FCS near OMP in Figure 5. It is seen that the distributions obtained from DLS (through CONTIN analysis)71 are erratic and they do not show any sequential variation with W0, while the distributions obtained from FCS (through GDM analysis) nicely follow a sequential variation in width and peak-size with W0 change near OMP (see also Figure 4). This comparison suggests that FCS is ideal for measuring size-distributions of MEDs at OMP where light scattering technique fails. At this juncture, one may argue that whether the differences observed really arise from the different quality of FCS and DLS data or from the different way of analyzing two data-sets – one using GDM which assumes a-priori Gaussian size-distribution and another using CONTIN which does use any a-priori assumption of shape-function. We believe that different analysis procedures would not affect the final results. This is because, in our previous report we had shown that GDM and MEMFCS analyses of FCS data provide very similar size-distribution of MEDs in solution.54 Unlike

Figure 4. Variation of peak-Rh with W0 of AOT-MEDs obtained from analysis of FCS data (solid circles with solid-lines through points), and DLS data (solid triangles with dotted lines through points). The peak-size variations with W0 are found to be nearly identical in all three different oils. The sizes obtained from DLS measurements are found to get deviated from the accurate ones near OMP. The OMP positions (indicated by colored vertical lines) are also found to shift toward lower W0 values with increase in carbon chain-length of the external oils. Error bars are shown in the plots.

GDM, MEMFCS analysis does not assume any model function a-priori, similar as in CONTIN analysis. MEMFCS fitting analysis of autocorrelation function seeks the best distribution of ai(τDi) where not only the χ2 is minimized, but also the entropy (S = ∑ , where Pi = ai(τDi)/ai(τDi)) is maximized.54,90 CONTIN analysis, on the other hand, is based on the inverse Laplace transformation which also does not assume any shape-function a-priori.78 The similar results obtained from GDM and MEMFCS analyses in our previous study54 fully justify the use of GDM analysis here. Moreover, the similar sizes obtained at W0 values (outside OMP region) from GDM analysis of FCS-data and CONTIN analysis of DLSdata further confirm that there is no effect of different data analysis procedures on the final results (see Figure 4 and Table 1). In fact, the drastically different MED-sizes obtained from DLS-data near OMP are real, which lie far beyond the error limits of the two measurements. Lastly, it should be noted that recent microsecond MD-simulation55 study on AOT-MEDs found polydispersity of AOT-MEDs in isooctane which is very similar as that obtained here (and also in our previous study).54 This again confirms that the size-distributions obtained through GDM analyses are correct. It is clear from above results that one has to be extremely cautious about the effect of OMP in order to explain the diffusion and hence, various size parameters of MEDs obtained from light scattering experiments. In fact, one of the most important findings of present study is that – we do not observe any effect of external-oil chain-length on the variation of peak-sizes with W0, although previous light scattering measurements showed drastic effect of oil chain-length on size of AOT-MEDs.44,48 Shah and co-workers found ~2 nm change in MED-sizes at W0 = 20 upon changing the continuous oil-phase from n-heptane to n-decane.44 They explained their observation based on the varying penetration propensity of oil-chains inside the AOT surfactant layer, which changes the radius-ofcurvature of droplets.44 As one can see from DLS data in Fig-



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Figure 5. Comparison of size (Rh) distributions of AOT-MEDs prepared in different oils near OMP: Distributions obtained from FCS (panels in left) and from DLS (panels in right). The size-distributions obtained from FCS show regular shifting (with monotonic change in widths) with W0 variation; while shifts and widths of distributions obtained from DLS measurements show irregular behavior near OMP.

ure 4, such a drastic variation in size can actually arise from the effect of OMP upon changing the oil-phase, especially at the W0 studied by Shah and co-workers.44 It is also clear from equation-1 that the OMP of AOT-MEDs in n-decane or in oils of higher chain-lengths will shift toward lower W0 values, which affect the measured size near W0 = 20 drastically. Hence, one would observe a false decrease in peak-size of MEDs near that W0.44 Similar decrease in size (at a different W0) was also reported by Neubert and co-workers.48 FCS data, which provide the accurate size information near OMP, do not show such effect of oil chain-length on size of AOT-MEDs. Nevertheless, we do observe a subtle effect of oil chain-length on the (average) polydispersity () of AOT-MEDs, which shows a small increase with increase in oil chain-length. This may possibly indicate only a subtle effect of oil-chain penetration inside AOT-surfactant-layer which eventually changes the size-heterogeneity by small amount instead of the peak-sizes of AOT-MEDs.

FCS Data for CTAB-MEDs: Having established that FCS can provide accurate size and size-distributions of AOTMEDs, we applied FCS to measure the size, size-distribution and polydispersity of quaternary CTAB-MEDs prepared in three different non-polar solvents – n-hexane, n-heptane and isooctane. Single-chain CTAB surfactants can form stable water-in-oil MEDs in non-polar solvents only in the presence of co-surfactants.32-37 A necessary geometric condition for the formation of water-in-oil MEDs is v/al > 1, where v is volume of hydrocarbon-tail of surfactant, a is polar-head area and l is fully extended chain-length of surfactant molecule.35,83 Most single-chain (cationic) surfactants can not satisfy this condition without the presence of co-surfactant. Co-surfactants adsorb at the water/surfactant interfacial region of MEDs increase the (average) volume of surfactant tails (v) and reduce the effective surface area (a). This provides the necessary condition for the formation of stable water-in-oil MEDs.35,82 Such arrangements of co-surfactants (1-butanol here) within the surfactant molecules (CTAB here) also screen the repulsive interactions between the head-groups of surfactants and modi-


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The Journal of Physical Chemistry water and surfactant (W0), and (3) molar ratio of co-surfactant and surfactant (P0).32-37,76,82 Although these structural aspects of quaternary MEDsystems are well-known,32-37,76,82 characterization of their sizeparameters, especially the size-distribution and polydispersity, is nearly absent in literature35 compared to the extensively studied AOT-MED systems. Mainly NMR,32-37 conductivity,76,83 and fluorescence83,84 measurements have been utilized to characterize the quaternary MEDs. Pulse gradient stimulated echo (PGSTE) NMR technique has been quite successful to provide the detailed diffusion characteristics of different components of these quaternary systems.32-37 Recent MD simulation, on the other hand, also provided new insight about the structural aspects of such MEDs.32 However, the frequently used light scattering techniques have rarely been explored in studying pure quaternary CTAB-MED systems;35 although such MEDs with embedded nanoparticles/nanorods have been characterized using DLS extensively.11,13,14 The reason could be the difficulty associated with detection of scattered signal from these MEDs (in pure form) in light scattering experiments because of their poor contrast,32 or could be due to the problem associated with the dilution of these quaternary systems.35,83

Figure 6. Variation of peak-size (Rh) with W0 of CTAB-MEDs at different 1-butanol/CTAB ratios (P0) in three different solvents obtained from FCS measurements: (A) n-hexane, (B) n-heptane and (c) isooctane. Data show drastic dependence of added cosurfactant (1-butanol) on the sizes of CTAB-MEDs. Panel (D) compares the peak-size variation with W0 of CTAB-MEDs depending on oil for P0 =20 (open circles) and P0 =35 (filled circles), which show also substantial effect of external oil on the sizes of CTAB-MEDs. See also Figures and Table in the Supporting Information. Error bars are show in the plots.

fy the surfactant packing parameter to form stable MEDs.35,82 By screening the repulsive forces, co-surfactants increase the compactness of molecules at the water/surfactant interface. Subsequently, the curvature and rigidity of surfactant layer increase. A minimum quantity of co-surfactant is always required to form the stable water-in-oil CTAB-MEDs.35,82 These quaternary MED systems can be characterized by mainly three parameters: (1) surfactant concentration, (2) molar ratio of

To obtain a comprehensive understanding of various size parameters of CTAB-MEDs, especially the size-distribution and polydispersity, we applied FCS to collect a large set of correlation data at (near) single droplet level (only 1 – 3 dyeembedded-droplets inside observation volume). We collected FCS data for CTAB-MEDs, prepared in n-hexane or n-heptane or isooctane, having different W0 and P0 values (see Figures S4, S5 and S6 in Supporting Information for fluorescence correlation curves and results of GDM analysis). The same SRhB is used as fluorescent marker in these MEDs. For the FCS measurements we varied objective collar between 0.17 and 0.19, where minimum diffusion times (D) were obtained for MEDs of different W0. The optimum depth of focal-point was found to be same (30 µm). GDM analysis of fluorescence correlation curves followed by calculation of size-distributions and polydispersity (assuming spherical shapes) provide W0 and P0 dependent size parameters of CTAB-MEDs in three different oils. Final results are included in Table S1 (in Supporting Information). Figure 6 plots the peak-size (Rh) variation with W0 for different P0 values in all the three oils. Similar to AOTMEDs, the Rh variations with W0 (for all P0 values except P0 = 10 in isooctane) are found to follow linear relationship till around W0 = 20, but beyond this W0 the Rh variations seem to deviate from linearity. The peak-Rh variations with W0 also show a decrease with increase in co-surfactant concentration (P0). This indicates that addition of co-surfactant (1-butanol) makes the droplet-size smaller because of larger compactness of surfactant layer, and thereby smaller uptake of water into their core. Similar effect of 1-pentanol on CTAB-MEDs size was also observed in previous PGSTE-NMR studies.36,37 However, several new findings originate from the present FCS data: At smaller co-surfactant content (lower P0) the MED-sizes increase upto a particular W0, but beyond this W0 peak-sizes slowly decrease while FWHM of size-distributions significantly increase (see Figure 6; and Table S1 in Supporting Information). The calculated polydispersity (for W0 > 20) shows large increase with W0 for MEDs with lower P0. This indicates that at lower P0 the CTAB-MEDs of larger W0 possess larger size and (possibly) shape heterogeneity in solution.



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However, for P0 > 20 the peak-sizes are found to increase with increasing W0 till the stage where stable CTAB-MEDs were formed. This clearly indicates that larger co-surfactant (1butanol) content stabilizes CTAB-MEDs to smaller sizes with smaller water uptake inside their core due to compactness of surfactant layer. For P0  20 the polydispersity is also found to decrease with increasing W0. This suggests that the higher cosurfactant content not only stabilizes the CTAB-MEDs, but also minimizes the size (and possibly) shape heterogeneity of CTAB-MEDs in solution. However, for P0  30 the overall polydispersity of MEDs is found to increase again. All these results indicate that P0 in the range of 20 – 25 makes MEDs with less size/shape heterogeneity. Not only that, for this range of P0 values one observes the largest change of peak-sizes with W0 variation (see Figure 6). Overall, the polydispersity values are found to be larger for CTAB-MEDs compared to AOT-MEDs (see Tables 1, and S1 in Supporting Information). Previously, quasi-elastic light scattering experiment on CTAB/1-pentanol/n-hexane/water MEDs found that the photon correlation data could be fitted with a single-exponential function, suggesting low degree of size-polydispersity of CTABMEDs in solution.35 However, the present FCS data could only be fitted well with a distribution model (GDM) which extracts large size-distributions and polydispersity of CTAB-MEDs in all three oils (see Table S1 in Supporting Information). In fact, recent MD simulation (of 45 ns) in CTAB/1-pentanol/n-hexane/water system found non-spherical structure of CTAB-MEDs with high eccentricity of ~0.9,32 while microsecond MD simulation of AOT-MEDs in isooctane found nearly spherical structure of AOT-MEDs (eccentricity ~0.1).55 These observations are in line with the present FCS data which indicate that unlike ternary AOT-MEDs, the quaternary CTAB-MEDs may also have large shapeheterogeneity along with the size-heterogeneity in solution. Moreover, the present FCS data indicate that the size and shape heterogeneities of CTAB-MEDs can be tuned by the amount of co-surfactant added into the system. Finally, we look at the effect of carbon chain-length of external-oil on the size of CTAB-MEDs: Figure 6D compares the peak-Rh variations with W0 in three oils for P0 = 20 and 35. It is clearly seen that unlike in AOT-MEDs, the increase of carbon chain-length of external-oil decreases the (peak) size of CTAB-MEDs at a particular W0 and P0. Other groups have also studied the effect of chain-lengths of co-surfactants and surfactants on the size of quaternary MEDs.82,85,86 The present FCS study looks at (similar) effect of chain-length of the external-oils on CTAB-MED size. Previously, it was shown that co-surfactants (alcohols) with longer chains allow formation of stable quaternary MEDs at lower concentration, compared to the alcohols having shorter chains.82,85 For a constant alcohol concentration, it was also found that longer-chain alcohols allow smaller water uptake inside polar core of cationic quaternary MEDs, leading to smaller size of MEDs.82,86 These results were explained based on the absolute value of a parameter R which is defined as the ratio of net interaction energy of surfactant with external-oil and the interaction energy of surfactant with water – both in presence of co-surfactant. The value of R should be > 1 for formation of stable water-in-oil MEDs.82,86,87 With increase in chain-length of external-oil, interaction energy of surfactants (and co-surfactants) with the oil-chain increases which eventually leads to the formation of smaller MEDs as observed here. Furthermore, the polydispersity values of CTAB-MEDs, as calculated from FCS data,

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reveal that there is substantial effect of W0 and P0 on the heterogeneity of CTAB-MEDs. The higher polydispersity observed for CTAB-MEDs, compared to AOT-MEDs, possibly suggest that CTAB-MEDs have larger size and shape heterogeneity compared to AOT-MEDs; however, it is still not clear how much the size and shape heterogeneities actually contribute to the overall polydispersity of quaternary CTAB-MEDs in solution. Certainly, experiments such as SANS and SAXS as well as extensive MD simulation studies (in hundreds of nanoseconds) on these quaternary MED systems are required to gain further knowledge on their complex size and shape heterogeneities in solution. Nevertheless, it is clear from the present study that the large variations of sizes and size-distributions (and shapes) with added co-surfactant (and water) of quaternary MED systems provide a much broader avenue for using them as nano-reactors for synthesizing various nanostructures, compared to ternary AOT-MED systems.11,13,14

CONCLUSION Present study showed that measurement of accurate size parameters, especially the size-distribution and polydispersity, of microemulsion droplets is not trivial. We showed here that the situation becomes even more complicated when a technique holds serious (technical) limitation for such studies. In such scenario the obtained results may not provide the accurate description of the system under investigation, and as shown, the results could be even misleading. Although substantial amount of data on various size parameters of ternary and quaternary water-in-oil MED systems have been reported in literature, this paper presented a comprehensive characterization of these MED systems in extremely dilute condition (near single droplet level). The FCS results showed sizes of ternary AOTMEDs are nearly independent of external oil-phase (at least in oils used here), though a subtle effect of external oil-chain on the size-polydispersity was observed. On contrary, a substantial effect of added co-surfactant (1-butanol) and external oil on the size, size-distribution and polydispersity of quaternary CTAB-MEDs was observed. The present study clearly showed how FCS can provide the accurate information of various size parameters of MEDs, where DLS fails. In fact, this study infers that it is better to obtain the correlation of fluorescence photons, rather than of scattered photons, originating from microemulsion droplets in solution to measure their accurate diffusion and size parameters. Nevertheless, we emphasize that the inability of DLS to provide accurate diffusion information of molecular-aggregates due to OMP problem will prevail only in cases of supramolecular assemblies which consist of multiple components of different refractive indices, such as in microemulsion droplets.

ASSOCIATED CONTENT AUTHOR INFORMATION Corresponding Authors [email protected]


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Notes

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The authors declare no competing financial interests.

15.

ACKNOWLEDGMENTS This work is supported by Department of Information Technology (DIT) and University Grants Commission (UGC), Government of India. We thank Prof. Ashok K. Ganguli (IITD) and his student Dr. Soma Sharma (IITD) for helping us in the DLS measurements. We thank Prof. Sudipta Maiti (TIFR) for providing the FCS data collection software. MFK and MKS thank CSIR for fellowships. Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org. Fluorescence correlation data showing dye-charge independence (Figure S1); objective correction-collar dependent correlation data (Figure S2); fits to correlation data validating use of 3D-dffusion model (Figure S3); correlation data and fitted sizedistributions of CTAB-MEDs in various conditions (Figures S4S6); fitted size-parameters of CTAB-MEDs (Table S1). (PDF)

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Measuring Size, Size Distribution, and Polydispersity of Water-in-Oil

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