Enhancement in Elastic Bending Rigidity of Polymer Loaded Reverse

Article Cite This: Langmuir XXXX, XXX, XXX-XXX

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Enhancement in Elastic Bending Rigidity of Polymer Loaded Reverse Microemulsions P. M. Geethu,† Indresh Yadav,‡ Vinod K. Aswal,‡ and Dillip K. Satapathy*,† †

Soft Materials Laboratory, Department of Physics, IIT Madras, Chennai 600 036, India Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India

‡

S Supporting Information *

ABSTRACT: Elastic bending rigidity of the surfactant shell is a crucial parameter which determines the phase behavior and stability of microemulsion droplets. For water-in-oil reverse microemulsions stabilized by AOT (sodium 1,4-bis(2-ethylhexoxy)-1,4-dioxobutane-2-sulfonate) surfactant, the elastic bending rigidity is close to thermal energy at room temperature (kBT) and can be modified by the presence of hydrophilic polymers. Here, we explore the influence of two polymers polyethylene glycol (PEG) and polyvinylpyrrolidone (PVP), both having nearly same size (radius of gyration, Rg) but different dipole moment, on elastic bending rigidity of waterAOT-n-decane reverse microemulsions via estimating the percolation temperatures (TP) and droplet radii using dielectric relaxation spectroscopy (DRS) and small-angle neutron scattering (SANS) techniques. Notably, an increase in TP is observed on introducing PEG and PVP polymers and is attributed to the adsorption of polymer chains onto the surfactant monolayer. The stability of the droplet phase of microemulsion after the incorporation of PEG and PVP polymers is confirmed by contrast matching SANS experiments. An enhancement in elastic bending rigidity of AOT surfactant shell amounting to ∼46% is observed upon incorporation of PVP into the droplet core, whereas for PEG addition, a smaller increase of about 17% is recorded. We conjecture that the considerable increase in elastic bending rigidity of the surfactant monolayer upon introducing PVP is because of the strong ion-dipole interaction between anionic AOT and dipoles present along the PVP polymer chains. Scaling exponents extracted from the temperature dependent electrical conductivity measurements and the frequency dependent scaling of conductivity at percolation indicate the dynamic nature of percolation for both pure and polymer loaded reverse microemulsions. The decrease in activation energy of percolation upon incorporating PEG and PVP polymer molecules also reflects the increased stability of microemulsion droplets against thermal fluctuations.

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(soft-confinement).4 Especially, reverse microemulsions loaded with polymers are widely investigated, because addition of polymers allows one to tailor and/or control the macroscopic properties and phase behavior of MEs. This is usually achieved by tuning the solubility of polymer in constituents of MEs and by playing with the molecular size and specific interactions of the added polymers. Polymer loaded reverse microemulsions (PLMEs) do find potential applications in enhanced oilrecovery by surfactant flooding,3,6 in food technology,7 in drug delivery,8 and in the biomedical field.9 In all of these aforementioned applications of PLMEs, the questions that need to be addressed are (i) whether the droplet phase of the microemulsion remains intact under the influence of added foreign molecules and (ii) how stable they are with respect to external perturbation such as temperature. A crucial parameter that determines the stability of microemulsion droplets is the elastic bending rigidity of surfactant monolayer which decorates the nanodomains of water in w/o microemulsions. Elastic bending rigidity of surfactant shell is known to play a decisive

INTRODUCTION Microemulsions (MEs) are thermodynamically stable, macroscopically homogeneous, liquid mixtures of water, oil, and surfactants, where the microscopic inhomogeneities will be present as nanodomains of water and oil. The spontaneous selfassembly and thermodynamic stability of microemulsions is governed by the drastic decrease of interfacial tension between water and oil phases by the surfactant molecules. Depending on the composition of water, oil, surfactants, and external parameters like temperature and pH, rich varieties of selfassembled microstructures can be obtained.1 The manifestation of nanodomains leads to different phases of microemulsion known as lamellar, bicontinuous and droplet, where in droplet phase, domains can be spherical water droplets dispersed in an oil matrix (w/o) or vice versa (o/w). In particular, the investigation of the droplet phase of microemulsions is not only interesting from a fundamental science point-of-view2 but also has attracted considerable attention for its manifold technological applications.3 Incorporation of different guest molecules like polymers, glass forming liquids, and proteins into the microemulsion core2,4,5 is found to have significant effects on properties of microemulsions and also on the dynamics of the guest molecules confined by the fluctuating soft surfactant shell © XXXX American Chemical Society

Received: September 1, 2017 Revised: October 12, 2017 Published: October 18, 2017 A

DOI: 10.1021/acs.langmuir.7b03104 Langmuir XXXX, XXX, XXX−XXX

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and the dipoles present in the polymer chains is one of the important factors that contributes to the increase in the elastic bending rigidity.10,32 It seems plausible that, by tailoring the ion-dipole interaction, the elastic bending rigidity of the surfactant monolayer and the stability of reverse microemulsions can be tuned/controlled and is scantly investigated. The present study focuses on the following aspects: the influence of different hydrophilic polymers having nearly similar size and appreciably different dipole moment on the percolation transition temperature, the phase stability, and the stiffness (elastic bending rigidity) of surfactant monolayer of reverse microemulsion droplets. In order to address these questions, the polymers polyethylene glycol (PEG) and polyvinylpyrrolidone (PVP) having appreciably different dipole moments33,34 have been incorporated into the model reverse microemulsion system water-AOT-n-decane. It has to be noted that both PEG (Mw = 4000 g/mol) and PVP (Mw = 8000 g/ mol) have almost the same number of monomers and nearly equal Rg, such that the relative area of the water−AOT interface occupied by PEG and PVP polymer chains are nearly the same. Interestingly, we observe an increase in elastic bending rigidity up to 46% for the case of PVP-loaded reverse microemulsions in comparison to pure reverse microemulsions, whereas the increase is 17% for PEG-loaded reverse microemulsions. Further, an increase in percolation temperature is observed for PEG-loaded and PVP-loaded reverse microemulsions in comparison to pure reverse microemulsions which indicates the enhancement in elastic bending rigidity. SANS technique is employed to investigate the structure and core radius of reverse microemulsion droplets with and without added polymer molecules. By determining the core radius (R) of droplets and the TP, elastic bending rigidity of the surfactant shell is estimated by following an established procedure for both pure and polymer loaded reverse microemulsions.25 The paper is organized as follows. First we discuss about the percolation phenomena observed in reverse microemulsions and the determination of TP, followed by the influence of two hydrophilic polymers, PEG and PVP, having different dipole moment, on TP. Next the structural investigations of polymer loaded reverse microemulsions performed using SANS are discussed. Then, we turn to address the generic percolation phenomena in pure and polymer loaded reverse microemulsions in detail by discussing the scaling laws of conductivity and the activation energy of percolation. Finally, we establish the increased stability of reverse microemulsions in the presence of added polymers by means of determining the elastic bending rigidity of the surfactant monolayer.

role in controlling the structure and dynamics of the microemulsions and also stabilizes the droplets against thermal fluctuations and entropy driven phase transitions.10−12 Therefore, a detailed understanding of the effect of added polymer molecules on elastic bending rigidity of surfactant shell is relevant for potential applications of PLMEs. A spectrum of experimental techniques like Kerr effect measurements,13,14 ellipsometry,15 neutron spin echo spectroscopy,16,17 and dielectric relaxation spectroscopy (DRS)18 were used to estimate the elastic bending rigidity of the surfactant monolayer and to determine the stability of the droplet phase of reverse microemulsions. Water-in-oil reverse microemulsions stabilized by the anionic, double tailed surfactant, AOT (sodium 1,4-bis(2-ethylhexoxy)-1,4-dioxobutane-2-sulfonate) have been used as model systems for estimating the elastic bending rigidity of the surfactant shell. All of these measurements unequivocally confirm that the elastic bending rigidity of AOT surfactant monolayer is of the order of kBT, and therefore, these nanosized emulsion droplets are highly sensitive to thermal fluctuations.19 On the other hand, a rapid increase of electrical conductivity (∼5 orders of magnitude) with a slight increase in temperature is observed for water-in-oil reverse microemulsions by using dielectric spectroscopy technique.18,20 This phenomenon is known as percolation transition and is directly related to the phase stability of microemulsion droplets.21−23 The effect of different polymers such as polyethylene glycol (PEG)18,24,25 and block copolymers like poly(styrene)-b-poly(ethylene glycol), 26 poly(propylene oxide)-polyglycerol,27 PEG-PI(polyisoprene)-PEG,28 on percolation transition and phase behavior of AOT stabilized reverse microemulsions have been investigated. A water-soluble polymer PEG, known to preserve the droplet structure of reverse microemulsions18,29 and available in a wide range of molecular weights, is chosen as an ideal additive to investigate polymer induced effects on reverse microemulsions.18,25,30 It is reported from the temperature dependent electrical conductivity measurements that, upon incorporation of PEG into the droplet core, the percolation temperature (TP) increases.18,19,25 This observation is corroborated by the stiffening of surfactant shell due to the adsorption of PEG at the surfactant/water interface. The presence of PEG adsorbed onto the surfactant monolayer at the water−surfactant interface is revealed by contrast matching small-angle neutron scattering (SANS) measurements.24,31 A noticeable increase in polydispersity of the droplets is reported upon introducing PEG polymer and is accounted for the adsorption of polymer chains at the surfactant monolayer. Effect of the interaction between added polymer chains and the surfactant monolayers on elastic bending rigidity and the overall phase stability of reverse microemulsions has been investigated in detail by choosing anionic and nonionic surfactants.25,31 For nonionic systems the addition of polymer is found to have no effects on percolation behavior and on the elastic bending rigidity of surfactant shell. For PEG-loaded reverse microemulsions with anionic surfactant AOT, an increase in percolation temperature is reported with the addition of polymer into the droplet core.31 An increase of about 10% in the elastic bending rigidity of surfactant shell has been reported on incorporation of PEG. AOT being an anionic surfactant attracts the dipoles in the polymer chains and thereby ensures the strong attachment of polymer molecules at the surfactant−water interface. Therefore, it is evident that strong ion−dipole interaction between the anionic surfactant

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MATERIALS AND METHODS

Reverse microemulsions with different compositions were prepared by mixing appropriate amounts of AOT surfactant (Sigma-Aldrich, 98% purity) and n-decane (Alfa Aesar, 99% purity), into which deionized Millipore water (σ = 5.5 × 10−8 S/cm) was added and shaken well for several minutes to obtain an optically clear solution. Two parameters, n[H2O] and the volume n[AOT] Vwater + VAOT , define the Vwater + VAOT + Vdecane

the molar ratio of water-to-surfactant W = fraction of the droplets ϕ =

Vdroplets Vtotal

=

composition of water-AOT-n-decane reverse microemulsions. The size of the water core of the microemulsion droplets depends linearly on W and is independent of ϕ for moderate droplet concentrations. The water core radius R for microemulsion droplets is related to W through R ≈ 1.4W Å.18,35 For the present investigation, microemulsions with ϕ = 0.1 and 0.3 and W between 30 and 40 were prepared, such that the corresponding droplet radii are in the range starting from 42 Å up to B


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Figure 1. (a) Measured electrical conductivity σ′ as a function of temperature for reverse microemulsions. The inflection point TP ≈ 29 °C which marks the percolation threshold and the critical point of phase separation TC ≈ 48 °C are shown. (b) The first derivative of logarithmic conductivity σ′ with respect to temperature (d ln σ′/dT, open triangles) and the real part of complex dielectric permittivity ϵ′ (open circles) as a function of temperature are shown. The quantity d ln σ′/dT is sharply peaked and its maximum is almost coinciding with the peak in ϵ′, which also marks the percolation threshold TP. All of the measurements are performed for reverse microemulsions with ϕ = 0.3 and W = 30 at an applied frequency of 104 Hz.

microemulsion with ϕ = 0.3 and W = 30, is shown in Figure 1a. DC conductivity is extracted from the real part of complex conductivity, σ*(ω) = iωϵ0ϵ*(ω), where, ω is the angular frequency, ϵ0 is the permittivity of vacuum and ϵ*(ω) is the complex permittivity of reverse microemulsions.38 In order to minimize the contributions from electrode polarization and dielectric relaxation, the electrical conductivity is measured at a frequency of 104 Hz, in the temperature range starting from 6 to 60 °C. At low temperature (T < 20 °C) a finite DCconductivity of the order of σ′ ≈ 10−8 S/cm is obtained. Although the major phase (oil) of the microemulsion has a negligible electrical conductivity, the observed conductivity is expected to originate from the charge fluctuations,39 i.e., the migration of charged water droplets in the electric field leading to a nonvanishing conductivity value. According to Feldman et al.40 water droplets dispersed in the oil phase do acquire charges by the spontaneous exchange of anionic surfactants present at the droplet interface and the positive Na + counterions released from AOT surfactants. Further, a steep increase in the DC conductivity is observed for a slight increase in temperature, and the temperature dependent DC conductivity shows a sigmoidal behavior, owing to the percolation transition in reverse microemulsions (Figure 1a). The drastic increase in conductivity at percolation transition is attributed to the formation of transient droplet clusters due to the attractive interaction between the droplets,41 which establish a pathway for the flow of electric charges.20,42 The percolation transition is characterized by a threshold temperature TP, which is measured as the maxima of the conductivity gradient and is found to be TP ≈ 29 °C for reverse microemulsions with W = 30 and ϕ = 0.3. Upon further increase in temperature, an abrupt decrease in DC conductivity is observed at TC ≈ 48 °C, which indicates the phase separation of microemulsion droplets.20 Figure 1b shows the temperature dependence of the first derivative of conductivity with respect to temperature, d ln σ′/dT and the dielectric permittivity ϵ′. The temperature dependent permittivity exhibits a local maxima close to the percolation temperature which is in-line with the previous reports.40,43 The peak in permittivity nearly coincides with the maximum of conductivity gradient (d ln σ′/dT) which further facilitates the unambiguous determination of the percolation transition temperature, TP ≈ 29 °C. Next, the influence of two different hydrophilic polymers, PEG and PVP, on the percolation transition temperature of the

56 Å. In all of the SANS measurements, D2O (Sigma-Aldrich, 99.9% pure) was used instead of H2O to obtain better contrast. Further, pure and PVP-loaded microemulsions with W = 33 and ϕ = 0.1 are prepared for SANS measurements under three different contrast conditions given as core contrast (DHH, D2O + AOT + n-decane), shell contrast (DHD, D2O + AOT + deuterated n-decane-d22) and droplet contrast (HHD, H2O + AOT + deuterated n-decane-d22). Here, to obtain DHD and HHD contrast, deuterated n-decane-d22 (Armar isotopes, Switzerland, 99.9% pure) was used. In order to investigate the influence of polymers having different dipole moment on water-AOT-n-decane reverse microemulsions, PEG (Mw = 4000 g/ mol, supplied by Sigma-Aldrich) and PVP (Mw = 8000 g/mol, supplied by Alfa Aesar), having a nearly equal number of monomers and almost = 11.4 Å and RPVP = 14.4 Å), were similar radius of gyration (RPEG g g dissolved in water and was mixed well with the stock solution prepared using n-decane and AOT surfactant. The concentration of polymer in reverse microemulsion is quantified as the average number of polymer chains per droplet, Z =

Npolymer Ndroplet

. In the present work, Z ≃ 1 is

maintained for all PLMEs. In order to investigate the percolation behavior of pure and polymer loaded reverse microemulsions, DRS measurements have been carried out in the frequency range from 1 Hz up to 40 MHz at different temperatures using a Novocontrol Alpha-N High Resolution Dielectric analyzer with active sample cell ZGS as the test interface. Here, a temperature stability better than ±0.1 K is achieved using Novocontrol Quatro Cryosystem. A gold coated parallel plate capacitor with Teflon spacers (BDS1308 model, Novocontrol, Germany) was used as the sample cell for the dielectric measurements. For structural characterization of pure and polymer loaded reverse microemulsions, SANS experiments were performed using SANS-I instrument at the Dhruva Reactor, Bhabha Atomic Research Centre, Mumbai, India.36 The mean wavelength (λ) of the incident neutron beam was 5.2 Å, with a resolution, Δλ/λ, of 15%. The scattering data were collected in the wave vector transfer, Q range of 0.017−0.35 Å−1 (Q = 4π sin(θ/2) /λ, where θ is the scattering angle). Samples were held in HELLMA quartz cells having thicknesses of 2 mm, and a one-dimensional (1-D) position sensitive detector was used to record the scattering data. The temperature of the samples was kept constant at 30 °C in all measurements. Data were corrected for background and empty cell contributions and normalized to absolute cross sectional units using standard procedure. SASfit software37 was used for fitting the measured scattering profiles.

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RESULTS Percolation in PLMEs: Electrical Conductivity Measurements. The variation of direct current (DC) electrical conductivity σ′, as a function of temperature for a reverse C


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the surfactant shell and stabilizes the droplets against thermal fluctuations. Further, for investigating the structural aspects of polymer loaded reverse microemulsions, SANS experiments are performed. Structural Investigations of PLMEs Using SANS. SANS is being extensively used to investigate the structure and interactions in microemulsions.19,27 The coherent differential scattering cross section per unit volume (dΣ/dΩ) as a function of momentum transfer, Q, is measured for pure and polymer loaded reverse microemulsions. For a collection of monodisperse interacting spherical droplets, dΣ/dΩ can be expressed as47

reverse microemulsions is investigated. The water-soluble PEG and PVP molecules possess significantly different dipole moments and are given as 1.0433 and 3.53 D,34,44 respectively (chemical structure of monomer of PEG and PVP are shown in Figure S1 of the Supporting Information). The radii of gyration (Rg) for PEG and PVP molecules are given by RPEG = 11.4 Å g and RPVP = 14.4 Å (RPEG and RPVP are obtained from SANS and g g g are shown in Figure S2 of the Supporting Information) and are smaller than the water core radius of reverse microemulsion droplets. The added polymers are completely dissolved in the water core of the reverse microemulsions. Neither the precipitation of the added polymers nor the turbidity of PLMEs are noticed upon addition of PEG and PVP (photographs showing the optically clear PVP and PEG-loaded reverse microemulsions are given in Figure S3 of the Supporting Information). The measured DC conductivities as a function of temperature for pure, PEG-loaded (Z = 1), and PVP-loaded (Z = 1) reverse microemulsion samples are shown in Figure 2. The behavior of the conductivity curve remains

dΣ (Q ) = nP(Q )S(Q ) + B dΩ

(1)

where n is the number density of microemulsion droplets and is related to volume fraction (ϕ) by the relation, n = ϕ/V, where V is the volume of an individual droplet of microemulsions. P(Q) is the orientational average of the square of the form factor and gives information about shape and size of the particles. S(Q) is the interparticle structure factor coming from the interference of neutrons scattered from different particles, and it describes the interactions between particles and their spatial arrangements. B is a constant that accounts for the incoherent scattering background. The intraparticle structure factor P(Q) is related to the single particle form factor F(Q) as P(Q ) = ⟨|F(Q )|2 ⟩

(2)

When the scatterers are spherical particles of radius R, F(Q) is expressed as F(Q ) = V (ρp − ρs )

3{sin(QR ) − QR cos(QR )} (QR )3

(3)

Figure 2. Electrical conductivities σ′ as a function of temperature for (i) pure reverse microemulsion (ϕ = 0.1 and W = 30), (ii) PEG-loaded reverse microemulsion (one polymer chain per droplet, Z = 1), and (iii) PVP-loaded reverse microemulsion (one polymer chain per droplet, Z = 1) are shown. The electrical conductivity is measured at an applied frequency of 104 Hz. The percolation threshold temperature TP for each measurement is indicated by solid arrows. The increase in TP upon introducing either PEG or PVP is clearly observed.

where ρp and ρs are the scattering length densities of particle (water droplet) and solvent, respectively. For the case of spherical core−shell particles, F(Q) is given as

qualitatively same for all the three cases, while the percolation temperature shifts to higher values upon introducing PEG (ΔTP = +1.6 °C) and further increases for PVP-loaded reverse microemulsions (ΔTP = +3.9 °C). PEG-loaded reverse microemulsions are known to show an increase in TP which is explained by taking into account the stiffening of AOT surfactant shell by the adsorption of PEG polymer chains at the water−AOT interface.2,18,19 Attractive electrostatic interactions between added PEG and AOT facilitate the adsorption of polymers onto the surfactant monolayer and was first discussed by de Gennes.45 A recent report on PEG-loaded reverse microemulsions provides direct evidence for the adsorption of a PEG polymer chain onto the AOT surfactant interface in water−AOT−n-decane reverse microemulsions from smallangle scattering measurements.46 They report a significant increase in Rg of the PEG polymer when it is confined inside the droplet core in comparison to the Rg of PEG in bulk state, which confirms the adsorption of polymer chains at the surfactant−water interface. The adsorption of polymer onto the surfactant monolayer in turn increases the interfacial rigidity of

where R is the core radius, Rd = R + δ is the droplet radius, and δ is AOT shell thickness. Δρcs is the difference in scattering length density between core and shell and Δρsm between shell and matrix. V1 and V2 are the volume of core and droplet (core + shell), respectively. The scattering length densities (SLD) of different components used in this study are given in Table S1(a) of the Supporting Information and are used to calculate the core and shell contrast with respect to the continuous oil matrix. The scattered intensity is averaged with a log-normal distribution in order to account for the polydispersity of microemulsion droplets. The interparticle structure factor S(Q) describes the correlation between the particles, and for noninteracting dilute systems S(Q) = 1. In the present study, SANS profiles for pure and polymer loaded microemulsions are fitted by assuming S(Q) ≈ 1 due to the following reasons: (i) there is no clear signature of S(Q) in the measured SANS profiles for pure and polymer-loaded microemulsions and (ii) the scattering profile for ϕ = 0.1 is found to be scaling with the measured SANS profile for a lower concentration ϕ = 0.05 as shown in Figure S4 of the Supporting Information.

3{sin(QR ) − QR cos(QR )} + V2Δρsm (QR )3 3{sin(QR d) − QR d cos(QR d)}

F(Q ) = V1Δρcs

(QR d)3

D

(4)


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Figure 3. Measured SANS profiles with fitted models for pure (Z = 0) and PVP loaded (Z = 1) microemulsions with ϕ = 0.1 and W = 33 under three different contrast conditions given as (a) core contrast (DHH), (b) surfactant shell contrast (DHD), and (c) droplet contrast (HHD). The schematics of microemulsions in DHH, DHD, and HHD contrast conditions are shown in panels d−f, where the hydrogenated components are shown in blue and deuterated components in yellow. The effective scattering contrast of AOT surfactant shell in the presence of deuterated decane is shown for DHD and HHD contrast as green.

Consequently, SANS profiles have been fitted only by taking the contribution of P(Q). Here, a nonlinear least-square method is used to fit the experimental scattering data with different theoretical models. In order to reveal the structural properties of reverse microemulsions in the presence of PVP polymer, contrast matching SANS measurements are performed for a particular composition of reverse microemulsion given by W = 33 and ϕ = 0.1. The SANS profiles together with fitted models for pure and PVP-loaded reverse microemulsions under three different contrast conditions are shown in Figure 3. In terms of water/ surfactant/oil, the different contrasts employed are given as (i) water core contrast (DHH; Figure 3a), (ii) surfactant shell contrast (DHD; Figure 3b), and (iii) droplet contrast (HHD; Figure 3c). For microemulsions in core contrast condition (DHH; Figure 3a), the scattering is mostly dominated by the D2O core. Here, the contribution of AOT surfactant shell toward scattering is neglected, since AOT surfactant shell has very small contrast (ρAOT − ρn−decane)2 in comparison to that of the D2O core (Table S1(a) in the Supporting Information). Consequently, the SANS profiles for pure and PVP-loaded microemulsions have been fitted by considering the form factor for spherical droplets given by eq 3. In presence of protonated PVP polymer, a slight increase in droplet radius as well as an increase in polydispersity is observed, which is in line with the previous reports for PEG-loaded reverse microemulsions10,48 and are given in Table 1. Herein, the contribution toward scattering from hydrated PVP polymer chain is negligible compared to the D2O core, and hence the scattering from polymer is neglected while modeling the SANS profiles. Further, in order to be sensitive to the AOT surfactant shell, SANS measurements have been performed in shell contrast condition (DHD), where AOT molecules and PVP polymer are protonated whereas water and decane are deuterated (Figure 3b). The peak from the core−shell structure is clearly visible in

Table 1. Droplet Radius and Polydispersity of Pure (Z = 0) and PVP-Loaded (Z = 1) Reverse Microemulsions, with Molar Ratio of Water to Surfactant W = 33 under Different Contrast Conditions Given by Core Contrast (DHH), Shell Contrast (DHD), and Droplet Contrast (HHD) as Estimated from SANS contrast DHH DHD HHD

no. of polymer chains per droplet (Z) 0 1 0 1 0 1

mean droplet radius R (Å) 45.0 46.9 45.0 46.9 46.4 48.2

± ± ± ± ± ±

0.3 0.4 0.3 0.4 0.4 0.6

polydispersity index 0.29 0.32 0.23 0.26 0.32 0.34

± ± ± ± ± ±

0.02 0.03 0.01 0.02 0.02 0.02

thickness of AOT shell δ (Å)

12.0 12.0 12.0 12.0

± ± ± ±

0.9 1.0 0.9 1.0

the scattering profiles. Consequently, the form factor for spherical core−shell particles as given by eq 4 is used to fit the scattering profiles from AOT shell. The polydispersity and shell thickness obtained from the best fit of the SANS data for pure and PVP-loaded reverse microemulsions are shown in Table 1. A slight increase in core radius and polydispersity can be noted in the presence of PVP polymer (Z = 1). Further, for higher concentration of PVP polymer (Z = 3), the polydispersity of droplets increases considerably as indicated by the highly smeared SANS profiles and is shown in Figure S5 of the Supporting Information. The polydispersity and shell thickness obtained from fitting of SANS profiles for pure and PVP-loaded reverse microemulsions (Z = 0, 1, and 3) are shown in Table S2 of the Supporting Information. Next, the topology of PVP loaded microemulsions is investigated in droplet contrast condition (HHD; Figure 3c). Here, deuterated decane is used as the continuous medium, and all other components are protonated. The form factor for the core−shell structure given by eq 4 is assumed to fit the scattering profiles, and the fitting E


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Figure 4. Measured SANS data together with fits (solid lines) for pure (Z = 0) and PVP-loaded reverse microemulsions (Z = 1) with water to surfactant molar ratios of W = 30 (a), 35 (b), 38 (c), and 40 (d). Volume fraction of droplets, ϕ = 0.1 for all cases.

35, 38, and 40 are shown in Figure 4a−d, respectively. The number of PVP chains added per droplet is kept fixed at one (Z = 1). The fitted profiles are calculated by taking into account the form factor for spherical water droplets and a log-normal distribution for their polydispersity. The parameters obtained from the best fit of measured SANS profiles are given in Table 2. A slight increase in core radius and polydispersity of

parameters are given in Table 1. Further we note that, in order to minimize the number of fitting parameters, SANS data in DHD contrast is fitted by keeping the core radius fixed to the value obtained from DHH contrast and shell parameters are used as fitting parameters. Next in HHD contrast, the surfactant shell thickness is kept fixed to the value obtained from the DHD contrast, and the core radius together with the scattering length density of shell are used as fitting parameters. Here, the SLD of surfactant shell is expected to be significantly different from the water core and AOT shell due to the penetration of deuterated decane in the hydrogenous AOT shell (Figure 3f). The scattering length densities for different regions of the microemulsion droplet under different contrast conditions are given in Table S1(b) of the Supporting Information. The SANS analysis in all three different contrast conditions are congruous, and the structural parameters of the microemulsion droplets are obtained reliably for both with and without the added polymer. Moreover, SANS measurements on pure and PVP-loaded microemulsions in all three different contrast conditions unequivocally confirm that the droplet structure remains intact upon PVP addition. For further measurements, pure and polymer loaded microemulsions are investigated in core contrast (DHH) condition. Next, the structural properties such as core radius and polydispersity of droplets for pure, PEG loaded, and PVP loaded microemulsions with different compositions (W) are determined from SANS measurements in DHH contrast. SANS data together with the fits for PEG-loaded reverse microemulsions are shown in Figure S6, and the parameters obtained from the best fit of measured SANS profiles are given in Table S3 of the Supporting Information. Further, the influence of PVP polymer on the shape and size of the reverse microemulsion droplets is addressed. SANS profiles together with fitted models for pure and PVP-loaded reverse microemulsions in DHH contrast condition for ϕ = 0.1 and W = 30,

Table 2. Droplet Radius and Polydispersity of Pure (Z = 0) and PVP-Loaded (Z = 1) Reverse Microemulsions, with Molar Ratios of Water to Surfactant of W = 30, 35, 38, and 40 as Estimated from SANS molar ratio of water to surfactant (W) 30 35 38 40

no. of polymer chains per droplet (Z) 0 1 0 1 0 1 0 1

mean droplet radius R (Å) 41.7 42.5 46.4 47.7 49.4 50.1 51.8 53.5

± ± ± ± ± ± ± ±

0.3 0.4 0.3 0.4 0.3 0.4 0.4 0.4

polydispersity index 0.29 0.32 0.29 0.32 0.29 0.31 0.30 0.31

± ± ± ± ± ± ± ±

0.02 0.03 0.02 0.03 0.02 0.03 0.03 0.03

microemulsion droplets is observed upon incorporation of PVP. The increase in polydispersity is significant for smaller droplets. The SANS measurements unambiguously confirm that the spherical structure of the droplets is preserved even after the incorporation of PVP polymer into the droplet. These observations are consistent with the earlier reports where an enhancement in droplet size as well as polydispersity has been reported upon introducing PEG, whereas the spherical shape of the microemulsion droplets remains largely unaffected.19,48 Scaling Laws of Conductivity and Activation Energy of Percolation. Next, the generic percolation phenomenon in F


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the scaling exponents s and μ are evaluated as a function of W and ϕ and is shown in Figure 6, panels a−c and d−f, respectively. The observed values of the exponents are in excellent agreement with the reported values for dynamic/ stirred percolation phenomena. Theoretical studies and experimental investigations report the values of exponents for dynamic percolation as, s ≈ 0.7−1.6 and μ ≈ 1.2−2.1.2,18 The dynamic percolation model takes into account the formation of finite transient droplet clusters owing to the attractive interactions between the droplets and their dissociation induced by thermal fluctuations. In dynamic percolation model, the huge-increase in electrical conductivity at TP is attributed to the transport of electrical charges through the hopping of ions between nearest neighbor droplet clusters.43,52 In our study, the dynamic percolation model is found to be valid for reverse microemulsions as well as for PEG and PVPloaded microemulsions. Thus, it is inferred that, though the addition of PEG and PVP into the microemulsions increase the percolation threshold temperature, the basic mechanism behind percolation transition remains unaffected. The frequency dependence of electrical conductivity at TP has been studied for microemulsions and PLMEs, and it further endorses the dynamic nature of percolation phenomena. Figure 7a−c show the frequency dependence of conductivity recorded at TP for pure, PEG-loaded, and PVP-loaded reverse microemulsions. It is observed that the DC conductivity becomes nearly independent of frequency below 25 kHz. However, for frequencies above 25 kHz, the conductivity scales as

pure as well as in PEG and PVP-loaded reverse microemulsions is investigated using electrical conductivity measurements. Though the percolation in microemulsions is an activated process,49,50 it is known that the electrical conductivity as a function of temperature follows a scaling law far below and above the percolation transition temperature, TP. The conductivity scaling law is given by43,51 σ ′ ∝ |TP − T |−s

for T < TP

σ ′ ∝ |T − TP| μ

for T > TP

(5)

where s and μ are the scaling exponents of conductivity. The log−log plot of conductivity σ′ versus the reduced temperature, T − TP TP

, is shown in Figure 5a−c for pure, PEG-loaded, and

PVP-loaded reverse microemulsions, respectively. After a rather flat region near TP, a well-defined power-law region in the conductivity plot is clearly observed on either side of TP. The scaling exponents s and μ are extracted from the best fit of the power-law regions with eq 5 and are shown in Table 3. Further,

σ ′ ≈ ωx

(6)

where x = μ/(s + μ) is valid within the experimental uncertainties. The parameter x is extracted from the best fit of the scaling-law region to eq 6. The linear fit to the scalinglaw region is shown in Figure 7, and the obtained values of x are tabulated in Table 3 for pure, PEG-loaded, and PVP-loaded reverse microemulsions. The values of x obtained for the PLMEs are also in agreement with the dynamic percolation model predicted for reverse microemulsions.43 Further, an estimate of the cluster rearrangement time τR at TP is obtained from the onset of scaling-law regime for pure and polymer loaded microemulsions and is listed in Table 3. The values of τR fit quite well to the experimentally reported values for reverse microemulsions.43 τR signifies the time scale associated with diffusion and rearrangement of water droplet clusters in the oil matrix. The effect of polymers on cluster rearrangement time τR at TP is observed to be negligible. Though the polymer molecules increase the stability of microemulsion droplets against thermal fluctuations, the dynamics of diffusion and rearrangement of droplet clusters at TP remain largely unaffected by the incorporation of polymers. This observation is not unexpected because the structure and size of the droplets mostly remains unaltered after the incorporation of polymers. Indeed, according to the Stokes−Einstein relation, the diffusion coefficient of a spherical particle mainly depends on its size, and therefore, it is expected that the τR will change only when the added polymers will significantly alter the size and/or shape of the droplets. The increase in τR with increase in droplet radius is observed for pure microemulsions with different W and is given in Figure S7 and Table S4 of the Supporting Information. Thus, the description of τR in relation with Stokes−Einstein relation and diffusion of ME droplets is justified. Having concluded unambiguously that the dynamic nature of percolation phenomena and the associated hopping of ions

Figure 5. log−log plot showing the scaling behavior of electrical conductivity σ′ above and below the percolation threshold temperature, TP, for (a) reverse microemulsion with ϕ = 0.3 and W = 30, (b) PEG-loaded reverse microemulsion (number of polymer chain per droplet, Z = 1), and (c) PVP-loaded reverse microemulsion (number of polymer chain per droplet, Z = 1). The straight lines are fits to log σ′ using eq 5. G


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Table 3. Conductivity Scaling Exponents, s, μ, and x and cluster rearrangement time τR, for pure, PEG-loaded, and PVP-loaded reverse microemulsions (ϕ = 0.3 and W = 30)a

a

sample

s

μ

x

τR(μs.)

ME ME + PEG ME + PVP

1.26 ± 0.01 1.48 ± 0.01 1.04 ± 0.01

1.67 ± 0.02 1.79 ± 0.02 2.05 ± 0.02

0.64 ± 0.01 0.62 ± 0.01 0.61 ± 0.01

0.69 ± 0.01 0.74 ± 0.01 0.77 ± 0.01

The number of polymer chains per droplet, Z = 1, is maintained for both PEG-loaded and PVP-loaded reverse microemulsions.

Figure 6. Scaling exponents s and μ as a function of water-to-surfactant ratio W for pure reverse microemulsion (a), PEG-loaded reverse microemulsion (b), and PVP-loaded reverse microemulsion (c). Volume fraction of droplets ϕ = 0.3 and is kept fixed for all measurements. Scaling exponents s and μ as a function of ϕ for pure reverse microemulsion (d), PEG-loaded reverse microemulsion (e), and PVP-loaded reverse microemulsion (f). Water to surfactant ratio W = 30 and is kept constant for all samples. The solid lines denote the acceptable range for upper bound and lower bound of s and μ reported in refs 2 and 18.

unit volume, R is the universal gas constant, and T is the absolute temperature. The variation of ln σ′ with inverse of absolute temperature, T−1, for pure, PEG-loaded, and PVPloaded reverse microemulsions is shown in Figure 8. From the slope of the linear portion of the curve, the activation energies Ea for all three systems are estimated to be about 1041 ± 13, 1012 ± 10, and 925 ± 14 kJ/mol, respectively. A decrease in Ea is observed when polymer molecules are incorporated into the microemulsion droplets. A noticeable decrease in Ea ≈ 120 kJ/ mol is recorded for the PVP-loaded reverse microemulsions, whereas the decrease is smaller for PEG-loaded microemulsions. According to Mathew et al.,49 the energy barrier for the mobility and diffusion of Na+ counterions through the charged surfactant shell is defined as activation energy. PEG and PVP polymer chains do get adsorbed onto the surfactant

between the droplet clusters hold good for PLMEs, next the energetics of percolation is studied by determining its activation energy. The interdroplet diffusion of the counterions (Na+) permeating across the surfactant shell proceeds through a steplike barrier, and the threshold energy associated with the permeability of the surfactant monolayer (membrane permeability) is usually known as the activation energy of percolation (Ea). Here, conductivity σ′ follows the Arrhenius-type equation49,50

⎛ −E ⎞ σ′ = A exp⎜ a ⎟ ⎝ RT ⎠

(7)

where A is a constant which depends on the thickness of the surfactant monolayer and the number of charge carriers per H


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Figure 7. log−log plot showing the electrical conductivity σ′ at TP as a function of frequency (ν) for (a) reverse microemulsion with ϕ = 0.3 and W = 30, (b) PEG-loaded reverse microemulsion (number of polymer chain per droplet, Z = 1), and (c) PVP-loaded reverse microemulsion (number of polymer chain per droplet, Z = 1). The straight lines are fits to log σ′ using eq 6.

Figure 8. Arrhenius plot of logarithmic electrical conductivity ln σ′ with inverse of absolute temperature T−1 for (a) pure reverse microemulsion, (b) PEG-loaded reverse microemulsion (Z = 1) and (c) PVP-loaded reverse microemulsion (Z = 1). For all three cases, W = 30 and ϕ = 0.3. The linear fit according to eq 7 is also shown.

⎛ 2πκ ⎞ ξp = a exp⎜ ⎟ ⎝ kBT ⎠

monolayer and screen the charges. Screening of charges at the surfactant head groups facilitates the free diffusion of Na+ ions between the droplets and thereby reduces the activation energy of percolation.53 The lowest value of activation energy observed for PVP-loaded microemulsion indicates the higher degree of screening of charges by PVP at the surfactant monolayer owing to the strong interaction between the AOT surfactant and PVP polymer chains. Elastic Bending Rigidity of the Surfactant Monolayer in PLMEs. The elastic bending rigidity κ of the surfactant monolayer is the key parameter which governs the stability of the droplet phase against thermal fluctuations and also controls the phase transitions in microemulsions. By measuring the structural (shape and size of the droplet) and thermodynamic properties (percolation temperature) of microemulsions, it is possible to estimate the κ by using the formalism developed by de Gennes and Meier.11,25 According to de Gennes, the spontaneous fluctuations of a random interface, which occurs at a smaller length scale, are quantified by the persistence length ξp. The ξp of a random interface is defined as the length scale over which the angular correlations between two points at the interface approaches zero (or strictly speaking, 1/e) and is mathematically given by11

(8)

where κ is the elastic bending rigidity of the interface and a is the lower cutoff in the wavelength of the undulations which is related to the size of the surfactant molecule. A similar expression for ξp but with a different numerical factor in the exponent, has been introduced by Peliti and Leibler54 based on renormalization group theory and is given as ⎛ 4πκ ⎞ ξp = a exp⎜ ⎟ ⎝ 3kBT ⎠

(9)

Gompper and Kroll55 modeled the phase behavior of selfavoiding fluid vesicles by using Monte Carlo simulations and arrived at the same expression for ξp as given in eq 9. Meier25 had used the concept of ξp to elucidate the form fluctuations, the percolation dynamics, and the stability of the droplet phase in reverse microemulsions. Moreover, an appropriate definition for ξp in the context of microemulsions has been put forward by Meier,25 as the upper limit of the length scale over which the oil/water interface remains constantly curved. Thus, if the microemulsion droplets have a radius R < ξp, it will be spherical, I


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Langmuir whereas when R > ξp, the structure will be nonspherical or bicontinuous. From eq 9, it can be inferred that ξp of the interface decays exponentially with increase of temperature. Accordingly, for microemulsions, the transition from R < ξp to R > ξp can be achieved by changing the temperature. The threshold temperature where the transition from the spherical droplet phase to the nonspherical droplet phase occurs is defined as the percolation transition temperature TP. Therefore, at T = TP, ξp ≈ R and eq 9 will transform to ⎛ 4πκ ⎞ ln R ∝ ⎜ ⎟ ⎝ 3kBTP ⎠

(10)

where R is the droplet radius in angstrom and TP is the percolation threshold temperature expressed in absolute scale. By measuring the dependence of TP on the size of droplets (radius R), the elastic bending rigidity of the surfactant monolayer, κ, can be estimated using eq 10. The logarithmic radius of the water core R obtained from SANS is plotted against the reciprocal of percolation temperature (TP) for pure, PEG-loaded, and PVP-loaded reverse microemulsions and are shown in Figure 9a−c, respectively. As predicted by eq 10, droplet radius R scales linearly with inverse temperature, and from the slope of the plot, κ ≈ 2.08 ± 0.04 kBT is obtained for pure microemulsions. It has been reported18 that the value of κ ranges from 0.2 to 3.8 kBT for AOT stabilized reverse microemulsions, and the obtained value of κ fits well in this range. Similarly, from Figure 9b the elastic bending rigidity of the surfactant monolayer for PEG-loaded microemulsions is found to be κ ≈ 2.43 ± 0.04 kBT. Thus, an increase in elastic bending rigidity of the surfactant shell ∼17%, in comparison to pure microemulsions, is observed when PEG polymer molecules are incorporated into the droplet core and is in good agreement with the reported literature values for PEGloaded reverse microemulsions.19,25 For PVP-loaded reverse microemulsions, the value of κ ≈ 3.04 ± 0.04 kBT is estimated from Figure 9c. A considerable increase in elastic bending rigidity of the surfactant shell amounting to ∼46% as compared to pure reverse microemulsions is obtained upon the addition of one PVP polymer molecule into the microemulsion droplet core. In fact, the augmented elastic bending rigidity for PVP incorporated microemulsions signifies the increased stability of spherical droplet phase against external thermal fluctuations. In the present study, the droplet size of pure MEs and PLMEs are measured at ambient temperature (∼30 °C), assuming that the droplet radius remains largely invariant with increase in temperature for pure microemulsions as well as for PLMEs when the concentration of polymer chains per droplet is small (here, for all cases, Z = 1). Recently, Kuttich et al.10 put forward the necessity for determining the droplet size at TP and reported a 3-fold increase in bending modulus when the droplet size measured at TP was taken into account for bending modulus estimation. However, the discrepancy in determination of bending modulus from the droplet size measured at room temperature and at TP is stronger for high concentrations of added polymers (Z = 2, 3, ...) and almost insignificant for pure microemulsions as well as low concentrations of added polymer (Z = 1). Here, the error involved in neglecting the temperature dependence of core radius R is estimated as ∼18%.

Figure 9. Logarithmic droplet core radius as a function of reciprocal of percolation temperature, TP, for (a) pure reverse microemulsion, (b) PEG-loaded reverse microemulsion (Z = 1), and (c) PVP-loaded reverse microemulsion (Z = 1), with droplet volume fraction ϕ = 0.1 and with different water to surfactant ratio, W. The lines show the fits according to eq 10.

nonionic PEG polymer molecules.19,25 For addition of PEG molecules up to three polymer chains per droplet, the increase in elastic bending rigidity of the surfactant monolayer is found to be moderate.19 Herein, we report a considerable increase in elastic bending rigidity for microemulsions, amounting to about 46% by adding one nonionic PVP polymer chain per droplet. The observed increase in elastic bending rigidity for PVP loaded MEs is attributed to the strong adsorption of PVP chains onto the AOT surfactant monolayer facilitated by the enhanced electrostatic interactions between anionic AOT and PVP polymer chains. The adsorption of nonionic (neutral) polymers onto the anionic surfactants is known in the literature and is discussed below. The thermodynamical favorable conditions for the adsorption of flexible neutral polymers onto the surfactant films have been spelled out by de Gennes.45 Further, Nagarajan56 has developed a unified thermodynamic theory which explains the association of nonionic polymer molecules with charged surfactant aggregates owing to the enhanced shielding of hydrophobic tail groups of surfactant molecules from water. From their detailed free energy calculations, the wrapping of

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DISCUSSION The elastic bending rigidity of reverse microemulsion droplets has been reported to increase up to 18% upon addition of J


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per monomer.33 The monomer of PVP has a permanent dipole moment of 3.53 D directed from O to C of the carbonyl group present at the side chain of the polymer molecule44 and is about three times higher than PEG. The effective interaction potential for the monovalent SO3− ion present in AOT and the dipoles present in PVP and PEG polymer chains is evaluated according to eq 11, as a function of distance, rd, inside the water droplet and is shown in Figure S8 of the Supporting Information. The interaction energy is found to be higher for PVP in comparison to PEG, for example, at a distance of 2 Å, from the surfactant molecule, the attractive interaction potential between AOT and PVP is about 15 times higher than that for PEG. The strong attraction between dipoles present in PVP polymer chains and ions at AOT surfactant governs the stronger adsorption of PVP polymer chains onto the AOT surfactant monolayer, which leads to the enhancement of elastic bending rigidity for PVPloaded microemulsions. Moreover, the canonical resonance structure of PVP forms a partial negative charge on oxygen atoms, which makes the polymer weakly cationic.32,60 Consequently, as Breuer and Robb reported,61 the reactivity of PVP polymer molecules with anionic surfactants is much higher in comparison to that of PEG. The presence of a higher dipole moment and the weakly cationic nature of PVP result in stronger interaction/reactivity of PVP polymer molecules with the AOT surfactant monolayer in comparison to PEG polymer chains. In conclusion, the enhanced stiffening/rigidification of the AOT surfactant monolayer is attributed to the strong adsorption of PVP polymer chains onto the surfactant monolayer owing to the enhanced ion−dipole interaction between the AOT and PVP molecules.

polymer chains around the surfactant−water interface have been emphasized. Furthermore, from the force profile measurements for emulsion droplets with charged surfactants in the presence of neutral polymers, Philip et al.57 have shown that, in the presence of charged surfactant molecules, the neutral polymer chains at the surfactant−water interface transform into partial polyelectrolytes. These weak polyelectrolyte chains stretch and decorate the surfactant layer by virtue of their intrachain electrostatic repulsion. From the present work, the increase in the percolation temperature of PLMEs, the decrease in activation energy of percolation and the scaling of Rg of added PVP chains with droplet size strongly indicate that the PVP polymer chains are getting adsorbed onto the surfactant monolayer at the interface. This adsorption of added polymer molecules onto the surfactant monolayer indeed increases the stiffness of the surfactant shells and stability of microemulsion droplets. Next, we turn to discuss the role of electrostatic interactions between the added polymers and anionic AOT in the enhancement of elastic bending rigidity of microemulsion droplets. An extensive investigation on surfactant−polymer complexes has been carried out by Saito,58 for the SDS surfactant-PVP polymer system. According to Saito, the electrostatic ion− dipole interaction between the polar sites in the polymer chains and the charged surfactants leads to the binding of the polymers onto the surfactant headgroups, and the polymer chains were found to position themselves parallel to the surfactant molecules. Further, Goddard32 has reported the interactions between neutral water-soluble polymers and charged surfactants, where the mechanism of formation of polymer−surfactant complexes has been addressed. It has been argued that, when a water-soluble polymer is incorporated into the surfactant aggregate, the association between the dipole of the hydrophilic group of the polymer and the ionic headgroup of the surfactant does occur. In light of these reports, the interactions of PEG and PVP with the anionic surfactant AOT have to be taken into account to get further insight into the enhanced interfacial rigidity and the phase stability of PLMEs. A considerable increase in elastic bending rigidity has been obtained for PVP-loaded microemulsions, in comparison to that of PEG-loaded microemulsions. Although, both the polymers PEG and PVP do get adsorbed onto the surfactant shell, the strength of the ion−dipole interaction between the added polymer and AOT decides the elastic bending rigidity of the surfactant shell and the stability of the microemulsions droplets. The electrostatic interaction between an electric dipole and a charged ion with valency Z, separated by a distance rd in a medium having relative permittivity ϵr, is directly proportional to the dipole moment (p⃗) as per the formula, Zepcos θ ϕ= , where θ is the angle between p⃗ and rd⃗ . In the 4πϵ ϵ r 2

■

The influence of two hydrophilic polymers PEG and PVP, having nearly the same number of monomers and similar Rg, on the percolation dynamics and the elastic bending rigidity, κ, of the reverse microemulsion droplets is investigated. Upon incorporation of PVP polymer chains into the microemulsion droplet, the elastic bending rigidity of the surfactant monolayer increases up to ∼46%, whereas for PEG-loaded microemulsions the corresponding increase is ∼17%. Moreover, an increase in percolation threshold temperature (TP) and decrease in activation energy of percolation (Ea) are observed for PLMEs and is attributed to the stiffening of surfactant monolayer by the adsorption of polymer chains at the surfactant−water interface. Notably, the increase in TP and κ and decrease in Ea are higher when PVP polymer chains are incorporated into the microemulsion droplet. We conjecture that the root cause for the considerable variation in TP, Ea, and κ for PVP-loaded microemulsions is the higher dipole moment of PVP molecules than that of PEG molecules. The increased dipole strength indeed leads to stronger interaction between the PVP molecules with the anionic AOT monolayer which facilitates the stronger adsorption of polymer chains onto the surfactant− water interface. Further, structural investigations using SANS for PLMEs confirm that the droplets remain intact upon the addition of PVP and PEG. Furthermore, the scaling exponents of conductivity evaluated for pure and polymer loaded microemulsions establish the dynamic picture of percolation in reverse microemulsions.

0 rd

presence of other molecules, the interaction between the ion and the dipole gets modified, and the effective interaction is given by the Boltzmann weighted interaction potential59

ϕeff =

−γ 2 6rd4

CONCLUSIONS

(11)

where γ is the strength parameter given as, γ = βZep/(4πϵ0ϵr), and β is the reciprocal of the thermodynamic temperature of a system. In PEG polymer chains, oxygen atoms are present at every third position of the polymer backbone which act as an electron donor and have an effective dipole moment of 1.04 D K


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(9) Zhao, X.; Tapec-Dytioco, R.; Tan, W. Ultrasensitive DNA Detection Using Highly Fluorescent Bioconjugated Nanoparticles. J. Am. Chem. Soc. 2003, 125, 11474−11475. (10) Kuttich, B.; Grefe, A. K.; Stühn, B. Changes in the Bending Modulus of AOT Based Microemulsions Induced by the Incorporation of Polymers in the Water Core. Soft Matter 2016, 12, 6400−6411. (11) De Gennes, P.; Taupin, C. Microemulsions and the Flexibility of Oil/Water Interfaces. J. Phys. Chem. 1982, 86, 2294−2304. (12) Helfrich, W. Elastic Properties of Lipid Bilayers: Theory and Possible Experiments. Z. Naturforsch., C: J. Biosci. 1973, 28, 693−703. (13) Van der Linden, E.; Geiger, S.; Bedeaux, D. The Kerr Constant of a Microemulsion for a Low Volume Fraction of Water. Phys. A 1989, 156, 130−143. (14) Meier, W. Kerr Effect Measurements on a Poly(oxyethylene) Containing Water-in-Oil Microemulsion. J. Phys. Chem. B 1997, 101, 919−921. (15) Binks, B. P.; Meunier, J.; Abillon, O.; Langevin, D. Measurement of Film Rigidity and Interfacial Tensions in Several Ionic SurfactantOil-Water Microemulsion Systems. Langmuir 1989, 5, 415−421. (16) Farago, B.; Richter, D.; Huang, J.; Safran, S.; Milner, S. Shape and Size Fluctuations of Microemulsion Droplets: the Role of Cosurfactant. Phys. Rev. Lett. 1990, 65, 3348. (17) Huang, J.; Milner, S.; Farago, B.; Richter, D. A Study of Dynamics of Microemulsion Droplets by Neutron Spin Echo Spectroscopy. Physics of Amphiphilic Layers; Springer: Berlin, 1987; pp 346−352. (18) Wipf, R.; Jaksch, S.; Stühn, B. Dynamics in Water-AOT-nDecane Microemulsions with Poly(ethylene glycol) Probed by Dielectric Spectroscopy. Colloid Polym. Sci. 2010, 288, 589−601. (19) Kuttich, B.; Falus, P.; Grillo, I.; Stühn, B. Form Fluctuations of Polymer Loaded Spherical Microemulsions Studied by Neutron Scattering and Dielectric Spectroscopy. J. Chem. Phys. 2014, 141, 084903. (20) Di Biasio, A.; Cametti, C.; Codastefano, P.; Tartaglia, P.; Rouch, J.; Chen, S. Phase Behavior of Dense Three-Component Ionic Microemulsions and Electrical Conductivity in the Lamellar Phase. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1993, 47, 4258. (21) Kim, M. W.; Huang, J. S. Percolationlike Phenomena in OilContinuous Microemulsions. Phys. Rev. A: At., Mol., Opt. Phys. 1986, 34, 719. (22) Jada, A.; Lang, J.; Candau, S. J.; Zana, R. Structure and Dynamics of Water-in-Oil Microemulsions. Colloids Surf. 1989, 38, 251−261. (23) Chen, S. H.; Chang, S. L.; Strey, R. Structural Evolution within the One-Phase Region of a Three-Component Microemulsion System: Water-n-decane-sodium-bis-ethylhexylsulfosuccinate (AOT). J. Chem. Phys. 1990, 93, 1907−1918. (24) Schübel, D.; Bedford, O. D.; Ilgenfritz, G.; Eastoe, J.; Heenan, R. K. Oligo-and Polyethylene Glycols in Water-in-Oil Microemulsions. A SANS Study. Phys. Chem. Chem. Phys. 1999, 1, 2521−2525. (25) Meier, W. Poly(oxyethylene) Adsorption in Water/Oil Microemulsions: A Conductivity Study. Langmuir 1996, 12, 1188− 1192. (26) Appel, M.; Spehr, T. L.; Wipf, R.; Moers, C.; Frey, H.; Stühn, B. Micellar Interactions in Water-AOT Based Droplet Microemulsions Containing Hydrophilic and Amphiphilic Polymers. J. Chem. Phys. 2013, 139, 184903. (27) Wipf, R.; Kraska, M.; Spehr, T.; Nieberle, J.; Frey, H.; Stühn, B. Interaction Between a Water-in-Oil Microemulsion and a LinearDendritic Poly(propylene oxide)-Polyglycerol Block Copolymer. Soft Matter 2011, 7, 10879−10888. (28) Blochowicz, T.; Gögelein, C.; Spehr, T.; Müller, M.; Stühn, B. Polymer-Induced Transient Networks in Water-in-Oil Microemulsions Studied by Small-Angle X-ray and Dynamic Light Scattering. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2007, 76, 041505. (29) Schübel, D.; Ilgenfritz, G. Influence of Polyethylene Glycols on the Percolation Behavior of Anionic and Nonionic Water-in-Oil Microemulsions. Langmuir 1997, 13, 4246−4250.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b03104. Chemical structure of the monomer of PEG and PVP. SANS profiles for PEG and PVP polymers dissolved in D2O. Optical photographs of pure, PEG-loaded, and PVP-loaded reverse microemulsion samples and of PEG in decane and PVP in decane samples. SANS data for microemulsions having volume fractions of ϕ = 0.05 and 0.1. Table showing the neutron scattering length density for different components used in the present study. SANS profiles and fitting parameters for pure and PVPloaded MEs (Z = 0 , 1, and 3) in DHD contrast. SANS profiles and fitting parameters for PEG-loaded microemulsions with W = 30, 35, and 38 and ϕ = 0.1. Plot and table showing cluster rearrangement time τR, for MEs with W = 20, 30, and 40 and ϕ = 0.3. The plot showing the effective interaction energy for the monovalent SO3− ion and the dipoles present in PVP and PEG polymer chains as a function of distances rd inside the water droplet. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91 (0) 44 2257 4899. ORCID

Vinod K. Aswal: 0000-0002-2020-9026 Dillip K. Satapathy: 0000-0002-3083-655X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS P.M.G. and D.K.S. thank Basavaraj M. Gurappa, Department of Chemical Engineering, IIT Madras for helpful discussions. This work is supported by funding from UGC-DAE Consortium For Scientific Research and NFSC scheme, IIT Madras.

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