Phase Behavior of Nonionic Microemulsions with Multi-end-capped

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Phase Behavior of Nonionic Microemulsions with Multi-end-capped Polymers and Its Relation to the Mesoscopic Structure Paula Malo de Molina,*,†,# Franziska Stefanie Ihlefeldt,† Sylvain Prévost,†,‡,∇ Christoph Herfurth,§,∥ Marie-Sousai Appavou,⊥ André Laschewsky,§,∥ and Michael Gradzielski*,† †

Stranski-Laboratorium für Physikalische und Theoretische Chemie, Institut für Chemie, Technische Universität Berlin, Strasse des 17 Juni 124, Sekr. TC7, 10623 Berlin, Germany ‡ Soft Matter Department, Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, 14109 Berlin, Germany § Fraunhofer Institut für Angewandte Polymerforschung IAP, Geiselbergstrasse 69, 14476 Potsdam-Golm, Germany ∥ Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24−25, 14476 Potsdam-Golm, Germany ⊥ Jülich Centre for Neutron Science (JCNS), Forschungszentrum Jülich GmbH, Outstation at MLZ, Lichtenbergstrasse 1, 85747 Garching, Germany S Supporting Information *

ABSTRACT: The polymer architecture of telechelic or associative polymers has a large impact on the bridging of self-assembled structures. This work presents the phase behavior, small angle neutron scattering (SANS), dynamic light scattering (DLS), and fluorescence correlation spectroscopy (FCS) of a nonionic oil-in-water (O/W) microemulsion with hydrophobically end-capped multiarm polymers with functionalities f = 2, 3, and 4. For high polymer concentrations and large average interdroplet distance relative to the end-toend distance of the polymer, d/Ree, the system phase separates into a dense, highly connected droplet network phase, in equilibrium with a dilute phase. The extent of the two-phase region is larger for polymers with similar length but higher f. The interaction potential between the droplets in the presence of polymer has both a repulsive and an attractive contribution as a result of the counterbalancing effects of the exclusion by polymer chains and bridging between droplets. This study experimentally demonstrates that higher polymer functionalities induce a stronger attractive force between droplets, which is responsible for a more extended phase separation region, and correlate with lower collective droplet diffusivities and higher amplitude of the second relaxation time in DLS. The viscosity and the droplet self-diffusion obtained from FCS, however, are dominated by the end-capped chain concentration.

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their solvophobic energy (∼1−1.2 kBT per CH2 group10). If the drops are further apart than the chain length, the polymer forms loops with two ends localized in the same droplet. When the drops are close enough (at a distance of the order of the end-to-end distance of the polymer), the polymer forms bridges with the two ends preferentially in different droplets. The formation of bridges leads to the formation of clusters of droplets and, above the polymer percolation concentration, an infinite network of droplets spans the entire volume leading to a significant increase of the viscosity.8 Such networks exhibit viscoelastic behavior generally with only one characteristic relaxation process that can be described by a Maxwell model.6,7 The relaxation time of the network depends on the length of the hydrophobic end-group, which determines the residence time of the end-group in the

INTRODUCTION Microemulsions (MEs) are homogeneous, thermodynamically stable, and finely dispersed mixtures of oil and water stabilized by a surfactant film.1 MEs may occur in the form of oil-in-water (O/W) and water-in-oil (W/O) droplets, or as bicontinuous structures.2 They are attractive formulations for applications where a highly interdispersed system is required, for instance as carriers of hydrophobic active agents, substrates, or enzymes in aqueous environments. Dilute microemulsions have the viscosity of its continuous component (or the average of both for the case of bicontinuous systems)3,4 irrespective of their structure and are, therefore, generally low viscous liquids. Many applications of microemulsions, however, require a precise control of their rheological properties. An effective way to enhance the viscosity of droplet microemulsions is by the addition of telechelic polymers,5−8 which typically are hydrophilic linear chains with two hydrophobic end-groups. The end-groups, or ”stickers”, partition into the microemulsion droplets uniformly9 due to © XXXX American Chemical Society

Received: March 4, 2015 Revised: April 15, 2015

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DOI: 10.1021/acs.langmuir.5b00817 Langmuir XXXX, XXX, XXX−XXX

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Figure 1. (a) Generic phase diagram of microemulsion with a linear polymer with two end stickers. The telechelic polymers can either loop on a single droplet or bridge two droplets leading to the formation of droplet clusters or a network above the percolation threshold. (b) Schematic representation of multiarm telechelic polymers with two, three, and four end-capped arms and chemical structure of dodecyl end-capped poly(N,Ndimethylacrylamide) (PDMA) with f arms.

hydrophobic end-cap, leading to viscosity increases of up to 6 orders of magnitude. The polymers were relatively long compared to the distance between the droplets and introduced an increasing repulsive interaction between the microemulsion droplets with increasing polymer concentration, regardless of the polymer architecture, without affecting the ME size. However, polymers with higher functionality are more efficient in bridging the droplets, as indicated by a stronger increase in viscosity and pronouncedly larger amplitudes for the cluster relaxation modes observed in DLS. Neutron spin−echo experiments showed that, with decreasing polymer functionality, there are less free ME droplets. Hence, the number of droplets in clusters is higher but the average cluster size is decreased; i.e., an individual cluster consists of a lower number of ME droplets.24 However, the effect of the number of end-capped arms of telechelic polymers on the phase behavior of polymer/ microemulsion mixtures and its relation to the interdroplet interaction, which is of practical and fundamental interest, has not yet been addressed. To fill this gap, here we present the phase behavior of a nonionic microemulsion with droplet size of 6.1 nm and end-capped PDMA polymers with two, three, and four end-capped arms (Figure 1b). We show that there is a systematic and pronounced shift of the phase boundary with the number of stickers per polymer. This is due to an increased attraction with increasing number of bridging arms as determined by SANS. In order to provide a full picture, we discuss the structure and interactions by SANS, viscosity, DLS, and fluorescence correlation spectroscopy (FCS) results along two lines of the phase diagram: (1) increasing the number of stickers per droplet r at a constant d/Ree and (2) increasing d/ Ree at a constant r.

microemulsion droplet, in a fashion similar to that wellestablished for micellar kinetics.11 Dynamic light scattering (DLS) measurements show a fast diffusive relaxation time associated with the collective diffusion of the droplets and a slow mode with a relaxation time of the same order of magnitude as the structural relaxation measured with rheology.12 In the cases where the polymer length is significantly larger than the interdroplet distance, DLS shows a rather complex behavior with various relaxation times requiring an additional relaxation mode for the description.12,13 Typically, the admixture of telechelic polymer does not lead to a significant change of the droplet size, as confirmed by small angle neutron and X-ray scattering (SANS/SAXS) results, but only to a change on their interaction potential.5,6,8,13−15 The interaction has three contributions: (1) The interaction between the droplets without polymer (excluded volume15 or Yukawa repulsion for charged surfactants16), (2) an entropic attraction induced by the bridging polymer, and (3) a soft repulsion caused by the self-excluding polymer chains between the droplets.17,18 Depending on the relative importance of these contributions, the net interaction is attractive or repulsive. If the net interaction is attractive enough, the system exhibits a phase separation between a fluid sol phase and a polymer rich network phase19 (Figure 1a). The attractive interaction that leads to phase separation has a purely entropic origin since the increase in polymer configurations overcomes the entropy loss due to the phase separation and the formation of a dense phase.20 Thus, it should not depend on the sticker length but only on the relative length of the polymer compared to the separation between the droplets. It was experimentally demonstrated that the end-group does not influence the phase behavior,19 but phase separation can be suppressed by introducing additional repulsive interactions.16 The effect of the polymer architecture on the structure and dynamics of ME networks has also been reported by studying the addition of hydrophobically end-capped multiarm poly(N,N-dimethylacrylamide) (PDMA) polymers (Figure 1b) to bridge a tetradecyldimethylamine oxide (TDMAO)/decane ME.21 These polymers were efficiently synthesized by reversible addition−fragmentation chain transfer (RAFT) polymerization.22,23 They are able to form networks with ME droplets, and the viscosity strongly increases with the length of the

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EXPERIMENTAL SECTION

Materials. Brij30 (C12H25EO4), Triton X100 (C14H22EO9.5), and n-decane (>98%) were purchased from Sigma-Aldrich. D2O (>99.9% isotopic purity) was obtained from Eurisotop. All chemicals were used as received without further purification; more details are given in the Supporting Information (SI). The multi- end-capped polymers were synthesized using RAFT polymerization. All details concerning synthesis and characterization of the polymers have been described before.23 B


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wavelength. In an FCS experiment, the fluctuations of fluorescence intensity over time inside a confocal volume are measured. The transversal radius ωxy = 0.4 μm and ellipticity S = 5 of the confocal volume were determined using the same experimental setup and measuring a solution of 0.62 nM of rhodamine 6G in MilliQ water assuming a diffusion coefficient value of 4.0 × 10−10 m2 s−1.28 The triplet state relaxation time appears at much shorter times, and it was not necessary to be taken into account.

Sample Preparation and Phase Behavior. The microemulsion was prepared by mixture of the oil (n-decane) and surfactants, Brij 30 and Triton X100, in D2O and stirring until the solution was homogeneous and transparent. The mass ratio Brij 30 to Triton X 100 (0.81) was chosen so that the cloud point of the microemulsion remains over 30 °C. A transparent and stable phase was found up to an oil to surfactant volume ratio of 0.72, when phase separation occurred (emulsification failure). Accordingly, we chose the oil to surfactant volume ratio to be 0.61, i.e., not too close to the phase boundary but still in the range of spherical microemulsion droplets. The microemulsion can be diluted over the range of 1−20% volume fraction, and the microemulsion droplets are spherical without significant variations in the droplet size (Figure 2). All samples in this study were prepared in D2O to avoid potential shifts in the phase behavior when exchanging the solvent to H2O and to allow for deriving a selfconsistent picture. Polymer−microemulsion mixtures were prepared by addition of polymer to a concentrated microemulsion solution and mixed mechanically. The samples were stored at 20 °C. The phase behavior was determined by visual inspection after several days of preparation, the time required for phase separation to take place. This time became longer when the samples were highly viscous. In practice, we could speed up the process by mild centrifugation of the samples. The samples which did not climb the walls of the sample container during vigorous vortex mixing were designated as the network phase. Small Angle Neutron Scattering. SANS measurements were done on the instrument KWS1 of the Jülich Center for Neutron Sciences at the Forschungs-Neutronenquelle Heinz Meier-Leibnitz (JCNS at FRMII, Munich, Germany),25 with scattered neutrons recorded on a 128 × 128 6Li scintillation detector with a CCDs detector of 68 × 68 cm2. A wavelength of 4.5 Å (full width at halfmaximum (fwhm), 10%) and sample-to-detector distances of 1.2, 7.7, and 20 m were employed with collimation at 4, 8, and 20 m, respectively, thereby covering a q-range of 0.03 < q < 5.2 nm−1. The data were reduced using the BerSANS software program,26 correcting measured intensities for the transmission, dead-time, detector background (with B4C as a neutron absorber at the sample position), sample background (empty cuvette), and the absolute scale (obtained from a tabulated value of a 1.5 mm sheet of Plexiglas). Samples were contained in quartz cuvettes (QX, Hellma) of 0.5, 1, or 2 mm thickness depending on the droplet concentration and measured at 25 °C. The incoherent background caused mainly by the protons was determined at high scattering angle, set as a constant and subtracted from the data. The data analysis of the experimental data with the model of polydisperse core−shell spheres with a hard sphere or a hard sphere and two Yukawa structure factor was done using implemented models in the National Institute of Standards and Technology IGOR software package.27 Dynamic Light Scattering. DLS measurements were performed at 25 °C using a setup consisting of an ALV/LSE-5004 correlator, an ALV CGS-3 goniometer, and a He−Ne Laser with 632.8 nm wavelength. Cylindrical sample cells were placed in an index matching toluene vat. Intensity autocorrelation functions were recorded at angles between 50° and 130°. In the case of Gaussian scatterers and ergodic systems the intensity autocorrelation function g2(t) measured in a homodyne experiment is related to the electric field autocorrelation function |g1(t)| by the Siegert relation as g(2)(t) = 1 + B|g(1)(t) |2, where B is an instrumental constant that reflects the deviations from ideal correlation and that has an ideal value of 0.33 in this setup. Viscosity. Viscosity measurements were done using a calibrated micro-Ostwald capillary viscometer (Schott) types Ic and IIc (diameter of Ic, 0.84 ± 0.01 mm; diameter of IIc, 1.50 ± 0.01 mm; capillary constant (K) for Ic, 0.03 mm2/s; K for IIc, 0.3 mm2/s; calibrated by the provider). The viscosity was calculated from the fluid flow time as η0 = ρKt, where η0 is the zero shear viscosity, ρ the sample density, K a calibration constant, and t the measured flow time. Fluorescence Correlation Spectroscopy. FCS measurements were performed with a Leica TCS SP5 II system. The hydrophobic tracer Nile red was excited with an Ar ion laser with 514 nm

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RESULTS AND DISCUSSION System Description. In this work we studied the addition of telechelic multiarm polymers to a nonionic O/W microemulsion consisting of Brij 30/Triton X100/decane (31.4/ 38.9/29.7 (wt %)) in D2O. In order to do so, we first characterized the microemulsion without polymer. Figure 2

Figure 2. SANS intensity patterns of the pure microemulsion system TX100/Brij30/decane/D2O for different core volume fractions ϕc. Lines: Fits using eq 1 for a core−shell-hard-sphere model (solid) and a core−shell-one-Yukawa (dashed). Inset: schematic representation of a ME droplet with an oil core radius Rc and hydrated PEO shell of effective thickness tsh.

shows the SANS patterns of the pure microemulsion for different droplet volume fractions. The scattering curves have a similar shape with an oscillation at q ∼ 0.8 nm−1, which is an indication that size and polydispersity of the microemulsion droplets are rather independent of concentration. With increasing droplet volume fraction a correlation peak appears that can be attributed to the steric repulsion of the droplets. In order to describe the SANS curves in a quantitative fashion, we employed a particle model, where the scattering intensity is given by I(q) = 1NV 2Δρ2 P ̅(q) S(̃ q)

(1)

1

where N is the number density of scatterers, V their volume, Δρ the difference between the coherent scattering length density of the particle and the one of the solvent, P̅(q) the form factor, and S̃(q) the effective structure factor that takes into account the interactions between the aggregates. Microemulsions with ethoxylated surfactants have a core−shell type structure with a core formed by hydrophobic chains and a shell composed of hydrated PEO chains29 (inset Figure 2). Here, the scattering length density of the core (ρc = −0.3 × 1010 cm −2) and the shell (ρsh = 4.4 × 1010 cm −2) are sufficiently different from one another and to that of the solvent (ρD2O = 6.36 × 1010 cm −2) that the ME droplet cannot be considered as a homogeneous sphere. Thus, we used a form factor for a core− shell sphere where the core radius has a Schulz−Zimm C


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Table 1. Polymer Parameters: Polymer Functionality f, Molar Mass as Weight (Mw) and Number Average (Mn) and Polydispersity Index (PDI) As Determined by GPC;23 DMA Units per Arm (n) As Calculated from Mn; and End-to-End Distance of Two Arms (Ree) polymer

f

Mw/KDa

Mn/KDa

PDI

n

Ree(2arms)/nm

(C12PDMA)2 (C12PDMA)3 (C12PDMA)4 (C12PDMA)3

2 3 4 3

25.3 36.5 51.8 92.3

22.4 30.2 40.5 61.4

1.13 1.21 1.28 1.50

109 99 99 203

14.7 13.9 13.7 20.2

Figure 3. Phase behavior of the microemulsion upon addition of (a) (C12PDMA)2, (b) (C12PDMA)3, and (c) (C12PDMA)4. There are three regions: fluid (black vertical lines), network (blue diamonds), and two phase region (red asterisks) (determined by visual inspection). (d) Combined phase diagram for f = 2, 3, and 4 of similar arm length and higher molecular weight (C12PDMA)3 (f = 3). Along lines A and B, viscosity, SANS, DLS, and FCS experiments were done.

The scattering curves were fitted to eq 1 using a model of polydisperse core−shell hard spheres. Within this model the scattering intensity is given by three adjustable parameters: R̅ c, σ, and tsh (which we assume to be fixed). The fits, represented by the solid lines in Figure 2, are in very good agreement with the experimental data. The best-fit parameters for the core radius and polydispersity (inset of Figure 2) vary very little with the droplet concentration. From these results we derive that R̅ c = 4.9 nm, σ ≈ 0.2, and tsh = 1.2 nm remain constant for all droplet core volume fractions between 0.003 and 0.07 within experimental accuracy. Only for the highest volume fraction there was a slight deviation in the low q regime that we attribute to an additional steric repulsion by the longer PEO chains of the surfactant Triton X100 typically observed for nonionic microemulsions with this surfactant at high concentrations.32 To this ME, we added hydrophobically end-capped PDMA polymers with different numbers of arms synthesized by RAFT polymerization.23 The polymers are based on hydrophilic PDMA blocks with n units and two, three, and four arms, with an aliphatic end chain of 12 carbon (dodecyl) units. The polymers with different numbers of arms were synthesized to

distribution with average size R̅ c and polydispersity σ, and the shell has a constant thickness tsh (details given in SI). The shell thickness depends on the PEO length, which here is a mixture of PEO4 and PEO9.5, and does not vary with the droplet concentration. For this reason, we fitted tsh for the lowest droplet volume fraction (where S(q)→1), obtaining a value of tsh = 1.2 nm, and kept it constant for all samples. The core radius is expected to decrease slightly with the volume fraction, according to microemulsion theory29 and thus should be a free parameter. The apparent structure factor S̃(q) is related to the true interparticle structure factor S(q) using the decoupling approximation30 S̃(q) = 1 + γ(S(q) − 1). The factor γ = ⟨F(q) ⟩2/⟨F(q)2⟩ (with P(q) ≡ ⟨ F(q) 2⟩) only depends on the molecular shape or polydispersity and is independent of the interaction. The simplest model for the structure factor S(q) of bare microemulsion droplets is the hard-sphere model that can be solved in the Percus−Yevick approximation to yield an analytical expression (SI eq S11),31 which depends only on the hard-sphere radius RHS = Rd = R̅ c + tsh and the volume fraction ϕHS = RHS3ϕc/R̅ c3. D


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Figure 4. (a) Viscosity as a function of the number of stickers per droplet at a constant core volume fraction ϕc = 0.067 (Lines: fits to eq 2 for f = 2 (solid line), f = 3 (dashed line), and f = 4 (dotted line); percolation, dashed−dotted line). (b) Viscosity as a function of the core volume fraction at a fixed number of stickers per droplet r = 2 (Lines: fits to eq 2 for no polymer (dotted−dashed line), f = 2 (solid line), f = 3 (dashed line), and f = 4 (dotted line)).

The two regions are separated by the percolation line (dotted line in Figure 3, here estimated by visual inspection) and at higher r and low ϕc by a two-phase region, with one dense (polymer rich) phase and a sol (polymer poor) phase. Similar phase behavior has also been observed for O/W microemulsions with linear end-capped poly(ethylene oxide) and was found to be independent of the end-cap group length.6,13 Conversely, the phase diagrams with polymers of different functionality differ with respect to the extent of the two-phase region. The phase boundaries of microemulsions with (C12PDMA)2, (C12PDMA)3, and (C12PDMA)4 are compared in Figure 3d. The phase transition at ϕc → 0 is at r ∼ 12 for f = 2, and r ∼ 7.5 for f = 3 and 4. In addition, the phase separation starts at higher volume fraction with higher number of arms per polymer. Overall the two-phase region is shifted to lower r and higher ϕc with higher polymer functionality, indicating that higher functionality polymers induce an increased effective attraction between the droplets. The variation from f = 2 to f = 3 is much more pronounced than from f = 3 to f = 4, which a priori can be attributed to the slightly larger length of the two arm polymer. In contrast, the percolation line is rather little affected by the polymer functionality f, and at high volume fraction it reaches a similar limiting r value of ∼3. To study the effect of the polymer length, we used a three arm polymer (C12PDMA)3 with a molecular weight 3 times higher (Figure 3d). Compared to its shorter analogue, the phase separation region is shifted to lower droplet volume fractions and higher r values as a result of a reduction of the entropic attraction when the polymer is longer.20 The higher molar mass also means that, for a given r, the polymer concentration must be higher and there are more self-excluded chains between the droplets, which may contribute to suppress phase separation driven by attractive interactions. Already the addition of small quantities of polymer to the microemulsion leads to a substantial increase in viscosity for all of the polymer architectures considered here. Figure 4 shows the viscosity variation along lines A and B in the phase diagram (Figure 3d). At a constant droplet volume fraction the viscosity increases with r in a similar way for all polymers (Figure 4a); i.e., there is no significant effect of the polymer architecture. At a fixed r, the viscosity also rises by increasing the droplet volume fraction (Figure 4b). This increase is very moderate in the absence of polymer as expected for the concentration

have very similar arm lengths, and for the three-arm polymer also one sample with about twice the arm length was produced. The ability of these polymers to form bridges with at least two of its stickers in different droplets depends on the end-to-end distance of two arms relative to the distance between the droplets. The length of the polymer can be estimated from the molecular parameters of the polymers (see Table 1) as the endto-end distance Ree of two arms free in solution, calculated as ⟨Ree2⟩ = 2nl2C∞, where n is the number of DMA units, l the length of a DMA monomer, and C∞ = 9.1 the characteristic ratio for PDMA in water.33 Essentially, bridging is possible if the distance between the droplets is similar or smaller than the end-to-end distance of the polymer Ree. Previous work concluded that the bridging attraction becomes already effective at interdroplet distances of 2.6 times Ree and shows its maximum at 1.3 times Ree,15 i.e., at distances substantially larger than the Ree. The distance between the centers of the droplets, assuming a primitive cubic packing, is defined as d = (4πR̅ c3/3ϕc)1/3, where R̅ c is the average core radius (R̅ c = 4.9 nm) and ϕc the core volume fraction. This is an approximation because the effective packing of droplets in solution may be other than cubic and it does not take into account the polydispersity of the microemulsion droplets, but nonetheless it should give a very good estimate. By tuning the microemulsion volume fraction we can continuously vary the distance between the surface of the droplets dsurf = d − 2 R̅ c such that it is larger than, equal to, or smaller than the end-to-end distance of the polymer (see also SI Figure S3). The number of hydrophobic (C12) stickers per droplet (r) is defined by r = 1Nst/1Nd, where 1Nst is the number density of stickers and 1Nd the number density of droplets (1Nd = 3ϕc/ 4πR̅ c3). Phase Behavior. Figure 3 shows the phase behavior of the nonionic microemulsion with added multiarm telechelic polymers with two, three, and four end-capped arms of similar length (see Table 1). The phase diagrams are given in terms of the number of C12 groups (stickers) per droplet as a function of the droplet core volume fraction. Although the three systems exhibit a different phase behavior, they also have some similarities. In all cases, there is a large monophasic region, which can be subdivided into two regions according to the rheological properties: a low viscous phase at low values of r and ϕc, and a highly viscous phase at higher values of r and ϕc. E


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Figure 5. (a) SANS patterns for MEs with a core volume fraction ϕc = 0.067 upon addition of (C12PDMA)2, (C12PDMA)3, and (C12PDMA)4. (b) SANS patterns for MEs with (C12PDMA)2, (C12PDMA)3, and (C12PDMA)4 at a fixed number of stickers per droplet r = 2 and various droplet volume fractions. Each data set is vertically shifted by a factor indicated next to the curve.

literature of nD2O/nEO = 6.36 The hydration of the PDMA chains was found to be around 98% in all the cases (SI Table S3), which is much higher than for PEO because of its higher hydrophilicity but also because the effective volume fraction increase with end-capped PDMA is not really a result of the bound water but rather due to the formation of decorated droplets and microemulsion clusters. Small Angle Neutron Scattering. To gain further insight into the microstructure and the polymer induced droplet− droplet interactions, we performed SANS measurements for microemulsions with added polymer along lines A and B in the phase diagram (Figure 3d). Figure 5a shows the scattering curves for microemulsions at a constant core volume fraction of 0.067 and increasing amounts of (C12PDMA)2, (C12PDMA)3, and (C12PDMA)4 (line A in Figure 3d). In the three cases, the curves are practically superimposed in the mid and high q regimes, indicating that the structure at smaller length scales, i.e., the structure of the microemulsion droplets, is the same. In addition, the unchanged position of the relative minimum at q ∼ 0.8 nm−1 is a further sign that the average size of the droplets does not change significantly in the presence of the polymer, in agreement with previous studies of microemulsions with endcapped polymers.5,6,8,19 The main differences in the scattering curves are present at smaller q values, where upon addition of polymer, a correlation peak appears, indicating repulsion between the droplets as a consequence of the presence of the polymer. For f = 3 and more so for f = 4, there is also a slight upturn of the intensity at still lower q suggesting either the presence of larger objects or an attractive interaction. In a second series of samples, we fixed the number of stickers per droplet to r = 2 for all different polymers and reduced the volume fraction of the microemulsion droplets, in order to increase the distance between the droplets relative to the polymer length. The scattering curves (Figure 5b) have again the same features at mid and high q from the droplet scattering with minimal variations on the position of the relative minimum at q ∼ 0.8 nm−1 due to the slight variations of the droplet size with composition. In the low q-regime there is an increase of the scattering intensity for the three arm and four arm polymers compared to the two arm polymer, indicative of more pronounced attractive interactions. With higher droplet volume fraction a correlation peak appears and becomes more pronounced at the highest volume fractions of 0.067.

dependence of hard spheres, while it becomes more prominent in the samples containing polymer. Generally, the increase in viscosity of microemulsion telechelic polymer mixtures as a function of the amount of bridging polymers follows the expression η = η0(rp − r) −k, where rp is the percolation concentration.6,8 Here the exponent is k = 2 in all three cases; Figure 4 shows the example of the best-fit for f = 2 to the equation η = 28(3.8−r) −2 mPa s. The value k = 2 is much higher than the value predicted by bond percolation theory k = 0.7. Percolation theory provides very good predictions of the elastic shear modulus and viscosity above the percolation concentration,6−8 where the fraction of bridges versus loops is expected to be maximal. Below the percolation concentration, however, loops are expected to be more frequent.34 Thus, the percolation model underestimates the viscosity increase because it only accounts for the bonds between droplets but not the formation of loops decorating droplets, which increase the effective volume fraction of the droplets that causes a viscosity increase. Such a viscosity increase with the effective volume fraction can be described using the empirical equation proposed by Thomas:35 η = η0[1 + 2.5ϕeff + 10.05ϕeff 2 + 0.00273 exp(16.6ϕeff )] (2)

where the effective volume fraction ϕeff is proportional to the number of stickers per droplet as ϕeff = ϕeff(r=0) +Pr, and in the case of varying the core volume fraction as ϕeff = Aϕc. The fits with eq 2 with only one parameter (A = ϕeff/ϕc or P = (ϕeff − ϕeff(r=0))/r) are in good agreement with the experimental data. The parameter describing the effective volume fraction for the ME without polymer A = 2.69 indicates that for the viscosity the droplets have an effective radius of 6.8 nm (when using Rc = 4.9 nm); i.e., here one sees the hydrated PEO headgroup. For a constant r = 2, the effective radius then is 8.51, 8.43, and 8.84 nm for f = 2, 3, and 4, respectively; i.e., it remains basically constant, and this increase of the effective radius can be attributed to the PDMA that extends into the aqueous surroundings of the microemulsion droplets. In addition, the hydration of the PEO chains from the surfactant and the PDMA chains from the end-capped polymers were obtained from the effective volume fraction parameters (see the SI). From the effective volume fraction for the ME without polymer A = 2.69, we can conclude to a hydration of 70%. This corresponds to 5.2 D2O molecules per EO monomer that compares well to the value reported in the F


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Figure 6. (a) Interaction potential for MEs at a constant core volume fraction ϕc = 0.067 and added polymers with varying r. (b) Interaction potential for MEs with added polymers at constant number of stickers per droplet r = 2 and varying ϕc. (c) Second virial coefficient as a function of r for ϕc = 0.067. (d) Second virial coefficient as a function of ϕc at a fixed number of stickers per droplet r = 2.

The scattering intensity results of the sum of the scattering of the droplets and of the polymer chains. It can be assumed that the scattering is dominated by the scattering of the droplets and the polymer contributes to the scattering to a rather small extent by the chain scattering at high q. Here the effect that the polymer addition has on the coherent scattering at high q is minimal (Figure 5), and thus the polymer contribution may be neglected. Therefore, the scattering intensity can be quantitatively described with eq 1 with P̅(q), the form factor of the microemulsion droplet, and S̃(q), the effective structure factor representing the interdroplet interactions. The interaction potential between the droplets induced by the presence of the polymer has been under debate in the past two decades in the literature. Theoretical work on the interaction potential of spheres linked by telechelic polymers18 predicts an attraction of the order of kBT at a separation slightly lower than the end-to-end distance of the free polymer. Porte et al. fitted SANS data of microemulsions linked with telechelic polymers with this model with relatively good agreement with the scattering curves. Still, they argued that the repulsive interactions due to the polymer chains between droplets were not properly accounted for in the model.16 In spite of the lack of an existing realistic model for the structure factor, simpler models such as a parabolic attraction,15 sticky hard sphere model,8 hard sphere,14 or hard sphere with steric repulsion21 have given very good quantitative agreement with the scattering data. From these studies, it is clear that the telechelic polymer induces both an attractive and a repulsive interaction between the droplets and the strength and range of those interactions depend on parameters such as the polymer concentration, the droplet volume fraction, and the length of the polymer. In order to account for this situation, we use an interaction

potential with a hard sphere and two Yukawa functions, one to account for the attraction and the other for the repulsion:

where x is the separation distance, Rd = Rc + tsh is the overall droplet radius, and K1 and K2 are the strength of the attraction and the repulsion part of the interaction, respectively. Z1 and Z2 are inversely proportional to the range of the interaction. The structure factor S(q) is solved numerically using the mean spherical approximation closure to solve the Ornstein−Zernike equation37 (details given in the SI). The fits of the scattering intensity to eq 1 with a model of polydisperse core−shell spheres with an interaction potential described by eq 3 are in very good agreement with the experimental data (Figure 5). In the fits we fixed tsh = 1.2 nm and ϕc and the scattering length densities of the core and the shell to the experimental conditions (see the SI), and fitted R̅ c, the polydispersity of the core σ, and the structure factor parameters K1, K2, Z1, and Z2. For the case of a constant droplet volume fraction, the polymer addition had no effect on the droplet size or polydispersity and only the structure factor parameters varied with polymer addition (SI Table S4). However, it is probably simpler to represent the interaction with the overall potential curves depicted in Figure 6a. The potential curves have a similar shape in all cases being repulsive at small separations and attractive at intermediate separations with a minimal value Umin. On one hand, an increasing amount of polymer (r) results in higher repulsion interactions due to the higher concentration of self-excluding PDMA chains. On the other hand, as r increases also the bridging attraction increases, which is reflected in the lower value of Umin, although G


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Figure 7. (a) Intensity autocorrelation function g2(t) − 1 at a scattering angle of 90° for MEs without and with (C12PDMA)2, (C12PDMA)3, and (C12PDMA)4 (r ∼ 3). The black lines correspond to the fits using eq 5. (b) FCS autocorrelation curves of microemulsion with (C12PDMA)2 (r = 3.17), (C12PDMA)3 (r = 3.30), and (C12PDMA)4 (r = 3.05). The lines are the fits with eq 6.

it is always rather shallow (well below kBT for ϕc = 0.067; see Figure 6a and SI Figure S6). It is interesting to note that the range of the attraction is between 12 and 18 nm, which is about the end-to-end distance of the polymers (see Table 1), i.e., in the expected range for attractive interaction induced by polymer bridging.15,18 The repulsive interactions are more prominent for the two arm polymer (which is slightly longer) than for f = 3 and f = 4 for a given r, whereas the depth of the well Umin increases significantly with f. At a fixed r and varying droplet volume fraction, the attractive interaction described by Umin decreases substantially with increasing droplet concentration (Figure 6b). Interestingly, Umin is of the order of 1 kBT for the most dilute case but then vanishes almost completely for the highest concentration, being in general more attractive for an increasing number of polymer arms. Also, the repulsive component increases with increasing droplet volume fraction. This clearly shows that the extent of attractive interaction decreases substantially as a function of the distance between the surfaces of the droplets dsurf for a given r. More importantly, the strength of the attractive interaction increases substantially with an increasing number of arms f. The counterbalancing attractive and repulsive interactions between the droplets can be accounted for with a single parameter, the dimensionless second virial coefficient B2, defined as B 2 (T ) =

2π Vd

∫0

∞

(1 − exp(−U (x)/kBT ))x 2 dx

increase of the microemulsion concentration leads to an increasing steric repulsion (Figure 6d) for all polymers but lower, more attractive, for higher polymer functionality. Figure 6d also shows the values of B2 for the higher molecular weight three arm polymer (SANS curves and fit results in the SI). Compared to the shorter three arm polymer, the values of B2 are higher for all droplet volume fractions in spite of the fact that the probability of forming bridges is higher for a longer polymer. Here, the additional repulsion is caused by the larger PDMA volume fraction per end-capped arm (SI Figure S3b), which leads to a higher steric repulsion. This relates to our previous results with multiarm telechelic and MEs where the length of the polymer was much larger compared to the interdroplet distance and the interaction was completely dominated by repulsion regardless of the polymer functionality.21 We can explain these results, at least qualitatively, in terms of the contributions of the end-capped polymer to the interaction potential. Specifically, the interaction between the droplets with added telechelic polymer has three contributions: (1) the interaction between the droplets without polymer, (2) an entropic attraction induced by the bridging polymer, and (3) a soft repulsion caused by the number of self-excluding chains between the droplets. Depending on the relative importance of these contributions, the net interaction is attractive or repulsive. Here, the interaction between the droplets without polymer does not change and we can focus on the other two contributions. The attractive interaction depends basically on the tendency to form bridges between the droplets.18 The probability of bridge formation increases with r,38 the polymer length Ree relative to the interdroplet distance dsurf,34,39 and f.21 The repulsive interaction, caused by self-excluding chains between the droplets, depends on the total volume fraction of the hydrophilic chains.17,32 Therefore, raising the polymer concentration at a given droplet volume fraction, increases both the number of bridges and the volume fraction of the hydrophilic chains and, thus, contributes to a rise in attraction and repulsion. Which one dominates the net interaction will be determined by the polymer length relative to the interdroplet distance and the polymer functionality. For polymers with Ree > dsurf there is a high probability for bridging but the volume fraction of polymer per bridge is higher and the interaction is dominated by repulsion. For large separations between

(4)

where Vd = 4πRd/3 is the volume of a droplet and Rd their radius obtained by SANS (Rd = R̅ c + tsh). B2 is very useful to describe the net interaction because the parameters describing the structure factor S(q) (K1, K2,Z1, and Z2) describe opposite effects but are not fully decoupled in their effect on the scattering curves. B2 for a pure hard sphere is 4 and will be higher if the net interaction is repulsive and lower when attractive. For a given microemulsion concentration (ϕc = 0.067) the second virial coefficient B2 as a function of r depends remarkably on the polymer functionality (Figure 6c). For f = 2 polymer an increasing repulsion is observed, while for f = 3 and f = 4, attractive interactions become increasingly prominent, the effect being somewhat more pronounced for f = 4. At a fixed r = 2 and polymers with similar length, the H


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obtained, which is slightly higher than the radius obtained by SANS (6.1 nm). This is mainly to be attributed to the fact that in SANS one only sees an effective thickness of the PEO shell of the surfactants, which here is a mixture of PEO4 and PEO9.5. The reduced collective diffusion coefficient Dcoll/Dcoll(ME) upon addition of two arm bridging polymer remains at first constant and then starts increasing with r (Figure 8). For higher

droplets, the number of bridges is small and the attraction is very weak. However, the excluded volume repulsion is even smaller, and the interaction energy is dominated by attraction. Most significantly, the attractive interaction between the droplets per end-capped arm is more pronounced for higher polymer functionality. Apparently, the branching points provided by the polymer force other microemulsion droplets that become connected to stay in the vicinity of the already connected droplets, thereby introducing an effective attraction, which is reflected in the phase diagram by an attractive phase separation. Dynamic Light Scattering and Fluorescence Correlation Spectroscopy. In order to gain further insight into the dynamic behavior of the investigated polymer microemulsion mixtures, we performed DLS measurements to probe the collective diffusion (Dcoll) and FCS to probe the self-diffusion (Dself) along one vertical line at ϕc = 0.067 of the phase diagram (line A in Figure 3d). Figure 7a depicts the intensity correlation function g 2 (t) for the pure microemulsion and with (C12PDMA)2, (C12PDMA)3, and (C12PDMA)4 with r ∼ 3. As to be expected, the pure microemulsion (r = 0) exhibits a single relaxation mode due to the diffusion of the droplets in the aqueous medium. The addition of polymer leads to a shift of the diffusive relaxation to longer relaxation times and most prominently to the appearance of additional, slower relaxation modes. Generally, the fast mode is associated with the concentration fluctuations of the microemulsion droplets and the intermediate mode with the network relaxation of the gel that is related to the terminal relaxation time and the selfdiffusion of the polymer. A third relaxation time has been observed when the polymer length is significantly larger than the interdroplet distance.12,13,21 Depending on the residence time of the stickers, the intermediate mode may drop out of the experimental window for the case of too long hydrophobic stickers.12,40 The autocorrelation curves curves were analyzed quantitatively in terms of a sum of a normal and one or two stretched exponential decays |g(1)(t )| = a f e−t / τf + ase−(t / τs)

βs

Figure 8. Reduced collective diffusion coefficient Dcoll/Dcoll(ME) (obtained with DLS) and self-diffusion coefficient Dself/Dself(ME) (obtained with FCS) for ME (ϕc = 0.067) with added (C12PDMA)2, (C12PDMA)3, and (C12PDMA)4 as a function of r.

functionalities (f = 3 and f = 4), Dcoll/Dcoll(ME) first decreases, and, after reaching a minimum, it starts growing again. This trend has been observed similarly in ME/telechelic mixture systems.8,14,21 Here, the depth of the minimum of Dcoll/ Dcoll(ME) is lower with higher polymer functionality, i.e., where SANS shows a more attractive interaction. In general, repulsive interactions in colloidal particles lead to a higher Dcoll and attractive ones to a lower Dcoll. Consequently, the change of Dcoll as a function of r and f follows the observations regarding the interactions deduced from the static scattering. The amplitude of the fast relaxation Af decreases with r as a consequence of the higher contribution of the slow relaxation (Figure 9a). Interestingly, this decrease is more pronounced with higher polymer functionality as previously observed for such systems.21 The second relaxation mode is not diffusive because it exhibits a q-dependence different from 2. The exponent describing the q-dependence of the relaxation time τs ∼ qns varies from 3 to 0 becoming smaller with higher r (Figure 9c). The angular dependence vanishes (ns = 0) for sufficiently high r, where this point comes earlier the larger the number of arms. The slow relaxation time (Figure 9b) is of the same order of magnitude but a factor 5 smaller in absolute value as found previously for a system with identical sticker length but larger Ree compared to the distance between the droplets.21 The slow relaxation time has been found to be strongly correlated to the structural relaxation time,14,42 which has led to the conclusion that the relaxation time is related to the process in which one polymer sticker changes from one droplet to another. Indeed, it is possible that if the polymer is long enough, entanglements contribute to an increase of the relaxation time. Here, the slow relaxation time increases with r and f (Figure 9b). Moreover, the stretching parameter β2 decreases with r for all polymer functionalities (Figure 9d). Complementary to DLS that gives information about collective diffusion, FCS provides insight into the self-diffusion of the labeled domains. Here we labeled the oil droplets with Nile red at a concentration of 2.5 nM. Then FCS was measured

(5)

where ai is the amplitude, τi the relaxation time, and βi the stretching parameter of the fast (i = f) and slow (i = s) modes. The sum of two exponentials was sufficient to describe all of the autocorrelation curves except for f = 2 and r ≥ 4.5, where a third exponential function with relaxation times τ3 ≥ 50 ms was necessary to describe the entire curve. In the following we will describe the fast and second relaxation modes. The fast relaxation time τf exhibits a q−2 dependence (see SI Figure S9) and is related to the collective diffusion of the microemulsion droplets.8,12 The collective diffusion coefficient is related to the fast relaxation time as Dcoll = 1/τfq2. At infinite dilution when the droplets can be regarded as non-interacting, Dcoll is related to the hydrodynamic radius RH through the Stokes−Einstein equation RH = kBT/6πηDcoll, where kB is the Boltzmann constant, T the temperature, and η the viscosity of the solvent. The diffusion coefficient of the pure microemulsion droplets increases linearly with the droplet volume fraction with a slope of 2.27 (see SI Figure S2), where for pure hard spheres a value of 1.45 would be expected, which shows that in the pure microemulsion the repulsive forces are largely due to the volume exclusion.41 From the extrapolation to zero concentration a value for the hydrodynamic radius RH ∼ 6.8 nm was I


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Figure 9. (a) Amplitude of the fast relaxation mode Af at a scattering angle of 90°, (b) second relaxation time τs at a scattering angle of 90° (dotted lines are a guide to the eye), (c) q-dependence exponent ns, and (d) stretching exponent of the second relaxation mode βs at a scattering angle of 90° as a function of the number of stickers per droplet, r.

as a function of r. Interestingly, the FCS correlation function exhibits only one relaxation time, contrary to the complex relaxation spectrum probed with DLS. The same observation for a 3 nm radius O/W microemulsion with (C18−PEO)2 added.8 The autocorrelation function G(t) is given by43 −1 α −0.5 ⎛ ⎛ t ⎞α ⎞ ⎛ 1 ⎛t ⎞ ⎞ G(t ) = G(0)⎜1 + ⎜ ⎟ ⎟ ⎜1 + 2 ⎜ ⎟ ⎟ ⎝τ⎠ ⎠ ⎝ ⎝ S ⎝τ⎠ ⎠

the arrest of the ME droplets by the formation of the polymer mediated network, which is fully effective for r > 3. A low constant value of Dself is reached for the situation where macroscopically one also observes a largely enhanced viscosity (and where the slow mode in DLS becomes prominent). Unlike the collective diffusion, the self-diffusion coefficient does not depend to a larger extent on f, similar to the trend observed in viscosity. This suggests that the self-diffusion of droplets slows down as the viscosity increases due to the formation of decorated droplets and clusters.

(6)

τ is the diffusion time, and S, the structure parameter, is the ratio of the longitudinal radius ωz to transversal radius ωxy of the confocal volume (S = ωz/ωxy). In this way, the diffusion coefficient of the fluorescently labeled droplets is Dself = ωxy2/ 4τ. In a crowded environment such as a polymer solution, the diffusion may become anomalous and the particle mean displacement then obeys a power law ⟨r2(t)⟩ = 6Γtα. The exponent α is the same as in eq 6. If it differs from 1, the diffusion is said to be anomalous, and if α < 1, it is subdiffusive. The effective diffusion coefficient in this case is defined by D(t) = Γtα−1. Anomalous diffusion takes place in crowded media, and this description has been used to describe FCS data of viscous systems.44 Here, α was found to be 1 for all polymers up to r ∼ 3−4 (see SI Figure S10), i.e., around the percolation concentration. This implies that the self-diffusion at small length scales is diffusive below the percolation concentration and becomes anomalous when the network is formed. The collective (DLS) and self-diffusion (FCS) coefficients are compared in Figure 8. The addition of bridging polymer leads to a rapid increase of the relaxation time in the fluorescence correlation functions (Figure 7b and 8). Dself (FCS) is correspondingly reduced much more strongly than Dcoll (DLS), and this effective ”arresting” of the mobility of the microemulsion droplets occurs in a similar fashion for the different polymers, requiring just a somewhat higher r for the two arm polymer. This means that in FCS one sees effectively

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CONCLUSIONS We investigated the effect of the polymer functionality on the phase behavior and mesoscopic properties of multiarm endcapped polymers in an oil-in-water microemulsion of TX100/ Brij 30/decane/water. We systematically varied the number of hydrophobic stickers per microemulsion droplet, the concentration of droplets, and the polymer functionality. The microemulsion/polymer mixtures exhibit a phase behavior as generally expected for such systems where, for polymer end-toend distances smaller than the interdroplet distance and high enough polymer concentrations, the entropic attraction of the bridging polymer causes phase separation. The phase separation boundary is shifted to lower number of stickers per droplet and higher droplet volume fractions by increasing the polymer functionality (number of end-capped arms), an indication for enhanced attractive interactions. Detailed analysis of SANS measurements demonstrates that the polymer induces an attractive interaction between the droplets due to bridging and soft repulsion caused by the hydrophilic chains between the droplets that was modeled with a two-Yukawa interaction potential. Through the calculation of the second virial coefficient, we quantify that polymers with higher functionality induce a larger net attractive interaction between the droplets that directly correlates with the shift of J


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the phase boundary. An increase of the polymer molecular weight results in an increased repulsion due to a higher concentration of self-excluding chains that leads to the suppression of phase separation. Dynamic light scattering experiments at a constant droplet volume fraction show, in addition to the collective diffusion of the droplets, a slow relaxation mode with increasing amplitude as the polymer has more end-capped arms. For sufficiently high r (∼4) the samples not only become very viscous and FCS results show a very low self-diffusion coefficient (reduced to 5− 10% of that of the free microemulsion droplets), but the slow relaxation mode of DLS becomes independent of the angle, thereby indicating a general nondiffusive structural relaxation process of the network. The collective diffusion correlates with the polymer induced interdroplet interactions and first decreases with r and then increases, where the minimum is lower with higher polymer functionality. However, the selfdiffusion decreases due to a reduced mobility of the droplets caused by the increase in viscosity and thus depends only on r and not significantly on the polymer functionality. In summary, we obtain a self-consistent picture regarding the change of the interparticle interactions in O/W microemulsions with the addition of bridging multiarm telechelic polymer and, in particular, by the number of interconnecting arms. These interactions explain also the observed dynamic behavior, the viscosity, and the macroscopic phase behavior. This then allows for a comprehensive description of such systems, which is very important when wanting to control the dynamics and rheology of microemulsion based systems.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Details on the SANS analysis and additional phase diagrams, viscosity, SANS, DLS, and FCS data. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b00817.

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AUTHOR INFORMATION

Corresponding Authors

*(P.M.M) E-mail: [email protected]. *(M.G.) E-mail: [email protected]. Present Addresses #

Department of Chemical Engineering, University of California Santa Barbara, 3357 Engineering II, Santa Barbara, CA 93106, USA. ∇ European Synchrotron Radiation Facility (ESRF), 71 Ave. des Martyrs, 38043 Grenoble Cedex, France. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are greatly indebted to Sam Safran for the inspiring discussion that got us to think about this problem. This work was funded by DFG Grants GR1030/9-1 and LA611/8-1. The SANS measurements on KWS-1 of JCNS (operating at FRMII, Munich) have been supported by the JCNS. The EU is thanked for funding the confocal microscope and its attached FCS unit through the EFRE program (EFRE 20072013 2/18). P.M.M. gratefully acknowledges a grant from DAAD-La Caixa. K


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Phase Behavior of Nonionic Microemulsions with Multi-end-capped

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