Impact of Diblock Copolymers on Droplet Coalescence, Emulsification

Article pubs.acs.org/Langmuir

Impact of Diblock Copolymers on Droplet Coalescence, Emulsification, and Aggregation in Immiscible Homopolymer Blends Jeremy N. Fowler,† Tonomori Saito,‡ Renlong Gao,‡ Eric S. Fried,† Timothy E. Long,‡ and David L. Green*,† †

Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, United States Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States

‡

S Supporting Information *

ABSTRACT: Using rheo-optical techniques, we investigated the impact of interfacial wetting of symmetric diblock copolymers (BCPs) on the coalescence and aggregation of polydimethylsiloxane (PDMS) droplets in immiscible polyethylene-propylene (PEP) homopolymers. Anionic polymerization was used to synthesize well-defined matrix homopolymers and symmetric 16 kg/mol-to-16 kg/mol PDMS-b-PEP diblock copolymers with low polydispersity (PDI ≈ 1.02) as characterized with size exclusion chromatography and nuclear magnetic resonance spectroscopy. Blends were formulated to match the viscosities between the droplets and the matrix. Moreover, molecular weights of these components were varied to ensure that the inner block of the copolymer inside the droplet was collapsed and dry, whereas the outer block of the copolymer outside of the droplet was stretched and wet. Droplet breakup and coalescence as well as interfacial tensions were measured using rheo-optical experiments with Linkam shearing stage and an optical microscope. Subsequent to droplet breakup at high shear rates, we found that the BCPs mitigated shear-induced coalescence at lower shear rates. Based on surface tension measurements, the stretching of the BCP increased in lower molecular weight matrices, causing the droplet surface to saturate at lower coverage in line with theoretical predictions. Droplet aggregation was detected with further reductions in shear rate, which was attributed to the dewetting or the expulsion of the matrix from a saturated brush. Ultimately, the regions of droplet coalescence and aggregation were scaled by balancing the forces of shear with those due to the attraction between BCP-coated droplets. brushes to particle dispersions in homopolymer melts.1−4 These studies show that wetting phase diagrams, derived through selfconsistent mean-field calculations and scaling theories,5 can be used to predict the conditions under which polymer-grafted nanoparticles should disperse or aggregate. On the basis of these diagrams, the brush assumes one of three states: (1) collapsed and unwetted (allophobic dewetting); (2) stretched and wetted (complete wetting); and (3) stretched and unwetted (autophobic dewetting). These states depend on brush surface coverage, Γ, and the swelling ratio, So = N/P, where P and N are the degrees of polymerization of the matrix and brush, respectively. Analogously, we seek to show that the swelling, or the stretching of the BCP in the droplet and matrix must be taken into account during compatibilization. Therefore, we formulated well-controlled blends of poly(dimethylsiloxane) (PDMS) droplets in hydrogenated polyisoprene matrices, i.e., poly(ethylene-co-propylene) (PEP). The droplets were compatibilized with symmetric PDMS-b-PEP diblock copolymers, where the molecular weight of each block was 16 kg/mol, i.e., 16k-to-16k

1. INTRODUCTION Our objective is to demonstrate how the wetting, or stretching, of diblock copolymers (BCPs) governs the rheology of polymer droplets in immiscible polymer blends. Blending immiscible polymers with BCPs is a cost-effective route to designing novel, high-performance polymer alloys that can greatly impact a wide variety of industries. Block copolymers, which segregate to the interface of the dispersed phase, serve to prevent droplet coalescence, which is crucial to the preparation of polymer alloys in advanced materials such as airplane and automotive parts, biomedical devices, and food packing where material properties (e.g., high mechanical strength, optical clarity, and chemical resistance) rely upon the even dispersion of emulsified droplets into the matrix. Moreover, lighter, cheaper and stronger components have far ranging benefits, such as increases in fuel efficiency, durability, and biocompatibility. Although droplet emulsification in bulk polymers has been studied in detail over the past 20 years, droplet dispersion in polymeric media still proves difficult and frequently results in coalescence into larger droplets, producing polymer alloys with suboptimal properties. To provide new insight into how the wetting of BCPs should impact droplet coalescence, we seek analogies to recent studies that fundamentally connect the conformation of polymer © 2011 American Chemical Society

Received: February 3, 2011 Revised: December 10, 2011 Published: December 12, 2011 2347

dx.doi.org/10.1021/la2037185 | Langmuir 2012, 28, 2347−2356

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Figure 1. (a) Schematic of a compatibilized polymer droplet and (b) schematic of wet/dry block copolymer brush at droplet/matrix interface.

of Shull and workers who quantified the adsorption of wet− dry BCP brushes at flat, immiscible homopolymer blend interfaces.10 They found that increasing So, or decreasing the molecular weight of the homopolymer that wets the BCP, causes the outer block of the BCP to stretch, which causes the BCP to fill, or saturate the blend interface at lower surface coverages, Γsat.10 To predict this correspondence, Shull adapted Liebler’s theory for polymer droplet emulsification;9 Shull’s application of Liebler’s work to flat interfaces is reasonable due to the low interfacial curvature of polymer droplets, where the droplet radius, R, is much greater than the BCP film thickness, L = LPEP + LPDMS, or R ≫ L. Based on the work of Shull and Leibler, a delicate balance should exist between the conformation of the wet−dry BCP brush in the film at the droplet interface and droplet rheology. Decreasing the matrix molecular weight, PPEP, or increasing outer droplet swelling ratio, So, in the film, should increase the stretching of the outer block of the BCP, or LPEP, which should reduce the BCP surface coverage, Γ. Based on the Gibbs adsorption equation, Γ = −(kBT)−1(∂σ/∂lnϕBCP)T, lower BCP coverage leads to smaller changes in Δσ, or higher surface tension, σ, as σ = σ0 − Δσ, where σ0 is the surface tension at uncompatbilized droplet/matrix interface. While higher surface tension should lead to increased droplet size as predicted by the Young−Laplace equation, ΔP = 2σ/R, decreases in the matrix molecular weight could offset the formation of larger droplets through the BCP stretching, which should mitigate coalescence and potentially lead to stable droplets.11 Thus, we seek to connect the stretching of the BCP at the external surface of droplets to their rheology. In general, the rheology of uncompatibilized droplets is governed by droplet breakup and coalescence at low Reynolds number, Re = γ̇ρR2/ηPEP < 1,12 where γ̇ is the shear rate, ρ is the matrix density, and ηPEP is the matrix viscosity. Droplet breakup is characterized by the capillary number, Ca, and as described by Taylor,13 Ca relates the relative importance of the viscous and surface tension stresses that control droplet deformation of

PDMS-b-PEP. Further, the hydrogenation of polyisoprene in the matrix and BCP significantly reduces oxidation of these constituents,6 enabling long-term studies. These studies were conducted at ambient conditions as blend components with glass transition temperatures of PEP = −71 °C7 and PDMS = −123 °C8 are melts at room temperature. (The schemes and protocols for polymer synthesis and characterization are listed in the Supporting Information.) Figures 1a and b displays a schematic of a polymer droplet compatibilized with the symmetric BCPs in which the inner and outer blocks are collapsed and stretched, respectively. In general, the conformation of the diblock copolymer depends on the molecular weights of the droplet (PPDMS), the inner block of the copolymer (NPDMS), the outer block of the copolymer (NPEP), and the matrix (PPEP) as defined by the swelling ratios inside and outside the droplet, or Si = NPDMS/PPDMS and So = NPEP/PPEP, respectively.9 To this end, we investigated how the wetting or stretching of the external brush impacts droplet rheology. Consequently, we formulated blends in which the internal swelling ratio inside the droplet is Si = NPDMS/PPDMS < 1, whereas outside the droplet, the external swelling ratio is So = NPEP/PPEP ≥ 1. This should allow the matrix polymer to penetrate and stretch the external copolymer brush with a thickness, LPEP, while the droplet polymer dewets from the internal block of the BCP with a thickness, LPDMS, leading to its collapse. As shown in the inset of Figure 1, this BCP conformation at the interface is known as a wet−dry brush, where LPEP > LPDMS,10 and the basic structure of this droplet is similar that of a polymer-grafted particle. In previous studies we find that placing these particles in polymer matrices of molecular weights lower than that of the grafts, i.e., So > 1, leads to increased brush stretching and particle stability.2,3 Analogously, we seek to discover whether increased emulsification and stability results upon placing droplets compatibilized with wet−dry BCPs in lower molecular weight matrices. Insight into the behavior of BCP films in wet−dry conformations at droplet surfaces can be gained from the studies 2348


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deformation, while controlling So governs the stretching of the outer PEP block. In contrast, the PDMS block with molecular weight (NPDMS) inside of the PDMS droplet will be “dry” given that molecular weight of the droplet (PPDMS) was selected such that of the swelling ratio inside the droplet was Si = NPDMS/ PPDMS ≤ 1. Thus, the effect of stretching of the PDMS block on droplet stability can be discounted, permitting us to quantify the impact of the BCP stretching at the exterior surface on droplet rheology in immiscible blends. Our hypothesis is that the swelling ratio affects BCP surface coverage, which significantly impacts the surface tension and morphology of the compatibilized droplets. As detailed in the Results and Discussion section, we find that increasing BCP coverage enhances emulsification and mitigates coalescence, similar to other researchers. In addition, we present a new finding: the aggregation of BCP-coated droplets toward low shear rates (γ̇ = 0.1−1 s−1). Support for the aggregation of BCP-coated droplets is given in past studies, which indicate that attractions between droplet interfaces can arise upon the expulsion of the matrix polymer from the BCP brush at surface saturation, similar to the behavior of polymer-grafted nanoparticles.

under external flow

Ca = (ηPEPγ̇)/(σ/R ) (1) Thus, Ca characterizes the evolution of the droplets as being a competition between the viscous stress (ηPEPγ̇) that deforms the droplet and the interfacial tension stress (σ/R) that restores the droplet back to its original shape. Based on a classical Newtonian dynamics, droplet breakup depends the viscosity ratio, p = ηPDMS/ηPEP, between the droplet and matrix phases; thus when Ca drops below a critical value, Cacrit(p), breakup ceases and coalescence begins. In our studies, the molecular weights of the matrices and droplets where chosen such that the droplet and matrix viscosities were equal, equating p = 1. Further, we focused on a range of shear rates for which only coalescence occurs, or Ca < Cacrit(p = 1). Coalescence is a multistep process. When droplets collide, the intervening fluid that separates the droplets drains away from the point of impact. If the fluid drains completely before the droplets move past each other, the droplets rupture and coalesce. For compatibilized blends, however, the addition of BCP facilitates emulsification by decreasing the surface tension and inhibiting coalescence.14,15 While no peer-reviewed study has been published on the impact of BCP conformation on droplet rheology, several investigators have focused on how BCP surface coverage mitigates droplet coalescence.16 At lower BCP coverage (Γ ≈ 0.02−0.04 chains/nm2), Briber and co-workers, Milner et al.,17 and van Puyvelde and co-workers18 indicate that coalescence inhibition results from the development of Marangoni stresses, or gradients in interfacial tension that immobilize the droplet interface, slowing film drainage and suppressing coalescence. This is exemplified by a decrease in the power-law slope, α, of the droplet radius with shear rate, or R ≈ γ̇−α where α ≈ 1.0 corresponds to an uncompatbilized droplet. Few analogies exist at lower coverage between the behaviors of BCPcoated droplets and polymer-grafted particles due to the mobility of the BCP at the droplet interface and the pinning of the graft polymer at the particle surface. However, at higher BCP coverage (Γ = 0.10−0.25 chains/nm2) analogies do exist between compatibilized droplets and grafted particles based on the rheological investigations of Macosko and co-workers,19−21 who indicate that the mechanism of coalescence suppression switches from Marangoni stresses to droplet stabilization through the formation of polymer brushes. Specifically, they assert that Marangoni stresses become irrelevant toward higher surface coverage as an interface packed with copolymer precludes its movement in response to flow. The immobility of the BCP film on droplets is analogous to that of polymers grafted to particles; thus, we anticipate that the penetration and stretching of the polymer at the external surface should control droplet and particle stability similarly. In all cases Macosko, Moldenaers, and their respective co-workers indicate that increases in BCP surface coverage increase droplet emulsification and stability.19−261 However, they did not explicitly connect droplet stability to the inner and outer swelling ratios, or Si and So, which control BCP conformation. Thus, we seek to relate how BCP stretching controls droplet rheology in polymer matrices in which rheo-optical measurements were made under ambient conditions. Special attention was placed on blend formulation by holding constant the droplet/matrix viscosity ratio p = ηPDMS/ηPEP = 1, while varying the swelling ratio outside of the droplet So = NPEP/PPEP ≥ 1 for the PEP block and matrices of molecular weights NPEP and PPEP, respectively. Constraining p facilitates control over droplet

2. EXPERIMENTAL METHODOLOGY 2.1. Materials, Chemicals, and Synthesis. Isoprene (Aldrich, 99%) was treated with dibutylmagnesium (Aldrich, 0.10 mM) and distilled under vacuum prior to use. Cyclohexane (Fisher Scientific, HPLC) was passed through an activated molecular sieve column (Aldrich, 60 Å mesh) and activated alumina column immediately prior to use. sec-Butyllithium 1.6 M solution in hexanes (secBuLi, FMC Lithium), nickel 2-ethylhexanoate (nickel octoate, Alfa Aesar), 1.0 M triethylaluminum in hexanes (Aldrich), citric acid (Aldrich, 98%), triethylamine (Aldrich, 99%), methanol (Fisher Scientific), and deuterated chloroform (CDCl3, Cambridge Isotope Laboratories) were used as received. Hexamethylcyclotrisiloxane (D3, Aldrich, 98%) was dried over calcium hydride (Aldrich, 95%) for 24 h and distilled under vacuum. Chlorotrimethylsilane (Aldrich, 99%) was treated with an aliquot of sec-butyllithium (Aldrich, 1.4 M) and distilled under vacuum prior to use. Higher distillation efficiency of D3 was achieved through dissolving D3 in cyclohexane with calcium hydride and distilled both at once under vacuum. Tetrahydrofuran (Fisher Scientific) was passed through Pure Solv MD-3 solvent purification system (Innovative Technology) prior to use. Methyl-terminated PDMS of molecular weights between 16 and 65 kg/mol were obtained from Dow-Corning and Gelest. 2.2. Polymer Synthesis and Characterization. Polyisoprene (PI) was synthesized via anionic polymerization in a 600 mL-capacity glass anionic reactor through the following steps.27 Isoprene (88 mL, 60 g) was syringed into the reactor that was maintained at a constant nitrogen pressure of 40 psi, and then sec-BuLi (12.49 mL, 20.0 mmol) was added to the solution to initiate the reaction, which was carried out for approximately 2 h, and subsequently terminated by adding nitrogen-degassed methanol. The synthesis of the symmetric PI-b-PDMS block copolymer was modified from a previously reported method.28 Isoprene (11.01 mL, 7.5 g) was syringed into the reactor at 50 °C, followed by the addition of sec-BuLi (0.28 mL, 0.442 mmol) to initiate the anionic polymerization, which proceeded for 2 h, during which a portion of the reaction mixture was taken out for PI characterization. Subsequently, D3 in cyclohexane (18.7 mL of 0.5 g/mL D3 solution, 9.4 g D3) was added to the reactor mixture, followed by stirring for 18 h at room temperature to ensure the crossover of the reaction from isoprenyllithium to lithium silanolate. THF (24 mL, 30 vol%) was then transferred to the reaction, and the mixture was then stirred at 4 °C in a refrigerator for 78 h. Subsequently, 1.2 fold of chlorotrimethylsilane was syringed into the mixture to terminate the reaction, after 10 min, an aliquot of triethylamine was added to scavenge acid, and then the solution was precipitated in methanol. The precipitation was repeated three times to remove salts and unreacted D3 monomer. 2349


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Table 1. Polymer Viscosity, Molecular Weights, and Swelling Ratios for the Polymer Blendsa polymer viscosities and ratios

polymer molecular weight and swelling ratios

PDMS viscosity, ηPDMS (Pa s)

PEP viscosity, ηPEP (Pa s)

viscosity ratio, p

PDMS MW, DPMDS (kg/mol)

PEP MW, PPEP (kg/mol)

internal ratio, Si = NPDMS/ DPDMS

external ratio, So = NPEP/PPEP

4.8 97.7

5.6 93.2

0.85 1.05

41.8 64.3

3 6

0.4 0.3

5.0 2.5

a

The molecular weight of each block of the symmetric BCP was 16 kg/mol. distance between the plates can range from 0 to 2500 μm. Two long working distance objectives were used at 20× and 50× magnifications in all experiments, and the temperature of the shearing stage was set to a constant temperature of 25 ± 1 °C for all experiments. 2.4.1. Steady-State Coalescence Experiments. Droplet coalescence was investigated by first breaking up the droplets at high shear and subsequently reducing the shear rate, allowing the droplets to coalesce to a steady-state size. Breakup was established through rapid shearing (e.g.,γ̇ = 200−1000 s−1), producing a similar initial starting size of small droplets at R ≈ 0.5 μm with a relatively narrow size distribution. Coalescence was induced upon reductions in shear rate, where steadystate sizes were observed after a prescribed amount of shear strain (e.g., 3000 strain units). Upon the cessation of flow, video images of the droplets were taken as soon as they became spherical (on the order of seconds) with a QICAM digital camera, which was automated by Linkam data acquisition software, Linksys 32. Subsequently, the droplets were sheared at a lower rate over the same shear strain, images were taken upon cessation of flow, and these steps were repeated until the droplets reached a maximum of 10 μm in diameter to avoid interactions with the quartz windows. Coalescence curves are customarily collected in this fashion, and droplet size hysteresis has not been observed upon increasing the shear rate to rebreak the droplets.32 The droplet size distribution was determined with image analysis using Vision Assistant 8.0, an extension program of Labview 8.0 from National Instruments. We employed the Danielson operator, which approximates the edge between a droplet and the surrounding phase a circle. Droplets having a diameter of at least 5 pixels were included in the calculation. The number average droplet radius was calculated as ∑n niR i R n = i =n 1 ∑i = 1 ni (2)

The PI and PI-b-PDMS polymers were hydrogenated to PEP and PEP-b-PDMS, respectively, by adding the matrix (60 g) or BCP (12 g) in cyclohexane (400 or 200 mL, respectively) and a preformed nickel catalyst (30 mL, 1.5 mmol) to a 600 mL reactor. The reactor was pressurized with hydrogen and vented three times, followed by pressurizing the reactor with hydrogen to 90 psi, heating the reactor to 50 °C, and stirring the contents for 24 h. The catalyst was subsequently removed from the polymer solution with citric acid washes, and the polymer solution was precipitated into methanol and dried in vacuo at room temperature. The unhydrogenated and hydrogenated polymers were then characterized using various method, which is included in the Supporting Information. In general, 1H NMR and size exclusion chromatography (SEC) were used to determine the molecular weights of the polymers including the symmetric PDMS-bPEP BCP which was 32 kg/mol, divided between 16k-to-16k blocks. Glass transition temperatures, crystallization temperatures, and melting temperatures were determined using a differential scanning calorimeter (DSC) Q100 (TA Instruments) at a heating rate of 10 °C/min under helium, where the glass transition temperatures are reported as the transition midpoint during the second heat. Thermogravimetric analysis (TGA) was conducted using a TA Instruments Hi-Res TGA 2950 thermogravimetric analyzer under N2 at a heating rate of 10 °C/min. The viscosities of the polymers were quantified using a TA Instruments AR2000 rheometer as listed in Table 1. The polymers were Newtonian, or having a viscosities that were independent of shear rate, within the range of shear rates in the study. The entanglement molecular weight for PDMS and PEP are 9600 and 5100 g/mol, respectively.29 2.3. Polymer Blend Formulation. The PEP and PDMS-b-PEP were blended with PDMS as listed in Table 1 where each PEP matrix was paired with a dispersed phase PDMS with essentially the same viscosity so that the dynamics of droplet deformation should scale similarly across all blends. In contrast, the matrix molecular weight was increased with respect to that of the BCP outer block, which should control its conformation.3,30 A physical compatibilization method was used to create the polymer blends where the BCP, PDMS, and PEP were blended together by hand with a spatula. The efficacy of this mixing method has been tested and deemed sufficient to completely mix the components.31 The blends were formulated to hold constant the volume fractions of the dispersed and matrix phases at 0.07 PDMS and 0.93 PEP, respectively. The volume fraction of the BCP, ϕbcp, was varied between 0 and 0.02; thus, the amounts of PDMS and PEP were adjusted according to maintain constant volume fractions of the dispersed and matrix phases. 2.4. Rheo-Optical Measurements. Rheo-optical measurements were first used to determine the impact of BCP addition on size of PDMS droplets as a function of applied shear. Second, droplet retraction experiments were carried to quantify the surface tension between the PDMS droplet and the PEP matrices. The first set of experiments permits us to determine how BCP addition impacts droplet emulsification, whereas the second set of measurements enable us to compute the interfacial coverage of BCP to connect how wetting of the BCP affects surface loading and droplet stability. Both sets of measurements were performed within a Linkham Scientific Instruments CSS-450 shear stage mounted on an Olympus BX51 microscope, which was operated in the phase contrast mode. The polymer sits between two parallel glass plates inside the stage; thus, the shearing stage operates in parallel plate geometry. The observation aperture is fixed at a radius of 7.5 mm from the bottom plate, according to the manufacturer’s specifications, and the gap

where the total number of droplets was approximately n = 500−8000.

2.4.2. Drop Retraction Experiments. The drop retraction method is useful for measuring the interfacial tension of fluid surfaces that cannot be accessed easily such as those of polymer droplets in immiscible polymer blends. A pulse shear lasting one second was applied to PDMS droplets whose uniform sizes were created with steady shear flow. Droplet deformation was kept below 15% to remain with the linear viscoelastic range of the materials.33 The retraction of the drop from a stretched state back to a spherical shape was captured using the QICAM digital camera at a rate of 35 frames/s. Vision Assistant 8.0 was used to measure the major and minor axes of the drops, L and B, respectively, which were then used to determine the drop deformability parameter, D33

D = D0 exp( − t /τd) (3) where D = (L − B)/(L + B) and D0 being the deformability parameter. The droplet relaxation time, τd, is defined as

τd =

ηeq R 0 (4)

σ

where R0 is the radius of the undistorted droplet and σ is the interfacial tension of the droplet. The equivalent viscosity is defined as

⎡ (2p + 3) + (19P + 16) ⎤ ηeq = ⎢ ⎥ηm 40(p + 1) ⎦ ⎣

(5) On the basis of the similarities between eqs 1 and 4, τd = γ̇ −1, which means that eq 4 corresponds to Ca = 1. 2350


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3. RESULTS AND DISCUSSION 3.1. Steady State Rheo-Optical Measurements for Droplet Breakup and Coalescence. We sought to quantify the impact of adding a symmetric 16 kg/mol-to-16 kg/mol PDMS-b-PEP BCP on the compatibilization of PDMS droplets in the PEP matrices listed in Table 1. In particular, the experiments were carried out to detect how the stretching of the outer copolymer block affects emulsification. The results of the steady-state coalescence experiments are shown in Figures 2 and 3, which correspond to measurements in the 6k and 3k

Figure 3. Number average droplet radius (Rn) with respect to shear stress (τ) and BCP volume fraction (ϕbcp) for all blends of PDMS and PDMS-b-PEP in 3 kg/mol PEP. The BCP is a symmetric 16 kg/mol to 16 kg/mol PDMS-b-PEP diblock copolymer.

PEP matrices, respectively. A common feature throughout the figures is that the sizes of the droplets in the uncompatibilized blends (i.e., those without BCP) are larger than those with BCP. Thus, very small amounts of BCP (e.g., ϕbcp ≤ 0.02) can have a large impact on drop emulsification.19 This impact can be more fully understood through a further examination of the results. In Figures 2 and 3 the number average droplet radii, Rn, are scaled with respect to the droplet shear stress, τ, in eq 6, which is adapted from Rother and Davis and takes into account the effects of the viscosity ratio, p, and size ratio, k = R1/R2, on droplet collisions in shear flow.34 The ratio, p, is obtained from Table 1, whereas we assume k = 1. 2 p + ) (k + 1)2 ( 3 γ̇η τ = 6π

(p + 1)

k

PEP

(6)

Equation 6 is proportional to the viscous interfacial stress, ηmγ̇PEP, within the numerator of eq 1. Based on the flow curves of Rn versus τ, the uncompatibilized and compatibilized blends displayed three distinct regimes with decreasing shear stress. These regimes are exemplified in the blends within the 6k PEP matrices in Figure 2, parts a and b, where Figure 2s shows the Rn of the PDMS droplets whose images from which the Rn are calculated are shown in Figure 2b. First, regardless of copolymer content, droplet breakup occurs at high shear stress, where PDMS droplet have the same approximate size (R ≈ 0.5 μm).35 In general, breakup occurs when the shearing stresses are much greater than the Laplace pressure of the droplets.32,36 Second, droplet coalescence occurs with decreases in shear stress, as evidenced by increases in droplet size. This regime is observed in the linear portion of Figures 2 and 3, where larger drops form due to droplet collisions.32,36 A typical characteristic of the uncompatibilized blends in Figures 2 and 3 is that they exhibit a slope of close to −1.0, i.e., the predicted correspondence between Rn and τ from eq 1. For each series of blends, the values of Rn as well as the slope between Rn and τ decrease with increases in BCP concentration, indicating that BCP addition enhances emulsification and mitigates coalescence.

Figure 2. (a) Number average droplet radius (Rn) with respect to shear stress (τ) and BCP volume fraction (ϕbcp) for all blends of PDMS and 16 kg/mol to 16 kg/mol PDMS-b-PEP in 6 kg/mol PEP. (b) Photographs of several blends made from the 6 kg/mol PEP matrix with BCP loading ranging from ϕbcp = 0 to 0.010. Shear stresses are at the lower end of those in part a. Scale bars are 50 μm. See Table 2 below for shear rates at which droplet aggregation detected. (c) Images of (a) aggregated droplets and (b) atomized or fully broken up droplets for the ϕbcp = 0.01 blend made with the 6 kg/mol PEP matrix. The image of the aggregated droplets was taken after shearing at γ̇ = 0.225 s−1 and image of the atomized droplets was taken after shearing at γ̇ = 12 s−1. Droplets broken up at higher shear rates aggregated into larger structures at lower shear rates. Close ups Atomized droplets are observed in the insets of (a) and (b). The BCP is a symmetric diblock copolymer of 16 kg/mol to 16 kg/mol PDMS-b-PEP. 2351


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aggregates. Based on this criteria, BCP volume fractions above ϕbcp = 0.010 in the 6 kg/mol PEP matrix and ϕbcp = 0.012 in the 3 kg/mol PEP matrix could not be analyzed due to droplet aggregation. Subsequently, a short-term shearing pulse was applied, causing the droplets to deform into ellipsoids, which subsequently retracted back to a spherical shape (Figure 4).

Third, a regime is reached where we observed the aggregation of the compatibilized droplets with further reductions in shear stress. This behavior was observed across all BCP loadings for the compatibilized blends in Table 1. In other words, with decreases in shear stress, the compatibilized droplets grew through shear-induced coalescence to a certain size, then aggregated, based on the amount of added BCP. Droplet aggregation was most easily observed at higher BCP loadings in our study. This is illustrated by viewing the top row of images in Figure 2b, corresponding to ϕbcp = 0.01 within the 6k PEP matrix in Figure 2a. This figure shows droplets broken up at higher shear stresses (τ ≈ 105 Pa). The droplets then underwent a brief range of coalescence to lower shear stresses (τ ≈ 104−105 Pa), and aggregated into elongated structures at stresses below (τ ≈ 104 Pa). Moreover, individual droplets, which form the elongated structures, can be observed in the aggregated structures as shown in the inset of Figure 2c. The shear stresses at which droplet aggregation was detected in Figures 2 and 3 coincide essentially with the last data point at the lowest shear stress of each BCP loading. Thus, depending on ϕbcp, shear-induced coalescence causes droplets grow to a certain critical size at which the compatibilized droplets aggregate. On the basis of experimental and theoretical studies,37−39 we speculate droplet aggregation is due to attractive interactions between the BCPs at the droplet interfaces that result from the expulsion of the matrix from the brush upon BCP surface saturation. To our knowledge, we are the first to document the aggregation of compatibilized polymer droplets in immiscible polymer matrices, and we discuss the mechanisms that control BCP surface saturation and droplet aggregation respectively in sections 3.2 and 3.3 below. 3.2. Drop Retraction Experiments to Quantify BCP Stretching and Surface Saturation. The results from the droplet retraction measurements were analyzed to show that decreasing the matrix molecular weight (i.e., increasing the swelling ratio, So, outside of the droplet) causes the BCP to saturate the blend interface at lower coverage, which impacts droplet stability. Thus, drop retraction experiments33 were conducted to quantify the interfacial tension (σ) at the droplet−matrix interface and the interfacial coverage of the BCP (Γ) as a function of the matrix molecular weight, which should affect the stretching of the block copolymer at the outer droplet surface. The Gibbs adsorption equation (eq 7) ties σ to Γ, whose saturation value (Γsat) should decrease with matrix molecular weight as fewer copolymers can fit at the droplet surface due to BCP stretching.9 The assumption of equilibrium facilitates the computation of the isotherm of the BCP, Γ = Γ(ϕBCP), through the equivalence of the chemical potential, μc, in matrix (eq 8) and the interface (eq 9) which has been derived by Shull and co-workers for wet−dry copolymer brushes.10 Substituting this relationship into eq 7 yields the surface equation of state σ = σ(Γ) for the BCP in eq 10. We also analyze our results by substituting a Langmuir monolayer adsorption isotherm (eq 12) into eq 7 to yield a more computationally friendly equation of state in eq 11 that we use to extract Γsat as well as develop a scaling theory for droplet aggregation in section 3.3. In this way, we elucidate how BCP stretching affects droplet stability by connecting the surface tensions from droplet retraction measurements to the BCP surface coverage for a wet−dry copolymer brush. Hence, droplet retraction experiments were carried out for each blend in Table 1 by first shearing the droplets to reach a steady-state size that was as large as possible without forming

Figure 4. Examples of images taken during the droplet retraction experiments. These specific micrographs are for the uncompatibilized PDMS droplets within the 6 kg/mol PEP matrix. L is the major axis of the droplet, and B is its minor axis.

Optimizing the shearing pulse, enabled us to lengthen the period of droplet retraction and determine the deformability parameter, D, in eq 3 for the droplet, which corresponds to measuring its major and minor axes, L and B, respectively as a function of time. The characteristic relaxation time, τd, was determined from the time evolution of D through eq 3. Thus, by knowing τd, the initial droplet size, Ro, and the matrix viscosity, ηm, the surface tension of the droplet/matrix interface, σ, can be determined from eq 3. Figure 5 shows the relaxations of the droplets with respect to the BCP volume fraction by plotting the natural log of the scaled

Figure 5. The scaled deformability parameter, ln(D/Do), with respect to the scaled retraction time, t/τd, for as a function of BCP volume fraction (ϕbcp) for the PDMS droplets in the 6 kg/mol PEP matrix. The BCP is a symmetric 16 kg/mol −16 kg/mol PDMS-b-PEP diblock copolymer.

deformability parameter, D/Do, as a function of the scaled retraction time, t/τd. Taking the inverse of the slopes from this plot yields τd from which the σ can be extracted. Based on the linearity of the fit of eq 3 to the data, the retraction rate was sufficiently slow to ensure that the deformation and retraction was within the linear viscoelastic range of the materials, satisfying a major requirement for using the droplet retraction method.33 Subsequently, the BCP interfacial coverage, Γ, was obtained from droplet retraction measurements through the Gibbs 2352


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adsorption equation, which connects Γ to changes in surface tension, σ, and bulk copolymer volume fraction, ϕbcp

Γ=−

⎞ ⎛ 1 ⎜ dσ ⎟ kbT ⎜⎝ d ln ϕ bcp ⎟⎠

(7)

where kb is the Boltzmann constant and T is the temperature. Based on the work of Shull, we predicted the adsorption isotherm of the wet−dry BCP brush by equating its chemical potential, μc, between the droplet and matrix phases. In the matrix phase, the BCP chemical potential is:10

μc kBT

≅ ln ϕ bcp − ϕ bcp + χNPDMS + 1 −

NPEP + NPDMS PPEP

(8)

where χ is the Flory parameter. The volume fraction of BCP (ϕbcp) and the degrees of polymerization for the PDMS block of the copolymer (NPDMS), the PEP block of the copolymer (NPEP), and matrix polymer (PPEP) are found in Table 1. The chemical potential at the droplet interface in which the brush of one block of the copolymer is wet (PPEP < NPEP) on one side of the interface and the brush of the other side is dry (PPDMS > NPDMS) is

Figure 6. Interfacial surface tensions of the PDMS droplets from drop retraction measurements within 3 kg/mol and 6 kg/mol PEP matrices. Dashed lines are fits of eq 10, the wet−dry BCP interfacial equation of state, to the data. The BCP is a symmetric 16 kg/mol to 16 kg/mol PDMS-b-PEP diblock copolymer.

1/3 ⎡ Γ ⎤ ⎡ 375 ⎤ ⎡⎢ NPEP ⎤⎥ ⎥+⎢ = 1 + ln⎢NPEP ⎥ ⎢⎣ ρ0 a ⎥⎦ ⎣ 32 ⎦ ⎢⎣ PPEP2/3 ⎥⎦ kBT

μc

⎡ Γ ⎤2/3 ⎡ Γ ⎤2 9 ⎥ ⎥ ×⎢ + NPDMS⎢ ⎢⎣ ρ0 a ⎥⎦ ⎢⎣ ρ0 a ⎥⎦ 2

(9)

where ρ0 is the segment density of the copolymer at approximately 8 chains/nm3 and a is the projected bond length at approximately 0.5 nm. The predicted Γ was determined by equating eqs 8 and 9, and adjusting χ to best fit the experimental Γ. The surface equation of state for the BCP is computed by10 2/3⎤ 2 ⎡⎛ Γ ⎞ 31/3 ⎛⎜ Nwet ⎞⎟⎛ Γ ⎞ ⎥ ⎜⎜ ⎟⎟ ⎟⎟ + 1 + σ = σ0 − k bT Γ⎢⎢⎜⎜ ⎜ ⎟ ρa 22/3 ⎝ Pwet 2/3 ⎠⎝ ρ0 a ⎠ ⎥⎦ ⎣⎝ 0 ⎠

(10)

which is obtained by substituting eqs 8 and 9 into eq 7. Figure 6 shows the interfacial tensions of the PDMS droplets in the 3k and 6k PEP matrices with respect of the ln of ϕbcp. The interfacial tension between the uncompatbilized PDMS/ PEP blends was 1.9 ± 0.1 mN/m, irrespective of molecular weight. A higher interfacial tension value of 3.2 mN/m has been reported between PDMS and polyisoprene (PI),40 in which PI is the unhydrogenated version of PEP. Thus, the hydrogenation of PI to PEP may reduce its interfacial tension with PDMS. Further, Figure 6 shows that increasing ϕbcp reduces σ, which occurs more dramatically in the 6k PEP matrix with the same 16k PDMS-b-16k PEP copolymer. The dashed and dotted lines are the predicted interfacial tensions for the wet−dry BCP brush from eq 10, which agree reasonably well with the experimental values. Figure 7 shows the adsorption isotherms for the symmetric BCP in 3k and 6k PEP matrices that were computed from eq 7. The dashed lines in Figure 8 are predictions from eqs 8 and 9 for a wet−dry BCP, which match the experimental results well. The nonlinear regression of these equations to the isotherms yield similar χ = 0.0860 and 0.0720 (with fitting error of ±0.0005 for both) for the blends in the 3k and 6k PEP

Figure 7. BCP interfacial coverage (Γ) with respect to BCP bulk volume fraction (ϕbcp). Lines are nonlinear least-squares fits of eqs 8 and 9 to the data with χ = 0.0860 and 0.0720 in 3k and 6k PEP, respectively. The BCP is a symmetric 16 kg/mol to 16 kg/mol PDMSb-PEP diblock copolymer.

matrices, respectively. The low χ values are expected, as the constituents of the BCP are only self-miscible with their chemically identical counterparts in the blends. Further, based on the correspondence of the experimental and theoretical isotherms in Figure 7, increasing the matrix molecular weight, PPEP, from 3k to 6k, increases the BCP interfacial coverage. This observation was further quantified by extracting the saturation coverage, Γsat, from assuming a Langmuir monolayer interfacial equation of state that is obtained from substituting the Langmuir adsorption isotherm

σ = σ0 + kbT Γsat(1 − Γ /Γsat) σ = σ0 + kbT Γsat(1 − KϕBCP) 2353

(11)


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however, the correspondence between So and Γ for the droplet imposes difficulty on relating BCP stretching to droplet stability. With further decreases in shear rate, however, we detect droplet aggregation, for which we postulate a mechanism from a list of phenomena that include van der Waals attraction, depletion flocculation, and interfacial dewetting. We discount the first two phenomena. Based on our previous studies of particle stability in semidilute and concentrated polymer solutions and melts, the presence of the polymer brush hinders close contact significantly reducing van der Waals attraction between the dispersed phase.2,3,42,43 Second, the probability of the depletion flocculation of droplets through the formation of BCP micelles is also low. Depletion flocculation would occur if micelles were excluded from the region between the droplets whose average separation distance would be within a micelle diameter. Assuming the BCPs form micelles with diameters D = 10−20 nm, this dimension is still less than the surface-to-surface separation distance at roughly h = 0.54 μm for R = 0.5 μm radius droplets at volume fraction, ϕ = 0.07. (We estimate the surface-to-surface separation distance as h = R((ϕm/ϕ)1/3 − 1), where ϕm = 0.63 for random close packing). Moreover, based on our interfacial tension measurements in Figure 7, micelle formation is not favored since σ did not flatten and become constant and independent of increases in ϕbcp, a characteristic of micelle formation. Thus, we postulate that dewetting, or expulsion of the matrix from the BCP brush drives droplet aggregation upon saturation of the blend interface. Based experimental and theoretical studies with polymer-grafted particles in semidilute and concentrated polymer solutions and melts, dewetting of the matrix can lead to the attraction between grafted interfaces as the matrix polymer seeks to maximize its conformational freedom and separate from the dispersed phase upon expulsion from the brush. Further, researchers have used self-consistent mean-field (SCF) calculations to predict that the expulsion of the matrix homopolymer from the BCP can lead to the attraction between compatibilized interfaces.37−39,44−46 Moreover, attractions between compatibilized droplets are more likely for monodisperse BCPs,37,45,46 such as the copolymer used in this study (PDI ≈ 1.02). 3.3. Droplet Aggregation Through Dewetting. To give support to the dewetting mechanism for droplet aggregation, we use a force balance between compatibilized droplets that permits us to relate the BCP surface coverage and shear rate at which we detect aggregation from our optical rheology measurements. The force balance in eq 14 relates the force of shear, Fs, on the left-hand side of the equation (LHS) to the forces at droplet contact at the onset of aggregation, Fc, on the right side of the equation (RHS)34

Figure 8. Phase diagram of scaled surface coverage (Γ/Γsat) with respect to scaled shear rate (γ̇/γ̇max) denoting regions of emulsification, coalescence, and aggregation of compatibilized polymer droplets in immiscible homopolymer matrices. Data are from micrographs at which droplet aggregation was detected and curve is nonlinear leastsquares fit of eq 15 to data with C = 4.6. The region below curve is that of emulsification and coalescence, where emulsification occurs with increasing BCP surface coverage (up arrow) and coalescence occurs with decreasing shear rate (left arrow). Region of droplet aggregation occurs above the curve. The BCP is a symmetric 16 kg/mol to 16 kg/ mol PDMS-b-PEP diblock copolymer.

KϕBCP Γ = Γsat 1 + KϕBCP

(12)

into the Gibbs adsorption equation (eq 7) where K in eqs 11 and 12 is the equilibrium constant, i.e., the ratio of the adsorption and desorption rate constants K = ka/kd. The fits of eqs 11 and 12 to the interfacial tensions and adsorption isotherms are included in the supplementary documents for the sake of brevity. Based on the goodness of the fit, Γsat = 0.079 chains/nm2 in 3k PEP, which increases to Γsat = 0.140 chains/ nm2 in 6k PEP. Thus, the nearly 2-fold increase in Γsat corresponds inversely with decreasing of the swelling ratio, So = NPEP/PPEP, outside of the droplet from So = 5.0 to 2.5, which should lead to a decrease in the stretching of the BCP outer block. We anticipate that further increases in PPEP should lead to further decreases in BCP stretching, which should result in a maximum interfacial coverage, Γmax, based on packing considerations41

Γmax =

υ̅1/3(N /n)1/2 υ̅N

2 p + ) (k + 1)2 ⎛ ( 3 lim F = 6π

(13)

s

where υ̅ is the equivalent monomer volume, N = 260 is the total degree of polymerization of the copolymer, and n = 1 for a diblock copolymer. Substituting the appropriate values into eq 13, yields Γmax = 0.25 chains/nm2, which should occur at the equivalence of the matrix and outer BCP block molecular weights, PPEP = NPEP, i.e, So = 1. Based on the studies of Macosko, we expect that saturation levels between Γsat = 0.079 and 0.140 chains/nm2 to mitigate Marangoni stresses and lead to an immobile drop interface. Thus, at higher coverage, we anticipate that the BCP-coated droplets will behave analogously to polymer-grafted particles;

⎜

(p + 1)

k

⎝

h→0

× γ̇ηmR2 sin 2 θ sin ϕ cos ϕ ⎛ δ⎞ = ⎜P − 3 ⎟ΔA = Fc ⎝ h ⎠

1 − A ⎞⎟ G ⎠

(14)

Several simplifications are made to relate this fundamental relation to Γ and γ̇. First, aggregation is assumed to occur along the centerline of equal-sizes droplets, which makes constant the angles of droplet orientation, θ and ϕ, the droplet radius, R, and the limiting values of the mobility functions A and G as the gap 2354


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Article

between the drops, h, approaches zero.34 Second, with respect to contact forces, the dynamic pressure is the Laplace pressure, P = 2σ/R, while we relate the attraction between droplets, δ, to the surface tension of the droplets through δ = 6πa2σ, where a is the projected bond length of the copolymer.34 Thus, we model the droplet aggregation as cohesion between interfaces.35 Further, because the area of contact, ΔA, is proportional to the droplet radius,34 we equate ΔA = CsR2 to enable the grouping of constants such as Cs, which is a function of h, and the cancelation of R. After integration and rearrangement eq 14 becomes

⎛2 ⎞ ⎜ − C1⎟Cs σ ≅ C 2 ηm γ̇* ⎝R ⎠

C = 4.6, lending support to our supposition that the dewetting of the matrix from the BCP causes compatibilized droplets to aggregate in shear flow. Mechanistically, aggregation begins at the balance between shear and attractive contact forces, the latter becoming apparent at higher coverage due to the monodisperse copolymer brush at the droplet interface.37−39 Further, for the materials in Table 1, Figure 8 represents a scaled phase diagram where the region of droplet coalescence and emulsification resides under the right side of the predicted curve, whereas the region of droplet aggregation lies above the left side of the same curve. The correspondence between experiment and theory in Figure 8 lends support to our observation in section 3.1 that all BCP-coated droplets aggregate following coalescence to a critical droplet size based on the BCP amount (ϕbcp) and applied shear (γ̇). Thus, immiscible polymer droplets with low ϕbcp coalesce to large sizes over a larger range of γ̇, whereas droplets emulsify with higher ϕbcp, but also aggregate at higher γ̇ most likely due to dewetting of the matrix from the BCP caused by its saturation.

(15)

where C1 = 6πa /h and C2 = f(p, k, θ, ϕ, A, G, h) from the RHS and LHS of eq 14, respectively. Because droplet attraction should predominate, C1 ≫ 2/R. Subsquently, substitution of eq 11 into eq 15 yields eq 16 2

ηm γ̇* = −

3

⎛ C1Cs Γ* ⎞ kBT Γsat ln⎜1 − ⎟ C2 Γsat ⎠ ⎝

(16)

4. CONCLUSIONS

to scale the surface coverage with respect to saturation within a polymer matrix, and Γ* is the coverage at aggregation. To scale eq 16 relative to the shear rate at droplet breakup, γ̇max, we assign, C = ηmγ̇maxC2/(C1CskbTΓsat), giving eq 17, the relationship between BCP surface coverage, Γ*, and shear rate at which droplet aggregation occurs, γ̇*

⎛ γ̇* ⎞ Γ* ⎟⎟ = 1 − exp⎜⎜ − C Γsat γ̇max ⎠ ⎝

Using rheo-optical methods, we studied the impact of symmetric diblock copolymers on the coalescence and aggregation of polymer droplets in immiscible homopolymer blends. Anionic polymerization was used to produce PEP homopolymers and symmetric 16 kg/mol-to-16 kg/mol PDMS-b-PEP copolymer of very low polydispersity, which was necessary to isolate the importance of interfacial wetting. Each compatibilized blend exhibited three distinct regimes. First, droplet breakup occurred at high shear rates; second, droplet coalescence resulted from subsequent decreases in shear rate; and third droplet aggregation followed upon further reductions in shear rate. Overall, very small quantities of copolymer were effective in emulsifying the droplets and suppressing coalescence, where the stretching of the BCP in lower molecular weight matrices reduced coalescence, increasing droplet stability. The analysis of drop retraction experiments match the theoretical predictions for wet−dry brush systems, showing that the stretching of the BCP at the outer droplet surface causes it to saturate at lower BCP coverage. The droplets grow through shear-induced coalescence to a critical size at which subsequent to surface saturation, the droplets aggregate. On the basis of our analysis, droplet aggregation is the result the polymer matrix dewetting from the copolymer brush, leading to the attraction between droplets toward lower shearing forces. We scale the regions of droplet coalescence, emulsification, and aggregation for our systems with a force balance to connect the forces of shear with those of attraction from the copolymer brush upon droplet contact from based on the interfacial coverage. Overall, our results indicate that a subtle balance is struck between shear-induced coalescence and interfacial wetting in the emulsification of polymer droplets in immiscible homopolymer matrices.

(17)

Table 2 and Figure 8 give the shear rates and surface coverages at droplet aggregations that are used to test eq 17. The shear rates Table 2. Shear Rates (γ̇*) at Which Droplet Aggregation Was Detecteda

matrix MW

droplet BCP BCP breakup saturation volume shear rate, coverage, fraction, γ̇max (s−1) Γsat (nm−2) ϕbcp

3k PEP

109.0

0.079

6k PEP

15.0

0.140

0 0.003 0.006 0.012 0.018 0 0.001 0.003 0.006 0.010

droplet aggregation shear rate, γ̇* (s−1)

droplet aggregation surface coverage, Γ* (nm−2)

not detected 13.5 19.5 37.5 45.0 not detected 1.4 3.0 6.0 7.5

0 0.030 0.044 0.063 0.071 0 0.040 0.087 0.115 0.130

a Γ* calculated from eqs 8 and 9 with χ = 0.086 and 0.072 in 3k and 6k PEP, respectively. The BCP is a symmetric 16 kg/mol to 16 kg/mol PDMS-b-PEP diblock copolymer.

were obtained from micrographs such as those in Figure 2b based on the criterion of seeing one or more aggregates in an image. Based on the volume fraction of BCP in the blend, the surface coverage at aggregation, Γ*, was determined using eqs 8 and 9 with χ = 0.0860 and 0.0720 in 3k and 6k PEP, respectively. Figure 8 shows that eq 17 agrees well with the experimental observations for the onset of droplet aggregation with a value of

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ASSOCIATED CONTENT

S Supporting Information *

Schemes and protocols for polymer synthesis and characterization. This material is available free of charge via the Internet at http://pubs.acs.org. 2355


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(35) Hiemenz, P.; Rajagopolan, R. Principles of Colloid and Surface Chemistry, 3rd ed.; Marcel Dekker: New York, 1997. (36) Ramic, A.; Stehlin, J.; Hudson, S.; Jamieson, A.; ManasZloczower, I. Macromolecules 2000, 33, 371−374. (37) Matsen, M. J. Chem. Phys. 1999, 110, 4658−4667. (38) Thompson, R.; Matsen, M. J. Chem. Phys. 2000, 112, 6863− 6872. (39) Thompson, R.; Matsen, M. Phys. Rev. Lett. 2000, 85, 670−673. (40) Kitade, S.; Ichikawa, A.; Imura, N.; Takahashi, Y.; Noda, I. J. Rheol. 1997, 41, 1039−1060. (41) Hudson, S.; Jamieson, A.; Burkhart, B. J. Colloid Interface Sci. 2003, 265, 409−421. (42) Dutta, N.; Green, D. L. Langmuir 2008, 24, 5260−5269. (43) Dutta, N.; Green, D. L. Langmuir 2010, in press. (44) Balazs, A. C.; Singh, C.; Zhulina, E. Macromolecules 1998, 31, 8370−8381. (45) Semenov, A. Macromolecules 1993, 26, 2273−2281. (46) Shull, K. J. Chem. Phys. 1991, 94, 5723−5738.

AUTHOR INFORMATION

Corresponding Author

*Tel:1-434-924-1302. Fax: 1-434-982-2658. E-mail: dlg9s@ virginia.edu.

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Impact of Diblock Copolymers on Droplet Coalescence, Emulsification

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