Dynamic Heterogeneity and Phase Separation Kinetics in Miscible

Sep 12, 2013 - Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7-D Arica, Chile. § Department of Physics, University of Ioannina, 45...
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Dynamic Heterogeneity and Phase Separation Kinetics in Miscible Poly(vinyl acetate)/Poly(ethylene oxide) Blends by Local Dielectric Spectroscopy Tomas P. Corrales,† David Laroze,†,‡ George Zardalidis,§ George Floudas,†,§ Hans-Jürgen Butt,† and Michael Kappl*,† †

Max Planck Institute for Polymer Research, D-55128 Mainz, Germany Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7-D Arica, Chile § Department of Physics, University of Ioannina, 45110 Ioannina, Greece ‡

S Supporting Information *

ABSTRACT: Local dielectric spectroscopy (LDS) was employed to analyze the miscible blend composed of poly(vinyl acetate) (PVAc) and poly(ethylene oxide) (PEO). The two homopolymers have very different relaxation times and glass transition temperatures. The aim was to study the dynamic heterogeneity in films as a function of the film thickness. Measurements of the local blend composition at the nanoscale have shown that LDS is sensitive to the dynamic heterogeneity. In thinner films, phase segregation occurs, and the kinetics of phase demixing was studied using as a probe the change in local composition. These results open new possibilities for studying interdiffusion and adhesion at polymer−polymer interfaces as a function of annealing temperature with LDS.

1. INTRODUCTION A key issue in the design of multicomponent materials for nanotechnology is knowledge of the local composition that imparts the final material properties at the nanoscale. A wellknown example is polymer blends where the final properties depend on the level of compatibility between the constituent homopolymers.1,2 The majority of polymer blends are immiscible and phase separate into micrometer size domains in contrast to a small number of blends that remain miscible down to the molecular level.3−7 Hence, it is essential to develop techniques that can probe the local composition at the nanoscale. One approach is based on probing the optical properties, for example, by combining laser scanning confocal microscopy and fluorescence correlation microscopy techniques. Recent efforts in this direction8 provided the local composition within the phase-separated domains as well as the interfacial width for an immiscible polymer blend. Another promising approach is by probing the local dielectric response of polymer films. In this respect, efforts by electrostatic force microscopy (EFM) allowed simultaneous mapping of the mechanical properties with respect to the topography/phase and the dielectric properties of polymeric films.9−20 EFM is based on the electrostatic interaction between a conductive atomic force microscopy (AFM) probe in close proximity with the sample that is supported by a flat conductive substrate. With EFM the dielectric properties of a film can be studied with a lateral resolution of few tens of nanometers. Therefore, the technique is also known as local dielectric © 2013 American Chemical Society

spectroscopy (LDS). Despite the powerful technique only a limited number of polymers have been investigated so far. The polymer which has been studied most is poly(vinyl acetate) (PVAc). The reason is the high dielectric strength (Δε = 4 at 333 K) and convenient glass transition temperature (Tg = 312 K) of PVAc. The method was successfully employed in studying the micrometer heterogeneities in immiscible polymer blends of polystyrene (PS) with PVAc.21−23 An extension of the method by Fumagalli et al.11 allowed mapping of the dielectric constant of a film by “nanoscale capacitance microscopy”, where the microscope was equipped with a subattofarad low-frequency capacitor detector. Riedel et al.18 employed EFM with phase imaging at a fixed frequency or with a double pass method and imaged the morphology and nanodielectric properties of the same PS/PVAc blend.22,24 This combination gave rise to the dielectric constant mapping of the films revealing micrometer size heterogeneities composed from PVAc inclusions within the PS matrix. In miscible polymer blends, however, the system is spatially homogeneous at such length scales. Nevertheless, miscible polymer blends are known to be dynamically heterogeneous. Dynamic heterogeneity here refers to the presence of distinct relaxation times in otherwise thermodynamically mixed blends.3−7 The fingerprint of dynamic heterogeneity is the Received: April 5, 2013 Revised: August 28, 2013 Published: September 12, 2013 7458

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reflectivity from the backside of the cantilever, metallic coatings were deposited on both sides of the cantilever. Oscillation of the AFM cantilever could be enforced by a driving voltage to a small piezo stack integrated in the commerical cantilever holder. This driving voltage was provided from a phase locked loop amplifier (PLLPro 2, RHK Technology, Troy) that was connected to the AFM controller (Nanoscope IIIa, Bruker) through a signal access module (Nanoscope SAM, Bruker). Using the PLL, we can image the samples in frequency modulation mode (FM-AFM). Additionally, we used this PLL to detect changes in the resonance frequency of the cantilever (Δf) due to the dielectric response of the polymer to an alternating voltage. The modulated Δf signal from the PLL was then fed into an external lockin amplifier (7280 DSP Signal Recovery, Ametek) to filter out its amplitude and phase. The alternating voltage applied between AFM tip and counter electrode was generated by the same lock-in and later amplified before charging the tip. A schematic of our experimental setup is shown in Figure S3. The lock-in amplifier detects modulations as low as 0.5 Hz, and this sets the lower limit of our LDS frequency sweep. The high frequency limit is given by the PLL electronics and the response time of the electrically interacting cantilever, which acts as a first order filter.17 By using a stiff cantilever (300 kHz) and a fast input filter for the PLL (100 kHz bandwidth), we optimize the reaction time of PLL and can track changes in Δf as fast a 100 μs; in other words, we can detect modulations of up to 10 kHz. Therefore, our current LDS setup has a final bandwidth limited to 4 decades (0.5 Hz−5 kHz). Although other methods have shown a broader bandwidth20 based on measuring direct tip−sample forces, it is generally accepted that LDS sensitivity is enhanced when measuring force gradients,9 which are proportional to changes in the resonance frequency (Δf). Principles of LDS Measurements. LDS can be implemented by an AFM equipped with a conductive cantilever located in close proximity to the sample. Both dc and ac bias voltages are applied between the conductive tip and the conductive sample that acts as a counter electrode. The applied electric field polarizes a sample volume near the tip. The technique is based on measuring the tip−sample capacitance in a quantitative way. The applied voltage V produces a force on the cantilever tip, F = 1/2V2 dC/dz, where z is the tip−sample distance and C the capacitance.14 This force can be measured either directly from the cantilever deflection signal or by measuring force gradients (dF/dz). The force field due to the interaction of the charged tip with the polarized sample volume results in a small but measurable change in cantilever resonance frequency (Δf). Force gradients are related to the change in the cantilever resonance frequency by Δf = −( f 0/2k) dF/dz, where f 0 is the resonance frequency of the cantilever in absence of external forces and k is its spring constant. When an alternating voltage (Vac) is applied between the tip and the counter electrode, a modulation of the Δf signal is produced by the dielectric response of the material. The second harmonic of this modulated signal (Δf 2ω) is related only to the tip− sample capacitance by10,28

dual relaxation processes that reflects the component segmental dynamics. In addition, concentration fluctuations7 give rise to the broadening of relaxation spectra as compared to the homopolymers. In this study, we employ the miscible blend composed from PVAc and poly(ethylene oxide) (PEO) possessing large dynamic asymmetry (difference in glass transition temperatures of homopolymers of about 100 K). PVAc/PEO blends have been investigated in the bulk as a function of composition, temperature,25,26 and pressure.27 These studies revealed that blends rich in PVAc are thermodynamically mixed yet are dynamically heterogeneous. Despite the good knowledge attained in the bulk, little is known on the behavior of such blends in films. In a polymer film, specific interactions of one component with the substrate may lead to phase demixing for certain film thicknesses. By employing LDS, we first demonstrate that the method is sensitive to the dynamic heterogeneity in films of PVAc/PEO blends. Second, we deduce the local blend composition at the nanoscale. In a third step, we follow the kinetics of phase demixing driven by PEO crystallization using the change in local dynamics as a probe. Thus, LDS can be employed in studying thermodynamically miscible blends where the relevant length scale controlling the segmental dynamics is of the order of the Kuhn length.

II. EXPERIMENTAL SECTION Samples and Sample Preparation. The PVAc (Mw = 59 400 g/ mol) and PEO (Mw = 32 500 g/mol, Mw/Mn = 1.09) used in this study were purchased respectively from Alfa-Aesar and Polymer Source Inc. PVAc/PEO blends with 5 and 10 wt % PEO (noted below as 95/5 and 90/10) were prepared from chloroform solutions, whereas toluene was used for pure PVAc samples. Films of PVAc and PVAc/PEO blends were prepared by spin-coating the solution onto flat surfaces. The final film thickness was controlled using rotation speeds of 2000−4000 rpm and solution concentrations of 1−10 mg/mL. For pure PVAc and the 95/5 blend gold-coated silicon substrates prepared by physical evaporation were used. A 5 nm chromium adhesion layer was first evaporated on a silicon substrate, after which 50 nm of gold is evaporated on top. In general, gold is a good substrate for thick samples when spin-coated from toluene or chloroform. For thinner samples (h < 200 nm), however, it was hard to obtain smooth films, since samples tended to dewet. Therefore, highly doped commercial silicon wafers Si(100) were used for all thin film samples to obtain uniform and stable films. In both cases the conductive substrates served as counter electrodes to allow application of a defined voltage between tip and sample. Subsequently, all samples were annealed in vacuum at Tg + 50 K for several days (3−6 days) to ensure the complete removal of solvent (toluene or chloroform). Films prepared from toluene or chloroform over gold or silicon with different thicknesses (h > 50 nm) do not show great differences in LDS loss tangent spectra as long as the films are correctly annealed (Figure S1, Supporting Information).15 Local Dielectric Spectroscopy Setup (LDS). A commercial Enviroscope AFM (Bruker, Santa Barbara, CA) was employed in this study. This AFM works within a hermetically sealed sample chamber that was flushed with dry nitrogen before all experiments in order to obtain a controlled dry atmosphere. Our AFM setup has a sample heating stage controlled with a commercial temperature controller (Lakeshore 331), with an accuracy of 0.1 K, and a maximum temperature of 458 K. Silicon cantilevers with a 300 kHz resonance frequency (k = 42 N/m) and a tip radius R < 5 nm were employed (Olympus OMCL-AC160TS-W2). The cantilevers including the tip were rendered electrically conductive by metal evaporation (5 nm chromium adhesion layer followed by 25 nm of gold). The final tip radius was R ∼ 30−40 nm as determined from SEM images (LEO 1530 Gemini) (Figure S2). To minimize thermal drift and to improve

⎛ f ⎞ d2C Δf2ω = − Vac 2⎜ 0 ⎟ 2 ⎝ 4k ⎠ dz

(1)

The phase-lag (δv) between the applied alternating voltage Vac and the observed frequency shift Δf 2ω contains the information on the dynamics of the system. We represent the phase lag data as the loss tangent function:

tan δv =

d2C″ /dz 2 d2C′/dz 2

(2)

Here, C′ and C″ are the real and imaginary part of the complex capacitance. The measured loss tangent can be analyzed using a capacitance model. According to Fumagalli et al.,11 the tip−sample capacitance for dielectric film of thickness h can be approximated by

⎛ R(1 − sin θ ) ⎞ C*(z , ω) = 2πε0R ln⎜1 + ⎟ z + h/ε*(ω) ⎠ ⎝ 7459

(3)

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In eq 3, R and θ are the effective tip apex radius and half of the cone angle of the tip, ε0 is the dielectric permittivity of vacuum, and ε*(ω) is the complex dielectric function of the polymer film. Given the form of the capacitance model, the loss tangent function (tan δv) is not equal to that measured using a double plate capacitor as in the latter case the loss tangent refers to the ratio of the dielectric loss to the dielectric permittivity (tan(δ) = ε″/ε′). Nevertheless, loss tangents measured with AFM (tan δv) give similar peak shapes as with a doubleplate capacitor. Relaxations times are obtained by expressing tan δv (eq 2) in terms of eq 3 and the empirical Havriliak−Negami function:29

* (ω , T ) = ε∞(T ) + εHN

Δε(T ) [1 + (iωτHN(T ))m ]n

1a. The loss tangent curves of the 95/5 and 90/10 PVAc/PEO blends are shown in Figure 1b,c.

(4)

where ε∞(T) is the high-frequency permittivity, τHN(T) is the characteristic relaxation time in this equation, Δε(T) = ε0(T) − ε∞(T) is the relaxation strength, and m and n (with limits 0 < m, mn ≤ 1) describe respectively the symmetrical and asymmetrical broadening of the distribution of relaxation times. From τHN, the relaxation time at maximum loss, τmax, is obtained analytically following

τmax

⎡ ⎢ sin = τHN⎢ ⎢⎣ sin

( 2 π+m2n ) ⎤⎥ ⎥ ( 2π+mn2n ) ⎥⎦

−1/ m

(5)

The loss tangent function (tan δv) was fitted using eqs 2, 3, and 4 with h, R, θ, ε0, ε∞, and z fixed. For ε∞ we used the measured value from our earlier DS measurements29 of ε∞ = 2.24. Four fitting parameters are employed, namely, τHN, Δε, m, and n. To obtain the experimental loss tangent curves, reference spectra were taken over a bare substrate at each temperature. For this, a scratch is made with a sharp syringe needle to locally remove the polymer film and uncover the bare substrate and record its spectra. The final loss tangent curve was obtained as tan δv = tan(δfilm − δbare). For each loss tangent curve, 6 frequency sweeps for both the bare substrate and the polymer film were recorded on a single spot and averaged within the frequency range from 0.5 Hz to 5 kHz. Each single sweep takes 8 min to complete. To position the tip at a fixed height (z) from the sample surface we first approach the surface in imaging mode (FM-AFM) using the Δf signal as our feedback, without applying a bias voltage to the tip. Typical approach set points are Δf ∼ −5 Hz. After imaging the region in FM-AFM mode, the instrument is switched to spectroscopy mode. Δf is recorded as a function of the vertical piezo-position while the tip is ramped toward and back from the surface. In order to position the tip at a defined distance from the surface, we recorded Δf versus distance curves with a defined ramp size of the vertical piezo movement. Using the trigger function of the force spectroscopy mode, we reverse the ramp at the same Δf value of about −5 Hz used as a set point for imaging. Leaving the piezo at the retracted position after such a piezo-movement ramp results in the final tip−sample distance above the polymer film of z = r + A, where r is the ramp size and A is the amplitude of oscillation of the cantilever. Tip−sample distances of z = 40−50 nm were typically used. To position the tip above the bare substrate for the reference spectra, the film thickness h was added to the total height (zbare = z + h), in order to record all spectra at the same distance from the substrate (i.e., supporting counter electrode). Once the tip was positioned at the correct height, all AFM feedbacks were turned off and we switched the alternating voltage on, sweeping it in frequency. Alternating voltages with amplitudes between 2 and 4 V were used. After each frequency sweep, the tip−sample distance was readjusted by another piezomovement ramp to compensate for possible drifts. Under such conditions we obtain a lateral resolution of ∼100 nm and a penetration depth within the film of ∼30 nm, as estimated from a finite element model for a 50 nm thick film (Figure S4).

Figure 1. Loss tangent curves for pure PVAc (top) and for PVAc/PEO blends with ratios 95/5 (middle) and 90/10 (bottom). Dashed lines represent fits obtained by combining eqs 2, 3, and 4. Pure PVAc loss tangent curves are shown for temperatures 323, 327, 331, 335, and 339 K. For the 95/5 blend curves correspond to 319, 323, 327, and 329 K. For the 90/10 blend, curves at 315, 319, 323, and 325 K are shown. The loss tangent curve at 323 K is highlighted in red.

The loss tangent curves of bulk PVAc and of the blends at 323 K are shown in red. There is a speed-up of the dynamics with decreasing PVAc content under isothermal conditions which is a direct consequence of dynamic heterogeneity. The latter is manifested by the dual relaxation processes reflecting PVAc and PEO segmental dynamics that are shifted relative to the homopolymers.27 Because of temperature limitations, in our experimental setup we can only access the PVAc segmental dynamics in PVAc-rich blends. The shape of loss tangent curves (Figure 2) exhibits a systematic broadening with decreasing PVAc concentration. The broadening is evident both from the low and high

III. RESULTS AND DISCUSSION Dynamic Heterogeneity. Loss tangent curves for pure PVAc at temperatures between 323 and 339 K with respective fits following the procedure outlined above are shown in Figure

Figure 2. Loss tangent curves for PVAc (spheres) and the blends with 95/5 (squares) and 90/10 (triangles) obtained at respective temperatures of 327, 321, and 315 K. For better comparison the curves where shifted vertically but not horizontally. 7460

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frequency sides of the peak. This is a manifestation of increasing concentration fluctuations in the blends.7 Using the procedure outlined in the Experimental Section, the PVAc segmental relaxation times at maximum loss were extracted and are plotted in Figure 3 in the usual Arrhenius representation.

Figure 3. Segmental relaxation times corresponding to the maximum of dielectric loss for pure PVAc (spheres) and PVAc/PEO blends with composition of 95/5 (squares) and 90/10 (triangles) measured by LDS. Dashed lines indicate VFT fits.

Figure 4. (a) Seaweed and dendritic finger-like structures that have grown from a scratch edge of a PVAc/PEO 90/10 film of 50 nm thickness at 323 K. (b) Local LDS spectra are recorded with the tip above of such a finger (positioned at the red triangle) and positioned at 1 μm (green circle) and 5 μm (blue square) away from it. (c) Loss tangent curves obtained at the indicated positions. The dashed lines are not fits but represent the pure PVAc (red) and PVAc/PEO 90/10 (blue) blend loss tangent curves obtained at the same temperature but from thicker films.

The τ(T) dependence conforms to the Vogel−Fulcher− Tammann (VFT) equation as τ = τ0 exp(B/(T − T0)), where τ0 is the relaxation time in the limit of very high temperatures, B is the activation parameter, and T0 the “ideal” glass transition temperature. The PVAc relaxation times in the PVAc/PEO blends are systematically shifted toward lower temperatures as in earlier measurements on bulk samples (lines) obtained from dielectric spectroscopy.27 Relaxation times and fitting parameters of our LDS experiments are compared to classical bulk dielectric spectroscopy results in the Supporting Information (Figures S5 and S6). We find that the relaxations times calculated from our fits show a slight enhancement of dynamics in blended films, while pure PVAc relaxation times follow closely its bulk counterpart. Although segmental relaxation times in immiscible polymer blends were studied earlier by LDS, it is the first time that the same method is employed to detect segmental dynamics and dynamic heterogeneities in miscible polymer blends. According to the self-concentration model of Lodge and McLeish,5 chain connectivity enhances the local concentration and the segmental dynamics of a given component in a miscible blend are biased toward the corresponding homopolymer. The relevant length scale for evaluating this selfconcentration (φS) is the Kuhn length of PVAc (lK = 1.36 nm). Successes and deficiencies of the model in predicting the segmental dynamics in miscible blends have been discussed in the literature.4,27,30−33 Phase Segregation and Dynamic Heterogeneity. In the thinner (∼50 nm) PVAc/PEO 90/10 films we find indications for phase separation driven by the local crystallization of PEO. Crystallization and phase separation in this case are induced by a scratch we had made on the film in order to obtain the bare substrate contribution (Figure 4a). Subsequent imaging of the scratch area using amplitude modulation AFM (AM-AFM) reveals seaweed and dendriticlike fingers of 4 nm in height (Figure 4b).34 Such fingers are formed within the temperature range from ambient temperature to 328 K. On heating, the already formed fingers disappear above 328 K. This transition temperature together

with the seaweed and dendritic-like appearance reveals that the objects are PEO crystals. The scratch of the sample provides a heterogeneous surface that induces the (heterogeneous) nucleation of PEO crystals. The PEO crystallization in miscible polymer blends has been studied earlier. In particular, the PEO crystallization has been studied in blends with PMMA in refs 31 and 35−37. We employed FM-AFM to image such finger-like structures at 323 K and record dielectric spectra by placing the tip at different positions relative to the finger. First, the tip is placed on top of the finger (indicated by the red triangle in Figure 4b), and the loss tangent is recorded and plotted in Figure 4c with triangles. In the same figure we include the pure PVAc and PVAc/PEO 90/10 loss tangent curves obtained at the same temperature but from thicker homogeneous films. We note that the loss tangent curve at this position peaks at ∼20 Hz, i.e., at a frequency much below that expected for a 90/10 blend composition (∼200 Hz). This suggests that PEO crystallization drives the phase separation in the vicinity of the dendritic-like fingers. Since the dielectric strength of the segmental process of PEO is negligible as compared to that of PVAc, we probed at this position the film under the PEO dendritic structures. The polymer film region below the PEO fingers is enriched in PVAc. To obtain an estimate for the blend composition in the film located below the PEO fingers, we proceed as follows. We first use the temperature and composition dependence of PVAc segmental relaxation times in the PVAc/PEO blend (Figure 3).27 Subsequently, within this Arrhenius relaxation map we locate the relaxation time corresponding to the spectrum recorded with the tip on top of the finger at 323 K (Figure 5). Assuming the same VFT parameters for B and τ0 as for PVAc, 7461

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probe neighboring areas of the finger front (1−5 μm). In effect, after taking spectra at 1 and 5 μm below the finger front, no significant finger growth was seen. Only several hours after the last frequency sweep, growth was clearly visible (Figure S8). Kinetics of Crystallization/Phase Separation. Because of the sensitivity of LDS in detecting local blend compositions, we employ the same method to probe the local composition during growth of dendritic PEO crystals. For this purpose we first image the film surface in FM-AFM mode followed by consecutive LDS spectra recorded at a fixed position and constant temperature (323 K). A small depression in the film is used as a reference landmark. Figure 6a depicts the depression Figure 5. Segmental relaxation times for PVAc (red line) and for the PVAc component in the PVAc/PEO blends with φPVAc = 0.95 (green line) and φPVAc = 0.90 (blue line). Solid lines represent fits to the VFT equation. The red triangle and green circle respectively give the relaxation times of spectra taken on top of the finger (Figure 4) and at 1 μm below it (at 323 K). The dashed lines are simulations of the VFT curves with fixed VFT parameters (τ0 and B) that pass though the measured data. In the inset the estimated glass transition temperatures (defined at τ = 100 s) are plotted as a function of φPVAc. The black line is the Fox equation, whereas the red solid line is the Lodge and McLeish model predictions for the PVAc (φS = 0.22) glass transition temperatures in the blends. Arrows depict the way to obtain the effective PVAc composition in the LDS spectra.

we estimate the glass transition temperature (defined at τ ∼ 100 s) for the blend located below the finger (Figure 5). The obtained glass transition temperature is then compared to the Tg(φ) dependence in the inset to Figure 5, which contains the Fox equation (black line) as well as the prediction from the selfconcentration model of Lodge and McLeish (red line) for the PVAc glass transition temperature in the blends.5,27 The obtained glass transition temperatures by LDS correspond to a local PVAc/PEO blend composition in the film located below the PEO fingers of about 99/1. Spectra taken on top of other fingers suggest a blend composition in the range from 100/0 to 99/1. The second tip position, indicated with the blue square in Figure 4b, is located some 5 μm away from the finger. The measured loss tangent (Figure 4c) at this position is nearly identical to that of the thick 90/10 PVAc/PEO film at the same temperature. On the other hand, placing the tip 1 μm away from the finger (green circle in Figure 4b) gives a loss tangent with a peak at intermediate frequencies with an effective PVAc/ PEO composition of 95/5. The gradual shift in peak position of the loss tangent with the relative tip−finger distance suggests the presence of a composition gradient with a PEO depletion zone around the finger structure. The PEO depletion zone extends to about 2 μm away from the finger-like structures, which is much larger than the lateral resolution of LDS. It is only beyond such distances that the nominal composition is recovered. Similar results were obtained when this experiment was repeated on top of finger-like structures obtained from other 90/10 blends of comparable thickness using different cantilevers (Figure S7). We point out that such needle-like fingers grow at a rate of ∼0.5 μm/h, as discussed below. Given that a single LDS frequency sweep takes 8 min, the finger front advances ∼60 nm during one single sweep. For each curve shown in Figure 4 we average three frequency sweeps, during which a maximum growth distance of ∼0.2 μm is expected. This growth distance is smaller than the distances at which we

Figure 6. Spatiotemporal kinetics of phase segregation in the PVAc/ PEO 90/10 film. (a) Panels i−iv: AFM images depicting the advancing finger front at 323 K recorded at different times (0, 4, 6, and 8 h). The white circle indicates the location where dielectric spectra are recorded during the experiment, and the white arrow in (i) points to a small depression in the film that is used as a reference landmark. (b) Timedependent loss tangent curves obtained after 4 h (circles), 6 h (squares), and 8 h (triangles). Dashed lines are not fits but give the measured dielectric spectroscopy spectra of the 90/10 (blue) and 95/5 (red) PVAc/PEO blends obtained at the same temperature but from thicker films.

position (white arrow), the chosen measurement point (white circle), and the growing finger front (Figure 6a, i−iv). The measurement position is located ∼2 μm left to the reference depression (white circle Figure 6a) and about 5 μm from the finger-like tip at time t = 0 h. All temporal spectra were taken at this same measurement point. The growth of the finger front was linear in time with an advancing speed of ∼0.5 μm/h (Figure S9). Loss tangent spectra recorded at different times show that the local blend composition changes as the finger approaches the measurement point (Figure 6b). Each curve shown in Figure 6b corresponds to an averaging time frame of 37 min, in which we record four spectra before the AFM image is taken. After 4 h, when the finger tip is ∼3 μm away from the reference point, the loss tangent peak position (∼300 Hz) and shape are reminiscent of that of the 90/10 PVAc/PEO blend; i.e., the local composition is still identical to the nominal blend composition. As the finger stretches out further toward the reference point, the loss tangent peak shifts to lower frequencies. Below about 1 μm the peak has shifted to around 7462

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100 Hz, and both the peak position and peak shape roughly match those of the 95/5 PVAc/PEO blend. Overall, these results indicate that PEO crystallization is the driving force for the gradient of concentration. Finger-like crystals of PEO are created on top of the PVAc-enriched underlying film. The crystals grow slowly and give rise to regions surrounding the fingers where the local blend composition changes in the course of time from the nominal blend composition to local compositions enriched in PVAc. From the tip radius R = 250 nm of the dentritic structures and their growth rate v = 0.5 μm/h, one can estimate the diffusion coefficient of PEO by using the equation R = 2.5(d0D/v)1/2, where d0 = 10−10 m is the capillary length.37,38 The obtained value of D = 1.4 × 10−14 m2/s compares reasonably well to the reported diffusion coefficients found for PEO diffusion in PEO/ PMMA blends37,39 or for interdiffusion across polymer− polymer interfaces.40−42

IV. CONCLUSIONS By employing LDS in the thermodynamically miscible blend PVAc/PEO, we have shown that the method is sensitive to the presence of dynamic heterogeneity in polymer films. Second, we were able to deduce the local blend composition at the nanoscale. Third, the local blend composition was used to quantitatively account for the kinetics of phase demixing in the thin films. Overall, LDS can be employed in studying thermodynamically miscible blends where the relevant length scale controlling the segmental dynamics is of the order of the Kuhn length. These results open new possibilities for LDS in studying polymer blend surface segregation, kinetics of phase separation, and even interdiffusion and adhesion at polymer− polymer interfaces as a function of annealing temperature.

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ASSOCIATED CONTENT

S Supporting Information *

Details on the LDS setup and measurements (effect of film thickness, solvent, etc.). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (M.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.P.C. was supported by a joint Deutscher Akademischer Austauschdienst (DAAD) − Becas Chile scholarship. D.L. acknowledges partial financial support from FONDECYT 1120764, Millennium Scientific Initiative, P 10-061-F, Basal Program Center for Development of Nanoscience and Nanotechnology (CEDENNA) and UTA-project 8750-12. G.F. acknowledges support during his sabbatical leave at the MPI-P. We also thank Dr. Javed Ally for his help with Comsol, Dr. Hung K. Nguyen for insightful discussions, and the technical support from RHK Technologies.

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REFERENCES

(1) De Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (2) Utracki, L.; Favis, B. Polymer Alloys and Blends; Marcel Dekker, Inc.: New York, 1989. 7463

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dx.doi.org/10.1021/ma4007158 | Macromolecules 2013, 46, 7458−7464