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Aug 16, 2017 - Interdiffusion only occurs in miscible systems, whereas no intermixing of the polymers occurs in immiscible ... Siebel, Scharfer, and S...
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Interdiffusion in Polymeric Multilayer Systems Studied by Inverse Micro-Raman Spectroscopy Sebastian M. Raupp,*,†,‡ David K. Siebel,† Paul G. Kitz,† P. Scharfer,†,‡ and W. Schabel† †

Institute of Thermal Process Engineering, Thin Film Technology, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany ‡ InnovationLab, Heidelberg, 69115 Heidelberg, Germany S Supporting Information *

ABSTRACT: Interdiffusion is likely to occur if two miscible polymeric films are in contact with each other in the presence of a solvent. This is e.g. relevant for the production of organic light-emitting diodes (OLEDs). Interdiffusion in OLED multilayer stacks has a great influence on the device performance. Yet, there is no study monitoring these interdiffusion processes. This is essential to gain fundamental knowledge about the predominant parameters influencing mass transfer between the present solids. In this work we demonstrate the application of inverse micro-Raman spectroscopy (IMRS) for in situ measurement of interdiffusion in polymeric multilayer systems. Interdiffusion only occurs in miscible systems, whereas no intermixing of the polymers occurs in immiscible systems. Given a miscible system, the average solvent content was found to be more important than the molecular weight of the polymers for the interdiffusion kinetics.

1. INTRODUCTION In various multilayer applications such as OLEDs, two polymers in the presence of one solvent are forming a ternary system in which interdiffusion occurs. So far the diffusion kinetics in such systems are not well understood. Studying interdiffusion in ternary polymer−polymer−solvent systems shares aspects of diffusion phenomena in polymer−solvent mixtures and those found in polymer−polymer systems. Diffusion in binray polymer−solvent systems has been studied intensively in the past century. Starting with the simplest case from binary polymer−solvent mixtures, it is always the aim to describe more complex multicomponent systems.1 The diffusion of small molecules in polymers was investigated by numerous groups in the past decades. In general, Fickian diffusion (case I), when diffusion is slower than relaxation processes, and case II diffusion with diffusion being faster than relaxation can be distinquished.2−4 Fickian diffusion occurs mostly if the system temperature is above the glass transition temperature.3 Vrentas et al.5−12 were focusing on the free-volume theory for calculating self-diffusion and mutual diffusion coefficients mainly in polystyrene−solvent systems with a quartz spring sorption balance.13−15 Modifications of the free-volume theory are reported by other authors.16−20 So far, diffusion coefficients of polymer solutions with mixtures of two21 and three22 organic solvents have been measured in the system poly(vinyl acetate) (PVAc)−toluene (TOL) and methanol by performing drying experiments with inverse micro-Raman spectroscopy (IMRS). Thomas and Windle23−27 developed a model for the case II diffusion28 which predicts polymer surface swelling in dependence of solvent exposure © XXXX American Chemical Society

time. They analyzed the system PMMA−methanol with optical microscopic analysis in detail. Kramer et al.29−33 performed further investigations of case II diffusion with ion beam methods (Rutherford backscattering spectrometry) mainly in polystyrene−solvent systems and applying the model of Thomas and Windle. Further work on case II diffusion was carried out by Scott,34 Park,35 Crank,36 Hopfenberg and Frisch,37,38 and others.39−43 Other theoretical descriptions of self-diffusion in polymer− solvent systems are the model by Rouse44−46 and the reptation model47,48 and its modifications.49−56 If the degree of polymerization is smaller than the entanglement length, the self-diffusion coefficient can be described by the Rouse theory which depends reciprocally on the molecular weight (Mw).57,58 For polymers, of which the degree of polymerization is larger than the entanglement length, the reptation model is applied in which the self-diffusion coefficient is proportional to Mw−2.4,59,60 In higher concentrated polymer solutions, the self-diffusion coefficient cannot be described by these models anymore. Brochard et al.61 and Binder62 developed the so-called “slow theory” to describe the interdiffusion of two polymers in melts in 1983. It is based on the general equation for diffusion which describes the flux of a component i in a general potential field. Further work on the slow theory has been performed by Higgins et al.63 with small-angle neutron scattering in Received: May 19, 2017 Revised: July 14, 2017

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Figure 1. Experimental setup for organic double-layer preparation. Knife coating and drying of polymer 1 (A) prior to coating of polymer 2 and merging of the films (B). In situ measurement of organic double-layer system after placing PTFE adhesive around the sample (C).

layer thicknesses, the results in polymeric model systems can be transferred to OLED fabrications, if suitable interdiffusion models can be developed. The goal of this work is to provide measurement data establishing a basis for future multicomponent polymer− solvent interdiffusion modeling. In this work we demonstrate that interdiffusion of two polymers in the presence of one solvent can be monitored in situ by IMRS on the micrometer scale. First, the influence of polymer miscibility on interdiffusion is considered. Additionally, the influence of polymer molar mass as well as solvent content on the interdiffusion process is investigated.

poly(methyl methacrylate) (PMMA) and chlorinated polyethylene blends. In contrast, the fast theory59,60,64 predicts a diffusion coefficient which depends on the diffusion of the faster moving component while the slow theory relates the diffusion coefficient to the diffusion of the slower component.65 So far, several experimental studies exist confirming either the slow63,66 or the fast theory.67,68 Both theories are still under discussion, as the effects of changing glass transition temperature with changing composition69−71 and consequently the influence on diffusion kinetics cannot always be regarded separately.72 Furthermore, these models cannot be directly transferred to ternary systems. Thompson et al.73 present the first, and to our knowledge, only study of polymer interdiffusion in the presence of a solvent by applying nuclear reaction analysis, which is the case under investigation in this work. They investigated the cyclohexane absorption in hydrogenous polystyrene (hPS) and deuteriopolysterene (dPS). A decreasing interdiffusion coefficient of dPS hPS−1 with increasing Mw of the hPS, the component with smaller molecular weight, was found. The diffusion coefficient increased with increasing temperature and was independent of the film thickness. An alternative to nuclear reaction analysis is IMRS. IMRS offers the possibility to monitor concentration profiles in polymeric systems in situ over time, with a spatial resolution of approximately 1 μm.74−76 Besides the interest in fundamental research on interdiffusion in polymeric multilayers, interdiffusion is also relevant for solution processing of OLEDs, coating, and welding of polymers with adhesives and functional coatings such as barrier foils.77 OLEDs consist of several functional layers in the nanometer range. A lot of effort has been spent in the past decade to bring this technology from laboratory scale to mass production.78−82 To increase processing speed and decrease the loss of material the manufacturing tends to a solution-based process.78−85 State of the art is a solution-based process, in which layer by layer is deposited with intermediated drying steps.79,80,82,85−90 Achieving multilayer architectures with welldefined interfaces (i.e., avoiding reduced efficiencies due to intermixing of the different functional layers) is the key challenge for a solution deposition process.79,91 A ternary system with two solids and one solvent is the simplest case considering OLED fabrication with a layer-by-layer process. Although OLED materials are not applicable to Raman spectroscopy, due to their strong optical activity and small

2. EXPERIMENTAL SECTION Materials. Toluene (TOL) was purchased from Merck KGaA (Darmstadt, Germany SeccoSolv, 99.9%). Poly(methyl methacrylate) (PMMA, poly(methyl 2-methylpropenoate), Mw 120 000 g mol−1), polystyrene (PS, poly(1-phenylethene), Mw 192 000 g mol−1), and poly(vinyl acetate) (PVAc, poly(1-acetyloxiethene), Mw 100 000 and 500 000 g mol−1) were supplied from Sigma-Aldrich (Taufkirchen, Germany). Low molecular weight PVAc (Mw 55 000−70 000 g mol−1) was purchased from Carl Roth (Karlsruhe, Germany). Densities, refractive indices, measured molecular weight, and polydispersity indices (PDI)s can be found in Tables S1 and S2. Sample Preparation. A double-layer system comprising two polymers and one solvent is applied in between two glass substrates, and interdiffusion is measured via IMRS. All polymers were kept under vacuum for 1 week to be completely dry prior to sample preparation. The polymer solutions were all prepared with 66.6 wt % TOL. Solely the high molecular weight PVAc with Mw 500 000 g mol−1 was dissolved in 79.5 wt % TOL to decrease viscosity and enable coatability. Samples were stirred for 1 week prior to the coating experiments in order to dissolve the polymers completely. The substrate thin glass slides (0.15 × 0.15 m2, thickness 150 μm, ZittThoma GmbH, Freiburg, Germany) were cleaned with acetone and isopropanol prior to the experiments. Knife coating was performed with a Zehnter coating applicator (Zehntner GmbH, Sissach, Switzerland) with a coating width of 100 mm. The coating gap was adjusted to 200 or 300 μm to obtain the desired film thickness. Coating velocity was adjusted to 1.3 cm s−1. A sample volume of approximately 2 mL was applied to ensure homogeneous coating over the whole area. For all experiments the desired film thickness of the complete system was in the range between 80 and 150 μm. In Figure 1 the experimental setup is described. The bottom layer is knife coated first and dried for 1 week at 50 °C to ensure a completely dry film (Figure 1A). The top layer is prepared just prior to the measurement and is knife coated on a second substrate (Figure 1B). Both layers are merged together and a PTFE adhesive tape is placed around the B

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Macromolecules sample edges to prevent solvent evaporation (Figure 1C). Therefore, no film shrinkage due to drying occurs over time. Afterward, the IMRS measurement is performed at 20 °C. The time between the first contact of the polymeric films and the start of the measurements was about 7 min. The first measurement is referred to t = 0 s. Substrates are kept in a temperature-controlled oven in between the measurements. With this setup we are able to monitor interdiffusion at a constant average solvent fraction while effects of dewetting and drying are excluded. Inverse Micro-Raman Spectroscopy. All spectra of the organic double-layer films were measured using inverse micro-Raman spectroscopy. The experimental setup has been described in former publications in detail.74,92 A temperature-controlled metal plate is used to keep the samples at 20 °C. A notch in the temperature-controlled metal plate enables optical accessibility. At various times so-called “depth scans” are performed: Raman spectra are acquired at different positions in the sample by shifting the objective lens. Spectra are measured beginning in the glass substrate below the polymer−solvent system followed by stepwise scanning through the whole film. By use of these spectra, a concentration profile through the complete sample can be extracted. The complete measuring time depends on the resolution, film thickness, and the exposure time and can vary from a few seconds to several minutes. For the measurements in this work, the measuring time was adjusted to 1 s. The total time per measured spectrum including shifting the focus and processing the data was 1.5 s. The first depth profiles were performed with a step size of 5 μm in order to decrease the duration of the measurement and monitor when the solvent has penetrated through the sample completely. All depth profiles in the later stage were measured with a resolution of 1 μm. As the spatial resolution is the most critical part in the experiments, it will be discussed later in a dedicated paragraph. All samples were measured repeatedly with increasing time intervals up to 400 h. The calibration procedure was performed according to the description of Scharfer et al.93 The local composition is derived quantitatively in terms of solvent loadings (g(solvent)·g(polymer)−1) and with the known density then given in volume fractions (ϕ(component (i)·v(total)−1). The spectra of the pure components are given in Figure 1S. The area of interest of the Raman shifts is 2700−3300 cm−1 for the analysis, and the resulting calibration curves are shown in Figures 2S−5S. As shown in previous works,21,76 there is a linear dependency of intensity with mass loading.94 From the slope of the regression line, the calibration constant for each ternary system can be found. As can be seen from Figures 3S−5S, binary as well as ternary samples are located on the regression line. Obviously for PS− PMMA−TOL no ternary samples are possible due to immiscibility of the polymers. The experimental error is quite low as the root-meansquare error R2 is higher than 98.2% for every system. In terms of volume fraction this is about 1 vol % of standard deviation, which is shown in Figures 6S−9S by plotting calculated volume fractions over the real volume fractions determined by weighed in quantities for the calibration samples. A worst case approximation for an error propagation is shown in these figures as well. The average solvent fraction (ϕ̅ S) is given for each experiment and displayed in the graph. Spatial Resolution of IMRS. To evaluate the spatial resolution of the IMRS, an opaque silicon wafer with a polished and defined sharp interface is measured. This is shown schematically in Figure 2. If the focal point of the objective had no spatial elongation, there should be just one signal directly at the surface of the wafer (position 2). Because of the expansion of the focal point a signal is already measured at position 1. The intensity goes down to zero again at position 3. Integrating the normalized intensity (normalized to an area of one) results in the correction function Ψ95 which can be found in the Supporting Information. With the help of the correction function it can be evaluated how the spatial resolution is affected by the elongation of the focal point. In Figure 3 two theoretical cases for the system PVAc−PMMA−TOL are shown. The concentration profiles in terms of volume fraction of each component are depicted. The colored, solid lines show the real profiles. With the correction function the profiles of theses samples, which would be measured by IMRS, are shown with the dashed line. It is of interest how the spatial

Figure 2. Intensity depth profiles for the measurement of an opaque silicon wafer. Left: normalized intensity over position with opaque silicon wafer. Right: the integration of the normalized intensity (solid line) results in the correction function Ψ (dashed line).

Figure 3. Theoretical concentration profiles for PVAc−PMMA−TOL for two different time steps t (t1 < t2). Time step t1 shows the ideal case of a sharp interface without any intermixing. The solid lines show the ideal profiles while the dashed line shows the real measurement due to the elongation of the focal point. elongation influences the measured profiles. For time step one (t1), which stands for the measurement of two separate layers with a defined interface, small deviations between the curves are observed. This is relevant for all starting conditions in the experiments as well as in the case for a system which shows no intermixing over the whole duration of the experiment. Because of the elongation of the focal point in the z-direction, the measured profiles even out, resulting in slightly rounded profiles. The deviation is about 2 or 3 vol %. This has to be taken into account as the original profiles could be misjudged to show a small degree of interdiffusion at the interface. A detailed discussion for real measurements will follow in Figure 5. Regarding time step two (t2) when the polymers already diffused to a certain extend into each other, almost no difference between the hypothetical profiles and the measured ones can be seen. Therefore, there is almost no difference between solid and dashed lines. A correction of the profiles is therefore not required anymore at this time step. We conclude that the spatial resolution of the measurement setup is high enough to monitor the concentration profiles and that a correction of the profiles is not required for judging the degree of intermixing beside the already discussed starting point. Glass Transition Temperature, Tg. Important for the interpretation of the results is the fact that all experiments are performed far above the glass transition temperature. Although the polymers provide different glass transition temperatures (PS: 80.85 °C;96 PMMA: 101 °C;97 PVAc: 29 °C96,98) the solvent influence consequently leads to glass transition temperatures in all systems of less than −50 °C for the present compositions, calculated by the Fox equation.99 In every sample more than 35 vol % of TOL is present. The calculations are shown in Figure S10 for all binary systems with a Tg of TOL −156.15 °C.102 These approximations are in accordance with experimental findings of Samus et al.,71 Savin et al.,70 and Yoshioka at al.69 As will be demonstrated, the solvent has already penetrated through the whole sample at the beginning of the measurement, so the effect of swelling can be neglected. C

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solvency,108,109 PMMA was easy to dissolve in TOL. The highresolution measurement after 12 min shows no difference compared to the measurement after 3 min. After 93 h there is still no interdiffusion of the polymers observable. The step in the solvent concentration is the same as after 12 min. A small change in film thickness of approximately 10 μm is observed while the total composition of the film does not change significantly. For this reason the change in thickness is assumed to be due to unsuppressed wetting and dewetting effects at the film edges, resulting in small thickness changes over longer time intervals. As the coating cannot cover the whole substrate a leveling of the films occurs as demonstrated in Figure S11. Levelling can occur over time as the films are not rigid but feature relatively high viscosities (>1 Pa s). To enable a better comparison of the different time steps, the concentration profile of the measurement after 93 h is shifted by 11 μm so that the interface stays at the same position. From the system PS−PMMA−TOL it is obvious that immiscible systems do not intermix even though the solvent is distributed over the whole film height. To demonstrate that no intermixing occurred, the profiles need to show a rectangular step as shown in Figure 3 on the left. Therefore, the concentration profiles of such an ideal system with two separate polymer layers were taken, and with the correction function Ψ the corresponding profiles of hypothetical measurements were calculated. The ideal step profile similar to the one in Figure 3 (left) and the profiles corrected with Ψ are shown in Figure 5 (left).The comparison of the real measurement and the corrected profiles is shown in Figure 5 (right).

3. RESULTS AND DISCUSSION First, the results of the immiscible system and the influence of spatial resolution are discussed, followed by the discussion of the miscible system and the influence of solvent content and molecular weight on the interdiffusion kinetics. Immiscible System. According to literature100,101 and verified by our own experiments, PS−PMMA−TOL forms an immiscible ternary system. While the binary polymer−TOL mixtures are soluble, the ternary system phase separates. The concentration profiles of a ternary PS−PMMA−TOL double layer are shown in Figure 4. For the measurements with 1 μm

Figure 4. Concentration profiles for the immiscible system of PS− PMMA−TOL at 20 °C. Different time steps are shown: PS (violet circles) (Mw 192 000 g mol−1), PMMA (blue triangles) (Mw 120 000 g mol−1), and TOL (orange diamonds).

resolution (after 12 min and 93 h) only every fifth data point is shown for better visibility. Position 0 refers to the position at the bottom of the film. The first diagram (top, left) in Figure 4 reveals that TOL is diffusing quickly from the upper layer to the bottom layer but has not reached the bottom glass substrate at this point. At the height of 61 μm, the volume fractions of the two polymers intersect. At first sight it seems that a small area of intermixing already exists. As discussed in the previous paragraph, this is due to the spatial resolution, and the concentration profiles are the ones of two polymer layers without any intermixing. A detailed discussion follows within Figure 5. The spatial resolution is mainly limited by the larger step size applied for the measurement at 0.5 and 3 min. After 3 min TOL is diffused through the whole system, and the volume fraction of TOL remains higher in PS than in PMMA. This is in accordance with the phase equilibrium, as the diffusion kinetics are so fast that the distribution regarding TOL solely depends on its interaction with the polymers and thus its thermodynamic behavior. According to the Flory−Huggins theory, the lower the Flory−Huggins interaction parameter χij, the higher the positive interactions. For PS−TOL (Mw 290 000 g mol−1, ϕ̅ S = 0.4) a value of χTOL,PS = 0.42 is given in the literature.103 With this χTOL,PMMA is calculated (see Supporting Information) to be 0.69, which is in accordance with the literature103 (χTOL,PMMA = 0.44−0.71). Although this value states a bad

Figure 5. Measured and with correction function Ψ calculated concentration profiles for the immiscible system of PS−PMMA−TOL at 20 °C for measurement time of 93 h. Left: the ideal step profile with its corresponding corrected step profile. Right: corrected step profile and real measurement. PS (violet circles, Mw 192 000 g mol−1), PMMA (blue triangles, Mw 120 000 g mol−1), and TOL (orange diamonds). Calculations with dashed lines and ideal step profile with solid lines in corresponding colors.

In Figure 5 (left) the influence of the special resolution of the IMRS is demonstrated as discussed in the previous section. Figure 5 (right) is an excerpt of the measurement after 93 h from Figure 4 showing the position in the film from 45 to 80 μm. In this case all points of measurement are shown with the spatial resolution of 1 μm without skipping any points. For each component the symbols do not differ significantly from the dashed lines. The points from the measurement scatter slightly around the dashed lines. This demonstrates that the measured profiles are almost ideally separated polymer layers without any intermixing at least in the range of micrometers, D

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Figure 6. Concentration profiles for the miscible system of PVAc−PMMA−TOL at 20 °C. Different average solvent contents are shown in each column. Time step t = 0 h (top row) and t = 170 h (bottom row). PVAc (green squares, Mw 100 000 g mol−1), PMMA (blue triangles, Mw 120 000 g mol−1), and TOL (orange diamonds).

Figure 7. Concentration profiles for the miscible system of PVAc−PMMA−TOL at 20 °C. Different molecular weights of PVAc are shown in each column. Time step t = 0 h (top row) and t = 400 h (bottom row). PVAc (green squares; Mw 55 000−70 000 g mol−1 (left), 100 000 g mol−1 (middle), and 500 000 g mol−1 (right)), PMMA (blue triangles, Mw 120 000 g mol−1), and TOL (orange diamonds).

S1), convection due to differences in densities of the polymers is not expected to occur. Influence of Solvent Content. PVAc with Mw 100 000 g mol−1 was chosen due to its similar molecular weight in comparison to PMMA. By changing the time in between knife coating of the fresh PMMA-TOL film and the merging of both films, the solvent content of the double-layer system can be changed due to solvent evaporation. Figure 6 shows three different experiments with average solvent contents in the range of ϕ̅ S = 0.49 (left) to 0.44 (middle) and 0.39 (right). The composition at the beginning is shown in the top row, and the situation after 170 h is illustrated in the bottom row. Because of the fast diffusion of TOL, the volume fraction of TOL is already in its thermodynamic equilibrium at the start of

which is sufficient to describe the interdiffusion processes in the polymer−polymer−solvent systems. Miscible System. In contrast to PS−PMMA−TOL, the system PVAc−PMMA−TOL offers a complete miscibility.104−106 The influence of temperature on miscibility was discussed by Crispim et al.104,107 Full miscibility is only observed at 30 °C, but the system becomes immiscible with increasing temperature at 50 °C. As the temperature is kept at 20 °C, time-dependent intermixing is expected to occur as the system is fully miscible. The influence of solvent content and the molecular size is investigated in Figures 6 and 7, respectively. Because of similar densities of PVAc (ρPVAc = 1186 kg m−3) and PMMA (ρPMMA = 1188 kg m−3) (see Table E

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component is present at any film height. Only a small gradient in TOL concentration exists with the TOL concentration decreasing toward the top of the film. For PVAc Mw 100 000 g mol−1 the TOL gradient is much more pronounced. Only a small amount of PVAc has reached the top, and only few PMMA molecules have reached the bottom of the film. For the high molecular weight PVAc only minor changes in the volume fractions can be observed after 400 h, indicating a comparably slow intermixing process. The step in TOL fraction is still present, and at positions below 50 μm no PMMA can be detected. Profiles are only slightly changed in the former top film, and the gradients in the polymer concentrations are still high. In general, the polymer profiles are not symmetric. Symmetric profiles are only expected in binary samples due to the conservation of volume. The more the molecular weights of the polymers differ, the stronger the asymmetry of the profiles. We assume that the smaller chain is more mobile and diffuses faster. Therefore, the gradient at the side of the less mobile chain is steeper and differences in concentration exist longer. In the case of PVAc (Mw 55 000−70 000 g mol−1) it should be PVAc, and in the case of PVAc (Mw 500 000 g mol−1) it should be PMMA, while for the case in the middle the difference is not so much. Considering the small molecular weight PVAc (Mw 55 000−70 000 g mol−1), molecules of the former dry bottom film (PVAc) diffuse into the top film while TOL instead of PMMA penetrates into the bottom film to fulfill the law of conservation of mass (or volume, if the excess volumes are zero). The profiles for the similar molecular weights of the polymers in the middle of Figure 7 are only slightly asymmetric. The system with the high molecular weight PVAc provides the highest ratio comparing the molecular weight of both polymers. As shown in Figure 7 on the right, PMMA (the smaller molecule in this case) does not diffuse in the PVAc film. This seems to be contrary to the observation for the other systems, but considering the higher mobility of PVAc due to higher TOL content in the PVAc film might explain the shape of the concentration profiles. Another reason could be the distribution of chain lengths in the sample, which is especially important for larger polymer chains. The longer the chains get the larger the PDI and therefore the distribution of chain lengths. A certain number of smaller chain lengths, which diffuse faster at the beginning, are present in PVAc (Mw 500 000 g mol−1) and may diffuse before the PMMA diffuses. As expected, interdiffusion is remarkably reduced when increasing the molecular weight of the polymeric components as a result of reduced mobility. Zone of Intermixing. To measure the degree of intermixing of the double layers, we propose a tangent method. This is shown schematically in Figure 8.

the measurement. PVAc has more attractive interactions with TOL as compared to PMMA, and therefore the solvent content in the PVAc films is higher. In the literature, several values can be found for the Flory−Huggins interaction parameters for PVAc−TOL and PMMA−TOL, as mentioned in the previous section. Schabel et al.110 give a composition-dependent Flory− Huggins interaction parameter χTOL,PVAc = −0.35ϕ̅ S + 0.85, which confirms our findings. At time step 0 h, the main difference between the various experiments is the volume fraction of TOL. Applying less TOL results consequently in a smaller film height. The gradient in the concentration profiles of PVAc and PMMA is again due to the elongation of the focal point, as discussed previously. After 170 h (second row) the system with the high TOL content is intermixed, and in every part of the film PVAc and PMMA are present. PVAc has reached the top of the film while PMMA has reached the bottom of the system. The profiles are not completely equalized, and therefore a slight gradient of TOL with decreasing volume fraction from bottom to top is observed. This is due to the higher PVAc content at the bottom of the film. For ϕ̅ S = 0.44 PVAc has penetrated the complete top of the film, while at the bottom a small area without PMMA still exists. The shape of the TOL gradient is similar to the one presented for ϕ̅ S = 0.49. In the case of ϕ̅ S = 0.39, intermixing of the polymers has only occurred over a zone of approximately 25 μm height. Because of the observed change in film thickness, the profiles were shifted. First chains of PVAc are reaching the top of the film while there is no PMMA at the bottom for more than 20 μm. The results demonstrate the importance of solvent content on the interdiffusion and that small changes of solvent content (in the experiments Δϕ̅ S = 0.05) change the polymer interdiffusion speed in the order of magnitudes. The solvent creates a free volume, which can be accessed by the polymer chains for their movement. This is in accordance with the observation from the free-volume theory111 and former experimental studies in polymer−solvent systems.19,21,22,76,112,113 Influence of Molar Mass. The miscible system PVAc− PMMA−TOL was used because PVAc is available in several molar weights. Experiments were chosen offering the same average solvent content to exclude this source of influence. The molecular weight of PMMA was kept constant in each experiment to be Mw 120 000 g mol−1. In Figure 7, three different PVAcs with molecular weights of PVAc Mw 55 000− 70 000 g mol−1 (left), Mw 100 000 g mol−1 (middle), and Mw 500 000 g mol−1 (right) were used for the experiments. For the interpretation of the experiments one has to take care about the relatively large PDIs (see Table S2). At the beginning of the experiments, interdiffusion is faster due to the smaller chains interdiffusing quicker than the larger ones. Afterward, interdiffusion speed will slow down as the longer chains present in the sample will result in a slower diffusion. The solvent step at the polymer interface in the beginning (first row) is similar in all of the three cases and confirms the findings from the previous section. Considering the profiles of the polymers, there is no significant difference between the samples initially, showing binary PVAc−TOL on the bottom and binary PMMA−TOL on the top of the double-layer system. In the second row the film composition is shown after 400 h. The films comprising the two smaller molecular weights of PVAc reveal that both polymers are found in every part of the film, indicating comparably fast intermixing processes. For PVAc Mw 55 000−70 000 g mol−1 almost 10 vol % of each

Figure 8. Tangent method for the evaluation of the intermixing zone. The tangents are fitted at the position where the profiles of the polymers intersect. F

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takes place. Because of the highest gradients at the beginning of the experiments resulting in high driving forces for the mass transfer process, the propagation speed has its highest value at the beginning. With decreasing gradients of the polymer volume fractions, the velocity of the intermixing processes decreases. Exemplarily we compare the times required for each system to reach ZIntermixing = 20 μm, which is shown in Table 1.

This method is applicable as long as there is an area with a constant volume fraction of both polymers on the top or the bottom of the film respectively (i.e., polymer A (green) did not reach the bottom or polymer B (blue) the top). As shown in Figure 3, the influence of the spatial resolution of the IMRS is so marginal that the elongation of the focal point does not really affect the tangent method as the tangents are fitted at the position where the profiles of the polymers intersect. The last data point measured in Figures 9 and 10 therefore signifies the

Table 1. Times Required for the Formation of an Intermixing Zone for ZIntermixing = 20 μm in Double Layers of the System PVAc Mw 100 000 g mol−1, PMMA Mw 120 000 g mol−1, and TOL Taken from Figure 9 average solvent content ϕ̅ S

time t [h]

0.49 0.41 0.39 0.35

2.1 27 66 did not reach 20 μm

Relating the time for each experiment for ZIntermixing = 20 μm to each other, the dependency on solvent volume fraction is much stronger than just linear. In Figure 10 eight experiments with three different molecular weights of PVAc in the system PVAc−PMMA−TOL are shown with minor differences in average solvent content. While for PMMA Mw 120 000 g mol−1 is fixed, the molecular weight of PVAc is changed. Three samples of Mw 55 000− 70 000 g mol−1 (squares) with the same average solvent content were measured showing almost identical results. In about 30 h, a value of ZIntermixing = 30 μm is reached. For Mw 100 000 g mol−1 (circles) and Mw 500 000 g mol−1 (triangles), slightly different solvent contents were found as shown with the changed color. The lighter the color, the less solvent content is present in the sample. Only in the case of the small molecular weight PVAc, three different samples with the same solvent content are shown. With increasing molecular weight and decreasing solvent content the intermixing zone increases slower due to the reduced propagation speed. As already shown, for the same molecular weight, the lower solvent content results in a smaller ZIntermixing value. Evaluating if the solvent content or the molecular weight has a bigger influence on the interdiffusion and ZIntermixing, one needs to consider the ratio of the molecular weight, which is approximately 5:8 (PVAc Mw 55 000−70 000 g mol−1 to Mw 100 000 g mol−1) and 1:8 (PVAc Mw 55 000−70 000 g mol−1 to Mw 500 000 g mol−1). The difference in penetration time for various values of Z Intermixing (regarding all samples with ϕ̅ S = 0.41) is approximately 1:2 (PVAc Mw 55 000−70 000 g mol−1 to Mw 100 000 g mol−1) and 1:21 (PVAc Mw 55 000−70 000 g mol−1 to Mw 500 000 g mol−1), which is approximately twice the factors given by the molecular weight although the values for the high molecular weight PVAc differ slightly more. The ratios differ more than the ones for the molecular weight. It is questionable if this is an indication toward a linear molecular weight dependency. The change in solvent content is much smaller (Δϕ̅ S = 0.02 or 0.03, respectively) than the change in molecular weight but its influence on the ZIntermixing value, and the propagation speed is in the same range by comparing the two PVAc Mw 100 000 g mol−1 samples or the two Mw 500 000 g mol−1 samples with the higher solvent contents. As mentioned in the discussion for Figure 6, the solvent content has the bigger influence on diffusion speed compared

Figure 9. Intermixing zone as a function of solvent content for the system PVAc Mw 100 000 g mol−1, PMMA Mw 120 000 g mol−1, and TOL over time. ϕ̅ S = 0.49: squares; ϕ̅ S = 0.41: circles; ϕ̅ S = 0.39: triangles; ϕ̅ S = 0.35: diamonds.

Figure 10. Intermixing zone width as a function of molar mass and solvent content for the system PVAc (Mw 55 000−70 000 g mol−1 (squares, blue), Mw 100 000 g mol−1 (circles, green), and Mw 500 000 g mol−1 (triangles, red)), PMMA (Mw 120 000 g mol−1), and TOL over time.

moment when one of the polymers is spread over the complete film height for the first time. ZIntermixing is defined as the distance between the two points where the tangents intersect with the abscissa (compare Figure 8). The initial width of the intermixing zone (ZIntermixing,0) differs slightly in the experiment due to the larger step width corresponding to a large spatial resolution chosen for the first measurements. This may cause an overestimation of the width of the intermixing zone. In Figure 9, the time-dependent values of ZIntermixing for four samples of PVAc−PMMA−TOL (PVAc Mw 100 000 g mol−1; PMMA Mw 120 000 g mol−1) with a variation of the TOL content are shown. The molecular weights of the components are kept constant. The intermixing zone increases over time for all samples. As expected, the higher the TOL content, the faster this process G

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to the molecular weight, enabling a higher mobility of the polymers.

4. CONCLUSION With the IMRS technique, interdiffusion was measured in situ in ternary polymer−polymer−solvent systems. Interdiffusion takes place if the system is miscible (in this study PVAc− PMMA−TOL) while immiscible systems such as PS−PMMA− TOL show no interdiffusion of the polymers. The solvent (TOL) diffuses within minutes through the complete dry film. According to the phase equilibrium, TOL concentration is higher in PS and PVAc films than in PMMA, which is in accordance with the literature. A stationary step gradient in solvent concentration exists as long as there is a sharp interface between the polymers. The more intermixing between the polymers occurs, the smaller the gradient in TOL concentration gets. A higher average solvent content results in faster interdiffusion. For polymers with a smaller molecular weight, interdiffusion was faster than for the ones with a larger molecular weight. Calculating the intermixing zone with a tangent method is a suitable method to illustrate interdiffusion kinetics of several samples in one plot. Regarding interdiffusion kinetics, solvent content has a bigger impact than the molecular weight. While molecular weight was found to have a lower influence on diffusion kinetics, the dependence of solvent content is much more enhanced than just a linear dependency. In our future work we aim at developing a model for predicting the interdiffusion behavior in the miscible system and finally transferring it from micro- to nanometer scale with respect to fabricating OLEDs.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b01037. Figures S1−S11; Tables S1 and S2 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (S.M.R.). ORCID

Sebastian M. Raupp: 0000-0003-1149-5232 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support via the project POESIE (Contract 13N13692) of the Federal Ministry of Education and Research. We thank all mechanics, assistants, and our students involved for contributing to this work. Special thanks go to Dr. Jürgen Schelter (University of Cologne, Cologne, Germany; Institute of Physical Chemistry) for conducting GPC measurements of the polymers.

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