From Micro to Nano Thin Polymer Layers: Thickness and

Article pubs.acs.org/Macromolecules

From Micro to Nano Thin Polymer Layers: Thickness and Concentration Dependence of Sorption and the Solvent Diffusion Coefficient Felix Buss,* Johannes Göcke, Philip Scharfer, and Wilhelm Schabel Institute of Thermal Process Engineering, Thin Film Technology, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131 Karlsruhe, Germany S Supporting Information *

ABSTRACT: From sorption experiments in literature it is known, that the solvent diffusion coefficient in nanoscale polymer layers decreases compared to its value in thicker films due to an increasing influence of the substrate. However, it is unclear whether this behavior is only related to thickness variation or also to concentration dependency, inadequate measurement routines, nonconsidered influence of phase-equilibrium or unsuitable data analysis. Here, we describe a measurement setup on the basis of a quartz crystal microbalance, that allows for a clear differentiation between the parameters thickness and concentration. For the material system poly(vinyl acetate)-methanol, sorption experiments with dry film thicknesses ranging from 50 to 685 nm on SiO2 and gold surfaces were conducted and analyzed using different evaluation methods. A comparison to micrometerscale data (30 μm) reveals that the phase equilibrium does not vary with film thickness, but the diffusion coefficient decreases by orders of magnitude due to both thickness (10−13 to 10−16 m2/s) and concentration (10−11 to 10−13 m2/s). On the basis of the different evaluation methods we propose a model that divides the diffusional characteristics in two zones: a top layer with bulk-like behavior and a substrate-near region where solvent diffusion is significantly slower. increasing impact of interface interactions.11−13 A common model suggests that polymer films can be divided into three characteristic zones: A top layer where the polymer can move freely at the free surface, a middle layer with bulk-like properties and a bottom layer close to the buried interface, where the polymer mobility changes due to interactions with the substrate.14,15 The thinner a film is, the more relevant the characteristics of the interface regions become and as a consequence the overall properties change. These confinement effects were first found by Keddie et al., who have demonstrated a change in PMMA glass transition temperature for thin layers in the range of 30 to 100 nm.16 Stimulated by these results, more recent studies focus on the change of crystallization dynamics,17 viscoelasticity,18,19 and phase separation dynamics.20 Similarly, the phase equilibrium and the solvent diffusion coefficient differ from their respective bulk values as the film thickness is decreased. Depending on the polymer−solvent− substrate interactions, the phase equilibrium changes: The water absorption of thin polyvinylpyrrolidone films decreases on hydrophobic hexamethyldisilazane, whereas it is unaffected if coated on hydrophilic silicon dioxide.21 An increase of relative water uptake was found for thin Nafion films (20−30 nm) on

1. INTRODUCTION Thin polymer layers are used in a wide variety of applications. In recent years organic electronics, thin biosensor devices, and layers that excel simple demands such as color variation or scratch resistance have attracted great attention and are under intense investigation.1,2 These materials have a high potential to be deposited by high throughput methods as they can be coated from scalable solution casting processes.3,4 The knowledge of the solvent mobility in such films is of high technological importance, since the desired functionality depends on the dynamics of the drying process.5−7 The faster a polymer solution dries, the less time the chains have to arrange into their thermodynamically favored order. For example organic photoactive layers consisting of P3HT:PCBM exhibit higher charge carrier mobility and absorb more light if the polymer chains can form inter- and intrachain crystallinity at low solvent evaporation rates.8 Trace solvent which is retained in the film can cause long-term property changes by structural rearrangement as polymer chains exhibit higher mobility in the presence of solvent molecules.9,10 To understand and tune such processing routines toward an optimum between processing speed and functionality, the dynamics of the solvent within the film, i.e., the binary diffusion coefficient, as well as the equilibrium solvent content, i.e., the phase equilibrium, at a given gas phase activity have to be known. As the film thickness of a polymer decreases toward its radius of gyration, the properties of the film change due to the © XXXX American Chemical Society

Received: July 24, 2015 Revised: October 12, 2015

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DOI: 10.1021/acs.macromol.5b01648 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules silicon dioxide.22 Spin-cast polystyrene films retain more residual solvent, as the film thickness decreases, suggesting a substrate-near solvent accumulation.23 Besides surface interactions, another common explanation is that solvent enters the substrate-near region in order to increase entropy which is reduced in the pure polymer film, since the chains are hindered to access all conformational states in the presence of a wall. However, no distinct theory is given in literature that predicts if and how the equilibrium solvent content changes at a given gas phase activity and type of surface as the polymer film thickness is reduced. The determination of solvent diffusion coefficients in micrometer scale polymer layers is well-established. It is known that its magnitude decreases toward low solvent content due to a decrease in free volume that promotes the mobility of solvent molecules.24 This behavior has not been verified for very thin polymer layers yet. To date, swelling experiments on thin polymer films are conducted using very large or undefined concentration steps and are often analyzed with a simplification of Crank’s theoretical solution to Fickian diffusion that is only valid for short time intervals and based on the assumption of constant diffusivities.25−28 Using that method, a sharp decrease for the values of solvent diffusion constants in nanoscale films have been determined with respect to their bulk properties.21,22 Approaches to explain this behavior are a lowered mobility of polymer molecules in vicinity to the polymer−substrate interface or a simultaneous rearrangement of chains into their thermodynamically favored order. However, it is unclear if the comparison of diffusion constants to their respective bulk value is correct, since they might be determined at different solvent contents in the film. It is also not clear to what extent the application of the solution for short times and the assumption of constancy of the diffusion coefficient distort the analysis. As a consequence, the experimental routines as well as the analytical methods have to be adapted to the idea of a concentrationdependent diffusion coefficient in order to further understand the mechanisms that hamper solvent mobility in thin polymer films. In summary, studies on the behavior of solvent mobility in polymer films under confining conditions lack detailed investigations that separate the presumably superimposing effects of changing phase equilibrium and diffusion coefficients, as well as a measurement procedure and analytical routine that allow for the determination of concentration-dependent mass transfer parameters. This work focuses on the determination of the phase equilibrium and concentration dependent diffusion coefficient of methanol in thin poly(vinyl acetate) (PVAc) films (50−684 nm). While these properties have been determined for films on the micrometer scale with different measurement techniques,29−34 only very little is known about their behavior in thin films. In this study we investigate the solvent uptake dynamics of thin PVAc films at different dry film thicknesses by means of a quartz crystal microbalance. We show that the diffusion coefficient is not a diffusion constant in this thickness range, but a concentration- and thickness-dependent variable, which deviates from the respective bulk behavior. These findings are highly important for the design of processing routines that include solvent-casting steps.

concentrations (1−10 wt %) and room temperature. The glass transition temperature of the pure polymer is Tg = 29−33 °C. Q-Sense QSX301 (gold surface) and QSX303 (SiO2 surface) quartz crystals, surface roughness 0.5 was taken to determine diffusion coefficients by the short time solution. As expected, the resulting value is lower since the first data point is already outside the validity interval of the method. However, it is still higher than at low activity, indicating concentration dependency. This increase in mobility is in agreement with the free volume theory by Vrentas and Duda, who state that the amount of the free volume decreases at low solvent content and therefore reduces the number of diffusion steps which are related to the magnitude of the diffusion coefficient.24 This behavior has been theoretically predicted39 and also experimentally measured.34,36,40,41 A fit over the entire experiment yields an even lower diffusion coefficient. However, this is not caused by only little data availability, but a kink in the curve after Mt/M∞ = 0.8 to a period of slower diffusion that cannot be mimicked by the fit function. This transition from fast to slow diffusion is also present at low activity, but not as pronounced indicating less difference in diffusion speed. A fit using the solution for long times, as depicted in Figure 5, confirms that the diffusion coefficient in the late stages of the sorption process is lowered by a factor of ∼190 as compared to the bulk value. This behavior cannot be related to concentration dependency, as the solvent concentration increases during the sorption process and is expected to increase methanol mobility in the PVAc film. The mechanisms behind this phenomenon are so far unidentified and will be discussed later. The same sorption steps as for the 488 nm sample were conducted at a 51 nm film, see Figure 6. Similarly, solvent uptake is faster at high activity as expected from bulk concentration dependency. For a decrease in thickness by a factor of 9.6 (488 to 51 nm) and an equal diffusion coefficient in both films, Fick’s law predicts an increase of 9.6 in initial slope and a speed-up by the same factor until the film reaches

Figure 5. Application of the solution for long times for a 488 nm thick PVAc-film on SiO2. The diffusion coefficient determind by this method is much lower than the respective bulk value (compare Figure 4a). The step was measured at activity aMeOH, corresponding to an average solvent content X̅ MeOH in the film.

Mt/M∞ = 0.5. In opposition to this expectation, the diffusion process at low activity in the thin film up to Mt/M∞ = 0.5 is slowed down by a factor of 1.8 (=1.22 s0.5/0.67 s0.5) as indicated by the arrows in Figures 4a and 6a. This difference is expressed by diffusion coefficients that are reduced by a factor of ∼1000 for the 51 nm thick film proving that in addition to concentration dependency the diffusion coefficient is also highly thickness-dependent. Again, a transition from fast to slow uptake kinetics is noted in the course of the sorption process, which is confirmed by the solution for long times. The results for the short time solution in Figure 7a show that for the three thickest layers (488, 198, 127 nm) the diffusion coefficient follows mostly the concentration-dependent bulklike behavior, as indicated by the comparative measurement at 30 μm. Open symbols, that represent a questionable application of the short time solution, are expected to shift to higher values E

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Figure 6. Sorption steps of a 51 nm thick PVAc film on SiO2 at (a) low and (b) high gas phase activity. Two different methods for the determination of diffusion coefficients are compared: the analytical solution for short times (blue dotted line) and for a fit over 180 s (green solid line). The arrow in part a indicates the instant when Mt/M∞ = 0.5 is reached. The steps were measured at different activities aMeOH, corresponding to an average solvent content X̅ MeOH in the film. Bulk data for comparison were taken from the literature.29,33,34

of solvent uptake. From Figure 6a we estimate the thickness of the bulk-like region to 27 nm by calculating the penetration depth of the solvent using the following approximation:42 h = (Dt)1/2. (D = 4.93 × 10−16 m2/s, t0.5 = 1.22 s0.5). The substratenear region is then calculated as the difference to dry film thickness, ∼ 24 nm. If this constant value for the substrate-near region is used for all investigated dry film thicknesses the values for the substrate-near diffusion coefficient coincide, see open symbols Figure7c. We therefore conclude that the substratenear region with lower mobility must be in the range of 25 nm and shows a constant average diffusion coefficient of D = 7.56 × 10−19 m2/s. Figure 8 illustrates the idea of impeded solvent diffusion in vicinity to the substrate. By the solution for short times the diffusion coefficient in the upper part of the film is analyzed. For the limit of sufficiently thick films this corresponds to the bulk-diffusion coefficient Dbulk of the layer due to high solvent content or if films are very thin. The diffusion coefficient within the vicinity of the substrate−polymer-interface Dint is quantified by the long time solution. The same trends are observed for experiments on gold substrates. All diffusion coefficients are summarized in Table S1. Validity of Boundary Conditions. The analysis above requires the absence of gas phase mass transport resistances and an instantaneous adjustment of phase equilibrium at the film surface. Both aspects are addressed in this section. Gas phase mass transport resistances appear if inert gas is present in the measurement setup. Experimentally, this is avoided by a vacuum step before starting data acquisition. In order to have an influence on the derivation of the diffusion coefficient, the gas phase mass transfer coefficient βg, i.e. the inverse mass transfer resistance, needs to be in the order of magnitude of the mass transfer coefficient βf in the polymer film.

and therefore toward bulk-behavior, if more data points were available. As this solution is valid for short times until the first solvent molecules reach the substrate, this method is sensitive to the upper part of the polymer film. Because of the transition from fast so slow uptake kinetics within a sorption step we suggest a substrate-near layer, where solvent diffusion is slower due to the lower polymer segment mobility. This assumption becomes clearer by the following analysis: diffusion coefficients that are determined over the entire experiment are expected to describe the entire sorption process and therefore not to be sensitive to any region within the polymer film. For the thickest 485 nm film, the first four points at low solvent activity coincide with bulk-behavior, confirming the validity of the analysis and the assumption of a largely uniform diffusion coefficient over film thickness (see Figure 7b). However, as the solvent content and therefore the bulk diffusion coefficient increase, the values of the diffusion coefficient remain at a constantly lower value compared to bulk behavior and the corresponding analysis of the short time solution. At high solvent content, where diffusion through a top layer with bulk-like properties is fast, the deviating character of the substrate-near layer is more pronounced leading to a decrease of the average diffusion coefficient calculated from the fit over the entire sorption step. This assumption is supported by the measurements on thinner polymer layers. Here, all diffusion coefficients are shifted to lower values with respect to bulk behavior. This can be explained by a smaller bulk-like region, leading to average diffusion coefficients that contain a higher proportion of the substrate-near diffusion characteristics and are therefore lower diffusion coefficients in total. The long time solution which is used at the late stages of the diffusion process is sensitive to the substrate-near region of the PVAc film. In all cases we calculate notably lower diffusion coefficients than with both the solution for short times and the overall process. The results are constant over solvent content but vary with film thickness (Figure 7c). This deviation in film thickness originates from eq 4 where the dry film thicknesses are used to calculate the diffusion coefficient. This is strictly not correct, since the substratenear region with its respective thickness governs the late stages

βg = F

Dg sg

=

Df sf

= βf

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Figure 8. Model of a thickness-dependent diffusion coefficient at constant solvent concentration. The polymer film is divided into two sublayers: A substrate-near region where diffusion is hindered due low chain mobility with a diffusion coefficient Dint and bulk-like layer with behavior known from experiments on micrometer scale films. For thick films bulk-like properties, Dbulk, are accessible via the analytical solution for short times. A fit over the whole sorption experiment yields an average diffusion coefficient Dav.

have an influence on the diffusion coefficient in the film. This is not reasonable, as the maximum distance between the evaporator and the QCM measurement cell is approximately 50 cm. A gas phase resistance can therefore be excluded. Despite Fickian diffusion dynamics where Mt/M∞ ∼ t0.5, case II diffusion (Mt/M∞ ∼ t) and non-Fickian dynamics, where Mt/M∞ ∼ tn with n ϵ (0.5,1),38,43 have been suggested for the description of solvent transport in polymeric systems. In the latter cases diffusion is superimposed by a relaxation process (e.g., polymer chain rearrangement), causing that the surface concentration C0 does not reach equilibrium C∞ instantaneously, but a lower value that relaxes toward equilibrium at a given rate k. Since our initial uptake processes are proportional to t0.5, we eliminate the idea of case II diffusion which is characterized by a predominance of relaxation dynamics. Twostage and sigmoidal diffusion, the latter being a special case of the former, describe states where solvent diffusion and relaxation occur at similar time scales. Their mathematical description is divided into a term of Fickian behavior and relaxation dynamics:

Figure 7. Concentration- and thickness-dependent diffusion coefficient of methanol in poly(vinyl acetate) on a SiO2 substrate at 40 °C resulting from different fit methods: (a) short time solution, (b) fit over 180 s of the experiment after Crank’s analytical solution, and (c) solution for long times. Open symbols in part a indicate where the solution is formally not valid due to insufficient data availability. Open symbols in part c correspond to a calculation of the long time solution with a constant thickness of the substrate-near layer (24 nm) for all experiments. The data coincide, the average value is given below at the associated dot-and-dashed line. Bulk data for comparison were taken from the literature.29,33,34

sg = s f

Dg Df

−4

= 51 nm ×

⎡ ⎢ tan( ψ ) exp( −ψϕ) Mt = ϕCF + (1 − ϕ)⎢1 − M∞ ψ ⎢ ⎣ ∞ 8 −∑ (2n + 1)2 π 2 2 2 n = 0 (2n + 1) π 1 − 4ψ

(

2.9 × 10 m /s = 150 m 9.87 × 10−14 m 2/s

)

⎤ ⎛ D(2n + 1)2 πt ⎞⎥ exp⎜ − ⎟⎥ 4h2 ⎠⎥ ⎝ ⎦

2

(7)

sg represents a measure for a hypothetical diffusion length in the gas phase, if the diffusion coefficients in the gas phase Dg and the film Df, and diffusion length in the film, i.e., film thickness, are known. Dg was calculated from the Fuller equation (p = 60 mbar at the lowest gas phase activity, air-methanol-mixture, T = 40 °C), Df and sf were taken from the 51 nm film. Hence a minimum gas phase diffusion length of 150 m is necessary to

ϕ=

C0 ; C∞

ψ=

kh2 D

(8)

Here ϕ is the dimensionless ratio between initial and final concentration at the air interface and ψ relates the characteristic times of relaxation and diffusion to each other (i.e., an inverse G

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Figure 9. (a) Fit of the two-stage diffusion model to a 51 nm methanol sorption into a 51 nm thick PVAc film (compare Figure 5a). (b) Diffusion coefficient for varying solvent content and dry film thickness resulting from two-stage analysis of the data. The step was measured at activity aMeOH, corresponding to an average solvent content X̅ MeOH in the film. Bulk data for comparison were taken from the literature.29,33,34

immobilized zone in vicinity to the substrate is suggested. This thickness is in accordance with the two-layer-model suggested in the Diffusion Coefficient section of this work. The absence of glass transition effects is supported by studies where a gradient in glass transition of poly(ethyl acetate) toward lower values in vicinity to silica particles has been found.45 Consequently, any PVAc film studied here is always in the rubbery state and the diffusion kinetics are most likely not influenced by a transition to the glassy state. By X-ray reflectivity measurements, Vignaud et al. identified a density increase of ultrathin polystyrene films due to a compacted polymer layer in vicinity to silicon wafer substrates.46 The miscalculation of layer thickness that is caused by higher density in thin layers does not contradict our findings. Higher densities in thin layers lead to thinner films. A reduction of film thickness even lowers the diffusion coefficients calculated from any of the eqs 3, 4, 5, or 8. This further supports our idea of a substrate-near influence zone with fundamentally different solvent transport dynamics.

Deborah number). CF is the Fickian part of the diffusion model, see eq 3. This model is usually used in the context of glass transition, when polymer chains rearrange into another order at a different time scale as diffusion occurs. Figure9a exemplarily shows a fit of the two-stage model to the 51 nm PVAc film. As expected from a mathematical point of view, the fit is of much higher accuracy, since in comparison to Cranks’ analytical solution eq 3 two additional fit parameters ϕ and ψ are introduced. Even though the better fit implies the presence of a two-stage process, we note that the surface concentration is reduced by a factor of ϕ ≈ 0.8−0.95 on SiO2 (Table S2), indicating a two-stage process that has only little influence on phase equilibrium. After the initial Fickian-type behavior the relaxation dynamics slow down the uptake process (ψ ≈ 0.01−0.1). The reduction of ϕ toward lower dry film thicknesses implies that thin film behavior differs from bulk properties. However, even if two-stage diffusion is assumed, the binary diffusion coefficient still shows concentration and−more importantly−thickness dependence (Figure 9b). If the change of phase equilibrium was only based on the characteristics of the polymer properties we would expect the same diffusion coefficient for all PVAc films, independent of dry film thickness. As this is not the case, phase equilibrium must also be thickness-dependent. However, ϕ decreases only slightly toward lower dry film thickness and can therefore not be responsible for a decrease of the diffusion constant of a factor of ∼1000. Even if phase equilibrium was a function of film thickness the two-stage model should yield equal diffusion coefficients, since the varying surface concentration is taken into account for every single experiment. Two-stage diffusion is often discussed in the context of glass transition. This influence of chain rearrangement was tried to eliminate by conducting experiments above glass transition temperature (T = 40 °C, Tg = 29−33 °C). An increase of solvent content in the course of activity increase additionally lowers the glass transition temperature, making the appearance of this effect less likely. Studies on the thickness dependent glass transition of PVAc films have been reported previously. Freely standing as well as PVAc films confined in a sandwich geometry between two Al electrodes showed deviations in glass transition temperature starting at a film thickness of ∼25 nm to a reduction of 6 K at 5.8 nm thick films.44 There, an

4. SUMMARY AND CONCLUSIONS In conclusion sorption experiments on PVAc with varying dry film thickness revealed that the diffusion coefficient is a thickness- and concentration-dependent parameter, whereas the phase equilibrium is independent of film thickness and the investigated substrate materials. For all investigated film thicknesses the diffusion coefficient decreases for lower solvent content as expected from the free volume theory. In thin films the solvent uptake takes place on a much lower time scale than in micrometer-scale layers. A comparison of the analytical solutions for short times, long times and a fit over the whole time scale of the sorption steps suggests the presence of two regions with different solvent mobility: a substrate-near region with a lowered and constant diffusion coefficient and a bulk-like region that reduces with decreasing film thickness. A timedependent surface concentration as modeled by two-stage diffusion cannot be entirely ruled out, but seems unlikely. Independent of the diffusion mechanism all models yield concentration- and thickness-dependent diffusion coefficients. A further analysis of the underlying mechanisms will have great impact on the design of processing routines of thin film devices, where the structural features and the respective film properties of solution-cast solid components strongly depend H

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(16) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Faraday Discuss. 1994, 98 (0), 219−230. (17) Frank, C. W.; Rao, V.; Despotopoulou, M. M.; Pease, R. F. W.; Hinsberg, W. D.; Miller, R. D.; Rabolt, J. F. Science (Washington, DC, U. S.) 1996, 273 (5277), 912−915. (18) Alsten, J. V.; Granick, S. Macromolecules 1990, 23 (22), 4856− 4862. (19) Bodiguel, H.; Fretigny, C. Macromolecules 2007, 40 (20), 7291− 7298. (20) Barnes, M. D.; Mehta, A.; Kumar, P.; Sumpter, B. G.; Noid, D. W. J. Polym. Sci., Part B: Polym. Phys. 2005, 43 (13), 1571−1590. (21) Vogt, B. D.; Soles, C. L.; Lee, H.-J.; Lin, E. K.; Wu, W.-l. Polymer 2005, 46 (5), 1635−1642. (22) Eastman, S. A.; Kim, S.; Page, K. A.; Rowe, B. W.; Kang, S. H.; Soles, C. L.; Yager, K. G. Macromolecules 2012, 45 (19), 7920−7930. (23) García-Turiel, J.; Jérôme, B. Colloid Polym. Sci. 2007, 285 (14), 1617−1623. (24) Vrentas, J. S.; Duda, J. L. J. Polym. Sci., Polym. Phys. Ed. 1977, 15 (3), 403−416. (25) Samanta, T.; Mukherjee, M. Macromolecules 2011, 44 (10), 3935−3941. (26) Vogt, B. D.; Soles, C. L.; Lee, H. J.; Lin, E. K.; Wu, W. L. Langmuir 2004, 20 (4), 1453−1458. (27) Zettl, U.; Knoll, A.; Tsarkova, L. Langmuir 2010, 26 (9), 6610− 6617. (28) Mukherjee, M.; Souheib Chebil, M.; Delorme, N.; Gibaud, A. Polymer 2013, 54 (17), 4669−4674. (29) Mamaliga, L.; Schabel, W.; Kind, M. Chem. Eng. Process. 2004, 43 (6), 753−763. (30) Wibawa, G.; Hatano, R.; Sato, Y.; Takishima, S.; Masuoka, H. J. Chem. Eng. Data 2002, 47 (4), 1022−1029. (31) Saure, R.; Schlünder, E. U. Chem. Eng. Process. 1995, 34 (3), 305−316. (32) Palamara, J. E.; Zielinski, J. M.; Hamedi, M.; Duda, J. L.; Danner, R. P. Macromolecules 2004, 37 (16), 6189−6196. (33) Schabel, W. Trocknung von Polymerfilmen - Messung von Konzentrationsprofilen mit der Inversen-Mikro-Raman-Spektroskopie. Ph.D. Thesis, University of Karlsruhe (TH): Karlsruhe, Germany, 2004. (34) Schabel, W.; Mamaliga, I.; Kind, M. Chem. Ing. Tech. 2003, 75 (1−2), 36−41. (35) Schmidt-Hansberg, B.; Baunach, M.; Krenn, J.; Walheim, S.; Lemmer, U.; Scharfer, P.; Schabel, W. Chem. Eng. Process. 2011, 50 (5−6), 509−515. (36) Jeck, S.; Scharfer, P.; Schabel, W.; Kind, M. Chem. Eng. Process. 2011, 50 (5−6), 543−550. (37) Schabel, W.; Scharfer, P.; Kind, M.; Mamaliga, L. Chem. Eng. Sci. 2007, 62 (8), 2254−2266. (38) Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, U.K., 1976. (39) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (40) Dupas, J.; Verneuil, E.; Van Landeghem, M.; Bresson, B.; Forny, L.; Ramaioli, M.; Lequeux, F.; Talini, L. Phys. Rev. Lett. 2014, 112 (18), 188302. (41) Hermes, H. E.; Sitta, C. E.; Schillinger, B.; Lowen, H.; Egelhaaf, S. U. Phys. Chem. Chem. Phys. 2015, 17 (24), 15781−15787. (42) Cussler, E. L. Diffusion. Cambridge University Press: Cambridge, U.K., 1997. (43) van der Wel, G. K.; Adan, O. C. G. Prog. Org. Coat. 1999, 37 (1−2), 1−14. (44) Serghei, A.; Tress, M.; Kremer, F. Macromolecules 2006, 39 (26), 9385−9387. (45) Berriot, J.; Montes, H.; Lequeux, F.; Long, D.; Sotta, P. Macromolecules 2002, 35 (26), 9756−9762. (46) Vignaud, G.; S. Chebil, M.; Bal, J. K.; Delorme, N.; Beuvier, T.; Grohens, Y.; Gibaud, A. Langmuir 2014, 30 (39), 11599−11608.

on the drying conditions. A diffusion coefficient which is decreased by orders of magnitude toward an interface or a coating substrate may have a significant influence on the final film properties, since after a given drying time the average solvent concentration in the film and at the interface may differ drastically. Technical drying times and the amount of trace solvent that are retained in a coating produced by a continuous roll-to-roll-process will increase.

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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.5b01648. Tables S1 and S2 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(F.B.) [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Part of this work was funded by the German Research Foundation (Deutsche Forschungsgemeinschaft−DFG) within the priority program 1355 “Elementary processes of organic photovoltaics” and parts of this work within a related project funded by the Karlsruhe Heidelberg Research Partnership (HEiKA).

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REFERENCES

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DOI: 10.1021/acs.macromol.5b01648 Macromolecules XXXX, XXX, XXX−XXX