Molecular dynamic simulations are used to investigate the structural effects of treating a glassy polymer thin film with solvents of varying quality and subsequently evaporating the solvent. Both a monodisperse film and a polydisperse film are studied for poor to good solvent conditions, including the limit in which the polymer film is fully dissolved. In agreement with previous studies, the dissolved polymer-solvent mixtures form a polymer-rich skin on top of the forming film during evaporation. In the case of the polydisperse films, a segregation of the lower molecular weight polymer to the film interface is observed. We provide a detailed, systematic analysis of the interface structure and properties during and after evaporation. We find that for non-dissolved films, the surface width of the film after solvent evaporation is enhanced compared to the case without solvent. Our results show that due to the kinetic arrest of the surface structure, the increased surface width is preserved after solvent evaporation for both mono- and polydisperse films. We conclude that it is important to take poor solvent effects into account for the surface morphology of already formed thin glassy films, an effect which is often neglected.
Thin polymer films and their surface properties are important for commercial applications such as coatings, membranes,1 composite materials and biomedical applications,2–4 and microelectronic devices and sensors5,6 Control of the surface properties like composition, roughness, and surface tension of the film is beneficial because they influence adhesion, wetting properties, and friction.7 For example, the efficiency of organic photovoltaic cells is directly dependent on their morphology and the distribution of components in the film.8,9
Common thin-film preparation techniques like spin coating often utilize solvents during various stages of processing from film formation to surface treatment.10,11 Suitable solvent mixtures can be designed for preferential solubility to certain components in a polymer mixture to create, e.g., layered structures or be selective with respect to molecular weight.12 Since solvent interactions can change the surface structure in complex ways, it is therefore important to systematically investigate how glassy polymer thin films are affected by the treatment of solvents of various qualities.
Many studies have been conducted on the effects of good solvents on film formation, which is the case most relevant to the deposition of a film from solution by solvent evaporation. Theoretical models13–15 as well as computer simulations16–18 show formation of a dense polymer skin on top of the initially dissolved film for suitable combinations of evaporation rate and polymer mobility and concentration. This polymer skin acts as a barrier for solvent evaporation, and in the case of glassy polymers, it can be under mechanical stress and could crack.18 In experiments, the polymer skin wrinkles and cracks when drying films and droplets.19,20
Considerably less attention has been given to cases involving poor solvents used to treat films after their formation. Exposure to different poor solvents has been shown to change the surface structure of thin glassy polystyrene films.21 Furthermore, it has been recently proposed that the partial dissolution of a glassy polymer film can be used to efficiently determine solvent qualities.12 In order to interpret such experimental observations, it is important to take into account the effects that solvents of poor quality have on already formed glassy polymer films. Yet, to our knowledge, there have been no systematic investigations of the effects of treating already formed glassy polymer films with solvents of different quality and subsequently evaporating the solvent.
In the present study, we utilize a simple bead-spring model with an explicit solvent to investigate changes in the surface structure of a glassy film as a function of the solvent quality. This coarse-grained model allowed us to access longer length and time scales than would be available to a more chemically detailed model, while still providing insights into the effects of solvent quality on thin-film surface structures.
Computer simulations allow us to control fully all microscopic interactions, which is not possible in experiments. Therefore, time-resolved, microscopically detailed resolution of the solvent influence on the surface during and after evaporation can be obtained. The formation of a film from a dense polymer-solvent solution is used as the upper limit for the investigated solvent conditions. We apply the simulation techniques developed for the evaporation of liquids with embedded nanoparticles22–25 to investigate the influence of evaporation and solvent quality on the surface roughness of the final film. This enables simulations of thin glassy polymer films and a liquid solvent layer on top with controlled evaporation rates.
We studied thin films of a model glass-forming flexible polymer. Each polymer chain consisted of N identical repeat units represented by beads of mass m and diameter σ that were connected linearly by springs. Nonbonded repeat units interacted with each other through the truncated and smoothed Lennard-Jones potential,
where r is the distance between particle centers, εij is the strength of the interaction between particles, and s(r) is a smoothing polynomial,
which ensures the pairwise potential and forces transition smoothly to zero at the truncation radius rc. In this work, we chose rc = 3 σ and began smoothing from rs = 2.5 σ for all nonbonded interactions. The interaction strength between repeat units of the polymer chains, εpp, was defined as the unit of energy, .
Bonded repeat units were connected by harmonic springs,
with bond length b0 = 0.9 σ and spring constant k0 = 1111 ε/σ2. A bond length less than σ was chosen in order to frustrate any crystallization that might occur in confinement.26,27 This choice of parameters is consistent with other recent studies of polymer thin films.26,28 The bulk polymer had a glass transition temperature Tg = 0.4 ε/kB, determined from the kink in the specific volume as a function of temperature for several cooling rates, as shown in the supplementary material. (Here, kB is Boltzmann’s constant.) This value of Tg is consistent with previously reported values for the chosen polymer model.26,28
The solvent was modeled by a single bead of identical size and mass to the repeating units in the polymer chain. The interaction between solvent beads was also given by the Lennard-Jones potential with the interaction strength εss = 0.5 ε scaled to give the vapor-liquid phase coexistence at temperatures where the polymer remained glassy. Specifically, the solvent coexistence densities at the glass transition temperature for the polymer were 0.77 m/σ3 for the liquid and 0.009 m/σ3 for the vapor phase as determined from the density profile. A modified Lorentz-Berthelot29,30 rule was employed for the Lennard-Jones cross-interaction between the polymer repeat units and the solvent,
This choice of combining rule allowed the solvent quality to be continuously adjusted through λ without affecting the polymer glass-transition temperature or the solvent vapor-liquid coexistence.
A smooth, structureless substrate supporting the thin film was modeled by a Lennard-Jones 9-3 potential,
where z is the distance between the particle center and the wall, εw is the strength of the interaction with the wall, and zc is the truncation distance normal to the surface. The substrate was placed at height −50 σ along the z-axis and made weakly attractive with parameters εw = 0.5 ε, σw = 0.5 σ, and zc = 3.0 σ to ensure that the polymer film wetted the substrate. An additional purely repulsive Lennard-Jones 9-3 potential with zc = (2/5)1/6σ was also placed at height 50 σ as a container wall. The overall layout of the systems studied is illustrated in Fig. 1.
The influence of the solvent quality on the film structure was first investigated for a monodisperse film containing 5500 chains of length N = 10 repeat units each. The thin film was placed in contact with 149 760 solvent particles of qualities spanning poor to good solvent conditions and including the dissolution limit (λ = 0.3, 0.5, 0.7, 0.9, 1.0, 1.05, 1.1, 1.15, 1.2, and 1.25). In addition, we also studied the structure of a film without any solvent on top, referred to as the λ = 0 case. A typical configuration and a density histogram of the system is shown in Fig. 1 for poor solvent conditions (λ = 0.3). The film thickness in all cases was h ≈ 15 σ, which was sufficient to create an initially bulk-like region in the middle of the film, as illustrated by the flat plateau region for the polymer density in Fig. 1.
The role of polymer polydispersity on the surface structure was investigated for varying solvent qualities using a binary mixture of 2750 polymers of length N = 5 and 2750 polymers of length N = 15 in contact with the same number of solvent particles. This simple bimodal distribution of polymers results in the same number-average chain length as for the monodisperse film. Since all polymer chains were short, we assumed that the glass transition temperature was not significantly influenced by the polydispersity. The average bulk density, and consequently the film height, was the same as for the monodisperse case. We considered three solvent conditions: a solvent which does not dissolve the film (λ = 1.0), a solvent that is capable of dissolving only the shorter polymer (λ = 1.1), and a solvent that dissolves the entire film (λ = 1.2). The choice of these values was based on the solubility behavior of the monodisperse film. By investigating both a monodisperse film and a polydisperse film, which are identical in all other parameters, the present study provides systematic insight into the influence of polydispersity, which is relevant in experiments.
III. SIMULATION METHODS
The initial configurations of polymer thin films in contact with solvents of different qualities were generated as follows: First, a polymer melt was created between the substrate and the wall using periodic boundaries in the x- and y-dimensions with edge lengths of 60 σ. The polymers were placed randomly into the box with a bond distance of 0.9 σ. Next, the “slow push off” method32–34 was used to remove the overlaps between the non-bonded repeat units. The repulsive Lennard-Jones interaction was slowly switched on during this process until all overlaps were removed. The polymers were equilibrated above the glass transition at temperature T = 1.0 ε/kB using molecular dynamics simulations with a Langevin thermostat (friction coefficient 0.1 m/τ) for at least 100 000 τ, where is the derived unit of time. Due to the slightly attractive interaction of the polymers and substrate, the polymer melt condensed onto it and formed a thin film. All simulations were performed on general-purpose graphics processing units (GPUs) using the HOOMD-blue simulation package35 with an integration time step of 0.002 τ. The time step was determined by monitoring the total energy drift for different values and then selecting the largest one consistent with long-term stability of the simulations. The chosen time step is consistent with the smaller time step used in Ref. 26.
The equilibrated melt was subsequently cooled to the bulk glass transition temperature T = 0.4 ε/kB at a linear cooling rate 6 10−5ε/kB/τ. To model the process of treating an already formed polymer thin-film with solvent, we then added solvent particles on top of the film. Solvent particles were randomly placed into sites of a face-centered cubic lattice at approximately the liquid density. The joined polymer-solvent system was then relaxed at T = 0.4 ε/kB for at least 12 000 τ, which was sufficiently long to ensure the formation of a liquid solvent film in coexistence with its vapor. The slow interdiffusion of the solvent in a glassy polymer thin film significantly increased the times needed for the solvent density to relax in some cases. For λ > 1.1, the solvent quality was sufficient to dissolve the polymer film. These systems were still equilibrated starting from the thin-film configuration because the dissolution limit was not precisely known beforehand, leading to even longer solvent-density relaxation times. We did not begin drying simulations until the polymer and solvent density histograms were no longer significantly changing, requiring simulations up to 820 000 τ in the case where the solvent quality is very close to the dissolution limit (λ > 1.15). Both smaller and larger values of λ equilibrated faster.
The final mixture typically consisted of three parts: a thin polymer film at the bottom wall, a liquid solvent phase in the middle of the box, and a solvent vapor above the liquid as shown in Fig. 1. The wall-polymer interactions ensured that the polymer film stayed adsorbed to the wall. Due to the favorable interactions of the solvent and polymer, the liquid phase of the solvent was always on top of the polymer film and a polymer-solvent interface formed, with a solvent vapor above the liquid solvent. For solvent conditions above the dissolution threshold, the polymer film was dissolved partly or entirely, creating a mixture of polymer and solvent with a solvent vapor on top.
Evaporation was modeled by periodically deleting a small number of solvent particles from a slab region at the top of the simulation box,22–25 as schematically illustrated in Fig. 1. Particles within a slab of thickness 20 σ at the top of the simulation box were defined as belonging to the deletion region. One randomly chosen particle was deleted from this slab every τ, leading to an evaporative flux of 2.77 10−4/σ2τ. When λ ≤ 1.1, the solvent particles in a slab region of thickness 15 σ above the polymer film were weakly coupled to a Langevin thermostat at T = 0.4 ε/kB with friction coefficient 0.1 m/τ. For larger λ values that fully dissolved the film, all solvent particles were weakly coupled to the thermostat, but the polymers remained decoupled. The simulations were stopped as soon as there were fewer than 100 solvent particles remaining in order to ensure temperature control was maintained. A single evaporation run typically took roughly six days on an NVIDIA Tesla K20 GPU. The chosen evaporation rate minimally disturbed the system, and the temperature remained roughly uniform during most of the simulations.
A. Solvent quality
The solvent quality will be reported in terms of the cross-interaction parameter λ as defined in Eq. (4). We found from our simulations that for our model, no polymers were dissolved when λ ≤ 1.1. Increasing λ resulted in an increased interface width, and at λ = 1.15, polymer chains started to dissolve from the interface. The solvent quality depends on the polymer molecular weight: a poor solvent for a high-molecular weight polymer may readily dissolve the same polymer at a lower molecular weight.12 Polymers with N = 10 were fully miscible with the solvent for λ > 1.15. Accordingly, λ was varied in our simulations from λ = 0.3 for poor solvent conditions up to λ = 1.25 for good solvent conditions.
Figure 2 shows representative snapshots of the monodisperse film surface for different values of λ below the solubility limit after treatment with the solvent but before evaporation (t = 0 τ) and at the end of the evaporation process (t = 180 000 τ). The repeat units are colored depending on their position relative to the interface (see Sec. IV C). As expected, the initial visible “roughness” of the interface increases with the solvent quality λ. Near the point where the solvent and polymers mix, the interfacial width is expected to broaden significantly. In the mean-field theory,36,37 the interfacial width scaling can be estimated by38
where ζ is the length scale of direct correlations and λc is the critical value. Here, we assume that the Flory-Huggins parameter χ is proportional to the solvent quality λ.39 The width is expected to increase until the polymers fully dissolve. This prediction is compared to simulation results in Sec. IV C.
B. Evaporation and film formation
The solvent was evaporated from the prepared films at a controlled rate. The evaporative flux was nearly constant during the simulations and deviated below the set rate only at the end of the simulations when there were few solvent particles remaining in the vapor phase. The time when this deviation occurred depended on the solvent quality, which influenced the amount of solvent trapped in the polymer films. Snapshots of the various dried monodisperse films are shown in Fig. 3 after evaporating for 140 000 τ. For the worst solvent qualities (λ ≤ 0.7), the solvent dewetted the polymer film when the liquid layer thickness was approximately 5–6 σ and formed droplets with finite contact angles that subsequently evaporated. Intermediate solvent qualities (0.7 < λ < 1.1) did not exhibit any dewetting, and the solvent dried essentially uniformly from the film surface. For the best solvent qualities (λ ≥ 1.1), some solvent particles became “stuck” to the film surface, and we were unable to completely evaporate the solvent during the accessible simulation times. This effect was most pronounced for the initially fully dissolved polymers, which evaporated to form swollen films compared to lower solvent qualities. The evaporation rate also slowed earliest and most quickly for these dissolved mixtures.
The time evolution of the polymer and solvent density profiles, shown in Fig. 4 for the monodisperse films, further demonstrates the influence of the solvent quality on film formation. All non-dissolved polymer films exhibited layering induced by the substrate as expected. Beyond this layering close to the wall, no additional spatial ordering was observed in any of the films considered here. For poor solvents, almost all solvent particles were removed after 140 000 τ, as seen in the upper row of Fig. 4. However, for better solvent qualities, there was a solvent-density peak that extended from the interface into the polymer film (middle row of Fig. 4), corresponding to the solvent that was initially partially mixed into the film and could not be removed. Qualitatively similar behavior was observed for the polydisperse films, shown in Fig. 5.
As expected,40 the shorter chains in the polydisperse films showed a slight tendency to segregate to the surface. Surface compositions differ from the bulk if the free energy of the system can be lowered by doing so. In a linear chain, a central repeat unit has two connecting chain parts, each having unfavorable interactions with the solvent. An end repeat unit, however, has only one chain emerging from it; therefore, the conformational entropy can be maximized by segregating chain ends at the interface.40 This effect is illustrated in Fig. 6, where the fraction of chain ends ϕend throughout the film at the end of the evaporation is shown. An enhancement of chain ends to about 0.5 at the flat substrate and 0.7 at the polymer-solvent interface can be seen. In addition, the solvent quality is slightly better for the shorter chains, resulting in further enhancement of the chain ends at the interface. The effective interfacial tension of the mixed films is therefore expected to be lower overall, resulting in rougher interfaces.
Figure 6 shows a polymer number density profile for λ = 1.1 at the end of the simulation at t = 401 500 τ, where the peak in density due to polymer accumulation is most pronounced. At this solvent quality, the small polymers are dissolved during equilibration and gather back onto the surface as the solvent is evaporated. Due to the partial dissolution and the reformation of the polydisperse film during the evaporation process, the surface width of this particular system stays very high. In fact, of all the film and solvent qualities in this study, this combination has the highest surface roughness after the solvent was evaporated. A snapshot of the film surface is shown as inset in Fig. 6. Some solvent molecules are trapped inside of the film at Lz ≈ 39 σ as well as on the surface at Lz ≈ 34 σ. Cases which use a solvent close to the dissolution limit on top of polydisperse films lead to an especially significant change in the surface structure of the film.
The time evolution of the density profiles was qualitatively different for the initially fully dissolved polymers, shown in the bottom rows of Figs. 4 and 5. As the solvent was evaporated from the dissolved mixture, a polymer-enriched layer formed at the drying interface. The height of this polymer-density peak initially grew before approaching a maximum value and forming a “crust” (or skin) layer.14–18,41 A significant amount of solvent remained trapped in the newly formed polymer film, partially due to the reduced mobility of the solvent through the skin layer.16
The formation of a skin layer was expected from the estimates of the Péclet number Pe = H/D for the evaporation process, where H is the initial height of the film, is the typical speed of the interface, and D is the diffusion coefficient of the polymers. When Pe 1, diffusion prevents the accumulation of polymers at the drying interface. When Pe 1, the polymer density increases near the drying interface, and a skin layer can eventually form. We determined D from the long-time limit of the mean-squared displacement of the dissolved polymer chains during equilibration and measured the interface speed from the simulations. For the monodisperse films, the estimated Péclet number was Pe ≈ 6.2, while Pe ≈ 4.4 and Pe ≈ 9.4 for N = 5 and N = 15 in the polydisperse films, respectively. Hence, in all cases, the well-dissolved chains were expected to form a skin layer during drying.
C. Interfacial properties
The positions and widths of the polymer-film interfaces were determined from the polymer density profiles by fitting them to a hyperbolic tangent form,37,42,43
where ρ1 and ρ2 are the densities in both phases, z0 is the position of the interface, and is the interfacial width. The density profiles were fit from the onset to the peak position plus 2.5 σ. In the case of the polydisperse film, the total number density of both polymers was used. The fitting procedure was performed for each snapshot taken every 100 τ during the evaporation. Our simulations then allow for the time-resolved interrogation of the interfacial properties, which can be challenging to obtain experimentally.
The influence of solvents of various qualities can be monitored during the evaporation process, as shown in Fig. 7. For poor solvents, the interface position stayed essentially the same during the evaporation run. Also, the interfacial width did not change significantly, as can be seen in Fig. 7(b). Their widths were roughly equal to the measured interfacial width = 0.311 σ for the film without any solvent on top. A small drop in the interface position can be observed at t 150 000 τ, which corresponds to the point where most of the solvent was removed from the thin-film surface. This drop is especially pronounced very close to the dissolution limit for the film with λ = 1.1.
The dissolved films reformed a thin film as the solvent was evaporated; however, they remained less dense than the films which were not dissolved. This is apparent by a larger interface position z0 in Fig. 7(a) and is due to the fact that these films contained a significant number of “trapped” solvent particles, even at the end of the accessible time scales of the simulations. As previously observed, an interface (the polymer-rich “crust”) quickly formed at about t 70 000 τ, indicated by a significant drop in z0. The polydisperse film exhibited qualitatively and quantitatively similar behavior as shown in Figs. 7(c) and 7(d). The long-time limit of the decrease in the film height is predicted14 to be h t−1/2, but we observed a slower decrease, confirming the simulation study in Ref. 17, which investigated a single solvent quality at an uncontrolled evaporation rate. This slower decrease can be explained with the position and concentration dependence of the solvent diffusion constant. A layer of enhanced mobility is found at the film interface, whereas the solvent diffusion decreases inside of the film as the solvent evaporates.17 Since the solvent diffuses in the polymer melt, the position and concentration dependence become more and more important close and below Tg.17 In experiments, the film thickness decreases rapidly at first during solvent evaporation and then slows down, which is associated with the glass transition, which decreases the diffusion.44 The trapping of solvent particles inside of the film below the glass transition temperature can be related to the increasing elastic modulus of the film.45 The exact determination of the glass transition in a system with changing concentration and slight evaporative cooling is challenging and requires further studies.
While previous studies investigated the process of film formation from evaporation from a good solvent, we focused on the influence of the solvent quality on the formed interface. The interfacial width was averaged over the first 5000 τ and the last 5000 τ of each trajectory. We confirmed that this choice of averaging window did not influence the reported results. The averaged initial width and final width are shown in Fig. 8. The initial interfacial width 0 showed a steep increase close to the dissolution limit (λ ≈ 1.1). Above this limit, it was not possible to determine an initial interfacial width by fitting Eq. (7) because the polymers were well dissolved. This behavior is expected from Eq. (6) because varying λ changes the solvent quality through the effective Flory-Huggins interaction parameter χ. Assuming λ is proportional to χ, Eq. (6) can be used to fit the interfacial width before evaporation, in Fig. 8. The critical exponent obtained from the fit was c = 0.46, very close to the mean field prediction of 1/2.
The interfacial width has an additional broadening due to capillary waves,42,46 which is not included in the mean-field estimation in Eq. (6). It has been shown that capillary waves are important for the stability of spin-coated films.47 The capillary wave spectrum depends on the lateral system size L and gives rise to a correction logarithmic in L. Quantifying this would require careful analysis,48 which we omit here since only one system size was investigated.
Figure 8 indicates that there was a small difference between the polydisperse and monodisperse films in terms of the initial width . The surface of the polydisperse films is slightly rougher than the monodisperse counterpart for all investigated solvent qualities. This was expected because the effective solvent quality is slightly higher for the shorter polymer, which segregates at the interface. The changed composition at the interface lowers the free energy of the system. For the polydisperse film, it is challenging to estimate the parameters for the mean-field scaling because not enough widths are available for fitting.
Although the initial interface width showed mean-field behavior as expected, the width at the end of the simulation exhibited distinct behavior for the monodisperse and polydisperse films. For the monodisperse films, was near 0.31 σ in case of poor solvents with λ ≤ 0.7. For solvents with larger values of λ, however, the interface had a slightly enhanced width of ≈ 0.51 σ. Both values are indicated by dashed lines in Fig. 8. Whether the solvent dewetted or not during the evaporation had no significant impact on the final width.
Figure 2 illustrates the difference in the width for the different solvent qualities further. In case of a poor solvent with λ = 0.7, only a very slight change in the surface morphology can be seen when solvent is placed on top of it. This corresponds to almost no change in the interfacial position and width during the evaporation of the solvent, as visible in Fig. 8. Better solvent qualities (λ = 1 and λ = 1.1) cause a drastic change in the surface roughness when placed on top of the glassy polymer film, as shown in the middle column of Fig. 2. Unlike the poor solvent, the interface morphology is visibly altered after evaporation, evident in the last column of Fig. 2.
If the solvent quality had no effect on the dried film’s surface structure, one would expect that the final width of the interface would be independent of the solvent quality and roughly equal to the width = 0.31 σ of the film without any solvent (λ = 0). The detailed insights provided by our simulations illustrate that for solvent qualities λ ≥ 0.7, this was not the case. Instead, the surface persisted to have an increased width. These poor solvents, which did not dissolve the film, increased the film interfacial width by nearly a factor of two. Although there is only a small absolute difference in the interface width, the resulting surface morphologies are distinctly different, as shown in Fig. 2 before treatment with the solvent and after evaporation. This enhancement to the film interface width persisted until the end of the simulation run, indicating a permanent change of the surface. That is likely due to kinetic arrest of the polymers, caused by glassy dynamics.
We studied the surface morphology of glassy polymer films covered with a liquid solvent before and during evaporation using large-scale molecular dynamics simulations. The simulations were motivated by recent experiments12 showing that even poor solvents have an effect on surface morphologies and suggesting that these can in turn be used to determine polymer-solvent interactions. The simulations provide unambiguous microscopic details for well-defined model systems, capturing also the dynamic evolution of the system as the solvent evaporates.
The initial width of the polymer interface as a function of the solvent quality followed the expected behavior and was in reasonable agreement with mean-field scaling predictions. As the solvent quality was increased, the interface broadened until the dissolution threshold was reached. The width of the interface after evaporation , however, was increased in comparison to the untreated film with no solvent on top. If the solvent had no permanent effect on the surface, one would have expected no difference between the final widths for different solvent qualities. The simulations provide microscopic insight and show clearly that even solvents which are below the dissolution threshold (considered poor in the framework of Flory-Huggins theory) still have an impact on the surface structure after application and evaporation of the solvent from a formed glassy polymer thin film, which is normally assumed to be negligible. The higher interfacial width of the films after evaporation is caused by kinetic arrest. Therefore it is especially important for experiments which aim to understand the surface morphology to take the influence of solvents on the surface structure into account.
In cases for which the thin film was dissolved and reformed during evaporation, a polymer-rich crust was obtained during drying. This effect is consistent with previous studies.14–18,41 The final films were less dense than the non-dissolved ones, while showing similar surface widths of ≈ 0.51 σ. As expected, no significant difference in the final films were found for different solvent qualities well above the dissolution limit. While deGennes18 showed that the resulting polymer-rich crust can crack due to mechanical stress, we did not observe any cracks in our simulations because the system size was too small for such macroscopic effects.
The effects of polydispersity on solvent interactions were investigated by performing additional simulations using a film with a mixture of two different chain lengths. In agreement with previous findings, the smaller polymers tended to accumulate slightly to the polymer-solvent surface. We additionally measured the interfacial width and illustrated that this segregation enhanced the interfacial width. Most importantly, our simulation study shows that polydisperse films exhibited increased surface roughness when treated with a solvent between the dissolution limits of the components. In this case, the smaller polymers dissolved and are assembled back onto the surface during evaporation, leaving a rough surface with enhanced interfacial width behind.
See supplementary material for the determination of the glass transition temperature of the bulk polymer.
We thank James Forrest for the initial inspiration for this work and for helpful suggestions. Financial support for this work was provided by the Princeton Center for Complex Materials (PCCM), a U.S. National Science Foundation Materials Research Science and Engineering Center (Award No. DMR-1420541). This research is a part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Award Nos. OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.