Interfacial and topological effects on the glass transition in
free-standing polystyrene films
Citation for published version (APA):
Lyulin, A., Balabaev, N. K., Baljon, A. R. C., Mendoza, G., Frank, C. W., & Yoon, D. Y. (2017). Interfacial and topological effects on the glass transition in free-standing polystyrene films. Journal of Chemical Physics, 146(20), 1-12. [203314]. https://doi.org/10.1063/1.4977042
DOI:
10.1063/1.4977042
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Interfacial and topological effects on the glass transition in free-standing
polystyrene films
Alexey V. Lyulin, Nikolay K. Balabaev, Arlette R. C. Baljon, Gerardo Mendoza, Curtis W. Frank, and Do Y. Yoon
Citation: The Journal of Chemical Physics 146, 203314 (2017); doi: 10.1063/1.4977042 View online: http://dx.doi.org/10.1063/1.4977042
View Table of Contents: http://aip.scitation.org/toc/jcp/146/20 Published by the American Institute of Physics
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THE JOURNAL OF CHEMICAL PHYSICS 146, 203314 (2017)
Interfacial and topological effects on the glass transition
in free-standing polystyrene films
Alexey V. Lyulin,1,a)Nikolay K. Balabaev,2Arlette R. C. Baljon,3Gerardo Mendoza,3 Curtis W. Frank,4and Do Y. Yoon4,a)
1Theory of Polymers and Soft Matter Group, Technische Universiteit Eindhoven, P.O. Box 513,
5600 MB Eindhoven, The Netherlands
2Institute of Mathematical Problems of Biology, Keldysh Institute of Applied Mathematics,
Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russia
3Department of Physics, San Diego State University, San Diego, California 92128, USA 4Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
(Received 25 October 2016; accepted 8 February 2017; published online 7 March 2017)
United-atom molecular-dynamics computer simulations of atactic polystyrene (PS) were performed for the bulk and free-standing films of 2 nm–20 nm thickness, for both linear and cyclic polymers comprised of 80 monomers. Simulated volumetric glass-transition temperatures (Tg) show a strong dependence on the film thickness below 10 nm. The glass-transition temperature of linear PS is 13% lower than that of the bulk for 2.5 nm-thick films, as compared to less than 1% lower for 20 nm films. Our studies reveal that the fraction of the chain-end groups is larger in the interfacial layer with its outermost region approximately 1 nm below the surface than it is in the bulk. The enhanced popu-lation of the end groups is expected to result in a more mobile interfacial layer and the consequent dependence of Tgon the film thickness. In addition, the simulations show an enrichment of backbone aliphatic carbons and concomitant deficit of phenyl aromatic carbons in the interfacial film layer. This deficit would weaken the strong phenyl-phenyl aromatic (π−π) interactions and, hence, lead to a lower film-averaged Tg in thin films, as compared to the bulk sample. To investigate the relative importance of the two possible mechanisms (increased chain ends at the surface or weakened π−π interactions in the interfacial region), the data for linear PS are compared with those for cyclic PS. For the cyclic PS, the reduction of the glass-transition temperature is also significant in thin films, albeit not as much as for linear PS. Moreover, the deficit of phenyl carbons in the film interface is compa-rable to that observed for linear PS. Therefore, chain-end effects alone cannot explain the observed pronounced Tgdependence on the thickness of thin PS films; the weakened phenyl-phenyl interac-tions in the interfacial region seems to be an important cause as well. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4977042]
I. INTRODUCTION
Understanding vitrification is a major challenge in soft condensed matter physics. This phenomenon is already hard to understand for simple liquids,1–5 while our present study is concerned with the glass transition in polymers, which can have many specific topologies, such as linear chains, rings, or branched structure. The possible kinetic pathways of cooperative molecular rearrangements are highly restricted in the glasses produced by vitrification of the low-molecular-weight compounds.6 By contrast, for polymers, the trans-formation from a liquid (polymer melt) to a solid (polymer glass) takes place in a continuous manner over a tempera-ture range. Its characteristic featempera-ture is that as temperatempera-ture is lowered, structural relaxation times and the polymer-melt vis-cosity increase rapidly up to a point where further structural relaxation becomes experimentally inaccessible.1,7–11
The glass transition temperature Tg is operationally defined as the temperature at which the viscosity reaches
a)Authors to whom correspondence should be addressed. Electronic addresses: a.v.lyulin@tue.nl and doyoon@stanford.edu
1012Pa·s, and the dominant relaxation time becomes ∼102s. Even though such a dramatic slowing down in the motion of chain segments is easily detectable,12–15 scattering exper-iments hardly show any accompanying change in the poly-mer static structure upon vitrification.16No unified theoretical understanding of the glass transition in polymers is yet avail-able. Nevertheless, it is one of the most important properties of amorphous polymers, both practically and theoretically. Even more difficult challenges can be expected when the glass transition is studied in thin polymer films rather than bulk polymeric systems.3,17,18A better understanding of the physics of polymers under confinement in general is relevant to fields as diverse as lubrication, filtration, enhanced oil recov-ery, and transport through membranes.19A porous medium, for example, can be used as a probe to gauge the character-istics of confined polymer systems.20Moreover, the study of the confinement-induced changes in the structure and dynam-ics of polymers may help elucidate the activity of biological polymers near cells.21
Many review articles have been published on the molec-ular mobility and glass transition phenomena in polymer thin films.3,17Here we highlight only those we believe to be
important for this study. Experimentally, it has been observed that the confinement due to the presence of supporting solid surfaces or/and free surfaces drastically changes the static as well as dynamic behavior of polymer chains in thin films with thicknesses below ∼100 nm. These experiments typi-cally use ellipsometry,22–24Brillouin light scattering,25X-ray reflectivity,26,27positron annihilation lifetime spectroscopy,28 neutron reflectivity,29 dielectric spectroscopy,30–32 or calori-metric33methods. The glass transition temperature is usually defined34as an abrupt change in the material’s thermal expan-sion coefficients or heat capacity upon cooling. As a result, the definition of Tgis not ambiguous. However, the difference in thermal expansion coefficients (or heat capacities) between the liquid and glass state could be substantially changed as the film thickness decreases below ∼100 nm.17Absolute val-ues of the thermal expansion coefficients themselves might change as well. Which thermal expansion coefficient, between that of a polymer liquid or of a glass, changes faster upon decreasing the film thickness has not yet been experimentally clarified.
It is significant that the polymer interfacial properties, structural or dynamic, are not the same at the interface with a supporting substrate as at a free surface. Studies of free-standing polymer films with two identical interfaces lack these issues, but they are experimentally very chal-lenging.37 Existence of two free interfaces should give rise to a much larger decrease of the glass transition tempera-ture with deceasing film thickness. This has been confirmed in the first experiments on free-standing polystyrene (PS) films.17
The decrease in glass transition temperature with decreas-ing film thickness observed for PS is most pronounced among all the polymers investigated so far.3,18 In contrast, poly(α-methyl styrene), PαMS, (its structure differs from PS by only one additional methyl group at the α-carbon of monomer unit) shows a drastically different behavior. For instance, Paeng and Ediger,18using a photobleaching technique, found that the mobile surface layer observed for the PS free-standing films is nearly absent in the case of PαMS. The authors suggest that some specific packing effects of PαMS chains and different monomer ordering at the film surface might be responsible for this absence. The spontaneous parti-cle embedment experiments, recently performed by Karim and McKenna38to obtain the surface compliance of PαMS films close to Tg, also show the PαMS surface remains mechani-cally stiff, which may be related to the observation of Paeng and Ediger.18In this regard, recent NEXAFS experiments39 show that in the case of PαMS the orientation of the phenyl rings at the film surface is much weaker than that observed for PS films, wherein the phenyl rings are preferentially oriented perpendicular to the film plane only at the top surface. How-ever, it is not clear how this surface orientation of the phenyl groups is related to the molecular mobility in the interfacial layer.
A popular theoretical explanation of the observed Tg decrease in thin, free-standing polymer films was suggested long ago by de Gennes.40He hypothesized that polymer chain ends are concentrated at the interfaces where they create lay-ers of higher segmental mobility. For thinner films, these
layers constitute a larger portion of the film. Hence, their statistical weight in the film-averaged glass transition tem-perature becomes more significant. This leads to a decrease of the glass transition temperature with decreasing film thick-ness. In this regard, it should be noted that the sliding model of de Gennes40 for thin film T
g was extensively and crit-ically studied. We note only that in the experiments that show a strong Tg dependence on film thickness, quite long polymers are often studied, with molecular weights above 100 000 (monomer units > 1000). In this case, the effect of the chain ends should have negligible effects. It is impor-tant to recognize that studies of cyclic polymers with no chain ends have not yet been carried out; these could pro-vide valuable insights into the film-thickness dependence of Tg.
Recently, thermodynamic models of the glass transition in confined polymers were proposed to describe the film-thickness dependence of Tg in free-standing thin films.41–43 They are based on the assumption of uniform segment density across the film thickness and, hence, do not take into account the possible non-uniform distribution of chain ends and/or strongly interacting chain moieties, such as phenyl groups of PS chains.
Therefore, the available experimental data and theoreti-cal models do not present a clear picture of the variation of
Tg reduction in thin (and especially free-standing) polymer films nor do they suggest a physical mechanism for this phe-nomenon. The underlying specific effects of free interface, polymer–substrate interactions, and monomer structure are difficult to delineate, and therefore, their individual contribu-tions are not well separated. Such a separation could be carried out via computer simulations,44–53but simulations introduce an additional complication: the cooling rates are much faster by a factor of ca. 1011than those used in experiments, which causes a shift in the glass transition temperature to higher val-ues.54 Moreover, the surprisingly strong dependence of T
g reduction in thin polymer films on the monomer structure, as shown by the experiments for PS versus PαMS, clearly demonstrates the critical need to carry out the simulations with full account of detailed monomer structures and their interactions. The experimentally observed Tg dependence on film thickness is most pronounced for PS.3,17,18In this regard, we note that molecular-dynamic simulations of the interfa-cial structure in glassy free-standing PS films have not been performed.
In the present study, we perform the first molecular-dynamics simulations of the united-atom model of atactic polystyrene (PS) in the bulk and in free-standing films in the vicinity of the glass transition temperature for both lin-ear and cyclic polymers. Our choice of PS is dictated by the fact that the experimentally reported confinement effects on the glass transition are most pronounced for this poly-mer.3,17,18 In this work, we use the united-atom approach in which hydrogen atoms are not modeled explicitly while still keeping a sufficient level of the chemical details. This allows us to simulate larger systems and implement slower cooling rates. Our main objective is to answer the follow-ing two questions on thermal and structural properties of PS films:
203314-3 Lyulin et al. J. Chem. Phys. 146, 203314 (2017)
(1) How large are the confinement effects (if any) for free-standing films of linear and cyclic PS on their Tg reduction and thermal expansivity, and what are the cor-responding roles of the chain ends and phenyl-phenyl (π−π) interactions?
(2) How can one compare the vitrification characteristics in free-standing films produced in silico and in vitro given the vastly different cooling rates in the two cases? In future work, we also plan to investigate how sensitive the interfacial properties (concentration of chain ends and phenyl rings, bond orientation) are to the atomistic details of PS versus PαMS, given the surprising experimental findings discussed above.
Here we report on our first results on structural and some thermal properties (glass transition temperature and expan-sion coefficients); the details of segmental dynamics will be a topic of a future publication. We also include some results of a united-atom model that slightly differs from that of PS. The structure of the paper is as follows. In Sec.II, the models and simulation algorithms are explained. In Sec.III, we present a careful consideration of the quality of the equilibration and finite-size effects and investigate the possible influence of the aging on the structural properties in the simulated time win-dow, followed by the discussion of the characteristics of the simulated PS bulk glass transition. Then we discuss the density profiles used to calculate the film density, which were used to extract the glass transition temperature. Finally, we discuss the reduction of Tg in films, as well as thermal expansion coef-ficients and the interfacial structural properties. The paper is finalized with Sec.IV.
II. SIMULATION ALGORITHM AND MODELS UNDER STUDY
Simulations have been performed for both linear and cyclic atactic PS. Both the bulk polymers and free-standing thin films were investigated. Each film consists of 8, 16, or 32 chains. Each chain contains 80 monomeric repeat units; hence, their molecular weight (ca. 8330) is below the entan-glement value. All bulk polymer samples contain 8 chains with 80 monomers per chain.
Periodic boundary conditions have been applied, in three dimensions in bulk, in two in free-standing films. Fig.1shows snapshots of two films, plus the monomeric structure in a united-atom presentation.
As in the previous studies,48–51,55–57 the united-atom model has been applied in the simulations. The hydrogen atoms were collapsed onto the corresponding carbons, and the combined atoms were treated as effective particles. The struc-ture of the PS monomer unit is shown in Fig.1(a). It consists of two backbone (–C–H–CH2–) atoms and the phenyl ring—the aromatic side group of six united atoms. The stereochemi-cal configurations of the aromatic groups were generated at random, so that the ratio of meso to racemic dyad ended up near unity. The configurations of the aromatic groups were generated independently for each polymer chain. In addition to the simulations of linear chains, cyclic polymers have been created. The corresponding bulk materials and films have been investigated as well. For cyclic polymers, the internal knots and
FIG. 1. (a) United-atom model of the PS monomer in the present study. All polymer chains have the same (80 monomers) degree of polymerization. Snap-shots are shown of the 2.5 nm-thick (b) and 10 nm-thick (c) free-standing PS films comprised of 8 and 32 PS chains, respectively. Periodic boundary condi-tions are not shown for clarity. T = 600 K. The vertical Z axis perpendicular to the film surfaces and the normal-to-phenyl-plane and backbone-chain vectors that are used to study the segmental orientation are also denoted. A simulation box of 70 Å (x) × 70 Å (y) × 200 Å (z) was used.
concatenation of the polymeric rings were prevented during the preparation step.
Interactions between the united atoms are given by the following potential: U=X i,j εij σij rij !12 −2 σij rij !6 +X i,j kl,ij rij−lij 2 +X i,j,k
kθ,ijkθijk−θ0,ijk2+X i,j,k,l
kφ,ijklcosnφijkl
. (1)
The first term denotes the non-bonded contribution, the sec-ond stretching, the third bending, and the last the torsional contribution. The PS united-atom force field is identical to the one employed in our previous studies of the glass transition in bulk PS;55–57 for details, see Refs.55–57and the references therein. No Coulombic interactions are taken into account. We also minimally modified the PS united-atom force field58(see below) to study the effects caused by the presence of addi-tional methyl side-groups attached to the α-carbon of chain backbone to mimic PαMS.
The velocity Verlet algorithm59 was used to integrate Newton’s equations of motion with a time step of 4 fs. The temperature was controlled using a collisional thermostat.60,61 All the simulated systems were initially equilibrated at 600 K (see the details in Sec.III Aof the paper). The polymer bulk simulations were started by placing the all-trans conforma-tions of 8 parallel chains in a large simulation box of 210
× 210 × 210 Å3 which corresponds to the density of
0.012 g/cm3. This periodic box was then compressed isotropi-cally with the velocity of 0.1 Å/ps until the density of 1 g/cm3 was reached. At the end of the compression, a short (about 500 ps) NVT run was performed, during which the box dimen-sions were fixed at about 50 Å in each direction. 50 Å is large compared to the chain individual gyration radius, which is about 20 Å for linear PS. In doing so, polymers will not overlap with themselves. Subsequently, the system was fur-ther equilibrated in the NpT ensemble at zero pressure using
a Berendsen barostat.59The pressure stayed fixed at zero for the bulk-production NpT simulations, which allowed the box size to fluctuate in response to temperature changes; see also Fig. S1 in thesupplementary material. The total equilibration time was about 1 µs. Eight independent samples were pre-pared in this way. All the following results were produced by the corresponding averaging over the independent sam-ples. The same procedure was used to prepare the samples of cyclic PS.
For free-standing film simulations, the equilibrated sam-ples of PS melts from above (T = 600 K, almost cubic boxes of about 50 × 50 × 50 Å3) were first compressed in the Z direc-tion and extended laterally with the velocity of 0.1 Å/ps. At the end of this stage, the lateral periodic box dimensions were kept fixed at 70 Å. After some NVT equilibration, the film was placed in the middle of a box in which the Z direction had been increased to 200 Å and the periodic boundary conditions removed in this direction. This way two free interfaces were created. All the film simulations have been performed in the NVT ensemble, keeping the size of these anisotropic boxes fixed. Note, however, that the effective pressure acting on the free surfaces equals zero, just like in the bulk simulations. The thicker films were produced by increasing the prepared configurations in the Z direction and providing some further equilibration. The film thickness (its dimension in the Z direc-tion) depends on the number of molecules. At T = 600 K, it is 100 Å for 32 chains, 50 Å for 16 chains, and 25 Å for 8 chains, all this for linear and cyclic polymer-films alike. For all films, the lateral box size was fixed at 70 Å. Equilibrated PS films with 8 and 32 chains are shown in Figs.1(b)and1(c), respectively.
In all simulated films, bulk density was observed in the very middle of the films. We tried to create thinner (12.5 Å), free-standing films, applying the same procedure as explained above, for the system with 4 polymer chains only. In this case, the monomer density in the middle of these films was almost one half of the corresponding values in the polymer bulk at the same temperature and zero pressure. Therefore, we did not continue with these 4-chain film simulations. To study thicker films (>10 nm) and achieve at the same time a com-promise with increasing computational expenses, the lateral dimensions of the 16-linear-chain PS films were decreased by a factor two, while the vertical box size was doubled. This made it possible to create free-standing films of about 20 nm thick.
Subsequently, all the samples, both the films and the bulk, were cooled at a velocity of 0.01 K/ps starting from T = 600 K. This simulated cooling is extremely fast compared to the cool-ing rates used in typical experiments, ca. 0.1 K/s. The effect of this simulated faster cooling, by a factor of ca. 1011, will be discussed later. The cooling was performed in a temperature range between 600 K (well above the glass-transition tem-perature for both polymers) and 240 K (well below the glass transition). For each system (linear and cyclic, in films and in bulk), a short 500 ps production run was subsequently per-formed at each selected sampling temperature, starting from the initial configurations obtained during the fast cooling run. During the production run, the polymer configurations were stored every 4 ps for further analysis. In order to improve
the statistics, the simulations were performed starting from eight independently generated and well-equilibrated samples at 600 K for each film and bulk sample investigated in this work.
III. RESULTS AND DISCUSSION A. Equilibration
Equilibration of all the PS samples has been performed at T = 600 K for about 1 µs, well above the glass-transition region (which is around 450 K under the fast cooling con-dition applied here; see below). Averaged auto-correlation functions for the chain end-to-end vector (and the char-acteristic ratios for different intermediate distances) were measured during the last 300 ns of the equilibration run, as shown in Fig. 2. For a PS melt at this high tempera-ture, it took about 280 ns for the end-to-end vector to relax sufficiently; the total equilibration time was a few times longer.
In order to quantify the equilibration further, the charac-teristic ratio CN = *R2 N Nl2 b + (2) was calculated in a bulk (linear) PS melt, as shown in Fig.2. Here R2N is the squared distance between two segments sep-arated by N backbone bonds and lbis the equilibrium length of the chemical bond in the backbone, lb = 0.153 nm.62The values of C∞ have been calculated by fitting CN vs 1/N, as suggested by Wittmer et al.,63,64CN = C∞
1 − αN−1/2 giv-ing C∞= 8.1 ± 0.2. This matches our previous simulations as well as available literature data;55–57 see also Fig. S2 in the
supplementary material. In thin films (not shown), the results are quite similar.
As was explained above, at each intermediate selected temperature short production runs of 500 ps were per-formed. Well above the glass transition, the polymer sys-tem is in equilibrium; the density (and other thermodynamic properties) remain constant on average and fluctuate around
FIG. 2. Characteristic ratio CNfor PS bulk at T = 600 K. The dashed line
shows the analytical asymptote,63,64see the text for details, with C∞= 8.1
±0.2. The inset shows the relaxation of the PS chain end-to-end vector at the same temperature. The solid line in the inset is the stretched exponential fit, which gives a relaxation time of about 280 ns.
203314-5 Lyulin et al. J. Chem. Phys. 146, 203314 (2017)
FIG. 3. (a) The time evolution of the PS bulk density well below (T = 320 K), close to (T = 420 K), and well above (T = 600 K) the simulated (linear) PS bulk glass transition temperature, Tg= 447 K. Aging effects lead to the increase of the polymer density and are seen below Tg. (b) The time evolution of the
normalized, monomer-monomer, van der Waals potential energy Uvdwwell below (320 K), and around (420 K) the glass transition temperature. The long-dashed
line is the stretched-exponential fit of the energy relaxation at T ∼ Tg, giving a relaxation time of about 20 µs. The horizontal level of no relaxation is highlighted
by the short-dashed line.
their equilibrium values. Upon approaching the glass tran-sition, aging phenomena (see, for example, Reference 65) become more and more pronounced. They lead to a slow increase of polymer density over time. The time evolution of density at different temperatures is shown in Fig.3(a)for PS bulk; to study this evolution, rather long runs of ∼300 ns have been carried out. Indeed, well above the glass tran-sition temperature, at T = 600 K, the density is on average constant. At T = 420 K, a temperature close to the glass tran-sition under the rapid cooling condition (Tg = 447 K), aging is quite pronounced: the density increases over time. At T = 320 K, well below the glass transition, aging was observed to occur extremely slowly. To estimate the characteristic aging time, the time evolution of the non-bonded (van der Waals) interactions was monitored. Fig.3(b)shows the time depen-dence of the normalized (to the initial value at the beginning of the production) monomer-monomer, van der Waals poten-tial energy for PS bulk, well below and around the bulk glass transition. A stretched exponential fit of this dependence (used here just for an illustration, as the final van der Waals energy will never reach zero) gives the characteristic aging time of about 20 µs. This value is much higher than the production time (500 ps) at each intermediate temperature, meaning that the density (and other statistical properties) can be consid-ered constant during the data production, even close to Tg, since the aging effects in the simulated time windows are negligible.
B. Bulk glass transition
The glass transition was simulated by monitoring the temperature dependence of the density or specific volume. NpT (p = 0) MD cooling runs have been carried out for bulk PS of both linear and cyclic chains, starting from T = 600 K, as shown in Fig. 4. A change in the thermal expan-sion coefficient upon cooling at 0.01 K/ps can be clearly observed in the simulated results. In Fig. 4(a), comparison with available PVT (Pressure-Volume-Temperature) measure-ments34 for linear PS of Mw = 9000 is also shown. It is obvious that in the high-temperature regime the simulated and experimental PS bulk densities are very close to each other. This validates the force field in use. We also checked for finite-size effects by simulating the larger PS box, dou-bling the amount of polymer chains. The density-temperature dependence is not changing (see Fig. S3 of thesupplementary material), and the produced glass-transition temperature remains the same. The thermal expansion coefficients from the high temperature region (the melt) and the low tempera-ture region (the glass) were obtained from the linear fits of the data in Fig.4.
The glass transition temperature is taken to be the tempera-ture at which the two fitted linear lines cross. The temperatempera-ture range of the fit was varied, and the error bars (see Table I
below) are calculated based on this variation. The transition temperature region itself is excluded from this fit. The vertical
FIG. 4. Simulated PVT results (specific volume–temperature dependencies) for bulk PS: (a) linear and (b) cyclic. Solid straight lines show the linear fits for the data well above and well below the glass-transition area. Vertical arrows indicate the Tg values. Experimental
results (see Reference36) for linear PS, Mw= 9000 at p = 1 atm, are also shown
TABLE I. Glass transition temperatures (K) (with error bars in parentheses) for all simulated polymers, both in the bulk and in films of various thicknesses denoted in parentheses. The error bars are calculated based on the variation of the temperature range of the linear fits.
Geometry Linear PS Cyclic PS
Bulk 447 (10) 454 (5)
Film (20 nm) 446 (5) · · ·
Film (10 nm) 443 (5) 433 (5)
Film (5 nm) 428 (5) 441 (5)
Film (2.5 nm) 391 (5) 413 (3)
arrows in Fig. 4 indicate the values of Tg obtained in this way. As seen in Fig. 4(a), the difference between the sim-ulated and the experimental Tg values is rather large, about 82 K. However, considering that the simulated cooling rate is extremely faster than that of typical experiments, by a fac-tor of ca. 1011, the estimated shift of Tg according to the well-known Williams-Landel-Ferry (WLF) equation66 with the universal values of C1 = 17.44 and C2 = 51.6 K is ca. 88 K.54If we apply the recently determined values of Vogel-Fulcher-Tammann parameters (B = 3288; T0 = 308 K) for PS with Mw of 90 000,67 the corresponding values of C2 = (Tg T0) = 57 K and C1 = B/2.303 C2 = 25,66 taking
Tg = 365 K from Fig.4(a), lead to the estimated Tg shift of 45 K. Therefore, the predicted Tgvalue of PS is found to be in good agreement with experiments considering the limits of applying the WLF equation. Moreover, very promising results (which are not a priori expected) are the values of the thermal expansion coefficients (see also the results in Fig.8 and the discussion). That is, very good agreement between the sim-ulations and the PVT experiments is observed—both in the melt (5.6 × 10 4 K 1 (exp) vs 4.7 × 10 4 K 1 (sim)) and in the glassy state (2.0 × 10 4 K 1 (exp) vs 2.3 × 10 4K 1 (sim)). The thermal expansions and the Tg values were also estimated for cyclic PS bulk. We believe that all the simulated thermal expansion coefficients (also those for films) can be directly compared with experiments (if available), in spite of the fact that the simulated glass-transition temperatures are very much shifted upwards as compared to the experimental data.
For cyclic PS, a slight shift to a higher (compared to the values for bulk samples of linear chains) value of the glass
transition temperature can immediately be observed. This is interesting and is consistent with the experimental observa-tions68 for PS, as well as the results of Kremer’s group for for polydimethylsiloxane (PDMS) melts69 that show a non-monotonic, non Fox-Flory, molecular-weight dependence of the glass transition temperature for cyclic polymers, which remains higher than that for linear polymers. These charac-teristics including the shift to the higher Tg values for cyclic polymers may be understood by thermodynamic arguments since the configurational entropy of the cyclic chains in melts is smaller than that of linear polymers.69
C. Monomer-density profiles
Film densities were calculated from monomer density profiles. Fig.5presents the results for PS films of 32 chains at different temperatures. All other films of different thicknesses show a similar behavior: the film thickness increases with the temperature, and, hence, the average film density decreases with temperature. The density reaches a plateau value in the middle of the film and drops near the free surfaces. We also checked for possible finite-size effects by narrowing the simu-lation box from 7 nm to 5 nm for the linear PS film composed of 8 chains. The corresponding film density profiles do not change; see Fig. S4 in thesupplementary material. The glass transition can be extracted by measuring the density in the mid-dle part of the film, or by measuring the film thickness (using Gibbs dividing surfaces or a similar criterion). In the present study, we closely follow the procedure suggested by some of us earlier.48Basically, the film density has been obtained from an average between the very last two peak values at the edges of the plateau region. The glass transition can also be calculated from the measurement of the film thickness48in analogy with experimental protocols. We have verified that this produces equivalent results (Fig. S5 in thesupplementary material com-pares the methods). It is important to note that for thick (above 10 nm) simulated films the density in the middle of the film is equal to the corresponding bulk density at the same tem-perature (see the horizontal lines in Fig.5(a)). For the 10 nm-thick cyclic PS films, the density profiles are very similar to those for linear-chain films, as can be seen in Fig.5(b). How-ever, for thinner films there is a difference, which leads to the different simulated glass-transition characteristics for thin films of linear and cyclic PS, as will be discussed below.
FIG. 5. (a) Film density profiles in a 10 nm-thick linear-PS film at different temperatures. Dashed horizontal lines show the simulated PS bulk density at 600 K and 240 K, respectively. A ver-tical arrow denotes the increased tem-perature. (b) Film density profiles for linear PS vs. cyclic ring PS well above (T = 600 K) and well below (T = 240 K) the glass transition. Larger oscillations in the middle of the film at low tem-perature reflect some monomer packing order in the horizontal film layers.
203314-7 Lyulin et al. J. Chem. Phys. 146, 203314 (2017)
FIG. 6. Temperature dependence of the specific volume for linear PS in the bulk and for films of two different thicknesses. The glass transition tempera-tures from linear fits (shown by the straight lines) are indicated. The ∼50 K decrease in Tgvalues is seen for the extremely thin (2.5 nm) films.
The interfacial layer thickness can also be calculated from plots as in Fig.5. For all the films in the simulated temperature range, the thickness of the interfacial layer is about 10 Å at 600 K and slightly (by 2-3 Å) decreases upon cooling. Other interfacial characteristics, such as the distribution profile of different chemical moieties and the segment orientations, will be discussed later in the manuscript.
D. Film glass transitions
The dependence of specific volume on temperature for linear PS is shown in Fig. 6. The corresponding curves for the cyclic analogues have also been simulated but are not presented. The numbers denoted in the figure indicate the sim-ulated glass transition temperatures, estimated as explained above, by using the linear fits to the data. It can immedi-ately be seen that thin films made of linear chains have decreased (as compared to bulk) values of Tg. For 2.5 nm-thick films, this decrease can be nearly 56 K. All the simulated glass transition temperatures of various film thicknesses, both for linear and cyclic polymers, are summarized in Table I
below.
For cyclic polymers, the confinement also leads to decreased glass transition temperatures with decreasing film thickness. The decrease is slightly weaker, however. This dif-ference, we believe, is due to a lack of chain ends. The same data are presented in Fig.7, which shows the thickness depen-dence of the glass-transition temperature. From the results of this figure and TableI, we also conclude that in general the
glass-transition temperature for cyclic polymers seems to be slightly higher than for linear ones, although this should be taken with some caution because of rather small differences and rather large error bars.
E. Thickness dependence of Tgfor PS films
As mentioned above, for both linear and cyclic PS films the simulated glass transition temperature decreases with decreasing film thickness. This is clearly seen in Fig. 7(a), where the thickness dependence of the normalized (to the simulated Tg of the corresponding bulk) film glass transition temperature is shown. In Fig.7(a),this dependence is fitted using the empirical equation35,49
Tg Hf = Tgbulk* , 1 − A Hf !δ + -, (3)
where Tgbulkis equal to the glass transition temperature in the corresponding bulk and Hf is the film thickness. The fit gives δ = 1.6 and A = 0.73 nm for the characteristic length, which is quite close to the (discussed earlier) thickness of the interfacial layer in these films.
Recent experiments of the Fakhraai group70on supported PS films show that there is a cooling rate, around 60 K/min, above which all the PS film glass transition temperatures vs film thickness data collapse onto each other. This seems to be true for other polymer systems as well.71 The data from Reference70obtained with (high) 120 K/min cooling rate for PS of Mw∼46 000 are normalized to the corresponding bulk
Tg, measured with the same cooling rate and are replotted in Fig. 7(a) for comparison. Given that these experiments were performed with supported films, we include the results obtained for supported PS films from a previous MD simula-tion study,49where a cooling rate of 0.01 K/ps was employed. The normalized experimental results70are in nice agreement with the simulations for the supported films, in spite of the huge difference in cooling rates. The fit (Eq. (3)) yields
A ∼ 0.1 nm, δ = 0.8 for both the simulated and
exper-imental data. These values are lower than those obtained for the simulated free-standing films. Thus, as compared to the simulated free-standing films, the film thickness depen-dence of Tg for the supported films is weaker. Note, never-theless, that the experimental data70 produced with a much slower cooling of 1 K/min show a stronger film thickness dependence, as replotted in Fig. 7(a). The most important observation in Fig. 7(a), however, may be that at very fast
FIG. 7. Film thickness dependence of the normalized (to the bulk) film glass transition temperature for (a) linear and (b) cyclic PS films. In (a), the experi-mental results of Fakhraai group70are also plotted for supported PS films. The grey circles in (a) show the simulated data for the supported PS films from a previous study.49The dashed lines in (a) are fits using Eq.(3). See the text for more details.
FIG. 8. The thickness dependence of the values of the PS thermal expansion coefficients in films of linear and cyclic PS, both in the melt (T = 600 K) and in the glassy (T = 300 K) state. Film thickness was measured at T = 600 K. The normalization was done to the corresponding (linear or cyclic) bulk values.
cooling rates the effect is noticeable only for very thin films <ca. 10 nm.
In the present work, we did not study the cooling rate effects on the simulated Tgsuppression; it was not our primary goal considering the enormous computational requirements. Due to the extremely high implemented cooling rates, the range of the confinement effects appears to be much shorter than that observed in experiments. In fact, it was not a priori obvi-ous that the comparison between simulations and experiments was at all possible. Although it may certainly be the case that the interfacial structural changes impact the magnitude of the observed Tg decrease, we still cannot exclude the possibil-ity that the features of the Tgsuppression may be different at experimental time scales. Indeed, the findings of Torkelson’s group31,72have suggested that the interfacial gradient in Tgis at least of order 10 nm at experimental time scales. Neverthe-less, the results in Fig.7demonstrate some agreement between simulations and available experiments.
Fig.7(b)shows that for cyclic PS the value of Tgdecreases by about 5% for the ∼10 nm-thick film as compared to the bulk value. Similar to the case of linear PS, further decreases of the glass transition temperature are observed for thinner films of cyclic PS, although our data exhibit larger error bars. F. Thermal expansion coefficients
Fig.8shows that the thermal expansion coefficients for linear and cyclic PS (10-nm thick) films are about 30% higher than in the bulk at 600 K (well above Tg). The absolute value of this coefficient changes only slightly with decreasing film thickness. In comparison, the absolute values of thermal expansion coefficients for the glassy films seem to remain nearly the same as that for the bulk sample, with no significant effect of the film thickness, within the statistical uncertainty of our data.
G. Distribution of chain ends
The decrease of the glass transition temperature in the films is definitely caused by the presence of free surfaces. In the interface region, both the static and dynamic characteris-tics of polymers differ from those of bulk systems and middle regions of films. The segmental dynamics is not analyzed in
the present study; however, we do observe an enhanced con-centration of the chain ends in the film interfacial layer. We investigated the location of the backbone vectors, defined as the vectors connecting the consecutive backbone CH2united atoms (see Fig.1(a)). The number of backbone vectors that are located at the end of the polymer chains, normalized by the total number of the backbone vectors in each 2 Å-thick subdivided layer, is shown for two temperatures in Fig.9. In the middle, bulk-like region of the film, this fraction is very close to 2 (ends)/80 (monomers) = 0.025. This corresponds to the homogeneous distribution of the chain ends and is inde-pendent of temperature. For all temperatures, we see that at the film surfaces a larger fraction of the backbone vectors are chain ends. As mentioned earlier, the interfacial regions are about 10 Å thick on each side, and the fraction of the chain ends in the interfacial regions increases from 0.06 at T = 600 K to 0.09 at T = 330 K. The strong increase of the chain-end frac-tion with decreasing temperature indicates that the chain-end segregation in the interfacial layer is driven primarily by the enthalpic effects of van der Waals attractions, rather than the confinement entropy effect.
Our observation regarding the chain-ends distribution is similar to that of Jain et al.45 in Monte Carlo simula-tions of a coarse-grained polymer-film model. It is hypoth-esized that the presence of more chain ends influences the dynamics of the interfacial layer and is responsible for a decrease in the glass transition temperature. The segmental dynamics of the film layers will be a subject for our future studies.
H. Orientation of polymer backbone and phenyl rings Besides the distribution of backbone vectors and phenyl groups, the orientation of the chain backbone and phenyl rings will also affect the local structure and chain mobility and, hence, the glass transition temperature. The orientation of the backbone is described by the chain vectors connecting the con-secutive CH2groups, and the orientation of the phenyl groups is denoted by the vector perpendicular to the phenyl ring plane, as shown by the arrows in Fig.1(a). The order parameter in Fig.10is plotted as a function of the position of these vectors.
FIG. 9. The fraction of the chain-end vectors plotted along the film thickness position (z-axis). Data are shown at high (600 K) and low (330 K) tempera-tures for a 10 nm-thick film of linear PS. The horizontal grey line draws, for comparison, the fraction (2/80) one expects when the chain end vectors are distributed uniformly; see the text for more details.
203314-9 Lyulin et al. J. Chem. Phys. 146, 203314 (2017)
FIG. 10. Orientation as a function of Z-position at T = 330 K for linear and cyclic PS (PSC). The orientation of the backbone (vector between CH2
groups) is given with respect to the Z axis. The orientation of the phenyl rings (measured as the alignment of the blue normal vector in Fig.1(a)) also relative to the Z axis. Half of the film is shown as the averaging has been performed with respect to the middle of the film.
The order is calculated as the second Legendre polynomial,
P2= 3 2 cos 2θ − 1 3 ! , (4)
where θ is the angle between the vector mentioned above and the film thickness (Z) direction. Hence, the order is 1 for vec-tors oriented perpendicular to the film surface and 1/2 for those oriented perfectly parallel to the surface. Given limited statistics and “frozen in” structures, the data are not perfectly symmetric around the middle of the film, and the averaging has been performed at the same distance from the middle of the film. From the data for linear PS and cyclic PS displayed in Fig.10, we can conclude the following:
(1) All the orientations in the middle part of the film are fully isotropic; the order parameter is very close to zero. (2) The orientation of the backbone vectors in the interfacial
layer differs for the two polymers, for all temperatures (only T = 330 K data are shown). The backbone vector tends to orient perpendicular to the surface for linear PS, at both below and above (not shown) the glass transition, and parallel to the surface for cyclic PS (PSC). This is caused by the segregation of PS chain-end vectors at the surfaces (Fig.9), which exhibit a strong preference for
the perpendicular orientation in contrast to the prefer-ence for the parallel orientation of other chain vectors at the surface. The parallel orientation of the cyclic PSC backbone at the surface of the film obviously results from the cyclic nature of these polymers with absence of ends.
(3) For both linear PS and cyclic PS, the vectors normal to the phenyl plane show preferential orientation parallel to the surface, indicating that “interfacial” phenyl rings tend to point normal to the surface, in good agreement with NEXAFS results and simulations for PS in39. I. Interfacial layers properties
In Fig.11, the united C-atom distribution functions, cal-culated separately for backbone C-atoms and phenyl C-atoms, are shown for 10 nm-thick films of linear PS (a) and cyclic PS (b), well above (T = 600 K) and close to (T = 450 K) the glass transition. A few conclusions can be drawn here:
(1) At the film surface, there is a higher probability of phenyl C-atoms of linear PS as compared with that of backbone atoms indicating that the phenyl rings are located outwards, in good agreement with the NEXAFS experiment.39This is also consistent with the snapshots of Fig.1.
(2) There is a pronounced peak in the backbone C-atom probability in the interfacial layer approximately 1 nm below the top surface, as shown by the dashed curves in Fig.11(a).This is accompanied by a deficit of phenyl C-atoms since the total film density in this layer is identical to the middle region (see Fig.5).
(3) The deficit of the phenyl rings in the interfacial layer slightly increases upon a decrease in temperature, as indicated by a larger excess of the backbone C-atoms seen in Fig.11(a).
(4) The observed deficit of the phenyl groups in the inter-facial layer is also seen for cyclic PS.
For both linear and cyclic PS, the deficit of the phenyl rings would decrease the corresponding phenyl-phenyl aromatic (π−π) interactions, which represent stronger segmental attrac-tions as compared with those of backbone aliphatic carbons. Such a loss of strong inter-segmental attractions would tend to result in greater segmental mobility in the melt, and hence
FIG. 11. Distribution for the backbone C-atoms (solid lines) and phenyl C-atoms (dashed lines) of 10-nm thick films of (a) linear PS, (b) cyclic PS, and (c) modified geometry. For the linear PS film, the results have been plotted for two temperatures, well above and close to the simulated glass-transition temperature. Plotted is the probability that backbone united C-atoms and phenyl C-atoms are located in each 1 Å thick sublayer. Half of the film is shown as the averaging has been performed with respect to the middle of the film. The additional united-atom groups of the modified geometry are not included in the calculation.
this may cause the observed reduction in the glass transition temperature in PS films.
J. Modification of backbone geometry
Fig.11(c)shows that upon a slight modification of the PS structure to mimic PαMS, the backbone and phenyl C-atoms do not exhibit any preferential location in the film. Our modified polymer geometry contains an additional CH3 united-atom group, which is bonded to the backbone α carbon of the PS monomer unit.
In addition, the equilibrium value of the Cα−−CH 2−−Cα valence angle, adapted following Sundarajan,58 is equal to 122◦. This valence angle is 109.5◦for the PS force field; our modification is clearly inspired by the previous work on PαMS.58 The lack of preferential location of both back-bone C-atoms and phenyl rings might cause a weaker thick-ness dependence of the Tg for PαMS films. However, at this point we can only conclude that the monomer structure really matters. Other data (not shown) indicate strong depen-dence of backbone and phenyl orientation on the monomer modification as well. A better tested and refined model is needed for further comparison between interfacial layer prop-erties of PS and PαMS and how these influence the glass transition.
IV. CONCLUSIONS
Using a molecular dynamics technique and employing a united-atom force field, for the first time we have simulated the reduction of the glass transition temperature of both lin-ear PS and cyclic PS in free-standing thin films. We show a good agreement with the reported experimental results, taking into account the huge differences in the implemented cooling rates. The density in the middle of the films is comparable to that of bulk systems, while it decreases at the film sur-face. The density in the present united-atom simulations also compares well with that obtained using the fully atomistic models.73
We find that for linear polymers the glass transition tem-perature decreases strongly with film thickness below 10 nm. This decrease must be due to the presence of free surfaces, as the interfacial properties, dynamics as well as static structure, differ from those of the bulk-like middle regions. As has been suggested in the literature,40,45we also observed an increase in the fraction of chain ends in the surface layer. The increased mobility of these free end-groups would cause a higher mobil-ity of the interfacial layers, thereby possibly decreasing Tg. Another explanation for the glass transition temperature reduc-tion in thin PS films is a weakened interacreduc-tion between strongly interacting aromatic phenyl rings. We find indeed that in a layer approximately 1 nm below the surface the density of backbone C-atoms peaks, while that of phenyl ring atoms dips. This will decrease the phenyl-phenyl aromatic (π−π) interactions between phenyl rings of PS chains in this interfacial layer and, hence, increase the chain mobility in this and adjoining layers. As a result, the interfacial layer of the PS film would exhibit higher mobility near Tgas compared with the bulk and this may be the source of the observed reduction in the glass-transition temperature in thin PS films, most pronounced among all the
polymers investigated so far.3,17,18All these effects have also been observed in fully atomistic simulations of PS.73
In order to test which of the two mechanisms, increase in the fraction of end groups versus weakening of phenyl-phenyl aromatic (π−π) interactions, is predominant, we compared the films comprised of linear and cyclic PS chains. For both polymers, the glass transition depends strongly on the film thickness, albeit this dependence is slightly weaker for cyclic PS. In addition, the preferential segregation of the backbone C-atoms and the concomitant deficit of phenyl C-atoms in the interfacial region are comparable for linear and cyclic PS films. Of course, the surface segregation of end groups and the pref-erence for vertical orientation of chain vectors in the interfacial layer are absent for the thin films of cyclic PS. Therefore, it is likely that the weakening of phenyl-phenyl aromatic (π−π) interactions in the interfacial layers could be responsible for the reduction of the glass transition temperature in thin PS films; the present results suggest a strong correlation between the film structural features and the Tgsuppression. However, in linear chains, the increase in the fraction of end groups at the film surface definitely has an additional effect and could be responsible for the stronger Tgreduction in linear PS films than in cyclic PS films. Moreover, details of segmental dynamics near Tgwould also be impacted by the non-uniform distribu-tion of aromatic phenyl rings. This will be the subject of a forthcoming publication. Nevertheless, our previous study48 of the monomer mobility in free-standing linear PS films, using a similar united-atom model, does show some correla-tion between the interfacial structural features and dynamically measured Tg suppression. The results of Ref.48reveal, for example, that interfaces affect α− and β-relaxation processes differently; the α relaxation rate is faster near the free surface and the small-scale structural β-relaxation is faster in the cen-ter of the film than near a free surface. A similar effect has been observed in experiments on PMMA by Torkelson and co-workers.72 The qualitative agreement of our preliminary studies of the segmental dynamics in these films with existing experimental data supports the validity of our computational model for PS.
The results for PS films are also compared with those for a slightly different chain geometry. We found that a small change, such as adding one methyl group to the α-carbon of the PS monomer unit, can give rise to significant differences in structural characteristics in the film surface. For instance, the enhanced density of backbone C-atoms and the accompanying deficit in phenyl C-atom density 1 nm below the free surface disappears. It will be interesting to see if this indeed affects the Tgreduction in thin films, since the π−π interactions are no longer weakened in the interfacial region. We plan to inves-tigate this question further with detailed atomistic, as well as united-atom, simulations of PαMS.
The large difference of surface layer mobility in glassy films of PS and PαMS has been observed in recent experi-ments.18,38The reason for such a strong dependence of glassy film behavior on chemical details of polymers is still poorly understood and computationally underexplored, and hence more detailed, extensive simulation studies are needed. More-over, we show that the agreement between experiments and simulations, regarding the film thickness dependence of Tg,
203314-11 Lyulin et al. J. Chem. Phys. 146, 203314 (2017)
is not only qualitatively but also semi-quantitatively satisfac-tory, when compared with experiments carried out at quite fast cooling rates.
SUPPLEMENTARY MATERIAL
Seesupplementary materialfor figures on the equilibra-tion process, finite size effects, and Tgdetermination. ACKNOWLEDGMENTS
The presented research is sponsored by the Stichting Nationale Computerfaciliteiten (National Computer Facili-ties Foundation, NCF), which is financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), through the usage of its supercomputer facilities. A.V.L. is grateful to the members of the Frank group and the staff of the chemical engineering department for their hospi-tality during his sabbatical stay at Stanford University. Very fruitful discussions with Z. Fakhraai, E. Glor, and J. Forrest, which led to the possibility to compare the simulations with their experimental data, are acknowledged. Helpful discus-sions with M. Ediger, G. McKenna, D. Vlassopoulos, K. Ngai, and D. Bedrov are also acknowledged.
1M. D. Ediger, C. A. Angell, and S. R. Nagel, “Supercooled liquids and
glasses,”J. Phys. Chem.100, 13200–13212 (1996).
2F. H. Stillinger and P. G. Debenedetti, “Glass transition thermodynamics
and kinetics,”Annu. Rev. Condens. Matter Phys.4, 263–285 (2013).
3M. D. Ediger and J. A. Forrest, “Dynamics near free surfaces and the glass
transition in thin polymer films: A view to the future,”Macromolecules47, 471–478 (2014).
4K. Binder and W. Kob, Glassy Materials and Disordered Solids (World
Scientific, Singapore, 2005).
5J.-L. Barrat, J. Baschnagel, and A. V. Lyulin, “Molecular dynamics
simulations of glassy polymers,”Soft Matter6, 3430–3446 (2010).
6C. Donati, J. F. Douglas, W. Kob, S. J. Plimpton, P. H. Poole, and
S. C. Glotzer, “Stringlike cooperative motion in a supercooled liquid,”Phys. Rev. Lett.80, 2338–2341 (1998).
7J. I. Brauman, “Glasses and amorphous materials,”Science 267, 1887
(1995).
8C. A. Angell, “Formation of glasses from liquids and biopolymers,”Science
267, 1924–1935 (1995).
9F. H. Stillinger, “A topographic view of supercooled liquids and glass
formation,”Science267, 1935–1939 (1995).
10B. Frick and D. Richter, “The microscopic basis of the glass transition in
polymers from neutron scattering studies,”Science267, 1939–1945 (1995).
11I. M. Hodge, “Physical aging in polymer glasses,”Science267, 1945–1947
(1995).
12Broadband Dielectric Spectroscopy, edited by F. Kremer and A. Sch¨onhals
(Springer, 2003).
13S. Peters, S. Napolitano, H. Meyer, M. W¨ubbenhorst, and J. Baschnagel,
“Modeling dielectric relaxation in polymer glass simulations: Dynamics in the bulk and in supported polymer films,”Macromolecules41, 7729–7743 (2008).
14S. Napolitano, V. Lupascu, and M. W¨ubbenhorst, “Temperature
depen-dence of the deviations from bulk behavior in ultrathin polymer films,”
Macromolecules41, 1061–1063 (2008).
15D. Cangialosi, A. Alegr`ıa, and J. Colmenero, “Route to calculate the length
scale for the glass transition in polymers,”Phys. Rev. E76, 011514 (2007).
16K. Binder, J. Baschnagel, S. B¨ohmer, and W. Paul, “Simulation of the
glass transition in polymeric systems: Evidence for an underlying phase transition?,”Philos. Mag. B77, 591–608 (1998).
17J. A. Forrest and K. Dalnoki-Veress, “The glass transition in thin polymer
films,”Adv. Colloid Interface Sci.94, 167–196 (2001).
18K. Paeng and M. D. Ediger, “Molecular motion in free-standing
thin films of poly(methylmethacrylate), poly(4-tert-butylstyrene), poly(α-methylstyrene), and poly(2-vinylpyridine),” Macromolecules 44, 7034–7042 (2011).
19C. Gay, P. G. de Gennes, E. Raphael, and F. Brochard-Wyart,
“Injec-tion threshold for a statistically branched polymer inside a nanopore,”
Macromolecules29, 8379–8382 (1996).
20Y. Wang and I. Teraoka, “Computer simulation of semidilute polymer
solu-tions in confined geometry: Pore as a microscopic probe,”Macromolecules 30, 8473–8477 (1997).
21Y. Ito, in Synthesis of Biocomposite Materials, edited by Y. Imanishi
(Chemical Rubber, Boca Raton, FL, 1992).
22J. L. Keddie, R. A. L. Jones, and R. A. Cory, “Size-dependent depression
of the glass transition temperature in polymer films,”Europhys. Lett.27, 59–64 (1994).
23S. Kawana and R. A. L. Jones, “Character of the glass transition in thin
supported polymer films,”Phys. Rev. E63, 021501 (2001).
24Z. Fakhraai, J. S. Sharp, and J. A. Forrest, “Effect of sample preparation on
the glass-transition of thin polystyrene films,”J. Polym. Sci., Part B: Polym. Phys.42, 4503–4507 (2004).
25J. A. Forrest, K. Dalnoki-Veress, and J. R. Dutcher, “Interface and chain
con-finement effects on the glass transition temperature of thin polymer films,”
Phys. Rev. E56, 5705–5716 (1997).
26T. Kanaya, T. Miyazaki, R. Inoue, and K. Nishida, “Thermal expansion
and contraction of polymer thin films,”Phys. Status Solidi B242, 595–606 (2005).
27R. Inoue, T. Kanaya, T. Miyazaki, K. Nishida, I. Tsukushi, and K. Shibata,
“Glass transition and thermal expansivity of polystyrene thin films,”Mater Sci. Eng. A442, 367–370 (2006).
28G. B. DeMaggio, W. E. Frieze, D. W. Gidley, Z. Ming, H. A. Hristov,
and A. F. Yee, “Interface and surface effects on the glass transition in thin polystyrene films,”Phys. Rev. Lett.78, 1524–1527 (1997).
29W. E. Wallace, N. C. Beck Tan, W. L. Wu, and S. Satija, “Mass density
of polystydrene thin films measured by twin neutron reflectivity,”J. Chem. Phys.108, 3798–3804 (1998).
30K. Fukao and Y. Miyamoto, “Glass transitions and dynamics in thin polymer
films: Dielectric relaxation of thin films of polystyrene,”Phys. Rev. E61, 1743–1754 (2000).
31D. R. Priestley, L. J. Broadbelt, J. M. Torkelson, and K. Fukao, “Glass
tran-sition and alpha-relaxation dynamics of thin films of labeled polystyrene,”
Phys. Rev. E75, 061806 (2007).
32A. Serghei, H. Huth, C. Schick, and F. Kremer, “Glassy dynamics in
thin polymer layers having a free upper interface,”Macromolecules41, 3636–3639 (2008).
33M. Y. Efremov, E. A. Olson, M. Zhang, Z. Zhang, and L. H. Allen, “Glass
transition in ultrathin polymer films: Calorimetric study,”Phys. Rev. Lett. 91, 085703 (2003).
34P. Zoller and D. J. Walsh, Standard Pressure-Volume-Temperature Data for
Polymers (Technomic, Lancaster, 1995).
35J. L. Keddie, R. A. L. Jones, and R. A. Cory, “Interface and surface effects
on the glass-transition temperature in thin polymer films,”Faraday Discuss. 98, 219–230 (1994).
36M. Tress, M. Erber, E. U. Mapesa, H. Huth, J. M¨uller, A. Serghei, C. Schick,
K.-J. Eichhorn, B. Voit, and F. Kremer, “Glassy dynamics and glass transition in nanometric thin layers of polystyrene,”Macromolecules43, 9937–9944 (2010).
37A. Serghei, “Challenges in glassy dynamics of polymers,” Macromol.
Chem. Phys.209, 1415–1423 (2008).
38T. B. Karim and G. B. McKenna, “Unusual surface mechanical
proper-ties of poly(α-methylstyrene): Surface softening and stiffening at different temperatures,”Macromolecules45, 9697–9706 (2012).
39J. L. Lenhart, D. A. Fischer, T. L. Chantawansri, and J. W. Andzelm,
“Sur-face orientation of polystyrene based polymers: Steric effects from pendant groups on the phenyl ring,”Langmuir28, 15713–15724 (2012).
40P. G. de Gennes, “Glass transitions in thin polymer films,”Eur. Phys. J. E
2, 201–205 (2000).
41R. P. White, C. C. Price, and J. E. G. Lipson, “Effect of interfaces on
the glass transition of supported and freestanding polymer thin films,”
Macromolecules48, 4132–4141 (2015).
42T. M. Truskett and V. Ganesan, “Ideal glass transitions in thin films: An
energy landscape perspective,”J. Chem. Phys.119, 1897–1900 (2003).
43W.-S. Xu and K. F. Freed, “Influence of cohesive energy and chain stiffness
on polymer glass formation,”Macromolecules47, 6990–6997 (2014).
44K. F. Mansfield and D. N. Theodorou, “Molecular dynamics simulation of
a glassy polymer surface,”Macromolecules24, 6283–6294 (1991).
45T. S. Jain and J. J. de Pablo, “Monte Carlo simulation of free-standing
polymer films near the glass transition temperature,”Macromolecules35, 2167–2176 (2002).
46A. R. C. Baljon, J. Billen, and R. Khare, “Percolation of immobile domains
in supercooled thin polymeric films,”Phys. Rev. Lett.93, 255701 (2004).
47J. Baschnagel and F. Varnik, “Computer simulations of supercooled polymer
melts in the bulk and in confined geometry,”J. Phys.: Condens. Matter17, R851–R953 (2005).
48A. R. C. Baljon, S. Williams, N. K. Balabaev, F. Paans, D. Hudzinskyy, and
A. V. Lyulin, “Simulated glass transition in free-standing thin polystyrene films,”J. Polym. Sci., Part B: Polym. Phys.48, 1160–1167 (2010); A. R. C. Baljon, R. B. DeGraaff, M. H. M. van Weert, and R. Khare, “Glass transition behavior of polymer films of nanoscopic dimension,”Macromolecules38, 2391 (2005).
49D. Hudzinskyy, A. V. Lyulin, A. R. C. Baljon, N. K. Balabaev, and M. A. J.
Michels, “Strong confinement effects on glass transition temperature in atactic polystyrene films,”Macromolecules44, 2299–2310 (2011).
50D. Hudzinskyy and A. V. Lyulin, “Confinement and shear effects for atactic
polystyrene film structure and mechanics,”Modell. Simul. Mater. Sci. Eng. 19, 074007 (2011).
51D. Hudzinskyy, M. A. J. Michels, and A. V. Lyulin, “Rejuvenation, aging,
and confinement effects in atactic-polystyrene films subjected to oscillatory shear,”Macromol. Theory Simul.22, 71–84 (2013).
52M. Solar, E. U. Mapesa, F. Kremer, K. Binder, and W. Paul, “The
dielec-tric α-relaxation in polymer films: A comparison between experiments and atomistic simulations,”Europhys. Lett.104, 66004 (2013).
53S.-J. Xie, H.-J. Qian, and Z.-Y. Lu, “The glass transition of polymers with
different side-chain stiffness confined in freestanding thin films,”J. Chem. Phys.142, 074902 (2015).
54N. J. Soni, P.-H. Lin, and J. Khare, “Effect of cross-linker length on the
ther-mal and volumetric properties of cross-linked epoxy networks: A molecular simulation study,”Polymer53, 1015–1019 (2012).
55A. V. Lyulin and M. A. J. Michels, “Molecular dynamics simulation of bulk
atactic polystyrene in the vicinity of Tg,”Macromolecules35, 1463–1472 (2002).
56A. V. Lyulin, N. K. Balabaev, and M. A. J. Michels, “Correlated
seg-mental dynamics in amorphous atactic polystyrene: A molecular dynamics simulation study,”Macromolecules35, 9595–9604 (2002).
57B. Vorselaars, A. V. Lyulin, and M. A. J. Michels, “Development of
hetero-geneity near the glass transition: Phenyl-ring-flip motions in polystyrene,”
Macromolecules40, 6001–6011 (2007).
58P. R. Sundararajan, “Configurational studies on poly-α-methylstyrene,”
Macromolecules10, 623–627 (1977).
59M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon
Press, Oxford, 1987).
60A. S. Lemak and N. K. Balabaev, “A comparison between
colli-sional dynamics and Brownian dynamics,” Mol. Simul. 15, 223–231 (1995).
61A. S. Lemak and N. K. Balabaev, “Molecular dynamics simulation of a
polymer chain in solution by collisional dynamics method,”J. Comput. Chem.17, 1685–1695 (1996).
62D. Y. Yoon, P. R. Sundararajan, and P. J. Flory, “Conformational
character-istics of polystyrene,”Macromolecules8, 776–783 (1975).
63J. P. Wittmer, H. Meyer, J. Baschnagel, A. Johner, S. Obukhov, L. Mattioni,
M. M¨uller, and A. N. Semenov, “Long range bond-bond correlations in dense polymer solutions,”Phys. Rev. Lett.93, 147801 (2004).
64J. P. Wittmer, P. Beckrich, H. Meyer, A. Cavallo, A. Johner, and
J. Baschnagel, “Intramolecular long-range correlations in polymer melts: The segmental size distribution and its moments,”Phys. Rev. E76, 011803 (2007).
65L. C. E. Struik, Physical Aging in Amorphous Polymers and Other Materials
(Elsevier, Amsterdam, 1978).
66J. D. Ferry, Viscoelastic Properties of Polymers (Wiley, New York,
1980).
67P. G. Santangelo and C. M. Roland, “Molecular weight dependence of
fragility in polystyrene,”Macromolecules31, 4581–4585 (1998).
68P. G. Santangelo, C. M. Roland, T. Chang, D. Cho, and J. Roovers,
“Dynam-ics near the glass temperature of low molecular weight cyclic polystyrene,”
Macromolecules34, 9002–9005 (2001).
69K. U. Kirst, F. Kremer, T. Pakula, and J. Hollingshurst, “Molecular
dynam-ics of cyclic and linear poly(dimethylsiloxanes),”Colloid Polym. Sci.272, 1420–1429 (1994).
70E. C. Glor and Z. Fakhraai, “Facilitation of interfacial dynamics in entangled
polymer films,”J. Chem. Phys.141, 194505 (2014).
71E. C. Glor, R. J. Composto, and Z. Fakhraai, “Glass transition dynamics
and fragility of ultrathin miscible polymer blend films,”Macromolecules 48, 6682–6689 (2015).
72R. D. Priestley, C. J. Ellison, L. J. Broadbelt, and J. M. Torkelson,
“Struc-tural relaxation of polymer glasses at surfaces, interfaces, and in between,”
Science309, 456–459 (2005).
73S. Lee, A. V. Lyulin, C. W. Frank, and D. Y. Yoon, “Interface characteristics
of polystyrene melts in free-standing thin films and on graphite surface from molecular dynamics simulations,” Polymer (submitted).
