Vapor Instantaneous Interfaces

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The Effect of Polymer/solid and Polymer/vapor Instantaneous Interfaces on the Interfacial Structure and Dynamics of Polymer Melt Systems Selemon Bekele, and Mesfin Tsige Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01554 • Publication Date (Web): 27 Jun 2016 Downloaded from http://pubs.acs.org on July 2, 2016

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The Effect of Polymer/solid and Polymer/vapor Instantaneous Interfaces on the Interfacial Structure and Dynamics of Polymer Melt Systems Selemon Bekele and Mesfin Tsige∗ Department of Polymer Science, The University of Akron, Akron, Ohio 44325

E-mail: [email protected]

Abstract Polymers are used in a wide range of applications that involve chemical and physical processes taking place at surfaces or interfaces which influence the interaction between the polymer material and the substance that comes into contact with it. Polymer surfaces are usually modified either chemically or physically for specific applications such as facilitating wetting, reducing friction and enhancing adhesion. The variety and complexity of surface and interfacial processes requires a molecular-level understanding of the structural and dynamical properties of the surface/interface layer to help in the design of materials with desired functional properties. Using molecular dynamics (MD) simulations, we investigate the structure and dynamics at the surface of polymer films. We find that the density profiles of the films as a function of distance relative to an instantaneous surface have a structure indicative of a layering at the polymer/vapor

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interface similar to the typical layered structure observed at the polymer/substrate interface. However, the interfacial molecules at the polymer/vapor interface have a higher mobility compared to that in the bulk while the mobility of the molecules is lower at the polymer/substrate interface. Time correlation of the instantaneous polymer/vapor interface show that surface fluctuations are strongly temperature dependent and are directly related to the mobility of polymer chains near the interface.

I. INTRODUCTION A wide range of polymeric materials have important applications in science and technology because of their versatile characteristics and their ability to be easily tailored for desired functionalities. Many of these applications are characterized by chemical and physical processes that take place at fluid/solid interfaces. As a result, interactions at the polymer/substrate interface are an essential area of study in biotechnology, nanotechnology, and in all forms of coating applications where the utility and reliability of the composite is largely determined by forces between the polymer and material which are a function of their surface characteristics. Whether the molecular surface of a polymer is glassy or not has implications in many applications. There is a large body of experimental and theoretical evidence that the properties of the free polymer surface play a crucial role in observed anomalies in the glass transition temperature of thin polymer films. 1 The glass transition temperature Tg of free standing and substrate supported polystyrene (PS) and polymethyl methacryalte (PMMA) thin films was found to deviate from its bulk value. 2–8 The combined effects of the substrate and free surface are often employed to interpret the Tg shifts observed in thin films. 9 In general, the consensus is that loss of configurational entropy due to the presence of a hard wall and packing constraints on interfacial chains coming from nearby chains in the bulk determine the structure of a melt near a hard wall. 10 The interplay between these two opposing effects results in an equilibrium structure where layering is observed in the interfacial region. Entropic and enthalpic arguments have also been forwarded to explain the higher mobility 2


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of surface molecules in terms of an increase in the number fraction of chain ends at the free surface. Experimental investigations by Tsui et al. 11 with polystyrene samples of molecular weights below and above the entanglement length indicated that the reduction in Tg of polymer thin films cannot be due to a surface mobile layer coming from segregated chain ends based on their observation that Tg is independent of chain entanglement and chain end distributions. The Tg of free-standing PMMA film as measured by Roth et al. 12 was found to be much less depressed than free-standing PS films. The surface mobility of PMMA films obtained by Li et al. 13 was found to be much lower than that of PS films reported by Yang et al. 14 . A microscopic level information on the interfacial structure is thus essential to gain insight into the relationship between structure, and thermodynamic and mechanical properties of polymers at interfaces. An important quantity in the investigation of interfaces is the average density profile ρ(z) measured in a direction perpendicular to the interface. The density distribution normal to a polymer/substrate interface is often characterized by an oscillatory profile near the substrate, with the amplitude of the density oscillations decreasing with increasing distance from the solid surface and extending up to tens of angstroms into the film. Within the bulk region of the film ρ(z) is constant. Density calculations are usually done relative to a fixed reference frame, which we refer to as the Laboratory Frame (LF). The polymer/vapor interfacial region is defined as the region spanning 10 − 90% of the density profile. Given the bulk density ρb and the chain length N , values of the chain end density profile scaled by N/ρb which are greater (or less) than one will indicate an enhancement (or depletion) of chain ends at a distance z from the reference surface. 15,16 However, in order to obtain the correct structural information, one needs to have a procedure to clearly determine the interface to characterize the structural and dynamic behaviors of interfacial molecules, the dynamics of the interface itself and the surface segregation of functional groups which play important roles in various surface phenomena such as contact angle hysteresis and tacticitydependent wettability. 17,18 Such an approach will greatly help to bring out unambiguously

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the differences between interfacial and bulk properties. Monte Carlo (MC) and molecular dynamics (MD) computer simulations have been extensively used since the late 1980s to study the structural and dynamic behavior of polymer surfaces and polymer/substrate interfaces. 1,15,16,19–22 While results from such analysis indicated an enhancement of chain ends at the polymer/substrate interface relative to the bulk, some also observed a relatively higher preference of chain end groups to segregate to the polymer/vapor interface. 15,16 Rissanou et al. carried out detailed molecular dynamics simulations to study the structural and dynamical properties of a free-standing polystyrene film supported by multiple graphene sheets. They show mass density profiles with layered structures near the graphene layers but falling to zero with a sigmoidal shape at the polystyrene/vapor interface. 23 MD simulations of polydimethylsiloxane (PDMS) films at silicon dioxide surfaces carried out by Tsige et al. 24 showed density profiles with oscillatory behavior near the solid-liquid interface with a sigmoidal shape which smoothly falls to zero at the PDMS/vapor interface. Their analysis also revealed that the PDMS terminal groups segregated near the solid/liquid interface but no enhancement was observed at the PDMS/vapor interface. Atomistic simulations by Tatek et al. of melt polystyrene adsorbed on graphite substrates 25 indicated a depletion of phenyl C6 H5 end groups at the PS/graphite interface. Pandey et. al. carried out all-atom MD simulations with short polyisoprene (PI) chains on graphite. The paper is mainly concerned with CG strategies for PI to account for interactions with the solid surface. 26 While they do not show the structure at the free PI/vapor interface, they have observed density profiles with layered structures near the graphite substrate. A recent study by Mortazavian et al. 27 used density profiles from molecular dynamics simulations to characterize the structure and mobility of polyvinyl acetate (PVA) polymers adsorbed on silica. The density profiles were calculated using the standard procedure described above. Of particular interest is the fact that the density profiles were shown to have a sigmoidal shape around the polymer/air interface, decreasing to zero over a distance of about 1 nm leading to the conclusion that a decreasing density at the polymer/air interface

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indicates a polymer region with a Tg lower than that for the bulk. The smooth decline of the density profile across a polymer/vapor interfacial region seems to be hiding information on the enhancement in the number of polymer end groups on the vapor side of a polymer melt which also contribute to the local density at the interface. Thus arises the need for other ways of looking at the system that may bring out unequivocally unique characteristics of the interfacial region without resorting to any normalization. There have been several methods developed over the last decade or so for the determination of fluid/fluid and fluid/vapor interfaces and the distribution of the associated interfacial molecules or atoms: the intrinsic sampling method (ISM), 28–33 the grid-based intrinsic profile method (GIP), 34–36 the identification of truly interfacial molecules method (ITIM), 37,38 the surface layer identification method (SLI), 39 and the method of Willard and Chandler. 40 Jorge et al. 41,42 have made an excellent assessment of the first four techniques mentioned above to determine the interface between two fluid phases and carried out an extensive study of density profiles for the water/CCl4 liquid-liquid interface using MD simulations. The global density profiles they obtained relative to a fixed reference frame show the often observed smoothing due to the capillary wave fluctuations of the interface while the intrinsic profiles relative to the interfaces determined by each method exhibited pronounced density enhancements in the interfacial region. Polymers that do not crystallize represent excellent model systems for studying amorphous material surfaces. In the present paper, we have used MD simulations to investigate the structure and dynamics of a free-standing atactic PMMA film and atactic PS film adsorbed on a graphite substrate, with both systems in the melt state. Our main objective is to explore the feasibility of these surface identification techniques to reconstruct the polymer/substrate, polymer/vapor or polymer/liquid interface and investigate local structural and dynamical properties relative to an instantaneous interface. Here, we focus on density profiles relative to an instantaneous surface which is computed using the ITIM method and the dynamics of the interfacial molecules. The results obtained with the GIP method are

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consistent with those from the ITIM technique and are presented in the supporting information. We show that the segregation of chain ends and the layering structure in the interfacial region observed with the traditional analysis methods can be clearly manifested if one carries out the calculation relative to an instantaneous surface computed at each time step of the simulation. In order to achieve equilibration within a reasonable computing time, we have investigated the structure and dynamics of both systems at temperatures far above their glass transition temperature. To our knowledge, these fully atomistic simulations are the first studies of polymer/solid and polymer/vapor systems taking into account the effect of the fluctuations in instantaneous interfaces.

II. SIMULATION DETAILS For this study, the graphite-supported PS film had 80 chains and the free-standing PMMA film had 64 chains. Each polystyrene chain was made up of 20 monomer units while each PMMA chain consisted of 40 monomer units. The simulation box size for the PMMA film is 71 Å × 77 Å × 200 Å and that of the graphite supported PS film is 54 Å × 51 Å × 220 Å where the films are exposed to more than 50 Å vacuum on both sides. The PMMA film thickness is ≈ 90 Å and that of PS is ≈ 120 Å. The radius of gyration of the PMMA is ≈ 25 Å and that of the PS is ≈ 17 Å each of which is about one third of the lateral dimensions of the simulation box. The box dimensions for each system were chosen to allow enough surface area for an individual chain to fully adsorb on the surface and sufficient film thickness to prevent chains from spanning the vertical dimension of the system. More details on equilibration and film preparation can be found in our previous work. 25,43,44 Periodic boundary conditions were imposed only in the X and Y directions. The OPLS-AA 45 force field, which was recently shown to capture structural and dynamical properties of PS and PMMA that are consistent with experimental results, 25 was used to model both PS and PMMA. The cutoff radius for the Lennard-Jones term was set to 12 Å. The particle-particle/particle-mesh Ewald (PPPM)

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algorithm was employed for the calculation of the Coulomb interactions. Both systems were equilibrated for more than 100 ns for the chains to diffuse through several times of their end-to-end distance and data were recorded every 2 ps for the last 10 ns. All simulations were carried out using the LAMMPS 46 MD package with an integration time step of 1 fs. For the surface calculations, we employed the ITIM technique which uses a probe sphere of a given radius that starts outside the region occupied by the system under study and is moved along test lines normal to plane of the interface and at different (x,y) positions until it comes in contact with the topmost or bottommost atoms of the system being probed. 37,38 We used a probe radius of 2.0 Å (see Figure S1 of the supporting information) and probe 2

lines centered at 1 × 1 Å grids covering the entire XY surface of the box. The probe was started from outside the polymer film and moved perpendicular to the film until it came within the van der Waal radius of a carbon atom. The surface thus determined is taken to be the z−position of the carbon atom plus (minus) the z-component of the vector joining the centers of the carbon atom and the probe for the top (bottom) surface. As an example, we show in Figure 1 the PS/vapor instantaneous interface generated using the ITIM technique for 520 K.

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Figure 1: PS/vapor instantaneous surface at T = 520 K generated using the ITIM technique.

III. RESULTS AND DISCUSSION The mass density profiles of PMMA and PS are shown in Figure 2. The dotted lines represent the standard density profiles obtained with respect to a fixed flat reference in the laboratory 7


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frame that is orthogonal to the surface normal. In the density calculations, the (x,y) position of each atom is used to determine the grid position (xsurf , ysurf ) on the surface closest to the atom and the relative z position defined as z = zatom − zsurf is used to construct the density profile normal to the x-y plane of the simulation box. For both systems, one can clearly see the usual sigmoidal shape at the polymer/vapor interfaces with the density decreasing to zero without exhibiting any structures. It is known 47–51 that the interfacial width is made up of an intrinsic part coming from density variations and a part due to capillary waves arising from thermal fluctuations. 2

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Figure 2: (Left) Mass density profile of PMMA film relative to an instantaneous PMMA/vapor surface. (Right) Mass density profile of PS film relative to an instantaneous PS/graphite (Left peaks) and PS/vapor (Right peak) surfaces. The dashed blue curve is the mass density profile relative to the fixed reference frame of the simulation box. The PS/graphite interface is near z = −60 Å and the PS/vapor interface is near z = 50 Å. The PMMA/vapor interface is near z = 40 Å and z = 0 Å corresponds to the middle of the PMMA film. The contribution of the capillary waves gives rise to an interfacial width that grows logarithmically with system size leading to a wider interface. The smooth decline of the density profile obtained in a standard analysis across the interface is thus attributed, in addition to the intrinsic surface roughness, to surface fluctuations because of capillary waves. When observed relative to an instantaneous interface, which effectively removes the effect of capillary waves, the distributions exhibit a dramatic enhancement at the polymer/vapor 8


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interface which does not show up in the traditional density profile with respect to the fixed reference frame of the simulation box. For the PMMA system shown on the left, the peak density values are of the order of 1.7 g/cm3 and 1.5 g/cm3 at 500 K and 560 K, respectively. Only the feature on one side of the film is presented here since the density profile relative to other side also shows similar characteristics. The density profile shows a substantial enhancement at the PMMA/vapor side in sharp contrast to the usual sigmoidal shape that density profiles assume in a traditional analysis. The density enhancement is confined to within about 6 Å of the interface. The lower temperature profile has some oscillations in the bulk, the one at higher temperature is relatively smoother because of the availability of more random arrangements of the chains. The plot on the right in Figure 2 displays the PS density profile with respect to the PS/graphite (left peaks) and PS/vapor (right peak) interfaces. The peak density values are of the order of 1.7 g/cm3 at both 500 K and 560 K. The peaks on the graphite side are similar to those observed in the standard analysis using the position of the graphite substrate as a reference. These peaks are followed by clear depletion regions followed by the familiar oscillations into the bulk. On the other hand, the density profile shows a substantial enhancement at the PS/vapor side. For both PMMA and PS, the density profiles corresponding to the higher temperature are lower in the bulk region and indicate a larger film thickness compared to those at the lower temperature which is expected of a melt system at a higher temperature. Our objective here is not to compare the various methods employed to construct instantaneous surfaces. However, a similar behavior is observed when employing a Grid based (GIP) method in which the instantaneous surface is constructed by finding the position of the atom with the maximum z-component in each grid. The corresponding mass density profiles are shown in Figure S2 of the supporting information. A long standing question related to the spatial distribution of the chains in a polymer melt is whether the end terminal groups and/or the middle monomers come to the surface or not.

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The wider interface in the presence of capillary waves which cause the smooth decline in the density profile also makes it difficult to say which groups preferentially come to the interface region. The calculation relative to an instantaneous interface helps in clearly identifying the groups that come to an interface as the effect of the capillary waves is removed by the procedure. On the left in Figure 3 is shown the distribution of the end terminal methyl (CH3 ), carbonyl (C=O) and methoxy (CH3 O) groups of PMMA. ×10-3 1 PMMA

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Figure 3: Distribution of end groups (number of end groups per unit area) for the PMMA film (Left) and PS film (Right) relative to an instantaneous surface. The black dash-dot curves in the bottom panels show the distribution of methoxy groups (Left) and the phenyl rings (Right) on the middle monomers of the polymer chains Since the lateral dimensions of the simulation box for PMMA and PS systems are different, we have normalized the number of end groups by the surface area for each system. The distributions for the two systems are seen to be comparable at any given temperature which is consistent with the surface tensions of PMMA and PS which have similar temperature dependence as predicted by Wu et al. 52 At both temperatures shown, there is a clearly enhanced distribution of the end groups at the PMMA/vapor interface. The enhancement is 10


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again confined to a region of about 6 Å around the interface. The distribution of end groups for the PS/graphite system are shown on the right in Figure 3 for the PS/vapor interface. The enhancement of the methyl, CH and phenyl (C6 H5 ) end groups at the PS/vapor interface is quite evident. A similar enhancement of the end groups has also been seen close to the PS/graphite interface (not shown here). The numbers of middle monomers are also somewhat enhanced at the PMMA/vapor and PS/vapor interfaces as shown by the black dashed curves in the bottom panels of Figure 3. This result clearly shows the advantage of carrying out such analysis relative to an instantaneous surface instead of the traditional analysis which requires normalization with respect to bulk properties and does not clearly bring out the interfacial structure as observed here. The results shown suggest that removing the capillary wave effect would help in identifying the functional groups that come to the surface. In order to understand the enhancement of the end terminal groups at the interfaces, we also calculated the probability of having one end of the chain at a distance z from the interfaces when the other end is already within 6 Å of a given interface. As shown in Figure 4, there is an enhanced probability for the other chain ends to also segregate to an interface for both systems. Note that the two systems consist of chains of different molecular weight, i.e, different chain lengths, hence the distance to the other end where P(z) falls to zero is consistent with the length of fully extended chain for both systems. Some part of the distribution that falls within the PMMA bulk is not shown since the focus is on the interfacial regions. For the PS/graphite system both interfaces are shown since they are different. On average, the probability of finding the other end within 6 Å of the PMMA/vapor interface is approximately 22% at 500 K and 35% at 560 K. Given one end is already within 6 Å of an interface, the PS system shows a similar behavior except that there is a higher probability of finding the other end on the graphite side (45%) than the vapor side (34%) at 520 K. At the temperature of 560 K, the probabilities are 48% at the PS/graphite interface and 17% on the vapor side. The low value at the higher temperature on the PS/vapor interface may

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be due to an increased mobility of the chains. 0.15 0.1

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Figure 4: Probability of finding a chain end as a function of z given the other chain end is within 6 Å of a polymer/vapor surface To gain further insight into the chain configurations in the interfacial regions, we calculated the conformational tensor defined as the second moment tensor of the end-to-end ~ given by the expression Cαβ = 3h Rα R2 β i for the chains with at least one distance vector R hR i 0

end in an interfacial region where α,β = x, y, z and hR02 i is the unperturbed mean-squared end-to-end distance in the bulk. Owing to symmetry in the x- and y-directions, it is expected that Cxx = Cyy and thus we report in Table 1 the components parallel (C|| ) and perpendicular (C⊥ = Czz ) to the substrate. Conformational tensor components for PS chains with both ends in the interfacial regions are given in Table S1 of the supporting information. For both systems, the magnitudes of the components of the tensor imply that the chains adopt a more or less flat conformation at the interfaces. For the PS system, the chain ends near the graphite interface are relatively more flattened than those on the vapor side. The picture that emerges is that there is a loss of configurational entropy at the PS/graphite interface because of the packing effect and the constraint imposed on the chains by the sub12


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Table 1: Conformational tensor components System T C|| Czz PMMA/vapor 500 K 1.38 0.64 560 K 1.82 0.54 PS/graphite

520 K 2.59 0.21 560 K 1.36 0.64

PS/vapor

520 K 1.66 0.87 560 K 1.45 1.06

strate. At the PS/vapor interface, there would be a gain in configurational entropy because of the enhanced number of chain ends with access to more free volume. This suggests that chains in the PS/vapor interfacial region have more freedom to change their conformations compared to the ones on the substrate side and thus a higher mobility of the chains on the vapor side is expected. In order to better understand the mobility of the atoms constituting the polymer chains we calculated atomic mean-squared displacements in the bulk and in the interfacial regions for both the PS and PMMA systems. We considered the atoms within 6 Å of the interfacial regions and those in a 6 Å thick layer in the bulk. The results are shown in Figure 5 for the PS (Top) and the PMMA (Bottom). The results indicate that the chains in the interfacial region have higher mobility than those in the bulk for both systems. However, the PS chains have a higher mobility compared to those of PMMA at the same temperature.

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t (ns) Figure 5: (Top) and (Middle) Mean-squared displacement for polystyrene atoms at the PS/vapor and PS/graphite interfaces, and those in the PS bulk at T = 560 K and T = 520 K respectively. (Bottom) Mean-squared displacement for PMMA atoms at the PMMA/vapor and in the PMMA bulk. The small vertical lines approximately indicate the point where the motion of the atoms changes from the ballistic to a sub-diffusive regime.

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PS @ 520 K

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t(ns) 2 Figure 6: (Top) Parallel (h∆r||2 i) and perpendicular (h∆r⊥ i = h∆z 2 i) components of the mean-squared displacement at the PS/vapor interface at T = 560 K (left) and T = 520 K (right). (Bottom) Parallel and perpendicular components of the mean-squared displacement at the PMMA/vapor interface at T = 560 K (left) and T = 500 K (right).

As shown in Figure 6, the diffusion is dominated by lateral motion in the x-y plane for the atoms in the interfacial regions. In Figure 5, the region in the initial few hundreds of femtoseconds corresponds to the fast local motion of the atoms in a polymer chain in which a particle moves ballistically during which h∆r2 i grows as t2 . The mean-squared displacement then transitions at similar times to a sub-diffusive behavior after which the atoms undergo a slower diffusive motion. One can clearly see in Figure 5 that, at both temperatures, the atoms in the three regions of the PS system (PS bulk, PS/vapor interface, and PS/graphite interface) exhibit marked differences in their mobility, the fastest being those at the PS/vapor interface. In the case of PMMA, the diffusion in the interfacial region and those in the bulk show similar behavior to the corresponding ones in the PS system. However, the over all dynamics in the case of PMMA is much slower than that in PS. In particular, the surface mobility of the atoms at the PMMA/vapor interface is much lower than that at the PS/vapor interface which is in agreement with the experimental findings by Li et al. 13 and Yang et al. 14 As the dynamics of the interfacial molecules has to be closely coupled to the dynamic 15


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behavior of the instantaneous interface, we calculated the time autocorrelation function arising from the spatial fluctuations in the instantaneous interface which is given by C(t)= 2

h∆sz (t)∆sz (0)i(Å ) where ∆sz (t) = sz (t) − hsi denotes the deviation of a given point on the interface from the mean position of the interface which is calculated by averaging over all interfacial positions determined by the ITIM method. The angle brackets represent an equilibrium average. A full quantitative study of C(t) (See Figures S4 and S5 of the supporting information) would consider the wave vector (~q) and temperature dependence of the surface relaxation modes in terms of the intermediate scattering function F (q, t) = hcos(~q · ∆~z)i where ∆~z = z(t) − z(0) and z(t) is the z−coordinate of a point on the interface. We focus here only on the wave vector averaged correlation function and will consider in future work the complete fourier components of C(t) which require more statistics and larger lateral system sizes in order to access the full range of q values in which molecular and continuum models of surface fluctuations can be tested. Figure 7 shows the normalized correlation functions for the PS/vapor and PMMA/vapor instantaneous interfaces. The correlation function for the PMMA/vapor system at T = 500 K is not shown as it does not decay enough on the time scale of our simulation. The correlations are characterized by a fast initial decay (not shown) followed by a slow relaxation which directly correlates to the behavior seen in the mean-squared displacement. To guage deviations from purely exponential behavior, the Kohlrausch-Williams-Watts (KWW) stretched-exponential function C(t) = A exp[−( τt )β ] has been used to fit the data for both systems. The parameter β is a measure of the non-exponential nature of the relaxation. The lines in Figure 7 are fits to the KWW function where the fits were restricted to ranges in which the data are statistically reliable (t < 0.6 ns for PMMA at T = 560 K, t < 0.4 ns for PS at T = 560 K, t < 0.3 ns for PS at T = 520 K). The values of β obtained for the PS/vapor system at T = 560 K and T = 520 K are 0.53 ± 0.01 and 0.63 ± 0.01, respectively. For the PMMA/vapor system, β = 0.39 ± 0.01. These values indicate that the surface relaxations are highly non-exponential. The relaxation times were calculated according to

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τc =

R∞ 0

C(t)dt = βτ Γ( β1 ) where Γ(x) is the gamma function. τc = 106±2 ps at T = 520 K and

τc = 98 ± 2 ps at T = 560 K, respectively, for the PS/vapor system. For the PMMA/vapor system, τc ∼ 1.32 ± 0.12 ns. We note that the PMMA/vapor interface relaxes more slowly as compared to the PS/vapor interface at the same temperature. The uncertainties indicated were estimated by varying the upper fit range to which the fits were found to be sensitive. A proper accounting of the errors requires more data for block averaging and was not done here for lack of statistics.

PMMA @560 K PS @520 PS @560 K

0.8

C(t)/C(0)

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0.6 0.4 0.2 0

10-2

t (ns)

10-1

Figure 7: Surface correlations for the PS/vapor interface at T = 520 K and T = 560 K, and for PMMA/vapor interface at T = 560 K. The dashed lines are the KWW stretched exponential fits to the data. The substantial mobility in the lateral direction along the interface observed from our mean-squared displacement calculations may explain why the interfacial chains are more mobile even when the density is higher. In spite of the higher density in the polymer/vapor interfacial region, the larger mobility of the atoms in the interfacial region observed in simulations and experiments may be explained by the dynamic nature of the instantaneous interface itself. This may also be a possible reason why the glass transition temperature of many glassy polymer thin films is lower than the corresponding bulk values.

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IV. SUMMARY We have studied density profiles of a free-standing PMMA film and a graphite supported PS film. The calculation of density profiles relative to an instantaneous interface removes the effect of surface fluctuations due to capillary waves and helps in clearly identifying the end terminal groups that come to an interface. Our results indicate that when plotted relative to the instantaneous interface, a substantial enhancement in the density profiles is observed at the polymer/vapor interface for both systems. This is in sharp contrast to the density profiles used by Mortazavian et al. 27 to make a correspondence with a mobile surface region at the polymer/vapor interface. The chain end distributions show an enhancement of chain ends at the PS/graphite interface which may be related to the constraint imposed by the graphite substrate on the possible configurations of the chains and packing effects. The polymer/vapor interface acts like a hard wall causing the polymer chain ends to cluster around the interface as clearly shown by the enhancement of end groups in the interfacial region for both PMMA/vapor and PS/vapor interfaces. Without some sort of interaction, the chains will continue to accumulate at the polymer/vapor interface to maximize their entropy and since there is no geometric constraint on the vapor side of the interface, the effect seen can be rationalized as a balance of enthalpic and entropic effects. 53 The results presented here will have serious implications for the glass transition temperature of thin polymer films as a glassy polymer is believed to have a mobile region near the free surface in comparison with the bulk. Based on the density profiles reported in this work, one would expect a denser polymer/vapor interface layer to lead to a slower dynamics in the interfacial region which suggests a higher glass transition temperature (Tg ) than that of the bulk. However, our results on the atomic mean-squared displacement in the PS/vapor interfacial region and the time autocorrelation function of the instantaneous interface indicate that the lower Tg values are probably a consequence of the dynamic nature of the interface. It seems a detailed study of the dynamics in the interfacial region, which can be clearly identified if the analysis is carried out relative to an instantaneous surface, is in order and a concerted 18


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effort in this direction from the polymer computational community may help in elucidating the glass transition behavior of supported and free-standing polymer films, in particular its dependence on film thickness.

Supporting Information Available See supporting information for additional information.

This material is available free of

charge via the Internet at http://pubs.acs.org/.

Acknowledgement This work was supported by the National Science Foundation (DMR-1410290). The authors would like to thank Gary Grest for helpful discussions and for a critical reading of the manuscript.

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Vapor Instantaneous Interfaces

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