Molecular Structure of Poly(methyl methacrylate) Surface II: Effect of

Oct 13, 2014 - Utilizing all-atom molecular dynamics (MD), we have analyzed the ... through sum frequency generation (SFG) spectroscopy alone. ... SFG...
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Molecular Structure of Poly(methyl methacrylate) Surface II: Effect of Stereoregularity Examined through All-Atom Molecular Dynamics Kshitij C. Jha,* He Zhu, Ali Dhinojwala, and Mesfin Tsige* Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States

Langmuir 2014.30:12775-12785. Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 09/10/18. For personal use only.

S Supporting Information *

ABSTRACT: Utilizing all-atom molecular dynamics (MD), we have analyzed the effect of tacticity and temperature on the surface structure of poly(methyl methacrylate) (PMMA) at the polymer−vacuum interface. We quantify these effects primarily through orientation, measured as the tilt with respect to the surface normal, and the surface number densities of the α-methyl, ester-methyl, carbonyl, and backbone methylene groups. Molecular structure on the surface is a complex interplay between orientation and number densities and is challenging to capture through sum frequency generation (SFG) spectroscopy alone. Independent quantification of the number density and orientation of chemical groups through all-atom MD presents a comprehensive model of stereoregular PMMA on the surface. SFG analysis presented in part I of this joint publication measures the orientation of molecules that are in agreement with MD results. We observe the ester-methyl groups as preferentially oriented, irrespective of tacticity, followed by the α-methyl and carbonyl groups. SFG spectroscopy also points to ester-methyl being dominant on the surface. The backbone methylene groups show a very broad angular distribution, centered along the surface plane. The surface number density ratios of ester-methyl to α-methyl groups show syndiotactic PMMA having the lowest value. Isotactic PMMA has the highest ratios of ester- to α-methyl. These subtle trends in the relative angular orientation and number densities that influence the variation of surface structure with tacticity are highlighted in this article. A more planar conformation of the syndiotactic PMMA along the surface (x−y plane) can be visualized through the trajectories from all-atom MD. Results from conformation tensor calculations for chains with any of their segments contributing to the surface validate the visual observation.

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INTRODUCTION

popular of these methods remains the traditional contact angle measurement preferred in part because of its simplicity. The loss of specific chemical information and additional complications in interpreting data that may also reflect the molecular rearrangement of the polymer surface upon contact with water limits surface characterization through the contact angle. For analysis in vacuum, X-ray photoelectron spectroscopy (XPS) is an attractive tool that offers chemical information on surface groups. However, small shifts in carbon binding energies serve as indicators of various hydrocarbon groups, and their differentiation is nontrivial. Sampling techniques such as attenuatedtotal-reflectance (ATR) infrared, while providing surface

Surface energy plays a critical role in determining the functionality of polymers, whether it be through utilization as commodity plastics or for high-end composite applications such as biomaterials. Wetting, adhesion, segregation, specific binding, and toxicity are all controlled to some measure by the surface energy. The proliferation of different end uses of PMMA from bone materials1 and MEMS2 to pharmaceutical systems3,4 makes the study of its surface behavior not only a basic scientific problem of interest but also one with immediate implications in material design. In contrast to the recent mining of surface properties for various applications, analyses of PMMA so far have focused largely on its bulk properties as a pure polymer or barrier properties in composites and blends.5−15 A plethora of surface characterization methods for polymers are available, each with its own set of challenges. The most © 2014 American Chemical Society

Received: June 16, 2014 Revised: October 8, 2014 Published: October 13, 2014 12775

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Figure 1. Chain orientation for different tacticities of PMMA at 560 K. We observe the effects of tacticity on the orientation of the chain at the air interface. Clearly, syndiotactic PMMA shows the most propensity for the chains to lie parallel to the surface.

be visually seen through an inspection of the trajectories. A sample snapshot for each tacticity at 560 K is shown in Figure 1. As observed in Figure 1, the overall chain orientation is a strong function of tacticity, and this may be a result of the packing of the chains in the bulk. We have quantified the anisotropy through the computation of the conformation tensor of the chains on the surface as a function of tacticity. Having analyzed the molecular structure of PMMA on the surface through SFG in paper I,36 we provide further insight by analyzing the subtle differences in interfacial structure with tacticity through all-atom MD. In the current study, we find the number density ratios of the ester-methyl to the α-methyl and carbonyl groups to be tacticity-dependent. We also find the relative orientation of the different chemical groups, especially the α- and ester-methyls, to be tacticity-dependent.

molecular information, analyze thicknesses that are larger than those affecting interfacial properties such as wetting and adhesion. Infrared−visible SFG has been widely used as a method of studying surfaces and interfaces. We have previously employed such analysis to probe the molecular structure of both polystyrene (PS)16 and PS/comb-polymer17 surfaces. The behavior of PMMA at polymer, water, and air interfaces has also been investigated by a number of groups using SFG.18−29 However, in these studies, conflicting accounts exist on the orientation of chemical groups for PMMA and the effect of annealing on changes in surface structure, especially in the work by Wang et al.30 and Tateishi et al.,27 both of whom utilized SFG for the characterization of the PMMA surface. Experimentally, there is ∼5−10 cm−1 resolution31−34 between the α- and estermethyl groups, and even systematic deuteration studies have given conflicting accounts of peak assignments20,29,30 and the manner in which the chemical groups orient themselves.31,33−35 This has necessitated the need for a careful delineation of the molecular structure on the surface of PMMA by combining SFG with models that complement the information available through spectroscopy. There is, thus, a clear case to be made for combining MD and SFG in order to understand the surface number densities and orientation of chemical groups such as αmethyl, ester-methyl, carbonyl, and the backbone methylene groups as surface applications become more common, and the segregation and wetting properties of the polymer gain increased the interest from the polymer community. In the first part of this joint publication, hereafter referred to as paper I,36 the molecular structure of PMMA at the air interface has been systematically analyzed using surface-sensitive SFG in conjunction with MD and ab initio models to aid in understanding the SFG results. The dominance of ester-methyl on the surface, irrespective of tacticity and temperature, is captured by SFG analysis. Spectra computed from the orientation distribution obtained from all-atom MD match the experimental spectra, providing a validation for the surface structure model hypothesized in the present study. Through this combination of all-atom MD simulations and SFG, we propose a model of chemical group orientation that shows both α- and ester-methyl and the carbonyl groups coming to the surface with the backbone methylene showing a broad distribution in orientation. The relative number density of the two methyl groups varies with tacticity and temperature, and these changes are captured through orientation and number density distributions obtained from all-atom MD simulations. The change in conformation on the surface with tacticity can also

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METHODS

Force Field Parameters. The interfacial behavior and dynamics of PMMA, along-with local relaxation and activation energies, have been validated through MD simulations using the optimized potentials for liquid simulations (OPLS) force field.15,37 OPLS has also been used to study the behavior of PMMA at graphene interfaces.38 The use of class I force fields such as OPLS has the additional advantage of affording equilibration over longer periods of time and has been used in the present study. Simulation Details. Chains of atactic (atac-), isotactic (iso-), and syndiotactic (syn-) PMMA were constructed in the Discover module of Materials Studio 6.0 from Accelrys Inc. and randomly placed in a box.39 The bulk of the polymer, thus constructed, was equilibrated at 600 K for 5 ns for each tacticity in an NPT ensemble with periodic boundary conditions in all directions. The initial equilibration generates a melt structure that is energetically stabilized with equilibrated bulk density at that temperature. A chain length of 40-mers was chosen because it balances the objectives of being long enough to distinguish between the tacticities while also being computationally efficient. To generate the film from the bulk, periodicity was maintained in the x and y directions while periodicity in the z direction was removed and was kept open to vacuum. Details of the method have been discussed in our previous work on polymer films.40,41 The box dimensions and the film thickness were chosen so that no chain interacts with both the top and bottom surfaces and a chain can fully adsorb on the surface. The thickness of the film for the different structures was initially about 90 Å along the z direction, with approximately 74 Å on both sides in the x−y plane. The total number of chains that satisfy these conditions for the system was found to be 64 for a chain length of 40-mers. MD simulations were also done for systems with a wider surface area (100 × 100 × 100 Å3) and double the thickness (74 × 74 × 180 Å3) at a few selected temperatures. The results were similar to the results obtained using the smaller system, which is used for all current analyses. 12776

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Figure 2. Density distribution along the PMMA film in the z direction at 560 K with z = 0 in the middle of the film. (Left) Mass density distribution of the films. (Right) Close-up view of the distribution for the upper 25 Å of the films to show the density variation with tacticity. A similar behavior is seen for temperatures from 500 to 560 K. The long time needed for PMMA equilibration has been mentioned as an issue in previous studies,5 and we found that a minimum of 100 ns at a given temperature was needed so that the ratios of the different chemical groups at the interface equilibrate to an average value that does not change with time. This is checked through the computation of the ratios of the number density of chemical groups at different times in the simulation, along with their orientation distribution. Both the ratios and the orientation distributions stabilize close to 100 ns. For each tacticity, the PMMA film was cooled from 600 to 300 K at a rate of 20 K/2 ns in the NVT ensemble. Selected temperatures of 500, 520, 540, and 560 K were run for simulation times longer than 100 ns (NVT), which would cause the total simulation time for a given tacticity to be greater than 0.4 μs. In running these simulations, we employed particle−particle particle−mesh (PPPM) Ewald summation with 10−5 accuracy and a 12 Å cutoff for van der Waals summation using the 12-6 potential. Because no chain leaves the interface, the choice of a longer cutoff for van der Waals is sufficient to capture the interfacial structure. All simulations were carried out using the LAMMPS code.42 Utilizing these simulation time protocols, the surface number density ratios of chemical groups were seen to equilibrate to an average value, and their variance with tacticity and temperature gave a measure of the surface structure of PMMA. Our discussion will mainly focus on 500 and 560 K, which represent the lower and higher ends of the temperature range. Sum Frequency Generation (SFG) Spectroscopy. To measure the response of the molecules on the surface, SFG mixes a visible laser beam with a tunable infrared (IR) beam. The approximation of the electric dipole yields a signal only through ordered species on the surface. Signal enhancement occurs through the overlap of the stretching vibrations of the surface molecules with the incident IR. The SFG setup and apparatus are detailed in paper I,36 alongside a discussion of its particular utility to resolve the ordering and orientation of chemical groups at the PMMA−air interface. Spectra were obtained for syn- and iso-PMMA for the solid and melt state (above Tg for synPMMA and above Tm for iso-PMMA). Through the angular distribution obtained from all-atom MD, SFG spectra were computed that match the experimental observations.

the mass density profile using partition bins of 1 Å in the z direction of the simulation cell. The masses of the atoms were summed over the partition volume, and density was calculated and averaged over the length of the trajectory at a given temperature. Figure 2 shows time-averaged mass density plots for the three tacticities at 560 K. The mass densities show two symmetric and smooth polymer−vacuum interfaces for all tacticities with the nature of the curve at the interfaces exhibiting tan hyperbolic behavior. The same behavior is observed for temperatures from 500 to 560 K. The average densities in the middle of the film are within 5% of experimental values43 and decrease with increasing temperature, as expected. The film thickness of iso-PMMA is slightly smaller, as can be seen in the left panel of Figure 2. This means that iso-PMMA has a higher density, which has also been observed experimentally and in simulations.5 Additionally, both Soldera et al.5 and Lu et al.,7 on the basis of density and free volume computations, respectively, argue for a more compact packing of iso-PMMA. Orientation on the Surface. Utilizing the vectors for orientation shown in Figure 3, we computed distribution plots for ⟨cos θ⟩ (Figure 4) to analyze the orientation of different chemical groups. All angles (θ) are given with respect to the z direction, which is normal to the film surface. Figure 4 also allows

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RESULTS AND DISCUSSION The characterization of the surface, followed by analyses of the orientation and number densities on the surface of the four chemical groups (ester-methyl, α-methyl, backbone methylene, and carbonyl) and their dependence on stereoregularity, is discussed in the following sections. We conclude with a discussion on the effect of tacticity on chain conformation on the surface. Mass Density Profile. The mass density represents the most straightforward way to characterize the surface. We computed

Figure 3. Vectors used for the computation of the orientation distribution for the PMMA film. Part of a PMMA polymer chain is shown. Angles are measured for the vectors with respect to the z direction that is normal to the surface. 12777

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Figure 4. Average cos θ values as a measure of the orientation for the three tacticities and two temperatures of 500 and 560 K. Values are shown for methylene, α-methyl, ester-methyl, and carbonyl groups.

Figure 5. Average cos θ for ester-methyl for the three tacticities at temperatures of 500 and 560 K.

us to characterize the surface. The point where the ⟨cos θ⟩ values start to show a monotonic increase (top part of the film) or decrease (bottom part of the film) can be termed the preferential onset of orientation. The surface is defined as the region beyond the preferential onset of orientation. We analyzed the preferential onset of orientation for all three tacticities and temperatures and found that utilizing a unique preferential onset of orientation as the starting point of the surface yields the same trends as utilizing the average of the top and bottom 1 nm for the film. Computation of orientation distributions for 1.5 and 2 nm reveal recovery to bulk behavior with the loss of the distinctions in chemical group orientation distributions. The recovery to bulk behavior happens very quickly after 1 nm, which further validates our choice of interface. Figure S1 in the Supporting Information shows the angular distribution in the middle of the film (at 500 K) that reflects bulk behavior, and beyond 1 nm, we observed a similar distribution.

The nature of the distribution is similar for 560 K and shows isotropic behavior with no differentiation in chemical group orientation, as expected. The ester-methyl group consistently shows the highest values of ⟨cos θ⟩ on the surface irrespective of the tacticity and temperature, followed by the α-methyl group (Figure 4). Also of interest is the methylene group, which shows the least-organized orientation of all of the chemical groups (α-methyl, ester-methyl, and carbonyl). This will be revisited in the orientational analysis for the top 1 nm as a function of angle. For a relative comparison across tacticities, we plotted the ⟨cos θ⟩ values for ester-methyl at two temperatures for the three tacticities (Figure 5). The results are very similar, indicating the invariance of orientation for the ester-methyl groups with tacticity and temperature. To estimate the spatial orientation on the surface, the angular distribution is plotted for the top 1 nm of the film (Figure 6). We 12778

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Figure 6. Angular distribution for the top 1 nm of the film for three different tacticities and two temperatures of 500 and 560 K. Values for α-methyl, ester-methyl, methylene, and carbonyl groups are shown. The errors are within 5%.

Figure 7. Angular distribution for the top 1 nm of the film for three different tacticities and for α-methyl, ester-methyl, methylene, and carbonyl groups at 560 K. The errors are within 5%. Similar distributions are observed for 500 K and are provided in the Supporting Information, Figure S1.

observe ester-methyl having the highest peaks, irrespective of tacticity. α-Methyl has a comparable peak to ester-methyl for synPMMA, where we also observe a shift in the methylene group away from all of the other chemical groups. A broad distribution of the methylene group is observed for all tacticities.

To compare the peak for different chemical groups across tacticities, we plotted the same distribution for each chemical group at two temperatures of 500 and 560 K (Figure 7 and Figure S2 in Supporting Information). For a given chemical group, Figure 7 is indicative of the effect of tacticity, which could be an 12779

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syn > atac > iso, α-methyl: iso > atac ≈ syn; methylene: syn > atac > iso, and carbonyl: syn ≈ atac>iso. The smaller the angle, the more the group is oriented toward the surface normal. Methylene groups orient almost along the plane, with the orientation being above the plane for atac- and iso-PMMA by 2−4° and below the plane by 1−2° for syn-PMMA. Only iso-PMMA has a greater αmethyl angle than carbonyl angle, implying that the carbonyl has the lowest angle with respect to the surface normal for isoPMMA. This shows the interplay between the surface number density and orientation. Syndiotactic PMMA has a higher relative carbonyl surface number density, as will be discussed in the next section, but iso-PMMA has the carbonyl group oriented more toward the normal. The interplay of orientation and number density between chemical groups determines the surface behavior of a polymer, which can be utilized as design principle for functional interfaces. Number Density on the Surface. To know how different chemical groups come to the surface with tacticity and temperature, it is instructive to look at the number densities. These were computed by using a slab length of 1 Å in a manner similar to the computation of mass densities by taking the number count instead of atomic masses. As seen in all distributions in Figure 8, at a certain point the number density of ester-methyl becomes greater than the number density of the α-methyl and methylene units (the crossover regime). This crossover regime (Figure 8) is similar to the preferential onset of orientation (Figure 4), which has been defined in the section on surface orientation. Hence, an average of 1 nm (top and bottom) is representative of both the crossover point and the preferential onset of orientation. The similarity between the crossover regime and the preferential onset may be specific to PMMA and needs to be tested for other polymeric systems in the future.

important design principle for acrylic surfaces. We observe synPMMA as having the highest peak of the three tacticities for αmethyl, whereas ester-methyl has the highest peaks for iso- and atac-PMMA. Carbonyl peaks are invariant for all tacticities, while there is a shift in the methylene peak to the right for syn-PMMA. The results from Figures 6 and 7 lead us to conclude that the ester-methyl has the most well-defined and narrow distribution whereas methylene orientation distributions are broad. The two methyl groups have similar distributions for syn-PMMA. There is also a shift toward the surface plane for the methylene group for syn-PMMA. Because the errors in the orientation distribution are within 5%, these distinctions are beyond the error bounds. The peaks are the most probable values. However, also useful are the average values for the angles, which were computed as a weighted average for the angular distribution. These values for the different groups are shown in Table 1. Table 1. Average Angle for Different Chemical Groups for Different Temperatures and Tacticitiesa tacticity isotactic syndiotactic atactic a

temperature (K)

estermethyl

αmethyl

methylene

carbonyl

500 560 500 560 500 560

67.6 68.0 73.9 74.1 71.5 69.1

80.4 82.2 77.9 76.6 75.9 78.7

88.2 85.9 89.5 91.0 89.6 86.3

76.1 78.8 79.2 80.3 79.3 80.3

The error is less than 0.1° for all values.

Table 1 quantifies the peak distribution behavior through tilt angles with respect to the surface normal, as seen in Figures 6 and 7. We observe that the ester-methyl orientation follows the trend

Figure 8. Number density vs tacticity and temperature for the upper part of the PMMA films for 500 and 560 K. The crossover regime, shown by a broken line in the top left distribution, is defined as the point where the number density of ester-methyl group exceeds that of the α-methyl units. It gives a picture of relative values of α-methyl to ester-methyl (and methylene) on the surface. 12780

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Figure 9. Distribution of ester-methyl (in blue) and α-methyl (in yellow) for different depths at the top interface at 560 K. The carbon for the chemical groups is highlighted. (A) atac-PMMA, (B) iso-PMMA, and (C) syn-PMMA depth profiles.

Figure 10. Ratio of ester-methyl to α-methyl plotted with distance from the top of the film as a function of temperature and tacticity.

The question arises as to how best to quantify relative number density effects. One way to look at it is through a visualization of trajectories. Figure 9 shows how the concentration of chemical groups changes as we travel from the surface to the more interior region of the film. There is an uneven distribution of chemical groups around 0.8−1 nm. For example, in panel B for isoPMMA, the spatial distribution of chemical groups can most clearly be visualized as uneven at 0.8 nm. As we go inside and approach the bulk, we observe a more uniform distribution. This

is consistent with our definition of the surface from both the surface orientation and number density distributions. The uneven distributions are a reflection of the surface roughness consisting of crests and troughs. It is to be stressed that the uneven distribution observed on the surface is not a consequence of finite size effects because we have observed the same nature of distribution of chemical groups even when we double the system size in our simulations. We also clearly observe that the ester-methyl group is in excess on the surface compared 12781

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Figure 11. Carbonyl and ester-methyl number density in the upper part of the film for different tacticities at 560 K.

Figure 12. Ratio of ester-methyl to carbonyl plotted with distance from the top of the film as a function of temperature and tacticity.

to α-methyl. The excess is apparent in the 0.8−1 nm region, beyond which there are similar numbers of chemical groups for both ester- and α-methyl. In the discussion of ratios that follows, the recovery to a similar distribution in the bulk of different chemical groups that may be depleted or in excess on the surface becomes evident. Figure 9 provides a clear visualization of this change in chemical group distribution. Another method to quantify relative number densities is to evaluate ratios of chemical groups as a function of distance from the surface. When these ratios are computed, it is to be noted that the number densities for the top or bottom 0.5 nm are extremely small and ratios of chemical groups in these regions can be misleading and unphysical. For example, we can see in the case of atac-PMMA 500 K in Figure 8 that surface number densities in the 43−48 Å range are too small to yield any measurable surface characteristics. Hence, our definition of the top of the film is after this region that is statistically significant in terms of number densities. We compute the ratios of the chemical groups from the sum of number densities starting from the top of the surface to a given point in the film. The ratios of the number density of estermethyl groups to α-methyl groups as a function of tacticity, temperature, and distance from the top of the film are shown in Figure 10 (500 and 560 K). In all cases, the ratio is greater than 1 on the surface, indicating that ester-methyl is in excess on the surface compared to αmethyl. The relative values of the ratio are also similar, with a decrease of as much as 7% with temperature. Figure 11 shows the surface number density of carbonyl groups compared to ester-methyl groups for the top part of the film as a function of tacticity at 560 K. The differences can be observed to a greater extent in examining the ratios of the

number density of ester-methyl groups to carbonyl groups at 500 and 560 K (Figure 12). In all cases, the values are greater than 1 on the surface, indicating that ester-methyl groups are present on the surface to a larger extent than are carbonyl groups. The overall trend is similar to what we observed for ratios of estermethyl to α-methyl groups (Figure 10), with the ester-methyl groups dominant irrespective of temperature and tacticity. It is interesting that the carbonyl groups are depleted near the surface, and this ratio may change for the PMMA surface in contact with water. The carbonyl group attracts the most participation from water, and the PMMA chain is said to reorient itself to maximize the water−carbonyl oxygen interaction.44 We discussed the carbonyl group separately from the other three chemical groups (ester-methyl, α-methyl, and methylene) because its hydrophilic character is greater and would impact the behavior of PMMA surfaces toward polar media, and its surface concentration may play an important role in determining the interfacial surface energy. Tacticity Effects on Conformation. Previous work on the stereoregularity of PMMA and its effect on the bulk glass transition11 suggests that the mobility of the side chain, specifically for iso-PMMA, leads to increased mobility of the backbone and a decreased glass transition. Another theory states that syn-PMMA has increased dipole−dipole interactions between the side chains,45,46 which restricts mobility, leading to a higher glass transition. Higher nonbond energy for the synPMMA has also been reported.47 It has been hypothesized that syn-PMMA possesses lower intramolecular energies whereas isoPMMA has lower intermolecular energies, leading to better packing.5 Analyses of free volume by Lu et al.7 indicate isoPMMA as the better-packed polymer. We propose that a more favorable steric distribution of chemical groups for iso-PMMA 12782

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Figure 13. Orientation of chains on the surface and bulk for iso-PMMA and syn-PMMA. Only a few representative chains have been highlighted to bring out the differences.

components in three Cartesian directions (x, y, and z) for chains with segments in the top 1 nm of the film and ⟨Ree2⟩0 is the meansquared end-to-end distance of the system in the bulk at the corresponding temperature. We observe that the anisotropy in the x−y plane (Cαα ≠ 1) is the highest for syn-PMMA with both Cxx and Cyy >1, implying a larger contribution to a planar conformation in the x−y (surface) plane as observed in Figure 13. We also observe that atac-PMMA has the largest mean-squared end-to-end distance in all directions, whereas iso-PMMA at 560 K appears to be closest to an isotropic distribution. Roughness computed for the interface gave similar values for both iso-PMMA and synPMMA of 0.5 ± 0.02 nm. However, it has to be noted that the roughness does not take into account the spatial distribution of the chains. It must be emphasized that all observations through all-atom simulations show subtle differences in orientation and ordering that would be very hard to characterize through empirical approaches. As expected, the spectra for syn-PMMA and isoPMMA match at the polymer−air interface for PMMA, as discussed in the first part of the joint publication.36 Coupled with insight provided by spectroscopy, our simulations have attempted to analyze the minimal differentials in surface orientation and number densities of chemical groups, alongwith their interplay, that could lead to changes in molecular structure on the surface of PMMA.

leads to better packing and may lead to faster dynamics. Our mass density computations also reveal a denser iso-PMMA. Higher surface activity, seen in our simulations through synPMMA being more planar on the surface, and the relative higher concentration of α-methyl in syn-PMMA is consistent with contact angle measurements.48,49 The glide-plane structure on the surface yields a more surface-active conformation,48 which is not possible for a helical conformation in which iso-PMMA prefers even in a melt state. In Figure 13, we observe that the surface orientation and number density of the chemical groups would also depend on the tacticity that is related to the packing of the chains. We observe for chains 1−6 for both polymers that syn-PMMA tends to coil and space itself on the surface. Atactic PMMA is in between these two behaviors. Because the orientation on the surface is markedly different than in the bulk, the patterns of the bulk may be transferred to the surface and vice versa, leading to oscillations in density observed in distribution plots. Coupled with control offered by the stereoregularity discussed in the current work, these could lead to tunable optical and lithographic properties, as have been explored in Langmuir−Blodgett films of PMMA for quite some time.50,51 Having observed chains with varying conformations on the surface, we have quantified the anisotropy in chain alignment by calculating diagonal elements of the conformational tensor for chains with any segments that are part of the top 1 nm of the film (Table 2). Similar behavior is observed for the bottom 1 nm. The conformation tensor is defined as52 Cαβ = 3⟨(ReeαReeβ)/ (⟨Ree2⟩0)⟩, where Reeα and Reeβ are the end-to-end distance

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CONCLUSIONS Through a combined investigation of the effect of stereoregularity on the relative number densities, it was observed that the ester-methyl groups come to the surface irrespective of the tacticity and temperature. We propose a preferential onset of orientation that is very close to the crossover regime to define the surface, where quantifiables in surface orientation and number densities paint a picture of the structure of PMMA. In this regime, through analyses of ratios of ester-methyl to α-methyl and carbonyl, it is observed that iso-PMMA has a greater degree of excess ester-methyl on the surface. In part I of the joint publication, we showed that the MD results could quantitatively match the SFG spectra observed in experiments. Even though the MD and SFG results show that ester-methyl groups are present in excess, SFG was not able to resolve the subtle differences as a function of tacticity. The differences in molecular hyperpolarization in addition to the values of orientation and number density are needed to explain the SFG results.

Table 2. Diagonal Elements of the Conformation Tensor for Chains in the Top 1 nm of the Film and the Mean-Squared End-to-End Distance of the System in the Bulk at the Corresponding Temperaturea tacticity isotactic syndiotactic atactic

a

temperature (K)

Cxx

Cyy

Czz

⟨Ree2⟩0 (Å2)

500 560 500 560 500 560

0.76 0.92 1.15 1.33 1.19 1.19

1.14 1.14 1.51 1.87 0.76 0.76

0.90 1.01 0.73 0.64 0.71 0.64

1492 ± 10 1178 ± 12 1117 ± 9 1403 ± 12 2996 ± 10 3809 ± 12

The deviation for the elements is less than 5%. 12783

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Visualization of the trajectories shows a planar conformation of syn-PMMA chains on the surface. A model for PMMA on the surface is presented that shows ester-methyl having the highest orientation and backbone methylene having the lowest orientation irrespective of tacticity, with the other two chemical groups (α-methyl and carbonyl) variously oriented per tacticity and temperature. Combining the surface orientation and number densities obtained from all-atom MD with SFG provides a detailed picture of the surface structure of PMMA and highlights the need for MD in combination with SFG to understand the number density and orientation of molecules at polymer surfaces and interfaces.

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ASSOCIATED CONTENT

S Supporting Information *

Angular distribution for the middle of the film for three different tacticities at 500 K that reflects bulk behavior. Angular distribution for the top 1 nm of the film for three different tacticities for α-methyl, ester-methyl, methylene, and carbonyl groups at 500 K. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by NSF grants DMR-0847580 (M.T.), DMR-1105370 (A.D.), and DMR-1006764 (A.D.). We thank Dr. Ram Bhatta and Alankar Rastogi for frutiful discussions and The University of Akron for additional support.

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REFERENCES

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