Local Structure Contributions to Surface Tension of a Stereoregular


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Local Structure Contributions to Surface Tension of a Stereoregular Polymer Kshitij C. Jha, Ali Dhinojwala, and Mesfin Tsige* Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States S Supporting Information *

ABSTRACT: We have used all-atom molecular dynamics (MD) simulations to calculate the surface tension of melt poly(methyl methacrylate) (PMMA) as a function of tacticity. Computation of surface tension using the Kirkwood-Buff approach required hundreds of nanoseconds of equilibration. The computed slopes of surface tension versus temperature are in very good agreement with reported experimental values. Using a rigorous treatment of the true interface, which takes into account the molecular roughness, we find that isotactic PMMA, in comparison to syndiotactic and atactic PMMA, shows a larger surface concentration of polar ester-methyl and carbonyl groups on the surface versus nonpolar α-methyl groups. A mechanistic hypothesis based on the helical nature of the isotactic PMMA chains, their relative flexibility, and their reported conformational energies is proposed to explain the trends in composition near the surface. We highlight here how surface composition and surface tension are controlled by both polarity and steric constraints imposed by tacticity.

T

surface plays a much more critical role compared to the bulk properties as thickness decreases. In this paper, we have implemented several important improvements for MD simulations of thin PMMA films. First, we have used force fields and parameters that have been validated by comparing with the surface structures determined using infrared-visible sum frequency generation spectroscopy.18,19 Second, we ran simulations for hundreds of nanoseconds to calculate equilibrated surface tension values as a function of temperature using the Kirkwood-Buff approach (augmented by a tail correction to account for long-range interactions). Third, we calculated the surface excess by using a true interface that takes into account the roughness of the simulated PMMA surface. The effect of surface properties of polymer surfaces on toxicity20 and biocompatibility21 are controlled by the orientation and surface concentrations of polar and nonpolar groups.22,23 This new approach provides us with a key insight into how chain conformations control the segregation of chemical groups, and how this leads to subtle

he conformations and configurations of poly(methyl methacrylate) (PMMA) stereoisomers have been topics of substantial research interest in order to gain insight into the effect of tacticity on the physical properties of this common polymer.1−5 Energetically unfavorable overlaps between the oxygens of the carbonyl and ester-methyl groups for different stereoregular forms provides a considerable barrier between trans−trans and trans−gauche conformers of the backbone chain.1,2,6 In addition, the cooperative motion of the side groups7 contributes to chain mobility and flexibility, which leads to comparatively large differences in glass transition temperature,3 dipole moments,8 and characteristic ratios1 between isotactic and syndiotactic forms. Here, we have used an all-atom molecular dynamics (MD) approach to study the differences in surface tension of free-standing thin films of PMMA as a function of tacticity. Ultrathin stereoregular PMMA films find applications in lithographic coatings and resists, geodesic lenses, nanoreactors, micro RNA detectors, and LEDs (where they enhance the LED quantum efficiency).9−11 Chemically modified forms of acrylates are also used as biomaterials12−14 and advanced filtration membranes.15−17 Knowledge of near-surface concentration of functional groups as a function of tacticity is required, as the © XXXX American Chemical Society

Received: August 27, 2015 Accepted: October 22, 2015

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ACS Macro Letters changes in surface tension. The simulation provides quantification that is often challenging to obtain through surfacesensitive spectroscopy and contact angle measurements. In particular, the contact angle measurements limit interpretations on near-surface composition in vacuum due to surface reconstruction in contact with liquids. All-atom molecular dynamics (MD) were performed on PMMA systems, of all three tacticities, comprising 40-monomer chains with an initial surface area of about 74 × 74 Å2 and a film thickness of about 90 Å. All structures were generated initially through the Discover module of Materials Studio 6.0 from Accelrys Inc. The chain length and box dimensions were chosen for optimal computational efficiency, allowing enough surface area for an individual chain to fully adsorb on the surface, sufficient thickness to prevent chains from spanning the vertical dimension of the systems, and allow for atactic conformer to have random placement of side groups, with an overall dyad replication probability of 0.5. To check the appropriateness of box dimensions, MD simulations were carried out for systems of overall greater dimensions (100 × 100 × 100 Å3), as well as one with double the thickness (74 × 74 × 180 Å3). The results obtained were similar to those for the smaller systems used in the current study. Total number of chains for our box size was 64 for each of the systems. Energetically stabilized melt structures were obtained through dynamics at 600 K with equilibrated bulk densities. After film formation from bulk the structures were cooled to 300 K with a cooling rate of 20 K/2 ns in the NVT ensemble. Select temperatures (500, 520, 540, 560 K) were run for additional hundreds of nanoseconds. Further details on equilibration and film formation can be found in our previous work.19 Particle− particle particle-mesh (PPPM) Ewald summation with 10−5 accuracy for electrostatic interactions was used. A 12 Å cutoff for van der Waals summation using the 12−6 potential was implemented. Integration time-step of 1 fs was used for all simulations. Periodic boundary conditions were maintained in all three directions, and removed in the z-direction after equilibration to obtain a film. The OPLS force field24 has been shown repeatedly to accurately reproduce the dynamics, structure and relaxation behavior of single-component systems of PMMA as well as blends.25−28 Modifications to the OPLSAA force field with a more accurate torsion potential for ester groups29 yield structure and dynamics properties that are close to those obtained through neutron scattering.30 The modified version has been used in the current study. The surface tension is computed following the KirkwoodBuff theory:31 L

Figure 1. Accumulated time averaged surface tension vs time for iso(black), syn- (green), and atac- (blue) PMMA at 540 K.

surface tension. Most of the prior work in the field utilizes simulated trajectories over tens of nanoseconds or less.32−36 Our work utilizes trajectories for a cumulative simulation time, for all systems and temperatures, of more than 4 μs (Figures 1 and 2). Tail corrections to the surface tension values in Figure 1

Figure 2. Surface tension vs temperature for iso- (squares), syn(circles), and atac- (triangles) PMMA after tail corrections. Maximum error values are within the symbol size (±0.15 dyn/cm). Broken lines are linear fits to the data.

are required to account for long-range interactions, and were computed from the mass density profile (ρ(z)),6 with ρ(z) being fit to an error function, the details of which can be found in our previous publication.37 The final, tail-corrected values of surface tension for PMMA at various temperatures are shown in Figure 2. The surface tension of isotactic (iso-) PMMA is higher than both syndiotactic (syn-) and atactic (atac-) PMMA. For instance, at 500 K, the surface tension values for iso-, syn-, and atac-PMMA are 26.5, 25.6, and 24.9 dyn/cm. The differences in surface tension lie outside a maximum error of ±0.15 dyn/cm. Using a linear fit (shown by solid lines in Figure 1), the values of the slope of surface tension versus temperature is found to be −0.076 (±0.007) for atactic, −0.081 (±0.004) for syndiotactic, and −0.085 (±0.003) for isotactic PMMA, respectively. Wu et al.,38 using a pendant drop method, measured the slope of surface tension versus temperature to be −0.076, which is in very good agreement with the MD results.

⟨p ⟩ + ⟨p ⟩

y γp = z [⟨pz⟩ − x ], where Lz is the length of the 2 2 simulation box in the z-direction, divided by 2 to account for

⟨p ⟩ + ⟨p ⟩

y represent symmetry of the two surfaces and ⟨pz⟩ and x 2 the time averaged normal and tangential pressure components, respectively. The plot of surface tension as a function of time is shown in Figure 1. To reach a well-equilibrated value of surface tension requires hundreds of nanoseconds of simulation time, and it can be observed from Figure 1 that at least the first 100 ns are not useful for statistical analyses. Previous MD simulations of bulk PMMA have pointed out the need for large equilibration times.32 This is one of the reasons why a number of simulation studies, that compare the effect of PMMA tacticity on energetics and dynamics, have not attempted to compute

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Figure 3. Chemical group ratios for (A) iso-/syn-, (B) iso-/atac-, and (C) syn-/atac-PMMA at 560 K in vacuum as a function of distance from the top surface, as measured through the local maxima.

differences in observed surface tension outlined above. The polymer film is probed from the local maximum of the grid. The value at a given depth is the cumulative sum up to the depth. The choice of “increment in probe depth” proved very sensitive in terms of characterizing the surface behavior (see SI, Figure S1, for a probe increment of 5 Å that misses the crests and troughs shown by choosing a probe increment of 1 Å). This carefully calibrated true interface approach provides a comprehensive picture in terms of relative chemical group ratios that is representative of the ultrathin PMMA film behavior at the vacuum interface. In Figure 3, we see ratios tend to converge around 10−15 Å with overlap occurring at approximately 20−25 Å for cases of both iso-/syn- and iso-/atac-PMMA. This point of convergence can be used to define the interface. All ratios remain above 1 for iso-/syn- and iso-/atac- as the presence of all chemical groups studied is enhanced at the surface of isotactic PMMA, in part due to reported higher density and better packing, and possibly in part due to better surface arrangement of chains. Once almost all chemical groups have been counted, the ratios equal 1, as expected (see SI, Figure S2). Note that as we move away from the bulk toward the extremities of the interface, the (absolute) density of the chemical groups decreases sharply visa-vis that of the bulk. Even so, we see higher presence of estermethyl chemical groups at the interface up to 1.5×, as represented in the iso-/atac- values. There are some distinct differences in the relative ratios of polar and nonpolar groups at the surface of iso-PMMA when compared with syn- and atac-PMMA. The α-methyl groups are relatively depleted and ester-methyl and carbonyl groups are in relative excess at the surface for iso-PMMA in comparison to syn-PMMA. This makes the iso-PMMA surface relatively more hydrophilic, which is consistent with the higher surface tension of iso- PMMA. The presence of ester-methyl groups dominating surface composition, in relation to α-methyl groups is also consistent with the surface composition measured using infrared-visible sum frequency generation spectroscopy (SFG).18,19 In comparison to iso-/syn-, the ratios for iso-/atac- are higher, implying much larger fraction of ester-methyl for isotactic PMMA (vs atactic PMMA). This contributes to atactic PMMA being the most hydrophobic of the three tacticities as represented by surface tension values. For a direct comparison, we analyze ratios of syn-/atac- shown in Figure 3C. We observe that syn-PMMA has a larger number for all chemical groups. There is a pronounced peak for α-methyl groups, which is

The experiments were carried out in a window of 373−453 K and did not analyze the effect of tacticity on surface tension. Temperatures exceeding 500 K in MD simulations are sufficiently above the glass transition for all three tacticities to have the requisite chain mobility to reach equilibrium states. A decrease in temperature of a few degrees would extend the simulation time required for equilibration to the point where all-atom MD would be infeasible for computing surface tension. The linear slope of surface tension versus temperature is very useful in extrapolating to the surface tension values at lower temperatures.38 Slopes of surface tension versus temperature, which represent the difference in entropy between the surface and the bulk, are similar for all three tacticities. The magnitude of the slopes shows a slight increase in value for isotactic (iso-) PMMA compared to syndiotactic (syn-) and atactic (atac-) PMMA and show the following general trend iso- > syn- > atac-. However, the slopes are not significantly different up to a 0.1 significance level (Supporting Information (SI), section S1). The nature of the helical chain, discussed in our mechanistic explanation, would allow isotactic PMMA to rearrange itself better at the interface, leading to higher changes in packing from the bulk. Small differences in surface tension can be attributed to experimental observations of differences in chain conformation, surface roughness, and near surface chemical composition with tacticity.39−42 To understand the relationship between conformation and surface composition, we first need to define the interface. In our previous work, we have reported the surface composition of PMMA surface by defining the first 1 nm as the surface region.19 However, the surface is not flat in these simulations and experimental results using both X-ray reflectometry and atomic force microscopy report a surface roughness of approximately 1 nm.11 In our previous work, we determined roughness to be approximately 5 Å for PMMA surfaces.19 The roughness in our context is due to capillary waves and the interface is not smooth as shown in our table of contents figure. To correct for this roughness, we traverse the contour of the polymer by using a 2 × 2 Å2 grid parallel to the interface. Different mesh sizes were used and 2 × 2 Å2 was the minimum grid size to capture molecular details. Any other ... smaller grid size shows voids. The computed ratios of chemical groups (α-methyl, estermethyl, and carbonyl) for iso-/syn-, iso-/atac-, and syn-/atacPMMA at 560 K as a function of depth are shown in Figure 3. Relative ratios with tacticity provide an explanation for 1236

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consistent with our previous observations on syn-PMMA having dominant α-methyl groups at the interface.19 It also demonstrates the competing effect of chemical group ratios: a larger relative concentration of the carbonyl and ester-methyl groups at the interface would be counterbalanced by increase in relative α-methyl group concentration. The increase in αmethyl groups at the syn-PMMA surface appears to increase with increasing temperature (SI, section S5). Previous studies using Lateral Force Microscopy and ATRFTIR spectroscopy have shown that the polar ester-methyl groups are on the same side for isotactic PMMA consequently making it relatively easier for the helical chains to reorient in the presence of a polar environment.6,41−43 The relative ease of orientation in polar environments is also attributed to the flexibility of the helical isotactic PMMA.6,44 Based on the above observations, the syn- stereomer is locked, with the hydrophobic groups pointing up toward the air surface, while the isoPMMA with its greater flexibility is able to reorient even if the energies are slightly unfavorable in order to pack itself better at the surface, indicating higher hydrophobicity for syn-PMMA. The atac-PMMA is free of these steric constraints and is able to rearrange to present the most favorable conformation with lesser penalties in comparison to the stereoregular forms. This implies that steric restrictions of chemical groups could be used to control surface energies of functional stereoregular acrylates. Measurement of contact angles for stereoregular PMMA (hence, their corresponding phobicity) remains an experimental challenge. So far, the results for contact angle measurements for stereoregular PMMA have been inconclusive.45−47 It has been hypothesized, however, that iso-PMMA is the most hydrophilic of the three tacticities and exhibits amphiphilic behavior.48 This is borne out in the most recent reported values,47 as well as in the corresponding utilization of differences in hydrophilicity, by the same research group,21 for application in biocompatible electrospun fibers. Computed surface tension values (Figure 2) follow the same trend, with iso- having the highest surface tension, implying a relatively higher presence of polar groups at the vacuum surface. It is also important to note that measurement of contact angle is not sufficient to make inferences on the surface energy of PMMA because of possible restructuring of the surfaces in contact with liquids and the fact that the measured angles are affected by surface roughness. Also, all measurements for contact angle have been done below glass transition and melting point, while the current study analyzes near-surface composition and surface tensions at much higher temperatures to allow for sufficient chain relaxation. In conclusion, we have shown that computation of surface tension for stereoregular PMMA requires equilibration over hundreds of nanoseconds. Furthermore, our values for slopes of surface tension versus temperature are in very good agreement with experiment. We have correlated the differences in surface tension of iso-, syn-, and atac-PMMA to the relative surface excess of polar ester-methyl and carbonyl groups and proposed a mechanistic hypothesis to explain the trends therein. Through a grid-based approach that takes into account the roughness of the polymer surface, we have shown that the trends in relative ratios for iso-/syn-, iso-/atac-, and syn-/atac- are qualitatively consistent with the expected interfacial behavior. We emphasize the importance of surface composition of polar and nonpolar groups in modulating surface behavior of polymer films.

Letter

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.5b00612. Values of surface tension, analysis of significant difference for slopes of surface tension with temperature, and details on computation of surface tension. Chemical group ratios for probe depth of 5 Å showing sensitivity to probe depth. Chemical group ratios showing decay to 1 as all groups are counted. Chemical group ratios for 500, 520, and 540 K. Details on viability of temperature range selected for analysis (PDF).



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was made possible by funding from ACS Petroleum Research Fund (ACS PRF 54801-ND5) and Procter & Gamble (K.C.J. and M.T.). A.D. acknowledges support from National Science Foundation (NSF DMR-1105370). The authors thank Dr. Selemon Bekele for help with visualization of the instantaneous surface, He Zhu, Emmanuel Anim-Danso, Nishad Dhopatkar, and Pushkar Sathe for fruitful discussions on approaches to spectroscopic characterization at polymer interfaces, and Dr. Gary Leuty, Dona Foster, Iskinder Arsano, and Jacob Hill for general comments on the paper.



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