Molecular Structure of Poly(methyl methacrylate) Surface. I.Combination of Interface-Sensitive Infrared−Visible Sum FrequencyGeneration, Molecular Dynamics Simulations, and ab InitioCalculationsHe Zhu, Kshitij C. Jha, Ram S. Bhatta, Mesfin Tsige, and Ali Dhinojwala*

Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States

*S Supporting Information

ABSTRACT: The chemical composition and molecularstructure of polymeric surfaces are important in understandingwetting, adhesion, and friction. Here, we combine interface-sensitive sum frequency generation spectroscopy (SFG), all-atom molecular dynamics (MD) simulations, and ab initiocalculations to understand the composition and the orientationof chemical groups on poly(methyl methacrylate) (PMMA)surface as a function of tacticity and temperature. The SFGspectral features for isotactic and syndiotactic PMMA surfacesare similar, and the dominant peak in the spectra correspondsto the ester-methyl groups. The SFG spectra for solid and meltstates are very similar for both syndiotactic and isotacticPMMA. In comparison, the MD simulation results show that both the ester-methyl and the α-methyl groups of syndiotactic-PMMA are ordered and tilted toward the surface normal. For the isotactic-PMMA, the α-methyl groups are less orderedcompared to their ester-methyl groups. The backbone methylene groups have a broad angular distribution and are disordered,independent of tacticity and temperature. We have compared the SFG results with theoretical spectra calculated using MDsimulations and ab initio calculations. Our analysis shows that the weaker intensity of α-methyl groups in SFG spectra is due to acombination of smaller molecular hyperpolarizability, lower ordering, and lower surface number density. This work highlights theimportance of combining SFG spectroscopy with MD simulations and ab initio calculations in understanding polymer surfaces.

■ INTRODUCTION

One of the simplest and still commonly used technique tocharacterize surfaces of polymers is the measurement of watercontact angle. Although this is a very simple technique to judgethe wettability of surfaces, it lacks molecular level sensitivity toidentify the chemical composition and molecular structure ofsurfaces. In addition, the rearrangement of molecules at thesurface after exposure to water complicates the interpretation ofcontact angle results.1 X-ray photoelectron spectroscopy (XPS),a vacuum-based technique, provides excellent informationregarding the elemental composition present at the surfaces.However, to identify different hydrocarbon groups (orbondings) is not trivial and relies on subtle shifts of carbonbinding energies in the high-resolution XPS analysis.2

Attenuated-total-reflectance infrared can be used to pick upmolecular fingerprints, but this technique samples a muchthicker layer than the surface region that affects wetting, surfaceenergy, and friction.3 In the past two decades, surface-sensitiveinfrared−visible sum frequency generation spectroscopy (SFG)has been used to study polymer surfaces,4−7 polymer/liquidinterfaces,7−11 polymer/metal or metal oxide interfaces,5,12−15

and polymer/polymer interfaces.12,16−19 SFG is a second-ordernonlinear optical technique, and under electric dipole

approximation, the SFG signal is only generated by the orderedmolecules at surfaces or interfaces and the contribution fromthe isotropic bulk is negligible. The SFG measurement involvesmixing a visible laser beam fixed in wavelength with a tunableinfrared (IR) beam. The SFG signals are enhanced when thescanning IR wavenumber overlaps with the stretchingvibrations of the chemical groups at the surface. By using acombination of different polarized input and output beams andthe location of resonance-enhanced peaks, SFG can be used toidentity chemical composition and orientation of chemicalgroups at interfaces. Particularly, this technique is useful instudying buried interfaces of polymers in contact with liquids orother solid surfaces.5,14

Poly(methyl methacrylate) (PMMA) is a widely used plasticdue to its transparency, good mechanical properties, andbiocompatibility. Especially, it has been used as bone cement,20

in intraocular lenses,21 and as a drug delivery material,22 whereunderstanding the surface molecular structure is of greatimportance. The surface of PMMA was characterized using

Received: June 16, 2014Revised: August 26, 2014Published: September 12, 2014

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SFG by Chen et al.,6 and the SFG spectra in SSP (s-polarizedSFG, s-polarized visible, and p-polarized IR) polarizationcombination showed a dominant peak at 2950−2955 cm−1,which was assigned to the ester-methyl side chain of PMMAand indicated ordered ester-methyl groups tilting towardsurface normal. Further analysis led the authors to concludethat the α-methyl groups tend to lie down in surface plane andas a result were not observed in the SSP spectra. They alsoconcluded that the methylene groups were disordered. Alsousing SFG technique, Tanaka et al.10 observed that theannealing temperature has a profound influence on the surfacestructure of PMMA and concluded that the backbonemethylene groups became ordered at the surface after beingannealed for long period of time at temperatures much higherthan the glass transition temperature of PMMA. However,strong methylene resonance was also observed using as-spunPMMA samples by both Tanaka et al.11 and Wang et al.,23

which suggested the high-temperature annealing was notnecessary for ordering the methylene groups. In addition, nomethylene resonance was observed in studies by Somorjai etal.13 and Chou et al.24 in which PMMA samples have beenannealed at or above 100 °C. With all the above observations, itis puzzling that hours of annealing at temperature much higherthan the Tg is needed for PMMA surface to equilibrate, as it isexpected that molecules on the surface relax much faster thanthe ones in the bulk.25 In addition, there are limited surfacestudies of PMMA as a function of tacticity, in spite of theimpact tacticity may have on the surface properties.26 RecentSFG study from Tanaka et al.7 concluded that syndiotacticPMMA (syn-PMMA) had both backbone methylene and ester-methyl groups ordered at the surface. In comparison, theisotactic PMMA (iso-PMMA) had only the ester-methyl groupsordered at the surface. Despite many studies on using SFG todetermine molecular structure of PMMA surface, the actualcomposition and orientation of chemical groups on PMMAsurface remains inconclusive.The difficulties in interpreting SFG spectra may result from

the fact that SFG intensity is proportional to the product ofthree main molecular parameters. The first parameter is themolecular hyperpolarizability, which depends on the IR dipoleand Raman polarizability derivatives, and this parameter can bedifferent for methylene, α-methyl, and ester-methyl groups oreven for the same molecular group in different chemicalenvironments. The second parameter is the concentration ornumber density of the chemical groups on the surface, whichmay not have the same stoichiometry as that in the bulk due tosurface segregation. The third parameter is the orientation ofthe chemical groups, which consists of two parts: the averageorientation and the width of the orientation distribution. It ischallenging to determine a unique solution for the average tiltangle and its distribution using the SFG results.6 In addition tothese three main parameters, the overlapping of hydrocarbonpeaks in the SFG spectra in the wavenumber range from 2800to 3100 cm−1 can also influence the interpretation of the SFGresults. Because of these complications, it is difficult to directlyuse the SFG results to determine the surface composition andorientation of chemical groups on the surface of polymericmaterials, especially in the case of PMMA.Recent advances in molecular dynamics (MD) have made it

possible to study polymer surfaces with atomistic details, whichcan complement the experimental SFG results. Previous MDstudy on atactic polystyrene surface revealed that the methylenegroups were weakly ordered and was able to explain why the

dominant signal in the SFG spectra was from the side chainphenyl groups.27 MD analysis in conjunction with SFGmeasurements helped in explaining the strong SFG signalassociated with the ordering of poly(dimethylsiloxane)(PDMS) methyl groups in contact with the methyl headgroups of the self-assembled monolayer.28 In addition topolymer surfaces, MD has also been used to explain the SFGspectra of interfacial water29 and aqueous solutions.30 In thisstudy, we have combined SFG, all-atom MD simulations, andab initio calculations to resolve the open questions regardingthe molecular structure of PMMA surfaces. The results of thiswork are divided into two papers. In this paper, we discuss theexperimental SFG results as a function of polymer tacticity andtemperature. In addition, we have used MD and ab initio resultsto calculate the SFG spectra for PMMA in SSP and SPSpolarization and compared them with the experimental results.In the second paper (paper II), we discuss the details of theMD simulation and also conclude with a more realistic pictureand in-depth analysis of the PMMA surface as a function ofpolymer tacticity and temperature.31

■ EXPERIMENTAL SECTIONMaterials and Sample Preparation. Syndiotactic PMMA of Mw

= 21 100 g/mol (PDI ≤ 1.03) and Mw = 467 000 g/mol (PDI ≤ 1.06)was purchased from Scientific Polymer Products. Since the SFGspectra features for 21 100 g/mol PMMA and 467 000 g/mol PMMAare found to be the same, the spectra shown for syn-PMMA in thisstudy are all from 21 100 g/mol PMMA samples. Isotactic PMMA ofMw = 250 000 g/mol was purchased from Polyscience. The d3-PMMA(Mn = 28 700 g/mol, Polymer Source, Inc.) has ester-methyl groupsdeuterated and is syndiotactic. The d5-PMMA (Mw = 27 600 g/mol,PDI ≤ 1.03, Polymer Source, Inc.) has methylene and α-methylgroups deuterated. PMMA tacticity was determined using protonNMR (Figure S1 in Supporting Information), while the tacticity of d5-PMMA cannot be determined by measuring the proton NMR spectraof ester-methyl groups.32

Sapphire prisms were used for the SFG experiments. Before spin-coating, the prisms were sonicated for 20 min in chloroform (99.9%,certified ACS, Fisher Scientific) and 20 min in toluene (99.5%, ARACS, Avantor Performance Materials). Then the prisms were driedwith N2, and the remaining hydrocarbon residues, if any, wereremoved by a final plasma treatment (Harrick Plasma, PDC-32G) for4 min. The prisms were used immediately for spin-coating the PMMAfilms. PMMA was dissolved in toluene (HPLC grade, 99.7%, AlfaAesar) of 2 wt % concentration and equilibrated overnight. ThePMMA solution was spun-coated on a sapphire prism using a spinspeed of 2000 rpm for a period of 1 min. After spin-coating, thesamples were quickly transferred into a home-built vacuum oven tominimize air-borne contamination and were annealed at 423 K for 12h under vacuum (10−5 mbar). For thickness measurement, sampleswere prepared using the same procedure on silicon wafers. The filmthicknesses of samples used in this study were ≈100 nm, measuredusing ellipsometry (J.A. Woolam Co. Inc. spectroscopic ellipsometer;control module: VB-400; monochromator: HS-190 high-speedmonochromator). The Tg’s of syn-PMMA and iso-PMMA were 402and 337 K, respectively (Figure S2 in Supporting Information,measured by differential scanning calorimetry (DSC) at a heating rateof 10 K/min). Tm of iso-PMMA was not detected by DSC, and byusing the relationship between Tm and molecular weight,33 wecalculated the Tm of iso-PMMA sample to be around 434 K. SFGspectra were collected at around 298 K (room temperature) for bothsyn- and iso-PMMA, below their Tg’s. Spectra were also collected at443 K for iso-PMMA, above its Tm, and 423 K for syn-PMMA, aboveits Tg. The high-temperature measurements were collected undervacuum (8 Torr) to reduce oxidation and degradation. Detailedinformation about the temperature controlled vacuum SFG setup canbe found in our previous publication.34

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SFG Measurements. The SFG spectra were collected using totalinternal reflection (TIR) geometry, where the incident angle can beadjusted to probe either the sapphire−polymer or polymer−airinterface. In this study we used a 60° sapphire prism and an incidentangle of 42° with respect to the surface normal to study the PMMA−air surface. Using the interference model, we have confirmed that at42° incident angle the contribution of the SFG signal from the buriedinterface is small for the conditions used in this study (SupportingInformation, Figure S10).5 SFG experimental details have beendescribed in previous publications.34,35

The theory of SFG has been explained in prior literature36−38 andwill not be detailed here. However, the formulas used for interpretingthe results of this work are outlined here.39

The SFG signal intensity in SSP and SPS polarization I(ω3 = ω1+ω2) depends on the electric-field components of the probing visiblebeam Ej(ω1) and IR beam Ek(ω2) as follows:

40

ω ω ω χ ω ω ω= + ∝ | |I E E( ) ( ) ( ) ( )ijk j k3 1 2 2 1 22

(1)

Here, χijk(ω2) (or χijk for simplicity) is a component of the second-order macroscopic susceptibility tensor, χ; where i, j, k = x, y, z (the labaxes). Ej(ω1) and Ek(ω2) represent the electric-field components onthe j and k direction for visible beam and IR beam, respectively, wherej, k = x, y, z. In this study, the SFG signal intensity was normalized tothe variation of incident IR as a function of scanning wavenumber, ω2.Each χijk is a sum of a nonresonant term and Q resonant terms (thefirst and second term of eq 2, respectively).

∑χ ω χω ω

= +− + Γ

Φ

=

A( ) e

iijk ijkq

Qijk q

q q2

NR i

1

,

2 (2)

In eq 2, Aijk,q, ωq, Φ, and Γq are the amplitude strength, resonantfrequency, relative phase of the nonresonant vibration to the resonantvibration, and damping constant, respectively, for the qth normal modevibration. χijk

NR is the nonresonant SFG susceptibility which does notvary with scanning wavenumber ω2. A total number of Q normal moderesonances are captured in the SFG spectra. The SFG spectra shownin this paper were fitted to eq 2.The Aijk,q’s have their origins in the molecular hyperpolarizability

tensor (β) components, which are as follows:41

∑β ωβ

ω ω=

− + Γ=

= il m n a b c( ) where , , , ,lmn

q

Qlmn q

q q2

1

,

2 (3)

Here, a, b, and c are axes of local symmetry coordinate, which isunique to each molecular group. The c-axis is conventionally taken tocoincide with the principal axis (or one of the axes) of each moleculargroup,42 while the a-axis has to be in the same plane with one of theC−H bonds. βlmn,q = Alm,qMn,q, where Alm,q is the lm component of theRaman polarizability tensor and Mn,q is the n component of the IRdipole moment vector.43 (Alm,q should not be confused the amplitudeAijk,q in eq 2.) Therefore, only those vibration modes that are bothRaman- and IR-active contribute to the hyperpolarizability tensor.The βlmn(ω2)’s (or βlmn’s for simplicity) can be projected on the lab

axes (xyz) by using the 27 × 27 projection coefficients Uijk:lmn.

∑β ω β ωΩ = Ω=

U( , ) ( ) ( )ijkl m n a b c

ijk lmn lmn2, , , ,

: 2(4)

ψ θ ϕΩ = Euler angles ( , , )

Note that these coefficients are a function of the Euler angles, Ω,which describe the orientation of the molecular axes (abc) with respectto the lab axes (xyz).37 (The angle ψ is the same as χ in ref 37.)The resonant portion of eq 2 is then a summation of the

appropriate (ijk) component of hyperpolarizability for all interfacialmolecules.38

∑ ∑ω ω

β ω− + Γ

= Ω=

A

i( , )

q

Qijk q

q qijk

1

,

2 molecules2

(5)

Ab Initio Calculations. A trimer of methyl methacrylate was usedas a model for calculating the molecular hyperpolarizability tensor forester-methyl, α-methyl, and methylene groups. The ab initiocalculations were performed using the Gaussian 09 suite of electronicstructure package.44 Initial input structure of a PMMA trimersurrounded by other trimers for ab initio calculations was determinedusing all-atom MD simulations. Second-order Møller−Plessetperturbation (MP2) theory combined with the basis set 6-31G(d)were employed in order to account for electron correlation effects.45 Atwo-layer ONIOM approach46,47 was then used for full optimization ofmolecular geometries. For the two-layer ONIOM calculations,ONIOM (MP2/6-31G(d):UFF) scheme, quantum mechanics wasused for the central methyl methacrylate unit and molecular mechanicsfor the remaining atoms. After a full optimization, vibrationalfrequencies were computed specifying “Freq = Raman” in the rootsection to account for both Raman and IR intensities using the sameONIOM method. From the central methyl methacrylate unit, both thedipole derivatives and the polarizability derivatives were obtained foreach vibrational mode in the calculation coordinates. Standard Eulertransformation matrices were used to transform these derivatives tothe local symmetry coordinates (a, b, and c) to obtain βlmn. Thenhyperpolarizability matrices, βijk, were calculated. The local symmetryaxes were chosen in accordance with their reduced vibrationalsymmetry. The c-axis was determined by vector addition of the C−H bond vectors on the same group. For the α-methyl and methylenegroups, the a-axis was chosen to be in the same plane with the C−Hbond, where the H atom, among all the H atoms from the samemolecular group, was the closest to the two oxygens of the estergroups. For ester-methyl groups, the a-axis was chosen to be in thesame plane with the C−H bond, where the H atom was furthest awayfrom the carbonyl oxygen. The b-axis was then determined and wasperpendicular to the a- and c-axes. The calculation showed that thesymmetric vibrations of α-methyl and ester-methyl were groups nolonger strictly C3v symmetry, and similarly the methylene symmetricvibration no longer retained its C2v symmetry.

Molecular Dynamics Simulation and SFG Spectra Calcu-lation. All-atom MD simulations were used to determine theorientation distribution of molecular groups (methylene, α-methyl,and ester-methyl) in a free-standing PMMA thin film. The surfacelayer thickness was determined to be around 1 nm based on moleculargroup density and orientation depth profiles. Simulation details areprovided in paper II of the joint publication which mainly focuses onresults obtained using MD simulations.31 To calculate the SFG spectra,the molecular hyperpolarizability was transformed from molecularlocal symmetry coordinate (a, b, and c) to the laboratory coordinate(x, y, and z) (eq 4). Each Aijk was calculated from βijk according to eq5. Finally, the SFG spectra was calculated using eqs 1 and 2. As thelocal electric field and the Fresnel factors are the same for ester-methyl,α-methyl, and methylene, |χijk(ω2)|

2 was taken to be proportional tothe SFG intensity in SSP and SPS polarization. The differences in thevibrational frequencies for symmetric vibrations (methylene, α-methyl,and ester-methyl) calculated from ab initio are within 3−5 cm−1

compared with the experimental values listed in Table 1. However, thedifferences were much larger for asymmetric vibrations (≈ 30−60cm−1). Because the accuracy of frequencies for asymmetric stretchingvibrations is not exactly the same as those measured using SFG, we

Table 1. Suggested PMMA Vibration Assignments6,48−51,54

wavenumber/cm−1 assignmenta

2850−2860 h/f(OCH3), h/f(CCH3), f(CH2)2880−2890 h/f(OCH3), h/f(CCH3)2930−2940 h/f(OCH3), s(CH2)2950−2960 s(OCH3), s(CCH3), as(CH2)2985−2995 as(OCH3), as(CCH3)3016 as(OCH3)

ah: harmonic vibration; f: Fermi related; s: symmetric stretch; as:asymmetric stretch.

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have used the experimentally measured peak assignments forcalculating the theoretical SFG spectra in SSP and SPS polarizations.

■ RESULTS AND DISCUSSIONIn this section, we first discuss the SFG results for iso-PMMAand syn-PMMA at solid and melt state. Second, the orientationdistribution of the methylene, α-methyl, and ester-methylgroups from MD simulations will be discussed. The resultsfrom the hyperpolarizability calculations are discussed in thesection on ab initio calculations. Finally, we will compare theSFG spectra calculated using MD simulations and ab initiocalculations with experimental results.Experimental SFG Spectra of iso-PMMA and syn-

PMMA. Figure 1 shows SFG spectra of iso-PMMA (A) andsyn-PMMA (B) in PPP, SPS, and SSP polarization. The datapoints shown as circles were collected at 298 K for both iso-and syn-PMMA in the solid state, below the Tg of both iso- andsyn-PMMA. The high-temperature data shown as squares werecollected at 443 K for iso-PMMA and 423 K for syn-PMMA, toensure that both polymers are in the melt state. The SPS andSSP spectra were scaled by a factor of 50 and 4, respectively, forcomparing the differences in spectral features as a function ofpolarization. Solid lines in Figure 1 are fits to the SFG spectrausing eq 2. The fitting parameters are provided in theSupporting Information (Table S2). It is important to notethat the SFG spectra in all three polarization combinations aresimilar for iso- and syn-PMMA (comparing Figures 1A and 1Bat the same temperature). The magnitudes of the SFG intensityfor iso- and syn-PMMA were comparable. In addition, the SFGspectra have similar features in the solid and melt states forboth iso- and syn-PMMA. In the PPP spectrum, a strong peakat 2950 cm−1 and several weak peaks from 2850 and 2920 cm−1

are observed. In the SSP spectra, 2955 cm−1 appears to be theonly dominant peak. In the SPS spectra, a broad peak centeredbetween 2980 and 2990 cm−1 is asymmetric in shape whichindicates signal interferences from nonresonant baseline andpotentially from a trace amount of adsorbed water.We have used previously published IR, Raman, and SFG

results for PMMA and partially deuterated PMMA for assigning

the peaks in the SFG spectra.6,48−52 The symmetric vibration ofester-methyl groups is assigned to 2950 cm−1. However, thetwo degenerate asymmetric vibrations assignments are still notresolved based on the IR and Raman measurements.48,49,51 Wehave assigned them to be 2990 and 3016 cm−1 based on SFGresults.6,53 The methylene symmetric and asymmetric vibra-tions are assigned to 2930 and 2960 cm−1, respectively.48−51

For α-methyl groups the assignments are not as straightfor-ward, and the symmetric and asymmetric vibrations have beenassigned to 2950 and 2995 cm−1, respectively.50 However, thepeaks at 2930, 2958, and 2995 cm−1 have also been assigned tothe symmetric and in-plane and out-of-plane asymmetricvibrations of α-methyl groups.51 The SFG experiments by Liuand Messmer observed only one peak at 2948 cm−1 in the SSPspectra for ester-methyl deuterated PMMA.52 In addition,polarized IR54 and Raman48 spectra indicated that the 2950cm−1 peak is due to a symmetric vibration. These twoobservations suggest that the 2950 cm−1 peak is due to thesymmetric vibration of α-methyl groups and the two degenerateasymmetric vibrations are too close and observed as a broadpeak around 2995 cm−1. Previous studies on d3-PMMA (ester-methyl group deuterated PMMA) have assigned the 2950 cm−1

peak to the symmetric α-methyl vibration.50,52,54 Thus, thedifferences in the assignment could be due to the mutualinfluence between methylene vibrations and α-methylvibrations. Our peak assignments are summarized in Table 1.Since the peak intensities and absorption frequencies are verysimilar in both IR and Raman spectra for both iso-PMMA andsyn-PMMA, we have used the same peak assignments for bothtacticities.48,54

Table 1 shows that the peaks for methylene, α-methyl, andester-methyl groups are very close to each other. Therefore, tohelp in identifying the origin of the peaks in the SFG spectra,we have also collected SFG spectra for partially deuteratedPMMA: d5- and d3-PMMA (Figure 2). These spectra werecollected in both the PPP and SSP polarizations at 298 K.Dramatic differences are observed in the spectra for d5- and d3-deuterated PMMA. The spectral features and SFG intensity ford5-PMMA are very similar to those collected for nondeuterated

Figure 1. SFG spectra of iso-PMMA (A) and syn-PMMA (B) in PPP, SPS, and SSP polarization. The spectra were collected at the solid state at 298K (circles) and at melt state (443 K for iso-PMMA and 423 K for syn-PMMA) (squares). Solid lines are fits to the experimental data using eq 2. SPSand SSP spectra were scaled by a factor of 50 and 4, respectively.

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PMMA (Figure 1). The SFG intensity for d3-PMMA was muchweaker and the symmetric vibration of α-methyl at 2950 cm−1

appears as an inflection point rather than a maximum point,indicating interferences between weak resonant and non-resonant signals.55 This observation confirms our assignmentof the peak around 2950 cm−1 in PPP and SSP polarization tobe mainly due to the symmetric vibration of ester-methylgroups. From the SFG spectra it appears that the PMMAsurface is composed of ester-methyl groups, while the backbonemethylene and α-methyl groups are disordered or not presentat the PMMA/air surface. However, this is misleading becausethe assignment for the α-methyl groups is very similar to that ofester-methyl, and all factors such as differences in the molecularhyperpolarizability, surface density, and orientation distribution

may influence the magnitude of the SFG peak. Therefore, wecannot use the SFG results alone to determine the surfacecomposition and molecular structure of the PMMA surface.

MD Results for PMMA Surface. We have used all-atommolecular dynamics simulation to determine the distribution oftilt angle from the surface normal, θ, and surface numberdensity of methylene, α-methyl, and ester-methyl groups foriso- and syn-PMMA. Figure 3 compares the orientationdistribution of all the molecular groups within the top 1 nmsurface layer for iso- and syn-PMMA at 300 K (A) and 480 K(B). Instead of using absolute surface number count as the y-axis, we normalized the number count at each tilt angle by thetotal number of each molecular group in the surface layer,which results in the probability of finding that molecular groupat that tilt angle. For calculating the distribution, we haveassumed that the molecules are isotropic in the other two Eulerangles. Therefore, for an random orientation, the distributionwill be broad and centered around 90°. This is what we observein the center of the PMMA film. Interestingly, these angulardistributions at 300 and 480 K are broad in nature and arequalitatively similar to each other. For ester-methyl and α-methyl the most probable orientation angle is less than 90°,suggesting that the majority of the ester-methyl and α-methylgroups are pointing toward the air. In comparison, thedistribution for methylene groups is much more broader, andthe average tilt angle is centered near 90°, indicating a randomdistribution. It is important to note that no crystallization ofPMMA was observed in the MD simulations due to the longsimulation time requirements of the process which, at thisstage, is inaccessible with all-atom simulations. However, wecan still compare the experimental and theoretical resultsbecause the surface is expected to be amorphous based on thegrazing X-ray diffraction measurements for iso-PMMA thinfilms.7

We have calculated the average cos(θ), ⟨cos(θ)⟩, for all themolecular groups within the 1 nm surface region to representan average orientation of these molecules (Table 2). We havealso calculated the composition of each molecular group at the

Figure 2. SFG spectra of d5-PMMA (squares) and d3-PMMA (circles)in PPP and SSP polarization at room temperature.

Figure 3. Orientation distribution data for ester-methyl (solid line), α-methyl (dotted line), and methylene (dashed line) at 300 K (A) and 480 K(B) for iso- and syn-PMMA.

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surface by normalizing its number count (in the 1 nm surfaceregion) to the total number count of all three molecular groupsin the same region, which is represented as C. In addition, weshow in Table 2 the product of each C and the corresponding⟨cos(θ)⟩, which serves as a good benchmark to judge therelative magnitude of the SFG signal that we should expect foreach molecular vibration by assuming that these moleculargroups to have similar hyperpolarizability values. Thisassumption is not critical if we only compare the results as afunction of tacticity and temperature for the same moleculargroup. We will discuss the hyperpolarizability calculations inmore detail in the next section. At 480 K, for iso-PMMA, the⟨cos(θ)⟩ of ester-methyl (OCH3), 0.55, is larger than that of α-methyl (CCH3), 0.41, which clearly indicates that the ester-methyl groups tilt more toward the surface normal than the α-methyl groups. Interestingly, for syn-PMMA the differencesbetween α-methyl ⟨cos(θ)⟩, 0.53, and ester-methyl ⟨cos(θ)⟩,0.54, are small. For both iso- and syn-PMMA, the values of⟨cos(θ)⟩ for methylene (CH2) are close to zero, indicatingdisordered methylene groups on the surface. In addition, foriso-PMMA, the surface molecular group composition of ester-methyl is 0.46, which is much higher than that of α-methylgroups, 0.29, while this difference is again smaller for syn-PMMA. The number count of methylene is the lowest for bothiso- and syn-PMMA. Based on the product of ⟨cos(θ)⟩ andmolecular group composition C, the SFG intensity of ester-methyl groups should be higher than that of α-methyl groups,and these differences should be larger for iso-PMMA than forsyn-PMMA (Table 2). Calculation results at 300 K suggest thesame trend. However, the hyperpolarizability of ester-methyland α-methyl may not be the same because their dipolederivatives could be different,56 and this analysis is discussedfurther in the next section.Ab Initio Calculation To Determine Molecular Hyper-

polarizability. Both the dipole moment and polarizabilityderivatives for normal mode vibrations were calculated, andtheir values after transformation into the local symmetrycoordinate of each molecular group are provided in Table S3 ofthe Supporting Information. The atom displacement analysisshows that the symmetric vibrations of both ester-methyl andα-methyl groups are distorted, which breaks their C3vsymmetry. The distortion may be caused by the interactionbetween the oxygen and hydrogen atoms of these methylgroups which results in the hydrogen atoms stretchingdifferently, depending on their distance from the oxygenatoms. We also observed that the absolute values of dipolederivatives along the c-axis in the local symmetry coordinate ofα-methyl were smaller than that of ester-methyl. Previous IRstudy of methyl group adjacent to different chemical groups

showed that the IR peak intensity, which is a measure of itsdipole derivative, has the following trend: ICH3−CO < ICH3−O <

ICH3−CH2. Because carbonyl is a strong polar group, it tends to

withdraw electrons from adjacent methyl or methylene groupsand reduces the magnitude of the dipole derivative.57 Theseobservations are consistent with the relative IR peak intensitiesof methyl acetate vibrations obtained both experimentally andusing normal-mode analysis.56,58 For PMMA, α-methyl groupsare not directly connected to the carbonyl groups; however, thebridging atom, a quaternary carbon, could still pass on theelectron-withdrawing effects to the nearby α-methyl andmethylene groups, which reduces the dipole derivative of thesymmetric vibration of α-methyl and methylene groups.57

Using our ab initio results, we have calculated the molecularhyperpolarizability tensor for methylene, α-methyl, and ester-methyl groups.Because it is difficult to directly compare the differences in

the molecular hyperpolarizability, we show an example onseparately identifying the effect of molecular hyperpolarizability,orientation distribution, and surface number density onvibration amplitude strength and SFG intensity. Here wecalculate the ratio of amplitude strength for the symmetricvibrations of α-methyl and ester-methyl, Ayyz,sCCH3

/Ayyz,sOCH3, by

using their individual molecular hyperpolarizability but thesame orientation distribution and surface number density(Table 3). This results in 29% reduction in the amplitude

strength for the α-methyl groups due to their lowerhyperpolarizability values. Then by only using the same surfacenumber density for both α-methyl and ester-methyl groups, wecalculate the combined effects of differences in molecularhyperpolarizability and orientation distribution on amplitudestrength ratio. This results in an overall reduction of α-methylsymmetric vibration amplitude strength to 59% for iso-PMMAcompared to 71% for syn-PMMA. Because the numberdensities of these two groups are also different, when wecorrect for all the three parameters, we obtain a reduction inamplitude strength to 33% for iso-PMMA compared to 55% forsyn-PMMA. Converting the amplitude strength to the ratio ofthe SFG intensity, we expect the SFG intensity of the α-methylgroups to be only 11% and 31% of the ester-methyl signals foriso-PMMA and syn-PMMA, respectively. Therefore, thesecalculations explain why in the SFG measurements we expect toobserve much weaker signal for the α-methyl symmetricvibration compared to the ester-methyl symmetric vibration,even though the molecular group orientation and surfacenumber density may not be significantly different, especially inthe case of syn-PMMA. The direct comparison between theexperimental and theoretical results is presented in the nextsection.

Calculation and Comparison of SFG Spectra Obtainedfrom MD and ab Initio Results. We have used the

Table 2. Averaged cos(θ) (⟨cos (θ)⟩), Fraction of theMolecular Group Composition (C), and Their Product forEach Molecular Group within the Top 1 nm Fraction ofSurface Region

⟨cos(θ)⟩ C ⟨cos(θ)⟩C

iso syn iso syn iso syn

300 K OCH3 0.55 0.55 0.43 0.40 0.24 0.22CCH3 0.31 0.54 0.31 0.36 0.10 0.19CCH2 0.10 0.04 0.26 0.24 0.03 0.01

480 K OCH3 0.55 0.54 0.46 0.43 0.25 0.23CCH3 0.41 0.53 0.29 0.34 0.12 0.18CCH2 0.09 0.17 0.25 0.23 0.02 0.04

Table 3. Effects of Hyperpolarizability (β), Orientation (θ),and Number Count (N) on the Magnitude Strength andIntensity Ratio of the Symmetric Vibration of α-Methyl tothe Symmetric Vibration of Ester-Methyl

Ayyz,sCCH3/Ayyz,sOCH3

Issp,sCCH3/Issp,sOCH3

β β + θ β + θ + N β + θ + N

iso-PMMA 0.71 0.53 0.33 0.11syn-PMMA 0.71 0.71 0.55 0.31

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distribution of the Euler tilt angle (θ) from MD simulations,the values of the molecular hyperpolarizability computed fromthe ab initio calculations, and the peak assignments summarizedin Table S4 of the Supporting Information to compute the SFGspectra in SSP and SPS polarization for iso-PMMA and syn-PMMA at 480 K (Figure 4A,B, dotted line). We have also

calculated the SSP spectra of both d5-PMMA and d3-PMMA(Figure 4C, dotted line). These spectra incorporate thecontributions from both symmetric and asymmetric vibrationsof all the three molecular groups: methylene, α-methyl, andester-methyl. We have assumed here that the molecules areisotropic in the other two Euler angles (ψ and ϕ). Although it isstill challenging to determine the peak width and nonresonantamplitude strength directly from MD simulations and ab initiocalculations, we estimate each vibration peak width by rescalingthe corresponding IR peak width with the ratio determined bynormalizing the IR peak width to the SFG peak width of ester-methyl symmetric vibration, which is the strongest peak in bothIR and SFG spectra. The nonresonant amplitude strength usedfor calculation is obtained by normalization to the resonantamplitude strength based on the ratio determined experimen-tally. For comparing the spectral features, we have plotted inFigure 4 the SPS data rescaled by a factor of 12.5 (the samerelative ratio we used in Figure 1). To compare the theoreticaland experimental SFG spectra, we rescaled the theoretical

amplitude strength to match that of the experimental resultsobtained for the SSP polarization. The same rescaling factorwas used for the SPS amplitude strength. For all cases, thecalculated SSP and SPS spectra have the same dominant peaksas the experimental ones. For iso- and syn-PMMA the peak at2955 cm−1 dominates the SSP spectra. As expected, asymmetricvibrations at 2990−3016 cm−1 are too weak in intensity to beobserved in SSP polarization. In SPS spectra, the asymmetricpeaks cannot be resolved as individual peaks and results in abroad peak around 2985 cm−1. To quantitatively compare therelative strength of the SSP and SPS spectra, we have alsocalculated the ratios of Aq(2955 cm−1, SSP)/Aq(2985 cm−1,SPS) to be 3.9 and 4.2 for iso- and syn-PMMA, respectively(Table S2, Supporting Information). We obtained the ratio of3.6 and 3.2 for iso- and syn-PMMA, respectively, from the MDresults. For the MD results we have included both the α-methyland ester-methyl symmetric vibration amplitude strengths tocalculate the combined Aq at 2955 cm−1 in SSP, included theirasymmetric vibration amplitude strengths for the Aq at 2985cm−1 in SPS, and excluded the asymmetric ester-methyl peak at3015 cm−1. A good match between the MD and experimentsfor SPS polarization suggests that the MD results are capturingnot only the spectral features correctly but also the relative ratioof the amplitude strengths for SPS and SSP polarizations.However, the broad featureless signals between 2800 and 2950cm−1 in the experimental SSP spectra of d3-PMMA are notcaptured in the theoretical prediction because in ourcalculations we have not included the Fermi-related vibrations,which are usually observed in SSP polarization.59 In addition,the weak SFG signal for d3-PMMA are strongly influenced bythe interference with the nonresonant background signals andpeaks from potentially adsorbed water.Each individual vibration peak of the three molecular groups

that contributed to SSP and SPS SFG spectra are shown inFigure 5 for both iso- and syn-PMMA. For both symmetric(dominant in SSP) and asymmetric vibrations (dominant inSPS), the SFG peak intensity from the α-methyl groups ismuch smaller than that from ester-methyl groups, as discussedbefore. In addition, the α-methyl peak intensity for syn-PMMAis stronger compared to iso-PMMA due to higher surfacenumber density and lower tilt angles with respect to the surfacenormal. However, we were unable to extract these informationfrom the SFG spectra due to the weak amplitude strength of α-methyl group vibrations and overlapping peak assignments ofα-methyl and ester-methyl groups. The contribution from themethylene groups is very small for both iso- and syn-PMMA inSSP and SPS polarizations. We calculated the SFG spectra at300 K for both polymers (Figures S7 and S8 in SupportingInformation), and no obvious spectral differences wereobserved as a function of temperature. We have also calculatedthe SFG spectra at 480 K using the alternate assignment for α-methyl groups at 2930 cm−1 (symmetric) and 2950 cm−1

(asymmetric). The theoretical results do not match experi-ments (Figure S9, Supporting Information), supporting theassignment of 2950 cm−1 for α-methyl symmetric mode. Wewould like to also point out that there are significant differencesin the surface structure as a function of tacticity (the complexbehavior of atactic-PMMA and this is discussed in paper II ofthis study31). However, these differences are not obvious in theSFG spectra because of the similarity in the peak assignmentsof α-methyl and ester-methyl groups and lower molecularhyperpolarizability of the α-methyl in comparison to the ester-methyl groups.

Figure 4. Calculated SFG spectra (dotted line) in SPS and SSPpolarization for iso-PMMA (A) and syn-PMMA (B). Calculated SFGspectra (dotted line) in SSP polarization for d5- and d3-PMMA (C).Experimental spectra are also shown as circles.

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Finally, we would like to compare these new results for iso-PMMA and syn-PMMA with those reported previously. First,the SFG results match with those reported in refs 6 and 19. Thedifference in the PPP spectra compared with ref 6 are due tothe differences in the experimental geometry (internalreflection geometry in this work and external reflectiongeometry in ref 6). The differences in the spectral featuresobserved in the SSP spectra for d3-PMMA, and the resultsreported in ref 19 could be due to different contributions of thenonresonance component to the overall SFG signal because ofthe differences in the substrates and SFG geometry used inthese two studies. However, the combined results from theMD, ab initio, and SFG clearly show that the α-methyl groupsare also ordered rather than oriented in the surface plane. Themore recent study by Tanaka et al.10 showed that the annealingtemperature had a substantial influence on the surface structurewhere methylene groups became more ordered at the surface.The results from the same group also indicated significantdifferences in the SFG spectra between iso- and syn-PMMA.These differences were explained by the difference in theordering of the methylene groups in the two systems. Here, wehave found the SFG spectra to be independent of temperatureand also tacticity. The MD results show differences in orderingbetween the α-methyl groups rather than methylene groups as afunction of tacticity. The MD results also show that themethylene groups are disordered at the surface, independent oftacticity and temperature, which suggests that the slowrearrangement of PMMA chains upon annealing cannot explainthe differences in the SFG results observed in previous studies.We are unable to explain the differences in these results, andperhaps this may be due to differences in polymer samples orpreparation conditions. More detailed analysis of the surfacestructure using MD simulation are provided in paper II of thisstudy.31

■ CONCLUSIONSWe have used SFG spectroscopy, all-atom MD simulations, andab initio calculations to study the molecular structure of PMMAsurface as a function of tacticity and temperature. The SFGspectra show only one major peak at 2952 cm−1 in SSP andPPP polarization, which suggests ordered ester-methyl groupsat the surfaces of both syn- and iso-PMMA. SFG spectra arevery similar for both iso- and syn-PMMA at both melt and solidstate. MD simulations show that both ester-methyl and α-methyl groups are ordered at the surface of syn- and iso-PMMA, even though experimental results show only onedominant peak in the SFG spectra. The syn-PMMA showsmuch higher orientational order of α-methyl groups incomparison to the iso-PMMA. In contrast, the methylenegroups are less ordered for both iso- and syn-PMMA. The SSPand SPS spectra were calculated based on the orientationdistribution of molecular groups determined by MDsimulations and the molecular hyperpolarizability tensor byab initio calculations. The SFG spectra calculated using theseresults match with the experimental data. The weak SFG peaksfor α-methyl vibrations overlap with strong ester-methylvibration peaks. Our work suggests that all four parameters(molecular hyperpolarizability, orientation distribution, surfacenumber density, and overlapping peak assignment) arenecessary for developing a comprehensive picture of molecularstructure at polymer surfaces. This study for the first timehighlights the advantages of using MD simulations and ab initiocalculations in conjunction with SFG to study polymer surfaces.This study also highlights that the SFG results alone are notsufficient in interpreting the molecular structure of polymersurfaces.

■ ASSOCIATED CONTENT*S Supporting InformationProton NMR spectra for iso-, syn-, and d3-PMMA, DSC curvesfor iso- and syn-PMMA, SFG spectra fits, dipole derivatives,

Figure 5. Figure shows the results of the calculated individual peak intensity for α-methyl, ester-methyl, and methylene groups to the SSP spectra (A,C) and SPS spectra (B, D). The results for iso-PMMA are shown in panels A and B, and syn-PMMA are shown in panels C and D. Color codes areused to indicate symmetric ester-methyl vibration (blue), symmetric α-methyl vibration (red), symmetric methylene vibration (black), asymmetricester-methyl vibrations (green and orange), asymmetric α-methyl vibrations (purple and yellow), and asymmetric methylene vibration (pink).

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polarizability derivatives, and hyperpolarizability tensors, IR andRaman spectra for d3-, d5-, and nondeuterated PMMA,parameters used in spectra calculation, and calculated SFGspectra for iso- and syn-PMMA at 300 and 480 K using analternate spectral assignments. This material is available free ofcharge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: ali4@uakron.edu (A.D.).

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We acknowledge the financial support from National ScienceFoundation (DMR-1105370 (A.D.), DMR-1006764 (A.D.),and DMR-0847580 (M.T.)). We appreciate the help fromJukuan Zheng, Shuangyi Sun, and Xiaoran Liu for the NMRcharacterization, the help from Nishad Dhopatkar for IRcharacterization, and the help from Gaurav Amarpuri forRaman characterization, which are shown in the SupportingInformation. We also thank Edward Laughlin for building thetemperature control stage as well as Alankar Rastogi for thehelpful discussion on ab intio calculations.

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