Structure and Dynamics of Octamethyl-POSS Nanoparticles

Article pubs.acs.org/JPCC

Structure and Dynamics of Octamethyl-POSS Nanoparticles Niina Jalarvo,†,‡ Olivier Gourdon,‡,& Georg Ehlers,§ Madhusudan Tyagi,∥ Sanat K. Kumar,⊥ Kerwin D. Dobbs,# Robert J. Smalley,# William E. Guise,# Anibal Ramirez-Cuesta,‡ Christoph Wildgruber,‡ and Michael K. Crawford*,# †

Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS), Outstation at Spallation Neutron Source (SNS), Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6473, United States ‡ Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6475, United States § Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6475, United States ∥ NIST Center for Neutron Research, Gaithersburg, Maryland 20879-8562, and Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, United States ⊥ Department of Chemical Engineering, Columbia University, New York, New York 10027, United States # DuPont Central Research and Development, Wilmington, Deleware 19880-0400, United States S Supporting Information *

ABSTRACT: Polyoligosilsesquioxanes (POSS) are a large family of Si−O cage molecules that have diameters of 1−2 nm and can be viewed as perfectly monodisperse silica nanoparticles. POSS can be synthesized with a wide variety of functional ligands attached to their surfaces. Here we report the results of a comprehensive study of the crystal structure and ligand dynamics of one of the simplest POSS nanoparticles, octamethyl-POSS or Si8O12(CH3)8, where the central Si8O12 cage is surrounded by eight methyl ligands. Neutron powder diffraction data highlight the presence of strongly temperature-dependent methyl group rotational dynamics. Vibrational spectra were measured using Raman and inelastic neutron scattering techniques, and the results of the measurements were compared with the predictions of density functional theory calculations. In particular, the inelastic neutron scattering spectra show the fundamental and first overtone transitions of the methyl torsional vibrations; these transitions are forbidden in both Raman and infrared spectroscopy for the molecule with its ideal octahedral symmetry. The energies of these transitions are used to determine the height of the torsional energy barrier. Direct measurements of the methyl group dynamics using quasielastic incoherent neutron scattering provide the hydrogen atom jump distance and the activation energy for rotation of the methyl groups. Together these results provide a detailed picture of the structure and ligand dynamics of this POSS molecule.

1. INTRODUCTION

10 nm). For these reasons, POSS nanoparticles have elicited much interest in the nanoscience community.1−5 In the pure state at room temperature different POSS exist as crystalline solids, amorphous solids, or even liquids, depending upon the nature of the organic ligands attached to the Si atoms. Large flexible ligands tend to discourage crystallization and lower the POSS melting temperature, but smaller ligands often lead to highly crystalline materials. The smallest possible ligand is of course hydrogen, and the structure of the crystalline POSS of formula H8Si8O12 (H-POSS) was previously solved using both X-ray6 and neutron diffraction.7 The crystal structures of a number of other POSS molecules have also been investigated as powders or single crystals using X-ray diffraction.1 To our knowledge, however, structure refinement based upon neutron

Polyoligosilsesquioxanes (POSS) are molecules composed of a silicon−oxygen cage (Si8O12) in which, for example, Si atoms occupy the corners of a cube and oxygen atoms are located on the edges (Figure 1). Each Si atom is bonded to three oxygen atoms but may have any one of a wide variety of potential ligands attached to the fourth position. The choice of ligands provides many useful properties, including selective solubility in organic or aqueous solvents, the ability to be dispersed in many polymers, and specific chemical reactivity that can be used to directly incorporate the POSS molecules into polymer backbones or side groups.1,2 POSS molecules can also be viewed as very small, perfectly monodisperse silica nanoparticles, with typical diameters on the order of 1−2 nm. Thus, they can be considered the smallest possible silica nanoparticles, with sizes that fall between typical solvent molecules (diameters of 0.2−0.5 nm) and the smallest commercially available silica nanoparticles (diameters generally greater than © 2014 American Chemical Society

Received: December 13, 2013 Revised: February 6, 2014 Published: February 7, 2014 5579

dx.doi.org/10.1021/jp412228r | J. Phys. Chem. C 2014, 118, 5579−5592

The Journal of Physical Chemistry C

Article

Figure 1. (a) View of the crystal structure of M-POSS looking down the hexagonal c axis. Si8O12 cages are represented as red cubes. Carbon atoms are black, and hydrogen atoms are yellow. Oxygen atoms have been omitted for clarity. Unit cell outline is shown in white. (b) M-POSS molecular structure at T = 12 K. Si atoms (blue) and oxygen atoms (red) form a cube-like cage, and the eight methyl (CH3) groups bonded to the Si atoms are shown in black (carbon atoms) and yellow (hydrogen atoms). H1 atoms are associated with the methyl groups that have C3 symmetry, while H2, H3, and H4 atoms belong to the methyl groups with C1 symmetry. Sizes of the atoms reflect the magnitudes of their thermal parameters. Positions of the H atoms were refined using anisotropic displacement parameters (ADPs). (c) M-POSS molecular structure at T = 300 K. Note the large hydrogen atom ADPs due to the presence of large amplitude torsional motions of the methyl groups. Si1 atoms are the larger blue spheres.

between the POSS molecules and the polymer chains. In combination with computational studies, vibrational and quasielastic spectra for POSS molecules dispersed in polymers could thus be used to determine the intermolecular contributions to the ligand torsional potential energy surfaces. Such characterization of POSS−polymer interactions would ultimately lead to a deeper understanding of the factors that control nanoparticle dispersion in polymer nanocomposites. In this article we describe the results of a comprehensive study of the structure and dynamics of the octamethyl-POSS (M-POSS) molecule Si8O12(CH3)8, where the eight ligands are methyl groups (Figure 1). This study utilized a number of experimental techniques, including neutron and synchrotron Xray powder diffraction, Raman spectroscopy, and inelastic and quasielastic neutron scattering (INS and QENS, respectively). Several earlier studies reported the results of X-ray diffraction measurements of M-POSS at room temperature,8,9 and one study described an electron diffraction determination of the structure in the gas phase.10 Our structural study goes well beyond these earlier results since neutrons scatter from

diffraction data has not been reported for any POSS other than the H-POSS molecule. POSS ligand dynamics have been explored computationally in a study of a POSS molecule whose ligands were isobutyl groups.5 Raman, NMR, and X-ray powder diffraction data, together with molecular dynamics simulations, provided evidence for rapid ligand dynamics leading to a structural phase transition at T = 330 K. However, important parameters that characterize the ligand dynamics, such as ligand rotational energy barriers and correlation times for internal rotations, were not determined in that study. We are not aware of any other studies of POSS molecules that explicitly investigated ligand dynamics. In addition to their fundamental interest, these studies are important for applications such as polymer nanocomposites, where the POSS ligands are selected to facilitate solubility and good nanoparticle dispersion in the polymer. Since the ligand conformational energy barriers generally have a significant intermolecular component, we expect the ligand dynamics and vibrational transition energies to be sensitive to the interactions 5580



Article

Bragg−Brentano mode, scanning between 3° and 35° twotheta with 0.0015° steps. 2.4. Raman Spectroscopy. Raman spectra were collected using a Horiba-JY Raman spectrometer with a fiber optic sampling head or a Raman microscope, both methods in backscattering geometry. Excitation wavelengths of 514 or 532 nm were supplied by an Ar-ion laser or a frequency-doubled Nd:YAG laser, respectively. The M-POSS sample was contained inside a quartz tube that was placed in a liquid He cooled cryostat or a small quantity of material was placed on the microscope sample stage and Raman spectra were collected using a 100× microscope objective. Laser powers of approximately 15−45 mW at the sample were used in the cryostat, but less than 10 mW was used for measurements with the microscope. The intensity of the spectra scaled linearly with laser power but otherwise did not change. This showed that sample heating due to the laser was not significant. Raman spectra were collected at various temperatures between 4.5 and 300 K over a Raman shift range of 100−4000 cm−1. Temperature stability was better than ±1 K. 2.5. Inelastic Neutron Scattering. INS is especially sensitive to vibrations that involve displacements of H atoms due to the large incoherent neutron scattering cross-section of hydrogen (80 barns, where 1 barn = 1 × 10−28 m2) compared to either incoherent or coherent cross sections for the other elements in M-POSS.13 The incoherent cross sections for C, O, and Si are approximately zero, and the coherent cross sections are between 2 and 6 barns.13 Thus, the inelastic or quasielastic neutron scattering spectra are dominated by the incoherent scattering from hydrogen atoms, providing an ideal probe of methyl group vibrations and dynamics. INS measurements were performed on both the VISION spectrometer14 and the Cold Neutron Chopper Spectrometer15 (CNCS) at the Spallation Neutron Source at Oak Ridge National Laboratory.16 VISION is an indirect geometry spectrometer that uses a wide range of incident neutron energies to probe vibrations from the elastic limit up to energy transfers as high as 500 meV (4000 cm−1). VISION provides an approximately constant energy resolution of ΔE/E ≈ 1−2% over the entire energy range. CNCS is a direct geometry spectrometer that measures both neutron energy transfer and momentum transfer, providing a good view of the dispersion (Q dependence) of vibrational mode energies. CNCS utilizes fixed energy incident neutrons, and the energy resolution depends upon the incident neutron energy and energy transfer. CNCS data were collected using incident neutron energies of 12 and 45 meV, yielding energy resolutions at the elastic line of 0.4 and 1.6 meV, respectively. The energy resolutions at finite energy transfers are better than those at zero energy transfer. The INS measurements covered the energy range below 41 meV (330.6 cm−1) with 45 meV incident energy and below 11 meV (95 cm−1) with 12 meV incident energy, which includes the regions where the fundamental and first overtone of the methyl torsional vibrations are expected, as well as the region where the external modes are found. For data collection on VISION and CNCS, the sample consisted of 1.24 g of M-POSS placed in a 7 mm diameter Al can that was loaded into a closedcycle He refrigerator (VISION) or a liquid He cryostat (CNCS). This sample thickness yielded a fairly low transmission of 10−20% but provided a significantly better signal-tonoise ratio than thinner samples. The thick sample will lead to a significant amount of multiple scattering which can affect the intensities of peaks but will have little effect on the energies or

hydrogen atoms significantly better than do X-rays or electrons, allowing us to determine the positions and anisotropic displacements of the hydrogen atoms. The results of this study thus provide a detailed understanding of the crystal structure, molecular vibrations, and methyl group dynamics of M-POSS, one of the simplest members of the POSS family of molecules that has attracted significant scientific and technological interest.1

2. EXPERIMENTAL SECTION 2.1. Materials. M-POSS was obtained from Hybrid Plastics and used without further purification. Differential scanning calorimetry, thermal gravimetric analysis, and X-ray powder diffraction were used to characterize the material. In agreement with earlier findings,1 we observed that this material sublimed at a temperature of approximately 200 °C (see Figure S1, Supporting Information). For that reason we limited our maximum QENS measurement temperature to 350 K (77 °C), well below the sublimation temperature. 2.2. Time-of-Flight Neutron Powder Diffraction. To investigate the structure of the M-POSS system, time-of-flight (TOF) neutron powder diffraction was performed at various temperatures on a ∼900 mg M-POSS sample that was loaded in a 6 mm diameter vanadium can. Neutron data were collected at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory on the high-resolution neutron powder diffractometer POWGEN. Further information on the design of POWGEN is given in ref 11 and references found therein. Data were collected at five temperatures: 300, 200, 125, 50, and 12 K. For each temperature data was collected using two different center wavelengths (CWLs). On the basis of the actual POWGEN detector configuration, CWLs of 1.599 and 3.731 Å were chosen. The first CWL covers d spacing from 0.29 to 3.09 Å and provides accurate information on the nuclear structure as well as the atomic displacement parameters (ADPs). The second CWL covers higher d spacing from 1.65 to 8.24 Å, revealing additional nuclear reflections. The crystal structure was refined at each temperature using JANA2006 software.12 Initial refinement used the M-POSS crystal structure determined by X-ray diffraction8 as a starting model. Refinements were performed using data from the two detector banks simultaneously (each of them being associated to a different CWL data set) to obtain unit cell parameters, atomic position, and ADPs. 2.3. Synchrotron X-ray Powder Diffraction. X-ray powder diffraction data were collected at the Advanced Photon Source at Argonne National Laboratory on the 5BMC bending magnet station of Sector 5 (DND-CAT). The diffractometer is a 2-circle Huber that includes a Soller slit and Ge 220 analyzer crystal. The monochromator is a Si 111 dual-crystal configuration. Data were collected in a quartz capillary at room temperature in transmission mode and in reflection (flatplate) geometry using a closed-cycle refrigerator at T = 12 and 300 K. For the low-temperature measurements the sample was mounted on a copper plate that was installed into an Advanced Research Systems cryostat that was controlled using a Lake Shore Cryotronics model 340 temperature controller. The Xray wavelengths used were 0.70824 Å for the transmission measurements and 0.708397 Å in reflection geometry. The capillary was rotated during the measurements to improve powder averaging, but the flat plate was not oscillated during the measurements in the closed-cycle refrigerator. Data was collected using a one-dimensional solid-state detector in 5581



Article

in Figure 1a.8 Lattice constants are a = b = 12.5077(7) Å and c = 13.0995(7) Å. There are three M-POSS molecules per crystallographic unit cell (Z = 3) but only one per Bravais cell. Despite the high concentration of hydrogen in the sample (46 atom %), neutron diffraction data of high quality were collected. Figure 2 shows the observed and calculated neutron

widths of vibrational transitions. INS spectra were collected at temperatures of T = 20 K on VISION and T = 5, 200, and 300 K on CNCS. 2.6. Computation of Molecular Vibrational Frequencies and Inelastic Neutron Scattering Spectra. All calculations were performed with density functional theory (DFT) methods within the Gaussian 09 suite of programs.17 Molecular structures were first optimized at the BP86/631G(d) level and then used in subsequent analytic vibrational frequency calculations at this same level of computation to ensure that these structures were indeed equilibrium ones. The pure BP86 functional18,19 was chosen mainly because of the enhanced performance gains of optimization and vibrational frequency calculations using this functional compared to B3LYP.20,21 The computed vibrational frequencies should be nearly equivalent to the corresponding gas-phase experimental values since the accepted scale factor is near unity for this level of computation.22,23 To calculate the inelastic neutron scattering spectrum for MPOSS, vibrational eigenvectors that were generated using the DFT calculation were input to the a-CLIMAX code,24 which generated the INS spectrum that would be expected for either the indirect geometry VISION spectrometer or the direct geometry CNCS. 2.7. Quasielastic Neutron Scattering. Similar to INS, QENS is very sensitive to low-energy dynamical processes that involve the motion of hydrogen atoms due to their large incoherent neutron scattering cross-section. QENS data were collected at the backscattering spectrometer BASIS25 at the Spallation Neutron Source (SNS). The center wavelength of the incident neutron beam was λ = 6.267 Å, the full width at half-maximum (fwhm) of the energy resolution at the elastic line was 3.4 μeV, and the accessible momentum transfer range was Q = 0.2−2.0 Å−1. Data analysis was limited to a dynamic range from −100 to +100 μeV, which is free from spurious scattering. Data sets were collected at temperatures ranging from T = 13 to 350 K. The lowest temperature data was used as the instrumental resolution function. Measured spectra were corrected for detector efficiency by normalizing to a vanadium standard and then interpolated to constant values of the momentum transfer, Q. An appropriate quantity of M-POSS powder (1.169 g) was evenly distributed in an aluminum foil packet placed in an annular cylindrical can, resulting in neutron transmission greater than 90% to reduce the contribution of multiple scattering but still maintain a reasonable level of quasielastic scattering. QENS data were also collected on the high-flux backscattering spectrometer (HFBS) at the NIST Center for Neutron Research.26 A neutron wavelength of 6.27 Å was used, and data were collected in fixed window mode to measure the elastic scattering as a function of temperature. In addition, quasielastic data were collected at low temperature (4 K) to check for the possible presence of transitions due to methyl group quantum mechanical rotational tunnelling. The resolution at the elastic line of HFBS is approximately 0.8 μeV, four times higher than the resolution at BASIS. The dynamic range of the HFBS spectrometer with the configuration used was from −17 to +17 μeV.

Figure 2. M-POSS neutron powder diffraction pattern obtained on POWGEN at 300 K for center wavelengths of (a) 1.599 and (b) 3.731 Å. Black lines are the measured diffraction pattern; red lines are the calculated profiles. Black tick marks indicate the positions of nuclear reflections. The difference curve is shown below in black on the same scale.

diffraction patterns collected on POWGEN at 300 K for the two detector banks. Refinement of the neutron data, which included background coefficients, scale factors, profile functions, absorption coefficients, atomic position parameters, and atomic displacement parameters, smoothly converged to a reasonable solution with a goodness of fit (gof) value of 1.9 (Rp= 1.82%) for 64 parameters (7 atomic parameters + 57 profile parameters). Anisotropic displacement parameters (ADPs) for the hydrogen atoms were introduced, and this drastically improved the quality of the refinement. The accuracy of the ADPs depends upon the high-resolution data obtained at very low d spacing (below 1 Å), as presented in Figure 2. A similar approach was used for the refinements at lower temperatures. (Table S1, Supporting Information, summarizes the refined atomic parameters and the equivalent ADPs for temperatures of 300, 200, 125, 50, and 12 K; Table S2, Supporting Information, lists bond distances and bond angles for T = 12 and 300 K, along with ADPs for the hydrogen atoms at those temperatures; Table S3, Supporting Information, lists some important nonbonded atom−atom distances). Figure S2, Supporting Information, shows the temperature dependence of the hexagonal lattice parameters. Table 1 lists the carbon− hydrogen distances for the two different methyl groups in the rhombohedral structure. These distances are rather short, as previously observed in single-crystal8 and X-ray powder

3. RESULTS AND DISCUSSION 3.1. Crystal Structure of M-POSS from Neutron and Xray Powder Diffraction. At 300 K, M-POSS adopts a rhombohedral crystal structure with space group R-3, as shown 5582



Article

Table 1. C−H Bond Lengths and H−H Distances for C3 and C1 Symmetry Methyl Groups at T = 300 and 12 K atom−atom distance C1−H1(a) C1−H1(b) C1−H1(c) H1−H1 C2−H2 C2−H3 C2−H4 H2−H3 H2−H4 H3−H4

length (Å) at T = 300 K C3 symmetry methyl groups 0.991(19) 0.99(4) 0.99(2) 1.55(3) C1 symmetry methyl groups 1.079(14) 1.024(16) 0.96(3) 1.728(16) 1.55(3) 1.65(3)

atures, T = 12 and 300 K, were indexed using the rhombohedral unit cell determined from the neutron diffraction data. Data collected at 300 K, however, showed an additional subtle splitting of a number of diffraction peaks, indicating that at room temperature the actual symmetry is lower than rhombohedral. This distortion is too small to be detected in our neutron diffraction data. However, our neutron diffraction refinements do show that the POSS Si8O12 cages undergo a small rhombohedral distortion that also changes sign and magnitude with temperature (Figure S5, Supporting Information), becoming largest at T = 300 K. Although we have no clear explanation for this observation, it may be at least partly due to the increasing rotational freedom of the methyl groups with temperature or to the relative torsional motions of the eight O3SiCH3 moieties that comprise each M-POSS cage.7 3.2. Vibrational Spectroscopy of M-POSS: Symmetry Analysis, Raman Spectroscopy, and DFT Calculations. In addition to the structural determinations at various temperatures described above, we used Raman spectroscopy to study the molecular vibrations of M-POSS. Before discussing the Raman data, we present the symmetry analysis for the expected vibrations, first assuming perfect octahedral (Oh) symmetry for the molecule and then accounting for the reduction of symmetry in the crystal. In Table 2 we show the irreducible representations for MPOSS in Oh symmetry. Since there are 52 atoms in the

length (Å) at T = 12 K 1.040(5) 1.040(9) 1.040(8) 1.708(8) 1.080(5) 1.059(7) 1.065(7) 1.74(8) 1.752(8) 1.705(8)

diffraction9 studies, where very short average C−H bond lengths of 0.875(30) and 0.872 Å were found, respectively. A gas-phase electron diffraction study10 yielded a more reasonable C−H bond length of 1.101(7) Å. Our values in Table 1 at T = 300 K fall roughly between the X-ray and electron diffraction values. We note here that our DFT calculations give for the optimized M-POSS molecular geometry a single C−H bond length of 1.103 Å (Figure S3, Supporting Information). The data presented in Table 1 warrants some additional discussion. The C−H bond lengths are rather short compared to those of methyl groups in other compounds, and the bond lengths become shorter with increasing temperature. Similar behavior has been observed for methyl groups in other compounds and is attributed to the effect of the torsional vibrations, increasingly excited to greater vibrational amplitudes at higher temperatures, reducing the apparent bond lengths.27−31 Although it is possible to correct for this effect27,28 using rigid body methods29−31 to find C−H bond lengths that are not foreshortened by the torsional motions, we instead use our data collected at a temperature of T = 12 K, where the torsional motions are fairly small (but not negligible), to determine approximate C−H bond lengths for the two methyl groups in the structure. We are specifically interested in the C− H bond lengths since they are expected to correlate with the C−H vibrational frequencies32−35 and can thus be used to help assign specific Raman bands to the two different methyl groups (see section 3.2). Figures 1b and 1c illustrate the structures of the POSS molecules using atomic ellipsoids for refinements at 12 and 300 K, respectively. Large ADPs for hydrogen atoms, especially at 300 K, are given by the refinements (Figure 1 and Table S2, Supporting Information). The shapes of the deformations and directions of the elongations are consistent with torsional motions of the methyl groups around their 3-fold or pseudo-3fold axes. In Figure S2, Supporting Information, we show the average hydrogen mean square displacements as a function of temperature based on the neutron powder diffraction refinements (values from Table S1, Supporting Information). The hydrogen mean square displacements show a strong deviation from the linear temperature behavior expected for a harmonic Debye−Waller factor.36 Inelastic and quasielastic neutron scattering were used to directly characterize the methyl group torsional potential energy surfaces and dynamics, as described in sections 3.3 and 3.4 below. High-resolution synchrotron X-ray powder diffraction patterns (Figure S4, Supporting Information) for two temper-

Table 2. Irreducible Representations and Activities for Vibrations of M-POSS (isolated molecule) with Oh Point Group Symmetry and in the R-3 Crystal Structure (C3i molecular site symmetry)a vibrational activity Raman infrared inactive nongenuine Raman infrared acoustic

irreducible representations Oh isolated molecule 5A1g + 7Eg + 10T2g 12T1u 2A2g + 7T1g + A1u + 5A2u + 6Eu + 8T2u T1g + T1u R-3 crystal 26Ag + 26Eg 25Au + 25Eu Au + Eu

a Note that the nongenuine vibrations (T1g + T1u) in the isolated molecule, corresponding to translations (T1u) or rotations (T1g) of the whole molecule, correlate with external modes in the crystal: the T1u translations become the Au + Eu acoustic modes, and the T1g rotations become the Ag + Eg rotational Raman modes.

molecule, there will be (3 × 52) − 6 = 150 vibrational normal modes. There are 22 Raman-active and 12 infrared-active vibrational modes. The molecule has a center of symmetry, so the Raman and infrared active vibrations are mutually exclusive. Due to the high molecular symmetry, many of the vibrational modes are doubly (E) or triply (T) degenerate. In addition, a large number of modes are inactive for either infrared or Raman spectroscopy but can be measured using inelastic neutron scattering, which does not suffer from restrictions due to selection rules.37 In the crystal, the rhombohedral symmetry both removes some of the degeneracies and causes the inactive modes to become either Raman or infrared active. In Table 2 we also provide the irreducible representations and spectroscopic activities for the vibrations of M-POSS in the rhombohedral 5583



Article

Figure 3. (a) Raman spectrum of M-POSS measured at T = 300 K using 532 nm laser excitation. Note the break and change of scale for the x axis. (b) Expanded view of the low-energy region of the Raman spectrum.

there will be 48 vibrational modes in total. Considering first the C−H stretching vibrations, each methyl group will contribute one symmetric stretch vibrational mode (νs) and one doubly degenerate asymmetric stretch vibrational mode (νas). Since there are eight methyls per M-POSS molecule, we expect there to be a set of 8 vibrations that consist of various linear combinations of the 8 symmetric modes and 16 vibrations that consist of various linear combinations of the 8 doubly degenerate asymmetric modes. These C−H stretching vibrations, 24 in total, are found near 3000 cm−1 and identified in Table S5, Supporting Information. According to the DFT calculations, the asymmetric stretch C−H modes have energies of 3072 cm−1 while the symmetric stretch modes have a lower energy of 2988 cm−1. We thus assign the observed 2997 and 2978 cm−1 Raman bands to the Eg and/or T2g asymmetric stretches and the 2917 cm−1 Raman band to the A1g and/or T2g symmetric stretch. In Oh symmetry, the Eg and T2g methyl asymmetric stretch Raman bands are degenerate (Table S5, Supporting Information), as are the A1g and T2g methyl symmetric stretch Raman bands. Consistent with this expectation, we observe a single symmetric stretch band at 2912 cm −1. However, two asymmetric stretch bands appear at 2997 and 2978 cm−1. We attribute these two bands to the two different methyl groups in the M-POSS crystal structure. The two methyl groups have different average C−H bond lengths (Table 1), which will lead to different vibrational energies.32−35 Two of the eight methyl groups in an M-POSS molecule in the crystal lie on the hexagonal c axis and have C3 site symmetry, while the other six methyl groups do not lie on symmetry axes or planes and thus have C1 site symmetry. We assign the more intense band at 2978 cm−1 to the six C1 symmetry methyl groups, which have longer average C−H bond lengths (Table 1) and thus a lower vibrational energy, and the 2997 cm−1 band to the two C3 symmetry methyl groups which have shorter average C−H bond lengths (Table 1) and thus a higher energy. For C3 symmetry the three C−H bonds in the methyl group are equivalent (Table 1), leading to a single degenerate (E) vibration at 2997 cm−1. On the other hand, in C1 symmetry the degenerate E vibration should be split due to the presence of three unequal C−H bond lengths for these methyl groups (Table 1), yielding two Raman bands near 2978 cm−1. However, we show below that near room temperature rapid methyl group rotations lead to the collapse (motional narrowing) of these split bands,43,44 so only a single band

R-3 crystal structure determined using a factor group analysis.38 Since a center of symmetry is also present in the R-3 space group the Raman and infrared modes remain mutually exclusive in the crystalline phase. (The same results can also be obtained by simply using correlation tables for the irreducible representations of the Oh symmetry group and the C3i (≡ S6) point symmetry group that characterizes the site symmetry of the three POSS molecules in the R-3 space group.) An important point to note is that there will be no factor group splitting of the vibrational modes in the crystal since there is only one POSS molecule per primitive (Bravais) unit cell. In Figure 3 we show the Raman spectrum of M-POSS measured at a temperature of 293 K. In order to assign the Raman bands to specific vibrations we performed calculations of the vibrational frequencies using DFT. These calculations provide a reasonably accurate prediction of vibrational energies and can serve as a guide to band assignments. Calculations were performed for an isolated molecule with Oh symmetry, while the actual vibrational frequencies were measured for the crystalline phase with lower (C3i) molecular site symmetry. This might lead to small differences between the observed and the predicted vibrational energies. Furthermore, the reduction of symmetry from the molecular symmetry of Oh to the site symmetry of C3i may also lead to additional Raman modes. However, since the M-POSS molecular distortions shown by the neutron diffraction data are rather small, the approximation of Oh molecular symmetry should be a reasonably good one. The calculated and observed Raman vibrational frequencies for M-POSS are listed in Table S5, Supporting Information. We find that our calculated Raman energies are in better agreement with the measured Raman bands located above 1000 cm−1 if a scaling factor of 0.974 is first applied to the calculated values. Scaling was generally not found to be necessary for the BP86/ 6-31G(d) level of calculation by extensive comparisons with experimental results for a large number of molecules,22 although for higher level computations frequency scaling is often required.39,40 In any case, the accuracy of the calculated vibrational frequencies is sufficiently good to provide reliable assignments for the methyl vibrations that are the main interest of our study. The methyl group vibrations which interest us are the C−H stretches located near 3000 cm−1 and the CH3 torsional vibrations that are generally found41,42 below 300 cm−1. Each methyl group will contribute 3N − 6 internal vibrations or 6 modes (3 bond stretching and 3 bond bending vibrations), so 5584



Article

Figure 4. (a) Inelastic neutron scattering spectrum of M-POSS measured at a temperature of T = 20 K using the VISION spectrometer. (b) Calculated inelastic neutron scattering spectrum of M-POSS. Calculated vibrational frequencies were not scaled. Shown in different colors are the fundamental transitions (0−1), first overtones (0−2), second overtones (0−3), and third overtones (0−4). Also shown are the contributions due to combination bands (W1−W4).

Figure 5. (a) Dynamic structure factor S(Q,E) for M-POSS measured at T = 5 K using CNCS at SNS. Since measurements were made on a polycrystalline sample, only the absolute magnitude of Q is determined. (b) Plot of S(Q,E) summed from Q = 3 to 7 Å−1 as a function of energy. The strong, narrow v = 0 → 1 and v = 0 → 2 torsional transitions at 19.4 and 37 meV correspond to nearly dispersionless internal molecular excitations that appear in S(Q,E).

active in the crystal (Table 2) but are expected to remain weak since the molecular polarizabilities and transition dipole moments are generally not much affected by these vibrations.42 The Raman spectrum in Figure 3 shows four strong, low-energy Raman modes at 39, 64, 159, and 209 cm−1. The most likely assignments for these modes are not to methyl torsions but to SiO3 torsional and symmetric Si−O−Si bending vibrations, based upon our calculations (Table S5, Supporting Information) and comparison with the Raman, IR, and neutron spectra37,45,46 of H8Si8O12. Thus, we now turn to INS to directly measure the torsional vibrations. 3.3. Vibrational Spectroscopy of M-POSS: Inelastic Neutron Scattering Measurements and DFT Calculations of Methyl Torsional Vibrations. INS is an excellent method for determining the torsional frequencies of methyl rotors in solids.47−50 Whereas the torsional transitions are often weak in infrared or Raman spectroscopy, they are generally strong in INS spectra.51,52 This is due to the large incoherent cross-section for hydrogen, the large hydrogen atom displacements involved in the torsional vibrations, and the low frequencies at which these vibrations are typically found. These characteristics make INS ideal for measuring these

appears, but at temperatures of roughly 200 K and below we indeed observe that the 2978 cm−1 band splits into two bands. The symmetry analysis for the methyl bending vibrations is similar to that for the stretching vibrations. The bending vibrations, 24 in total, will be found in the 1200−1500 cm−1 region and are listed in Table S5, Supporting Information. Thus, the stretching and bending vibrations account for all of the methyl internal vibrations. We are particularly interested in the methyl torsional vibrations, since they are directly related to the methyl group rotations and the rotational potential energy surface. Since there are 8 methyl groups per POSS molecule, there will be 8 vibrations in the molecule that are various combinations of the individual methyl torsions. These eight torsional modes will have the following species in Oh symmetry: A2g + T1g + A1u + T2u. It is important to note that the methyl torsions are not infrared or Raman active in Oh symmetry. Of course, as described above, the M-POSS crystal actually has R-3 space group symmetry, with each of the three M-POSS molecules in the crystallographic unit cell located on sites with C3i point symmetry. A factor group38 or correlation42 analysis then shows that the torsional vibrations will become infrared or Raman 5585



Article

vibrations. For methyl groups directly attached to carbon atoms the torsions are typically found in the 25−40 meV (200−320 cm−1) region,41,42 while for methyl groups bonded to Si atoms the torsions are found between 12 and 25 meV (96−200 cm−1)52 due to generally weaker rotational potentials. In Figure 4 we show the INS spectrum of M-POSS measured using the VISION spectrometer, and in Figure 5 we show comparable data measured with the CNCS spectrometer with the incident neutron energy of 45 meV. (Data collected with 12 meV incident neutron energy is shown in Figure S6, Supporting Information.) In Figure 4 we also show the calculated INS spectrum. We used the DFT eigenvectors and eigenvalues and the aCLIMAX program to predict the intensities and locations of the peaks in the spectrum. Since the incoherent scattering from hydrogen atoms dominates the scattering from other atoms, the INS spectrum accentuates the vibrations in which the hydrogen atoms strongly participate, such as the methyl torsions. Also, since there are no selection rules for the neutron-induced vibrational transitions, all of the fundamentals, overtones, and combination bands can appear, appropriately weighted by the neutron scattering cross sections of the vibrating atoms. The calculated spectrum in Figure 4 is very similar to the measured spectrum, providing good evidence for the mode assignments we made in Table S5, Supporting Information. The torsional transition, located at 19.4 meV (157 cm−1), is the most intense band in the spectrum. On the basis of the calculated spectrum, the second most intense peak is the first overtone of the torsional transition at 37 meV. We note that the measured fundamental torsional transition energy is a factor of 1.13 higher than the value predicted by the DFT calculation. This observation can be understood since the DFT calculation is performed for an isolated molecule, but intermolecular interactions can have a significant effect on the torsional energy barrier and the torsional vibration frequency.53 The narrow widths of the torsional transitions in Figures 4 and 5 reflect the lack of frequency dispersion with wave vector displayed in the 2-D dynamic structure factor S(Q,ω) plot in Figure 5. It is also interesting that the location of the first overtone of the methyl torsion, 37 meV (298.4 cm−1), is significantly below the value of twice the fundamental transition energy of 38.8 meV (313 cm−1) expected for a simple harmonic torsional potential. We can readily account for these values using a more realistic 3-fold torsional potential energy function for the methyl groups54 V (θ ) =

V3 (1 − cos 3θ ) 2

Figure 6. Diagram of the 3-fold methyl torsional potential for MPOSS, V(θ) = (V3/2(1 − cos 3θ)) (black curve), along with a harmonic potential (red curve) that was fitted to the lower section of the 3-fold potential. Also shown are the torsional transitions that were measured using INS, the methyl rotational activation energy (Eact) measured using QENS, and the 3-fold barrier height V3.

H=

(3)

and the free rotor wave functions are given by

ψn(θ ) =

1 ±inθ e 2π

(4)

Here I = (ℏ2/2B) is the methyl rotational constant and B = 654 μeV (5.3 cm−1). Equation 2 can be solved numerically,55 and the eigenvalues for the torsional energy levels and resulting transition energies can be used to determine the value of the barrier height. This procedure yields V3 = 74.4 meV (600 cm−1 or 7.18 kJ/mol). This value for V3 accurately reproduces both the 19.4 and the 37 meV torsional transitions. Note that the torsional energy levels are 3-fold degenerate. This degeneracy will be lifted by tunnelling matrix elements between the potential energy wells to yield two levels for each torsional level, one singly degenerate and the other doubly degenerate. The tunnel splittings for the ground, first, and second excited torsional levels are also given by the calculation as 0.1, 4.9, and 94.7 μeV, respectively. The ground state tunnel splitting is less than the energy resolution of either backscattering spectrometer used in this study, and the excited state splittings are also less than the resolution of the time-of-flight spectrometer. Thus, it is not possible to use these neutron scattering techniques to measure the tunneling rates in octamethyl POSS. It is possible, however, to measure the ground state tunnel splitting using NMR techniques56 since the longitudinal relaxation times (T1) for the methyl protons are significantly shortened by tunneling. 3.4. Methyl Group Rotational Dynamics from Quasielastic Neutron Scattering. To probe the microscopic hydrogen dynamics, the temperature-dependent elastic incoherent neutron scattering contribution to the dynamic structure factor was measured on HFBS at the NIST Center for Neutron Research, operating the spectrometer in the fixedwindow scan mode.26 An important quantity derived from these data is ⟨r2⟩, the average mean-square displacement (MSD) of the atoms in the structure, which can be estimated using a Gaussian approximation57 for the elastic component of the dynamic structure factor Sel(Q,ω = 0)

(1)

where θ is the torsion angle and V3 is the height of the potential barrier, as illustrated in Figure 6. This function, in the limit of small torsional oscillations (or low vibrational excitation), can be approximated by a harmonic potential as shown in Figure 6 but rapidly deviates from the harmonic form for larger displacements. We can now use the two torsional transition energies to determine the barrier height separating the equivalent methyl group orientations. If the torsional potential is composed of the 3-fold term only the energy levels are given by the solutions of the Schrodinger equation54 Hψn(θ ) = Enψn(θ )

V −ℏ2 d2 + 3 (1 − cos 3θ ) 2 2I dθ 2

(2)

where 5586


The Journal of Physical Chemistry C Sel(Q , ω = 0) = Ae−[

Q 2Δr 2 ] 6

Article

the spectrometer’s elastic energy resolution limit, and as a result the apparent MSD increases strongly, as can be seen in Figure 7. This signals the onset of 3-fold rotational diffusion of the methyl groups within the time/energy window of HFBS, and we therefore expect significant quasielastic scattering to be present above 60 K. At temperatures above T = 150 K, the methyl rotations are very rapid and the quasielastic scattering, now broad compared to the dynamic range of HFBS, does not contribute significantly to the elastic signal. Without the contribution of the anharmonic methyl rotations, the MSD is again linear since the Debye−Waller factor behaves as expected for harmonic vibrations. The linear temperature dependence above T = 150 K thus shows that there are no additional motions occurring, other than the methyl rotations, in the temperature and Q range we explored. An example of the quasielastic data measured at BASIS at T = 200 K is shown in Figure 8 (data at additional temperatures are shown in Figure S7, Supporting Information). Quasielastic broadening was observed at temperatures from 100 to 350 K, indicating the presence of thermally activated methyl group rotations. As expected, the elastic intensities decrease and the quasielastic intensities increase at higher Q values. The reason for this behavior is that the methyl dynamics are localized in real space. The width of the QE component stays constant over the measured Q range for each temperature, also indicating localized reorientations of the methyl groups. With decreasing temperature, the width of the quasielastic component is reduced. The QENS spectra were fitted by a least-squares method using a phenomenological approach to describe the CH3 reorientations, with the following dynamic structure factor

(5)

The Gaussian approximation is valid if all the scattering atoms in the material have the same isotropic MSD, which of course is not true for M-POSS. However, the scattering is heavily weighted by scattering from hydrogen due to its large incoherent neutron scattering cross-section, so using a single MSD is in fact reasonable. Despite this simplification, the Gaussian approximation may still not be fully justified even for the hydrogen atoms in M-POSS since their MSDs are not isotropic (see Figure 1c), and there are two crystallographically distinct sets of methyl groups in the crystal which could have different MSDs. Nevertheless, we used eq 5 to extract ⟨r2⟩ values at each temperature, and the results are shown in Figure 7. The values we obtain are the MSDs within the elastic energy

Figure 7. Mean-square-displacement ⟨r2⟩ for the methyl group hydrogen atoms measured using a fixed-window scan on HFBS. The large increase above T = 60 K is due to the onset of thermally activated methyl group rotations.

⎛ 1 Δ(Q ) ⎞ Sphe(Q , ω) = f ⎜p1 δ(ω) + p2 ⎟ ⊗ R(Q , ω) ⎝ π ω 2 + Δ2 ⎠

resolution58 of HFBS (0.8 μeV), i.e., reflecting methyl rotational dynamics that are characterized by correlation times that are less than 5−10 ns. Despite the approximations in the MSD analysis, these data provide a good overview of the temperature-dependent dynamics of M-POSS. At temperatures below T = 60 K, the MSD increases linearly with temperature due to the increase of the Debye−Waller factor for the methyl hydrogen atoms, as expected for harmonic vibrations. At temperatures above T = 60 K, the methyl rotational dynamics occur on a time scale shorter than the 5−10 ns determined by

Here the key fit parameters are Δ, p1, and p2: the width of the QE component and the weights of the elastic and quasielastic components, respectively. The first term in parentheses in eq 6 represents the elastic (delta function) component, and the second term is the quasielastic (Lorentzian) component. Both components are convoluted (represented by the symbol ⊗) with the experimentally determined resolution function R(Q,ω). B(Q,ω) is the linear inelastic background that reproduces qualitatively the contribution to the spectra from very fast, and therefore very broad in frequency (or energy),

+ B(Q , ω)

(6)

Figure 8. Experimental dynamic structure factor S(Q,ω) from QENS data for M-POSS at T = 200 K for three Q values: (a) 0.3, (b) 1.3, and (c) 1.9 Å−1. Also shown are the results of fitting eq 6 to the data. Data points are shown as open circles with error bars, the elastic resolution function is the solid black line, the Lorentzian quasielastic component is shown in red, and the total fitted curve is shown in blue. In the insets the spectra are shown with the strong elastic scattering component on scale. Note the differences in vertical scale for the three main plots and the inset plots. 5587



Article

which resulted in a methyl H−H distance of 1.58 ± 0.05 Å, in good agreement with our neutron diffraction data (Table 1), which yields an average H−H distance of 1.62 ± 0.03 Å. Although this model accounts relatively well for the data and shows that the different methyl groups in the M-POSS molecule undergo similar rotations around their symmetry axes, systematic deviations between the fit and the experimental data points are observed in the low-Q region at each temperature. This is primarily due to multiple scattering, which becomes more important at low Q.59 Multiple scattering can, in principle, be accounted for in the data analysis, although not in a simple way.59 Such corrections will be small, on the order of 2−4% for the correlation times or activation energy.60 For that reason we did not correct our data for multiple scattering. The rotational diffusion of methyl groups can be treated as an activated process that is described by a simple Arrhenius law61,62

quasielastic components, and f is a scale factor. Figure 8 also shows the results of fitting eq 6 to the experimental spectra at 200 K. This function can describe the experimental data well at temperatures from 150 to 300 K. As we pointed out before, the M-POSS crystal structure contains methyl groups with C1 and C3 point group symmetries. For that reason we also tested a model with two Lorentzian functions for the quasielastic component, but the quality of the fit using this model was no better than the model with one Lorentzian. We therefore assume that, despite the different symmetries, the two methyl groups have similar rotational dynamics and rotational residence times. To determine the geometry of the reorientations of the methyl groups, the elastic incoherent structure factor (EISF) was extracted from the fits to the QENS spectra. The EISF is denoted as A0 and defined as59 A 0 (Q ) =

p1 (Q ) p1 (Q ) + p2 (Q )

(7)

Γ(T ) = Γ0e−Eact / kBT

where p1 and p2 are the elastic and quasielastic intensities, respectively. Symmetric methyl groups rotate around their C3 axes, and this motion can be described with a 3-site jump model, where the hydrogen atoms for each methyl group are located on 3 sites equally spaced on a circle. The EISF for this model is59 1 A3sites(Q ) = [1 + 2j0 (Qd)] (8) 3

(9)

where Γ(T) is the full width at half-maximum (fwhm) of the quasielastic scattering at temperature T, Γ0 is the attempt frequency, and Eact is the rotational activation energy (Figure 6). Figure 10 shows an Arrhenius plot of eq 9: log Γ(T) is

where d is the jump distance separating the hydrogen atoms undergoing the rotational diffusion and j0 is the spherical Bessel function of order zero. Figure 9 shows the EISF extracted according to eq 7 from the QENS data measured at different temperatures. We can clearly

Figure 10. Arrhenius plot for the fwhm of the Lorentzian quasielastic component plotted as a function of inverse temperature. Slope of the line yields the activation energy for methyl group rotation in M-POSS, and the y intercept is equal to the attempt frequency for the methyl group to make a 120° rotation.

plotted as a function of inverse temperature. The resulting activation energy for methyl reorientations around the C3 axes is 5.12 ± 0.07 kJ/mol (equal to 53.1 meV or 428 cm−1). In a simple model, the value for the rotational activation energy should be equal to the 3-fold barrier height V3 minus the ground state (zero-point) torsional energy of the methyl group (Figure 6). In that case Eact = 74.4 meV − 1/2(19.4 meV) = 64.7 meV or 6.24 kJ/mol. The value determined by the QENS measurements is significantly smaller than this value. There are two possible reasons for this discrepancy. One is the contribution of rotational tunnelling to methyl group rotation, which is known to reduce the apparent activation energy.62 The more likely explanation is that the torsional potential energy barrier is temperature dependent. The value of V3 was determined by INS measurements at T = 20 K, whereas the QENS measurements used to determine Eact were made at

Figure 9. EISF A0(Q) for M-POSS defined by eq 7. Shown are the experimental points from 150 to 300 K (error bars are smaller than the symbols) and the calculated results for the 3-site model for methyl reorientations defined by eq 8 (red line).

see that the data for all temperatures from 150 to 300 K are consistent, indicating that methyl groups undergo similar reorientations in this temperature range. The EISF for methyl reorientations around the C3 symmetry axes described by eq 8 is shown in Figure 9 with a red line. The jump distance was varied to yield the best fit of eq 8 to the experimental data, 5588



Article

temperatures between T = 150 and 300 K. Our neutron diffraction data show that not only does the structure expand with increasing temperature (Figure S2, Supporting Information) but the POSS cages also exhibit distortions from perfect cubic symmetry that change as a function of temperature (Figure S5, Supporting Information). These structural changes will affect the intermolecular and intramolecular interactions and thus could modify the methyl torsional potentials. Further measurements are needed to directly evaluate the possibility that the energy barrier varies with temperature. The Arrhenius plot in Figure 10 also provides the attempt frequency Γ0 for the rotations, equal to 0.744 meV. Methyl rotational attempt frequencies are generally found to lie in the range of 2−5 meV,63 so this value is also quite a bit lower than expected. A possible origin for the lower attempt frequency in M-POSS would be the presence of methyl−methyl coupling in the M-POSS crystal structure.63 For example, QENS studies63 of methyl halides have found that both methyl fluoride (CH3F) and methyl chloride (CH3Cl) have attempt frequencies that lie below those of the bromide and iodide. This was attributed to coupling between methyl rotations on different molecules. Our neutron diffraction refinements show relatively close proximity of the methyl groups of adjacent M-POSS molecules in the crystal lattice (C−C distances of 3.77−4.34 Å and H−H distances as short as 3.26 Å). This observation suggests that methyl−methyl coupling could indeed be present, as has been observed in organic crystals that contain methyl groups separated by similar distances.63−65 Measurements of the methyl tunnel frequencies using NMR techniques would provide valuable information about such coupling and the role of tunnelling in M-POSS.56 The fwhm of the Lorentzian function for 3-site jumps is proportional to the methyl rotational jump rate: fwhm = 3τr−1. Here τr is the rotational correlation time for the methyl groups. In Table 3 we list the quasielastic line widths and the

Figure 11. C−H stretch region of the Raman spectrum measured at five temperatures. Note the splitting of the peak at 2970 cm−1 with decreasing temperature. Laser excitation wavelength was 514 nm.

intensities, and widths at each temperature (examples are shown in Figure S8, Supporting Information). The resulting temperature-dependent positions and widths of the Raman bands associated with the C−H stretches are shown in Figure S9, Supporting Information. From Figures 11 and S9, Supporting Information, it can be seen that the band splitting vanishes above temperatures of 150−200 K. There is no obvious sign of any (structural) phase transition in the Raman data, consistent with our X-ray and neutron diffraction data, nor do any other peaks in the spectrum split in a similar fashion. It thus seemed reasonable to attempt to treat the data using the correlation function formalism that was developed to describe the temperature-dependent splitting of methyl asymmetric stretching bands in the infrared spectra of n-alkanes.44 From ref 44 the normalized infrared or Raman peak splitting is given by

Table 3. fwhm of the Quasielastic Components and the Corresponding Jump Rates and Rotational Correlation Times (τr) for the Methyl Group Rotations around the 3Fold Axes temp. (K)

fwhm (μeV)

jump rate (μeV)

τr (ps)

150 175 200 225 250 300

12.7 21.4 33.4 48.0 64.6 96.5

4.23 7.13 11.1 16 21.5 32.2

993.5 588.9 377.4 262.5 195.0 130.6

S(T ) =

Δω(T ) = Δω(0)

1−

n2 B α coth 2 2 νt

1−

n2 B 2 νt

(10)

In eq 10 the variables are Δω(T) = frequency splitting of Raman bands at temperature T, α = hνt/kBT, where νt is the methyl torsional frequency, h is Planck’s constant, and kB is Boltzmann’s constant, n is the non-3-fold part of the effective stretch−torsion coupling potential, with typical values44 of 4 or 5, and B = 5.3 cm−1. We use our lowest temperature data, collected at T = 4.5 K, to determine an approximate value for the zero-temperature splitting Δω(0). The splitting at higher temperatures is then normalized by this low-temperature value and plotted in Figure 12. In Figure 12 we also show a fit of eq 10, varying only the torsional frequency vt, to the measured temperature-dependent normalized splitting of the Raman bands. We only show curves calculated with n = 5, which yielded better fits than n = 4, and with torsional frequencies of 100, 152 (best fit value), and 180 cm−1. The best-fit value of 152 cm−1 agrees with the value of 157 cm−1 determined from our INS measurements. Thus, the reduction of the Raman band splitting with increasing temperature is consistent with the model of motional

corresponding jump rates and correlation times for the methyl group reorientations around their C3 axes. These values are comparable to those reported for methyl group rotation in other solids having similar energy barriers.59 3.5. Low-Temperature Raman Spectroscopy. In order to search for possible effects of methyl group dynamics on the Raman spectra, we also collected a series of spectra at temperatures between 4.5 and 300 K. Several examples are shown in Figure 11. One obvious effect of cooling the sample is the splitting of the Raman band near 2970 cm−1, which we associate with the asymmetric stretch of the C1 symmetry methyl groups in the crystal. In our analysis of the C−H stretch region of the Raman spectra, we fit each spectrum to a sum of Lorentzians in order to extract values for the band positions, 5589



■

Article

AUTHOR INFORMATION

Corresponding Author

*Phone (302)695-3045. E-mail michael.k.crawford@dupont. com. Present Address &

Los Alamos National Laboratory Lujan Center (LANSCELC) TA-53, Building 622, Room 318, P.O. Box 1663, MS H805 Los Alamos, NM 87545.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

■

Figure 12. Temperature dependence of the normalized splitting of the 2970 cm−1 asymmetric stretch Raman band below T = 150 K. Also shown are the predictions of eq 10 with n = 5 and three different values for the torsional vibration frequency. Best-fit curve yields νt = 151.7 cm−1 (shown in black).

ACKNOWLEDGMENTS A portion of this research at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC0206CH11357. We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing some of the neutron research facilities used in this work. This work utilized facilities supported in part by the National Science Foundation under Agreement No. DMR-0944772. S.K.K. thanks the National Science Foundation (DMR-1006514) for partial support of this research. We thank Professor Herbert L. Strauss of the Chemistry Department, University of California, Berkeley for very helpful discussions concerning analysis of the variable-temperature Raman data and Dr. John J. Rush of the NIST Center for Neutron Research for illuminating discussions concerning our neutron scattering data. Identification of commercial products does not imply endorsement by the National Institute of Standards and Technology nor does it imply that these are the best for the purpose.

narrowing due to thermal excitation of the methyl rotations.44 The less than optimal quality of the fit in Figure 12, however, suggests that additional mechanisms contribute to the peak splitting. The derivation of eq 10 in ref 44 includes intramolecular interactions only, specifically the stretch−torsion coupling, but other intramolecular or intermolecular interactions might also contribute to the peak splitting/collapse.44 These additional interactions could be modified by thermal excitation of low-energy intramolecular vibrations (as listed in Table S5 and shown in Figure S6, Supporting Information) or intermolecular translational or rotational phonons in the crystal lattice, leading to more rapid Raman band collapse with increasing temperature than is predicted by eq 10.

4. CONCLUSIONS We presented the results of a study of the structure and methyl group dynamics of a simple POSS molecule, octamethyl-POSS or Si8O12(CH3)8 (M-POSS). Neutron diffraction data clearly show the presence of large amplitude methyl torsional vibrations. Inelastic and quasielastic neutron scattering measurements were used to determine the torsional transition energies and rotational dynamics of the methyl groups, along with the magnitude of the 3-fold methyl rotational energy barrier. These results, for a POSS molecule with simple methyl ligands, serve as a basis from which to analyze the structures and dynamics of other POSS molecules with more complex ligands as well as POSS molecules dispersed in polymer matrices, where perturbations of the ligand vibrations and dynamics by the polymer matrix can provide insight into the polymer−nanoparticle interactions.

■

■

ABBREVIATIONS M-POSS, octamethyl-POSS; INS, inelastic neutron scattering; QENS, quasielastic neutron scattering; DFT, density functional theory

■

REFERENCES

(1) Cordes, D. B.; Lickiss, P. D.; Rataboul, F. Recent Developments in the Chemistry of Cubic Polyhedral Silsequioxanes. Chem. Rev. 2010, 110, 2081−2173. (2) Kopesky, E. T.; Haddad, T. S.; Cohen, R. E.; McKinley, G. H. Thermomechanical Properties of Poly(methyl methacrylate)s Containing Tethered and Untethered Polyhedral Oligomeric Silsesquioxanes. Macromolecules 2004, 37, 8992−9004. (3) Liang, K.; Li, G.; Toghiani, H.; Koo, J. H.; Pittman, C. U., Jr. Cyanate Ester/Polyhedral Oligomeric Silsesquioxane (POSS) Nanocomposites: Synthesis and Characterization. Chem. Mater. 2006, 18, 301−312. (4) Fina, A.; Tabuani, D.; Frache, A.; Camino, G. Polypropylene− Polyhedral Oligomeric Silsesquioxanes (POSS) Nanocomposites. Polymer 2005, 46, 7855−7866. (5) Croce, G.; Carniato, F.; Milanesio, M.; Boccaleri, E.; Paul, G.; van Beek, W.; Marchese, L. Understanding the Physico-Chemical Properties of Polyhedral Oligomeric Silsesquioxanes: A Variable Temperature

ASSOCIATED CONTENT

S Supporting Information *

Neutron diffraction refinement results and structural data, bond distances and angles, selected nonbonded distances, atom positions and site symmetries, complete table of vibrations, Raman correlation times, TGA data, additional INS and QENS data, Raman peak fits, Raman band positions and line widths versus temperature. This material is available free of charge via the Internet at http://pubs.acs.org. 5590



Article

Multidisciplinary Study. Phys. Chem. Chem. Phys. 2009, 11, 10087− 10094. (6) Auf der Heyde, T. P. E.; Bürgi, H.-B.; Bürgy, H.; Törnroos, K. W. The Crystal and Molecular Structure of the Symmetrical Silasesquioxane H8Si8O12 at 100 K, a Molecular Building Block of Some Zeolites. Chimia 1991, 45, 38−40. (7) Törnroos, K. W. Octahydridosilasesquioxane Determined by Neutron Diffraction. Acta Crystallogr. 1994, C50, 1646−1648. (8) Koellner, Von G.; Müller, U. Verfeinerung tier Struktur yon (SiCH3)8O12. Acta Crystallogr. 1989, C45, 1106−1107. (9) Handke, B.; Jastrzębski, W.; Mozgawa, W. Kowalewska. Structural Studies of Crystalline Octamethylsilsesquioxane (CH3)8Si8O12. A. J. Mol. Struct. 2008, 887, 159−164. (10) Wann, D. A.; Less, R. J.; Rataboul, F.; McCaffrey, P. D.; Reilly, A. M.; Roberton, H. E.; Lickiss, P. D.; Rankin, D. W. H. Accurate GasPhase Experimental Structures of Octasilsesquioxanes (Si8O12X8; X = H, Me). Organometallics 2008, 27, 4183−4187. (11) Huq, A.; Hodges, J. P.; Gourdon, O.; Heroux, L. POWGEN: A Third-Generation High Resolution High-Throughput Powder Diffraction Instrument at the Spallation Neutron Source. Z. Kristallogr. Proc. 2011, 1, 127. (12) Petricek, V.; Dusek, M.; Palatinus, L. Jana2006: The Crystallographic Computing System; Institute of Physics: Praha, Czech Republic, 2006. (13) In International Tables for Crystallography; Wilson, A. J. C., Ed.; Kluwer Academic Publishers: Boston, MA, 1992; Vol. C (Mathematical, Physical and Chemical Tables). Also see the NIST Neutron Cross Section Database: http://www.ncnr.nist.gov/resources/n-lengths/. (14) Seeger, P. A.; Daemen, L. L.; Larese, J. Z. Resolution of VISION, a Crystal-Analyzer Spectrometer. Nuclear Instrum. Methods Phys. Res. A 2009, 604, 719−728. (15) Ehlers, G.; Podlesnyak, A. A.; Niedziela, J. L.; Iverson, E. B.; Sokol, P. E. The New Cold Neutron Chopper Spectrometer at the Spallation Neutron Source: Design and Performance. Rev. Sci. Instrum. 2011, 82, 085108−1−085108−6. (16) Mason, T. E.; Abernathy, D.; Anderson, I.; Ankner, J.; Egami, T.; Ehlers, G.; Ekkebus, A.; Granroth, G.; Hagen, M.; Herwig, K.; et al. The Spallation Neutron Source in Oak Ridge: A Powerful Tool for Materials Research. Physica B 2006, 385−386, 955−960. (17) Frisch, M. J.; et al. Gaussian 09, revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. (18) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behaviour. Phys. Rev. A 1988, 38, 3098. (19) Perdew, J. P. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B 1986, 33, 8822−8824. (20) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623−11627. (21) Hertwig, R. H.; Koch, W. On the Parameterization of the Local Correlation Functional. What is Becke-3-LYP? Chem. Phys. Lett. 1997, 268, 345−351. (22) Scott, A. P.; Radom, L. Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors. J. Phys. Chem. 1996, 100, 16502−16513. (23) Irikura, K. K.; Johnson, R. D., III; Kacker, R. N. Uncertainties in Scaling Factors for ab Initio Vibrational Frequencies. J. Phys. Chem. A 2005, 109, 8430−8437. (24) Ramirez-Cuesta, A. J. aCLIMAX 4.0.1, The New version of the Software for Analyzing and Interpreting INS Spectra. Comput. Phys. Commun. 2004, 157, 226-238 (25) Mamontov, E.; Herwig, K. W. A Time-of-Flight Backscattering Spectrometer at the Spallation Neutron Source, BASIS. Rev. Sci. Instrum. 2011, 82, 085109−1−085109−10.

(26) Meyer, A.; Dimeo, R. M.; Gehring, P. M.; Neumann, D. A. The High-Flux Backscattering Spectrometer at the NIST Center for Neutron Research. Rev. Sci. Instrum. 2003, 74, 2759−2777. (27) Wilson, C. C. Interesting Proton Behaviour in Molecular Structures. Variable Temperature Neutron Diffraction and ab Initio Study of Acetylsalicylic Acid: Characterising Librational Motions and Comparing Protons in Different Hydrogen Bonding Potentials. New J. Chem. 2002, 26, 1733−1739. (28) Wilson, C. C. Variable Temperature Study of the Crystal Structure of Paracetamol (p-hydroxyacetanilide), by Single Crystal Neutron Diffraction. Z. Kristallogr. 2000, 215, 693−701. (29) Trueblood, K. N.; Dunitz, J. D. Internal Molecular Motions in Crystals. The Estimation of Force Constants, Frequencies and Barriers from Diffraction Data. A Feasibility Study. Acta Crystallogr. 1983, B39, 120−133. (30) Schomaker, V.; Trueblood, K. N. Correlation of Internal Torsional Motion with Overall Molecular Motion in Crystals. Acta Crystallogr. 1998, B54, 507−514. (31) Schomaker, V.; Trueblood, K. N. On the Rigid-Body Motion of Molecules in Crystals. Acta Crystallogr. 1968, B24, 63−76. (32) McKean, D. C.; Duncan, J. L.; Blatt, L. CH Stretching Frequencies, Bond Lengths and Dissociation Energies. Spectrochim. Acta 1973, 29A, 1037−1049. (33) Larrson, J. A.; Cremer, D. Theoretical Verification and Extension of the McKean Relationship Between Bond Lengths and Stretching Frequencies. J. Mol. Struct. 1999, 485−486, 385−497. (34) McKean, D. C.; Biedermann, S.; Bürger, H. CH Bond Lengths and Strengths, Unperturbed CH Stretching Frequencies, from Partial Deuteration Infrared Studies: t-Butyl Compounds and Propane. Spectrochim. Acta 1974, 30A, 845−857. (35) McKean, D. C.; Saur, O.; Travert, J.; Lavalley, J. C. Isolated CH Stretching Frequencies, CH Bond Lengths and Strengths in Ethyl and Isopropyl Halides. Spectrochim. Acta 1975, 31A, 1713−1719. (36) James, R. W. The Optical Principles of the Diffraction of X-Rays; Cornell University Press: Ithaca, NY, 1965. (37) Marcolli, C.; Lainé, P.; Bühler, R.; Calzaferri, G.; Tomkinson, J. Vibrations of H8Si8O12, D8Si8O12, and H10Si10O15 As Determined by INS, IR, and Raman Experiments. J. Phys. Chem. B 1997, 101, 1171− 1179. (38) Fateley, W. G., Dollish, F. R., McDevitt, N. T., and Bentley, F. R. Infrared and Raman Selection Rules for Molecular and Lattice Vibrations: The Correlation Method; Wiley-Interscience: New York, 1972. (39) Merrick, J. P.; Moran, D.; Radom, L. An Evaluation of Harmonic Vibrational Frequency Scale Factors. J. Phys. Chem. A 2007, 111, 11683−11700. (40) Anderson, M. P.; Uvdal, P. New Scale Factors for Harmonic Vibrational Frequencies Using the B3LYP Density Functional Method with the Triple-ζ Basis Set 6-311+G(d,p). J. Phys. Chem. A 2005, 109, 2937−2941. (41) Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand: Princeton, NJ, 1945; Vol. II (Infrared and Raman Spectra of Polyatomic Molecules). (42) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; Dover: New York, 1980. (43) MacPhail, R. A.; Snyder, R. G.; Strauss, H. L. Motional Collapse of Methyl Group Vibrational Bands. J. Am. Chem. Soc. 1980, 102, 3976. (44) MacPhail, R. A.; Snyder, R. G.; Strauss, H. L. The Motional Collapse of the Methyl C−H Stretching Vibration Bands. J. Chem. Phys. 1982, 77, 1118−1137. (45) Bärtsch, M.; Bornhauser, P.; Calzaferri, G.; Imhof, R. H8SisO12: A Model for the Vibrational Structure of Zeolite A. J. Phys. Chem. 1994, 98, 2817−2831. (46) Bornhauser, P.; Calzaferri, G. Normal Coordinate Analysis of H8Si8O12. Spectrochim. Acta 1990, 46A, 1045−1056. (47) Rush, J. J.; Taylor, T. I.; Havens, W. W. Rotational Freedom of Ammonium Ions and Methyl Groups by Cross Section Measurements with Slow Neutrons. J. Chem. Phys. 1962, 37, 234−238. 5591



Article

(48) Rush, J. J.; Taylor, T. I. Neutron Scattering Study of Hindered Rotational Motions and Phase Transitions in Hexamethylbenzene. J. Chem. Phys. 1966, 44, 2749−2754. (49) Rush, J. J. Cold Neutron Study of Hindered Rotations in Solid and Liquid Methylchloroform, Neopentane, and Ethane. J. Chem. Phys . 1967, 46, 2285−2291. (50) Takehuchi, H.; Allen, G.; Suzuki, S.; Dianoux, A. J. Low Frequency Vibrations in Solid n-Butane and n-Hexane by Incoherent Inelastic Neutron Scattering. Chem. Phys. 1980, 51, 197−203. (51) Jayes, L.; Hard, A. P.; Sene, C.; Parker, S. F.; Jayasooriya, U. A. Vibrational Spectroscopic Analysis of Silicones: A Fourier TransformRaman and Inelastic Neutron Scattering Investigation. Anal. Chem. 2003, 75, 742−746. (52) Mitchell, P. C. H.; Parker, S. F.; Ramirez-Cuesta, A. J.; Tomkinson, J. Vibrational Spectroscopy with Neutrons; World Scientific: Hackensack, NJ, 2005. (53) Dimeo, R. Visualization and Measurement of Quantum Rotational Dynamics. Am. J. Phys. 2003, 71, 885−893. (54) Lister, D. G.; Macdonald, J. N.; and Owen, N. L. Internal Rotation and Inversion: An Introduction to Large Amplitude Motions in Molecules; Academic Press: New York, 1978. (55) Azuah, R. T.; Kneller, L. R.; Qiu, Y.; Tregenna-Piggott, P. L. W.; Brown, C. M.; Copley, J. R. D.; Dimeo, R. M. DAVE: A Comprehensive Software Suite for the Reduction, Visualization, and Analysis of Low Energy Neutron Spectroscopic Data. J. Res. Natl. Inst. Stand. Technol. 2009, 114, 341−358. (56) Prager, M.; Heidemann, A. Rotational Tunneling and Neutron Spectroscopy: A Compilation. Chem. Rev. 1997, 97, 2933−2966. (57) Rahman, A.; Singwi, K. S.; Sjolander, A. Theory of Slow Neutron Scattering by Liquids. I. Phys. Rev. 1962, 126, 986−996. (58) Vural, D.; Glyde, H. Intrinsic Mean-Square Displacement in Proteins. Phys. Rev. E 2012, 86, 011926-1−011926-11. (59) Bee, M. Quasielastic Neutron Scattering; Adam Hilger: Philadelphia, PA, 1988. (60) Lechner, R. E.; Badurek, G.; Dianoux, A. J.; Hervet, H.; Volino, F. On the Rotational Motion of the Ammonium Ion in the CsCl− Type Phase of NH4Br: Results from Quasielastic Neutron Scattering. J. Chem. Phys. 1980, 73, 934−939. (61) Clough, S.; Heidemann, A.; Horsewill, A. J.; Lewis, J. D.; Paley, M. N. J. The Rate of Thermally Activated Methyl Group Rotation in Solids. J. Phys. C: Solid State Phys. 1982, 15, 2495−2508. (62) Kowalewski, J.; Liljefors, T. On the Relationship Between the Potential Barrier and the Activation Energy for the Internal Rotation of a Methyl Group. Chem. Phys. Lett. 1979, 64, 170−174. (63) Kirstein, O.; Prager, M.; Grimm, H.; Buchsteiner, A.; Wischnewski, A. Quasielastic Neutron Scattering Experiments Including Activation Energies and Mathematical Modeling of Methyl Halide Dynamics. J. Chem. Phys. 2007, 127, 094504−1−094504−7. (64) Fillaux, F.; Carlile, C. J.; Kearley, G. J. Inelastic-NeutronScattering Study at Low Temperature of the Quantum Sine-Gordon Breather in 4-Methyl-Pyridine with Partially Deuterated Methyl Groups. Phys. Rev. B 1991, 44, 12280−12293. (65) Nair, S.; Dimeo, R. M.; Neumann, D. A.; Horsewill, A. J.; Tsapatsis, M. Methyl Rotational Tunneling Dynamics of p-Xylene Confined in a Crystalline Zeolite Host. J. Chem. Phys. 2004, 121, 4810−4819.

5592


Structure and Dynamics of Octamethyl-POSS Nanoparticles

Recommend Documents