Comparison of the electronic structure of two polymers with strong dipole ordering

Two diff erent polymers, with large local electric dipoles, are compared: copolymers of polyvinylidene fl uoride with trifl uoroethylene [P(VDF-TrFE, 70%:30%)] and polymethylvinylidenecyanide (PMVC). While the diff erent local point group symmetries play a key role, both crystalline polymers exhibit intra-molecular band structure, though the Brillouin zone critical points diff er. Polyvinylidene fl uoride [PVDF; -(CH2-CF2)n-] copolymers with trifl uoroethylene [TrFE;(CHF-CF2)-] can form highly ordered crystalline ferroelectric ultrathin polymer fi lms, as has been demonstrated by x-ray and neutron scattering [1-4], scanning tunnelling microscopy [1, 5-8], low energy electron diff raction [1, 8] and band mapping [1, 8]. Although not always evident in scanning tunnelling microscopy, the band structure shows a characteristic super-periodicity dominated by -(CH2-CF2)2-or -(CH2-CF2)-(CHF-CF2)`dimer’ pairs [1, 8] in the ferroelectric phase. Th e copolymer poly(vinylidene fl uoride with trifl uoroethylene: 70%:30%) [P(VDF-TrFE, 70:30)], in spite of the low overall symmetry, does show all the characteristics of high local symmetry and symmetry selection rules. Th e eff ects are quite signifi cant in photoemission [9, 10] and electron energy loss spectroscopy [4, 9-11]. By comparing the copolymer P(VDF-TrFE, 70:30) to the highly dipole-ordered polymer polymethylvinylidenecyanide (PMVC) we can see the infl uence of local point group symmetry on the intra-molecular band structure. Th e results summarized here show that PMVC Journal of Physics: Condensed Matter L 155 Published in J. Phys.: Condens. Matter 18:13 (5 April 2006), pp. L155-L161. doi:10.1088/0953-8984/18/13/L01 http://www.iop.org/EJ/journal/JPhysCM © 2006 IOP Publishing Ltd. Used by permission. L 156 Letter to the Editor: J. Phys.: Condens. Matter (-(CH(CH3)-C(CN)2)n-) has a much lower local point group symmetry than polyvinylidene fl uoride, although not a copolymer system. Th e very thin crystalline P(VDF-TrFE, 70:30) and PMVC fi lms were formed by Langmuir-Blodgett (LB) monolayer deposition from a water subphase. Th e P(VDF-TrFE, 70:30) copolymer with weight-averaged molecular weight (Mw) = 100 000 was dissolved at 0.05 wt% in dimethylsulfoxide. Th e PMVC polymer with weight-averaged molecular weight (Mw) = 2780 was dissolved at 0.07 wt% in a 90:10 mixture of chloroform and dimethylsulfoxide. For each material, a monolayer was dispersed on the surface of a NIMA model 622C LB trough fi lled with ultra-pure (>18 M Ω-cm) water and compressed to a surface pressure of 5 mN m 1. Th e LB fi lms were deposited on substrates of freshly cleaved pyrolytic graphite wafers by the horizontal (Schaefer) variation of the LB technique, repeated fi ve times to make a fi lm of fi ve nominal monolayers (ML). Film preparation methods were described in greater detail in [12]. Previous studies showed that P(VDF-TrFE 70:30) LB fi lms produced under these conditions had an average thickness of 1.8 nm per ML [13]. Prior x-ray diff raction [1, 2], neutron diff raction [4] and scanning tunnelling microscopy [1, 5-8] studies of the P(VDF-TrFE 70:30) LB fi lms showed that they are highly crystalline and planar, with a crystalline orientation and the polymer chains predominantly parallel to the substrate, but showing little lamellar folding. Th roughout this work, we used nominally 5 ML fi lms of P(VDF-TrFE, 70:30) and PMVC on graphite for the angle-resolved ultraviolet photoemission spectroscopy (UPS) and inverse photoemission spectroscopy (IPES) experiments. Th e electron spectroscopy measurements of P(VDF-TrFE, 70:30) were taken at a sample temperatures of 200 K, well below the 353 K bulk ferroelectric phase transition of this material (80 °C) [1, 2, 7], and at room temperature for PMVC. For scanning tunnelling microscopy (STM), the images were recorded at 295 K from polymer fi lms nominally 2 and 3 ML thick on graphite substrates, for P(VDF-TrFE) and PMVC respectively. Th e STM imaging conditions for P(VDFTrFE) were Vtip bias = 0.10 V, I = 0.21 nA. Th e imaging conditions for PMVC were Vtip bias = 0.10 V, I = 0.2 nA. Th e UPS and IPES spectra were taken to study the molecular orbital placement of both occupied and unoccupied orbitals of the polymers. In both photoemission and inverse photoemission measurements, the binding energies are referenced with respect to the Fermi edge of gold or tantalum, in intimate contact with the sample surface. Th e IPES were obtained by using electrons with variable incident energy while measuring the emitted photons at a fi xed energy (9.7 eV) using a Geiger-Müller detector [1, 8]. Th e instrumental linewidth is ~400 meV, as described elsewhere [1, 8]. Th e light polarization dependent angle-resolved UPS were found using synchrotron light at 55 eV photon energy, dispersed by a 3 m toroidal grating monochromator, at the Center for Advanced Microstructures and Devices (CAMD) in Baton Rouge, Louisiana, employing a hemispherical electron energy analyser with an angular acceptance of ± 1°, as described in detail elsewhere [14-16]. All angles (both light incidence angles as well as the photoelectron emission angles) reported herein are with respect to the normal to the substrate surface. Because of the highly plane polarized nature of the dispersed synchrotron light through the toroidal grating monochromator, the large light incidence angles result in a vector potential A more parallel to the surface normal (p-polarized light), while smaller light incidence angles result in the vector potential A residing more in the plane of the surface (s-polarized light) in the geometry of our experiment. Th e polarization dependence can be related to the photoemission selection rules resulting in changes in the cross-section of symmetry-specifi c molecular orbitals. Th e details of selection rule formalism are laid out elsewhere [9, 17-19]. Th eoretical calculations of the electronic structure of short segments of P(VDF-TrFE) and PMVC were undertaken by NDO-PM3 (neglect of diff erential overlap, parametric method 3) Letter to the Editor: J. Phys.: Condens. Matter L 157 with the HyperChem package [20, 21]. Geometric optimization of the system was performed by obtaining the lowest unrestricted Hartree-Fock (UHF) energy states: the structures of the short chain segments are shown as insets to fi gure 1. A calculated density of states (DOS) was obtained by applying equal Gaussian envelopes of 1 eV full width half maximum to each molecular orbital (to account for the solid state broadening in photoemission) and then summing. Th is calculated density of states, together with a rigid energy shift of 5.3 eV applied to the calculated electronic structure, is in generally good agreement with the combined photoemission and inverse photoemission data from both P(VDF-TrFE, 70:30), taken at 200 K, and PMVC, recorded at 295 K, as seen in fi gure 1. Th e calculations do not account for photoemission and inverse photoemission matrix element eff ects, so that the comparison with ultraviolet photoemission must be considered only qualitative, but the comparison of theory with experiment, shown in fi gure 1, is suffi cient to exclude the presence of a signifi cant number of gauche bonds (i.e. such bonds must be below 5%). Th e electronic structures of both P(VDF-TrFE, 70:30), at 200 K, and PMVC, at 295 K, are indicative of systems in the all-trans Figure 1. Th e combined UPS (left) and IPES (right) spectra, along with the calculated molecular orbitals (bottom black lines) and model density of states without any corrections for matrix element or cross-section eff ects (red line), are shown for P(VDFTrFE) copolymer (a) and PMVC (b). Th e photoemission spectra were taken with the photoelectrons collected normal to the surface, while the inverse photoemission spectrum was taken with the electrons at normal incidence. Th e insets show schematic representations of chain segments of P(VDF-TrFE) in (a) and PMVC in (b). L 158 Letter to the Editor: J. Phys.: Condens. Matter confi guration, with the dipoles all aligned. Structural phases that look like `paraelectric’ and `antiferroelectric’ phases are considered very unlikely, though antiparallel packing of chains cannot be excluded on the basis of a comparison of photoemission and inverse photoemission with theory. Figure 2. Th e surface structure of crystalline (left) P(VDF-TrFE) and (right) PMVC Langmuir-Blodgett fi lms as ascertained from scanning tunnelling microscopy. Th e scanning tunnelling microscope images, recorded at 295 K, are of nominally 2 and 3 ML fi lms on graphite substrates, for P(VDF-TrFE) and PMVC respectively. Th e image sizes are 4.4 nm × 4.4 nm for P(VDF-TrFE) and 4.8 nm × 4.8 nm for PMVC. Arrows indicate chain direction. Figure 3. Th e light polarization photoemission spectra were recorded at a photon energy of 55 eV and 295 K for PMVC. Th e 70° light incidence angle results in E more along the surface normal (red), while a 45° light incidence angle refl ects E with components along the surface normal and in the plane of the surface (black). Th e spectra were taken with the photoelectrons collected at normal emission, to preserve the highest possible point group symmetry. For comparison, the light polarization dependence of P(VDF-TrFE) is shown in the inset (adapted from [9]), for 170 K and light incidence angles of 70° and 45°, as indicated. Letter to the Editor: J. Phys.: Condens. Matter L 159 Th e gap between the highest occupied (HOMO) to lowest unoccupied molecular orbital (LUMO) derived from the combined photoemission and inverse photoemission spectra (fi gure 1) indicates that P(VDF-TrFE, 70:30) should be a slightly better dielectric than PMVC, in the absence of structural considerations. Th is expectation that P(VDF-TrFE) is a better insulator is because the HOMO-LUMO gap is slightly larger for P(VDF-TrFE, 70:30). In addition, the position of the Fermi level within the HOMO-LUMO gap is closer to the lowest unoccupied band edge for PMVC and there is a greater DOS at the lowest unoccupied band edge for PMVC, when compared with that of P(VDF-TrFE). Th e surface crystallinity of P(VDF-TrFE, 70:30), grown by the Langmuir-Blodgett technique, has been well established by STM techniques [1, 5-8], as already noted. On a cleaved graphite substrate, a 5 ML PMVC fi lm is seen to be similarly crystalline by scanning tunnelling microscopy, as shown in fi gure 2. Th e in-plane spacing between the polymer chains is distributed from 3.5 to 4.3 Å for P(VDF-TrFE, 70:30), which is somewhat smaller than is generally observed in the bulk crystal structure of P(VDF-TrFE, 70:30) [2, 22, 23]. Along the chain, as determined from the STM images, the spacing between monomers is about 2.5 ± 0.1 Å, in good agreement with the bulk crystal structure of P(VDF-TrFE, 70:30) [2, 22, 23]. Th e uniformity of the images tends to exclude antiparallel packing of PMVC and P(VDF-TrFE) chains at the surface. In spite of the high level of apparent crystalline order, there is very little dependence of the valence band photoemission spectra for PMVC on the incident light polarization (fi gure 3), unlike the considerable light polarization dependent photoemission observed for P(VDFTrFE) [9]. For comparison, the signifi cant light polarization dependence of P(VDF-TrFE) is shown in the inset (adapted from [9]) in fi gure 3. For molecules with high symmetry with respect to the surface normal, the partial cross-section for photoemission varies according to the orientation of the light vector potential A and the symmetry of the initial state ψi, assuming that the fi nal state wavefunction ψf is fully symmetric, as when the photoelectrons are collected along the surface normal [17-19]. Th is insensitivity of the photoemission to light polarization eff ects suggests that PMVC has a much lower local point group symmetry with respect to the surface normal, than P(VDF-TrFE, 70:30). PMVC does exhibit signifi cant intra-molecular band structure, particularly in the unoccupied states (fi gure 4), in spite of the low local point group symmetry. Th e angle dependent inverse photoemission spectra have been further analysed to determine the dispersion (change in binding energy) as a function of wavevector k||, parallel to the plane of the surface. Th e wavevector parallel to the surface of the fi lm follows: where the value of k|| (the wavevector parallel with the surface) can be calculated from the kinetic energy (Ekin) of the incident electron and the incidence angle θ, in the case of inverse photoemission [8, 9, 17-19]. Angle-resolved inverse photoemission spectra, taken along the molecular chains, show evidence of considerable dispersion. Th e conduction band dispersion of the lowest unoccupied molecular orbital states, with k||, along the high symmetry direction is shown in fi gure 4. Th e dispersion of the fi rst unoccupied molecular orbital feature along the polymer chain for the P(VDF-TrFE) in the ferroelectric phase [2], at 200 K, and room temperature for the PMVC was abstracted from the angle-resolved IPES recorded from multiple samples. Th e amplitudes of the conduction band dispersion L 160 Letter to the Editor: J. Phys.: Condens. Matter are about 1.5 and 2 eV for P(VDF-TrFE) and PMVC, respectively. Th e real space crystalline periodicity of the conduction band dispersion of P(VDF-TrFE) is clearly shorter than for PMVC, judging by the fact that the period in k|| space for P(VDF-TrFE) is 1.3 Å –1, while, for PMVC the period is 0.9 Å –1 in k|| space. As noted previously [1, 8], the length of the Brillouin zone for P(VDF-TrFE) of 1.3 ± 0.4 Å –1 is very close to the value 1.255 Å –1 which corresponds to 4.8 ± 0.2 Å or about twice that of the dimer–(CH2–CF2)n– separation of 2.5 Å in real space. For PMVC, the length of the Brillouin zone along the chains is 0.9 ± 0.6 Å –1 in k|| space, close to 0.84 Å –1, which corresponds to three times the dimer distance in real space or 7 ± 0.5 Å. Th e reason why the size of the unit cell of PMVC in real space is 7 ± 0.5 Å may be a natural arrangement of the methyl groups or, as has been suggested for P(VDF-TrFE) [1, 5, 6, 8], due to some subtle local arrangements of dipole orientation. It is very clear from scanning tunnelling microscopy (fi gure 3) and band structure (fi gure 4) that PMVC, like P(VDF-TrFE), can be highly ordered when the fi lms are prepared by the Langmuir-Blodgett technique. Indeed, the absence of signifi cant light polarization eff ects in photoemission, combined with the high level of crystallinity, tends to indicate that an overall low symmetry matters less than local symmetry and dipole ordering. Figure 4. Th e band dispersion, from angle-resolved inverse photoemission, of the unoccupied feature closest to the Fermi level, along the polymer chains. Th e dashed lines indicate the diff erent positions of the Brillouin zone centres and Brillouin zone edges between P(VDF-TrFE) copolymer and PMVC. Letter to the Editor: J. Phys.: Condens. Matter L 161 Th is work was supported by the National Science Foundation through grant CHE-0415421 and the NSF `QSPINS’ MRSEC (DMR 0213808). Th e Center for Advanced Microstructures and Devices (CAMD) is funded by the Louisiana Board of Regents.