Article pubs.acs.org/JPCA
Polarized Raman Spectroscopy of Oligothiophene Crystals To Determine Unit Cell Orientation John C. Heckel,†,∥ Andrew L. Weisman,‡,∥ Severin T. Schneebeli,§,⊥ Michelle Lynn Hall,§,¶ Leif J. Sherry,†,# Sarah M. Stranahan,† Kateri H. DuBay,§ Richard A. Friesner,*,§ and Katherine A. Willets*,† †
Department of Chemistry and Biochemistry and Center for Nano and Molecular Science, The University of Texas at Austin, Austin, Texas 78712, United States ‡ Department of Applied Physics and Applied Mathematics and §Department of Chemistry, Columbia University, New York, New York 10027, United States S Supporting Information *
ABSTRACT: Raman spectra were recorded experimentally and calculated theoretically for bithiophene, terthiophene, and quaterthiophene samples as a function of excitation polarization. Distinct spectral signatures were assigned and correlated to the molecular/unit cell orientation as determined by X-ray diffraction. The ability to predict molecular/unit cell orientation within organic crystals using polarized Raman spectroscopy was evaluated by predicting the unit cell orientation in a simulated terthiophene crystal given a random set of simulated polarized Raman spectra. Polarized Raman spectroscopy offers a promising tool to quickly and economically determine the unit cell orientation in known organic crystals and crystalline thin films. Implications of our methodologies for studying individual molecule conformations are discussed.
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the morphologies of crystals and thin films including optical polarization microscopy,17 low energy ion scattering,18 ellipsometry,19,20 extended X-ray absorption fine structure,21 Fourier transform infrared absorption,22 and Raman spectroscopy.23−39 Polarized Raman spectroscopy and microscopy in particular offer relatively inexpensive and fast optical methods to extract structural information from a crystal or film while also accommodating many different sample shapes and sizes with theoretical diffraction-limited resolution. Several research groups have proposed and demonstrated the utility of polarized Raman spectroscopy for characterizing the morphologies of different materials. Specific examples include estimating the molecular orientation in copper phthalocyanine thin films,23 conjugated polymer thin films,31 polymer− electrode interfaces,33 and nylon 6 filaments.30 Still other examples include relating molecular orientation to the Raman spectra of liquid-crystalline composites,24 nucleotide embedded stretched poly(ethylene) matrices,27 6,13-bis[(triisopropylsilyl)ethynyl]-pentacene-embedded polystryrene blends,26 and strained graphene monolayers.35 Polarized Raman spectroscopy has also been demonstrated to differentiate between crystalline and amorphous silicon films,28 detect strain defects in diamond single crystals,25 study polymorphism in organic crystals,36−39 and determine the degree of molecular order in poly(3-hexylthiophene) films.32 In
INTRODUCTION π-Conjugated polymers and oligomers continue to be an intensely studied class of materials due to their diverse properties including photoluminescence,1 electroluminescence,2 electrical conduction,3 and semiconduction.4 In particular, polythiophenes, polythiophene derivatives, and oligothiophenes have proven to be particularly well-suited for applications in organic electronic devices such as light-emitting diodes,2,5 field effect transistors,6 and photovoltaic cells.7,8 It is well-known that the performance of organic electronic devices is highly influenced by the morphology of the active materials within the device: crystallinity,9,10 the orientation of crystalline regions in a polycrystalline film,11,12 the number of molecules in the unit cell (Z),13 and the degree of molecular disorder14 can all strongly affect device performance. Therefore, a fast and accurate method to determine structural information about oligo/polythiophene crystals and thin films at the molecular level would be quite advantageous. The most rigorous method to determine structural information from a crystalline material is X-ray diffraction (XRD). However, XRD is expensive, time-consuming, provides poor spatial resolution, and is typically not suited to characterize samples other than single crystals or crystalline powders. Grazing incidence XRD can be used to measure structural information from samples such as alkyl substituted polythiophene12,15 and oligothiophene16 films with high depth resolution (25 °C) inside the XRD instrument caused the surface of the crystal to melt slightly when the crystal was transferred to the cold stream within the instrument, leading to the rounded edges of the crystal observed in Figure 4A. However, the XRD spectra were recorded at −120 °C, so no further melting occurred during data collection, and the slightly melted surfaces did not affect the bulk crystalline state within the sample, based upon our ability to resolve the crystal structure. A second 2T crystal (2T-2) that was grown concurrently with 2T-1 was also analyzed by polarized Raman microscopy, as shown in Figure 5. Despite 2T-1 and 2T-2 being the same material (crystalline 2T), their polarized Raman scattering behavior was markedly different (Figure 5, Table 1). Though MM1 showed low scattering intensity relative to MM2 in 2T-1 (Aavg = 22.4), the two Raman intensities are comparable in 2T2 (A = 1.2). Moreover, the modulation depth of MM2 in 2T-1 (M2,avg = 0.94) was about 2 times higher than the modulation depth of MM2 in 2T-2 (M2 = 0.46). The contrast in the marker mode behavior between the two crystals suggests that the individual 2T molecules in the two different crystals were
Figure 5. (A) Polarized Raman spectra from crystal 2T-2. (B) Polar plots showing the Raman intensities of MM1 and MM2 (radial axis) as ψ is varied from 0° to 350°. 6810
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results are very promising of the utility of marker modes to interpret the orientation of 2T molecules and in particular, the orientation of the unit cell within the crystals. Correlated Polarized Raman and Molecular Orientation: Experiment and Theory. Because of the instability of crystalline 2T at room temperature, correlating the orientation of its unit cell with the polarized Raman signatures is difficult, and we therefore shifted our focus to the more stable oligothiophenes, 3T and 4T. Crystals of 3T and 4T were grown by vacuum sublimation and characterized with XRD. It was determined that the 3T sample was a single crystal of the low temperature phase64,65 and the 4T sample was a single crystal of the high temperature polymorph66 (3T: P21/c, a = 15.24 Å, b = 5.64 Å, c = 25.87 Å, β = 98.05°, and Z = 8; 4T: P21/c, a = 14.15 Å, b = 5.68 Å, c = 9.02 Å, β = 98.59°, and Z = 2). Polarized Stokes Raman scattering spectra were recorded from both crystals, with the crystal oriented at two positions with respect to the optical (z) axis: one in which the flat edge of the crystal was roughly orthogonal to the z-axis (zperp, Figures 6A, S-1A, Supporting Information) and one in which the flat edge was aligned parallel to the z-axis (zparallel, Figures 7A, S-2A, Supporting Information). In each case, the orientation of the molecules with respect to the crystal is fixed, but their orientation with respect to the lab frame is changing; this allows us to probe the orientation dependence of the polarized Raman signal in more detail. For all calculations from this point on, we assume that the individual molecules adopt the 180° planar conformation, which, as mentioned previously, is the conformation oligothiophenes tend to adopt in crystalline form. Terthiophene. Figures 6 and 7 show the different polarized Raman response for 3T from the zperp and zparallel crystal orientations, respectively. Figure 6A shows the orientation of the crystal in the lab frame (x, y, z, where the +z axis is out of the plane of the page) and Figure 6B shows the projection of the individual molecules within the crystal as measured by XRD, relative to the same lab frame. The experimentally measured polarized Raman data indicates that the two marker modes have similar intensities (Figure 6C). The polar plot data for the two marker modes, shown in Figure 6E and summarized in Table 2, demonstrate that the polarization-sensitivity of the two marker modes is out-of-phase by 75°. Next, we simulated the Raman spectra for this geometry of 3T, on the basis of the orientations of the molecules within the unit cell with respect to the lab frame, as determined by XRD (Figure 6B). 3T has eight molecules in the unit cell with four unique orientations. The Euler angles associated with each of the four unique molecular orientations were determined from the rotated XRD data shown in Figure 6B, and polarized Raman spectra were calculated for each. The final Raman spectrum was generated by averaging the four spectra together and is shown in Figure 6D. Polar plots for MM1 and MM2 were also constructed and are plotted as solid lines in Figure 6E. For these plots, the maximum intensities of the dominant mode (here, MM1) were set equal and all other mode intensities were scaled accordingly. The Raman parameters for MM1 and MM2 from the calculated spectra are summarized in the first two columns of Table 2. We note that the theory is able to reproduce the general trends in the data: notably, the modulation depth of MM1 is less than the modulation depth of MM2, the amplitude is less than 1, and the difference in the phase of the two marker modes is ∼75°. Although the experimental and calculated values of M and φ do not show perfect agreement, we believe
Figure 6. (A) Bright-field image of the 3T crystal (zperp) with lab frame coordinate axes on bottom left (+z axis coming out of the page). (B) Molecular orientation of individual 3T molecules within the unit cell with respect to the lab frame as determined by XRD. The crystal is represented as a yellow polygon. (C) Experimental and (D) simulated polarized Raman spectra from the circled region in (A). (E) Polar plots of measured MM1 and MM2 Raman intensities as a function of the excitation polarization (data points). The solid lines correspond to the simulated Raman data points.
this to be due to imperfect registration between the orientation of the crystal in the XRD and its orientation on the optical microscope, leading to ±15° error in the assignment of the crystal orientation with respect to the lab frame. After rotating the crystal to the zparallel position as shown in Figure 7A, we observe that the intensity of MM1 drops dramatically relative to MM2 (Figure 7C), but now the phase values appear nearly identical (Figure 7E). This observed marker mode behavior is due to the change in the orientation of the molecules with respect to the lab frame (e.g., comparing Figures 6B and 7B). The theoretical Raman spectra and associated polar plots for MM1 and MM2 based upon the new molecular orientation were also calculated (Figure 7D,E, respectively). The parameters associated with MM1 and MM2 are summarized in the last two columns of Table 2, and we note that, once again, theory is able to reproduce the general trends on the basis of the given orientation of the 6811
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given the associated error in determining the crystal orientation within the lab frame, this is excellent agreement between experiment and theory. Quaterthiophene. Next we investigated crystals of 4T, which have two molecules per unit cell, each with a unique orientation. As with 3T, we observe a similar dependence between the polarized Raman response we measure and the orientation of the crystal. Table 3 summarizes the parameters Table 3. Parameters for Raman Marker Modes for 4T Sample 4T, zperp marker mode 1
marker mode 2
molecules within the unit cell. Moreover, for this orientation, most experimental and theoretical values agree to better than 10%, except for the modulation depth of MM1. Nonetheless, Table 2. Parameters for Raman Marker Modes for 3T Sample
marker mode 1
marker mode 2
ν (cm−1) M1 φ1 (°) ν (cm−1) M2 φ2 (°) A φ2 − φ1 (°)
3T, zparallel
expt
theory
expt
theory
687 0.43 99.7 1456 0.72 24.8 0.80 −74.9
695 0.56 118.6 1505 0.96 43.8 0.20 −74.8
687 0.73 154.3 1456 0.93 154.7 28 0.4
695 0.88 162.2 1505 1.00 163.0 32 0.8
expt
theory
expt
theory
687 0.35 137.4 1454 0.80 139.1 5.2 1.7
698 0.71 119.1 1492 1.00 122.2 22 3.1
687 0.77 160.4 1454 0.81 161.5 19 1.1
698 0.91 165.7 1492 1.00 167.0 39 1.3
associated with the Raman marker modes for both the experimental and theoretical data (associated crystal/molecule orientation and spectral data are presented in the Supporting Information, Figures S-1 and S-2). As before, we are able to reproduce the general trends in the experimental data with the calculated Raman data, although imperfect registration between the XRD and optical lab frames produces error in the determination of the orientation of the individual molecules in the unit cell, resulting in slight differences between the experimental and theoretical data. We note that for both crystal orientations, the difference in phase between MM1 and MM2 is similar, but the individual phase values for MM1 and MM2 change as the crystal rotates; this is reproduced well by the simulated Raman data. We also find that for both orientations, the intensity of MM2 is stronger than MM1, as indicated by A values >1. General Trends in Marker Mode Intensity. For all three molecules studied (2T, 3T, and 4T), all calculated CC stretch modes within 1400−1700 cm−1 (MM2 included) reduced to at least 1 order of magnitude smaller than MM1 when the molecule and optical axes were aligned. This agreed with a general trend we noticed from both the simulated and experimental data: although MM2 generally dominated MM1 in amplitude, for orientations in which the long axis of the molecule was nearly parallel to the optical axis, the modes became roughly the same intensity (as in Figure 6). Figure 8 illustrates this relationship using simulated Raman data for the marker modes for different single molecule orientations relative to the optical axis. In the “parallel” alignment (rotation angle of 90°), the modes in the range of 1400−1700 cm−1 approach near-zero amplitudes compared to those below 1400 cm−1 (such as MM1). Conversely, even a small deviation from this “parallel” alignment significantly increases the intensity of the modes in the 1400−1700 cm−1 range relative to the lower modes. The sensitivity of the spectra to the orientation near the “parallel” alignment along with the aforementioned ±15° registration difficulty is most likely why it was more difficult to achieve agreement between experiment and theory in the 1400−1700 cm−1 region. We also found that the longer the molecule, the larger this degree of spectral sensitivity to
Figure 7. (A) Bright-field image of the 3T crystal (zparallel) with lab frame coordinate axes on bottom left (+z axis coming out of the page). (B) Molecular orientation of individual 3T molecules within the unit cell with respect to the lab frame as determined by XRD. The crystal is represented as a yellow polygon. (C) Experimental and (D) simulated polarized Raman spectra from the circled region in (A). (E) Polar plots of measured MM1 and MM2 Raman intensities as a function of the excitation polarization (data points). The solid lines correspond to the simulated Raman data points. The plot on the right is zoomed in to show the MM1 data more clearly.
3T, zperp
ν (cm−1) M1 φ1 (°) ν (cm−1) M2 φ2 (°) A φ2 − φ1 (°)
4T, zparallel
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and then averaged over the spectrum of each of the four unique molecular orientations within the unit cell. All spectra were calculated for a backscattering geometry, with no polarization filters in front of the detector. We thus obtained intensity vs polarization curves for each normal vibrational mode in the spectrum for a given unit cell orientation. Unlike the experimental data, where we focused on two marker modes, here we expanded the set of marker modes to include all 51 vibrational modes with frequencies above 100 cm−1 (including the C−H stretch modes near 3200 cm−1). By fitting each of the 51 polarized Raman intensities to eq 7, we obtained three parametersmodulation depth, phase, and amplitudefor each of the 51 marker modes. The amplitude parameters were calculated relative to the intensity of the lowest-frequency mode. We repeated this process for each unit cell orientation, ending up with 3 × 51 = 153 parameters for each of the Npool unit cell orientations. We called this set of parameters the “pool” set. We then generated Ntest = 100 random unit cell orientations and calculated a set of 153 parameters for each of these orientations, in the same manner as for the pool set. We therefore ended up with 153 parameters for each of Ntest unit cell orientations, calling this set of parameters the “test” set. Finally, we created a very basic, nonfitted scoring function for matching the parameters associated with each “test” orientation to its best match from the “pool” set (see Supporting Information, section 5), to rank the unit cell orientations in the pool set given a set of parameters for any of the unit cell orientations in the test set. The “best” rankings (i.e., 1, 2, 3, etc.) correspond to Euler angles of orientations from the “pool” set being as close as possible to the Euler angles of the current “test” orientation. Because the incident polarization angle is unique up to only 180° due to the symmetry of the electric field vectors, in principle a single set of 153 parameters can correspond to two possible unit cell orientations: one rotated 180° about the optical axis with respect to the other. Therefore, in the following results, we count a pair of such unit cell orientations as a single “match” to a given set of parameters. For example, say that for a given set of test parameters the following four best-matched unit cell orientations were obtained from the pool set (where the three values represent the associated Euler angles of the unit cell): match 1: [15, 30, 240] match 2: [195, 30, 240] match 3: [280, 160, 10] match 4: [100, 160, 10]
Figure 8. Calculated marker mode intensities of individual oligothiophene molecules rotated with respect to the optical axis (vertical blue axes in the molecule insets). Solid lines correspond to MM1, and dashed lines correspond to MM2, calculated for (blue) 2T, (green) 3T, and (red) 4T. Note the marked increase in intensity of MM2 upon even a small deviation from the “parallel” alignment represented here by 90°. Also note the logarithmic scaling of the intensity axis.
deviation from the “parallel” alignment (Figure 8). These observations justify our choice of the two marker modes that we have analyzed. Moreover, they allow us to assign structural features related to the 2T data shown previously (Figures 4 and 5). We further note that the superlinear increase in MM2 intensity with oligomer length agrees with refs 56 and 61 and the same appears to be true for MM1. We find that the intensity increase in both modes is exponential, except for the nearly “parallel” alignment of the optical and molecule axes, where the intensity of MM2 in 2T overtakes that of 3T and 4T and the type of increase in MM1 becomes ambiguous (Figure 8). In crystal 2T-1 shown in Figure 4, MM1 is much less intense than MM2, indicating that the molecules in the crystal must have a strong in-plane alignment (i.e., orthogonal to the optical axis). On the other hand, crystal 2T-2 in Figure 5 has polarized Raman spectra in which MM1 and MM2 have comparable intensities, indicating that the molecules in this crystal must be more strongly aligned with the optical axis. We also note that this intensity trend is true for other bands, as suggested by our calculations: multiple modes under 1400 cm−1 are enhanced relative to the higher energy modes in crystal 2T-2 compared to 2T-1. Crystal Orientation Determination from Polarized Raman Spectra. Having shown that theory is able to reproduce the experimentally observed polarization-dependent Raman spectra using experimentally determined molecular orientations, we next asked the question of whether theory could help predict molecular orientation given a set of Raman parameters. To this end, we simulated how well we could determine the orientation of a 3T unit cell given its simulated Raman spectra and the orientations of the molecules inside the unit cell. First, we defined the unit cell as a collection of four unique orientations of the individual 3T molecules, each contributing to the overall Raman spectrum of the unit cell. We then varied the Euler angles of the unit cell over a range of Npool = 119 952 Euler angles to represent a complete, unique, and uniform set of general unit cell orientations. For each unit cell orientation, we simulated the Stokes Raman spectrum for each individual molecule over a range of polarization angles (ψ = 0, 3, ..., 177),
The first pair of unit cell orientations (matches 1 and 2) and the second pair (matches 3 and 4) would be ranked as one and two, respectively. See Supporting Information for complete details on the matching algorithm and how ranking was performed. For the set of 153 parameters corresponding to each unit cell orientation in the test set, the pairs of unit cell orientations in the pool set were ranked using our scoring function. We defined the “true” match in the pool set to be the pair of orientations very similar to the known test orientation by requiring each of the Euler angles of the true match to be within typically ±5° of the actual test Euler angles. The “true” match corresponded to the first orientation that would allow an experimentalist to make only minor changes to the crystal to obtain the true orientation. No significant modifications were allowed, such as any sort of rotation (however minor) about an 6813
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In considering prospects for analyzing more complex systems than those considered here, it is important to begin by summarizing the sources of noise in both the calculations and experimental data. The DFT calculations do not perfectly reproduce experimental vibrational frequencies; there are a number of factors that likely contribute to discrepancies, including (1) the use of single molecule calculations rather than calculations that would include the crystalline environment (e.g., periodic boundary condition DFT methods or the use of large clusters containing neighboring molecules) and (2) intrinsic errors in the DFT functional employed. Both of these issues can be addressed in principle: the former by employing larger models or solid state DFT approaches as noted above and the latter by scaling force constants as is common in the DFT literature. 67−69 Obtaining better frequency agreement would further assist in automating the orientation-determination process. However, as long as one can match the peaks in the DFT spectrum with those in the experimental spectrum, exact matching of calculated and experimental frequencies is not critical to the determination of structural information, which is much more dependent upon comparisons of the computed and experimental Raman intensities as a function of polarization angle. These intensities appear to track quite well in all cases examined herein. Improvements may further be made to the calculated Raman intensities by moving outside the double harmonic approximation, relaxing assumptions of mechanical and/or electrical harmonicity. It should be noted that the theoretical approximation of the molecular crystal modes and spectra by the modes/spectra of the constituent nontumbling planar molecules, ignoring packing effects completely, was quite good; as mentioned, mode frequencies were still useful, and the agreement of the mode intensities with our experimental results was excellent. Such good approximations have been proposed by for example ref 41 and evidenced by for example ref 70. Though it is plausible that the use of a plane-wave electronic structure code would yield even better results, one of the largest physical additions it would make would be phonons corresponding to wavelengths larger than the molecule size (i.e., vibrational modes that are not internal to the individual molecules and thus cannot be determined from our method of approximating the crystal modes by the molecular modes). Raman spectra in the lattice phonon region recorded from pentacene36 and oligothiophene38,39 crystals did show several modes that changed intensity and position at different excitation polarizations. However, the degree to which phonon mode intensity fluctuates with excitation polarization compared to intramolecular mode intensity fluctuation with excitation polarization is unclear at this time. In this study we noted some issues associated with the experimental data that likely contribute significantly to the discrepancies between the experimental and predicted Raman spectra. One challenge we faced in these studies was imperfect registration between the XRD laboratory frame and the optical laboratory frame, introducing error into our structural assignments. This is a significant challenge for any correlated optical/ structure experiment, yet our Raman data indicate that we may ultimately be able to circumvent this issue by using theoretically calculated Raman data to predict the structure on the basis of matching the polarized response of experimentally measured Raman data. Assigning the Euler angles of individual molecules within each unit cell based on the XRD data also introduced an
axis (aside from rotating by 180° to obtain the other member of the pair, of course). This matching was performed manually, checking each determined match using 3D plots of the orientations (relative to the lab frame) of the four uniquely oriented molecules in the unit cell. As shown in Table 4, for 87 Table 4. Results of the Orientation-Determination Algorithm rank of true pair of orientations
no. of test cases (Ntest = 100 total cases) obtaining that rank
1 2 3 4 ≥5
87 11 1 1 0
out of our 100 test unit cell orientations, the algorithm found the true pair of matches in the pool set to be ranked number one. For the 13 out of 100 test unit cell orientations that were not determined perfectly, 11 found the true pair of unit cell orientations to be ranked number two, one found the true pair to be ranked number three, and the last found the true pair to be ranked number four. Thus, in our test of determining the unit cell orientation given simulated Raman spectra, we usually determined the roughly correct pair of unit cell orientations as our first guess, and we always determined the correct pair of unit cell orientations by our fourth guess. When the “true” pair of orientations was not found to be ranked first, the orientations that ranked better than the true pair, i.e., false positives, did so most often because the correct contributions to the average spectra came from the wrong molecules within the unit cell. The other false positive orientations ranked better because they were rotated about an axis orthogonal to the optical axis yet appeared similar when viewed down the optical axis. Thus, both types of false positive orientations were due to the symmetry of the molecules and unit cell.
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DISCUSSION We have shown that we can identify marker modes of oligothiophenes that are dependent upon torsional orientation and vary systematically in the mode intensity as a function of the polarization angle of the excitation light relative to the sample. Theoretical calculations reproduce the experimental marker mode Raman intensity data with good, if not perfect, accuracy; furthermore, at least in a simple idealized test case, structure can be inferred from the spectra with excellent reliability. Although there are sources of noise in the experiment, the systematic behavior can be readily perceived above the noise level and matches the results from theoretical calculations in a robust and consistent fashion. The results shown here are highly encouraging with regard to the possibility of employing polarized Raman spectroscopy to extract useful information concerning unit cell orientation, key torsional conformations, percentage of molecules at a 0° torsion angle (as opposed to the lower-energy 180° conformation), local morphology within polymorphic crystals, degree of crystallinity or presence of tumbling molecules in a partially ordered sample, and distribution of molecules within the unit cell for crystalline and polycrystalline materials composed of conjugated polymers. 6814
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that polarized Raman spectroscopy can make an important, even central, contribution to this effort. Further experiments on increasingly heterogeneous systems should provide indications as to how far the method can be pushed forward.
additional error source, although we estimate this error to be much smaller than the error in registration described above (
