Rubrene

Rubrene molecule (5,6,11,12 - tetraphenylnaphthacene) as it is found in orthorhombic rubrene crystals

The rubrene molecule is basically the tetracene molecule with four wings. Its family are the polycyclic aromatic hydrocarbons. When rubrene molecules combine to build orthorhombic crystals, the molecules have a centrosymmetric structure with 2/m symmetry, as shown in the figure (their tetracene backbone acquires a twist when the molecules are free from constrains). Symmetry considerations imply that transitions between electronic ground state and first excited state can only be mediated by electromagnetic radiation that is polarized parallel to the 2-fold symmetry axis of the molecule (the M axis), which is in the plane of the tetracene backbone and perpendicular to its long axis.

This is a very important point when it comes to understanding the most common rubrene crystals, which have an orthorhombic structure with all molecules (all of them!) aligned with their 2-fold symmetry axis M parallel to each other, and generally perpendicular to the natural large facet of rubrene crystals grown by vapor transport. This molecular packing is completely different from that found in tetracene crystals, to which rubrene crystals are often compared, and it has a profound effect on the optical properties of rubrene

Figure 1: A single rubrene molecule with the definition of its L,M,N molcular axes (top.) Facets of single-crystal rubrene (bottom.)

How rubrene molecules assemble in orthorhombic rubrene crystals

We grow rubrene crystals using vapor transport. Rubrene molecules are sublimated inside a 1 inch diameter fused silica tube, where pure argon gas is made to flow, at a low rate, through a temperature gradient that slowly allows the walls of the silica tube to cool, causing the vapor-phase molecules to assemble into a crystalline form after some of them stick to the surface of the cube. Rubrene crystals have an orthorhombic unit cell with lattice parameters a = 1.44 nm, b = 0.718 nm, and c = 2.69 nm. The most common crystal shapes are platelets with extended surfaces perpendicular to the c-direction and crystals elongated in the b direction but with short dimensions in the a and c directions. As-grown rubrene crystals have facets that form a typical angle of 63.5 degrees to the b axis when observing the ab plane, and 75 degrees with respect to the b axis from the bc plane (see figure 3.)

The major difference between rubrene and tetracene crystals is that in rubrene every single molecule in the crystal is oriented in such away that the tetracene backbone has its short axis (The 'M' direction) parallel to the crystallographic c-axis, which is the axis perpendicular to the large flat surfaces in as-grown crystals. Combine this with the fact that selection rules based on molecular symmetries tell us that photon absorption and emission with no phonon involvement is only allowed for light polarized along this 'M' direction, and we have recipe for enormous anisotropy of optical properties. The crystal structure itself and the way as grown crystals are formed combine to effectively hide the dominant and very strong absorption and emission of c-polarized light. This can easily lead to confusing results (strong enhancement of fluorescence in coincidence with tiny surface defects, strong dependence of spectral shape from experimental setup) in unsophisticated experiments that do not take this property in account.

Two facets of the rubrene single crystal, abplane view seen top left, and bc plane on top right. Molecular packing structure of rubrene is seen to be a herring bone pattern (bottom image.)

But this molecular orientation also makes it possible to apply an external field (like a magnetic field) to the crystal in such a way that it has the exact same direction for every single molecule in the crystal, something that cannot be done with a close relative to rubrene, the tetracene crystals. This simplifies the analysis of the effects of a magnetic field oriented perpendicular to the large surfaces of rubrene crystals, because it has the same effects on all molecules, determining for example the frequency of fluorescence quantum beats after pulsed illumination.

The ab surface of a tiny rubrene crystal

Another aspect of the molecular packing of rubrene crystal is the fact that there is a specific direction where the molecules are close to each other. This makes transport in the crystal an essentially one-dimensional affair, with electrons, holes, and excitons having a larger ability to move along those closely packed molecular columns in what we call the "b" direction. Rubrene has a high room-temperature charge carrier mobility for an organic crystal (10 - 40 cm^2/Vs for holes in field-effect transistors) and a high photoconductivity (which is actually caused by triplet exciton dissociation!). We have also found long-range diffusion of triplet excitons in the same direction, which is largely due to the long triplet exciton lifetime in rubrene (100 microseconds) and leads to an average diffusion length of triplet excitons of 4 micrometers along the direction of close molecular packing.

Finally, photon absorption in rubrene crystals leads to singlet excitons. The high binding energy of singlet excitons in molecular crystals does not allow for dissociation of the excitons into free carriers, which can then either recombine to the ground state while emitting a photon, or undergo a fission process into two spin-entangled triplet excitons, a process that is allowed because the energy of one triplet exciton in rubrene is about half that of a singlet exciton. It turns out that fission is much more probable than photon emission, and therefore the vast majority of photoexcitations in rubrene results in triplet exciton pairs. And since a triplet exciton has half the energy of a singlet exciton in rubrene, it becomes possible for two triplets to merge, and to re-create a singlet state, and this singlet state can then emit a photon. All this leads to a complicated time-dependence for the fluorescence observed after pulsed photoexcitation, to fluorescence quantum beats, to an intensity-dependent quantum-yield, and to the possibility of observing triplet-exciton diffusion directly under the microscope.

See also:

• Light, Excitons, and transport in Organic Molecular Crystals.
• The rubrene crystal.
• Absorption and luminescence spectroscopy.
• Singlet Exciton Fission.
• Triplet Exciton Fusion.
• Quantum Beats.
• Triplet Exciton Diffusion and Fusion.
• Global Spin Decoherence in a Triplet-Pair population.

References:

• H. Najafov, I. Biaggio, T.-K. Chuang, M. K. Hatalis, “Exciton dissociation by a static electric field followed by nanoscale charge transport in PPV polymer films,” Phys. Rev. B 73, (2006).
• H. Najafov, I. Biaggio, V. Podzorov, M. F. Calhoun, M. E. Gershenson, “Primary Photoexcitations and the Origin of the Photocurrent in Rubrene Single Crystals,” Phys. Rev. Lett. 96, 0566004 (2006).
• H. Najafov, B. Lyu, I. Biaggio, V. Podzorov, “Investigating the origin of the high photoconductivity of rubrene single crystals,” Phys. Rev. B 77, 125202 (2008).
• H. Najafov, B. Lyu, I. Biaggio, V. Podzorov, “Two mechanisms of exciton dissociation in rubrene single crystals,” Appl. Phys. Lett. 96, 183302 (2010).
• P. Irkhin and I. Biaggio, “Direct imaging of anisotropic exciton diffusion and triplet diffusion length in rubrene single crystals,” Phys. Rev. Lett. 107, 017402 (2011).
• A. Ryasnyanskiy and I. Biaggio, “Triplet exciton dynamics in rubrene single crystals,” Phys. Rev. B 84, 193203 (2011).
• P. Irkhin, A. Ryasnyanskiy, M.Koehler, I. Biaggio, “Absorption and photoluminescence spectroscopy of rubrene single crystals,” Phys. Rev. B 86, 085143 (2012).
• I. Biaggio, P. Irkhin, “Extremely efficient exciton fission and fusion and its dominant contribution to the photoluminescence yield in rubrene single crystals,” Appl. Phys. Lett. 103(26), 263301 (2013).
• P. Irkhin, I. Biaggio, “Two-photon absorption spectroscopy of rubrene single crystals,” Phys. Rev. B 89, 201202(R) (2014).
• K. A. Ward, B. R. Richman, I. Biaggio, “Nanosecond pump and probe observation of bimolecular exciton effects in rubrene single crystals,” Appl. Phys. Lett. 106(22), 223302 (2015).
• P. Irkhin, I. Biaggio, T. Zimmerling, M. Döbeli, B. Batlogg, “Defect density dependent photoluminescence yield and triplet diffusion length in rubrene,” Appl. Phys. Lett. 108(6), 063302 (2016).
• Eric A. Wolf, Drew M. Finton, Vincent Zoutenbier, Ivan Biaggio, “Quantum beats of a multiexciton state in rubrene single crystals,” Appl. Phys. Lett. 112, 083301 (2018).
• D.M. Finton, E.A. Wolf, V.S. Zoutenbier, K.A. Ward, I. Biaggio, “Routes to singlet exciton fission in rubrene crystals and amorphous films,” AIP Advances 9 (9), 095027 (2019).
• Eric A. Wolf, Ivan Biaggio, “Geminate exciton fusion fluorescence as a probe of triplet exciton transport after singlet fission,” Phys. Rev. B Letters 103 (20), L201201 (2021).
• Gerald Curran III, Zachary Rex, Casper Xallan Wilson, Luke J. Weaver, Ivan Biaggio, Ivan Biaggio, “Persistence of spin coherence in a crystalline environment,” Phys. Rev. Lett. 133, 056901 (2024).