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This paper 1) reviews the α-plane representation of a type-2 fuzzy set (T2 FS), which is a representation that is comparable to the α-cut representation of a type-1 FS (T1 FS) and is useful for both theoretical and computational studies of and for T2 FSs; 2) proves that set theoretic operations for T2 FSs can be computed using very simple α-plane computations that are the set theoretic operations for interval T2 (IT2) FSs; 3) reviews how the centroid of a T2 FS can be computed using α-plane computations that are also very simple because they can be performed using existing Karnik Mendel algorithms that are applied to each α-plane; 4) shows how many theoretically based geometrical properties can be obtained about the centroid, even before the centroid is computed; 5) provides examples that show that the mean value (defuzzified value) of the centroid can often be approximated by using the centroids of only 0 and 1 α-planes of a T2 FS; 6) examines a triangle quasi-T2 fuzzy logic system (Q-T2 FLS) whose secondary membership functions are triangles and for which all calculations use existing T1 or IT2 FS mathematics, and hence, they may be a good next step in the hierarchy of FLSs, from T1 to IT2 to T2; and 7) compares T1, IT2, and triangle Q-T2 FLSs to forecast noise-corrupted measurements of a chaotic Mackey-Glass time series.Index Terms-α-Plane, centroid, Mackey-Glass time series, quasi-type-2 fuzzy logic systems (Q-T2 FLSs), set theoretic operations, type-2 fuzzy sets (T2 FSs).

We have performed a comprehensive study of chemical synthesis, crystal growth, crystal quality, and electrical transport properties of isotopically substituted rubrene-d 28 single crystals (D-rubrene, C 42 D 28 ). Using a modified synthetic route for protonated-rubrene (H-rubrene, C 42 H 28 ), we have obtained multigram quantities of rubrene with deuterium incorporation approaching 100%. We found that the vaporgrown D-rubrene single crystals, whose high qualities were confirmed by X-ray diffraction and atomic force microscopy, maintained the remarkable transport properties originally manifested by H-rubrene crystals. Specifically, field-effect hole mobility above 10 cm 2 V −1 s −1 was consistently achieved in the vacuum-gap transistor architecture at room temperature, with an intrinsic band-like transport behavior observed over a broad temperature range; maximum hole mobility reached 45 cm 2 V −1 s −1 near 100 K. Theoretical analysis provided estimates of the density and characteristic energy of shallow and deep traps presented in D-rubrene crystals. Overall, the successful synthesis and characterization of rubrene-d 28 paves an important pathway for future spin-transport experiments in which the H/D isotope effect on spin lifetime can be examined in the testbed of rubrene.

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We use spectrally-resolved magneto-electroluminescence (EL) measurements to study the energy dependence of hyperfine interactions between polaron and nuclear spins in organic LEDs. Using layered devices based on Bphen/MTDATA -a well-known exciplex emitter -we show that the increase in EL emission intensity I due to small applied magnetic fields of order 100 mT is markedly larger at the high-energy blue end of the EL spectrum (∆I/I ∼11%) than at the low-energy red end (∼4%). Concurrently, the widths of the magneto-EL curves increase monotonically from blue to red, revealing an increasing hyperfine coupling between polarons and nuclei and directly providing insight into the energy-dependent spatial extent and localization of polarons.Several recent experiments have shown that small applied magnetic fields B on the order of 10-100 mT can induce substantial (∼10%) changes in the total light intensity emitted by organic light-emitting diodes (OLEDs) [1][2][3][4][5][6][7][8][9][10][11][12][13]. While initially surprising in view of the fact that the polymers and small molecules used in OLEDs are primarily composed of non-magnetic atoms (H, C, N), it was quickly appreciated that hyperfine spin interactions underpinned these phenomena. Specifically, the coupling of the electron and hole polaron spin to the many nuclear spins in the host material generates randomly-oriented local effective magnetic fields about which electron and hole polaron spins can precess. This precession leads to spin mixing between singlet and triplet polaron-pair states, which are precursors to exciton or exciplex formation in an OLED. Applied fields B suppress this hyperfineinduced mixing, altering the population balance between singlet and triplet excitons or exciplexes, which in turn modifies the electroluminescence (EL) efficiency.The detailed dependence of EL intensity on B allows direct insight into not only the rates of singlet and triplet exciton/exciplex formation, but also reveals the strength of hyperfine coupling and therefore provides a measure of the spatial extent (size) of the electron and hole polarons.In magneto-EL studies to date [1][2][3][4][5][6][7][8][9][10][11][12][13], only the total (spectrally-integrated) EL intensity was measured as a function of B. However, OLED emission spectra typically span a very broad wavelength range, reflecting the fact that excitons and exciplexes form over a wide range of energies, and with varying degrees of localization for which different hyperfine couplings may be expected. Here we spectrally resolve the magneto-EL from MTDATA/Bphen OLEDs -a well known exciplex emitter -and show that the increase in EL intensity due to B is significantly larger at the high-energy blue side of the spectrum than at the low-energy red side. Most importantly, the widths of the magneto-EL curves increase by over a factor of two from blue to red, directly revealing an increasingly strong hyperfine coupling and providing insight into the energy-dependent spatial extent and localization of the emitting states.Figu...

Massé, A.; Friederich, P.; Symalla, F.; Liu, F.; Meded, V.; Coehoorn, R.; Wenzel, W.; Bobbert, P.A. Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA):Massé, A., Friederich, P., Symalla, F., Liu, F., Meded, V., Coehoorn, R., ... Bobbert, P. A. (2017). Effects of energy correlations and superexchange on charge transport and exciton formation in amorphous molecular semiconductors: an ab initio study. Physical Review B, 95(11), 1-11. [115204]. DOI: 10.1103/PhysRevB.95.115204 General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. In this study, we investigate on the basis of ab initio calculations how the morphology, molecular on-site energies, reorganization energies, and charge transfer integral distribution affect the hopping charge transport and the exciton formation process in disordered organic semiconductors. We focus on three materials applied frequently in organic light-emitting diodes: α-NPD, TCTA, and Spiro-DPVBi. Spatially correlated disorder and, more importantly, superexchange contributions to the transfer integrals, are found to give rise to a significant increase of the electric field dependence of the electron and hole mobility. Furthermore, a material-specific correlation is found between the HOMO and LUMO energy on each specific molecular site. For α-NPD and TCTA, we find a positive correlation between the HOMO and LUMO energies, dominated by a Coulombic contribution to the energies. In contrast, Spiro-DPVBi shows a negative correlation, dominated by a conformational contribution. The size and sign of this correlation have a strong...

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