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Reversible electronic energy transfer (homo-FRET) in cyclic multichromophoric systems is studied for sets of n identical fluorophores arranged in regular polygons (triangle, square, pentagon, etc.). A general analytic expression for the anisotropy decay is obtained for a regular polygon of any order, under the assumptions of isotropic interaction and nearest-neighbor FRET. A graphical way of connecting the decay form and polygon geometry based on the Frost circle is also presented. The consequences of the relaxation of these assumptions on the anisotropy decay are also discussed and analyzed in detail for the heptagon.

The chemiluminescence of several naphthalene-based luminol analogues is characterized and compared with that of luminol. The compounds produce a strong greenish or green-yellow chemiluminescence in alkaline aqueous and nonaqueous solutions by reaction with hydrogen peroxide in the presence of hexacyanoferrate (III). The results point to the possibility of increasing the sensitivity of analytical methods currently based on luminol. The photophysics of the oxidation products is also studied. The solubility of some of the new compounds in aqueous solution is significantly increased using a nonionic surfactant Triton X-100. Increase of the chemiluminescence intensity in aqueous micellar media was observed. The location of the oxidation product 3-aminophthalate in the external hydrophilic shell of the micelle was established using its intrinsic fluorescence by iodide. The described luminol analogues may prove of interest in forensic and other applications.

Direct O-alkylation of p-tert-butyldihomooxacalix[4]arene (1) with N-(bromopropyl)- or N-(bromoethyl)phthalimides and K2CO3 in acetonitrile was conducted under conventional heating (reflux) and using microwave irradiation and ball milling methodologies. The reactions afforded mono- and mainly distal di-substituted derivatives in the cone conformation, in a total of eight compounds. They were isolated by column chromatography, and their conformations and the substitution patterns were established by NMR spectroscopy (1H, 13C, COSY and NOESY experiments). The X-ray structures of four dihomooxacalix[4]arene phthalimide derivatives (2a, 3a, 3b and 5a) are reported, as well as their photophysical properties. The microwave (MW)-assisted alkylations drastically reduced the reaction times (from days to less than 45 min) and produced higher yields of both 1,3-di-substituted phthalimides (3a and 6a) with higher selectivity. Ball milling did not reveal to be a good method for this kind of reaction.

Thermally activated delayed fluorescence (TADF) molecules offer nowadays a powerful tool in the development of novel organic light emitting diodes due to their capability of harvesting energy from non-emissive triplet states without using heavy-metal complexes. TADF emitters have very small energy difference between the singlet and triplet excited states, which makes thermally activated reverse intersystem crossing from the triplet states back to the singlet manifold viable. This mechanism generates a long-lived delayed fluorescence component which can be explored in the sensing of oxygen concentration, local temperature, or used in time-gated optical cell-imaging, to suppress interference from autofluorescence and scattering. Despite this strong potential, until recently the application of TADF outside lighting devices has been hindered due to the low biocompatibility, low aqueous solubility and poor performance in polar media shown by the vast majority of TADF emitters. To achieve TADF luminescence in biological media, careful selection or design of emitters is required. Unfortunately, most TADF molecules are not emissive in polar media, thus complexation with biomolecules or the formation of emissive aggregate states is required, in order to retain the delayed fluorescence that is characteristic of these compounds. Herein, we demonstrate a facile method with great generalization potential that maintains the photophysical properties of solvated dyes by combining luminescent molecules with polymeric nanoparticles. Using an established swelling procedure, two known TADF emitters are loaded onto polystyrene nanoparticles to prepare TADF emitting nanomaterials able to be used in live-cell imaging. The obtained particles were characterized by optical spectroscopy and exhibited the desired TADF emission in aqueous media, due to the polymeric matrix shielding the dye from solvent polarity effects. The prepared nanoparticles were incubated with live human cancer cells and showed very low cytotoxicity and good cellular uptake, thus making fluorescence microscopy imaging possible at low dye concentrations.

Thermally activated delayed fluorescence (TADF) has revolutionized the field of organic light emitting diodes owing to the possibility of harvesting non-emissive triplet states and converting them in emissive singlet states. This mechanism generates a long-lived delayed fluorescence component which can also be used in sensing oxygen concentration, measuring local temperature, or on imaging. Despite this strong potential, only recently TADF has emerged as a powerful tool to develop metal-free long-lived luminescent probes for imaging and sensing. The application of TADF molecules in aqueous and/or biological media requires specific structural features that allow complexation with biomolecules or enable emission in the aggregated state, in order to retain the delayed fluorescence that is characteristic of these compounds. Herein we demonstrate a facile method that maintains the optical properties of solvated dyes by dispersing TADF molecules in nanoparticles. TADF dye-doped silica nanoparticles are prepared using a modified fluorescein fluorophore. However, the strategy can be used with many other TADF dyes. The covalent grafting of the TADF emitter into the inorganic matrix effectively preserves and transfers the optical properties of the free dye into the luminescent nanomaterials. Importantly, the silica matrix is efficient in shielding the dye from solvent polarity effects and increases delayed fluorescence lifetime. The prepared nanoparticles are effectively internalized by human cells, even at low incubation concentrations, localizing primarily in the cytosol, enabling fluorescence microscopy imaging at low dye concentrations.

Valorisation of industrial low-value waste residues was preconized. Hence, carbon dots (C-dots) were synthesized from wastewaters of the cork industry&mdash, an abundant and affordable, but environmentally-problematic industrial effluent. The carbon nanomaterials were structurally and morphologically characterised, and their photophysical properties were analysed by an ensemble of spectroscopy techniques. Afterwards, they were successfully applied as highly-sensitive fluorescence probes for the direct detection of haemproteins. Haemoglobin, cytochrome c and myoglobin were selected as specific targets owing to their relevant roles in living organisms, wherein their deficiencies or surpluses are associated with several medical conditions. For all of them, remarkable responses were achieved, allowing their detection at nanomolar levels. Steady-state and time-resolved fluorescence, ground-state UV&ndash, Vis absorption and electronic circular dichroism techniques were used to investigate the probable mechanisms behind the fluorescence turn-off of C-dots. Extensive experimental evidence points to a static quenching mechanism. Likewise, resonance energy transfer and collisional quenching have been discarded as excited-state deactivating mechanisms. It was additionally found that an oxidative, photoinduced electron transfer occurs for cytochrome c, the most electron-deficient protein. Besides, C-dots prepared from citric acid/ethylenediamine were comparatively assayed for protein detection and the differences between the two types of nanomaterials highlighted.

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Phasor plots (plots of the Fourier sine transform vs. the Fourier cosine transform, for one or several angular frequencies) of the fluorescence intensity decay are being increasingly used in studies of homogeneous and heterogeneous systems. In this work, the phasor approach is applied to monomer-excimer systems with a focus on mixed decays, i.e. decays with both monomer and excimer contributions. The phasors of mixed decays fall on a straight line delimited by the excimer and monomer phasors. With a fixed concentration, and by continuously increasing the emission wavelength, the phasor moves from pure monomer to pure excimer. At a certain intermediate wavelength, which is concentration-dependent, the phasor crosses the universal semicircle and the decay becomes single exponential. This is an interesting case of an exponential decay not corresponding to a single fluorescent species. All results are demonstrated experimentally with pyrene in methylcyclohexane at room temperature, for which a full phasor picture emerges, combining in a single diagram monomer, excimer and mixed decays measured at several concentrations, showing the graphical power of the phasor approach.

Treatment of trans-[PtCl2(NCR)2] 1 (R = Me (1a), Et (1b), o-ClC6H4 (1c), p-ClC6H4 (1d), p-(HCdouble bond; length as m-dashO)C6H4 (1e), p-O2NC6H4CH2 (1f)) with 1,3-diiminoisoindoline HNdouble bond; length as m-dashCC6H4C(NH)double bond; length as m-dashNH 2 gives access to the corresponding (1,3,5,7,9-pentaazanona-1,3,6,8-tetraenato)Pt(II) complexes [PtCl{NHdouble bond; length as m-dashC(R)Ndouble bond; length as m-dashC(C6H4)NCdouble bond; length as m-dashNC(R)double bond; length as m-dashNH}] 3a–f, in good yields (65–70%). The reaction of trans-[PdCl2(NCMe)2] 4a with 2 furnishes (1,3,5,7,9-pentaazanona-1,3,6,8-tetraenato)Pd(II) complex [PdCl{NHdouble bond; length as m-dashC(Me)Ndouble bond; length as m-dashC(C6H4)NCdouble bond; length as m-dashNC(Me)double bond; length as m-dashNH}] 5a, in good yield (65%). However, the reaction of trans-[PdCl2(NCR)2] 4 (R = Ph (4b), p-MeC6H4CH2 (4c), p-(HCdouble bond; length as m-dashO)C6H4 (4d), p-O2NC6H4CH2 (4e)) with 2 gives a number of unidentified products. The compounds 3a–f and 5a were characterized by IR, 1H, 13C and DEPT-135 NMR spectroscopies, elemental analyses and, in the case of the Pt(II) complex [PtCl{NHdouble bond; length as m-dashC(Me)Ndouble bond; length as m-dashC(C6H4)NCdouble bond; length as m-dashNC(Me)double bond; length as m-dashNH}] 3a, also by X-ray diffraction analysis. Compounds 3a and 3b were also characterized by UV–Vis absorption and luminescence emission spectroscopies. Emission quantum yields of ca. 3 × 10−3 were obtained in dichloromethane solution, and luminescence lifetimes are in the order of the tens of nanoseconds. Both compounds also exhibited luminescence in solid state (polystyrene matrix), with luminescence lifetimes in the order of hundreds of nanoseconds. peerReviewed

The intrinsic electronic absorption and fluorescence properties of several multifluorophoric dihomooxacalix[4]arenes are studied. The contributions of phenyl and/or benzyl groups (lower rim) and p-tert-butylphenyl ethers (upper rim) to the absorption and fluorescence are established. Fluorescence titrations were undertaken to investigate the calixarene complexes with nitrate and hydrogen sulfate. A comparison with UV-Vis titrations in the same concentration range showed that similar values for the association constants are obtained by both techniques. Fluorescence is thus demonstrated to be a good method for the determination of calixarene–anion association constants.

A complete set of criteria for the classification, design, and selection of optimal thermally activated delayed fluorescence (TADF) emitters, for both photoluminescence and electroluminescence applications, is presently unavailable. In this work, and as a contribution toward this aim, a detailed characterization of TADF photophysical kinetics is presented, contrasting TADF in photoluminescence and TADF in electroluminescence. Two different types of TADF are identified: One-way and two-way TADF. It is shown that, for a given efficiency, one-way TADF allows lower rates of reverse intersystem crossing, an aspect that may be significant with respect to stability and roll-off issues. Graphical and quantitative indicators of singlet–triplet interconversion and photophysical efficiency are obtained and applied to the photoluminescence of eosin, coronene, and fullerenes and to the electroluminescence of several TADF emitters specifically designed for organic light emitting diodes. Relations for the photoluminesce...

The purpose of this chapter is to summarize the state of art of fluorescence-based explosive sensors in a simple way, focusing especially on the research progress. Importantly, the advances in this field are organized in the different strategies and improvements in the exploitation of fluorescence explosives detection. Mechanisms of fluorescence explosives detection are reviewed, not only fluorescence-quenching-based mechanisms but also some novel mechanism which are applied in explosives detection. We also focused our discussion on several fluorescent probes that can be used for the detection of explosives, in this way the discussion is organized based on their structures. Some design and data treatment requirements for obtaining an optical sensor are discussed, including statistical analysis and signal modelling. At the end of the chapter, future directions and perspectives are presented and discussed.

Aeronautical industry deals with extremely complex and sensitive issues, the most critical of which being arguably aircraft safety during flight. For a variety of reasons and through different pathways, the integrity of an airplane might be compromised in such a way that passengers and crew might be at risk. In the case of military aircraft, this risk is largely aggravated in war zones.

In this work, N-N′-diaryl-perylene-3,9-diamine (PDA) derivatives featuring different alkoxyl substituents at the para position of the N-aryl rings were synthesized and employed as emitters in solution processed organic light emitting diodes. Their physical properties were studied by UV-Vis absorption, fluorescence, differential scanning calorimetry, photo-electron yield spectroscopy and cyclic voltammetry, and were correlated with the OLED performance. Changing the length of the alkoxyl groups influences the PDAs' thermal properties, their bulk crystallinities and affects the performance of the respective OLEDs. The OLED emission spectra are red-shifted up to wavelengths of 800 nm, covering a spectral emission regime formerly inaccessible by other PDA derivatives.

Phasor plots of the fluorescence intensity decay (plots of the Fourier sine transform versus the Fourier cosine transform, for one or several angular frequencies) are being increasingly used in studies of homogeneous and heterogeneous systems. In this work, the phasor approach is applied to monomer-excimer kinetics. The results obtained allow a clear visualization of the information contained in the decays. The monomer phasor falls inside the universal circle, whereas the excimer phasor lies outside it, but within the double-exponential outer boundary curve. The monomer and excimer phasors, along with those corresponding to the two exponential components of the decays, fall on a common straight line and obey the generalized lever rule. The clockwise trajectories described by both phasors upon monomer concentration increase are identified. The phasor approach allows discussing in a single graphic not only the effect of concentration but also that of rate constants, including the evolution from irreversible kinetics to fast excited-state equilibrium upon a temperature increase. The obtained results are applied to the fluorescence decays of pyrene monomer and excimer in methylcyclohexane at room temperature. A straightforward method of monomer-excimer lifetime data analysis based on linear plots is also introduced.

Thermally activated delayed fluorescence (TADF) of 12C70 and 13C70 was observed up to 140 °C in a p-tert-butyldihomooxacalix[4]arene solid matrix, a temperature range significantly higher than that of previous TADF quantitative studies. An effective singlet-triplet energy gap of 29 kJ/mol and triplet formation quantum yields of 0.97 and 0.99 were measured for 12C70 and 13C70, respectively. The photophysical properties of the two fullerenes in this new matrix are comparable to those obtained in polystyrene at a lower temperature range. Calixarenes are proposed to be suitable matrices for high temperature TADF studies and applications.

The phosphorescence and thermally activated delayed fluorescence (TADF) lifetimes of

Phasor plots of the fluorescence intensity decay (plots of the Fourier sine transform vs the Fourier cosine transform, for one or several angular frequencies) are being increasingly used, namely, in fluorescence lifetime imaging microscopy (FLIM) of cells, tissues, and surfaces, but are also relevant for the characterization of homogeneous (e.g., solution) systems. In this work, the construction of the phasor plot using time domain data is discussed, including the effect of the instrument response function (IRF). A deconvolution method in the Fourier space is described. The results obtained are applied to fluorescence decays of aqueous fluorescein (basic form) in the presence of concentrated potassium iodide. The effect of the impulse is clearly shown, in accordance with model predictions. Deconvolution in the Fourier space works well for lifetimes at least 1 order of magnitude higher than the IRF time width.

The kinetics of the luminescence concentration depolarization of molecules in a medium is studied theoretically. It is shown that the concentration depolarization kinetics is well described by a stretched exponential function of time, r(t)/r 0 ≈ exp[−b(t/τ)β], where r(t) and r 0 are the luminescence anisotropy values at time moments t and t = 0, respectively. The parameters b and β allow the determinnation of the penetration depth of the molecules in the medium.

Luminescence decay functions describe the time dependence of the intensity of radiation emitted by electronically excited species. Decay phasor plots (plots of the Fourier sine transform vs. the Fourier cosine transform, for one or several angular frequencies) are being increasingly used in fluorescence, namely in lifetime imaging microscopy. In this work it is shown that the universal semicircle, locus of all exponential decay functions, can be viewed as the weighted sum of two spiraling phasors, one corresponding to a truncated exponential and the other to a shifted exponential. The geometric details of this recomposition are discussed. With area normalization, the decay functions form a subset in the universe of one-sided probability density functions, the same being valid for the phasor plots, which are parametric plots of the respective characteristic functions.

Luminescence decay functions describe the time dependence of the intensity of radiation emitted by electronically excited species. Decay phasor plots (plots of the Fourier sine transform vs. the Fourier cosine transform, for one or several angular frequencies) are being increasingly used in fluorescence, namely in lifetime imaging microscopy (FLIM). In this work, a detailed study of the sum of two exponentials decay function is carried out revealing that sub-exponential, super-exponential and unimodal decays have different phasor signatures. A generalization of the lever rule is obtained, and the existence of an outermost phasor curve corresponding to intermediate-like decays is demonstrated. A study of the behavior of more complex decay functions (sum of three exponentials, stretched and compressed exponentials, phosphorescence with reabsorption and triplet–triplet annihilation, fluorescence with quantum beats) allows concluding that a rich diversity of phasor plot patterns exists. In particular, super-exponential decays can present complex shapes, spiraling at high frequencies. The concept of virtual phasor is also introduced.

Molecular radiative transport, consisting in consecutive emission–absorption events by atoms or molecules of the same species, is studied in the case of excited-state absorption, a situation relevant to the phosphorescence of polycyclic aromatic hydrocarbons. This type of transfer differs in a number of ways from the better studied atomic resonance and molecular fluorescence cases, and leads to decays with a very distinctive form. A simple 1D model is introduced and used to discuss qualitatively the phosphorescence build-up and the phosphorescence decay in the presence of reabsorption. A new empirical phosphorescence decay law is also presented and justified on the basis of a phenomenological equation. The phosphorescence build-up and the phosphorescence decay in the presence of reabsorption are discussed and confronted with experimental results obtained for both normal and perdeuterated coronene.

The luminescence decay of a species in an absorbing medium whose optical thickness changes with time, as occurs with triplet-triplet absorption following excitation cut-off, is studied theoretically and experimentally. A general luminescence decay function based on a distribution of optical thicknesses is presented. A simple decay function previously used empirically is shown to result from an exponential distribution of optical thicknesses. The general approach introduced allows the adequate description of the phosphorescence decays of two polycyclic aromatic hydrocarbons, coronene and triphenylene (normal and perdeuterated forms for both molecules), in polymer films in the presence of excited-state absorption.

Luminescence decay functions describe the time dependence of radiation emitted by a sample after excitation. An overview of the mathematical aspects and systematics of luminescence decays is presented. In particular, super-exponential (faster-than-exponential) decays are defined and the possibility of their observation in single species physicochemical systems discussed. It is shown that this type of behavior can be both spontaneous and induced (by acting upon the system in real time). Spontaneous super-exponentiality is identified for the first time in experimental decays, these being phosphorescence decays affected by triplet–triplet absorption.

The dependence of the luminescence quantum yield of linear polymer molecules that contain chromophores at the ends on the number of units of polymer chain is studied. Numerical calculations for the dipole-dipole energy transfer between chromophores show that an increase in the chain length by a factor of 2 leads to a several-fold increase in the luminescence quantum yield depending on the ratio of the Forster radius to the radius of polymer coil. An approximate formula is derived for the adequate analysis of the dependence at the Forster radius that is significantly less than the radius of polymer coil. The dependence of the luminescence quantum yield of linear polymer molecules on the length of the statistical segment (unit) at a constant total length of the chain is also studied.

The phosphorescence decay under the effect of significant excited-state absorption has a distinctive signature: it is initially concave, switching to convex (pure exponential decay) after a certain time. A simple one-parameter decay function satisfactorily reproducing the experimental decays is discussed, and some of its peculiar mathematical properties analyzed.

Resonance energy transfer (RET), both radiative and nonradiative, is a well-known process in the molecular fluorescence field. On the other hand, RET has been much less explored in connection with phosphorescent systems. We have recently studied in detail phosphorescence reabsorption (radiative transfer) of polycyclic aromatic hydrocarbons in the presence of excited-state absorption. In this case, reabsorption of phosphorescence results from triplet-triplet (T-T) absorption overlapping the emission spectrum, i.e. Tn ← T1 radiative transitions, and not from absorption by ground state molecules, owing to the forbidden nature of the Tn←S0 radiative transitions. In this way, all absorbing molecules are already in the T1 state, and are generated in the first place by the external source, whose intensity and spatial distribution completely determines the set of allowed sites for excitation diffusion. The excitation moves from one triplet, that returns to the ground state, to another, that undergoes the fast sequence T1→Tn→T1 and thus remains unchanged, hence the elementary process for radiative transfer is T1 + T1 → S0 + T1. The process may take place a number of times. In this mechanism there is no radiation imprisonment, only a peculiar type of inner filter effect, as the emitted photon is lost and does not reach the detector. Unlike the fluorescence reabsorption process, phosphorescence reabsorption depends significantly on the excitation intensity, which determines the number and spatial distribution of triplets. Furthermore, the reabsorption probability is time-dependent, as the T-T absorption contribution to the optical thickness of the medium continuously decreases with time, after excitation cut-off: For sufficiently long times, the phosphorescence absorption probability is negligible, and the decay becomes exponential. However, for shorter times the decay has a distinctive form, displaying an initial concavity when reabsorption is significant [3,4]. For sufficiently high concentrations (typically around 0.01 M), nonradiative transfer of the type T1 + T1 → S0 + Tn (the final triplet state after relaxation being T1) by the dipole-dipole mechanism can also occur. Here, the phosphorescence decay is affected owing to an increase of the nonradiative decay rate. This process is sometimes called long-range triplet-triplet annihilation. For even higher concentrations (typically around 0.1 M) a significant fraction of molecules is so close that the exchange interaction is now operative. In this way, for high excitation intensities short-range triplet-triplet annihilation, T1 + T1 → S0 + S1, eventually preceded by triplet energy migration, T1 + S0 → S0 + T1, comes into play. The phosphorescence decay is again affected and delayed fluorescence may be observed. In this work, we discuss radiative and nonradiative transfer of energy owing to triplet-triplet absorption, including the effect of dimensionality. [1] D. L. Andrews and A. A. Demidov eds., Resonance Energy Transfer, Wiley, Chichester, 1999. [2] B. Valeur and M. N. Berberan-Santos, Molecular Fluorescence. Principles and Applications, Wiley-VCH, Weinheim, 2nd ed., 2012. [3] T. Palmeira, M. N. Berberan-Santos, J. Lumin. 158 (2015) 510-518. [4] T. Palmeira, A. Fedorov, M. N. Berberan-Santos, ChemPhysChem 16 (2015) 640-648.

Here, a comprehensive photophysical investigation of a the emitter molecule DPTZ‐DBTO2, showing thermally activated delayed fluorescence (TADF), with near‐orthogonal electron donor (D) and acceptor (A) units is reported. It is shown that DPTZ‐DBTO2 has minimal singlet–triplet energy splitting due to its near‐rigid molecular geometry. However, the electronic coupling between the local triplet (3LE) and the charge transfer states, singlet and triplet, (1CT, 3CT), and the effect of dynamic rocking of the D–A units about the orthogonal geometry are crucial for efficient TADF to be achieved. In solvents with low polarity, the guest emissive singlet 1CT state couples directly to the near‐degenerate 3LE, efficiently harvesting the triplet states by a spin orbit coupling charge transfer mechanism (SOCT). However, in solvents with higher polarity the emissive CT state in DPTZ‐DBTO2 shifts below (the static) 3LE, leading to decreased TADF efficiencies. The relatively large energy difference between the 1CT and 3LE states and the extremely low efficiency of the 1CT to 3CT hyperfine coupling is responsible for the reduction in TADF efficiency. Both the electronic coupling between 1CT and 3LE, and the (dynamic) orientation of the D–A units are thus critical elements that dictate reverse intersystem crossing processes and thus high efficiency in TADF.

A new diethylenetriamine-derived macrocycle known as L, bearing 2-methylquinoline arms and containing m-xylyl spacers, was prepared in good yield by a one-pot [2 + 2] Schiff base condensation procedure, followed by reduction with sodium borohydride. Up to now this is the first hexaazamacrocycle with appended fluorophore units. Single-crystal X-ray diffraction determination of the dinuclear zinc(II) complex of L showed that metal centers are located at about 7.20(2) Å from one another. This complex exhibits only weak fluorescence in aqueous solution, but the addition of 1 equiv of pyrophosphate (PPi) caused a 21-fold enhancement of the fluorescence intensity. The sensor response is linear up to a value of 10 μM HPPi(3-) and has a detection limit of 300 nM. The receptor behaves as a highly selective sensor for pyrophosphate as other anions, including phosphate, phenylphosphate (PhP), adenosine monophosphate (AMP), adenosine diphosphate (ADP), and adenosine triphosphate (ATP), failed to induce any fluorescence change and practically do not affect the fluorescence intensity of the sensor in the presence of HPPi(3-). Competition titrations carried out in aqueous solution at pH 7.4 [in 20 mM 3-(N-morpholino)propanesulfonic acid (MOPS) buffer] by spectrofluorometry revealed a high association constant value of 6.22 log units for binding of PPi by the dinuclear zinc(II) receptor, one of the highest reported values for colorimetric/fluorometric sensors able to work under real aqueous physiological conditions, while association constant values for binding of the other phosphorylated substrates are in the 5.51-4.03 log unit range.