Ionic liquids in a multiscale study

Trotz des hohen Interesse an Ionischen Flüssigkeiten wird das zielgerichtete Design und die Anwendung Ionischer Flüssigkeiten durch fehlendes grundlegendes Verständnis erschwert. Deshalb wurde die Balance der molekularen Wechselwirkungen in Ionischen Flüssigkeiten studiert, um die Eigenschaften dieser zu verstehen und die Kraftfeldentwicklung im Rahmen des Multiskalenansatzes zu systematisieren. Es wurden reine Imidazolium-basierte Ionische Flüssigkeiten, Mischungen mit kleinen Molekülen und eine protische Ionische Flüssigkeit mit ab-initio-Methoden, hauptsächlich Car-Parrinello-Molekulardynamik, untersucht. Weiterhin wurden Eigenschaften der Flüssigphase mit denen von Ionenpaaren verglichen.rnIm Fokus standen die molekularen elektrostatischen Eigenschaften und es wurde gezeigt, dass Coulomb-Wechselwirkungen zu einzigartigen Charakteristika führten. So waren die Ionen-Nettoladungen stets reduziert, die molekularen Dipolmomentverteilungen sehr breit, elektronische Polarisation war entscheidend. Die elektrostatischen Eigenschaften waren allgemein lokal auf molekularen Größen- und Zeitskalen und hingen stark von Phasenzustand und Zusammensetzung ab. Für andere molekulare Eigenschaften, wie der Neigung zu dispersiven Kontakten oder Wasserstoffbrücken, wurde gezeigt, dass sie einen entscheidenden Einfluss auf die Feinstruktur Ionischer Flüssigkeiten hatten. Das Gleichgewicht der Wechselwirkungen zeigte sich auch in Leistungsspektren, die sich aus den ab-initio-Molekulardynamiksimulationen ergaben. Diese boten einen neuen Weg für den Vergleich zum Experiment und für einen Einblick in die schnelle Dynamik Ionischer Flüssigkeiten.

Hadronic matrix elements in lattice QCD

The lattice formulation of Quantum ChromoDynamics (QCD) has become a reliable tool providing an ab initio calculation of low-energy quantities. Despite numerous successes, systematic uncertainties, such as discretisation effects, finite-size effects, and contaminations from excited states, are inherent in any lattice calculation. Simulations with controlled systematic uncertainties and close to the physical pion mass have become state-of-the-art. We present such a calculation for various hadronic matrix elements using non-perturbatively O(a)-improved Wilson fermions with two dynamical light quark flavours. The main topics covered in this thesis are the axial charge of the nucleon, the electro-magnetic form factors of the nucleon, and the leading hadronic contributions to the anomalous magnetic moment of the muon. Lattice simulations typically tend to underestimate the axial charge of the nucleon by 5 − 10%. We show that including excited state contaminations using the summed operator insertion method leads to agreement with the experimentally determined value. Further studies of systematic uncertainties reveal only small discretisation effects. For the electro-magnetic form factors of the nucleon, we see a similar contamination from excited states as for the axial charge. The electro-magnetic radii, extracted from a dipole fit to the momentum dependence of the form factors, show no indication of finite-size or cutoff effects. If we include excited states using the summed operator insertion method, we achieve better agreement with the radii from phenomenology. The anomalous magnetic moment of the muon can be measured and predicted to very high precision. The theoretical prediction of the anomalous magnetic moment receives contribution from strong, weak, and electro-magnetic interactions, where the hadronic contributions dominate the uncertainties. A persistent 3σ tension between the experimental determination and the theoretical calculation is found, which is considered to be an indication for physics beyond the Standard Model. We present a calculation of the connected part of the hadronic vacuum polarisation using lattice QCD. Partially twisted boundary conditions lead to a significant improvement of the vacuum polarisation in the region of small momentum transfer, which is crucial in the extraction of the hadronic vacuum polarisation.

Solvatochromic and Thermochromic Studies of Tryptanthrin

Solvatochromism and thermochromism describe how a solvent or environment affects the photophysical behavior of a photoluminescent solute. The most common use of solvatochromism is as a probe in which the polarity of a solvent in which a solvatochromic solute is dissolved can be spectroscopically measured. Solvatochromic and thermochromic studies of tryptanthrin in several different solvents are reported. Absorption and corrected emission spectra for tryptanthrin at ~10-6 M concentrations are reported in four aprotic and nine alcoholic solvents. The absorption spectra are relatively unaffected by changes in solvent polarity and by differences in the hydrogen bonding ability of the alcoholic solvents. The emission spectra are much more affected by changes in solvent polarity and hydrogen bonding ability. In aprotic solvents, emission energy decreases and emission intensity increases with increasing solvent polarity. In the alcoholic solvents, emission energy also decreases with increasing solvent polarity. However, emission intensity for the alcoholic solvents varies significantly from the aprotic solvents over similar polarity ranges. This suggests that in the alcoholic solvents, hydrogen bonding ability correlates better than polarity to emission energy and intensity trends. The absorption and emission data in the aprotic solvents were also used to estimate the ground and emitting excited state dipole moments for tryptanthrin. The value obtained for the ground state dipole moment (2.37 D) agrees with theoretical results (2.06 D) and a previously reported experimental value (2.0 D). Attempts to explain previously reported results and conclusions with respect to the solvatochromic behavior of the aromatic carbonyls fluorenone and benzo(b)fluorenone were explored in an attempt to understand the solvatochromic response of tryptanthrin. Such attempts include models dependent on non-radiative decay pathways like intersystem crossing, internal conversion, and hydrogen bonding interactions.

Frequency-domain source localization shows state-dependent diazepam effects in 47-channel EEG

The topic of this study was to evaluate state-dependent effects of diazepam on the frequency characteristics of 47-channel spontaneous EEG maps. A novel method, the FFT-Dipole-Approximation (Lehmann and Michel, 1990), was used to study effects on the strength and the topography of the maps in the different frequency bands. Map topography was characterized by the 3-dimensional location of the equivalent dipole source and map strength was defined as the spatial standard deviation (the Global Field Power) of the maps of each frequency point. The Global Field Power can be considered as a measure of the amount of energy produced by the system, while the source location gives an estimate of the center of gravity of all sources in the brain that were active at a certain frequency. State-dependency was studied by evaluating the drug effects before and after a continuous performance task of 25 min duration. Clear interactions between drug (diazepam vs. placebo) and time after drug intake (before and after the task) were found, especially in the inferior-superior location of the dipole sources. It supports the hypothesis that diazepam, like other drugs, has different effects on brain functions depending on the momentary functional state of the brain. In addition to the drug effects, clearly different source locations and Global Field Power were found for the different frequency bands, replicating earlier reports (Michel et al., 1992).

Pyroelectric and piezoelectric scanning microscopy applied to reveal the bipolar state of 4-iodo-4′-nitrobiphenyl (INBP)

Two recent scanning probe techniques were applied to investigate the bipolar twin state of 4-iodo-4′-nitrobiphenyl (INBP) crystals. Solution grown crystals of INBP show typically a morphology which does not express that of a mono-domain polar structure (Fdd2, mm2). From previous X-ray diffraction a twinning volume ratio of [similar]70 : 30 is now explained by two unipolar domains (Flack parameter: 0.075(29)) of opposite orientation of the molecular dipoles, joined by a transition zone showing a width of [similar]140 μm. Scanning pyroelectric microscopy (SPEM) demonstrates a continuous transition of the polarization P from +P into −P across the zone. Application of piezoelectric force microscopy (PFM) confirms unipolar alignment of INBP molecules down to a resolution of [similar]20 nm. A previously proposed real structure for INBP crystals built from lamellae with antiparallel alignment is thus rejected. Anomalous X-ray scattering was used to determine the absolute molecular orientation in the two domains. End faces of the polar axis 2 are thus made up by NO2 groups. Using a previously determined negative pyroelectric coefficient pc leads to a confirmation also by a SPEM analysis. Calculated values for functional group interactions (DA), (AA), (DD) and the stochastic theory of polarity formation allow us to predict that NO2 groups should terminate corresponding faces. Following the present analysis, INBP may represent a first example undergoing dipole reversal upon growth to end up in a bipolar state.

Solvation-Driven Charge Transfer and Localization in Metal Complexes

In any physicochemical process in liquids, the dynamical response of the solvent to the solutes out of equilibrium plays a crucial role in the rates and products: the solvent molecules react to the changes in volume and electron density of the solutes to minimize the free energy of the solution, thus modulating the activation barriers and stabilizing (or destabilizing) intermediate states. In charge transfer (CT) processes in polar solvents, the response of the solvent always assists the formation of charge separation states by stabilizing the energy of the localized charges. A deep understanding of the solvation mechanisms and time scales is therefore essential for a correct description of any photochemical process in dense phase and for designing molecular devices based on photosensitizers with CT excited states. In the last two decades, with the advent of ultrafast time-resolved spectroscopies, microscopic models describing the relevant case of polar solvation (where both the solvent and the solute molecules have a permanent electric dipole and the mutual interaction is mainly dipole−dipole) have dramatically progressed. Regardless of the details of each model, they all assume that the effect of the electrostatic fields of the solvent molecules on the internal electronic dynamics of the solute are perturbative and that the solvent−solute coupling is mainly an electrostatic interaction between the constant permanent dipoles of the solute and the solvent molecules. This well-established picture has proven to quantitatively rationalize spectroscopic effects of environmental and electric dynamics (time-resolved Stokes shifts, inhomogeneous broadening, etc.). However, recent computational and experimental studies, including ours, have shown that further improvement is required. Indeed, in the last years we investigated several molecular complexes exhibiting photoexcited CT states, and we found that the current description of the formation and stabilization of CT states in an important group of molecules such as transition metal complexes is inaccurate. In particular, we proved that the solvent molecules are not just spectators of intramolecular electron density redistribution but significantly modulate it. Our results solicit further development of quantum mechanics computational methods to treat the solute and (at least) the closest solvent molecules including the nonperturbative treatment of the effects of local electrostatics and direct solvent−solute interactions to describe the dynamical changes of the solute excited states during the solvent response.

Attenuated T2 relaxation by mutual cancellation of dipole–dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution

Fast transverse relaxation of 1H, 15N, and 13C by dipole-dipole coupling (DD) and chemical shift anisotropy (CSA) modulated by rotational molecular motions has a dominant impact on the size limit for biomacromolecular structures that can be studied by NMR spectroscopy in solution. Transverse relaxation-optimized spectroscopy (TROSY) is an approach for suppression of transverse relaxation in multidimensional NMR experiments, which is based on constructive use of interference between DD coupling and CSA. For example, a TROSY-type two-dimensional 1H,15N-correlation experiment with a uniformly 15N-labeled protein in a DNA complex of molecular mass 17 kDa at a 1H frequency of 750 MHz showed that 15N relaxation during 15N chemical shift evolution and 1HN relaxation during signal acquisition both are significantly reduced by mutual compensation of the DD and CSA interactions. The reduction of the linewidths when compared with a conventional two-dimensional 1H,15N-correlation experiment was 60% and 40%, respectively, and the residual linewidths were 5 Hz for 15N and 15 Hz for 1HN at 4°C. Because the ratio of the DD and CSA relaxation rates is nearly independent of the molecular size, a similar percentagewise reduction of the overall transverse relaxation rates is expected for larger proteins. For a 15N-labeled protein of 150 kDa at 750 MHz and 20°C one predicts residual linewidths of 10 Hz for 15N and 45 Hz for 1HN, and for the corresponding uniformly 15N,2H-labeled protein the residual linewidths are predicted to be smaller than 5 Hz and 15 Hz, respectively. The TROSY principle should benefit a variety of multidimensional solution NMR experiments, especially with future use of yet somewhat higher polarizing magnetic fields than are presently available, and thus largely eliminate one of the key factors that limit work with larger molecules.

Lipid monolayer image dipoles.

A simple model is described for calculating the electrostatic energy of lipid domains at the air-water interface, taking account of dipole-dipole repulsions between the lipid molecules themselves, as well as interactions between the molecular dipoles and image dipoles in the subphase. The model assumes that the molecular dipoles within the monolayer arise from the terminal methyl groups of the hydrophobic hydrocarbon chains of the lipid molecules, and that on average they are oriented perpendicular to the plane of the monolayer. With this model the role of the subphase is to enhance rather than suppress the effects of dipole-dipole repulsions.

Junções moleculares e agregados de nanobastões de ouro: um estudo SERS

A Espectroscopia Raman Intensificada pela Superfície (SERS) é um efeito de intensificação da intensidade Raman de uma molécula adsorvida numa superfície metálica nanoestruturada. Esta característica permite a utilização do SERS na caracterização vibracional de sistemas como junções moleculares (JM) (JM são sistemas constituídos de fios moleculares sintetizados em junções do tipo metal|fiomolecular|metal) e, no entendimento de quais características morfológicas de agregados metálicos mais influenciariam no sinal SERS obtido. Portanto, esta tese apresenta os seguintes objetivos: (a) síntese e caracterização de substratos SERS ativos, nanoesferas (AuNE) e nanobastões (AuNB) de ouro e eletrodo de ouro ativado eletroquimicamente; (b) síntese e caracterização SERS de fios moleculares em JM; (c) estudo do acoplamento plasmônico entre as superfícies metálicas em JM; (d) correlação entre SERS - morfologia de agregados individuais de AuNB. Os fios moleculares estudados foram os da família das oligofeniliminas (OPI) e, no melhor do nosso entendimento, esta foi a primeira vez que fios moleculares desta família foram caracterizados por Raman e SERS. As JM apresentaram um comportamento SERS não esperado. Enquanto para o modo vibracional, v(CS), a intensidade da banda se apresentou constante com o aumento do espaçamento entre as nanoestruturas metálicas (para distâncias de até 5 nm), o modo vibracional, β(CH), teve a intensidade de sua banda aumentada. Este comportamento foi explicado considerando a diferente natureza da interação dos plasmons nas JM, sendo estas interações do tipo, ressonância de plasmon de superfície (LSPR) - dipolo imagem, para ambos os modos. No entanto, para o modo β(CH) existe também uma intensificação extra devido ao aumento da polarizabilidade dos fios moleculares com o aumento do número de unidades. A correlação SERS - morfologia dos agregados de AuNB indicam que, para agregados onde predominam interações ponta a ponta, os espectros SERS apresentavam uma maior intensidade quando comparados com aqueles em que interações lado a lado predominavam. No entanto, este comportamento não foi observado para agregados contendo mais do que cinco nanopartículas onde estes dois tipos de interações ocorrem indicando que deve existir um acoplamento dos plasmons destes dois tipos de interações contribuindo para maiores valores de intensidade SERS.

Efeito do macrodipolo sobre a estabilidade térmica de derivados de 1,3,5-tricarboxamida-ciclo-hexano

1,3,5-tricarboxamida-ciclo-hexano são compostos capazes de se autoagregarem formando colunas supramoleculares as quais se mantêm unidas não só devido às interações das cadeias laterais mas também devido às ligações de hidrogênio de cada um dos três grupos amida por monômero. Cada monômero possui momento de dipolo elétrico associado aos grupos amida. Quando as amidas dos vários monômeros dentro da mesma coluna estão apontadas para a mesma direção, os momentos de dipolo individuais de todas as amidas se somam formando elevado dipolo ao longo do eixo da coluna, chamado de macrodipolo, o qual influencia as interações intercolunares. Neste trabalho foram investigadas quatro conformações as quais diferem entre si em relação à orientação dos grupos carbonila: a conformação Up-Up contém grupos carbonilas paralelos dentro das colunas e colunas paralela, a conformação Up-Down possui grupos carbonilas paralelos dentro das colunas e colunas antiparalelas, a conformação Intra-Up-Up contém grupos carbonilas antiparalelos dentro das colunas e colunas paralelas e a conformação Intra-Up-Down possui grupos carbonilas antiparalelos dentro das colunas e colunas antiparalelas. Foi usado Dinâmica Molecular Clássica para investigar o efeito das interações macrodipolo-macrodipolo das quatro diferentes conformações sobre a estabilidade térmica de três diferentes compostos derivados de 1,3,5-tricarboxamida-ciclo-hexano. Foi verificado que as conformações com colunas antiparalelas tendem a ser ligeiramente mais estáveis do que as conformações com orientação paralela. O efeito da orientação dos grupos carbonila dentro das colunas sob a estabilidade do material está relacionado a vários fatores, tais como cargas atômicas parciais, arranjo colunar ou natureza das cadeias laterais, e os resultados não são tão diretos como quando se compara as orientações entre colunas. Outro tópico investigado foi o comportamento do material durante a transição da fase colunar para a fase desordenada. As colunas podem se desmontar em três diferentes formas: elas podem completamente se desintegrar rapidamente, podem primeiro se desintegrar lentamente e então perder a ordem colunar ou primeiro perdem a ordem colunar e então se desmontam em um processo demorado. Tais comportamentos estão associados com as interações dentro e entre colunas.

Dinâmica das configurações de formação e inibição das chuvas no Rio Grande do Norte: caracterização hidroclimática do estado

This study aimed to evaluate the influence of the main meteorological mechanisms trainers and inhibitors of precipitation, and the interactions between different scales of operation, the spatial and temporal variability of the annual cycle of precipitation in the Rio Grande do Norte. Além disso, considerando as circunstâncias locais e regionais, criando assim uma base científica para apoiar ações futuras na gestão da demanda de água no Estado. Database from monthly precipitation of 45 years, ranging between 1963 and 2007, data provided by EMPARN. The methodology used to achieve the results was initially composed of descriptive statistical analysis of historical data to prove the stability of the series, were applied after, geostatistics tool for plotting maps of the variables, within the geostatistical we opted for by Kriging interpolation method because it was the method that showed the best results and minor errors. Among the results, we highlight the annual cycle of rainfall the State which is influenced by meteorological mechanisms of different spatial and temporal scales, where the main mechanisms cycle modulators are the Conference Intertropical Zone (ITCZ) acting since midFebruary to mid May throughout the state, waves Leste (OL), Lines of instability (LI), breeze systems and orographic rainfall acting mainly in the Coastal strip between February and July. Along with vortice of high levels (VCANs), Complex Mesoscale Convective (CCMs) and orographic rain in any region of the state mainly in spring and summer. In terms of larger scale phenomena stood out El Niño and La Niña, ENSO in the tropical Pacific basin. In La Niña episodes usually occur normal or rainy years, as upon the occurrence of prolonged periods of drought are influenced by EL NIÑO. In the Atlantic Ocean the standard Dipole also affects the intensity of the rainfall cycle in State. The cycle of rains in Rio Grande do Norte is divided into two periods, one comprising the regions West, Central and the Western Portion of the Wasteland Potiguar mesoregions of west Chapada Borborema, causing rains from midFebruary to mid-May and a second period of cycle, between February-July, where rains occur in mesoregions East and of the Wasteland, located upwind of the Chapada Borborema, both interspersed with dry periods without occurrence of significant rainfall and transition periods of rainy - dry and dry-rainy where isolated rainfall occur. Approximately 82% of the rainfall stations of the state which corresponds to 83.4% of the total area of Rio Grande do Norte, do not record annual volumes above 900 mm. Because the water supply of the State be maintained by small reservoirs already are in an advanced state of eutrophication, when the rains occur, act to wash and replace the water in the reservoirs, improving the quality of these, reducing the eutrophication process. When rain they do not significantly occur or after long periods of shortages, the process of eutrophication and deterioration of water in dams increased significantly. Through knowledge of the behavior of the annual cycle of rainfall can have an intimate knowledge of how it may be the tendency of rainy or prone to shortages following period, mainly observing the trends of larger scale phenomena

Influência da interação dipolar nas fases magnéticas de nanopartículas esféricas com estrutura núcleo@camada

Bi-magnetic core@shell nanoparticle has attracted attention several researchers because great applicability that they offer. The possibility of combining different functionalities of magnetic materials make them a key piece in many areas as in data processing permanent magnets and biomagnetics sistems. These nanoparticles are controlled by intrinsic properties of the core and shell materials as well as the interactions between them, besides size and geometry effects. Thus, it was developed in this thesis a theoretical study about dipolar interaction contribution between materials different magnetic properties in bi-magnetic core@shell nanoparticles conventional spherical geometry. The materials were analyzed CoFe2O4, MnFe2O4 e CoFe2 in various combinations and sizes. The results show that the impact of the core dipole field in the shell cause reverse magnetization early its, before of the core, in nanoparticle of CoFe2O4(22nm)@CoFe2(2nm), thereby causing a decrease coercivity field of 65% in comparection with simple nanoparticle of CoFe2O4 (HC=13.6 KOe) of same diameter. The large core anisotropy in conventional nanoparticle makes it the a stable dipolar field source in the shell, that varies length scale of the order of the core radius. Furthermore, the impact of dipolar field is greatly enhanced by the geometrical constraints and by magnetics properties of both core@shell materials. In systems with core coated with a thin shell of thickness less than the exchange length, the interaction interface can hold reversal the shell occurring an uniform magnetization reversal, however this effect only is relevant on systems where the dipole field effects is weak compared with the exchange interaction.

Influência da interação dipolar nas fases magnéticas de nanopartículas esféricas com estrutura núcleo@camada

Bi-magnetic core@shell nanoparticle has attracted attention several researchers because great applicability that they offer. The possibility of combining different functionalities of magnetic materials make them a key piece in many areas as in data processing permanent magnets and biomagnetics sistems. These nanoparticles are controlled by intrinsic properties of the core and shell materials as well as the interactions between them, besides size and geometry effects. Thus, it was developed in this thesis a theoretical study about dipolar interaction contribution between materials different magnetic properties in bi-magnetic core@shell nanoparticles conventional spherical geometry. The materials were analyzed CoFe2O4, MnFe2O4 e CoFe2 in various combinations and sizes. The results show that the impact of the core dipole field in the shell cause reverse magnetization early its, before of the core, in nanoparticle of CoFe2O4(22nm)@CoFe2(2nm), thereby causing a decrease coercivity field of 65% in comparection with simple nanoparticle of CoFe2O4 (HC=13.6 KOe) of same diameter. The large core anisotropy in conventional nanoparticle makes it the a stable dipolar field source in the shell, that varies length scale of the order of the core radius. Furthermore, the impact of dipolar field is greatly enhanced by the geometrical constraints and by magnetics properties of both core@shell materials. In systems with core coated with a thin shell of thickness less than the exchange length, the interaction interface can hold reversal the shell occurring an uniform magnetization reversal, however this effect only is relevant on systems where the dipole field effects is weak compared with the exchange interaction.

Time-domain simulation of wave-induced ship motions by a Rankine panel method

In this thesis, a numerical program has been developed to simulate the wave-induced ship motions in the time domain. Wave-body interactions have been studied for various ships and floating bodies through forced motion and free motion simulations in a wide range of wave frequencies. A three-dimensional Rankine panel method is applied to solve the boundary value problem for the wave-body interactions. The velocity potentials and normal velocities on the boundaries are obtained in the time domain by solving the mixed boundary integral equations in relation to the source and dipole distributions. The hydrodynamic forces are calculated by the integration of the instantaneous hydrodynamic pressures over the body surface. The equations of ship motion are solved simultaneously with the boundary value problem for each time step. The wave elevation is computed by applying the linear free surface conditions. A numerical damping zone is adopted to absorb the outgoing waves in order to satisfy the radiation condition for the truncated free surface. A numerical filter is applied on the free surface for the smoothing of the wave elevation. Good convergence has been reached for both forced motion simulations and free motion simulations. The computed added-mass and damping coefficients, wave exciting forces, and motion responses for ships and floating bodies are in good agreement with the numerical results from other programs and experimental data.

Mixing of 0(+) and 0(-) observed in the hyperfine and Zeeman structure of ultracold Rb-2 molecules

We study the combination of the hyperfine and Zeeman structure in the spin-orbit coupled A(1)Sigma(+)(u) = b(3)Pi(u) complex of Rb-87(2). For this purpose, absorption spectroscopy at a magnetic field around B = 1000 G is carried out. We drive optical dipole transitions from the lowest rotational state of an ultracold Feshbach molecule to various vibrational levels with 0(+) symmetry of the A - b complex. In contrast to previous measurements with rotationally excited alkali-dimers, we do not observe equal spacings of the hyperfine levels. In addition, the spectra vary substantially for different vibrational quantum numbers, and exhibit large splittings of up to 160 MHz, unexpected for 0(+) states. The level structure is explained to be a result of the repulsion between the states 0(+) and 0(-) of b(3)Pi(u), coupled via hyperfine and Zeeman interactions. In general, 0(-) and 0(+) have a spin-orbit induced energy spacing Delta, that is different for the individual vibrational states. From each measured spectrum we are able to extract Delta, which otherwise is not easily accessible in conventional spectroscopy schemes. We obtain values of Delta in the range of +/- 100 GHz which can be described by coupled channel calculations if a spin-orbit coupling is introduced that is different for 0(-) and 0(+) of b(3)Pi(u).