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Lectio praecursoria
- 1. Properties of molecules in weak and strong magnetic fields Maria Dimitrova University of Helsinki Department of Chemistry 7.11.2019 1 Lectio praecursoria
- 2. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Magnetic fields • Angular momentum • Magnetic properties of molecules • Magnetically induced currents • Molecules in strong magnetic fields • Summary 7.11.2019 2 Contents
- 3. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 3 Magnetic field lines
- 4. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 4 Electromagnetic induction: Faraday’s law 𝐼𝑖𝑛𝑑 𝐵𝑒𝑥𝑡
- 5. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 5 Electromagnetic induction: The Biot-Savart law 𝐼 𝐵𝑖𝑛𝑑
- 6. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 6 Magnetic field induced by a closed current loop 𝐵𝑖𝑛𝑑 𝐵𝑖𝑛𝑑 𝐼
- 7. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 7 Magnetism and molecules N S
- 8. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • The electron is spinning around the nucleus; • There is angular momentum associated with the rotational motion 7.11.2019 8 Angular momentum: classically 𝒑 = 𝑚𝒗 𝑭 → 𝑳 = 𝒓 × 𝒑
- 9. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • An electron has an intrinsic spin magnetic moment • Spin angular momentum is associated with it 7.11.2019 9 Electron spin
- 10. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • The electron is not a point particle • Electronic motion does not have a trajectory • Angular momentum can only take certain values • It is an important characteristic of the electronic state 7.11.2019 10 Angular momentum: quantum-mechanically
- 11. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 11 Energy splitting of orbitals with the same angular momentum 𝐸 𝐵
- 12. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 12 Splitting of the spin states 𝐸 𝐵
- 13. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Diamagnetic • Expel the magnetic field lines • Energy increases in a magnetic field → repelled by magnets • Closed-shell systems • Paramagnetic • Enhance the magnetic field lines • Energy decreases in a magnetic field → attracted by magnets • Non-zero orbital or spin angular momentum • Closed-shell paramagnetism • Due to magnetically induced currents 7.11.2019 13 Magnetic response of materials
- 14. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria Orders of magnitude 𝟏 𝒂. 𝒖. = 𝟐𝟑𝟓 𝟎𝟎𝟎 𝑻 𝟏𝟎−𝟏𝟕 𝑩 𝟎 (brain) 𝟏𝟎−𝟏𝟎 𝑩 𝟎 (Earth’s MF) 𝟏𝟎−𝟖 𝑩 𝟎 (fridge magnet) 𝟏𝟎−𝟔 𝑩 𝟎 (sunspot) 7.11.2019 14 Pictures: Wikimedia Commons Orders of magnitude of magnetic fields > 𝟏 𝑩 𝟎 (neutron star) 𝟏𝟎−𝟑 𝑩 𝟎 (lab magnet) 𝟏𝟎−𝟒 𝑩 𝟎 (NMR) 𝟏𝟎−𝟓 𝑩 𝟎 (Nd magnet)
- 15. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • At 10 T the melting point of H2O and D2O are higher by 5.6 mK and 21.8 mK respectively • The viscosity and surface tension of water increase • Hydrogen bonds become stronger 7.11.2019 15 Molecules in external magnetic fields Iwasaka, Ueno, J. Appl. Phys. 83 (1998) 6459. Inaba, Saitou, Tozaki, Hayashi, J. Appl. Phys. 96 (2004) 6127. Ghauri, Ansari, J. Appl. Phys. 100 (2006) 1066101. Fujimura, Iino, J. Appl. Phys. 103 (2008) 124903.
- 16. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • At ~1 T carbon nanotubes grow in higher quality due to alignment with the magnetic field lines • Quantum Hall effect in carbon nanotubes and graphene • The electrons in some semiconductors act as if the magnetic field is very strong 7.11.2019 16 Molecules in external magnetic fields Kordás et al. Chem. Mater. 19 (2007) 787 Bellucci et al. J. Phys. Condens. Matter 19 (2007) 395017. Novoselov et al. Nature 438 (2005) 197. Murdin et al. Nat. Comm. 4 (2013) 1469.
- 17. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • On white dwarfs (0.2 T – 100 kT, 8000 − 16 000 K) • Confirmed small molecular species on white dwarf stars: • Molecular hydrogen H2 • Neutron stars (104 − 1011 T) • Orbitals become like needles • Predicted: Hydrogen molecular ion H2 + • Predicted: hydrogen polymer molecular chains 7.11.2019 17 Extreme magnetic fields Xu, Jura, Koester, Klein, Zuckerman. Astrophys. J. 766 (2013) L18. Khersonskii. Astrophysics and Space Science 98 (1984) 255. De Melo, Ferreira, Brandi, Miranda. Phys. Rev. Lett. 73 (1976) 676. Lai, Salpeter, Shapiro. Phys. Rev. A. 45 (1992) 4832.
- 18. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Near atomic nuclei • Around chemical bonds • Inside molecular rings • Around the whole molecule 7.11.2019 18 Magnetically induced currents
- 19. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 19 Experimental methods limited Source: DOI: 10.1016/j.polymer.2004.05.025
- 20. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Schrödinger equation: 7.11.2019 20 Solution: computational chemistry − ℏ2 2𝑚 𝛻2 Ψ + VΨ = 𝐸Ψ
- 21. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 21 Aromaticity • Benzene isolated by Michael Faraday (1825) • Its structure? Michael Faraday's sample of benzene at the Royal Institution Source: www.rigb.org
- 22. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 22 An aromatic molecule?
- 23. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 23 Hückel’s empirical rule for aromaticity Antiaromatic: 4𝑛 𝜋 electrons Aromatic: (4𝑛 + 2) 𝜋 electrons
- 24. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 24 Ring currents in linear molecules
- 25. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 25 Ring currents in linear molecules
- 26. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 26 Ring currents in benzene
- 27. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 27 Ring currents in pentalene
- 28. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 28 Ring currents in pentalene 0.5 𝑎0 above the molecular plane
- 29. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 29 Ring currents in pentalene 1 𝑎0 above the molecular plane
- 30. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 30 Ring currents in dibenzopentalene
- 31. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Place an integration plane and calculate the strength of the current flux through it 7.11.2019 31 Quantifying the ring-current strength There are no sources or sinks – charge is conserved
- 32. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Global and local current pathways 7.11.2019 32 Toroidal carbon nanotubes K. Reiter, F. Weigend, L. N. Wirz, M. Dimitrova, D. Sundholm. J. Phys. Chem. C. 123 (2019) 15354.
- 33. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 33 Helical currents in toroidal carbon nanotubes K. Reiter, F. Weigend, L. N. Wirz, M. Dimitrova, D. Sundholm. J. Phys. Chem. C. 123 (2019) 15354.
- 34. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Deeper understanding of the electronic structure of the molecule • Optoelectronics • Dyes • Solar cells 7.11.2019 34 Applications
- 35. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 35 Let’s put the molecule in a strong magnetic field! − ℏ2 2𝑚 𝛻2 Ψ + VΨ = 𝐸Ψ Problems: • Standard quantum-chemistry are not suitable • Electronic structure becomes complicated • Accuracy • Computationally more demanding
- 36. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • The p orbital in C in 𝐵 = 0 (left) and 𝐵 = 10 𝐵0 (right) 7.11.2019 37 Atomic orbitals in extreme magnetic fields = 2 350 517 𝑇 (a couple billion fridge magnets)
- 37. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 38 C atom: triplets and quintets -39 -38.8 -38.6 -38.4 -38.2 -38 -37.8 -37.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 E,[H] B/B0 Triplets: dashed lines; quintets: solid lines.
- 38. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Convergence to different states • Slow (<1 s vs 16 min for CH4) 7.11.2019 39 Accuracy of calculations S. Lehtola, M. Dimitrova, D. Sundholm. Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields. Mol. Phys. (2019) 𝐵𝑒𝐻+ , B∥
- 39. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 40 CH, 𝑩 = 0.7 𝑩 𝟎 -39.5 -39.3 -39.1 -38.9 -38.7 -38.5 -38.3 -38.1 0.8 1.8 2.8 3.8 4.8 5.8 E,[Eh] r, [a0] B parallel, doublet B perp, doublet B parallel, quartet B parallel, quartet B parallel, quartet B perp, quartet B perp, quartet B parallel, sextet B parallel, sextet B perp, sextet B perp, sextet
- 40. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • CH, CH2, CH3 and CH4 investigated for 𝐵 = [0; 𝐵0] • Bound states exist in 𝐵 ⊥ C − H • High-spin configurations (only 1s2 paired) 7.11.2019 41 C – H fragments Molecule 𝑬 𝒃𝒊𝒏𝒅 at 0.9 𝑩 𝟎, [kcal/mol] CH 4.0 CH2 7.6 CH3 11.4 CH4 16.0
- 41. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria • Magnetically induced currents arise • Molecules have a preferred direction with respect to the magnetic field • The order of states changes • High spin multiplicity is favoured • Bonds form between electrons with parallel spins 7.11.2019 43 Summary
- 42. Maria Dimitrova | Properties of molecules in weak and strong magnetic fields Lectio praecursoria 7.11.2019 44
Editor's Notes
- Faraday's Law Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated.
- In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law that André-Marie Ampère discovered in 1823[1]) relates the integrated magnetic field around a closed loop to the electric current passing through the loop. In physics, specifically electromagnetism, the Biot–Savart law (/ˈbiːoʊ səˈvɑːr/ or /ˈbjoʊ səˈvɑːr/)[1] is an equation describing the magnetic field generated by an electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The law is valid in the magnetostatic approximation, and is consistent with both Ampère's circuital law and Gauss's law for magnetism.[2] It is named after Jean-Baptiste Biot and Félix Savart who discovered this relationship in 1820. The Biot–Savart law is used for computing the resultant magnetic field B at position r generated by a steady current I (for example due to a wire): a continual flow of charges which is constant in time and the charge neither accumulates nor depletes at any point. The law is a physical example of a line integral, being evaluated over the path C in which the electric currents flow. The equation in SI units is[3] B ( r ) = μ 0 4 π ∫ C I d l × r ′ | r ′ | 3 {\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\int _{C}{\frac {Id\mathbf {l} \times \mathbf {r'} }{|\mathbf {r'} |^{3}}}} where d l {\displaystyle d\mathbf {l} } is a vector whose magnitude is the length of the differential element of the wire in the direction of conventional current, r ′ = r − l {\displaystyle \mathbf {r'} =\mathbf {r} -\mathbf {l} } , the full displacement vector from the wire element ( l {\displaystyle \mathbf {l} } ) to the point at which the field is being computed ( r {\displaystyle \mathbf {r} } ), and μ0 is the magnetic constant. Alternatively: B ( r ) = μ 0 4 π ∫ C I d l × r ^ ′ | r ′ | 2 {\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\int _{C}{\frac {Id\mathbf {l} \times \mathbf {{\hat {r}}'} }{|\mathbf {r'} |^{2}}}} where r ^ ′ {\displaystyle \mathbf {{\hat {r}}'} } is the unit vector of r ′ {\displaystyle \mathbf {r'} } . The symbols in boldface denote vector quantities. Magnetic responses applications The Biot–Savart law can be used in the calculation of magnetic responses even at the atomic or molecular level, e.g. chemical shieldings or magnetic susceptibilities, provided that the current density can be obtained from a quantum mechanical calculation or theory.
- Weak field (Zeeman effect) If the spin-orbit interaction dominates over the effect of the external magnetic field, L → {\displaystyle \scriptstyle {\vec {L}}} and S → {\displaystyle \scriptstyle {\vec {S}}} are not separately conserved, only the total angular momentum J → = L → + S → {\displaystyle \scriptstyle {\vec {J}}={\vec {L}}+{\vec {S}}} is. The spin and orbital angular momentum vectors can be thought of as precessing about the (fixed) total angular momentum vector J → {\displaystyle \scriptstyle {\vec {J}}} . The (time-)"averaged" spin vector is then the projection of the spin onto the direction of J → {\displaystyle \scriptstyle {\vec {J}}} : S → a v g = ( S → ⋅ J → ) J 2 J → {\displaystyle {\vec {S}}_{avg}={\frac {({\vec {S}}\cdot {\vec {J}})}{J^{2}}}{\vec {J}}} and for the (time-)"averaged" orbital vector: L → a v g = ( L → ⋅ J → ) J 2 J → . {\displaystyle {\vec {L}}_{avg}={\frac {({\vec {L}}\cdot {\vec {J}})}{J^{2}}}{\vec {J}}.} Strong field (Paschen–Back effect) The Paschen–Back effect is the splitting of atomic energy levels in the presence of a strong magnetic field. This occurs when an external magnetic field is sufficiently strong to disrupt the coupling between orbital ( L → {\displaystyle {\vec {L}}} ) and spin ( S → {\displaystyle {\vec {S}}} ) angular momenta. This effect is the strong-field limit of the Zeeman effect. When s = 0 {\displaystyle s=0} , the two effects are equivalent. m l {\displaystyle m_{l}} and m s {\displaystyle m_{s}} are still "good" quantum numbers.
- Weak field (Zeeman effect) If the spin-orbit interaction dominates over the effect of the external magnetic field, L → {\displaystyle \scriptstyle {\vec {L}}} and S → {\displaystyle \scriptstyle {\vec {S}}} are not separately conserved, only the total angular momentum J → = L → + S → {\displaystyle \scriptstyle {\vec {J}}={\vec {L}}+{\vec {S}}} is. The spin and orbital angular momentum vectors can be thought of as precessing about the (fixed) total angular momentum vector J → {\displaystyle \scriptstyle {\vec {J}}} . The (time-)"averaged" spin vector is then the projection of the spin onto the direction of J → {\displaystyle \scriptstyle {\vec {J}}} : S → a v g = ( S → ⋅ J → ) J 2 J → {\displaystyle {\vec {S}}_{avg}={\frac {({\vec {S}}\cdot {\vec {J}})}{J^{2}}}{\vec {J}}} and for the (time-)"averaged" orbital vector: L → a v g = ( L → ⋅ J → ) J 2 J → . {\displaystyle {\vec {L}}_{avg}={\frac {({\vec {L}}\cdot {\vec {J}})}{J^{2}}}{\vec {J}}.} Strong field (Paschen–Back effect) The Paschen–Back effect is the splitting of atomic energy levels in the presence of a strong magnetic field. This occurs when an external magnetic field is sufficiently strong to disrupt the coupling between orbital ( L → {\displaystyle {\vec {L}}} ) and spin ( S → {\displaystyle {\vec {S}}} ) angular momenta. This effect is the strong-field limit of the Zeeman effect. When s = 0 {\displaystyle s=0} , the two effects are equivalent. m l {\displaystyle m_{l}} and m s {\displaystyle m_{s}} are still "good" quantum numbers.
- 1 𝐺= 10 −4 𝑇 Fowler et a1 (1960) reported a field of 1400 T lasting for 2 ps. This technique has the disadvantage of being self-destructive. The stress in the containing chambers and the thermal heating by eddy currents during pulses limit the steady fields which are possible in the laboratory. This limit depends somewhat on the available materials, but is typically about 50 T. The magnetic pressure (B218.r) may be written numerically as P = 3.9 x 105 B2, where P is in N m-2 and B in T. Thus at a field of 0.5 T the magnetic pressure is about io5 N m-2 (about 1 atm). At 103 T the pressure is 3.9 x 1011 N m-2, about equal to the pressure at the centre of the Earth! Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from the Earth's interior out into space, where it meets the solar wind, a stream of charged particles emanating from the Sun. Its magnitude at the Earth's surface ranges from 25 to 65 microteslas (0.25 to 0.65 gauss).[3] Approximately, it is the field of a magnetic dipole currently tilted at an angle of about 11 degrees with respect to Earth's rotational axis, as if there were a bar magnet placed at that angle at the center of the Earth. The North geomagnetic pole, located near Greenland in the northern hemisphere, is actually the south pole of the Earth's magnetic field, and the South geomagnetic pole is the north pole. The magnetic field is generated by electric currents due to the motion of convection currents of molten iron in the Earth's outer core driven by heat escaping from the core, a natural process called a geodynamo. The magnetosphere is the region above the ionosphere that is defined by the extent of the Earth's magnetic field in space. It extends several tens of thousands of kilometers into space, protecting the Earth from the charged particles of the solar wind and cosmic rays that would otherwise strip away the upper atmosphere, including the ozone layer that protects the Earth from harmful ultraviolet radiation. The Earth and most of the planets in the Solar System, as well as the Sun and other stars, all generate magnetic fields through the motion of electrically conducting fluids.[47] The Earth's field originates in its core. The mechanism by which the Earth generates a magnetic field is known as a dynamo.[47] The magnetic field is generated by a feedback loop: current loops generate magnetic fields (Ampère's circuital law); a changing magnetic field generates an electric field (Faraday's law); and the electric and magnetic fields exert a force on the charges that are flowing in currents (the Lorentz force).[51] These effects can be combined in a partial differential equation for the magnetic field called the magnetic induction equation, ∂ B ∂ t = η ∇ 2 B + ∇ × ( u × B ) , {\displaystyle {\frac {\partial \mathbf {B} }{\partial t}}=\eta \nabla ^{2}\mathbf {B} +\nabla \times (\mathbf {u} \times \mathbf {B} ),} where u is the velocity of the fluid; B is the magnetic B-field; and η=1/σμ is the magnetic diffusivity, which is inversely proportional to the product of the electrical conductivity σ and the permeability μ .[52] The term ∂B/∂t is the time derivative of the field; ∇2 is the Laplace operator and ∇× is the curl operator. The first term on the right hand side of the induction equation is a diffusion term. In a stationary fluid, the magnetic field declines and any concentrations of field spread out. If the Earth's dynamo shut off, the dipole part would disappear in a few tens of thousands of years.[52] In a perfect conductor ( σ = ∞ {\displaystyle \sigma =\infty \;} ), there would be no diffusion. By Lenz's law, any change in the magnetic field would be immediately opposed by currents, so the flux through a given volume of fluid could not change. As the fluid moved, the magnetic field would go with it. The theorem describing this effect is called the frozen-in-field theorem. Even in a fluid with a finite conductivity, new field is generated by stretching field lines as the fluid moves in ways that deform it. This process could go on generating new field indefinitely, were it not that as the magnetic field increases in strength, it resists fluid motion.[52] Jupiter's magnetosphere is the largest and most powerful of any planetary magnetosphere in the Solar System, and by volume the largest known continuous structure in the Solar System after the heliosphere. Wider and flatter than the Earth's magnetosphere, Jupiter's is stronger by an order of magnitude, while its magnetic moment is roughly 18,000 times larger. Magnetic moment 2.83 × 1020 T·m3 Equatorial field strength 776.6 μT (7.766 G) highly magnetized neutron stars with surface magnetic fields of order B∼10^15 G -> 10^ 𝐵 ~ 10 15 𝐺= 10 11 𝑇= 10 6 𝑎.𝑢. Clinical MRI: 0.5 – 3 T white dwarfs: 10^1 –10^5 T; neutron stars 10^8 –10^9 T; magnetars 10^10 T At B > B0 magnetic interaction overpowers Coulomb forces
- https://doi.org/10.1016/j.molstruc.2009.08.037 Abstract In this paper, the experimental results on the effects of a magnetic field on water are reported. Purified water was circulated at a constant flow rate in a magnetic field. After this treatment, the physicochemical properties of water were changed, shown as the decrease of surface tension and the increase of viscosity over the treatment time. The water is more stable by magnetic treatment with less molecular energy and more activation energy, as shown from the calculation based on the results. The correlation time was calculated in terms of spin–lattice relaxation time of proton NMR, which verified that the rotational motions got slow down after magnetic treatments. A two-phase model was set up to prove that the proportion of free water molecules was reduced. The results suggested that the average size of water clusters became larger by magnetic treatments. Magnetic field increases the surface tension of water - IOPscience iopscience.iop.org/article/10.1088/1742-6596/156/1/012028/meta The surface tension increased by 1.83 ± 0.18 % at the magnetic field of 10 T. As for artificial effects and possible contributions to the surface tension increase, it seems most likely that the stabilization of hydrogen bonds increases the bulk Helmholtz's free energy, at least at the surface, which thereby increases ... The surface tension of water under high magnetic fields Journal of Applied Physics 103, 124903 (2008); https://doi.org/10.1063/1.2940128
- https://pubs.acs.org/doi/abs/10.1021/cm062196t Magnetic-Field Induced Efficient Alignment of Carbon Nanotubes in Aqueous Solutions A droplet of carboxyl-functionalized carbon nanotube solution dispensed on a Si surface (a), which is placed in moderate magnetic field and dried (b). Carbon nanotubes having iron catalyst nanoparticles in their inner-tubular cavity align in the solution and, in the course of the drying process, form a ring-shaped deposit of highly ordered nanotubes being parallel with the external magnetic field (d). Meanwhile, nanotubes without ferromagnetic impurities deposit on the inner areas of the droplet's footprint and have no alignment (c). The demonstrated method enables ordering of CNTs in solutions, deposition of aligned structures on smooth surfaces and poses an alternative separation of ferromagnetic (iron-contaminated) nanotubes from the pure ones. 0.5 – 1 T strength http://iopscience.iop.org/article/10.1088/0953-8984/19/39/395017 The recent observation of the integer quantum Hall effect in planar graphene [1, 2] has attracted much attention on the effects of a perpendicular magnetic field in two-dimensional (2D) carbon compounds. In these systems the sp2 bonding produces the arrangement of the carbon atoms in a honeycomb lattice, giving rise to electron quasiparticles with conical dispersion around discrete Fermi points.
- A white dwarf, also called a degenerate dwarf, is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to that of the Sun, while its volume is comparable to that of Earth. A white dwarf's faint luminosity comes from the emission of stored thermal energy; no fusion takes place in a white dwarf wherein mass is converted to energy.[ White dwarfs are thought to represent the end point of stellar evolution for main-sequence stars with masses from about 0.07 to 10 M☉.[4][106] The composition of the white dwarf produced will depend on the initial mass of the star. Current galactic models suggest the Milky Way galaxy currently contains about ten billion white dwarfs.[107] Such densities are possible because white dwarf material is not composed of atoms joined by chemical bonds, but rather consists of a plasma of unbound nuclei and electrons. There is therefore no obstacle to placing nuclei closer than normally allowed by electron orbitals limited by normal matter.[23] Eddington wondered what would happen when this plasma cooled and the energy to keep the atoms ionized was no longer sufficient.[38] This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle.[39] At zero temperature, therefore, electrons can not all occupy the lowest-energy, or ground, state; some of them would have to occupy higher-energy states, forming a band of lowest-available energy states, the Fermi sea. This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy.[38][40] Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure.[38][41] This electron degeneracy pressure supports a white dwarf against gravitational collapse. The pressure depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is much greater than that of a low-mass white dwarf and that the radius of a white dwarf decreases as its mass increases.[1] most white dwarfs are thought to be composed of carbon and oxygen, spectroscopy typically shows that their emitted light comes from an atmosphere which is observed to be either hydrogen or helium dominated. White dwarfs are thought to be the final evolutionary state of stars whose mass is not high enough to become a neutron star, which would include the Sun and over 97% of the other stars in the Milky Way.[4], § 1. After the hydrogen-fusing period of a main-sequence star of low or medium mass ends, such a star will expand to a red giant during which it fuses helium to carbon and oxygen in its core by the triple-alpha process. If a red giant has insufficient mass to generate the core temperatures required to fuse carbon (around 1 billion K), an inert mass of carbon and oxygen will build up at its center. After such a star sheds its outer layers and forms a planetary nebula, it will leave behind a core, which is the remnant white dwarf.[5] Usually, white dwarfs are composed of carbon and oxygen. If the mass of the progenitor is between 8 and 10.5 solar masses (M☉), the core temperature will be sufficient to fuse carbon but not neon, in which case an oxygen–neon–magnesium white dwarf may form.[6] Stars of very low mass will not be able to fuse helium, hence, a helium white dwarf[7][8] may form by mass loss in binary systems. http://iopscience.iop.org/article/10.1088/2041-8205/766/2/L18/meta DISCOVERY OF MOLECULAR HYDROGEN IN WHITE DWARF ATMOSPHERES Check! https://link.springer.com/10.1007/s11214-015-0152-0 https://aasnova.org/2017/03/10/building-magnetic-fields-in-white-dwarfs/ : though the object begins as a fluid composed primarily of an ionized mixture of carbon and oxygen (and a few minor species like nickel and iron), it gradually crystallizes as its temperature drops. The crystallized phase of the white dwarf is oxygen-rich — which is denser than the liquid, so the crystallized material sinks to the center of the dwarf as it solidifies. As a result, the white dwarf forms a solid, oxygen-rich core with a liquid, carbon-rich mantle that’s Rayleigh-Taylor unstable: as crystallization continues, the solids continue to sink out of the mantle. These planets’ magnetic fields (Earth and Jupiter) are similarly thought to be generated by convective dynamos powered by the cooling and chemical separation of their interiors Neutron stars: http://www.if.ufrgs.br/hadrons/reisenegger1.pdf The magnetic field strength on the surface of neutron stars ranges from c. 104 to 1011 tesla http://adsbit.harvard.edu//full/1988Ap%26SS.147..107G/0000107.000.html Molecules in white dwarfs He atmosphere, sometimes C2 but usually no other molecules CH stars https://en.wikipedia.org/wiki/CH_star Hydrogen Molecule Ion in Strong Magnetic Fields C. P. Melo, R. Ferreira, H. S. Brandi, and L. C. M. Miranda Phys. Rev. Lett. 37, 676 – Published 13 September 1976 Orbitals become like needles
- Electrons are not circling around randomly
- Benzene was isolated by Michael Faraday in 1825 but defining its molecular structure turned out to be a challenge. Many structural formulae were suggested, including a prism-like structure. Fig. 1 The first sample of benzene, isolated in 1825 by Michael Faraday. It was isolated from an oily reside left by the production of coal gas and was first named bicarburet of hydrogen. Benzene is a colourless liquid at room temperature. This sample is on display at the Royal Institution, London.
- One of the first classes taught in organic chemistry tells about aromatic molecules. So they think – yes! I know this! But… In the 19th century the term aromatic molecule referred to organic residues with usually unpleasant odour
- Hückel suggested an empirical rule to classify a molecule as aromatic. When a molecule possesses (4𝑛+2) 𝜋 electrons it behaves similarly to benzene. A contrasting property called antiaromaticity occurs when the number of 𝜋 electrons is equal to 4𝑛.
- The molecule is bound as a sextet in perpendicular field. The minimum lies at about 4.0 bohr (E = 0.010622 H = 6.67 kcal/mol) -38.5538 -37.8613 -39.045 -39.0618 -39.4225 True min of B_y @ 4.03164062 bohr, E = -39.433155442677, E_bind = 10.64 mH, 6.676726 kcal/mol
- Most closed-shell molecules are diamagnetic. Their energy increases in an applied field and the induced currents oppose the field. The energy of paramagnetic molecules decreases in a MF. Eventually all molecules become diamagnetic. The magnetizability tensor can be diagonalized to find the optimal direction of the magnetic field vector. Modelling strong MF in solid state: B. N. Murdin et al., Nat. Commun. 4, (2013) 1469. The study of the behaviour of atoms in the presence of magnetic fields is a long established branch of spectroscopy, dating from the discovery by Zeeman in 1896 of the splitting of spectral lines into components when a light source was placed between the poles of an electromagnet. Lorentz in 1897 developed the classical theory of the motion of an electron undergoing simple harmonic motion in the presence of a superimposed magnetic field. His theory predicted that all spectral lines would show ‘normal’ Lorentz triplet splitting, but many lines were found which showed more complicated (‘anomalous’) splittings. These were explained by the work of Lande in 1923 on multiplet structure and the discovery by Uhlenbeck and Goudsmit in 1925 of the spin and magnetic moment of the electron. The splitting of a spectral line into components in the presence of a (small) magnetic field became known as the Zeeman effect. The quantum theory of the Zeeman effect was developed by many workers. (from Rep. Prog. Phys. 1977 40 105-154, R H Gavstang, Atoms in high magnetic fields (white dwarfs)) nuclear spin: H, C, F = 0.5; Cl, Br = 1.5 Paschen-Back Effect In the presense of an external magnetic field, the energy levels of atoms are split. This splitting is described well by the Zeeman effect if the splitting is small compared to the energy difference between the unperturbed levels, i.e., for sufficiently weak magnetic fields. This can be visualized with the help of a vector model of total angular momentum. If the magnetic field is large enough, it disrupts the coupling between the orbital and spin angular momenta, resulting in a different pattern of splitting. This effect is called the Paschen-Back effect. In the weak field case the vector model at left implies that the coupling of the orbital angular momentum L to the spin angular momentum S is stronger than their coupling to the external field. In this case where spin-orbit coupling is dominant, they can be visualized as combining to form a total angular momentum J which then precesses about the magnetic field direction. In the strong-field case, S and L couple more strongly to the external magnetic field than to each other, and can be visualized as independently precessing about the external field direction. (http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/paschen.html)