4/4/11. Particles possess intrinsic angular momentum. Spin angular momentum is quantized (it can only take on discrete values)

Transcription

1 For the completely filled shells, subshell (4d 10 ) the orbital magnetic momentum is zero; for the 5s orbital M L is also zero. Hypothesis: the argent atom possesses no magnetic momentum >> they move in an inhomogeneous magnetic field along the same path. Particles possess intrinsic angular momentum. Spin angular momentum is quantized (it can only take on discrete values) The electron possesses an intrinsic angular momentum and an intrinsic magnetic momentum: spin S intrinsic angular momentum M s intrinsic magnetic momentum Electrons, protons and neutrons are particles having a spin angular momentum of 1/2. Any substance with unpaired electron(s) on incompletely filled shells/subshells is paramagnetic: the net magnetic momentum differs from zero. E.g.: free radicals (singlet oxygen, hydroxyl-radical), stable free radicals (nitroxide derivatives), Fe 3+, Mn 2+, Ni 2+. If there are unpaired protons or neutrons in a nucleus, then the net nuclear spin (the intrinsic nuclear magnetic momentum) differs from zero. 1

2 µ: elemi mágneses momentum Q: Does the magnetic moment (µ) point to the direction of the external magnetic field (Bo)? Q: Does the magnetic moment (µ) point to the direction of the external magnetic field (Bo)? A: Not! Angular momentum and gyroscopic precession The precession angular velocity (Larmor frequency) is proportional to Bo. In the absence of magnetic field the states of the electron-spin or the nuclear-spin are energetically equivalent, called degenerated. In the presence of magnetic field the energy states split into energetically differing states: Zeemann-splitting; distribution of the particles between the different energy states can be described by the Boltzmann distribution. Boltzmann-distribution: a.) thermal equilibrium; b.) energy minimum, c.) entropy maximum (random dist.) n 2 n 1 = e Δε / kt 2

3 4/4/11 The extent of the Zeemann-splitting (Δε) is proportional the magnetic field strength (H) At appropriate magnetic field-strength excitation of the electrons/protons from the ground state to the excited state can be achieved by electromagnetic radiation in the frequency range of GHz (ESR) or MHz (NMR). E β> ΔE=konstans*B0 ΔE B0 ΔE=γħB0 γ [radian/st] α> A possible measurement technique of the ESR/NMR spectroscopy: detection of a signal proportional to the absorbed energy under excitation with Continuous electromagnetic -Wave radiation (CW) due to the local field strength (different molecular environment/interactions) different nuclei or electrons take up energy at slightly different excitation energies (Δε); the extent of the absorption is proportional to the concentration of the electrons, nuclei able to absorb the applied excitation energy; the ESR/NMR spectrum is defined as: the signal proportional to the absorbed energy as the function of the excitation energy (Δε) or the equivalent frequency (ν) or the magnetic field (H). The field strength of the externally applied magnetic field will be modified by the local interactions (on tissue or even molecular level) local magnetic field. > The excitation frequency depends on the > environment of the excited electron-, nuclear spin. 3

4 Spin-lattice relaxation: T1 or longitudinal relaxation time Spin-spin relaxation: T2 or transversal relaxation time After the exciting EM radiation pulse the particles tend to get rid of the extra energy. The energy is dissipated through the interactions with atoms in the environment (lattice). Mz returns to its starting equilibrium state with increasing amplitude Time constant: T1 1) Spins are rotating at the same phase (y direction) Mxy max : Forced statespins diverge (phase loss) Equidistant spread of spins in the xy-plane Mxy = 0 Exponencially decay of net magnetic momentum (and induced voltage in receiver) Time constant: T2 A Fourier-transform decomposes a function into oscillatory functions. Reference signal Signals due to protons in different chemical environment 1.) A spektrumvonalak relativ amplitudói Etanol CH 3 -CH 2 -OH Signal amplitude is proportional to the absorption, proton concentration Peak of the reference compound (at constant frequency/magnetic field strength) chemical shift Depends on the group where the hydrogen atom bounds to (e.g.: CH 3, CH 2, etc.). 2.) A spektrumvonalak kémiai eltolódásai 3.) a vonalak finomszerkezete 4

5 A vizsgált rendszer saját (intrinsic) paramágneses centruma, vagy a kívülről bejuttatott (extrinsic) paramágneses centrum alapján van lehetőség az ESR spektrumok felvételére. Sejtmembránba inkorporált paramágneses zsírsav paramágneses zsírsav izotóniás sóoldatban Spektrális információk: 5