Electron spin relaxation due to small-angle motion: Theory for the canonical orientations and application to hierarchic cage dynamics in ionomers

Abstract

Analytical expressions for transverse electron spin relaxation induced by small angle motion were derived for the first time within an anisotropic model for rotational diffusion by using an approximation of the spin Hamiltonian and its variation during reorientation that is valid close to the canonical orientations. The dependence of the decay of the stimulated echo on such motion was studied by extensive Monte Carlo simulations and regimes were identified in which the time constant of this decay is related to parameters of the anisotropic diffusion model by simple equations. For testing these theoretical findings and obtaining insight into hierarchical cage dynamics in soft matter, high-field electron paramagnetic resonance (EPR) measurements were performed at a frequency of 94 GHz where the canonical orientations for nitroxide spin labels are well resolved. A combination of continuous wave EPR, saturation recovery measurements, and measurements of the decay of primary and stimulated electron spin echoes was employed to cover time scales from a few picoseconds up to several microseconds. Ionic spin probes attached by electrostatic interactions to the surface of ionic clusters in ionomers were used as a model system in which slow cage reorientation can be studied in the glass transition region of the polymer (0.64<T/T-g<1.05). Three hierarchical reorientation processes of the spin probe were observed on different time scales. The spin probe undergoes fast intramolecular libration on the time scale of a few picoseconds, it experiences a local rearrangement of the cage on the time scale of hundreds of nanoseconds and it performs cooperative reorientation coupled to the structural relaxation of the glassy matrix over time scales comparable to or longer than several microseconds in the glass transition region. (C) 2003 American Institute of Physics

Molecular dynamics of nitroxides in glasses as studied by multi-frequency EPR

“…11,12,21,23 -25 At temperatures above T g , the relaxation is more and more induced by slow (¾10 6 s) molecular orientational diffusion. 8,13,17,26 Nevertheless, ambiguities in the interpretation of ED-EPR data remained for temperatures close to the glass transition where the regimes of slow unrestricted motion and fast restricted motion may overlap. To obtain further insight into the character of the motional process that dominates the transverse relaxation at this temperature, we performed measurements of the transverse relaxation rates at different resonant frequencies ω o (S(3 GHz)-, X(9.5 GHz)-, W(95 GHz)-and G(180 GHz)-bands).…”

“…In the expressions, and c are the pulse separation time and the motional correlation time respectively. The parameters A, B and C, which contain the field dependence of the echo-decay functions, are: A D 2 e ∂ H/∂ 2 D/3, with the electron gyromagnetic ratio e , the diffusion coefficient of the orientational motion D and the angular gradient of the Hamiltonian, ∂H/∂ / H 0 ; B D 2 F/ c ) 1 17 By deriving expressions for the echo decays at the canonical g-matrix positions, the authors found monoexponential decay functions with relaxation rates showing a square-root dependence on the external magnetic field (Eqns 13-15, A1-A3 in Ref. 17).…”

Signatures of the fast dynamics in glassy polystyrene by multi-frequency, high-field electron paramagnetic resonance of molecular guests

“…HF-EPR is widely used in polymer science [10,11,19,[41][42][43][44]. One major feature is the remarkable orientation resolution [44] due to increased magnitude of the anisotropic Zeeman interaction leading to a wider distribution of resonance frequencies [45]. Recently, HF-EPR studies evidenced the exponential distribution of the energy barriers of the deep structure of the energy landscape [19] as well as clear signatures of the onset of fast motion in glassy PS [43,44] in full agreement with neutron [1][2][3][4][5] and Raman scattering [6][7][8][9].…”

“…B 0 ffi 3T corresponding to Larmor frequencies about 95 GHz (W band), [37,38] or even larger frequencies [19,39,40]. HF-EPR is widely used in polymer science [10,11,19,[41][42][43][44]. One major feature is the remarkable orientation resolution [44] due to increased magnitude of the anisotropic Zeeman interaction leading to a wider distribution of resonance frequencies [45].…”

CW EPR, echo-detected EPR, and field-step ELDOR study of molecular motions of nitroxides ino-terphenyl glass: Dynamical transition, dynamical heterogeneity and β-relaxation

“…Different approaches in EPR were employed: continuous-wave (CW) EPR [1][2][3][4], including high-field CW EPR [5,6], echo-detected (ED) EPR [7][8][9][10][11][12], stimulated echo decay [13,14], field-step electron-electron double resonance (FS ELDOR) [15][16][17][18][19][20], pulsed two-dimensional EPR [21], and some others. EPR allows addressing the important issues of molecular dynamics 638 s.A. Dzuba et al in glasses, such as the mechanism of motion of individual guest molecules, the cooperative nature of motion, temperature dependence of motion, the relation to glass transition, the distribution of correlation times, ~tynamical heterogeneity and others.…”