Anomalous Molecular Displacement Laws in Porous Media and Polymers Probed by Nuclear Magnetic Resonance Techniques

How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance

“…By superimposing, over two short time intervals, an additional magnetic field with a large gradient, the displacement of the nuclei (and hence of the molecules in which they are contained) in the time span between these two "gradient pulses" is recorded in a phase shift of their orientation in the plane perpendicular to the magnetic field with respect to the mean orientation. Hence, the distribution of the diffusion path lengths appears in the distribution of these phase shifts and, consequently, in the vector sum of the magnetic moments of the individual spins, i.e., in the magnetization [2,[20][21][22]. Since it is this magnetization which is recorded as the NMR signal, molecular diffusion leads to an attenuation of the signal intensity during the PFG NMR experiments which is the larger the larger the displacements in the time interval between these two gradient pulses are.…”

“…Further, the initial condition of a process described by Eqs. (19) to (21) has to be chosen in such a manner that for the initial time t = 0 the particles are located at a given position x and are already distributed stationarily between the regions. This is obvious since neither p ′ 1 (k) nor p ′ 2 (k) depends on t which would be necessary to converge to the stationary distribution.…”

“…The exchange between these two diffusive regions is simulated by a jump process governed by a master equation with jump rates w nm , which describe a transition from region m to n (m, n = 1, 2). The inverse of the jump rates w nm yields the mean dwell time τ m τ 1 = 1 w 21 and τ 2 = 1 w 12 (25) for which particles remain in region m. Further, the stationary distribution between the regions π 1 = w 12 w 12 + w 21 and π 2 = w 21…”

Evaluation of bacterial proliferation with a microfluidic-based device: Antibiochip

“…Comparing the absolute values of the pellet areas, the behavior of the 22-and 36-µm-thick channels was very similar, while the 11-µm-thick channels showed a lower particle concentration. This is a well-known phenomenon due to anomalous diffusion when the channel size and particle size are not very different [1,2].…”

“…Angle of the V-shaped channels (in degrees) 11 22 36 90° 70° 60° Filling of the channels -+ ++ + + - (2) The shape of the pellet after centrifugation +/-++ + (1) + (1) ++ - (2) The texture of the pellet after centrifugation +/-+ +/-+ (1) ++ - (2) (1) Instability of the pellet (2) Presence of air bubbles in the microchannel.…”