Effect of Stochastic Dynamics on the Nuclear Magnetic Resonance in a Field Gradient

Tóthová, Jana; Lisý, V.

doi:10.12693/aphyspola.131.1111

Cited by 3 publications

(7 citation statements)

References 17 publications

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“…The magnetization of spins is modulated by a field gradient g(t). General formulas for the attenuation function S(t) of the observed NMR signal that are applicable to any kind of stochastic motion of spins, including their dynamics with memory, have been obtained in [28,29,31]. In the evaluation of S(t) it was assumed that the studied random processes are stationary in the sense that the autocorrelation function of a fluctuating dynamical variable x at times t and t' depends only on the time difference t -t':…”

Section: Attenuation Of the Nmr Signals Due To Brownian Motionmentioning

confidence: 99%

“…Possible memory effects in the shorter-time particle dynamics are ignored or incorrectly taken into account. The aim of our recent papers [28][29][30][31] was to overcome this limitation and to calculate the all-time attenuation functions of the NMR signals from spin-bearing particles resulting from the BM with memory. We have considered the Brownian particles in Maxwell fluids [28,29] and the BM with hydrodynamic memory [30].…”

Section: Introductionmentioning

confidence: 99%

“…Both these quantities characterize the fractal environment for the Brownian particle and do not depend on its radius R. Let us assume that R decreases. The second term in D  , which is proportional to 31 R   is expected to grow. This is possible if   1/3, i.e., not   1, as initially assumed in the fractional BM model.…”

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confidence: 99%

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NMR signals within the generalized Langevin model for fractional Brownian motion

Lisý

Tóthová

2018

Physica A: Statistical Mechanics and its Applications

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The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the longtime limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S(t) for an ensemble of spinbearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S(t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

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Section: Attenuation Of the Nmr Signals Due To Brownian Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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NMR signals within the generalized Langevin model for fractional Brownian motion

Lisý

Tóthová

2018

Physica A: Statistical Mechanics and its Applications

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“…It seems natural to apply NMR methods to follow such unusual BM. However, as discussed in [3][4][5], the mathematical description of suitable NMR experiments in the literature is valid only for long times when the particles are in diffusion regime (normal or anomalous). The only exception is the memoryless Langevin model for which correct interpretations of the NMR experiments have been proposed [6].…”

Section: Introductionmentioning

confidence: 99%

“…Possible memory effects in the shorter-time particle dynamics are ignored or incorrectly taken into account. The aim of our recent papers [3][4][5]7] was to overcome this limitation and to calculate the all-time attenuation functions of the NMR signals from spin-bearing particles resulting from the BM with memory. We have considered the Brownian particles in Maxwell fluids [3,7] and the BM with hydrodynamic memory [4].…”

Section: Introductionmentioning

confidence: 99%

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

Lisý

Tóthová

2018

EPJ Web Conf.

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Abstract. Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.

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Scanning Electrochemical Microscopy and Hydrodynamic Voltammetry Investigation of Charge Transfer Mechanisms on Redox Active Polymers

Burgess

Hernández‐Burgos

Simpson

et al. 2015

J. Electrochem. Soc.

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We recently showed that viologen-based redox active polymers (RAPs) with molecular weights between 21 and 318 kDa are attractive charge storage materials as anolytes for size-selective non-aqueous redox flow batteries. Here, we characterize the electron transfer mechanisms of these RAPs, as well as a ferrocene based catholyte RAP, in acetonitrile/Li + electrolyte. We utilized scanning electrochemical microscopy (SECM) and rotating disk electrode (RDE) voltammetry to measure the rate of electron transfer and the rate of charge hopping between neighboring pendants along the insulating backbone of RAPs. The electron transfer kinetics of a 271 kDa ferrocene RAP mimic the facile kinetics of its monomer repeating unit. In contrast, viologen RAPs displayed RDE and SECM signatures that suggest a preceding chemical step to electron transfer. Viologen RAPs adsorb strongly to the electrode surface and create a redox active film that controls the rate of electron transfer via self-exchange. In addition, finite element simulations including a preceding chemical step demonstrated that a purely mass-transfer limited model is insufficient to recreate the viologen RAP feedback SECM response. Non-aqueous redox flow batteries (NRFBs) are emerging technologies for electrical energy storage, and are an attractive alternative to their aqueous counterparts. [1][2][3][4][5][6] The choice of organic solvents with voltage windows larger than that required for the electrolysis of water enables the use of a larger variety of redox molecules and electrolyte systems, where the combination of high solubility and higher reaction potentials leads to increased energy density. A major challenge in NRFBs is to increase the conductivity of the electrolyte through the commonly used ion exchange membrane. In response to this challenge, our groups recently reported on a new size-selective concept in flow batteries where a porous separator replaces poorly performing ion exchange membranes.7-9 These porous separators are coupled to high energy density redox active polymers (RAPs) that replaced small molecules as charge storage media. RAPs consist of an unconjugated polymer backbone densely decorated with redox active pendants. We previously reported on the electrochemical characterization of viologen-based RAPs with molecular weight between 21 and 318 kDa, which displayed hydrodynamic radii between 4 and 7 nm. Increasing the size of RAPs decreased transport through Celgard which was used as a porous separator. However, we are also interested in understanding the impact of size on the rate and mechanisms of charge transfer and transport on RAPs to determine their ultimate performance limit. 10RAPs displayed attractive electrochemical properties such as similar standard reduction potentials than those of the parent monomer, efficient bulk electrolysis with up to +98% of redox groups reversibly accessible, and high solubility of up to 2.8 M with quantitative electrode reactivity even when at 1.0 M. Despite these promising features, little is known about el...

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Effect of Stochastic Dynamics on the Nuclear Magnetic Resonance in a Field Gradient

Cited by 3 publications

References 17 publications

NMR signals within the generalized Langevin model for fractional Brownian motion

NMR signals within the generalized Langevin model for fractional Brownian motion

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

Scanning Electrochemical Microscopy and Hydrodynamic Voltammetry Investigation of Charge Transfer Mechanisms on Redox Active Polymers

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