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Ion exchange chromatography separates charged molecules from a solution by reversibly exchanging them with mobile, or 'active', ions associated with the oppositely charged stationary phase. This method can be used to separate ions, soften and deionize water, and purify solutions. The polymers comprising the ion-exchange column are high-molecular-weight and chemically stable polymers, crosslinked to be porous and essentially insoluble. They are also functionalized with either acidic or...
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Probing numerical Laplace inversion methods for two and three-site molecular exchange between interconnected pore

Emilia V Silletta1, María B Franzoni1, Gustavo A Monti1

  • 1Universidad Nacional de Córdoba, Facultad de Matemática, Física, Astronomía y Computación, Córdoba, Argentina; CONICET, IFEG, Córdoba, Argentina.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|December 4, 2017
PubMed
Summary

Two-dimension Nuclear Magnetic Resonance relaxometry accurately analyzes pore interactions. The fast iterative shrinkage-thresholding algorithm (FISTA) offers superior precision over the Butler-Reeds-Dawson (BRD) method for complex porous systems.

Keywords:
Molecular exchangeNMR methodsNumerical inverse Laplace transformPolymeric porous networkPore size distribution

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Area of Science:

  • Materials Science
  • Analytical Chemistry
  • Physical Chemistry

Background:

  • Two-dimension Nuclear Magnetic Resonance (2D NMR) relaxometry is crucial for studying pore interactions, primarily in inorganic materials.
  • Data analysis typically involves 2D numerical inversion to generate T2-T2 maps, with various algorithms developed over time.

Purpose of the Study:

  • To compare the performance of the Butler-Reeds-Dawson (BRD) algorithm and the fast iterative shrinkage-thresholding algorithm (FISTA) for 2D NMR data inversion.
  • To evaluate these algorithms under varying exchange dynamics, pore sizes, and signal-to-noise ratios (SNR).

Main Methods:

  • Development of a theoretical model to test BRD and FISTA algorithms.
  • Application of algorithms to simulated two- and three-site porous media with varied exchange rates and pore sizes.
  • Testing algorithms on a challenging organic system (water in hierarchical porous polymeric networks).

Main Results:

  • The BRD algorithm demonstrated accuracy only under specific exchange parameter conditions.
  • The FISTA method provided precise results across all tested parameters, except in extreme signal-to-noise ratio scenarios.
  • Molecular exchange rates in a hierarchical porous polymeric network were successfully determined.

Conclusions:

  • FISTA is a more robust and precise algorithm for 2D NMR relaxometry data analysis compared to BRD, especially for complex systems.
  • The study validates FISTA's applicability to real-world organic porous materials.
  • Algorithm choice significantly impacts the accuracy of pore interaction analysis in NMR relaxometry.