The art of fitting ordinary differential equations models to experimental results

Sebastião, Pedro J.; Beira, Maria Jardim; Cordeiro, Rui Miguel Oliveira; Kumar, Anant; Fernandes, J.; Ferraz, A.; Gonçalves, L. N.

doi:10.1088/1361-6404/ac563a

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…The solid lines in Figure 5 present the best fit of the model to the experimental data, while the dashed lines reflect the contribution of individual relaxation mechanisms. We used a web-based solution for professional model fitting 29 created and described by Sebastiao 30 to analyze the data.…”

Section: Thermal Properties the Thermal Stability Of The [Mim]mentioning

confidence: 99%

Evidence for NMR Relaxation Enhancement in a Protic Ionic Liquid by the Movement of Protons Independent of the Translational Diffusion of Cations

Knapkiewicz,

Jankowska,

Swiergiel

et al. 2024

J. Phys. Chem. B

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The molecular dynamics, thermal stability, and ionic conductivity were studied in the protic ionic liquid 1methylimidazolium bis(trifluoromethylsulfonyl)imide ([MIm]-[TFSI]). The relaxation of the 1 H spin−lattice of cations in the measured frequency range (10 kHz to 20 MHz) and temperature (298 to 343 K) is sensitive mainly to slow processes occurring in the molecular dynamics of protic ionic liquid and dominated by the contribution of intermolecular translational diffusion. Molecular rotations give only a constant contribution and become significant in the higher frequency range. An interesting feature is the observed enhancement of the 1 H spin−lattice relaxation below 0.03 MHz attributed to the exchange of protons (order of 10 −5 s) between imidazolium cations. The measurements of the self-diffusion coefficient of hydrogen atoms of cation from 298 to 343 K additionally confirm the observed phenomenon. The coefficient for exchangeable protons −NH is higher than for the cation. The nuclear magnetic resonance (NMR) experiments provide unambiguous evidence for proton transport decoupled from molecular diffusion of ions and support the conclusion that the charge transport mechanism in the studied PIL includes contributions from both the vehicular and Grotthus mechanisms. The protic ionic liquid is thermally stable to about 573 K as shown by thermogravimetric analysis and its electrical conductivity is 5 × 10 −2 S/cm at 423 K.

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Section: Thermal Properties the Thermal Stability Of The [Mim]mentioning

confidence: 99%

Evidence for NMR Relaxation Enhancement in a Protic Ionic Liquid by the Movement of Protons Independent of the Translational Diffusion of Cations

Knapkiewicz,

Jankowska,

Swiergiel

et al. 2024

J. Phys. Chem. B

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“…In Figures 4 and 5, the model fitting results produced by the Master module of the online platform fitteia ® [37] are presented. Figure 4 show the results obtained for pure water and the CA/SiO 2 -22 G20 and GT-hydrated membranes.…”

Section: Model Fittingmentioning

confidence: 99%

Water Molecular Dynamics in the Porous Structures of Ultrafiltration/Nanofiltration Asymmetric Cellulose Acetate–Silica Membranes

et al. 2022

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This study presents the characterization of water dynamics in cellulose acetate–silica asymmetric membranes with very different pore structures that are associated with a wide range of selective transport properties of ultrafiltration (UF) and nanofiltration (NF). By combining 1H NMR spectroscopy, diffusometry and relaxometry and considering that the spin–lattice relaxation rate of the studied systems is mainly determined by translational diffusion, individual rotations and rotations mediated by translational displacements, it was possible to assess the influence of the porous matrix’s confinement on the degree of water ordering and dynamics and to correlate this with UF/NF permeation characteristics. In fact, the less permeable membranes, CA/SiO2-22, characterized by smaller pores induce significant orientational order to the water molecules close to/interacting with the membrane matrix’s interface. Conversely, the model fitting analysis of the relaxometry results obtained for the more permeable sets of membranes, CA/SiO2-30 and CA/SiO2-34, did not evidence surface-induced orientational order, which might be explained by the reduced surface-to-volume ratio of the pores and consequent loss of sensitivity to the signal of surface-bound water. Comparing the findings with those of previous studies, it is clear that the fraction of more confined water molecules in the CA/SiO2-22-G20, CA/SiO2-30-G20 and CA/SiO2-34-G20 membranes of 0.83, 0.24 and 0.35, respectively, is in agreement with the obtained diffusion coefficients as well as with the pore sizes and hydraulic permeabilities of 3.5, 38 and 81 kg h−1 m−2 bar−1, respectively, reported in the literature. It was also possible to conclude that the post-treatment of the membranes with Triton X-100 surfactants produced no significant structural changes but increased the hydrophobic character of the surface, leading to higher diffusion coefficients, especially for systems associated with average smaller pore dimensions. Altogether, these findings evidence the potential of combining complementary NMR techniques to indirectly study hydrated asymmetric porous media, assess the influence of drying post-treatments on hybrid CA/SiO2 membrane’ surface characteristics and discriminate between ultra- and nano-filtration membrane systems.

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Parameter estimation in the stochastic SIR model via scaled geometric Brownian motion

Sánchez-Monroy,

Riascos-Ochoa,

Bustos

2024

Chaos, Solitons & Fractals

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The art of fitting ordinary differential equations models to experimental results

Cited by 4 publications

References 23 publications

Evidence for NMR Relaxation Enhancement in a Protic Ionic Liquid by the Movement of Protons Independent of the Translational Diffusion of Cations

Evidence for NMR Relaxation Enhancement in a Protic Ionic Liquid by the Movement of Protons Independent of the Translational Diffusion of Cations

Water Molecular Dynamics in the Porous Structures of Ultrafiltration/Nanofiltration Asymmetric Cellulose Acetate–Silica Membranes

Parameter estimation in the stochastic SIR model via scaled geometric Brownian motion

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