Related terms:
- Mugineic Acid
- Phosphonate
- Pyruvate
- Point Group T
- NMR Spectroscopy
- Aqueous Solution
Applications of NMR Techniques in the Development and Operation of Proton Exchange Membrane Fuel Cells
Liuming Yan, ... Baohua Yue, in Annual Reports on NMR Spectroscopy, 2016
4.3 Proton Dynamics in Organic Acid Salts
The organic phosphate and phosphonate are also investigated as proton-conducting materials. For example, Traer et al. characterized two model salts, benzimidazolium phosphate and benzimidazolium methane phosphonate, and concluded that the phosphate anion dynamics contributes to long-range proton transport, whereas the mobility of the polymer itself is not a contributing factor based on solid-state 1H DQF NMR and 31P CODEX NMR [49]. A three-site jump for methane phosphonate anion was identified as a zigzag pathway of proton transport through the phosphonate salt crystallites based on 31P CODEX NMR and 1H variable temperature MAS NMR. In addition, they also characterized a series of benzimidazole-alkyl phosphonate salts using high-resolution 1H solid-state MAS NMR, DQ MAS NMR, and 31P CODEX NMR spectroscopy, and concluded that the alkyl group slows down the correlation times for anion reorientation at ambient temperature, but the lowered lattice energy of the salt and thus lowered the activation energy allow good dynamics at intermediate temperatures [50].
In addition, the Traer group also studied the proton-conducting dynamics of imidazole methylphosphonate. The 31P CODEX NMR showed that the rotation of the methylphosphonate has a low activation energy implying that the motion of the anion is not impeded by the solid-state structure. 31P CODEX and variable temperature 1H MAS NMR spectra confirmed that ionic conductivity is facilitated by dynamics at the bifurcated hydrogen bonds between anions, with a time scale of 57±4ms at ambient temperature for rotation of the phosphonate about the C3v axis [51]. In the solid acid rubidium methane phosphonate (RMP) and the hydrated crystal RMP·2H2O, they observed two different types of acidic protons as well as the water protons in the lamella using 1H MAS NMR, and established proton proximities by solid-state 1H DQF NMR [52]. The variable temperature 1H MAS NMR showed that the dehydrated RMP powder has no phase transition, and no significant proton dynamics in the temperature range 250–350K, while the RMP·2H2O has high proton mobility at relatively low temperature (~330K) and a proton transport mechanism that uniquely relies on crystalline water. This group also investigated proton mobility in polyvinazene and its sulfonated derivatives using 1H solid-state MAS NMR, and the activation energy for transportation of hydrogen-bonded protons using variable temperature experiments [53].
Zhu et al. observed several orders of magnitude enhancement in the proton conductivity by addition of triflic acid (HTf) to the guanidinium triflate (GTf) solid-state matrix. The 1H and 19F solid-state MAS NMR measurements show no apparent effect on local molecular mobility of the GTf matrix by the addition of HTf at room temperature, however, fast ion exchange between the GTf matrix and the HTf at higher temperatures. The exchange rate, quantified by continuum T2 fitting analysis, increases with increasing temperature with an activation energy at about 58.4kJmol−1 [54].
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Applications III. Materials Science, Nanoscience, Polymer Science and Surface Chemistry
Walid Al Maksoud, ... Jean Marie Basset, in Comprehensive Organometallic Chemistry IV, 2022
14.13.3.4 Understanding alkane metathesis with a bi-metallic catalyst
Over the period of time, the TON in alkane metathesis was substantially improved; [Ta]
H=60 to [W]=CH2=260 in propane metathesis, 150 in n-decane metathesis, and 450 in cyclooctane metathesis with [(
SiO)W(CH3)5].159,161,164 During the catalytic reaction it was understood that the critical step is the dehydrogenation of alkane to olefin which plays the important role to determine the efficiency of the alkane metathesis reaction. If the dehydrogenation step can be improved, then the reactivity can be enhanced, resulting in higher TON.
To increase the efficiency of the catalyst in alkane metathesis reaction, for the first time, a bi-metallic catalyst was designed where one part of the catalyst could help for improved dehydrogenation of alkanes to olefin, and at the same time, it should not affect the olefin metathesis catalyst to carry out metathesis reaction. In the bi-metallic catalyst, group IV metals like Zr and Ti were used for the dehydrogenation, and W was used as a metathesis catalyst. At first, Zr(Np)4 and W(CH3)6 were grafted on the surface of silica sequentially to form [(SiO)W(CH3)5/(SiO)ZrNp3] (Scheme 8).148 The supported complex was characterized by solid-state NMR (Fig. 17). The NMR double-quantum (DQ) and triple quantum (TQ) study showed strong autocorrelation peaks for WCH3 groups and [Zr] neopentyl groups, which confirms that the grafted W(CH3)6 and Zr(Np4) are in close proximity to each other on the surface. Along with the expected autocorrelation peaks, another cross-correlation peak is observed corresponds to the methyl peak of [Zr](CH2C(CH3)3) and [W]CH3 thus confirming that of [W]CH3 and [Zr](CH2C(CH3)3) are in close vicinity to each other (Fig. 17). The corresponding hydrides of [(SiO)W(CH3)5/(SiO)ZrNp3] were prepared by reacting molecular hydrogen at room temperature or by heating at 100°C for 12 to 15h.
Scheme 8. Synthetic scheme of a bi-metallic [W]/[Zr] and [W/Ti] precursor catalyst.
The bi-metallic pre-catalyst was used for n-decane metathesis with an improved TON of 1436. A broad range of products were observed as expected. To further improve the reactivity of bi-metallic catalyst, in place of Zr, Ti metal was introduced, and a new variant of the bi-metallic catalyst [(SiO)W(CH3)5/(SiOTiNp3)] was prepared.165 The bi-metallic catalyst was fully characterized by advanced solid-state NMR, IR, elemental analysis, and gas quantification method. The [W]/[Ti] bi-metallic pre-catalyst was used for propane metathesis reaction in batch reactor conditions and continuous flow reactor conditions. In batch reactor conditions, a TON of 1800 was achieved, whereas in flow reactor conditions, a TON of 10,000 was achieved. This is the highest obtained TON till date by any alkane metathesis catalyst known so far (Fig. 20).165
Fig. 20. Turnover number vs. time for pre-catalyst [(SiO)W(CH3)5]/[(SiO)TiNp3] (0.34wt%W and 1.02wt% Ti)(violet color), the physical mixture of [(SiO)W(CH3)5] and [(SiO)TiNp3] (0.27wt%W, 1.05wt% Ti)(green color), and a layer of [(SiO)W(CH3)5] (1.1wt% Ti) followed by a layer of [(SiO)W(CH3)5] (0.34wt%W) (red color). TON is expressed in moles of propane transformed per mole of W.
NMR characterization of both the [W]/[Zr] and [W]/[Ti] bi-metallic catalyst gives an impression that both the surface organometallic fragments (SOMFs) like W and Zr in the case of [W]/[Zr] and W and Ti in [W]/[Ti] bi-metallic catalysts are very close to each other. To understand the effect of togetherness of the metals known as synergistic effect of the metal fragments, three catalyst beds were prepared: (1) the [W]/[Ti] catalyst bed, (2) a bed of mechanically mixed [(SiO)W(CH3)5+(SiO)TiNp3] and (3) a layer of [(SiO)W(CH3)5 and (SiO)TiNp3 separated by a layer of glass wool.165 In all the cases, the metal loading was kept constant. At the end of the reaction with all above mentioned catalysts, it was found that the grafted catalyst [(SiO)W(CH3)5/(SiO)TiNp3] produced a TON approximately 10,000 better than both of the mixture of [(SiO)W(CH3)5+(SiO)TiNp3] and the layer of [(SiO)W(CH3)5] and (SiO)TiNp3] (TONs are 5204 and 639) (Fig. 20).165 This study proved that when both the catalysts are grafted on the surface, they have very unique way of functioning, which enhances their activity in the alkane metathesis reaction.165
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NMR of Inorganic Nuclei
Cory M. Widdifield, Navjot Kaur, in Comprehensive Inorganic Chemistry III (Third Edition), 2023
9.15.2.10 Doped/Lithiated nanoparticles
9.15.2.10.1 Carbon-doped MgB2
The discovery that pristine MgB2 was a type-II superconductor (Tc=39K)123 heralded a vast array of studies on the material, as well as numerous MgB2-containing derivatives. One method of improving the properties (i.e., critical fields and critical-current density) of MgB2 involves doping with a carbon source, such as SiC, although there is not a consensus as to why such doping improves these properties. To clarify the mechanism by which carbon improves these properties and to establish the location of 13C in the lattice, Bounds etal. used solid-state 11B and 13C NMR experiments on carbon-doped MgB2 nanoparticles in both the normal and superconducting states.124 Carbon doping was done using chemical vapor deposition with 99% enriched 13C2-ethylene gas, and hence all carbon-doped MgB2 samples were enriched in the NMR-active 13C nuclide. Using powder XRD and magnetic susceptibility measurements, the nanoparticle sample composition was established as approximately MgB1.9513C0.05. At room temperature, several NMR experiments were performed (using B0=9.4 or 14.1T), including: (i) 11B MQMAS; (ii) 11B and 13C MAS; and (iii) 13C-13C double-quantum recoupling. Experiments at cryogenic temperatures were performed under static (i.e., non-spinning) conditions at B0=4.7 or 8.5T. At room temperature, the 11B MAS NMR spectrum of MgB1.9513C0.05 was dominated by a peak at 95ppm with no evidence of oxidation to B2O3. Compared to MgB2, there appeared to be a second low-intensity peak at a lower chemical shift value, but this was not clearly resolved. The 13C MAS NMR spectrum was composed of a single resolved carbon site at a shift of 200ppm. Boron-11 MQMAS NMR experiments on MgB1.9513C0.05 demonstrated that the 11B environments were less ordered than in pristine MgB2, and a second 11B peak at 70ppm was assigned to B4C. The 13C-13C double-quantum NMR experiments did not yield any signal after ca. 60,000 scans, which the authors reasoned meant that the 13C sites were isolated. At cryogenic temperatures (5K–80K), the authors observed signal broadening at both 13C and 11B sites as the temperature decreased (Fig.36).
Fig.36. NMR peak shapes of MgB1.9513C0.05 as a function of temperature. (A) 11B NMR spectra at fields of 8.5 and 4.7T. (B) 13C NMR spectra at fields of 8.5 and 4.7T.
Adapted minimally from Bounds, R. W.; Pavarini, E.; Paolella, M.; Young, E.; Heinmaa, I.; Stern, R.; Carravetta, M. Study of 11B and 13C NMR on Doped MgB2 in the Normal and in the Superconducting State. Phys. Rev. 2018, 97, 014509. DOI: 10.1103/PhysRevB.97.014509, and under the terms of the Creative Commons CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).In addition to the broadening effects, it was clear that the 11B sites experienced a significant shift in their resonance frequency at B0=4.7T, which was attributed to the Meissner effect. On top of these trends, the authors also observed, for a given fixed B0, a decrease in the 11B and 13C shift value as the temperature was reduced, which was ascribed to Knight shift decay. As 11B environments were generally more affected when compared against 13C, this was taken as evidence that 11B were within the vortex field distribution, while 13C occupy the vortex cores. Spin-lattice relaxation measurements were performed for both 11B and 13C at 4.7T and 8.5T at various temperatures. Both nuclides deviated from Korringa’s law below the critical temperature with R<1, which demonstrated that ferromagnetic correlations were present. Spin susceptibility measurements and results from ab initio calculations were presented, and when all the information was taken in concert, it was concluded that carbon substituted for boron when generating MgB1.9513C0.05 and there was no support for models that involved defect formation.
9.15.2.10.2 Aluminum-doped MnO2
Wang and co-workers used insitu 23Na NMR experiments to study the intercalation/deintercalation of sodium ions (and associated degradation process) for aluminum-doped MnO2 nanoparticles that were being developed as battery electrodes.125 Relative to MnO2 nanoparticles that did not involve Al doping, Al-doped nanoparticles had a much greater specific capacitance and possessed excellent cycling stability. By recording the 23Na NMR spectra, the authors were able to resolve a narrow band, attributed to sodium cations in the electrolyte, and a much broader band, which was assigned to intercalated Na+. It was observed that the broad band changed slightly as each cycle progressed, which the authors assigned to a fast structural change. On top of this was a slower change in the average chemical shift of the broad band signal, which moved slightly to lower chemical shifts as the cycle number increased. Supported with data from other experimental techniques (XPS, cycling voltammetry, SEM, and HRTEM) the authors speculated that repeated Na+ intercalation/deintercalation may induce a pulverization process in the MnO2 nanoparticle electrode surface, and that doping with Al3+ somehow slows down this degradation pathway.
9.15.2.10.3 Lithiated Sn (LixSn)
High capacity, safe, and portable energy storage solutions are very desirable, with a bewildering array of potential solutions being developed, although nearly all have certain caveats that hinder their widespread application. For example, due to several favorable properties, tin anodes are being developed as they can form stable intermetallic compounds with lithium. The drawback with this material is its severe capacity fade. Unfortunately, the mechanism that accompanies this capacity fade is not well described and therefore deriving potential remedies is problematic. Hence, Lopez etal. used operando 7Li NMR and ex situ 7Li MAS NMR experiments, coupled with pair distribution function (PDF) methods, to study the electrochemical lithiation and delithiation of tin nanoparticles.126 The derivative of the operando 7Li NMR data with respect to time was also taken to generate a derivative Operando (dOp) NMR spectrum.127 Over the course of one lithiation half-cycle, the authors observed the formation (and removal) of many different components, including: Li0 (removal only), Li2Sn5, Li2Sn3, LiSn, Li7Sn3, Li13Sn5, and Li7Sn2. During the initial stages of delithiation, a resonance at δ(7Li)∼16ppm (labeled as D′) was observed to occur alongside a removal peak associated with the highly lithiated Li7Sn2 phase. As the line shape associated with the D′ phase was highly dissimilar to any phase observed upon lithiation, the authors took a conservative approach when assigning it, but made an initial assignment as a Li13Sn5 phase that possessed many lithium site vacancies. Using operando and ex situ 7Li NMR experiments, the authors observed that the intensity of this signal increased as a function of the cycle number (Fig.37).
Fig.37. (A) Operando 7Li NMR 2D spectra of 11 cycles of a Sn electrode cell at a sweep rate of 50μVs−1. (B) Ex situ 7Li MAS NMR spectra of Sn samples cycled to D′ at a sweep rate of 50μVs−1 after 2 (black), 9 (red), and 13 (blue) complete cycles, lithiated to 0.2V and then delithiated to 0.58V to form D′. The MAS NMR of the cell at 2cycles shows intense resonances at 42 and 32ppm corresponding to the two non-exchanging crystallographic sites of LiSn, and a resonance at 15.8ppm corresponding to the D′. As more cycles are performed, a decrease in the intensity of the LiSn resonance and an increase in the intensity of the D′ resonance is observed.
Republished with permission of the Royal Society of Chemistry from Lopez, J. L. L.; Grandinetti, P. J.; Co, A. C. Phase Transformations and Capacity Fade Mechanism in LixSn Nanoparticle Electrodes Revealed by Operando 7Li NMR. J.Mater. Chem. A 2019, 7, 10781–10794. DOI: 10.1039/C9TA03345A. Copyright 2019 with permission conveyed through Copyright Clearance Center, Inc.As the number of cycles increased, the 7Li NMR peak associated with Li0 dendrites was progressively lower in intensity after complete delithiation. As such, the authors stated that lithium appeared to become trapped in the D′ phase on progressive cycling. Using PDF data, it was found that a model corresponding to a vacancy-rich Li7−ζSn3 phase (85.7%) and a LiSn phase (14.3%) yielded the best fit to the data. Addition of phases such as Li13Sn5 and Li5Sn2 did not improve the agreement between the model and the PDF data. At the completion of each cycle, the number of 7Li nuclei in the Li7−ζSn3 phase increased, and the cell capacity decreased. Further, although the 7Li NMR signal associated with a solid electrolyte interface grew rapidly during the first few cycles, it soon reached a nearly constant value and thus could not be fully responsible for the capacity fade. Capacity fade was found to only occur during delithiation and not during lithiation. It was concluded that the capacity fade was due to particles losing contact with the carbon-rich binder material. Surprisingly, the disconnected phases appeared to reconnect upon full lithiation.
9.15.2.10.4 Doped α-NaYF4
Developing on pioneering studies involving nanophase NaYF4,128–130 Augustine and co-workers used wide line 19F and 23Na NMR experiments to probe various local environments in NaYF4 nanoparticles doped with Yb3+ and Er3+.131 These materials have potential applications in areas that require long-lasting light emission at specific wavelengths. Although bulk characterization of these materials can be easily performed using alternative methods, the authors selected 19F NMR experiments to elucidate the local structure and/or distributions of the trivalent lanthanide atoms. Due to the paramagnetic nature of the samples, the 19F NMR data were acquired under static conditions over a very broad frequency range, spanning 350–375MHz, and using an applied magnetic field of 9.4T. In addition to collecting 19F NMR spectra, 19F T1 values were measured. While broad 19F NMR spectra were expected, the authors found that the 19F NMR line width of their α-NaY0.8Er0.2F4 sample was at least 66,450ppm (Fig.38).
Fig.38. Wide line 19F NMR spectra for α-NaY0.7Yb0.3F4 (A), α-NaY0.97Er0.03F4 (B), and α-NaY0.8Er0.2F4 (C).
Reprinted with permission from Martin, M. N.; Newman, T.; Zhang, M.; Sun, L. D.; Yan, C. H.; Liu, G. Y.; Augustine, M. P. Using NMR Relaxometry to Probe Yb3+-Er3+ Interactions in Highly Doped Nanocrystalline NaYF4 Nanostructures. J.Phys. Chem. C 2019, 123, 10–16. DOI: 10.1021/acs.jpcc.8b07553. Copyright 2019, American Chemical Society.To isolate the various contributions to the 19F spin-lattice relaxation rates, the following equation was used:
where the first term on the right-hand side of the equation is meant to capture the spin-lattice relaxation in the absence of any paramagnetic dopant atoms and spin diffusion. The x and y parameters correspond to the mol % of added Yb3+ and Er3+, respectively. All R-containing parameters in the above equation were determined by fitting different sets of experimental data using a least-squares approach. As such, wide line 19F NMR experiments served as a sensitive probe of both dopant ion identity and concentration. Discussion was provided to support a Yb3+-Er3+ interaction at high doping levels, and absence of 19F-19F spin diffusion due to paramagnetic quenching. Sodium-23 solid-state NMR spectra were found to be generally insensitive to both dopant identity and concentrations, but there was a correlation between dopant concentrations and the 23Na T1 values.
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Quantification of pyruvate with special emphasis on biosensors: A review
Chandra Shekhar Pundir, ... Reeti Chaudhary, in Microchemical Journal, 2019
2.6 Proton nuclear magnetic resonance method
Spectroscopy using proton nuclear magnetic resonance (H′NMR) spectroscopy method illustrates detection method whereby, images were constructed utilizing proton double quantum nuclear magnetic resonance based on the metabolite of interest such as pyruvate and one such method for the detection of pyruvate was proposed by Hill in 2013 [27], whereby a comparison of the kinetics of pyruvate–lactate exchange in SW1222 colorectal cancer cells was experimented on the basis of the following reaction (Fig. 2).The method is useful for analyzing samples under in-vivo and in-vitro conditions but unable to decipher absolute pyruvate concentration.
Fig. 2. Representation of pyruvate-lactate exchange [27].
Table 1 summarizes the principles and analytical parameters of the above methods for quantitative analysis of pyruvate in biological materials.
Table 1. A comparison of various conventional methods for determination of pyruvate.
| S. No. | Methods | Principle/Based on | Limit of detection (mM) | Working range (mM) | Response time/incubation period | Correlation with standard method (R2) | Interference by metabolite | CV (%) | Samples | Reference |
|---|---|---|---|---|---|---|---|---|---|---|
| 1. | Spectrophotometric/colorimetric | Determination of DNPH (2,4-dinitrophenylhydrazine) carbonyls at 420 nm | 0.05 | 0.05–2.20 | 120 min, 8 min | ND | ND | 1.7 | Onion pungency | [10,11] |
| 2. | Enzymic fluorimetric | Detection of change of fluorescence due to altered concentrations of NADH | ND | 0.01–10 | 40 min | 0.982 | ND | 0.4–4.4 | Extracts of blood/human saliva | [6] |
| 3. | Fluorimetric | Oxidation of nonfluorescentAmplex Red to highly fluorescent resorufin. | 0.000005 | 0.0000010–0.000015 | ND | 0.995 | 6.8 (2-oxobutyrate); 8.7% (oxaloacetate) | ND | Cell extracts | [21] |
| 4a. | HPLC | Automated system based on formation and detection of 2,4 dinitrophenylhydrazine | ND | 0–0.008 | 41 min/sample | 0.99 | Negligible | 0.9 | Onion bulbs | [13] |
| 4b. | HPLC (Fluorimetric) | Fluorimetric detection based on quinoxalinol derivatives | 0.01 | 0.01–3 | <12 min per sample | 0.996 | ND | <6 and < 11 | Blood samples | [22] |
| 4c. | HPLC (Reverse-phase HPLC) | Detection of pyruvate using C18 reversed-phased column and a UV-Visible diode array detector | 0.001 | 0.003–1 | ND | 0.9998 | Negligible interference | 1.5 | Human Sweat | [24] |
| 5. | Gas chromatography | Gas chromatography–mass spectrometry in selected ion monitoring (SIM) mode and detection of methoxime/tert-butyldimethylsilyl derivatives | 0.0004 | 0.0004–0.015 | ND | 0.9991 | ND | ND | Human plasma | [25] |
| 6. | LC-MS | Ionization and separation of ions based on mass/charge ratio | 0.02 | 0.02–5 | <1 min | 0.9447 | ND | 5.7, 7.3 | Dried blood spots of pediatric patients | [20] |
| 7. | Mass spectral analysis | Detection of a colored complex (potassium adduct) by reaction between hydrazine and potassium hydroxide | 0.25 | 0.25–6 | 30 min | 0.99 | ND | ND | Onion juice | [26] |
| 8. | Proton NMR | In-vitro 1H NMR assay, using [3-13C]pyruvate, and compared the measured kinetics with a hyperpolarized 13C NMR assay, using [1-13C]pyruvate, under the same conditions in | ND | 0.017–0.042 | ND | ND | 0.993 | ND | Human colorectal carcinoma SW1222 cells/healthy male rats | [27,28] |
Abbreviations: NADH-Nicotinamide adenine dinucleotide phosphate, NMR - Nuclear magnetic resonance, HPLC - High performance liquid chromatography, LC-MS - Liquid chromatography with mass spectrometry.
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A comprehensive review on polymer single crystals—From fundamental concepts to applications
Samira Agbolaghi, ... Farhang Abbasi, in Progress in Polymer Science, 2018
2.2 Single crystal growth theories and simulations
One of the primary theories describing the formation of PSCs from dilute solution was given by Lauritzen and Hoffman [213]. The Hoffman theory, depending on the relative rates of nucleation and spreading, realized three different types of growth regimes, i.e., regimes I, II, and III [214]. It was demonstrated that the initial lamellar thickness was controlled by entropic barriers rather than enthalpic factors considered in the Lauritzen-Hoffman’s (LH) theory [215,216]. Some aspects of LH theory were also reviewed [146]. The LH theory was applicable for the lamellar growth kinetics of poly(bisphenol A octane ether) (BA-C8) crystals in regimes I and II, but not regime III [217]. An interpretation of regime transitions was proposed by Hu and Cai on the basis of the intramolecular-crystal-nucleation model for a better understanding of both experimental and simulation observations [218].
The chain diffusion coefficients in the solution crystallized species were determined by Yao et al. [219]. Single molecule fluorescence microscopy and molecule tracking techniques were applied to study the diffusion of single PEO chains in its monolayers on solid substrates, before and after the crystallization process. The results showed a strong correlation between the crystallization process and chain diffusion [220].
The modeling of transient nucleation in the isothermal thickening of polymer lamellar crystals was substantiated by Liu et al. [221]. Linear lateral growth, lamellar thickening, and slipping of monomers along chain direction were directly observed in the large-scale and long-time molecular dynamics (MD) simulations carried out by Luo and Sommer [222]. Other groups have worked on the lamellar thickening as well [43,223–225]. The existence of precursor state at the growth front is physically reasonable, but is difficult to be observed just by the snapshots. Many previous MD simulations have not found precursor states near the growth front [226–228], or their evidence has not been so clear [229]. The temperature behavior of the equilibrium crystal thickness was discussed in the undercooled state [230]. Wang et al. [231] demonstrated that the thickening rate increased with temperature because the thickening process incurred an activation energy barrier for chain-sliding diffusion. Ren et al. [232] carried out some simulations on the thin film single crystals.
The chain folding structure and adjacent re-entry site was determined by Hong and Miyoshi [39,40] using 13C −13C double quantum (DQ) NMR combined with selective 13C isotope labeling. The two-dimensional (2D) folded crystals and the chain–chain distances have been also investigated [233,234]. Bärenwald et al. [235] revealed that the fold surface had no strong effect on the time scale of the local chain flip process. The dynamic Monte Carlo simulation of lattice polymers was adopted to visualize the transitions from extended- to once-folded-chain growth, from once- to twice-folded growth, and so on [236]. Possible mechanisms for the transition were discussed regarding the entropy of chain folding directions [237]. The dynamic Monte Carlo simulations of lattice polymers melting from a metastable chain-folded lamellar single crystal were also reported [232]. The crystal growth and morphology of i-PB-1 were studied to investigate the properties of end surface of chain folded crystals [238,239]. The facets and the clear sectorization of chain folding were visualized through simulating the formation of semidilute solution-grown crystallites [240]. The reversible melting of lamellar polymer crystals on their fold-end surfaces was also taken into account [241]. Moreover, Zhang and Muthukumar [242] represented a Monte Carlo-based anisotropic aggregation model, in which each lattice unit demonstrated a single-folded chain in a dilute solution.
Xu et al. [113] performed dynamic Monte Carlo simulations to demonstrate that the thickness of a lamellar single crystal was fluctuating around some mean values. The primary nucleation and crystal growth of a single chain from different dilute solutions were studied by Monte Carlo simulations. In the solution growth environments, the solvent qualities affected the nucleation mechanism, crystal morphology, and thickening process [243]. A coil-globule transition and crystallization occured by changing the solvent quality [244]. Except a direct first-order transition due to the strong interaction between the monomers [245,246], the normal phase transition of a single polymer chain benefited from the collapse and the crystallization protocol [219,247].
Monte Carlo was utilized to simulate the power-law dependence of lamellar crystal melting on the heating rate [248,249]. This power-law dependence was also experimentally detected by the ultra-fast chip-calorimeter measurements [250,251]. Recently, Toda et al. [252] using fast-scanning chip-calorimeter measurements proved that the crystal thickening via melting-recrystallization destroyed the power-law dependence of superheating at low heating rates.
Dynamic Monte Carlo simulations of quasi-1D lamellar crystal growth in polymer solutions demonstrated a linear relationship between the crystal growth rate and the polymer concentration [253]. In the solution environments, the polymer chains depleted in the solution space upon the crystal growth, and the crystal growth rate decreased over time. This model considered some kinetic features in the morphology evolution of PSCs, whereas it did not take the kinetics of quasi-1D crystal growth into account, especially under the effect of chain lengths [242]. Dynamic Monte Carlo simulations based on a simple lattice polymer model [254] were capable of predicting the intrinsic crystal growth behaviors, e.g., the phenomenon of molecular segregation on crystal growth [255]. Molecular dynamics simulations were reported for PE to the fast crystallization process in the nanoseconds scale [256]. The coexistence of melting and growth during heating was also proved via molecular dynamics simulations for the semicrystalline entangled polymers [257]. Meanwhile, the solution of the system of equations and simulation of the shape of single crystals of PE, a-PVDF, and PEO represented a good agreement with the experimental data [258].
Estimating the lateral habit of single crystals and their lattice under particular crystallization conditions has been a critical problem for both theory and practice [259]. Development of the computational methods for predicting the single crystal shape was originated from a demand for avoiding the formation of needle-like crystals in the commercial processing of some low molecular compounds [260]. The chain unfolding certainly resulted in the lattice vacancies which need to be filled. The thickening of the monolayer of PEO with hydroxyl end groups after complete crystallization could lead to the shrinkage of the lateral size of monolayer crystals [221]. The molten molecules might climb up the top surface of the crystalline monolayer and, then, diffuse to the voids [261].
The free energy profiles for the crystallization process were quantitized based on the multiple wells corresponding to a determined number of folds [262]. The free energy barrier and nucleation rate were calculated as a function of temperature and were also compared with linear PE-based experiments [263]. The effects of the amount and type of short chain branches on both non-isothermal kinetics and semicrystalline structures were also evaluated [264]. The surface free energy was determined for PEO [265] and i-PB-1 crystals [266–272]. The intramolecular secondary nucleation model was proposed by Hu et al. [273] to describe the free energy barrier for the growth kinetics of lamellar polymer crystals. The metastability of lamellar structures was regarded in Janeschitz-Kriegl model describing the free energy of a lamellar crystal [274].
The physical origin of PSC growth was discussed based on the phase field model by Wang et al. [275]. The phase field theory was also utilized to study the phase transition kinetics in mesoscale [276]. Wang et al. [277] performed a novel phase field model with taking into account the physical conceptions about polymer cell parameter and crystal plane. The technique of isochronous decoration was used to prepare the stripped single crystal morphology by Dubreuil et al. [278]. Another novel three-dimensional phase field model was established by combining the cellular automaton method with the general phase field model, in which different steric structures or discretization methods were related to the lattice parameters of s-PP single crystals [279].
Other applications of Monte Carlo method are described in the upcoming paragraphs. Monte Carlo simulations indicated that edge-on and flat-on lamellae are developed in thin films with repulsive and attractive interactions with the substrate, respectively [280]. Hu et al. [281] performed Monte Carlo simulation-based studies on the growth of shish-kebab structures grown during the polymer crystallization. The structural fluctuations which happened on the lamellar surfaces were also realized by Monte Carlo simulations [282]. Furthermore, the dynamic Monte Carlo simulations were scrutinizingly used to study the molecular level structures of individual chains during crystallization [218,222], anisotropic driving forces, confinement effects and kinetics of the quasi-1D fibril crystal growth of diblock copolymers in the solutions with both feeding and depleting modes [205] and the quasi-1D growth kinetics of lamellar crystals in homopolymer solutions [253].
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