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Keywords = theory and models of crystal growth

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20 pages, 4322 KiB  
Article
The 1D Hybrid Material Allylimidazolium Iodoantimonate: A Combined Experimental and Theoretical Study
by Hela Ferjani, Rim Bechaieb, Diego M. Gil and Axel Klein
Inorganics 2025, 13(7), 243; https://doi.org/10.3390/inorganics13070243 - 15 Jul 2025
Viewed by 544
Abstract
The one-dimensional (1D) Sb(III)-based organic–inorganic hybrid perovskite (AImd)21[SbI5] (AImd = 1-allylimidazolium) crystallizes in the orthorhombic, centrosymmetric space group Pnma. The structure consists of corner-sharing [SbI6] octahedra forming 1D chains separated by allylimidazolium cations. Void [...] Read more.
The one-dimensional (1D) Sb(III)-based organic–inorganic hybrid perovskite (AImd)21[SbI5] (AImd = 1-allylimidazolium) crystallizes in the orthorhombic, centrosymmetric space group Pnma. The structure consists of corner-sharing [SbI6] octahedra forming 1D chains separated by allylimidazolium cations. Void analysis through Mercury CSD software confirmed a densely packed lattice with a calculated void volume of 1.1%. Integrated quantum theory of atoms in molecules (QTAIM) and non-covalent interactions index (NCI) analyses showed that C–H···I interactions between the cations and the 1[SbI5]2− network predominantly stabilize the supramolecular assembly followed by N–H···I hydrogen bonds. The calculated growth morphology (GM) model fits very well to the experimental morphology. UV–Vis diffuse reflectance spectroscopy allowed us to determine the optical band gap to 3.15 eV. Density functional theory (DFT) calculations employing the B3LYP, CAM-B3LYP, and PBE0 functionals were benchmarked against experimental data. CAM-B3LYP best reproduced Sb–I bond lengths, while PBE0 more accurately captured the HOMO–LUMO gap and the associated electronic descriptors. These results support the assignment of an inorganic-to-organic [Sb–I] → π* charge-transfer excitation, and clarify how structural dimensionality and cation identity shape the material’s optoelectronic properties. Full article
(This article belongs to the Section Inorganic Materials)
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32 pages, 5807 KiB  
Article
Influence of Nucleating Agents on the Crystallization, Thermal, and Mechanical Properties of Poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (P3HBHHx)
by Anyi Jin, Germán Pérez, Luis J. del Valle and Jordi Puiggalí
Appl. Sci. 2025, 15(11), 6120; https://doi.org/10.3390/app15116120 - 29 May 2025
Viewed by 674
Abstract
This study investigates the impact of various nucleating agents on the crystallization behavior, thermal stability, and mechanical properties of poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (P3HBHHx) with 6 mol% 3-hydroxyhexanoate (3HHx) units. Nucleating agents, including boron nitride (BN), poly(3-hydroxybutyrate) (PHB), talc, ultrafine cellulose (UFC), and an [...] Read more.
This study investigates the impact of various nucleating agents on the crystallization behavior, thermal stability, and mechanical properties of poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (P3HBHHx) with 6 mol% 3-hydroxyhexanoate (3HHx) units. Nucleating agents, including boron nitride (BN), poly(3-hydroxybutyrate) (PHB), talc, ultrafine cellulose (UFC), and an organic potassium salt (LAK), were incorporated to enhance the crystallization performance. Differential scanning calorimetry (DSC) revealed that BN and PHB significantly increased the crystallization temperature and reduced the crystallization time by half, with BN exhibiting the highest nucleation efficiency. Isothermal kinetics modeled using the Avrami and Lauritzen–Hoffman theories confirmed faster crystallization and reduced nucleation barriers in nucleated samples. Polarized optical microscopy (POM) revealed that the nucleating agents altered the spherulite morphology and increased the growth rates. Under fast cooling, only BN induced crystallization, confirming its superior nucleation activity. Thermogravimetric analysis (TGA) indicated minimal changes in thermal stability, while mechanical testing showed a slight reduction in stiffness without compromising the tensile strength. Overall, BN emerged as the most effective nucleating agent for enhancing the P3HBHHx crystallization kinetics, providing a promising strategy for improving processing efficiency and reducing the cycle times in industrial applications. Full article
(This article belongs to the Section Applied Biosciences and Bioengineering)
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26 pages, 5179 KiB  
Article
Thermally Induced Phenomena in Amorphous Nifedipine: The Correlation Between the Structural Relaxation and Crystal Growth Kinetics
by Roman Svoboda
Molecules 2025, 30(1), 175; https://doi.org/10.3390/molecules30010175 - 4 Jan 2025
Cited by 2 | Viewed by 1218
Abstract
The particle size-dependent processes of structural relaxation and crystal growth in amorphous nifedipine were studied by means of non-isothermal differential scanning calorimetry (DSC) and Raman microscopy. The enthalpy relaxation was described in terms of the Tool–Narayanaswamy–Moynihan model, with the relaxation motions exhibiting the [...] Read more.
The particle size-dependent processes of structural relaxation and crystal growth in amorphous nifedipine were studied by means of non-isothermal differential scanning calorimetry (DSC) and Raman microscopy. The enthalpy relaxation was described in terms of the Tool–Narayanaswamy–Moynihan model, with the relaxation motions exhibiting the activation energy of 279 kJ·mol−1 for the temperature shift, but with a significantly higher value of ~500 kJ·mol−1 being obtained for the rapid transition from the glassy to the undercooled liquid state (the latter is in agreement with the activation energy of the viscous flow). This may suggest different types of relaxation kinetics manifesting during slow and rapid heating, with only a certain portion of the relaxation motions occurring that are dependent on the parameters of a given temperature range and time frame. The DSC-recorded crystallization was found to be complex, consisting of four sub-processes: primary crystal growth of αp and βp polymorphs, enantiotropic βp → βp′ transformation, and βpp′ → αp recrystallization. Overall, nifedipine was found to be prone to the rapid glass-crystal growth that occurs below the glass transition temperature; a tendency of low-temperature degradation of the amorphous phase markedly increased with decreasing particle size (the main reason being the increased number of surface and bulk micro-cracks and mechanically induced defects). The activation energies of the DSC-monitored crystallization processes varied in the 100–125 kJ·mol−1 range, which is in agreement with the microscopically measured activation energies of crystal growth. Considering the potential correlations between the structural relaxation and crystal growth processes interpreted within the Transition Zone Theory, a certain threshold in the complexity and magnitude of the cooperating regions (as determined from the structural relaxation) may exist, which can lead to a slow-down of the crystal growth if exceeded. Full article
(This article belongs to the Special Issue Exclusive Feature Papers in Physical Chemistry, 2nd Edition)
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14 pages, 2173 KiB  
Article
Crystallization Kinetics of Tacrolimus Monohydrate in an Ethanol–Water System
by Suoqing Zhang, Jixiang Zhao, Ming Kong, Jiahui Li, Mingxuan Li, Miao Ma, Li Tong, Tao Li and Mingyang Chen
Crystals 2024, 14(10), 849; https://doi.org/10.3390/cryst14100849 - 28 Sep 2024
Viewed by 1140
Abstract
Nucleation and growth during the crystallization process are crucial steps that determine the crystal structure, size, morphology, and purity. A thorough understanding of these mechanisms is essential for producing crystalline products with consistent properties. This study investigates the solubility of tacrolimus (FK506) in [...] Read more.
Nucleation and growth during the crystallization process are crucial steps that determine the crystal structure, size, morphology, and purity. A thorough understanding of these mechanisms is essential for producing crystalline products with consistent properties. This study investigates the solubility of tacrolimus (FK506) in an ethanol–water system (1:1, v/v) and examines its crystallization kinetics using batch crystallization experiments. Initially, the solubility of FK506 was measured, and classical nucleation theory was employed to analyze the induction period to determine interfacial free energy (γ) and other nucleation parameters, including the critical nucleus radius (r*), critical free energy (G*), and the molecular count of the critical nucleus (i*). Crystallization kinetics under seeded conditions were also measured, and the parameters of the kinetic model were analyzed to understand the effects of process states such as temperature on the crystallization process. The results suggested that increasing temperature and supersaturation promotes nucleation. The surface entropy factor (f) indicates that the tacrolimus crystal growth mechanism is a two-dimensional nucleation growth. The growth process follows the particle size-independent growth law proposed by McCabe. The estimated kinetic parameters reveal the effects of supersaturation, temperature, and suspension density on the nucleation and growth rates. Full article
(This article belongs to the Special Issue Crystallization Process and Simulation Calculation, Third Edition)
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16 pages, 28139 KiB  
Article
The Influence of the Aggressive Medium upon the Degradation of Concrete Structures: Numerical Model of Research
by Ibragimov Ruslan, Shakirzyanov Farid, Kayumov Rashit and Korolev Evgeny
Buildings 2024, 14(6), 1762; https://doi.org/10.3390/buildings14061762 - 11 Jun 2024
Cited by 1 | Viewed by 1012
Abstract
This article discusses the impact of the aggressive environment on the pattern of pore distribution, strength, and mass absorption of investigated samples. For this purpose, a physical and numerical research model has been developed based on Fick’s second law and Zhurcov’s theory. Consequently, [...] Read more.
This article discusses the impact of the aggressive environment on the pattern of pore distribution, strength, and mass absorption of investigated samples. For this purpose, a physical and numerical research model has been developed based on Fick’s second law and Zhurcov’s theory. Consequently, computer tomography research revealed that pore redistribution was revealed in test samples due to exposure. The degradation model is proposed assuming that in the first stage of interaction between concrete constructions and aggressive medium, the product of interaction is accumulated in the surface of structures and pores. Interaction products in the form of needle-shaped crystals grow in time and create additional stress in the body of the structure, resulting in partial distribution of the surface of the structure due to the growth. In this state, the excretion of dissolved substances (in the form of citrate and calcium acetate), leaching of Ca(OH)2, and decalcination of CSH lead to a decrease in the strength of cement stone. Based on the developed numerical models, the dependences of aggressive environment impact on the on the parameters of the structure of cement composites at different exposure times were obtained. For the samples obtained during the activation of Portland cement in the electromagnetic mill, energy parameters of the destruction process are 1.85–2.2 times heavier than the control compositions. The samples obtained by activating Portland cement in the electromagnetic mill have a higher susceptibility to an aggressive environment (they absorb 1.8 times more energy per unit of time for structure transformation). However, the higher U-energy barrier (1.85 times greater than the control composition) provides both a longer term of exploitation and a lower kinetics of the change in the strength of the material. Full article
(This article belongs to the Special Issue Research on Concrete and Cement-Based Materials)
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26 pages, 16372 KiB  
Article
Halogen Bond via an Electrophilic π-Hole on Halogen in Molecules: Does It Exist?
by Pradeep R. Varadwaj
Int. J. Mol. Sci. 2024, 25(9), 4587; https://doi.org/10.3390/ijms25094587 - 23 Apr 2024
Cited by 10 | Viewed by 2118
Abstract
This study reveals a new non-covalent interaction called a π-hole halogen bond, which is directional and potentially non-linear compared to its sister analog (σ-hole halogen bond). A π-hole is shown here to be observed on the surface of halogen in halogenated molecules, which [...] Read more.
This study reveals a new non-covalent interaction called a π-hole halogen bond, which is directional and potentially non-linear compared to its sister analog (σ-hole halogen bond). A π-hole is shown here to be observed on the surface of halogen in halogenated molecules, which can be tempered to display the aptness to form a π-hole halogen bond with a series of electron density-rich sites (Lewis bases) hosted individually by 32 other partner molecules. The [MP2/aug-cc-pVTZ] level characteristics of the π-hole halogen bonds in 33 binary complexes obtained from the charge density approaches (quantum theory of intramolecular atoms, molecular electrostatic surface potential, independent gradient model (IGM-δginter)), intermolecular geometries and energies, and second-order hyperconjugative charge transfer analyses are discussed, which are similar to other non-covalent interactions. That a π-hole can be observed on halogen in halogenated molecules is substantiated by experimentally reported crystals documented in the Cambridge Crystal Structure Database. The importance of the π-hole halogen bond in the design and growth of chemical systems in synthetic chemistry, crystallography, and crystal engineering is yet to be fully explicated. Full article
(This article belongs to the Special Issue Noncovalent Interactions: New Developments in Experiment and Theory)
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14 pages, 2251 KiB  
Article
Impact of Schwoebel Barriers on the Step-Flow Growth of a Multicomponent Crystal
by Alexey Redkov
Crystals 2024, 14(1), 25; https://doi.org/10.3390/cryst14010025 - 26 Dec 2023
Cited by 3 | Viewed by 1842
Abstract
The step-flow and spiral growth of a multicomponent crystal are considered from vapors, taking into account the different possible Schwoebel barriers for each component within the Burton-Cabrera-Frank model. Analytic expressions for the final growth rates of such a multicomponent crystal are determined while [...] Read more.
The step-flow and spiral growth of a multicomponent crystal are considered from vapors, taking into account the different possible Schwoebel barriers for each component within the Burton-Cabrera-Frank model. Analytic expressions for the final growth rates of such a multicomponent crystal are determined while considering the kinetic properties of all the individual components and growth conditions. Possible instabilities inherent in the presence of several components are studied, and a stability criterion for the multicomponent case is proposed. It is shown that, in certain cases, nucleation of nanoislands of pure components behind the moving steps can initiate, significantly distorting the growth process. The criterion for the occurrence of such an unstable regime is found. Full article
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18 pages, 5830 KiB  
Article
Supramolecular Structure, Hirshfeld Surface Analysis, Morphological Study and DFT Calculations of the Triphenyltetrazolium Cobalt Thiocyanate Complex
by Essam A. Ali, Rim Bechaieb, Rashad Al-Salahi, Ahmed S. M. Al-Janabi, Mohamed W. Attwa and Gamal A. E. Mostafa
Crystals 2023, 13(11), 1598; https://doi.org/10.3390/cryst13111598 - 19 Nov 2023
Cited by 4 | Viewed by 2126
Abstract
Polymorphism is a prevalent occurrence in pharmaceutical solids and demands thorough investigation during product development. This paper delves into the crystal growth and structure of a newly synthesized polymorph (TPT)2[CoII(NCS)4], (1), where TPT is triphenyl tetrazolium. The [...] Read more.
Polymorphism is a prevalent occurrence in pharmaceutical solids and demands thorough investigation during product development. This paper delves into the crystal growth and structure of a newly synthesized polymorph (TPT)2[CoII(NCS)4], (1), where TPT is triphenyl tetrazolium. The study combines experimental and theoretical approaches to elucidate the 3D framework of the crystal structure, characterized by hydrogen-bonded interactions between (TPT)+ cations and [Co(NCS)4]2− anions. Hirshfeld surface analysis, along with associated two-dimensional fingerprints, is employed to comprehensively investigate and quantify intermolecular interactions within the structure. The enrichment ratio is calculated for non-covalent contacts, providing insight into their propensity to influence crystal packing interactions. Void analysis is conducted to predict the mechanical behavior of the compound. Utilizing Bravais-Friedel, Donnay-Harker (BFDH), and growth morphology (GM) techniques, the external morphology of (TPT)2[CoII(NCS)4] is predicted. Experimental observations align well with BFDH predictions, with slight deviations from the GM model. Quantum computational calculations of the synthesized compounds is performed in the ground state using the DFT/UB3LYP level of theory. These calculations assess the molecule’s stability and chemical reactivity, including the computation of the HOMO-LUMO energy difference and other chemical descriptors. The study provides a comprehensive exploration of the newly synthesized polymorph, shedding light on its crystal structure, intermolecular interactions, mechanical behavior, and external morphology, supported by both experimental and computational analyses. Full article
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35 pages, 6220 KiB  
Article
Effects of Structural Relaxation of Glass-Forming Melts on the Overall Crystallization Kinetics in Cooling and Heating
by Jürn W. P. Schmelzer, Timur V. Tropin and Christoph Schick
Entropy 2023, 25(11), 1485; https://doi.org/10.3390/e25111485 - 26 Oct 2023
Cited by 4 | Viewed by 1553
Abstract
In the theoretical treatment of crystallization, it is commonly assumed that the relaxation processes of a liquid proceed quickly as compared to crystal nucleation and growth processes. Actually, it is supposed that a liquid is always located in the metastable state corresponding to [...] Read more.
In the theoretical treatment of crystallization, it is commonly assumed that the relaxation processes of a liquid proceed quickly as compared to crystal nucleation and growth processes. Actually, it is supposed that a liquid is always located in the metastable state corresponding to the current values of pressure and temperature. However, near and below the glass transition temperature, Tg, this condition is commonly not fulfilled. In such cases, in the treatment of crystallization, deviations in the state of the liquid from the respective metastable equilibrium state have to be accounted for when determining the kinetic coefficients governing the crystallization kinetics, the thermodynamic driving force of crystallization, and the surface tension of the aggregates of the newly evolving crystal phase including the surface tension of critical clusters considerably affecting the crystal nucleation rate. These factors may greatly influence the course of the overall crystallization process. A theoretical analysis of the resulting effects is given in the present paper by numerical solutions of the J(ohnson)–M(ehl)–A(vrami)–K(olmogorov) equation employed as the tool to model the overall crystallization kinetics and by analytical estimates of the crystallization peak temperatures in terms of the dependence on cooling and heating rates. The results are shown to be in good agreement with the experimental data. Possible extensions of the theory are anticipated and will be explored in future analysis. Full article
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12 pages, 2663 KiB  
Article
Can Nanowires Coalesce?
by Vladimir G. Dubrovskii
Nanomaterials 2023, 13(20), 2768; https://doi.org/10.3390/nano13202768 - 16 Oct 2023
Viewed by 1588
Abstract
Coalescence of nanowires and other three-dimensional structures into continuous film is desirable for growing low-dislocation-density III-nitride and III-V materials on lattice-mismatched substrates; this is also interesting from a fundamental viewpoint. Here, we develop a growth model for vertical nanowires which, under rather general [...] Read more.
Coalescence of nanowires and other three-dimensional structures into continuous film is desirable for growing low-dislocation-density III-nitride and III-V materials on lattice-mismatched substrates; this is also interesting from a fundamental viewpoint. Here, we develop a growth model for vertical nanowires which, under rather general assumptions on the solid-like coalescence process within the Kolmogorov crystallization theory, results in a morphological diagram for the asymptotic coverage of a substrate surface. The coverage is presented as a function of two variables: the material collection efficiency on the top nanowire facet a and the normalized surface diffusion flux of adatoms from the NW sidewalls b. The full coalescence of nanowires is possible only when a=1, regardless of b. At a>1, which often holds for vapor–liquid–solid growth with a catalyst droplet, nanowires can only partly merge but never coalesce into continuous film. In vapor phase epitaxy techniques, the NWs can partly merge but never fully coalesce, while in the directional molecular beam epitaxy the NWs can fully coalesce for small enough contact angles of their droplets corresponding to a=1. The growth kinetics of nanowires and evolution of the coverage in the pre-coalescence stage is also considered. These results can be used for predicting and controlling the degree of surface coverage by nanowires and three-dimensional islands by tuning the surface density, droplet size, adatoms diffusivity, and geometry of the initial structures in the vapor–liquid–solid, selective area, or self-induced growth by different epitaxy techniques. Full article
(This article belongs to the Special Issue New Advances in Nanowires and Quantum Dots)
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17 pages, 4131 KiB  
Article
CuO Nanoparticles and Microaggregates: An Experimental and Computational Study of Structure and Electronic Properties
by Lorenzo Gontrani, Elvira Maria Bauer, Alessandro Talone, Mauro Missori, Patrizia Imperatori, Pietro Tagliatesta and Marilena Carbone
Materials 2023, 16(13), 4800; https://doi.org/10.3390/ma16134800 - 3 Jul 2023
Cited by 8 | Viewed by 2582
Abstract
The link between morphology and properties is well-established in the nanoparticle literature. In this report, we show that different approaches in the synthesis of copper oxide can lead to nanoparticles (NPs) of different size and morphology. The structure and properties of the synthesized [...] Read more.
The link between morphology and properties is well-established in the nanoparticle literature. In this report, we show that different approaches in the synthesis of copper oxide can lead to nanoparticles (NPs) of different size and morphology. The structure and properties of the synthesized NPs are investigated with powder X-ray diffraction, scanning electron microscopy (SEM), and diffuse reflectance spectroscopy (DRS). Through detailed SEM analyses, we were able to correlate the synthetic pathways with the particles’ shape and aggregation, pointing out that bare hydrothermal pathways yield mainly spheroidal dandelion-like aggregates, whereas, if surfactants are added, the growth of the nanostructures along a preferential direction is promoted. The effect of the morphology on the electronic properties was evaluated through DRS, which allowed us to obtain the electron bandgap in every system synthesized, and to find that the rearrangement of threaded particles into more compact structures leads to a reduction in the energy difference. The latter result was compared with Density Functional Theory (DFT) computational models of small centrosymmetric CuO clusters, cut from the tenorite crystal structure. The computed UV-Vis absorption spectra obtained from the clusters are in good agreement with experimental findings. Full article
(This article belongs to the Special Issue Oxide/Hydroxide-Based Materials and Their Application)
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31 pages, 5107 KiB  
Article
Primary Growth Behavior of Sulfur Particles through the Throttle Valve in the Transmission System of High Sulfur Content Natural Gas
by Gang Liu, Duo Chen, Bo Li and Changjun Li
Energies 2023, 16(7), 2976; https://doi.org/10.3390/en16072976 - 24 Mar 2023
Cited by 2 | Viewed by 1991
Abstract
The deposition of sulfur particles in gathering and transportation pipeline system can cause serious safety problems and economic losses. When the high sulfur content natural gas (HSCNG) flows through the throttle valve of the gathering and transportation system, it will cause the supersaturation [...] Read more.
The deposition of sulfur particles in gathering and transportation pipeline system can cause serious safety problems and economic losses. When the high sulfur content natural gas (HSCNG) flows through the throttle valve of the gathering and transportation system, it will cause the supersaturation of elemental sulfur in the gas phase, and then the sulfur crystal nuclei and sulfur particles will appear in the pipeline system. Studying the initial growth behavior of sulfur crystal nuclei and sulfur particles can lay a necessary prerequisite for the accurate prediction of sulfur particle deposition in high sulfur content natural gas gathering and transportation (HSCNGGT) pipelines. Based on the homogeneous nucleation theory in crystallization kinetics, a mathematical model of elemental sulfur nucleation was established. Taking the throttling condition in the process of HSCNGGT as an example, the effects of temperature, pressure and H2S concentration in HSCNG on the critical nucleation radius and nucleation rate of elemental sulfur were explored. The results show that: (1) after the supersaturation of elemental sulfur, sulfur crystal nuclei with nanoscale radius will be precipitated. The temperature and pressure after throttling have great influence on the nucleation radius, and the influence of H2S concentration on the nucleation radius is more complex. (2) The temperature, pressure and H2S concentration after throttling also have great influence on the nucleation rate. By solving the growth kinetics model of sulfur particles based on Brownian condensation, it is found that the nano-sized sulfur crystal nuclei can grow into micron-sized sulfur particles in a very short time. Full article
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25 pages, 6693 KiB  
Article
Non-Isothermal Crystallization Kinetics of PBSu/Biochar Composites Studied by Isoconversional and Model Fitting Methods
by Katerina Papadopoulou, Evangelia Tarani, Konstantinos Chrissafis, Ondřej Mašek and Dimitrios N. Bikiaris
Polymers 2023, 15(7), 1603; https://doi.org/10.3390/polym15071603 - 23 Mar 2023
Cited by 8 | Viewed by 2735
Abstract
Non-isothermal crystallization of Poly(butylene succinate) (PBSu)/biochar composites was studied at various constant cooling rates using differential scanning calorimetry. The analysis of the kinetics data revealed that the overall crystallization rate and activation energy of the PBSu polymer were significantly influenced by the addition [...] Read more.
Non-isothermal crystallization of Poly(butylene succinate) (PBSu)/biochar composites was studied at various constant cooling rates using differential scanning calorimetry. The analysis of the kinetics data revealed that the overall crystallization rate and activation energy of the PBSu polymer were significantly influenced by the addition of biochar. Specifically, the PBSu/5% biochar composite with a higher filler content was more effective as a nucleation agent in the polymer matrix, as indicated by the nucleation activity (ψ) value of 0.45. The activation energy of the PBSu/5% biochar composite was found to be higher than that of the other compositions, while the nucleation activity of the PBSu/biochar composites decreased as the biochar content increased. The Avrami equation, which is commonly used to describe the kinetics of crystallization, was found to be limited in accurately predicting the non-isothermal crystallization behavior of PBSu and PBSu/biochar composites. Although the Nakamura/Hoffman–Lauritzen model performed well overall, it may not have accurately predicted the crystallization rate at the end of the process due to the possibility of secondary crystallization. Finally, the combination of the Šesták–Berggren model with the Hoffman–Lauritzen theory was found to accurately predict the crystallization behavior of the PBSu/biochar composites, indicating a complex crystallization mechanism involving both nucleation and growth. The Kg parameter of neat PBSu was found to be 0.7099 K2, while the melting temperature and glass transition temperature of neat PBSu were found to be 114.91 °C and 35 °C, respectively, very close to the measured values. The Avrami nucleation dimension n was found to 2.65 for PBSu/5% biochar composite indicating that the crystallization process is complex in the composites. Full article
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13 pages, 1009 KiB  
Article
The Modeling of Self-Consistent Electron–Deformation–Diffusion Effects in Thin Films with Lattice Parameter Mismatch
by Oleh Kuzyk, Olesya Dan’kiv, Ihor Stolyarchuk, Roman Peleshchak and Yuriy Pavlovskyy
Coatings 2023, 13(3), 509; https://doi.org/10.3390/coatings13030509 - 25 Feb 2023
Viewed by 2345
Abstract
In our work, the model of self-consistent electron–deformation–diffusion effects in thin films grown on substrate with the mismatch of lattice parameters of the contacting materials is constructed. The proposed theory self-consistently takes into account the interaction of the elastic field (created by the [...] Read more.
In our work, the model of self-consistent electron–deformation–diffusion effects in thin films grown on substrate with the mismatch of lattice parameters of the contacting materials is constructed. The proposed theory self-consistently takes into account the interaction of the elastic field (created by the mismatch of lattice parameters of the film and the substrate, and point defects) with the diffusion processes of point defects and the electron subsystem of semiconductor film. Within the framework of the developed model, the spatial distribution of deformation, concentration of defects, conduction electrons and electric field intensity is investigated, depending on the value of the mismatch, the type of defects, the average concentrations of point defects and conduction electrons. It is established that the coordinate dependence of deformation and the concentration profile of defects of the type of stretching (compression) centers, along the axis of growth of the strained film, have a non-monotonic character with minima (maxima), the positions of which are determined by the average concentration of point defects. It is shown that due to the electron–deformation interaction in film with a lattice parameter mismatch, the spatial redistribution of conduction electrons is observed and n-n+ transitions can occur. Information about the self-consistent spatial redistribution of point defects, electrons and deformation of the crystal lattice in semiconductor materials is necessary for understanding the problems of their stability and degradation of nano-optoelectronic devices operating under conditions of intense irradiation. Full article
(This article belongs to the Special Issue Recent Advances in Semiconducting Thin Films)
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29 pages, 690 KiB  
Article
Kinetics of Precipitation Processes at Non-Zero Input Fluxes of Segregating Particles
by Jürn W. P. Schmelzer, Timur V. Tropin and Alexander S. Abyzov
Entropy 2023, 25(2), 329; https://doi.org/10.3390/e25020329 - 10 Feb 2023
Cited by 1 | Viewed by 1762
Abstract
We consider the process of formation and growth of clusters of a new phase in segregation processes in solid or liquid solutions in an open system when segregating particles are added continuously to it with a given rate of input fluxes, Φ. [...] Read more.
We consider the process of formation and growth of clusters of a new phase in segregation processes in solid or liquid solutions in an open system when segregating particles are added continuously to it with a given rate of input fluxes, Φ. As shown here, the value of the input flux significantly affects the number of supercritical clusters formed, their growth kinetics, and, in particular, the coarsening behavior in the late stages of the process. The detailed specification of the respective dependencies is the aim of the present analysis, which combines numerical computations with an analytical treatment of the obtained results. In particular, a treatment of the coarsening kinetics is developed, allowing a description of the development of the number of clusters and their average sizes in the late stages of the segregation processes in open systems, which goes beyond the scope of the classical Lifshitz, Slezov and Wagner theory. As is also shown, in its basic ingredients, this approach supplies us with a general tool for the theoretical description of Ostwald ripening in open systems, or systems where the boundary conditions, like temperature or pressure, vary with time. Having this method at one’s disposal supplies us with the possibility that conditions can be theoretically tested, leading to cluster size distributions that are most appropriate for desired applications. Full article
(This article belongs to the Special Issue 150th Anniversary of Gibbs Publication of Geometrical Thermodynamics)
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