ASSESSMENT OF THE INFLUENCE OF THE THERMODYNAMIC FACTOR ON THE CRYSTALLIZATION PROCESS IN A VACUUM APPARATUS

2021 ◽  
Author(s):  
Е.В. СЕМЕНОВ ◽  
А.А. СЛАВЯНСКИЙ ◽  
В.А. ГРИБКОВА ◽  
Д.П. МИТРОШИНА ◽  
Н.Н. ЛЕБЕДЕВА
Keyword(s):  
Phase Transformations ◽  
Crystallization Process ◽  
Physical Factor ◽  
Supersaturated Solution ◽  
Crystal Formation ◽  
Two Phase ◽  
Software Products ◽  
Diffusive Mass Transfer ◽  
Vacuum Apparatus ◽  
Technology Of Production

Особенность состояния системы жидкость–твердое тело в метастабильном растворе вещества состоит в том, что она (система) претерпевает два фазовых превращения в вакуум-аппарате (ВА) – кристаллообразование и растворение, требующие экспериментального изучения и описания в силу их важности при совершенствовании технологии производства кристаллического сахара. Однако и теоретическое обоснование фазовых превращений в метастабильном растворе разработано недостаточно. В статье предпринята попытка количественно поставить и решить проблему учета возникающего при проведении обработки метастабильного сахарсодержащего раствора повышения температуры в результате конденсации молекул на центре концентрации при пересыщении в ВА. В качестве основы численного моделирования поставленной задачи использовали программные продукты информационной среды Mathcad. С использованием модели диффузионного массопереноса сахарозы в пересыщенном растворе к затравке был разработан алгоритм расчета зависимости массы сахарозы от времени проведения процесса кристаллизации. На примере сахарозы дана оценка влияния физического фактора – выделяющейся при кристаллообразовании теплоты на расчет теплового баланса и производительности ВА. The peculiarity of the state of the liquid-solid system in a metastable solution of a substance is that it (the system) undergoes two phase transformations in a vacuum apparatus (VA) – crystal formation and dissolution, requiring experimental study and description due to their importance in improving the technology of production of crystalline sugar. However the theoretical justification of phase transformations in a metastable solution has not been sufficiently developed. The article attempts to quantify and solve the problem of taking into account the temperature increase that occurs during the processing of a metastable sugar-containing solution as a result of condensation of molecules at the concentration center during supersaturation in VA. Software products of the Mathcad information environment were used as the basis for numerical modeling of the task. Using a model of diffusive mass transfer of sucrose in a supersaturated solution to the seed, an algorithm was developed for calculating the dependence of the sucrose mass on the time of the crystallization process. On the example of sucrose, an assessment of the influence of a physical factor – the heat released during crystallization on the calculation of the thermal balance and the productivity of the VA is given.

Optimal control of thermal processes with phase transitions

2021 ◽  
Author(s):  
Yury Evtushenko ◽  
Vladimir Zubov ◽  
Anna Albu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Crystallization Process ◽  
Automatic Differentiation ◽  
Phase Interface ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Phase ◽  
Metal Solidification

The optimal control of the metal solidification process in casting is considered. Quality of the obtained detail greatly depends on how the crystallization process proceeds. It is known that to obtain a model of a good quality it is desirable that the phase interface would be as close as possible to a plane and that the speed of its motion would be close to prescribed. The proposed mathematical model of the crystallization process is based on a three dimensional two phase initial-boundary value problem of the Stefan type. The velocity of the mold in the furnace is used as the control. The control satisfying the technological requirements is determined by solving the posed optimal control problem. The optimal control problem was solved numerically using gradient optimization methods. The effective method is proposed for calculation of the cost functional gradient. It is based on the fast automatic differentiation technique and produces the exact gradient for the chosen approximation of the optimal control problem.

Lithium electrochemical deintercalation from O2-LiCoO2: structural study and first principles calculations

2002 ◽  
Vol 756 ◽  
Author(s):  
D. Carlier ◽  
A. Van der Ven ◽  
G. Ceder ◽  
L. Croguennec ◽  
M. Ménétrier ◽  
...  
Keyword(s):  
Phase Transformations ◽  
Density Functional ◽  
Driving Forces ◽  
Charge Ordering ◽  
Ionic Exchange ◽  
Two Phase ◽  
Entropy Maximization ◽  
Vacancy Ordering ◽  
Voltage Curve ◽  
Ordered Phases

ABSTRACTWe present a detailed study of the O2-LiCoO2 phase used as positive electrode in lithium batteries. This phase is a metastable form of LiCoO2 and is prepared by ionic exchange from P2-Na0.70CoO2. The O2-LiCoO2 system presents interesting fundamental problems as it exhibits several phase transformations upon lithium deintercalation that imply either CoO2 sheet gliding or lithium/vacancy ordering. Two unusual structures are observed: T#2 and O6. The T#2 phase was characterized by X-ray, neutron and electron diffraction, whereas the O6 phase was only characterized by XRD.In order to better understand the structures and the driving forces responsible for the phase transformations involved in lithium deintercalation, we combine our experimental study of this system with a theoretical approach. The voltage-composition curve at room temperature is calculated using Density Functional Theory combined with Monte Carlo simulations, and is qualitatively in good agreement with the experimental voltage curve over the complete lithium composition range. Pseudopotential and thermodynamic calculations both show that two tetrahedral sites have to be considered for Li in the T#2 structure. The calculated voltage curve thus exhibits a two-phase O2/T#2 region that indicates that this phase transformation is driven by the entropy maximization and not by a non-metal to metal transition. We also predict two ordered phases for Li1/4CoO2 (O2) and Li1/3CoO2 (O6) and show that the formation of the O6 phase is not related to Li staging or Co3+/Co4+ charge ordering.

scholarly journals Used of Chemically Modified Titanium Dioxide Particles to Mediate the Non-isothermal Cold Crystallization of Poly(latic acid)

2020 ◽  
Vol 64 (2) ◽  
Author(s):  
J. A. Gonzalez-Calderon ◽  
Guadalupe Mendoza ◽  
M. G. Peña-Juárez ◽  
Elias Perez
Keyword(s):  
Titanium Dioxide ◽  
Glass Transition ◽  
Transition Temperature ◽  
Glass Transition Temperature ◽  
Chemical Modification ◽  
Dicarboxylic Acid ◽  
Crystallization Process ◽  
Polymer Chains ◽  
Cold Crystallization ◽  
Crystal Formation

In this work, the effect of the chemical modification of titanium dioxide particles on the non-isothermal crystallization process of polylactic acid (PLA) was studied. Cold crystallization in some polymers occurs above the glass transition temperature (Tg) when the polymer chains gain sufficient mobility to organize themselves into the ordered structure (i.e. the crystal structure) by folding the chains. Cold crystallization in general is caused by the ordering of the molecular chains in the crystalline PLA due to the increased mobility during heating. Through an analysis of the cool crystallization process in DSC at different cooling rates, it was observed that the behavior of PLA and its composites made with titanium dioxide, neat and functionalized with dicarboxylic acids, can be described through the models used for crystallization of the polymer carrying out during cooling, such as Mo’s and Jeziorny’s model. In addition, it was determined that the chemical modification of TiO2 performed with silane increases the crystallization rate in the last step of the process; while the chemical modification with dicarboxylic acid has an accelerated effect on the crystal formation process attributed to the affinity between the aliphatic part of this group and the polymer chains. Also, it was shown that the inclusion of the silanized particles has no effect on the energy requirement compared to the pure PLA process; however, the addition of particles with the dicarboxylic acid decreases the energy value required to complete the crystalline state due to affinity at the surface to immobilize the polymer chains. Finally, it is emphasized that the activation energy required to perform the crystallization of PLA and its composites has positive values, which is an indicator that the crystallization was performed while heating, after reaching and passing the glass transition temperature and before melting.

New in situ solid-state NMR techniques for probing the evolution of crystallization processes: pre-nucleation, nucleation and growth

2015 ◽  
Vol 179 ◽  
pp. 115-140 ◽  
Author(s):  
Colan E. Hughes ◽  
P. Andrew Williams ◽  
Victoria L. Keast ◽  
Vasileios G. Charalampopoulos ◽  
Gregory R. Edwards-Gau ◽  
...  
Keyword(s):  
Solid State ◽  
Liquid State ◽  
Solid State Nmr ◽  
Crystallization Process ◽  
Solid Particles ◽  
Crystal Formation ◽  
Nmr Studies ◽  
Nmr Techniques ◽  
Solid Phases

The application of in situ techniques for investigating crystallization processes promises to yield significant new insights into fundamental aspects of crystallization science. With this motivation, we recently developed a new in situ solid-state NMR technique that exploits the ability of NMR to selectively detect the solid phase in heterogeneous solid–liquid systems (of the type that exist during crystallization from solution), with the liquid phase “invisible” to the measurement. As a consequence, the technique allows the first solid particles produced during crystallization to be observed and identified, and allows the evolution of different solid phases (e.g., polymorphs) present during the crystallization process to be monitored as a function of time. This in situ solid-state NMR strategy has been demonstrated to be a powerful approach for establishing the sequence of solid phases produced during crystallization and for the discovery of new polymorphs. The most recent advance of the in situ NMR methodology has been the development of a strategy (named “CLASSIC NMR”) that allows both solid-state NMR and liquid-state NMR spectra to be measured (essentially simultaneously) during the crystallization process, yielding information on the complementary changes that occur in both the solid and liquid phases as a function of time. In this article, we present new results that highlight the application of our in situ NMR techniques to successfully unravel different aspects of crystallization processes, focusing on: (i) the application of a CLASSIC NMR approach to monitor competitive inclusion processes in solid urea inclusion compounds, (ii) exploiting liquid-state NMR to gain insights into co-crystal formation between benzoic acid and pentafluorobenzoic acid, and (iii) applications of in situ solid-state NMR for the discovery of new solid forms of trimethylphosphine oxide and l-phenylalanine. Finally, the article discusses a number of important fundamental issues relating to practical aspects, the interpretation of results and the future scope of these techniques, including: (i) an assessment of the smallest size of solid particle that can be detected in in situ solid-state NMR studies of crystallization, (ii) an appraisal of whether the rapid sample spinning required by the NMR measurement technique may actually influence or perturb the crystallization behaviour, and (iii) a discussion of factors that influence the sensitivity and time-resolution of in situ solid-state NMR experiments.

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