Sublimation Kinetics Research Articles

A combined experimental-mathematical study on the kinetics of dry ice sublimation under different airflow velocities and blowing modes

The sublimation rate of dry ice, crucial for its cooling performance, is typically influenced by environmental temperature, pressure, and specific surface area. However, the effect of wind speed under forced air convection is not well understood, and current sublimation kinetic models inadequately capture this influence, leading to discrepancies between simulations and experiments. This study examines the sublimation kinetics of static dry ice particles under varying wind speeds and blowing modes. A mathematical model was developed to determine the sublimation kinetic parameters by integrating the Clausius-Clapeyron equation, mass transfer theory, and hybrid particle swarm optimization (HPSO) algorithm. These parameters were then used to create a cooling model for a small insulated box, and the results were validated against experimental data. The findings show that increasing wind speed enhances the sublimation rate of dry ice, with upward-blowing conditions resulting in higher rates than side-blowing conditions. The model’s predictions closely match experimental data, with a maximum mass change deviation of less than 3 % and a maximum temperature deviation of less than 4 °C, demonstrating high reliability.

Thermophysical properties of lunar regolith simulant LHS-1 and ice sublimation kinetics in its mixtures with frozen water

A recently developed lunar regolith simulant LHS-1 is used currently to advance the technologies for water extraction from icy regolith in the polar regions of the Moon. However, thermophysical properties of LHS-1 at low temperatures have not been studied yet, which hinders the development of these technologies. It is also unclear whether experimental data on the rate of ice sublimation in LHS-1/ice mixtures can be applied to the actual icy regolith of the Moon. In the present paper, the specific heats and thermal diffusivities of LHS-1 and its finer version LHS-1D were studied at low temperatures using differential scanning calorimetry and laser flash analysis. The thermal diffusivities of LHS-1 and LHS-1D have been measured in the temperature range of 148−300 K in a helium environment at pressures of about 90 kPa and less than 1 Pa. The reduced pressure decreased the thermal diffusivity by several times owing to the decreased role of helium in the heat transfer during the test. The thermal diffusivity also decreased with increasing temperature and decreasing particle size. The specific heats of dry simulants have been measured in the temperature range of 110−320 K. The obtained values are close to the specific heats of the Apollo regolith samples at the same temperatures. The specific heats of LHS-1 and LHS-1D, mixed with water, have been measured in the temperature range of 110−340 K. The theoretically expected increase in specific heat due to the addition of 3 − 5 wt % ice was within the experimental error. The ice sublimation rates in LHS-1/ice and LHS-1D/ice mixtures have been measured at temperatures of 240, 247, and 258 K at pressure of 4 Pa. The sublimation rate decreases with time for all samples, which may be associated with increasing vapor pressure over the subliming surface as the sublimation front propagates downward. The analysis of the obtained data has shown that the area of the subliming surface is much less than the surface area of the simulant particles. This should be taken into account when the results of experiments with simulant/ice mixtures are applied to the actual icy regolith on the Moon.

Degradation kinetics and service performance prediction of CoSb3-based skutterudite thermoelectric device

Predictable service performance is essentially required for practical applications of thermoelectric (TE) power generators. Sublimation at TE material surface and chemical reaction/diffusion at electrode interface are the major causes for the performance degradation of TE devices. The synergistic effect of surface and interface behaviors coupled with temperature gradient makes the degradation relationship much more complicated, and the accurate prediction of service performance very challenging. In this work, we systematically investigated the sublimation kinetics for p-type Ce0.9Fe3CoSb12 and n-type Yb0.3Co4Sb12 skutterudites. A service performance prediction model (SPPM) is proposed to illustrate the service performance profiles of TE device, in which an equivalent circuit approach is applied to quantitatively link the kinetic parameters of structure and composition evolutions at both surface and interface to the output performance of device. It is found that, the performance degradation is mainly caused by the interfacial structure evolution at early stage, while the influence of surface sublimation becomes dominant in long-term service. The SPPM simulation results are well verified by the long-term evaluation tests of single-leg devices under temperature gradients, demonstrating its potential application to the engineering design of TE power generators.

Surface Rearrangement and Sublimation Kinetics of Supported Gold Nanoparticle Catalysts

Heterogeneous catalysts consisting of supported metallic nanoparticles typically derive exceptional catalytic activity from their large proportion of undercoordinated surface sites which promote adsorption of reactant molecules. Simultaneously, these high energy surface configurations are unstable, leading to nanoparticle growth or degradation and eventually a loss of catalytic activity. Surface morphology of catalytic nanoparticles is paramount to catalytic activity, selectivity, and degradation rates, however it is well-known that harsh reaction conditions can cause the surface structure to change. Still, limited research has focused on understanding the link between nanoparticle surface facets and degradation rates or mechanisms. Here, we study a model Au supported catalyst system over a range of temperatures using a combination of in situ transmission electron microscopy, kinetic Monte Carlo simulations, and density functional theory calculations to establish an atomistic picture of how variations in surface structures and atomic coordination environments lead to shifting evolution mechanisms as a function of temperature. By combining experimental results, which yield direct observation of dynamic shape changes and particle sublimation rates, with computational techniques, which enable understanding the fundamental thermodynamics and kinetics of nanoparticle evolution, we illustrate a two-step evolution mechanism in which mobile adatoms form through desorption from low-coordination facets and subsequently sublimate off the particle surface. By understanding the role of temperature in the competition between surface diffusion and sublimation, we are able to show how individual atomic movements lead to particle scale morphological changes and rationalize why sublimation rates vary between particles in a system of nearly identical nanoparticles.

Mass Accommodation of Water on Ice at Environmentally Relevant Temperatures: Insights from Fast Scanning Calorimetry.

Using a conceptually simple, quasi-adiabatic, fast scanning calorimetry technique, we have investigated the sublimation kinetics of ice films with thicknesses ranging from 14 to 400 nm at environmentally relevant temperatures, between 223 and 268 K. The technique enables accurate determination of ice sublimation rates into vacuum under the conditions of free molecular flow during rapid yet quasistatic heating. The measured sublimation fluxes yield the vapor pressure of the ice samples, which is indistinguishable from that derived from experiments under near-equilibrium conditions. Thus, in agreement with the microscopic reversibility principle, we conclude that the mass accommodation coefficient of water by ice is unity and temperature-independent in the temperature range of the studies. We discuss these findings in the context of current computational and theoretical research into the chemistry and physics of aqueous interfaces.

O2 Oxidation and Sublimation Kinetics of Single Silicon Nanoparticles at 1200–2050 K: Variation of Reaction Rates, Evolution of Structural and Optical Properties, and the Active-to-Passive Transition

Sublimation and O2 etching kinetics for a series of individual silicon (Si) nanoparticles (NPs) were studied for NP temperatures (TNP) from 1200 to 2050 K using a single NP mass spectrometry technique. Sublimation was significant for TNP > 1700 K, with rates reasonably well fit to Arrhenius kinetics but evolving, particularly during initial heating. O2 etching efficiencies varied from NP-to-NP and with changing TNP, but they also evolved dramatically over time. For TNP ≤ 1500 K, NPs were observed to passivate after losing 30–50% of the initial NP mass. At higher TNP, etching efficiency decreased over time but never passivated. Interestingly, bulk Si passivation has not been observed for the range of TNP and O2 pressures used here, and a model was developed to test the effects of several NP-specific mechanistic parameters on both the initial and time-dependent etching behavior. The optical properties of the hot NPs were also found to evolve as the NPs etched, particularly during the initial fast mass loss, and correlations between emission intensities and etching kinetics were examined.

Evaluation of Sublimation Kinetics for Phenolic Impregnated Carbon Ablator

Recession analyses of stagnation tests conducted in NASA Ames Research Center arcjet facilities with surface heat fluxes high enough for carbon char to sublimate are performed and compared with data. The axisymmetric recession computations are based on both the finite-rate gas–surface interaction model and the standard chemical equilibrium surface ablation model. The finite-rate gas–surface interaction model is studied using three different sets of sublimation coefficients, which are obtained through direct measurements. The standard chemical equilibrium ablation model is established through the tables. The ablating material used in these arcjet tests is phenolic impregnated carbon ablator. The prediction of axisymmetric surface recession is achieved by implicitly coupling a material thermal response code and a flow code. The material thermal response code used in this study is the Two-Dimensional Implicit Thermal-Response and Ablation program, which predicts charring material thermal response and shape change. The flow code solves the reacting Navier–Stokes equations using the data parallel line relaxation method. The recession predictions for three selected arcjet conditions with various base radii are presented. The effect of sticking coefficient for carbon sublimation on recession prediction is investigated, and the prediction discrepancy between finite-rate and chemical equilibrium models is examined and discussed in detail.

High-Temperature Oxidation of Single Carbon Nanoparticles: Dependence on the Surface Structure and Probing Real-Time Structural Evolution via Kinetics.

O2 oxidation and sublimation kinetics for >30 individual nanoparticles (NPs) of five different feedstocks (graphite, graphene oxide, carbon black, diamond, and nano-onion) were measured using single-NP mass spectrometry at temperatures (TNP) in the 1100-2900 K range. It was found that oxidation, studied in the 1200-1600 K range, is highly sensitive to the NP surface structure, with etching efficiencies (EEO2) varying by up to 4 orders of magnitude, whereas sublimation rates, significant only for TNP ≥ ∼1700 K, varied by only a factor of ∼3. Its sensitivity to the NP surface structure makes O2 etching a good real-time structure probe, which was used to follow the evolution of the NP surface structures over time as they were either etched or annealed at high TNP. All types of carbon NPs were found to have initial EEO2 values in the range near 10-3 Da/O2 collision, and all eventually evolved to become essentially inert to O2 (EEO2 < 10-6 Da/O2 collision); however, the dependence of EEO2 on time and mass loss was very different for NPs from different feedstocks. For example, diamond NPs evolved rapidly and monotonically toward inertness, and evolution occurred in both oxidizing and inert atmospheres. In contrast, graphite NPs evolved only under oxidizing conditions and were etched with complex time dependence, with multiple waves of fast but non-monotonic etching separated by periods of near-inertness. Possible mechanisms to account for the complex etching behavior are proposed.

Role of sublimation kinetics of ammonia borane in chemical vapor deposition of uniform, large-area hexagonal boron nitride

Hexagonal boron nitride (h-BN) is a critical 2D insulator used as a substrate, gate dielectric, or encapsulation layer for graphene and other 2D materials and their van der Waals heterostructures. It is also promising as an active layer in single-photon emitters and other photonic devices. With the chemical formula H3N-BH3, ammonia borane is the most attractive precursor for up-scalable growth of large-area h-BN, using chemical vapor deposition given its stoichiometric B:N ratio, high stability under ambient conditions, nontoxicity, and high solubility in common solvents. Here, the synthesis of large-area (100 × 150 mm2) crystalline hexagonal boron nitride layers by thermal activation and decomposition of the precursor ammonia borane is presented. We describe two different reaction pathways for h-BN synthesis, providing evidence for dissimilarities in the sublimation kinetics of ammonia borane and how these differences critically influence the growth of h-BN. This understanding helps us accelerate h-BN production, reuse precursors, and reduce machine runtime, paving the way for upscalability. Moreover, our work provides a consistent unified view explaining the diverse deposition conditions reported in the literature for h-BN grown by CVD using ammonia borane as a precursor.

In situ observation of the solid solution-induced sublimation of CuAg Janus nanoparticles

Bimetallic Janus nanostructures (JNs) have attracted much interest because of their promising potential applications induced by unique interface effects, especially in catalysis. Catalytic stability acts a role as significant as catalytic efficiency in the potential applications of catalysts. However, the response of bimetallic JNs to high temperature has been poorly investigated due to their complex structure and sublimation kinetics. Herein, the thermal stability and sublimation mechanisms of CuAg JNs are studied through in situ annealing experiments performed in an aberration-corrected FEI Titan 80-300 transmission electron microscope operated at 300 kV. It is proven that CuAg JNs begin to sublimate until the temperature increases to 800 °C, although Ag nanostructures can always begin to sublimate at temperatures as low as 500 °C. Interestingly, Cu and Ag atoms sublimate simultaneously with a molar ratio likely to preserve at approximately 1 because Cu partially dissolves into the Ag phase at higher temperatures. Furthermore, a rational atomic motion mechanism is proposed to explain the phase transition in which the solid solution forms and the whole special sublimation process. These in situ observations promise to be helpful for understanding the evolutionary behaviors of bimetallic JNs under high temperatures arising in catalytic processes and other applications.

Sublimation Behavior of Industrial Grade Molybdenum Trioxide

Volatilization loss of molybdenum trioxide (MoO3) always takes place during the synthesis of Mo-containing alloying steel in the steelmaking process. In this work, the sublimation kinetics and mechanism of MoO3 in the range of 1273 to 1373 K were analyzed, in which the methods of model fitting, FE-SEM, EDS, and thermodynamic calculation were adopted. The results showed that sublimation of high-purity MoO3 (defined as the case III) and industrial grade MoO3 with the thickness of 3 mm (defined as the case II) were mainly controlled by the chemical reaction on the surface; increasing the thickness of industrial grade MoO3 to 7 mm (defined as the case I), the diffusion model was obeyed, instead. Activation energies of the three cases were extracted to be 127.489 (case III), 197.418 (case II), and 89.76 kJ/mol (case I), respectively. With the adoption of lever principle, the weight ratio of melting (from solid to liquid) to vaporization (from liquid to gas) during the whole volatilization process was estimated, i.e., 2.52:1 for case III, 0.84:1 for case II, and 5.89:1 for case I. The possible sublimation mechanism of industrial grade MoO3 was also proposed.

Sublimation Anisotropic Etching of Silicon Carbide in Aluminum Nitride Vapors

Specific features of sublimation etching of crystalline silicon carbide (SiC) in the presence of aluminum nitride (AlN) vapors have been reported. The etching is shown to be essentially anisotropic. Abnormally high speed of sublimation in a lateral direction, which weakly depends on surface orientation and polarity, is revealed through increasing artificial holes and flattening out surface elevations prepared in the shape of rectangular mesa structures. A high-rate etching is observed at outcrops of micropipes and closed-core screw dislocations, which leads to the formation of pits on () C-terminated faces. During annealing, the pits evolve into holes that might provoke the formation of pores inside free-standing AlN layers grown in one process with the sublimation of SiC substrates. The sublimation kinetics of a Si-terminated face is evidently different from that of a C-terminated face. It is found that a liquid phase is formed on the etched surfaces and it plays a key role in interpreting the etching anisotropy on SiC crystal faces of different orientations. It is shown that the sublimation of mesa-shaped SiC substrates can be used with the aim of optimizing the fabrication of thick freestanding AlN layers.

Sublimation Kinetics for Individual Graphite and Graphene Nanoparticles (NPs): NP-to-NP Variations and Evolving Structure-Kinetics and Structure-Emissivity Relationships

A single nanoparticle (NP) mass spectrometry method was used to measure sublimation rates as a function of nanoparticle temperature (TNP) for sets of individual graphite and graphene NPs. Initially, the NP sublimation rates were ∼400 times faster than those for bulk graphite, and there were large NP-to-NP variations. Over time, the rates slowed substantially, though they remained well above the bulk rate. The initial activation energies (Ea values) were correspondingly low and doubled, as a few monolayers worth of material was sublimed from the surfaces. The high initial rates and low Ea values are attributed to large numbers of edge, defect, and other low coordination sites on the NP surfaces, and the changes are attributed to atomic-scale "smoothing" of the surface by preferential sublimation of the less stable sites. The emissivity of the NPs also changed after heating, more frequently increasing. The emissivity and sublimation rates were anticorrelated, leading to the conclusion that high densities of low-coordination sites on the NP surfaces enhance sublimation but suppress emissivity.

Reducing the Sublimation Tendency of Ligustrazine through Salt Formation

Two new salts of ligustrazine (tetramethylpyrazine, TMP) with the sweeteners, saccharine (SAC) and acesulfame (ACS), have been synthesized through the anion exchange reaction. Single crystals of the new forms were prepared, and their structures were determined. The stability of the new salts against heat and humidity was tested and compared to the commercial hydrochloride and phosphate salts. The sublimation kinetics at various temperatures was analyzed using the Arrhenius equation. The results indicated that TMP-ACS exhibits significantly reduced sublimation tendency and hygroscopicity, which make it a more suitable salt for developing a tablet with acceptable shelf stability than the salts currently used in commercial products.

Non-Isothermal Sublimation Kinetics of 2,4,6-Trinitrotoluene (TNT) Nanofilms.

Non-isothermal sublimation kinetics of low-volatile materials is more favorable over isothermal data when time is a crucial factor to be considered, especially in the subject of detecting explosives. In this article, we report on the in-situ measurements of the sublimation activation energy for 2,4,6-trinitrotoluene (TNT) continuous nanofilms in air using rising-temperature UV-Vis absorbance spectroscopy at different heating rates. The TNT films were prepared by the spin coating deposition technique. For the first time, the most widely used procedure to determine sublimation rates using thermogravimetry analysis (TGA) and differential scanning calorimetry (DSC) was followed in this work using UV-Vis absorbance spectroscopy. The sublimation kinetics were analyzed using three well-established calculating techniques. The non-isothermal based activation energy values using the Ozawa, Flynn–Wall, and Kissinger models were 105.9 ± 1.4 kJ mol−1, 102.1 ± 2.7 kJ mol−1, and 105.8 ± 1.6 kJ mol−1, respectively. The calculated activation energy agreed well with our previously reported isothermally-measured value for TNT nanofilms using UV-Vis absorbance spectroscopy. The results show that the well-established non-isothermal analytical techniques can be successfully applied at a nanoscale to determine sublimation kinetics using absorbance spectroscopy.

A freeze-drying microscopy study of the kinetics of sublimation in a model lactose system

Freeze drying microscopy has been used to probe the lyophilisation kinetics of lactose solutions of various concentrations, at temperatures ranging from −50°C to −30°C and under a constant pressure of 1Pa. Sublimation front velocities were determined by recording a sequence of video images of the sublimation and analysing the frontal progression using MATLAB. Initial experiments showed poor reproducibility. To combat this, silver iodide (AgI) was added as an ice nucleator, which raised nucleation temperatures and improved reproducibility when compared to non-AgI experiments. The lower supercooling on nucleation when AgI was used also produced larger ice crystals, which enabled the crystal microstructure of the more dilute samples to be more clearly observed. This showed long thin crystals, and the orientation of these crystals with respect to the direction of the frontal movement strongly affected frontal progression rates, which explained the earlier reproducibility problems. A twin resistance mass transfer model, comprising a fixed edge resistance and a resistance which increased with frontal depth, was able to describe the sublimation kinetics. The edge resistance first increased and then decreased with solids content. The resistance per unit depth increased exponentially with solids content, so much so that there is an optimal solids content in relation to the rate of production of dried material. Resistances were also much higher when crystals were oriented with their major axis perpendicular to the direction of frontal movement. Freeze drying rates were approximately proportional to the saturation vapour pressure of water, however the long-held belief that water vapour pressure is the main driving force for mass transfer in freeze-drying systems may be an oversimplification as this only reflects driving forces in the vapour phase (pores) rather than within the solid.

Surface Energy and Surface Stability of Ag Nanocrystals at Elevated Temperatures and Their Dominance in Sublimation-Induced Shape Evolution.

The surface energy and surface stability of Ag nanocrystals (NCs) are under debate because the measurable values of the surface energy are very inconsistent, and the indices of the observed thermally stable surfaces are apparently in conflict. To clarify this issue, a transmission electron microscope is used to investigate these problems in situ with elaborately designed carbon-shell-capsulated Ag NCs. It is demonstrated that the {111} surfaces are still thermally stable at elevated temperatures, and the victory of the formation of {110} surfaces over {111} surfaces on the Ag NCs during sublimation is due to the special crystal geometry. It is found that the Ag NCs behave as quasiliquids during sublimation, and the cubic NCs represent a featured shape evolution, which is codetermined by both the wetting equilibrium at the Ag-C interface and the relaxation of the system surface energy. Small Ag NCs (≈10 nm) no longer maintain the wetting equilibrium observed in larger Ag NCs, and the crystal orientations of ultrafine Ag NCs (≈6 nm) can rotate to achieve further shape relaxation. Using sublimation kinetics, the mean surface energy of Ag NCs at 1073 K is calculated to be 1.1-1.3 J m-2 .

Impact of Ice Morphology on Design Space of Pharmaceutical Freeze-Drying

It has been known that the sublimation kinetics of a freeze-drying product is affected by its internal ice crystal microstructures. This article demonstrates the impact of the ice morphologies of a frozen formulation in a vial on the design space for the primary drying of a pharmaceutical freeze-drying process. Cross-sectional images of frozen sucrose–bovine serum albumin aqueous solutions were optically observed and digital pictures were acquired. Binary images were obtained from the optical data to extract the geometrical parameters (i.e., ice crystal size and tortuosity) that relate to the mass-transfer resistance of water vapor during the primary drying step. A mathematical model was used to simulate the primary drying kinetics and provided the design space for the process. The simulation results predicted that the geometrical parameters of frozen solutions significantly affect the design space, with large and less tortuous ice morphologies resulting in wide design spaces and vice versa. The optimal applicable drying conditions are influenced by the ice morphologies. Therefore, owing to the spatial distributions of the geometrical parameters of a product, the boundary curves of the design space are variable and could be tuned by controlling the ice morphologies.

In Situ Observation on Dislocation-Controlled Sublimation of Mg Nanoparticles.

Sublimation is an important endothermic phase transition in which the atoms break away from their neighbors in the crystal lattice and are removed into the gas phase. Such debonding process may be significantly influenced by dislocations, the crystal defect that changes the bonding environment of local atoms. By performing systematic defects characterization and in situ transmission electron microscopy (TEM) tests on a core--shell MgO-Mg system, which enables us to "modulate" the internal dislocation density, we investigated the role of dislocations on materials' sublimation with particular focus on the sublimation kinetics and mechanism. It was observed that the sublimation rate increases significantly with dislocation density. As the density of screw dislocations is high, the intersection of screw dislocation spirals creates a large number of monatomic ledges, resulting in a "liquid-like" motion of solid-gas interface, which significantly deviates from the theoretically predicted sublimation plane. Our calculation based on density functional theory demonstrated that the remarkable change of sublimation rate with dislocation density is due to the dramatic reduction in binding energy of the monatomic ledges. This study provides direct observation to improve our understanding on this fundamental phase transition as well as to shed light on tuning materials' sublimation by "engineering" dislocation density in applications.

Influence of Operating Conditions on the Freeze-Drying of Frozen Particles in a Fixed Bed and Modeling Data

Experimental runs have been carried out to investigate the influence of shelf temperature and total gas pressure in the chamber on the primary drying sublimation kinetics of a packed bed of frozen spherical particles of a model 16.6% (w/w) sucrose solution. Sublimation kinetics determined, in situ and on line, by weighing continuously the freeze-dried sample, were observed to increase with the total gas pressures and with the shelf temperatures. A physical model, based on the hypothesis that two “sublimation fronts” advancing at the same time from the bottom of the bed, due to the contact heat flux, and from the top of the bed, due to radiation heat flux, was proposed. Fair agreement was found between simulated and experimental data.