Sublimation Rate Research Articles

Stability of massive ground ice bodies in University Valley, McMurdo Dry Valleys of Antarctica: Using stable O–H isotope as tracers of sublimation in hyper-arid regions

To date, studies of the stability of subsurface ice in the McMurdo Dry Valleys of Antarctica have been mainly based on climate-based vapor diffusion models. In University Valley (1800m), a small glacier is found at the base of the head of the valley, and adjacent to the glacier, a buried body of massive ice was uncovered beneath 20–40cm of loose cryotic sediments and sandstone boulders. This study assesses the origin and stability of the buried body of massive ice by measuring the geochemistry and stable O–H isotope composition of the ice and applies a sublimation and molecular diffusion model that accounts for the observed trends. The results indicate that the buried massive ice body represents an extension of the adjacent glacier that was buried by a rock avalanche during a cold climate period. The contrasting δ18O profiles and regression slope values between the uppermost 6cm of the buried massive ice (upward convex δ18O profile and SD-18O=5.1) and that below it (progressive increase in δ18O and SD-18O=6.4) suggest independent post-depositional processes affected the isotope composition of the ice. The upward convex δ18O profile in the uppermost 6cm is consistent with the ice undergoing sublimation. Using a sublimation and molecular diffusion model, and assuming that diffusion occurred through solid ice, the sublimation rate needed to fit the measured δ18O profile is 0.2 ⋅ 10−3mm yr−1, a value that is more similar to net ice removal rates derived from 3He data from cobbles in Beacon Valley till (7.0 ⋅ 10−3mm yr−1) than sublimation rates computed based on current climate (0.1–0.2mm yr−1). We suggest that the climate-based sublimation rates are offset due to potential ice recharge mechanisms or to missing parameters, particularly the nature and thermo-physical properties of the overlying sediments (i.e., temperature, humidity, pore structure and ice content, grain size).

Modeling vapor diffusion within cold and dry supraglacial tills of Antarctica: Implications for the preservation of ancient ice

We modeled water–vapor diffusion within Mullins till, a relatively dry supraglacial till in southern Victoria Land, Antarctica, that rests directly on Mullins Glacier, purportedly one of the oldest alpine glaciers in the world. Like most supraglacial tills in cold-desert environments, Mullins till contains three characteristic facies: a weathered facies representing the oxidation of iron-bearing minerals and the physical disintegration of surface rocks; a sand-wedge facies representing the episodic infill of thermal cracks associated with contraction-crack polygons; and an underlying fresh facies representing the addition of englacial debris (sourced from rockfall) as overlying ice sublimes. Using a one-dimensional model for Fickian vapor diffusion through porous media, we show that the rate of subsurface ice sublimation varies by ~ 5.5% beneath till facies and that over timescales of 10 5 years diffusion through “porous” sand wedges contributes to the development of deep troughs surrounding high-centered polygons. Applying site-specific meteorological data collected over a four-year period, we show that ice loss at the stagnant terminus of Mullins Glacier is ~ 6.6 × 10 −5 m a −1, a value that (although low and assuming an ice thickness of ~ 150 m) is consistent with complete ice loss under current environmental forcing in ~ 2.5 Ma. Our sensitivity tests indicate that the vast majority of sublimation occurs during the summer months. Calculated summertime losses drop to zero with either a reduction in soil and ice surface temperatures of ~ 6.4 °C or an increase in atmospheric relative humidity from 44% to 75%, both of which could arise from an increase in cloud cover over Mullins Glacier. Sublimation responses to meteorological forcing are not uniform across Mullins Glacier. A summer increase in soil temperature of 2 °C results in negligible change in ice sublimation at Mullins terminus, but a 27% increase in ice loss in upper Mullins Valley. The key factor is the thickness of Mullins till, which is greater near the glacier terminus. For till thicknesses exceeding ~ 25 cm, non-linear variations in soil temperature result in downward vapor fluxes, capable of producing thin, cm-scale lenses of secondary pore that cap the surface of buried glacier ice. This downward vapor flow, sourced from modern snowfall and/or elevated atmospheric relative humidity, is one of the key factors that enable long-term preservation of buried glacier ice. Overall, our results highlight the subtle relations among changes in till texture, till thickness, and meteorological forcing on the rate of subsurface ice loss and provide insight into the plausible range of conditions under which multi-million-year-old ice can exist beneath thin supraglacial tills, <~50-cm thick, in southern Victoria Land, Antarctica.

Characterizing the Freeze–Drying Behavior of Model Protein Formulations

The freeze-drying behavior of three model proteins, namely, lysozyme, BSA, and IgG, has been studied using a variety of techniques under two different primary drying conditions (shelf temperatures of -25°C and +25°C, respectively) in an amorphous formulation. Manometric temperature measurements were used to characterize product temperature (T (pr)), sublimation rates, and product resistance (R (p)) during primary drying. Biophysical techniques such as circular dichroism, fluorescence, and Fourier transform infrared spectroscopy were used to study protein conformation. Size exclusion chromatography was used to monitor the formation of high-molecular-weight species (HMWS) over time on storage, and cake morphology was studied using scanning electron microscopy. The differences in the freeze-drying behavior of the three proteins were more evident at higher protein concentrations, where the protein significantly influences the behavior of the formulation matrix. However, these differences were minimized in the aggressive mode and were insignificant at lower protein concentrations where excipients dominated the freeze-drying behavior. Differences in cake morphology were observed between the two drying conditions employed as well as between the three proteins studied. The stability and the protein structure, however, were equivalent for the protein cakes generated using the two different primary drying conditions.

Sublimation Rate of TNT Microcrystals in Air

Reliable measurements of the sublimation rate of nonuniform layers of trinitrotoluene (TNT) microcrystals were carried out using a quartz crystal microbalance (QCM). The sample layer was prepared by precipitation of TNT from a well-defined volume of its solution in acetonitrile. The TNT solution was placed on the QCM electrode surface to form the precipitated layer of TNT microcrystals. It is shown that the kinetics of small TNT particles sublimation is controlled by the molecular diffusion in air. The sublimation process is well described by simple diffusion expressions that are discussed in the literature for both individual hemispherical-shaped microcrystals and disk-shaped layers. Expressions describing particle size evolution in time were derived based on this diffusion model. It is shown that the expressions developed can be used to simulate particle sublimation in a wide size range, including very small sub-micrometer particles.

The evolution of exposed ice in a fresh mid-latitude crater on Mars

Recent observations of the surface of Mars have shown several fresh mid-latitude craters. Some of these craters show exposed ice (Byrne, S. et al. [2009]. Science 325, 1674–1676.). In some craters, albedo of ice slowly decreases, while in others, it remains nearly constant. We attempt to determine influence of the regolith structure on the rate of sublimation of ice. For this purpose we performed numerical simulations describing evolution of the exposed ice in model craters located at middle latitudes. We consider a new model for the structure and evolution of the material at- and beneath the crater floors. In contrast to the previous study by Dundas and Byrne (Dundas, C.M., Byrne, S. [2010]. Icarus 206, 716–728.) we do not investigate sublimation of dirty ice, and the related formation of a sublimation lag. Instead, we consider sublimation of a pure ice layer on top of layered regolith. In our model the observed reflectivity decreases due to the sublimation-driven changes of the optical properties of thinning clean ice. This offers an alternative to the deposition of the dust embedded in ice (sublimation lag). We have shown that in our model among many parameters affecting ice sublimation rate, volumetric fraction of water ice in the subsurface beneath the crater has the strongest influence. Hence observed darkening of the ice patch on the crater floor might be sufficient to determine the content of water ice in the subsurface. Our calculations show that an albedo decrease of fresh ice patches in mid-latitude craters can be explained by either strong dust sedimentation or, if this is excluded, by sublimation of a thin layer of water ice from the regolith with large thermal inertia. This is consistent with a large volumetric fraction of water ice beneath the crater floor and contributes to evidence for an extended subsurface water reservoir on Mars. The overall conclusion of our work is that a thin post-impact surface ice coating over ice-rich ground beneath the crater floors is consistent with the observations.

On the Use of a Dual-Scale Model to Improve Understanding of a Pharmaceutical Freeze-Drying Process

The evolution of product temperature and of residual ice content in the various vials of a batch during a freeze-drying process can be significantly affected by local conditions around each vial. In fact, vapor fluid dynamics in the drying chamber determines the local pressure that, taking into account the heat flow from the shelf and, eventually, radiation from chamber surfaces, is responsible for the sublimation rate and product temperature. These issues have to be taken into account when using mathematical simulation to predict the evolution of the product as a consequence of the operating conditions (recipe design), as well as during the scale-up of a recipe obtained in a small-scale equipment to a large-scale unit. In this framework, a dual-scale model can significantly improve the understanding for pharmaceuticals freeze-drying processes: it couples a three-dimensional model, describing the fluid dynamics in the chamber, and a second mathematical model, either mono- or bi-dimensional, describing the drying of the product in each vial. Thus, it can be profitably used to gain knowledge about process dynamics, and to improve the design of the equipment, as well as the performance of the control system of the process.

Migration of air bubbles in ice under a temperature gradient, with application to “Snowball Earth”

To help characterize the albedo of “sea glaciers” on Snowball Earth, a study of the migration rates of air bubbles in freshwater ice under a temperature gradient was carried out in the laboratory. The migration rates of air bubbles in both natural glacier ice and laboratory‐grown ice were measured for temperatures between −36°C and −4°C and for bubble diameters of 23–2000 μm. The glacier ice was sampled from a depth near close‐off (74 m) in the JEMS2 ice core from Summit, Greenland. Migration rates were measured by positioning thick sections of ice on a temperature gradient stage mounted on a microscope inside a freezer laboratory. The maximum and minimum migration rates were 5.45 μm h−1 (K cm−1)−1 at −4°C and 0.03 μm h−1 (K cm−1)−1 at −36°C. Besides a strong dependence on temperature, migration rates were found to be proportional to bubble size. We think that this is due to the internal air pressure within the bubbles, which may correlate with time since close‐off and therefore with bubble size. Migration rates show no significant dependence on bubble shape. Estimates of migration rates computed as a function of bubble depth within sea glaciers indicate that the rates would be low relative to the predicted sublimation rates, such that the ice surface would not lose its air bubbles to net downward migration. It is therefore unlikely that air bubble migration could outrun the advancing sublimation front, transforming glacial ice to a nearly bubble‐free ice type, analogous to low‐albedo marine ice.

Product mass transfer resistance directly determined during freeze-drying cycle runs using tunable diode laser absorption spectroscopy (TDLAS) and pore diffusion model

The pore diffusion model is used to express the dry layer mass transfer resistance, , as a function of the ratio re/τ, where re is the effective pore radius and τ is the tortuosity factor of the dry layer. Using this model, the effective pore radius of the dry layer can be estimated from the sublimation rate and product temperature profiles measured during primary drying. Freeze-drying cycle runs were performed using the LyoStar II dryer (FTS Systems), with real-time sublimation rate profiles during freeze drying continuously measured by tunable diode laser absorption spectroscopy (TDLAS). The formulations chosen for demonstration of the proposed approach include 5% mannitol, 5% sucrose, 5% lactose, 3% mannitol plus 2% sucrose, and a parenteral nutrition formulation denoted VitaM12. The three different methods used for determination of the product resistance are: (1) Using both the sublimation rate and product temperature profiles, (2) using the sublimation rate profile alone, and (3) using the product temperate profile alone. Unlike the second and third methods, the computation procedure of first method does not need solution of the complex heat and mass transfer equations.

Development of a Magnesium and Zinc Hall-Effect Thruster

§This paper describes what are believed to be the first demonstrations of Hall-effect thrusters operating on magnesium and zinc propellant. Pathfinding experiments were performed using consumable anodes that were machined from solid magnesium and zinc, which sublimated under the heat load from the discharge plasma and delivered propellant gas to the thruster. Therefore the magnesium and zinc anodes served as the acceleration electrode and also served as the propellant supply. A retarding potential analyzer was used to obtain plume diagnostics during early operation of the experiments, showing reasonable acceleration of the propellant ions. Two main issues were expected and encountered with the solid magnesium and zinc anodes – 1) the zinc anode displayed localized melting causing liquid zinc to accumulate in the discharge channel and 2) the crude scheme did not feature any means to actively control the sublimation rate of the metal propellant. A new porous anode with internal propellant reservoir was designed and built that could be refilled with either propellant, eliminating liquid intrusion into the discharge channel. A scheme developed earlier for bismuth thrusters was employed wherein shim anodes were implemented to shift discharge current to and from the main anode to control the main anode temperature and hence the metal propellant sublimation rate. Results are reported showing stable operation of a thruster using a porous anode with magnesium propellant for more than 100 minutes. Also demonstrated was the ability of the shim anode scheme to actively control the propellant mass flow rate.

Chemically assisted vapour transport for bulk ZnO crystal growth

A chemically assisted vapour phase transport (CVT) method is proposed for the growth of bulk ZnO crystals. Thermodynamic computations have confirmed the possibility of using CO as a sublimation activator for enhancing the sublimation rate of the feed material in a large range of pressures (10 −3 to 1 atm) and temperatures (800–1200 °C). Growth runs in a specific and patented design yielded single ZnO crystals up to 46 mm in diameter and 8 mm in thickness, with growth rates up to 400 μm/h. These values are compatible with an industrial production rate. N type ZnO crystals ( μ=182 cm 2/(V s) and n=7 10 15 cm −3) obtained by this CVT method (Chemical Vapour Transport) present a high level of purity (10–30 times better than hydrothermal ZnO crystals), which may be an advantage for obtaining p-type doped layers ([Li] and [Al] <10 +15 cm −3). Structural (HR-XRD), defect density (EPD), electrical (Hall measurements) and optical (photoluminescence) properties are presented.

Choked flow and importance of Mach I in freeze-drying process design

Occasionally the freeze drying cycle conditions are developed on a small scale dryer that result in a water vapor flux during primary drying that the full-scale equipment cannot handle, resulting in loss of the ability to control chamber pressure. A primary cause of loss of pressure control is a phenomenon commonly described as “choked flow”, where the required mass transfer through the duct connecting the drying and condenser chamber cannot be maintained at the control pressure. Water vapor flow rate increases as the condenser pressure decreases, but it can continue to do so only until the velocity of water vapor reaches speed of sound (i.e., Mach I) at the duct exit. The flow is then said to be choked, and any further increase in water vapor flow rate results in an increase in chamber pressure (i.e., loss in chamber pressure control). Sublimation tests were carried out in Lyostar II freeze-dryer (SP Industries, NY) to predict the occurrence of choked flow. A capacitance manometer was installed in the “condenser chamber” and differential pressure ( P c − P cd ) was measured as a function of sublimation rate ( P c =chamber pressure and P cd =condenser pressure). Water vapor flow rate was measured by Tunable Diode Laser Absorption Spectroscopy (TDLAS) methodology, with a check by gravimetric data. Flow of water vapor in the duct connecting chamber and the condenser was modeled using computational fluid dynamics software (Fluent 6.3). The critical pressure ratio ( K⁎= P c / P cd ) has been identified as an important variable that determines the onset of choked flow during primary drying. This ratio can be calculated given the mass flux. For our freeze-dryer, K* greater than 2.5 (for P c <150 mTorr) resulted in choked flow. The gas velocity indeed reaches Mach I limit at the duct exit under the choked flow conditions, as modeled by Fluent. Using the differential pressure measurements, the throat connecting the chamber and the condenser can be used as an “in process” mass flow meter to measure sublimation rate under non-choked flow conditions during primary drying without interrupting the process. Also, TDLAS is a useful tool for determination of sublimation rate even at very high mass flux.

The initial responses of hot liquid water released under low atmospheric pressures: Experimental insights

Experiments have been performed to simulate the shallow ascent and surface release of water and brines under low atmospheric pressure. Atmospheric pressure was treated as an independent variable and water temperature and vapor pressure were examined as a function of total pressure variation down to low pressures. The physical and thermal responses of water to reducing pressure were monitored with pressure transducers, temperature sensors and visible imaging. Data were obtained for pure water and for solutions with dissolved NaCl or CO 2. The experiments showed the pressure conditions under which the water remained liquid, underwent a rapid phase change to the gas state by boiling, and then solidified because of removal of latent heat. Liquid water is removed from phase equilibrium by decompression. Solid, liquid and gaseous water are present simultaneously, and not at the 611 Pa triple point, because dynamic interactions between the phases maintain unstable temperature gradients. After phase changes stop, the system reverts to equilibrium with its surroundings. Surface and shallow subsurface pressure conditions were simulated for Mars and the icy satellites of the outer Solar System. Freezing by evaporation in the absence of wind on Mars is shown to be unlikely for pure water at pressures greater than c. 670 Pa, and for saline solutions at pressures greater than c. 610 Pa. The physical nature of ice that forms depends on the salt content. Ice formed from saline water at pressures less than c. 610 Pa could be similar to terrestrial sea ice. Ice formed from pure water at pressures less than c. 100 Pa develops a low thermal conductivity and a ‘honeycomb’ structure created by sublimation. This ice could have a density as low as c. 450 kg m −3 and a thermal conductivity as low as 1.6 W m −1 K −1, and is highly reflective, more akin to snow than the clear ice from which it grew. The physical properties of ice formed from either pure or saline water at low pressures will act to reduce the surface temperature, and hence rate of sublimation, thereby prolonging the lifespan of any liquid water beneath.

Investigating sublimation and the effect of an imaging gas in a VPSEM

In this paper we present an investigation into the possible link between the pressure of the gas in the surrounding environment and the rate of ice sublimation in a VPSEM (variable pressure scanning electron microscope). Although this is mainly significant to an electron microscopist working in a variable pressure environment, it is relevant to people working at low pressures who wish to have control over the rate of sample dehydration where the input of water vapour is not a viable alternative.

Sublimation crystal growth of yttrium nitride

The sublimation–recombination crystal growth of bulk yttrium nitride crystals is reported. The YN source material was prepared by reacting yttrium metal with nitrogen at 1200 °C and 800 Torr total pressure. Crystals were produced by subliming this YN from the source zone, and recondensing it from the vapor as crystals at a lower temperature (by 50 °C). Crystals were grown from 2000 to 2100 °C and with a nitrogen pressure from 125 to 960 Torr. The highest rate was 9.64×10 −5 mol/h (9.92 mg/h). The YN sublimation rate activation energy was 467.1±21.7 kJ/mol. Individual crystals up to 200 μm in dimension were prepared. X-ray diffraction confirmed that the crystals were rock salt YN, with a lattice constant of 4.88 Å. The YN crystals were unstable in air; they spontaneously converted to yttria (Y 2O 3) in 2–4 h. A small fraction of cubic yttria was detected in the XRD of a sample exposed to air for a limited time, while non-cubic yttria was detected in the Raman spectra for a sample exposed to air for more than 1 h.

Use of Manometric Temperature Measurements (MTM) to Characterize the Freeze-Drying Behavior of Amorphous Protein Formulations

The freeze-drying behavior and cake morphology of a model protein in an amorphous formulation were studied at varying protein concentrations using conservative (-25 degrees C) and aggressive (+25 degrees C) shelf temperatures at constant chamber pressure during primary drying. The two cycles were characterized by manometric temperature measurements (MTM) in a SMART freeze dryer that estimates the sublimation rate (dm/dt), product temperature at the freeze-drying front (T(p-MTM)) and product resistance (R(p)) during a run. The calculated sublimation rates (dm/dt) were 3-4 times faster in the aggressive cycle compared to the conservative cycle. For conservatively dried cakes R(p) increased with both dry layer thickness and protein concentration. For aggressively dried cakes (where freeze-drying occurs at the edge of microcollapse), R(p) also increased with protein concentration but was independent of the dry layer thickness. The sublimation rate was influenced by R(p), dry layer thickness and T(p-MTM) in the conservative cycle, but was governed mainly by T(p-MTM) in the aggressive cycle, where R(p) is independent of the dry layer thickness. The aggressively dried cakes had a more open and porous structure compared to their conservatively dried counterparts.

Blowing Snow Fluxes in the Cariboo Mountains of British Columbia, Canada

The Cariboo Mountains form the northern extension of the Columbia Mountains, spanning a distance of about 300 km in central British Columbia (BC), Canada. Cool air temperatures, abundant snowfall, and strong winds (especially above treeline and along exposed ridges) would suggest frequent and intense blowing snow events. The occurrence of intense blowing snow episodes is confirmed by automated wind and snow depth measurements at several sites in the area. Simulations conducted with a numerical model forced by meteorological observations recorded from 2006 to 2009 reveal a high frequency of blowing snow episodes at three high-elevation sites in the Cariboo Mountains. This process is especially prominent on the exposed ridge of Browntop Mountain (elevation of 2031 m a.s.l.) where snow transport by wind is calculated to occur as much as two-thirds of the time during some winter months. Simulated blowing snow fluxes remain high at this site with monthly transport and sublimation rates reaching 5301 Mg m−1 and 31 mm snow water equivalent (SWE), respectively. Blowing snow is also shown to be a dominant process in snow accumulation at the upper Castle Creek Glacier site (elevation of 2105 m a.s.l.), with strong winds generating sharp declines in snow depth and the erosion of more than 200 cm of snow depth during two successive winters. The results presented in this study suggest that blowing snow contributes significantly to snow accumulation and the mass balance of glaciers in BC’s Cariboo Mountains.

On resolving the statistical and calorimetric entropies of glass and non-crystalline solids, and the residual entropy problem

Abstract In statistical terms, the configurational entropy, S conf , of a structure of fixed configuration is zero, i.e., its Ω = 1 in the Boltzmann equation, S conf = k B ln Ω . On that basis, a recent discussion has drawn two inferences: (a) S conf is lost when a liquid vitrifies and thus a glass has no residual entropy, S res , and (b) structural relaxation of a glass would first increase its S conf with time from its zero value and then decrease S conf to the equilibrium value, thus causing the slope of its free energy against time plot to abruptly decrease after a certain time period. Both conclusions conflict with the classical, textbook analysis of the calorimetric data, and with the experimental findings. To evaluate the merits of these conclusions, we use the difference between the free energy of glass (and of supercooled liquid) and its crystal phase. If the inferences based on the statistical view are valid, (i) this difference would show a gap between the glass and supercooled liquid in the T g range, (ii) the slope of the plot of this difference against T would be much less at T T g than at T > T g , and (iii) annealing would decrease this difference by a relatively large amount. After constructing such plots from the known C p data, we propose that measurement of the vapor pressure, sublimation rate, solubility, chemical reaction rate, and emf of a cell made from glassy-metal electrodes may be useful for testing whether or not S conf is lost on vitrification. The data available provide no support for the entropy-loss view.

The behavior of powder sublimation in the long-term PVT growth of SiC crystals

The effect of different temperature distribution in powder on the powder sublimation was investigated by experiments and simulations. On the one hand, appropriately large temperature difference in the powder will contribute to high growth rate when the mass transportation between the powder and the seed proceeds smoothly. Nevertheless, the recrystallization at the bottom of powder will reduce the available powder in the growth and should be avoided. On the other hand, when the temperature difference in the powder is so large that the rate of sublimation of the powder increases beyond the normal limit of the rate of mass transportation between the powder and the seed, the mass transportation in the powder will be obstructed and even the crystal growth will be interrupted.

First principle lattice energy calculations for enantiopure and racemic crystals of α-(trifluoromethyl)lactic acid: Is self-disproportionation of enantiomers controlled by thermodynamic stability of crystals?

The lattice energies for the enantiopure and racemic crystals of α-(trifluoromethyl)lactic acid were calculated by a combination of the DFT calculations with the periodic boundary condition and the MP2 calculations of the interactions with neighboring molecules. The lattice energies calculated for the two crystals (−16.56 and −17.35 kcal/mol, respectively) show that the racemic crystals are thermodynamically more stable, although the racemic crystals sublime faster than the enantiopure crystals. The calculations suggest that the relative thermodynamic stability is not the cause of the faster sublimation rate of the racemic crystals compared with the enantiopure crystals. Although the crystals have hydrogen-bonding networks, the dispersion interactions contribute to the lattice energies significantly. The MP2 calculations for the evaluation of the dispersion interactions with the neighboring molecules are important for an accurate evaluation of the lattice energies. The relative thermodynamic stability of the two crystals is not determined solely by the hydrogen bonds. The interactions with other neighboring molecules also play important roles in determining the relative stability. We demonstrate that the geometry optimization is essential for an accurate evaluation of the lattice energy by the first principle calculation. The interaction energies calculated using the structure by X-ray diffraction often have large errors.

Investigation of Formulation and Process of Lyophilised Orally Disintegrating Tablet (ODT) Using Novel Amino Acid Combination.

Lyophilised orally disintegrating tablets (ODTs) have achieved a great success in overcoming dysphagia associated with conventional solid dosage forms. However, the extensive use of saccharides within the formulation limits their use in treatment of chronic illnesses. The current study demonstrates the feasibility of using combination of proline and serine to formulate zero sacharide ODTs and investigates the effect of freezing protocol on sublimation rate and tablets characteristics. The results showed that inclusion of proline and serine improved ODT properties when compared to individual counterparts. Additionally, annealing the ODTs facilitated the sublimation process and shortened the disintegration time.