This is a working overview of sublimation, written for readers who want more than a one-paragraph summary but less than a textbook.
Reviewed 2026-03-22. Anything still debated is marked as such rather than presented as settled.
Lyophilization, or freeze-drying, removes water from a material by freezing it and then lowering pressure so ice changes directly to vapor. The process relies on sublimation, the phase transition from solid to gas without an intervening liquid state. It is used for heat-sensitive materials that would degrade in conventional drying. The three stages are freezing, primary drying, and secondary drying, each with distinct temperature and pressure requirements. In practice, cycle design balances these variables.
Freezing determines ice crystal structure and pore size, which affect drying speed and product uniformity. Rapid freezing creates small crystals, while slow freezing creates larger crystals and often faster sublimation. During primary drying, chamber pressure is held below the vapor pressure of ice, and shelf temperature supplies heat for sublimation. The ice front recedes, leaving a porous matrix. Thermal limits such as collapse and eutectic temperatures set safe boundaries for formulation. These limits vary with solute composition and concentration.
Secondary drying removes bound water that remains after ice sublimation. Shelf temperature is raised gradually while pressure remains low, reducing water content to a target range. Over-drying can cause brittleness or electrostatic issues, while under-drying affects stability. The endpoint is often judged by pressure rise tests, temperature measurements, or water content analysis. Scale-up depends on matching heat and mass transfer across equipment sizes. Small changes in shelf temperature or pressure can alter cycle length substantially.
The process relies on the phase diagram of water, where the triple point marks the conditions at which ice, liquid water, and vapor coexist. By maintaining pressure below this point, typically around 0.01 to 0.1 millibar, sublimation becomes the dominant mechanism. Formulations often include excipients such as sugars or polymers that act as lyoprotectants and bulking agents. These additives help preserve the structure of the active ingredient and prevent collapse during drying. The choice of excipient and freezing rate influences the final cake morphology and stability.
Industries use lyophilization for pharmaceuticals, biological products, and food preservation. In the pharmaceutical sector, it extends the shelf life of injectable drugs, vaccines, and proteins that are unstable in aqueous solution. Food manufacturers apply freeze-drying to coffee, fruits, and ready meals to retain flavor and texture. The process is energy-intensive and requires specialized equipment, which limits its use to high-value products. Ongoing research examines how formulation and process parameters affect the quality of the final dried product.
| Property | Value | Notes |
|---|---|---|
| Process name | Lyophilization or freeze-drying | Both terms appear in technical standards and literature. |
| Phase transition | Sublimation | Solid ice becomes vapor without a liquid step. |
| Typical chamber pressure | 0.05-0.5 mbar | Range depends on product temperature and equipment. |
| Typical product temperature | -40 °C to -10 °C | Measured during primary drying; formulation sets limits. |
| Water content after drying | 0.5-3% w/w | Target varies by material and stability needs. |
Freeze-drying is distinct from simple evaporation and from spray drying. Evaporation removes water at temperatures above freezing, while spray drying rapidly dries droplets in a heated gas stream. Lyophilization avoids high temperatures, which can be useful for heat-sensitive materials such as proteins, vaccines, and some foods. The porous cake produced by sublimation dissolves or rehydrates more quickly than a dense dried mass. Not all materials tolerate freezing or the pH shifts that can occur as solutes concentrate during ice formation.
Lyophilization removes water from a frozen material by sublimation under reduced pressure. The process begins with freezing, which converts liquid water into ice and fixes the structure of the sample. After freezing, primary drying lowers pressure so ice changes directly to vapor without passing through a liquid phase. Secondary drying then removes bound water that remains after ice sublimation. The result is a dry, porous solid that often retains its original shape.
The low pressure used during drying allows water vapor to move from the ice surface to a cold condenser. Energy supplied as heat drives sublimation but must stay below the collapse temperature of the frozen matrix. If the product becomes too warm, the frozen structure may soften or melt, reducing pore formation and slowing drying. Formulations often include bulking agents, stabilizers, or buffers to support a rigid cake. The final moisture content depends on formulation, freezing rate, and the length of secondary drying.
The process generally proceeds in three stages: freezing, primary drying, and secondary drying. During freezing, controlled cooling converts water into ice and may also crystallize or vitrify solutes. In primary drying, the pressure is lowered below the triple point, and heat is supplied so ice sublimes directly to vapor. Secondary drying removes water that remains bound to the solid matrix, yielding a low final water content. Product temperature must stay below the collapse or glass transition temperature to maintain structure. Cycle design therefore balances shelf temperature, chamber pressure, and time.
Freeze-drying is used for materials whose activity or structure depends on low temperature and low water content. Examples include certain biologics, diagnostic reagents, starter cultures, coffee, and porous inorganic precursors. The dried product forms a cake whose porosity aids rapid wetting and dissolution. Main drawbacks are high energy use, long cycle times, and sensitivity to formulation and equipment variation. Questions remain about how freezing rates and ice morphology affect batch uniformity, especially when moving from laboratory to production scale.
Lyophilization is a dehydration technique in which a product is frozen and the solvent is removed under reduced pressure. The low pressure allows ice to sublimate directly into vapor without passing through a bulk liquid phase. This differs from conventional drying, where heat drives evaporation and can damage heat-sensitive structures. The process is used for biological materials, pharmaceutical formulations, and some foods. Its main advantage is preservation of porous structure and rapid reconstitution.
Freezing is the first stage and sets the ice structure that later becomes the pore network. The formulation is cooled below its freezing point, often with a controlled ramp, and solutes concentrate as ice forms. Primary drying then lowers chamber pressure and supplies heat to sublime the ice. The product temperature must stay below its collapse or eutectic temperature to prevent structural loss. Secondary drying raises the temperature modestly to remove bound water and achieve a low residual moisture.
The ability to quantitate the βhCG level is useful in monitoring germ cell and trophoblastic tumors, follow-up care after miscarriage, and diagnosis of and follow-up care after treatment of ectopic pregnancy. The lack of a visible fetus on vaginal ultrasound after βhCG levels reach 1500 mIU/mL is strongly indicative of an ectopic pregnancy. Still, even an hCG over 2000 IU/L does not necessarily exclude the presence of a viable intrauterine pregnancy in such cases. As pregnancy tests, quantitative blood tests and the most sensitive urine tests usually detect hCG between 6 and 12 days after ovulation. It must be taken into account, however, that total hCG levels may vary in a very wide range within the first 4 weeks of gestation, leading to false results during this period. A rise of 35% over 48 hours is proposed as the minimal rise consistent with a viable intrauterine pregnancy.
It is believed that the tyrosine amino acid found along the amino acid sequence of alpha-sarcin allows for the specificity when alpha-sarcin binds to the rRNA. It is the alcohol group found on the tyrosine amino acid that allows for this binding. This was determined in tests that removed the alcohol group, replacing tyrosine with phenylalanine, and the binding affinity was greatly reduced. The region of the DNA that makes alpha-sarcin is highly conserved, along with the corresponding sequence on the targeted ribosome. The corresponding sequence on the targeted ribosome is a centered around a guanine nucleotide located on what is called the "bulged-G motif".
Caesium-134 is found in spent nuclear fuel but is not produced by nuclear weapon explosions, as it is only formed by neutron capture on stable Cs-133, which is only produced by beta decay of Xe-133 with a half-life of 3 days. Cs-134 has a half-life of 2 years and may be a major source of gamma radiation in the first 20 years after discharge. Caesium-135 is a long-lived fission product with much weaker radioactivity. Neutron capture inside the reactor transmutes much of the xenon-135 that would otherwise decay to Cs-135. Caesium-137, with a half-life of 30 years, is the main medium-lived fission product, along with Sr-90. Cs-137 is the primary source of penetrating gamma radiation from spent fuel from 10 years to about 300 years after discharge. It is the most significant radioisotope left in the area around Chernobyl.
A study shows most extensively the neuro-molecular mechanics of how a fungal parasite affects behavior of insects. A study found that, of 70,000 monitored species, some 48% are experiencing population declines from human activity, whereas only 3% have increasing populations. By publishing virome-related results, researchers close a major gap in the accumulating research into centenarians' microbiome characteristics for life extension. 16 May – A software tool called Allegro is reported to accurately simulate 44 million atoms, running on the Perlmutter supercomputer. 17 May Astronomers confirm the existence of MACS1149-JD1 (JD1), one of the farthest known galaxies from Earth. Scientists report, based on genetic studies, a more complicated pathway of human evolution than previously understood. According to the studies, humans evolved from different places and times in Africa, instead of from a single location and period of time. The newly discovered exoplanet LP 791-18 d is theorised to be covered with volcanoes, due to the extreme gravitational pull of a super-Earth in the same system. A study proposes school curricula start including useful basic life support, noting that e.g. complemented video lessons could be effective. 18 May Astronomers map the paths of potentially hazardous asteroids for the next 1,000 years. At least 28 asteroids of 1 km diameter or larger are found to have non-zero probabilities of a 'deep encounter' with Earth. A study reports that more than 50% of freshwater lakes and reservoirs lost volume since 1992 due to human and climatic drivers.
Sources: en.wikipedia.org
If the incircle is tangent to the sides AB, BC, CD, DA at T1, T2, T3, T4 respectively, and if N1, N2, N3, N4 are the isotomic conjugates of these points with respect to the corresponding sides (that is, AT1 = BN1 and so on), then the Nagel point of the tangential quadrilateral is defined as the intersection of the lines N1N3 and N2N4. Both of these lines divide the perimeter of the quadrilateral into two equal parts. More importantly, the Nagel point N, the "area centroid" G, and the incenter I are collinear in this order, and NG = 2GI. This line is called the Nagel line of a tangential quadrilateral. In a tangential quadrilateral ABCD with incenter I and where the diagonals intersect at P, let HX, HY, HZ, HW be the orthocenters of triangles AIB, BIC, CID, DIA. Then the points P, HX, HY, HZ, HW are collinear.
"Molecular mechanisms of insulin resistance and associated diseases". Clinica Chimica Acta. 375 (1–2): 20–35. doi:10.1016/j.cca.2006.07.005. PMID 16956601. Tomazic, J; Karner, P; Vidmar, L; Maticic, M; Sharma, PM; Janez, A (2005). "Effect of metformin and rosiglitazone on lipid metabolism in HIV infected patients receiving protease inhibitor containing HAART". Acta Dermatovenerologica Alpina, Pannonica et Adriatica. 14 (3): 99–105. PMID 16200335. Tomažič, Janez; Silič, Anja; Karner, Primož; Vidmar, Ludvik; Matičič, Mojca; Poljak, Mario; Ihan, Alojz; Janež, Andrej (2004). "Lipodystrophy and metabolic abnormalities in Slovenian HIV-infected patients". Wiener Klinische Wochenschrift. 116 (21–22): 755–9. doi:10.1007/s00508-004-0268-9. PMID 15628647. S2CID 24715784. Tomazic, M.; Janez, A.; Sketelj, A.; Kocijancic, A.; Eckel, J.; Sharma, P. (2002). "Comparison of alterations in insulin signalling pathway in adipocytes from type II diabetic pregnant women and women with gestational diabetes mellitus". Diabetologia. 45 (4): 502–8. doi:10.1007/s00125-002-0791-z. PMID 12032625. (Retracted) Hevener, A.; Reichart, D.; Janez, A.; Olefsky, J. (2002). "Female Rats Do Not Exhibit Free Fatty Acid-Induced Insulin Resistance". Diabetes. 51 (6): 1907–12. doi:10.2337/diabetes.51.6.1907. PMID 12031980. Hevener, A. L.; Reichart, D.; Janez, A.; Olefsky, J. (2001). "Thiazolidinedione Treatment Prevents Free Fatty Acid-Induced Insulin Resistance in Male Wistar Rats". Diabetes. 50 (10): 2316–22. doi:10.2337/diabetes.50.10.2316. PMID 11574414. Ravnik-Oblak, M; Janez, A; Kocijanicic, A (2001).
Initial rate experiments. When an enzyme is mixed with a large excess of the substrate, the enzyme-substrate intermediate builds up in a fast initial transient. Then the reaction achieves a steady-state kinetics in which enzyme substrate intermediates remains approximately constant over time and the reaction rate changes relatively slowly. Rates are measured for a short period after the attainment of the quasi-steady state, typically by monitoring the accumulation of product with time. Because the measurements are carried out for a very short period and because of the large excess of substrate, the approximation that the amount of free substrate is approximately equal to the amount of the initial substrate can be made. The initial rate experiment is the simplest to perform and analyze, being relatively free from complications such as back-reaction and enzyme degradation. It is therefore by far the most commonly used type of experiment in enzyme kinetics. Progress curve experiments. In these experiments, the kinetic parameters are determined from expressions for the species concentrations as a function of time. The concentration of the substrate or product is recorded in time after the initial fast transient and for a sufficiently long period to allow the reaction to approach equilibrium. Progress curve experiments were widely used in the early period of enzyme kinetics, but are less common now. Transient kinetics experiments. In these experiments, reaction behaviour is tracked during the initial fast transient as the intermediate reaches the steady-state kinetics period.
As a result, people with a history of cardiovascular disease may derive benefit from statins irrespective of their cholesterol levels (total cholesterol below 5.0 mmol/L [193 mg/dL]), and in men without cardiovascular disease, there is benefit from lowering abnormally high cholesterol levels ("primary prevention"). Primary prevention in women was originally practiced only by extension of the findings in studies on men, since, in women, none of the large statin trials conducted prior to 2007 demonstrated a significant reduction in overall mortality or in cardiovascular endpoints. Meta-analyses have demonstrated significant reductions in all-cause and cardiovascular mortality, without significant heterogeneity by sex.
Vitamins occur in a variety of related forms known as vitamers. The vitamers of a given vitamin perform the functions of that vitamin and prevent symptoms of deficiency of that vitamin. Vitamins are those essential organic molecules that are not classified as amino acids or fatty acids. They commonly function as enzymatic cofactors, metabolic regulators or antioxidants. Humans require thirteen vitamins in their diet, most of which are actually groups of related molecules (e.g. vitamin E includes tocopherols and tocotrienols): vitamins A, C, D, E, K, thiamine (B1), riboflavin (B2), niacin (B3), pantothenic acid (B5), pyridoxine (B6), biotin (B7), folate (B9), and cobalamin (B12). The requirement for vitamin D is conditional, as people who get sufficient exposure to ultraviolet light, either from the sun or an artificial source, synthesize vitamin D in the skin.
Sources: en.wikipedia.org
=== Campaigning === Heseltine was not one to befriend and gossip with colleagues or backbenchers. He did not regard this as an insurmountable problem, as neither Heath nor Thatcher had been particularly "clubbable" either. From about the mid-1970s, he began a campaign of addressing local associations, sometimes using a helicopter to speak to several in one day. Heseltine had often had a reputation for being very cold and aloof with backbench MPs and party activists (Steven Norris said that after a visit to his constituency in 1983, local activists used a poster of Heseltine as a dartboard). However, in 1986–1990 he was a frequent visitor to local constituency dinners, although he usually attacked Labour rather than the Conservative government, and he used his wealth to afford a chauffeur and a helicopter. Heseltine campaigned in 100 constituencies in the 1987 election, attracting more publicity than many Cabinet ministers, although seldom mentioning Thatcher by name. During this period Heseltine enjoyed excellent relations with the media: among TV journalists he was in regular touch with Elinor Goodman of Channel 4 News (herself a former Haymarket employee), James Mates of ITN (son of his lieutenant Michael Mates) and John Cole, whilst among print journalists he was close to his old friend Anthony Howard (Deputy Editor of the Observer), Peter Jenkins, and especially close to Anthony Bevins of The Independent and the young Alastair Campbell of the Daily Mirror.
== Biography == Palmer was born in Port of Spain on the twin island Republic of Trinidad and Tobago. He is fluent in English and became a U.S. citizen. Palmer earned a chemical engineering degree at Howard University in Washington D.C in 1993 and his doctorate in chemical and biomolecular engineering at Johns Hopkins University in 1998. After completing postdoctoral work at Johns Hopkins University in 1999, Palmer joined the Chemistry Department faculty at Howard University. In 2001, he left for the University of Notre Dame to become assistant professor of chemical and biomolecular engineering. In 2006, after five years, he moved to Ohio State University to become associate professor of chemical and biomolecular engineering, and was promoted to full professor in 2012. He served as interim department chair in 2014–2015. In 2015, he was named Chair of the William G. Lowrie Department of Chemical and Biomolecular Engineering and served until 2019. In March 2020, the Ohio Board of Regents named Palmer, "Ohio Eminent Scholar," a statewide endowed chair. In August 2021, Palmer was appointed Associate Dean for research, charged with directing the College of Engineering's $138 million research enterprise.
== Limitations of model == AIDA, like other model-based approaches, is not sufficiently accurate to be used for individual patient simulation or glycemic prediction. Therefore, as the program makes clear, it is not intended for insulin therapy planning and can only be used for teaching, self-learning, demonstration, or research purposes. While the AIDA software can simulate a wide variety of insulin dosage and diet (nutrition) adjustments, it should be stressed that the purpose of AIDA is to create a learning environment for communicating and training intuitive thinking when dealing with such adjustments. In this respect AIDA appears most of use for recreating clinical situations in diabetes care, rather than trying to predict best outcome.
The Don Cossacks flag 3:4 was inaugurated during the Don Cossacks assembly in Novocherkassk, Don Republic, on 4 May 1918 under chiefing of Ataman Pyotr Krasnov. The flag has three colours: blue, yellow, and red. The flag is similar to that of the Ukrainian State, also established in 1918, which the Don Republic bordered to its west.
Sources: en.wikipedia.org
Conventional drying uses heat to evaporate liquid water, often at temperatures that can degrade sensitive materials. Lyophilization freezes the material first and then removes water by sublimation under vacuum. This avoids prolonged exposure to liquid water and high heat.
Lowering pressure reduces the boiling point of water and allows ice to sublimate at temperatures below freezing. Vacuum also limits convective heat transfer, so heat is usually supplied by shelves or radiation. The pressure must stay below the vapor pressure of ice at the product temperature.
The cycle typically includes freezing, primary drying, and secondary drying. Freezing solidifies water and sets the pore structure; primary drying removes bulk ice; secondary drying removes bound water. Some cycles add annealing or pre-freezing steps.
Conventional drying uses heat to evaporate water from a material, while lyophilization freezes the material and removes water by sublimation under vacuum. This avoids the liquid phase and reduces thermal damage to sensitive substances. The result is a porous cake that reconstitutes quickly.