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Physico-chemical Processes that Occur During Freezing

1. Introduction

Lyophilization respectively freeze-drying is an important and well-established process to improve the long-term stability of labile drugs, especially therapeutic proteins.[1] About 50% of the currently marketed biopharmaceuticals are lyophilized, representing the most common formulation strategy.[2] In the freeze-dried solid state chemical or physical degradation reactions are inhibited or sufficiently decelerated, resulting in an improved long-term stability.[3] Besides the advantage of better stability, lyophilized formulations also provide easy handling during shipping and storage. [1]

A traditional lyophilization cycle consists of three steps; freezing, primary drying and secondary drying.[1] During the freezing step, the liquid formulation is cooled until ice starts to nucleate, which is followed by ice growth, resulting in a separation of most of the water into ice crystals from a matrix of glassy and/or crystalline solutes.[4-5] During primary drying, the crystalline ice formed during freezing is removed by sublimation. Therefore, the chamber pressure is reduced well below the vapor pressure of ice and the shelf temperature is raised to supply the heat removed by ice sublimation.[6] At the completion of primary drying, the product can still contain approximately 15% to 20% of unfrozen water, which is desorbed during the secondary drying stage, usually at elevated temperature and low pressure, to finally achieve the desired low moisture content.[7]

In general, lyophilization is a very time- and energy-intensive drying process.[8]  Typically, freezing is over within a few hours while drying often requires days. Within the drying phase, secondary drying is short (~hours) compared to primary drying (~days).[1, 4] Therefore, lyophilization cycle development has typically focused on optimizing the primary drying step, i.e., shortening the primary drying time by adjusting the shelf temperature and/or chamber pressure without influencing product quality.[5, 9] Although, freezing is one of the most critical stages during lyophilization, the importance of the freezing process has rather been neglected in the past.[10]

The freezing step is of paramount importance. At first, freezing itself is the major desiccation step in lyophilization [6] as solvent water is removed from the liquid formulation in the form of a pure solid ice phase, leading to a dramatic concentration of the solutes.[11-12] Moreover, the kinetics of ice nucleation and crystal growth determine the physical state and morphology of the frozen cake and consequently the final properties of the freeze-dried product.[11-13] Ice morphology is directly correlated with the rate of sublimation in primary and secondary drying.[14] In addition, freezing is a critical step with regard to the biological activity and stability of the active pharmaceutical ingredients (API), especially pharmaceutical proteins.[1]

While simple in concept, the freezing process is presumably the most complex but also the most important step in the lyophilization process.[10] To meet this challenge, a thorough understanding of the physico-chemical processes, which occur during freezing, is required. Moreover, in order to optimize the freeze drying process and product quality, it is vital to control the freezing step, which is challenging because of the random nature of ice nucleation. However, several approaches have been developed to trigger ice nucleation during freezing.

The purpose of this review is to provide the reader with an awareness of the importance but also complexity of the physico-chemical processes that occur during freezing. In addition, currently available freezing techniques are summarized and an attempt is made to address the consequences of the freezing procedure on process performance and product quality. A special focus is set on the critical factors that influence protein stability. Understanding and controlling the freezing step in lyophilization will lead to optimized, more efficient lyophilization cycles and products with an improved stability.

2. Physico-chemical fundamentals of freezing

The freezing process first involves the cooling of the solution until ice nucleation occurs. Then ice crystals begin to grow at a certain rate, resulting in freeze concentration of the solution, a process that can result in both crystalline and amorphous solids, or in mixtures.[11] In general, freezing is defined as the process of ice crystallization from supercooled water.[15] The following section summarizes the physico-chemical fundamentals of freezing.

At first, the distinction between cooling rate and freezing rate should be emphasized. The cooling rate is defined as the rate at which a solution is cooled, whereas the freezing rate is referred to as the rate of postnucleation ice crystal growth, which is largely determined by the amount of supercooling prior to nucleation.[16-17] Thus, the freezing rate of a formulation is not necessarily related to its cooling rate.[18]

2.1 Freezing phenomena: supercooling, ice nucleation and ice crystal formation

In order to review the physico-chemical processes that occur during freezing of pure water, the relationship between time and temperature during freezing is displayed in figure 1. When pure water is cooled at atmospheric pressure, it does not freeze spontaneously at its equilibrium freezing point (0°C).[19] This retention of the liquid state below the equilibrium freezing point of the solution is termed as “supercooling”.[19] Supercooling (represented by line A) always occurs during freezing and is often in the range of 10 to 15°C or more.[12, 18] The degree of supercooling is defined as the difference between the equilibrium ice formation temperature and the actual temperature at which ice crystals first form and depends on the solution properties and process conditions.[1, 6, 11, 20] As discussed later, it is necessary to distinguish between “global supercooling”, in which the entire liquid volume exhibits a similar level of supercooling, and “local supercooling”, in which only a small volume of the liquid is supercooled.[14] Supercooling is a non-equilibrium, meta-stable state, which is similar to an activation energy necessary for the nucleation process.[21] Due to density fluctuations from Brownian motion in the supercooled liquid water, water molecules form clusters with relatively long-living hydrogen bonds [22] almost with the same molecular arrangement as in ice crystals.[11, 15] As this process is energetically unfavorable, these clusters break up rapidly.[15] The probability for these nuclei to grow in both number and size is more pronounced at lowered temperature.[15] Once the critical mass of nuclei is reached, ice crystallization occurs rapidly in the entire system (point B).[15, 21-22]  The limiting nucleation temperature of water appears to be at about -40°C, referred to as the “homogeneous nucleation temperature”, at which the pure water sample will contain at least one spontaneously formed active water nucleus, capable of initiating ice crystal growth.[11] However, in all pharmaceutical solutions and even in sterile-filtered water for injection, the nucleation observed is “heterogeneous nucleation”, meaning that ice-like clusters are formed via adsorption of layers of water on “foreign impurities”.[6, 11] Such “foreign impurities” may be the surface of the container, particulate contaminants present in the water, or even sites on large molecules such as proteins.[23-24] Primary nucleation is defined as the initial, heterogeneous ice nucleation event and it is rapidly followed by secondary nucleation, which moves with a front velocity on the order of mm/s through the solution. [14, 25] Often secondary nucleation is simply referred to as ice crystallization, and the front velocity is sometime referred to as the crystallization linear velocity.[14]

Once stable ice crystals are formed, ice crystal growth proceeds by the addition of molecules to the interface.[22] However, only a fraction of the freezable water freezes immediately, as the supercooled water can absorb only 15cal/g of the 79cal/g of heat given off by the exothermic ice formation.[12, 22] Therefore, once crystallization begins, the product temperature rises rapidly to near the equilibrium freezing point.[12, 26] After the initial ice network has formed (point C), additional heat is removed from the solution by further cooling and the remaining water freezes when the previously formed ice crystals grow.[12] The ice crystal growth is controlled by the latent heat release and the cooling rate, to which the sample is exposed to.[22] The freezing time is defined as the time from the completed ice nucleation to the removal of latent heat (from point C to point D). The temperature drops when the freezing of the sample is completed (point E).[21]

The number of ice nuclei formed, the rate of ice growth and thus the ice crystals` size depend on the degree of supercooling.[14, 20] The higher the degree of supercooling, the higher is the nucleation rate and the faster is the effective rate of freezing, resulting in a high number of small ice crystals. In contrast, at a low degree of supercooling, one observes a low number of large ice crystals.[14, 19] The rate of ice crystal growth can be expressed as a function of the degree of supercooling.[23]  For example for water for injection, showing a degree of supercooling of 10°C +/- 3°C, an ice crystal growth rate of about  5.2cm/s results.[23] In general, a slower cooling rate leads to a faster freezing rate and vice versa. Thus, in case of cooling rate versus freezing rate it has to be kept in mind “slow is fast and fast is slow”.

Nevertheless, one has to distinguish between the two basic freezing mechanisms. When global supercooling occurs, which is typically the case for shelf-ramped freezing, the entire liquid volume achieves a similar level of supercooling and solidification progresses through the already nucleated volume.[12, 14] In contrast, directional solidification occurs when a small volume is supercooled, which is the case for high cooling rates, e.g. with nitrogen immersion. Here, the nucleation and solidification front are in close proximity in space and time and move further into non-nucleated solution. In this case, a faster cooling rate will lead to a faster freezing rate.[12, 14]

Moreover, as ice nucleation is a stochastically event [6, 18], ice nucleation and in consequence ice crystal size distribution will differ from vial to vial resulting in a huge sample heterogeneity within one batch.[6, 14, 27] In addition, during freezing the growth of ice crystals within one vial can also be heterogeneous, influencing intra-vial uniformity.[5]

Up to now, 10 polymorphic forms of ice are described. However, at temperatures and pressures typical for lyophilization, the stable crystal structure of ice is limited to the hexagonal type, in which each oxygen atom is tetrahedrally surrounded by four other oxygen atoms.[23] The fact that the ice crystal morphology is a unique function of the nucleation temperature was first reported by Tammann in 1925.[28] He found that frozen samples appeared dendritic at low supercoolings and like “crystal filaments” at high supercooling. In general, three different types of growth of ice crystals around nuclei can be observed in solution[15]: i) if the water molecules are given sufficient time, they arrange themselves regularly into hexagonal crystals, called dendrites; ii) if the water molecules are incorporated randomly into the crystal at a fast rate, “irregular dendrites” or axial columns that originate from the center of crystallization are formed; iii) at higher cooling rates, many ice spears originate from the center of crystallization without side branches, referred to as spherulites. However, the ice morphology depends not only on the degree of supercooling but also on the freezing mechanism. It is reported that “global solidification” creates spherulitic ice crystals, whereas “directional solidification” results in directional lamellar morphologies with connected pores.[12, 14] While some solutes will have almost no effect on ice structure, other solutes can affect not only the ice structure but also its physical properties.[19] Especially at high concentrations, the presence of solutes will result in a depression of the freezing point of the solution based on Raoults`s Law and in a faster ice nucleation because of the promotion of heterogeneous nucleation, leading to a enormously lowered degree of supercooling.[21]

2.2 Crystallization and vitrification of solutes

The hexagonal structure of ice is of paramount importance in lyophilization of pharmaceutical formulations, because most solutes cannot fit in the dense structure of the hexagonal ice, when ice forms.[23] Consequently, the concentration of the solute constituents of the formulation is increased in the interstitial region between the growing ice crystals, which is referred to as “cryoconcentration”.[11-12] If this separation would not take place, a solid solution would be formed, with a greatly reduced vapor pressure and the formulation cannot be lyophilized.[23] The total solute concentration increases rapidly and is only a function of the temperature and independent of the initial concentration.[4] For example, for an isotonic saline solution a 20-fold concentration increase is reported when cooled to -10°C and all other components in a mixture will show similar concentration increases.[4] Upon further cooling the solution will increase to a critical concentration, above which the concentrated solution will either undergo eutectic freezing or vitrification.[7]

A simple behavior is crystallization of solutes from cryoconcentrated solution to form an eutectic mixture.[19] For example, mannitol, glycine, sodium chloride and phosphate buffers are known to crystallize upon freezing, if present as the major component.[12] When such a solution is cooled, pure ice crystals will form first. Two phases are present, ice and freeze-concentrated solution. The composition is determined via the equilibrium freezing curve of water in the presence of the solute (figure 2). The system will then follow the specific equilibrium freezing curve, as the solute content increases because more pure water is removed via ice formation. At a certain temperature, the eutectic melting temperature (Teu), and at a certain solute concentration (Ceu), the freezing curve will meet the solubility curve. Here, the freeze concentrate is saturated and eutectic freezing, which means solute crystallization, will occur.[7, 19] Only below Teu, which is defined as the lowest temperature at which the solute remains a liquid the system is completely solidified.[19] The Teu and Ceu are independent of the initial concentration of the solution.[7] In general, the lower the solubility of a given solute in water, the higher is the Teu.[19] For multicomponent systems, a general rule is that the crystallization of any component is influenced, i.e. retarded, by other components.[11] In practice, analogous to the supercooling of water, only a few solutes will spontaneously crystallize at Teu.[11] Such delayed crystallization of solutes from a freezing solution is termed supersaturation and can lead to an even more extreme freeze concentration.[11] Moreover, supersaturation can inhibit complete crystallization leading to a meta-stable glass formation, e.g. of mannitol.[12, 23] In addition, it is also possible that crystalline states exist in a mixture of different polymorphs or as hydrates.[11] For example, mannitol can exist in the form of several polymorphs (a, b and d) und under certain processing conditions, it can crystallize as a monohydrate.[11]

The phase behavior is totally different for polyhydroxy compounds like sucrose, which do not crystallize at all from a freezing solution in real time.[11] The fact that sucrose does not crystallize during freeze-concentration is an indication of its extremely complex crystal structure.[11] The interactions between sugar -OH groups and those between sugar -OH groups and water molecules are closely similar in energy and configuration, resulting in very low nucleation probabilities.[11] In this case, water continues to freeze beyond the eutectic melting temperature and the solution becomes increasingly supersaturated and viscous.[11] The increasing viscosity slows down ice crystallization, until at some characteristic temperature no further freezing occurs.[11] This is called glassification or vitrification.[18]  The temperature at which the maximal freeze-concentration (Cg`) occurs is referred to as the glass transition temperature Tg`.[11, 29] This point is at the intersection of the freezing point depression curve and the glass transition or isoviscosity curve, described in the “supplemented phase diagram” [30] or “state diagram” (figure 2).[11] Tg´ is the point on the glass transition curve, representing a reversible change between viscous, rubber-like liquid and rigid, glass system.[19] In the region of the glass transition, the viscosity of the freeze concentrate changes about four orders of magnitude over a temperature range of a few degrees.[19] Tg` depends on the composition of the solution, but is independent of the initial concentration.[4, 11, 27]  For example, for the maximally freeze concentration of sucrose a concentration of 72-73% is reported.[31] In addition to Tg` the collapse temperature (Tc) of a product is used to define more precisely the temperature at which a structural loss of the product will occur. In general Tc is several degrees higher than Tg`, as the high viscosity of the sample close to Tg` will prevent .[10] The glassy state is a solid solution of concentrated solutes and unfrozen, amorphous water. It is thermodynamically unstable with respect to the crystal form, but the viscosity is high enough, in the order of 1014 Pa*s, that any motion is in the order of mm/year.[4, 11, 29]

The important difference between eutectic crystallization and vitrification is that for crystalline material, the interstitial between the ice crystal matrix consists of an intimate mixture of small crystals of ice and solute, whereas for amorphous solutes, the interstitial region consists of solid solution and unfrozen, amorphous water.[19, 23] Thus, for crystalline material nearly all water is frozen and can easily be removed during primary drying without requiring secondary drying.[19] However, for amorphous solutes, about 20% of unfrozen water is associated in the solid solution, which must be removed by a diffusion process during secondary drying.[19] Moreover, the Teu for crystalline material or the Tg` respectively Tc for amorphous material define the maximal allowable product temperature during primary drying.[19] Eutectic melting temperatures are relatively high compared to glass transition temperatures, allowing a higher product temperature during primary drying, which results in more efficient drying processes.[19] If the product temperature exceeds this critical temperature crystalline melting or amorphous collapse will occur, resulting in a loss of structure in the freeze-dried product, which is termed “cake collapse”.[11, 19]

2.3 Phase separation and other types of freezing behavior

A characteristic property of multicomponent aqueous solutions, especially when at least one component is a polymer, is the occurrence of a liquid-liquid phase separation during freezing into two liquid equilibrium phases, which are enriched in one component.[11, 19] This phase separation behavior has been reported for aqueous solutions of polymers such as PEG/dextran or PVP/dextran but is also reported for proteins and excipients.[32-33] When a critical concentration of the solutes is reached, the enthalpically unfavorable interactions between the solutes exceed the favorable entropy of a solution with complete miscibility.[34] Another proposed explanation is that solutes have different effects on the structure of water, leading to phase separation.[35]

Besides the separation into two amorphous phases, two other types of phase separation are stated in literature; crystallization of amorphous solids and amorphization from crystalline solids.[18] Crystallization of amorphous solids often occurs when metastable glasses are formed during freezing. In this case, e.g. upon extremely fast cooling, a compound that normally would crystallize during slower freezing is entrapped as an amorphous, metastable glass in the freeze-concentrate.[12, 23] However, with subsequent heating above Tg`, it will undergo crystallization, which is the basis for annealing during freeze-drying (see 3.3).[19] Without annealing, the metastable glass can crystallize spontaneously out of the amorphous phase during drying or storage.[18] Amorphization from crystalline solids, that can be buffer components or stabilizers, predominantly occurs during the drying step and not during the freezing step.[18, 36]

Additionally, lyotropic liquid crystals, which have the degree of order between amorphous and crystalline, are reported to form as a result of freeze-concentration. However, their influence on critical quality attributes of the lyophilized product are not clarified.[19] Moreover, clathrates, also termed gas hydrates, are known to form, especially in the presence of non-aqueous co-solvents, when the solute alters the structure of the water.[23]

3. Modifications of the freezing step

As aforementioned, the ice nucleation temperature defines the size, number and morphology of the ice crystals formed during freezing. Therefore, the statistical nature of ice nucleation poses a major challenge for process control during lyophilization. This highlights the importance of a controlled, reproducible and homogeneous freezing process. Several methods have been developed in order to control and optimize the freezing step. Some of them only intend to influence ice nucleation by modifying the cooling rate. Others just statistically increase the mean nucleation temperature, while a few allow a true control of the nucleation at the desired nucleation temperature.

3.1 Shelf-ramped freezing

Shelf-ramped freezing is the most often employed, conventional freezing condition in lyophilization.[37] Here, at first, the filled vials are placed on the shelves of the lyophilizer and the shelf temperature is then decreased linearly (0.1°C/min up to 5°C/min, depending on the capacity of the lyophilizer) with time.[37-38] As both water and ice have low thermal conductivities and large heat capacities and as the thermal conductivity between vials and shelf is limited, the shelf-ramped cooling rate is by nature slow.[11] In order to ensure the complete solidification of the samples, the samples must be cooled below Tg` for amorphous material respectively below Teu for crystalline material. Traditionally, many lyophilization cycles use a final shelf temperature of -50°C or lower, as this was the maximal cooling temperature of the freeze-drier.[7] Nowadays, it is suggested to use a final shelf temperature of -40°C if the Tg` or Teu is higher than -38°C or to use a temperature of 2°C less than Tg` and Teu.[1] Moreover, complete solidification requires significant time.[11] In general, the time for complete solidification depends on the fill volume; the larger the fill volume the more time is required for complete solidification.[11] Tang et al.[1]  suggest that the final shelf temperature should be held for 1 h for samples with a fill depth of less than or equal to 1 cm or 2 h for samples with a fill depth of greater than 1 cm. Moreover, fill depth of greater than 2 cm should be avoided, but if required, the holding time should be increased proportionately.

In order to obtain a more homogeneous freezing, often the vials are equilibrated for about 15 to 30 min at a lowered shelf temperature (5°C – 10°C) before the shelf temperature is linearly decreased.[1] Here, either the vials are directly loaded on the cooled shelves or the vials are loaded at ambient temperature and the shelf temperature is decreased to the hold temperature. [1, 5, 9] Another modification of the shelf-ramped freezing is the two-step freezing, where a “supercooling holding” is applied.(7) Here, the shelf temperature is decreased from room temperature or from a preset lowered shelf temperature to about -5 to -10°C for 30 to 60min hold. This leads to a more homogenous supercooling state across the total fill volume.[1, 5] When the shelf temperature is then further decreased, relatively homogeneous ice formation is observed.[5]

In general, shelf-ramped frozen samples show a high degree of supercooling but when the nucleation temperature is reached, ice crystal growth proceeds extremely fast, resulting in many small ice crystals.[9, 39] However, the ice nucleation cannot be directly controlled when shelf-ramped freezing is applied and is therefore quite random.[4] Thus, one drawback of shelf-ramped freezing is that different vials may become subject to different degrees of supercooling, typically about +/- 3°C about the mean.[4] This results in a great variability in product quality and process performance.[4] Moreover, with the shelf-ramped freezing method it is not practical to manipulate the ice nucleation temperature as the cooling rates are limited inside the lyophilizer and the degree of supercooling might not change within such a small range.[1, 14]

3.2 Pre-cooled shelf method

When applying the pre-cooled shelf method, the vials are placed on the lyophilizer shelf which is already cooled to the desired final shelf temperature, e.g. -40°C or -45°C.[1, 13-14] It is reported that the placement of samples on a pre-cooled shelf results in higher nucleation temperatures (-9,5°C) compared to the conventional shelf-ramped freezing (-13.4°C).[14] Moreover, with this lowered degree of supercooling and more limited time for thermal equilibration throughout the fill volume, the freezing rate after ice nucleation is actually slower compared to shelf-ramped freezing.[40]  In addition, a large heterogeneity in supercooling between vials is observed for this method.[14] A distinct influence of the loading shelf temperature on the nucleation temperature is described in literature.[13-14] Searles et al.[14] found that the nucleation temperatures for samples placed on a shelf at -44°C were several degrees higher than for samples placed on a -40°C shelf. Thus, when using this method the shelf temperature should be chosen with care.

3.3 Annealing

Annealing is defined as a hold step at a temperature above the glass transition temperature.[12] In general, annealing is performed to allow for complete crystallization of crystalline compounds and to improve inter-vial heterogeneity and drying rates.[1, 19] Tang et al.[1] proposed the following annealing protocol: when the final shelf temperature is reached after the freezing step, the product temperature is increased to 10 to 20°C above Tg` but well below Teu and held for several hours. Afterwards the shelf temperature is decreased to and held at the final shelf temperature. Annealing has a rigorous effect on the ice crystal size distribution [17, 41] and can delete the interdependence between the ice nucleation temperature and ice crystal size and morphology. If the sample temperature exceeds Tg`, the system pursues the equilibrium freezing curve and some of the ice melts.[12, 41] The raised water content and the increased temperature enhance the mobility of the amorphous phase and all species in that phase.[12] This increased mobility of the amorphous phase enables the relaxation into physical states of lower free energy.[12] According to the Kelvin equation ice crystals with smaller radii of curvature will melt preferentially due to their higher free energy compared to larger ice crystals.[12, 37, 41] Ostwald ripening (recrystallization), which results in the growth of dispersed crystals larger than a critical size at the expense of smaller ones, is a consequence of these chemical potential driving forces.[12, 41] Upon refreezing of the annealed samples small ice crystals do not reform as the large ice crystals present serve as nucleation sites for addition crystallization.[41] The mean ice crystal radius rises with time1/3 during annealing.[37, 41] A consequence of that time dependency is that the inter-vial heterogeneity in ice crystal size distribution is reduced with increasing annealing time, as vials comprising smaller ice crystals “catch up” with the vials that started annealing containing larger ice crystals.[12, 17, 37, 41] Searles et al.[41] found that due to annealing multiple sheets of lamellar ice crystals with a high surface area merged to form pseudo-cylindrical shapes with a lower interfacial area. In addition to the increase in ice crystal size, they observed that annealing opened up holes on the surface of the lyophilized cake. The hole formation is explained by the diffusion of water from melted ice crystals through the frozen matrix at the increased annealing temperature. Moreover, in the case of meta-stable glass formation of crystalline compounds, annealing facilitates complete crystallization.[42] Above Tg` the meta-stable glass is re-liquefied and crystallization occurs when enough time is provided. Furthermore, annealing can promote the completion of freeze concentration (devitrification) as it allows amorphous water to crystallize.[41] This is of importance when samples were frozen too fast and water capable of crystallization was entrapped as amorphous water in the glassy matrix. In addition, the phenomenon of annealing also becomes relevant when samples are optimal frozen but are then kept at suboptimal conditions in the lyophilizer or in a freezer before lyophilization is performed.[11]

3.4 Quench freezing

During quench freezing, also referred to as vial immersion, the vials are immersed into either liquid nitrogen or liquid propane (ca. -200°C) or a dry ice/ acetone or dry ice/ ethanol bath (ca. -80°C) long enough for complete solidification and then placed on a pre-cooled shelf.[9, 16] In this case the heat-transfer media is in contact with both the vial bottom and the vial wall [10], leading to a ice crystal formation that starts at the vial wall and bottom. This freezing method results in a lowered degree of supercooling but also a high freezing rate as the sample temperature is decreased very fast, resulting in small ice crystals. Liquid nitrogen immersion has been described to induce less supercooling than slower methods [9, 37, 39] , but more precise this faster cooling method induces supercooling only in a small sample volume before nucleation starts and freezes by directional solidification.[12, 14]  While it is reported that external quench freezing might be advantageous for some applications [39], this uncontrolled freezing method promotes heterogeneous ice crystal formation and is not applicable in large scale manufacturing.[7]

3.5 Directional freezing

In order to generate straight, vertical ice crystallization, directional respectively vertical freezing can be performed. Here, ice nucleation is induced at the bottom of the vial by contact with dry ice and slow freezing on a pre-cooled shelf is followed.[9] In this case, the ice propagation is vertically and lamellar ice crystals are formed.[9]

A similar approach, called unidirectional solidification, was described by Schoof et al. [43]. Here each sample was solidified in a gradient freezing stage, based on the Power-Down principle, with a temperature gradient between the upper and the lower cooling stage of 50 K/cm, resulting in homogenous ice-crystal morphology.

3.6 Ice-fog technique

In 1990, Rowe [44] described an ice-fog technique for the controlled ice nucleation during freezing. After the vials are cooled on the lyophilizer shelf to the desired nucleation temperature, a flow of cold nitrogen is led into the chamber. The high humidity of the chamber generates an ice fog, a vapor suspension of small ice particles. The ice fog penetrates into the vials, where it initiates ice nucleation at the solutio

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