The ice nucleation temperature determines the primary drying rate of lyophilization for samples frozen on a temperature‐controlled shelf

The Ice Nucleation Temperature Determines the Primary Drying Rate of Lyophilization for Samples Frozen on a Temperature-Controlled Shelf JAMES A. SEARLES,1,2 JOHN F. CARPENTER,3 THEODORE W. RANDOLPH1 1

Center for Pharmaceutical Biotechnology and Department of Chemical Engineering, University of Colorado, Boulder, Colorado 80309

2

Vaccine Technology and Engineering, Merck & Company, Inc., West Point, Pennsylvania 19486

3

Center for Pharmaceutical Biotechnology and Department of Pharmaceutical Sciences, School of Pharmacy, University of Colorado Health Sciences Center, Denver, Colorado 80262 Received 16 May 2000; revised 16 December 2000; accepted 19 December 2000

ABSTRACT: The objective of this study was to determine the in¯uence of ice nucleation temperature on the primary drying rate during lyophilization for samples in vials that were frozen on a lyophilizer shelf. Aqueous solutions of 10% (w/v) hydroxyethyl starch were frozen in vials with externally mounted thermocouples and then partially lyophilized to determine the primary drying rate. Low- and high-particulate-containing samples, ice-nucleating additives silver iodide and Pseudomonas syringae, and other methods were used to obtain a wide range of nucleation temperatures. In cases where the supercooling exceeded 58C, freezing took place in the following three steps: (1) primary nucleation, (2) secondary nucleation encompassing the entire liquid volume, and (3) ®nal solidi®cation. The primary drying rate was dependent on the ice nucleation temperature, which is stochastic in nature but is affected by particulate content and the presence of ice nucleators. Sample cooling rates of 0.05 to 18C/min had no effect on nucleation temperatures and drying rate. We found that the ice nucleation temperature is the primary determinant of the primary drying rate. However, the nucleation temperature is not under direct control, and its stochastic nature and sensitivity to dif®cult-to-control parameters result in drying rate heterogeneity. Nucleation temperature heterogeneity may also result in variation in other morphology-related parameters such as surface area and secondary drying rate. Overall, these results document that factors such as particulate content and vial condition, which in¯uence ice nucleation temperature, must be carefully controlled to avoid, for example, lot-to-lot variability during cGMP production. In addition, if these factors are not controlled and/or are inadvertently changed during process development and scaleup, a lyophilization cycle that was successful on the research scale may fail during large-scale production. ß 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:860±871, 2001 Keywords: freezing; nucleation; secondary nucleation; ice; lyophilization; freeze-drying; silver iodide (AgI); Snomax; Pseudomonas syringae; hydroxyethyl starch (HES); particulate; process development; scaleup

INTRODUCTION

Correspondence to: T.W. Randolph (Telephone: 303-4924776; Fax: 303-492-4341; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 90, 860±871 (2001) ß 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association

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The freezing step is of paramount importance in freeze-drying. It dictates ice crystal morphology and size distribution, which in turn in¯uence several critical parameters. For example, the method of freezing has been found to in¯uence protein aggregation,1±4 primary drying rate,5±8

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ICE NUCLEATION TEMPERATURE DETERMINES LYOPHILIZATION DRYING RATE

secondary drying rate,9 extent of product crystallinity,10 and surface area11±13 of the lyophilized product. Prior to discussing earlier work on the effect of freezing conditions and solutes on ice crystals and lyophilization cycle performance, we ®rst need to de®ne the nomenclature used in the current paper. Primary nucleation is the initial (heterogeneous) ice nucleation event. Secondary nucleation follows primary nucleation, and moves with a velocity on the order of mm/s to encompass some portion of the liquid volume.14±16 This event stops when the liquid temperature approaches the equilibrium freezing temperature. Often secondary nucleation is referred to simply as crystallization, and the front velocity is sometimes referred to as the crystallization linear velocity.14±16 We will refer to it as the secondary nucleation front velocity. Subsequent to secondary nucleation, solidi®cation is completed relatively slowly as the heat of crystallization is transferred from the solidi®cation interface through the already-solidi®ed layer and the vial bottom to the shelf. We will refer to two basic types of freezing mechanisms. In the ®rst, global supercooling, the entire liquid volume achieves a similar level of supercooling, and the secondary nucleation zone encompasses the entire liquid volume. Solidi®cation then progresses through the alreadynucleated volume. In contrast, directional solidi®cation occurs when a small portion of the volume is supercooled to the point of primary and secondary nucleation. The nucleation and solidi®cation fronts are in close proximity in space and time, with the front moving into non-nucleated liquid. Tammann reported in 1925 that the ice crystal morphology is a unique function of the nucleation temperature.17 He observed that the velocity of the secondary nucleation front ®rst increased with the extent of supercooling, then decreased at high supercoolings due to viscosity effects. The ice crystal morphology was not a unique function of the nucleation front velocity, as evidenced by the similar velocities observed at high and low supercoolings. However, the morphologies were distinct, with samples frozen at low supercoolings appearing dendritic and those frozen at high supercoolings being ``crystal ®laments''.17 Therefore, over a wide range of supercoolings, a given secondary nucleation front velocity could result in two distinct morphologies: one at high supercooling, and one at low supercooling.

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Luyet and Rapatz found a variety of ice crystal morphologies in the freezing of various aqueous solutions, including hexagonal, dendritic, and dispersed spherulitic morphologies.18,19 The morphology was dependent on the freezing temperature, solute, and concentration. For example, in glycerol solutions, the ice morphology shifted from hexagonal to ``irregular'' and then to spherulitic with increasing supercooling. Kochs et al. studied the effects of the directional solidi®cation process on ice morphology for samples of 10% hydroxyethyl starch (HES) in a freeze-drying microscope.20 They found that the primary dendritic spacing was proportional to the product vÿ1/4
Gÿ1/2, where n is the interface velocity, and G is the temperature gradient at the interface. They also established a linear relationship between the lamellar spacing and the primary drying rate. In a companion paper, they examined effect of freezing conditions on the primary drying rate for 23-mL samples and found higher primary drying rates for samples that had been frozen with slower post-nucleation cooling rates during solidi®cation.21 It is also well established that ice crystal size is inversely correlated to the extent of supercooling.22 Both ice crystal morphology and size distribution exert considerable control over the diffusion and viscous ¯ow of water vapor from the ice interface to the top of the dried region within the cake.20 Consider a bundle of capillaries of different sizes, with an imposed concentration and/or pressure gradient and ¯ow limited to the lumen of the capillaries (not the intercapillary spaces). For Knudsen diffusion, the ¯ow per unit area will be proportional to / , where the brackets refer to an average over the pore size distribution. Viscous ¯ow probably operates in parallel with Knudsen diffusion given the presumed pressure gradient between the ice interface and the vial headspace. In this case, the ¯ow per unit area will be proportional to / .23 In both cases, but especially for viscous ¯ow, a decrease in the average pore radius will result in decreased vapor ¯ux per unit of crosssectional void area. In addition, the presence of dead-end and interconnected pores contributes to the tortuosity of the dried cake. Cakes with a better connected ice crystal morphology with more direct vapor ¯ow paths toward the top of the cake will have higher primary drying rates. Roy and Pikal established an early linkage between the ice nucleation temperature and the subsequent primary drying rate.24 They found JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 7, JULY 2001

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that sample vials with internally placed thermocouples nucleated at higher temperatures and completed primary drying sooner than samples without thermocouples. Common methods of sample freezing (listed in decreasing order of achievable cooling rate) include liquid-nitrogen immersion or spraying, placement on a pre-chilled freeze-dryer shelf, or a temperature ramp on a freeze-dryer shelf. The most common method of quantifying actual freezing rate is to measure the temperature at a representative location within the sample and use its average cooling rate post nucleation.24 By this method of measurement, the solidi®cation front velocity generally correlates with the cooling rate. However, as discussed in detail later, some fundamental distinctions must be made between the global supercooling and directional solidi®cation types of freezing. Freezing by immersion into liquid nitrogen has been shown to result in greater ice crystal surface areas than shelf-ramp freezing11±13 and slower primary drying. Hsu et al.12 studied various freezing rates for shelf-ramp freezing. They obtained lower cooling rates by using greater vial ®ll volumes and calculated the freezing rate as the post-nucleation cooling rate, as already noted. The nucleation temperatures correlated with the subsequent cooling rate in that supercooling to lower temperatures resulted in faster postnucleation cooling rates. They also found greater product surface areas with higher cooling rates. Pikal et al.25 found that formulations with lower surface areas exhibited slower secondary drying rates. In this study, we have examined the effect of nucleation temperature during shelf freezing on the freezing mechanism and primary drying rate. Further, we examined the effect of sample particulate content, vial scoring, and the addition of ice nucleating agents on nucleation temperatures and drying rates. We found both global

supercooling and directional solidi®cation can occur with shelf-ramp freezing, but that the latter only occurs with the aid of ice-nucleating agents.

MATERIALS AND METHODS In all of the experiments described here, aqueous solutions of HES (Viastarch1, Fresenius; Linz, Austria) were freeze-dried in a laboratory scale lyophilizer (Dura Stop, FTSjKinetics, Stone Ridge, NY). The HES mean molecular weight, water content, and NaCl content were 259,700 Da, 4.64%, 0.11%, respectively. After 0.22-mm ®ltration and vacuum degassing, 2 mL of 10% (w/v) HES solution were added to each 5-mL tubing vial (i.d. ˆ 1.8 cm; The West Company, Lionville, PA). Neither trays nor shelf borders were used during freeze-drying for any of the experiments. Table 1 summarizes the experimental groups for this study. Vials were either low particulate (groups A, D±F), scored (group B), or high particulate (group C). Low-particulate vials were removed from the sealed manufacturer's package within a laminar ¯ow hood. A metal scribe was used to scratch the bottom interior surface of lowparticulate vials for the scored group. Highparticulate vials were manually washed then rinsed three times with distilled, deionized, and 0.22±mm-®ltered water, then air-dried in the laboratory (outside of a laminar ¯ow hood). All stoppers were fully closed subsequent to ®lling and were not raised until after freezing was complete. Pseudomonas syringae and silver iodide (AgI) were used as ice nucleants. The P. syringae samples (group F) contained 0.001% (w/v) Snomax1 (Telemet, Inc.; Hunter, NY). Silver iodide (AgI) samples (group E) were seeded with 1 mg of ®ne AgI powder (Fisher Scienti®c; Pittsburgh, PA) added to the vial after ®lling. Most of the AgI remained ¯oating on the meniscus, whereas

Table 1. Summary of Experimental Groups and Conditions for the Individual Sample Freezing Study ID

Name

Vial

Ice Nucleant

Freezing Method

Number of Samples 35 22 21 22 24 17

A

Control

Low particulate

None

B

Scored

None

C D E F

High particulate Pre-Cooled Shelf AgI P. syringae

Low particulate, Scored High Particulate Low particulate Low particulate Low particulate

Shelf Ramp (various rates) Shelf Ramp

None None AgI P. syringae

Shelf Ramp Pre-Cooled Shelf Shelf Ramp Shelf Ramp

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ICE NUCLEATION TEMPERATURE DETERMINES LYOPHILIZATION DRYING RATE

P. syringae was suspended in solution, imparting a slightly cloudy appearance to the sample. Samples frozen on the freeze-dryer shelf with a constant shelf cooling rate (groups A±C, E±F) were ®rst equilibrated on a 08C shelf for 15 min, then the shelf temperature was ramped down to its minimum temperature of ÿ 458C. Samples in the control group (A) were frozen at various shelf ramp rates, resulting in pre-nucleation sample cooling rates of 0.05 to 18C/min. The pre-nucleation sample cooling rate was calculated as the average rate of sample temperature decrease for 20 min immediately preceding ice nucleation. The pre-cooled shelf group (B) was frozen by placing the samples on a freeze-dryer shelf that had been pre-cooled to between ÿ40 and ÿ448C. Samples were moved to a ÿ708C freezer once their temperature was below ÿ308C, which was considered suf®ciently low to avoid annealing effects because it is well below the glass transition temperature (Tg0 ) of the freeze-concentrated HES, which is ÿ158C.21 Sample temperatures were monitored during shelf freezing by adhering a thin 36-gauge thermocouple to each vial with a small piece of aluminum tape. The thermocouple was placed on the exterior side of the vial halfway between the liquid meniscus and the vial bottom. Thermocouples were used externally to avoid serving as ice nucleation sites.24 Thermagon Sil-less 431 thermal compound was used to provide good thermal contact between the thermocouple and the vial (Thermagon; Cleveland, OH). Vials did not contact each other during freezing. Experiments with vials instrumented with interior and exterior thermocouples veri®ed the accuracy of external thermocouples for determining the nucleation temperature. Sample temperatures were saved in a computer ®le at intervals of 5 to 20 s. To determine their primary drying rates, preweighed samples were partially dried at a pressure of 200 mmHg (mTorr) and shelf temperature of ÿ208C. The vials were stoppered after 5±6 h of primary drying, over which time interval 20±50% of the crystalline water had sublimed. The samples were re-weighed on removal from the freeze-dryer, and the primary drying rate was calculated using the weight lost during the partial drying. Previous experiments had shown that samples located on or near the edge of the sample array would dry faster than those on the interior due to heat transfer from the chamber walls of the freeze-dryer (data not shown). To ensure compar-

863

able heat transfer to all samples during primary drying, the sample array was surrounded by one layer of water-containing vials, then by a 2.5'' high multilayer thermal shield. The shield was constructed of 20 layers of 75-mm thick Mylar1 ®lm with a 0.1-mm thick re¯ective vapor-deposited aluminum layer on each side. Dacron1 netting was placed between the layers to prevent physical contact. One-quarter-inch squares of 3M1 966 adhesive transfer tape placed at 1-foot intervals adhered the layers together. The re¯ective ®lm and netting were kindly donated by Sheldahl (North®eld, MN), and the tape was donated by 3M (St. Paul, MN). Shelf spacing was set to allow a 14-inch gap between the top of the shield and the bottom of the shelf above for ef®cient water vapor ¯ow. Samples for morphological study of cakes were taken through primary drying at the aforementioned conditions, then secondary drying was completed at a pressure of 50 mTorr with a 0.028C/min shelf temperature ramp to 358C. HES forms strong cakes, which were broken cleanly using two pairs of tweezers and then sputtercoated with gold using a Polaron SEM Coating System (Watford, UK). The plugs were imaged with an ISI model SX-30 scanning electron microscope.

RESULTS Freezing Observations A typical freezing thermogram is shown in Figure 1, including the sample and the shelf temperatures (thin and thick traces, respectively). The sample cooled at a rate similar to that of the shelf, with the sample temperature remaining 7±88C above that of the shelf (area A of Figure 1). Point B is the onset of nucleation, de®ned as the nadir temperature just prior to the sharp increase to ÿ18C, and point C is the completion of nucleation and the onset of solidi®cation. Primary and secondary nucleation occurred in rapid succession, and the former was not observable either by eye or on the thermogram except as the starting point of secondary nucleation. As solidi®cation progressed to completion, the sample temperature gradually equilibrated with that of the shelf. During freezing of samples without nucleating agents (groups A±D), primary and secondary nucleation were apparent as the initiation and spread of a translucent region throughout the JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 7, JULY 2001

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bottom at ÿ1.2 to ÿ2.78C, and secondary nucleation only extended several millimeters into the solution. Samples containing P. syringae froze by directional solidi®cation because secondary nucleation was con®ned to the bottom of the vial, and for the bulk of the volume, the nucleation and ®nal solidi®cation interfaces were in close proximity in time and space. Nucleation Temperatures and Drying Rates

Figure 1. Sample (Ð) and shelf temperatures (Ð) during shelf freezing. A, B, and C on the sample temperature trace identify the pre-nucleation cooling rate, nucleation temperature, and completion of nucleation, respectively. The nucleation temperature of this sample is ÿ148C.

liquid volume. Nucleation of these groups occurred from ÿ8.0 to ÿ18.58C. The crystallization front moved from the point of nucleation (usually on the bottom of the vial) throughout the liquid volume at a velocity of several millimeters per second. This velocity increased with the extent of supercooling. Several investigators have observed similar nucleation velocities and temperature dependencies in aqueous solutions.14±16 It is conceivable that the initial nucleation front consisted of crystals that were small enough to be invisible, and that the visible front was the growth of these crystals to visible size. Samples seeded with AgI nucleated in the center of the meniscus (on which most of the AgI remained) at temperatures from ÿ5.0 to ÿ7.48C. The crystallization front sometimes contained needle-like structures that advanced several millimeters ahead of the interface. In samples seeded with P. syringae, primary nucleation occurred at many points at once on the vial

Figure 2 shows the nucleation temperatures for the control, high particulate vial, pre-cooled shelf, AgI, and P. syringae groups (A, C±F), and Table 2 contains the median nucleation temperatures for each group. Referring to the nucleation temperature histograms in Figure 2, samples in groups C and D nucleated over a wide range of temperatures, whereas the other groups were more homogeneous. High-particulate samples, which were exposed to the uncontrolled high particulate environment of the laboratory, caused nucleation at generally higher temperatures than their lowparticulate counterparts. The nucleation temperature distribution of those samples that were scored was not statistically different than that of the control group. Median nucleation temperatures for groups nucleated with AgI and P. syringae (E and F) were ÿ6.1 and ÿ1.88C, respectively. These values are consistent with previous applications to ice nucleation from the melt.26,27 Placement of samples on a pre-cooled shelf (group D) resulted in higher and much less consistent nucleation temperatures than the control group (A). Samples placed upon a shelf at ÿ448C nucleated over a wide range, including temperatures several degrees above those seen for the samples placed on a ÿ408C shelf (data not shown). This result indicates a great sensitivity of the nucleation temperature to the shelf temperature for precooled shelf freezing. The primary drying rate correlates strongly with the nucleation temperature. Figure 3 shows

Table 2. Median Nucleation Temperatures and Drying Rates ID A B C D E F

Name Control Scored High particulate Pre-Cooled Shelf AgI P. syringae

Symbol

Median Nucleation Temperature, 8C

Median drying Rate, mg hrÿ1

X } * O & ~

ÿ13.4 ÿ13.1 ÿ11.4 ÿ9.5 ÿ6.1 ÿ1.8

79 85 81 90 102 126

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ICE NUCLEATION TEMPERATURE DETERMINES LYOPHILIZATION DRYING RATE

Figure 2. Nucleation temperature histograms: (‡) control; (*) high-particulate vials; (*) pre-cooled shelf; (&) AgI; (~) P. syringae. The nucleation temperature is affected by the presence of particulate and known ice nucleators. Freezing on a pre-cooled shelf results in a wide range of nucleation temperatures.

this dependence as a plot of the drying rate versus nucleation temperature. The line is a linear regression of the data from groups A through E. There is a sharp in¯ection in drying rate at the highest nucleation temperatures for the samples containing P. syringae (group F), suggesting a different freezing mechanism and a relaxed dependence on the nucleation temperature. Control group samples (low-particulate vials, no ice nucleants) were frozen over a range of shelfcooling rates. Figure 4 shows both the primary drying rate and the nucleation temperatures

Figure 3. Primary drying rate as a function of nucleation temperature: (‡) control; (}) scored vials; (*) high-particulate vials; (*) pre-cooled shelf; (&) AgI; (~) P. syringae. The primary drying rate is 4% lower for each degree of additional supercooling.

865

Figure 4. Primary drying rate (*) and nucleation temperature (*) versus the pre-nucleation sample cooling rate. The effect of the pre-nucleation vial- (and shelf-) cooling rate is small compared with the overall impact of the nucleation temperature, as shown in Figure 3.

plotted as a function of the pre-nucleation sample temperature cooling rate. Cooling rates ranged from 0.05 to 18C/min, and did not have a signi®cant effect on the nucleation temperature or the primary drying rate. Morphology Panels A and B of Figure 5 show photomicrographs of the control group, which nucleated at the lowest temperatures. A spherulitic morphology is visible, in which the formation of spheroidal ice crystals concentrated the amorphous phase into a sponge-like matrix, with chambers on the order of 100 mm in diameter. The wall between adjacent chambers often contains a hole, which would allow water vapor ¯ow during drying. Addition of AgI resulted in an interesting mixed morphology. These samples, which nucleated at the top of the sample, had mixed orientation packets of lamellar structures that are interrupted by spheroids (5C). The lower left portion of the panel reveals regular spheroidal structure similar to the control group (5A and B). In the micrograph of the bottom of the sample (panel 5D), one can see mixed spheroidal and lamellar structures. Addition of P. syringae almost eliminated supercooling to allow directional solidi®cation JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 7, JULY 2001

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Figure 5. SEM micrographs of dried plugs for the control (A, top of cake; B, bottom of cake), AgI (C, top of cake; D, bottom of cake), and P. syringae (E, top of cake; F, bottom of cake). Cake cross-sections at 908 to the vial axis. The scale bar in panel A applies to all panels.

with completely lamellar morphology (panels 5E and F). The sample was divided into regions, within each of which the lamellar structure orientation was consistent and frequently such that the lamellae were perpendicular to the closest vial surface. At the top of the sample (panel 5E), the end plate of a packet is exposed, revealing the distinct lamellar morphology at the packet boundary in which the lamellae formed in JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 7, JULY 2001

the direction of heat ¯ow. In panel 5F and the lower right of panel 5E, the lamellae themselves are visible, with spacing on the order of tens of micrometers.

DISCUSSION Groups A±E (Table 1) nucleated and froze via the global supercooling mechanism, and the P. syr-

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867

solidi®cation and the primary drying rate for the P. syringae group (F), probably due to the narrow range of cooling rates (data not shown). Extent of Crystallization at Nucleation

Figure 6. Predicted fraction of bulk freezable water solidi®ed (Ð) and predicted depth of completelysolidi®ed layer along the vial interior ( - - ) for the global supercooling mechanism of freezing. Although only a small portion of freezable water crystallizes during primary and secondary nucleation, the number of nuclei formed during these events determines the ®nal morphology.

ingae group (F) froze by directional solidi®cation. The nucleation temperature cutoff between the two mechanisms was between ÿ2.7 and ÿ5.18C, which were the lowest and highest nucleation temperatures for the P. syringae (F)- and AgI (E)containing samples, respectively. Application of this cutoff is limited to the particular vials, ®ll volume, concentration, solute(s), and range of shelf-cooling rates used. Figure 3 reveals a clear direct dependence of the drying rate on the nucleation temperature. This dependence is most clearly elucidated, however, by the use of nucleation agents to achieve high nucleation temperatures. The correlation between drying rate and nucleation temperature is especially strong when groups A±E are considered. Because it was frozen via directional solidi®cation, the P. syringae-containing group resulted in a completely lamellar morphology. The wide distribution of drying rates resulting from a very narrow range of nucleation temperatures in this sample group leads us to conclude that phenomena other than the nucleation temperature are in¯uencing the drying rate. The effect of freezing parameters on the freeze-drying rate in directionally solidi®ed solute systems has already been well characterized20,21 and is a function of the cooling rate. Our results show a weak correlation between the cooling rate during

For supercooling of 58C and greater, secondary nucleation was observed to encompass the entire sample volume. However, it can easily be shown that the samples were not completely frozen at this point. Figure 6 shows the predicted mass fraction of freezable water that crystallizes during nucleation (x). It was calculated using an adiabatic enthalpy balance around the vial contents during nucleation, in which the extent of supercooling is used to absorb the heat of crystallization up to the equilibrium freezing point: xˆ

mwn …Tf ÿ Tn †CPw ˆ mwf … 1 ÿ C=C0g †
Hm

…1†

where mwn is the mass of water crystallized at nucleation, mwf is the mass of freezable water, Tf is the equilibrium freezing point of water in the presence of the solute at weight fraction C, Tn is the temperature at which nucleation occurs, CPw is the heat capacity of water, C is the mass fraction of solute in the solution (mass of solute/ total mass), Cg0 is the mass fraction of solute in the maximally freeze concentrated amorphous phase (a characteristic of the solvent/solute system), and DHm is the heat of fusion for water. Tf was set to 08C because freezing point depression is negligible. The estimate of x is an average over the entire volume and it assumes complete freezeconcentration. It does not account for decreasing Tf as the solution is concentrated, because in the range of nucleation temperatures observed, the concentration C is estimated to increase only from 0.09 to 0.12. The value of Cg0 used was 0.696,28 resulting in 87% of the water available for crystallization (in agreement with Korber et al.29). As seen in Figure 6, over the ÿ5 to ÿ198C range of nucleation temperatures observed in this study, only 7± 27% of the freezable water in the bulk of the sample could have crystallized. The thickness of the solidi®ed layer along the glass was estimated and is shown in Figure 6 as the dashed trace. It was calculated by considering the heat capacity of the vial in contact with the liquid, in which the available latent heat of the vial is used to completely solidify a layer of the sample adjacent to the vial. The thickness increases faster at higher supercoolings because greater JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 7, JULY 2001

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Figure 7. Dependence of the cooling rate during solidi®cation on the nucleation temperature: (‡) control; (}) scored vials; (&) AgI; (~) P. syringae. The cooling rate during solidi®cation (the post-nucleation cooling rate) depends on the nucleation temperature, and it is the nucleation temperature, not the cooling rate during solidi®cation, that determines the morphology and therefore the drying rate.

supercooling also increases the extent of crystallization in the bulk liquid, increasing the penetration depth of the vial-driven solidi®cation. In the range of nucleation temperatures observed in this study, the predicted penetration distance is < 2% of the vial inner radius. Ice Morphology is Controlled by the Nucleation Temperature for Global Supercooling To determine the freezing parameters that control the ice and concentrated solute phase morphologies, one must ®rst identify the freezing mechanism. In this paper we have de®ned directional solidi®cation and global supercooling mechanisms, and we suggest that just as they result in distinct morphologies (lamellar versus spherulitic, respectively), the factors controlling those morphologies differ between the two mechanisms. In directional solidi®cation, the interface velocity is a major determinant of the characteristic dendrite spacing.20,30,31 In a 1993 paper, Kochs et al.21 applied the cooling rate during solidi®cation as a surrogate measurement for the solidi®cation interface velocity. They stated that their 23 mL samples froze by directional solidi®cation, and they found that higher cooling rates resulted in slower primary drying.21 Like Kochs et al.,21 we have used the primary drying rate during lyophilization as an indicator of ice crystal morphology and size. However, we observed that in the absence of ice nucleators, our 2-mL samples freeze by global supercooling and it JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 7, JULY 2001

appears that the cooling rate during solidi®cation is not the parameter controlling the morphology. As already discussed, the global supercooling freezing mechanism consists of (1) primary heterogeneous nucleation, (2) secondary nucleation throughout the liquid volume, and (3) ®nal solidi®cation. Which of these three steps determines the morphology of the ice and concentrated amorphous phases? The initial ice crystal size distribution and number density are functions of the temperature at which nucleation occurs, as well as the nature and concentration the solute.32 We suggest that the initial crystal number and morphology are preserved through the solidi®cation process because solidi®cation does not cause the nucleation of new crystals; rather the existing crystals grow. Consider the following: (a) the present system requires extensive supercooling for nucleation, (b) ®nal solidi®cation progresses through an already nucleated volume, and (c) any local supercooling is removed from the solute phase by the growth of neighboring crystals. The number density and size distribution of ice crystals formed at primary and secondary nucleation will therefore dominate the morphology and size distribution of the crystals through solidi®cation. Therefore, we do not expect the velocity of the ®nal solidi®cation interface or the cooling rate during solidi®cation to be the controlling factors; rather, they are also determined by the nucleation temperature. When analyzed in terms of the cooling rate during solidi®cation, our data does show the tendency that slower post-nucleation sample cooling rates result in higher primary drying rates (data not shown), but this is a result of the linkage between nucleation temperature and the postnucleation drying rate, as seen in Figure 7. While standing on a shelf that is cooled at a constant rate, samples, which freeze later and therefore at lower nucleation temperatures, will have a greater temperature driving force for ®nal solidi®cation. Consider a sample that nucleates at ÿ108C when the shelf is at ÿ158C. On nucleation, the sample temperature rises to just below 08C. There is a 158C driving force between the sample and the shelf for ®nal solidi®cation. However, a sample that nucleates at a temperature of ÿ208C when the shelf is at ÿ258C, solidi®cation will be driven by a 258C temperature difference between the sample and the shelf. However, the crystal size distribution and morphology can change during the post-nuclea-

ICE NUCLEATION TEMPERATURE DETERMINES LYOPHILIZATION DRYING RATE

tion, pre-solidi®cation interval. After secondary nucleation, the ice/solution slurry (sometimes referred to as mushy zone) exists at temperatures very close to the equilibrium freezing point of the ice. In this state, Ostwald ripening will cause large crystals to grow at the expense of small ones,33 and high surface area dendritic structures and plates will break down into cylinders and spheroids with less surface area.34,35 Consequently, whereas nucleation establishes the basic crystal morphology and size distribution, the ice crystal structure may evolve into more thermodynamically stable structures before solidi®cation.34 However, the extent of post-nucleation ripening is still determined by the nucleation temperature because samples that nucleate at higher temperatures will have a slower solidi®cation front velocity. So although post-nucleation annealing probably also plays a role, its in¯uence is uniquely determined by the nucleation temperature for samples frozen in vials on a temperature-ramped shelf. We therefore propose that the nucleation temperature is the primary determinant of ice crystal structure and surface area. Given the manner in which freezing on lyophilizer shelves is conducted (either with cooling the shelves after samples are place on them or using pre-cooled shelf freezing resulting in global supercooling), the velocities of the secondary nucleation and solidi®cation interfaces and the cooling rate during solidi®cation are all determined by the nucleation temperature. Critical Cooling Rate We suggest that for a given formulation, vial geometry, and volume of ®ll, there is a critical cooling rate below which samples freeze by global supercooling and above which they freeze by directional solidi®cation. Large thermal gradients will promote directional solidi®cation because secondary nucleation will encompass only those areas of the liquid volume with suf®cient supercooling. Higher volumes of ®ll and large vial height-to-diameter aspect ratios will therefore increase the tendency toward directional solidi®cation when samples are frozen on a freeze-dryer shelf. Liquid nitrogen immersion causes extreme temperature gradients along the vial bottom and sides, resulting in directional solidi®cation from those surfaces inward. Samples frozen below their critical cooling rate will freeze by global supercooling, and their

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drying rates are primarily determined by the nucleation temperature. We would expect that at extremely low cooling rates, the post-nucleation annealing phenomenon just discussed would cause a more pronounced effect in those samples nucleating earlier, further increasing the drying rates of those samples relative to those nucleating later. However, we do not expect such a mechanism is controlling in the present case because we expect that the magnitude of that phenomenon would be sensitive to the cooling rate. Slower cooling rates would further exaggerate the drying rate difference between the samples for which nucleation occurred at high and low temperatures, and we did not observe this effect. We therefore propose the existence of three cooling-rate ranges: (1) cooling rates higher than the critical cooling rate lead to directional solidi®cation, (2) cooling rates lower than the critical cooling rate result in freezing by global supercooling, and (3) at very low cooling rates freezing is still by global supercooling, but post-nucleation, pre-solidi®cation annealing plays a role in further exaggerating the primary drying rate difference between the early- and late-nucleating samples. We expect the ®rst and third ranges to be affected by the cooling rate, but as we have shown, the intermediate range is not cooling rate sensitive. Implications The nucleation of water and aqueous solutions is stochastic Ð the same droplet will nucleate over a temperature range of up to 28C when repeatedly cycled.36 In addition to this inherently chaotic behavior, the stochastic nature of freezing is further ampli®ed by sample-to-sample heterogeneity in glass surface condition and particulate loading. The nucleation temperature is therefore under only limited control and is subject to deviations due to the presence of unseen particulates, vial surface conditions, and the stochastic nature of nucleation. Heterogeneity in nucleation temperatures, within a set of samples or between different processing lots, will result in heterogeneous drying rates and cake surface areas. In addition, the resulting alterations in the lyophilized cake (e.g., variable residual moisture levels) may cause variability in the stability of protein products. The control group (A), which utilized low particulate samples frozen on a shelf that was ramped slowly down in temperature, nucleated from ÿ8 to ÿ168C and dried at rates from 69 to JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 7, JULY 2001

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100 mg/h. Although these results may be more heterogeneous than those obtained in cGMP production, it is expected that considerable variation will still occur. Production lots will each possess a distribution around a slightly different mean because of varying production conditions and vial lots. We have observed that the nucleation temperatures of samples placed in vials from different packages from the manufacturer could differ by up to several degrees (data not shown). Also, the presence of operators has been found to be a signi®cant source of particulates,37 so the proximity of an operator during ®lling could result in atypically high particulate loading for a number of samples within a lot and may lead to a subset of samples within a lot nucleating earlier and drying faster. Recommendations Care must be taken through the process development and technology transfer sequence to avert unintended modi®cations to the lyophilized product morphology, surface area, the amount of protein lost to aggregation, and drying rate due to unintended effects on the freezing step. For example, lyophilization development runs may be conducted in environments higher in environmental particulate burdens than in ®nal production scale cGMP vial washing, depyrogenation, ®lling, loading, freezing, and lyophilization facilities, or may be conducted with discarded lots of product. The development engineer may be tempted to use aggregated protein, unsuitable for other uses, for lyophilization studies. However, the aggregated protein may promote ice nucleation, resulting in higher than normal drying rates and lower surface area. Future Studies A companion paper addresses the use of annealing to (a) eliminate drying rate heterogeneity caused by variation in nucleation temperatures, (b) optimize the primary drying rate, and (c) simultaneously determine the Tg0 values of a large number of formulations.39 Further study is needed on the effects of various freezing methods and rates on the secondary drying and reconstitution steps.

NOMENCLATURE mwf mtot

mass of freezable water, g total mass of solution, g

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 90, NO. 7, JULY 2001

C Cg0 CPw
Hm Tf Tn v G Tg0

mass fraction of solute in the solution mass fraction of solute in the maximally freeze concentrated amorphous phase heat capacity of water, J/g8C heat of fusion for water, J/g equilibrium freezing temperature of water in the presence of the solute, 8C nucleation temperature,8C interface velocity, m/s temperature gradient at the interface, 8C/mx glass transition temperature of maximally freeze-concentrated amorphous phase, 8C average of the squares of pore radii, m2

ACKNOWLEDGMENTS Funding was provided by the National Science Foundation (grant #BES 9816975) and the Colorado Institute for Research in Biotechnology. JAS was funded by Merck and Company, Inc. through an employee fellowship. The authors also thank FTSjKinetics for generous donations of funding and equipment.

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