Combining Solid-State and Solution Calorimetry for the Gibbs Free

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Combining Solid-State and Solution Calorimetry for the Gibbs Free Energy Calcula-tion of Polymorphs to Determine the Relative Stability and Solubility. Daniel Hsieh, Daniel Roberts, Thorsten Rosner, Tamar Rosenbaum, Chiajen Lai, and Qi Gao Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.5b00443 • Publication Date (Web): 10 Nov 2015 Downloaded from http://pubs.acs.org on November 27, 2015

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Crystal Growth & Design

Combining Solid-State and Solution Calorimetry for the Gibbs Free Energy Calculation of Polymorphs to Determine the Relative Stability and Solubility Daniel Hsieh1,*, Daniel Roberts1, Thorsten Rosner2,Tamar Rosenbaum1, Chiajen Lai1, Qi Gao1 1

Drug Product Science and Technology, Bristol-Myers Squibb Co., New Brunswick, NJ, 08903, USA 2 Chemical Development, Bristol-Myers Squibb Co., New Brunswick, NJ 08903, USA

* Corresponding author: Tel: +1 732 227 7488 1 Squibb Drive, Bristol-Myers Squibb Company, New Brunswick, NJ 08903 E-mail address: [email protected]

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ABSTRACT: A novel pure component approach using HyperDSC for the relative stability determination was reported in 2012 [1]. The accuracy of this approach depends upon the accurate physical properties of the amorphous and crystalline phases, including heat capacity and heat of fusion. However, it has been encountered that the heat of fusion for some pharmaceutical compounds cannot be accurately determined due to thermal decomposition or recrystallization upon melting even at very high heating rate. Hence, we report here two new methods for accurate heat of fusion determination using a combination of solid-state and solution calorimetry, determining the heat of solution at temperatures much lower than the melting point, thus avoiding decomposition or recrystallization. The theoretical derivation and experimental procedure for these two methods are reported in this study. The theoretical derivation of thermodynamic equations relates the solid-state and solution approaches. The experimental approach focuses on the use of solution calorimetry to measure the enthalpy difference between the amorphous and crystalline phases or between the polymorphs. A system composed of five polymorphs has been used to verify the methodology and its extension. The heat of fusion for the five polymorphs determined from the new methods are in good agreement with those from HyperDSC. A phase diagram using the heat of fusion determined from this study can be generated to rank the relative stability among the five polymorphs as a function of temperature. Keywords: polymorph, Gibbs free energy, HyperDSC™, solution calorimetry, thermodynamics

I. Introduction Determining relative stability for multi-polymorph compounds is very important to chemical processes and product development in the pharmaceutical industry to ensure the selection of stable polymorphs with consistent bioavailibilty. A method for such determination using a novel pure component free energy calculation has been successfully developed1. This method, as shown in Figure 1, incorporates both experimental and theoretical approaches. HyperDSC™ was used for the measurement of thermal data including the heat capacity (Cp), melting temperature (Tm), glass transition temperature (Tg) and the heat of fusion (∆Hf). With conventional DSC – which uses a relatively low heating rate (10-20°C/min) – recrystallization can occur during the melt, resulting in inaccurate and irreproducible data2. However, due to the high heating rate of HyperDSC™ (up to 750°C/min), recrystallization can be avoided; thus in most of the cases the heat of fusion for polymorphs can be reliably measured3. In addition, the heat capacity for crystalline polymorphs and amorphous materials can be accurately measured via HyperDSC™ over a wide temperature range. The accurate thermal data for the pure components, combined with the derived thermodynamic model1 provide the basis for the determination of the relative stability of the polymorphs over the desired temperature range, greatly aiding efforts in process and product development.


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Figure 1: Summary of Free Energy Calculation Concepts from Pure Component using HyperDSC™

Although HyperDSC™ offers an innovative approach for the calculation of Gibbs free energy1, it relies on the ability to accurately and reproducibly calculate heat of fusion of all polymorphs at the melt. For most pharmaceutical products, the high heating rate of HyperDSC™ is able to suppress decomposition and recrystallization, resulting in accurate heat of fusion values. However, two extreme cases have been encountered during product development in which the accurate heat of fusion measurement becomes untenable. One case involves the rapid chemical decomposition of the drug substance upon melting even at a high heating rate of 500°C/min. The other case entails the instantaneous recrystallization of the drug substance upon melting at the maximum heating rate of HyperDSC™, 750 °C/min. These two cases are schematically described in Figure 2. Figure 2(a) shows the determination of heat of fusion from single melt while Figure 2(b) shows the melt coupled with either recrystallization or thermal decomposition to make the accurate heat of fusion measurement not feasible. Hence the objective of this study was to develop methods that can address these limitations by determining the heat of fusion from the enthalpy data at lower temperatures via solution calorimetry such that form change, recrystallization and thermal decomposition are far less likely to occur. After the accurate heat of fusion is obtained, it can be used for the determination of relative stablility of polymorphs. Two methods have been developed and the theoretical and experimental approaches of these are presented in this study. The theoretical approach includes the derivation of thermodynamic equations which relate the heat of fusion to the enthalpy data at lower temperature. On the basis of this derivation, the thermal data required to determine the heat of fusion values are identified and collected. The experimental approach includes the setup and validation of the aforementioned data collection strategies. A polymorphic system composed of 5 polymorphs1 is used to verify the procedures. The phase digram in terms of Gibbs free energy difference with respect to the selected polymorph as a function of temperature is generated by using the heat of fusion from these new procedures and is compared with that from the purely solid-state method. The methodology presented in this study for the determination of heat of fusion and the relative stability of polymorphs is different from those in the literature4,5,6. First of all, no solubility of polymorph in solvent is required for the determination of heat of fusion or for the crossover (transition) temperature of a pair of polymorphs exhibiting enantiotropic behavior. No assumption on heat capacity was made because the heat capacity of each polymorph can be accurately measured via HyperDSC in this study. However, amorphous 3 ACS Paragon Plus Environment


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material is needed for the determination of the heat of fusion from two methods proposed in this study. After the heat of fusion and the heat capacity are known, the difference in Gibbs Free Energy of polymorphs as a function of temperature can be calculated via thermodynamic equations derived by authors1 to determine the relative stability and solubility of polymorphs at various temperatures.

Figure 2. (a) Accurate heat of fusion measurement from the single melt. (b) Inaccurate heat of fusion measurement due to multiple melt/recrystallizaton and melt/decomposition II.

MATERIALS AND METHODS

2.1 Compound 459 and Solvent. The amorphous phase and five polymorphs N1 to N5 of Compound 4597 were used in this study. The crystallization processes of these polymorphs have been described in detail1. The solvent used for the heat of mixing study is DMF. The solubility of Compound 459 in DMF at 25°C is higher than 0.45 g/cc.

2.2 PXRD. The form of the five polymorphs and the amorphous of compound 459 were checked by using PXRD. Powder X-Ray Diffraction data were collected using a Bruker-AXS D8 Discover with GADDS system. The x-ray generator was operated at 40 kV and 40 mA with a Cu target (CuKα λ=1.5418 Å), Göbel mirror optics with a 0.5 mm snout collimator, and Hi-Star Detector set at 175 mm sample-detector distance. Integration was set at 3–33 °2θ with a data collection time of 600s s. Data were analyzed using MDI Jade 9. 2.3 DSC. Conventional DSC was performed with a TA Instruments DSC Q2000 under a 50 mL/min N2 purge. Samples in the weight range of 2-5 mg were scanned at 10-20°C/min in hermetic Aluminum (Al) pans. The temperature and heat flow were calibrated using indium (In). The melting and eutectic-melting data reported were the average of two measurements. The melting temperatures were the onset of melting endotherms. Estimated standard error was ±0.05°C for temperature and ±0.1 kJ/mol for heat flow. 4 ACS Paragon Plus Environment

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2.4 Hyper-DSC. HyperDSC data was collected on a PerkinElmer 8500 (HyperDSC) under a 20 mL/min purge (He or N2); cooling was provided by a PerkinElmer Intracooler II with ballistic cooling. Analysis was performed using Pyris software (V4.02). The use of Hyper-DSC for measuring the heat capacity and heat of fusion of compound 459 has been described in detail1. 2.5 Solution Calorimetry. Omnical Insight calorimeter (Omnical Inc. Stafford, TX) was used for the measurement of heat of mixing. Four 15 mL glass vials equipped with magnetic stir bars were charged with 0.9 g of the desired compound. The vials were sealed with a screw cap with septa and placed into the Insight calorimeter for thermal equilibration together with an empty 15 ml glass vial for the reference cell. For each vial in the calorimeter a 2mL syringe with needle was filled with 2 mL DMF and the syringe was placed into the calorimeter, piercing the vial septa, for thermal equilibration at 25°C. Thermal equilibration was typically reached after 40 min and the content of the syringes was injected into the glass vials simultaneously while the thermal event was recorded. As soon as the heat flow returned to the baseline, the vials were removed from the instrument and visually inspected for complete dissolution of the solids. The heat flow data were integrated based on a point to point baseline.

2.6 Method I: Heat of Fusion from Enthalpy Difference between Amorphous and Crystalline Phase at Low Tempertaure and Heat Capacity This method is most applicable for cases in which the compounds will decompose at the melting point and hence, the accurate heat of fusion cannot be obtained through a conventional solid-state approach. The thermodynamic derivation for this method is illustrated in Figure 3, the enthalpy vs. temperature for both amorphous and crystalline phases. Two polymorphs NA and NB are used in this illustration and NA has a higher melting temperature than NB. For the calculation of the enthalpy difference between the amorphous phase and the crystalline phase, a reference state is selected in which the enthalpy of the amorphous phase at the melting temperature of NA is set as zero, as indicated in Figure 3.

Figure 3. Method I: Heat of Fusion Calculated from Enthalpy Difference between Amorphous and Crystalline Phase at Low Temperature and Heat Capacity 5 ACS Paragon Plus Environment


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To determine the heat of fusion for NB, a thermodynamic pathway composed of five steps is conceived and illustrated in Figure 3. The first 4 steps are used to determine the enthalpy of NB at the melting temperature of NB and the last step, step 5, is used to determine the enthalpy difference between the amorphous phase and the crystalline phase, which is the heat of fusion of NB. The thermodynamic derivation of these five steps are expressed as follows:

= − − ∗ − ∗ − ∗ + ∗

(1)

The four terms on the right-hand-side of equation (1) present the enthalpy changes from step 1 to step 4, respectively, to determine the enthalpy of NB at the melting temperature of NB. The description of symbols or abbreviations used in the derivation and figures is provided at the end of this paper.

The thermodynamic derivation for step 5 is expressed in equation (2). ∆

= −

=

=

−

∗ − ∗ +

∗ − ∗ + ∗ (

+

∗

− )

−

∗

(2)

The first term on the right-hand-side of equation (2) is the enthalpy difference between the crystalline phase NB and the corresponding amorphous phase at low temperature (low temperature, as discussed here, is merely relative and refers to a temperature below any observable thermal events). This difference can be measured via solution calorimetry. The second term on the right-hand-side of equation (2) is the enthalpy difference between NB and the corresponding amorphous phase over a temperature range from low temperature to the melting temperature of NB. Since the heat capacities as a function of temperature of both crystalline and amorphous phases were accurately measured previously via HyperDSC1, this enthalpy difference can be calculated. The above mentioned equation (2) clearly shows that the determination of the heat of fusion requires the use of both solid-state calorimetry such as HyperDSC and solution calorimetry with a high degree of accuracy and reproducibility. Method II: Heat of Fusion from Enthalpy Difference between Two Crystalline Phases at Low Tempertaure and Heat Capacity. This method is most applicable for cases in which one of the polymorphs is stable at its melting temperature and, therefore, its heat of fusion can be measured accurately. The thrermodynamic derivation of this method is illustrated in Figure 4, the enthalpy vs. temperature for amorphous and two crystalline phases. Two polymorphs NA and NB are used in this illustration and NA has a higher melting temperature than NB. The heat of fusion for NA can be accurately measured.


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Figure 4. Method II: Heat of Fusion Calculated from Enthalpy Difference between Two Crystalline Phases at Low Tempertaure and Heat Capacity. For the calculation of the enthalpy difference between the amorphous phase and the crystalline phase or between two crystalline phases, a reference state is selected in which the enthalpy of the amorphous phase at the melting temperature of NA is set as zero, as indicated in Figure 4. To determine the heat of fusion for NB, a total of five steps are involved as noted in Figure 4. The first 4 steps are used to determine the enthalpy of NB at the melting temperature of NB and the last step, step 5, is used to determine the enthalpy difference between the amorphous phase and the crystalline phase, which is the heat of fusion of NB. The thermodynamic derivation of these five steps are expressed as follows:

=

−∆

−

∗

−

∗ − ∗ + ∗

(3)

The four terms on the right-hand-side of equation (3) present the enthalpy changes from step 1 to step 4, respectively to determine the enthalpy of NB at the melting temperature of NB. The thermodynamic derivation for step 5 to determine the heat of fusion for NB is expressed in equation (4) as follows: ∆

= −

= −

−

−

−∆

−

= ∆ + ∗ − ∗ −

∗

∗

−

∗ − ∗

( − ) −


+

∗

( − ) (4)


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The first term on the right-hand-side (RHS) of equation (4) is the heat of fusion of polymorph NA and is determined from solid-state calorimetry such as HyperDSC. The second term on the RHS of equation (4) is the enthalpy difference between two polymorphs NA and NB and it can be determined from the solution calorimetry. The third term on the RHS of equation (4) is the enthalpy difference between NA and NB over the temperature range from low temperature to the melting temperature of NB. The last term on the RHS of equation (4) is the enthalpy difference between the amorphous phase and the crystalline phase of NA over the temperature range from the melting temperature of NB to the melting temperature of NA. The last two terms on the RHS of equation (4) can be calculated since the heat capacities of the amorphous phase, crystalline phase of NA and NB as a function of temperature are known and previously reported1. Solution Calorimetry: Determination of Enthalpy Difference . The theoretical basis of the use of solution calorimetry for the enthalpy difference between amorphous and crystalline phases or between two polymorphs can be illustrated by using the following thermodynamic derivations: The heat of mixing of amorphous material and solvent can be expressed as follows: ! = (, #, $ + $ ! ) − $ (, #) − $ ! ! (, #)

(5)

Where L and S represent amorphous material and solvent respectively; H presents enthalpy WL = weight of amorphous phase WS = weight of solvent ! = heat of mixing as amorphous material and solvent are mixed together Similarly, the heat of mixing of polymorph NA and solvent can be expressed as follows: = (, #, $ + $ ! ) − $ (, #) − $ ! ! (, #) !

(6)

Where $ = weight of polymorph NA

When the same weight of amorphous material and crystalline material is used, $ = $ , the enthalpy of the solution for both becomes equal and this relationship is expressed as follows: (, #, $ + $ ! ) = (, #, $ + $ ! )

(7)

Equation (7) is valid because when both amorphous and crystalline phases are fully and separately dissolved in the same solvent, the two resulting solutions have the same composition, temperature and pressure; hence the enthalpy for each solution is equal as shown in equation (7). By using equation (7), the subtraction of equation (6) from equation (5) yields the following expression: ! ( − )/$ = (, #) − (, #) !

(8)

The first two terms on the left-hand-side of equation (8) present the difference between the heat of mixing for amorphous material and solvent system and the heat of mixing for crystalline material NA and solvent system. The RHS of equation (8) presents the enthalpy difference between the amorphous phase and the crystalline phase. Since the heat of mixing can be measured by using solution calorimetry, it follows that the enthalpy between the crystalline phase and amorphous phase can be determined.


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Figure 5. Schematic diagram to demonstrate the determination of the enthalphy difference between the crystalline phase and amorphous phase from the heat of solution difference via solution calorimetry The physical meaning of equation (8) can be illustrated in Figure 5. Two mixing processes are presented in this figure. One is the mixing of the crystalline material NA and a solvent. The other is the mixing of amorphous material (melt) with a solvent. Both mixing processes are conducted at low temperature. Since the enthalpy is a state function, the mixing of crystalline material NA with a solvent can be divided into two steps: the first step is to melt the crystalline material NA into an amorphous material. The heat required for this melting is the enthalpy difference between the crystalline phase and amorphous phase. The second step is the mixing of the amorphous material (melt) with a solvent, as shown on the left-hand side, which is identical to mixing process of amorphous material with a solvent on the right-hand side. Therefore, as the heat of mixing of amorphous material and a solvent is compared with that of crystalline material NA and a solvent, the difference between them is the enthalpy difference between the amorphous material and crystalline material NA, as shown in equation (8). By using the above-mentioned methodology, the enthalpy difference between NA and NB can be expressed as follows: ( − )/$ = (, #) − (, #) !

!

(9)

Comparison between Method I and Method II. Method I using equation (2) is most applicable for polymorphs which will decompose at the melting points while Method II using equation (4) is most applicable when the heat of fusion for one of the polymorphs is available. Hence, the information and the material required for each method are different as shown in Table 1.



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Table 1. Method I and Method II Comparison Item

Method I

Method II

Amorphous

NA

Amorphous material required for Cp for amorphous

Solution calorimetry and heat capacity measurement Over a temp. range from T* to TmNB

Heat capacity measurement

Enthalpy difference between amorphous and crystalline at T*

Yes

Over a temp. range from TmNB to TmNA No

Enthalpy difference between two polymorphs

No

Yes

Heat of fusion for one polymorph

No

Yes

Reference material

Proper application of Method I needs measuring the enthalpy difference between amorphous and crystalline phases and hence the reference material is the amorphous. In contrast, Method II requires measuring the enthalpy difference between NA (with an accurate heat of fusion) and other polymorphs; hence, the reference material is NA. As far as the amount of amorphous material is concerned, Method I requires amorphous material for heat of mixing (around 5 g) and for the heat capacity measurement (around 1g) while Method II requires amorphous material solely for heat capacity measurement (around 1 g). The amorphous and crystalline materials need to be checked for phase purity before the measurement of the heat of mixing. As shown in Figure 6, the amorphous material exhibits some partial crystallization after 12 hours of the formation of the amorphous material from the quench of the melt. However, there is no detectable spontaneous crystallization within the first 2 hours after the amorphous material is prepared. Therefore, during this two hour period, the solution calorimetry data for the amorphous material must be collected to obtain an accurate heat of mixing.


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Figure 6. Meta-Stability of Amorphous Material Similarly, the form of the polymorph needs to be checked against the simulated XRD as shown in Figure 7 (polymorph N5 as an example) to ensure phase purity for accurate heat of mixing.

Figure 7. XRD of N-5 Simulated vs. Experimental III. RESULTS AND DISCUSSION 3.1 Heat of Mixing. Heat of mixing for amorphous and crystalline materials was measured at 25°C in DMF via solution calorimetry. A typical result from this measurement is shown in Figure 8, the heat flow vs. time for both amorphous material and crystalline material N3. The heat of mixing for amorphous material and DMF is exothermic (negative wrt heat of mixing) while the heat of mixing for crystalline material N3 (and other polymorphs not shown) with DMF is endothermic (positive wrt heat of mixing). This measurement is considered complete when the heat flow signal returns back to baseline after the mixing process. The value of the heat of mixing is determined from the integration of the heat flow over the mixing time.



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Figure 8. Heat of Mixing Mesurement Four experimental samples (& = 4) were used for each material to obtain an average value of the heat of mixing for each solid compound. The results of the heat of mixing for amorphous and all five polymorphs are shown in Table II. The deviation of the measurement between the four samples for each material is less than or equal to 2 %. The heat of mixing provided in Table 2 can be used for the calculation of the enthalpy difference between the amorphous and crystalline phase at 25°C in Method I and for the calculation of the enthalpy difference between polymorphs at 25°C in Method II.

Table 2. Results of Heat of Mixing at 25°°C Form

Heat of Mixing, J/g (n=4)

Deviation of Measurement, %

N1

-26.10

±1.1

N2

-20.55

±2.0

N3

-40.24

±0.8

N4

-35.94

±0.7

N5

-37.00

±0.9

Amorphous

+15.06

±1.1

Two examples are given here to illustrate how to determine the enthalpy difference from the heat of mixing from Table 3. The first example is for the amorphous and crystalline pair and the second example is for two polymorphs. Equation (8) shows that the enthaply difference between crystalline and amorphous phases is equal to the difference in heat of mixing. The heat of mixing for amorphous and DMF is +15.06 J/g and for N3 and DMF is - 40.24 J/g which means the difference in heat of mixing between them is 55.30 J/g, which is the value on the LHS of equation (8). This implies that the enthalpy of crystalline N3 is lower than that of amorphous by 55.30 J/g. For two polymorphs, the heat of mixing for N3 and DMF is 40.24 J/g and the heat of mixing for N2 and DMF is 20.55 J/g, which means the difference in heat of mixing between them is 19.69 J/g, 12 ACS Paragon Plus Environment

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which is the value on the LHS of equation (9). This implies that the enthalpy of N2 is higher than that of N3 by 19.69 J/g at 25⁰C. 3.2 Heat of Fusion from Method I and Method II. The heat of fusion determination from Method I is illustrated in Figure 9 by using amorphous and polymorph N3 as an example. Since polymorph N2 has the highest melting point 421.8K (148.6°C) among the five polymorphs1, the reference state for the calculation of the heat of fusion is selected such that the enthalpy of the amorphous phase at 421.8 K is zero as shown in Fig. 9.

Figure 9. Heat of Fusion determined from Method I By using the first 4 steps in Method I, the enthalpy of the polymorph N3 at the melting temperature of N3 can be determined from equation (1). The enthalpy differences from step 1, 2, and 4 are calculated since the heat capacity for amorphous and for polymorph N3 are known1. The value of the enthalpy difference between the amorphous material and polymorph N3 at 25°C, 55.30 J/g (22.42 KJ/Mol) used in step 3 is obtained from the heat of mixing measurement via solution calorimetry (Table 2). After the enthalpy of N3 at its melting temperature 395 K(121.8°C) is determined, the heat of fusion of N3 can be calculated from step 5 in Method I, which is the enthalpy difference between the amorphous and the crystalline phase at the melting temperature. The enthalpy of the amorphous at the melting temperature of N3 is calculated from the integration of the heat capacity of amorphous1 from the melting temperation of N2 to N3. Figure 9 is used to explain the physical meaning of the heat of fusion determination step by step via Method I. The value of the heat of fusion for each polymorph can be simply calculated by using equation (2). The heat of fusion determination from Method II can be illustrated in Figure 10 by using polymorph N2 and N3 as an example. N2 is selected as the reference material in Method II because it is stable at its melting temperature and its heat of fusion can be measured from either HyperDSC or conventional DSC1. Similar to Method I, the reference state for the calculation of the heat of fusion is selected such that the enthalpy of the amorphous at 421.8 K is zero as shown in Fig. 10.



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Figure 10. Heat of Fusion determined from Method II By using the first 4 steps in Method II, the enthalpy of the polymorph N3 at the melting temperature of N3 can be determined from equation (3). Since the heat of fusion of N2 is known, the enthalpy of N2 at N2 melting temperature can be determined, which is referred as step 1. The enthalpy differences from step 2 and step 4 are calculated since the heat capacity for N2 and N3 and for poare known1. The value of the enthalpy difference between N2 and N3 at 25°C, 19.69 J/g, which is the value on the LHS of equation (9). This implies that the enthalpy of N2 is higher than that of N3 by 19.69 J/g. (Table II). After the enthalpy of N3 at its melting temperature 395 K(121.8°C) is determined, the heat of fusion of N3 can be calculated from step 5 in the extended Method, which is the enthalpy difference between the amorphous and the crystalline phase. The enthalpy of the amorphous at the melting temperature of N3 is calculated from the integration of the heat capacity of amorphous1 from the melting temperation of N2 to N3. Figure 10 is used to explain the physical meaning of the determination of heat of fusion step by step via Method II. The value of the heat of fusion for each polymorph can be simply calculated by using equation (4). The heat of fusion for five polymorphs N1 to N5 from both Methods is summarized in Table 3 and is compared with the heat of fusion determined from Hyper DSC1. Table 3 shows that the heat of fusion of N1 to N5 determined from both Methods is very close to that from HyperDSC and the deviation is less than 2%. Hence, it is fair to conclude that both Methods I and II can be used for the determination of heat of fusion.

Table 3. Comparison of Heat of Fusion from HyperDSC vs. Method I and Method II Hyper DSC Form

KJ/mole

Method I KJ/mole

Method II

%, deviation wrt to value from HyperDSC 14

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KJ/Mol

%, deviation wrt to value from HyperDSC

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N1 N2


34.55

-1.3

-0.45

34.10 35.34

35.05

-1.4

35.20

-0.95

35.56

36.06

+1.4

36.27

+1.9

37.03

37.46

+1.15

37.62

+1.6

35.34

33.9 35.17

N5

35.54

N4 N3

-1.7

0%

3.3 Phase Diagram. The heat of fusion for polymorphs N1 to N5 from both Methods coupled with thermodynamic equations and the heat capacity of these polymorphs and amorphous1 can be used to generate the phase diagrams in terms of ∆G vs. temperature as shown in Figure 11. These two phase diagrams are nearly identical and the only difference is slight variation the crossover temperature.

Figure 11. ∆G vs. Temperature from Method I and Method II As the phase diagram using the heat of fusion directly measured via HyperDSC1is compared with that from both Methods, as shown in Figure 12, small differences in terms of crossover temperature (Table 4) and relative stability (Table 5) are summarized.

Figure 12. ∆G vs. Temperature from HyperDSC vs. from Method I Table 4. Crossover Temperature Comparison from Four Different Methods

N1/N3

Competitive Slurrying

HyperDSC

Method I

Method II

60-70

66

75

72



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N2/N3

25-35

36

41

40

N4/N3

40-55

54

52

52

N5/N3

N/A

125

120

120

N5/N1

>55

52

55

52

N5/N4

40-50

42

23*

22*

N5/N2

15-30

27

22

22

As far as the crossover temperature is concerned, these three phase diagrams are in good agreement except for N5/N4 pair (Table 4). As far as the relative stablility ranking is concerned (Table 5), these three phase diagrams exhibit the same stability ranking except the relative ranking at 30°C. This is due to a higher ∆G difference between N3 and N5 and the shift of the crossover temperature between N2 and N3 when heat of fusion from both Methods is used. Figure 13 shows that the heat of fusion for N3 and N4 measured from both Methods is higher than those from HyperDSC while the heat of fusion for N5 and N1 measured from both Methods is lower than those from HyperDSC. This is likely the major source of discrepancy in the phase diagram. Table 5. Relative Stability Ranking from Three Methods T, °C

Hyper DSC

Method I

Method II

Note

30

N3>N2>N5>N4>N1

N3>N2>N4>N5>N1

N3>N2>N4>N5>N1

Same except N4 and N5

45

N2>N3>N4>N5>N1

N2>N3>N4>N5>N1

N2>N3>N4>N5>N1

Same

60

N2>N4>N3>N1>N5

N2>N4>N3>N1>N5

N2>N4>N3>N1>N5

Same

100

N2>N4>N1>N3>N5

N2>N4>N1>N3>N5

N2>N4>N1>N3>N5

Same


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Figure 13. Comparison of Heat of Fusion from Three Methods The combination of solid-state and solution calorimetry developed in this study has demonstrated that heat of fusion can be accurately determined for pharmaceutical compounds in which thermal decomposition or recrystallization upon melting may occur by using solid-slate calorimetry. Hence, the methodology using pure components for the stability ranking developed by authors1 previously can be employed for all pharmaceutical compounds. The relative solubility is related to the Gibbs free energy difference between each polymorph and the reference polymorph N3 in this study which is calculated and displayed in Figures 11 and 12. The mathematical expression for this relationship was provided in details by authors8. Figure 14 shows the logic flow diagram on how to use various methods for the phase diagram generation. When the direct measurement of heat of fusion is feasible via HyperDSC, this situation has been demonstrated by authors earlier1. However, when the direct measurement of heat of fusion is not feasible, the methods developed in this study need to be employed.



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Figure 14. Logic Flow Diagram for Heat of Fusion Measurement and Stability Phase Diagram Generation 3.4 Verification of Methodology with Different System. Compound 4591 with 5 polymorphs has been used to demonstrate the two methodologies proposed in this study for heat of fusion determination. To further verify the approaches, a different polymorphic system was used. Compound 158 with a molecular weight of 309.3 g/gmol, including two major polymorphs N2 and N3, was selected as a second system to verify the methodology proposed in this study. The PXRD overlay of N2 and N3 is shown in Figure 15. Since the making of amorphous material of compound 158 is not possible from melt quenching due to rapid formation of crystalline material from amorphous, only Method II is used to verify the methodology. Since the melting temperature and heat of fusion for both N2 and N3 are available, either one can be used as the reference to determine the heat of fusion of the other via Method II. However, N3 is selected as the polymorph for the determination of the heat of fusion of polymorph N2 because N3 has a higher melting temperature to make the calculation simpler.

Figure 15. The PXRD of polymorphs N2 and N3 of compound 158. 18 ACS Paragon Plus Environment

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The melting temperature and the heat of fusion for N2 and N3 of compound 158, as measured by Hyper DSC, are shown in Table 6. Table 6. Melting Temperature and Heat of Fusion for Polymorphs N2-N3 of Compound 158 Polymorph Melting Temperature, K Heat of Fusion, KJ/mol N2 376.97±0.60 42.58±0.38 N3 381.74±0.23 36.01±0.71 (n=5) (n=5) The heat of mixing for the two polymorphs with NMP (N-Methyl Pyrrolidinone) was measured. The amount of NMP used for each run is 3 ml and the amount of crystalline material used for each run is around 0.65g. The results of the mixing are presented in Table 7. Table 7. Heat of Mixing for Compound 158 at 25°C Form Average Heat of Mixing, J/g (n=4) N2 -66.5538 N3 -54.5826

Standard Deviation of Measurement, % 0.28 1.36

The results of heat of mixing show that the enthalpy of N2 is lower than that of N3 by 11.97 J/g (3.7 KJ/Mol) at 25°C. The heat capacity of N2, N3 and liquid were measured by HyperDSC following ASTM standard method (E1269-05, 2005). The results of this measurement are shown in Table 8 and Figure 16. Table 8. Heat Capacity/Temperature Correlation for Polymorphs N2 and N3 of Compound 158 Material Cp equation (T in K), KJ/(Mol K) R2 (Correlation Coefficient) N2 -0.023984 + 0.0010572*T 0.98121 N3 -0.051259 + 0.0012102*T 0.99472 Sub cooled Liquid -0.33914 + 0.002245*T 0.99905 The heat capacity data including N2, N3 and liquid can be correlated well with a linear relationship with temperature, as shown in Table 8. It should be noted that the liquid heat capacity of Compound 158 was measured at temperatures above the melting temperature of N3 (381.74 K). The results of this measurement were correlated with a linear function of temperature as shown in Table 8. This linear equation was then used to generate the heat capacity of liquid below the melting temperature for amorphous (sub-cooled liquid) below the melting temperature. The heat capacity of the sub cooled liquid (Amorphous material in the rubbery state) can be used to determine the enthalpy of amorphous and to calculate the relative stability of two polymorphs1.



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Figure 16. Heat capacity of polymorphs N2, N3 and amorphous material of compound 158. Since the polymorph N3 has a higher melting temperature than N2, as shown in Table 6, the enthalpy of the amorphous at the melting temperature of N3 is selected as the reference point, the enthalpy of the amorphous at this temperature is chosen as zero, as shown in Figure 17. By using 5 steps proposed in Method II, the enthalpy of N2 can be calculated. The value of the heat of fusion of N2 determined from thes 5 steps of Method II is 41.13 KJ/mol, which is very close to the value of the heat of fusion of N2 directly determined from HyperDSC 42.58 KJ/mol (Table 6). The difference is less than 3.5% from the value determined from HyperDSC.


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Figure 17. Heat of Fusion determined from Method II. Since the thermal properties such as melting temperature, heat of fusion and heat capacity for N2/N3 as well as the heat capacity of sub cooled liquid are generated, the relative stability of N3 with respect to N2 as a function of temperature (phase diagram) can be calculated1. The results of this calculation are shown in Fig. 18. Two relative stability curves are presented in this figure: one is using the heat of fusion of N2 from HyperDSC (direct method) and the other is using the heat of fusion of N2 from method II. Both curves show that N2 and N3 are enantiotropically related: N2 is more stable than N3 as the temperature is below the crossover temperature and N3 is more stable than N2 as the temperature is above the crossover temperature. The crossover temperature from the direct method (HyperDSC) is 80°C, slightly higher than that from Method II, 74°C. The relative stability of N3 with respect to N2 predicted from direct method (HyperDSC) or from Mehtod II, as shown in Figure 18, is consistent with the experimental finding. N3 is prepared from the melting of N2 followed by gradual cooling. This proves that N3 is more stable than N2 at elevated temperatures.



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Figure 18. ∆G vs. Temperature from HyperDSC vs. from Method II 3.5 Impact of the Selection of Amorphous Material on Heat of Fusion and Relative Stability When the amorphous material is at temperatures above the glass transition temperature, it is in a rubbery (Sub cooled) state which is considered an equilibrium state; hence, the enthalpy of the amorphous material above the glass transition temperature is a function of temperature only, as shown in Figure 19. In contrast, when this amorphous material is below the glass transition temperature, it is in a glassy state which is not at equilibrium because the enthalpy level of the glassy material is dependent upon how this amorphous material is cooled or how this amorphous material is prepared. For example, the amorphous material could be made from melt and quench process or from the spray drying process, resulting in different enthalpy level as shown in Figure 19 for amorphous material I (from R to O) or amorphous material II (from R to O’). In addition, the state of the amorphous material may change with time as shown in Figure 6. Since the amorphous material is selected as the reference for the indirect method to determine the heat of fusion, it is important to know how to obtain accurate heat of fusion from this indirect method. A few procedures are needed to ensure accuracy: First, the amorphous material might change with time. As shown in Figure 6, there was no change in PXRD pattern in the first two hours after the amorphous material was made from the melt and quench process, but some partial crystallization was observed between 2 and 12 hours as shown in Figure 6. This means that all the measurements including the heat capacity of amorphous material, the glass transition temperature and the heat of mixing for amorphous material via solution calorimetry need to be completed within 2 hours after the amorphous material is prepared. Second, the accurate measurement of heat capacity as a function of temperature and the glass transition temperature are needed to determine the enthalpy of the amorphous material below the glass transition temperature, as shown in Figure 19, from point Q through R to O. The heat capacity data as a function of temperature was generated via HyperDSC, following ASTM Standard Test Method for Determining Specific Heat Capacity by DSC1. 22 ACS Paragon Plus Environment

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Third, the heat of mixing measurement needs to be conducted to accurately determine the enthalpy difference between the amorphous material and the crystalline material. It should be noted that the same amorphous material needs to be used for both solution calorimetry and HyperDSC. The heat of fusion generated from this indirect method for 5 polymorphs of compound 459 are close to those from the direct method via HyperDSC as shown in Table 3, with a deviation less than 2%. It is important to know the impact of the selection of amorphous material on heat of fusion determination and the relative stability. This impact can be illustrated by Figure 19. When amorphous material I is used for the heat of fusion measurement, the enthalpy of this amorphous material is located at position O and the enthalpy difference between this amorphous material and the crystalline material NB, determined from solution calorimetry, is used to locate the enthalpy of the crystalline material NB at the temperature T*, designated at point B. Since the heat capacity of NB as a function of temperature is known, the heat of fusion of NB can be determined from the enthalpy difference between the amorphous and NB. By using the same procedure, the heat of fusion of other polymorphs such as NA can be determined. Since the amorphous material is not at equilibrium, the enthalpy of this material (I) may change to a new and different value, located as position O’ as amorphous material II. When this new material (II) is used for heat of mixing via solution calorimetry, the enthalpy difference between the amorphous material II and NB might be different from that between the amorphous material I and NB, resulting in a different enthalpy value for NB, as designated as point C. The enthalpy difference between B and C is designated as ∆. The value for ∆ could be positive or negative. Since the heat capacity of NB as function of temperature is known, the enthalpy of NB change from point C to C’ can be calculated, resulting in a heat of fusion for NB different from that from using amorphous material I and this difference is ∆, as shown in Figure 19.

Figure 19. Enthalpy Change Due to the Selection of Amorphous Material N

The heat of fusion for NB, which is the distance between P and B’, can be designated as (∆Hf B )I. The superscript I indicates that the heat of fusion is determined from using amorphous material I as the reference. N Similarly, the heat of fusion for NB, which is the distance between P and C’, can be designated as (∆Hf B )II. The superscript II indicates that the heat of fusion is determined from using amorphous material II as the reference. 23 ACS Paragon Plus Environment


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Same notation can be applied for polymorph NA. With these designations, the impact of the selection of amorphous material on heat of fusion and the relative stability can be derived mathematically as follows: ++

+

∆ = ∆ + ∆ ++

(10)

+

∆ = ∆ + ∆

(11)

When equation (11) is subtracted from equation (10), the result of this subtraction is expressed as follows: N

II

II

N

N

I

I

N

∆Hf B -∆Hf A =∆Hf B -∆Hf A

(12)

Equation (12) shows that the difference in the heat of fusion between the two polymorphs is the same regardless of the selection of the amorphous material. This relationship is very important because it will be used to determine the impact of the selection of amorphous material on the relative stability. The Gibbs free energy difference between polymorphs NA and NB on the basis of the amorphous material was described in details by the authors1. These differences between polymorph NA and NB for amorphous material I and for amorphous material II are expressed in the following two equations (13) and (14), respectively.

(/ − / )+ = (∆/ )+ = (∆ − ∆0 )+

=

−

56 − 4

−

56

+ ∆

−

∆89

7 + 4

+ ∆ +

−

∆89

+

1 + 2

5:;

7 + 4 4 −

56

=

−

56 − 4

−

56

+ ∆

−

∆89

7 + 4

++ ∆ +

−

∆89

++

5:;

7 + 4 4 −

1 + 2

56

7 7 (13)

(/ − / )++ = (∆/ )++ = (∆ − ∆0 )++

3

3

7 7 (14)

It should be noted that the heat capacities for polymorphs NA and NB and for the amorphous material above the glass transition temperature are used in both equations (13) and (14). Since the amorphous material above the glass transition temperature is in equilibrium, its heat capacity is independent of the selection of the amorphous material. Therefore, when equation (13) is subtracted from equation (14), all the terms related to the heat capacities can be eliminated and the result of this subtraction is expressed in the following equation: ++

++

+

+

(/ − / )++ − (/ − / )+ = >∆ − ∆ ? − >∆ − ∆ ? 24

ACS Paragon Plus Environment

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− 24


∆89

++

∆89

7 −4

++

7 3 + 24

∆89

+

∆89

7 −4

+

73

(15)

When equations (10) to (12) are used, the equation (15) can be reduced to a simple relationship between the difference in Gibbs free energy due to the selection of the amorphous material:

(/ − / )++ − (/ − / )+ = − @

∆

−

∆

A

(16)

Equation (16) shows that the difference in Gibbs free energy between using amorphous material I and using amorphous material II is attributed to the difference in entropy only. The Gibbs free energy is composed of two parts, enthalpy and entropy. It is interesting to note that although the selection of the amorphous material will determine the value of the enthalpy of the polymorphs, as shown in Fig. 19, the enthalpy difference between two polymorphs is the same regardless of the selection of the amorphous material. This is because the enthalpy variation ∆ caused by using different amorphous material is cancelled out as shown in equation (12). The rearrangement of equation (16) yields:

(/ − / )++

=

(/ − / )+ − @

∆

−

∆

A

(17)

Equation (17) shows that the impact of the selection of the amorphous material on the relative stability between two polymorphs can be calculated if the value for ∆ is known. 4 CONCLUSIONS New methods combining solid-state and solution calorimetry on the base of derived thermodynamic equations have been developed to determine the heat of fusion from heat of solution at low temperature. It has been demonstrated that the heat of fusion for five polymorphs determined from the new methods are in good agreement with those from HyperDSC. The new method can be used for the determination of the relative stability and solubility for cases of thermal decomposition and re-crystallization upon melting. Two compounds have been used to verify the methods proposed in this study. Acknowledgments The authors are grateful to the Senior Leadership Team at Bristol-Myers Squibb Co. for providing support to accomplish this work. Mr. Dave Norman from PerkinElmer is greatly acknowledged for his generous technical assistance on the use of HyperDSC. HyperDSC is a registered trademark of PerkinElmer Inc. All Rights Reserved. References 1. Hsieh, D.S.;Huang, J.;Roberts, D.;Gao, Q.;Ng, A.;Erdemir, D.;Leahy, D.;Li, J.;Huang, M.;Lai, C. Determination of the Relative Stability of a Multipolymorph System via a Novel Pure Component Free Energy Calculation. Cryst. Growth and Des, 2012, 12, 5481. 25 ACS Paragon Plus Environment


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2. Verdonck, E.;Schaap, K.;Thomas, L.C. A discussion of the principles and applications of Modulated Temperature DSC (MTDSC). Int J Pharm. 1994, 192, 3. 3. McGregor, C.; Saunders, M.H.;Buckton, G.; Saklatvala, R.D. The use of high-speed differential scanning calorimetry (Hyper-DSCTM) to study the thermal properties of carbamazepine polymorphs. Thermocim Acta, 2004, 417, 231. 4. Behme, R.; Brooke, D. Heat of Fusion Measurement of a Low Melting Polymorph of Carbamazepine That Undergoes Multiple-Phase Changes During Differential Scanning Calorimetry Analysis. J. Pharm. Sci 1991,80, 986. 5. Gu, C.H; Grant, D. Estimating the Relative Stability of Polymorphs and Hydrates from Heats of Solution and Solubility Data. J. Pharm. Sci. 2001, 90, 1277. 6. Urakami, K.; Shono, Y.; Higashi, A.; Umemoto, K.; Godo, M. A Novel Method for Estimation of Transition Temperature for Polymorphic Pairs in Pharmaceuticals Using Heat of Solution and Solubility Data. Chem. Pharm. Bull. 2002,50, 263. 7. Leahy, D.; Li, J.;Sausker, J.; Zhu,J.;Fitzgerald,M.;Lai,C.;Buono,F.G.;Braem,A.;de Mas,N.;Manaloto,Z.; Lo,E.;Merkl,W.;Su,B.N.;Gao,Q.;Ng,A.;Hartz,A. Development of an Efficient Synthesis of Two CRF Antagonists for the Treatment of Neurological Disorders. Organic Process Research & Development. 2010, 14, 1221. 8. Hsieh, D. S.; Sarsfield, B.;Davidovitch, M.;DiMemmo, L.;Chang, S.Y.;Kiang, S. Use of Enthalpy and Gibbs Free Energy to Evaluate the Risk of Amorphous Formation. J. Phar. Sci. 2010, 99, 4096-4105.

Abbreviations Abbreviation Cp G H NA NB P S T Tg Tm T* Hmix ∆Hf W Superscript L LS NAS NA NB Subscript f mix

Description Heat Capacity Gibbs free energy Enthalpy Polymorph A Polymorph B Pressure Solvent Temperature Glass transition temperature Melting temperature Low temperature at which re-crystallization will not occur Heat of mixing Heat of fusion Weight

Amorphous Material Amorphous material and solvent System Polymorph NA and Solvent System Polymorph A Polymorph B

fusion Mixing 26 ACS Paragon Plus Environment

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phase diagram using the heat of fusion determined from this study can be generated to rank the relative stability among the five polymorphs as a function of temperature.


Combining Solid-State and Solution Calorimetry for the Gibbs Free

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