Effect of Manufacturing Methods Used in the Stability of Amorphous Solid Solutions and Predictions to Test them

With the advent of combinatorial chemistry and high throughput screening of drug molecules, poorly water soluble molecules have been entering the development stage as new drug candidates. The poor aqueous solubility of these molecules is one of the limiting factors for them to succeed as a new drug product. This had led to converting these drugs in most cases are crystalline to amorphous solid dispersion with use of amorphous polymers to improve the solubility. Although amorphous solid dispersion of a poorly water drug can improve the solubility, careful selection of polymer is a necessity in order to stabilize the high energy nature of the amorphous solid dispersion. Miscibility of a drug and a polymer is important. With specific interaction between the drug and the polymer, the dispersion can remain miscible much longer. Another factor that needs to be considered when formulating an amorphous solid dispersion is the amount of drug that is incorporated into the polymer. Over saturating the polymer with the drug can cause instability of the dispersion and crystallization may occur which will lead to reduced solubility. In this work, effects of processing method, polymer selection and the drug concentrations for the preparation of amorphous solid dispersion as well as prediction of drug-polymer miscibility have been studied. Hot melt extrusion (HME), rotary evaporation (Rot) and spray drying (SD) processing methods used in the study with Eudragit E 100 (EPO), HPMCAS LF and PVPVA 64 polymers. Drug concentration was another factor that was explored. The objective of this dissertation were: (1) to prepare amorphous solid dispersion of nifedipine with polymers (2) to characterize the solid dispersions (3) to determine the factors which contributes to successful amorphous solid dispersion (4) to evaluate prediction methods used to study drug and polymer miscibility and solubility (5) to use a thermodynamic prediction model to determine solubility of nifedipine at room temperature. In the first manuscript, amorphous solid dispersions of nifedipine and polymers were prepared. Physical and chemical characterizations of the solid dispersions indicated solid dispersions prepared with EPO polymer were unstable although intrinsic dissolution rates (IDR) of those samples had higher rates than those prepared with HPMCAS LF or PVPVA 64 polymers. The instability was explained by the lack of specific hydrogen bond interaction while the high IDR was explained by the low glass transition temperature (Tg) of the polymer. With lower Tg, molecular mobility would be higher and therefore the drug could dissolve at a faster rate. ANOVA analysis of factorial design showed all factors (process, polymer and drug concentration) affected the IDR. Further optimization of experiments may be necessary to determine the dominant factor for improving IDR. In the second manuscript, we have calculated three different ways to calculate the Flory-Huggins interaction parameter, χ. Although using melting point depression approach and solubility parameter of a drug and a polymer are common to estimate the miscibility of the two, there were assumptions that needed to be addressed. We have modified the melting point depression approach by calculating a better estimate of volume fractions needed to calculate the interaction parameter. In the third manuscript, we have taken a recently published thermodynamic prediction model, which can estimate the stable drug concentration that can be incorporated into an amorphous solid dispersion at room temperature, to predict the solubility of nifedipine with EPO, HPMCAS LF and PVPVA 64 polymers in amorphous solid dispersions prepared by HME, Rot and SD processes. The predictions showed less stable nifedipine concentration could be incorporated into HME processed solid dispersions than samples prepared by Rot or SD processes. Overall, nifedipinePVPVA 64 solid dispersion prepared by SD method was predicted to incorporate nifedipine concentration up to 30 % w/w.

these drugs in most cases are crystalline to amorphous solid dispersion with use of amorphous polymers to improve the solubility.
Although amorphous solid dispersion of a poorly water drug can improve the solubility, careful selection of polymer is a necessity in order to stabilize the high energy nature of the amorphous solid dispersion. Miscibility of a drug and a polymer is important. With specific interaction between the drug and the polymer, the dispersion can remain miscible much longer. Another factor that needs to be considered when formulating an amorphous solid dispersion is the amount of drug that is incorporated into the polymer. Over saturating the polymer with the drug can cause instability of the dispersion and crystallization may occur which will lead to reduced solubility.
In this work, effects of processing method, polymer selection and the drug concentrations for the preparation of amorphous solid dispersion as well as prediction of drug-polymer miscibility have been studied. Hot melt extrusion (HME), rotary evaporation (Rot) and spray drying (SD) processing methods used in the study with Eudragit E 100 (EPO), HPMCAS LF and PVPVA 64 polymers. Drug concentration was another factor that was explored.
The objective of this dissertation were: (1) to prepare amorphous solid dispersion of nifedipine with polymers (2) to characterize the solid dispersions (3) to determine the factors which contributes to successful amorphous solid dispersion (4) to evaluate prediction methods used to study drug and polymer miscibility and solubility (5) to use a thermodynamic prediction model to determine solubility of nifedipine at room temperature.
In the first manuscript, amorphous solid dispersions of nifedipine and polymers were prepared. Physical and chemical characterizations of the solid dispersions indicated solid dispersions prepared with EPO polymer were unstable although intrinsic dissolution rates (IDR) of those samples had higher rates than those prepared with HPMCAS LF or PVPVA 64 polymers. The instability was explained by the lack of specific hydrogen bond interaction while the high IDR was explained by the low glass transition temperature (T g ) of the polymer. With lower T g , molecular mobility would be higher and therefore the drug could dissolve at a faster rate. ANOVA analysis of factorial design showed all factors (process, polymer and drug concentration) affected the IDR. Further optimization of experiments may be necessary to determine the dominant factor for improving IDR.
In the second manuscript, we have calculated three different ways to calculate the Flory-Huggins interaction parameter, χ. Although using melting point depression approach and solubility parameter of a drug and a polymer are common to estimate the miscibility of the two, there were assumptions that needed to be addressed. We have modified the melting point depression approach by calculating a better estimate of volume fractions needed to calculate the interaction parameter.
In the third manuscript, we have taken a recently published thermodynamic prediction model, which can estimate the stable drug concentration that can be incorporated into an amorphous solid dispersion at room temperature, to predict the solubility of nifedipine with EPO, HPMCAS LF and PVPVA 64 polymers in amorphous solid dispersions prepared by HME, Rot and SD processes. The predictions showed less stable nifedipine concentration could be incorporated into HME processed solid dispersions than samples prepared by Rot or SD processes. Overall, nifedipine-PVPVA 64 solid dispersion prepared by SD method was predicted to incorporate nifedipine concentration up to 30 % w/w.

Introduction
Amorphous solid dispersions are one of the forms used in the pharmaceutical industry to manipulate poorly water soluble drug molecules; to improve their solubility in aqueous media and to achieve higher level of bioavailability. In an amorphous solid dispersion, the hydrophobic drug is dispersed in an amorphous hydrophilic polymer carrier by different means. The action of the polymer is twofold: to stabilize the amorphous state of the drug and to improve the dissolution of the drug (1)(2)(3)(4)(5)11). In some cases, the use of polymer have shown to prevent precipitation of the drug from a supersaturated solution created as the result of higher solubility of the amorphous form compared to the crystalline one. (6,7) In the literature, the effects of processing methods on the final product properties are rarely mentioned; for example, etravirine was processed by two different methods; via film casting, and solvent evaporation and the effects of methodologies used on the final solid dispersions were compared (7).
Weuts et al., studied the changes occurred in the melt and the spray dried powder and they found that melting process provided a higher miscibility and longer stability whereas the spray drying method was not sufficient to produce stable products (8).
Patterson et al. mentioned the differences in the drug properties obtained by quench cooling and ball milling methods. However, the effects of each method used, were different on each of the drugs used for testing (9).
Amorphous solid dispersion can be prepared by several methods such as physical manipulation (i.e. milling) (9, 10), precipitation from solvents (11), melting (9,12,13) and solvent removal (11,13). The two most commonly used amorphous processing methods in the pharmaceutical industry are melting (fusion) and solvent removal. The fusion method employs high temperatures to melt both the drug and the polymer together; disperse the drug molecules throughout the polymer matrix and quench cool the mixture by either extruding the mixture or by placing the molten mixture in an ice bath or liquid nitrogen. The solvent removal method can produce an amorphous solid dispersion by dissolving a poorly water soluble drug and a polymer in the same organic solvent. In most cases a type of alcohol is used as a solvent and then the solvent is removed by evaporation, lyophilization, vacuum drying or supercritical condition respectively.
Comparison of the effects of the processing methods, including the effects of different polymers used on the final products has been studied very little. We believe that the methods that we have selected will produce products of different characteristics. The reasoning behind this can be, for example, to investigate the differences in the rate of solvent evaporation for rotary evaporation compared to spray drying. In spray drying the solvent can evaporate from the droplets of drug-polymer combination in "milliseconds" which can lead to a successful solid dispersion (13 (11). The crystallization temperature of itraconazole reported for the two processing methods showed that the onset of crystallization for the film casted samples were lower which meant that the solid dispersions prepared by this process gave less stable products by influencing the crystallization behavior of the drug in the polymer.
In this study, amorphous solid dispersions of nifedipine (NIF), which is a calcium channel blocker, used for the treatment of high blood pressure and to control angina, with three different polymers, Eudragit E 100 [Poly(butyl methacrylate-co-(2demethylaminoeethyl) methacrylate-co-methyl methacrylate)], HPMCAS LF (hydroxypropylmethylcellulose acetate succinate), PVPVA 64 (polyvinyl pyrrolidone vinyl acetate) coprecipites. They were prepared by using hot melt extrusion (HME), spray drying (SD) and rotary evaporation (Rot). The processed formulations were analyzed for physical, thermal and chemical properties by using modulated differential scanning calorimetry (MDSC), Fourier transform infrared spectroscopy (FT-IR), powder X-ray diffraction (PXRD). The intrinsic dissolution rates were also measured to relate properties obtained with the solubility of the final product.

MATERIALS
The API (Active pharmaceutical ingredient) used was, nifedipine (NIF) purchased from RIA International (East Hanover, NJ). Eudragit E-100 (EPO) polymer which was kindly provided by Evonik (Parsippany, NJ), HPMCAS LF from Shin-Etsu Chemical   Table I lists the physical-chemical properties of the drug and the polymers.

Hot Melt Extrusion (HME)
Physical mixtures of NIF and EPO were prepared using a mortar and pestle with drug In this machine, the physical mixture went into the extruder through the funnel on the left hand side and softened with the temperature applied and extrudes out from the flush hole. The extrusion screw speed was set to 50 RPM throughout the experiments and no shear force was additionally applied to the mixture.

Rotary Evaporation (Rot)
The same physical mixtures prepared for HME were used for rotary evaporation. In this spray dryer, the solution is atomized from (1) while nitrogen is continuously supplied from (2). The atomized droplets are dried in the heated chamber (3) and are collected in the collection vessel through cyclone in (4). Smaller particles are removed from the nitrogen flow by a filter located in (5) and the gas flows out to (6) to be condensed to collect the solvent.
In our experiments, the pump speed was set to 24%, inlet temperature to 7 C, and aspirator to 90% on the control panel. The two-fluid nozzle was used to allow compressed air to disperse the pumped liquid into fine droplets. An electronic heater was used to heat the nitrogen gas which would dry the droplets to evaporate the solvent. The droplets would continue to dry in the spray cylinder and, a cyclone created, separated the particles into the collection container or into the outer filter.
Aspirator located at the end of the spray dryer was used to generate the nitrogen flow and to collect the used solvent into the cooling block.
Materials collected were transferred into an amber colored vial and were kept in desiccators until further analysis.

Modulated differential scanning calorimetry (MDSC)
NIF-polymer samples were thermally analyzed with a MDSC instrument Q2000 (TA Instruments, New Castle, DE). Samples to be scanned were weighed (6-8 mg) and placed in to aluminum pans with lids. Heating was controlled throughout the measurement and the samples were heated from room temperature up to 20-30°C above the melting point of the pure drug at a rate of 5°C/ minute unless noted otherwise. The samples were kept at the highest temperature for two minutes and then cooled down to -50°C at -50°C/minute cooling rate. The samples were kept at the lowest temperature for a maximum of 2 minutes and then heated up to 20-30 °C above the melting point of the drug.

Fourier transform-infrared spectroscopy (FT-IR)
FT-IR used was Nicolet 6700 FT-IR spectrometer (Thermo Scientific, Waltham, MA) to collect infrared spectra. The FT-IR was equipped with Smart Orbit ATR (Attenuated Total Reflection) objective lens with a diamond crystal in reflection mode. OMNIC software program was used to analyze the data.

Powder X-ray diffraction (PXRD)
PXRD was performed by using X-ray diffraction obtained with Bruker D8 XRD. The samples were analyzed using Cu, K α radiation to determine the crystalline or amorphous phases of the drugs. The X-Ray pattern was collected in the angular range of < 2θ < 40° in the step scan mode (step width 0.02°, scan rate °/ per minute).

Intrinsic dissolution rate determination (IDR)
Dissolution studies using solid dispersions samples obtained, which contained 5, 10, 20 and 40% w/w NIF and the three polymers respectively, were prepared by HME, Rot and SD, were conducted to determine the intrinsic dissolution rates. USP II apparatus with an amber vessel was used for the study.

Products Obtained with Hot Melt Extrusion (HME)
In HME, we observed significant changes at the -NH stretch and the C=O of the ester groups with the wavelength changing at 3318 cm -1 and at1676 cm -1 peaks which agrees with previous reporting (23) Table , suggesting a one-phase amorphous solid dispersion, a melting endotherm seen at 6 C which was preceded with a recrystallization peak of the NIF-EPO sample indicated thermal instability; crystallization of NIF was not apparent in the XRD data, Fig. 1-6. There was also a melting endotherm that was observed at 6 C of the NIF-HPMCAS LF sample at 40 % drug concentration, which was not preceded by a recrystallization peak. This may suggest that there were small nifedipine clusters in the solid dispersion that did not convert to amorphous form that had melted while the sample was heated in the DSC instrument, see  They were too small to be detected by the XRD.
The findings from the XRD can suggest the possible limitation of high-angle x-ray diffraction. The presence of the melting endotherm may be the result of applied heat resulted in an unstable amorphous solid dispersion by the DSC, which caused recrystallization of the drug.
When the dissolution rates of the samples obtained with HME were investigated (Table III ), it is seen that the increasing dissolution rates are obtained with increasing drug concentrations with EPO and HPMCAS LF. This is an expected finding.
However, with PVPVA 64 polymer, dissolution rates are not following the same path.
The reason may be that the high solubility of PVPVA 64 in water compared to EPO and HPMCAS LF. When the polymer engulfing the nifedipine molecules in a solid dispersion dissolves immediately, it exposes the drug molecules to the dissolution medium resulting high concentration of drug, which may be the reason of rapid crystallization and precipitation resulting lower intrinsic dissolution rate.

Products obtained with Rotary evaporation (Rot)
Rotary evaporation also caused hydrogen bonding of nifedipine with; HPMAS and PVPVA 64, see Figs. 1-8 and 1-9. However, the DSC data, with PVPVA 64, Fig 1-0, demonstrates the presence of two glass transition temperatures. The first appears at .0 C and the second at 2 . 7 C. Although the X-ray diffractions showed amorphous product at all drug concentrations, shown in Fig. 1-11, the DSC data may indicate the presence of two amorphous phases, one being the drug-rich, the other being the polymer rich regions since the change in the glass transition temperatures have shifted from a lower temperature to a higher one that is closer to the glass transition temperature of the polymer. Occurrence of two glass transition temperature regions could be the result of phase separation of the amorphous solid dispersions.
This was suggested by Rumondor et al. (16). For PVPVA polymer, dissolution rates appear to be random and not consistent with increasing drug concentration. As explained earlier, the two glass transition regions seen in Fig. 1-10, the possible phase separated nifedipine may be the cause for inconsistent trend.

Products Obtained with Spray Drying (SD)
Spray dried samples showed no interaction between nifedipine and EPO but showed strong interaction between nifedipine and PVPVA 64 at 2937 cm -1 and 1698 cm-1 .
Similar interactions were seen given in Intrinsic dissolution rates of the samples prepared with this method are given in Table   III.
Increasing EPO and HPMCAS LF increase the IDR. However PVPVA 64 at 20 and 40 % drug concentration demonstrates lower rates than the lower drug concentrations.
This could be due to the highly water-soluble nature of the PVPVA polymer that the supersaturation that is caused with the release of high concentration of nifedipine may result in a reversion of amorphous nifedipine to crystalline state. Since PVPVA 64 does not have the same inhibition property as HPMCAS LF, the released nifedipine may have crystallized in the dissolution media.
Over all , spray drying process can incorporate 20% of drug in the solid dispersion regardless of the type, molecular weight and structure of the polymers used.

Intrinsic Dissolution Rates Comparison
In Fig. 1 in terms of yielding a high intrinsic dissolution rate. Since process conditions were not optimized for preparing the amorphous solid dispersions, optimization of each process and using design of experiments may provide the answer to this question.

Discussions
The results from the IDR experiments show that NIF-EPO samples prepared by HME or SD have higher dissolution rate. The slightly acidic nature of nifedipine results in the higher intrinsic dissolution rate in an acidic aqueous medium as shown with amorphous solid dispersions prepared with EPO at all three processing methods.
Overall, the higher drug loading resulted in faster dissolution rates across all three polymers and processing methods.
The MDSC measurements, resulted with a melting endotherm appearing at the drug loading of 20%,w/w, as it is seen in NIF-EPO systems Fig. 1 should be above 50°C of the storage temperature to keep the system stable [28]. With the high molecular mobility environment, the high intrinsic dissolution rate may not translate to sustained supersaturated nifedipine solution but may result in fast precipitation of the reverted crystal nifedipine.

Conclusion
Amorphous solid dispersions of NIF with three polymers via HME, Rot and SD were made. The highest IDR was achieved when NIF-EPO sample was prepared by spray drying and second highest IDR with HME, with 40% drug loading. The reasons of the differences obtained were explained. However, these samples may not be the best candidates to proceed for formulation due to their unstable amorphous character. In that case, NIF-PVPVA 64 samples may be a better choice which the polymer has a better stabilizing ability compared to EPO polymer .

Introduction
Most of the poorly water soluble drugs have crystalline structures. Therefore they are challenging to prepare as pharmaceutical formulations due to the low solubility which leads to low bioavailability. In many cases for such a drug, this property can be the limiting factor minimizing the success of the product.
There have been numerous techniques used to formulate such drugs by improving their solubility by manipulating the morphological and other physical-chemical properties. One such technique is to prepare an amorphous solid dispersion of a drug in a water soluble polymer. Compared to the crystalline state, a drug in an amorphous state has higher solubility in a solution due to the higher energy state which is the result of greater entropy and free energy [1]. However in the amorphous form, the drug is thermodynamically unstable for the same reason.
Suitable polymers can modify crystallinity of the drug and degree of crystallization thus, improve the thermodynamic stability.
The purpose of producing an amorphous solid dispersion of a drug in an amorphous polymer is to improve the bioavailability of the drug. In this way, high therapeutic concentrations can be incorporated into the formulation. In many cases, if therapeutic concentration is high, the supersaturation state is created. Flory-Huggins interaction parameter, χ, is defined as " the thermodynamic interaction energy of a solvent and a solute" [6] and has been used as a predictive tool to determine the interaction between a drug and a polymer in the molten state.
The calculated χ can tell whether the drug will be miscible with the polymer used where (χ<0). Very little or no interaction will produce a (χ>0) value. In a strong interaction state between the drug and polymer, the amorphous mixture of the drug will remain stable much longer than if there was no interaction with the polymer.
olubility parameters, δ, show similar values for similarly structured solvents and solutes which can be used to select a better solvent for a solute to make a solution.
Solubility parameter can be used to predict the solubility of the solid drug in the polymer in the solid form.
olubility parameter, δ, is defined as the square root of cohesive energy density which is related to the change in the internal energy per volume of a substance eq. (2).

+0.34……………………………………..…( )
where χ is the interaction parameter, v is the volume of each lattice site, R is the gas constant and T is the absolute temperature. The first term is the enthalpy contribution and 0.34 is the value for entropy.
Flory-Huggins theory is based on the Gibbs free energy and it is used to determine the thermodynamic miscibility of a solute in a solvent system shown in eq. (6) ……………………………………………… (6) where entropy of mixing will usually be positive due to mixing of two components but depending on the sign of ΔH mix . The miscibility can be favored when ΔG mix is negative, where, the solute will readily solubilize in the solvent. They will not mix if ΔG mix is positive.
Eq. (5) can be rewritten to determine the interaction parameter shown in eq. (1).
In eq. (1), since the number of moles and volume fraction will always remain as positive values, the sign of the enthalpy term will be determined by the value of the interaction parameter, χ. Therefore, calculating the Flory-Huggins interaction parameter can be useful to predicting the solubility of a component in a system.

Calculations based on melting point depression
Marsac et al. [7] have argued that sometimes specific hydrogen bonding between a drug and a polymer contributes to the miscibility which cannot be distinguished by Therefore the melting point depression method was more specifically used to calculate the interaction parameter instead of using solubility parameter [7]. The idea is based on the two compounds' melting point temperature to be specific to its structure and thus mixing of the two should be predicted. The interaction parameter χ can be calculated by using the eq. (7): .…. (7) where T M is the melting point temperature of the drug in the mixture or in its pure state indicated by "mi " and "pure" respectively, ΔH fus is the heat of fusion of a drug, m is the degree of polymerization and Φ is the volume fraction.
This approach has been used quite frequently since it is a convenient and practicable because melting points can be easily determined by the differential scanning calorimeters. However, it must be mentioned that the interaction parameter, χ, is both temperature and concentration dependent which means that the value of χ can change with change in either temperature or concentration of the drug present in the polymer [6]. However, these are not taken into consideration with the melting point depression method where χ is calculated using a set of drugpolymer mixtures with decreasing drug concentrations which alters the melting point temperature in return. To obtain the interaction parameter, χ, with one set of temperature and concentration, another approach has to be taken.

Calculations based on heat of fusion
In this study, heat of fusion of the undissolved drug in the polymer will be used to determine the equilibrium solubility. Using this value we can calculate the solubility of the drug in the polymer which will be used to calculate the actual volume fraction of the dissolved drug in the drug-polymer mixture. The Flory- Huggins interaction parameter, χ, have been calculated for a drug-polymer system of nifedipine with three polymers: (Eudragit E 100, hydroxypropyl methylcellulose acetate succinate and poly (vinyl pyrrolidone vinyl acetate) by using the melting point depression approach with the actual volume fraction of drug in the mixture and one annealing temperature that is specific for one measurement at a time.
The Flory-Huggins theory eq. (6) takes into account of the size differences between a small molecule (i.e. drug) and a larger molecule (i.e. polymer) by accepting that the segments of the polymer chain are in equal size as the smaller molecule (drug). Since then, research groups have taken this work and applied to crystalline drug and amorphous polymer systems to calculate the interaction parameters [6][7][8][9][10][11][12]. The idea is that when a crystalline drug is mixed in an amorphous polymer and they are miscible, the chemical potential of the drug will be smaller than the pure drug which will be shown through a depression in the melting point of the drug in the mixture. However, it must be noted again that the interaction parameter, χ, is dependent on drug concentration (melting of the drug at a specific volume fraction) and the melting temperature of each combination. With the melting point depression approaches these two are not constant throughout which can lead to overestimated value of χ than the actual one.
In this paper, an amorphous solid dispersion of a drug and a polymer that are "miscible" means that the amorphous drug and amorphous polymer e ist as a onephase by a liquid-liquid mixing of the two components in the molten state [5].

Solubility parameter calculations
Solubility parameters of nifedipine and polymers were calculated using Eqs. Hildebrand and cott's method eq. (4) was used to calculate the interaction parameter.

Determination of χ by the use of melting point depression
In an amorphous solid dispersion, mixing of a crystalline drug which has a high melting temperature with an amorphous polymer having some miscibility with the drug, will lower the melting temperature of the drug in a mixture containing increasing amounts of polymer furthermore. Their melting point temperature should be determined individually and placed in eq. (7).

Development of formula to determine nifedipine solubility with heat of fusion measurements
In Once the solubility of nifedipine in a given polymer is determined, the interaction parameter, χ, can be further obtained by using eq. (15).

…………………………( )
The solubility parameters of the polymers and nifedipine were calculated using the Hoftyzer and Van Krevalen method and are reported in Table 2. Each solubility parameter component can be calculated using the equations shown below: In the aforementioned equation, F di is molar attraction constant due to dispersion component, F di is molar attraction constant due to dispersion component and V is the molar volume of substance.

Results
Once the solubility parameters were calculated, Flory-Huggins interaction parameters were calculated using eq. (4) and are reported in Table 2.   Table 1 show that HPMCAS LF has the highest Tg and this polymer property is dominating the miscibility of the drug-polymer mixture.
As the annealing temperature increases, the interaction parameter, χ, obtained in the heat of fusion as well as melting point depression show a decreasing trend except for nifedipine-HPMCAS LF combination around and 6 C, which could be explained by the insignificant differences created by small increase of temperature from to 6 C. When these two are grouped and compared with the interaction parameter value calculated at 30 C, the same decreasing trend can be seen.
The decreasing trend in the interaction parameter values can be explained by the increase in polymer mobility and flexibility at elevated temperatures.
Following the annealing processes of drug polymer mixtures, melting points were measured and used to calculate the interaction parameter as well shown in Table 3 under melting point depression.

Discussions
The χ values calculated by each method, heat of fusion and melting point depression as well as from solubility parameters are shown in Table 2 [17,20]. For example, the solubility parameter calculations may not be as accurate or specific to the state (crystalline vs. amorphous) of the compound as it should be and it could change with changes in the temperature of the system. Since the solubility parameter values used for the calculation were taken at a lower temperature than the annealing temperature, this discrepancy may be explained. Also it has been suggested that solubility parameter may change with the change in system's temperature [ 7] and suggested earlier, it does not differentiate specific bonding interaction that could contribute to a stable mixture [21]. With this in mind, the results obtained using the solubility parameter calculations show a deviation from the interaction parameters calculated using the other two methods. In general, χ values calculated by melting point depression were lower than the χ calculated by heat of fusion method. This could be so, because the heat of fusion method takes into consideration only the dissolved portion of the drug and only that particular amount is used to calculate the actual weight fraction. Melting point depression does not take into account the actual weight fraction of the dissolved drug which leads to a gross over estimation of solubilized drug in each drug-polymer system.
The second problem with the use of melting point depression approach is that the temperatures used to calculate χ keep changing with the change in drug fraction in each system. Since χ is temperature dependent, it would be a better choice to use one temperature setting (i.e. the heat of fusion approach) than to use a range of temperatures.
Since the melting point depression method calculates the interaction parameter from a slope where the change in temperature is plotted against the change in the fraction of the polymer, the χ obtained from the slope is neither from one temperature nor a single concentration. Therefore, the melting point depression There was a trend that could be observed with using the heat of fusion method especially with the PVPVA 64 polymer where the increase in the annealing temperature resulted in a smaller interaction parameter, χ, value whereas the melting point depression method does not show that trend but does the opposite with increasing values. This shows that the melting point depression method is not sensitive to temperature change of the system.

Conclusions
We have been able to show that by annealing a drug in a polymer before obtaining the melting point depression temperature of nifedipine in polymer systems and calculate the solubility of the drug in polymer, we can correct the overestimated volume fraction of the actual dissolved drug in the polymer. Also by using an annealing method, there is only one temperature value that was used throughout the experiment. These have been done in order to stay true to the obtaining the    forms. By dispersing the drug molecularly in a polymer matrix, given that the interaction between the drug and the polymer is not too strong, the dissolution and/ or apparent solubility of the drug which will lead to greater absorption and bioavailability of the drug can be increased [1][2][3][4][5][6][7][8].
There are two important criteria when preparing a solid dispersion of a drug in an amorphous polymer. Firstly; the drug must be molecularly miscible with the polymer. Drug concentration can also affect the stability of the drug in the system i.e. with high drug concentration, the solid dispersion becomes unstable. The equilibrium solubility of the crystalline drug will be much less than the solubility of amorphous drug. The amorphous drug will have an e perimentally determined "apparent" solubility and not an equilibrium solubility since the amorphous drug will be metastable.
There have been various approaches to understand the miscibility of a drug and a polymer in an amorphous solid dispersion [9][10][11][12][13][14]. These include measurement of the changes in the glass transition temperatures [9][10][11], determination of Flory-Huggins interaction parameter by using melting point depression method or solubility parameters [12][13][14], measuring the miscibility of a drug in a monomer or oligomer of the same polymer [14] or using a hot stage microscope to visibly determine miscibility of the melt [9]. However, there are limitations to the methods mentioned above such as: (1) Polymers used in these experiments tend to have high glass transition temperatures which reduce the molecular mobility in the solid dispersion. They will be highly viscous and may not be suitable to determine miscibility on a hot stage microscope.
(2) Determining miscibility with the use of a liquid monomer or an oligomer will limit the types of polymers that can be used to determine miscibility. Also there are assumptions that can interfere with the accuracy of such monomers, i.e. the interaction of a drug with a monomer will be the same as the drug with the polymer which could be different from drug-oligomer n this paper, the term "solubility" is referred to the solubility of a crystalline drug in a polymer as an amorphous molecular dispersion (solid form), where the chemical potential of the solid state of the drug is equal to its liquid state. "Miscibility" is referred to that amount of liquefied drug that can mix with a liquid polymer. Since the temperature at which this mixing occurs is much higher than the glass transition temperature at this condition, reaching equilibrium state is very difficult.
The solubility of a drug in a solid dispersion can be expressed with the change in the chemical potential (Δµ) of its pure form. f Δμ of the drug in the solid dispersion is lower than the Δμ of the pure drug, the drug present in the solid dispersion will dissolve fully and the final concentration of the drug will be its apparent solubility.
The term "apparent solubility" refers to a metastable or supersaturated solution which may initially contain high concentration of the drug and over time reduced concentrations that are thermodynamically stable. f Δμ of the solid dispersion is higher than that of the pure drug, then some of the drug dissolved as solid dispersion will revert back to the pure crystals in the polymer matrix and precipitate. The maximum amount of drug that can be loaded in a solid dispersion is, when μ of the drug in the solid solution is equal to μ of the drug at a solid state [10]. This is the highest stable concentration of drug in a drug-polymer matrix that can be achieved.
In addition to the methods determining miscibility of a crystalline drug with a polymer discussed, there are other methods that have been developed to estimate the drugpolymer miscibility by using Flory-Huggins solution Theory [15], which were carried out by measuring melting point depression or solubility parameter [12][13][14]. The calculation of χ according to solubility parameter and melting point depression were already explained in the previous paper [16]. However, these authors have explained the solid-solid solubility by using data obtained when both components were in the liquid state.
For predicting amorphous solubility of a drug in a solid polymer, a temperature that is close to the room temperature (2 C) should be used to mimic the real-life conditions. ot all methods used utilize this temperature. n such cases, solubility parameter (δ) can be used. The only problem in its use is that; it does not take into account the specific secondary bondings in the calculations. To incorporate information of these bondings is important since they increase miscibility of a drug with a polymer.
Another predictive method published recently, proposed a thermodynamic model to calculate the miscibility of a drug at room temperature [8].  where P is pressure.
The plot of change in Gibbs free energy versus drug concentration while normalizing each by the weight of polymer in the formulation, we will be able to obtain the slope shown in Eq. 5. Since we have different drug and polymer weight fractions for each formulation, ΔG SS should be calculated per gram of formulation. By plotting the right hand side of Eq. 6 against the drug weight fraction, the slope can be determined. Flory-Huggins interaction parameter, χ, can be determined using solubility parameter, δ, of a drug and a polymer as shown in Eq.7 which is based on Hansen's idea to correlate solubility to cohesive energy [17]. The solubility parameter can be calculated by using the method developed by van Krevelen and Hoftyzer as shown in Eq. 7 [18].
where V is molar volume per structure unit where δ is the solubility parameter and d, p and h represents dispersion, polar and hydrogen bonding, respectively. Solubility parameter components δ d , δ p and δ h can be calculated as shown in Eqs. 9-11. where F is the group contribution from dispersion where E is the molar cohesive energy. Louis, MO).

Hot melt extrusion (HME)
Physical mixtures of NIF and EPO were prepared using a mortar and pestle with drug loadings of 5, 10, 20 and 40 % w/w. The mixture was then extruded using Haake Minilab micro compounder (Thermo Scientific, Waltham, MA). The extruded material was ground and sized through a # 40 sieve. The physical mixture went into the extruder through the funnel on the left hand side and softened with the temperature applied and extrudes out from the flush hole. The extrusion screw speed was set to 50 RPM throughout the experiments and no shear force was additionally applied to the mixture.

Rotary evaporation (Rot)
The same physical mixtures prepared for HME were used for rotary evaporation. 5-10 grams of the physical mixture was dissolved in 50-100 mL of methylene chloride, with HPMCAS LF methanol had to be used as solvent, and the solvent was removed by using a rotary evaporator apparatus Büchi Rotavapor from Buchi (New Castle, DE). The samples were collected by removing the foamy film created on inside of the flask with a metal spatula and ground by using a mortar and pestle. The particles were sized through a # 40 sieve.

Spray drying (SD)
Mini hours at 40 C. The true density was measured using AccuPyc 1340 (Micrometrics, Norcross, GA) and Helium gas used as the analyzer gas with 10 repeated cycles. The true density measurements were used to determine the theoretical change in glass transition temperatures using Gordon-Taylor equation of solid dispersions and compare them to experimentally determined glass transition temperatures.
The samples were analyzed using Cu K α radiation to determine the crystalline or amorphous phases of the drugs. The X-Ray pattern was collected in the angular range of < 2θ < 40° in the step scan mode (step width 0.02°, scan rate 1°/ per minute)

Estimation of the stable drug load in a polymer mixture
The estimation for the most stable drug loads were calculated using Bellantone's method described in [8]. The Flory-Huggins interaction parameter were determined using heat of fusion method which was previously reported, melting point depression method and with the use of solubility parameters.

Results and Discussions
The Flory-Huggins interaction parameter, χ, obtained for each polymer was calculated using Eq. 6 and the results are shown in Table I. From the interaction parameter obtained with A 64, it is observed that the product has the lowest χ therefore it will show the highest miscibility. PVPVA 64 will be the most likely candidate to form a stable amorphous solid dispersion with nifedipine.
The changes in total Gibbs free energy against nifedipine weight fractions were calculated and plotted in Figs. 3-1 a- [16]. ΔG 1 and ΔG 2 were found the same in but ΔG 3 differs in each application. However, the slopes the changes appear to be very small meaning that they are not sensitive enough to detect the stable concentration. In the total change in Gibbs free energy of nifedipine-EPO solid dispersions processed by HME, shown in Fig. 3 is not the most important factor to determine the solubility of nifedipine in the polymers used as it has been suggested by Pajula et al. [12] and Marsac et al. [14].
Changes in the enthalpy and entropy of a crystalline drug to an amorphous solid dispersion may be the result of different bond modes or another translational change for the stabilization of the amorphous solid dispersions.
There are some evidence of phase separation occurring in the higher drug concentration with some of the nifedipine-polymer combinations. In Figs 3-3, 3-4, 3-8 and 3-9 which show the prediction models of solid dispersions prepared by Rot and SD for NIF-EPO and HME and Rot for NIF-PVPVA 64, there were sudden change in the slopes of ΔG/w 2 vs. drug weight fraction plots which could be the indication of existence of two separate phases [18]. At the concentration region above 20 %, amorphous nifedipine may be coexisting with crystalline nifedipine. This was confirmed with XRD analysis for 40% drug concentration of Rot processed NIF-EPO sample but not for the other samples. With the use of DSC, melting endotherms were present for 20 and 40 % Rot and SD processed NIF-EPO samples but none was present in the NIF-PVPVA 64 samples. Therefore, it is possible that phase separation of nifedipine and EPO can occur. However, NIF-PVPVA 64 solid dispersions may require further testing to confirm the existence of the two phases. Since these predictions are made for determining suitable drug concentration that will remain stable over the period of pharmaceutical products' shelf life, we need to select the drug concentration where there is only one, amorphous, phase present. ΔG 3 component which was accepted as the main variable in the former to be a small contributor compared to ΔG 1 solubility estimations, was found that its contribution was small compared to ΔG 1 .