- Email: [email protected]
solvent mixtures
Journal Pre-proofs Phase behavior of pharmaceutically relevant polymer/solvent mixtures Stefanie Dohrn, Christian Luebbert, Kristin Lehmkemper, Samuel O. Kyeremateng, Matthias Degenhardt, Gabriele Sadowski PII: DOI: Reference:
S0378-5173(20)30049-1 https://doi.org/10.1016/j.ijpharm.2020.119065 IJP 119065
To appear in:
International Journal of Pharmaceutics
Received Date: Revised Date: Accepted Date:
7 November 2019 16 January 2020 17 January 2020
Please cite this article as: S. Dohrn, C. Luebbert, K. Lehmkemper, S.O. Kyeremateng, M. Degenhardt, G. Sadowski, Phase behavior of pharmaceutically relevant polymer/solvent mixtures, International Journal of Pharmaceutics (2020), doi: https://doi.org/10.1016/j.ijpharm.2020.119065
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Elsevier B.V. All rights reserved.
Phase behavior of pharmaceutically relevant polymer/solvent mixtures Stefanie Dohrn1, Christian Luebbert1, Kristin Lehmkemper2, Samuel O. Kyeremateng2‡, Matthias Degenhardt2 and Gabriele Sadowski1* 1Department
of Biochemical and Chemical Engineering, Laboratory of Thermodynamics, TU
Dortmund University, Emil-Figge-Str. 70, D-44227 Dortmund, Germany. 2 AbbVie
Deutschland GmbH & Co. KG, Global Pharmaceutical R&D, Knollstraße, D-67061 Ludwigshafen am Rhein, Germany.
ABSTRACT
In the pharmaceutical industry, polymers are used as excipients for formulating poorly water-soluble active pharmaceutical ingredients (APIs) in so-called “amorphous solid dispersions” (ASDs). ASDs can be produced via solvent-based processes, where API and polymer are both dissolved in a solvent, followed by a solvent evaporation step (e.g. spray drying). Aiming at a homogeneous API/polymer formulation, phase separation of the components (API, polymer, solvent) during solvent evaporation must be avoided. The latter is often determined by the phase behavior of polymer/solvent mixtures used for ASD processing. Therefore, this work investigates the polymer-solvent interactions in these mixtures. Suitable polymer/solvent combinations investigated in this work comprise the pharmaceutically relevant polymers poly(vinylpyrrolidone)
1
(PVP), poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64), and hydroxyppropyl methylcellulose acetate succinate 126G (HPMCAS) as well as the solvents acetone, dichloromethane (DCM), ethanol, ethyl acetate, methanol, and water. Based on vapor-sorption experiments demixing of solvents and polymers were predicted using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). These were found to be correct for all investigated solvent/polymer mixtures. Acetone, DCM, ethanol, methanol, and water were found to be completely miscible with PVPVA64. DCM, ethanol, methanol, and water were found to be completely miscible with PVP K90, while none of the investigated solvents was appropriate for avoiding immiscibility with HPMCAS. In addition, the impact of temperature, polymer molecular weight, and solvent-mixture composition on miscibility was successfully predicted using PC-SAFT. Thus, the proposed methodology allows identifying suitable solvents or solvent mixtures relevant for solvent-based preparations of pharmaceutical ASD formulations with low experimental effort. Graphical abstract:
KEYWORDS: amorphous solid dispersion, solvent selection, HPMCAS, PVP, PVPVA64, liquid-liquid phase separation, miscibility gap, PC-SAFT
2
1
INTRODUCTION The oral drug delivery development of low water-soluble active pharmaceutical ingredients
(APIs) is a major challenge in pharmaceutical development. An established strategy to overcome this limitation is embedding the amorphous API in a polymer, generating a so-called amorphous solid dispersion (ASD) 1,2. These formulations might be produced via a solvent-based process, e.g. spray drying 3, by rapidly evaporating the solvent from a solution of both, API and polymer in a common solvent. A homogenous and stable drug product is only obtained if polymer, API, and solvent remain intimately mixed during the entire process including dissolution of the solutes and solvent evaporation. However, the selection of inappropiate solvents can lead to unwanted immiscibility of polymer and solvent resulting in two coexisting liquid phases (liquid-liquid equilibirium (LLE)) 4. Several works reported a decisive solvent-influence on the final drug product. Mugheirbi et al. reported solvent-influence on the homogeneity of the final Itraconazole/HPMC ASD and the dissolution behavior of Itraconazole 5. Costa et al. found an unexpected solvent impact on the crystallinity of praziquantel/poly(vinylpyrrolidone) formulations 6. Luebbert et al. 4 explained the solvent influence in solvent-based processed ASDs using phase diagrams of the API/polymer/solvent systems and emphasized the phase behavior of the polymer/solvent system as the main factor for API/polymer/solvent phase separation. Inhomogeneous API/polymer formulations can be the result of solvent-induced phase separation during the preparation step caused by inappropriate polymer/solvent systems used for ASD preparation. Completely miscible polymer/solvent systems do not show phase separation and were therefore found to be appropriate for solvent-based ASD processing.
3
Many polymer/solvent systems are known to undergo phase separation into two liquid phases (e.g. polystyrene/acetone 7,8). This liquid-liquid demixing of polymer/solvent systems has been successfully described by thermodynamic models accounting for the chain-like architecture of polymers, such as the Flory-Huggins theory 9,10, the lattice-cluster theory developed by Dudowicz and Freed 11, and the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) developed by Gross and Sadowski 12,15. The selection of appropriate solvents for given polymers is a typical task in polymer science, where modeling is often performed via the classic Flory-Huggins model previous works
12,19–21,
13–18.
As shown in
the thermodynamic model PC-SAFT is a better alternative to the Flory-
Huggins model, particularly for mixtures showing hydrogen-bond interactions
22.
Moreover, in
contrast to the Flory-Huggins model, PC-SAFT is an equation-of-state and thus explicitly accounts for volume changes due to mixing as well as for changes in temperature and concentration. PC-SAFT can very well describe the solubility of APIs in organic solvents
23,
water 22 and
polymers 24, the influence of humidity on API solubility in polymers 22,25, and the miscibility of API/polymer/solvent systems 4,25. For the development of HPMCAS-based ASDs, the identification of co-solvents is an important topic since this polymer is immiscible with pure solvents commonly used in pharmaceutical production. Solvent selection for these systems using the Flory-Huggins model was already discussed in literature 26,27. Duarte et al. 26 used a DCM/MeOH-mixture 80/20% w/w in case of a HPMCAS/itraconazole ASDs. Sturm et al. 28 investigated the often-used mixture of acetone and water for that purpose.
4
This work investigated the phase behavior of polymer/solvent mixtures aiming at identifying appropriate solvents and solvent mixtures of varying compositions that do not demix with a given polymer. In addition, the influence of temperature and of polymer molecular weight on the miscibility gap were assessed. PC-SAFT was used to model the solvent-vapor sorption in polymers and LLEs in polymer/solvent systems, thus being able to identify suitable pharmaceuticallyrelevant polymer/solvent mixtures and compositions to avoid immiscibility during and after ASD preparation.
2
MODELING
The thermodynamic equilibrium between two liquid phases L1 and L2 is characterized by the equality of the chemical potentials μi of each component i in the two phases according to Eq. (1). L2 μL1 i = μi
(1)
This leads to Eq.s (2) - (4) where the chemical potential of each component (polymer, solvent 1, and solvent 2 if solvent mixtures are considered) is expressed as the product of its mole fraction x and activity coefficient for each of the phases L1 and L2.
L1 L2 L2 xL1 polymer γpolymer = xpolymer γpolymer
(2)
L1 L2 L2 xL1 solvent1 γsolvent1 = xsolvent1 γsolvent1
(3)
L1 L2 L2 xL1 solvent2 γsolvent2 = xsolvent2 γsolvent2
(4)
The solvent-vapor sorption in a polymer can be calculated via Eq. (5) assuming that the investigated polymers are fully amorphous and have a negligible vapor pressure.
5
xLsolventγLsolvent = aSolvent =
psolvent pLV o, solvent
(5)
The thermodynamic activity of the solvent asolvent in the liquid phase equals the ratio of the solvent partial pressure psolvent and the vapor pressure of the pure solvent
pLV o, solvent
at given
temperature. The solvent activity of water is usually called “relative humidity” (RH). The activity coefficient i (Eq. (2)-(4)) accounts for the non-idealities in the polymer/solvent mixture and is defined as the ratio of the fugacity coefficients of component i in the mixture φLi and as pure component φLoi at given temperature and pressure (Eq. (6)): γLi
=
φLi φLoi
(6)
The fugacity coefficients φ were obtained via PC-SAFT from the residual chemical potential μres i , the Boltzmann constant kB and the compressibility factor z according to Eq. (7). ln φLi =
μres i kB T
― ln z
(7)
The residual chemical potential μres i and the compressibility factor z (Eq. (8)) are obtained from the residual Helmholtz energy ares (Eq. (9)).
z=1+ρ
μres i kB ⋅ T
=
ares +z―1+ kB ⋅ T
∂ares ∂ρ
( )
(8) T,x
ares kB ⋅ T
( )
ares kB ⋅ T
( )
( )∑( ) ∂
∂xi
∂
n
―
xj ⋅
j
(9)
∂xj
The residual Helmholtz energy ares is determined in PC-SAFT by summing up individual contributions according to Eq. (10)29.
6
(10)
ares = ahc + adisp + aassoc
The hard-chain contribution ahc accounts for the volume of the molecules and is calculated using the pure-component parameters segment number
mseg i
and segment diameter σi, the dispersion
contribution adisp accounts for van der Waals attractions of the molecules and requires the dispersion energy parameter ui/kB. Hydrogen bonding is accounted by the association contribution aassoc. Hydrogen-bond forming molecules require the number of association sites Niassoc as well as AiBi
two additional parameters, namely the association energy ε
AiBi
/kB and the association volume κ
.
To predict mixture properties, mixing rules of Berthelot-Lorenz and Wolbach-Sandler30 are used to calculate the segment diameter σij (Eq. (11)), the dispersion energy uij/kB (Eq. (12)), the crossassociation parameter εAiBj/kB (Eq. (13)), as well as the cross-association volume AiBj (Eq. (14)). 1 σij = ⋅ (σi + σj) 2
(11)
uij = (1 ― kij) ui uj
(12)
1 εAiBj = ⋅ (εAiBi + εAjBj) 2
(13)
κAiBj = κAiBi κAjBj
((
2σiiσjj σii + σjj
))
3
(14)
The binary interaction parameter kij in Eq. (12) corrects for the deviation of the dispersion energy between unlike segments from the geometric mean of the pure-component parameters and is usually determined based on experimental data of the binary system. In this work, the phase equilibria could be well described with kij values either being constant or linearly dependent on temperature according to (Eq. (15)).
7
(15)
kij = kij, m T(K) + kij, b
The kij values for solvent/polymer pairs in this work were fitted to sorption data of the solvent in the polymer, see section 4.2. The maximum absolute deviation (MAD) and average absolute deviation (AAD) of the calculated solvent sorption (in weight fractions wi) in the polymer from the experimentally-determined one was calculated according to Eq.s (16)-(17) to evaluate the accuracy of the PC-SAFT modeling.
MAD = max |wcalc, i ― wexp,i|
(16)
i, = i,nexp
1 AAD = nexp
nexp
∑ |w
(17) calc, i
― wexp, i|
i=1
All pure-component parameters used in this work are summarized in Table 1. Table 1: PC-SAFT pure-component parameters of the compounds investigated in this work
Å)
M (g/mol)
mseg/M (mol/g)
ui/kB (K)
Nassoc
PVP K2531
25700
0.0407
2.710
205.599
0
0.02
231/231
PVP K90
1220000
0.0407
2.710
205.599
0
0.02
10977/10977
PVPVA6432
65000
0.0372
2.947
205.271
0
0.02
653/653
HPMCAS22
150000
0.0489
2.889
298.047
1602.3
0.02
931/931
acetone33
58.08
0.0498
3.228
247.42
0
0.01
1/1
DCM34
84.93
0.0266
3.338
274.20
ethanol19
46.07
0.0517
3.1771
198.24
2653.4
0.0324
1/1
EtAc29
88.11
0.0401
3.3079
230.8
0
0.01
1/1
methanol19
32.04
0.0476
3.23
188.9
2899.5
0.0352
1/1
watera
18.015
0.0669
water*
353.95
2425.7
0.0451
1/1
AB
/kB (K)
AB
8
Water has a temperature-dependent segment diameter water = 2.792 + 10.11 exp(-0.01755 T)-1.417 exp(0.01146 T) 35 a
All binary interaction parameters kij used in this work are summarized in Table 2. Table 2: Binary interaction parameters kij used in this work
Polymer
Solvent
kij,b
kij,m (K-1)
Ref.
AAD (-)
MAD (-)
PVP
acetone
0.0113
0
4
PVP
DCM
-0.042
0
4
PVP
ethanol
-0.070
0
4
PVP
EtAc
0.026
0
this work
0.01
0.03
PVP
methanol
-0.130
0
this work
0.02
0.05
PVP
water
-0.1483
0
36
PVPVA64
acetone
0.015
-0.000027
this work
0.02
0.06
PVPVA64
DCM
-0.014
0
this work
0.01
0.03
PVPVA64
ethanol
-0.040
0
this work
0.02
0.04
PVPVA64
EtAc
0.014
0
this work
0.02
0.05
PVPVA64
methanol
-0.08
0
this work
0.07
0.2
PVPVA64
water
-0.156
0
24
HPMCAS
acetone
-0.045
0
this work
0.01
0.03
HPMCAS
DCM
-0.055
0
this work
0.01
0.01
HPMCAS
ethanol
-0.080
0
this work
0.004
0.008
HPMCAS
EtAc
-0.068
0
this work
0.01
0.07
HPMCAS
methanol
-0.110
0
this work
0.01
0.022
HPMCAS
water
-0.045
0
this work
0.01
0.01
water
acetone
-0.075
0
37
9
3
EXPERIMENTS
3.1
Materials
The polymers (Fig. 1) PVP with a molar mass of 1,220,000 g mol-1 (Kollidon®K90) and 25,700 g mol-1 (Kollidon®K25) and the copolymer PVPVA64 (Kollidon®VA64) with a molar mass of 65,000 g mol-1 were purchased from BASF (Ludwigshafen, Germany). PVP K12 with a molar mass of 2,500 g mol-1 was purchased from Carl Roth GmbH (Karlsruhe, Germany). HPMCAS (126 G) with a molar mass of 150,000 g mol-1 was purchased from Dow (Bomlitz, Germany). The polymers were stored in vacuum chambers to prevent water sorption from the environment. Acetone (purity 99,8%), DCM (purity 99,9%), ethanol (purity 99,99%), EtAc (purity 99,9%) and methanol (purity 99,9%) were purchased from Merck KGaA (Darmstadt, Germany). All substances were used without further purification.
Fig. 1: Chemical structures of polymers (a) PVP; (b) PVPVA64 and c) HPMCAS (126G)
3.2 3.2.1
Methods Measuring vapor sorption in polymers
The solvent vapor sorption in PVP, PVPVA64, and HPMCAS was measured using a dynamic vapor sorption (DVS) device (DVS Resolution) from Surface Measurement Systems (London,
10
UK) with an accuracy of ±0.1 µg. The solvent partial pressure was generated by mixing dry nitrogen gas (purity ≥ 99.999%) with organic vapor, using electronic mass-flow controllers and speed-of-sound sensors. The relative solvent partial pressure (pi/poiLV(T)) was adjusted in a range from 0-0.95 (Eq. (5)) at the temperature T = 25 °C. In a first step, 3-10 mg of the polymer was exposed to pure nitrogen and dried for about 500 minutes. Then the sample was exposed to a certain solvent partial pressure and the increasing sample mass was detected over time. At samplemass changes per minute smaller than 0.002 [mg min-1], thermodynamic equilibrium was assumed and the measurement at that pressure step was terminated. 3.2.2
Qualitative estimation of miscibility gaps
The occurrence of the predicted miscibility/immiscibility in the polymer/solvent systems was visually validated in solvent-screening experiments. In a stirred, temperature-controlled (accuracy ±0.1 K) glass vessel, a total of 20 g solvent and polymer was weighed in with a polymer mass fraction wpolymer = 5 wt% and stored for 4 weeks. In polymer/solvent systems with immiscibility, two liquid phases were observed visually. 3.2.3
Quantitative determination of miscibility gaps
90 wt% solvent and 10 wt% polymer were mixed with a total mass of 5 g in a sample vial, stirred for 1 week and afterwards stored for 4 weeks at 25 °C. Samples (0.3 g) from both phases were transferred into individual sample vials and weighed with an analytical balance (accuracy 0.1 mg). Solvent and polymer concentrations in the phase separated liquid phases were quantified gravimetrically. For that purpose, the solvent was evaporated by drying the samples under vacuum for 1 week. Complete evaporation was assumed when further weight loss was smaller than 0.1 mg. The mass fraction of polymer wpolymer was obtained from the weight loss upon drying, which
11
corresponds to the solvent mass (msolvent), and the residual mass corresponding to the mass of the
(
polymer (mpolymer) wpolymer =
mpolymer
).
msolvent + mPolymer
Additionally, for polymer/solvent mixtures identified to phase separate, the solvent concentration in the polymer-rich phase was determined gravimetrically by an isothermal DVS method, established in this work. For that, the DVS pan was filled with 95wt% solvent and 5 wt% polymer (about 35 mg in total) and afterwards equilibrated in the pan inside a closed glass vessel for 4 weeks at T = 25 °C undergoing phase separation in the pan. Afterwards the pan with the demixed sample was transferred into the DVS, in which the solvent partial pressure was set to zero. The time-dependent decrease of the sample mass due to solvent evaporation at T = 25 °C was measured. At the beginning of the experiment, the solvent evaporated quickly from the solvent-rich upper phase.
Fig. 2: Time-dependent mass of a demixed polymer/solvent system stored at T = 25 °C and dry condition (psolvent = 0). Light and dark branches depict the measured masses; the dashed lines illustrate the gradient change.
Fig. 2 shows the measured mass of the demixed PVP/acetone system as function of time. Two phases coexisted in the DVS pan, one being known to be approximately pure acetone4 at the top of the pan and the other being PVP-rich at the bottom of the pan (L1 and L2 in Fig. 2). At the beginning of the experiment, solvent evaporation was fast since phase L1 consisting of almost pure
12
acetone quickly evaporates at the dry conditions in the DVS. Within these first six minutes, the total sample mass decreased from the initial value of 33.312 mg to 2.121 mg. The abrupt decrease of evaporation rate or slope of the curve (in the scheme after six minutes) occurred due to the complete evaporation of acetone from the upper phase. After that, acetone started to evaporate (much slower) from the highly viscous polymer-rich phase (Phase L2). The mass at the time of gradient change is assumed to be the total mass of phase L2 in the pan. The dry polymer mass at the end of the fully drying was used to calculate the solvent amount in the polymer-rich phase L2 with following equation:
wL2, solvent =
4
massat gradient change - massdry polymer
(18)
massat gradient change
RESULTS
4.1
Vapor-sorption measurements
Time-dependent vapor sorption experiments were performed for acetone, DCM, EtAc, ethanol, methanol, and water in the polymers PVP K90, PVPVA64, and HPMCAS at solvent activities between 0.1 and 0.95. The results are listed in Table 3 and shown in Fig. 3. Table 3: Equilibrium sorption of acetone, DCM, ethanol, EtAc, methanol, and water in the three polymers PVP K90, PVPVA64 and HPMCAS at 25°C measured via dynamic vapor sorption
PVP K90 asolvent [-]
PVPVA64 wsolvent [-]
asolvent [-]
HPMCAS wsolvent [-]
asolvent [-]
wsolvent [-]
13
acetone
DCM
ethanol
EtAc
0.100
0.012
0.100
0.010
0.100
0.011
0.300
0.037
0.300
0.044
0.300
0.034
0.450
0.071
0.450
0.083
0.450
0.056
0.600
0.128
0.600
0.140
0.600
0.083
0.750
0.204
0.749
0.197
0.750
0.137
0.900
0.297
0.850
0.281
0.850
0.189
0.900
0.330
0.900
0.231
0.100
0.037
0.100
0.062
0.100
0.043
0.300
0.230
0.300
0.163
0.300
0.121
0.450
0.305
0.450
0.236
0.500
0.177
0.600
0.369
0.600
0.313
0.600
0.242
0.750
0.450
0.750
0.392
0.750
0.354
0.850
0.509
0.850
0.452
0.850
0.422
0.900
0.541
0.900
0.486
0.900
0.461
0.100
0.021
0.100
0.024
0.100
0.015
0.300
0.125
0.300
0.081
0.300
0.042
0.450
0.171
0.450
0.115
0.450
0.068
0.600
0.243
0.600
0.167
0.600
0.099
0.750
0.333
0.750
0.238
0.750
0.143
0.850
0.406
0.850
0.3011
0.850
0.189
0.900
0.472
0.900
0.343
0.900
0.221
0.100
0.004
0.100
0.003
0.100
0.021
0.300
0.012
0.300
0.013
0.300
0.059
0.450
0.021
0.450
0.042
0.450
0.094
0.600
0.036
0.600
0.104
0.600
0.133
14
methanol
water
0.750
0.063
0.750
0.153
0.750
0.190
0.950
0.133
0.850
0.204
0.850
0.251
0.900
0.251
0.900
0.294
0.100
0.058
0.100
0.036
0.100
0.016
0.300
0.132
0.300
0.083
0.300
0.042
0.450
0.183
0.450
0.120
0.450
0.063
0.600
0.233
0.600
0.157
0.600
0.085
0.750
0.281
0.750
0.196
0.750
0.107
0.850
0.333
0.850
0.222
0.900
0.144
0.900
0.429
0.900
0.237
0.083
0.040
0.082
0.020
0.092
0.005
0.277
0.095
0.276
0.050
0.293
0.015
0.426
0.149
0.426
0.078
0.440
0.023
0.577
0.201
0.576
0.12
0.583
0.038
0.731
0.272
0.730
0.185
0.727
0.064
0.833
0.341
0.833
0.253
0.820
0.099
0.885
0.393
0.886
0.307
0.867
0.129
15
Fig. 3: Experimental vapor sorption of acetone, DCM, ethanol, EtAc, methanol, and water at solvent activity steps between asolvent = 0.1 and 0.95 at 25 °C in the polymers (a) PVP K90 (b) PVPVA64 and (c) HPMCAS
Both, the time dependence of solvent uptake and the finally reached equilibrium values at each solvent activity can be seen in Fig. 3. The equilibrium was reached at the end of each sorption step when the sample mass was constant over time. As it was expected
28,38,39,
the rate of solvent
sorption as well as the amount of absorbed solvent differ for each solvent/polymer system and both increase with higher solvent activities. Especially below the glass transition, the solvent diffusion into a polymer is significantly slower than above the glass transition 38. Increasing solvent partial pressures lead to increased solvent concentrations in the polymer sample thus lowering the glass transition temperatures, which are significantly higher than room temperature for the pure polymers (PVP K90: Tg = 173 °C, PVPVA64: Tg = 111 °C, HPMCAS: Tg = 120 °C). This leads to a faster solvent sorption at higher solvent activities, which is most obvious for PVP K90/DCM, PVPK90/ethanol, PVPVA64/acetone, or PVPVA64/ethanol. Considering polymer/water systems, the sorbed amount of water increases with increasing hydrophilicity of the polymer and is therefore highest in PVP and lowest in HPMCAS, as expected from literature 32 (see Table 3). 4.2
Vapor-sorption modeling
The experimentally-determined amounts of absorbed solvent in the polymers as function of solvent activities lead to so-called sorption isotherms as illustrated for water in Fig. 4. These isotherms were modeled using PC-SAFT (Eq.(5) and parameters from Table 1) and used for fitting the binary PC-SAFT interaction parameters between polymers and solvents listed in Table 2.
16
Fig. 4: Water sorption in PVP K90 as function of water activities (relative humidities) at 25 °C. The measured timedependent water content is shown in (a), the resulting sorption isotherm is shown in (b). Symbols denote measured equilibrium points, the line in (a) is the measured time-dependent sorption and the line in (b) is the PC-SAFT calculation using Eq.(5). Dashed lines connect the sorption equilibrium points of diagram (a) with those of the sorption isotherm (b).
Fig. 4a shows the sorption of water vapor in PVP K90, experimentally determined in a wateractivity range of 0.083 < awater < 0.885 (Table 3) The PC-SAFT interaction parameter kij was fitted to these measurements (Table 2) and the vapor-sorption modeling shown in Fig. 4b is in good agreement with the experimental data (AAD = 0.0318).
Fig. 5: Solvent sorption in PVP K90 at 25 °C (a) DCM (triangles) and water (circles) determined in this work, (b) ethanol (triangles) and methanol (squares) determined in this work and literature data39 for ethanol (stars) and methanol (circles). All lines are PC-SAFT calculations using Eq. (5).
17
Fig. 5a shows experimental and modeled sorption isotherms of water and DCM in PVP K90. PVP K90 is the most hydrophilic polymer compared to PVPVA64 and HPMCAS, absorbing an amount of wwater = 0.393 at awater = 0.9 (90% RH). For the DCM sorption in PVP K90, a deviation between measurement and calculation (kij not fitted in this work) was observed at high DCM activities. This can be explained by high DCM evaporation rates inside the DVS measurement cell, leading to a slight temperature decrease during the measurement and a systematic experimental error for DCM activities aDCM > 0.6. This experimental problem is always expected for very volatile solvents, particularly at high solvent activities. At lower solvent activities, the agreement between the experiments and the PC-SAFT modeling is quite good. In Fig. 5b the sorption isotherms of ethanol, methanol in PVP measured in this work are compared to literature data 39 (PVP Mw = 10,000 g mol-1) which are in good agreement with the data measured in this work (PVP Mw = 1,220,000 g mol-1). Moreover, it can be seen that the sorption isotherms are again well described with PC-SAFT using the kij values from Table 2. 4.3
Prediction of the polymer/solvent miscibility gaps based on sorption data
After all PC-SAFT parameters have been obtained from literature (pure-component parameters) or fitted to sorption data (polymer/solvent binary parameters), the occurrence of miscibility gaps was predicted using Eq. (2). These predictions revealed complete miscibility for the systems PVP/water, PVP/DCM, PVP/ethanol, and PVP/methanol in the entire composition range at T = 25 °C.
18
Fig. 6: PVP K90/acetone at T=25°C. (a) Sorption isotherm of PVP/acetone, (b) Phase diagram of PVP/acetone with PC-SAFT predicted liquid-phase separation (LLE). Filled symbols denote experimental sorption data, half-filled symbols denote liquid-phase concentrations, measured using the sorption approach described in 3.2.3). The lines are calculated with PC-SAFT (vapor sorption ((a) and (b)) and miscibility gap (b)). The bar on the right-hand side of a) indicates a miscibility gap predicted via PC-SAFT.
Fig. 6a shows the sorption isotherm for PVP/acetone modeled with PC-SAFT by fitting the kij to the experimental data. From the sorption measurement itself it does not become clear, whether immiscibility (liquid-liquid demixing; LLE) occurs or not. However, using the same set of parameters, PC-SAFT predicts the occurrence of a huge miscibility gap indicated by a bar next to the right y-axis of Fig. 6a. The complete phase behavior of the PVP/acetone system is shown in Fig. 6b, containing the experimental vapor-sorption data and their PC-SAFT correlation as well as the predicted miscibility gap. The prediction of the latter was validated by concentration measurements in the polymer-rich liquid phase at 1 bar (see section 3.2.3). The solvent concentration in the polymer-rich phase was found to be wL1,acetone = 0.48 ± 0.02 whereas the other phase was almost pure acetone wL2,acetone ≈1. As to be seen from Fig. 6, PC-SAFT not only qualitatively predicts the occurrence of a miscibility gap in the PVP/acetone system, but even quantitatively correctly describes both the concentrations of the solvent-lean phase L1 and of the solvent-rich phase L2.
19
Fig. 7 shows the vapor-sorption isotherms in the systems PVP/acetone, PVP/EtAc, and PVPVA/EtAc as well as the PC-SAFT predicted miscibility gaps.
Fig. 7: Sorption isotherms of solvent/polymer systems at T = 25°C (a) PVP/acetone (circles) and PVP/EtAc (squares) (b) PVPVA64/EtAc (squares). Symbols are experimental data points, the lines are calculated with PC-SAFT. Bars on the right-hand sides indicate PC-SAFT predicted miscibility gaps.
Fig. 7a shows the experimental sorption isotherms of acetone and EtAc in PVP as well as the PC-SAFT correlation of these data. Moreover, PC-SAFT predicts a miscibility gap for all of these systems at solvent concentrations higher than wacetone = 0.505 for acetone and higher than wEtAc = 0.134 for EtAc. Fig. 7b shows the sorption isotherm of EtAc in PVPVA64 and a predicted miscibility gap for EtAc concentrations higher than wEtAc = 0.460.
20
Fig. 8: Sorption isotherms of the solvent/polymer systems at 25°C. (a) HPMCAS/acetone (circles), HPMCAS/DCM (triangles), HPMCAS/EtAc (squares) and HPMCAS/water (diamonds) (b) HPMCAS/ethanol (triangles) and HPMCAS/methanol (squares). Symbols are experimental data points, lines are calculated with PCSAFT. Bars on the right-hand sides indicate PC-SAFT predicted miscibility gaps.
Fig. 8a shows the sorption isotherms of HPMCAS with DCM, EtAc, acetone and water in a solvent-activity range asolvent = 0.1 to 0.9 as well as the PC-SAFT predicted miscibility gaps. The solvent-rich phases are predicted to always consist of negligibly small HPMCAS amounts (wsolvent = 0.999), while the solvent amount in the polymer-rich phases varies (wDCM = 0.577; wEtAc = 0.374; wacetone = 0.291; wwater = 0.218). Fig. 8b shows the sorption isotherms of HPMCAS with the alcohols ethanol and methanol in an activity range from asolvent = 0.1 to 0.9. The solvent amounts in the polymer-rich phase were predicted to be wethanol = 0.357 and wmethanol = 0.299 at 25°C. Table 4 summarizes the PC-SAFT predictions for miscibility gaps in the investigated polymer/solvent combinations. No phase separation was predicted for the polymer/solvent systems PVPVA64/acetone, PVPVA64/DCM, PVPVA64/ethanol, PVPVA64/methanol, PVPVA64/water, PVP K90/DCM, PVP K90/ethanol, PVP K90/methanol, PVP K90/methanol, and PVP K90/water. Therefore, acetone, DCM, ethanol, methanol and water are predicted to be appropriate solvents for preparing ASDs with PVPVA64, whereas DCM, ethanol, methanol, and water are appropriate
21
solvents for ASD preparation with PVPK90. In contrast, PC-SAFT predicts a miscibility gap for the systems PVP/acetone, PVP/EtAc, PVPVA64/EtAc, HPMCAS/DCM, HPMCAS/acetone, HPMCAS/EtAc, HPMCAS/ethanol, HPMCAS/methanol, and HPMCAS/water. Table 4: PC-SAFT calculated miscibility gaps (x) and appropriate polymer/solvent combinations () at T = 25 °C.
DCM
ethanol
methanol
water
acetone
EtAc
PVPVA64
x
PVPK90
x
x
HPMCAS
x
x
x
x
x
x
None of the investigated solvents was predicted to be completely miscible with HPMCAS and thus, all investigated solvents were found to be inappropriate for preparation of HPMCAS-based ASDs. PC-SAFT predicted miscibility gaps of EtAc with all investigated polymers which therefore seem to be rather inappropriate for solvent-based ASD production, followed by acetone which was predicted to be immiscible with PVPK90 and HPMCAS. DCM as well as the alcohols ethanol and methanol were predicted to be particularly suitable for preparing ASDs based on PVPVA64 and PVP K90. 4.4
Validation of PC-SAFT-predicted miscibility gaps
The PC-SAFT prediction for miscible/immiscible polymer/solvent combinations was experimentally validated via visual screening. This was performed for all combinations listed in Table 4 via mixing 95 wt% solvent and 5 wt% polymer. The occurrence of immiscibility was detected visually; pictures of all polymer/solvent mixtures are shown in Fig. 9.
22
Fig. 9: Validation of PC-SAFT predicted miscibility gaps for PVP K90, PVPVA64, and HPMCAS with acetone, DCM, ethanol, EtAc, methanol, and water at 25°C. The homogeneous polymer/solvent mixtures are on the left-hand side, polymer/solvent mixtures showing a miscibility gap are on the right-hand side.
The first row of Fig. 9 shows the results of the visual solvent screening for PVPVA64. PVPVA64 was found to be completely miscible with acetone, DCM, ethanol, methanol, and water and only showed immiscibility with EtAc. The solvent screening of PVP K90 (average molar mass Mw = 1,220,000 g/mol) (Fig. 9, second row) showed fully-miscible systems for the solvents DCM, ethanol, methanol, and water, whereas immiscibility occurred with acetone and EtAc. The solvent screening for HPMCAS (Fig. 9, third row) revealed that HPMCAS is immiscible with all solvents investigated. Immiscibility was either identified by two clearly separated phases (PVPVA64/EtAc, PVP/acetone, PVP/EtAc), by the occurrence of turbidity (HPMCAS/DCM, HPMCAS/ethanol, HPMCAS/methanol, HPMCAS/acetone, HPMCAS/EtAc) or by the segregation of particles at the bottom of the vial (HPMCAS/water). Although the visual appearance of the liquid coexisting
23
phases differs slightly for the investigated mixtures, the phenomenon as such was the same in all cases. Thus, the PC-SAFT prediction (Table 4) of miscibility/immiscibility was successfully validated by the experiments for all investigated solvent/polymer combinations. After the PC-SAFT predictions on immiscibility were qualitatively validated, also the predicted concentrations in the two coexisting phases were experimentally also validated. For that purpose, the PVP/acetone results of the novel sorption approach described above (section 3.2.3) were compared with results earlier
4
obtained after separating the two equilibrated liquid phases and
determining their concentrations gravimetrically, where no PVP could be quantified in the solventrich phase (wPVP≈0), while the coexisting acetone-lean phase contained wPVP = 0.485 4. The sorption approach proposed in this work resulted in an acetone concentration wacetone ≈ 0.501 which in perfect agreement with the previous measurements. The sorption approach was therewith found to be particularly advantageous for measuring the concentrations in highly-viscous polymerrich phases of a phase-separated polymer/solvent mixture containing negligible amount of polymer in the solvent-rich phase. 4.5
Influence of the polymer molecular weight on the miscibility gap
The molecular weight of the polymer significantly influences the miscibility gap of polymer/solvent systems 40. In order to investigate the influence of polymer molecular weight on the size of the miscibility gap, the miscibility gap was predicted with PC-SAFT by solving Eqs. 2-4 for different PVP molecular weights ranging from 1,000 g mol-1 to 1,220,000 g mol-1 with acetone in a temperature range of -100 °C to 250 °C (Fig. 10). The same pure-component parameters and binary parameters as given in Table 1 and Table 2 were used for this prediction. Only the PVP segment number and the number of PVP association sites were varied according to the varying molecular weights (e.g. segment number 40.7/association sites 9/9 and segment
24
number 49.654/association sites 10977/10977 for PVPs with 1,000 g mol-1 and 1,220,000 g mol-1, respectively).
Fig. 10: Miscibility gaps of PVP/acetone as function of PVP molecular weight. (a) PC-SAFT predictions for different PVP molecular weights 1:Mw = 1,220,000 g mol-1; 2: Mw = 25,700 g mol-1; 3:Mw = 8,000 g mol-1; 4: Mw = 4,000 g mol-1; 5:Mw = 3,000 g mol-1; 6:Mw = 2,500 g mol-1; 7: Mw = 1,000 g mol-1 (b) experimental validation at 25°C for PVP K90 and PVP K25 showing immiscibility and PVP K12 being fully miscible with acetone.
As shown in Fig. 10, PC-SAFT predicts that the width of the miscibility gap increases with increasing molecular weight of PVP. Low PVP molecular weights show two miscibility gaps: one at low temperatures (below the upper critical solution temperature (UCST) of 21.05 °C for PVP with 2,500 g mol-1), where the miscibility gap width decreases with increasing temperature and one at high temperatures (above the lower critical solution temperature (LCST) 240 °C for PVP with 2,500 g mol-1), where the miscibility gap width increases with increasing temperature. At room temperature (T = 25 °C), this leads to a miscibility gap for all PVP grades with molecular weights higher than 4,000 g mol-1. PVP with molecular weights ≥8,000 g/mol shows an hourglass behavior, meaning that the miscibility gap spreads over the whole temperature range, first decreasing and then increasing with increasing temperature.
25
Very small molecular weight PVP grades (Mw = 2,500 g mol-1) are expected to be completely miscible in the entire concentration range in the investigated temperature range of T = 0 °C – 50 °C. To validate the PC-SAFT predictions, samples of PVP with different molecular weights were mixed in 1:10 weight ratios with acetone and examined visually for miscibility. At room temperature, immiscibility was observed for both PVP K90 and PVP K25, while no miscibility gap was observed for PVP K12 (Fig. 10 b). The experimental data are thus in perfect agreement with the influence of the molecular weight on miscibility predicted by PC-SAFT. 4.6
Identifying appropriate solvent mixtures for avoiding miscibility gaps
From the results described above it turned out that HPMCAS is immiscible with all considered solvents. Thus, using an acetone/water solvent mixture was investigated as a promising option for the preparation of HPMCAS-based ASDs28. Fig. 11 shows the result of the PC-SAFT predictions for the phase behavior of the ternary HPMCAS/acetone/water system for entire solvent-mixture compositions at 25 °C. HPMCAS forms a wide miscibility gap with both solvents, water and acetone (see also section 4.4).
26
Fig. 11: Phase behavior of the HPMCAS/acetone/water system at T = 25°C. Gray lines are the PC-SAFT predicted tie-lines of the (gray-filled) miscibility gaps whereas predicted homogeneous region are white. Symbols are experimental feed points in the ternary mixture. Empty circles denote homogeneous mixtures; half-filled circles denote mixtures showing phase separation.
For the ternary system of HPMCAS with the two-solvent mixture, two distinct regions of immiscibility are predicted. , According to the tie lines shown in Fig. 11, the amount of HPMCAS in the solvent-rich phases is negligibly small for both regions, while the amount of HPMCAS in the polymer-rich phases depends on the composition of the solvent mixture. Furthermore, it becomes clear that HPMCAS forms homogenous solutions in solvent mixtures with water/acetone ratios between 0.3 and 0.48. For example, a mixture of 5 wt% HPMCAS, 65 wt% acetone, and 30 wt% water is predicted to be completely homogeneous. The predicted phase diagram was experimentally verified by mixing HPMCAS, water, and acetone in different ratios expected to be inside and outside of the predicted miscibility gaps. These mixtures were then controlled for turbidity as discussed in section 4.4. It was observed that those samples predicted to be located inside the miscibility gap indeed showed two phases and appeared turbid while those samples predicted to be located in the homogenous region indeed showed one
27
clear liquid phase, even those of higher HPMCAS concentrations (e.g. wHPMCAS = 0.3). Thus, the PC-SAFT prediction for the phase behavior of a solvent mixture with HPMCAS was found to be in excellent agreement with the experimental findings. Using this thermodynamic approach, it is possible to find appropriate composition of solvent mixtures for HPMCAS although it is immiscible with each of the two pure solvents. Processing of HPMCAS-based ASDs from using this solvent mixture is therefore possible as long as the mixture stays within the homogeneous region during the entire drying process.
5
CONCLUSION Unwanted phase separation needs to be avoided during the ASD production. As already shown
earlier, this demixing is strongly affected by the polymer/solvent phase behavior. Homogeneous ASDs are only prepared via solvent-based methods (e.g. spray drying), if polymer and solvent remain intimately mixed during the entire production process including dissolution of the polymer and solvent evaporation4. However, the selection of inappropiate solvents can lead to unwanted phase separation, which is often caused by the immiscibility of the polymer/solvent systems used for ASD processing. The miscibility of the technically-relevant solvents acetone, DCM, ethanol, EtAc, methanol, and water was investigated with the polymers PVP, PVPVA64, and HPMCAS to identify appropriate and
inappropriate
solvents
for
ASD
preparation.
PC-SAFT
was
used
to
predict
miscibility/immiscibility for all polymer/solvent combinations. For that purpose, PC-SAFT interaction parameters between polymers and solvents were fitted to solvent-sorption experiments. Based on the predictions, the solvents acetone, DCM, ethanol, methanol, and water were predicted to be appropriate solvents for preparing ASDs based on PVPVA64, whereas DCM, ethanol,
28
methanol, and water were found to be appropriate solvents for ASD preparation using PVPK90. Phase separation was predicted for EtAc with PVPVA64 and neither acetone nor EtAc were predicted to be appropriate solvents for ASDs based on PVPK90. None of the investigated solvents was predicted to be appropriate for preparing ASDs based on HPMCAS. For
all
investigated
solvent/polymer
combinations,
the
PC-SAFT
predictions
on
miscibility/immiscibility were found to be in qualitative and even quantitative agreement with the experiments performed in this work. Besides gravimetric measurements, the solvent-sorption approach was found to be particularly advantageous for measuring solvent concentrations in highly-viscous, polymer-rich phases of a phase-separated polymer/solvent mixture. The influence of polymer molecular weight on the miscibility gap was predicted with PC-SAFT considering PVP/acetone mixtures with different PVP molecular weights ranging from PVP K12 (2,500 g mol-1) to PVP K90 (1,220,000 g mol-1). Acetone formed the largest miscibility gap with PVP K90 followed by PVP K25 (25,700 g mol-1), whereas PVP K12 was predicted to be completely miscible with acetone. This behavior was experimentally validated at room temperature. As all investigated solvents were found to be immiscible with HPMCAS, PC-SAFT was used to predict whether acetone/water mixtures were appropriate for ASD preparation using this polymer. Although both, acetone and water were individually immiscible with HPMCAS, solvent mixtures of certain acetone/water ratios were predicted to completely dissolve HPMCAS. Again, these findings could be validated by experiments. PC-SAFT thus shows great potential for identifying appropriate solvents and solvent mixtures for ASD preparation with minimal experimental effort.
29
AUTHOR INFORMATION Corresponding Authors *Phone: +49 231 755 2635, Fax: +49 231 755 2572, E-Mail: [email protected] ‡Phone:
+49 621 589 4940, Fax: +49 621 589 3092, E-Mail:
[email protected]
DISCLOSURE This study was funded by AbbVie. AbbVie participated in the study design, research, data collection, analysis and interpretation of data, as well as writing, reviewing, and approving the publication. S.K., M.D., and K.L. are AbbVie employees and may own AbbVie stock/options. G.S. is professor, C.L. is post doc and S.D. is PhD student at the Department for Biochemical and Chemical Engineering of TU Dortmund University and they have no conflict of interest to report. ABBREVIATIONS a
Helmholtz energy [J/mol]
Ai,Bi
association sites A and B of molecule
API
active pharmaceutical ingredient
assoc
association
ASD
amorphous solid dispersion
DCM
dichloromethane
30
disp
dispersion
EtAc
ethyl acetate
hc
hard-chain
HPMCAS
Hydroxypropyl Methyl Cellulose Acetate Succinate 126G
kB
Boltzmann constant
kij
binary interaction parameter
L
liquid
LLE
liquid-liquid equilibrium
m
mass [g]
mseg
segment number
Mw
molecular weight [g mol−1]
Nassoc
number of association sites
p
pressure [bar]
PC-SAFT
perturbed-chain statistical associating fluid theory
PVP
poly(vinylpyrrolidone)
PVPVA64
poly(vinylpyrrolidone-co-vinyl acetate)
R
universal gas constant [8.1345 J mol−1 K−1]
res
residual
T
temperature [K]
u/kB
dispersion-energy parameter [K]
V
vapor
w
mass fraction
x
mole fraction
z
compressibility factor
γ
activity coefficient
µ
chemical potential
31
6
φ
fugacity coeffient
εAiBi/ kB
association-energy parameter [K]
κAiBi
association-volume parameter
ρ
density [g cm−1]
σ
segment diameter [Å]
References
(1) Leuner, C. Improving drug solubility for oral delivery using solid dispersions. Eur. J. Pharm. Biopharm. 2000, 50, 47–60. (2) Vasconcelos, T.; Marques, S.; das Neves, J.; Sarmento, B. Amorphous solid dispersions: Rational selection of a manufacturing process. Adv. Drug Delivery Rev. 2016, 100, 85–101. (3) Guy Van den Mooter. The use of amorphous solid dispersions: A formulation strategy to overcome poor solubility and dissolution rate. Drug Discovery Today 2012, 9, 79-85. (4) Luebbert, C.; Real, D.; Sadowski, G. Choosing Appropriate Solvents for ASD Preparation. Mol. Pharm. 2018, 15, 5397–5409. (5) Mugheirbi, N. A.; Mosquera-Giraldo, L. I.; Borca, C. H.; Slipchenko, L. V.; Taylor, L. S. Phase Behavior of Drug-Hydroxypropyl Methylcellulose Amorphous Solid Dispersions Produced from Various Solvent Systems: Mechanistic Understanding of the Role of Polymer using Experimental and Theoretical Methods. Mol. Pharm. 2018, 15, 3236–3251. (6) Costa, E. D.; Priotti, J.; Orlandi, S.; Leonardi, D.; Lamas, M. C.; Nunes, T. G.; Diogo, H. P.; Salomon, C. J.; Ferreira, M. J. Unexpected solvent impact in the crystallinity of praziquantel/poly(vinylpyrrolidone) formulations. A solubility, DSC and solid-state NMR study. Int. J. Pharm. 2016, 511, 983–993. (7) A. R. Shultz and P. J. Flory. Phase Equilibria in Polymer-Solvent Systems. J. Am. CHem. Soc. 1952, 74, 4760–4767.
32
(8) Pappa, G. D.; Voutsas, E. C.; Tassios, D. P. Liquid−Liquid Phase Equilibrium in Polymer−Solvent Systems: Correlation and Prediction of the Polymer Molecular Weight and the Pressure Effect. Ind. Eng. Chem. Res. 2001, 40, 4654–4663. (9) Flory, P. J. Thermodynamics of High Polymer Solutions. J. Chem. Phys. 1942, 10, 51–61. (10) Huggins, M. L. Thermodynamic properties of solutions of long-chain compounds. Ann. N. Y. Acad. Sci. 1942, XLIII, 1–32. (11) Freed, K. F. Extension of lattice cluster theory to strongly interacting, self-assembling polymeric systems. J. Chem. Phys. 2009, 130, 61103. (12) Tumakaka, F.; Gross, J.; Sadowski, G. Modeling of polymer phase equilibria using Perturbed-Chain SAFT. Fluid Phase Equilib. 2002, 194-197, 541–551. (13) Patterson, D. Polymer compatibility with and without a solvent. Polym. Eng. Sci. 1982, 22, 64–73. (14) Meng, F.; Dave, V.; Chauhan, H. Qualitative and quantitative methods to determine miscibility in amorphous drug-polymer systems. Eur. J. Pharm. Sci. 2015, 77, 106–111. (15) James S. Vrentas, J. Larry Duda, and Shan T. Hsieh. Thermodynamic properties of some amorphous polymer-solvent systems. Ind. Eng. Chem. Prod. Res. Dev. 1983, 22, 326–330. (16) Dudowicz, J.; Freed, K. F.; Douglas, J. F. Communication: Cosolvency and cononsolvency explained in terms of a Flory-Huggins type theory. J. Chem. Phys. 2015, 143, 131101. (17) Drain, K. F.; Murphy, W. R.; Otterburn, M. S. Solvents for Polypropylene: Their selection for a recycling process. Conservation & Recycling 1983, 6, 107–122. (18) Koningsveld, R. Liquid-liquid equilibria in multicomponent polymer systems. Discuss. Faraday Soc. 1970, 49, 144.
33
(19) Gross, J.; Sadowski, G. Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Ind. Eng. Chem. Res. 2002, 41, 5510–5515. (20) Tumakaka, F.; Gross, J.; Sadowski, G. Thermodynamic modeling of complex systems using PC-SAFT. Fluid Phase Equilib. 2005, 228-229, 89–98. (21) Kleiner, M.; Tumakaka, F.; Sadowski, G.; Latz, H.; Buback, M. Phase equilibria in polydisperse and associating copolymer solutions: Poly(ethene-co-(meth)acrylic acid)–monomer mixtures. Fluid Phase Equilib. 2006, 241, 113–123. (22) Lehmkemper, K.; Kyeremateng, S. O.; Heinzerling, O.; Degenhardt, M.; Sadowski, G. Impact of Polymer Type and Relative Humidity on the Long-Term Physical Stability of Amorphous Solid Dispersions. Mol. Pharm. 2017, 14, 4374–4386. (23) Ruether, F.; Sadowski, G. Modeling the solubility of pharmaceuticals in pure solvents and solvent mixtures for drug process design. J. Pharm. Sci. 2009, 98, 4205–4215. (24) Lehmkemper, K.; Kyeremateng, S. O.; Heinzerling, O.; Degenhardt, M.; Sadowski, G. Long-Term Physical Stability of PVP- and PVPVA-Amorphous Solid Dispersions. Mol. Pharm. 2017, 14, 157–171. (25) Luebbert, C.; Sadowski, G. Moisture-induced phase separation and recrystallization in amorphous solid dispersions. Int. J. Pharm. 2017, 532, 635–646. (26) Duarte, Í.; Santos, J. L.; Pinto, J. F.; Temtem, M. Screening methodologies for the development of spray-dried amorphous solid dispersions. Pharm. Res. 2015, 32, 222–237. (27) Newman, A. Pharmaceutical Amorphous Solid Dispersions; John Wiley & Sons, Inc 2015. (28) Sturm, D. R.; Chiu, S.-W.; Moser, J. D.; Danner, R. P. Solubility of water and acetone in hypromellose acetate succinate, HPMCAS-L. Fluid Phase Equilib. 2016, 429, 227–232.
34
(29) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244–1260. (30) Wolbach, J. P.; Sandler, S. I. Using Molecular Orbital Calculations To Describe the Phase Behavior of Cross-associating Mixtures. Ind. Eng. Chem. Res. 1998, 37, 2917–2928. (31) Ji, Y.; Paus, R.; Prudic, A.; Lübbert, C.; Sadowski, G. A Novel Approach for Analyzing the Dissolution Mechanism of Solid Dispersions. Pharm. Res. 2015, 32, 2559–2578. (32) Lehmkemper, K.; Kyeremateng, S. O.; Degenhardt, M.; Sadowski, G. Influence of LowMolecular-Weight Excipients on the Phase Behavior of PVPVA64 Amorphous Solid Dispersions. Pharm. Res. 2018, 35, 25. (33) Tumakaka, F.; Sadowski, G. Application of the Perturbed-Chain SAFT equation of state to polar systems. Fluid Phase Equilib. 2004, 217, 233–239. (34) Tihic, A.; Kontogeorgis, G. M.; Solms, N. von; Michelsen, M. L. Applications of the simplified perturbed-chain SAFT equation of state using an extended parameter table. Fluid Phase Equilib. 2006, 248, 29–43. (35) Fuchs, D.; Fischer, J.; Tumakaka, F.; Sadowski, G. Solubility of Amino Acids: Influence of the pH value and the Addition of Alcoholic Cosolvents on Aqueous Solubility. Ind. Eng. Chem. Res. 2006, 45, 6578–6584. (36) Prudic, A.; Ji, Y.; Luebbert, C.; Sadowski, G. Influence of humidity on the phase behavior of API/polymer formulations. Eur. J. Pharm. Biopharm. 2015, 94, 352–362. (37) Cassens, J. Modellierung thermodynamischer Eigenschaften pharmazeutischer Substanzen in Lösungsmitteln und Lösungsmittelgemischen. PhD thesis, TU Dortmund, Dortmund, 2013. (38) Krüger, K.-M.; Sadowski, G. Fickian and Non-Fickian Sorption Kinetics of Toluene in Glassy Polystyrene. Macromolecules 2005, 38, 8408–8417.
35
(39) Zafarani-Moattar, M. T.; Samadi, F. Determination of Solvent Activity in Poly(vinylpyrolidone) + Methanol, + Ethanol, + 2-Propanol, + and 1-Butanol Solutions at 25 °C. J. Chem. Eng. Data 2004, 49, 1475–1478. (40) Siow, K. S.; Delmas, G.; Patterson, D. Cloud-Point Curves in Polymer Solutions with Adjacent Upper and Lower Critical Solution Temperatures. Macromolecules 1972, 5, 29–34.
36
Stefanie Dohrn: Conceptualization, Methodology, Investigation, Writing- Original Draft, Visualization, Formal analysis Christian Luebbert: Methodology, Conceptualization, Writing: Review and editing, Kristin Lehmkemper: Conceptualization, Writing: Review and editing, Formal analysis Samuel O. Kyeremateng: Conceptualization, Writing: Review and editing, Funding acquisition, Supervision Matthias Degenhardt: Writing: Review and editing, Funding acquisition, Resources Gabriele Sadowski: Software, Data Curation, Project Administration, Resources, Writing: Review and editing, Supervision.
37
Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
38
S0378-5173(20)30049-1 https://doi.org/10.1016/j.ijpharm.2020.119065 IJP 119065
To appear in:
International Journal of Pharmaceutics
Received Date: Revised Date: Accepted Date:
7 November 2019 16 January 2020 17 January 2020
Please cite this article as: S. Dohrn, C. Luebbert, K. Lehmkemper, S.O. Kyeremateng, M. Degenhardt, G. Sadowski, Phase behavior of pharmaceutically relevant polymer/solvent mixtures, International Journal of Pharmaceutics (2020), doi: https://doi.org/10.1016/j.ijpharm.2020.119065
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Elsevier B.V. All rights reserved.
Phase behavior of pharmaceutically relevant polymer/solvent mixtures Stefanie Dohrn1, Christian Luebbert1, Kristin Lehmkemper2, Samuel O. Kyeremateng2‡, Matthias Degenhardt2 and Gabriele Sadowski1* 1Department
of Biochemical and Chemical Engineering, Laboratory of Thermodynamics, TU
Dortmund University, Emil-Figge-Str. 70, D-44227 Dortmund, Germany. 2 AbbVie
Deutschland GmbH & Co. KG, Global Pharmaceutical R&D, Knollstraße, D-67061 Ludwigshafen am Rhein, Germany.
ABSTRACT
In the pharmaceutical industry, polymers are used as excipients for formulating poorly water-soluble active pharmaceutical ingredients (APIs) in so-called “amorphous solid dispersions” (ASDs). ASDs can be produced via solvent-based processes, where API and polymer are both dissolved in a solvent, followed by a solvent evaporation step (e.g. spray drying). Aiming at a homogeneous API/polymer formulation, phase separation of the components (API, polymer, solvent) during solvent evaporation must be avoided. The latter is often determined by the phase behavior of polymer/solvent mixtures used for ASD processing. Therefore, this work investigates the polymer-solvent interactions in these mixtures. Suitable polymer/solvent combinations investigated in this work comprise the pharmaceutically relevant polymers poly(vinylpyrrolidone)
1
(PVP), poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64), and hydroxyppropyl methylcellulose acetate succinate 126G (HPMCAS) as well as the solvents acetone, dichloromethane (DCM), ethanol, ethyl acetate, methanol, and water. Based on vapor-sorption experiments demixing of solvents and polymers were predicted using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). These were found to be correct for all investigated solvent/polymer mixtures. Acetone, DCM, ethanol, methanol, and water were found to be completely miscible with PVPVA64. DCM, ethanol, methanol, and water were found to be completely miscible with PVP K90, while none of the investigated solvents was appropriate for avoiding immiscibility with HPMCAS. In addition, the impact of temperature, polymer molecular weight, and solvent-mixture composition on miscibility was successfully predicted using PC-SAFT. Thus, the proposed methodology allows identifying suitable solvents or solvent mixtures relevant for solvent-based preparations of pharmaceutical ASD formulations with low experimental effort. Graphical abstract:
KEYWORDS: amorphous solid dispersion, solvent selection, HPMCAS, PVP, PVPVA64, liquid-liquid phase separation, miscibility gap, PC-SAFT
2
1
INTRODUCTION The oral drug delivery development of low water-soluble active pharmaceutical ingredients
(APIs) is a major challenge in pharmaceutical development. An established strategy to overcome this limitation is embedding the amorphous API in a polymer, generating a so-called amorphous solid dispersion (ASD) 1,2. These formulations might be produced via a solvent-based process, e.g. spray drying 3, by rapidly evaporating the solvent from a solution of both, API and polymer in a common solvent. A homogenous and stable drug product is only obtained if polymer, API, and solvent remain intimately mixed during the entire process including dissolution of the solutes and solvent evaporation. However, the selection of inappropiate solvents can lead to unwanted immiscibility of polymer and solvent resulting in two coexisting liquid phases (liquid-liquid equilibirium (LLE)) 4. Several works reported a decisive solvent-influence on the final drug product. Mugheirbi et al. reported solvent-influence on the homogeneity of the final Itraconazole/HPMC ASD and the dissolution behavior of Itraconazole 5. Costa et al. found an unexpected solvent impact on the crystallinity of praziquantel/poly(vinylpyrrolidone) formulations 6. Luebbert et al. 4 explained the solvent influence in solvent-based processed ASDs using phase diagrams of the API/polymer/solvent systems and emphasized the phase behavior of the polymer/solvent system as the main factor for API/polymer/solvent phase separation. Inhomogeneous API/polymer formulations can be the result of solvent-induced phase separation during the preparation step caused by inappropriate polymer/solvent systems used for ASD preparation. Completely miscible polymer/solvent systems do not show phase separation and were therefore found to be appropriate for solvent-based ASD processing.
3
Many polymer/solvent systems are known to undergo phase separation into two liquid phases (e.g. polystyrene/acetone 7,8). This liquid-liquid demixing of polymer/solvent systems has been successfully described by thermodynamic models accounting for the chain-like architecture of polymers, such as the Flory-Huggins theory 9,10, the lattice-cluster theory developed by Dudowicz and Freed 11, and the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) developed by Gross and Sadowski 12,15. The selection of appropriate solvents for given polymers is a typical task in polymer science, where modeling is often performed via the classic Flory-Huggins model previous works
12,19–21,
13–18.
As shown in
the thermodynamic model PC-SAFT is a better alternative to the Flory-
Huggins model, particularly for mixtures showing hydrogen-bond interactions
22.
Moreover, in
contrast to the Flory-Huggins model, PC-SAFT is an equation-of-state and thus explicitly accounts for volume changes due to mixing as well as for changes in temperature and concentration. PC-SAFT can very well describe the solubility of APIs in organic solvents
23,
water 22 and
polymers 24, the influence of humidity on API solubility in polymers 22,25, and the miscibility of API/polymer/solvent systems 4,25. For the development of HPMCAS-based ASDs, the identification of co-solvents is an important topic since this polymer is immiscible with pure solvents commonly used in pharmaceutical production. Solvent selection for these systems using the Flory-Huggins model was already discussed in literature 26,27. Duarte et al. 26 used a DCM/MeOH-mixture 80/20% w/w in case of a HPMCAS/itraconazole ASDs. Sturm et al. 28 investigated the often-used mixture of acetone and water for that purpose.
4
This work investigated the phase behavior of polymer/solvent mixtures aiming at identifying appropriate solvents and solvent mixtures of varying compositions that do not demix with a given polymer. In addition, the influence of temperature and of polymer molecular weight on the miscibility gap were assessed. PC-SAFT was used to model the solvent-vapor sorption in polymers and LLEs in polymer/solvent systems, thus being able to identify suitable pharmaceuticallyrelevant polymer/solvent mixtures and compositions to avoid immiscibility during and after ASD preparation.
2
MODELING
The thermodynamic equilibrium between two liquid phases L1 and L2 is characterized by the equality of the chemical potentials μi of each component i in the two phases according to Eq. (1). L2 μL1 i = μi
(1)
This leads to Eq.s (2) - (4) where the chemical potential of each component (polymer, solvent 1, and solvent 2 if solvent mixtures are considered) is expressed as the product of its mole fraction x and activity coefficient for each of the phases L1 and L2.
L1 L2 L2 xL1 polymer γpolymer = xpolymer γpolymer
(2)
L1 L2 L2 xL1 solvent1 γsolvent1 = xsolvent1 γsolvent1
(3)
L1 L2 L2 xL1 solvent2 γsolvent2 = xsolvent2 γsolvent2
(4)
The solvent-vapor sorption in a polymer can be calculated via Eq. (5) assuming that the investigated polymers are fully amorphous and have a negligible vapor pressure.
5
xLsolventγLsolvent = aSolvent =
psolvent pLV o, solvent
(5)
The thermodynamic activity of the solvent asolvent in the liquid phase equals the ratio of the solvent partial pressure psolvent and the vapor pressure of the pure solvent
pLV o, solvent
at given
temperature. The solvent activity of water is usually called “relative humidity” (RH). The activity coefficient i (Eq. (2)-(4)) accounts for the non-idealities in the polymer/solvent mixture and is defined as the ratio of the fugacity coefficients of component i in the mixture φLi and as pure component φLoi at given temperature and pressure (Eq. (6)): γLi
=
φLi φLoi
(6)
The fugacity coefficients φ were obtained via PC-SAFT from the residual chemical potential μres i , the Boltzmann constant kB and the compressibility factor z according to Eq. (7). ln φLi =
μres i kB T
― ln z
(7)
The residual chemical potential μres i and the compressibility factor z (Eq. (8)) are obtained from the residual Helmholtz energy ares (Eq. (9)).
z=1+ρ
μres i kB ⋅ T
=
ares +z―1+ kB ⋅ T
∂ares ∂ρ
( )
(8) T,x
ares kB ⋅ T
( )
ares kB ⋅ T
( )
( )∑( ) ∂
∂xi
∂
n
―
xj ⋅
j
(9)
∂xj
The residual Helmholtz energy ares is determined in PC-SAFT by summing up individual contributions according to Eq. (10)29.
6
(10)
ares = ahc + adisp + aassoc
The hard-chain contribution ahc accounts for the volume of the molecules and is calculated using the pure-component parameters segment number
mseg i
and segment diameter σi, the dispersion
contribution adisp accounts for van der Waals attractions of the molecules and requires the dispersion energy parameter ui/kB. Hydrogen bonding is accounted by the association contribution aassoc. Hydrogen-bond forming molecules require the number of association sites Niassoc as well as AiBi
two additional parameters, namely the association energy ε
AiBi
/kB and the association volume κ
.
To predict mixture properties, mixing rules of Berthelot-Lorenz and Wolbach-Sandler30 are used to calculate the segment diameter σij (Eq. (11)), the dispersion energy uij/kB (Eq. (12)), the crossassociation parameter εAiBj/kB (Eq. (13)), as well as the cross-association volume AiBj (Eq. (14)). 1 σij = ⋅ (σi + σj) 2
(11)
uij = (1 ― kij) ui uj
(12)
1 εAiBj = ⋅ (εAiBi + εAjBj) 2
(13)
κAiBj = κAiBi κAjBj
((
2σiiσjj σii + σjj
))
3
(14)
The binary interaction parameter kij in Eq. (12) corrects for the deviation of the dispersion energy between unlike segments from the geometric mean of the pure-component parameters and is usually determined based on experimental data of the binary system. In this work, the phase equilibria could be well described with kij values either being constant or linearly dependent on temperature according to (Eq. (15)).
7
(15)
kij = kij, m T(K) + kij, b
The kij values for solvent/polymer pairs in this work were fitted to sorption data of the solvent in the polymer, see section 4.2. The maximum absolute deviation (MAD) and average absolute deviation (AAD) of the calculated solvent sorption (in weight fractions wi) in the polymer from the experimentally-determined one was calculated according to Eq.s (16)-(17) to evaluate the accuracy of the PC-SAFT modeling.
MAD = max |wcalc, i ― wexp,i|
(16)
i, = i,nexp
1 AAD = nexp
nexp
∑ |w
(17) calc, i
― wexp, i|
i=1
All pure-component parameters used in this work are summarized in Table 1. Table 1: PC-SAFT pure-component parameters of the compounds investigated in this work
Å)
M (g/mol)
mseg/M (mol/g)
ui/kB (K)
Nassoc
PVP K2531
25700
0.0407
2.710
205.599
0
0.02
231/231
PVP K90
1220000
0.0407
2.710
205.599
0
0.02
10977/10977
PVPVA6432
65000
0.0372
2.947
205.271
0
0.02
653/653
HPMCAS22
150000
0.0489
2.889
298.047
1602.3
0.02
931/931
acetone33
58.08
0.0498
3.228
247.42
0
0.01
1/1
DCM34
84.93
0.0266
3.338
274.20
ethanol19
46.07
0.0517
3.1771
198.24
2653.4
0.0324
1/1
EtAc29
88.11
0.0401
3.3079
230.8
0
0.01
1/1
methanol19
32.04
0.0476
3.23
188.9
2899.5
0.0352
1/1
watera
18.015
0.0669
water*
353.95
2425.7
0.0451
1/1
AB
/kB (K)
AB
8
Water has a temperature-dependent segment diameter water = 2.792 + 10.11 exp(-0.01755 T)-1.417 exp(0.01146 T) 35 a
All binary interaction parameters kij used in this work are summarized in Table 2. Table 2: Binary interaction parameters kij used in this work
Polymer
Solvent
kij,b
kij,m (K-1)
Ref.
AAD (-)
MAD (-)
PVP
acetone
0.0113
0
4
PVP
DCM
-0.042
0
4
PVP
ethanol
-0.070
0
4
PVP
EtAc
0.026
0
this work
0.01
0.03
PVP
methanol
-0.130
0
this work
0.02
0.05
PVP
water
-0.1483
0
36
PVPVA64
acetone
0.015
-0.000027
this work
0.02
0.06
PVPVA64
DCM
-0.014
0
this work
0.01
0.03
PVPVA64
ethanol
-0.040
0
this work
0.02
0.04
PVPVA64
EtAc
0.014
0
this work
0.02
0.05
PVPVA64
methanol
-0.08
0
this work
0.07
0.2
PVPVA64
water
-0.156
0
24
HPMCAS
acetone
-0.045
0
this work
0.01
0.03
HPMCAS
DCM
-0.055
0
this work
0.01
0.01
HPMCAS
ethanol
-0.080
0
this work
0.004
0.008
HPMCAS
EtAc
-0.068
0
this work
0.01
0.07
HPMCAS
methanol
-0.110
0
this work
0.01
0.022
HPMCAS
water
-0.045
0
this work
0.01
0.01
water
acetone
-0.075
0
37
9
3
EXPERIMENTS
3.1
Materials
The polymers (Fig. 1) PVP with a molar mass of 1,220,000 g mol-1 (Kollidon®K90) and 25,700 g mol-1 (Kollidon®K25) and the copolymer PVPVA64 (Kollidon®VA64) with a molar mass of 65,000 g mol-1 were purchased from BASF (Ludwigshafen, Germany). PVP K12 with a molar mass of 2,500 g mol-1 was purchased from Carl Roth GmbH (Karlsruhe, Germany). HPMCAS (126 G) with a molar mass of 150,000 g mol-1 was purchased from Dow (Bomlitz, Germany). The polymers were stored in vacuum chambers to prevent water sorption from the environment. Acetone (purity 99,8%), DCM (purity 99,9%), ethanol (purity 99,99%), EtAc (purity 99,9%) and methanol (purity 99,9%) were purchased from Merck KGaA (Darmstadt, Germany). All substances were used without further purification.
Fig. 1: Chemical structures of polymers (a) PVP; (b) PVPVA64 and c) HPMCAS (126G)
3.2 3.2.1
Methods Measuring vapor sorption in polymers
The solvent vapor sorption in PVP, PVPVA64, and HPMCAS was measured using a dynamic vapor sorption (DVS) device (DVS Resolution) from Surface Measurement Systems (London,
10
UK) with an accuracy of ±0.1 µg. The solvent partial pressure was generated by mixing dry nitrogen gas (purity ≥ 99.999%) with organic vapor, using electronic mass-flow controllers and speed-of-sound sensors. The relative solvent partial pressure (pi/poiLV(T)) was adjusted in a range from 0-0.95 (Eq. (5)) at the temperature T = 25 °C. In a first step, 3-10 mg of the polymer was exposed to pure nitrogen and dried for about 500 minutes. Then the sample was exposed to a certain solvent partial pressure and the increasing sample mass was detected over time. At samplemass changes per minute smaller than 0.002 [mg min-1], thermodynamic equilibrium was assumed and the measurement at that pressure step was terminated. 3.2.2
Qualitative estimation of miscibility gaps
The occurrence of the predicted miscibility/immiscibility in the polymer/solvent systems was visually validated in solvent-screening experiments. In a stirred, temperature-controlled (accuracy ±0.1 K) glass vessel, a total of 20 g solvent and polymer was weighed in with a polymer mass fraction wpolymer = 5 wt% and stored for 4 weeks. In polymer/solvent systems with immiscibility, two liquid phases were observed visually. 3.2.3
Quantitative determination of miscibility gaps
90 wt% solvent and 10 wt% polymer were mixed with a total mass of 5 g in a sample vial, stirred for 1 week and afterwards stored for 4 weeks at 25 °C. Samples (0.3 g) from both phases were transferred into individual sample vials and weighed with an analytical balance (accuracy 0.1 mg). Solvent and polymer concentrations in the phase separated liquid phases were quantified gravimetrically. For that purpose, the solvent was evaporated by drying the samples under vacuum for 1 week. Complete evaporation was assumed when further weight loss was smaller than 0.1 mg. The mass fraction of polymer wpolymer was obtained from the weight loss upon drying, which
11
corresponds to the solvent mass (msolvent), and the residual mass corresponding to the mass of the
(
polymer (mpolymer) wpolymer =
mpolymer
).
msolvent + mPolymer
Additionally, for polymer/solvent mixtures identified to phase separate, the solvent concentration in the polymer-rich phase was determined gravimetrically by an isothermal DVS method, established in this work. For that, the DVS pan was filled with 95wt% solvent and 5 wt% polymer (about 35 mg in total) and afterwards equilibrated in the pan inside a closed glass vessel for 4 weeks at T = 25 °C undergoing phase separation in the pan. Afterwards the pan with the demixed sample was transferred into the DVS, in which the solvent partial pressure was set to zero. The time-dependent decrease of the sample mass due to solvent evaporation at T = 25 °C was measured. At the beginning of the experiment, the solvent evaporated quickly from the solvent-rich upper phase.
Fig. 2: Time-dependent mass of a demixed polymer/solvent system stored at T = 25 °C and dry condition (psolvent = 0). Light and dark branches depict the measured masses; the dashed lines illustrate the gradient change.
Fig. 2 shows the measured mass of the demixed PVP/acetone system as function of time. Two phases coexisted in the DVS pan, one being known to be approximately pure acetone4 at the top of the pan and the other being PVP-rich at the bottom of the pan (L1 and L2 in Fig. 2). At the beginning of the experiment, solvent evaporation was fast since phase L1 consisting of almost pure
12
acetone quickly evaporates at the dry conditions in the DVS. Within these first six minutes, the total sample mass decreased from the initial value of 33.312 mg to 2.121 mg. The abrupt decrease of evaporation rate or slope of the curve (in the scheme after six minutes) occurred due to the complete evaporation of acetone from the upper phase. After that, acetone started to evaporate (much slower) from the highly viscous polymer-rich phase (Phase L2). The mass at the time of gradient change is assumed to be the total mass of phase L2 in the pan. The dry polymer mass at the end of the fully drying was used to calculate the solvent amount in the polymer-rich phase L2 with following equation:
wL2, solvent =
4
massat gradient change - massdry polymer
(18)
massat gradient change
RESULTS
4.1
Vapor-sorption measurements
Time-dependent vapor sorption experiments were performed for acetone, DCM, EtAc, ethanol, methanol, and water in the polymers PVP K90, PVPVA64, and HPMCAS at solvent activities between 0.1 and 0.95. The results are listed in Table 3 and shown in Fig. 3. Table 3: Equilibrium sorption of acetone, DCM, ethanol, EtAc, methanol, and water in the three polymers PVP K90, PVPVA64 and HPMCAS at 25°C measured via dynamic vapor sorption
PVP K90 asolvent [-]
PVPVA64 wsolvent [-]
asolvent [-]
HPMCAS wsolvent [-]
asolvent [-]
wsolvent [-]
13
acetone
DCM
ethanol
EtAc
0.100
0.012
0.100
0.010
0.100
0.011
0.300
0.037
0.300
0.044
0.300
0.034
0.450
0.071
0.450
0.083
0.450
0.056
0.600
0.128
0.600
0.140
0.600
0.083
0.750
0.204
0.749
0.197
0.750
0.137
0.900
0.297
0.850
0.281
0.850
0.189
0.900
0.330
0.900
0.231
0.100
0.037
0.100
0.062
0.100
0.043
0.300
0.230
0.300
0.163
0.300
0.121
0.450
0.305
0.450
0.236
0.500
0.177
0.600
0.369
0.600
0.313
0.600
0.242
0.750
0.450
0.750
0.392
0.750
0.354
0.850
0.509
0.850
0.452
0.850
0.422
0.900
0.541
0.900
0.486
0.900
0.461
0.100
0.021
0.100
0.024
0.100
0.015
0.300
0.125
0.300
0.081
0.300
0.042
0.450
0.171
0.450
0.115
0.450
0.068
0.600
0.243
0.600
0.167
0.600
0.099
0.750
0.333
0.750
0.238
0.750
0.143
0.850
0.406
0.850
0.3011
0.850
0.189
0.900
0.472
0.900
0.343
0.900
0.221
0.100
0.004
0.100
0.003
0.100
0.021
0.300
0.012
0.300
0.013
0.300
0.059
0.450
0.021
0.450
0.042
0.450
0.094
0.600
0.036
0.600
0.104
0.600
0.133
14
methanol
water
0.750
0.063
0.750
0.153
0.750
0.190
0.950
0.133
0.850
0.204
0.850
0.251
0.900
0.251
0.900
0.294
0.100
0.058
0.100
0.036
0.100
0.016
0.300
0.132
0.300
0.083
0.300
0.042
0.450
0.183
0.450
0.120
0.450
0.063
0.600
0.233
0.600
0.157
0.600
0.085
0.750
0.281
0.750
0.196
0.750
0.107
0.850
0.333
0.850
0.222
0.900
0.144
0.900
0.429
0.900
0.237
0.083
0.040
0.082
0.020
0.092
0.005
0.277
0.095
0.276
0.050
0.293
0.015
0.426
0.149
0.426
0.078
0.440
0.023
0.577
0.201
0.576
0.12
0.583
0.038
0.731
0.272
0.730
0.185
0.727
0.064
0.833
0.341
0.833
0.253
0.820
0.099
0.885
0.393
0.886
0.307
0.867
0.129
15
Fig. 3: Experimental vapor sorption of acetone, DCM, ethanol, EtAc, methanol, and water at solvent activity steps between asolvent = 0.1 and 0.95 at 25 °C in the polymers (a) PVP K90 (b) PVPVA64 and (c) HPMCAS
Both, the time dependence of solvent uptake and the finally reached equilibrium values at each solvent activity can be seen in Fig. 3. The equilibrium was reached at the end of each sorption step when the sample mass was constant over time. As it was expected
28,38,39,
the rate of solvent
sorption as well as the amount of absorbed solvent differ for each solvent/polymer system and both increase with higher solvent activities. Especially below the glass transition, the solvent diffusion into a polymer is significantly slower than above the glass transition 38. Increasing solvent partial pressures lead to increased solvent concentrations in the polymer sample thus lowering the glass transition temperatures, which are significantly higher than room temperature for the pure polymers (PVP K90: Tg = 173 °C, PVPVA64: Tg = 111 °C, HPMCAS: Tg = 120 °C). This leads to a faster solvent sorption at higher solvent activities, which is most obvious for PVP K90/DCM, PVPK90/ethanol, PVPVA64/acetone, or PVPVA64/ethanol. Considering polymer/water systems, the sorbed amount of water increases with increasing hydrophilicity of the polymer and is therefore highest in PVP and lowest in HPMCAS, as expected from literature 32 (see Table 3). 4.2
Vapor-sorption modeling
The experimentally-determined amounts of absorbed solvent in the polymers as function of solvent activities lead to so-called sorption isotherms as illustrated for water in Fig. 4. These isotherms were modeled using PC-SAFT (Eq.(5) and parameters from Table 1) and used for fitting the binary PC-SAFT interaction parameters between polymers and solvents listed in Table 2.
16
Fig. 4: Water sorption in PVP K90 as function of water activities (relative humidities) at 25 °C. The measured timedependent water content is shown in (a), the resulting sorption isotherm is shown in (b). Symbols denote measured equilibrium points, the line in (a) is the measured time-dependent sorption and the line in (b) is the PC-SAFT calculation using Eq.(5). Dashed lines connect the sorption equilibrium points of diagram (a) with those of the sorption isotherm (b).
Fig. 4a shows the sorption of water vapor in PVP K90, experimentally determined in a wateractivity range of 0.083 < awater < 0.885 (Table 3) The PC-SAFT interaction parameter kij was fitted to these measurements (Table 2) and the vapor-sorption modeling shown in Fig. 4b is in good agreement with the experimental data (AAD = 0.0318).
Fig. 5: Solvent sorption in PVP K90 at 25 °C (a) DCM (triangles) and water (circles) determined in this work, (b) ethanol (triangles) and methanol (squares) determined in this work and literature data39 for ethanol (stars) and methanol (circles). All lines are PC-SAFT calculations using Eq. (5).
17
Fig. 5a shows experimental and modeled sorption isotherms of water and DCM in PVP K90. PVP K90 is the most hydrophilic polymer compared to PVPVA64 and HPMCAS, absorbing an amount of wwater = 0.393 at awater = 0.9 (90% RH). For the DCM sorption in PVP K90, a deviation between measurement and calculation (kij not fitted in this work) was observed at high DCM activities. This can be explained by high DCM evaporation rates inside the DVS measurement cell, leading to a slight temperature decrease during the measurement and a systematic experimental error for DCM activities aDCM > 0.6. This experimental problem is always expected for very volatile solvents, particularly at high solvent activities. At lower solvent activities, the agreement between the experiments and the PC-SAFT modeling is quite good. In Fig. 5b the sorption isotherms of ethanol, methanol in PVP measured in this work are compared to literature data 39 (PVP Mw = 10,000 g mol-1) which are in good agreement with the data measured in this work (PVP Mw = 1,220,000 g mol-1). Moreover, it can be seen that the sorption isotherms are again well described with PC-SAFT using the kij values from Table 2. 4.3
Prediction of the polymer/solvent miscibility gaps based on sorption data
After all PC-SAFT parameters have been obtained from literature (pure-component parameters) or fitted to sorption data (polymer/solvent binary parameters), the occurrence of miscibility gaps was predicted using Eq. (2). These predictions revealed complete miscibility for the systems PVP/water, PVP/DCM, PVP/ethanol, and PVP/methanol in the entire composition range at T = 25 °C.
18
Fig. 6: PVP K90/acetone at T=25°C. (a) Sorption isotherm of PVP/acetone, (b) Phase diagram of PVP/acetone with PC-SAFT predicted liquid-phase separation (LLE). Filled symbols denote experimental sorption data, half-filled symbols denote liquid-phase concentrations, measured using the sorption approach described in 3.2.3). The lines are calculated with PC-SAFT (vapor sorption ((a) and (b)) and miscibility gap (b)). The bar on the right-hand side of a) indicates a miscibility gap predicted via PC-SAFT.
Fig. 6a shows the sorption isotherm for PVP/acetone modeled with PC-SAFT by fitting the kij to the experimental data. From the sorption measurement itself it does not become clear, whether immiscibility (liquid-liquid demixing; LLE) occurs or not. However, using the same set of parameters, PC-SAFT predicts the occurrence of a huge miscibility gap indicated by a bar next to the right y-axis of Fig. 6a. The complete phase behavior of the PVP/acetone system is shown in Fig. 6b, containing the experimental vapor-sorption data and their PC-SAFT correlation as well as the predicted miscibility gap. The prediction of the latter was validated by concentration measurements in the polymer-rich liquid phase at 1 bar (see section 3.2.3). The solvent concentration in the polymer-rich phase was found to be wL1,acetone = 0.48 ± 0.02 whereas the other phase was almost pure acetone wL2,acetone ≈1. As to be seen from Fig. 6, PC-SAFT not only qualitatively predicts the occurrence of a miscibility gap in the PVP/acetone system, but even quantitatively correctly describes both the concentrations of the solvent-lean phase L1 and of the solvent-rich phase L2.
19
Fig. 7 shows the vapor-sorption isotherms in the systems PVP/acetone, PVP/EtAc, and PVPVA/EtAc as well as the PC-SAFT predicted miscibility gaps.
Fig. 7: Sorption isotherms of solvent/polymer systems at T = 25°C (a) PVP/acetone (circles) and PVP/EtAc (squares) (b) PVPVA64/EtAc (squares). Symbols are experimental data points, the lines are calculated with PC-SAFT. Bars on the right-hand sides indicate PC-SAFT predicted miscibility gaps.
Fig. 7a shows the experimental sorption isotherms of acetone and EtAc in PVP as well as the PC-SAFT correlation of these data. Moreover, PC-SAFT predicts a miscibility gap for all of these systems at solvent concentrations higher than wacetone = 0.505 for acetone and higher than wEtAc = 0.134 for EtAc. Fig. 7b shows the sorption isotherm of EtAc in PVPVA64 and a predicted miscibility gap for EtAc concentrations higher than wEtAc = 0.460.
20
Fig. 8: Sorption isotherms of the solvent/polymer systems at 25°C. (a) HPMCAS/acetone (circles), HPMCAS/DCM (triangles), HPMCAS/EtAc (squares) and HPMCAS/water (diamonds) (b) HPMCAS/ethanol (triangles) and HPMCAS/methanol (squares). Symbols are experimental data points, lines are calculated with PCSAFT. Bars on the right-hand sides indicate PC-SAFT predicted miscibility gaps.
Fig. 8a shows the sorption isotherms of HPMCAS with DCM, EtAc, acetone and water in a solvent-activity range asolvent = 0.1 to 0.9 as well as the PC-SAFT predicted miscibility gaps. The solvent-rich phases are predicted to always consist of negligibly small HPMCAS amounts (wsolvent = 0.999), while the solvent amount in the polymer-rich phases varies (wDCM = 0.577; wEtAc = 0.374; wacetone = 0.291; wwater = 0.218). Fig. 8b shows the sorption isotherms of HPMCAS with the alcohols ethanol and methanol in an activity range from asolvent = 0.1 to 0.9. The solvent amounts in the polymer-rich phase were predicted to be wethanol = 0.357 and wmethanol = 0.299 at 25°C. Table 4 summarizes the PC-SAFT predictions for miscibility gaps in the investigated polymer/solvent combinations. No phase separation was predicted for the polymer/solvent systems PVPVA64/acetone, PVPVA64/DCM, PVPVA64/ethanol, PVPVA64/methanol, PVPVA64/water, PVP K90/DCM, PVP K90/ethanol, PVP K90/methanol, PVP K90/methanol, and PVP K90/water. Therefore, acetone, DCM, ethanol, methanol and water are predicted to be appropriate solvents for preparing ASDs with PVPVA64, whereas DCM, ethanol, methanol, and water are appropriate
21
solvents for ASD preparation with PVPK90. In contrast, PC-SAFT predicts a miscibility gap for the systems PVP/acetone, PVP/EtAc, PVPVA64/EtAc, HPMCAS/DCM, HPMCAS/acetone, HPMCAS/EtAc, HPMCAS/ethanol, HPMCAS/methanol, and HPMCAS/water. Table 4: PC-SAFT calculated miscibility gaps (x) and appropriate polymer/solvent combinations () at T = 25 °C.
DCM
ethanol
methanol
water
acetone
EtAc
PVPVA64
x
PVPK90
x
x
HPMCAS
x
x
x
x
x
x
None of the investigated solvents was predicted to be completely miscible with HPMCAS and thus, all investigated solvents were found to be inappropriate for preparation of HPMCAS-based ASDs. PC-SAFT predicted miscibility gaps of EtAc with all investigated polymers which therefore seem to be rather inappropriate for solvent-based ASD production, followed by acetone which was predicted to be immiscible with PVPK90 and HPMCAS. DCM as well as the alcohols ethanol and methanol were predicted to be particularly suitable for preparing ASDs based on PVPVA64 and PVP K90. 4.4
Validation of PC-SAFT-predicted miscibility gaps
The PC-SAFT prediction for miscible/immiscible polymer/solvent combinations was experimentally validated via visual screening. This was performed for all combinations listed in Table 4 via mixing 95 wt% solvent and 5 wt% polymer. The occurrence of immiscibility was detected visually; pictures of all polymer/solvent mixtures are shown in Fig. 9.
22
Fig. 9: Validation of PC-SAFT predicted miscibility gaps for PVP K90, PVPVA64, and HPMCAS with acetone, DCM, ethanol, EtAc, methanol, and water at 25°C. The homogeneous polymer/solvent mixtures are on the left-hand side, polymer/solvent mixtures showing a miscibility gap are on the right-hand side.
The first row of Fig. 9 shows the results of the visual solvent screening for PVPVA64. PVPVA64 was found to be completely miscible with acetone, DCM, ethanol, methanol, and water and only showed immiscibility with EtAc. The solvent screening of PVP K90 (average molar mass Mw = 1,220,000 g/mol) (Fig. 9, second row) showed fully-miscible systems for the solvents DCM, ethanol, methanol, and water, whereas immiscibility occurred with acetone and EtAc. The solvent screening for HPMCAS (Fig. 9, third row) revealed that HPMCAS is immiscible with all solvents investigated. Immiscibility was either identified by two clearly separated phases (PVPVA64/EtAc, PVP/acetone, PVP/EtAc), by the occurrence of turbidity (HPMCAS/DCM, HPMCAS/ethanol, HPMCAS/methanol, HPMCAS/acetone, HPMCAS/EtAc) or by the segregation of particles at the bottom of the vial (HPMCAS/water). Although the visual appearance of the liquid coexisting
23
phases differs slightly for the investigated mixtures, the phenomenon as such was the same in all cases. Thus, the PC-SAFT prediction (Table 4) of miscibility/immiscibility was successfully validated by the experiments for all investigated solvent/polymer combinations. After the PC-SAFT predictions on immiscibility were qualitatively validated, also the predicted concentrations in the two coexisting phases were experimentally also validated. For that purpose, the PVP/acetone results of the novel sorption approach described above (section 3.2.3) were compared with results earlier
4
obtained after separating the two equilibrated liquid phases and
determining their concentrations gravimetrically, where no PVP could be quantified in the solventrich phase (wPVP≈0), while the coexisting acetone-lean phase contained wPVP = 0.485 4. The sorption approach proposed in this work resulted in an acetone concentration wacetone ≈ 0.501 which in perfect agreement with the previous measurements. The sorption approach was therewith found to be particularly advantageous for measuring the concentrations in highly-viscous polymerrich phases of a phase-separated polymer/solvent mixture containing negligible amount of polymer in the solvent-rich phase. 4.5
Influence of the polymer molecular weight on the miscibility gap
The molecular weight of the polymer significantly influences the miscibility gap of polymer/solvent systems 40. In order to investigate the influence of polymer molecular weight on the size of the miscibility gap, the miscibility gap was predicted with PC-SAFT by solving Eqs. 2-4 for different PVP molecular weights ranging from 1,000 g mol-1 to 1,220,000 g mol-1 with acetone in a temperature range of -100 °C to 250 °C (Fig. 10). The same pure-component parameters and binary parameters as given in Table 1 and Table 2 were used for this prediction. Only the PVP segment number and the number of PVP association sites were varied according to the varying molecular weights (e.g. segment number 40.7/association sites 9/9 and segment
24
number 49.654/association sites 10977/10977 for PVPs with 1,000 g mol-1 and 1,220,000 g mol-1, respectively).
Fig. 10: Miscibility gaps of PVP/acetone as function of PVP molecular weight. (a) PC-SAFT predictions for different PVP molecular weights 1:Mw = 1,220,000 g mol-1; 2: Mw = 25,700 g mol-1; 3:Mw = 8,000 g mol-1; 4: Mw = 4,000 g mol-1; 5:Mw = 3,000 g mol-1; 6:Mw = 2,500 g mol-1; 7: Mw = 1,000 g mol-1 (b) experimental validation at 25°C for PVP K90 and PVP K25 showing immiscibility and PVP K12 being fully miscible with acetone.
As shown in Fig. 10, PC-SAFT predicts that the width of the miscibility gap increases with increasing molecular weight of PVP. Low PVP molecular weights show two miscibility gaps: one at low temperatures (below the upper critical solution temperature (UCST) of 21.05 °C for PVP with 2,500 g mol-1), where the miscibility gap width decreases with increasing temperature and one at high temperatures (above the lower critical solution temperature (LCST) 240 °C for PVP with 2,500 g mol-1), where the miscibility gap width increases with increasing temperature. At room temperature (T = 25 °C), this leads to a miscibility gap for all PVP grades with molecular weights higher than 4,000 g mol-1. PVP with molecular weights ≥8,000 g/mol shows an hourglass behavior, meaning that the miscibility gap spreads over the whole temperature range, first decreasing and then increasing with increasing temperature.
25
Very small molecular weight PVP grades (Mw = 2,500 g mol-1) are expected to be completely miscible in the entire concentration range in the investigated temperature range of T = 0 °C – 50 °C. To validate the PC-SAFT predictions, samples of PVP with different molecular weights were mixed in 1:10 weight ratios with acetone and examined visually for miscibility. At room temperature, immiscibility was observed for both PVP K90 and PVP K25, while no miscibility gap was observed for PVP K12 (Fig. 10 b). The experimental data are thus in perfect agreement with the influence of the molecular weight on miscibility predicted by PC-SAFT. 4.6
Identifying appropriate solvent mixtures for avoiding miscibility gaps
From the results described above it turned out that HPMCAS is immiscible with all considered solvents. Thus, using an acetone/water solvent mixture was investigated as a promising option for the preparation of HPMCAS-based ASDs28. Fig. 11 shows the result of the PC-SAFT predictions for the phase behavior of the ternary HPMCAS/acetone/water system for entire solvent-mixture compositions at 25 °C. HPMCAS forms a wide miscibility gap with both solvents, water and acetone (see also section 4.4).
26
Fig. 11: Phase behavior of the HPMCAS/acetone/water system at T = 25°C. Gray lines are the PC-SAFT predicted tie-lines of the (gray-filled) miscibility gaps whereas predicted homogeneous region are white. Symbols are experimental feed points in the ternary mixture. Empty circles denote homogeneous mixtures; half-filled circles denote mixtures showing phase separation.
For the ternary system of HPMCAS with the two-solvent mixture, two distinct regions of immiscibility are predicted. , According to the tie lines shown in Fig. 11, the amount of HPMCAS in the solvent-rich phases is negligibly small for both regions, while the amount of HPMCAS in the polymer-rich phases depends on the composition of the solvent mixture. Furthermore, it becomes clear that HPMCAS forms homogenous solutions in solvent mixtures with water/acetone ratios between 0.3 and 0.48. For example, a mixture of 5 wt% HPMCAS, 65 wt% acetone, and 30 wt% water is predicted to be completely homogeneous. The predicted phase diagram was experimentally verified by mixing HPMCAS, water, and acetone in different ratios expected to be inside and outside of the predicted miscibility gaps. These mixtures were then controlled for turbidity as discussed in section 4.4. It was observed that those samples predicted to be located inside the miscibility gap indeed showed two phases and appeared turbid while those samples predicted to be located in the homogenous region indeed showed one
27
clear liquid phase, even those of higher HPMCAS concentrations (e.g. wHPMCAS = 0.3). Thus, the PC-SAFT prediction for the phase behavior of a solvent mixture with HPMCAS was found to be in excellent agreement with the experimental findings. Using this thermodynamic approach, it is possible to find appropriate composition of solvent mixtures for HPMCAS although it is immiscible with each of the two pure solvents. Processing of HPMCAS-based ASDs from using this solvent mixture is therefore possible as long as the mixture stays within the homogeneous region during the entire drying process.
5
CONCLUSION Unwanted phase separation needs to be avoided during the ASD production. As already shown
earlier, this demixing is strongly affected by the polymer/solvent phase behavior. Homogeneous ASDs are only prepared via solvent-based methods (e.g. spray drying), if polymer and solvent remain intimately mixed during the entire production process including dissolution of the polymer and solvent evaporation4. However, the selection of inappropiate solvents can lead to unwanted phase separation, which is often caused by the immiscibility of the polymer/solvent systems used for ASD processing. The miscibility of the technically-relevant solvents acetone, DCM, ethanol, EtAc, methanol, and water was investigated with the polymers PVP, PVPVA64, and HPMCAS to identify appropriate and
inappropriate
solvents
for
ASD
preparation.
PC-SAFT
was
used
to
predict
miscibility/immiscibility for all polymer/solvent combinations. For that purpose, PC-SAFT interaction parameters between polymers and solvents were fitted to solvent-sorption experiments. Based on the predictions, the solvents acetone, DCM, ethanol, methanol, and water were predicted to be appropriate solvents for preparing ASDs based on PVPVA64, whereas DCM, ethanol,
28
methanol, and water were found to be appropriate solvents for ASD preparation using PVPK90. Phase separation was predicted for EtAc with PVPVA64 and neither acetone nor EtAc were predicted to be appropriate solvents for ASDs based on PVPK90. None of the investigated solvents was predicted to be appropriate for preparing ASDs based on HPMCAS. For
all
investigated
solvent/polymer
combinations,
the
PC-SAFT
predictions
on
miscibility/immiscibility were found to be in qualitative and even quantitative agreement with the experiments performed in this work. Besides gravimetric measurements, the solvent-sorption approach was found to be particularly advantageous for measuring solvent concentrations in highly-viscous, polymer-rich phases of a phase-separated polymer/solvent mixture. The influence of polymer molecular weight on the miscibility gap was predicted with PC-SAFT considering PVP/acetone mixtures with different PVP molecular weights ranging from PVP K12 (2,500 g mol-1) to PVP K90 (1,220,000 g mol-1). Acetone formed the largest miscibility gap with PVP K90 followed by PVP K25 (25,700 g mol-1), whereas PVP K12 was predicted to be completely miscible with acetone. This behavior was experimentally validated at room temperature. As all investigated solvents were found to be immiscible with HPMCAS, PC-SAFT was used to predict whether acetone/water mixtures were appropriate for ASD preparation using this polymer. Although both, acetone and water were individually immiscible with HPMCAS, solvent mixtures of certain acetone/water ratios were predicted to completely dissolve HPMCAS. Again, these findings could be validated by experiments. PC-SAFT thus shows great potential for identifying appropriate solvents and solvent mixtures for ASD preparation with minimal experimental effort.
29
AUTHOR INFORMATION Corresponding Authors *Phone: +49 231 755 2635, Fax: +49 231 755 2572, E-Mail: [email protected] ‡Phone:
+49 621 589 4940, Fax: +49 621 589 3092, E-Mail:
[email protected]
DISCLOSURE This study was funded by AbbVie. AbbVie participated in the study design, research, data collection, analysis and interpretation of data, as well as writing, reviewing, and approving the publication. S.K., M.D., and K.L. are AbbVie employees and may own AbbVie stock/options. G.S. is professor, C.L. is post doc and S.D. is PhD student at the Department for Biochemical and Chemical Engineering of TU Dortmund University and they have no conflict of interest to report. ABBREVIATIONS a
Helmholtz energy [J/mol]
Ai,Bi
association sites A and B of molecule
API
active pharmaceutical ingredient
assoc
association
ASD
amorphous solid dispersion
DCM
dichloromethane
30
disp
dispersion
EtAc
ethyl acetate
hc
hard-chain
HPMCAS
Hydroxypropyl Methyl Cellulose Acetate Succinate 126G
kB
Boltzmann constant
kij
binary interaction parameter
L
liquid
LLE
liquid-liquid equilibrium
m
mass [g]
mseg
segment number
Mw
molecular weight [g mol−1]
Nassoc
number of association sites
p
pressure [bar]
PC-SAFT
perturbed-chain statistical associating fluid theory
PVP
poly(vinylpyrrolidone)
PVPVA64
poly(vinylpyrrolidone-co-vinyl acetate)
R
universal gas constant [8.1345 J mol−1 K−1]
res
residual
T
temperature [K]
u/kB
dispersion-energy parameter [K]
V
vapor
w
mass fraction
x
mole fraction
z
compressibility factor
γ
activity coefficient
µ
chemical potential
31
6
φ
fugacity coeffient
εAiBi/ kB
association-energy parameter [K]
κAiBi
association-volume parameter
ρ
density [g cm−1]
σ
segment diameter [Å]
References
(1) Leuner, C. Improving drug solubility for oral delivery using solid dispersions. Eur. J. Pharm. Biopharm. 2000, 50, 47–60. (2) Vasconcelos, T.; Marques, S.; das Neves, J.; Sarmento, B. Amorphous solid dispersions: Rational selection of a manufacturing process. Adv. Drug Delivery Rev. 2016, 100, 85–101. (3) Guy Van den Mooter. The use of amorphous solid dispersions: A formulation strategy to overcome poor solubility and dissolution rate. Drug Discovery Today 2012, 9, 79-85. (4) Luebbert, C.; Real, D.; Sadowski, G. Choosing Appropriate Solvents for ASD Preparation. Mol. Pharm. 2018, 15, 5397–5409. (5) Mugheirbi, N. A.; Mosquera-Giraldo, L. I.; Borca, C. H.; Slipchenko, L. V.; Taylor, L. S. Phase Behavior of Drug-Hydroxypropyl Methylcellulose Amorphous Solid Dispersions Produced from Various Solvent Systems: Mechanistic Understanding of the Role of Polymer using Experimental and Theoretical Methods. Mol. Pharm. 2018, 15, 3236–3251. (6) Costa, E. D.; Priotti, J.; Orlandi, S.; Leonardi, D.; Lamas, M. C.; Nunes, T. G.; Diogo, H. P.; Salomon, C. J.; Ferreira, M. J. Unexpected solvent impact in the crystallinity of praziquantel/poly(vinylpyrrolidone) formulations. A solubility, DSC and solid-state NMR study. Int. J. Pharm. 2016, 511, 983–993. (7) A. R. Shultz and P. J. Flory. Phase Equilibria in Polymer-Solvent Systems. J. Am. CHem. Soc. 1952, 74, 4760–4767.
32
(8) Pappa, G. D.; Voutsas, E. C.; Tassios, D. P. Liquid−Liquid Phase Equilibrium in Polymer−Solvent Systems: Correlation and Prediction of the Polymer Molecular Weight and the Pressure Effect. Ind. Eng. Chem. Res. 2001, 40, 4654–4663. (9) Flory, P. J. Thermodynamics of High Polymer Solutions. J. Chem. Phys. 1942, 10, 51–61. (10) Huggins, M. L. Thermodynamic properties of solutions of long-chain compounds. Ann. N. Y. Acad. Sci. 1942, XLIII, 1–32. (11) Freed, K. F. Extension of lattice cluster theory to strongly interacting, self-assembling polymeric systems. J. Chem. Phys. 2009, 130, 61103. (12) Tumakaka, F.; Gross, J.; Sadowski, G. Modeling of polymer phase equilibria using Perturbed-Chain SAFT. Fluid Phase Equilib. 2002, 194-197, 541–551. (13) Patterson, D. Polymer compatibility with and without a solvent. Polym. Eng. Sci. 1982, 22, 64–73. (14) Meng, F.; Dave, V.; Chauhan, H. Qualitative and quantitative methods to determine miscibility in amorphous drug-polymer systems. Eur. J. Pharm. Sci. 2015, 77, 106–111. (15) James S. Vrentas, J. Larry Duda, and Shan T. Hsieh. Thermodynamic properties of some amorphous polymer-solvent systems. Ind. Eng. Chem. Prod. Res. Dev. 1983, 22, 326–330. (16) Dudowicz, J.; Freed, K. F.; Douglas, J. F. Communication: Cosolvency and cononsolvency explained in terms of a Flory-Huggins type theory. J. Chem. Phys. 2015, 143, 131101. (17) Drain, K. F.; Murphy, W. R.; Otterburn, M. S. Solvents for Polypropylene: Their selection for a recycling process. Conservation & Recycling 1983, 6, 107–122. (18) Koningsveld, R. Liquid-liquid equilibria in multicomponent polymer systems. Discuss. Faraday Soc. 1970, 49, 144.
33
(19) Gross, J.; Sadowski, G. Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Ind. Eng. Chem. Res. 2002, 41, 5510–5515. (20) Tumakaka, F.; Gross, J.; Sadowski, G. Thermodynamic modeling of complex systems using PC-SAFT. Fluid Phase Equilib. 2005, 228-229, 89–98. (21) Kleiner, M.; Tumakaka, F.; Sadowski, G.; Latz, H.; Buback, M. Phase equilibria in polydisperse and associating copolymer solutions: Poly(ethene-co-(meth)acrylic acid)–monomer mixtures. Fluid Phase Equilib. 2006, 241, 113–123. (22) Lehmkemper, K.; Kyeremateng, S. O.; Heinzerling, O.; Degenhardt, M.; Sadowski, G. Impact of Polymer Type and Relative Humidity on the Long-Term Physical Stability of Amorphous Solid Dispersions. Mol. Pharm. 2017, 14, 4374–4386. (23) Ruether, F.; Sadowski, G. Modeling the solubility of pharmaceuticals in pure solvents and solvent mixtures for drug process design. J. Pharm. Sci. 2009, 98, 4205–4215. (24) Lehmkemper, K.; Kyeremateng, S. O.; Heinzerling, O.; Degenhardt, M.; Sadowski, G. Long-Term Physical Stability of PVP- and PVPVA-Amorphous Solid Dispersions. Mol. Pharm. 2017, 14, 157–171. (25) Luebbert, C.; Sadowski, G. Moisture-induced phase separation and recrystallization in amorphous solid dispersions. Int. J. Pharm. 2017, 532, 635–646. (26) Duarte, Í.; Santos, J. L.; Pinto, J. F.; Temtem, M. Screening methodologies for the development of spray-dried amorphous solid dispersions. Pharm. Res. 2015, 32, 222–237. (27) Newman, A. Pharmaceutical Amorphous Solid Dispersions; John Wiley & Sons, Inc 2015. (28) Sturm, D. R.; Chiu, S.-W.; Moser, J. D.; Danner, R. P. Solubility of water and acetone in hypromellose acetate succinate, HPMCAS-L. Fluid Phase Equilib. 2016, 429, 227–232.
34
(29) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244–1260. (30) Wolbach, J. P.; Sandler, S. I. Using Molecular Orbital Calculations To Describe the Phase Behavior of Cross-associating Mixtures. Ind. Eng. Chem. Res. 1998, 37, 2917–2928. (31) Ji, Y.; Paus, R.; Prudic, A.; Lübbert, C.; Sadowski, G. A Novel Approach for Analyzing the Dissolution Mechanism of Solid Dispersions. Pharm. Res. 2015, 32, 2559–2578. (32) Lehmkemper, K.; Kyeremateng, S. O.; Degenhardt, M.; Sadowski, G. Influence of LowMolecular-Weight Excipients on the Phase Behavior of PVPVA64 Amorphous Solid Dispersions. Pharm. Res. 2018, 35, 25. (33) Tumakaka, F.; Sadowski, G. Application of the Perturbed-Chain SAFT equation of state to polar systems. Fluid Phase Equilib. 2004, 217, 233–239. (34) Tihic, A.; Kontogeorgis, G. M.; Solms, N. von; Michelsen, M. L. Applications of the simplified perturbed-chain SAFT equation of state using an extended parameter table. Fluid Phase Equilib. 2006, 248, 29–43. (35) Fuchs, D.; Fischer, J.; Tumakaka, F.; Sadowski, G. Solubility of Amino Acids: Influence of the pH value and the Addition of Alcoholic Cosolvents on Aqueous Solubility. Ind. Eng. Chem. Res. 2006, 45, 6578–6584. (36) Prudic, A.; Ji, Y.; Luebbert, C.; Sadowski, G. Influence of humidity on the phase behavior of API/polymer formulations. Eur. J. Pharm. Biopharm. 2015, 94, 352–362. (37) Cassens, J. Modellierung thermodynamischer Eigenschaften pharmazeutischer Substanzen in Lösungsmitteln und Lösungsmittelgemischen. PhD thesis, TU Dortmund, Dortmund, 2013. (38) Krüger, K.-M.; Sadowski, G. Fickian and Non-Fickian Sorption Kinetics of Toluene in Glassy Polystyrene. Macromolecules 2005, 38, 8408–8417.
35
(39) Zafarani-Moattar, M. T.; Samadi, F. Determination of Solvent Activity in Poly(vinylpyrolidone) + Methanol, + Ethanol, + 2-Propanol, + and 1-Butanol Solutions at 25 °C. J. Chem. Eng. Data 2004, 49, 1475–1478. (40) Siow, K. S.; Delmas, G.; Patterson, D. Cloud-Point Curves in Polymer Solutions with Adjacent Upper and Lower Critical Solution Temperatures. Macromolecules 1972, 5, 29–34.
36
Stefanie Dohrn: Conceptualization, Methodology, Investigation, Writing- Original Draft, Visualization, Formal analysis Christian Luebbert: Methodology, Conceptualization, Writing: Review and editing, Kristin Lehmkemper: Conceptualization, Writing: Review and editing, Formal analysis Samuel O. Kyeremateng: Conceptualization, Writing: Review and editing, Funding acquisition, Supervision Matthias Degenhardt: Writing: Review and editing, Funding acquisition, Resources Gabriele Sadowski: Software, Data Curation, Project Administration, Resources, Writing: Review and editing, Supervision.
37
Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
38