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Influence of polymeric excipients on the solubility of aspirin: Experimental measurement and model prediction
Journal Pre-proof Influence of polymeric excipients on the solubility of aspirin: Experimental measurement and model prediction Dongxu Wu, Yuanhui Ji PII:
S0378-3812(19)30512-6
DOI:
https://doi.org/10.1016/j.fluid.2019.112450
Reference:
FLUID 112450
To appear in:
Fluid Phase Equilibria
Received Date: 10 August 2019 Revised Date:
25 December 2019
Accepted Date: 30 December 2019
Please cite this article as: D. Wu, Y. Ji, Influence of polymeric excipients on the solubility of aspirin: Experimental measurement and model prediction, Fluid Phase Equilibria (2020), doi: https:// doi.org/10.1016/j.fluid.2019.112450. 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. © 2019 Published by Elsevier B.V.
Dongxu Wu: Writing - Original Draft, Methodology, Data Curation , Formal analysis Yuanhui Ji *: Writing - Review & Editing, Conceptualization, Supervision, Resources
Model Prediction Comparison
Solubilization Effect
UNIQUAC> NRTL>Wilson
Ternary System
0.0025
xcal(mol/mol)
0.0020
Water Excipients
API
0.0015
0.0010
0.0005
0.0000 0.0000
0.0005
0.0010
0.0015
xexp(mol/mol)
0.0020
0.0025
Influence of Polymeric Excipients on the Solubility of Aspirin: Experimental Measurement and Model Prediction Dongxu Wu, Yuanhui Ji *
Jiangsu Province Hi-Tech Key Laboratory for Biomedical Research, School of Chemistry and Chemical Engineering, Southeast University, Nanjing, 211189, People’s Republic of China
KEYWORDS: Solubility, Polymeric Excipients, Model Prediction, Thermodynamics, Ternary systems
*E-mail: [email protected]; [email protected]
ABSTRACT: In this work, the solubility of aspirin at 293.15-313.15 K was measured in several aqueous systems where one excipient out of PEG 6000, PEG 400, PVP K25, HPMC E3 and poloxamer 188 was present. It was found that PVP K25 had the strongest solubilizing ability and the solubility enhancement of aspirin by poloxamer 188 was greatly affected by temperature. In addition, the Wilson, NRTL and UNIQUAC models were employed to predict the solubility of aspirin in various organic solvents as well as in different mixtures of polymeric excipients and water through interaction parameters obtained from experimental data. The average ARDs of
1
Wilson, NRTL, and UNIQUAC models were 0.0300, 0.0318, 0.0305 for the binary aspirin-solvent systems, respectively, and those were 0.4214, 0.1166, 0.0861 for the ternary aspirin-polymer-water systems. UNIQUAC model among these three models was found to have excellent performance for solubility prediction of aspirin in solvents and polymer-water solutions.
1. Introduction The solubility data of active pharmaceutical ingredients (APIs) is one of the important foundations for the development of new pharmaceuticals and the preparation of formulations. The poor water solubility of APIs causes various difficulties in the development of pharmaceuticals [1, 2]. In practical applications, the addition of pharmaceutical excipients is often employed to enhance the API solubility [3-5]. The influence of excipients on dissolution and crystallization of APIs has also drawn great attention of researchers [6, 7]. Although excipients have been widely applied in various formulations for many water-insoluble APIs, the dissolution mechanism of these APIs in the existence of excipients was not clear. Moreover, the solubility data of APIs is very essential in pharmaceutical research [8-10]. However, the solubility data of poorly water-soluble APIs in excipient-aqueous solutions is very limited. Especially during the initial period of pharmaceutical discovery, a small amount of APIs synthesized or extracted is required for a large number of preliminary biological experiments,
2
leading to the lack of APIs for the solubility measurement and thus a serious deficiency of solubility data [11, 12]. Aspirin is a classic non-steroidal anti-inflammatory drug (NSAID) with poor water solubility [13]. NSAIDs are extensively applied in the treatment of painful diseases in therapeutics because of their anti-inflammatory, antipyretic and analgesic effects [14, 15]. However, most NSAIDs have a serious adverse effect on the gastrointestinal tract while exerting therapeutic effects [16, 17]. It has been reported that the adverse drug reactions of NSAID can be improved by adding excipients [18-20]. In addition, the improvement of water solubility of NSAIDs by excipients has also been declared in literature [8]. Therefore, to choose appropriate excipients is of great significance in formulation studies. Toxicity and irritation are important criteria for the selection of pharmaceutical excipients [21]. Polyethylene glycol (PEG) 6000, PEG 400, polyvinylpyrrolidone (PVP) K25, hydroxypropyl methylcellulose (HPMC) E3 and poloxamer 188 are common pharmaceutical excipients with low toxicity and low irritant, which are typical neutral polyether copolymer, N-vinyl amides copolymer, nonionic cellulose mixed ethers polymer and block copolymer, respectively. They are also widely used in oral and external preparations as well as in cosmetics and food products [22-25]. Most of them have good solubility in water and have a strong ability to form water-soluble complexes with active substances. Besides, they are often employed for the improvement of the solubility of poorly water-soluble APIs [23, 26]. Paus et al., Prudic et al. and
3
Ji et al. found that the solubility of indomethacin and naproxen was improved by PEG and PVP [6, 8, 9]. In recent years, Wilson, Non-Random Two Liquid (NRTL) and UNIversal QUasi-Chemical (UNIQUAC) models are widely applied in liquid-liquid equilibrium (LLE) and vapor-liquid equilibrium (VLE) as well as for activity coefficient calculation of binary and ternary systems [27-33]. However, there are few studies on solid-liquid equilibrium (SLE) of ternary systems by applying these models, especially on API-polymer-water systems. SLE equation is combined with the activity coefficient model for parameter regression and calculation. Not only the accuracy but also the simplicity of the calculation should be considered in the selection of the model. These models do not require additional experimental data between APIs and polymeric excipients and solvent to predict the solubility of the API in aqueous solutions of polymeric excipients, which greatly improves the ease of use of the model [34].
4
Figure 1. Chemical structures of aspirin (a), polyvinylpyrrolidone (b), polyethylene glycol (c), hydroxypropyl methylcellulose (d) and poloxamer (e).
In this work, we selected aspirin as an API, PEG 6000, PEG 400, PVP K25, HPMC E3 and poloxamer 188 as excipients to measure and compare the solubility of aspirin in aqueous solutions of these excipients so as to explore the influence of polymeric excipients on API solubility in aqueous medium. The chemical structures of aspirin and polymers are presented in Figure 1. At the same time, Wilson, NRTL and UNIQUAC models were employed to correlate and calculate the solubility of aspirin in binary and ternary systems at different temperatures. By comparing the calculation accuracy of the three models in these systems, the optimal models in different systems were obtained. This work would provide important fundamental data and be
5
helpful for selecting appropriate polymeric excipients in the research and development of new API formulations.
2. Materials and methods 2.1. Substances Aspirin (purity > 99%) was purchased from Aladdin Co., Ltd (Shanghai, China). PEG 6000 with Mw of 6000 g/mol, and PEG 400 with Mw of 400 g/mol were purchased from Energy Chemical Co., Ltd (Shanghai, China). PVP K25 with Mw of 24000 g/mol was purchased from Macklin Co., Ltd (Shanghai, China). HPMC E3 (USP 2910, 2% Viscosity: 3mpa.s, Methoxy: 28-30%, Hydroxypropyl: 7.0-12%) with Mw of 6092 g/mol was purchased from Aladdin Co., Ltd (Shanghai, China). Poloxamer 188 with Mw of 8350 g/mol was purchased from Maya Reagent Co., Ltd (Jiaxing, Zhejiang Province, China). Characterization of the substances is listed in Table 1. All chemicals were used without further purification. A Miyoshi ultrapure water machine was used to filter, deionize and distill water for all aqueous solutions. Table 1. Characterization of the substances.a
Substance
CAS No.
Source
Molecular weight (g/mol)
Acetylsalicylic acid (Aspirin)
50-78-2
Aladdin Co., Ltd
180.16
>0.99
HPLCb
25322-68-3
Energy Chemical Co., Ltd
6000
-
-
Polyethylene glycol (PEG 6000)
Mass fraction purity
Analysis method
6
25322-68-3
Energy Chemical Co., Ltd
400
-
-
Polyvinylpyrrolidone (PVP K25)
9003-39-8
Macklin Co., Ltd
24000
-
-
Hydroxypropyl methylcellulose (HPMC E3)
9004-65-3
Aladdin Co., Ltd
6092
-
-
Polyethylene-polypropylene glycol (Poloxamer 188)
9003-11-6
Maya Reagent Co., Ltd
8350
-
-
Water
7732-18-5
Lab made
18.01
Ultra-pure
Resistivity
Polyethylene glycol (PEG 400)
a
As stated by the supplier.
b
High performance liquid chromatography 2.2. Solubility measurement In a 100 mL glass container with a heating jacket, 75 mL of ultrapure water or an aqueous
medium containing each excipient with different mass fractions (2wt%, 5wt%, 8wt%, 10wt%) was added. It was heated to the desired temperature (temperatures from 293.15 to 313.15 K, with an interval of 5 K). Then excess aspirin was added into each medium and mixed by using a magnetic stirrer at 600 rpm. To prevent nucleation and crystallization of aspirin, the syringe (10 mL) with a needle and a Polyethersulfone resin (PES) filter (mesh size Ø 0.45 µm) was preheated. To make sure a thermodynamic equilibrium, the mixtures were stirred and kept for at least 48 hours, samples were then taken from the solution and appropriately diluted by water, and analyzed by a UV-vis spectrophotometer (PerkinElmer Lambda 365) at 224.15 nm. The concentrations of aspirin were determined through the required absorbance/concentration 7
calibration curves (the coefficient of determination R2 was higher than 0.9995 for each calibration curve), which were generated from the standard solutions with different concentrations of aspirin we prepared. The solubility of aspirin in each media was measured according to the method described in previous work [8]. The sample concentrations were measured again after 72 h to ensure that the concentration of aspirin reached saturation at 48 h.
3. Model description 3.1. Solid-liquid equilibrium modeling The solid-liquid equilibrium equation is shown in Eq. (1) [34]. ln ( γ Sat x Sat ) =
∆ fus H 1 1 1 − − R Tm T RT
∫
T
Tm
∆C p dT +
1 T ∆C p dT R ∫Tm T
(1)
xSat and γSat are the solubility in mole fraction and the activity coefficient of the API in the saturated solution, respectively. ∆
H and Tm are the melting enthalpy and the melting
temperature, respectively. ∆Cp is the difference in heat capacity between the solid and the supercooled melt, and ∆Cp is usually negligible as it is small enough [34, 35]. Moreover, when the component is difficult to present polymorphic transitions and the pure compounds are immiscible in the solid phase, Eq. (1) can be derived as a simplified thermodynamic equation only relating to the ∆ ln x1 =
∆ fus H R
H and Tm of the solute as shown in Eq. (2).
1 1 − − ln γ 1 Tm T
(2)
According to the simplified SLE equation, the API solubility is calculated by the melting temperature, melting enthalpy and activity coefficient of API. Local compositional models, such 8
as Wilson, NRTL, and UNIQUAC models, can describe the activity coefficient of a solute as a function of temperature and solute composition. 3.2. Wilson model In 1964, based on local composition, Wilson proposed Wilson activity coefficient model [36]. Eq. (3) is the Wilson model of the multi-component system. n n Λ ki x k ln ( γ i ) = 1 − ln ∑ ( Λ ij x j ) − ∑ n j k ∑ j ( Λ kj x j )
(3)
In Eq. (3), Λij can be expressed as: Λ ij =
∆λ exp − ij Vi RT
Vj
(4)
In Eq. (4), Λ ≠ Λ , Λ = Λ = 1, ∆
is the energy parameter of the binary interaction, Vm
represents the molar volume of component i and component j [37]. According to Eq. (3), for a ternary system, the Wilson model can be written as Eq. (5).
ln(γ 1 ) = 1 − ln( x1 + Λ12 x2 +Λ13 x3 ) −
Λ31 x3 x1 Λ21 x1 − − x1 + Λ12 x2 +Λ13 x3 Λ21 x1 +x2 + Λ23 x3 Λ31 x1 + Λ32 x2 +x3
(5)
3.3. NRTL model In 1968, Renon and Prausnitz combined Scott two-fluid theory with the local composition concept proposed by Wilson to derive the NRTL model [38]. Equation 6 is the NRTL model of the multi-component system. n
ln(γ i ) =
∑xτ j =1 n
j
ji
G ji
∑ xk Gki k =1
n xmτ mj Gmj ∑ n xG + ∑ n j ij τ ij − m =1n j =1 xk Gkj xk Gki ∑ ∑ k =1 k =1
(6)
9
Gij and
are given in Eqs. (7)-(8).
Gij = exp ( −α ijτ ij )
τ ij =
gij − g jj RT
=
(7)
∆gij
(8)
RT
As shown in Eqs. (7)-(8), Gii =Gjj =1 , ∆gii =∆gjj =0 , αij =αji , α is relative to the non-randomness of the mixture. If α=0, the mixing of the components is completely random. A large number of experimental data for binary system shows that α varies from 0.2 to 0.47 [38]. For the ternary system, the NRTL model can be written as Eq. (9).
( G21 x2 + G31 x3 ) ⋅ (τ 21G21 x2 + τ 31G31 x3 ) + τ12G12 x22 + (τ12 − τ 32 )G12G32 x2 x3 2 2 ( x1 + G21 x2 + G31 x3 ) ( G12 x1 + x2 + G32 x3 )
ln(γ 1 ) = +
τ 13G13 x32 + (τ 13 − τ 23 )G13G23 x2 x3
( G13 x1 + G23 x2 + x3 )
(9)
2
3.4. UNIQUAC model In 1975, based on the local composition and statistical mechanics, Abrams and Prausnitz proposed UNIQUAC equation, which extended Guggenheim's quasi-chemical theory [39]. The multi-component UNIQUAC model is shown in Eq. (10). φ Z θ φ ln γ i = ln i + qi ln i + li − i xi xi 2 φi
The φi =
θi =
φ,
θ , l and
ri xi
∑
n
∑
n
j =1
rj x j
q i xi j =1
qjxj
τ
n
∑x l j =1
j j
θ jτ ij n n + qi 1 − ln ∑ θ jτ ji − ∑ n j =1 j =1 ∑ k =1θ kτ kj
(10)
in the equation can be expressed as Eqs. (11)-(14). (11)
(12)
10
li =
Z ( ri − qi ) −( ri −1) 2
(13)
uij − u jj RT
τ ij = exp −
φi
and
θi
(14)
refer to the volume parameter and surface area parameter of the pure component i,
respectively, and Z stands for the lattice coordination number, Z=10. For ternary systems, the UNIQUAC model is shown in Eq. (15).
φ ( x l + x2 l2 + x3l3 ) φ Z θ ln γ 1 = ln 1 + q1 ln 1 + l1 − 1 1 1 x1 x1 2 φ1 θ 3τ 13 θ1 θ 2τ 12 + q1 1 − ln (θ1 + θ 2τ 21 + θ 3τ 31 ) − − − θ1 + θ 2τ 21 + θ 3τ 31 θ1τ 12 + θ 2 + θ 3τ 32 θ1τ 13 + θ 2τ 23 + θ 3
(15)
Table 2. Group contribution parameters of aspirin and solvents in UNIQUAC model. Aspirin
Water
Ethanol
Acetone
2-Propanol
1,2-Propanediol
ri
6.06
0.92
2.1055
2.5735
2.7791
3.5524
qi
4.792
1.4
1.972
2.336
2.508
3.4
Vm (cm3/mol)
133.45
18.01
58.39
74.03
76.40
73.45
The values of
ri and qi of API and solvents can be obtained from the Dortmund Database
(DDB) [40]. (see Table 2). The values of
ri and qi of polymers are calculated from Eqs.
(16)-(17) [41, 42]. The results are shown in Table 3.
ri = 0.029281 Vm qi =
(Z − 2) ri 2(1 − b i ) + Z Z
(16) (17)
11
means the molar volume of the pure component. The
values of polymers are
calculated by the group contribution method [41, 42]. Z stands for the coordination number, Z=10.
bi is the volume factor of the component i, bi =1 [41].
Table 3. Group contribution parameters of polymers in UNIQUAC model. PEG 6000
PEG 400
PVP K25
HPMC E3
Poloxamer 188
ri
153.57
10.41
614.29
128.33
223.28
qi
122.86
8.33
491.43
102.66
178.63
Vm(cm3/mol)
5244.76
355.40
20979.02
4382.73
7625.57
Although all three models are based on the theory of local composition, they are quite different. From the model equation, we can see that NRTL has no entropic term and Wilson has an implicit entropic term. UNIQUAC has obvious entropic term [43]. 3.5. Parametric regression and accuracy analysis According to Eq. (18), the Levenberg-Marquardt algorithm is used to minimize the objective function for parameter estimation [44]. In this work, MATLAB software is employed to calculate all the interaction parameters. xi,exp − xi,cal Fobj = ∑ xi,exp k =1 n
2
k
(18)
The calculation accuracy of the thermodynamic model is evaluated by the average relative deviation (ARD) and the root mean square deviation (RMSD) between the experimental and calculated values.
12
ARD =
1 n xi,exp − xi,cal ∑ x n i=1 i ,exp
(19) 1
2 2 1 n RMSD = ∑ ( xi ,cal − xi ,exp ) n i =1
(20)
In Eqs. (19)-(20), xi,cal is the solubility calculated by the model in mole fraction, xi,exp is the experimentally measured solubility in mole fraction, and n is the number of experimental data points.
4. Results and discussions 4.1. Influence of polymer type on aspirin solubility At 293.15-313.15 K, the solubility of aspirin in PEG 6000, PEG 400, PVP K25, HPMC E3, and poloxamer 188 aqueous solutions with various mass fractions (2wt%, 5wt%, 10wt%) was presented in Figure 2. In all systems, the solubility of aspirin was a function of polymer content, polymer type and temperature. As presented in Figure 2, the solubility of aspirin was significantly affected by the existence of polymeric excipients. In most systems with different temperatures and polymer concentrations, the solubility of aspirin was improved compared to that in water, which was consistent with the enhancement of API solubility by polymeric excipients as mentioned in the literatures. Paus et al. found that the addition of PVP K25 enhanced the solubility of indomethacin and naproxen better than PEG 6000 [8]. Soni et al. observed higher solubility of indomethacin with the existence of PEG 6000 compared to PEG 400 [45], which was in agreement with the solubilization ability of PVP K25, PEG 6000 and 13
PEG 400 for aspirin in present experimental observations. In general, PVP K25 and poloxamer 188 had better solubilization effects on aspirin than PEG 6000, HPMC E3 and PEG 400. It should be noted that PVP K25 showed the best solubilization capability. It can be ascribed to the strong capability of PVP K25 to establish hydrogen bonding with aspirin [8, 46].
Figure 2. At 293.15-313.15 K, the solubility of aspirin in water (square), and in aqueous solutions containing 2wt% (a), 5wt%(b) and 10wt% (c) of PVP K25 (circle), PEG 6000 (inverted triangle), PEG 400 (diamond), HPMC E3 (triangle) and poloxamer 188 (star). 14
4.2. Influence of temperature on aspirin solubility Figure 2 illustrated that there was an apparent positive correlation between the solubilization effect of polymer and temperature in an aqueous solution with various polymer contents (2wt%, 5wt%, 10wt%), which was most pronounced in the case of poloxamer 188 as the polymeric excipient. The increase of the solubility of aspirin at 313.15 K in an aqueous solution containing 2wt%, 5wt% and 10wt% of poloxamer 188 was about 16.3 times, 11.2 times and 5.0 times as much as that at 293.15 K. When it came to other polymers, the solubility increase of aspirin at 313.15 K in water with the existence of 2wt%, 5wt% and 10wt% of them was less than 6 times as much as that at 293.15 K. The temperature had an outstandingly greater impact on poloxamer 188 than other polymers causing the solubilization effect of poloxamer 188 progressively superior to other polymers with increasing temperature. Al-Saden et al. demonstrated that the intrinsic viscosity of poloxamer 188 in aqueous solution decreased with increasing temperature [47]. Although the poloxamer 188 system was not monodisperse, its dispersion declined with the increase of temperature. Moreover, poloxamer 188 is an amphiphilic structure of the block arrangement of propylene oxide (PO) and ethylene oxide (EO) [48, 49]. The increase in temperature leads to the continuous dehydration of PO and EO chains. Below room temperature, both PO and EO blocks in poloxamer 188 are hydrated and are relatively water-soluble. PO blocks begin to dehydrate and become insoluble as the temperature rises leading to the micelle formation [48]. The monomolecular micelles of the temperature-increasing system aggregate into aggregates of different sizes, thus affecting the solubilization of poloxamer 188 [50]. 15
4.3. Influence of polymer concentration on aspirin solubility In order to reveal the role of the polymer concentration on the solubilization effect of polymers for API, the solubility of aspirin in aqueous solutions with several polymer concentrations (2wt%, 5wt%, and 10wt%) was compared as shown in Figure 3. Additionally, as for PVP K25, which showed better solubilization performance, the concentration of 8wt% was also considered here. It was observed from Figure 3 that when the concentration of polymer was 2wt%, the solubility of aspirin almost did not increase compared with that in water, and even was found to decrease slightly at 293.15 K. As the concentration of polymer increased, the solubility of aspirin was observed to increase at each temperature, i.e., there was a positive correlation between the solubility of aspirin and the polymer concentration. For instance, at the temperature of 313.15 K, the increments of aspirin solubility in aqueous solutions with the poloxamer 188 concentration of 10wt% was about 7.0 times and 2.3 times as high as those of 2wt% and 5wt%, respectively. The increments of aspirin solubility in aqueous solutions with the PEG 6000 concentration of 10wt% was around 9.1 and 2.6 times as much as those of 2wt% and 5wt%, respectively. The increments of aspirin solubility in aqueous solutions with the PEG 400 concentration of 10wt% was nearly 13.8 and 3.1 times as much as those of 2wt% and 5wt%, respectively. Besides, the solubilizing effect of polymer appeared to enhance with the increase in temperature. Temperature synergized with the polymer concentration to improve the solubility of aspirin. It should be noted that it was rather difficult to precisely measure the solubility of aspirin in the aqueous solution with 10wt% of HPMC at 313.15 K because of its high viscosity. Furthermore, it has also been observed in the 16
literature that the solubility of API was found to decrease as the viscosity of HPMC rose [51, 52]. Therefore, the solubility of aspirin in the aqueous solution with 10wt% HPMC wasn’t measured at 313.15 K in this work.
17
Figure 3. At 293.15-313.15 K，solubility of aspirin in aqueous solutions with 2wt% (triangle), 5wt% (diamond), 10wt% (star) PEG 6000(a), PEG 400(b), HPMC E3(c), poloxamer 188(d) and 18
2wt% (triangle), 5wt% (diamond), 8wt% (circle), 10wt% (star) PVP K25(e) and ultra-pure water (square).
4.4 Model prediction of binary systems The melting temperature and melting enthalpy of aspirin were reported in the literature as
T fus =408.65 K and ∆H fus =33.509 kJ/mol [53]. The solubility data of aspirin in ethanol, acetone, 2-propanol and 1,2-propanediol was obtained in the literature at the temperature range of 290.6-336.6 K [54]. In present work, the experimental solubility of aspirin in ultrapure water was determined at 293.15-313.15 K. When the temperature is higher than room temperature, the solubility of aspirin in aqueous solution reported in this work is slightly higher than that of References 55 and 56 (see Figure S1) [55, 56]. It may be caused by the following reasons: our measurement time (48 h for stirring, 2 h for settling and PES filter for filtering) is longer than that (about 1 h for stirring and 24 h for settling) in the Literature 56. In our experiments, we found that the solid-liquid equilibrium was not reached for only 24 h. The sample concentrations were measured again after 72 h to ensure that the concentration of aspirin is the equilibrium solubility at 48 h. In addition to that, the method reported in the literature is titration with sodium hydroxide after adding phenolphthalein indicator, which probably have some influence on aspirin equilibrium solubility. Aspirin has a pKa of 3.5 and is a poorly water-soluble weak acid, the use of a pH meter or a conductance meter would be better for the requirement of more precise results. In addition, when the studied temperature is higher than room temperature, it is 19
possible to appear precipitation of drug solids during titration, which might lead to a slightly smaller experimental result. Literature 55 only reported the aspirin solubility at 298.15 K, and it did not include the experimental deviation. As provided in Table S1 (Supporting Information), the binary interaction parameters of Wilson, NRTL and UNIQUAC model were regressed according to our experimental data. Meanwhile, the solubility of aspirin was predicted at such temperatures in above organic solvents and water. Figure 4 provides the predicted aspirin solubility in various solvents by using Wilson, NRTL and UNIQUAC models compared with the experimental data.
Figure 4. The solubility of aspirin in ethanol (star), acetone (left triangle), 2-propanol (right triangle), 1,2-propanediol (hexagon) and water (square). The symbols indicate the aspirin solubility obtained experimentally in this work or literature, and the lines indicate the calculated values of the aspirin solubility by using Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models. 20
Table 4. The RMSD and the ARD between the calculated and experimental aspirin solubilities in binary systems. Wilson
NRTL
UNIQUAC
ARD
RMSD×103
ARD
RMSD×103
ARD
RMSD×103
H2O
0.0568
0.0382
0.0578
0.0360
0.0562
0.0400
Ethanol
0.0025
0.4039
0.0030
0.4531
0.0143
2.6945
Acetone
0.0313
4.2142
0.0399
5.3440
0.0118
1.6912
2-Propanol
0.0099
1.7586
0.0097
1.7330
0.0191
3.2415
1, 2-Propanediol
0.0494
5.9695
0.0486
5.8687
0.0513
6.2254
Average
0.0300
2.4769
0.0318
2.6869
0.0305
2.7785
The ARD and RMSD of aspirin solubility in water, ethanol, acetone, 2-propanol and propylene glycol were summarized in Table 4, which were obtained by comparing the experimental aspirin solubility data with the predicted values of Wilson, NRTL, and UNIQUAC models. According to Table 4, the average ARDs of Wilson, NRTL and UNIQUAC models were 0.0300, 0.0318 and 0.0305, respectively. Besides, all the ARDs of above three models were below 6%. It indicated that the solubility of aspirin in water and such four organic solvents were well predicted by Wilson, NRTL and UNIQUAC models. For above five binary API-solvent systems, the average ARD and RMSD of Wilson model were 0.03 and 2.4769×10-3, respectively, which represented that the Wilson model possessed the best prediction accuracy. 4.5 Model prediction of ternary systems 21
The interaction parameters of the Wilson, NRTL and UNIQUAC models for ternary systems were regressed based on the experimentally determined solubility data of aspirin at 293.15-313.15 K in aqueous solutions in presence of 10wt% polymeric excipients (PVP K25, PEG 6000, PEG 400, HPMC E3 and poloxamer 188). In 2wt%, 5wt% polymer-water solutions, the concentration of polymer is relatively small, its value will be much smaller especially when described in mole fraction for the model calculation. Parameters regressed from mixtures at 10% polymer concentration can reflect the interactions between polymers and drug. Model parameters were listed in Tables 5-7. Table 5. Interaction parameters within Wilson model of ternary API-water-polymer systems.
λ12 − λ22
λ21 −λ11
λ13 − λ33
λ31 −λ11
λ23 − λ33
λ32 − λ22
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
PEG 6000
-3677.0
-10480.4
28685.9
30321.7
116.3
-5262.5
PEG 400
-2719.9
-12582.9
23459.6
10766.1
8.3
308.5
PVP K25
-3381.5
-11664.7
15795.4
12512.3
866.5
-1235.4
HPMC E3
-4828.4
18971.3
53043.0
52427.9
-18760.5
-12567.0
Poloxamer 188
-3264.7
-12468.6
19309.6
16357.2
-272.0
-2490.8
Table 6. Interaction parameters within NRTL model of ternary API-water-polymer systems.
g12 − g22 g21 − g11 g13 − g33 g31 − g11 -1
(J·mol )
-1
(J·mol )
-1
(J·mol )
-1
(J·mol )
g23 − g33 g32 − g22 -1
(J·mol )
α
-1
(J·mol ) 22
PEG 6000
-4651.0
-20960.1
86039.7
10511.4
-76.3
4641.6
0.4
PEG 400
4078.1
-2998.0
11677.8
8382.6
-82.3
-4060.9
0.47
PVP K25
-4793.8
-23795.1
78332.8
10354.7
27.9
4791.8
0.47
HPMC E3
-5374.8
-18587.9
72153.2
12074.3
-97.1
5359.0
0.47
Poloxamer 188
-3764.7
-17464.3
75009.9
9947.6
2.1
3760.2
0.47
Table 7. Interaction parameters within UNIQUAC model of ternary API-water-polymer systems.
u12 −u22
u21 −u11
u13 −u33
u31 −u11
u23 − u33
u32 − u22
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
PEG 6000
-863.6
1204.0
-1095.3
2093.6
6499.4
693.9
PEG 400
-3519.8
527.7
-70.3
793.5
19384.3
-3247.6
PVP K25
-388.8
404.2
-344.9
966.5
8917.7
290.1
HPMC E3
5281.8
9436.2
11811.2
-1986.7
6731.0
-5450.8
Poloxamer 188
-251.4
435.8
-94.2
704.6
11394.0
109.1
In order to evaluate the reliability and the predictive performance of above three models, the solubility of aspirin at five temperatures was calculated in different polymer aqueous solutions by substituting above parameters into corresponding model equations. The results were summarized in Tables S3 and S4.
23
In addition, we calculated the solubility of aspirin at 273.15-323.15 K in various polymer-water solutions through the same method and the results are shown in Figures 5-9 with a comparison with the experimental data.
Figure 5. At 293.15-313.15 K, the experimental values (including error bars) of aspirin solubility in PVP K25 aqueous solutions with PVP K25 mass fractions of 2wt% (a), 5wt% (b), 8wt% (c) and 10wt% (d). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models. 24
Figure 6. At 293.15-313.15 K, the solubility of aspirin in PEG 6000 aqueous solutions with PEG 6000 mass fractions of 2wt% (a), 5wt% (b) and 10wt% (c). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models.
25
Figure 7. At 293.15-313.15 K, the solubility of aspirin in PEG 400 aqueous solutions with PEG 400 mass fractions of 2wt% (a), 5wt% (b) and 10wt% (c). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models.
26
Figure 8. At 293.15-313.15 K, the solubility of aspirin in HPMC E3 aqueous solutions with HPMC E3 mass fractions of 2wt% (a), 5wt% (b) and 10wt% (c). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models.
27
Figure 9. At 293.15-313.15 K, the solubility of aspirin in poloxamer 188 aqueous solutions with mass fractions of 2wt% (a), 5wt% (b) and 10wt% (c). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models.
As shown in Figures 5-9, the experimental solubility of aspirin were compared with the predicted results of NRTL, UNIQUAC and Wilson models in the aqueous solutions with PVP K25 (2wt%, 5wt%, 8wt% and 10wt%), PEG 6000 (2wt%, 5wt% and 10wt%), PEG 400 (2wt%, 28
5wt% and 10wt%), HPMC E3 (2wt%, 5wt% and 10wt%) and poloxamer 188 (2wt%, 5wt% and 10wt%), respectively. It is intuitively observed that both NRTL and UNIQUAC models predict the solubility of aspirin at 273.15-320.15K in aqueous solutions in the presence of 2wt%, 5wt%, 8wt% and 10wt% of above five polymer excipients. The Wilson model showed the worst predictive performance as it only described well the aspirin solubility in aqueous solutions with 10wt% polymer solutions, but it did not have a good predictive capability in other API-polymer-water systems. All of the three models showed poor prediction in aqueous solutions with HPMC. For the UNIQUAC model, which had the best predictive performance, its predicted results in HPMC systems (2wt% and 5wt%) were found to be significantly higher than the experimental solubility data. The high viscosity of the HPMC aqueous solutions as mentioned in Section 4.3 might affect the dissolution of aspirin, and even make it difficult to measure the API solubility accurately. Table 8. The ARD and RMSD between the experimental and calculated API solubilities in ternary systems. NRTL
Wilson
UNIQUAC
ARD
RMSD×104
ARD
RMSD×104
ARD
RMSD×104
2wt% PEG6000
0.7823
5.5196
0.0795
0.4986
0.0440
0.4706
5wt% PEG6000
0.4749
3.9898
0.0628
0.4988
0.0447
0.4711
10wt% PEG6000
0.0182
0.2065
0.0191
0.2124
0.0196
0.2308
2wt% PEG400
0.8202
5.6454
0.1924
1.4137
0.0472
0.3917
29
5wt% PEG400
0.5203
4.0239
0.1193
0.9892
0.0270
0.2680
10wt% PEG400
0.0103
0.1417
0.0138
0.2413
0.0226
0.3141
2wt% PVPK25
0.7907
5.7889
0.0681
0.5079
0.1217
1.0048
5wt% PVPK25
0.4978
4.6558
0.1007
0.9604
0.0663
0.5137
8wt% PVPK25
0.1834
2.3585
0.0896
1.3116
0.0817
0.8197
10wt% PVPK25
0.0814
0.8499
0.0958
1.4296
0.0878
0.9851
2wt% HPMCE3
0.7325
5.0559
0.4391
2.8516
0.3259
1.8479
5wt% HPMCE3
0.4270
3.5511
0.3399
2.6380
0.1339
0.9848
10wt% HPMCE3
0.0376
0.3285
0.0295
0.2735
0.0314
0.2663
2wt% Poloxamer188
0.7996
5.9598
0.0934
0.8336
0.1312
0.8848
5wt% Poloxamer188
0.5038
5.0329
0.0605
0.7002
0.1095
0.9178
10wt% Poloxamer188
0.0618
2.1895
0.0622
2.2057
0.0828
1.9743
Average
0.4214
3.4561
0.1166
1.0979
0.0861
0.7716
Figure 10. At 293.15-313.15 K, the ARD between the calculated aspirin solubility by Wilson, NRTL and UNIQUAC models and the experimental solubility of aspirin in aqueous solutions of 30
PEG 6000 (2wt%, 5wt% and 10wt%), PEG 400 (2wt%, 5wt% and 10wt%), poloxamer 188 (2wt%, 5wt% and 10wt%), PVP K25 (2wt%, 5wt%, 8wt% and 10wt%) and HPMC E3( 2wt%, 5wt% and 10wt%).
The ARD and RMSD between the experimental and calculated API solubilities in ternary systems were summarized in Table 8 and Figure 10. It was observed that the ARDs of these models decreased gradually with the increase of the concentration of polymers. The average ARDs of Wilson, NRTL and UNIQUAC models in aqueous solutions with 2wt% polymer were 0.7851, 0.1745 and 0.1340, respectively. The average ARDs of the three models in aqueous solutions with 5wt% polymer were 0.4848, 0.1366 and 0.0763, respectively. The average ARDs of the three models in aqueous solutions with 10wt% polymer were 0.0419, 0.0441 and 0.0488, respectively. It was found that the solubility of aspirin was well predicted by the UNIQUAC and NRTL model in aqueous solutions with the polymer concentration of 2wt%, 5wt% and 10wt% and of 5wt% and 10wt%, respectively. While for Wilson model, it was almost impossible to achieve its prediction under the polymer concentration of 2wt% and 5wt%. UNIQUAC model was found to have the highest prediction accuracy in PEG aqueous solutions with an average ARD of 0.0342. The prediction accuracy of NRTL model in poloxamer 188 aqueous solutions was slightly higher than UNIQUAC model and the average ARD of the former was 0.0720 and that of the latter was 0.1078. Interestingly, the average ARDs of the three models in aqueous solutions with 10wt% polymer were quite close and the Wilson model was observed to possess 31
the smallest ARD, which suggested that the Wilson model had better regression performance than the other two models in the aqueous solutions with the polymer concentration of 10wt%. Overall, the average ARD of each model obeyed the following order: Wilson model (0.4214) > NRTL model (0.1166) > UNIQUAC model (0.0861) implying that UNIQUAC model had the best prediction performance. The prediction accuracy of UNIQUAC model for different polymer-water systems followed the order: PEG 400> PEG 6000> PVP K25> poloxamer 188> HPMC E3.
5. Conclusions In this work, the influence of polymeric excipients on the solubility of aspirin was systematically investigated through both experimental measurement and thermodynamic model prediction. The experimental results demonstrated that the solubility of aspirin was enhanced with the existence of polymeric excipients and PVP K25 showed the best solubilizing capability. The solubilization effect of polymers was observed to be positively correlative with the temperature and the polymer concentration. Particularly, the solubilizing ability of poloxamer 188 was most affected by temperature. The Wilson, NRTL, and UNIQUAC models were found to successfully correlate and predict the solubility of aspirin in binary systems. The model parameters were obtained from the experimental data at a certain polymer concentration and were used to predict the solubility of the drug in aqueous solutions with other polymer concentrations, and UNIQUAC model achieved best prediction performance from binary systems to ternary systems. However, Wilson 32
model had low ability to predict aspirin solubility for ternary systems even using the model parameters obtained from the experimental data at 10% polymer concentration. It is essential to accurately predict the solubility of API in aqueous solutions in the presence of various polymers (with different polymer concentration) at various temperatures for the screening of polymeric excipients.
Associated content Supporting information.
The following files are available free of charge.
Interaction parameters and predicted results of Wilson, NRTL and UNIQUAC models for API-solvent binary systems. And experimental data and calculated values of aspirin solubility in API- polymer ternary systems. (DOCX)
Author information Corresponding author
*E-mail: [email protected]; [email protected]
*Tel: +86-13951907361
Notes
The authors declare no competing financial interest.
33
Acknowledgment The authors gratefully acknowledge the financial support for this study from the National Natural Science Foundation of China (Grant No.: 21606043, 21776046), the Fundamental Research Funds for the Central Universities (Grant No.: 2242019K40145), the Six Talent Peaks Project in Jiangsu Province (Grant No.: XCL-079), and the Recruitment Program for Young Professionals (the Thousand Youth Talents Plan).
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42
HIGHLIGHTS
The effects of five polymers on API solubility at various temperatures were compared
Local composition model was applied from binary system to ternary system
Local composition model was applied to predict aspirin-polymer-water systems
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:
S0378-3812(19)30512-6
DOI:
https://doi.org/10.1016/j.fluid.2019.112450
Reference:
FLUID 112450
To appear in:
Fluid Phase Equilibria
Received Date: 10 August 2019 Revised Date:
25 December 2019
Accepted Date: 30 December 2019
Please cite this article as: D. Wu, Y. Ji, Influence of polymeric excipients on the solubility of aspirin: Experimental measurement and model prediction, Fluid Phase Equilibria (2020), doi: https:// doi.org/10.1016/j.fluid.2019.112450. 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. © 2019 Published by Elsevier B.V.
Dongxu Wu: Writing - Original Draft, Methodology, Data Curation , Formal analysis Yuanhui Ji *: Writing - Review & Editing, Conceptualization, Supervision, Resources
Model Prediction Comparison
Solubilization Effect
UNIQUAC> NRTL>Wilson
Ternary System
0.0025
xcal(mol/mol)
0.0020
Water Excipients
API
0.0015
0.0010
0.0005
0.0000 0.0000
0.0005
0.0010
0.0015
xexp(mol/mol)
0.0020
0.0025
Influence of Polymeric Excipients on the Solubility of Aspirin: Experimental Measurement and Model Prediction Dongxu Wu, Yuanhui Ji *
Jiangsu Province Hi-Tech Key Laboratory for Biomedical Research, School of Chemistry and Chemical Engineering, Southeast University, Nanjing, 211189, People’s Republic of China
KEYWORDS: Solubility, Polymeric Excipients, Model Prediction, Thermodynamics, Ternary systems
*E-mail: [email protected]; [email protected]
ABSTRACT: In this work, the solubility of aspirin at 293.15-313.15 K was measured in several aqueous systems where one excipient out of PEG 6000, PEG 400, PVP K25, HPMC E3 and poloxamer 188 was present. It was found that PVP K25 had the strongest solubilizing ability and the solubility enhancement of aspirin by poloxamer 188 was greatly affected by temperature. In addition, the Wilson, NRTL and UNIQUAC models were employed to predict the solubility of aspirin in various organic solvents as well as in different mixtures of polymeric excipients and water through interaction parameters obtained from experimental data. The average ARDs of
1
Wilson, NRTL, and UNIQUAC models were 0.0300, 0.0318, 0.0305 for the binary aspirin-solvent systems, respectively, and those were 0.4214, 0.1166, 0.0861 for the ternary aspirin-polymer-water systems. UNIQUAC model among these three models was found to have excellent performance for solubility prediction of aspirin in solvents and polymer-water solutions.
1. Introduction The solubility data of active pharmaceutical ingredients (APIs) is one of the important foundations for the development of new pharmaceuticals and the preparation of formulations. The poor water solubility of APIs causes various difficulties in the development of pharmaceuticals [1, 2]. In practical applications, the addition of pharmaceutical excipients is often employed to enhance the API solubility [3-5]. The influence of excipients on dissolution and crystallization of APIs has also drawn great attention of researchers [6, 7]. Although excipients have been widely applied in various formulations for many water-insoluble APIs, the dissolution mechanism of these APIs in the existence of excipients was not clear. Moreover, the solubility data of APIs is very essential in pharmaceutical research [8-10]. However, the solubility data of poorly water-soluble APIs in excipient-aqueous solutions is very limited. Especially during the initial period of pharmaceutical discovery, a small amount of APIs synthesized or extracted is required for a large number of preliminary biological experiments,
2
leading to the lack of APIs for the solubility measurement and thus a serious deficiency of solubility data [11, 12]. Aspirin is a classic non-steroidal anti-inflammatory drug (NSAID) with poor water solubility [13]. NSAIDs are extensively applied in the treatment of painful diseases in therapeutics because of their anti-inflammatory, antipyretic and analgesic effects [14, 15]. However, most NSAIDs have a serious adverse effect on the gastrointestinal tract while exerting therapeutic effects [16, 17]. It has been reported that the adverse drug reactions of NSAID can be improved by adding excipients [18-20]. In addition, the improvement of water solubility of NSAIDs by excipients has also been declared in literature [8]. Therefore, to choose appropriate excipients is of great significance in formulation studies. Toxicity and irritation are important criteria for the selection of pharmaceutical excipients [21]. Polyethylene glycol (PEG) 6000, PEG 400, polyvinylpyrrolidone (PVP) K25, hydroxypropyl methylcellulose (HPMC) E3 and poloxamer 188 are common pharmaceutical excipients with low toxicity and low irritant, which are typical neutral polyether copolymer, N-vinyl amides copolymer, nonionic cellulose mixed ethers polymer and block copolymer, respectively. They are also widely used in oral and external preparations as well as in cosmetics and food products [22-25]. Most of them have good solubility in water and have a strong ability to form water-soluble complexes with active substances. Besides, they are often employed for the improvement of the solubility of poorly water-soluble APIs [23, 26]. Paus et al., Prudic et al. and
3
Ji et al. found that the solubility of indomethacin and naproxen was improved by PEG and PVP [6, 8, 9]. In recent years, Wilson, Non-Random Two Liquid (NRTL) and UNIversal QUasi-Chemical (UNIQUAC) models are widely applied in liquid-liquid equilibrium (LLE) and vapor-liquid equilibrium (VLE) as well as for activity coefficient calculation of binary and ternary systems [27-33]. However, there are few studies on solid-liquid equilibrium (SLE) of ternary systems by applying these models, especially on API-polymer-water systems. SLE equation is combined with the activity coefficient model for parameter regression and calculation. Not only the accuracy but also the simplicity of the calculation should be considered in the selection of the model. These models do not require additional experimental data between APIs and polymeric excipients and solvent to predict the solubility of the API in aqueous solutions of polymeric excipients, which greatly improves the ease of use of the model [34].
4
Figure 1. Chemical structures of aspirin (a), polyvinylpyrrolidone (b), polyethylene glycol (c), hydroxypropyl methylcellulose (d) and poloxamer (e).
In this work, we selected aspirin as an API, PEG 6000, PEG 400, PVP K25, HPMC E3 and poloxamer 188 as excipients to measure and compare the solubility of aspirin in aqueous solutions of these excipients so as to explore the influence of polymeric excipients on API solubility in aqueous medium. The chemical structures of aspirin and polymers are presented in Figure 1. At the same time, Wilson, NRTL and UNIQUAC models were employed to correlate and calculate the solubility of aspirin in binary and ternary systems at different temperatures. By comparing the calculation accuracy of the three models in these systems, the optimal models in different systems were obtained. This work would provide important fundamental data and be
5
helpful for selecting appropriate polymeric excipients in the research and development of new API formulations.
2. Materials and methods 2.1. Substances Aspirin (purity > 99%) was purchased from Aladdin Co., Ltd (Shanghai, China). PEG 6000 with Mw of 6000 g/mol, and PEG 400 with Mw of 400 g/mol were purchased from Energy Chemical Co., Ltd (Shanghai, China). PVP K25 with Mw of 24000 g/mol was purchased from Macklin Co., Ltd (Shanghai, China). HPMC E3 (USP 2910, 2% Viscosity: 3mpa.s, Methoxy: 28-30%, Hydroxypropyl: 7.0-12%) with Mw of 6092 g/mol was purchased from Aladdin Co., Ltd (Shanghai, China). Poloxamer 188 with Mw of 8350 g/mol was purchased from Maya Reagent Co., Ltd (Jiaxing, Zhejiang Province, China). Characterization of the substances is listed in Table 1. All chemicals were used without further purification. A Miyoshi ultrapure water machine was used to filter, deionize and distill water for all aqueous solutions. Table 1. Characterization of the substances.a
Substance
CAS No.
Source
Molecular weight (g/mol)
Acetylsalicylic acid (Aspirin)
50-78-2
Aladdin Co., Ltd
180.16
>0.99
HPLCb
25322-68-3
Energy Chemical Co., Ltd
6000
-
-
Polyethylene glycol (PEG 6000)
Mass fraction purity
Analysis method
6
25322-68-3
Energy Chemical Co., Ltd
400
-
-
Polyvinylpyrrolidone (PVP K25)
9003-39-8
Macklin Co., Ltd
24000
-
-
Hydroxypropyl methylcellulose (HPMC E3)
9004-65-3
Aladdin Co., Ltd
6092
-
-
Polyethylene-polypropylene glycol (Poloxamer 188)
9003-11-6
Maya Reagent Co., Ltd
8350
-
-
Water
7732-18-5
Lab made
18.01
Ultra-pure
Resistivity
Polyethylene glycol (PEG 400)
a
As stated by the supplier.
b
High performance liquid chromatography 2.2. Solubility measurement In a 100 mL glass container with a heating jacket, 75 mL of ultrapure water or an aqueous
medium containing each excipient with different mass fractions (2wt%, 5wt%, 8wt%, 10wt%) was added. It was heated to the desired temperature (temperatures from 293.15 to 313.15 K, with an interval of 5 K). Then excess aspirin was added into each medium and mixed by using a magnetic stirrer at 600 rpm. To prevent nucleation and crystallization of aspirin, the syringe (10 mL) with a needle and a Polyethersulfone resin (PES) filter (mesh size Ø 0.45 µm) was preheated. To make sure a thermodynamic equilibrium, the mixtures were stirred and kept for at least 48 hours, samples were then taken from the solution and appropriately diluted by water, and analyzed by a UV-vis spectrophotometer (PerkinElmer Lambda 365) at 224.15 nm. The concentrations of aspirin were determined through the required absorbance/concentration 7
calibration curves (the coefficient of determination R2 was higher than 0.9995 for each calibration curve), which were generated from the standard solutions with different concentrations of aspirin we prepared. The solubility of aspirin in each media was measured according to the method described in previous work [8]. The sample concentrations were measured again after 72 h to ensure that the concentration of aspirin reached saturation at 48 h.
3. Model description 3.1. Solid-liquid equilibrium modeling The solid-liquid equilibrium equation is shown in Eq. (1) [34]. ln ( γ Sat x Sat ) =
∆ fus H 1 1 1 − − R Tm T RT
∫
T
Tm
∆C p dT +
1 T ∆C p dT R ∫Tm T
(1)
xSat and γSat are the solubility in mole fraction and the activity coefficient of the API in the saturated solution, respectively. ∆
H and Tm are the melting enthalpy and the melting
temperature, respectively. ∆Cp is the difference in heat capacity between the solid and the supercooled melt, and ∆Cp is usually negligible as it is small enough [34, 35]. Moreover, when the component is difficult to present polymorphic transitions and the pure compounds are immiscible in the solid phase, Eq. (1) can be derived as a simplified thermodynamic equation only relating to the ∆ ln x1 =
∆ fus H R
H and Tm of the solute as shown in Eq. (2).
1 1 − − ln γ 1 Tm T
(2)
According to the simplified SLE equation, the API solubility is calculated by the melting temperature, melting enthalpy and activity coefficient of API. Local compositional models, such 8
as Wilson, NRTL, and UNIQUAC models, can describe the activity coefficient of a solute as a function of temperature and solute composition. 3.2. Wilson model In 1964, based on local composition, Wilson proposed Wilson activity coefficient model [36]. Eq. (3) is the Wilson model of the multi-component system. n n Λ ki x k ln ( γ i ) = 1 − ln ∑ ( Λ ij x j ) − ∑ n j k ∑ j ( Λ kj x j )
(3)
In Eq. (3), Λij can be expressed as: Λ ij =
∆λ exp − ij Vi RT
Vj
(4)
In Eq. (4), Λ ≠ Λ , Λ = Λ = 1, ∆
is the energy parameter of the binary interaction, Vm
represents the molar volume of component i and component j [37]. According to Eq. (3), for a ternary system, the Wilson model can be written as Eq. (5).
ln(γ 1 ) = 1 − ln( x1 + Λ12 x2 +Λ13 x3 ) −
Λ31 x3 x1 Λ21 x1 − − x1 + Λ12 x2 +Λ13 x3 Λ21 x1 +x2 + Λ23 x3 Λ31 x1 + Λ32 x2 +x3
(5)
3.3. NRTL model In 1968, Renon and Prausnitz combined Scott two-fluid theory with the local composition concept proposed by Wilson to derive the NRTL model [38]. Equation 6 is the NRTL model of the multi-component system. n
ln(γ i ) =
∑xτ j =1 n
j
ji
G ji
∑ xk Gki k =1
n xmτ mj Gmj ∑ n xG + ∑ n j ij τ ij − m =1n j =1 xk Gkj xk Gki ∑ ∑ k =1 k =1
(6)
9
Gij and
are given in Eqs. (7)-(8).
Gij = exp ( −α ijτ ij )
τ ij =
gij − g jj RT
=
(7)
∆gij
(8)
RT
As shown in Eqs. (7)-(8), Gii =Gjj =1 , ∆gii =∆gjj =0 , αij =αji , α is relative to the non-randomness of the mixture. If α=0, the mixing of the components is completely random. A large number of experimental data for binary system shows that α varies from 0.2 to 0.47 [38]. For the ternary system, the NRTL model can be written as Eq. (9).
( G21 x2 + G31 x3 ) ⋅ (τ 21G21 x2 + τ 31G31 x3 ) + τ12G12 x22 + (τ12 − τ 32 )G12G32 x2 x3 2 2 ( x1 + G21 x2 + G31 x3 ) ( G12 x1 + x2 + G32 x3 )
ln(γ 1 ) = +
τ 13G13 x32 + (τ 13 − τ 23 )G13G23 x2 x3
( G13 x1 + G23 x2 + x3 )
(9)
2
3.4. UNIQUAC model In 1975, based on the local composition and statistical mechanics, Abrams and Prausnitz proposed UNIQUAC equation, which extended Guggenheim's quasi-chemical theory [39]. The multi-component UNIQUAC model is shown in Eq. (10). φ Z θ φ ln γ i = ln i + qi ln i + li − i xi xi 2 φi
The φi =
θi =
φ,
θ , l and
ri xi
∑
n
∑
n
j =1
rj x j
q i xi j =1
qjxj
τ
n
∑x l j =1
j j
θ jτ ij n n + qi 1 − ln ∑ θ jτ ji − ∑ n j =1 j =1 ∑ k =1θ kτ kj
(10)
in the equation can be expressed as Eqs. (11)-(14). (11)
(12)
10
li =
Z ( ri − qi ) −( ri −1) 2
(13)
uij − u jj RT
τ ij = exp −
φi
and
θi
(14)
refer to the volume parameter and surface area parameter of the pure component i,
respectively, and Z stands for the lattice coordination number, Z=10. For ternary systems, the UNIQUAC model is shown in Eq. (15).
φ ( x l + x2 l2 + x3l3 ) φ Z θ ln γ 1 = ln 1 + q1 ln 1 + l1 − 1 1 1 x1 x1 2 φ1 θ 3τ 13 θ1 θ 2τ 12 + q1 1 − ln (θ1 + θ 2τ 21 + θ 3τ 31 ) − − − θ1 + θ 2τ 21 + θ 3τ 31 θ1τ 12 + θ 2 + θ 3τ 32 θ1τ 13 + θ 2τ 23 + θ 3
(15)
Table 2. Group contribution parameters of aspirin and solvents in UNIQUAC model. Aspirin
Water
Ethanol
Acetone
2-Propanol
1,2-Propanediol
ri
6.06
0.92
2.1055
2.5735
2.7791
3.5524
qi
4.792
1.4
1.972
2.336
2.508
3.4
Vm (cm3/mol)
133.45
18.01
58.39
74.03
76.40
73.45
The values of
ri and qi of API and solvents can be obtained from the Dortmund Database
(DDB) [40]. (see Table 2). The values of
ri and qi of polymers are calculated from Eqs.
(16)-(17) [41, 42]. The results are shown in Table 3.
ri = 0.029281 Vm qi =
(Z − 2) ri 2(1 − b i ) + Z Z
(16) (17)
11
means the molar volume of the pure component. The
values of polymers are
calculated by the group contribution method [41, 42]. Z stands for the coordination number, Z=10.
bi is the volume factor of the component i, bi =1 [41].
Table 3. Group contribution parameters of polymers in UNIQUAC model. PEG 6000
PEG 400
PVP K25
HPMC E3
Poloxamer 188
ri
153.57
10.41
614.29
128.33
223.28
qi
122.86
8.33
491.43
102.66
178.63
Vm(cm3/mol)
5244.76
355.40
20979.02
4382.73
7625.57
Although all three models are based on the theory of local composition, they are quite different. From the model equation, we can see that NRTL has no entropic term and Wilson has an implicit entropic term. UNIQUAC has obvious entropic term [43]. 3.5. Parametric regression and accuracy analysis According to Eq. (18), the Levenberg-Marquardt algorithm is used to minimize the objective function for parameter estimation [44]. In this work, MATLAB software is employed to calculate all the interaction parameters. xi,exp − xi,cal Fobj = ∑ xi,exp k =1 n
2
k
(18)
The calculation accuracy of the thermodynamic model is evaluated by the average relative deviation (ARD) and the root mean square deviation (RMSD) between the experimental and calculated values.
12
ARD =
1 n xi,exp − xi,cal ∑ x n i=1 i ,exp
(19) 1
2 2 1 n RMSD = ∑ ( xi ,cal − xi ,exp ) n i =1
(20)
In Eqs. (19)-(20), xi,cal is the solubility calculated by the model in mole fraction, xi,exp is the experimentally measured solubility in mole fraction, and n is the number of experimental data points.
4. Results and discussions 4.1. Influence of polymer type on aspirin solubility At 293.15-313.15 K, the solubility of aspirin in PEG 6000, PEG 400, PVP K25, HPMC E3, and poloxamer 188 aqueous solutions with various mass fractions (2wt%, 5wt%, 10wt%) was presented in Figure 2. In all systems, the solubility of aspirin was a function of polymer content, polymer type and temperature. As presented in Figure 2, the solubility of aspirin was significantly affected by the existence of polymeric excipients. In most systems with different temperatures and polymer concentrations, the solubility of aspirin was improved compared to that in water, which was consistent with the enhancement of API solubility by polymeric excipients as mentioned in the literatures. Paus et al. found that the addition of PVP K25 enhanced the solubility of indomethacin and naproxen better than PEG 6000 [8]. Soni et al. observed higher solubility of indomethacin with the existence of PEG 6000 compared to PEG 400 [45], which was in agreement with the solubilization ability of PVP K25, PEG 6000 and 13
PEG 400 for aspirin in present experimental observations. In general, PVP K25 and poloxamer 188 had better solubilization effects on aspirin than PEG 6000, HPMC E3 and PEG 400. It should be noted that PVP K25 showed the best solubilization capability. It can be ascribed to the strong capability of PVP K25 to establish hydrogen bonding with aspirin [8, 46].
Figure 2. At 293.15-313.15 K, the solubility of aspirin in water (square), and in aqueous solutions containing 2wt% (a), 5wt%(b) and 10wt% (c) of PVP K25 (circle), PEG 6000 (inverted triangle), PEG 400 (diamond), HPMC E3 (triangle) and poloxamer 188 (star). 14
4.2. Influence of temperature on aspirin solubility Figure 2 illustrated that there was an apparent positive correlation between the solubilization effect of polymer and temperature in an aqueous solution with various polymer contents (2wt%, 5wt%, 10wt%), which was most pronounced in the case of poloxamer 188 as the polymeric excipient. The increase of the solubility of aspirin at 313.15 K in an aqueous solution containing 2wt%, 5wt% and 10wt% of poloxamer 188 was about 16.3 times, 11.2 times and 5.0 times as much as that at 293.15 K. When it came to other polymers, the solubility increase of aspirin at 313.15 K in water with the existence of 2wt%, 5wt% and 10wt% of them was less than 6 times as much as that at 293.15 K. The temperature had an outstandingly greater impact on poloxamer 188 than other polymers causing the solubilization effect of poloxamer 188 progressively superior to other polymers with increasing temperature. Al-Saden et al. demonstrated that the intrinsic viscosity of poloxamer 188 in aqueous solution decreased with increasing temperature [47]. Although the poloxamer 188 system was not monodisperse, its dispersion declined with the increase of temperature. Moreover, poloxamer 188 is an amphiphilic structure of the block arrangement of propylene oxide (PO) and ethylene oxide (EO) [48, 49]. The increase in temperature leads to the continuous dehydration of PO and EO chains. Below room temperature, both PO and EO blocks in poloxamer 188 are hydrated and are relatively water-soluble. PO blocks begin to dehydrate and become insoluble as the temperature rises leading to the micelle formation [48]. The monomolecular micelles of the temperature-increasing system aggregate into aggregates of different sizes, thus affecting the solubilization of poloxamer 188 [50]. 15
4.3. Influence of polymer concentration on aspirin solubility In order to reveal the role of the polymer concentration on the solubilization effect of polymers for API, the solubility of aspirin in aqueous solutions with several polymer concentrations (2wt%, 5wt%, and 10wt%) was compared as shown in Figure 3. Additionally, as for PVP K25, which showed better solubilization performance, the concentration of 8wt% was also considered here. It was observed from Figure 3 that when the concentration of polymer was 2wt%, the solubility of aspirin almost did not increase compared with that in water, and even was found to decrease slightly at 293.15 K. As the concentration of polymer increased, the solubility of aspirin was observed to increase at each temperature, i.e., there was a positive correlation between the solubility of aspirin and the polymer concentration. For instance, at the temperature of 313.15 K, the increments of aspirin solubility in aqueous solutions with the poloxamer 188 concentration of 10wt% was about 7.0 times and 2.3 times as high as those of 2wt% and 5wt%, respectively. The increments of aspirin solubility in aqueous solutions with the PEG 6000 concentration of 10wt% was around 9.1 and 2.6 times as much as those of 2wt% and 5wt%, respectively. The increments of aspirin solubility in aqueous solutions with the PEG 400 concentration of 10wt% was nearly 13.8 and 3.1 times as much as those of 2wt% and 5wt%, respectively. Besides, the solubilizing effect of polymer appeared to enhance with the increase in temperature. Temperature synergized with the polymer concentration to improve the solubility of aspirin. It should be noted that it was rather difficult to precisely measure the solubility of aspirin in the aqueous solution with 10wt% of HPMC at 313.15 K because of its high viscosity. Furthermore, it has also been observed in the 16
literature that the solubility of API was found to decrease as the viscosity of HPMC rose [51, 52]. Therefore, the solubility of aspirin in the aqueous solution with 10wt% HPMC wasn’t measured at 313.15 K in this work.
17
Figure 3. At 293.15-313.15 K，solubility of aspirin in aqueous solutions with 2wt% (triangle), 5wt% (diamond), 10wt% (star) PEG 6000(a), PEG 400(b), HPMC E3(c), poloxamer 188(d) and 18
2wt% (triangle), 5wt% (diamond), 8wt% (circle), 10wt% (star) PVP K25(e) and ultra-pure water (square).
4.4 Model prediction of binary systems The melting temperature and melting enthalpy of aspirin were reported in the literature as
T fus =408.65 K and ∆H fus =33.509 kJ/mol [53]. The solubility data of aspirin in ethanol, acetone, 2-propanol and 1,2-propanediol was obtained in the literature at the temperature range of 290.6-336.6 K [54]. In present work, the experimental solubility of aspirin in ultrapure water was determined at 293.15-313.15 K. When the temperature is higher than room temperature, the solubility of aspirin in aqueous solution reported in this work is slightly higher than that of References 55 and 56 (see Figure S1) [55, 56]. It may be caused by the following reasons: our measurement time (48 h for stirring, 2 h for settling and PES filter for filtering) is longer than that (about 1 h for stirring and 24 h for settling) in the Literature 56. In our experiments, we found that the solid-liquid equilibrium was not reached for only 24 h. The sample concentrations were measured again after 72 h to ensure that the concentration of aspirin is the equilibrium solubility at 48 h. In addition to that, the method reported in the literature is titration with sodium hydroxide after adding phenolphthalein indicator, which probably have some influence on aspirin equilibrium solubility. Aspirin has a pKa of 3.5 and is a poorly water-soluble weak acid, the use of a pH meter or a conductance meter would be better for the requirement of more precise results. In addition, when the studied temperature is higher than room temperature, it is 19
possible to appear precipitation of drug solids during titration, which might lead to a slightly smaller experimental result. Literature 55 only reported the aspirin solubility at 298.15 K, and it did not include the experimental deviation. As provided in Table S1 (Supporting Information), the binary interaction parameters of Wilson, NRTL and UNIQUAC model were regressed according to our experimental data. Meanwhile, the solubility of aspirin was predicted at such temperatures in above organic solvents and water. Figure 4 provides the predicted aspirin solubility in various solvents by using Wilson, NRTL and UNIQUAC models compared with the experimental data.
Figure 4. The solubility of aspirin in ethanol (star), acetone (left triangle), 2-propanol (right triangle), 1,2-propanediol (hexagon) and water (square). The symbols indicate the aspirin solubility obtained experimentally in this work or literature, and the lines indicate the calculated values of the aspirin solubility by using Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models. 20
Table 4. The RMSD and the ARD between the calculated and experimental aspirin solubilities in binary systems. Wilson
NRTL
UNIQUAC
ARD
RMSD×103
ARD
RMSD×103
ARD
RMSD×103
H2O
0.0568
0.0382
0.0578
0.0360
0.0562
0.0400
Ethanol
0.0025
0.4039
0.0030
0.4531
0.0143
2.6945
Acetone
0.0313
4.2142
0.0399
5.3440
0.0118
1.6912
2-Propanol
0.0099
1.7586
0.0097
1.7330
0.0191
3.2415
1, 2-Propanediol
0.0494
5.9695
0.0486
5.8687
0.0513
6.2254
Average
0.0300
2.4769
0.0318
2.6869
0.0305
2.7785
The ARD and RMSD of aspirin solubility in water, ethanol, acetone, 2-propanol and propylene glycol were summarized in Table 4, which were obtained by comparing the experimental aspirin solubility data with the predicted values of Wilson, NRTL, and UNIQUAC models. According to Table 4, the average ARDs of Wilson, NRTL and UNIQUAC models were 0.0300, 0.0318 and 0.0305, respectively. Besides, all the ARDs of above three models were below 6%. It indicated that the solubility of aspirin in water and such four organic solvents were well predicted by Wilson, NRTL and UNIQUAC models. For above five binary API-solvent systems, the average ARD and RMSD of Wilson model were 0.03 and 2.4769×10-3, respectively, which represented that the Wilson model possessed the best prediction accuracy. 4.5 Model prediction of ternary systems 21
The interaction parameters of the Wilson, NRTL and UNIQUAC models for ternary systems were regressed based on the experimentally determined solubility data of aspirin at 293.15-313.15 K in aqueous solutions in presence of 10wt% polymeric excipients (PVP K25, PEG 6000, PEG 400, HPMC E3 and poloxamer 188). In 2wt%, 5wt% polymer-water solutions, the concentration of polymer is relatively small, its value will be much smaller especially when described in mole fraction for the model calculation. Parameters regressed from mixtures at 10% polymer concentration can reflect the interactions between polymers and drug. Model parameters were listed in Tables 5-7. Table 5. Interaction parameters within Wilson model of ternary API-water-polymer systems.
λ12 − λ22
λ21 −λ11
λ13 − λ33
λ31 −λ11
λ23 − λ33
λ32 − λ22
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
PEG 6000
-3677.0
-10480.4
28685.9
30321.7
116.3
-5262.5
PEG 400
-2719.9
-12582.9
23459.6
10766.1
8.3
308.5
PVP K25
-3381.5
-11664.7
15795.4
12512.3
866.5
-1235.4
HPMC E3
-4828.4
18971.3
53043.0
52427.9
-18760.5
-12567.0
Poloxamer 188
-3264.7
-12468.6
19309.6
16357.2
-272.0
-2490.8
Table 6. Interaction parameters within NRTL model of ternary API-water-polymer systems.
g12 − g22 g21 − g11 g13 − g33 g31 − g11 -1
(J·mol )
-1
(J·mol )
-1
(J·mol )
-1
(J·mol )
g23 − g33 g32 − g22 -1
(J·mol )
α
-1
(J·mol ) 22
PEG 6000
-4651.0
-20960.1
86039.7
10511.4
-76.3
4641.6
0.4
PEG 400
4078.1
-2998.0
11677.8
8382.6
-82.3
-4060.9
0.47
PVP K25
-4793.8
-23795.1
78332.8
10354.7
27.9
4791.8
0.47
HPMC E3
-5374.8
-18587.9
72153.2
12074.3
-97.1
5359.0
0.47
Poloxamer 188
-3764.7
-17464.3
75009.9
9947.6
2.1
3760.2
0.47
Table 7. Interaction parameters within UNIQUAC model of ternary API-water-polymer systems.
u12 −u22
u21 −u11
u13 −u33
u31 −u11
u23 − u33
u32 − u22
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
(J·mol-1)
PEG 6000
-863.6
1204.0
-1095.3
2093.6
6499.4
693.9
PEG 400
-3519.8
527.7
-70.3
793.5
19384.3
-3247.6
PVP K25
-388.8
404.2
-344.9
966.5
8917.7
290.1
HPMC E3
5281.8
9436.2
11811.2
-1986.7
6731.0
-5450.8
Poloxamer 188
-251.4
435.8
-94.2
704.6
11394.0
109.1
In order to evaluate the reliability and the predictive performance of above three models, the solubility of aspirin at five temperatures was calculated in different polymer aqueous solutions by substituting above parameters into corresponding model equations. The results were summarized in Tables S3 and S4.
23
In addition, we calculated the solubility of aspirin at 273.15-323.15 K in various polymer-water solutions through the same method and the results are shown in Figures 5-9 with a comparison with the experimental data.
Figure 5. At 293.15-313.15 K, the experimental values (including error bars) of aspirin solubility in PVP K25 aqueous solutions with PVP K25 mass fractions of 2wt% (a), 5wt% (b), 8wt% (c) and 10wt% (d). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models. 24
Figure 6. At 293.15-313.15 K, the solubility of aspirin in PEG 6000 aqueous solutions with PEG 6000 mass fractions of 2wt% (a), 5wt% (b) and 10wt% (c). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models.
25
Figure 7. At 293.15-313.15 K, the solubility of aspirin in PEG 400 aqueous solutions with PEG 400 mass fractions of 2wt% (a), 5wt% (b) and 10wt% (c). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models.
26
Figure 8. At 293.15-313.15 K, the solubility of aspirin in HPMC E3 aqueous solutions with HPMC E3 mass fractions of 2wt% (a), 5wt% (b) and 10wt% (c). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models.
27
Figure 9. At 293.15-313.15 K, the solubility of aspirin in poloxamer 188 aqueous solutions with mass fractions of 2wt% (a), 5wt% (b) and 10wt% (c). The symbols indicate the experimental aspirin solubility data and the lines indicate the corresponding calculated results by Wilson (dash line), NRTL (dash dot line), and UNIQUAC (solid line) models.
As shown in Figures 5-9, the experimental solubility of aspirin were compared with the predicted results of NRTL, UNIQUAC and Wilson models in the aqueous solutions with PVP K25 (2wt%, 5wt%, 8wt% and 10wt%), PEG 6000 (2wt%, 5wt% and 10wt%), PEG 400 (2wt%, 28
5wt% and 10wt%), HPMC E3 (2wt%, 5wt% and 10wt%) and poloxamer 188 (2wt%, 5wt% and 10wt%), respectively. It is intuitively observed that both NRTL and UNIQUAC models predict the solubility of aspirin at 273.15-320.15K in aqueous solutions in the presence of 2wt%, 5wt%, 8wt% and 10wt% of above five polymer excipients. The Wilson model showed the worst predictive performance as it only described well the aspirin solubility in aqueous solutions with 10wt% polymer solutions, but it did not have a good predictive capability in other API-polymer-water systems. All of the three models showed poor prediction in aqueous solutions with HPMC. For the UNIQUAC model, which had the best predictive performance, its predicted results in HPMC systems (2wt% and 5wt%) were found to be significantly higher than the experimental solubility data. The high viscosity of the HPMC aqueous solutions as mentioned in Section 4.3 might affect the dissolution of aspirin, and even make it difficult to measure the API solubility accurately. Table 8. The ARD and RMSD between the experimental and calculated API solubilities in ternary systems. NRTL
Wilson
UNIQUAC
ARD
RMSD×104
ARD
RMSD×104
ARD
RMSD×104
2wt% PEG6000
0.7823
5.5196
0.0795
0.4986
0.0440
0.4706
5wt% PEG6000
0.4749
3.9898
0.0628
0.4988
0.0447
0.4711
10wt% PEG6000
0.0182
0.2065
0.0191
0.2124
0.0196
0.2308
2wt% PEG400
0.8202
5.6454
0.1924
1.4137
0.0472
0.3917
29
5wt% PEG400
0.5203
4.0239
0.1193
0.9892
0.0270
0.2680
10wt% PEG400
0.0103
0.1417
0.0138
0.2413
0.0226
0.3141
2wt% PVPK25
0.7907
5.7889
0.0681
0.5079
0.1217
1.0048
5wt% PVPK25
0.4978
4.6558
0.1007
0.9604
0.0663
0.5137
8wt% PVPK25
0.1834
2.3585
0.0896
1.3116
0.0817
0.8197
10wt% PVPK25
0.0814
0.8499
0.0958
1.4296
0.0878
0.9851
2wt% HPMCE3
0.7325
5.0559
0.4391
2.8516
0.3259
1.8479
5wt% HPMCE3
0.4270
3.5511
0.3399
2.6380
0.1339
0.9848
10wt% HPMCE3
0.0376
0.3285
0.0295
0.2735
0.0314
0.2663
2wt% Poloxamer188
0.7996
5.9598
0.0934
0.8336
0.1312
0.8848
5wt% Poloxamer188
0.5038
5.0329
0.0605
0.7002
0.1095
0.9178
10wt% Poloxamer188
0.0618
2.1895
0.0622
2.2057
0.0828
1.9743
Average
0.4214
3.4561
0.1166
1.0979
0.0861
0.7716
Figure 10. At 293.15-313.15 K, the ARD between the calculated aspirin solubility by Wilson, NRTL and UNIQUAC models and the experimental solubility of aspirin in aqueous solutions of 30
PEG 6000 (2wt%, 5wt% and 10wt%), PEG 400 (2wt%, 5wt% and 10wt%), poloxamer 188 (2wt%, 5wt% and 10wt%), PVP K25 (2wt%, 5wt%, 8wt% and 10wt%) and HPMC E3( 2wt%, 5wt% and 10wt%).
The ARD and RMSD between the experimental and calculated API solubilities in ternary systems were summarized in Table 8 and Figure 10. It was observed that the ARDs of these models decreased gradually with the increase of the concentration of polymers. The average ARDs of Wilson, NRTL and UNIQUAC models in aqueous solutions with 2wt% polymer were 0.7851, 0.1745 and 0.1340, respectively. The average ARDs of the three models in aqueous solutions with 5wt% polymer were 0.4848, 0.1366 and 0.0763, respectively. The average ARDs of the three models in aqueous solutions with 10wt% polymer were 0.0419, 0.0441 and 0.0488, respectively. It was found that the solubility of aspirin was well predicted by the UNIQUAC and NRTL model in aqueous solutions with the polymer concentration of 2wt%, 5wt% and 10wt% and of 5wt% and 10wt%, respectively. While for Wilson model, it was almost impossible to achieve its prediction under the polymer concentration of 2wt% and 5wt%. UNIQUAC model was found to have the highest prediction accuracy in PEG aqueous solutions with an average ARD of 0.0342. The prediction accuracy of NRTL model in poloxamer 188 aqueous solutions was slightly higher than UNIQUAC model and the average ARD of the former was 0.0720 and that of the latter was 0.1078. Interestingly, the average ARDs of the three models in aqueous solutions with 10wt% polymer were quite close and the Wilson model was observed to possess 31
the smallest ARD, which suggested that the Wilson model had better regression performance than the other two models in the aqueous solutions with the polymer concentration of 10wt%. Overall, the average ARD of each model obeyed the following order: Wilson model (0.4214) > NRTL model (0.1166) > UNIQUAC model (0.0861) implying that UNIQUAC model had the best prediction performance. The prediction accuracy of UNIQUAC model for different polymer-water systems followed the order: PEG 400> PEG 6000> PVP K25> poloxamer 188> HPMC E3.
5. Conclusions In this work, the influence of polymeric excipients on the solubility of aspirin was systematically investigated through both experimental measurement and thermodynamic model prediction. The experimental results demonstrated that the solubility of aspirin was enhanced with the existence of polymeric excipients and PVP K25 showed the best solubilizing capability. The solubilization effect of polymers was observed to be positively correlative with the temperature and the polymer concentration. Particularly, the solubilizing ability of poloxamer 188 was most affected by temperature. The Wilson, NRTL, and UNIQUAC models were found to successfully correlate and predict the solubility of aspirin in binary systems. The model parameters were obtained from the experimental data at a certain polymer concentration and were used to predict the solubility of the drug in aqueous solutions with other polymer concentrations, and UNIQUAC model achieved best prediction performance from binary systems to ternary systems. However, Wilson 32
model had low ability to predict aspirin solubility for ternary systems even using the model parameters obtained from the experimental data at 10% polymer concentration. It is essential to accurately predict the solubility of API in aqueous solutions in the presence of various polymers (with different polymer concentration) at various temperatures for the screening of polymeric excipients.
Associated content Supporting information.
The following files are available free of charge.
Interaction parameters and predicted results of Wilson, NRTL and UNIQUAC models for API-solvent binary systems. And experimental data and calculated values of aspirin solubility in API- polymer ternary systems. (DOCX)
Author information Corresponding author
*E-mail: [email protected]; [email protected]
*Tel: +86-13951907361
Notes
The authors declare no competing financial interest.
33
Acknowledgment The authors gratefully acknowledge the financial support for this study from the National Natural Science Foundation of China (Grant No.: 21606043, 21776046), the Fundamental Research Funds for the Central Universities (Grant No.: 2242019K40145), the Six Talent Peaks Project in Jiangsu Province (Grant No.: XCL-079), and the Recruitment Program for Young Professionals (the Thousand Youth Talents Plan).
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HIGHLIGHTS
The effects of five polymers on API solubility at various temperatures were compared
Local composition model was applied from binary system to ternary system
Local composition model was applied to predict aspirin-polymer-water systems
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: