International Journal of Pharmaceutics 485 (2015) 277–287

Influence of excipients on solubility and dissolution of pharmaceuticals

Raphael Paus, Anke Prudic, Yuanhui Ji *TU Dortmund, Department of Biochemical and Chemical Engineering, Laboratory of Thermodynamics, Emil-Figge Str. 70, D-44227 Dortmund, Germany

A R T I C L E I N F O

Article history:Received 26 January 2015Received in revised form 27 February 2015Accepted 2 March 2015Available online 5 March 2015

Chemical compounds studied in this article:Indomethacin (PubChem CID: 3715)Naproxen (PubChem CID: 156391)Polyethylene glycol (PubChem CID: 174)Polyvinylpyrrolidone (PubChem CID: 6917)Mannitol (PubChem CID 6251)

Keywords:DissolutionExcipientsThermodynamicsSolubilityPC-SAFTChemical potential gradientPoorly soluble APIs

A B S T R A C T

In this work, solubilities and dissolution profiles of the active pharmaceutical ingredients (APIs)indomethacin and naproxen were measured in water in the presence of one excipient out of polyethyleneglycol (PEG) 2000, 6000 and 12000, polyvinylpyrrolidone (PVP) K 25 and mannitol. It was found that thesolubility of indomethacin and naproxen was increased with an addition of the selected excipients, whichwas also predicted by the perturbed-chain statistical associating fluid theory (PC-SAFT). The two-stepchemical-potential-gradientty model was applied to investigate the dissolution mechanism ofindomethacin and naproxen in water in the presence of the excipient. It was found that the dissolutionmechanisms of indomethacin and naproxen were changed by the presence of excipients. Although thesolubility of the API was increased by the addition of excipients, the dissolution rate of the API wasdecreased in some cases. This was mainly due to the combination of the molecular interactions betweenthe API and the polymer with the influence of the excipients on the kinetic part (rate constant of thesurface reaction or diffusion of the API or both) of API dissolution as function of PEG molar mass as well asof the API type. Based upon the determined rate constants, the dissolution profiles were modeled with ahigh accuracy compared with the experimental data.

ã 2015 Elsevier B.V. All rights reserved.

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International Journal of Pharmaceutics

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1. Introduction

Many active pharmaceutical ingredients (APIs) show a lowsolubility and slow dissolution in aqueous solutions. As a result, theoral bioavailability of these poorly soluble APIs is often quite low.Therefore, several formulation strategies were developed toenhance the aqueous solubility and dissolution rate of these APIs.Within the formulation process, excipients are commonly used.Different polymers, e.g., polyethylene glycol (PEG) and polyvinyl-pyrrolidone (PVP), were reported to be suitable formulationmaterials for many poorly soluble APIs (Caron et al., 2010; Joshiet al., 2004; Kochling et al., 2007; Lakshman et al., 2008;Papadimitriou et al., 2012; Windbergs et al., 2009). Moreover,sugars, e.g., mannitol, are often used for pharmaceutical for-mulations (Liao et al., 2005; Littringer et al., 2013). However, so far,the detailed influencing mechanism of these excipients on APIsolubility and dissolution is far from being well explained. As thedissolution process of many poorly soluble APIs often showscomplex dynamic characteristics, an accurate description of their

* Corresponding author. Tel.: +49 231 755 3199; fax: +49 231 755 2572.E-mail addresses: Yuanhui.Ji@bci.tu-dortmund.de, yuanhuiji@aliyun.com (Y. Ji).

http://dx.doi.org/10.1016/j.ijpharm.2015.03.0040378-5173/ã 2015 Elsevier B.V. All rights reserved.

dissolution profiles and an appropriate analysis of their dissolutionmechanism turn out to be difficult (DeAlmeida et al.,1997; Lu et al.,2011). Additionally, the presence of excipients, which mightinfluence the dissolution mechanism of APIs, complicates theanalysis and prediction of the specific API dissolution profile. Basedon the approach proposed by Noyes and Whitney, (1897), severalmodels, in most cases, empirical approaches (Costa et al., 2001;DeAlmeida et al., 1997; Gibaldi and Feldman, 1967; Higuchi, 1961,1963; Higuchi et al., 1958; Hopfenberg, 1976; Korsmeyer et al.,1983; Mooney et al., 1981a,b) were developed to describe thedissolution profiles of APIs. Mooney et al. (1981a,b); Mooney et al.(1981a,b) investigated the dissolution of several weak acid APIsunder unbuffered and buffered conditions from a rotating disk dieand proposed a model for describing the initial steady-statedissolution rate of those APIs based on the Fick’s second law ofdiffusion. In this model, a diffusion-controlled mass transport ofthe investigated APIs was assumed, in which simple, instan-taneously established reaction equilibria were considered across apostulated diffusion layer (Mooney et al., 1981a,b). However, forthe investigation on the influence of excipients on API dissolution,these models need to be combined with an appropriatethermodynamic model to take into account the molecularinteractions between API and water, between API and the excipient

278 R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287

as well as between the excipient and water. In previous works,based on the work of Ji et al. (2010) and Lu et al. (2011), a two-stepchemical-potential-gradient model in which the molecular inter-actions of the systems were accounted for was developed todescribe the dissolution profiles and to analyze the dissolutionmechanism of poorly soluble crystalline APIs and their formula-tions under various conditions (Ji et al., 2015; Paus et al., 2015).Within this model, two consecutive steps, namely the surfacereaction and diffusion, were considered and expressed in terms ofthe chemical potential gradient of the API (the thermodynamicdriving force) and the corresponding rate constants (from kineticaspect). In this paper, the two-step chemical-potential-gradientmodel was used to analyze the influencing mechanism ofexcipients on the dissolution of APIs in water.

In this work, indomethacin and naproxen were selected asmodel APIs. PEG with different molar masses (PEG 2000, PEG6000 and PEG 12000), PVP with a molecular weight of 25,000 g/mol (PVP K 25) and mannitol were selected as model excipients.The chemical structures of the APIs and excipients are shown inFig. 1. In literature, PVP and PEG were reported to show a highinfluence on the aqueous solubility of poorly-soluble APIs(Afrasiabi Garekani et al., 2003; Bettinetti and Mura, 1994;Cadwallader and Madan, 1981; Mura et al., 1996). Mura et al.(1996) investigated the influence of PEGs with different molarmasses on the aqueous solubility of naproxen. They found that byaddition of 2 wt% of PEG 4000 in the solution, the solubility ofnaproxen was increased by more than two times. As during APIdissolution, the amount of excipients is commonly quite smallcompared to the amount of solvent (intestinal fluid) and as a highinfluence of 2 wt% of PEG on API solubility was already reported inliterature, in this work, the solubility and dissolution profiles ofindomethacin and naproxen in water in the presence of 2 wt% ofthe model excipients were measured. As the perturbed-chainstatistical associating fluid theory (PC-SAFT (Gross and Sadowski,2001)) was already successfully applied to calculate thethermodynamic properties of APIs in polymers (Prudic et al.,2014a,b, 2015b), solvents and solvent mixtures (Ruether andSadowski, 2009, 2011) under various conditions, it was applied todescribe the influence of excipients on API solubility (thermody-namic aspect). The two-step chemical-potential-gradient modelwas applied to analyze the influencing mechanism of excipientson API dissolution (kinetic aspect) by accounting for theinteractions between the API and the excipient, the API andwater as well as the interactions between the excipient and watervia PC-SAFT (Gross and Sadowski, 2001). Finally the dissolution

Fig. 1. Chemical structures of indomethacin (a), na

profiles of the APIs were modeled and compared with theexperimental findings.

2. Theory

2.1. Two-step chemical-potential-gradient model

As introduced in previous works (Ji et al., 2010, 2015;Paus et al., 2015), two main consecutive steps are involved inthe API dissolution process. In the first step the disintegration ofthe API crystals and the hydration of the API molecules take place.This step is called surface reaction. For this step, the chemicalpotential gradient of the API between the solid phase mS

API and thesolid–liquid interface mI

API is the thermodynamic driving force ofthe surface reaction. For the second step, the diffusion of thehydrated API molecules from the solid–liquid interface into thebulk phase of the medium takes place. Here the chemical potentialgradient of the API between the solid–liquid interface mI

API and thebulk phase mB

API, is the thermodynamic driving force of diffusion.The rates of surface reaction and diffusion are described inEqs. (1) and (2).

JAPI ¼ V � dcBAPIdt

� 1A¼ ks

mSAPIRT

�mIAPIRT

!(1)

JAPI ¼ kdmI

APIRT

�mBAPIRT

� �(2)

In Eq. (1), JAPI is the dissolution rate of the API in mol/(m2 s), V is thevolume of the dissolution medium in m3; A is the surface area ofthe dissolving API in contact with the dissolution medium in m2,cBAPI is the concentration of the API in the bulk phase of the mediumin mol/m3 and t is the time in s. In Eqs. (1) and (2), T is thetemperature in K and R is the ideal gas constant in J/(mol K). mS

API,mI

API and mBAPI are the chemical potentials of the API in the solid

phase, at the solid–liquid interface and in the bulk phase in J/mol,respectively. ks and kd are the rate constants of the surface reactionand diffusion in mol/(m2 s), respectively.

Based on the values of ks and kd within Eqs. (1) and (2), the ratecontrolling step of API dissolution can be determined. The APIdissolution is controlled by the surface reaction in the case ofks< kd and it is controlled by diffusion if kd< ks. In the case of ksequal to or similar to kd both steps are important for APIdissolution.

proxen (b), PEG (c), PVP (d) and mannitol (e).

Table 1Melting temperature, melting enthalpy and the difference in the solid and liquidheat capacities of indomethacin and naproxen used within this work.

API TSL0API DhSL

0APIDcSLpAPI

Ref.

[K] [kJ/mol] [J/(mol K)]

Indomethacin 433.25 39.3 116.95 (Paus et al., 2015)Naproxen 429.47 31.5 87.44 (Paus et al., 2015)

R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287 279

The chemical potential of the API at the solid–liquid interface isdetermined by the Statistical Rate Theory developed by Dejmekand Ward (Dejmek and Ward, 1998; Ward et al., 1982). This theorydescribes the instantaneous API transport rate across thesolid–liquid interface according to Eq. (3).

JAPI ¼ ke expmS

API � mIAPI

RT

!� exp

mIAPI � mS

APIRT

!( )(3)

In Eq. (3), ke is the equilibrium exchange rate of the API moleculesbetween the solid and the liquid phase in mol/(m2 s). As a detailedderivation of the equilibrium exchange rate can be found inliterature (Dejmek and Ward, 1998; Ji et al., 2015; Paus et al., 2015;Ward et al., 1982), it is only briefly introduced in this paper. Theequilibrium exchange rate of the API between the solid and liquidphase per unit area of the interface can be described according toEq. (4).

ke ¼ xLAPIa1afffiffiffiT

pþ xLAPIa2;af 0:51

ffiffiffiffiffiffiffiv3

n

rd2 (4)

In Eq. (4), xLAPI is the API solubility in the media in mole fraction, a1

and a2 are the proportionality constants, ; is a constant fraction ofmolecules that strike the solid surface, af describes the fraction ofthe area of the solid–liquid interface available for the transport ofmolecules from the medium, T is the temperature of the system inK, v is the stirring speed in round/s, n is the kinematic viscosityof the medium in m2/s and d is the thickness of the diffusion layerin m.

The chemical potential of the API in the solid phase mSAPI, as used

in Eqs. (1) and (3) can be calculated by the solid–liquid equilibrium(SLE). Here, the chemical potential of the API in the solid phase isequal to that in its saturated solution mI

API (Eq. (5)).

mSAPI ¼ mL

API ¼ mL0API � RT lnðaLAPIÞ (5)

In Eq. (5), aLAPI is the API activity in the saturated solution, mL0API is

the chemical potential of the API in the standard state (here thepure liquid API).

The chemical potentials of the API at the solid–liquid interfacemI

API and in the bulk phase mBAPI required in Eqs. (1)–(3) can be

expressed as shown in Eqs. (6) and (7).

mIAPI ¼ mL

0APIþRTlnðaIAPIÞ (6)

mBAPI ¼ mL

0APIþRTlnðaBAPIÞ (7)

In Eq. (6), aIAPI is the activity of the API at the solid–liquid interface.In Eq. (7), aBAPI is the activity of the API in the bulk phase of themedium. In this work, the required API activities (see Eqs. (5)–(7))are calculated using the thermodynamic model PC-SAFT (Grossand Sadowski, 2002b) according to Eq. (8).

aAPI ¼ xAPIgAPI (8)

In Eq. (8), xAPI is the mole fraction of the API in the solution and gAPIthe corresponding API activity coefficient. Based on Eqs. (4)–(7),Eqs. (1)–(3) can be described in terms of the API activity (see Eqs.(9)–(11)).

JAPI ¼ ks ln aLAPI � ln aIAPI� �

(9)

JAPI ¼ kd ln aIAPI � ln aBAPI� �

(10)

JAPI ¼ xLAPI a1afffiffiffiT

pþ xLAPI a2;af 0:51

ffiffiffiffiffiffiffiv3

n

rd2

!aLAPIaIAPI

� aIAPIaLAPI

!(11)

In Eqs. (9)–(11), the parameters K1 (K1 = a1af) and K2

(K2 ¼ a2;afd2), as well as kd and ks were fitted to the experimentalAPI dissolution profiles based on Eqs. (9)–(11).

Finally, based on Eqs. (9) and (10), the dissolution rate of the APIcan be described in terms of the rate constant of the whole APIdissolution kT and the chemical potential gradient of the APIbetween the solid phase and the bulk phase according to Eq. (12).

JAPI ¼ kTmS

API � mBAPI

RT

!¼ kT ln aLAPI � ln aBAPI

� �(12)

In Eq. (12), kT can be expressed in terms of the surface-reaction rateconstant ks and the diffusion rate constant kd (see Eq. (13)).

kT ¼ 11=kdþ1=ks

(13)

2.2. Solid–liquid equilibrium

Based on the SLE (Prausnitz et al., 1998), the temperature-dependent solubility of an API in a solution was calculatedaccording to Eq. (14).

xLAPI ¼1

gLAPI

exp �DhSL0APIRT

1 � T

TSL0API

!(

�DcSL0pAPI

Rln

TSL0API

T

!� TSL

0API

Tþ1

!)(14)

In Eq. (14), xLAPI is the solubility of the API in the solution in molefraction, gL

API is the activity coefficient of the API in the saturatedsolution, which is used to account for the influence of the solvent

and excipient on API solubility in the solution. TSL0API, DhSL0API and

DcSLp0API are the caloric properties of the API, namely the meltingtemperature in K, melting enthalpy in J/mol and the difference inthe solid and liquid API heat capacities in J/(mol K), respectively.T is the temperature in K and R is the universal ideal gas constant.In this work, the caloric properties of the selected APIs were takenfrom previous works, as summarized in Table 1.

As the excipients, the API and water show different physico-chemical properties due to their different molecular interactionsand shapes, the activity coefficient of the API is often quite differentfrom one and has to be considered within the solubilitycalculations (see Eq. (14)). In this work, the API activity coefficientwas calculated as function of temperature and medium composi-tion using PC-SAFT (Gross and Sadowski, 2001).

2.3. PC-SAFT

Within PC-SAFT, the residual Helmholtz energy ares of thesystem is calculated as a sum of various contributions (Gross andSadowski, 2001, 2002a) resulting from the repulsion of the hardchain (ahc), van der Waals attractions (adisp, disp stands fordispersion) and hydrogen bondings (aassoc, where assoc stands forassociation), according to Eq. (15).

280 R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287

ares ¼ ahcþadispþaassoc (15)

Within PC-SAFT, each molecule is described as a chain ofsegments with a segment number of mseg

i and a segment diameterof si. The van der Waals interactions are described by thedispersion energy parameter ui/kB. Here, kB is the Boltzmannconstant in J/K. For molecules, which can form hydrogen bonds,two additional parameters, the association-energy parametereAiBi=kB and the association-volume parameter kAiBi, are required.Additionally, the number of association sites Nassoc

i within amolecule has to be determined.

To describe thermodynamic properties of binary mixtures, e.g.,mixtures between API, excipient and water, the Berthelot–Lorentzmixing rules are applied for the segment diameter and thedispersion energy of the mixture of different molecules. Thesegment diameter and the dispersion energy for a mixture of twocomponents i and j are given in Eqs. (16) and (17).

sij ¼12si þ sj� �

(16)

uij ¼ ð1 � kijÞffiffiffiffiffiffiffiffiffiuiuj

p(17)

A correction for the deviation of the interaction energy of unlikesegments from the geometric mean is made by the binaryinteraction parameter kij, as introduced in Eq. (17). In some cases,this parameter is determined as function of temperature(see Eq. (18)).

kij Tð Þ ¼ kij; slope � ðT=K � 298:15Þ þ kij; 298:15 K (18)

For systems in which cross association occurs, the cross-association interactions between two associating components canbe described by the combination rules proposed by Wolbach andSandler (Eqs. (19) and (20)) (Wolbach and Sandler, 1998).

eAiBj ¼ 12eAiBiþeAjBj

� �(19)

kAiBj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikAiBi kAjBj

p 2 � ffiffiffiffiffiffiffiffiffiffisisj

psiþsj� �

( )3

(20)

2.4. PC-SAFT pure-component parameters

In this work, the PC-SAFT pure-component parameters ofindomethacin, naproxen, water and the selected excipients weretaken from literature (Fuchs et al., 2006; Held et al., 2013; Prudicet al., 2015a, 2014a,b; Stoychev et al., 2009) and are summarizedin Table 2.

Table 2Molar mass and PC-SAFT pure-component parameters of naproxen, indomethacin, PEG

Substance M msegi

si ui/kB eAiBi

(g/mol) (�) (Å) (K) (K)

Naproxen 230.26 8.110 2.939 229.45 934Indomethacin 357.79 14.283 3.535 262.79 886PEG 2000 2000 101.2 2.899 204.6 1799PEG 6000 6000 303.6 2.899 204.6 1799PEG 12000 12000 607.2 2.899 204.6 1799PVP K 25 25700 1045.21 2.710 205.59 0Mannitol 182.17 7.230 2.935 227.03 5000Water 18.015 1.2047 2.793a 353.945 2425

a The expression swater = 2.7927 + 10.11 � exp(�0.01775 � T) � 1.417 � exp(�0.01146 �

2.5. PC-SAFT binary interaction parameters

In this work, the binary interaction parameters between theAPI and water, the API and PVP K 25 as well as those betweenmannitol and water were taken from literature (Held et al., 2013;Paus et al., 2015,b; Prudic et al., 2014a,b). For PVP K 25/watersystem, a temperature-independent binary interaction parameterwas estimated by Prudic et al. (2015a) to describe the watersorption of PVP K 25 (vapor–liquid equilibrium) at 298.15 K. Inthis work, in order to improve the accuracy of predicted APIsolubility in water/PVP K 25 solution, temperature-dependentbinary interaction parameters between PVP K 25 and water wereestimated by fitting them to the solubility data of indomethacin inwater containing 2 wt% of PVP K 25 and these parameters werefurther used for predicting the solubility of naproxen in watercontaining 2 wt% of PVP K 25. As proposed by Prudic et al. (2014a)the binary interaction parameter between indomethacin and PEGwith different molar masses can be set to zero. As the APIsolubility in water in the presence of PEG was found to be stronglydependent on the PEG molar mass, a binary interaction parameterbetween water and PEG as function of PEG molar mass wasconsidered according to Eq. (21) and it was fitted to indomethacinsolubility in PEG/water solutions.

kPEG; water ¼ k � MPEG þ 0:086 (21)

In Eq. (21), k is a parameter which was estimated as �0.23 �10�4mol/g and MPEG is the molar mass of the polymer PEG ing/mol. Additionally, a temperature-dependent binary interactionparameter between naproxen and PEG was fitted to the solubilitydata of naproxen in the PEG 12000/water solution and it wasfurther used for the prediction of naproxen solubility in the PEG2000/water and PEG 6000/water solutions. The binary interactionparameter between the selected APIs and mannitol was set to zero.All the binary interaction parameters between API and water andbetween API and the excipient as well as between the excipientand water are summarized in Table 3.

3. Materials

Crystalline indomethacin (purity �99%) was purchased fromSigma–Aldrich Co., LLC (Germany). Naproxen (purity >99%) waspurchased from TCI Deutschland Co., LLC (Germany). PEG 2000was purchased from Merck (Germany), PEG 6000 from ProlaboVWR (Germany), and PEG 12000 from Sigma–Aldrich Co., LLC(Germany). PVP K 25 (Kollidon1 K 25) was purchased from BASF(Ludwigshafen, Germany). Mannitol (purity >98%) was purchasedfrom Sigma–Aldrich Co., LLC (Germany). All substances were usedas obtained without any further purification. Water was filtered,deionized and distilled using a Millipore purification system andused for all experiments.

2000, 6000 and 12000, PVP K 25, mannitol and water used within this work.

=kB kAiBi Nassoci Ref.

(�) (�)

.19 0.02 2/2 (Prudic et al., 2014b)

.44 0.02 3/3 (Prudic et al., 2014a)

.8 0.02 2/2 (Stoychev et al., 2009)

.8 0.02 2/2 (Stoychev et al., 2009)

.8 0.02 2/2 (Stoychev et al., 2009) 0.0451 231/231 (Prudic et al., 2015a; Prudic et al., 2014a) 0.1 6/6 (Held et al., 2013).671 0.0451 1/1 (Fuchs et al., 2006)

T) was used (Fuchs et al., 2006).

Table 4Measured kinematic viscosities (including standard deviations) of the selectedmedia at 310.15 K.

System n [mm2/s] Deviation

Water/mannitol 0.493 �0.012Water/PEG 2000 0.843 �0.008Water/PEG 6000 0.995 �0.032Water/PEG 12000 1.178 �0.007Water/PVP K 25 0.967 �0.003

R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287 281

4. Methods

4.1. API solubility measurement

Solubility measurements of indomethacin and naproxen inwater in the presence of one excipient out of PEG 2000, PEG 6000,PEG 12000, PVP K 25 and mannitol were carried out in 100 mlglass vessels with a heating jacket in a temperature range of288.15–313.15 K. For this purpose, an excess of the crystalline APIwas added into each medium (water containing 2 wt% of eachexcipient) and mixed with a magnetic stirrer at 600 rpm. After 96 h(thermodynamic equilibrium was ensured by a constant APIconcentration), the solubility was measured at each temperature.For sampling, syringes (10 ml) and needles were used. To preventAPI nucleation (if necessary), both, the syringe and the needle waspreheated prior to sampling. The sample (2–3 ml) was filtered by aPES filter with a mesh size of Ø 0.45 mm and then immediatelyanalyzed by the UV–vis spectroscopy (Analytic Jena Specord 210Plus spectrophotometer, Jena, Germany) at a wavelength of 331 nmfor naproxen and 320 nm for indomethacin according to theprocedure described in previous works (Paus et al., 2015). Eachmeasurement was performed in a triplicate and the mean valuewas reported.

4.2. Kinematic viscosity measurement of solutions

According to Eq. (11) the viscosities of the solutions in thepresence of the excipients were required for dissolution modeling.Therefore, the viscosities of the aqueous media containing 2 wt% ofeach excipient were measured using a MGW Lauda viscosimeter(Lauda-Königshofen, Germany) at 310.15 K (accuracy �0.01 K)according to the approach proposed by Ubbelohde (1937). Eachmeasurement was performed in triplicate and the mean value isreported. The temperature-dependent viscosity data of pure waterwere taken from literature (Kestin et al., 1978) and correlated bythe following function: n/(m2/s) = 2.248 � 10�10 (T/�C)2� 3.195 �10�8 (T/�C) + 1.572 � 10�6.

4.3. API dissolution measurement

The intrinsic dissolution profiles of indomethacin and naproxenin water in the presence of 2 wt% of each excipient (PEG 2000,6000, 12000, PVP K 25 and mannitol) were measured using arotating disk system (USP II). For this purpose a cylindrical tablet

Table 3Binary interaction parameters kij’s between API and water and between API and the ex

Component i Component j kij(T) = kij� (T

Indomethacin Mannitol 0

PEG 2000 0

PEG 6000 0

PEG 12000 0

PVP K 25 �0.000633 �Water 0.0001691 �

Naproxen Mannitol 0

PEG 2000 �0.043 � (T/PEG 6000 �0.043 � (T/PEG 12000 �0.043 � (T/PVP K 25 0.000128 � (

8Water 0.0002269 �

Water Mannitol �0.00022 �

PEG 2000 0.04

PEG 6000 �0.052

PEG 12000 �0.154

PVP K 25 0.002667 � (

(Ø = 8 mm) of pure API (200 mg � 1 mg) was pressed with acompressive force of 2 kN into the disk using a manual tabletpress device (Brütsch/Rüegger AG, Zurich, Switzerland). Within anexperiment the disk was rotated at a stirring speed of 50 rpm in theprepared media at 310.15 K (accuracy �0.3 K). The temperature andthe stirring speed were monitored during each experiment. Eachmedia was prepared by dissolving a defined mass of each excipientin water to generate a solution containing 2 wt% of each excipient.Sample analysis was conducted in spectrometer flow cells whichwere circulated with the dissolution media at 25 ml/min using apiston pump (SOTAX CY 7-50, Allschwil, Switzerland). APIconcentrations were measured at the same wavelengths as usedin the solubility measurements. Data analysis was performed bythe use of the WinSOTAX plus dissolution software (SOTAX Co.,LLC, Allschwil, Switzerland). Each measurement was performed ina triplicate and the mean value was reported.

5. Results and discussions

5.1. Kinematic viscosity of the selected media

The kinematic viscosities of the selected media at 310.15 K weremeasured according to the procedures described in Section 4.2.The measured results including the standard deviations aresummarized in Table 4.

For a better comparison of the measured kinematic viscositiesof different media, the measured results and the kinematicviscosity of pure water at 310.15 K are also shown in Fig. 2. Asshown in Fig. 2, the kinematic viscosities of the aqueous solutionsin the presence of 2 wt% PVP K 25, PEG 2000, PEG 6000 and PEG12000 are obviously higher than that of pure water. For the mediacontaining selected PEGs with different molar masses, theviscosity increases with an increase in the molar mass of PEG.Here, the viscosity of water containing 2 wt% PEG 12000 is around

cipient as well as between the excipient and water used within this work.

/K � 298.15) � kij, 298.15 K Ref.

this work(Prudic et al., 2014a)(Prudic et al., 2014a)(Prudic et al., 2014a)

(T/K � 298.15) � 0.09653 (Prudic et al., 2014b) (T/K � 298.15) � 0.05948 (Paus et al., 2015)

this workK � 298.15) + 0.07955 this workK � 298.15) + 0.07955 this workK � 298.15) + 0.07955 this workT/K � 298.15) � 0.09154 (Prudic et al., 2014b)

(T/K � 298.15) + 0.006475 (Paus et al., 2015)

(T/K � 298.15) � 0.0492 (Held et al., 2013)this workthis workthis work

T/K � 298.15) � 0.148 (Prudic et al., 2015a)/this work

Fig. 2. Kinematic viscosities of the selected media at 310.15 K.

282 R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287

1.7 times as high as that of pure water at 310.15 K. The aqueousmedia containing 2 wt% PVP K 25 and that containing 2 wt% PEG6000 show nearly the same kinematic viscosity. In the case of themedia in the presence of 2 wt% mannitol, the kinematic viscosity islower than that of pure water.

The measured viscosities of the selected media at 310.15 Kare further used for the dissolution mechanism analysis based onEqs. (9)–(11).

5.2. Measured API solubility in water in the presence of excipients

The measured aqueous solubility of indomethacin andnaproxen in water in the presence of 2 wt% of each excipient isshown in Fig. 3(a)–(d). As shown in this figure, the solubility ofboth APIs is obviously influenced by the presence of excipients.In all cases, the API solubility is a function of temperature aswell as of excipient type in water. For a comparison the

Fig. 3. (a) Solubility of indomethacin in water (Paus et al., 2015) (gray hollow stars), in wa(dark gray triangles). (b) Solubility of indomethacin in water (Paus et al., 2015) (gray sta(light gray pentagons) and in water with 2 wt% of PEG 12000 (light gray hollow squares).

of mannitol (hollow circles), in water with 2 wt% of PVP K 25 (dark gray triangles). (d) Solu2000 (gray circles), in water with 2 wt% of PEG 6000 (light gray pentagons) and in water wof API solubility in water and in water with 2 wt% of PEG 2000, 6000 and 12000 (full lines)K 25 (dashed lines) using PC-SAFT.

temperature-dependent solubility of indomethacin and naproxenin pure water (taken from a previous work (Paus et al., 2015)) isalso included in Fig. 3. As observed in Fig. 3(a), the presence of2 wt% of PVP K 25 increases the solubility of indomethacin inwater. At a temperature of 313.15 K, indomethacin solubility is1.4 times as high as that in pure water. The observed increase inthe aqueous solubility of indomethacin by adding PVP was alsoreported in literatures for several other APIs (Afrasiabi Garekaniet al., 2003; Bettinetti and Mura, 1994; Cadwallader and Madan,1981; Tros de Llarduya et al., 1998). This shows that ourexperimental observations agree with the results in theliteratures. Generally, an increase in API solubility in water wasobserved with an increase in PVP concentration in the aqueousmedia (Afrasiabi Garekani et al., 2003; Tros de Llarduya et al.,1998). This phenomenon might be mainly attributed to the highability of PVP to form hydrogen bonds with the APIs (AfrasiabiGarekani et al., 2003). The presence of 2 wt% of mannitol in waterhas no obvious influence on the solubility of indomethacin. Only aslight increase in the solubility of indomethacin is observed atlower temperatures. As shown in Fig. 3(b), the presence of 2 wt%of PEG in water has obvious influence on the solubility ofindomethacin as function of PEG molar mass and it follows theorder: PEG 2000 > PEG 6000 > PEG 12000. The solubility ofindomethacin in water in the presence of 2 wt% of PEG 2000 isaround 3 times at 313.15 K as high as that in pure water. In case ofthe presence of 2 wt% of PEG 6000 in water the indomethacinsolubility is 1.5 times as high as that in pure water at 313.15 K andit remains nearly the same in case of the presence of 2 wt% ofPEG 12000 as that in pure water.

As shown in Fig. 3(c) and (d) almost the same trend is observedfor the solubility of naproxen in water in the presence of 2 wt% ofeach excipient. Here again, the solubility of naproxen in water in

ter with 2 wt% of mannitol (light hollow circles), and in water with 2 wt% of PVP K 25rs), in water with 2 wt% of PEG 2000 (gray circles), in water with 2 wt% of PEG 6000(c) Solubility of naproxen in water (Paus et al., 2015) (gray stars), in water with 2 wt%bility of naproxen in water (Paus et al., 2015) (gray stars), in water with 2 wt% of PEGith 2 wt% of PEG 12000 (light gray squares). The lines represent the modeling results, in water with 2 wt% of mannitol (dotted lines), as well as in water with 2 wt% of PVP

Table 5The maximum relative deviation (MRD) as well as the average relative deviation(ARD) of the calculated and experimental API solubilities in the selected media.

API System ARD (%) MRD

Indomethacin Water 7.55a 14.52Water/mannitol 11.66 30.12Water/PVP K 25 4.74 10.44Water/PEG 2000 8.45 14.58Water/PEG 6000 10.69 19.97Water/PEG 12000 7.91 21.79

Naproxen Water 2.38a 6.72Water/mannitol 10.41 16.91Water/PVP K 25 13.48 32.86Water/PEG 2000 5.98 13.38Water/PEG 6000 7.20 13.45Water/PEG 12000 4.98 9.28

a taken from (Paus et al., 2015).

R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287 283

the presence of 2 wt% of PVP K 25 is around 2 times at 313.15 K ashigh as that in pure water. Bettinetti and Mura (1994) alsoobserved an increase in the aqueous API solubility in the presenceof PVP. This shows again that our observations agree with theresults in the literature. The enhancement of naproxen solubilityby adding 2 wt% of PVP K 25 in water might be also attributed to thehigh ability of PVP to form hydrogen bonds with naproxen. For themedia in the presence of 2 wt% of mannitol the solubility ofnaproxen is only slightly influenced. Here, the solubility ofnaproxen is around 1.17 times as high as that in pure water at310.15 K. As shown in Fig. 3(d), the solubility of naproxen in waterwith 2 wt% of PEG is highly increased and is more increased withincreasing temperature compared to that in pure water. Here again,the solubility of naproxen in water with different PEGs is a functionof PEG molar mass. With an increase in the molar mass of the PEG,the solubility of naproxen is decreased (PEG 2000 > PEG6000 > PEG > 12000). At 313.15 K, the solubility of naproxen inwater in the presence of 2 wt% of PEG 2000 is around 3.4 times ashigh as that in pure water. For the media with 2 wt% of PEG 6000and with 2 wt% of PEG 12000, the naproxen solubility is around 2.8times and 2.4 times, respectively as high as that in pure water.Mura et al. (1996) investigated the effect of PEGs with differentmolar masses of 4000, 6000 and 20000 on the aqueous solubilityof naproxen. They also observed an increase in the API solubilitywith a decrease in the molar mass of the PEG which was mainlyattributed to the formation of hydrogen bonds between the API andthe polymer resulting in an improved local API solubilization.Additionally, the API-polymer interactions were found to bedecreased with an increase in the polymer molar mass (Mura et al.,1996). This also helps to explain why the aqueous solubility ofindomethacin and naproxen was decreased with increasing PEGmolar mass.

Compared to indomethacin solubility (see Fig. 3(a) and (b)), thepresence of PEG with a higher molar mass shows a significantlyhigher influence on the aqueous naproxen solubility.

5.3. Modeling results of API solubility in water in the presence ofexcipients

The solubility of indomethacin and naproxen in all systems wasmodeled by PC-SAFT (see Sections 2.2–2.5) and the modelingresults are also included in Fig. 3(a)–(d). As presented in Fig. 3, themodeling results are in good accordance to the experimental data.

To evaluate the accuracy of the modeling results, the maximumrelative deviation (MRD) as well as the average relative deviation(ARD) between the calculated and experimental API solubilitywere calculated according to Eqs. (22) and (23).

MRD ¼ 100 � maxi¼1; nexp jxcalc; i � xexp; i

xexp; ij (22)

ARD ¼ 100 � 1nexp

Xnexp

i¼1

jxcalc; i � xexp; i

xexp; ij (23)

In Eqs. (22) and (23), xexp, i is the experimental API solubility inmole fraction, xcalc, i is the calculated API solubility in mole fractionand nexp is the number of experimental solubility data points. Theresults are summarized in Table 5.

As presented in Table 5, the MRD and ARD analysis shows thatthe modeling results are in good accordance to the experimentaldata. In all cases except for the naproxen/water/PVP K 25 systemthe ARD is below 12%, which indicates the good performance ofPC-SAFT for the solubility calculation of indomethacin andnaproxen in water in the presence of 2 wt% of selected excipients.Only in the case of naproxen in water in the presence of 2 wt% of

PVP K 25 a higher deviation (13.48%) between the modeling resultsand the experimental data is observed. However, one has to keep inmind that the modeling results for the naproxen/water/PVP K25system were fully predicted as all the pure-component parametersand binary interaction parameters were determined from binarysystems (Prudic et al., 2014b, 2015a). Additionally it has to bementioned that the aqueous solubility of these APIs is very low forall of the selected systems (xLAPI < 1.5 �10�5mol/mol in theselected temperature range).

5.4. Measured API dissolution profiles in water in the presence ofexcipients

The experimental dissolution profiles of indomethacin andnaproxen were measured within a time range of 240 min at310.15 K according to the procedures described in Section 4.3. Themeasured dissolution profiles of indomethacin and naproxen inwater in the presence of 2 wt% of PVP K 25, 2 wt% of mannitol andin the presence of 2 wt% of PEGs are shown in Fig. 4(a). For acomparison, the dissolution profiles of indomethacin andnaproxen in pure water (taken from a previous work(Paus et al., 2015)) are also included in this figure. As presentedin Fig. 4(a), the dissolution profiles of both APIs, indomethacinand naproxen are influenced by the presence of the excipients.From Fig. 4(a) it becomes obvious, that the dissolution rateof indomethacin is increased by the presence of 2 wt% ofPVP K 25 and mannitol compared to that in pure water. Here,indomethacin shows the highest dissolution rate in water in thepresence of 2 wt% of mannitol. As also shown in Fig. 4(a), thedissolution rate of indomethacin in water containing differentPEGs decreases with an increase in the molar mass of PEG. Thesame trend is observed for the influence of the different PEGs onnaproxen dissolution.

As shown in Fig. 4(a), naproxen dissolution rate increases withaddition of both excipients PVP K 25 and mannitol compared tothat in pure water, and the highest dissolution rate of naproxen isobserved in PVP K 25 solution. In the presence of 2 wt% of PEG6000, naproxen dissolution rate is similar to that in pure waterwhile naproxen dissolution rate decreases with an addition of 2 wt% of PEG 12000 in water. In the presence of 2 wt% of PEG 2000 theobserved naproxen dissolution rate is higher than that in purewater. The experimental investigations on indomethacin andnaproxen dissolution in the media containing different excipientsshow that the presence of excipients plays an important role on thedissolution rate of the selected APIs. In the next section, theinfluence mechanism of the excipients on indomethacin andnaproxen dissolution will be discussed in detail.

Fig. 4. (a) Dissolution profiles of selected APIs at 310.15 K and 50 rpm: indomethacin in water (dark gray stars) (Paus et al., 2015), in water with 2 wt% of PVP K 25 (hollowtriangles), in water with 2 wt% of mannitol (light gray pentagons), in water with 2 wt% of PEG 2000 (light gray cycles), in water with 2 wt% of PEG 6000 (hollow hexagons) andin water with 2 wt% of PEG 12000 (light gray squares); naproxen in water (black stars) (Paus et al., 2015), in water with 2 wt% of PVP K 25 (gray triangles), in water with 2 wt% ofmannitol (gray pentagons), in water with 2 wt% of PEG 2000 (gray cycles), in water with 2 wt% of PEG 6000 (gray hexagons) and in water with 2 wt% of PEG 12000 (graysquares); (b) surface-reaction rate constant ks and diffusion rate constant kd of indomethacin and naproxen in water (Paus et al., 2015), in water with 2 wt% of mannitol, inwater with 2 wt% of PVP K 25, in water with 2 wt% of PEG 2000, in water with 2 wt% of PEG 6000 and in water with 2 wt% of PEG 12000 at 310.15 K and 50 rpm.

284 R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287

5.5. Dissolution mechanism of indomethacin and naproxen in water inthe presence of excipients

The dissolution mechanism of indomethacin and naproxen inwater in the presence of 2 wt% of each excipient was analyzedusing the two-step chemical-potential-gradient model as intro-duced in Section 2.1. As shown in Eq. (12), the dissolution rate ofindomethacin and naproxen JAPI depends on two main factors.Firstly the thermodynamic driving force, which is described by thechemical potential gradient of the API mS

API � mBAPI and secondly the

kinetic aspect, which is described in terms of the rate constant kT.The latter is a function of the surface-reaction rate constant ks andthe diffusion rate constant kd of the API. The aim of this section is todiscuss the influence of the excipients on the dissolution of the APIin water from both aspects, the thermodynamic driving force andthe kinetic aspect.

The surface-reaction rate constant ks and the diffusion rateconstant kd of indomethacin and naproxen were fitted to theirexperimental dissolution profiles in the media containing 2 wt% ofeach excipient (Section 5.4). For the data analysis, it was assumedthat the volume of the dissolution medium, the viscosity of themedium and the surface area of the tablet remain constant duringeach measurement.

Table 6Fitted parameters ks,kd, K1, K2 and calculated rate constant of the whole API dissolutexperimental dissolution profiles.

System kd k1 = a1af

Indomethacin/water (Paus et al., 2015) 9.69 � 10�07 1.35 �10�03

Indomethacin/water/PEG 2000 1.01 �10�06 9.61 �10�06

Indomethacin/water/PEG 6000 8.13 � 10�07 8.13 �10�07

Indomethacin/water/PEG 12000 5.86 � 10�07 8.85 �10�04

Indomethacin/water/PVP K 25 4.86 � 10�07 9.74 �10�04

Indomethacin/water/mannitol 1.20 � 10�06 5.90 � 10�03

Naproxen/water (Paus et al., 2015) 3.70 � 10�06 8.99 � 10�04

Naproxen/water/PEG 2000 1.40 � 10�06 3.37 � 10�04

Naproxen/water/PEG 6000 1.26 � 10�06 9.08 � 10�04

Naproxen/water/PEG 12000 1.09 � 10�06 1.68 � 10�04

Naproxen/water/PVP K 25 2.17 � 10�06 3.83 � 10�04

Naproxen/water/mannitol 4.09 � 10�06 2.88 � 10�05

The corresponding values of ks and kd for indomethacin andnaproxen dissolution are shown in Fig. 4(b). The rate constants ofindomethacin and naproxen dissolution in water were taken froma previous work (Paus et al., 2015). The detailed values of theparameters ks, kd and K1 and K2 (as introduced in Section 2.1) andthe ARD (%) between the calculated and experimental dissolutiondata are also listed in Table 6.

Although the thermodynamic driving force mSAPI � mB

API ofindomethacin in water and in water with 2 wt% of mannitol isnearly the same (see Fig. 3(a)) at 310.15 K, the dissolution rate ofindomethacin in water in the presence of mannitol is obviouslyhigher than that in pure water, as observed in Fig. 4(a). The mainreason for this is the higher rate constants of both surface reactionand diffusion for indomethacin dissolution in water in thepresence of 2 wt% of mannitol compared to those in pure wateras shown in Fig. 4(b). In mannitol solution, the surface-reactionrate constant of indomethacin is around 1.8 times and the diffusionrate constant is around 1.2 times as high as those in pure water. Theenhancement of the diffusion rate constant for indomethacindissolution in mannitol solution might be related to the decrease inthe viscosity of mannitol solution compared to that of pure water(see Fig. 2). The increase of the surface-reaction rate constant ofindomethacin dissolution in mannitol solution might be due to

ion kT and the average relative deviation (ARD) between the calculated and the

K2 ¼ a2;af d2 ks kT ARD%

1.82 � 10�04 2.80 � 10�07 2.17 � 10�07 17.524.39 � 10�05 4.67 � 10�07 3.19 � 10�07 11.874.64 �10�05 2.73 �10�07 2.05 �10�07 5.218.63 �10�05 1.35 �10�07 1.10 � 10�07 12.761.36 � 10�03 1.05 �10�06 3.32 � 10�07 16.612.15 �10�04 5.08 � 10�07 3.57 � 10�07 6.591.39 � 10�04 1.73 � 10�06 1.18 � 10�06 16.353.39 � 10�04 3.24 �10�06 9.78 � 10�07 12.253.15 �10�04 3.01 �10�06 8.88 � 10�07 8.153.89 � 10�04 2.77 � 10�06 7.82 �10�07 8.841.75 �10�03 4.49 � 10�06 1.46 � 10�06 14.351.05 �10�04 1.82 � 10�06 1.26 � 10�06 14.43

R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287 285

the improvement of hydration of indomethacin by addition ofmannitol. Nevertheless the dissolution of indomethacin inboth pure water and mannitol solution is controlled bysurface reaction which indicates a slow disintegration ofindomethacin crystals from the crystal lattice and a slow hydrationof the indomethacin molecules. In the case of indomethacindissolution in water in the presence of 2 wt% of PVP K 25, theobserved increase in indomethacin dissolution rate comparedto that in pure water can be explained from two differentaspects. Firstly the increase in the thermodynamic drivingforce mS

IND � mBIND due to the higher solubility of indomethacin

in PVP K 25 solution (see Fig. 3(a)) and secondly the increase inhe surface-reaction rate constant. As shown in Fig. 4(b), thesurface-reaction rate constant of indomethacin in PVP K 25solution is around 4 times as high as that in pure water. However,the diffusion rate constant of indomethacin molecules into thebulk phase of the PVP K 25 solution is decreased by the presence of2 wt% of PVP K 25 in water. This can be related to the increase inthe viscosity of the media (see Fig. 2) and the interactionsbetween PVP K 25 and indomethacin. This leads to a changein the dissolution mechanism of indomethacin in PVP K 25 solutionfrom surface-reaction controlled in pure water to diffusioncontrolled.

As observed in Fig. 4(a), the dissolution rate of indomethacinin water in the presence of 2 wt% of PEG 2000 is slightly increasedcompared to that in pure water. This again can be related to twomain aspects: firstly the increase in the thermodynamic drivingforce due to the higher solubility of indomethacin in PEG 2000solution than that in pure water (see Fig. 3(b)) and secondly theincrease in the surface-reaction rate constant from the kineticaspect (1.6 times as high as that in pure water as shown inFig. 4(b)) due to an improvement of the disintegration ofindomethacin crystals from the crystal lattice and of thehydration of the indomethacin molecules. It was found inFig. 4(b) that the diffusion rate constant of indomethacin inPEG 2000 solution is nearly the same as that in pure water. For thedissolution of indomethacin in water in the presence of 2 wt% ofPEG 6000 and PEG 12000, the dissolution rate of indomethacin isslower than that in water in the presence of 2 wt% of PEG 2000.For the dissolution of indomethacin in PEG 6000 solution, thedissolution rate of indomethacin is nearly the same as that in purewater. Although the thermodynamic driving force of indometha-cin dissolution in PEG 6000 and PEG 12000 solutions is increaseddue to the higher solubility of indomethacin in these solutions,the rate constants from the kinetic aspect are decreased due tothe addition of the two excipients. As shown in Fig. 4(b), both thesurface-reaction rate constant and the diffusion rate constant ofindomethacin dissolution are decreased with an addition of PEG12000. For the dissolution of indomethacin in PEG 12000solution, the surface-reaction rate constant of indomethacindissolution is nearly half of that in pure water, which might bedue to the influence of PEG 12000 on the mass transport ofindomethacin molecules at the solid–liquid interface. Addition-ally, the diffusion rate constant of indomethacin dissolution isdecreased due to the combination of the molecular interactionsbetween the API and the polymer with the increase in theviscosity of the medium with addition of PEG 12000. The decreasein both rate constants finally leads to a slower indomethacindissolution in PEG 12000 solution compared to that in pure water.For the dissolution of indomethacin in all PEG solutions, it iscontrolled by the surface reaction, which shows that thedissolution rate of indomethacin can be further enhanced mainlyby the improvement of the disintegration of indomethacincrystals from the crystal lattice and of the hydration of theindomethacin molecules.

As observed in Fig. 4(a), the dissolution rate of naproxen inPVP K 25 solution and in mannitol solution is obviously higherthan that in pure water. From the dissolution–mechanismanalysis this can be explained by two main aspects. Firstly thehigher thermodynamic driving force due to the increase in thenaproxen solubility in water with addition of both excipients(see Fig. 3(c)) and secondly the increase in the surface-reactionrate constant of naproxen in PVP K 25 solution and in bothrate constants of naproxen in mannitol solution from kineticaspect. In the presence of 2 wt% of PVP K 25 the correspondingsurface-reaction rate constant of naproxen is nearly 2.6 timesas high as that in pure water. Although the diffusion-rateconstant of naproxen is decreased with an addition of PVP K25, which leads to a diffusion-controlled dissolution process ofnaproxen, the increase in the surface-reaction rate constant aswell as in thermodynamic driving force of naproxen dissolutionleads to the higher naproxen dissolution rates than that inpure water.

For naproxen dissolution in mannitol solution, the surface-reaction rate constant of naproxen dissolution is nearly the same asthat in pure water. However, the improved diffusion of naproxenmolecules into the bulk phase of the media due to the lowerviscosity of the medium (see Fig. 2) leads to a higher dissolutionrate compared to that in pure water.

As observed in Fig. 4(a), the same trend for the influence ofPEGs on naproxen dissolution in water is observed as that onindomethacin dissolution. With an increase in the molar mass ofthe PEG, the dissolution rate of naproxen decreases. In PEG 2000solution, the dissolution rate of naproxen is slightly higherthan that in pure water. While in PEG 6000 solution, theobserved naproxen dissolution rate is nearly identical to that inpure water. For naproxen dissolution in PEG 12000 solution, thedissolution rate of naproxen is decreased compared to that inpure water although the solubility of naproxen is increasedwith an addition of PEG 12000 (see Fig. 3(d)). For the dissolutionof naproxen in water in the presence of PEGs, the rate constantsfrom kinetic aspect play an important role on naproxendissolution. Although the thermodynamic driving force isincreased due to the higher solubility of naproxen in waterin the presence of PEGs (see Fig. 3(d)), the diffusion rateconstant is highly decreased with the addition of PEGs,which leads to a change in the dissolution mechanism fromsurface-reaction controlled to diffusion controlled. Although thesurface-reaction rate constant of naproxen in PEG 2000 solutionis nearly 2 times as high as that in pure water, the diffusion rateconstant is decreased. For naproxen dissolution in PEG 6000solution, the diffusion rate constant is only one third of thatin water. However, there is an increase in the correspondingsurface-reaction rate constant, which explains why the observednaproxen dissolution rate in PEG 6000 solution is similar to thatin pure water. For naproxen dissolution in PEG 12000 solution,the decrease in both the surface-reaction rate constant and thediffusion rate constant (below one third of that in pure water)of naproxen leads to the lower dissolution rate of naproxen(see Fig. 4(b)).

The dissolution-mechanism analysis shows that the dissolutionrate of poorly soluble indomethacin and naproxen can be improvedfrom both thermodynamic aspect (solubility) and kinetic aspect(rate constants of surface reaction or diffusion or both) withaddition of mannitol and PVP K 25.

For API dissolution in PEG solutions, although the solubility ofthe APIs may be obviously increased, their dissolution rates can bedecreased due to the change in the surface-reaction rate constantand diffusion rate constant of the APIs as function of PEG molarmass as well as of API type.

Fig. 5. (a) Dissolution profiles of indomethacin (dark gray stars) (Paus et al., 2015), in water with 2 wt% of PVP K 25 (hollow triangles), in water with 2 wt% of mannitol (lightgray pentagons), in water with 2 wt% of PEG 2000 (light gray cycles), in water with 2 wt% of PEG 6000 (hollow hexagons) and in water with 2 wt% of PEG 12000 (light graysquares) from a rotating disk at 310.15 K and 50 rpm; (b) dissolution profiles of naproxen in water (black stars) (Paus et al., 2015), in water with 2 wt% of PVP K 25 (graytriangles), in water with 2 wt% of mannitol (gray pentagons), in water with 2 wt% of PEG 2000 (gray cycles), in water with 2 wt% of PEG 6000 (gray hexagons) and in water with2 wt% of PEG 12000 (gray squares) from a rotating disk at 310.15 K and 50 rpm; the dotted black line, the dashed black line, the full black line, the dashed gray line, the full grayline and the dotted gray line represent the calculated dissolution profiles of the APIs in water, in water with 2 wt% of mannitol, in water with 2 wt% of PVP K25, in water with2 wt% of PEG 2000, in water with 2 wt% of PEG 6000, in water with 2 wt% PEG 12000 using the two-step chemical-potential-gradient model, respectively.

286 R. Paus et al. / International Journal of Pharmaceutics 485 (2015) 277–287

5.6. Calculation of API dissolution profiles in water in the presence ofexcipients

The dissolution profiles of indomethacin and naproxen in waterin the presence of each excipient were calculated according toEq. (12). The determined rate constants of the surface reaction ksand diffusion kd were used for the calculation of the rate constantof the whole API dissolution kT according to Eq. (13). The detailedvalues of ks, kd, and kT are summarized in Table 6. The calculateddissolution profiles of indomethacin and naproxen in water in thepresence of each excipient are shown in Fig. 5(a) and (b). Forcomparison, the dissolution profiles of indomethacin andnaproxen in pure water are also included in Fig. 5. As presentedin Fig. 5(a) and (b), the calculated dissolution profiles are in goodaccordance to the experimental data, which is also verified by thecalculated low ARDs as summarized in Table 6. This shows that thetwo-step chemical-potential-gradient model can be used to wellrepresent the dissolution profiles of the selected APIs in water inthe presence of excipients.

6. Conclusions

In this work, the temperature-dependent solubility ofindomethacin and naproxen and the dissolution profiles of thesetwo APIs were measured in water in the presence of 2 wt% of eachexcipient out of PVP K 25, PEG 2000, PEG 6000, PEG 12000 andmannitol. It was found that the solubility of indomethacin andnaproxen was increased with addition of the selected excipients,which was also predicted by the PC-SAFT. It was also found thatthe presence of 2 wt% of both, mannitol and PVP K 25 increasesthe dissolution rate of both APIs. However, in the presence ofdifferent PEGs, a decrease in the dissolution rates of both APIs wasobserved with an increase in the molar mass of the PEG. With theanalysis of the dissolution mechanism of indomethacin andnaproxen in water in the presence of each excipient using thetwo-step chemical-potential-gradient model, it was found thatthe dissolution mechanisms of indomethacin and naproxen canbe changed by the addition of the different excipients. Althoughthe presence of mannitol showed a slight influence on APIsolubility (the thermodynamic driving force of API dissolution),the API dissolution rate was obviously increased due to theincrease of both rate constants of surface reaction and diffusion.The presence of PVP K 25 mainly increases the thermodynamicdriving force and the surface-reaction rate constant of the APIs

but decreases the diffusion rate constant of the APIs, which mightbe due to the combination of the molecular interactions betweenthe API and the polymer with the higher viscosity of PVP K25solution than that of pure water. For API dissolution in PEGsolutions, although the solubility of the APIs were observed to beobviously increased, their dissolution rates were decreased due tothe change in the surface-reaction rate constant and diffusion rateconstant of the APIs as function of PEG molar mass as well as ofAPI type.

Based on the obtained rate-constants of surface reaction anddiffusion, the dissolution profiles of indomethacin and naproxenin all of the selected systems were calculated in good accordanceto the experimental findings. This work shows that the two-stepchemical-potential-gradient model combined with PC-SAFT canbe used to analyze the influencing mechanism of differentexcipients on the dissolution of poorly-soluble APIs and tocalculate the API dissolution profiles in water in the presence ofexcipients with a high accuracy compared to the experimentaldata.

Acknowledgments

We would like to acknowledge the financial support from theAlexander von Humboldt Foundation (Dr. Yuanhui Ji) as well asthat from the CLIB Graduate Cluster Industrial Biotechnology(Anke Prudic). We would like to thank Lisa Vahle for assisting withsome solubility measurements. We would also like to thank thereviewers for their helpful advice.

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