A Rheological Approach for Predicting Physical Stability of Amorphous Solid Dispersions

Abstract

Miscibility is an important indicator of physical stability against crystallization of amorphous solid dispersions (ASDs). Currently available methods for miscibility determination have both theoretical and practical limitations. Here we report a method of miscibility determination based on the overlap concentration, c*, which can be conveniently determined from the viscosity-composition diagram. The determined c* values for ASDs of two model drugs, celecoxib and loratadine, with four different grades of polyvinylpyrrolidone (PVP), were correlated strongly with the physical stability of ASDs. This result suggests potential application of the c* concept in guiding the design of stable high drug loaded ASD formulations. A procedure is provided to facilitate broader adoption of this methodology. The procedure is easy to apply and widely applicable for thermally stable binary drug/polymer combinations.

Introduction

In recent years, there has been an increasing number of small molecule drug candidates with poor aqueous solubility and low oral bioavailability. Amorphous forms of such drugs have drawn considerable interest because of their solubility advantage.1, 2 However, pure amorphous drug is thermodynamically unstable and tends to convert to the more stable crystalline counterpart.³ Amorphous solid dispersions (ASDs), formulated by molecularly dispersing an amorphous drug with a polymer, are used to improve physical stability.4, 5, 6

Although no first principles model exists to predict the enhanced physical stability of ASDs, several viewpoints have been expressed: (1) polymeric matrices sterically hinder and impede crystallization of amorphous drugs and disrupt self-association of drug aggregates⁷; (2) incorporating a polymer with a higher glass transition temperature (T_g) than that of the amorphous drug raises the T_g of an ASD, reducing molecular mobility3, 8; and (3) drug/polymer combinations with relatively strong intermolecular interactions provide a route to physical stabilization.7, 9 In all of these viewpoints, it is assumed that drug and polymer are dispersed homogenously at the molecular level, i.e. they are miscible.¹⁰

In the ASD literature, a miscible ASD is taken to consist of a single homogeneous phase with physical properties distinct from those of pure components.¹¹ With this definition, an ASD consisting of a dilute dispersion of disconnected polymer chains in a “sea” of drug would be considered to be “immiscible.” The miscibility limit is then the highest drug concentration above which an ASD is divided into a polymer rich domain and a pure amorphous drug domain.

(Before proceeding, we note that the ASD literature definition of miscibility is somewhat different from that used in physical chemistry. In the latter case, a miscible binary system is defined as “as stable homogeneous mixture which exhibits macroscopic features of a single-phase material.”¹² A dilute solid dispersion (low polymer concentration) would be considered to be miscible under this definition. We shall adhere to the ASD literature definition of miscibility in the present work.)

Since it is widely suggested that miscibility is an important indicator of stability against crystallization when a drug is formulated as an ASD, many experimental techniques have been applied to investigate it by identifying heterogeneous domains when the critical drug concentration is exceeded.13, 14, 15 One technique relies on determining the number of glass transition events. However, multiple glass transition events may be obscured when drug and polymer have similar T_g values, when domain sizes are very small (less than 20–30 nm), or when remixing takes place during heating.¹⁶ Other methods applied to evaluate miscibility of ASDs include spectroscopic techniques, including Raman,¹⁶ solid-state nuclear magnetic resonance (ssNMR),¹⁷ Fourier-transform infrared (FTIR),¹⁸ and fluorescence¹⁹; imaging techniques, including polarized light microscopy (PLM),²⁰ fluorescence microscopy,¹⁹ scanning electron microscopy,²¹ transmission electron microscopy,18, 22 and atomic force microscopy²³; and their combinations. Although useful, these techniques can only provide qualitative information regarding drug-polymer miscibility and they are not universally applicable or accessible for routine use.¹⁵

Complementing the experimental techniques, the most popular theoretical scheme for determining miscibility is the Flory-Huggins theory, which is based on the mean field assumption.24, 25, 26, 27 In this theory, the free energy of mixing per lattice site, $F_{mix}$, is given by

$$\frac{F_{mix}}{k_{B}T}=\frac{\varphi }{N}\text{ln}\varphi +\left(1-\varphi \right)\text{ln}\left(1-\varphi \right)+\chi \varphi \left(1-\varphi \right)$$

where k_B is Boltzmann's constant, T is absolute temperature, ϕ is the volume fraction of polymer, N is the ratio of molar volume of the polymer to that of the drug, and χ is the Flory-Huggins interaction parameter. In this model, polymer acts as a solvent for the drug, and the miscibility limit is identified with the amorphous solubility of drug in polymer. The drug loading corresponding to the miscibility limit can be estimated by the intersection of the T_g curve and the spinodal curve,¹⁰ which is obtained by taking the second derivative of Eq. (1) with respect to ϕ, if χ is inferred from the following:

$$\left(\frac{1}{T_{\mathrm{m}}^{\text{mix}}}-\frac{1}{T_{\mathrm{m}}^{\text{pure}}}\right)=\frac{-R}{\Delta H_{fus}}\left[\text{ln}\left(1-\varphi \right)+\left(1-\frac{1}{N}\right)\varphi +\chi {\varphi }^2\right]$$

where $T_m^{mix}$ is the melting temperature of crystalline drug/polymer dispersions, $T_m^{\text{pure}}$ is the melting temperature of the pure drug, R is the gas constant, and $\Delta H_{\text{fus}}$ is the heat of fusion of crystalline drug.²⁶

The accuracy of investigating miscibility of ASDs using Flory-Huggins theory is limited by three problems: (1) Flory-Huggins theory assumes that the drug/polymer solution is at equilibrium, but this only holds when temperature is above T_g of the ASD. Hence, miscibility below T_g can be predicted only by extrapolation or modeling¹⁰; (2) practically, different experimental conditions, including uniformity, particle size of drug/polymer crystalline dispersions, and different DSC heating rates, may lead to significantly different inferred χ values²⁸; and (3) Flory-Huggins theory assumes a mean field, with uniform $\varphi$. This stipulation does not hold in a dilute solution of polymer in drug, since each polymer chain consists of contiguous monomers occupying sites in the same neighborhood, and regions between these locales are vacant of polymer.²⁹ This is reflected in the second term on the right-hand side of Eq. (3) obtained by expanding Eq. (1) at small $\varphi$,

$$\frac{F_{mix}}{k_{B}T}=\frac{\varphi }{N}ln\varphi +\frac{1}{2}{\varphi }^2\left(1-2\chi \right)+\frac{1}{6}{\varphi }^3+O\left(\varphi \right)$$

where the monomer-monomer interaction ${\varphi }^2$ means $〈{\varphi }^2〉$, rather than ${〈\varphi 〉}^2$.30, 31, 32 Note that linear terms in $\varphi$ are ignored for simplicity. Therefore, the Flory-Huggins theory is best applied when polymer concentration is sufficiently high, and fluctuations can be neglected. To accurately describe miscibility of an ASD with a low polymer concentration (high drug loading), a method based on a different theory is needed.

Here we propose a rheology based method of miscibility determination of ASDs guided by the concept of the overlap concentration, c*, is the concentration of a polymer solution for which the concentration of monomers inside a polymer coil is the same as the macroscopic average concentration, which was introduced by de Gennes and others in the 1970s.30, 33 We consider the small molecule drug, not the polymer, to be the solvent.³⁴ When the polymer concentration is sufficiently low, polymer coils are separated from each other leading to polymer-rich and pure amorphous drug domains. When the polymer concentration exceeds c*, polymer coils overlap and interpenetrate, the polymer in drug solution becomes semidilute/concentrated, and it can be regarded as a single homogeneous phase at the molecular level. Hence, c* of polymer in an ASD is treated as the polymer loading corresponding to a pseudo-phase boundary.

The concentration c* can be estimated as the point (actually a narrow range) where there is an abrupt change in slope of the viscosity-composition diagram when the drug/polymer mixture (ASD) is in the molten state.³⁵ Importantly, c* is also a threshold, below which ASDs, when quenched to ambient conditions, will be physically unstable, while above c* the polymer will stabilize the amorphous drug against crystallization for long periods of time. In the present work, we demonstrate these principles using two poorly water-soluble model drugs, celecoxib (CEL) and loratadine (LOR), and four different grades (molecular weights) of polyvinylpyrrolidone (PVP).

In a recent publication we estimated c* as the reciprocal of the intrinsic viscosity of the molten ASD system.³⁴ While the latter estimation was shown to be useful for the drug/polymer systems that were studied, we believe the present method to be more general. We also show here, for the first time, that ASDs formulated with polymer concentrations exceeding c* retain their physical stability over long time periods at ambient conditions.