## Dry Powder Inhalers

The 1987 Montreal protocol (4) initially limited the use of CFC propellants and then banned them by 2009 in the United States (51). In addition, degradation kinetics of therapeutic biomolecules is slower in the solid state than in the liquid state. Combined with bypassing the "first-pass effect" of hepatic metabolism and drug degradation in the gastrointestinal tract, the lungs have been an attractive route of administration of sensitive biomacromolecules in the solid state. The forces of interaction between particles present barriers to their flow and dispersion. The major forces of interaction are van der Waals, electrostatic, and capillary forces (52).

Van der Waals forces are derived from the energy of interaction between two molecules, Vss. These can be derived from London's theory as follows:

where a is the polarizability, h is Planck's constant, and v0, the characteristic frequency. Because v is found in the UV region of the absorption spectra and plays a key role in optical dispersion, the intermolecular London-van der Waals forces are also called dispersion forces. These forces operate at short ranges but when integrated over all molecules give rise to large interparticulate forces.

The dipole-induced dipole interactions are summed over all atoms and expressed as the Hamaker constant (A). The total molecular potential, t/m, for two perfectly spherical particles with diameters d\ and d2 for particles 1 and 2, respectively, is

where z is the shortest interparticulate distance. The Hamaker constant is given by

where and n2 are molecular densities and Css is the London-van der Waals constant. Two dissimilar materials, with Hamaker constants An and A22, interact as follows:

Equation (10) may be applied when z <C D = did2/(di + d2). This is not a practical limitation, but an applicable equation can be obtained by differentiating equation (10) with respect to z.

The attractive force (F) is dependent on the Hamaker constant and the shortest distance between the particles, z. F may be decreased by decreasing A or increasing z. Theoretically, the Hamaker constant can be decreased by decreasing the densities of the two interacting particles. Since the separation distance plays a significant role in van der Waals attraction, any means to increase this distance will reduce the attractive force and increase the ease of dispersion. Surface roughening and the use of spacers can increase interparticulate separation with the improved particle dispersion.

Electrostatic forces are smaller than van der Waals forces for conducting particles, but most pharmaceutical products are poor conductors. Therefore, electrostatic charge must be considered. Two adjacent solid surfaces give rise to a contact potential and, in turn, interfacial electrostatic attractive forces that increase interparticulate interfacial interactions (52,53) and, consequently, powder aggregation. Surface electrostatic charge phenomena play an important role in aerosol dispersion and delivery of respirable particles in the solid state (53). Particle collisions and surface contacts give rise to contact charging and additional surface electrostatic interactions. Triboelectric (frictional) charging, a potential difference between two interacting particles in motion having different work functions, further contributes to electrostatic interactions. The potential difference causes electrons to migrate from the body that has a smaller work function to that with a larger work function until equilibrium is achieved. A reduction in charge does not always occur on contact with another particle whether the latter is charged or

Nanometer separation >

Figure 5 Illustration of interfacial electrostatic attraction between two particles.

Nanometer separation >

Figure 5 Illustration of interfacial electrostatic attraction between two particles.

uncharged. A persistent charge will induce an equal and opposite charge on neighboring particles or surfaces, as depicted in Figure 5. This induced electrical force on a particle may be expressed as follows:

where q is the charge on the particle and h is the separation distance between the adhering particles in a dielectric medium, e.

The Coulomb equation describes triboelectric charging (Fc) between a spherical particle and an adjacent uncharged particle.

\6neoh2

where R is the particle radius, q the charge, h the separation distance, and £q the permittivity of vacuum. This Coulomb attraction between two solid-state particles, illustrated in Figure 5, reduces to zero in a humid environment because of decharging of the system, but attractive forces then become complicated by capillary forces of interaction.

In the presence of a potential difference, particles of different work functions are brought into contact by a force of attraction defined as follows:

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