## N

H> 1.000E+01 o e <s a 1.000E+00 1.000E-01 1.000E-02 1.000E-03

Figure 4 Techniques of particle size detection and their limits.

Figure 4 Techniques of particle size detection and their limits.

particularly colloidal particles, QELS is the preferred technique. Two theories dominate the theory of light scattering—the Fraunhofer and Mie. According to the Fraunhofer theory, the particles are spherical, nonporous, and opaque; diameter is greater than wavelength, particles are distant enough from each other, have random motion, and all the particles diffract the light with the same efficiency, regardless of size and shape. The Mie theory takes into account the differences in refractive indices between the particles and the suspending medium. If the diameter of the particles is above 10 mm, then the size produced by utilizing each theory is essentially the same. However, discrepancies may occur when the diameter of the particles approaches that of the wavelength of the laser source.

The following are the values reported from diffraction experiments:

• D (v, 0.1) is the size of particles for which 10% of the sample is below this size.

• D (v, 0.5) is the volume (v) median diameter, of which 50% of the sample is below and above this size.

• D (v, 0.9) is the size of the particle for which 90% of the sample is below this size.

• D [4, 4] is the equivalent volume mean diameter calculated using:

• D [3,2] is the surface area mean diameter; also known as the Sauter mean, where d = diameter of each unit.

• Log difference represents the difference between the observed light energy data and the calculated light energy data for the derived distribution.

• Span is the measurement of the width of the distribution, and is calculated using

The dispersion of the powder is important in achieving reproducible results. Ideally, the dispersion medium should have the following characteristics:

• have a suitable absorbancy

• not swell the particles

• disperse a wide range of particles

• slow sedimentation of particles

• allow homogeneous dispersion of the particles

In terms of sample preparation, it is necessary to deggregate the samples, so that the primary particles are measured. To achieve this, the sample may be sonicated, although there is a potential problem of the sample being disrupted by the ultrasonic vibration. To check for this, it is recommended that the particle dispersion be examined by optical microscopy.

Although, laser light diffraction is a rapid and highly repeatable method in determining the particle size distributions of pharmaceutical powders, the results obtained can be affected by the particle shape. The laser light scattering generally reports broader size distribution compared with image analysis. In addition, the refractive index of the particles can introduce an error of 10% under most circumstances, and should be accounted for. Another laser-based instrument, relying on light scattering, is the aerosizer. The aerosizer measures particles one at a time in the range of 0.20-700 mm. The particles may be in the form of a dry powder or may be sprayed from a liquid suspension as an aerosol. The particles are blown through the system and dispersed in air to a preset count rate. The aerosizer operates on the principle of aerodynamic time of flight. The particles are accelerated by a constant, known force caused by the airflow, and are forced through a nozzle at nearly sonic velocity. Smaller particles are accelerated at a greater rate than large particles as a result of a greater force-to-mass ratio. Two laser beams measure the time of flight through the measurement region by detecting the light scattered by the particles. Statistical methods are used to correlate the start and stop times of each particle in a particular size range (channel) through the measurement zone. The time of flight is used in conjunction with the density of the particles, and calibration curves are established to determine the size distribution of the sample.

### Surface Area

As the surface area exposed to the site of administration determines the speed with which a particle dissolves in accordance with the Noyes-Whitney equation, these determinations are important. In addition, in those instances where the particle size is difficult to measure, a gross estimation of the surface area is the second best parameter to characterize the drug. The most common methods of surface area measurement, including gas adsorption (nitrogen or krypton), based on what is most commonly described as the Braunauer, Emmet, and Teller (BET) method, is applied either as a multipoint or single-point determination.

Adsorption is defined as the concentration of gas molecules near the surface of a solid material. The adsorbed gas is called adsórbate, and the solid where adsorption takes place is known as the adsorbent. Adsorption is a physical phenomenon (usually called physisorption) that occurs at any environmental condition (pressure and temperature), but it becomes measurable only at very low temperatures. Thus physisorption experiments are performed at very low temperatures, usually at the boiling temperature of liquid nitrogen at atmospheric pressure. Adsorption takes place because of the presence of an intrinsic surface energy. When a material is exposed to a gas, an attractive force acts between the exposed surface of the solid and the gas molecules. The result of these forces is characterized as physical (or van der Waals) adsorption, in contrast to the stronger chemical attractions associated with chemisorption. The surface area of a solid includes both the external surface and the internal surface of the pores.

Because of the weak bonds involved between the gas molecules and the surface (<15 KJ/mol), adsorption is a reversible phenomenon. Gas physisorp-tion is considered nonselective, thus filling the surface step-by-step (or layer by layer) depending on the available solid surface and the relative pressure. Filling the first layer enables the measurement of the surface area of the material, because the amount of gas adsorbed when the monolayer is saturated is proportional to the entire surface area of the sample. The complete adsorption/ desorption analysis is called an adsorption isotherm. The six IUPAC (International Union for Physical and Applied Chemistry) standard adsorption isotherms are shown in Figure 5; they differ because the systems demonstrate different gas/solid interactions (4) .

Figure 5 The six types of International Union for Physical and Applied Chemistry isotherms. The type I isotherm is typical of microporous solids and chemisorption isotherms. Type II is shown by finely divided nonporous solids. Types III and V are typical of vapor adsorption (i.e., water vapor on hydrophobic materials). Types V and VI feature a hysteresis loop generated by the capillary condensation of the adsorbate in the mesopores of the solid. The rare type VI, the step-like isotherm, is shown by nitrogen adsorbed on special carbon.

Figure 5 The six types of International Union for Physical and Applied Chemistry isotherms. The type I isotherm is typical of microporous solids and chemisorption isotherms. Type II is shown by finely divided nonporous solids. Types III and V are typical of vapor adsorption (i.e., water vapor on hydrophobic materials). Types V and VI feature a hysteresis loop generated by the capillary condensation of the adsorbate in the mesopores of the solid. The rare type VI, the step-like isotherm, is shown by nitrogen adsorbed on special carbon.

Once the isotherm is obtained, a number of calculation models can be applied to different regions of the adsorption isotherm to evaluate the specific surface area (i.e., BET, Dubinin, Langmuir, and the like) or the micro- and mesopore volume and size distributions (i.e., Barett-Joyner-Halenda, Dubinin-Radushkevich, Horvath and Kawazoe, Saito and Foley, and the like).

The surface area of a solid material is the total surface of the sample that is in contact with the external environment. It is expressed as square meters per gram of dry sample. This parameter is strongly related to the pore size and the pore volume, that is, the larger the pore volume, the larger the surface area, and the smaller the pore size, the higher the surface area. The surface area results from the contribution of the internal surface area of the pores along with the external surface area of the solid or the particles (in case of powders). Whenever a significant porosity is present, the fraction of the external surface area to the total surface area is small.

The BET isotherm for type II adsorption processes (typical for pharmaceutical powders) is given by:

where P is the partial pressure of the adsorbate, V is the volume of gas adsorbed at pressure p, Vmon is the volume of the gas at monolayer coverage, Po is the saturation pressure and c is related to the intercept. Thus, by plotting P/V (Po — P) versus P/Po, a straight line of slope c — 1/cVmon and intercept 1/cVmon will be obtained. The total surface area is thus:

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