PHYSICAL STABILITY OF COARSE SUSPENSIONS

4. PHYSICAL STABILITY OF COARSE SUSPENSIONS

Parenteral coarse suspensions are not, strictly speaking, colloidal systems, because they exhibit settling under the force of gravity. However, principles of colloidal science are useful in understanding the physical stability of these sys- tems, particularly regarding flocculation behavior.

The interface between the suspended solid and the liquid phase plays an important role in determining the stability of suspensions. The interfacial free energy is an expression of the degree of preference of a molecule of the dispersed solid for its bulk relative to its interface. This interfacial free energy is always positive, meaning that energy must be put into the system in order to create the free energy; for example, through mechanical milling. When this energy is removed and the suspension is formulated, thermodynamics takes over and tends to drive the system toward its more stable, lower free energy state. While thermodynamics will ultimately win, appropriate manufacturing techniques and rational for- mulation can often result in a system that is, for practical pharmaceutical purposes, ‘‘stable.’’

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The angle that a liquid makes with a solid surface is called the contact angle, and contact angles yield useful infor- mation about the solid surface. Generally, liquids are consid- ered non-wetting if the contact angle is larger than 90 , and wetting if the contact angle is < 90 . Complete wetting results in a contact angle of 0 . To measure the contact angle, the solid can be pressed into a flat wafer using a Carver press, a defined volume of liquid is applied to the surface, and the contact angle is measured using a contact angle goniometer. An image of the drop is examined using a lens with adjustable cross-hairs, where one cross-hair is aligned with the surface, and the other is rotated until it forms a tangent to the drop. The contact angle is read directly. For a detailed discussion of characteri- zation of solid surfaces by measurement of contact angle, the reader is referred to Evans and Wennerstrom (16).

The greater the percentage of molecules at the surface; that is, the smaller the particle size, the more important sur- face properties are in determining the stability of the system. Nature tends to reduce this free energy to zero by various means. One is reduction of the interfacial area by the growth of larger particles at the expense of smaller ones. This phe- nomenon is known as Ostwald ripening. This is expressed quantitatively by the Ostwald–Freundlich equation:

ln C 1 =C 2 ¼ ð2Mg=rRTÞð1=R 1 2 Þ

where C 1 and C 2 are the solubilities of particles of radius R 1 and R 2 , respectively, M represents molecular weight, g is the surface energy of the solid in contact with solution, r is the density of the solid, R is the gas constant, and T is the absolute temperature. Use of this equation predicts that the solubility of a 0.2-mm particle is about 13% higher than the same solid when present as a 20-mm particle.

Another way that nature tries to reduce the free energy of the system is by aggregation of dispersed particles as attractive forces overcome repulsive forces. Successful formu- lation of suspensions generally depends on the scientist’s appreciation for the importance of surface properties of the system. For example, understanding the role of surface charge characteristics allows formulation such that a floccu-

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lated network of particles is formed that can be easily resus- pended with gentle agitation. Adsorption of small hydrophilic colloids or non-ionic polymers may stabilize the system by increasing its interaction with water or sterically hindering particles from approaching closely enough that repulsive forces are replaced by attractive ones, resulting in caking of the suspended solid.

When the solid powder is added to the vehicle, it is agi- tated vigorously, and this agitation may be in the form of further particle size reduction by wet milling. Dispersion refers to the extent to which the solid exists as individual par- ticles, as opposed to clumps or aggregates of particles. The extent to which a uniform distribution of particles is main- tained is referred to as the dispersion stability. The particles will settle at a rate described by Stoke’s law:

V ¼d 2 ðr s l Þg=18Z where V is the settling velocity, d is the particle diameter, r s

and r l are densities of the solid and liquid phases, respec- tively; g is the gravitational constant, and Z is the viscosity of the liquid phase. This equation suggests several ways to reduce settling. One way is to reduce the particle diameter, another is to minimize the density difference between the liquid and solid phases by increasing the specific gravity of the vehicle, and another is to increase the viscosity of the vehicle. From the standpoint of formulating a parenteral suspension, however, increasing the density or the viscosity of a vehicle to a point where settling is prevented is not practical, since the resulting suspension would not be syringeable. Settling must be accepted, and efforts should focus on formulation conditions that result in easy resuspen- sion of the solids with gentle shaking.

When two colloidal particles undergoing Brownian motion approach each other, they experience two types of interaction— static forces arising from attractive van der Waals forces and electrostatic interaction, and hydrodynamic forces mediated by the vehicle. The attractive static forces include dipole– dipole, dipole-induced dipole, and van der Waals forces. van

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der Waals forces are quantum mechanical in origin, and are always attractive, irrespective of charge effects. These are very

short range forces, and vary inversely with r 6 , where r is the distance between particles. Opposing these attractive forces is electrostatic repulsion arising from the fact that the surface of the suspended solid is generally charged. This charge may arise from ionization of surface ionizable groups (amines or carboxylic acid groups, most commonly), from adsorption of molecules that impart a charge, or perhaps from charge generated by particle size reduction operations. Repulsion can also be caused by adsorption of polymers that sterically inhibit close approach of particles. The layer of fixed charges at the surface, called the Stern layer, is characterized by

both a charge density and a surface potential (F 0 ). Direct measurement of F 0 is uncertain. Instead a quantity called the zeta potential (z) is measured. The zeta potential is mea- sured by a variety of electrokinetic methods, and represents the electrical potential at the slip plane, or the effective hydrodynamic radius of the particle.

Interaction between charges that are fixed at the surface and those that are free in solution plays an important role in the stability of colloidal systems. The electrolyte solution is characterized by the charge and concentration of electrolytes as well as the dielectric constant of the medium. The combina- tion of the charged surface and the neutralizing layer of coun- ter ions is said to constitute an electrical double layer. The thickness of the double layer is expressed by

1 X 2 2 1 =k =2 ¼ ðeKT=e

where 1 =k is the Debye length, e is the dielectric constant of the medium, K is the Boltzman constant, n i is the number of ions of type i per unit volume near the surface, e is the charge on an electron and z i is the valence of the electrolyte. Note the strong dependence of the Debye length on the valence of the electrolyte.

Figure 2 is a potential energy diagram representing the attractive forces, the repulsive forces, and the net interaction potential between colloidal particles. The diagram shows that

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Figure 2 Forces of interaction between colloidal particles.

attractive forces predominate at very short interparticle dis- tances. If no repulsive forces exist, the particles can come together in the primary minimum. Depending on the depth of the primary minimum, the aggregation can be either reversible or irreversible. However, for most pharmaceutical suspensions, aggregation in the primary minimum is usually irreversible; that is, the solid cannot be redispersed by simple shaking. Electrostatic repulsion creates an energy barrier opposing approach of particles closely enough to reach the pri- mary minimum. The thickness of the electrical double layer determines the rate at which electrostatic repulsion decreases with increasing distance between particles. The net potential energy curve has a maximum. The size of this maximum, rela- tive to the thermal energy of the system (expressed as kT, where k is the Boltzman constant), determines the ability of

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particles to reach the primary minimum. If the size of the potential energy barrier is very large compared with kT, then the primary minimum is inaccessible, and the system is kineti- cally stable. The net potential energy curve may contain a secondary minimum at a relatively large interparticulate distance. Aggregation in this secondary minimum gives rise to a loosely structured network of particles, and the aggrega- tion is readily reversible by shaking. Such floccules are reported to display fractal properties.

Flocculation is an important property of any coarse suspension, and the pharmaceutical scientist should under- stand both the properties of flocculated suspensions and the forces that mediate the aggregation state of suspensions. In flocculated suspensions, particles are loosely aggregated by electrostatic forces, such that the suspension consists of a loose network of particles. This ensemble of particles, or floc, settles relatively rapidly, and forms a clear boundary between the precipitate and the supernatant. The sediment is loosely packed, and a hard, dense cake is not formed. As

a result, the solid is easy to redisperse. In a deflocculated sus- pension, particles exist as separate entities. The rate of set- tling is slow, and dependent on the particle size. Since there are minimal repulsive forces between particles, even- tually a hard, dense sediment is formed which is difficult, or perhaps impossible, to redisperse.

DLVO (for Derjaguin, Landau, Verwey, and Overbeek, the scientists who published the original theory of colloidal stability in the 1940s) theory states that colloidal stability is determined by a balance between electrical double layer repulsion, which increases exponentially with decreasing distance between particles, and van der Waals forces of attraction. The practical lessons to be learned from DLVO theory are primarily that: (i) ionic strength of the vehicle is

a dominant factor controlling flocculation of the system, and (ii) adsorption of polymers can be used to sterically stabilize

a suspension by preventing two particles from approaching closely enough to aggregate in the primary minimum. The reader is referred to the chapter by Burgess in this book on physical stability of dispersed systems.

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