Dispersion methods.

The breakdown of coarse material may be carried out by the use of a colloid mill or ultrasonics.

Condensation methods.

These involve the rapid production of supersaturated solutions of the colloidal material under conditions in which it is deposited in the dispersion medium as colloidal particles and not as a precipitate. The supersaturation is often obtained by means of a chemical reaction that results in the formation of the colloidal material. For example, colloidal silver iodide may be obtained by reacting together dilute solutions of silver nitrate and potassium iodide; colloidal sulphur is produced from sodium thiosulfate and hydrochloric acid solutions; and ferric chloride boiled with excess of water produces colloidal hydrated ferric oxide.

A change of solvent may also cause the production of colloidal particles by condensation methods. If a saturated solution of sulphur in acetone is poured slowly into hot water, the acetone vaporizes, leaving a colloidal dispersion of sulphur. A similar dispersion may be obtained when a solution of a resin, such as benzoin in alcohol, is poured into water.

Ultrafiltration.

By applying pressure (or suction), the solvent and small particles may be forced across a membrane whilst the larger colloidal particles are retained. The process is referred to as ultrafiltration. It is possible to prepare membrane filters with known pore size and use of these allows the particle size of a colloid to be determined. However, particle size and pore size cannot be properly correlated because the membrane permeability is affected by factors such as electrical repulsion, when both the membrane and particle carry the same charge, and particle adsorption which can lead to blocking of the pores.

Electrodialysis.

An electric potential may be used to increase the rate of movement of ionic impurities through a dialysing membrane and so provide a more rapid means of purification. The concentration of charged colloidal particles at one side and at the base of the membrane is termed electrodecantation.

Size distribution.

Within the size range of colloidal dimensions specified above, there is often a wide distribution of sizes of the dispersed colloidal particles. The molecular weight or particle size is therefore an average value, the magnitude of which is dependent on the experimental technique used in its measurement. When determined by the measurement of colligative properties such as osmotic pressure, a number average value, M_n, is obtained which, in a mixture containing n₁, n₂, n₃, … moles of particle of mass M₁, M₂, M₃, … respectively, is defined by:

(5.1)

In the light-scattering method for the measurement of particle size, larger particles produce greater scattering and the weight rather than the number of particles is important, giving a weight-average value, M_w, defined by:

(5.2)

In Equation 5.2, m₁, m₂, and m₃ … are the masses of each species, and m_i is obtained by multiplying the mass of each species by the number of particles of that species; that is, m_i = n_iM_i. A consequence is that M_w > M_n, and only when the system is monodisperse will the two averages be identical. The ratio M_w/M_n expresses the degree of polydispersity of the system.

Shape.

Many colloidal systems, including emulsions, liquid aerosols and most dilute micellar solutions, contain spherical particles. Small deviations from sphericity are often treated using ellipsoidal models. Ellipsoids of revolution are characterized by their axial ratio, which is the ratio of the half-axis a to the radius of revolution b (see Fig. 5.1). Where this ratio is greater than unity, the ellipsoid is said to be a prolate ellipsoid (rugby ball shaped), and when less than unity an oblate ellipsoid (discus-shaped).

High molecular weight polymers and naturally occurring macromolecules often form random coils in aqueous solution. Clay suspensions are examples of systems containing plate-like particles.

Brownian motion.

Colloidal particles are subject to random collisions with the molecules of the dispersion medium with the result that each particle pursues an irregular and complicated zigzag path. If the particles (up to about 2 µm diameter) are observed under a microscope or the light scattered by colloidal particles is viewed using an ultramicroscope, an erratic motion is seen. This movement is referred to as Brownian motion after Robert Brown who first reported his observation of this phenomenon with pollen grains suspended in water.

Diffusion.

As a result of Brownian motion, colloidal particles spontaneously diffuse from a region of higher concentration to one of lower concentration. The rate of diffusion is expressed by Fick’s First Law. One form of this relationship is shown in Equation 5.3.

(5.3)

where dm is the mass of substance diffusing in time dt across an area A under the influence of a concentration gradient dC/dx (the minus sign denotes that diffusion takes place in the direction of decreasing concentration). D is the diffusion coefficient and has the dimensions of area per unit time. The diffusion coefficient of a dispersed material is related to the frictional coefficient, f, of the particles by Einstein’s Law of Diffusion:

(5.4)

where k_B is the Boltzmann constant and T temperature.

Therefore, as the frictional coefficient is given by the Stokes equation:

(5.5)

where η is the viscosity of the medium and a the radius of the particle (assuming sphericity), then:

(5.6)

N_A is the Avogadro constant, R is the universal gas constant and k_B = R/N_A. The diffusion coefficient may be obtained by an experiment measuring the change in concentration, via refractive index gradients, when the solvent is carefully layered over the solution to form a sharp boundary and diffusion is allowed to proceed. A more commonly used method is that of dynamic light scattering which is based on the frequency shift of laser light as it is scattered by a moving particle, the so-called Doppler shift. The diffusion coefficient can be used to obtain the molecular weight of an approximately spherical particle, such as egg albumin and haemoglobin, by using Equation 5.5 in the form:

(5.7)

where M is the molecular weight and is the partial specific volume of the colloidal material.

Sedimentation.

Consider a spherical particle of radius a and density σ falling in a liquid of density ρ and viscosity η. The velocity v of sedimentation is given by Stokes’ Law:

(5.8)

where g is acceleration due to gravity.

If the particles are only subjected to the force of gravity then, due to Brownian motion, the lower size limit of particles obeying Equation 5.8 is about 0.5 µm. A stronger force than gravity is therefore needed for colloidal particles to sediment and use is made of a high-speed centrifuge, usually termed an ultracentrifuge, which can produce a force of about 10⁶ g. In a centrifuge, g is replaced by ω²x, where ω is the angular velocity and x the distance of the particle from the centre of rotation.

The ultracentrifuge is used in two distinct ways in investigating colloidal material. In the sedimentation velocity method, a high centrifugal field is applied, up to about 4 × 10⁵ g, and the movement of the particles, monitored by changes in concentration, is measured at specified time intervals. In the sedimentation equilibrium method, the colloidal material is subjected to a much lower centrifugal field until sedimentation and diffusion tendencies balance one another, and an equilibrium distribution of particles throughout the sample is attained.

Osmotic pressure.

The determination of molecular weights of dissolved substances from colligative properties such as the depression of freezing point or the elevation of boiling point is a standard procedure. However, of the available methods, only osmotic pressure has a practical value in the study of colloidal particles because of the magnitude of the changes in the properties. For example, the depression of freezing point of a 1% w/v solution of a macromolecule of molecular weight 70 000 Da is only 0.0026 K, far too small to be measured with sufficient accuracy by conventional methods and also very sensitive to the presence of low molecular weight impurities. In contrast, the osmotic pressure of this solution at 20 °C would be 350 N m⁻² or about 35 mm of water. Not only does the osmotic pressure provide an effect that is measurable, but also the effect of any low molecular weight material, which can pass through the membrane, is virtually eliminated.

However, the usefulness of osmotic pressure measurement is limited to a molecular weight range of about 10⁴−10⁶ Da; below 10⁴ Da the membrane may be permeable to the molecules under consideration and above 10⁶ Da the osmotic pressure will be too small to permit accurate measurement.

If a solution and solvent are separated by a semi-permeable membrane, the tendency to equalize chemical potentials (and hence concentrations) on either side of the membrane results in a net diffusion of solvent across the membrane. The pressure necessary to balance this osmotic flow is termed the osmotic pressure.

For a colloidal solution the osmotic pressure, Π, can be described by:

(5.12)

where C is the concentration of the solution, M the molecular weight of the solute and B a constant depending on the degree of interaction between the solvent and solute molecules.

Thus a plot of Π/C versus C is linear with the value of the intercept at C → 0 giving RT/M enabling the molecular weight of the colloid to be calculated. The molecular weight obtained from osmotic pressure measurements is a number-average value.

A potential source of error in the determination of molecular weight from osmotic pressure measurements arises from the Donnan membrane effect. The diffusion of small ions through a membrane will be affected by the presence of a charged macromolecule that is unable to penetrate the membrane because of its size. At equilibrium, the distribution of the diffusible ions is unequal, being greater on the side of the membrane containing the non-diffusible ions. Consequently, unless precautions are taken to correct for this effect or eliminate it, the results of osmotic pressure measurements on charged colloidal particles such as proteins will be invalid.

Viscosity.

Viscosity is an expression of the resistance to flow of a system under an applied stress. An equation of flow applicable to colloidal dispersions of spherical particles was developed by Einstein:

(5.13)

where η_o is the viscosity of the dispersion medium and η the viscosity of the dispersion when the volume fraction of colloidal particles present is ϕ.

A number of viscosity coefficients may be defined with respect to Equation 5.13. These include relative viscosity:

(5.14)

and specific viscosity:

(5.15)

Since volume fraction is directly related to concentration, Equation 5.15 may be written as:

(5.16)

where C is the concentration expressed as grams of colloidal particles per 100 mL of total dispersion and k is a constant. If η is determined for a number of concentrations of macromolecular material in solution and η_sp/C is plotted versus C then the intercept obtained on extrapolation of the linear plot to infinite dilution is known as the intrinsic viscosity [η].

This constant may be used to calculate the molecular weight of the macromolecular material by making use of the Mark–Houwink equation:

(5.17)

where K and α are constants characteristic of the particular polymer-solvent system. These constants are obtained initially by determining [η] for a polymer fraction whose molecular weight has been determined by another method such as sedimentation, osmotic pressure or light scattering. The molecular weight of the unknown polymer fraction may then be calculated. This method is suitable for use with polymers, such as dextrans used as blood plasma substitutes.

Light scattering.

When a beam of light is passed through a colloidal sol (dispersion of very fine particles), some of the light may be absorbed (when light of certain wavelengths is selectively absorbed, a colour is produced), some is scattered and the remainder is transmitted undisturbed through the sample. Due to the light scattered, the sol appears turbid; this is known as the Tyndall effect. The turbidity of a sol is given by the expression:

(5.18)

where I_o is the intensity of the incident beam, I that of the transmitted light beam, l the length of the sample and τ the turbidity.

Light-scattering measurements are of great value for estimating particle size, shape and interactions, particularly of dissolved macromolecular materials, as the turbidity depends on the size (molecular weight) of the colloidal material involved. Measurements are simple in principle but experimentally difficult because of the need to keep the sample free from dust, the particles of which would scatter light strongly and introduce large errors.

As most colloids show very low turbidities, instead of measuring the transmitted light (which may differ only marginally from the incident beam), it is more convenient and accurate to measure the scattered light, at an angle (usually 90°) relative to the incident beam. The turbidity can then be calculated from the intensity of the scattered light, provided the dimensions of the particle are small compared to the wavelength of the incident light, by the expression:

(5.19)

R₉₀ is known as the Rayleigh ratio after Lord Rayleigh who laid the foundations of the light-scattering theory. The light-scattering theory was modified for use in the determination of the molecular weight of colloidal particles by Debye who derived the following relationship between turbidity and molecular weight:

(5.20)

C is the concentration of the solute and B an interaction constant allowing for non-ideality. H is an optical constant for a particular system depending on the refractive index change with concentration and the wavelength of light used. A plot of HC/τ against concentration results in a straight line of slope 2B. The intercept on the HC/τ axis is 1/M, allowing the molecular weight to be calculated. The molecular weight derived by the light-scattering technique is a weight-average value.

Light-scattering measurements are particularly suitable for finding the size of the micelles of surface-active agents and for the study of proteins and natural and synthetic polymers.

For spherical particles, the upper limit of the Debye equation is a particle diameter of approximately one-twentieth of the wavelength λ of the incident light; that is, about 20–25 nm. The light-scattering theory becomes more complex when one or more dimensions exceed λ/20 because the particles can no longer be considered as point sources of scattered light. By measuring the light scattering from such particles as a function of both the scattering angle θ and the concentration C, and extrapolating the data to zero angle and zero concentration, it is possible to obtain information on not only the molecular weight but also the particle shape.

Because the intensity of the scattered light is inversely proportional to the fourth power of the wavelength of the light used, blue light (λ = 450 nm) is scattered much more than red light (λ = 650 nm). With incident white light, a scattering material will therefore tend to be blue when viewed at right angles to the incident beam, which is why the sky appears to be blue, the scattering arising from dust particles in the atmosphere.

Ultramicroscopy.

Colloidal particles are too small to be seen with an optical microscope. Light scattering is employed in the ultramicroscope first developed by Zsigmondy, in which a cell containing the colloid is viewed against a dark background at right angles to an intense beam of incident light. The particles, which exhibit Brownian motion, appear as spots of light against the dark background. The ultramicroscope is used in the technique of microelectrophoresis for measuring particle charge.

Electron microscopy.

The electron microscope, capable of giving actual pictures of the particles, is used to observe the size, shape and structure of colloidal particles. The success of the electron microscope is due to its high resolving power, defined in terms of d, the smallest distance by which two objects are separated yet remain distinguishable. The smaller the wavelength of the radiation used, the smaller is d and the greater the resolving power. An optical microscope, using visible light as its radiation source, gives a d of about 0.2 µm. The radiation source of the electron microscope is a beam of high-energy electrons having wavelengths in the region of 0.01 nm; d is thus about 0.5 nm. The electron beams are focused using electromagnets and the whole system is under a high vacuum of about 10⁻³–10⁻⁵ Pa to give the electrons a free path. With wavelengths of the order indicated, the image cannot be viewed directly, so the image is displayed on a monitor or computer screen.

A major disadvantage of the electron microscope for viewing colloidal particles is that normally only dried samples can be examined. Consequently, it usually gives no information on solvation or configuration in solution and, moreover, the particles may be affected by sample preparation. A recent development which overcomes these problems is environmental scanning electron microscopy (ESEM) which allows the observation of material in the wet state.

Electrical properties of interfaces.

Most surfaces acquire a surface electric charge when brought into contact with an aqueous medium, the principal charging mechanisms being as follows.

The electrical double layer.

Consider a solid charged surface in contact with an aqueous solution containing positive and negative ions. The surface charge influences the distribution of ions in the aqueous medium; ions of opposite charge to that of the surface, termed counter-ions, are attracted towards the surface, ions of like charge, termed co-ions, are repelled away from the surface. However, the distribution of the ions will also be affected by thermal agitation which will tend to redisperse the ions in solution. The result is the formation of an electrical double layer made up of the charged surface and a neutralizing excess of counter-ions over co-ions (the system must be electrically neutral) distributed in a diffuse manner in the aqueous medium.

The theory of the electric double layer deals with this distribution of ions and hence with the magnitude of the electric potentials which occur in the locality of the charged surface. For a fuller explanation of what is a rather complicated mathematical approach, the reader is referred to a textbook of colloid science (e.g. Shaw 1992). A somewhat simplified picture of what pertains from the theories of Gouy, Chapman and Stern follows.

The double layer is divided into two parts (see Fig. 5.2a): the inner, which may include adsorbed ions, and the diffuse part where ions are distributed as influenced by electrical forces and random thermal motion. The two parts of the double layer are separated by a plane, the Stern plane, at about a hydrated ion radius from the surface; thus counter-ions may be held at the surface by electrostatic attraction and the centre of these hydrated ions forms the Stern plane.

The potential changes linearly from ψ_o (the surface potential) to ψ_δ, (the Stern potential) in the Stern layer and decays exponentially from ψ_δ to zero in the diffuse double layer (Fig. 5.2b). A plane of shear is also indicated in Figure 5.2. In addition to ions in the Stern layer, a certain amount of solvent will be bound to the ions and the charged surface. This solvating layer is held to the surface, and the edge of the layer, termed the surface or plane of shear, represents the boundary of relative movement between the solid (and attached material) and the liquid. The potential at the plane of shear is termed the zeta, ζ, or electrokinetic, potential and its magnitude may be measured using microelectrophoresis or any other of the electrokinetic phenomena. The thickness of the solvating layer is ill-defined and the zeta potential therefore represents a potential at an unknown distance from the particle surface; its value, however, is usually taken as being slightly less than that of the Stern potential.

In the discussion above, it was stated that the Stern plane existed at a hydrated ion radius from the particle surface; the hydrated ions are electrostatically attracted to the particle surface. It is possible for ions/molecules to be more strongly adsorbed at the surface, termed specific adsorption, than by simple electrostatic attraction. In fact, the specifically adsorbed ion/molecule may be uncharged as is the case with non-ionic surface-active agents. Surface-active ions specifically adsorb by the hydrophobic effect and can have a significant effect on the Stern potential, causing ψ_o and ψ_δ to have opposite signs, as in Figure 5.3a, or for ψ_δ to have the same sign as ψ_o but be greater in magnitude, as in Figure 5.3b.

Figure 5.2b shows an exponential decay of the potential to zero with distance from the Stern plane. The distance over which this occurs is 1/κ, referred to as the Debye–Hückel length parameter or the thickness of the electrical double layer. The parameter κ is dependent on the electrolyte concentration of the aqueous media. Increasing the electrolyte concentration increases the value of κ and consequently decreases the value of 1/κ; that is, it compresses the double layer. As ψ_δ stays constant this means that the zeta potential will be lowered.

As indicated earlier, the effect of specifically adsorbed ions may be to lower the Stern potential and hence the zeta potential without compressing the double layer. Thus the zeta potential may be reduced by additives to the aqueous system in either (or both) of two different ways.

Electrokinetic phenomena.

This is the general description applied to the phenomena that arise when attempts are made to shear off the mobile part of the electrical double layer from a charged surface. There are four such phenomena: namely, electrophoresis, sedimentation potential, streaming potential and electroosmosis. All of these electrokinetic phenomena may be used to measure the zeta potential but electrophoresis is the easiest to use and has the greatest pharmaceutical application.