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2004/12/31

Dispersing Powders in Liquids


-- 4: Particle Structure --


When you pour a powder out of a container onto a flat surface, you often find that it is agglomerated into clumps. Some clumps fall apart under their own weight as they tumble, while others may not break unless they are hit with a hammer. The term {\sl particle} means an assemblage of solid matter which translates and rotates as a rigid unit, with no translational or rotational motion of the constituent parts with respect to the whole.
Before attempting to disperse a powder in a liquid, you should determine the structure of the starting powder and get a clear description of what sort of particle size and structure is required in the end-use application. Many discussions between marketing representatives, plant supervisors, technical support people, particle size analysts, and academic researchers suffer from great confusion because of differences in nomenclature or conceptualization of the structure of the solid particles.
The term "particle" is used very loosely, and it may be used to refer to either a single crystal or a loosely bound clump of smaller units. It does not imply that anything is either nonporous or agglomerated or dispersed to the maximum extent. Many other terms in slurry technology are also used loosely, so you must be quite careful to establish at the beginning of a discussion just what others mean for each term. Drawings can be very helpful for describing the structures found for the starting powder, intermediate states, and the final dispersion.


Levels of Particle Structure

There are often several levels of structure in a clump. Small primary particles are often cemented together by rather strong forces to form medium-size aggregates which are bound by moderate forces to form large agglomerates. These may be collected by weak forces into large and tenuous flocs. As we go from lower to higher level structures, the strength of bonding decreases, the void (nonsolid) fraction within the clump boundaries increases, and the degree of structural complexity increases.

People who are not familiar with slurry technology often do not realize how complex a clump of particles can be. They may believe that a single pass through a low energy process such as screening breaks the feed material down to fundamental particles. This is rarely the case. More experienced workers know that while loosely bound clumps may be broken up by a low energy process to moderate size particles, these are usually agglomerates of still smaller particles. The specialist will always insist upon examining the powder with a microscope (or electron microscope) so as to determine the structure in detail. The purpose of this section is to discuss the most common particle structures and to describe how they are formed in industrial processes.

The terminology for describing the structure of particles often seems somewhat confused because there are a wide variety of different structures that can be formed from the wide variety of chemical compositions in this world. The terms listed below describe structures typical of different regions in the continuum of bond energies and contact areas that may be formed. There are no sharply defined dividing lines between the regions. Many specialists use variants of the terminology presented, since what one specialist considers to be a relatively weak bond may be considered by others to be a relatively strong bond.



Fundamental Particles

Fundamental particles are the lowest level of structure -- having the highest degree of crystal lattice or structural homogeneity, the highest density, and the lowest void fraction For crystalline materials the fundamental particles are single crystal domains. It is important to note that even a particle that looks like a single, nonporous, unagglomerated crystal may in fact be made up of several single crystal domains; for example, magnetic particles are generally made up of microdomains with different orientations. The boundaries and orientations of these domains change in response to exposure to an external magnetic field.

For noncrystalline solids we can define the fundamental structural elements to be those regions that are homogeneously solid (with no voids down to the atomic packing level) and cut from the solid continuum into relatively convex shapes by imaginary cut-planes of minimum area. Thus, the regions on each side of a pore would be separate fundamental units and a porous or sintered clump would be a high-level structure made up of many fundamental units.


Fig. 2.1a -- Varieties of Single Particle Structure



Twins and Mosaics

Twinned crystals are made up of two (relatively perfect) crystal domains that are joined at a plane which forms a symmetry element. Thus there is a large angle between the major axes of the two crystal domains. Twins are usually formed during the the initial precipitation of a solid. The exterior of a primary particle usually grows by addition of solution material at kinks or shelves or screw dislocations in the surface, so the exterior atomic plane is not flat. Rapid growth about a dislocation can produce a twinned crystal. Polarized light microscopy can usually distinguish twinned crystals from single crystals.

Mosaics are made up of multiple crystal domains which have only small differences in angle between their major axes so that the crystal planes meet at the grain boundary (also called a domain boundary) with only a small mismatch in lattice parameters. In those cases where these domains have dimensions comparable to the wavelength of x-rays (0.001 to 10 nm), then the broadening of lines in an x-ray powder diffraction pattern can be used to characterize the size of the grains that make up the mosaic.

Semicrystalline polymeric materials have regions of crystallinity adjacent to regions of amorphous (glassy) structure. These may be considered to be mosaics. A polymer chain that is part of the crystalline region may also be part of the amorphous region, so the regions may be bound together very strongly along the plane separating the two regions, with little or no void fraction.



Aggregates and Porous Particles

An aggregate is a clump of fundamental particles that are strongly bonded through a region that is not planar or involves some voids, so there is significantly imperfect contact between the particles. See Chapter 1 for a discussion of differences between European and American terminology. Aggregates may be crystals joined across rough faces, porous materials, clumps of particles held together by extensive precipitation bridges or heavily sintered structures for which the cross sectional area of the regions joining the fundamental particles is larger than the surface area which is exposed to void space.

A precipitation bridge forms when precipitation occurs at the point where two particles make contact in a floc or a packed bed of material. A heteroprecipitation bridge or gel bond forms when a solid different from the core particle precipitates at the contact points. This may occur when a coating agent is applied to an incompletely dispersed slurry or when a soluble salt precipitates out during the drying of a filtercake.

The contact points between primary particles can deform under pressure to increase the area of contact between particles in a packed bed. Sintering occurs when surface material migrates to broaden the contact area and fuse the structures of two originally distinct particles. This is called thermal sintering or pressure sintering according to which variable was used to produce the effect. Sintering is most commonly applied to amorphous materials such as glasses or metals. The surface migration rate increases exponentially with temperature, and sintering can occur within reasonable contact times at (absolute) temperatures as low as 70% of the solid's melting point.


Fig. 2.1b -- Varieties of Clump Structure



Agglomerates or Strong Flocs

A strong floc is a clump of particles with large areas in close proximity but not in intimate contact. Direct contact may be prevented by surface roughness, a scale of reaction products, or an adsorbed coating of surfactant or vehicle molecules. Even though the interparticle bonding here is weaker than for direct lattice bonds, it can hold such flocs together up to quite high shear. Since these tight flocs are held together over large contact areas, they have a small void fraction.

Weak Flocs

Aggregates and agglomerates have rough surfaces, so when they collide, the area available for direct contact is limited. The bonding energy that can be attained per unit mass is low. Bonding will also be weak if the particles have thick coatings that prevent the particles from getting close enough to attract strongly or if the interparticle forces are inherently weak (as for nonpolar polymer particles dispersed in an organic liquid). Weak flocs usually have rather open structures with high void fractions. Light stirring can redisperse weak flocs, and the weight of sediment in a settling mass can break the bonds between the particles, allowing them to collapse into a more compact configuration.

Tangles

Long fibers have extended, flexible structures that can twist about to become entangled to hold the particles together mechanically. The void fraction of such tangles is generally high. Although the attraction between the fibers may be weak, an essentially infinite time would be required for the random motion in a stirred slurry to bring them into configurations that would enable them to disengage from the tangle. This complex configuration dependence for deagglomeration means that the particles are entropically agglomerated rather than enthalpically agglomerated.

Adsorbed-Vapor Agglomeration

The flow and clumping of hygroscopic powders are critically dependent on the relative humidity. Clumping is dependent on the partial pressure of any vapor that could be adsorbed, but water vapor is most common cause of agglomeration by adsorption. A hygroscopic (water-adsorbing) solid adsorbs water, often as a surface film that increases the bonding between particles. The strength of agglomeration depends on the relative humidity of air and its diffusion into the powder. Since a vapor is best adsorbed or condensed at contact points, fine powders with many contact points per unit mass are more sensitive to humidity than coarse particles are. At high humidities so much moisture is adsorbed that liquid bridges form.

The adsorbed water may dissolve the surface or any residual salts deposited on the surface. If this solution later evaporates, the dissolved material will reprecipitate to form precipitation bonds. Several options that may reduce the sensitivity to humidity are to

  • Chemically treat the surface to make it less hygroscopic.

  • Coat the powder with a small amount of hydrophobic liquid. First check to see that this liquid does not by itself cause unacceptable clumping.

  • Disperse over the core powder a small amount of a hydrophobic shield powder that is at least ten times smaller in diameter than the first. The shields act as an anticaking agent by preventing contact between the surfaces of the core particles. The shield particles are chosen so that they will not condense or sinter.


Liquid-Bridge Agglomerates

Particles may be held together in agglomerates by a liquid that wets the contact points. Some examples are
1) liquid in a filtercake
2) water wetting the particle contacts in a damp storage bin
3) oil drops added to agglomerate coal particles in a coal-water slurry.


Fig. 2.2 -- Shoreline on a Liquid Bridge

When a liquid drop wets the contact point between two spheres of equal diameter dp [m] as in Fig. 3, the shoreline length [m] (one for each sphere) of the solid-liquid-gas contact is

lshore = p dp sin jshore

where jshore [rad] is the angle defined by a line drawn from the particle-particle contact point to one particle's center and then to a point on the shoreline for that particle. The total agglomerative force due to liquid bridging Fagglom [N] depends on jshore, the contact angle q [rad] (the angle between the surface tangent and the liquid tangent at the shoreline), and the surface tension of the liquid gl [N/m]. Rigorous analysis produces two terms that sum to approximately

Fagglom = Fcoh + Fsurf ~ p dp gl cos q

Fcoh is the cohesive (negative) force based on the curvature of the liquid-vapor meniscus. It is a complicated function, but for small values of g, the term

Fcoh ~ Fagglom (1 - sin ji) / cos j

dominates the sum (Hunter 1987 [see reference list] pages 287-290). Fsurf is the component of gl (along the shoreline of both particles) in the direction of the line of particle centers. Fsurf = Fagglom sin2 j and is small until j is rather large. Fagglom depends strongly on the particle diameter and only weakly on the amount of liquid in the meniscus (related to j).



Solid-Bridge Agglomerates

Particles of one material may become cemented together by the solids that precipitate as liquid evaporates during tray drying of wet filtercake or spray drying of a slurry. Because the surface tension causes the last remaining solution to be held as liquid bridges rather than as droplets on particle surfaces, the solids precipitate in the places best suited to cause cementation of the particles into a clump. Many medicinal and agricultural powders use water-soluble binders to provide solid bridges in tablets and granules.

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