Wall forces

At short interparticle distances, the van der Walls forces show that two metallic particles will be mutually attracted. In the absence of repulsive forces opposed to the van der Walls forces the colloidal metal particles will aggregate. Consequently, the use of a protective agent able to induce a repulsive force opposed to the van der Walls forces is necessary to provide stable nanoparticles in solution. The general stabihzation mechanisms of colloidal materials have been described in Derjaguin-Landau-Verway-Overbeck (DLVO) theory. [40,41] Stabilization of colloids is usually discussed... 

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

The study of how fluids interact with porous solids is itself an important area of research [6], The introduction of wall forces and the competition between fluid-fluid and fluid-wall forces, leads to interesting surface-driven phase changes, and the departure of the physical behavior of a fluid from the normal equation of state is often profound [6-9]. Studies of gas-liquid phase equilibria in restricted geometries provide information on finite-size effects and surface forces, as well as the thermodynamic behavior of constrained fluids (i.e., shifts in phase coexistence curves). Furthermore, improved understanding of changes in phase transitions and associated critical points in confined systems allow for material science studies of pore structure variables, such as pore size, surface area/chemistry and connectivity [6, 23-25],... 

Fr is the radial die wall force that develops because the powder is in a confined environment (i.e., not able to spread outward as pressure is applied down upon it because it is residing within the die). The coefficient of friction at the die wall, iw, is due to the shearing adhesion that occurs along the die a as the powder is made more dense and compressed. The following relationship between and FD, iw, and Fr is found to exist ... 

The force of tablet ejection from the die, Fr, is a function of both and the residual die wall force, RD WF, that exists after decompression. As the friction decreases, one will obviously see a corresponding drop in Fr. It is important to remember here that it is desirable for Fr to be as low as possible so that minimal damage is imparted to both the tablet and the tooling. 

Slopes BC and CD = function of elastic recovery Lines OC and OE = function of (residual die wall force) RDWF... 

The side wall is the same as the front wall, spanning vertically from foundation to roof. Because the highest loads are on the front wall, a side wall analysis would only be necessary to check the interaction of in-plane and out-of-plane shear wall forces, This calculation will be for a wall segment, Lt, 1 foot wide (0.3 m). 

Adsorption/chemisorption at the surface (adsorption of gas molecules occurs on the solid surface because of attractive forces between them). Gas molecules approaching the surface may lose some of their momentum (in the component normal to the surface) and become trapped in the potential well. The energy required to overcome the attractive potential barrier of the surface and the attraction of neighbouring molecules is the heat of adsorption (Van der Wall forces) and several monolayers may be adsorbed. However, if there is some interaction or electron transfer between the gas molecule and the surface (forming, e.g., a surface compound), it is defined as chemisorption. The heat of chemisorption is usually greater than the heat of adsorption. The extent of chemisorption depends upon the specific nature of the solids and gases. 

The use of compaction simulators was first reported in 1976. Since then, a variety of simulators have been developed. Hydraulic simulators, as well as mechanical simulators, are available to characterize raw materials, drug substances, and formulations, as well as to predict material behavior on scale-up. The appeal of simulators is due to the fact that they purport to provide the same compaction profile as experienced on a tablet press while using only gram or even milligram quantities of powders. Compaction simulators can achieve high speeds, as would be experienced on a production tablet press, and can be instrumented to measure a variety of parameters, including upper and lower punch force, upper and lower punch displacement, ejection force, radial die wall force, take-off force, etc. Summaries on the uses of simulators and tablet press instrumentation can be found in (19,20). 

Another example of the use of DOE during pilot studies is the study of factors affecting the ejection and take-off force. Measurement of ejection force and take-off force will determine if the formula is sufficiently lubricated. Ejection force is measured as an indication of the release of the tablet from the die wall forces, and the take-off force related to the adhesion forces to the punch face. Take-off force is an appropriate measurement to determine if a formula has a tendency to stick. Based on these designs, an optimal formula, including the lubricant level, and process can be predicted for scale-up (Figs. 12 and 13). 

Fig. 6.2 Effect of different long cut-offs on the average number of H-bonds formed by water molecules as a function of distance from the bottom of the simulated systems solid line, 14 A dashed line, 18 A dash dot line, 30 A. The lipids reside in the region below the dotted line at 47.5 A and the dotted line at 89 A represents the cut-off of the boundary wall force. (Adapted from Fig. 6 of ref. 31 with permission from the American Institute of Physics).

The amount adsorbed at each pressure can be obtained by integrating the equilibrium density profile p(r) and subtracting the quantity of adsorptive which would be present in the absence of wall forces p0(r). The integration limits depend on the pore geometry, for example, in the case of slit-shape pores, the densities are only functions of the normal distance (z) from the wall thus,... 

Adsorption Theory of Adhesion. The adsorption theory states that adhesion results from molecular contact between two materials and the surface forces that develop. Adhesion results from the adsorption of adhesive molecules on the substrate and the resulting attractive forces, usually designated as secondary or van der Walls forces. For these forces to develop, the respective surfaces must not be separated more than 5 angstroms (A) in distance. Therefore, the adhesive must make intimate, molecular contact with the substrate surface. 

After intimate contact is achieved between adhesive and adherend through wetting, it is believed that permanent adhesion results primarily through forces of molecular attraction. Four general types of chemical bonds are recognized as being involved in adhesion and cohesion electrostatic, covalent, and metallic, which are referred to as primary bonds, and van der Walls forces, which are referred to as secondary bonds. 

String-wound These cartridge filters consist of a string of polypropylene (or cotton, nylon, jute, polyester, and so forth) wound around a central core. String-wound cartridge filters rely on Van der Walls forces to capture small particles. These filters suffer from the potential to unload particles at higher pressure drops. Additionally, a slower flow rate is recommended for these filters, about 2 -3 gpm per 10-inch equivalent. 

Besides upper punch force, lower punch force, die wall force [63-65], ejection force [66], and tablet scraper force can be measured. Die wall force measurement will be discussed separately. 

Die Wall Force Measurement During compression of the powder the forces are evolving not only at the punches but also at the die wall [63-65], Therefore die wall force measurement complements upper and lower force measurement. Since the compression process occurs axially, these radially evolving forces are smaller than the forces at the punches. Measurement of die wall force allows, for example, for indication on die wall friction, tablet capping, and lamination. Instrumentation for... 

One example most recently developed is a split die consisting of three sections (Figure 10) [64], Integrating the sensing web in a thin middle layer isolates stress measurement to a narrow band around the tablet and gives much closer approximation to the true stress. Further die wall force measurement is linear and independent of tablet height and position as it is uncoupled from all other die wall stresses and strains. Further it is designed in the shape of a conventional die and can be mounted without modification into a die table. 

Laich,T., and Kissel,T. (1995), Axial die-wall force minimum. Influences and significance for elastic behavior of single components and binary mixtures of excipients, Pharm. Ind. 57(2), 174-182. 

In the theory developed by Derjaguin and Landau (24) and Verwey and Overbeek (25.) the stability of colloidal dispersions is treated in terms of the energy changes which take place when particles approach one another. The theory involves estimations of the energy of attraction (London-van der Walls forces) and the energy of repulsion (overlapping of electric double layers) in terms of inter-oarticle distance. But in addition to electrostatic interaction, steric repulsion has also to be considered. 

After decompression, the tablet remains in the die until it is ejected. During this time, a residual die wall force is exerted by the tablet on the die wall. Tablet ejection is defined by three stages ... 

Radial and axial die-wall force measurements also provide an insight into the compaction mechanism of the material and may indicate a die-wall binding (sticking) that is, in effect, a negative pull on lower punch. The radial die-wall pressure due to friction is material-specific and is more evenly distributed inside the die with an addition of a lubricant. Instrumentation of the die presents a technological challenge because pressure is distributed non-linearly with respect to tablet position inside the die and depends on tablet thickness. " ... 

Schrank-Junghani, H. Bier, H.P. Sucker, H. The measurement of die wall forces to determine the minimum concentration of lubricant needed for tablet formulations. Acta Pharm. Technol. 1984, 30 (3), 224—234. 

Instrumented punches and dies, which enable online measurement of forces on the punch and relative displacement or acceleration, electrical resistance, and acoustic release as well as measurement of die wall forces, are special tools used exclusively in research they are discussed in a separate chapter. 

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