Cohesion

Cohesiveness of a powder is a compound measurement and its fundamental origin lies in the propensity of the individual particles to stick together. 

It follows, therefore, that the tensile strength tests reported in section 4.5 should also be included in this section, as a direct way of measuring cohesion. All of the other ways are, therefore, indirect in that they measure other properties related to or as a consequence of the internal cohesion forces. 

The tensile strength described in section 4.5 is the most direct way of assessing cohesiveness because it measures the internal adhesion properties independent of the mechanical interactions of a shear plane. From the practical point of view, however, such interactions do occur in powder flow and handling and it is perhaps 

An instrument which attempts to measure cohesion was originally developed at Warren Springs Laboratory and is now available from Ajax Equipment (Bolton) Ltd. It is designed to aid the assessment of flow properties of bulk solids in that it measures the cohesive strength of samples of powders in varied states of compaction, from lightly settled conditions to firm compacts. It attempts to measure directly cohesion as defined in section 4.1.2, i.e. the shear stress at failure, with no normal load acting upon the surface of failure. 

These conditions represent circumstances in powder storage and handling where the material is not confined by boundary walls or adjacent masses of product so that, in order to fail, it does not have to overcome externally applied forces or constraints but merely the strength developed by prior compaction of the powder. 

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Asphaltenes are obtained in the laboratory by precipitation in normal heptane. Refer to the separation flow diagram in Figure 1.2. They comprise an accumulation of condensed polynuclear aromatic layers linked by saturated chains. A folding of the construction shows the aromatic layers to be in piles, whose cohesion is attributed to -it electrons from double bonds of the benzene ring. These are shiny black solids whose molecular weight can vary from 1000 to 100,000. 

Additives acting on the pour point also modify the crystal size and, in addition, decrease the cohesive forces between crystals, allowing flow at lower temperatures. These additives are also copolymers containing vinyl esters, alkyl acrylates, or alkyl fumarates. In addition, formulations containing surfactants, such as the amides or fatty acid salts and long-chain dialkyl-amines, have an effect both on the cold filter plugging point and the pour point. 

Derive the expression (in terms of the appropriate works of adhesion and cohesion) for the spreading coefficient for a substance C at the interface between two liquids A and B. 

The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range. 

Most solid surfaces are marred by small cracks, and it appears clear that it is often because of the presence of such surface imperfections that observed tensile strengths fall below the theoretical ones. For sodium chloride, the theoretical tensile strength is about 200 kg/mm [136], while that calculated from the work of cohesion would be 40 kg/mm [137], and actual breaking stresses are a hundreth or a thousandth of this, depending on the surface condition and crystal size. Coating the salt crystals with a saturated solution, causing surface deposition of small crystals to occur, resulted in a much lower tensile strength but not if the solution contained some urea. 

The statement was made that the work of adhesion between two dissimilar substances should be larger than the work of cohesion of the weaker one. Demonstrate a basis on which this statement is correct and a basis on which it could be argued that the statement is incorrect. 

The behavior of insoluble monolayers at the hydrocarbon-water interface has been studied to some extent. In general, a values for straight-chain acids and alcohols are greater at a given film pressure than if spread at the water-air interface. This is perhaps to be expected since the nonpolar phase should tend to reduce the cohesion between the hydrocarbon tails. See Ref. 91 for early reviews. Takenaka [92] has reported polarized resonance Raman spectra for an azo dye monolayer at the CCl4-water interface some conclusions as to orientation were possible. A mean-held theory based on Lennard-Jones potentials has been used to model an amphiphile at an oil-water interface one conclusion was that the depth of the interfacial region can be relatively large [93]. 

Cortona P 1992 Direct determination of self-consistent total energies and charge densities of solids A study of the cohesive properties of the alkali halides Phys. Rev. B 46 2008... 

Figure Cl. 1.6. Minimum energy stmctures for neutral Si clusters ( = 12-20) calculated using density functional theory witli tire local density approximation. Cohesive energies per atom are indicated. Note tire two nearly degenerate stmctures of Si g. Ho K M, Shvartsburg A A, Pan B, Lu Z Y, Wang C Z, Wacher J G, Fye J L and Jarrold M F 1998 Nature 392 582, figure 2.

Ultimately, the surface energy is used to produce a cohesive body during sintering. As such, surface energy, which is also referred to as surface tension, y, is obviously very important in ceramic powder processing. Surface tension causes liquids to fonn spherical drops, and allows solids to preferentially adsorb atoms to lower tire free energy of tire system. Also, surface tension creates pressure differences and chemical potential differences across curved surfaces tlrat cause matter to move. 

Sintering invoives the densification and microstmcture deveiopment that transfonns the iooseiy bound particies in a powder compact into a dense, cohesive body [, 70, 71, 72 and 73]. The end-... 

It is remarkable that only two descriptors were needed in this method. However, this equation is mostly only of historical interest as it is of little use in modem dmg and combinatorial library design because it requires a knowledge of the compound s experimental melting point which is not available for virtual compounds. Several methods exist for estimating log P [1-14], but only a few inroads have been made into the estimation of melting points. The melting point is a key index of the cohesive interactions in the solid and is still difficult to estimate. 

Loh most likely mixed up the internal pressure with the cohesive eneigy density. See (a) Dack, M. 

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

The solubility parameter is not calculated directly. It is calculated as the square root of the cohesive energy density. There are a number of group additivity techniques for computing cohesive energy. None of these techniques is best for all polymers. 

If the concentration of junction points is high enough, even branches will contain branches. Eventually a point is reached at which the amount of branching is so extensive that the polymer molecule becomes a giant three-dimensional network. When this condition is achieved, the molecule is said to be cross-linked. In this case, an entire macroscopic object may be considered to consist of essentially one molecule. The forces which give cohesiveness to such a body are covalent bonds, not intermolecular forces. Accordingly, the mechanical behavior of cross-linked bodies is much different from those without cross-linking. 

We shall devote a considerable portion of this chapter to discussing the thermodynamics of mixing according to the Flory-Huggins theory. Other important concepts we discuss in less detail include the cohesive energy density, the Flory-Krigbaum theory, and a brief look at charged polymers. 

The quantity AU JV° is the internal energy of vaporization per unit volume and is called the cohesive energy density (CED) of component i. The square root of the CED is generally given the symbol 6j for component i. 

Table 8.2 Values of the Cohesive Energy Density (CED) for Some Common Solvents and the Solubility Parameter 6 for These Solvents and Some Common Polymers...

For benzene at 25°C this becomes AU = 33,900 - 8.314 (298) = 31,400 J mol". The molar volume of a compound is given by V° = (molecular weight)/ (density). For benzene at 25°C, this becomes V° = 78.0/0.879 = 88.7 cm mol". Tlie cohesive energy density is simply the ratio AUy/V°, but in evaluating this numerically, the question of units arises. By convention, these are usually expressed in calories per cubic centimeter, so we write... 

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