Number of contact points

Whereas a maximum number of contact points between PVC grains is desired to achieve mechanical stability, this prevents higher porosities. Typical values for porosity are 30 - 35 percent therefore the electrical resistance is rather high, i.e., 170 mQcm2, despite thin 0.3 mm backwebs for top qualities. As mentioned, the range is very wide — even considerably higher electrical resistances are sometimes acceptable, e.g., in areas where cold crank performance is of no significant importance. 

These grafted polymers, though anchored covalently at one end, act like loosely adsorbed polymers of the same nature, except that their number of contact points per molecule will be small and the chains extend further in to the fluid. 

In trying to formulate DMP-754, Badway et al. (51) investigated binary blends as well as compacts of DMP-754 (Fig. 2) with anhydrous lactose and concluded that compaction of the blends resulted in an increase in the amount of hydrolysis seen (Table 5). Badway et al. postulated that this result was due to an increase in the number of contact points between the drug and the lactose resulting in an increased rate of moisture transfer leading to degradation. 

Experimental support on the validity of Eq. 4.7-2 was presented by Spencer et al. (32), who also proposed a theoretical derivation based on considering a discrete number of contact points between solids and containing walls. They assumed isotropic stress distribution (K = 1) and obtained an expression identical to Eq. 4.7-2... 

If we introduce heterochiral units in a homochiral octamer, the number of such hydrogen bonds would be diminished, with an increase in the energy of the cluster. Additionally, the homochiral octamer shows an alternate pattern of ammonium and carboxylate groups, being an eight point contact surface, which would be disrupted by introducing heterochiral units, decreasing the number of contact points. 

N is the number of chemical units in one chain) [42] the resulting mean number of contact points of one chain with the silica surface is N1/2 [11, 12]. The NMR sensitivity... 

Cohesion. This test is used for very fine powders (below 70 pm). Material is passed through three vibrating sieves in series. The material left on each sieve is weighed and a cohesion index is determined from the relative amounts retained. Carr19 defined cohesion as the apparent surface force acting on the surface of powders, which are composed of millions of atoms. The number of points of contact within the powder mass determines the effect of this force. Thus, cohesiveness increases with decreasing particle size, since the number of contact points increases as the particle size decreases. 

This publication arranges the published papers on adsorption of polymers with special regard to experiment and theory. A summary of all investigated systems is given. The experimental methods are outlined and the amounts adsorbed are discussed as a function of the system and experimental parameters (polymer, adsorbent, solvent, molecular, concentration, time, weight and temperature). Calculated and experimental amounts of saturation, the number of contact points per molecule adsorbed, the thickness of the adsorbed layer, the adsorption isotherms, the heats of adsorption, the effects of desorption are compared. Assumptions on the structur of the adsorbed layer and the mechanism of polymer adsorption are made and discussed. 

Na being the total number of aggregates and (, being the average number of contact points to neighboring aggregates ... 

With a suspension containing a distribution of particle sizes, one cannot replace a by the average particle size, since the number of contact points N in a floe is greater than that calculated using an average particle size. With a polydisperse suspension it is difficult to calculate the number of contacts without knowledge of the exact particle size distribution. Since this was not available in the present system, no attempt was made to calculate Xg (and hence compare it with the experimental value). However, the trend in p p correlates very well... 

The average number of contact points between particles increases as bulk density increases, and the interparticulate forces at these contact points must be overcome to produce a dispersed aerosol cloud. Therefore, a powder of low bulk density may be more easily dispersed as an aerosol than an otherwise identical powder of high bulk density. 

Improvements upon the theories require more detailed treatment of intramolecular as well as intermolecular interactions. As we mentioned in the previous section, use of Mayer /-functions has been made by Yamakawa and others to take intramolecular excluded volume effects into consid ation. However, in their calculation, parts of macromolecules between two consecutive contact points of two molecules are replaced always by Gaussian-free chains. While this approximation may be correct for a small number of contact points for very long molecules, it certainly invalidates the /-function expansion itself for higher orders. On the other hand, our results in the previous section indicate clearly that collective interactions of two macromolecules play important roles in explaining the molecular weight dependence of Ag. 

In addition to drug dissolution and bioavailability, the properties of a powder bed can be strongly influenced by particle size. As the particle size decrea.ses, the number of contact points between particles in a given volume of material drastically increases. For example, if 1 g of material with a density 1 g/cm were densely packed with six contact points per particle, then 10 and l(X)pm diameter spherical particles would have about ll.5x I o and ll.5x 10 contact points/g, respectively. In other word.s, the smaller... 

The efficiency of a ball mill depends on the number of contact points between the balls... 

Clearly, depends on the volume fraction of the dispersion, as well as the particle size distribution (which determines the number of contact points in a floe). Therefore, for quantitative comparison between various systems, it must be ensured that the volume fraction of the disperse particles is the same, and that the dispersions have very similar particle size distributions. also depends on the strength of the flocculated structure - that is, the energy of attraction between the droplets - and this in turn depends on whether the flocculation is in the primary or secondary minimum. Flocculation in the primary minimum is associated with a large attractive energy, and this leads to higher values of when compared to values obtained for secondary minimum flocculation (weak flocculation). For a weakly flocculated dispersion, as is the case for the secondary minimum flocculation of an electrostatically stabilised system, the deeper the secondary minimum the higher the value of (at any given volume fraction and particle size distribution of the dispersion). 

The increase in conductivity can be explained in terms of an initial significant increase in the number of contacting points between fibers. The refining process, which causes shearing and slitting of the fibers, increases the specific area of the fibers and the number of interfiber contacts that can serve as... 

The number of heterogeneous contacts Nab can be easily estimated. It is equal to the number of contact points associated with A molecules multiplied by a probability pB that a neighbor of molecule A is molecule B, that is. 

A segment perpendicular to a surface results in an effective steric barrier, while the number of contact points with the interface influences the strength of adsorption. For example, flexible caseins have numerous proline residues, so they have little ordered secondary structure and no intramolecular crosslink. As a result, caseins are able to adopt a number of different conformational states when being adsorbed at the oil-water interface. They are usually adsorbed at the interface in such a way that considerable portions of their structures protruding into the aqueous phase are available (Dickinson, 1992). On the other hand, serum milk proteins, such as p-lg and a-lactalbumin (a-la), bind relatively close to the interface and do not protrude... 

---