Bimodal spheres

In summary, a method has been developed for the placement of bimodal sphere distributions within three-dimensional boundaries. The bimodal distribution is created from the combination of two sphere populations, where each population represents a distinct distribution. The efficient packing of a bimodal distribution of spheres can produce a high volume of the discrete phase in a toughened plastic and a corresponding small interparticle distance. However, combining two materials containing equal discrete-phase volumes of monosized spheres to make a bimodal system does not decrease interparticle... 

Encapsulation via the layer-by-layer assembly of multilayered polyelectrolyte (PE) or PE/nanoparticle nanocomposite thin shells of catalase in bimodal mesoporous silica spheres is also described by Wang and Caruso [198]. The use of a bimodal mesoporous structure allows faster immobilization rates and greater enzyme immobilization capacity (20-40 wt%) in comparison with a monomodal structure. The activity of the encapsulated catalase was retained (70 % after 25 successive batch reactions) and its stability enhanced. 

All catalysts are either it-in. cylinder or sphere. Catalyst B has a bimodal pore size distribution. The average pore diameter is defined as 40,000 x pore volume (ml/g) divided by nitrogen surface area (m2/g). 

The evidence for single-electron transfer (SET) in the reactions of lithium aluminium hydride (LAH) with hindered primary alkyl iodides is overwhelming. A study has now shown for the first tune that SET may also be involved in reactions of LAH with unhindered, unsubstituted primary alkyl iodides, the particular substrate studied being 1-iodoctane.98 A theory of the rates of, k 2 reactions and then relation to those of outer-sphere bond-rapture electron transfers has been presented in detail.99 A unified approach is introduced in which there can be a flux density for crossing the transition state, which is either bimodal, one part leading to, k 2 and the other to ET products, or... 

Figure 2. Bimodal distributions of suspensions containing mixtures of a) 1.09 and 2.99 pm, b) 1.09 and 2.02 pm latex spheres measured by TS.

Several approaches towards the synthesis of hierarchical meso- and macro-porous materials have been described. For instance, a mixture that comprised a block co-polymer and polymer latex spheres was utilized to obtain large pore silicas with a bimodal pore size distribution [84]. Rather than pre-organizing latex spheres into an ordered structure they were instead mixed with block-copolymer precursor sols and the resulting structures were disordered. A similar approach that utilized a latex colloidal crystal template was used to assemble a macroporous crystal with amesoporous silica framework [67]. 

Figure 6.3 Relative viscosity as a function of the fraction of large spheres in a bimodal distribution of particle sizes with a 5 1 ratio of diameters, at various total volume percentages of particles. The arrow P Q illustrates the 50-fold reduction in viscosity that occurs when monosized particles in a 60 vol% suspension are replaced by a 50-50 mixture of large and small spheres. The arrow P S shows that if monosized spheres are replaced by a bimodal size distribution, the concentration of spheres can be increased from 60% to 75% without increasing the viscosity. (Reprinted from Barnes et al., An Introduction to Rheology (1989), with kind permission from Elsevier Science - NL, Sara Burger-hartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

Figure 12 shows Chong et al. (28) data for monodisperse and bidisperse (bimodal) suspension systems. In a bidisperse suspension, the volume fraction of small spheres (diameter d) in the mixture is kept constant at 25% of the total solids. The figure shows that the viscosity of a bidisperse suspension is a strong function of the particle size ratio, d/D, where D is the diameter of the large particles. The viscosity decreases substantially by decreasing d/D at a given total solids concentration. The data for the unimodal system fall well above the bimodal suspensions. Also, the effect of particle size distribution decreases at lower values of total solids concentration. 

Figure 13 illustrates another very interesting point. Here the relative viscosity of a bimodal suspension is plotted as a function of volume percent of small spheres in total solids. At any given total solids concentration, the relative viscosity decreases initially with the increase in volume percent of small spheres, and then it increases with further increase in small spheres. The minimum observed in the relative viscosity plots of a bimodal suspension is quite typical. There are no fundamental reasons why a similar behavior would not be true for emulsions. 

The maximum packing fraction cp. can be easily calculated for monodisperse rigid spheres. For an hexagonal packing

random packing (Pp = 0.64. The maximum packing fraction increases with polydisperse suspensions for example, for a bimodal particle size distribution (with a ratio of 10 1), 0.8. 

A potential advantage in toughness results from the more efficient packing of spheres in a bimodal system (5). However, even when the volume of the... 

There is a need to be able to calculate interparticle distance and other parameters from geometric models of bimodal and conventional systems. This paper explains how computer programs for the placement of spheres in a three-dimensional space have been modified to accommodate bimodal distributions. Examples of models composed of simple bimodal particle distributions are presented to illustrate the technique. 

Figure 2. Bimodal-distribution model, seen in a perspective view, of sphere placement in a 35-pm3 three-dimensional space. Distribution 1 2.0-pm average diameter, 0.4-pm standard deviation, 2.0% discrete-phase volume, 192 particles. Distribution 2 8.0-pm average diameter, 0.8-pm standard deviation, 6.2% discrete-phase volume, 9 particles.

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