Maximum Number of Particles

A second important difference between the batch reactor model and the CSTR model is the prediction of a maximum number of particles for the CSTR as a function of mean residence time. This maximum is readily determined hy setting the derivative dN/d6), obtained from Eq- (11), equal to zero and solving for N. The result of this computation is... 

Nearly all particles are likely to be produced in the first reactor. The size of this reactor will influence the number of particles formed. If a maximum number of particles is desired this first reactor will be operated at a relatively small mean residence time and thus will be smaller than the other reactors in the system. 

In the above, the sum over A has the upper limit of infinity. This is clearly correct in the thermod5mamic limit. However, for a system with finite volume, V, depending on the hard core size of its constituents, there will be a maximum number of particles, M V), that can be packed in volume V. Then, for all N such that N > M(V), the value of (-PW) becomes infinity and all terms in the Nsum with N> M(V) vanish. Thus, provided the inter-particle interactions contain a strongly repulsive part, the jV sum in the above discussion can be extended to infinity. 

Grade Maximum number of particles greater than 0.5 micrometre Suggested microbiological quality CFU per cubic metre... 

Class of cleanliness Maximum number of particles permitted per cubic M 2 .5// >5/jm Maximum number of viable microorganisms permitted per cubic M Recommended minimum air changes per hour... 

Levels of cleanliness have been established as classes , an industry convention. The class number measures the maximum number of particles per cubic meter that may be present. It does not represent the number of organisms. 

The above trend was confirmed by Hull and Kitchener [39] using a rotating disc coated with a negative film and negative polystyrene latex particles. The number of polystyrene particles deposited was found to increase with increasing NaCl concentration, reaching a maximum at CnsO > 10 mol dm . The ratio of maximum number of particles deposited Nmax to the number deposited at any other NaCl concentration Nj (the so-called stability ratio W) was calculated and plotted versus NaCl concentration. 

Goebel et al. [107] have reported that the particle concentration reaches a maximum at very low conversion (below 1%). This agrees well with the concept of an emulsifier-free emulsion polymerization of conventional monomers in which the maximum number of particles below 5% appears. Beyond this critical conversion, the number of particles starts to decrease due to the particle association. The strong association of particles results from the low stability of small particles. The same results were found by other groups [76,108,109] in which a strong flocculation of latex particles led to a decrease of particle concentration with conversion. 

Moreover, the PE nano particles are spherical in shape, which are confirmed from AFM, TEM and SEM (Figures 2-4). Supplementary information to be noted, there is always a distribution of particle size of PE nano particles and these distributions are shown in the histogram [Figures 2(e) and 3(c)]. AFM shows maximum numbers of particles are of 75-100 nm with population of 50%, and 100% in between 60- 250 nm. From TEM the maximum numbers of particles are of 50-60 nm sized with 50% population, 62% of below 100 nm and 100% in between 30-260 nm. Additional studies from SEM images [Figure 4] show that the micron sized PE particles are spherical in morphology. These AFM and TEM microscopy results show that there is no pronounced variation with the average particle size of spherical PE nano particles. It is also noticed from the microscopy analysis that micro and nano particles are separated from each other. 

Figure 2. (a) Displays 2D view of few of PE nano particles obtained from AFM topography, (b) displays 3D view of the same. Figure 2(c) is another AFM photograph of PE nano particles, (d) displays 3D view of the same. Figure (e) particle size distribution of nano sphere PE. The maximum numbers of particles are of 80 nm sized. 50 % PE particles are below 100 nm sized, and all are in between 60-250 nm sized. 

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