Monodisperse particles coagulation

In this system using a polystyrene containing block copolymer, the polystyrene segment should readily partition into the lipophilic polystyrene particle core while the poly(FOA) or PDMS block is solubilized in the CO2 continuous phase to provide steric stabilization and prevent coagulation. In comparison of the polystyrene-b-poly(FOA) diblock copolymers to the polystyrene-b-PDMS diblock copolymers, it was found that the use of a polystyrene-b-PDMS stabilizer gives much more monodisperse particles. This most likely arises from the synthetic technique employed in the surfactant synthesis. The blocks in the polystyrene-b-PDMS block copolymers have a much narrower polydispersity than the blocks in the polystyrene-b-poly(FOA) block copolymers. It was noted that the particles obtained in... 

To simplify the calculations, it is assumed that the concentrations, mobilities, and other properties of the positive and negative ions are equal and that the concentrations of the tons and charged particles have reached a steady slate. We consider a group of particles of uniform size no coagulation occurs,. so a polydisperse aerosol can be treated as a set of uncoupled monodisperse particles. The rates at which ions of both signs attach to particles are assumed to be independent ol each other. In the steady state, ions are generated and destroyed at the same rate by attachment to particles. Calculations indicate that ion recombination is not an important mechanism for ion loss in the atmosphere (Bricard and Pradel, Ii966). 

The theory of coagulation will be presented in two steps. At first, we will develop an expression describing the rate of collisions between two monodisperse particle populations consisting of N particles with diameter Dpl and N2 with diameter Dp2. In the next step a differential equation describing the rate of change of a full coagulating aerosol size distribution will be derived. 

Finally, it could be considered that the spherical monodisperse particles are formed by secondary coagulation of the primary particles [46,48,49]. 

Electrolytes. Electrolytes are added for several reasons. For example, they can control the pH (buffers), which prevents hydrolysis of the surfactant and maintains the efficiency of the initiator. The addition of electrolytes can lead to more monodisperse particles but also to coagulation. 

Soapless seeded emulsion copolymerization has been proposed as an alternative method for the preparation of uniform copolymer microspheres in the submicron-size range [115-117]. In this process, a small part of the total monomer-comonomer mixture is added into the water phase to start the copolymerization with a lower monomer phase-water ratio relative to the conventional direct process to prevent the coagulation and monodispersity defects. The functional comonomer concentration in the monomer-comonomer mixture is also kept below 10% (by mole). The water phase including the initiator is kept at the polymerization temperature during and after the addition of initial monomer mixture. The nucleation takes place by the precipitation of copolymer macromolecules, and initially formed copolymer nuclei collide and form larger particles. After particle formation with the initial lower organic phase-water ratio, an oligomer initiated in the continuous phase is... 

Perikinetic Coagulation. If colloidal particles are of such dimensions that they are subject to thermal motion, the transport of these particles is accomplished by this Brownian motion. Collisions occur when one particle enters the sphere of influence of another particle. The coagulation rate measuring the decrease in the concentration of particles with time, N (in numbers/ml.), of a nearly monodisperse suspension corresponds under these conditions to the rate law for a second order reaction (15) ... 

The potential energy barrier to coagulation can be reduced to zero by the addition of excess electrolyte, which creates a situation in which every encounter between the particles leads to permanent contact. The theory of rapid (diffusion-controlled) coagulation was developed by Smoluchowski110. For a monodispersed sol containing... 

Let us consider a system of monodispersed aerosol particles. Because of the collisions between the particles, they will coagulate to form doublets. The rate of formation of a doublet depends, of course, on the particle radius, the particle density, the viscosity and temperature of the suspending medium, the Hamaker constant, and the particle number concentration. If the rate of formation of a doublet is itnuch less than its rate of dissociation, the doublets are unstable. These unstable doublets attain... 

For the case of coagulation of particles of two different sizes, it is possible to follow the same approach as given for the monodisperse case except that d is replaced with + d2)/2 and 2D is replaced with Dt + D2. Then the coagulation coefficient Kl2 becomes... 

The second method for aerosol coagulation in turbulent flows arises because of inertial differences between particles of different sizes. The particles accelerate to different velocities by the turbulence depending on their size, and they may then collide with each other. This mechanism is unimportant for a monodisperse aerosol. For a polydisperse aerosol of unspecified size distribution, Levich (1962) has shown that the agglomeration rate is proportional to the basic velocity of the turbulent flow raised to the 9/4 power, indicating that the agglomeration rate increases very rapidly with the turbulent velocity. Since very small particles are rapidly accelerated, this mechanism also decreases in importance as the particle size becomes very small, being most important for particles whose sizes exceed 10-6 to 10"4 cm in diameter. In all cases brownian diffusion predominates when particles are less than 10-6 cm in diameter. 

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