Monomers diffusion flux

Note that for Dd > Z>a,c and Z>a < i)a,c, the flux is positive and negative, respectively. The characteristic time of the exchange of monomer from droplets during Ostwald ripening (t x) is given by relation 27, where < mc is the dimensionless solubility of the monomer in the continuous phase (i mco = C McoV mon) and Dmc is the monomer diffusion coefficient in the continuous phase. 

When surfactant molecules adsorb at an interface, the concentration of monomers in the subsurface layer decreases, which leads to release of monomers from the neighboring micelles, or to then-complete decomposition. The decrease in the concentrations of monomers and micelles gives rise to corresponding diffusion fluxes from the bulk of solution toward the subsurface layer (Figure 4.7). In general, the role of the micelles as sources and carriers of monomers leads to a marked acceleration of surfactant adsorption. 

The flux of monomers diffusing from the droplets to the particles will decrease as the former reservoirs are depleted, but reasonable calculations lead to the expectation that the arrival rate at the particle-water interface will exceed the usage rate even when more than 90% of the monomer has already left the droplets. 

In rheological experiments, that is, when the surface layer is periodically compressed and expanded around the equilibrium state, we also meet the situation that molecules desorb from the interface, increasing the local concentration of monomers such that micelles have to either take up molecules or form new micelles. In this case, a diffusion flux of monomers and micelles from and to the interface exists, depending on the respective situation at the interface [16, 25]. The peculiarities of the micellar kinetics in various systems are discussed in several papers however, the general principles hold [30-34]. 

No monomer transport through the solid catalyst support is considered. The diffusivity Z)PV in Eq. (73) is only a formal notation because the flux between the void phase V and the polymer P (or P ) micro-elements is calculated from the assumption of no accumulation and sorption equilibrium at the phase interface. 

In other words, if rd,2> d,D the difference in chemical potential is positive and the monomer will diffuse from 1 to 2. This process is schematically represented in Fig. 6. Point A represents the initial size of the monomer droplets. Equilibrium exists only if all of the droplets have the same size. In the case where a smaller droplet is created (symbolized by point B), monomer will flow from B to A (positive flux to A, or />0) as a result of the difference in chemical potential, making B smaller and smaller. The opposite happens for a bigger droplet (point C), which will become bigger and bigger. In other terms, point A is an unstable equilibrium. This process is usually referred to as monomer ripening. 

Since the nitroxide and the carbon-centered radical diffuse away from each other, termination by combination or disproportionation of two carbon-centered radicals cannot be excluded. This will lead to the formation of dead polymer chains and an excess of free nitroxide. The build-up of free nitroxide is referred to as the Persistent Radical Effect [207] and slows down the polymerization, since it will favor trapping (radical-radical coupling) over propagation. Besides termination, other side reactions play an important role in nitroxide-mediated CRP. One of the important side reactions is the decomposition of dormant chains [208], yielding polymer chains with an unsaturated end-group and a hydroxyamine, TH (Scheme 3, reaction 6). Another side reaction is thermal self-initiation [209], which is observed in styrene polymerizations at high temperatures. Here two styrene monomers can form a dimer, which, after reaction with another styrene monomer, results in the formation of two radicals (Scheme 3, reaction 7). This additional radical flux can compensate for the loss of radicals due to irreversible termination and allows the poly-... 

The rate of transmembrane diffusion of ions and molecules across a membrane is usually described in terms of a permeability constant (P), defined so that the unitary flux of molecules per unit time [J) across the membrane is 7 = P(co - f,), where co and Ci are the concentrations of the permeant species on opposite sides of membrane correspondingly, P has units of cm s. Two theoretical models have been proposed to account for solute permeation of bilayer membranes. The most generally accepted description for polar nonelectrolytes is the solubility-diffusion model [24]. This model treats the membrane as a thin slab of hydrophobic matter embedded in an aqueous environment. To cross the membrane, the permeating particle dissolves in the hydrophobic region of the membrane, diffuses to the opposite interface, and leaves the membrane by redissolving in the second aqueous phase. If the membrane thickness and the diffusion and partition coefficients of the permeating species are known, the permeability coefficient can be calculated. In some cases, the permeabilities of small molecules (water, urea) and ions (proton, potassium ion) calculated from the solubility-diffusion model are much smaller than experimentally observed values. This has led to an alternative model wherein permeation occurs through transient hydrophilic defects, or pores , formed by thermal fluctuations of surfactant monomers in the membrane [25]. 

We may compare results presented here with those obtained in two types of inductively coupled reactors [, 3]. One is the reactor we have used for many years [4], in which the portion of the reactor inserted into the r.f. coil is smaller than the main portion of the reactor, in which plasma polymer is collected. Monomer flux is directed into the main portion of the reactor, not through the r.f. coil. Electron bombardment of plasma polymer and substrate is reduced in this way [ ]. Active species are formed mainly under the r.f. coll and are transported by diffusion to the entire volume of the reactor. Interaction of these non-polymerizable energy carrying species (e.g. electrons, excited atoms) with the monomer entering the reactor leads to plasma polymerization [ ]. 

A further requirement of a CCRO membrane is that it should have an open, microporous sublayer structure. Such membranes allow effective diffusion of ethanol into the membrane from a recirculation solution supplied on the permeate side of the membrane. In our survey of various flat-sheet and hollow-fiber membranes, a monomer-derived polyamide composite membrane designated 3N8 was identified which satisfied this requirement. Other membranes tested either exhibited small or no measurable flux increases with permeate-side recirculation and are thus not suited to CCRO applications. 

To describe the transport within the gel, one assumes that a free species i of charge number zj is convected at the solvent velocity v and diffuses with a coefficient Di 4>), which depends on the volume fraction occupied by the polymeric network, whereas the deprotonated form A of the monomer, attached to the network, is advected at velocity vp and does not difiuse. To account for the permittivity and for the tortuosity of this network at 1, the following approximation Bi((t>) = Doi(l — 2(j>) was used [42], whereas for the friction coefficient of this network, the Ogston law, given by Eq. (9.28), was again employed. The fluxes of the free species and of the ions A are, respectively, given by the two equations... 

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