Radical entry rate coefficient

It is accepted that the radical entry rate coefficient for miniemulsion droplets is substantially lower than for the monomer-swollen particles. This is attributed to a barrier to radical entry into monomer droplets which exists because of the formation of an interface complex of the emulsifier/coemulsifier at the surface of the monomer droplets [24]. The increased radical capture efficiency of particles over monomer droplets is attributed to weakening or elimination of the barrier to radical entry or to monomer diffusion by the presence of polymer. The polymer modifies the particle interface and influences the solubility of emulsifier and coemulsifier in the monomer/polymer phase and the close packing of emulsifier and co emulsifier at the particle surface. Under such conditions the residence time of entered radical increases as well as its propagation efficiency with monomer prior to exit. This increases the rate entry of radicals into particles. 

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

Guo et al. [29] have estimated the entry rate coefficient, k a, of radicals into micelles (microemulsion droplets) to be 7xl05 cm3 mol-1 s 1, which is several orders of magnitude smaller than ka, the entry rate coefficient into the polymer particles. This was ascribed to the difference of the surface area of microemulsion droplets and polymer particles. The condensed interface layer or the possibly high zeta-potential of the surface of the microemulsion droplets may hinder the entry of radicals. 

Adams, et al. [89] could find no evidence of differing efficiency of entry between charged and uncharged radicals or of any effect of the extent of surface coverage with emulsifier or of ionic strength collisional or diffusive entry models predicted entry rate coefficients which were too large. Subsequently Maxwell, et al. [60] concluded that the rate-determining process was the time required for an initiator radical to add two styrene residues in the aqueous phase and thereby acquire sufficient hydrophobic character to adsorb onto a latex particle. 

The various second-order entry rate coefficients for entry into particles and micelles by initiator-derived and exit-derived radicals are assumed to obey the... 

Another component of the entry rate coefficient can be from re-entry of radicals which have exited (desorbed) from another particle. Desorbed radicals will have arisen from some transfer reaction inside a particle, and are thus unlikely to be charged, and hence will be lipophilic. Hence once a desorbed radical in the aqueous phase meets the surface of a particle, it is likely to penetrate immediately into the interior of the particle its probability of entry into a monomer-rich region is unity. Denoting these radicals as E, one has... 

Although iterative numerical solution of Equations (5.10)-(5.13) is trivial, insight can be obtained from the analytic solution obtained when it is assumed that kp,aq is independent of the degree of polymerization (note, however, that this simplification is not likely to be quantitatively accurate). The resulting formula was also obtained, in a somewhat different context, in the simplest version of the Hansen-Ugelstad-Fitch-Tsai (HUFT) theoiy for particle formation [26,27], and may be expressed either as the entry rate coefficient for radicals derived directly from initiator, or alternatively as the initiator efficiency, /mi, ... 

At very low polymer volume fractions, the entry follows Smoluchowski kinetics Sm = 1), whereas for polymer volume fractions greater than 0.1% Smis increased (Figure 25.4). The BD simulations reveal an almost linear dependence of the radical capture rate coefficient on the polymer volume fraction in the dispersion, cf. Equation 25.26 ... 

The entry model of Maxwells et al. was derived from and/or supported by data on the influence of particle surface characteristics (charge, size) on the entry rate coefficient [312]. It was assumed that the aqueous radicals became surface active when the degree of polymerization reached 2-3. This was based on thermodynamic considerations of the entering species. 

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

In this set of equations, n is the number of reaction loci per arbitrary volume of reaction system which contain i propagating radicals, cr is the average rate of entry of radicals into a single reaction locus, xr is the volume of the reaction locus, A. is the rate coefficient for the mutual termination of radicals, and k is a composite constant which quantifies the rate at which radicals are lost from reaction loci by first-order processes. For convenience we put kju s x ... 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

On the other hand, Nomura and Harada [14] proposed a kinetic model for the emulsion polymerization of styrene (St), where they used Eq. 7 to predict the rate of radical entry into both polymer particles and monomer-swollen micelles. In their kinetic model, the ratio of the mass-transfer coefficient for radical entry into a polymer particle kep to that into a micelle kem> K lk,... 

On the other hand, Casey and Morrison et al. [52,96] derived the desorption rate coefficient for several limiting cases in combination with their radical entry model, which assumes that the aqueous phase propagation is the ratecontrolling step for entry of initiator-derived free radicals. Kim et al. [53] also discussed the desorption and re-entry processes after Asua et al. [49] and Maxwell et al. [ 11 ] and proposed some modifications. Fang et al. [54] discussed the behavior of free-radical transfer between the aqueous and particle phases (entry and desorption) in the seeded emulsion polymerization of St using KPS as initiator. 

The usual population balance methods are used to derive this equation thus entry into an particle creates an N - particle, and so on note in particular that transfer occurs with a rate coefficient of since / is that for transfer of a single free radical, and we here have two distinguishing free radicals. 

An important further contribution to the analysis of steady-state reacticm systems has been made by Ugclstad et d. (1967), They have shown how account can be taken of the likely possihillty that radicals that exit from the reaction loci contribute to the stationary concentration of free radicals in the external phase which is available for entry into a reaction loci. For this purpose, it is necessary to distinguish blmolecular mutual termination between radicals that occurs in the reaction loci (i.e., within polymer/ monomer particles) from that which occurs in the external phase. The rate at which the former reaction occurs is characterized by the rate coefficient the rate of the latter reaction by. The total rate of entry of radicals into all loci within unit volume of reaction system is then expressed as the sum of three contributions. The first derives from the rate of formation of new "acquirable radicals within the external phase the second derives from the rate at which acquirable radicals become present in the external phase by the process of exit from the loci the third (which is negative) allows for the fact that radicals can be lost from the external phase by bimolecular mutual termination within the external phase. The resultant equation is... 

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