Monomer activities, concentration

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

McGarrity and Ogle examined the aggregation of BuLi in THF by using H and Li NMR spectroscopy and determined that BuLi exists as a tetramer in equilibrium with a dimer in THF. Activation and equilibrinm parameters were measured for the tetramer-dimer equilibrium (equation 2). No evidence was obtained for a monomer at concentrations of BuLi down to 0.1 mM. ... 

Figures 3-21 and 3-22 show results in the ATRP polymerization of styrene using 1-phenylethyl bromide as the initiator, CuBr as catalyst (activator), and 4,4-di-5-nonyl-2,2 -bipyridine as ligand [Matyjaszewski et al., 1997]. Figure 3-21 shows the decrease in monomer concentration to be first-order in monomer, as required by Eq. 3-223. The linearity over time indicates that the concentration of propagating radicals is constant throughout the polymerization. The first-order dependencies of Rp on monomer, activator, and initiator and the inverse first-order dependence on deactivator have been verified in many ATRP reactions [Davis et al., 1999 Patten and Matyjaszewski, 1998 Wang et al., 1997].

For copolymerizations proceeding by the activated monomer mechanism (e.g., cyclic ethers, lactams, /V-carboxy-a-amino acid anhydrides), the actual monomers are the activated monomers. The concentrations of the two activated monomers (e.g., the lactam anions in anionic lactam copolymerization) may be different from the comonomer feed. Calculations of monomer reactivity ratios using the feed composition will then be incorrect. 

Perhaps the answer lies in the introduction o-f another process in the system which relies only on monomer activities in a known -fashion. The sur-face tension method already mentioned (4> relies on the -fact that surface tension is determined solely by monomer concentrations. However, the plateau surface tension is not terribly sensitive to monomer composition in many cases of interest. An aggregate formation process which can be much more sensitive is adsorption of surfactants on hydrophilic (13-15) or hydrophobic (see Chapter 17) surfaces. 

One possibility is that the concentration of monomers in the endoplasm is too low to produce dimers and that the monomers are concentrated in the periplasmic space by active transport. Evidence against active transport was obtained in episomal transfer of the structural gene from E. coli to S. typhimurium (26). Even though S. typhimurium does not synthesize alkaline phosphatase, the enzyme was produced by the heterogenote and appeared in the periplasmic space. Schlesinger and Olsen (26) argued that it is unlikely that S. typhimurium would have a transport system for alkaline phosphatase monomers because it does not normally make the enzyme. 

The Mass Action Model The mass action model represents a very different approach to the interpretation of the thermodynamic properties of a surfactant solution than does the pseudo-phase model presented in the previous section. A chemical equilibrium is assumed to exist between the monomer and the micelle. For this reaction an equilibrium constant can be written to relate the activity (concentrations) of monomer and micelle present. The most comprehensive treatment of this process is due to Burchfield and Woolley.22 We will now describe the procedure followed, although we will not attempt to fill in all the steps of the derivation. The aggregation of an anionic surfactant MA is approximated by a simple equilibrium in which the monomeric anion and cation combine to form one aggregate species (micelle) having an aggregation number n, with a fraction of bound counterions, f3. The reaction isdd... 

If one considers solely the consecutive equilibria, the concentration of monomer can only increase with increasing total amphiphile concentration even above the CMC. (Apart from the trivial decrease in the monomer concentration calculated on the total volume which may arise when the micelles occupy a substantial volume fraction). However, if one realizes that micelles are not only composed of amphiphile, the result may be different. Thus counterion binding helps to stabilize the micelles and for ionic surfactants it can be predicted that the monomer activity may decrease with increasing surfactant concentration above the CMC. Good evidence for a decreasing monomer concentration above the CMC has been provided in the kinetic investigations of Aniansson et al.104), and recently Cutler et al.46) demonstrated, from amphiphile specific electrode studies, that the activity of dodecylsulfate ions decreases quite appreciably above the CMC for sodium dodecylsulfate solutions (Fig. 2.14). 

Kinetic models referred to as adsorption models have been proposed, especially for olefin polymerisation with highly active supported Ziegler-Natta catalysts, e.g. MgCl2/ethyl benzoate/TiCU AIR3. These models include reversible processes of adsorption of the monomer (olefin coordination at the transition metal) and adsorption of the activator (complexation via briding bonds formation). There are a variety of kinetic models of this type, most of them considering the actual monomer and activator concentrations at the catalyst surface, m and a respectively, described by Langmuir-Hinshelwood isotherms. It is to be emphasised that M and a must not be the same as the respective bulk concentrations [M] and [A] in solution. Therefore, fractions of surface centres complexed by the monomer and the activator, but not bulk concentrations in solution, are assumed to represent the actual monomer and activator concentrations respectively. This means that the polymerisation rate equation based on the simple polymerisation model should take into account the... 

Change in the main monomer activity, e.g. by adding a monomer that is highly reactive to the Surfmer at the end of the polymerization process or by an intrinsic change in the comonomer activity because of concentration effects... 

Polymerization of Methyl Methacrylate and Other Vinyl Monomers Activated by Low Concentrations of S02... 

Recently, this salt (being a model of one of the possibie isomeric forms of the active centers in polyacetals) was used to initiate the polymerization of 1,3-dioxolane and 1,3-dioxepane. According to the H- and C-NMR spectra, the following species coexist in equilibrium at 70 C when 1,3-dioxolane is used (measurements were performed below monomer equilibrium concentration when polymerization was not possible ) ... 

The precise experimental conditions for the measurements of chain lifetimes of polyethylene with the TiCl4/Al(i-Bu2 )H catalyst are not explicitly stated, but there is clear evidence for a steady increase in lifetime with polymerization time. For an average lifetime of 4 min after 40 min polymerization time, the instantaneous values were 4 min after 18 min polymerization and 10 min after 40 min polymerization. As the concentration of active centres remains almost steady after a sharp initial fall, the increase cannot be accounted for wholly by changes in the monomer/active sites ratio. The explanation may lie in a reduced rate of chain transfer with increase in conversion, as has been found for propene with a-TiClj/AlEt2 Cl [121]. In accord with this view average chain lifetimes of polypropene have been calculated to increase with conversion [123]. 

The fourth factor determining polymerization rate is the monomer concentration in the particles. For some monomers the ratio of monomer to polymer in the particles is about constant during part of the polymerization. Smith (57) suggested that this results from a balance between the eflFect on the monomer activity of the dissolved polymer and the eflFect of interfacial tension of the very small particles. This equilibrium was put in a quantitative form by Morton, Kaizerman, and Altier (44), who derived the following equation by combining an expression for the interfacial free energy of the particle with the Flory-Huggins equation for the activity of the solvent (monomer) in the monomer-polymer particle. 

Considering a polymerizing emulsion system at its distribution balance, the three phases must show the same monomer activity the monomer-polymer particles, the micellar phase, and the water phase. Both monomer-polymer particles and the organic part of the micelles are lipophilic, and, therefore, compete for monomer. It does not seem plausible to assume that equal monomer activities in these two phases belong to monomer concentrations which differ by several orders of magnitude. Therefore it is likely that new particles are formed also after the disappearance of the pure monomer phase, provided there is a micellar phase, and enough monomer in the monomer-polymer particles as well. 

Mass balances of the polymerization products have been performed for the whole set of polymerization reactions, where both the initiator and activator concentrations have been varied from 0.3 to 1.5 moles over 100 moles of CL. In Table I the data related to the maximum monomer conversion and the high polymer yield are given as functions of the active species concentration (initiator and activator), which are present in equimolar amount in the polymerizing mixture. For almost all systems, monomer conversion and polymer yield are higher than 98 and 95%, respectively. In such concentration range of active species, yield fluctuations are less than 1.5% in terms of monomer conversion and less then 2.0% for the high polymer yield. 

The other extreme case (local torch regime) is realized at relatively high values of R (type B) (tank stirred reactor). Active sites deactivates having no time for diffusion into reaction volume peripheral parts that in this case are the slip zones of non-reacted monomer. As a consequence specific, complex in configuration fields of monomer, active sites concentrations and temperature are formed. Reaction doesn t reach reactor s walls and product yield due to monomer slipping is always lower than 100% [38,39]. 

Aveyard and coworkers (47, 48) have stressed the importance of monomer activity when simple surfactants are used as demulsifiers. For a commercial demulsifier the interfacial tension between oil/water seems to pass through a minimum for NaCl concentrations between zero and 1 M. According to Menon and Wasan (55), AOT has been found to have a cmc at approximately 300 ppm in a water/oil system with asphaltenes present. This means that in our destabilization tests, where the concentration of AOT is up to 100 ppm, the results correspond with the con-... 

The increase on graft yield can be also attributed that keratin forms a charge transfer complex with HEMA molecules, so it is possible increase monomer activity at higher concentrations of HEMA which leads homopolymerization. 

The first order dependence of the rate on the monom.er concentration shows, as in the case of EVE, that solvation by the monomer is not significant. The similarity of the rates in bulk and benzene imply, as with EVE, that solvation by the polymer chain is taking place. The faster rates and lower activation energies compared with EVE would suggest that the more bulky isopropyl grour makes such solvation... 

Fig. 10. Determination of the monomer activity and concentration from the surface pressure isotherms for Hept4NCl solutions in benzene at the interface with water...

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