Local monomer

The apparent terminal model reactivity ratios are then r => aK and c =rR, K It follows that rABVBf = rABrBA - const. The bootstrap effect does not require the terminal model and other models (penultimate, complex participation) in combination with the bootstrap effect have been explored.103,1 4215 Variants on the theory have also appeared where the local monomer concentration is a function of the monomer feed composition.11[Pg.431]

In the present work the Cl procedure ( ) employed includes single, double, and higher excited configurations, and can treat in a natural way, using the localized monomer basis orbitals, intra- as well as inter-molecular excitations. States which arise from such monomer-based excitations can then be interpreted in terms of their locally-excited, excitonic, CT, or "mixed" character. Details as to the nature of the dimer states have been discussed in our earlier works (7, 8). 

Despite the complex interaction between the components of a catalyst recipe, for example consisting of catalyst, co-catalyst, electron donors (internal and external), monomers, chain-transfer agents such as hydrogen, and inert gases and the catalyst support, the local polymer production rate rate (polymerization rate) in a given volume, Rp (kg polymer hr"1), can often be described by a first-order kinetic equation with respect to the local monomer concentration near the active site, cm (kgm"3), and is first order to the mass of active sites ( catalyst ) in that volume, m (kg) ... 

The present model is based on several assumptions (i) the possible configurations of the grafted chain are described by a random walk (ii) their free energy densities are expressed as functions of the local monomer volume fraction alone (iii) the configurations of minimum energy dominate the partition function of the system (iv) only the configurations with monomers distributed between the surface and the position of the last monomer of the chain, assumed to be the farthest one, are taken into account. The latter assumption basically implies that the probability that the most distant monomer from the surface reaches the distance z is equal to the probability that the last monomer of the chain reaches this distance this approximation clearly fails when z is in the vicinity of the surface. However, in swollen brushes the behavior of the monomers in the vicinity of the surface is less important than the behavior of the distant monomers, which are primarily responsible for the brush thickness and for the interactions between brushes. 

We present here the results of such a systematic investigation on the dependence of the self-diffusion coefficient of flexible polymer chains as a function of P and N, conducted on polydimethylsiloxane (PDMS). This model polymer is well above its glass temperature at room temperature (Ta = - 120°C), so that one can expect that spurious effects associated with the variation of the free volume and of the local monomer-monomer friction coefficient with the molecular weights of the chains are minimised. 

An important question is to decide how far one can believe that a self-diffusion coefficient varying like N is characteristic of reptation. It has been argued that additional molecular weight dependences could exist and compensate for departures from the N 2 law [48 to 52]. Such an effect can come from the local monomer-monomer friction coefficient w hich appears as a prefactor in equation 8, hidden in the diffusion coefficient D. Several processes can combine and lead to a local friction which is molecular weight dependent, and W hich decreases when the polymer molecular weight is decreased. This is, for example, the... 

This shows the way that the local monomer concenfration, c, varies from the centre of the chain (x = 0) to either end. The excluded-volume forces on the chain create a potential energy y/ sensed by each repeat unit, which depends on and on a volume parameter Vg that controls their magnitude ... 

Figure 1.3. Comparison of the change in local monomer concentration with distance from the chain centre for a random chain in solution and in the melt. Adapted from Strobl (1996).

The influence of the lyotropic morphology on polymerization rates was studied for a variety of monomers with different polarity and amphiphiUcity [54] in lyotropic phases of dodecyltrimethylammonium bromide in water. The confined geometry of the resulting aggregates has a strong impact on the local monomer concentration and diffusion properties and therefore also on the polymerization kinetics. 

To describe the coil-globule transition in the vicinity of the Flory temperature, in 1968 Lifshitz8 proposed an original method which amounts to expressing the free energy of a polymer in terms of the local monomer concentration. This method was subsequently reexamined and developed in various articles.2 We shall describe it here but, for reasons of convenience, we shall use a slightly different formalism. 

In order to calculate the entropy S C of a real chain in terms of the local monomer concentration C(r), we set the corresponding Brownian chain in an external potential V(r), the result being that the mean link concentration at point r is C(r). In this case, the entropy of the chain is a function of the potential but, on the other hand, there is a relation between P (r) and C(r) and consequently the entropy can be re-expressed in terms of C(r). First, let us study the statistical state of the chain. The weight associated with a Brownian chain of area S is given by (see Chapter 2)... 

Note that the (diffusion of micelles does not influence the dynamic surface elasticity. This fact can be easily explained if we take into account that any increase of the total micellar concentration is accompanied by a decrease of the relative changes of Cm. Hence, changes of the local monomer concentration are partly compensated at the expense of micelles, when the adsorption and desorption processes are determined by diffusion of monomers normal to the interface. However, the corresponding local relative changes of the micellar concentrations are negligible when Cm is sufficiently large. 

It is possible that equilibrium morphology is not obtained because the movement of the polymer chains is not fast enough to reach that equilibrium within the time-frame of the reaction this is kinetic control of morphology. The kinetic parameters influence the rate of formation of a certain morphology [27, 28], which is basically determined by the interfacial tensions [29]. The parameters of importance are the rate of formation of the polymer (parameters are propagation rate coefficient, and the local monomer and radical concentrations) and the rate of diffusion of the polymer chains (parameters are viscosity in the locus of polymerization, molar mass and topology of the polymer chain). Both the rate of formation and the rate of diffusion of a polymer chain are, for example, affected by the mode of addition of the monomer and initiator. An increased rate of addition of the monomer will lead to a lower instantaneous conversion and thus a lower viscosity in the particle, which in turn increases the rates of diffusion and leads to different morphologies. 

Alternatively, implementing (40) and (41) leads to a quite different picture for the star structure. Here, the elastic tension in the arms is determined by the local monomer-monomer repulsion only at the edge of the corona, r = I . At r < 7 the arms are stretched more strongly, due to an excess pulling force exerted by the terminal parts of the arms. Therefore, the polymer density profile Cp r,N,R) and the chemical potential A(A,7 ) depend explicitly on N (or the star size R) [123]. 

Solis, F.J., Weiss-Malik, R. Vernon, B. 2005, Local monomer activation model for phase behavior and calorimetric properties of LCST gel-forming polymers . Macromolecules, vol. 38, no. 10, pp. 4456-4464. 

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