Polymer notations Particle

Table 3.4 presents the catalytic properties of PAHAPS colloids containing Pd nanoparticles in selective hydrogenations of DHL and DMEC. Polymer notations in Table 3.4 are consistent with those presented in Ref.[86]. One can see that the higher activity was observed for the PAHAPS catalysts where nanoparticles were formed by N2H4-%H20 reduction revealing that the particles formed at the edges... 

The microscopic mass balance of polymer functional groups and volatile components given in Eqs. (27) has to be modified in order to take into account the variable reaction volume due to polymer crystallization. Here we do not follow the notation in Ref. 74 rather, we use concentrations and rates of reaction per unit volume of amorphous phase instead of concentrations per unit volume of particle [A ]p = [A ]/(l — and so on, in order to use the same kinetic rate laws [Eqs. (49)] as in the melt. 

We start with a microscopic polymer model, whose state is specifiedby a point in 6N-dimensional phase space, z e f with z = (ri,.... r pj,.... p ), a short notation for the positions and momenta of all N particles. The model is described by the microscopic Hamiltonian H(z) with inter- and intramolecular interactions. The coarse-grained model eliminates some of the (huge number of) microscopic degrees of freedom. The level of detail that is retained is specified by the choice of coarsegrained variables x = (xi,..., ) with... 

The notation is that of Butler, Gordon and Malcolm. The reader unfamiliar with the power of the cascade approach to polymer statistics will gain a better insight into its fundamentals from a recent paper (cf. also v/hich generalises the earlier formulae to embrace, e.g., the particle scattering functions through the notion of a trail-weighting function, which is of wide utility. ... 

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