Chain length, distribution, simulation

From several number chain length distributions simulated for pulsed laser polymerization for a great variety of experimental parametersl l which were converted to chromatographic dimensions and subsequently submitted to the infiuence of BB by applying the Tung equationl l correction functions were deduced. The comparison of the input values for the point of infiection and the maximum lead to the following correction functions ... 

Finally, the poljmier is processed in an extruder, where polymer properties (such as the chain length distribution) are adjusted by means of a sequence of different functional zones of the extruder. Further modifications of the polymer properties can be achieved by adding additives to the polymer melt. The extrusion step can be simulated by a special purpose tool called MOREX [146, 394]. Given geometry data of the extruder, it calculates the required energy demand and the properties of the resulting polymer. In addition, it can be used to calculate the vapor stream of -caprolactam which can be stripped of if a considerable amount of e-caprolactam is present in the polymer melt. 

In a subsequent study, the reinforcing particles were randomly distributed within the PDMS matrix. One effect of the filler was to increase the end-to-end separation of the chains. These results on the chain-length distributions are in agreement with some subsequent neutron scattering experiments on silicate-filled PDMS. The polymers contained silica particles that were surface treated to make them inert to the polymer chains, as was implicitly assumed in the simulations. These experimental results also indicated chain extension when the particles were relatively small, and chain compression when they were relatively large. 

Butte, A., Storti, G., MorbideUi, M., 2002. Evaluation of the chain length distribution in free-radical polymerization, 1. Bulk polymerization. Macromol. Theory Simul. 11, 22-36. 

This interesting phenomenon is further illustrated in Figure 8 for the simulated fractionation of a model polymer into five fractions. The dotted lines indicate the chain-length distributions of the polymer in the polymer-lean phase. 

Fig. 8. Simulated chain-length distributions for precipitation fractionation of a model polsmier sample that follows Flory-Schultz s distribution with = 1000. The following parameters were used to simulate the fractionation J = 1 x 10 and a =3 x 10 , 4.5 X 10 , 6.75 X 10 , 1.01 x 10 and 1.52 x 10 .

The first set of simulations has been performed using a constant value of kt. In this specific case all radicals thus exhibit the exact same probability for termination irrespective of their chain length. Broadening processes that lead to a certain dispersity in the radical chain-length distribution can by definition not influence the kinetics of such a system. These simulations are therefore not meant to test equation 3.8 but rather to show the ease and... 

Fig. 3.20 Simulation of polymerisation within a dropiet at a diffusion coefficient Z = 10 " m /s radial profiles of number and mass average of the polymer s chain length distribution upper plot kinetics according to the basic equations in Table 3.1, whereas below the modified schcane for propagation and termination has been applied in the lower row the literature model of mrunent...

In calculations the moments can be treated as concentrations. Kinetic simulation of radical polymerization to evaluate dispcrsitics typically involves evaluation of the moments rather than the complete distribution. This method of moments is accurate as long as the kinetics are independent of chain length. 

The 327-670 GHz EPR spectra of canthaxanthin radical cation were resolved into two principal components of the g-tensor (Konovalova et al. 1999). Spectral simulations indicated this to be the result of g-anisotropy where gn=2.0032 and gi=2.0023. This type of g-tensor is consistent with the theory for polyacene rc-radical cations (Stone 1964), which states that the difference gxx gyy decreases with increasing chain length. When gxx-gyy approaches zero, the g-tensor becomes cylindrically symmetrical with gxx=gyy=g and gzz=gn. The cylindrical symmetry for the all-trans carotenoids is not surprising because these molecules are long straight chain polyenes. This also demonstrates that the symmetrical unresolved EPR line at 9 GHz is due to a carotenoid Jt-radical cation with electron density distributed throughout the whole chain of double bonds as predicted by RHF-INDO/SP molecular orbital calculations. The lack of temperature... 

Single hydrophobic-amphiphilic (HA) copolymers with the same HA composition but with different distribution of H and A units along the main hydrophobic chain were also simulated [212]. In particular, regular copolymers comprising H and A units in alternating sequence, regular multiblock copolymers composed of H and A blocks of equal lengths, and the quasirandom protein-like copolymers with a quenched primary structure were studied. These copolymers are schematically depicted in Fig. 24b,c, and d. 

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