Polymer chain, displacement

Silica particles do not induce any modification of the stress state in the material, and so no extended plasticity in the matrix. Naiiosized silica particles can be considered as a modifier of polymer chain displacement, and not as a reinforcement filler. There is adsorption of PP on silica surface and consequent reduction of molecular mobility with a large increase of elastic modulus. We do not observe any process zone, and mechanisms as particle/matrix decohesion as well as crack pinning or blunting are not effective. 

Many simulations attempt to determine what motion of the polymer is possible. This can be done by modeling displacements of sections of the chain, Monte Carlo simulations, or reptation (a snakelike motion of the polymer chain as it threads past other chains). These motion studies ultimately attempt to determine a correlation between the molecular motion possible and the macroscopic flexibility, hardness, and so on. 

Figure 2.8 Model for the displacement of a polymer chain in relation to a hole H.

Without implying anything about the shape of the tube, it is clear that it has the same length as the polymer chain itself, that is, nlo. This is the displacement of interest in calculating the escape time from the tube. Therefore Eq. (2.63) becomes... 

Displacement of a volatile with a nonvolatile alcohol is an important reaction for curing paint films with amino cross-linkers and amino resias on textile fabrics or paper. FoUowiag is an example of a methoxymethyl group on an amino resia reacting with a hydroxyl group of a polymer chain. 

These models are designed to reproduce the random movement of flexible polymer chains in a solvent or melt in a more or less realistic way. Simulational results which reproduce in simple cases the so-called Rouse [49] or Zimm [50] dynamics, depending on whether hydrodynamic interactions in the system are neglected or not, appear appropriate for studying diffusion, relaxation, and transport properties in general. In all dynamic models the monomers perform small displacements per unit time while the connectivity of the chains is preserved during the simulation. 

Again, the OLMC bead-spring model (Sec. IIB 2) is used, with a host matrix of an equilibrated dense solution of polymer chains quenched at different concentrations Cots. Eq. (7) for the probability IF of a random monomer displacement in direction Ax, Ay, Az is given by... 

Homopolymerization of the olefin occurred if its basicity was higher than that of 2-furaldehyde, i.e. the initiator displacement from the complex was strong and thereafter only occasional inclusion of aldehyde in the growing polymer chain took place 2-furaldehyde units in the products were less than 5%. This situation was observed with acenaphthylene and N-vinylcarbazole. 

Fig. 78.—Radial distribution function W r) of the chain displacement vectors for the same polymer chains as in Fig. 77. W(r) is expressed in A"h...

Kuhn has shown how a real polymer chain may be approximated by an equivalent freely jointed chain. Instead of taking the individual bonds as statistical elements, one may for this purpose choose sequences of m bonds each. In Fig. 79, arbitrarily chosen statistical elements consisting of five bonds are indicated, the displacement vectors for these elements being shown by the dashed lines. The direction assumed by a statistical element will be nearly independent of the direction of the preceding element, provided the number m of bonds per... 

Parameter characterizing the Gaussian distribution of the end-to-end (displacement) length of a polymer chain (Chap. X et seq.). 

The difference in activity between metal carbon bonds in (VIII) and (XXXI) could also explain why only one benzyl group per metal atom is used. On kinetic grounds alone, quite apart from other objections to two polymer chains growing from one metal atom, the probability of a second benzyl group being displaced can only be comparable to the probability of chain termination. 

Fig. 21 Mean-square displacement vs. evolution time for 16-mers with an occupation density of 0.9375 in a 32-sized cubic lattice. The triangles are for four middle chain units, the circles are for the mass center, and the crosses are for the chain units relative to the center of mass. The lines with slopes of 1.0 and 0.5 indicate the scaling expected according to the Rouse model of polymer chains [56]... 

For an estimate of the ultimate shear strength, r0, of a single domain based on the lattice parameters we use a simple shear plane system proposed by Frenkel [19]. As shown in Fig. 19 it consists of a linear array of periodic force centres resembling the polymer chain. According to this model the relation between the relative displacement x along the shear direction and the shear stress is given by... 

Returning to ion-pair zirconocene catalysts, the initiation of the polymerisation process requires the displacement of the anion so that the alkene can be coordinated. The mobility of the anion is therefore an important factor and has become the focus of a number of detailed investigations. The original mechanistic scheme of alkene insertion and polymer chain growth (Scheme 8.4) implied dissociation of the anion and formation of a 14-electron cationic intermediate, which then reacted... 

In the crystal structure of the polymer phase (Fig. 17a), the polymer chains are aligned along the c-axis and the distance (3.71 A) between the centres of adjacent cyclobutane and pyrazine rings corresponds to half the c-axis repeat of the unit cell. For comparison between the monomer and polymer structures, an overlay plot of these structures is shown in Fig. 17b. It is clear that the solid-state reaction is associated with only very small atomic displacements at the site of the [2-1-2] photocyclization reaction (the displacement of the carbon atoms of the C=C double bonds of monomer molecules on forming the cyclobutane ring of the polymer is only ca. 0.8 A for one pair of carbon atoms and ca. 1.6 A for the other pair). Such small displacements are completely in accord with the assignment of this solid-state reaction as a topochemical transformation [124—127] (in which the crystal structure of the reactant monomer phase imposes geometric control on the pathway of the... 

During the last several years, a significant effort has been devoted to incorporating heterocyclic units into the backbone of PAE. When heterocyclic units are placed within the arylene ether polymer chain, certain properties such as strength, modulus and glass transition temperature (Tg) generally increase. Aromatic nucleophilic displacement and electrophilic reactions have been used to synthesize poly(arylene ether)s containing heterocyclic units (PAEH). 

The simulation of polymer chains attached at one end to an inert interface ("tails") Is described, using a combination of Monte-Carlo techniques and the RIS scheme. Four types of chains that exhibit different structural and geometrical characteristics are examined PE, POM, POE, and PDMS. The overall effects on the conformation of the attached chains arising from the presence of the interface are qualitatively similar. The chains are significantly extended, as measured by the mean square displacement, in the direction normal to the interface, but essentially unaffected parallel to the interface. A comparison Is made of intramolecular excluded volume with excluded volume arising from an impenetrable interface. It is shown that the two types of excluded volume exhibit qualitatively different effects on the conformation. 

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