Configuration of chains

Santos also scrutinized the polymer-like behavior of the constructed stream lines. Two characteristics were analyzed the second moment of the end-to-end distance distribution, (r2)0, which characterizes the spatial configurations of chain molecules, and the radius of gyration, Rg, that indicates how the... 

Both investigated systems are melts of polybead chains at a temperature of 473 K. Configurations of chain length ranging from 24 beads to 100 beads at a density of 0.75 g/cm3 (this corresponds to a comparable real system of polyethylene at a pressure of 1 bar) have been successfully embedded. The hard-sphere radius was 2.2 A, corresponding approximately to a van-der-Waals ra-... 

The present theoretical approach to rubberlike elasticity is novel in that it utilizes the wealth of information which RiS theory provides on the spatial configurations of chain molecules. Specifically, Monte Carlo calculations based on the RIS approximation are used to simulate spatial configurations, and thus distribution functions for end-to-end separation r of the chains. Results are presented for polyethylene and polydimethylsiloxane chains most of which are quite short, in order to elucidate non-Gaussian effects due to limited chain extensibility. 

Figure 13-2 Schematic representation of the configuration of chains in gutta-percha (trans-1,4-polyisoprene)...

Fig. 10.1. One-dimensional metal model of interacting 2/ z-electrons in polymer chain from C-C- bonds of equal length [9] (a) the configurations of chain with repeat union (a). 2/jz-electrons are indicated by black dots (b) energy band scheme for 2/ z-electrons EF Fermi energy.

Let us now analyze how the interactions between brushes occur in the present model. Our system is described by the statistical average of all possible configurations of chains that start from opposite surfaces and end up at the distances z and z2, respectively. For each possible path that is not reflected by the opposite wall, it is assumed that the monomers of the chains grafted on surfaces 1 and 2 are distributed between 0 and z and between z2 and 2d, respectively. The paths that are reflected by the opposite walls have the monomers distributed everywhere between 0 and 2d. Only the configurations that minimize the Flory—Huggins free energy are taken into account. Since a complete evaluation of all possible combinations is quite tedious, we will focus... 

Figure 7. Local volume fractions of the monomers for two configurations of chains which end up at Z and z-i, respectively (a) simple addition of the volume fractions of the brushes (b) configuration that minimizes the Flory— Huggins mixing free energy for the conditions mentioned in the text.

Another characteristic feature of polyethyleneterephthalate is almost plane configuration of chains and presence of two centres of symmetiy on each repeat unit [188], These two features cause the ability of PETP to crystallization [189], Crystallization of PETP flows with formation of spherulite structure leading to polymer turbidity. 

Starches made from stem tubers of plants have various chemical components and structures. According to the different configurations of chains in their molecules, starch can be divided into amylose (with straight chain) and amylopectin polymer (branched or gelatinized). The characteristics of these two kinds of starch are as follows (Table 5.23a). 

Restrictions imposed by a lattice moreover can lead to errors in the calculation. The lattice model assumes that segments of the polymer chain occupy successive cells in the lattice. This may not allow for configurations of chains where cells adjacent to filled cells may be occupied by portions of molecules such as side groups [10]. 

Here, >j(i)jt(2)( ) is the contribution from the configuration of chains 1 and 2 shown in Figure 6-3b, in which beads i (l) and k (2) are in direct contact, and that from the configuration shown in Figure 6-3c, in which chain 3 is in contact with chain 2 directly at one point. Fourier transformation of eq 2.47 followed by summation over all beads of chains 1 and 2 yields... 

We have shown that this classification is sufficiently simple and general to include most important polymer solid mesophases identified so far. We are aware, however, that our classification of mesomorphic polymers, as well as alternative ones based on the different kinds of disorder which may occur in crystalline polymers, may not be exhaustive, since in many cases different kinds of disorder are interrelated and simultaneously present. For instance, in the case of polyacrylonitrUe, the irregular configuration of chains deter-... 

Transition from local chain parameters to system properties is realized in self-consistent field approach. This is evidenced in classical works such as the Flory - Huggins model [ 1 ] implicitly and later explicitly in a number of papers of de Gennes and co workers [16]. Considering possible configurations of chains in a... 

Equation (7) is the reason why the sampling of SAWs is so difficult. Note that all configurations of chains with N steps on the lattice that obey the excluded volume condition should have equal a priori probability to occur in the generated sample. A straightforward way to realize this is simple random sampling One carries out a construction of a RW, as in Fig. la,... 

That the stress originates within the chains comprising the network is well established by the evidence cited. The conclusion receives indirect, but equally compelling, support from the investigations on the configurations of chains in the bulk polymer,as pointed out above. 

---