Effective Kuhn segment length

It does not affect the exponents in the equation (i.e.. the dependence of on N), however, but simply introduces a prefactor. This suggests a different approach, where we consider the number of adjacent bonds whose combinations of allowed rotations essentially behave like a freely jointed unit when taken collectively. We would then have Nx effective segments each of length lp known as the Kuhn segment length (Figure 8-36), defined in Equation 8-12 ... 

Figure 11.18. Effects of crosslinking on the brittle fracture stress of styrene-divinylbenzene copolymers. Note the catastrophic embrittlement at very high crosslink densities (i.e., at an average number of repeat units between crosslinks less than the Kuhn segment length of 8 repeat units). The data point (not shown) for the uncrosslinked limit (polystyrene) is at (°°,41).

For quantitative description of the segmental dynamics of the components in the miscible blends, both concentration fluctuation and self-concentration effects should be consistently incorporated in the model. This approach has already been examined by Kumar et al. (1996), Kamath et al. (1999), and Colby and Lipson (2005). In particular, the model by Colby and Lipson adopted the value ( 1 nm) comparable to the Kuhn segment length to reasonably describe the segmental relaxation time and mode distribution for both PI and PVE components in PI/PVE blends. 

Figures 6 and 7 show the results of numerical inversion for the case where there are no traps, i.e. T Figure 6 illustrates the effect of statistical chain stiffness. As the Kuhn segment length a increases relative to R the chain becomes stiffer and more expanded, causing to decrease and the decay of the initial...

Intermolecular interactions determining the force /(r) with which a segment from a chain acts on a segment from another one are approximated by a hard sphere interaction with a certain diameter d comparable with the Kuhn segment length h. The entanglement effects or the topological interactions are the consequence of chain connectivity and excluded-volume intermolecular interactions. 

The theoretical background of the confinement effect in (artificial) tubes was recently examined in detail with the aid of an analytical theory as well as with Monte Carlo simulations [70]. The analytical treatment referred to a polymer chain confined to a harmonic radial tube potential. The computer simulation mimicked the dynamics of a modified Stockmayer chain in a tube with hard pore walls. In both treatments, the characteristic laws of the tube/reptation model were reproduced. Moreover, the crossover from reptation (tube diameter equal to a few Kuhn segment lengths) to Rouse dy-... 

Here is the effective, or Kuhn, length, N is the number of Kuhn segments in the chain, and Q is a constant factor, which does not depend on R. The value of Q depends on what exactly we mean by Pat(R). It can be two things, either the total number of conformations with the given R (in some... 

In our computer studies of the conformational behavior of the shell-forming chains, we used MC simulations [91, 95] on a simple cubic lattice and studied the shell behavior of a single micelle only. Because we modeled the behavior of shells of kinetically frozen micelles, we simulated a spherical polymer brush tethered to the surface of a hydrophobic spherical core. The association number was taken from the experiment. The size of the core, lattice constant (i.e., the size of the lattice Kuhn segment ) and the effective chain length were recalculated from experimental values on the basis of the coarse graining parameterization [95]. 

Fig. 47. Spin-lattice relaxation dispersion for a chain of 1 =1,600 Kuhn segments (of length b) confined to a randomly coiled tube with a harmonic radial potential with varying effective diameters d. The data were calculated with the aid of the harmonic radial potential theory [70]. c is a constant. At low frequencies the curves visualize the crossover from Rouse dynamics depending on the effective tube diameter. The latter case is described by a Tj dispersion proportional to characteristic for limit (II)de of the tube/ reptation model...

Taking into account (2.17) we can find the required correlation length Lkor, which shows the distance from the chosen Kuhn segment where the orientational effects stop ... 

---