Stretched chains

Tlim is the limiting value for a fully stretched chain and should correspond to the Rouse relaxation time when there is no deformation, t must equal the Zimrn... 

A discontinuous coil to stretch transition is evident at sc = 0.000725. The transition point sc was found by using two different initial conformations as described above. For values lower than ec> the random chain will eventually coil, form a folded chain crystalline structure and stay in that conformation until the end of the run for relatively long run times. On the other hand, a prestretched chain would fluctuate and eventually form a crystallized folded chain that is stable. Similarly, for flow rates higher than sCy a pre-stretched chain will never coil and a random chain will eventually stretch. 

Some of the chains, when in contact with the shish, will stretch almost completely. However, these highly stretched chains are not dominant compared to the highly folded bundles that form crystalline kebabs around the shish. Also, none of the highly stretched chains formed a structure with part of it stretched and attached to the shish and part of it in folded crystalline lamella. The formation of kebabs in these simulations is clearly growth of lamellae, nucleated on the shish. 

At x > xcr, the network is in the very expanded state. The size of the chain between two junction points, R, is proportional to m R = aR0 ma/a /2 as it is for fully stretched chain. The reason for such an essential expansion is the osmotic pressure of counter ions which originates from their translational entropy. Trom the entropy consideration counter ions would like to leave the network, however, this is forbidden due to the condition of total electroneutrality. This effect was for the first time described in Ref. [7]. 

As LjP = A is the projection of the monomer unit on the axis of the stretched chain, the final relation reads ... 

A simple scaling model of block copolymer micelles was derived by de Gennes (1978). He obtained scaling relations assuming uniformly stretched chains for the core radius, RB, of micelles with association number p.This model can be viewed as a development of the Alexander de Gennes theory (Alexander 1977 de Gennes 1976,1980) for polymer brushes at a planar interface, where the density profile normal to the interface is a step function. In the limit of short coronal (A) chains (crew-cut micelles) de Gennes (1978) predicted... 

In Fig. 23, d is plotted against MB, the molecular weight of dimethylsiloxane blocks, for various dispersions. As can be seen, above MB = 10 x 103 d falls between the two limiting lines corresponding to the fully stretched chain model and the random coil model, while below MB = 10 x 103, 6 is closer to the former model than to the latter. 

By varying the distance between nearest adsorption sites, rs, one can control the composition variation period of the synthesized copolymer. From the chemical correlators defined by Eq. 16, it is easy to find the average number of segments in the repeating chain sections, N, for different rs values. It is instructive to analyze the relation between N and rs. As expected, a power law N oc is observed. It is clear that exponent //. in this dependence should be between //, = 1 (for a completely stretched chain) and //. = v 1 with v 0.6 (for a random coil with excluded volume [75]). The calculation [95] yields yu 1.33 for N > 15. This supports the aforementioned assumption that the repeating chain sections are strongly stretched between the adsorption sites. The same conclusion can be drawn from the visual analysis of typical snapshots similar to that presented in Fig. 22. 

This model, however, is only valid for chain molecules at zero Kelvin. When 7V 0 the chain parts possess thermal energy vibration causes them to move in random directions, which always results in a contraction of the stretched chain. The chain tends to a state of higher probability, and eventually reaches a fully unoriented random conformation, as described in 2.4 ( random walk conformation ). To... 

Fig. 10. Conformational map of glycyl-L-alanine. The locations of the right- and left-handed a-helices are denoted by an, and ccl, respectively. The fully-stretched chain is located at the origin. The full and dashed lines represent the boundaries of sterioally allowed regions for this dipeptide, as calculated by Ramachandran et al. (1963a) with two different sets of assumptions about van der Waals contact distances.

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