Velocity chains

Since the tube friction factor measures the force needed to impart a unit velocity to the chain along the tube direction, we can think of applying this force, one segment at a time, to the diffusing chain. Since the friction factor per segment is f, Eq. (2.65) becomes... 

Aside from the side chains, the movement of the backbone along the main reptation tube is still given by Eq. (2.67). With the side chains taken into account, the diffusion velocity must be decreased by multiplying by the probability of the side-chain relocation. Since the diffusion velocity is inversely proportional to r, Eq. (2.67) must be divided by Eq. (2.69) to give the relaxation time for a chain of degree of polymerization n carrying side chains of degree of polymerization n ... 

This reaction terminates growth of a chain but there is no net loss in the radical concentration and it does not therefore affect the velocity of the reaction.)... 

The above-mentioned models differ in the relation that is derived between the rate of pull-out of the individual chain and the crack velocity. These models also differ in their interpretation of the threshold stress and the threshold toughness (Go). Also, V is expected to be dependent on the configuration of the connector chain at the interface. The value of v when connector chain crosses the interface just once is higher than the value when the chain forms multiple stitches, even though Go is not altered. When the chain forms multiple stitches, the block and tackle effect ensures that the viscous processes dominate even at lower velocities, and V is reduced by a factor of N from the value obtained from the single crossing case. These models are discussed by Brown and coworkers [45,46]. 

The term aK2v", derived from reptation theory, describes the velocity-dependent energy necessary to fracture the bulk adhesive. K2 is the consistency which relates the viscosity to the shear rate for a non-newtonian fluid. a = TtraL fh", with r being the chain radius, L the chain length, a the density of chains crossing over the fracture plane, and h is the distance between the chain and reptation tube. 

In order to examine the permeability of the porous medium, it is useful to study the average velocity of the chain... 

For intermediate drift rates (4 < BN < 8), when chain conformations are already distorted, deviates from linear behavior and goes through a maximum at some critical value Bf. of the field, confirming earlier findings by Pandey et al. [103,104]. This critical bias B at which the velocity starts to decrease depends rather weakly on the density Cobs, turns out to be reciprocal to chain length A, implying that only when the total force, /c = B,N 9, acting upon the whole driven molecule, exceeds a certain threshold, which does not depend on the size of the macromolecule, the chains start to get stuck in the medium. 

One could assume that this characteristic behavior of the mobility of the polymers is also reflected by the typical relaxation times r of the driven chains. Indeed, in Fig. 28 we show the relaxation time T2, determined from the condition g2( Z2) = - g/3 in dependence on the field B evidently, while for B < B t2 is nearly constant (or rises very slowly), for B > Be it grows dramatically. This result, as well as the characteristic variation of with B (cf. Figs. 27(a-c)), may be explained, at least phenomenologically, if the motion of a polymer chain through the host matrix is considered as consisting of (i) nearly free drift from one obstacle to another, and (ii) a period of trapping, r, of the molecule at the next obstacle. If the mean distance between obstacles is denoted by ( and the time needed by the chain to travel this distance is /, then - (/ t + /), whereby from Eq. (57) / = /Vq — k T/ DqBN). This gives a somewhat better approximation for the drift velocity... 

Of samples swollen with ethylene diamine, the graft yield at a 50 1 liquor ratio increases as the concentration of ethylene diamine increases. This is due to the increase of decrystallization of swollen samples, which helps the penetration velocity of the chemicals through the cellulosic chains. Graftability of the samples treated with 100% ethylene diamine is lower that of the sample treated with 75%. This is due to the dissolution of low DP chains and some of the hemicelluloses, which is detectable by the increase in DP of the sample teated with 100% ethylene diamine. 

The maximum at 223 nm is remarkably high, though the chain is relatively short. Also remarkable is the higher folding velocity in comparison to the use of single-chain collagen-peptide models as shown in Fig. 22. The folding is also completely reversible. 

Usually, the transition of polymer systems into the oriented state occurs as a result of deformation e.g. upon exposure to external stress. When the polymers undergo deformation both the macromolecule as a whole and its parts (segments) can undergo orientation. The rates of these orientation processes are very different and, hence, the orienting forces affect first of all the orientation of chain segments and subsequently that of a chain molecule as a whole. However, by varying the extension velocity and the temperature, only the overall orientation process may predominate, thus extension of all chains occurs in a single act. 

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