Contour length of polymer

Contour length of polymer chain (cm) in Chapter 4 Onsager coefficient... 

Eventually, one should also note that even in the case of dead polymers one has also observed a variation of the gyration radius (i g) with D, which goes through a minimum as D —> 0 [48] although the contour length of the chains L does not change. Thus computer simulations, being capable of... 

Since the contour length of a fully extended C — C chain is lmax = Nlp, a polymer molecule can be stretched in the extreme by a factor of lmax/R or N1/2 from its equilibrium value. 

At this point a third intermediate approach deserves mentioning. It is due to Allegra [43] who proposed that polymer crystallization is controlled by a metastable equilibrium distribution of intramolecular clusters, the so-called bundles , forming in the liquid phase. These subsequently aggregate to the side surfaces of the crystals, driven by van der Waals interactions. The lamellar thickness is determined by the average contour length of the loops within the bundles. Although the model can... 

Of course, the network strands cannot be stretched completely. Stretching ratios of 1.4 for PC [31, 90] and of 1.3 for epoxy polymers [37] have been reported. The chain contour length of the strands is an appropriate measure for a simple estimation of the number of strands that are stretched across the deformation zone. The chain contour length of the strands is assumed to be proportional to... 

Root-mean-square end-to-end distance, which effectively takes account of the average distance between the first and the last segment in the macromolecule, and is always less that the so-called contour length of the polymer. This latter is the actual distance from the beginning to the end of the macromolecule travelling along the covalent bonds of the molecule s backbone. Radius of gyration, which is the root-mean-square distance of the ele-... 

The small ratio of lamellar thickness to the contour length of a polymer molecule clearly implies that chains must fold back and forth into stems with chain direction essentially perpendicular to the lamellar surface, as originally declared by Storks. The large surfaces of the lamellae containing the chain folds are called fold surfaces, and the thin surfaces are called lateral surfaces. 

Here N is the number of chains in unit volume of the rubber and T is the absolute temperature. Note that the chain is defined here as part of a long polymer molecule between neighboring cross-linking points. The fundamental assumptions made in deriving Eq. (28) are that all chain ends are displaced to new positions by affine transformation when the rubber is deformed, that there are no intermolecular interactions, and that the end-to-end distance of each chain is much smaller than the contour length of the chain. 

Block copolymers consist of chemically distinct polymer chains that are tethered together to form a single macromolecule. If the individual blocks are immiscible when they are unattached, phase separation will also normally occur in the case of the copolymer, with morphologies that depend on the relative composition of the separate block species, and their manner of attachment (diblocks, triblocks, stars, etc.). This is a result of the physical connection of the blocks, which prevents them from separating over distances greater than the contour lengths of the respective blocks. The result is a microphase separation with adjacent domains that are richer in either of the chemical species. 

The decrease in the hydrodynamic radius coincides with the first inflection point of the potentiometric titration a further and significantly smaller decrease might be assumed at the second inflection point. At pH 4 spherical structures with a maximal radius of approximately 120 nm are observed. As the contour length of the polymer chain is only 140 nm these spherical aggregates most probably do not represent simple spherical micelles. More likely vesicles are formed. At pH 10 also spherical aggregates are found, which appear to be less uniform than the ones formed under acidic conditions. at basic conditions the maximal radius was determined to be about 100 nm. 

Let us assume that the solution of semiflexible macromolecules occupies the volume V. Let i be the polymer volume fraction in the solution. Then, the average concentration of segments is c = 4 fibrpd3, the total number of segments N = Vc, and, finally, the average concentration of macromolecules is c//L, where L denotes the contour length of one macromolecule. 

Now we apply these equations to determine the time td required for a polymer chain to diffuse out of its tube. Naturally, the contour length of the tube is defined by the length of the chain, lc, so based on the diffusion equations we can write (Equations 13-69) ... 

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