Polymer contour length

Wu D, Lenhardt JM, Black AL, Akhremitchev BB, Craig SL (2010) Molecular stress relief through a force-induced irreversible extension in polymer contour length. J Am Chem Soc 132 15936-15938... 

PVP47 Cylindrical brush polymer Contour length L = 100 nm 3.9 = 2,800 lOONTnm... 

Dependence of Rg (nm) of Et - PVP - Br on Specificity of Counterion from Added Saif. Polymer Contour Length L = 1000 nm... 

In the limit that the number of effective particles along the polymer diverges but the contour length and chain dimensions are held constant, one obtains the Edwards model of a polymer solution [9, 30]. Polymers are represented by random walks that interact via zero-ranged binary interactions of strength v. The partition frmction of an isolated chain is given by... 

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-... 

X 10 N and the value obtained by the simplest form, 1.45 X 10 " N m n = 918 and a = 0.31 nm for Equation 21.1). These comparisons imphed that the measurements were consistent with the theoretical predictions. The deviation between the rupture length of 260.9 nm and the fitted-contour length indicated that the polymer chain was not fully stretched at the rupture event. The reason for this was that the rupture event was a stochastic process and was dependent on many factors such as pulling speed, bond strength, and temperature. The vahdity of the freely jointed (FJC) model (dashed fine) was also checked ... 

When interaction and physical phenomena length scales become comparable to or larger than the size of the structure, as, for example, with polymer contour chain length, the system may exhibit unusual behavior and generate novel arrangements not accessible in bulk. 

Ordered conformation. Figure 1. shows representative electron micrographs of samples A, B, C, and D vacuum dried from xanthan solutions under ordering conditions as specified in the legend. Xanthan samples A -D appear as unbranched, uniformly thick, convoluted chains. The contour length varies from molecule to molecule as expected for a polydisperse polymer. The electron micrographic... 

Finally, a further unsolved problem should be mentioned. If we compare the plateau moduli of different polymer melts and relate them to the Kuhn length and to the density, this relation can also be adequately described with the scaling model, if an exponent a near 3 is chosen [73]. It is not known why this exponent is different if the contour length density is varied by dilution in concentrated solution or by selecting polymer chains of different volume. 

In order to estimate whether the true molar masses of the dendronized polymers are larger or smaller than the GPC molar masses reported in Table 1, it is useful to recall that the separation in a GPC experiment is based on the hydro-dynamic volume (Vn) of macromolecules. For flexible coils, Vn depends on the chain length (i. e. contour length) L = MxbxMo1 according to... 

The applied strain is affine and the whole of the tube is deformed along with the polymer. As the strain is infinitesimally small the contour length is unaltered. At very short times / after the strain is applied, t < re tr the stress is relaxed as a Rouse chain. At short times we can make an approximation and replace our sum by an integral ... 

---