Length, contour

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... 

In which X is the average monomer interpenetration distance, L is the contour length of interdiffused chains and n(t) is the number of chains diffused at time t. The time and molecular weight dependence of these molecular properties are given in Table 1. 

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... 

Effective molecular mass between crosslinks tvtc/kg mol 1 Tensile yield strength cry/MPa Energy release rate Gic/Jm 2 Half crack opening displacement w = 6/2 = Gic/2cry w/pm Chain contour length (Eq. 7.9) lc/nm... 

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... 

Small angle X-ray scattering Rg, chain contour length, L solution conformation and flexibility If M is also known, can provide mass per unit length Ml [5]... 

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-... 

A thiol-terminated PS was used as a sample in the experiment. It was based on a living polymerized carboxyl-terminated PS with M = 93,800 and Mu = 100,400. The polydispersity was Mp( /M = 1.07. The degree of polymerization was about 900 and, thus, its contour length was about 220 nm. The thiol groups were substimted for the carboxylic ends using 1,10-decanedithiol by means of thiolester bonding, anticipating the preferential interaction between... 

X is the extension length at an external load of F Ip and L are persistence and contour lengths, respectively. 

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 ... 

In the case of filled rubbers, the network is represented by a huge chain of contour length L = NL, where N is the number of primary chains of length L. The observable (macroscopic) free energy is given by Equation 22.9, where Z(n) is the replicated partition function that is estimated by functional integration over the continuous chain conformations ... 

The foregoing discussion of equivalent chains requires merely that its root-mean-square end-to-end distance shall equal that of the real chain. In order to define completely the equivalent chain, its contour lengths may also be required to coincide with that of the real chain. 

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