Chain-length-dependent perturbation

Freed et al. [42,43], among others [44,45] have performed RG perturbation calculations of conformational properties of star chains. The results are mainly valid for low functionality stars. A general conclusion of these calculations is that the EV dependence of the mean size can be expressed as the contribution of two terms. One of them contains much of the chain length dependence but does not depend on the polymer architecture. The other term changes with different architectures but varies weakly with EV. Kosmas et al. [5] have also performed similar perturbation calculations for combs with branching points of different functionalities (that they denoted as brushes). Ohno and Binder [46] also employed RG calculations to evaluate the form of the bead density and center-to-end distance distribution of stars in the bulk and adsorbed in a surface. These calculations are consistent with their scaling theory [27]. 

Expansion is considered for finite, regular polyethylene stars perturbed by the excluded volume effect. An RIS model is used for the chain statistics. The number of bonds in each branch ranges up to 10 240, and the functionality of the branch point ranges up to 20. The form of the calculation employed here provides a lower bound for the expansion. If the number, n, of bonds in the polymers is heid constant, expansion is found to decrease with increasing branch point functionality. Two factors dictate the manner in which finite stars approach the limiting behavior expected for very large stars, These two factors are the chain length dependence at small n of the characteristic ratio and of fa -a3) / n1/2. 

Theoretical Calculations.- A molecular interpretation of the chain-length dependent thermotropic behaviour of saturated symmetrical-chain phosphatidylcholine bilavers has been put forward. Thermodynamic parameters of the thermal phase-transition were found to be linearly related to a perturbation parameter and could be used to predict the minimum number of carbon atoms in the acvl chain needed for a bilayer phase-transition to occur. A model has been developed, consistent with NMR data, for hydrocarbon-chain dynamics in lipid bilayers. Involving concerted rotations around at least two C-C bonds at a... 

A soft twist with a helicity reversal was also proposed by Taylor and coworkers for the case of polytetrafluoroethylene (PTFE) [25, 26]. The ambi-dextron , as it was termed, came naturally as a result of the equations of motion for the system. The difference to the other soft twists, already discussed, is a chain-length dependence. Free motion of the perturbation is only possible when there is a high ratio of free ends to stems in the crystal lamella, as is the case for PTFE. 

Increasing chain length changes the general features of the fi, q plots rather drastically. For v = 10 the range of random replication appears to be substantially wider (Figure 11). The (fi, q curves are almost horizontal on both sides of the maximum irregularity condition at q = 0.5. In addition, the transitions from direct to random replication and from random to complementary replication are rather sharp. We are now in a position to compare the minimum accuracy of replication that we derived in Section III by perturbation theory with the exact population dependence on q. From Eqs. (III.l) and (III.4) we find (D = 0 k = 0,1,. . . , n)... 

The experimental measures of these molecular electric properties involve oscillating fields. Thus, the frequency-dependence effects should be considered when comparing the experimental results . Currently, there are fewer calculations of the frequency-dependent polarizabilities and hyperpolarizabilities than those of the static properties. Recent advances have enabled one to study the frequency dispersion effects of polyatomic molecules by ab initio methods In particular, the frequency-dependent polarizability a and hyperpolarizability y of short polyenes have been computed by using the time-dependent coupled perturbed Hartree-Fock method. The results obtained show that the dispersion of a increases with the increase in the optical frequency. At a given frequency, a and its relative dispersion increase with the chain length. Also, like a, the hyperpolarizability y values increase with the chain length. While the electronic static polarizability is smaller than the dynamic one, the vibrational contribution is smaller at optical frequencies. ... 

Takahashi reported the first halogold(l) isonitrile systems (141 R = H, OC ,H2, + i). Depending on the chain length, the ligands with R = H showed nematic and SmA mesophases, between ca. 70 and 85 °C, while the complex showed SmA and SmC phases at elevated temperatures (170-270 In order to perturb the strong intermolecular... 

The on rate constant, /c+, is diffusion-controlled and depends little on surfactant and micelle size (cf. Table 19.5). The off rate constant, on the other hand, is strongly dependent on alkyl chain length, micelle size, etc. Because of the co-operativity in micelle formation there is a very deep minimum in the size distribution curve. This leads to a two-step approach to equilibrium after a perturbation. In a fast step, quasiequilibrium is reached under the constraint of a constant total number of micelles. The redistribution of unimers between abundant micelles is a fast process. In order to reach a true equilibrium, the number of micelles must change. Because of the stepwise process, this also involves the very rare intermediate micelles. Therefore, this process is slow. 

Molten polymers flow like (highly viscous) ordinary liquids when they are acted upon by very slow perturbations. However, at slightly higher frequencies co, they behave like a rubber. The threshold frequency coj = 1/t that separates the two spectral regions is strongly dependent on the chain length... 

This much is readily evident. Assessment of the magnitude of the perturbation of the configuration and its dependence on chain length require a more penetrating examination. 

---