Chain-end effects

G. Henn, D. J. Bucknall, M. Stamm, P. Vanhoorne, R. Jerome. Chain end effects and dewetting of thin polymer films. Macromolecules 29 4305 313, 1996. 

These treatments of periodic parts of the dipole moment operator are supported by several studies which show that, for large oligomeric chains, the perturbed electronic density exhibits a periodic potential in the middle of the chain whereas the chain end effects are related to the charge transfer through the chain [20-21]. Obviously, approaches based on truncated dipole moment operators still need to demonstrate that the global polarization effects are accounted for. In other words, one has to ensure that the polymeric value corresponds to the asymptotic limit of the oligomeric results obtained with the full operator. 

Another interesting chiral chain end effect is exhibited by the helical polymer block co-polymer, poly(l,l-dimethyl-2,2-di-/z-hexylsilylene)- -poly(triphenylmethyl methacrylate), reported by Sanji and Sakurai (see Scheme 7) and prepared by the anionic polymerization of a masked disilene.333 The helical poly(triphenylmethyl methacrylate) block (PTrMA) is reported to induce a PSS of the same sign in the poly(di- -propylsilylene) block in THF below — 20 °C, and also in the solid state, by helicity transfer, as evidenced by the positive Cotton effect at 340 nm, coincident with a fairly narrow polysilane backbone UV absorption characteristic of an all-transoid-conformation. This phenomenon was termed helical programming. Above 20°C, the polysilane block loses its optical activity and the UV absorption shifts to 310 nm in a reversible, temperature-dependent effect, due to the disordering of the chain, as shown in Figure 45. 

Sequence 3 examines chain-end effects on DNA dynamics. It contains the coumarin probe one base pair removed from the end of the sequence. This chain end sequence has the same base pair sequence as the normal sequence, but with entire sequence, including the coumarin, shifted towards one terminus. The Stokes shifts from the two sequences are displayed on a relative Stokes shift scale in Fig. 2b. 

So far, the effects of the chain ends were neglected in our stochastic model for the restricted chain. Therefore, n must be much larger than the number of steps needed to form the largest excluded polygon. The partition function, which incorporates the chain-end effects and which could be also employed for exact statistical description of short non-self-intersecting chains can be obtained as follows Assume, as before, that we eliminate only lowest-order polygons of t steps. Therefore, the first t — 1 steps in the chain are described as a sequence of independent events. Eq (9), then, will be replaced by... 

The partition function, given by Eqs. (15-17) for chains with no chain-end effects, and by Eqs. (20-23) for chains with end effects, is restricted to the chain models in which only the lowest-order polygons are excluded. We can extend the derivation of these partition functions to a more general case, in which we eliminate all polygons of sizes t or less and restrict nearest-neighbor interactions to contacts which are separated by t — 1 and fewer chain elements. 

When the propagating metal carbene complex does not have a predetermined vacant ligand position, but is instead trigonal-bipyramidal or tetrahedral, it may still behave like the octahedral model provided that the ligands other than the carbene offer an asymmetric environment which controls the direction of approach of the monomer. If this is not the case there will not be a favoured direction of approach unless the chain-end effect comes into play. 

The PRISM (Polymer-Reference-Interaction-Site model) theory is an extension of the Ornstein-Zernike equation to molecular systems [20-22]. It connects the total correlation function h(r)=g(r) 1, where g(r) is the pair correlation function, with the direct correlation function c(r) and intramolecular correlation functions (co r)). For a primitive model of a polyelectrolyte solution with polymer chains and counterions only, there are three different relevant correlation functions the monomer-monomer, the counterion-counterion, and the monomer-counterion correlation function [23, 24]. Neglecting chain end effects and considering all monomers as equivalent, we obtain the following three PRISM equations for a homogeneous and isotropic system in Fourier space ... 

Narrows, if M lMn > 2 Broadens, if My, Mn < 2 Enhances rate initially chain end effect, then weak branch points... 

With the help of the above-described apparatus, Francois et al.16 discovered a characteristic effect in linear polymer solutions. A preliminary study had already shown to these authors that the partial volume per mass and the branching ratio are related. A measurement of partial volumes per mass should in principle show a chain-end effect. This effect was observed however, another unexpected effect appeared. 

The chain-end effect is observed for low polymerization degrees (N < 102). We note that, for N > 102, the partial volume varies less in poor solvent than in good solvent. 

The role of proton transfer was also investigated. The rate constant of LRET decreases with increasing pH between pH 4 to 6 and then is constant between pH 7 and 11 (156). No chain-end effect is observed by adding lysine residues at both ends of the peptides. Replacing tryptophan by N-methyl tryptophan, the rate of LRET becomes one order of magnitude higher, however the P value is the same (159). The authors conclude that proton transfer is not rate-determining. 

The resulting isotactic Bernoullian model (this is a true Bernoullian model, as the chain end effect is neglected) gives the calculated pentad distribution reported in Table 13. Each pentad contains two symmetric contributions for example, the mmmm pentad derives from the two possibilities... 

In a blend solution, the interaction parameter x of the Flory-Huggins theory is zero (the chain end effect is negligible) and independent of temperature. Otherwise, a temperature-dependent x can lead to a thermorhe-ologically complex behavior of the polymer solution sj tem, which would disallow the apphcation of the time-temperature superposition principle. A theoretical analysis indicates that if M M2, the system is free of the excluded volume effect that will cause the component-two chain to expand in other words, the chain coil remains Gaussian. Here, we consider polystyrene blend solutions with Mi slightly smaller than Mg (= 13,500 for polystyrene). In such a system, the condition M > M2 can be easily satisfied. Furthermore, the solvent, being chains of more than ten Rouse... 

The NMR spectrum of MEEP at an operating frequency of 30 MHz exhibits a major resonance at 5 63.1 (THF-dg) with a full-width at half maximum linewidth (Avi/2) of 75 Hz (Figure 1). A minor resonance in the P NMR spectra downfield (0 to -5 ppm region) of the major resonance is also observable in the N NMR spectra (5 71.9). Similar resonances are observed in the P and N NMR spectra of the related N HPP. These downfield resonances are consistent with polymer chain-end effects. 

The influence of the penultimate member of the growing polymer chain (what is called the penultimate effect) has been often discussed as a cause of deviations from the simple copolymerization equation, especially in the case of strongly polar monomers. Very accurate experiments at very low monomer ratios must be carried out to establish such influences and to correspondingly modify the simple copolymerization equation. However, the penultimate chain end effect can often be better explained by the formation of CT complexes (see Figure 22-11). In this case, the CT complexes function as third monomer. 

With the usual assumptions [steady-state principle, no penultimate chain end effect (see Section 22.4.2), no influence of chain length on the polymerization equilibrium], the following equation is derived for the case of one reversible (monomer 1) and one irreversible homopolymerization step with two irreversible heteropropagation steps ... 

In free radical copolymerizations, all the assumptions summarized in Section 22.1.1 are generally valid, i.e., bimolecular propagation mechanism, absence of the penultimate chain end effect or depolymerization, high degree of polymerization, and identity of overall and effective concentrations. Deviations were discussed in Sections 22.4.2 and 22.4.5. Table 22-3 contains the reactivity ratios for the free radical copolymerization of some monomer pairs that behave normally. 

Deviations from normal copolymerization behavior can be caused not only by a penultimate chain end effect but also by the formation of charge transfer complexes. Definitive charge transfer complexes can be formed by two monomer molecules of widely different polarities, i.e., an electron donor and an electron acceptor. The presence of such complexes can frequently be inferred from accentuated bands in the visible and ultraviolet spectra. 

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