Disordered polymers

This is the entropy of the disordered polymer when the latter entirely fills the lattice. 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

A similar comparison can be made with cis-poly(isoprene), natural rubber, by taking advantage of the fact that the polymer is very slow to crystallize [164], Consequently, the comparison can be made between the supercooled, noncrystalline polymers at 0°C and the semi-crystalline polymer (31% crystalline) at the same temperature. The Tlc values for each of the five carbons involved were again found to be the same for the completely disordered polymer and the semicrystalline one, so that a similar conclusion can be made with regard to their chain structure. 

This branch of polymer physics is closely connected to another of I.M. Lif-shitz favorite directions in physics, namely, the theory of disordered systems [73]. The situation when different samples have only statistical similarity is typical for the physics of chaos, and many concepts I.M. Lifshitz developed are also quite naturally applied in the physics of disordered polymers. The idea of self-averaging in general and self-averaging of free energy [74], in particular, are examples of such concepts. 

This term describes the phenomena of stereoisomerism observable in short chain segments. Microtacticity considerations can be applied to stereoregular polymers, to sequences of partially regular polymers, and to highly disordered polymers, both from the qualitative and quantitative points of view. This approach is the most appropriate and complete for the structural study of real polymers. 

We will want to know two things about the conformations of disordered polymer chains the average distance apart of the chain ends or, as we say, the end-to-end distance, and the distribution of end-to-end distances. Obtaining the average is easier for most students to understand, so we will do that first. This problem is similar to a number of others in physics that can be related to a random walk or random flight. 

So far we have focused on disordered polymer chains. Now we turn to the question of order and morphology. Morphology is a word that was stolen from the world of biology and botany, where it means the study... 

Discuss the limitations of the freely jointed and rotating bond model for a disordered polymer chain. 

Another challenging project would be to put more effort in developing techniques capable of predicting electronic spectra of substitutionally disordered polymers. For example, these methods could be valuable for the investigation of copolymers of various types (26) ... 

Many more subtleties arise when we have to deal with phase boundaries, and particularly the boundary between crystalline and disordered polymer, whether the latter is the phase from which a crystal grows, or the disordered layer at the surface of crystal lamellae in the final state. This, in one way or another, is what we are concerned with in much the largest section of our Discussion, from Point s paper almost to the end. 1 would like to emphasize that the most important restriction on randomness in these situations, whether we are considering statistical equilibrium or kinetic restrictions on the attainment of equilibrium, is not self-exclusion but mutual exclusion. 

Wide-angle X-ray scattering techniques can provide direct information on key features such as crystallinity, preferred orientation, phase identification and compositional analysis.. zfs jjoj-g detailed analysis can yield details of local chain conformations and packing arrangements in both crystalline and disordered polymers. ... 

Reversible energy transfer between monomeric and dimeric forms of rhoda-mine 6G in ethylene glycol has been observed" and the concentration dependence of the overall fluorescence quantum yield has been modelled by Monte-Carlo simulations. Triplet energy transfer in disordered polymers has been analyzed on the basis of Bassler s model in which the trap energies have a Gaussian distribution." Energy transfer has also been observed in mono-layers and for photoswitchable molecular triads." The structural requirements for efficient energy transfer from a carotenoid to chlorophyll have been... 

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