Other Transitions and Relaxations

The glass transition temperature of copolymers depends on the mass functions Wa and wb of A and B monomeric units, the probabilities p of occurrence of AA, AB, and BB diads, and on their corresponding glass transition temperatures. Considering (rG)BA = (rc )AB, the following can be used empirically  

Polymers may possess a series of other transition and relaxation temperatures besides the glass transition and melting temperatures. Such temperatures may lie either above or below the glass transition temperature. Like the glass transition temperature, these temperatures also depend on the frequency of the method of measurement. 

As the temperature of a polymer is lowered continuously, the sample may exhibit several second-order transitions. By custom, the glass transition is designated the a transition, and successively lower temperature transitions are called the - - transitions. One important second-order transition appears above Tg, designated the (liquid-liquid) transition. Of course, if the polymer is semicrystalhne, it will also melt at a temperature above Tg. 

2 Side-Chain Motions The above considers main-chain motions. Many polymers have considerable side-chain foliage, and these groups can, of course, have their own motions. 

A major difference between main-chain and side-chain motions is the toughness imparted to the polymer. Low-temperature main-chain motions act 

As illustrated in Rgure 8.17 (50), the Tn transition occurs above the glass transition and is thought to represent the onset of the ability of the entire polymer molecule to move as a unit (9,51,52). Above Tn, physical entanglements play a much smaller role, as the molecule becomes able to translate as a whole unit. 

Although there is much evidence supporting the existence of a Tn (51-53), it is surrounded by much controversy (54-57). Reasons include the strong dependence of Tn on molecular weight and an analysis of the equivalent 

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As a practical example, take the use of a polymer in some biomedical apphcations such as an implant device, in which the polymer surface will continually contact blood or other body fluids. Classic surface studies using contact angle measurements, wetting phenomena. X-ray photoelectron spectroscopy, or other analytical techniques may indicate that the material should be biocompatible and not cause problems such as blood platelet deposition and clot formation and immune responses. Typical surface analyses, however, are not or cannot normally be carried out under conditions of use. Under such conditions, surface transitions and relaxations may occur with time that will transform the polymer surface into one that is no longer biocompatible from the standpoint of blood or other body fluid interactions. The result could be catastrophic for the recipient of the transplant or implant made of such material. 

The steady state is disturbed and the system exhibits transient behavior when at least one of its parameters is altered under an external stimulus (perturbation). Transitory processes that adjust the other parameters set in (response) and at the end produce a new steady state. The time of adjustment (transition time, relaxation time) is an important characteristic of the system. 

Perhaps not surprisingly, the most thorough NMR studies of Knight shifts, Korringa relaxation, metal-insulator transitions, and the NMR of the dopant nuclei themselves have been carried out for doped silicon. Since few semiconductors other than PbTe, which presents a considerably more complicated case, have been studied in such detail, it is worthwhile here to summarize salient points from these studies. They conveniently illustrate a number of points, and can shed light on the behavior to be expected in more contemporary studies of compound semiconductors, which are often hindered by the lack of availability of a suite of samples of known and widely-varying carrier concentrations. 

An electronically-excited species is usually associated with an excess of vibrational energy in addition to its electronic energy, unless it is formed by a transition between the zero-point vibrational levels (v = 0) of the ground state and the excited state (0 —> 0 transition). Vibrational relaxation involves transitions between a vibrationally-excited state (v > 0) and the v = 0 state within a given electronic state when excited molecules collide with other species such as solvent molecules, for example S2(v = 3) - Wr> S2(v = 0). 

One may consider the relaxation process to proceed in a similar manner to other reactions in electronic excited states (proton transfer, formation of exciplexes), and it may be described as a reaction between two discrete species initial and relaxed.1-7 90 1 In this case two processes proceeding simultaneously should be considered fluorescence emission with the rate constant kF= l/xF, and transition into the relaxed state with the rate constant kR=l/xR (Figure 2.5). The spectrum of the unrelaxed form can be recorded from solid solutions using steady-state methods, but it may be also observed in the presence of the relaxed form if time-resolved spectra are recorded at very short times. The spectrum of the relaxed form can be recorded using steady-state methods in liquid media (where the relaxation is complete) or using time-resolved methods at very long observation times, even as the relaxation proceeds. 

Chompff and Duiser (232) analyzed the viscoelastic properties of an entanglement network somewhat similar to that envisioned by Parry et al. Theirs is the only molecular theory which predicts a spectrum for the plateau as well as the transition and terminal regions. Earlier Duiser and Staverman (233) had examined a system of four identical Rouse chains, each fixed in space at one end and joined together at the other. They showed that the relaxation times of this system are the same as if two of the chains were fixed in space at both ends and the remaining two were joined to form a single chain with fixed ends of twice the original size. 

As opposed to the liquid-crystal transformation, the liquid-glass transformation is not a phase transition and therefore it can not be characterized by a certain transition temperature. Nevertheless, the term "the vitrification temperature , Tv, is widely used. It has the following physical meaning. As opposed to crystallization, vitrification occurs when the temperature changes continuously, i.e. over some temperature interval, rather than jump-wise. Inside this interval, the sample behaves as a liquid relative to some of the processes occurring in it, and as a solid relative to other processes occurring in it. The character of this behaviour is determined by the ratio between the characteristic time of the process, t, and the characteristic relaxation time of the matrix, x = t//G, where tj is the macroscopic viscosity and G is the matrix elasticity module. If t x, then the matrix should be considered as a solid relative to the process, and if t > x it should be considered as a liquid. The relation tjx = 1 can be considered as the condition of the matrix transition from the liquid to the solid (vitreous) state, and the temperature Tv at which this condition is realized as the temperature of vitrification. Evidently, Tv determined by such means will be somewhat different for the processes with different characteristic times t. However, due to the rapid (exponential) dependence of the viscosity rj on T, the dependence of Tw on t (i.e. on the kind of process) will be comparatively weak (logarith-... 

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