Motion segmental

In this case it is more convenient to calculate the following time correlation function, 

The bracket in the last expression represents the average over A (0- To 

To solve this, we need the initial condition and the boundary condition  

This result is easily derived, for if r the polymer segment remains in the initial tube, so that if the chain moves (r) dong the tube, the mean square displacement in the three-dimensional space is given by a( (0l) (see eqn (6.2)). Hence 0(s, s t) is given by 

Hence the diffusion constant Da of the centre of mass is given as 

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To the extent that the segmental friction factor f is independent of M, then Eq. (2.56) predicts a first-power dependence of viscosity on the molecular weight of the polymer in agreement with experiment. A more detailed analysis of f shows that segmental motion is easier in the neighborhood of a chain end because the wagging chain end tends to open up the structure of the melt and... 

Unlike SSBR, the microstmcture of which can be modified to change the polymer s T, the T of ESBR can only be changed by a change in ratio of the monomers. Glass-transition temperature is that temperature where a polymer experiences the onset of segmental motion (7). 

A crystalline or semicrystalline state in polymers can be induced by thermal changes from a melt or from a glass, by strain, by organic vapors, or by Hquid solvents (40). Polymer crystallization can also be induced by compressed (or supercritical) gases, such as CO2 (41). The plasticization of a polymer by CO2 can increase the polymer segmental motions so that crystallization is kinetically possible. Because the amount of gas (or fluid) sorbed into the polymer is a dkect function of the pressure, the rate and extent of crystallization may be controUed by controlling the supercritical fluid pressure. As a result of this abiHty to induce crystallization, a history effect may be introduced into polymers. This can be an important consideration for polymer processing and gas permeation membranes. 

Homogeneous nucleation occurs when, as a result of statistically random segmental motion, a few segments have adopted the same conformation as they would have in a crystallite. At one time it was considered that the likelihood of the formation of such nuclei was greatest just above the transition temperature... 

In the case of polymer molecules where the dipoles are not directly attached to the main chain, segmental movement of the chain is not essential for dipole polarisation and dipole movement is possible at temperatures below the glass transition temperature. Such materials are less effective as electrical insulators at temperatures in the glassy range. With many of these polymers, e.g., poly(methyl methacrylate), there are two or more maxima in the power factor-temperature curve for a given frequency. The presence of two such maxima is due to the different orientation times of the dipoles with and without associated segmental motion of the main chain. 

The importance of polymer segmental motion in ion transport has already been referred to. Although classical Arrhenius... 

Mahabadi and O Driscolm considered that segmental motion and center of mass diffusion should be the dominant mechanisms at low conversion. They analyzed data for various polymerizations and proposed that k, J should be dependent on chain length such that the overall rale constant obeys the expression ... 

More complex models for diffusion-controlled termination in copolymerization have appeared.1 tM7j Russo and Munari171 still assumed a terminal model for propagation but introduced a penultimate model to describe termination. There are ten termination reactions to consider (Scheme 7.1 1). The model was based on the hypothesis that the type of penultimate unit defined the segmental motion of the chain ends and their rate of diffusion. 

Robeson et al. studied the secondary loss transitions of a series of poly(arylene ether)s using a torsion pendulum.15 They found that the secondary loss transitions are closely related to the segmental motion of the aryl ether bonds. The secondary... 

In solution the molecules of a polymer undergo various segmental motions, changing rapidly from one conformation to another, so that the molecule itself effectively takes up more space than the volume of its segments alone. As we have seen, the size of the individual molecules depends on the thermodynamic quality of the solvent in good solvents chains are relatively extended, whereas in poor solvents they are contracted. 

The intercept, 1/Po, is called the anisotropy of the molecule and is an indication of the nonrotational depolarization of the molecule. This intrinsic depolarization is due to the segmental motion of the fluorophores within the molecule the depolarization due to energy transfer and the angular difference in transition dipole moments of the absorbing and emitting states. 

For motion of entire molecular strands, consisting of n segments, to take place in 0.1 s, the frequency of segmental motion must be much faster than 0.1 s by a factor of or more. This rate is achieved only at a temperature well above Tg for typical values of n, of the order of 100. Thus, fully rubber-like response will not be achieved until the test temperature is Tg + 30°C, or even higher. (On the other hand, for sufficiently slow movements that take place over several hours or days, an elastomer would still be able to respond at temperatures below the conventionally dehned glass transition temperature.)... 

In these complexes, the cations coordinate with the oxygen atoms of the backbone and, under the influence of an electrical potential, they are transferred from an oxygen atom to another through the amorphous region of the polymer assisted by the segmental motion of the polymer backbone. 

For the investigation of polymer systems under spatial confinement, fluorescence microscopy is a powerful method providing valuable information with high sensitivity. A fluorescence microscopy technique with nanometric spatial resolution and nanosecond temporal resolution has been developed, and was used to study the structure and dynamics of polymer chains under spatial confinement a polymer chain in an ultra-thin film and a chain grafted on a solid substrate. Studies on the conformation of the single polymer chain in a thin film and the local segmental motion of the graft polymer chain are described herein. 

AVi/2 Segmental motions, order parameters, exchange rates... 

The increase in the length of the side chain results normally in an internal plasticization effect caused by a lower polarity of the main chain and an increase in the configurational entropy. Both effects result in a lower activation energy of segmental motion and consequently a lower glass transition temperature. The modification of PPO with myristoyl chloride offers the best example. No side chain crystallization was detected by DSC for these polymers. 

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