Segmental Asymmetric Relaxation

At the equilibrium,/dH =/dL, see Fig. 33.3 one can derive the rules for the segmental corporative asymmetric relaxation. Letting and be the respective force constants and Sda and Sdi the corresponding displacements, the k, and (5t/x satisfy the relation 

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Compression stiffens the softer phonons and softens the stiffer phonons as a consequence of the asymmetric relaxation of the bond segments. 

Above the -relaxation process, the 2,4-TDI/PTMO polymer displayed a short rubbery plateau at a storage modulus of about 5 MPa while 2,6-TDI/PTMO was capable of crystallization, as evidenced by the ac-loss process. This difference in dynamic mechanical properties demonstrates the effect of a symmetric diisocyanate structure upon soft-segment properties. As previously discussed, single urethane links can sometimes be incorporated into the soft-segment phase. The introduction of only one of these diisocyanate molecules between two long PTMO chains inhibits crystallization if the diisocyanate is asymmetric. In the case of a symmetric diisocyanate, soft-segment crystallization above Tg can readily occur. The crystals formed were found to melt about 30°C below the reported melting point for PTMO homopolymer, 37°-43°C (19), possibly because of disruption of the crystal structure by the bulky diisocyanate units. 

The observation that a macromolecular brush gets stretched as the side chains get adsorbed on a flat surface provides a means to stimulate molecular motility by desorption of the brush molecule or a segment of it. If the molecule is in a subsequent period allowed to relax to the adsorbed stretched state it will eventually do a step forward. This is depicted schematically in Figure 28 as a sort of a creep motion. Here, the desorbed state might be characterized as an excited state whose formation requires input of energy. In the case that the structure of the surface and of the molecule favor relaxation into a distinct direction, i.e., in the case of an asymmetric potential, the motion of the molecule can be become directed. 

The assumption that the contraction process is ideally adiabatic, while perhaps not entirely permissible practically, seems indicated by modern theory of the behavior of molecular chains, which pictures these as undergoing, when freed of restraints, a sort of segmental diffusion, much like the adiabatic expansion of an ideal gas into a vacuum (155). In the case of the molecular chain, it diffuses to the most probable, randomly coiled configuration, which is much less asymmetric, hence shorter, than an initially extended chain. Because rubber most nearly presents this ideal behavior, those fibers which develop increased tension (a measure of the tendency toward assumption of the contracted form) when held isometrically under conditions of increasing temperature (favoring the diffusion ) are said to be rubber-like. Most normal elastic solids upon stress are strained from some stable structure and relax as the temperature is raised. 

At rest, the conformation of a flexible chain in dilute solution looks like a coil with spherical symmetry in the long-term. However, its instantaneous shape is asymmetric [125], which means the chain rotates along a streamline of a flow field with velocity gradient. The hydrodynamic drag force from the friction between the chain segments and the solvent molecules can deform the coil from its equilibrium shape. On the other hand, the conformation of the polymer chain is variable and changing all the time because of thermal fluctuation (Brownian motion of the solvent). So the shape of the chain in the flow field depends on how quickly the solvodynamic force deforms the chain and how slow the whole chain relaxes. This evolves two timescales. 

On going from the isotropic to the anisotropic LC state, the orientation-dependent attractive interactions come into play [125,126] while the steric interactions (the excluded-volume effect) between the mesogenic rods are relaxed [127]. In the LC state, all molecules are required to take an asymmetric shape. Accordingly, chain segments adopt a unique conformer distribution called a nematic conformation [26,93-95,102,103,105]. The Y-Vsp relation determined in the aforementioned studies may be used to examine the mean-field potentials effective in nematic as well as isotropic hquids. After Frank [128] and HUdebrand and Scott [2,129], the intermolecular interaction potentials such as... 

Retention in the separation segment of the FIA-HFFF channel is expected to be equivalent to that observed in a conventional asymmetrical channel system, if complete hydrodynamic relaxation can be obtained. It will follow basic principles, as shown by the retention ratio, R, given by... 

The HS relaxation temperature was affected by the symmetry of the reactants and by the E value in the rubbery plateau for the urea group concentration and steric hindrance. As shown by Marcos [224], the copolymers were very sensitive to the linkage between HS and SS segments. The use of asymmetric diisocyanates lead to a large domain boundary mixing while symmetric diisocyanates determined a sharper boundary. Higher HS percent crystallinity has been observed in PUs with linear, aliphatic HS compared to those made of aromatic diisocyanates [177,188],... 

Such PU molecular structure assumed, a priori, the possible manifestation of several dynamic modes within the glass transition, in particular, because of the different positions of segments within a PPG crosslink regarding rigid junctions. However, DMA and dielectric relaxation spectrometry (DRS) techniques exhibited only one broad relaxation region for PU glass transition, for instance, the asymmetric mechanical loss peak extending from —60°C to 50°C, with Tmax —30°C (Fig. 9). 

Fig. 33.3 Forces and relaxation dynamics of the segmented 0 H-0 bond. Asymmetric and coupling relaxation dynamics of the master-slave-segmented 0 H-0 bond in water ice under applied stimulus. Short-range interactions of intramolecular H-O bond exchange interaction, intermolecular 0 H non-bond vdW interaction (broken red lines), interelectron-pair Coulomb repulsion (broken white lines), forces of Coulomb repulsion /q, deformation recoveryand the force driving relaxation acting on the electron pairs (small dots). H atom is the coordinate origin. Because of the strength disparity, Mi] > lAdnl the Coulomb repulsion makes the Adg and the A l shift in the same direction by different amounts (Reprinted with permission from [14])...

MD results show the general trend of pressure-induced 0 H shortening and H-O lengthening. An extrapolation of the MD-derived polynomial expressions leads to the proton symmetrization occurring at 58.6 GPa with the 0-0 distance of 0.221 nm, which is in good accordance with measurements of 59 GPa and 0.220 nm [10]. Therefore, it is confirmed that the proton symmetrization arises from the pressure-induced asymmetric segmental relaxation. 

The flexible, polarizable, and segmented 0 H-0 H-bond forms a pair of asymmetric, Coulomb repulsion coupled, H-bridged oscillators, whose relaxation in length and energy and the associated electron entrapment and polarization determines the anomalies of water ice. 

Dewetting is not a surface sensitive technique. In particular, the height of the rim is not controlled by a possible high mobility surface layer. Dewetting involves the displacement of whole polymer chains and takes place across the entire film thickness. Moreover, at the used dewetting temperature, the film behaved like an elastic body, as demonstrated by the asymmetric shape of the rim. Stress relaxation could therefore, only occur by motion on the level of chain segments. 

The a- and ajS-processes are characterized by a broad asymmetric dielectric relaxation spectrum, which can be well represented by the Kohlrausch Williams-Watts (KWW) decay function (cf. eqn. (4.17)). The major factor leading to the broad DR spectra for a- and ajS-relaxations is that chain segments relax in cooperation with their environment. In order to explain the mechanism of this relaxation, the concepts of defect diffusion and free-volume fluctuation are used. For example, Bendler has proposed a model in which the KWW function is interpreted as the survival probability of a frozen segment in a swarm of hopping defects with a stable waiting-time distribution At for defect motion. 

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