Linear molecular motion

This section begins with a brief description of the basic light-molecule interaction. As already indicated, coherent light pulses excite coherent superpositions of molecular eigenstates, known as wavepackets , and we will give a description of their motion, their coherence properties, and their interplay with the light. Then we will turn to linear and nonlinear spectroscopy, and, finally, to a brief account of coherent control of molecular motion. 

It is likely that there will always be a distinction between the way CAD/CAM is used in mechanical design and the way it is used in the chemical process industry. Most of the computations requited in mechanical design involve systems of linear or lineatizable equations, usually describing forces and positions. The calculations requited to model molecular motion or to describe the sequence of unit operations in a process flow sheet are often highly nonlinear and involve systems of mixed forms of equations. Since the natures of the computational problems are quite different, it is most likely that graphic techniques will continue to be used more to display results than to create them. 

Fig. 26. Observed and calculated 2H spectra of the amorphous regions of drawn (A sb 9) linear polyethylene for various angles p0, cf. Fig. 25. The data were taken at 143 K in order to freeze in molecular motion...

Again because of the crosslinks, such brittle behaviour occurs whatever the temperature unlike brittle materials based on linear polymers, there is no temperature at which molecular motion is suddenly freed. In other words, the Tg, if there is one, does not produce dramahc changes in mechanical properties so that the material is changed from one that undergoes brittle behaviour to one that exhibits so-called tough behaviour. 

Various types of power law relaxation have been observed experimentally or predicted from models of molecular motion. Each of them is defined in its specific time window and for specific molecular structure and composition. Examples are dynamically induced glass transition [90,161], phase separated block copolymers [162,163], polymer melts with highly entangled linear molecules of uniform length [61,62], and many others. A comprehensive review on power law relaxation has been recently given by Winter [164],... 

Eontanella and co-workers studied the effect of high pressure variation on the conductivity as well as the H, H, and O NMR spectra of acid form Nafionl 17 membranes that were exposed to various humidities. Variation of pressure allows for a determination of activation volume, A V, presumably associated with ionic and molecular motions. Conductivities (a) were obtained from complex electrical impedance diagrams and sample geometry, and A V was determined from the slope of linear isothermal In a versus p graphs based on the equation A E = —kJ d In a/d/j] t, where p is the applied pressure. At room temperature, A Ewas found to be 2.9 cm mol for a sample conditioned in atmosphere and was 6.9 cm mol for a sample that was conditioned in 25% relative humidity, where the latter contained the lesser amount of water. 

The large scale molecular motions which take place in the rubber plateau and terminal zones of an uncross-linked linear polymer give rise to stress relaxation and thereby energy dissipation. For narrow molecular weight distribution elastomers non-catastrophic rupture of the material is caused by the disentanglement processes which occur in the terminal zone, e.g., by the reptation process. In practical terms it means that the green strength of the elastomer is poor. 

Materials with properties intermediate between those of elastomers and fibers are grouped together under the term plastics. Thus plastics exhibit some flexibility and hardness with varying degrees of crystallinity. The molecular requirements for a plastic are that (1) if it is linear or branched, with little or no cross-linking, it be below its T (2) if it is amorphous and/or crystalline, it be used below its Tm, or (3) if it is cross-linked, the cross-linking be sufficient to severely restrict molecular motion. 

The changes in structure that must occur create a barrier to electron transfer. In order to understand the origin of the barrier and to treat it quantitatively, it is necessary to recall that the structural changes at each reactant can be resolved into a linear combination of its normal vibrational modes. The normal modes constitute a complete, orthonormal set of molecular motions into which any change in intramolecular structure can be resolved. 

A pseudo solid-like behavior of the T2 relaxation is also observed in i) high Mn fractionated linear polydimethylsiloxanes (PDMS), ii) crosslinked PDMS networks, with a single FID and the line shape follows the Weibull function (p = 1.5)88> and iii) in uncrosslinked c/.s-polyisoprenes with Mn > 30000, when the presence of entanglements produces a transient network structure. Irradiation crosslinking of polyisoprenes having smaller Mn leads to a similar effect91 . The non-Lorentzian free-induction decay can be a consequence of a) anisotropic molecular motion or b) residual dipolar interactions in the viscoelastic state. 

The polymers considered in Sects. 4 to 6, i.e. polyethylene fere-phthalalc), bisphenol A polycarbonate and aryl-aliphatic polyamides, are linear polymers or copolymers without side chains, in which molecular motions occur in the glassy state. Detailed analysis of the transitions, mostly the ft transition, reveals that several processes are involved in this ft transition and that the co-... 

The mechanical properties of poly(methyl methacrylate), PMMA, have been studied for quite a long time and, in addition to its industrial interest, PMMA constitutes a kind of reference material. Indeed, among the amorphous linear polymers it represents an intermediate between the very brittle polystyrene and the tough bisphenol A polycarbonate considered in Sect. 4. Furthermore, as shown in [1] (Sect. 8.1), the molecular motions responsible for its large p transition are precisely identified, as well as the nature of the cooperativity that develops in the high temperature range of the p transition. 

A much simpler picture emerges in the time domain. The corresponding autocorrelation function, depicted in Figure 8.4, exhibits three well resolved recurrences with very small amplitudes. The recurrence times 2"i, T2, and T3 are incommensurable which indicates that they reflect different types of molecular motion. Since the recurrences are well separated we can write S(t) as a sum S(t) = Si(t), i = 0,..., 3, with So representing the main peak at t = 0. The Fourier transformation is linear so that the absorption cross section also splits into four individual terms,... 

Exclusively mechanically interlocked linear polymer blends, typically, are not thermodynamically phase stable. Given sufficient thermal energy (Tuse>Tg), molecular motion will cause disentanglement of the chains and demixing to occur. To avoid phase separation, crosslinking of one or both components results in the formation of a semi-IPN or full-IPN, respectively. Crosslinking effectively slows or stops polymer molecular diffusion and halts the phase decomposition process. 

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