Molecular motions, character

A basic theme throughout this book is that the long-chain character of polymers is what makes them different from their low molecular weight counterparts. Although this notion was implied in several aspects of the discussion of the shear dependence of viscosity, it never emerged explicitly as a variable to be investi-tated. It makes sense to us intuitively that longer chains should experience higher resistance to flow. Our next task is to examine this expectation quantitatively, first from an empirical viewpoint and then in terms of a model for molecular motion. 

We thus see that the RFOT theory provides a rather complete picture of vitrification and the microscopies of the molecular motions in glasses. The possibility of having a complete chart of allowed degrees of freedom is veiy important, because it puts strict limitations on the range of a priori scenarios of structural excitations that can take place in amorphous lattices. This will be of great help in the assessment of the family of strong interaction hypotheses mentioned in the introduction. To summarize, the present theory should apply to all amorphous materials produced by routine quenching, with quantitative deviations expected when the sample is partially crystalline. The presence and amount of crystallinity can be checked independently by X-ray. It is also likely that other classes of disordered materials, such as disordered crystals, will exhibit many similar traits, but of less universal character. 

Given the character of the water-water interaction, particularly its strength, directionality and saturability, it is tempting to formulate a lattice model, or a cell model, of the liquid. In such models, local structure is the most important of the factors determining equilibrium properties. This structure appears when the molecular motion is defined relative to the vertices of a virtual lattice that spans the volume occupied by the liquid. In general, the translational motion of a molecule is either suppressed completely (static lattice model), or confined to the interior of a small region defined by repulsive interactions with surrounding molecules (cell model). Clearly, the nature of these models is such that they describe best those properties which are structure determined, and describe poorly those properties which, in some sense, depend on the breakdown of positional and orientational correlations between molecules. 

NMR and EPR techniques provide unique information on the microscopic properties of solids, such as symmetry of atomic sites, covalent character of bonds, strength of exchange interactions, and rates of atomic and molecular motion. The recent developments of nuclear double resonance, the Overhauser effect, and ENDOR will allow further elucidation of these properties. Since the catalytic characteristics of solids are presumably related to the detailed electronic and geometric structure of solids, a correlation between the results of magnetic resonance studies and cata lytic properties can occur. The limitation of NMR lies in the fact that only certain nuclei are suitable for study in polycrystalline or amorphous solids while EPR is limited in that only paramagnetic species may be observed. These limitations, however, are counter-balanced by the wealth of information that can be obtained when the techniques are applicable. 

As pointed out above with relation to the data at 87 °C, the Tic of the crystalline-amorphous interphase is appreciably longer than that of the amorphous phase, suggesting the retention of the helical molecular chain conformation in the interphase. We also note that a Tic of 65-70 s for the crystalline phase is significantly shorter than that for other crystalline polymers such as polyethylene and poly-(tetramethylene oxide), whose crystalline structure is comprised of planar zig-zag molecular-chain sequences. In the crystalline region composed of helical molecular chains, there may be a minor molecular motion in the TiC frame, with no influence on the crystalline molecular alignment that is detected by X-ray diffraction analyses. Such a relatively short TiC of the crystalline phase may be a character of the crystalline structure that is formed by helical molecular chain sequences. 

Note, however that the concepts about the lipid membrane as the isotropic, structureless medium are oversimplified. It is well known [19, 190] that the rates and character of the molecular motion in the lateral direction and across the membrane are quite different. This is true for both the molecules inserted in the lipid bilayer and the lipid molecules themselves. Thus, for example, while it still seems possible to characterize the lateral movement of the egg lecithin molecule by the diffusion coefficient D its movement across the membrane seems to be better described by the so-called flip-flop mechanism when two lipid molecules from the inner and outer membrane monolayers of the vesicle synchronously change locations with each other [19]. The value of D, = 1.8 x 10 8 cm2 s 1 [191] corresponds to the time of the lateral diffusion jump of lecithin molecule, Le. about 10 7s. The characteristic time of flip-flop under the same conditions is much longer (about 6.5 hours) [19]. The molecules without long hydrocarbon chains migrate much more rapidly. For example for pyrene D, = 1.4x 10 7 cm2 s1 [192]. 

The rate and character of the molecular motions of both the molecules embedded in the lipid bilayer and lipid molecules themselves are strongly dependent on the temperature [19, 203], At a certain temperature tm, the gel-liquid crystal phase transition is known to occur for the membrane made of a synthetic lipid. For example, tm = 41.5 °C for the membranes from DPL. In the vesicles formed by a mixture of lipids, e.g. egg lecithin, the phase transition occurs smoothly rather than jumpwise and starts below 0 °C. Note that the permeability of lipid membranes increases notably upon transition from the liquid crystal state to the gel state [204]. 

The deficiency is rectified in Figure 3.24 by taking suitable sums and differences of the motions of Figure 3.23. For molecular motions these transformations correspond to the orthog-onalization of the like symmetry linear combinations, which occur as repetitions. Note that this particular example is an especially favourable one, as it is a single-orbit problem and is also one where the vibrational character contains not more than one copy of any irreducible symmetry, so the forms of all the vibrational modes are entirely determined by symmetry. In a more general case, symmetry considerations provide a basis for the normal modes rather than the modes themselves. 

Depending on the character of the molecular motions, one can distinguish several physical situations. In most cases, the molecules are trapped in relatively deep potential wells. Then, they perform small translational and orientational oscillations around well-defined equilibrium positions and orientations. Such motions are reasonably well described by the harmonic approximation. The collective vibrational excitations of the crystal, which are considered as a set of harmonic oscillators, are called phonons. Those phonons that represent pure angular oscillations, or libra-tions, are called librons. For some properties it turns out to be necessary to look at the effects of anharmonicities. Anharmonic corrections to the harmonic model can be made by perturbation theory or by the self-consistent phonon method. These methods, which are summarized in Section III under the name quasi-harmonic theories, can be considered to be the standard tools in lattice dynamics calculations, in addition to the harmonic model. They are only applicable in the case of fairly small amplitude motions. Only the simple harmonic approximation is widely used the calculation of anharmonic corrections is often hard in practice. For detailed descriptions of these methods, we refer the reader to the books and reviews by Maradudin et al. (1968, 1971, 1974), Cochran and Cowley (1967), Barron and Klein (1974), Birman (1974), Wallace (1972), and Cali-fano et al. (1981). 

In a series of impressive publications. Maxwell [65] [66] [67] [68] provided most of the fundamental concepts constituting the statistical theory recognizing that the molecular motion has a random character. When the molecular motion is random, the absolute molecular velocity cannot be described deterministically in accordance with a physical law so a probabilistic (stochastic) model is required. 

Time-resolved optical experiments rely on a short pulse of polarized light from a laser, synchrotron, or flash lamp to photoselect chromophores which have their transition dipoles oriented in the same direction as the polarization of the exciting light. This non-random orientational distribution of excited state transition dipoles will randomize in time due to motions of the polymer chains to which the chromophores are attached. The precise manner in which the oriented distribution randomizes depends upon the detailed character of the molecular motions taking place and is described by the orientation autocorrelation function. This randomization of the orientational distribution can be observed either through time-resolved polarized fluorescence (as in fluorescence anisotropy decay experiments) or through time-resolved polarized absorption. 

The applicability of the Enskog theory for high pressures is explained by the vortical character of the thermal motion of molecules. For molecular motions presented in Fig. 1 the relative motion of two neighboring molecules is only essential. In this case all molecules being on some sphere (circle) interact with their neighbors on the next spheres (circles) identically. So, the conditions for the applicability of two-particle approximation arise. 

In general, if the NMR line has any Lorentzian character to it, the second moment is not an ideal parameter for study because so much of the crucial information is lost in the wings of the spectrum. A line can be considered to be a Gaussian when S /CSg) =3. When such difficulties exist, it may be easier to get the true second and fourth moments from the FID as will be described shortly. For discussions of moments of Lorentzian-like lines, the relationship between the true moment and the measurable moment, and which component of the second moment is affected by molecular motion, see Abragam (Appendix A), Sections IV.II.B, IV.IV.A, X.V.A. 

According to initial findings on batch reactors, both in solution and in the molten state, the role of the reaction time in overall yield of the process was too far to be neglected (39) (Fig. 13.10). In order to check that point and also the role stereospecificity could play in the reaction extension, that is the molecular motion possibilities of the macromolecular coreactant, atactic polypropylene was chosen to be modified by grafting maleic anhydride in the same mode as before for isotactic polypropylene. The influence of the temperature of the process had also to be checked because the atactic polymer could not be processed at the same temperature as the isotactic one due to its nature. Results were fully discussed elsewhere (40). Figure 13.11 exhibits the dynamic and unsteady character of the grafting process. 

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