Polymer dynamics chain modes

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

As indicated by Eqs. (3.41) and (3.55), the molecular translational motion and the internal modes of motion of a Rouse chain ultimately depend on the diffusion constant of each individual Rouse bead, D = kT/ The diffusion of a Brownian particle (Eq. (3.3)) can be simulated by the random walk model as shown in Appendix 3.D, which in turn can be used to introduce the diffusion process into different discrete-time models of polymer dynamics (Chapters 8 and 16-18). 

In the previous chapter, we discussed the dynamics of a polymer in a fixed network. We shall now discuss the polymer dynamics in concentrated solutions and melts. In these systems, though aU polymers are moving simultaneously it can be argu that the reptation picture will also hold. Consider the motion of a certain test polymer arbitrarily chosen in melts. If the test polymer moves perpendicularly to its own contour, it drags many other chains surrounother hand the movement of the test polymer along its contour will be much easier. It will be thus plausible to assume that the polymer is confined in a tube-like region, and the major mode of the dynamics is reptation. 

Figure 3-15. Example of a dynamical situation of a polyme ylene chain -(CH2)n- which contains defects consisting of CDt groups and of CH3 units at either ends. The motion of CD2 rocking occurs in a gap and does not couple with the host lattice, thus generating localized modes on the contrary the frequencies of both external deformation and umbrella motions of the CH3 group occur in the frequency range spanned by the dispersion curves of the host lattice coupling takes place and resonance modes are generated.

All in all, the Rouse model provides a reasonable description of polymer dynamics when the hydrodynamic interactions, excluded volume effects and entanglement effects can be neglected a classical example of its applicability is short-chain polymer melts. Since the Rouse model is exactly solvable for polymer chains, it represents a basic reference frame for comparison with more involved models of polymer dynamics. In particular, the decouphng of the dynamics of the Rouse chain into a set of independently relaxing normal modes is fundamental and plays an important role in other cases, such as more complex objects of study, or in other models, such as the Zimm model. 

The dielectric (e" and M") spectra and the relaxation frequencies of the p relaxation are similar to the mechanical spectra (J" and E", respectively) and the corresponding relaxation rate over a wide temperatures range (Muzeau et al. 1991 Perez et al. 1999). These observations suggest that the underlying mechanisms for the local electrical and mechanical relaxation processes in PMMA are similar. Clearly, this is not always the case for polymers, since all modes of motion of a polymer chain are not dielectrically active. When rotational diffusion occurs about a variety of different axes among which only a few reorient a dipole, the shape of the relaxation and the average rates of relaxation in a dielectric measurement may and will differ from those in a mechanical test. Dielectric, dynamic mechanical, and DSC glass transition... 

In this chapter, we have used broadband dielectric spectroscopy (BDS) and rheology to study properties of linear polymers. We have focused our study on the large chain dynamics (normal mode), described by the reptational tube theory and the Rouse model when the polymer is entangled or not, respectively. 

Below we will discuss numerous NMR relaxometry applications to polymers. The information on the type of segment-internal fluctuations, chain modes or center-of-mass displacements is contained in the autocorrelation functions in the time domain or, equivalently, in the spectral density in the frequency domain according to Eq. 29. In order to probe characteristic features of polymer dynamics it is therefore of interest to measure the frequen-... 

Before deepening the discussion of the experimental features of component B referring to the chain-mode regime, we will first consider a series of semiempirical studies corroborating the existence of the three dynamic components and other polymer characteristics one has to keep in mind when interpreting experimental polymer data. Such general characteristics can favorably be elucidated with the aid of transverse relaxation. 

The range of motions available to a polymer spans the high-frequency secondary relaxations, involving motion of pendant groups, to the slow so-called chain modes, which reflect motion over large (>10 nm) distances. The slowest relaxation process is the terminal mode, corresponding to motion of the entire molecule. These dynamics can be illustrated with an example, poly(vinylethylene) (PVE), an elastomer also known as 1, 2-polybutadiene. 

Most properties of linear polymers are controlled by two different factors. The chemical constitution of tire monomers detennines tire interaction strengtli between tire chains, tire interactions of tire polymer witli host molecules or witli interfaces. The monomer stmcture also detennines tire possible local confonnations of tire polymer chain. This relationship between the molecular stmcture and any interaction witli surrounding molecules is similar to tliat found for low-molecular-weight compounds. The second important parameter tliat controls polymer properties is tire molecular weight. Contrary to tire situation for low-molecular-weight compounds, it plays a fimdamental role in polymer behaviour. It detennines tire slow-mode dynamics and tire viscosity of polymers in solutions and in tire melt. These properties are of utmost importance in polymer rheology and condition tlieir processability. The mechanical properties, solubility and miscibility of different polymers also depend on tlieir molecular weights. 

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