Network structure relaxation

From a practical point of view, it is advantageous that critical gel properties depend on molecular parameters. It allows us to prepare materials near the gel point with a wide range of properties for applications such as adhesives, absorbents, vibration dampers, sealants, membranes, and others. By proper molecular design, it will be possible to tailor network structures, relaxation character, and the stiffness of gels to one s requirements. 

As measurements show ( I anaka et al.. 1973), the relaxation time of the density of a PA.A netw ork is r = (l)q ) with D as 10 cm /s while that of the thermal diffusion of water is r-y = ([)-jq ) with Dp 1.1 10 cm s, whence it follows that thermal diffiisioM is faster than polymer network structure relaxation. Consequently, in the time scale characteristic for tlie fluctuations in polymer network structure, temperature can be regarded cunslant and the process is isothermal (not adiabatic, as in the case of. Mandelshtam-Krillouiii s scattering). 

Measurement of the equilibrium properties near the LST is difficult because long relaxation times make it impossible to reach equilibrium flow conditions without disruption of the network structure. The fact that some of those properties diverge (e.g. zero-shear viscosity or equilibrium compliance) or equal zero (equilibrium modulus) complicates their determination even more. More promising are time-cure superposition techniques [15] which determine the exponents from the entire relaxation spectrum and not only from the diverging longest mode. 

The reduction in stress which takes place in a test strip of rubber held at constant elongation. Stress relaxation measurements are used in the study of the ageing of rubber vulcanisates, the degradation of the network structure resulting in a reduction of the tension. 

Stress decay (relaxation) measurements of propellant binders are a way to obtain insight into the network structure of binder systems (29). In addition, high hysteretical losses appear to be associated with good tensile properties. Figure 5 shows a normalized stress-decay vs. time plot of a polyurethane elastomer. If the reference stress, [Pg.105]

As regards the dynamics of the fluid composition, the experimental results are very difficult to understand [66,67]. We expect that, if the pore size b is very large, the diffusion constant should first behave as in bulk near-critical fluids, but it will cross over to a value of order kBTZb/Gntis 2, being the correlation length (see Eq. (6.67) below). It would also be interesting to find whether the time correlation function of c would be influenced by structural relaxation of network (see Sect 6.2). 

The plateau region appears when the molecular weight exceeds Mc [(Mc)soln. for solutions], and is taken to be a direct indication of chain entanglement. Indeed the presence of a plateau may be a more reliable criterion than r 0 vs M behavior, especially in solutions of moderate concentration where viscosity may exhibit quite complex concentration and molecular weight behavior. It is postulated that when M greatly exceeds Mc, a temporary network structure exists due to rope-like interlooping of the chains. Rubber-like response to rapid deformations is obtained because the strands between coupling points can adjust rapidly, while considerably more time is required for entire molecules to slip around one another s contours and allow flow or the completion of stress relaxation. 

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. 

In the case under consideration different physical structures were realized due to the formation of the polymer network in the surface layers the filler surface, as usually happens in filled systems. As is known79, this induces considerable changes in the structure of the material. It is also possible that in these conditions a more defective network structure is formed. These results show that even the purely physical factors influencing the formation of the polymer network in the interface lead to such changes in the relaxation behavior and fractional free-volume that they cannot be described within the framework of the concept of the iso-free-volume state. It is of great importance that such a model has been devised for a polymer system that is heterogeneous yet chemically identical. 

The analytical techniques discussed previously can be used to study the EPDM network as such or its formation in time as well as to determine relationships between the network structure and the properties of the vulcanisates. In a preliminary approach some typical vulcanised EPDM properties, i.e., hardness, tensile strength, elongation at break and tear strength, have been plotted as a function of chemical crosslink density (Figure 6.6). The latter is either determined directly via 1H NMR relaxation time measurements or calculated from the FT-Raman ENB conversion (Table 6.3). It is concluded that for these unfilled, sulfur-vulcanised, amorphous EPDM, the chemical crosslink density is the main parameter determining the vulcanisate properties. It is beyond the purpose of this review to discuss these relationships in a more detailed and theoretical way. 

Cross-link density and parameters relating to the network structure can be measured by NMR by analysis of the transverse relaxation decay (cf. Section 1.3) and the longitudinal relaxation in the rotating frame [67]. Combined with spatial resolution, the model-based analysis of relaxation yields maps of cross-link density and related parameters [68]. Often the statistical distribution of relaxation parameters over all pixels provides a reduced data set with sufficient information for sample characterization and discrimination [68]. 

The use of solid-state NMR magnetisation relaxation experiments to characterise network structures in various rubbery materials is reviewed in this chapter. Comprehensive reviews of high-resolution NMR techniques can be found elsewhere [21-23, 30-35]. 

Network Structure Analysis by Means of NMR Transverse Magnetisation Relaxation... 

Solid-state NMR magnetisation relaxation experiments provide a good method for the analysis of network structures. In the past two decades considerable progress has been made in the field of elastomer characterisation using transverse or spin-spin (T2) relaxation data [36-42]. The principle of the use of such relaxation experiments is based on the high sensitivity of the relaxation process to chain dynamics involving large spatial-scale chain motion in elastomers at temperatures well above the Tg and in swollen networks. Since chain motion is closely coupled to elastomer structure, chemical information can also be obtained in this way. 

The results of the T2 relaxation studies prove that this method is a very useful technique for the quantitative characterisation of network structures, while the more sophisticated NMR techniques, which also determine the residual dipole-dipole interactions [31, 53-60], provide specific information for the chemical structure and molecular mobility, which may be useful in determining mechanisms of molecular motions and refining interpretations of the non-selective T2 relaxation method, especially for composite materials. 

Network structures have been quantitatively determined by means of real-time XH NMR T2 relaxation experiments for several polymers [174-178]. The effect of the curing conditions on sol and gel fractions and the spatial heterogeneity of the network structure has been studied for polyethylene [174], polyacrylamide [175], PDMS [176], BR [177], epoxy resins [178] and EPDM [179]. 

Network structure analysis is discussed in Chapters 7, 8,10 and 13. These chapters deal with the characterisation of the structure of chemical and physical networks, rubber-filler physical network, network defects and its heterogeneity using NMR relaxation techniques and NMR imaging. 

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