Relaxation crosslink density

Time-crosslink density superposition. Work of Plazek (6) and Chasset and Thirion (3, 4) on cured rubbers suggests that there is one universal relaxation function in the terminal region, independent of the crosslink density. Their results indicate that the molar mass between crosslinks might be considered as a reducing variable. However, these findings were obtained from compliance measurements on natural rubber vulcanizates,... 

Where p defines the shape of the hole energy spectrum. The relaxation time x in Equation 3 is treated as a function of temperature, nonequilibrium glassy state (5), crosslink density and applied stresses instead of as an experimental constant in the Kohlrausch-Williams-Watts function. The macroscopic (global) relaxation time x is related to that of the local state (A) by x = x = i a which results in (11)... 

In the case of crosslinked polymers, the global relaxation time X has to be generalized by including a shift factor for the crosslink density (av)... 

Figure 5. Shear relaxation modulus of NR as a function of crosslink density at 25°C.

The above models describe a simplified situation of stationary fixed chain ends. On the other hand, the characteristic rearrangement times of the chain carrying functional groups are smaller than the duration of the chemical reaction. Actually, in the rubbery state the network sites are characterized by a low but finite molecular mobility, i.e. R in Eq. (20) and, hence, the effective bimolecular rate constant is a function of the relaxation time of the network sites. On the other hand, the movement of the free chain end is limited and depends on the crosslinking density 82 84). An approach to the solution of this problem has been outlined elsewhere by use of computer-assisted modelling 851 Analytical estimation of the diffusion factor contribution to the reaction rate constant of the functional groups indicates that K 1/x, where t is the characteristic diffusion time of the terminal functional groups 86. ... 

To approach this problem from our theory, we extend our Feh Eq. (3.6), to the case in which the crosslink density is weakly inhomogeneous as v(jc0) = v0 + <5v(jt0) P3]. The correlation of the deviation <5v(jc0) s short-ranged in the relaxed state as... 

Reaction-induced phase separation is certainly also the reason for which an inhomogeneous structure is observed for photocured polyurethane acrylate networks based on polypropylene oxide (Barbeau et al., 1999). TEM analysis demonstrates the presence of inhomogeneities on the length scale of 10-200 nm, mostly constituted by clusters of small hard units (the diacrylated diisocyanate) connected by polyacrylate chains. In addition, a suborganization of the reacted diisocyanate hard segments inside the polyurethane acrylate matrix is revealed by SAXS measurements. Post-reaction increases the crosslink density inside the hard domains. The bimodal shape of the dynamic mechanical relaxation spectra corroborates the presence of a two-phase structure. 

Unrelaxed and relaxed moduli for each transition. Let us recall that, generally, the ratio E (unrelaxed)/ E (relaxed) is higher than 10 for the a transition (it is a decreasing function of the crosslink density), whereas it is generally lower than 2 for secondary transitions where it does not depend directly on crosslink density but rather on the mechanical activity of the corresponding molecular motions. 

Crosslink density directly affects E0 (through rubber elasticity), and has an indirect influence on E (through the antiplasticization effect). Cole-Cole plots open the way to analyzing the distribution of relaxation times (the exponents a and y or % or % are linked to the width of the distribution of relaxation times). According to the results of Table 11.3, these exponents seem to depend more on the molecular-scale structure (they vary almost... 

Results presented in Fig. 13.8 could have been interpreted as an effect of crosslink density on toughening. But this is an incorrect concept, because crosslink density can be increased by the use of a low-molar-mass aliphatic diepoxide. This would decrease the matrix Tg and increase its toughenabil-ity, in spite of the increase in crosslink density. But also, it may be stated that at the same Tg — T, other factors related to the chemical structure, such as sub-Tg relaxations, will play a role on toughening mechanisms. 

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. 

The relative contribution of each of these types of network junctions to the overall crosslink density in silica-filled PDMS was estimated by means of T2 relaxation experiments [113, 118-121], To determine the relative contributions of the different types of network... 

The time it takes for the temperature of a sample to stabilise in an NMR probe can also be determined in real-time XH NMR Tj relaxation experiments, because at vulcanisation temperatures Tj is only slightly affected by a moderate crosslink density [22, 180, 181]. The T2 data obtained in the aforementioned experiments were used for determining an increase in the density of chemical crosslinks upon vulcanisation time (Figure 10.18) [179]. The method can also be used in kinetic studies of the vulcanisation of filled and oil-extended rubbers. 

A major focus of this chapter is the effect of network formation and network density on the relaxation times of the H and 13C nuclei in the NMR experiment. The changes in relaxation times can be exploited to obtain information about crosslink density and chain motion, and must be taken into account in the design of experiments to determine changes in chemical structure. In this section we examine how crosslinking changes the transverse (T2) relaxation times of nuclei, and how this information can be of use. Two different approaches have been taken in the literature, namely changes in T2 can be used to estimate crosslink density, or used to develop and verify models of chain motion. 

Measurement of Crosslink Density from Transverse Relaxation Decays... 

The fractions of protons decaying according to relaxation functions Rx and R2 are given by fj and f2. In molten polymers this relationship has long been exploited to provide a measure of the crosslink density in many polymer systems [64-83]. The form of the decay functions has been the subject of much discussion, however, it is often observed that Rj and R2 can be approximated by simple exponential decay functions. It is generally accepted that the protons with short relaxation times are those directly attached to or adjacent to crosslink points. As an example Figure 13.4 shows the decays of transverse... 

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