Short chain relaxations

PVF displays several transitions below the melting temperature. The measured transition temperatures vary with the technique used for measurement. T (L) (lower) occurs at —15 to —20 " C and is ascribed to relaxation free from restraint by crystallites. T (U) (upper) is in the 40 to 50°C range and is associated with amorphous regions under restraint by crystallites (63). Another transition at —80° C has been ascribed to short-chain amorphous relaxation and one at 150°C associated with premelting intracrystalline relaxation. 

Under these conditions, Eq. (32) indicates the maximum extent to which a particular mode p can reduce S(Q,t) as a function of the momentum transfer Q. Figure 10 presents the Q-dependence of the mode contributions for PE of molecular weights Mw = 2000 and Mw = 4800 used in the experiments to be described later. Vertical lines mark the experimentally examined momentum transfers. Let us begin with the short chain. For the smaller Q the internal modes do not influence the dynamic structure factor. There, only the translational diffusion is observed. With increasing Q, the first mode begins to play a role. If Q is further increased, higher relaxation modes also begin to influence the... 

Fig. 3.2 Development of Schain(Q>0 for different times (a) and the normalized relaxation function 5chain(Q>0/ chain(Q) ( ) for QRg=l, 2,... 6. The dashed lines contain only the intrachain relaxation whereas the solid lines include the centre-of-mass diffusion. Note that for short chains and for small Q the diffusion dominates the observed dynamics (Reprinted with permission from [40]. Copyright 2003 Springer, Berlin Heidelberg New York)...

Recently a very detailed study on the single chain dynamic structure factor of short chain PIB (M =3870) melts was undertaken with the aim to identify the leading effects limiting the applicability of the Rouse model toward short length scales [217]. This study was later followed by experiments on PDMS (M =6460), a polymer that has very low rotational barriers [219]. Finally, in order to access directly the intrachain relaxation mechanism experiments comparing PDMS and PIB in solution were also carried out [186]. The structural parameters for both chains were virtually identical, Rg=19.2 (21.3 A). Also their characteristic ratios C =6.73 (6.19) are very similar, i.e. the polymers have nearly equal contour length L and identical persistence lengths, thus their conformation are the same. The rotational barriers on the other hand are 3-3.5 kcal/mol for PIB and about 0.1 kcal/mol for PDMS. We first describe in some detail the study on the PIB melt compared with the PDMS melt and then discuss the results. 

In the low Q-regime RPA describes well the static structure factor for the short chain melt, where the ODT is sufficiently far away (kN 7). In the dynamics we would expect the diblock breathing mode to take over around QRg 2 (Q=0.04 A ). Instead, deviations from Rouse dynamics are already observed at Q values as high as QR =5. At QJ g=3 a crossover to a virtually Q-independent relaxation rate about four to five times faster than the predicted breathing mode is found. This phenomenon is only visible under h-d labelUng. Under single chain contrast (see below) these deviations from RPA are not seen. Thus, the observed fast relaxation mode must be associated with the block contrast. 

Furthermore, it may be seen that for all the normal modes of relaxation, including the most rapid, the freely jointed chain model and the Rouse model are identical if we set n = N + 1 that is, the relaxation time xp of the pth normal mode of a freely-jointed chain is the same as that of a Rouse marcromolecule composed of N + 1 subchains, each of mean square end-to-end length b2. Moreover, for the special choice a = 0, Eq. (10) is true for arbitrarily large departures from equilibrium. We thus seem to have confirmed analytically the discovery of Verdier24 that quite short chains executing a stochastic process described by Eqs. (1) and (3) on a simple cubic lattice display Rouse relaxation behavior. Of course, Verdier s Monte Carlo technique permits study of excluded volume effects, quite beyond the range of our present efforts. 

The type of molecular information that can be obtained from measurements of the fast relaxation time is illustrated in Table 5.1 where data for a series of sodium alkylsulfates are presented. One can see that for micelles of short-chain surfactants,... 

Relaxation of long and short chains in binary blends. 

The first relaxation process (designated A hereafter) corresponds to a Rouse-like relaxation of chain segments between entanglement points. It is assumed that the entanglement points remain fixed during the time-scale of this relaxation and that no diffusion of monomers through the slip-links is allowed in such short times. The associated relaxation time,, is related to a monomeric friction coefficient, to thie number of monomers between... 

In order to test whether the chain ends or the central part are responsible for this behaviour, the orientation of both blocks has been compared to that of linear chains. The relaxation of chains ends in the star polymer and in copol5uners PS DH 184 and PS DHD 500 is compared in Figure 11. The short time orientation is similar for the 3 materials, but the end of an arm relaxes slower than that of the PS DHD 500 copolymer although the involved length is... 

Binary blends composed of deuterated short chains and of entangled hydrogenated long polyst3Tene chains have been investigated. The relaxational behaviour of the short chains has been analysed as a function of their molecular weight. Additionally, attention has been focussed on the role of the short chain concentration on the orientational relaxation of the long chains. 

The short chains with MRouse chains with relaxation times on the order of the experimental time-scale. For example, the Rouse times of PSD3 and of PSDIO are approximately 9s and 19s seconds, respectively at 115°C [35,36]. Consequently, the residual orientation at long times for these chains can be attributed to orientational coupling interactions with the long chains of the polymer matrix. Similar orientational correlations have been observed on various systems by NMR spectroscopy studies of stretched elastomers where even dissolved solvent molecules and free chains were shown to possess a very short-length scale local orientation [37]. 

The cooperative nature of the orientational relaxation in asymmetric binary blends has been further investigated through the analysis of the effect of the short chain concentration, for a given short chain length, Mw = 10 000. 

Master curves of the orientational relaxation of the long chains are presented in Figure 18. The long chain relaxation in the pure polymer is compared to that in the blends which contain increasing concentrations of short chains. 

One convenient strategy to interpret these results is to review the molecular characteristics of binary blends as extracted from polymer melt rheology [40]. The influence of short chains (M < Me) is to effectively decrease the plateau modulus and the terminal relaxation times as compared to the pure polymer. Consequently, the molecular weight between entanglements... 

Infrared dichroism has been successfully applied to characterize the orientational relaxation of linear and branched polyst3rrene chains as well as binary blends of long and short chains. By deuterating some chains or parts of chains, infrared spectroscopy provides a method of analyzing the orientational behaviour of the different species and consequently probe the molecular relaxation mechanisms. 

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