Segmental orientation correlation

An important property of the self-avoiding chain is that the segment orientational correlation function decays at large distances not exponentially, like in ideal chain (eqn [7]), but as a power-law function ... 

At the same time, the segment rotational motions also become severely limited. Steric collisions of the chain with the neighbours cause, at first, departure of the segment orientation correlation function from a single exponential decay function characteristic of a free chain, and on further increase of concentration the segment dynamics change completely. 

Thus about 5% of the volume is occupied by bundle-like regions. More generally, one could say that about 5% of all polymer segments are correlated in orientation. This seems a plausible result, although the length of the correlated region, L, of about 10000 A is perhaps rather... 

As a first approximation we postulate the existence of an equally sized hard core volume located in the center of each cylinder that defines the excluded volume per segment, according to the degree of interpenetration of neighboring cylinders. This simple construction includes complicated local intersegmental configurations, but it imposes a unique local orientation correlation of segments within the domains of a PE melt The shape of those impenetrable correlation cylinders is assumed also to be cylindrical. 

B. Amram, L. Bokobza, P. Sergot, and L. Monnerie, Effect of temperature on intermolecular orientational correlations between chain segments in strained poly-isoprene A Fourier transform infrared dichroism investigation, Macromolecules, 23, 1212 (1990). 

There are two major theoretical approaches to the understanding of orientational ordering of extended chain polymers one is a model wherein rod-shaped particles are confined to a lattice under the restriction that segments may not overlap with one another the other utilizes a virial expansion that accounts for mutual orientational correlations and interactions of pairs, triplets, etc. of elongated particles at varied concentrations. 

The evolution of the experimental anisotropy as a function of the temperature is shown in Fig. 8. As expected, the decay rate increases as the temperature increases. For the highest temperature (t > 50 °C), it can be noticed that the anisotropy decays from a value close to the fundamental anisotropy of DMA to almost zero in the time window of the experiment (about 60 ns). This means that the initial orientation of a backbone segment is almost completely lost within this time. This possibiUty to directly check the amplitude of motions associated with the involved relaxation is a very useful advantage of FAD. In particular, it indicates that in the temperature range 50 °C 80 °C, we sample continuously and almost completely the elementary brownian motion in polymer melts. Processes too fast to be observed by this technique involve only very small angles of rotation and cannot be associated with backbone rearrangements. On the other hand, the processes too slow to be sampled concern only a very low residual orientational correlation, i.e. they are important only on a scale much larger than the size of conformational jumps. 

To summarize, it must be assumed that amorphous PC does not exhibit strong intermolecular spatial and orientational correlations between chain segments. This result is consistent with the fact that PC chains are highly entangled (see Sect. 4.2). It is believed that, up to the present time, insufficient experimental evidence has been provided to prove the existence of some sort of molecular organization in glassy poly-... 

Equation 2.9 indicates that the orientation correlation of the tangents at contour points 5 and s diminishes exponentially with the contour length As = s — s l between the two points, and the decay is more rapid for smaller q, i.e., for more flexible chains. Thus, in a Gaussian chain (q = 0), there exists no correlation between the orientations of any paired segments. On the other hand, in a rod chain, the reverse is the case as can be intuitively understood. 

One of the features of a free flexible polymer is that any pair of its segments virtually have no orientation correlation unless they are situated very close on the chain. Its segments thus tend to wriggle almost isotropically. In order to have a flexible chain reptate, this tendency of the segments has to be suppressed so that all the segments displace along a curve at the same speed. A nmve... 

With polymers, as well as with liquids of non-s Aerical molecules, the extent of short range order present is demonstrated more clearly by the degree of spatial orientational correlation exhibited among neighboring segments, subchains, or molecules. We characterize [2] the spatial orientation correlation by means of... 

It is noted that a similar approach carried out for polyethytene leads to an activation energy of 13.6 0.4 kJ/mol, for the relaxation of short (6-8 bonds) chain segments, regardless of the constraints imposed by chain connectivity [105]. This is in good agreement with the value 13.8kJ ol obtained by Brownian dynamics simulations of PE chains, and with NMR measurements of perfluoroalkane chains by Matsuo and Stodonayer, in which the mean orientational correlation times for C-F and C-H bends are found to have equal activation energies of about 12 kJ/mol. The barrier for internal rotation about typical CH2-CH2 bonds is slightly over 12 kJ/mol, from spectroscopic data and conformational analysis [3,106,107]. This value is exactly reproduced in the present theoretical treatment... 

Polymer chain segment orientation angle Correlation time... 

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