Polymer melts single chain structure factor

The first static property characterizing the system is the pVT behavior, which was already discussed in the last section. Besides this thermodynamic information, an amorphous polymer melt is mainly characterized through two types of structural information the single chain structure factor and the overall structure factor of the melt. 

The standard approximation for the tJi k) has been to invoke the Flory ideality hypothesis. Although this is not on as firm a footing as in the melt case, it is a good first approximation, and is useful because the self-consistent determination of intramolecular and intermolecular correlations is a demanding task in polymer blends. The monomer structure is input to the theory through the single chain structure factors, something which is difficult to do in other liquid state theories. 

Figure 35 Single-chain structure factor from a PEE melt at 473 K. The numbers along the curves represent the experimental 0-values in A. The solid lines are a joint fit with the Rouse model (eqn [61]). From Richter, D. Monkenbusch, M. Arbe, A. etal. Adv. Polym. Sci. 2005, 174,1-221. ...

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. 

The above derivation can also be applied to colloidal or polymer-based liquids and is then used to calculate the so-called form factors of soft matter samples. The major difference between a monoatomic liquid and a polymer chain in the melt or in solution is that the total structure factor consists of two parts. The first is the inter-particle structure factor and the second the intra-particle structure factor. This second part is also often called the particle form factor P(q). Using Eq. (2.38) it is straightforward to calculate P(q) for a given soft matter sample. A good example is the form factor of a single polymer coil in a melt [88, 92]. The pair correlation function of such a coil is given by... 

Another strong point of the simulation approach is its ability to selectively change parts of the model Hamiltonian. In this way one can compare a chemically realistic model of PB with a freely rotating chain version of the same polymer and does not have to switch to a completely different polymer with some of the same properties like is unavoidable in experiments [33]. With this approach we could establish that identical structure on the two-body correlation function level (single chain and liquid structure factors) does not imply identical dynamics which raises questions on the applicability of the mode-coupling theory of the glass transition to polymer melts. 

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