Homopolymer melts

PRISM (polymer reference interaction-site model) method for modeling homopolymer melts... 

In a somewhat wider sense, one can define amphiphiles as molecules in which chemically very different units are linked together. For example, the structures formed by A B block copolymers in demixed A and/or B homopolymer melts and their phase behavior are very similar to those of classical amphiphiles in water and/or oil [13,14]. Copolymers are used not only to disperse immiscible homopolymer phases in one another, but also to create new, mesoscopically structured materials with unusual and interesting properties [15]. 

Rouse behavior observed on PI homopolymer melts has to be modified if the labelled (protonated) PI species are replaced by diblock copolymers of proto-nated PI and deuterated polystyrene (PS) [46]. The characteristic frequency Q(Q) is slowed down considerably due to the presence of the non-vanishing X-parameter. Thus, the reduction is stronger at smaller Q-values or at larger length scales than in the opposite case. In addition, as a minor effect, Q(Q) becomes dependent on both friction coefficients per mean square monomer length, //2, valid for PI and for PS. 

Again, at high Q the RPA predicts that the dynamics of arm A is identical to the Rouse motion of an A polymer in an A homopolymer melt. At low Q, Ai(Q) turns into a breathing mode with a non-vanishing relaxation rate at Q=0, as the collective mode A3(Q). 

Block copolymers of this composition are completely amorphous when isolated in the usual manner, by adding the polymer solution to a large volume of methanol or other antisolvent. They show a single Tg = 226°C. The T/s of the two homopolymers are too close (225° for DMP (17) and 230°C for DPP (11)) to permit the observation of separate transitions for the DMP and DPP portions of the blocks. The DPP portion of the block crystallizes when heated to approximately 290°C, as does the DPP homopolymer. Melting of the crystalline DPP, which occurs at 480°C in the homopolymer, could not be observed in the copolymer because of the onset of decomposition at approximately 450°C. 

In Figure 10.13 the Raman signals have been scaled by a single factor C that adjusts them to lie on top of the birefringence measurements. It is observed that the C-C bond dynamics follow the birefringence response, which is not surprising for a homopolymer melt. 

Acetal resins are those homopolymers (melting point ca. 175°C, density ca. 1.41) and copolymers (melting point ca. 165°C, density ca. 1.42) where the backbone or main structural chain is completely or essentially composed of repeating oxymethylene units (-CH20-)n. The polymers are derived chiefly from formaldehyde (methanal, CH2=0), either directly or through its cyclic trimer, trioxane or 1,3,5-trioxacyclohexane. 

The PRISM approach for modeling homopolymer melts, based on the pioneering work of Curro and Schweizer,ii -i 9 g continuous space, liquid state methodology suited for the study of equilibrium properties of polymer chains. The technique is based on integral equation methods that have been generalized to deal with macromolecules. 

Various approaches may be taken to study the packing of chains in a homopolymer melt using PRISM. The degree of coarse graining allows the study of various phenomena, from long-range universal aspects to quantitative comparisons with experiment where detailed chemical structure is important. 

PAN homopolymer melts at approximately 320 °C whereby melting refers to the endothermic breaking up of the highly ordered crystalline regions. The high melting point has been related to molecular stiffness (cf. Sect. 2.1). 

Fig. 15. Approximate mapping of a chemically realistic polymer (polyethylene in this example) to the bond fluctuation model on the (simple cubic) lattice. In this coarse-graining one integrates n successive chemical monomers (e.g. n = 3) into one effective monomer which blocks 8 adjacent sites on the simple cubic lattice (or 4 on the square lattice in d = 2 dimensions) from occupation by other monomers. The chemical bonds 1, 2, 3 then correspond to effective bond I, bonds 4, 5, 6 to effective bond II. Some information on the chemical structure can be kept indirectly by using suitable distributions P (9) for the angle between subsequent effective bonds, but so far this has been done for homopolymer melts only [94-99]. In the simplest version of the bond fluctuation model [84-88] studied for blends in d = 3 dimensions [88, 91, 92, 99], bond lengths t are allowed to fluctuate freely from i = 2 to t = v/l0, with t = being excluded to maintain that chains do not cut through each other in the course of the random hops of the effective monomers. From Binder [95]...

As demonstrated before, the shifting involves three shift factors, one horizontal, usually expressed as aj, = b rip(T)/rip(Tp), where b = p T /pT is the hrst vertical shift factor that originates in the thermal expansion of the system (p is density). The subscript o indicates reference conditions, dehned by the selected reference temperature T, usually taken in the middle of the explored T-range. For homopolymer melts, as well as for amorphous resins, the two shift factors, aj, and b.j, are sufficient. However, for semi-crystalline polymers, a second vertical factor, v., has been found necessary — it accounts for variation of the crystallinity content during frequency scans at different temperatures [Ninomiya and Ferry, 1967 Dumoulin, 1988]. 

The linear viscoelastic behavior of the pure polymer and blends has already been described quantitatively by using models of molecular dynamics based on the reptation concept [12]. To describe the rheological behavior of the copolymers in this study, we have selected and extended the analytical approach of Be-nallal et al. [13], who describe the relaxation function G(t) of Hnear homopolymer melts as the sum of four independent relaxation processes [Eq. (1)]. Each term describes the relaxation domains extending from the lowest frequencies (Gc(t)) to the highest frequencies (Ghf( )), and is well defined for homopolymers in Ref [13]. 

The fact that real chains cannot cross over themselves and therefore do interact at distances greater than the Kuhn link length is often called the excluded-volume effect and it leads to an expected increase in the RMS chain length and to a change in the way that it depends on n. Later it will be seen that the effect is not important in changing /"nns or its dependence on n in homopolymer melts or in solids, but the fact that the chains cannot interpenetrate each other nevertheless has important effects on their mechanical properties. 

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