Polyethylene characteristic ratio

The molecule is either fully flexible or semi-flexible. The fully flexible chains are generally harder to crystallize than semi-flexible chains [35]. In the latter part of the paper (Sect. 5), where we discuss crystallization from the melt, we consider a semi-flexible chain, the flexibility of which is adjusted to reproduce the characteristic ratio of real polyethylene. We there make the... 

Table 2.1 illustrates the magnitudes of the characteristic ratio found for typical polymers in dilute solution. The relatively simple polyethylene oxide), (PEO), chain is fairly flexible whereas the cellulosic chain has... 

A further expansion of the average dimensions of the coil results when one assumes that rotation around single bonds is not free but is still independent of the rotation around the adjacent bonds. Let us take as an example a polyethylene chain On the base of each of the two cones of formula 70, three positions are identified, T, G", and G, differently populated according to the energy difference E = Eq — Ej and the temperature. The characteristic ratio is then written ... 

Expansion is considered for finite, regular polyethylene stars perturbed by the excluded volume effect. An RIS model is used for the chain statistics. The number of bonds in each branch ranges up to 10 240, and the functionality of the branch point ranges up to 20. The form of the calculation employed here provides a lower bound for the expansion. If the number, n, of bonds in the polymers is heid constant, expansion is found to decrease with increasing branch point functionality. Two factors dictate the manner in which finite stars approach the limiting behavior expected for very large stars, These two factors are the chain length dependence at small n of the characteristic ratio and of fa -a3) / n1/2. 

The characteristic ratio, C, is evaluated by RIS theory for polyethylene chains that contain randomly placed short branches. The size of the short branches ranges from methyl to octyl. Calculations are restricted to chains with few branches, where C is nearly a linear function of branch content. The calculations provide numerical values for (3 In C / d Pb)0, where P/, is the probability that a repeat unit has a short branch and zero as a subscript denotes the initial slope. 

Figure 2. Generalized characteristic ratio C q) plotted vs. qjn for three typical polymers polyethylene (PE) at 400 K [11, 21], atactic polystyrene (PS) at 300 K. [14], and poly(dimethyl-siloxane) (PDMS) at 350 K [15],...

The numerical value of Flory s characteristic ratio depends on the local stiffness of the polymer chain with typical numbers of 7-9 for many flexible polymers. The values of the characteristic ratios of some common polymers are listed in Table 2.1. There is a tendency for polymers with bulkier side groups to have higher C c, owing to the side groups sterically hindering bond rotation (as in polystyrene), but there are many exceptions to this general tendency (such as polyethylene). 

Fig. 6.12 Plot of melting temperature against characteristic ratio for indicated polymers. (1) Polyethylene (2) i-poly(propylene) (3) i-poly(isopropyl acrylate) (4) s-poly(isopropyl acrylate) (5) i-poly(methyl methacrylate) (6) s-poly(methyl methacrylate) (7) poly(dimethyl siloxane) (8) poly(diethyl siloxane) (9) poly(dipropyl siloxane) (10) poly(cis-l,4-isoprene) (11) poly(trans-l,4-isoprene) (12) poly(cis-1,4-butadiene) (13) poly(trans-1,4-butadiene) (14) poly(caprolactone) (15) poly(propiolactone) (16) poly(pivalolactone) (17) poly(oxymethylene) (18) poly(ethylene oxide) (19) poly(trimethylene oxide) (20) poly(tetramethylene oxide) (21) poly(hexamethylene oxide) (22) poly(decamethylene oxide) (23) poly(hexamethylene adipamide) (24) poly(caprolaetam) (25) poly(ethylene terephthalate) (26) poly(ethylene sulfide) (27) poly(tetrafluoroethylene) (28) i-poly(styrene) (29) poly(acrylonitrile) (30) poly(l,3-dioxolane) (31) poly(l,3-dioxopane) (32) poly(l,3-dioxocane) (33) bisphenol A-poly(carbonate).

Fig. 5. Characteristic ratio of ethyl branched polyethylenes as a function of 1-butene content SoUd symbols are RIS values for statistic weights t = 0 ( ) and 0.43 ( ). Open symbols represent various experimental values from sources listed in [161]. Reprinted with permission from Macromolecules, 24 6205 (1991). Copyright 1991 American Chemical Society...

Swell Ratio Parameter for Prediction of Chemically Crosslinked Low Density Polyethylene Foam Expansion Characteristics... 

Characteristics of the Graft Polymerization Process. Under certain polymerization conditions such as when the vinyl chloride/polyethylene ratio is high, heterogeneous products are obtained in the sense that, beside the polyethylene grains gorged with PVC, independent suspension PVC particles are formed. Since the optimum conditions for production of PVC and graft copolymers are not necessarily identical, it is advantageous to avoid the formation of these independent PVC particles. 

Catalysts and catalytic supports are often formulated from aluminas owing to their low cost, and their thermal, chemical and mechanical stability [27], To this end, nonionic surfactant templating with polyethylene oxide surfactants was used to synthesize mesoporous alumina [28], Partially ordered mesoporous materials with wormhole channels were obtained - this seems to be a characteristic of templating with nonionic surfactants. Cationic surfactants have recently been found to template mesoporous aluminum oxide with pore sizes that could be fine-tuned by varying the molar ratio of the reactants [29]. The material obtained was thermally stable to 900 °C and exhibited a narrow pore size distribution. 

First, the rate of shear, which is not linear with the shearing stress due to the non-Newtonian behaviour, varies with the different types of polymer. The processability of different polymers with an equal value of the MI may therefore differ widely. An illustration of this behaviour is given in Fig. 15.14. Furthermore the standard temperature (190 °C) was chosen for polyethylenes for other thermoplastics it is often less suitable. Finally, the deformation of the polymer melt under the given stress is also dependent on time, and in the measurements of the melt index no corrections are allowed for entrance and exit abnormalities in the flow behaviour. The corrections would be expected to vary for polymers of different flow characteristics. The length-diameter ratio of the melt indexer is too small to obtain a uniform flow pattern. 

---