Steady Branched polymers

The greater melt viscosities observed for some branched polymers, as compared with linear ones of the same MW, are not accounted for by current theories, as indicated in Section 5. The greater values of the steady state compliance mentioned above is also unexpected theory (128) would suggest a difference in the opposite sense. 

The results shown in Figures 7 and 9 also indicate that the sensors based on the poly(ethylene oxide) and siloxane-ethylene oxide branch polymer systems can operate efficiently at relatively low applied potentials. In fact, the sensors containing these polymers show steady-state glucose responses at a potential of +100 mV (vs. SCE) which are similar to the response of the best poly(siloxane)-based sensor at +300 mV. This is an important consideration because lower operating potentials are often advantageous in real measurements, where easily oxidizable interfering species are usually present. 

Most concentrated structured liquids shown strong viscoelastic effects at small deformations, and their measurement is very useful as a physical probe of the microstructure. However at large deformations such as steady-state flow, the manifestation of viscoelastic effects—even from those systems that show a large linear effects—can be quite different. Polymer melts show strong non-linear viscoelastic effects (see chap. 14), as do concentrated polymer solutions of linear coils, but other liquids ranging from a highly branched polymer such as Carbopol, through to flocculated suspensions, show no overt elastic effects such as normal forces, extrudate swell or an increase in extensional viscosity with extension rate [1]. 

The low-frequency limiting viscoelastic behavior is thus governed by the sums S1 and 82- Values of these, together with 1S2/5 and the first two relaxation time ratios, are given in Table 9-II for several choices of h and other parameters. The greatest differences are seen in the ratio 82/8 to which the steady-state compliance Je is proportional. The table also includes some data for branched polymers which will be discussed in Section 8. 

In Section 3.4 it was explained that polymers having very well defined structures can be prepared by means of anionic polymerization, and this technique has been widely used to prepare samples for rheological study. This has been a particularly fruitful approach to the study of the elfects of various types of long-chain branching structure on rheological behavior. Linear viscoelastic properties are very sensitive to branching. In this section we review what is known about the zero-shear viscosity, steady-state compliance, and storange and loss moduli of model branched polymers. 

For a linear chain or an arm on a branched polymer, there is a least one free end, and retraction occurs rapidly, with a time constant controlled by the Rouse time of the chain. Therefore, for the simplest type of branched polymer, the star, we do not expect the nonlinear properties to be qualitatively different from those of linear polymers. This, indeed, appears to be the case. In step-shearing deformations, the damping function of star polymers [79-81] has been found to be nearly identical to that of linear polymers (shown in Fig. 11.2). Likewise, in steady... 

The other argument which opposes to the previous argument is based on fundamental viscoelastic studies with monodispersed polymers, where the only variable is the long branch, linear versus equal-arm star branch molecule. The steady state compliance of the branched polymer is lower than that of the linear polymer therefore, the steady state memory in the former is less than that in the latter. This means the extrudate swell of the branched polymer is less than that of the linear polymer. 

Biesenberg, J. S. etal., J. Polym. Eng. Sci., 1976,16, 101-116 Polymerisation of methyl methacrylate initiated by oxygen or peroxides proceeds with a steady increase in velocity during a variable induction period, at the end of which a violent 90°C exotherm occurs. This was attributed to an increase in chain branching, and not to a decrease in heat transfer arising from the increasing viscosity [ 1 ]. The parameters were determined in a batch reactor for thermal runaway polymerisation of methyl methacrylate, initiated by azoisobutyronitrile, dibenzoyl peroxide or di-ferf-butyl peroxide [2],... 

Star-shaped polymer molecules with long branches not only increase the viscosity in the molten state and the steady-state compliance, but the star polymers also decrease the rate of stress relaxation (and creep) compared to a linear polymer (169). The decrease in creep and relaxation rate of star-shaped molecules can be due to extra entanglements because of the many long branches, or the effect can be due to the suppression of reptation of the branches. Linear polymers can reptate, but the bulky center of the star and the different directions of the branch chains from the center make reptation difficult. 

It became clear in the early development of the tube model that it provided a means of calculating the response of entangled polymers to large deformations as well as small ones [2]. Some predictions, especially in steady shear flow, lead to strange anomaUes as we shall see, but others met with surprising success. In particular the same step-strain experiment used to determine G(t) directly in shear is straightforward to extend to large shear strains y. In many cases of such experiments on polymer melts both Hnear and branched, monodisperse and polydisperse,the experimental strain-dependent relaxation function G(t,Y) may be written... 

For polymer melts where the low shear rate limiting viscosity value is r ), r 3t]0 (14). Examples of extensional viscosity growth, either to a steady t](i ) value or to a strainhardening-like mode, are shown in Fig. 3.6 for the linear nonbranched polystyrene (PS), a high density polyethylene (HDPE) that is only slightly branched with short branches, and a long chain-branched low density polyethylene (LDPE) (15). 

Kraus has studied the steady flow and dynamic viscosity of the following branched butadiene t) ene block copolymers (88)3, (88)3, (88)4 in comparison with 888 and 888 copolymers. He has found higher viscosities (at constant molecular weight and total styrene content for polymers terminated by styrene blocks) for the former inespective of branchii, but for copolymers of equal molecular weight the viscosity is smaller for branched than for linear copolymer. Kraus has also studied the effect of free polybutadiene molecules on the viscoelastic behaviour of branched (88)4 block copolymers which consist of styrene domains in a butadiene matrix and verified De Gennes s theory of reptation ... 

One of the obvious features of the oxidation of polypropylene is the formation of hydroperoxides (reaction (3) in Scheme 1.55) as a product. The initiation of the oxidation sequence is usually considered to be thermolysis of hydroperoxides formed during synthesis and processing (shown as the bimolecular reaction (1 ) in Scheme 1.55). The kinetics of oxidation in the melt then become those of a branched chain reaction as the number of free radicals in the system continually increases with time (ie the product of the oxidation is also an initiator). Because of the different stabilities of the hydroperoxides (e.g. p-, s- and t- isolated or associated) under the conditions of the oxidation, only a fraction of those formed will be measured in any hydroperoxide analysis of the oxidizing polymer. The kinetic character of the oxidation will change from a linear chain reaction, in which the steady-state approximation applies, to a branched-chain reaction, for which the approximation might not be valid since the rate of formation of free radicals is not... 

Commercial random SBR polymers (solution SBR) prepared by alkyllithium-initiated polymerization typically have 32% cis-, A-, 41% trans-, A-, and 27% vinyl-microstructure compared to 8% cw-1,4-, 74% trans-, A-, and 18% vinyl-microstructure for emulsion SBR with the same comonomer composition [3, 221]. Solution SBRs typically have branched architectures to eliminate cold flow [17, 49]. Compared to emulsion SBR, solution random SBRs require less accelerator and give higher compounded Mooney, lower heat buildup, increased resilience, and better retread abrasion index [3]. Terpolymers of styrene, isoprene, and butadiene (SIBR) have been prepared using a chain of single-stirred reactors whereby the steady-state concentration of each monomer and Lewis base modifier at any degree of conversion could be controlled along the reactor chain [3, 222-224]. 

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