Short linear polymer melts

To test the Rouse prediction that viscosity is proportional to chain length, viscosity data at constant friction coefficient must be used instead of viscosity data at constant temperature. If the coefficient of thermal expansion of the free volume af m Eq. (8.131) were independent of chain 

The simplest way to correct viscosity data to constant friction coefficient is to first fit the temperature dependence of viscosity of each individual sample to the WLF equation [Eq. (8.134)], which determines 5//q. At a given reference temperature, sufficiently long chains have the same 5//o and progressively lower values of 5//o are obtained for shorter chains, since they have more free volume at a given temperature. The viscosity data at the reference temperature can then be corrected to the friction coefficient of the long chains at the reference temperature using Eq. (8.133). Viscosity data subjected to such a correction are shown in Fig. 8.17 for polybutadiene, polyisobutylene and polystyrene, roughly 

120 K above their glass transitions. All linear polymer melts have viscosity proportional to molar mass (ry M) for sufficiently short chains, when the data are determined at a constant friction coefficient as opposed to isothermal data. Longer chains have entanglement effects (discussed in Chapter 9) and have The full chain length dependence of 

Equation (8.136) is tested in Fig. 8.17 (solid curves) and found to describe the molar mass dependence of constant friction coefficient viscosity data for all three of these linear polymers. The critical molar mass Me for entanglement effects in viscosity is always a factor of 2-4 larger than the entanglement molar mass Mg. that was defined in Eq. (7.47). 

As an illustration of the Rouse model, consider the polydisperse mixture of polymers produced by random branching with short chains between branch points. The molar mass distribution and size of the branched polymers in this critical percolation limit were discussed in Section 6.5. Close to the gel point, some very large branched polymers (with M 10 ) are formed and the intuitive expectation is that such large branched polymers would be entangled. However, recall that hyperscaling requires 

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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). 

The zero-shear viscoelastic properties of concentrated polymer solutions or polymer melts are typically defined by two parameters the zero-shear viscosity (f]o) and the zero-shear recovery compliance (/ ). The former is a measure of the dissipation of energy, while the latter is a measure of energy storage. For model polymers, the infiuence of branching is best established for the zero-shear viscosity. When the branch length is short or the concentration of polymer is low (i.e., for solution rheology), it is found that the zero-shear viscosity of the branched polymer is lower than that of the linear. This has been attributed to the smaller mean-square radius of the branched chains and has led to the following relation... 

It was observed that up to about 25% conversion, the polymerization of diallyl o-phthalate is linear with time and initiator concentration. As the process continues, a cross-linked gel forms. The polymer formed up to 25% conversion has a melting point of about 90°C, is soluble, and is less unsaturated than would be expected for a linear polymer. Therefore, it was presumed that the prepolymers consisted of a main chain with a number of short branches [30]. 

In accordance with the conclusion done from the Eq. (9), which determines an average variance of a step of the SARW trajectories for the linear polymeric chain via average probability to discover the occupied cell, it kept true for any polymeric chain into the concentrated solutions and melts, but at this the p value should be additionally depended on the concentration of polymer. Let us show also, that the main Eqs. (25) and (28) for the concentrated solutions are kept in the previous form (for short the term melt will be used as the need arises). 

Such a difference can be ascribed to the presence of dimeric or longer, repeated p-oxybenzoyl units along the chain in the random copolyester, whereas in the ordered sequence copolyester every p-oxybenzoyl unit exists in a monomeric unit connected to the bent 1,6-naphthalenediol moiety on one side resulting in a too short linear segment to render the polymer the ability to form a mesophase in melt. 

The a values (26-28 kJ/mol) reported for 3/MAO-catalyzed copolymers are considered to represent the properties of linear polymers in which only short-chain branching influences the melt behavior [46]. The calculated tjo values are close to the measured values, and the flow activation energy E increases slightly with comonomer incorporation, as expected for a polymer with short-chain branching. 

Phenolic Resins - Phenol-formaldehyde tackifying resins are linear short chain polymers which have limited heat stability, and so may cause discoloration if used in hot melt systems. 

Figure 5.2 Relaxation moduli of three samples of a linear polymer A) an unentangled molten sample, B) an entangled,monodisperse molten sample,C) an entangled, polydisperse molten sample, and D) acrosslinked sample. At short times,all the samples relax first by a glassy mechanism and then by Rouse relaxation involving only very short segments of the chain (log scales). The unentangled melt then flows in the terminal zone.The entangled, monodisperse melt has a plateau modulus followed by terminal relaxation, while in the polydisperse melt the plateau zone of the longest molecules overlaps with the terminal zones of the shorter molecules.

Chemically, rubber is dr-l,4-polyisoprene, a linear polymer, having a molecular weight of a few tens of thousands to almost four million, and a wide molecular-weight distribution. The material collected fi om the rubber tree is a latex containing 30-40% of submicron rubber particles suspended in an aqueous protein solution, and the rubber is separated by coagulation caused by the addition of acid. At room temperature, natural rubber is really an extremely viscous liquid because it has a Tg of —70°C and a crystalline melting point of about —5°C. It is the presence of polymer chain entanglements that prevents flow over short time scales. 

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