Branching rheological behaviour

Rheological behaviour, viscosity and plasticity under given conditions are affected by the nature of the polymer, the average molecular weight, its distribution, and the molecular structure, branching, stereo-arrangement... 

Accordingly, siloxy-substituted complexes have been found to give polymers with rheological behaviour indicative of long-chain branching [44, 60, 61, 83, 84], but the relations between molar mass, PD and the low shear-rate rheological behaviour are distinctive to each catalyst [83]. 

The extent of LCB and its distribution depends mainly on the catalyst system and the conditions used in the polymerisation. Polymerisation conditions (monomer and comonomer concentration, type of catalyst, temperature and concentration of transfer agents) are important variables to be taken into account when one is looking at the rheological behaviour of the polymers. By decreasing the ethene concentration and increasing the polymerisation time in the reactor the LCB frequency can be enhanced [59, 81]. The polymers made with these catalysts have a complex branching structure composed of comb and tree structures of different lengths. 

We study here the case of a branched polyethylene (LDPE FN 1010), characterized by long chain branching, whose rheological behaviour has been previously described in Chapter II-l. Compared to linear LLDPE, it exhibits strain-hardening in elongational situations and higher values of first normal stress difference. 

The LLDPE material is an ethylene-butene copolymer, containing 4 % of butene. The LDPE polymer is known to involve long ehain branching while LLDPE has a rather low content of branches, which are known to be short. These structures explain why large differences could be expected in their rheological behaviour in shear and elongation and, consequently, in complex flow situations. The molecular characteristics of both samples are given in Section II -1. 

On the other hand, a power law relaxation in rheology cannot be a sure indication for a gelation threshold. Self-similar relaxations has been associated with selfsimilar structures on the molecular and supermolecular level as well as for suspensions and emulsions (Winter and Mours 1997). Similarities between gelation and long-chain branching viscoelastic behaviour have been also discussed (Garcia-Franco et al. 2001). 

The archetypical example of a branched polymer is low density polyethylene (LDPE), the product of radical polymerization at high temperature and pressure. That LDPE is significantly branched was first suspected because of the influences of polymerization conditions upon the crystallinity of the polymer and upon its rheological behaviour in the melt and in solution. Confirmation was provided by IR analysis which indicated a considerable excess of methyl groups ideally, the maximum number of such groups would be two per molecule, corresponding to the end-groups of a linear alkane. 

Romanini, D., Savadori, A., and Gianotti, G., Long chain branching in low density polyethylene. 2. Rheological behaviour of the polymers, Pofymer, 21,1092-1101 (1980). 

High molar mass epoxy prepolymers containing rabber dispersions based on carboxyl-terminated butadiene-acrylonitrile copolymer were prepared from initially miscible solution of low molar mass epoxy prepolymers, bisphenol A and carboxyl-terminated NBR. During chain extension inside a twin screw extruder due to epoxy-phenoxy and epoxy-carboxy reactions, a phase separation process occurs. Epoxy-phenoxy and epoxy-carboxy reactions were catalysed by triphenylphosphine. The effect of reaction parameters (temperature, catalyst, reactant stoichiometry) on the reactive extrasion process were analysed. The structure of the prepolymers showed low branching reactions (2-5%). Low molar mass prepolymers had a Newtonian rheological behaviour. Cloud-point temperatures of different reactive liquid butadiene aciylonitrile random copolymer/epoxy resin blends were measured for different rubber concentrations. Rubber... 

The branch of science which is concerned with the flow of both simple (Newtonian) and complex (non-Newtonian) fluids is known as rheology. The flow characteristics are represented by a rheogram, which is a plot of shear stress against rate of shear, and normally consists of a collection of experimentally determined points through which a curve may be drawn. If an equation can be fitted to the curve, it facilitates calculation of the behaviour of the fluid. It must be borne in mind, however, that such equations are approximations to the actual behaviour of the fluid and should not be used outside the range of conditions (particularly shear rates) for which they were determined. 

The challenge within our programme is to follow up the consequences of the tube model for the non-linear rheology of branched polymers - would such a theoretical framework lead to any understanding of the special behaviour of, for example, LDPE in complex flows We build up our tools as before in the context of linear polymers. 

A branch of physics that is called rheology studies the behaviour of solids and liquids under mechanical stress, which manifests itself by deformation of soHds and by flow of Hquids under appHed forces. The relationship between rheological and organoleptic properties of foods is the subject of psychorheology. 

Molten polymers are viscoelastic materials, and so study of their behaviour can be complex. Polymers are also non-ideal in behaviour, i.e. they do not follow the Newtonian liquid relationship of simple liquids like water, where shear-stress is proportional to shear strain rate. Unlike Newtonian liquids, polymers show viscosity changes with shear rate, mainly in a pseudoplastic manner. As shear rate increases there is a reduction in melt viscosity. This is true of both heat-softened plastics and rubbers. Other time-dependent effects will also arise with polymer compounds to complicate the rheological process behaviour. These may be viscosity reductions due to molecular-mass breakdown or physical effects due to thixotropic behaviour, or viscosity increases due to crosslinking/branching reactions or degradation. Generally these effects will be studied in rotational-type rheometers and the extrusion-type capillary rheometer. 

---