Polypropylene modelling

N. Kaprinidis, P. Shields, and G. Leslie, Antimony free flame retardant systems containing Flamestab NOR 116 for polypropylene modelling. In Flame Retardants 2002, Interscience Communications, London, 2002, pp. 107-111. 

Loos J, Schimanski T, Hoffman J, Peijs T and Lemstra P J (2001) Morphological investigations of polypropylene single-fiber reinforced polypropylene model composites. Polymer 42 3827-3834. 

Mayo FR. Relative reactivities in oxidations of polypropylene and polypropylene models. Macromolecules 1978 11 942-6. 

This has been done for polyethylene, polyisobutylene and polypropylene models, for instance, by prescribing spheres of a chosen diameter around each interaction site, or by using Voronoi polyhedra to define the unoccupied space. The free volume fraction,can be defined by... 

Construct such a model for isotactic polypropylene. Estimate the volume of an isobutyl group on the scale of your model and examine whether interference between successive substituents would occur if this were the R group present. 

Fig. 2. (a) Chain conformation of isotactic polypropylene, and (b) model of a polypropylene spheruHte. 

Polypropylene molecules repeatedly fold upon themselves to form lamellae, the sizes of which ate a function of the crystallisa tion conditions. Higher degrees of order are obtained upon formation of crystalline aggregates, or spheruHtes. The presence of a central crystallisation nucleus from which the lamellae radiate is clearly evident in these stmctures. Observations using cross-polarized light illustrates the characteristic Maltese cross model (Fig. 2b). The optical and mechanical properties ate a function of the size and number of spheruHtes and can be modified by nucleating agents. Crystallinity can also be inferred from thermal analysis (28) and density measurements (29). 

Antioxidants may be assessed in a variety of ways. For screening and for fundamental studies the induction period and rate of oxidation of petroleum fractions with and without antioxidants present provide useful model systems. Since the effect of oxidation differs from polymer to polymer it is important to evaluate the efficacy of the antioxidant with respect to some property seriously affected by oxidation. Thus for polyethylene it is common to study changes in flow properties and in power factor in polypropylene, flow properties and tendency to embrittlement in natural rubber vulcanisates, changes in tensile strength and tear strength. 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

The model has also been found to work well in describing the mechanics of the interface between the semicrystalline polymers polyamide 6 and polypropylene coupled by the in-situ formation of a diblock copolymer at the interface. The toughness in this system was found to vary as E- where E was measured after the sample was fractured (see Fig. 8). The model probably applied to this system because the failure occurred by the formation and breakdown of a primary craze in the polypropylene [14],... 

The grade of polypropylene whose creep curves are given in Fig. 2.5 is to have its viscoelastic behaviour fltted to a Maxwell model for stresses up to 6 MN/m and times up to ICKX) seconds. Determine the two constants for the model and use these to determine the stress in the material after 900 seconds if the material is subjected to a constant strain of 0.4% throughout the 900 seconds. 

The creep curve for polypropylene at 4.2 MN/m (Fig. 2.5) is to be represented for times up to 2 X 10 s by a 4-element model consisting of a Maxwell unit and a Kelvin-Voigt unit in series. Determine the constants for each of the elements and use the model to predict the strain in this material after a stress of 5.6 MN/m has been applied for 3 x 10 seconds. 

Example 5.1 Applying the Carreau model to polypropylene, the following constants are known at 190°C. 

Gas phase olefin polymerizations are becoming important as manufacturing processes for high density polyethylene (HOPE) and polypropylene (PP). An understanding of the kinetics of these gas-powder polymerization reactions using a highly active TiCi s catalyst is vital to the careful operation of these processes. Well-proven models for both the hexane slurry process and the bulk process have been published. This article describes an extension of these models to gas phase polymerization in semibatch and continuous backmix reactors. 

More recently, two-state E/B models have been proposed by Chujo and Doi (9.10) for the analysis of polypropylene. Similar E/B models were proposed by Cheng(11) and Asakura, et al(12) for polybutylene. For copolymers, two-state B/B models have been proposed for ethylene-propylene copolymers,(11,13-15) and propylene-butylene copolymers.(11,13) Recently, Cheng(11) generalized these multi-state models and developed computer methodology for the general analysis of such systems. A number of polymer systems were treated. 

Elucidation of degradation kinetics for the reactive extrusion of polypropylene is constrained by the lack of kinetic data at times less than the minimum residence time in the extruder. The objectives of this work were to develop an experimental technique which could provide samples for short reaction times and to further develop a previously published kinetic model. Two experimental methods were examined the classical "ampoule technique" used for polymerization kinetics and a new method based upon reaction in a static mixer attached to a single screw extruder. The "ampoule technique was found to have too many practical limitations. The "static mixer method" also has some difficult aspects but did provide samples at a reaction time of 18.6 s and is potentially capable of supplying samples at lower times with high reproducibility. Kinetic model improvements were implemented to remove an artificial high molecular weight tail which appeared at high initiator concentrations and to reduce step size sensitivity. 

Kinetic Model Development Our kinetic model for the degradation of polypropylene Q.) is based upon the following reaction mechanism ... 

Very low molecular weight polypropylenes are now known to be useful industrial additives (8). Such polymers can be made by using very high concentrations of peroxide in the degradation. Extension of the model to high initiator concentrations is therefore of practical interest, o The model was found to be sensitive to step size in reaction time used. 

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