magnets

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Polymeric magnets have special propertieswhich make them commercially important,including: solvent resistance controllability of magnetic strength fabrication into complex-shapesPolymeric magnets can be made by usingmagnetic particles in a polymer matrix. Onesuch example is ’Mulberin’, made by ICI byputting particles of ’Magnaquench’ (NdFeB),usually in Nylon 12. The packing fraction is55-76% by volume; the magnetic alloy fillersare plate-like, with dimensions about 200µm.To gain maximum magnetic strength, thehighest possible volume fraction of fillerwould be desired. However, this leads topoor mechanical properties. The shape ofthe filler can also have adverse effects on themagnetic strength, and plate-like particleshave been shown to give better interparticlecontacts than spherical particles.Orientational order of the fillers is alsoimportant, since a random configuration offillers can reduce the net energy product ofthe final magnet.A new approach - MacroPacSimulation can be used to predict propertiesthat are difficult to measure experimentally,giving reliable results and new insights.Composite moulding could be improved ifgood simulations of high volume fractioncomposites were available - especially fornon-spherical filler shapes. To date mostwork has concentrated on the dilute case,where the volume fraction is low - but thisdoesn’t represent the high loading present inmany industrial processes.MacroPac simulates the packing of particlesin the dense regime, setting up a simulation’box’ which can have hard, soft or periodicboundaries. Using ’hard’ boundaryconditions, you can see how the surface ofthe mould is likely to affect fibre packing andorientation. Periodic boundaries are suited tomodelling the bulk of the sample. Orientationeffects, including any local ordering, can bepredicted. By changing the aspect ratio, theeffect of this important parameter on theachievable packing fractions can beinvestigated rapidly on your computer.

Packing Magnetic Particles in CompositesModelling the behaviour of plate-like particlesin polymeric composites has been undertakenby Dr Wai Chee Lam, working in the group ofProfessor Ken Evans at Liverpool University,UK.

The Magnaquench particles were modelledas parallelograms, or rhomboids, since thesemost closely matched the particle shapeobserved by electron microscopy. Figure 1shows how Lam decided on the appropriateparticle shape.

"Good Fit""No Good"

Derivation of particle shapes

Figure 1. Choosing Particle Shapes

Improving Polymeric MagnetsWith MacroPacOnce the basic particle shape was

determined, a random packing of the plate-like particles was undertaken, with variationallowed in the length, width, thickness andangle between the length and width vectors.Each plate is built up of a number of spheresas illustrated in Figure 2.

Both 2D and 3D packings were carried out byLam. He varied key parameters - such as theangle between the two sides of the plates, Ω -to see what effect these had on the packingfraction. Essentially, the smaller the angle Ω,the smaller the volume fraction which couldbe achieved through random packing. Thelargest volume fractions which were achievedranged from about 20% (for Ω = 10o) to 50%(when Ω = 90o).

Figure 3. Packing Rhombohedral PlatesA typical packing is shown in Figure 3, takenfrom the MacroPac program for particles of asingle size. The effect of including differentsizes, via a bimodal distribution, can also beinvestigated, with control of the relativenumbers of large and small particles in thesimulation. The simulation using a bimodalsquare plate packing distribution gavepacking fractions which were in qualitativelygood agreement with ICI packing results on’Magnaquench’ particles.

MacroPac gives the starting point forunderstanding a number of features of thesystem. For example, in the case ofpolymeric magnets, the orientation of themagnetic

Figure 2. MacroPac sphere representationof ’Magnaquench’ particle

particles is crucial to the overall performance.Integrated within MacroPac is an orientationanalysis, which defines an orientationalparameter for each particle, and also definesan average orientational parameter for thewhole packing configuration.

MacroPac’s contacts analysis is alsoimportant in understanding polymericmagnets, since it is the starting point for apercolation study. And of course, this alsorelates to thermal and electrical conductivity,which could be important in differentadvanced composite systems.