The Model of the Small Ferrogel Sample with Representation of Polymer Matrix as Lennard-Jones fluid with Elastic Cross-Links

Purpose. To develop a model of small sample of the ferrogel with non-prescribed internal structure, which allows to account excluded volume of polymer matrix and permits noticeable filler rearrangements under external magneto-mechanical load, and simultaneously, has sufficient numerical efficiency.  

Methods and approaches. The model is based on a coarse-grained molecular dynamics approach. Ferrogel is represented as system of spherical objects of two types –  single-domain magnetic particles and polymer “blobs” – bound by Lennard-Jones interaction and network of elastic bonds. The later has random and coherent internal structure, which is formed at the initial stage of the calculation, and ensures elastic response of the sample. The influence of the thermofluctuations on the ferrogel is accounted through Langevin thermostat.

Results. The series of calculations for submicron samples with various concentration of monodisperse magnetic nanoparticles were performed. The dependencies of the average sample magnetic moment, obtained in the simulation of quasi-static magnetization cycles, shows, particularly, that for considered model dipolar interaction promotes magnetization. Then, numerical experiments on the uniaxial mechanical stretching were performed 1) for non-magnetized samples and 2) in the presence of a permanent magnetic field. It is found, that magnetization reinforces material elastic module, especially in case when the field is parallel to stretching direction. 

Concluson. There is proposed a model of the small ferrogel sample with representation of gel matrix as LennardJones fluids crosslinked by elastic bonds. Test calculations with samples with various concentration of magnetic filler prove the numerical efficiency and physical propriety of the model. The further development of the model are related to increasing of amount of magnetic particles and identification of mechanical model parameters based to experimental data regarding real ferrogel behavior.

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