Thermodynamics of interacting magnetic nanoparticles

Abstract

We apply the concepts of stochastic thermodynamics combined with the transition state theory to develop a framework for evaluating local heat distributions across the assemblies of interacting magnetic nanoparticles (MP) subject to time-varying external magnetic fields. We show that additivity of entropy production in the particle state-space allows separating the entropy contributions and evaluating the heat produced by the individual MPs despite interactions. Using MP chains as a model system for convenience, without losing generality, we show that the presence of dipolar interactions leads to significant heat distributions across the chains. Our study also suggests that the typically used hysteresis loops cannot be used as a measure of energy dissipation at the local particle level within MP clusters, aggregates or assemblies, and explicit evaluation of entropy production based on appropriate theory, such as developed here, becomes necessary.

How size, shape and assembly of magnetic nanoparticles give rise to different hyperthermia scenarios

“…Another key aspect defining the heating performance is the particle assembling, as it is often observed that particles tend to aggregate after cell internalisation, 41 which may completely define their heat release in comparison with the randomly dispersed case. [42][43][44][45] The assembling process is defined by a complex interplay between a broad range of parameters, including the media properties (viscosity, pH), the nanoparticle characteristics (size, shape, anisotropy), the field parameters (frequency and amplitude) and, obviously, the sample concentration see e.g. Bakuzis et al and references therein.…”

Disentangling local heat contributions in interacting magnetic nanoparticles

“…used to evaluate the hysteresis loops of ensembles, including kinetic Monte Carlo techniques 16,17 and an equivalent Master equation model, 18,19 which are suitable for the typical timescales of magnetic hyperthermia experiments (tens to hundreds of kHz). These approaches require an evaluation of reversal probabilities to traverse over energy barriers, which is not a trivial task in the presence of magnetic interactions even between just two particles 20 and involves various approximations.…”

“…16,22 This approach, however, is not correct due to the fact that an individual nanoparticle does not form an isolated system and does work on its interacting counterpart. Our recent consideration of the thermodynamics of interacting nanoparticles 19 showed that also within a statistical approach -rather than a dynamical approach as described here -one can not evaluate released heat from individual particle hysteresis loops and an explicit evaluation of entropy production is necessary.…”

Finding the Limits of Magnetic Hyperthermia on Core-Shell Nanoparticles Fabricated by Physical Vapor Methods

“…Furthermore, the assembling of the nanocubes in a chainlike fashion increases the correlation length, thus modifying the response to external stimuli [8,10,54]. This effect stems from the dependence of the entropy and dipolar interactions on the length of the chain, although the particular details will depend also on the chain orientation with respect to the field direction [52]. For instance, monodisperse iron-oxide NPs of 44 nm in size, assembled into chains, have achieved a heating performance of around 2 kW per Fe gram (1.5 kW/g nanoparticle) under a 24 kA/m and 765 kHz, while the same nonassembled control samples show typical iron-oxide SLP values below 500 W/g [14].…”