How to estimate local heat dissipation of interacting magnetic nanoparticles

subjected to an applied magnetic field?

C. Munoz-Menendez, D. Serantes, S. Ruta, O. Hovorka, K. Livesey, O. Chubykalo-Fesenko, R. W. Chantrell and D. Baldomir

04/03/2017

Motivation

L.A. Tai, et. al., Nanotechnology, 2009, 20, 135101

Magnetic fluid hyperthermia Heat mediated drug delivery

A. Andrade, et. al., Biomedical Enineering- Frontiers and Challenges, 2011

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ACS Nano 2011

Cell damage with no global temperature rise?

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A. Riedinger, et. al., Nano Lett., 2013, 13, 2399–2406 J. T. Dias, et. al., Angew. Chem., Int. Ed., 2013, 52, 11526–11529

ACS Nano 2011

Unprecedented huge local ΔT gradients at the NPs’ nanoenvironment

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A. Riedinger, et. al., Nano Lett., 2013, 13, 2399–2406 J. T. Dias, et. al., Angew. Chem., Int. Ed., 2013, 52, 11526–11529

ACS Nano 2011

NEED TO STUDY LOCAL HEATING BESIDES THE GLOBAL ONE

How to evaluate local heating?

𝑆𝐿𝑃 = 𝐻𝐿 · 𝑓

H

Inverted loops Negative area?

How to evaluate local heating?

H H

𝐻𝑑𝑖𝑝𝑜𝑙𝑎𝑟 modifies 𝐻𝑙𝑜𝑐𝑎𝑙: 𝜇 𝑠𝑚𝑎𝑙𝑙 flips if 𝐻𝑙𝑜𝑐𝑎𝑙 > 𝐻𝐶

𝜇

Hd+H=Hloc

Hd+H=Hloc

𝜇

D1 = 20 nm D2 = 10 nm

𝐻𝑎𝑝𝑝𝑧 D

𝑀𝑆𝑉1𝑧 𝑀𝑆𝑉2𝑧

Simple case:

Premiss: Global area IS dissipated heat

kMC* 𝐸𝑇 = 𝐸𝐾 + 𝐸𝑍 + 𝐸𝐷

* S. Ruta, O. Hovorka, R. Chantrell, ‘Unified model of hyperthermia via hysteresis heating in systems of interacting magnetic nanoparticles’, Sci. Rep., 2015, 5

Local areas cannot be used to estimate local heat

Local areas cannot be used to estimate local heat

How to estimate local heat?

Let us analyze energy jumps

𝐴

𝑖

=

Let us analyze energy jumps

Global area is recovered from ‘A’ jumps and from ‘A’+’B’ jumps

Global area is only recovered from ‘A’+’B’ jumps

Influence of the big particle (minor loop)

Wobbling of 𝜇 𝑏𝑖𝑔 has to be considered for recovering

the correct global energy dissipation

Summary

• Experiments show the need to study local heating

• Local inverted hysteresis loops appear for strong interacting conditions

• Local areas do not account for local dissipated heat

• Energy jumps of individual NPs are a promising way to access local information

Global vs. local heating

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‘The role of size polydispersity in magnetic fluid hyperthermia: average vs. local infra/over-heating effects’, C. Munoz-Menendez, et. al., Phys. Chem. Chem. Phys., 2015, 17, 27812–27820

‘Self-consistent description of spin-phonon dynamics in ferromagnets’, P. Nieves, D. Serantes, O. Chubykalo-Fesenko, Phys. Rev. B, 2016, 94, 014409

Temperature effect kMC for T>0K

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‘Distinguishing between heating power and hyperthermic cell-treatment efficacy in magnetic fluid hyperthermia’, C. Munoz-Menendez, et. al., 2016, Soft Matter, 12, 8815-8818