Engelmann Ulrich M, Shalaby Ahmed, Shasha Carolyn, Krishnan Kannan M, Krause Hans-Joachim
Department of Medical Engineering and Applied Mathematics, FH Aachen University of Applied Sciences, 52428 Jülich, Germany.
Department of Physics, University of Washington, Seattle, WA 98195, USA.
Nanomaterials (Basel). 2021 May 11;11(5):1257. doi: 10.3390/nano11051257.
Dual frequency magnetic excitation of magnetic nanoparticles (MNP) enables enhanced biosensing applications. This was studied from an experimental and theoretical perspective: nonlinear sum-frequency components of MNP exposed to dual-frequency magnetic excitation were measured as a function of static magnetic offset field. The Langevin model in thermodynamic equilibrium was fitted to the experimental data to derive parameters of the lognormal core size distribution. These parameters were subsequently used as inputs for micromagnetic Monte-Carlo (MC)-simulations. From the hysteresis loops obtained from MC-simulations, sum-frequency components were numerically demodulated and compared with both experiment and Langevin model predictions. From the latter, we derived that approximately 90% of the frequency mixing magnetic response signal is generated by the largest 10% of MNP. We therefore suggest that small particles do not contribute to the frequency mixing signal, which is supported by MC-simulation results. Both theoretical approaches describe the experimental signal shapes well, but with notable differences between experiment and micromagnetic simulations. These deviations could result from Brownian relaxations which are, albeit experimentally inhibited, included in MC-simulation, or (yet unconsidered) cluster-effects of MNP, or inaccurately derived input for MC-simulations, because the largest particles dominate the experimental signal but concurrently do not fulfill the precondition of thermodynamic equilibrium required by Langevin theory.
磁性纳米颗粒（MNP）的双频磁激发能够增强生物传感应用。本文从实验和理论角度对此进行了研究：测量了暴露于双频磁激发下的MNP的非线性和频分量随静态磁偏置场的变化。将处于热力学平衡的朗之万模型拟合到实验数据中，以推导对数正态核心尺寸分布的参数。这些参数随后被用作微磁蒙特卡罗（MC）模拟的输入。从MC模拟得到的磁滞回线中，对和频分量进行数值解调，并与实验和朗之万模型预测结果进行比较。从后者我们得出，大约90%的频率混合磁响应信号是由最大的10%的MNP产生的。因此，我们认为小颗粒对频率混合信号没有贡献，这得到了MC模拟结果的支持。两种理论方法都能很好地描述实验信号形状，但实验和微磁模拟之间存在显著差异。这些偏差可能是由于布朗弛豫（尽管在实验中受到抑制，但仍包含在MC模拟中）、MNP的（尚未考虑的）团簇效应，或者是MC模拟的输入推导不准确，因为最大的颗粒主导了实验信号，但同时不满足朗之万理论要求的热力学平衡前提。
