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The Second-order Phase Transition in the Measurement of Susceptibility-temperature Curve of Ferroflu

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Tutor: KongLi
School: Huazhong University of Science and Technology
Course: Control Science and Engineering
Keywords: ferrofluid,magnetic susceptibility,inverse susceptibility versus temperture curv
CLC: R318.0
Type: PhD thesis
Year:  2011
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Abstract:
Aiming at the two key problems of temperature measurement and RF heating efficiency in magnetic induction hyperthermia for cancer therapy, this dissertation studies the statistical thermodynamics behavior of ferrofluid in the biomedical temperature range by means of Monte Carlo simulation and experimental testing. From the study, we find a second-order phase transition phenomenon of cluster disruption modulated by temperature, which provides the theoretical basis for modifying the magnetic nanoparticle temperature measurement model and designing the heating system in cancer hyperthermia.The main research achievements of this dissertation are as follows:(1) Propose a particle size estimation method based on discretization of the magnetization curve to obtain the cluster type information in ferrofluid. This method is from the prospects of magnetic measurement and information theory, which is different from the current optic and acoustic methods. According to the solved particle size distribution function, we find that the content of dimer is larger than any other types of clusters, but there are still some trimers or polymers coexisting in the ferrofluid.(2) Using the Monte Carlo method to study the impact of temperature on the cluster disruption behavior. The Metropolis and Cluster-moving algorithms are adopted in the Monte Carlo method to simulate the two-dimentional ferrofluid system with interparticle interactions under small external magnetic field and thus the characterization of clusters at different temperatures is obtained. The results show that the content of different types of clusters consisting of different number of particles reduces with increasing the temperature, which indicates the clusters disrupt when temperature increases; and the polymers may disrupt gradually to monomers; meanwhile, different clusters with the same type could have different magnetic moments.(3) Establish the second order phase transition model of cluster disruption, and obtain a modified model of the inverse susceptibility versus temperature and the transition temperature of cluster disruption. Based on the Landau’s theory of second-order phase transition, by choosing the volume fraction of clusters as an order parameter, the second-order phase transition model of cluster disruption is deduced. According to this model, we modify the classical Langevin model which only describes a non-interaction system by including both of the contributions from monomers and clusters, and thus establish a mathematical model of the relationship of inverse susceptibility and temperature. Because the clusters disrupt in ferrofluid, the inverse susceptibility versus temperature curve measured from the sample in the temperature range of 300-340 K does not obey the linear relationship described by Curie law, but shows an up-bending superlinearity. The nonlinearity of experimental data and the theoretical analysis confirm with each other, based on this, we obtain the transition temperature of clusters disrupting to monomers.(4) Establish a model to describe the relationship between the frequency of AC magnetic field and the cluster disruption transition temperature; analyze the method of promoting the magnetic nanoparticle’s heating efficiency. From the experimental data of the inverse susceptibility versus temperature cuve under low-frequency AC applied field, we find that the transition temperature which characterizes the cluster disruption process decreases with the increasing frequency, i.e., the higher the frequency is, the more energy the cluster disruption process can get, which makes the clusters disrupt at a lower heating temperature. The nonlinear fitting results using the modified Langevine model at different frequencies shows that the mathematical model describing the relationship between the transition temperature of cluster disruption and the AC field frequency explains the quantitative relationship of the frequency and transition temperature very well. Therefore, designing a ferrofluid sample with low cluster disruption transition temperature could be a possible way to improve heating efficiency, and meanwhile choose a proper frequency to make the clusters disrupt at a low temperature and let them work in the monomer state to heat the tumors.
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