磁流体磁化率—温度测量中的二阶相变现象
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摘要
本论文针对肿瘤磁感应热疗中的温度测量和射频加热效率等关键问题,借助蒙特卡罗仿真和实验测试等手段研究磁流体在生物医学温度窗口内的统计热力学行为,最终发现磁纳米粒子受温度调制的聚集体分离二阶相变现象,为活体内磁纳米粒子温度测量模型的修正及肿瘤热疗法加热系统的设计提供理论依据。论文的主要研究工作如下：
(1)提出基于磁化曲线离散化的粒径分析方法获取了磁流体中聚集体类型的信息。该方法不同于现有的光学、声学等实验方法,而是从磁学测量和信息理论的角度获取粒径分布中隐含的聚集体信息,发现磁流体中二聚体含量占优势,仅有少量三聚体和多聚体存在。
(2)采用蒙特卡罗模拟方法研究温度对磁流体中聚集分离行为的影响。基于Cluster-moving算法的Metropolis蒙特卡罗模拟方法,通过仿真磁纳米粒子间存在相互作用的情况下二维磁流体系统的行为,得到了不同温度下的磁纳米粒子聚集体型貌。研究发现,组成聚集体的粒子个数以及聚集体的体积分数均随温度的升高而减小,说明聚集体中的粒子发生了分离,且较多粒子组成的聚集体是逐步分裂成单体的；同时,相同类型的不同聚集体可能具有不同的磁矩。
(3)建立基于聚集体分离二阶相变过程的温度模型,得到磁化率倒数与温度的具体函数关系,以及聚集体分离的相变温度。在朗道二阶相变理论的基础上,通过选择聚集体的体积分数作为序参量,推导聚集体分离的二阶相变模型,并由此对描述无相互作用的单体磁纳米粒子磁化曲线的经典朗之万方程进行修正,从而建立了基于聚集体分离二阶相变的磁化率倒数与温度的数学模型。由于磁流体中的聚集体发生分离,300～340 K温度范围内磁流体样品的磁化率倒数与温度的关系不符合居里定律描述的线性关系,而是呈现向上弯曲的非线性。实验数据的非线性与理论推导相互印证,据此可得到聚集体完全分离成单体的相变温度。
(4)建立交变磁场频率与聚集体分离相变温度的数学模型,分析提高热疗法中磁纳米粒子加热效率的方法。低频交变磁场激励下的磁流体磁化率倒数与温度的实验曲线发现,表征聚集体分离过程的临界温度随随频率的升高而减小,即频率越高提供给聚集体分离的能量越大,使得只需要较低的加热温度就能使聚集体完全分离成单体。非线性拟合结果表明,聚集体分离的相转变临界温度与交变磁场频率之间的数学模型较好地解释了二者之间的定量关系。因此可通过设计具有较低聚集体分离相变温度的磁流体来提高热疗效率,并选择合适的频率,使聚集体在较低温度时就能完全分离成单体,从而工作在单体状态下继续加热。
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.
(1)提出基于磁化曲线离散化的粒径分析方法获取了磁流体中聚集体类型的信息。该方法不同于现有的光学、声学等实验方法,而是从磁学测量和信息理论的角度获取粒径分布中隐含的聚集体信息,发现磁流体中二聚体含量占优势,仅有少量三聚体和多聚体存在。
(2)采用蒙特卡罗模拟方法研究温度对磁流体中聚集分离行为的影响。基于Cluster-moving算法的Metropolis蒙特卡罗模拟方法,通过仿真磁纳米粒子间存在相互作用的情况下二维磁流体系统的行为,得到了不同温度下的磁纳米粒子聚集体型貌。研究发现,组成聚集体的粒子个数以及聚集体的体积分数均随温度的升高而减小,说明聚集体中的粒子发生了分离,且较多粒子组成的聚集体是逐步分裂成单体的；同时,相同类型的不同聚集体可能具有不同的磁矩。
(3)建立基于聚集体分离二阶相变过程的温度模型,得到磁化率倒数与温度的具体函数关系,以及聚集体分离的相变温度。在朗道二阶相变理论的基础上,通过选择聚集体的体积分数作为序参量,推导聚集体分离的二阶相变模型,并由此对描述无相互作用的单体磁纳米粒子磁化曲线的经典朗之万方程进行修正,从而建立了基于聚集体分离二阶相变的磁化率倒数与温度的数学模型。由于磁流体中的聚集体发生分离,300～340 K温度范围内磁流体样品的磁化率倒数与温度的关系不符合居里定律描述的线性关系,而是呈现向上弯曲的非线性。实验数据的非线性与理论推导相互印证,据此可得到聚集体完全分离成单体的相变温度。
(4)建立交变磁场频率与聚集体分离相变温度的数学模型,分析提高热疗法中磁纳米粒子加热效率的方法。低频交变磁场激励下的磁流体磁化率倒数与温度的实验曲线发现,表征聚集体分离过程的临界温度随随频率的升高而减小,即频率越高提供给聚集体分离的能量越大,使得只需要较低的加热温度就能使聚集体完全分离成单体。非线性拟合结果表明,聚集体分离的相转变临界温度与交变磁场频率之间的数学模型较好地解释了二者之间的定量关系。因此可通过设计具有较低聚集体分离相变温度的磁流体来提高热疗效率,并选择合适的频率,使聚集体在较低温度时就能完全分离成单体,从而工作在单体状态下继续加热。
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.
引文
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