Dielectric fluctuations in force microscopy: noncontact friction and frequency jitter.
Dielectric fluctuations in force microscopy: noncontact friction and frequency jitter.
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DOI：
10.1063/1.2932254
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发表时间：
2008-06
期刊：
影响因子：
--
通讯作者：
Showkat M. Yazdanian;J. Marohn;Roger F Loring
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文献类型：
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作者：
Showkat M. Yazdanian;J. Marohn;Roger F Loring
在电磁力显微镜中，带电探针在样品表面上方几十到几百纳米处振荡，提供了对分子材料弛豫的直接机械检测。非接触摩擦，即探针运动的阻尼，反映了探针谐振频率处的介电函数，而探针频率的波动是由较慢的分子运动引起的。我们提出了两种测量的统一理论图景，它将非接触摩擦和频率抖动的功率谱与样品的介电特性和实验几何形状联系起来。每个观测值都与电场波动相关的平衡相关函数有关，这是由样品的介电连续体模型的两种替代互补策略决定的。第一种方法是根据时变的外部电荷分布计算与电介质极化有关的响应函数。第二种方法采用麦克斯韦方程的随机形式，其中包含波动的电极化，在没有外部电荷分布的情况下直接计算平衡相关函数。这种方法包括与辐射传播有关的效应。在与相关辐射波长相比尖端样品距离小的实验相关限制下，两种方法产生相同的结果。测量了超灵敏悬臂梁的频率波动功率谱，并测量了聚甲基丙烯酸甲酯薄膜上的非接触摩擦，以估计实验可检测到的最小频率抖动。该聚合物的预测抖动显示超过该阈值，证明了测量的可行性。
Electric force microscopy, in which a charged probe oscillates tens to hundreds of nanometers above a sample surface, provides direct mechanical detection of relaxation in molecular materials. Noncontact friction, the damping of the probe's motions, reflects the dielectric function at the resonant frequency of the probe, while fluctuations in the probe frequency are induced by slower molecular motions. We present a unified theoretical picture of both measurements, which relates the noncontact friction and the power spectrum of the frequency jitter to dielectric properties of the sample and to experimental geometry. Each observable is related to an equilibrium correlation function associated with electric field fluctuations, which is determined by two alternative, complementary strategies for a dielectric continuum model of the sample. The first method is based on the calculation of a response function associated with the polarization of the dielectric by a time-varying external charge distribution. The second approach employs a stochastic form of Maxwell's equations, which incorporate a fluctuating electric polarization, to compute directly the equilibrium correlation function in the absence of an external charge distribution. This approach includes effects associated with the propagation of radiation. In the experimentally relevant limit that the tip-sample distance is small compared to pertinent wavelengths of radiation, the two methods yield identical results. Measurements of the power spectrum of frequency fluctuations of an ultrasensitive cantilever together with measurements of the noncontact friction over a poly(methylmethacrylate) film are used to estimate the minimum experimentally detectable frequency jitter. The predicted jitter for this polymer is shown to exceed this threshold, demonstrating the feasibility of the measurement.