應用於奈米金粒子布朗運動量測溫度之演算法之評估

An evaluation of algorithm for temperature measurement by detecting the Brownian motion of gold nanoparticles

李佳諺(Jia-Yan Lee)

指導教授 ： 孫珍理

國立臺灣大學/工學院/機械工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201803269

摘要

本研究中探討應用奈米金粒子的Brownian motion量測微流道中流體溫度之表現。我們使用內含直徑150 nm與300 nm奈米金粒子之溶液，在不同的放大倍率下，記錄粒子之Brownian motion影像後，分析粒子位移以估算流體溫度。我們首先使用PTV追蹤單一粒子的軌跡，再利用超統計 (superstatistics) 方法來修正傳統Brownian motion公式在極小時間間隔之誤差，並探討倍率與粒徑變化對PTV分析之影響，找出最佳參數，最後嘗試利用PIV並搭配修正過之Brownian motion公式進行溫度量測與比較。
當系統誤差降低到可接受之範圍時，我們定義此時之時間間隔為臨界時間間隔 (threshold time interval)。實驗之結果顯示，當時間間隔很小時，粒子位移量之機率密度函數 (PDF) 不是Gaussian分佈而是指數分佈，此時粒子之擴散係數不再為常數。但當時間間隔大於臨界時間間隔時，粒子之擴散過程符合傳統Brownian motion的定義，故溫度之系統誤差會大幅降低。此外，我們發現隨著倍率增加，臨界時間間隔亦逐漸增加。這是因為高倍物鏡其工作距離較短且數值孔徑較大，再加上奈米金粒子因表面電漿共振 (surface plasmon resonance) 而自發光，因此高倍物鏡所接收到的光較多。較亮的粒子影像在分析粒子中心位置時，會因有限的曝光時間的影響而產生較大的誤差，因此當倍率較大時，需要較大的時間間隔來使誤差降低。隨著粒子粒徑增加，其擴散係數逐漸減小，較大粒徑之奈米金粒子因此較不容易跑出對焦平面，故可得較清晰之粒子影像，進而使臨界時間間隔較小。若為較小粒徑之奈米金粒子，因其擴散係數大，故容易離開對焦平面而使粒子影像模糊，導致在推估溫度時，其誤差較大，使臨界時間間隔增大。唯一的例外是當倍率為20時，因較大粒徑之奈米金粒子影像過亮而產生過曝，誤差大幅上升，進而使其臨界時間間隔大幅上升。
當時間間隔很小時，我們發現使用峰度修正可以有效的降低因超統計所產生之誤差，提高溫度量測在時間間隔很小時之準確性，並降低臨界時間間隔。因此，我們嘗試利用PIV並搭配峰度修正來推估全域溫度。PIV之結果顯示，推估之全域平均溫度相當準確，但具有約7°C之標準差，其原因猜測為粒子定位之誤差所造成。從實驗結果可歸納出，當倍率為6.3，粒徑為300 nm並使用峰度修正時，會有最小的臨界時間間隔 0.03 s。

關鍵字

粒子追蹤測速 ； 布朗運動 ； 溫度量測 ； 峰度修正

並列摘要

This study attempts to improve the accuracy of temperature estimation by detecting the Brownian motion of gold nanoparticles. The superstatistical behavior of Brownian motion is considered, and the influences of optical setup and nanoparticle size are explored. We find that there exists a threshold time interval at which systematic error drops below an acceptable level. According to the diffusing diffusivity model, the probability density function resembles a non-Gaussian shape for very short time interval, leading to a significant deviation from the Einstein equation. When the time interval exceeds the threshold value, systematic error remains diminutive. In addition, increasing the magnification factor leads to an augmentation of the threshold time interval. Although objective with higher magnification usually has a larger numerical aperture and better light-gathering capability, its shorter working distance results in less light attenuation. As a result, brighter nanoparticle images are acquired and motion blur leads to greater error in identifying the particle center. Therefore, a longer time interval is required so that the traveling distance of nanoparticle is sufficient to reduce this effect, in contrast, nanoparticle size plays a more complicated role in temperature estimation. The higher diffusion coefficient makes smaller nanoparticles move away from the focus plane more easily and the blur particle images result in threshold time interval for M = 6.3 and 10. Nevertheless, larger nanoparticle becomes too bright under M = 20 and motion blur becomes an issue due to over exposure. At small time interval, we find that the kurtosis correction successfully reduces the substantial error produced by the conventional Einstein-Stokes equation. The employment of the kurtosis correction proves to estimate temperature more accurately from displacement of particle in shorter duration. This opens the possibility of applying particle image velocimetry to realize full-field temperature evaluation from Brownian displacements of particles. The PIV results show that a ±1°C accuracy of full-field temperature can be achieved with a standard deviation of 7°C. We speculate that the error may be caused by locating the particle center. In this study, we find that analyzing Brownian motion of gold nanoparticles with a diameter of 300 nm under a magnification factor of 6.3 results in the smallest threshold time interval of 0.03 s.

並列關鍵字

PTV ； Brownian motion ； temperature measurement ； kurtosis correction

參考文獻

[1] D. Ross-Pinnock and P. G. Maropoulos, "Review of industrial temperature measurement technologies and research priorities for the thermal characterisation of the factories of the future," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 230, no. 5, pp. 793-806, 2016 (10.1177/0954405414567929).

[2] P. R. N. Childs, J. R. Greenwood, and C. A. Long, "Review of temperature measurement," Review of Scientific Instruments, vol. 71, no. 8, pp. 2959-2978, 2000 (10.1063/1.1305516).

[3] C. D. S. Brites, P. P. Lima, N. J. O. Silva, A. Millán, V. S. Amaral, F. Palacio, and L. D. Carlos, "Thermometry at the nanoscale," Nanoscale, vol. 4, no. 16, pp. 4799-4829, 2012 (10.1039/C2NR30663H).

[4] C. Bergaud, "Thermometry in micro and nanofluidics," in Thermometry at the Nanoscale : Techniques and Selected Applications, L. D. Carlos and F. Palacio, Eds. London: Royal Society of Chemistry, 2015, pp. 461-492.

[5] C. Wang, R. Xu, W. Tian, X. Jiang, Z. Cui, M. Wang, H. Sun, K. Fang, and N. Gu, "Determining intracellular temperature at single-cell level by a novel thermocouple method," Cell Research, vol. 21, pp. 1517-1519, 2011 (10.1038/cr.2011.117).