熱泳及擴散泳分別指粒子在溫度及濃度梯度下之移動,而熱泳及擴散泳之耦合可衍生成熱擴散阱(TDT)。本論文以單粒子追蹤技術去探討TDT之物理機制。我們發現TDT之位能阱在平行加熱表面及垂直加熱表面方向有不同的對稱性,同時亦提出一唯象模型來了解TDT之行為。更發現平行加熱面上的捕捉力與被捕捉粒子的大小平方成正比,從而推斷捕捉力是從滲透壓梯度引起。論文第二部分探索在穩定非平衡体系中隨機軌跡之可逆性及熱交換漲落。我們發現粒子軌跡遵守類似細部平衡之關係,並以實驗驗證之。同時我們對熱傳輸提出一漲落關係。

Thermophoresis and Diffusiophoresis refers to particle migration due to the presence of a temperature and solute concentration gradient respectively.Coupling of Thermophoresis and Diffusiophoresis leads to trapping of colloidal particles in polymer solutions, termed thermodiffusiophoretic trap (TDT). In the first part of this thesis I study the physical mechanism of the TDT via single particle tracking to probe the trapping potential of the TDT. Due to the presence of a heating surface, I found that the trapping potentials to have different form with a symmetric potential for the in-plane trapping and a semi-Mexican hat potential for the transverse trapping. A phenomological model is proposed to understand this trapping behavior. Moreover I found that the in-plane trapping force scaling with a2 for both steadystate and non-steady state measurements where a is the colloid radius. This result suggest that the trapping force is due to the osmotic pressure gradient across the colloid which is caused by the concentration gradient of the solute particles. In the second part of the thesis I study reversibility of stochastic trajectories and heat exchange fluctuation of a particle in a Non-Equilibrium Steady State (NESS) where the NESS is formed due to the presence of a spatial gradient of an intensive thermodynamic variable. Extending the work of Sekimoto on Stochastic Energetics, and under this force balance condition we found that a Detailed Balance (DB) like relation is still obeyed by the particle trajectories. I verified experimentally this DB-like relation for a particle confined in a TDT and a particle locally trapped by an Optical tweezer but with a net heat flux across it (OTT). Furthermore, a Fluctuation like relation is proposed for the heat transfer fluctuation under a mean heat flux which I have experimentally verified for the OTT system.

[1] Wurger, A. Rep. Prog. Phys. 73, 126601 (2010). viii, 2, 5, 6, 28
[2] deGroot, S. R. and Mazur, P. Non-Equilibrium Thermodynamics. Dover
Publications, Inc., New York, (2011). 1, 2, 3, 5, 7, 40, 41, 55
[3] Ritort, F. Comptes Rendus Physique 8, 528–539 (2007). 1, 26, 54, 68
[4] Cross, M. and Greenside, H. Pattern Formation and Dynamics in Nonequi-
librium Systems. Cambridge University Press, London, (2009). 1
[5] Onsager, L. Phys. Rev. 37, 405–426 (1931). 1
[6] Onsager, L. Phys. Rev. 38, 2265–2279 (1931). 1
[7] Miller, D. Chem. Rev. 60, 15–37 (1960). 1
[8] Anderson, J. L. Ann. Rev. of Fluid Mech. 21, 61–99 (1989). 2, 4, 5, 38, 41,
72
[9] Piazza, R. J.Phys.: Condens. Matter 16, S4195S4211 (2004). 2
[10] Piazza, R. and Parola, A. J. Phys.: Condens. Matter 20, 153102 (2008). 2,
13
[11] Duhr, S. and Braun, D. PNAS 103, 19678 (2006). 3, 7, 14, 18, 23, 41
[12] Astumian, R. D. PNAS 104, 3–4 (2007). 3, 5, 27
[13] Duhr, S. and Braun, D. Phys. Rev. Lett. 96, 168301 (2006). 3
[14] Dhont, J., Wiegand, S., Duhr, S., and Braun, D. Langmuir 23, 1674–1683
(2007). 3
[15] Bringuier, E. and Bourdon, A. Phys. Rev. E. 67, 011404 (2003). 3
[16] Ruckenstein, E. J. Colloid Interface Sci. 83, 77 (1981). 3
[17] Piazza, R. Soft Matter 4, 1740–1744 (2008). 4, 27, 41, 65
[18] Rasuli, S. and Golestanian, R. Phys. Rev. Lett. 101, 108301 (2008). 4
[19] Braibanti, M., Vigolo, D., and Piazza, R. Phys. Rev. Lett. 100, 108303
(2008). 4
[20] Weinert, F. and Braun, D. Phys. Rev. Lett. 101, 168301 (2008). 4
[21] Wurger, A. C. R. Mecanique (2013). 4
[22] Duhr, S. and Braun, D. arXiv:cond-mat/0609554v1 (2006). 5
[23] Palacci, J., Abecassis, B., Cottin-Bizonne, C., Ybert, C., and Bocquet, L.
Phys. Rev. Lett. 104, 138302 (2010). 5
[24] Abecassis, B., Cottin-Bizonne, C., Ybert, C., Ajdari, A., and Bocquet, L.
Nature Materials 7, 785789 (2008). 5
[25] Abecassis, B., Cottin-Bizonne, C., Ybert, C., Ajdari, A., and Bocquet, L.
New J. Phys. 11, 075022 (2009). 5
[26] Cordova-Figueroa, U. M. and Brady, J. Phys. Rev. Lett. 100, 158303 (2008).
5, 6, 39
[27] Julicher, F. and Prost, J. Eur. Phys. J. E 29, 2736 (2009). 5
[28] Anderson, J. L., Lowell, M. E., and Prieve, D. C. J. Fluid Mech. 117,
107–121 (1982). 5, 29
[29] Astumian, R. D. and Brody, R. J Phys Chem B. 113, 11459–62 (2009). 6,
43, 44, 57, 60, 75, 76
[30] Reinmller, A., Schope, H. J., and Palberg, T. Langmuir 6, 17381742 (2013).
6, 39
[31] Ghorayeb, K. and Firoozabadi, A. AIChE J. 46, 883–891 (2000). 7
[32] Gans, B., Kita, R., Muller, B., and Wiegand, S. J. Chem. Phys. 118, 8073
(2003). 7
[33] Gans, B., Kita, R., Wiegand, S., and Luettmer-Strathmann, J. Phys. Rev.
Lett. 91, 245501 (2003). 7
[34] Kita, R., Wiegand, S., and Luettmer-Strathmann, J. J. Chem. Phys. 121,
3874 (2004). 7, 8, 14
[35] Jiang, H., Wada, H., Yoshinaga, N., and Sano, M. Phys. Rev. Lett. 102,
208301 (2009). 8, 11, 12, 14, 18, 23, 24, 72
[36] Crocker, J. C., Matteo, J. A., Dinsmore, A. D., and Yod, A. G. Phys. Rev.
Lett. 82, 4352–4355 (1999). 10
[37] Moffitt, J. R., Chemla, Y. R., Smith, S. B., and Bustamante, C. Annual
Review of Biochemistry 77, 205–228 (2008). 10
[38] Smith, S. B., Finzi, L., and Bustamante, C. Science 258, 1122–1126 (1992).
10
[39] Pethig, R. Biomicro
uidics 4, 022811 (2010). 10
[40] Braun, D., Goddard, N. L., and Libchaber, A. Phys. Rev. Lett. 91, 158103
(2003). 11
[41] Deng, H. D., Li, G., Liu, H. Y., Dai, Q. F., Wu, L. J., Lan, S., Gopal, A. V.,
Trofimov, V. A., and Lysak, T. M. Opt Express 20, 9616–23 (2012). 11
[42] Maeda, Y. T., Buguin, A., and Libchaber, A. Phys. Rev. Lett. 107, 038301
(2011). 11, 12, 18, 23, 24, 74
[43] Putnam, S. A. and Cahill, D. G. Langmuir 21, 53175323 (2005). 13
[44] Giglio, M. and Vendramini, A. Appl. Phys. Lett. 25, 555 (1974). 14
[45] K¨ohler, W. and Sch¨afer, R. New Developments in Polymer Analytics II.
Springer, Berlin, (2000). 14
[46] Qian, H., Sheetz, M. P., and Elson, E. L. Biophys. J. 60, 910–921 (1991).
18
[47] Arines, J. and Ares, J. OPTICS J. 27, 497 (2002). 18
[48] Jenkins, F. and White, H. Fundamentals of Optics; 4 edition. McGraw-Hill
Science/Engineering/Math, USA, (2011). 18, 20
[49] Rogers, S. S., Waigh, T. A., Zhao, X., and Lu, J. R. Phys. Biol. 4, 220227
(2007). 18
[50] Zhang, Z. and Menq, C. H. Applied Optics 47, 2361 (2008). 20
[51] Speidel, M., Jon´aˇs, A., and Florin, E.-L. Optics Letters 28, 69–71 (2003).
20
[52] Holyst, R., Bielejewska, A., Szymanski, J., Wilk, A., Patkowski, A., Gapinski,
J., Zywocinski, A., Kalwarczyk, T., Kalwarczyk, E., Tabaka, M.,
Ziebacz, N., and Wieczorek, S. Phys. Chem. Chem. Phys. 11, 9025 (2009).
32, 38, 73
[53] Prieve, D. Adv. Colloid and Interface Science 82, 93–125 (1999). 32
[54] Seifert, U. Phys. Rev. Lett. 95, 040602 (2005). 40
[55] Jarzynski, C. Eur. Phys. J. B 64, 331340 (2008). 40
[56] Bustamante, C., Liphardt, J., and Ritort, F. Phys. Td. 58, 43–48 (2005). 41
[57] Seifert, U. Eur. Phys. J. B 64, 423–431 (2008). 41
[58] Jarzynski, C. Phys. Rev. Lett. 78, 2690 (1997). 41
[59] Gallavotti, G. and Cohen, E. Phys. Rev. Lett. 71, 2401 (1995). 41, 68
[60] Seitaridou, E., Inamdar, M., Phillips, R., Ghosh, K., and Dill, K. J. Phys.
Chem. B 111, 2288–2292 (2007). 41, 42
[61] Ghosh, K., Dill, K., Inamdar, M., Seitaridou, E., and Phillips, R. Am. J.
Phys. 74, 123–133 (2006). 42, 43
[62] Criado-Sanchoa, M., Casas-Vzquezb, J., and Joub, D. Phys. Lett. A 373,
33013303 (2009). 42
[63] Sekimoto, K. Stochastic Energetics. Springer-Verlag, Berlin, (2010). 44, 54,
66, 75
[64] Jackson, J. D. Classical Electrodynamics. Wiley, New York, (1998). 45
[65] Ashkin, A. Phys. Rev. Lett. 24, 156159 (1970). 45
[66] Ashkin, A., Dziedzic, J. M., Bjorkholm, J. E., and Chu, S. Opt. Lett. 11,
288290 (1986). 45
[67] W¨ordemann, M. Structured Light Fields: Applications in Optical Trapping,
Manipulation, and Organisation (Springer Theses). Springer, New York,
(2012). 46, 47, 49
[68] Nelson, P. Biological Physics. W. H. Freeman, New York, (2007). 46
[69] Svoboda, K. and Block, S. M. Annu. Rev. Biophys. Biomol. Struct. 23,
247–85 (1994). 46, 47, 49
[70] Visscher, K., Gross, S. P., and Block, S. M. IEEE J. Sel. Top. Quant. Elect.
2, 1066 (1996). 47
[71] Hale, G. and Querry, M. Appl. Opt. 12, 555 (1973). 49
[72] Gibson, J. L., Duncan, B. D., Watson, E. A., and Loomis, J. S. Opt. Eng.
43, 23122321 (2004). 49
[73] Shaevitz, J. W. A Practical Guide to Optical Trapping.
https://sites.google.com/site/shaevitzlab/links, (2006). 50
[74] Lanon, P., Batrouni, G., Lobry, L., and Ostrowsky, N. Europhys. Lett. 54,
28–34 (2001). 54
[75] Volpe, G., Helden, L., Brettschneider, T., Wehr, J., and Bechinger, C. Phys.
Rev. Lett. 104, 170602 (2010). 54
[76] Doi, M. and Edwards, S. F. The Theory of Polymer Dynamics. Clarendon
Press, Oxford, (1999). 55, 56
[77] Bier, M., Der´enyi, I., Kostur, M., and Astumian, R. D. Phys. Rev. E 59,
6422 (1999). 60, 71
[78] Feitosa, K. and Menon, N. Phys. Rev. Lett. 92, 164301 (2004). 69
[79] Garnier, N. and Ciliberto, S. Phys. Rev. E 71, 060101 (2005). 69
[80] Wurm, F. and Kilbinger, A. Angew Chem Int Ed Engl. 45, 8412–21 (2009).
74
[81] K¨ummel, F., B. t. Hagen, R. W., Buttinoni, I., R. Eichhorn, G. V., L¨owen,
H., and Bechinger, C. Phys. Rev. Lett. (accepted) (2013). 74
[82] Golestanian, R., Liverpool, T., and Ajdari, A. Phys. Rev. Lett. 94, 220801
(2005). 74
[83] Jiang, H. R., Yoshinaga, N., and Sano, M. Phys. Rev. Lett. 105, 268302
(2010). 74, 77
[84] Buttinoni, I., Volpe, G., K¨ummel, F., Volpe, G., and Bechinger, C. J. Phys.:
Condens. Matter 24, 284129 (2012). 74, 77
[85] Ebbens, S. J. and Howse, J. R. Soft Matter 6, 726–738 (2010). 74
[86] Dzubiella, J., Lowen, H., and Likos, C. N. Phys. Rev. Lett. 91, 248301
(2003). 77
[87] Khair, A. and Brady, J. Proc. R. Soc. A 463, 223 (2007). 78