臺灣博碩士論文加值系統

由於奈米科技與材料製備技術被廣泛研發，奈米孔道之特殊離子傳輸行為及其應用備受關注。
第一章中，探討填入高度帶電之聚電解質對於pH可調控之分支型奈米孔道之離子傳輸行為以及其離子整流的影響。當高度帶負電之聚電解質僅填入奈米孔道之主幹端，且溶液pH值低於奈米材料之等電點時，主幹端由填入之負電聚電解質主導，同時分支端奈米孔道表面帶正電，此情形下之奈米通道類似一個二極體，進而造成高達850之離子整流比(在+/- 1伏特)的絕佳表現。另外，將聚電解質僅填入奈米孔道之分支端亦可達到相似的效果，但若整個奈米孔道皆填滿聚電解質，離子整流現象將會被抑制。以上研究成果已發表於Journal of Colloid and Interface Science。
第二章中，我們發現極短的奈米孔道在表面電性極強時，仍可在鹽濃差發電系統中有良好的發電量以及離子選擇性。一般而言，奈米孔道的長度越短，孔道的阻力越小，此有利於鹽濃差發電；然而，過短的孔道將會使離子選擇性大幅降低，進而影響發電表現。透過尋找更高表面帶電的材料或是調控孔道表面電性，將可使極短的奈米孔道在高鹽濃差時亦有絕佳的離子選擇性及發電表現。此外，我們也深入探究箇中機制，發現在極短的奈米孔道鹽濃差發電系統中，發電表現係由靠近帶電孔道表面之反離子流所主導，而非孔道進出口之有效濃度差。因此，若將此推論進行推廣，我們可發現當極短的奈米孔道有著遠大於電雙層重疊尺寸的孔道半徑時，雖然離子選擇性隨之下降，但受惠於孔道阻力變小且離子電流增加，仍可保有一定水準的發電效果。此研究成果已發表於Electrochimica Acta。

Due to the fast progress in nanofabrication techniques, materials having nanoscaled structures are used widely in versatile studies and applications.
The overlapping of the electric double layer (EDL) in a nanochannel yields many interesting and significant electrokinetic phenomena such as ionic current rectification (ICR), which occurs only at a relatively low bulk salt concentration (~1 mM) where the EDL thickness is comparable to the nanochannel size. In an attempt to raise this concentration to higher levels and the ICR performance improved appreciably, a branched nanochannel filled with polyelectrolytes (PEs) is proposed in chapter 1. We show that these objectives can be achieved by choosing appropriate PE. For example, if the stem side of an anodic aluminum oxide nanochannel is filled with polystyrene sulfonate (PSS) an ICR ratio up to 850 can be obtained at 1 mM, which was not reported in previous studies. Taking account of the effect of electroosmotic flow, the underlying mechanisms of the ICR phenomena observed are discussed and the influences of the solution pH, the bulk salt concentration, and how the region(s) of a nanochannel is filled with PE examined. We show that the ICR behavior of a branched nanochannel can be modulated satisfactorily by filling highly charged PE and the solution pH.
In chapter 2, an eco-friendly energy generation system is considered. Due to its extremely low resistance, using membrane-based nanopore of only several nanometers in length, known as ultrashort nanopore (ultrathin membrane) in salinity gradient power (SGP) seems promising. However, its poor ion selectivity, especially at high salt concentrations becomes disadvantageous. Adopting a continuum model, we show that this difficulty might be circumvented by considering a 2-D material having an extremely high surface charge density. Through raising the surface charge density, both the electric power and the transference number can both be enhanced effectively. For example, for a cylindrical nanopore having length 2 nm, radius 2 nm and surface charge density -1000 mC/m2, the transference number can approach ca. 0.97 and the electric power ca. 200 pW if the salt concentration ratio across the nanopore is (1000/1), much higher than previous reported values of 3.13 pW in similar systems having longer pores (~1000 nm) and lower surface charge density (~-60 mC/m2). The underlying mechanisms of the present novel SGP system are investigated in detail for the first time. In particular, the profiles for the concentration of ions and its flux inside the nanopore are examined to explain the ion transport phenomena observed. Anomalously, if the surface charge density is sufficiently high (e.g., -1000 mC/m2), a nanopore of radius as large as 50 nm can still generate appreciable electric power (ca. 45 pW).

致謝………………………………………………………………………………………I
中文摘要………………………………………………………………………………...II
Abstract …………..…………………………………………………………………....III
Contents………...…………………………………………………………………..…..V
List of Figures…………………………...……………………………………………..VI
Chapter 1 Regulating the Ionic Current Rectification Behavior of Branched Nanochannels by Filling Polyelectrolytes…………………….…………….......………..1
Chapter 2 Ultrashort Nanopores (2-D Materials) of Large Radius Can Generate Anomalously High Salinity Gradient Power…………………………..……………….38
Conclusion………...……………………………………………………….…………..68

Chapter 1
[1] H. Kimizuka, K. Koketsu, Ion transport through cell membrane, J. Theor. Biol. 6 (1964) 290-305.
[2] B. Hille, Ionic channels in excitable membranes - current problems and biophysical approaches, Biophys. J. 22 (1978) 283-294.
[3] N. Unwin, The structure of ion channels in membranes of excitable cells, Neuron 3 (1989) 665-676.
[4] Y. Kamiyama, J. Israelachvili, Effect of pH and salt on the adsorption and interactions of an amphoteric polyelectrolyte, Macromolecules 25 (1992) 5081-5088.
[5] H. Grib, L. Bonnal, J. Sandeaux, R. Sandeaux, C. Gavach, N. Mameri, Extraction of amphoteric amino acids by an electromembrane process. pH and electrical state control by electrodialysis with bipolar membranes, J. Chem. Technol. Biot. 73 (1998) 64-70.
[6] J.E. Rothman, J. Lenard, Membrane asymmetry, Science 195 (1977) 743-753.
[7] M.S. Bretscher, Membrane structure - some general principles, Science 181 (1973) 622-629.
[8] C.C. Harrell, Z.S. Siwy, C.R. Martin, Conical nanopore membranes: controlling the nanopore shape, Small 2 (2006) 194-198.
[9] F. Xia, W. Guo, Y. Mao, X. Hou, J. Xue, H. Xia, L. Wang, Y. Song, H. Ji, Q. Ouyang, Y. Wang, L. Jiang, Gating of single synthetic nanopores by proton-driven DNA molecular motors, J. Am. Chem. Soc. 130 (2008) 8345-8350.
[10] M. Ali, P. Ramirez, H.Q. Nguyen, S. Nasir, J. Cervera, S. Mafe, W. Ensinger, Single cigar-shaped nanopores functionalized with amphoteric amino acid chains: experimental and theoretical characterization, ACS Nano 6 (2012) 3631-3640.
[11] J.M. Perry, K. Zhou, Z.D. Harms, S.C. Jacobson, Ion transport in nanofluidic funnels, ACS Nano 4 (2010) 3897-3902.
[12] P.Y. Apel, I.V. Blonskaya, O.L. Orelovitch, P. Ramirez, B.A. Sartowska, Effect of nanopore geometry on ion current rectification, Nanotechnology 22 (2011) 175302.
[13] J.P. Hsu, H.H. Wu, C.Y. Lin, S. Tseng, Ion current rectification behavior of bioinspired nanopores having a pH-tunable zwitterionic surface, Anal. Chem. 89 (2017) 3952-3958.
[14] Y. Kong, X. Fan, M. Zhang, X. Hou, Z. Liu, J. Zhai, L. Jiang, Nanofluidic diode based on branched alumina nanochannels with tunable ionic rectification, ACS Appl. Mater. Interfaces 5 (2013) 7931-7936.
[15] C.Y. Li, Z.Q. Wu, C.G. Yuan, K. Wang, X.H. Xia, Propagation of concentration polarization affecting ions transport in branching nanochannel array, Anal. Chem. 87 (2015) 8194-8202.
[16] L. Zaraska, E. Kurowska, G.D. Sulka, M. Jaskuła, Porous alumina membranes with branched nanopores as templates for fabrication of Y-shaped nanowire arrays, J. Solid State Electrochem. 16 (2012) 3611-3619.
[17] H. Jo, N. Haberkorn, J.A. Pan, M. Vakili, K. Nielsch, P. Theato, Fabrication of chemically tunable, hierarchically branched polymeric nanostructures by multi-branched anodic aluminum oxide templates, Langmuir 32 (2016) 6437-6444.
[18] R.B. Schoch, J. Han, P. Renaud, Transport phenomena in nanofluidics, Rev. Mod. Phys. 80 (2008) 839-883.
[19] M. Miansari, J.R. Friend, L.Y. Yeo, Enhanced ion current rectification in 2D graphene-based nanofluidic devices, Adv. Sci. (Weinh) 2 (2015) 1500062.
[20] M.L. Kovarik, K. Zhou, S.C. Jacobson, Effect of conical nanopore diameter on ion current rectification, J. Phys. Chem. B 113 (2009) 15960-15966.
[21] T. Yamamoto, M. Doi, Electrochemical mechanism of ion current rectification of polyelectrolyte gel diodes, Nat. Commun. 5 (2014) 4162.
[22] H.S. White, A. Bund, Ion current rectification at nanopores in glass membranes, Langmuir 24 (2008) 2212-2218.
[23] W.J. Lan, D.A. Holden, H.S. White, Pressure-dependent ion current rectification in conical-shaped glass nanopores, J. Am. Chem. Soc. 133 (2011) 13300-13303.
[24] Z. Siwy, Y. Gu, H.A. Spohr, D. Baur, A. Wolf-Reber, R. Spohr, P. Apel, Y.E. Korchev, Rectification and voltage gating of ion currents in a nanofabricated pore, Europhys. Lett. 60 (2002) 349-355.
[25] J. Gao, W. Guo, D. Feng, H. Wang, D. Zhao, L. Jiang, High-performance ionic diode membrane for salinity gradient power generation, J. Am. Chem. Soc. 136 (2014) 12265-12272.
[26] M. Ali, S. Mafe, P. Ramirez, R. Neumann, W. Ensinger, Logic gates using nanofluidic diodes based on conical nanopores functionalized with polyprotic acid chains, Langmuir 25 (2009) 11993-11997.
[27] W. Guo, H. Xia, L. Cao, F. Xia, S. Wang, G. Zhang, Y. Song, Y. Wang, L. Jiang, D. Zhu, Integrating ionic gate and rectifier within one solid-state nanopore via modification with dual-responsive copolymer brushes, Adv. Funct. Mater. 20 (2010) 3561-3567.
[28] H. Daiguji, Y. Oka, K. Shirono, Nanofluidic diode and bipolar transistor, Nano Lett. 5 (2005) 2274-2280.
[29] I. Vlassiouk, Z.S. Siwy, Nanofluidic diode, Nano Lett. 7 (2007) 552-556.
[30] R. Karnik, C. Duan, K. Castelino, H. Daiguji, A. Majumdar, Rectification of ionic current in a nanofluidic diode, Nano Lett. 7 (2007) 547-551.
[31] L. Wen, J. Ma, Y. Tian, J. Zhai, L. Jiang, A photo-induced, and chemical-driven, smart-gating nanochannel, Small 8 (2012) 838-842.
[32] K. Xiao, L. Chen, Z. Zhang, G. Xie, P. Li, X.Y. Kong, L. Wen, L. Jiang, A tunable ionic diode based on a biomimetic structure-tailorable nanochannel, Angew. Chem. Int. Ed. Engl. 56 (2017) 8168-8172.
[33] I. Boussouar, Q. Chen, X. Chen, Y. Zhang, F. Zhang, D. Tian, H.S. White, H. Li, Single nanochannel platform for detecting chiral drugs, Anal. Chem. 89 (2017) 1110-1116.
[34] J.H. Yuan, F.Y. He, D.C. Sun, X.H. Xia, A simple method for preparation of through-hole porous anodic alumina membrane, Chem. Mater. 16 (2004) 1841-1844.
[35] S. Wu, F. Wildhaber, O. Vazquez-Mena, A. Bertsch, J. Brugger, P. Renaud, Facile fabrication of nanofluidic diode membranes using anodic aluminium oxide, Nanoscale 4 (2012) 5718-5723.
[36] O. Jessensky, F. Müller, U. Gösele, Self-organized formation of hexagonal pore arrays in anodic alumina, Appl. Phys. Lett. 72 (1998) 1173-1175.
[37] C.Y. Li, F.X. Ma, Z.Q. Wu, H.L. Gao, W.T. Shao, K. Wang, X.H. Xia, Solution-pH-modulated rectification of ionic current in highly ordered nanochannel arrays patterned with chemical functional groups at designed positions, Adv. Funct. Mater. 23 (2013) 3836-3844.
[38] A.P. Li, F. Muller, A. Birner, K. Nielsch, U. Gosele, Hexagonal pore arrays with a 50-420 nm interpore distance formed by self-organization in anodic alumina, J. Appl. Phys. 84 (1998) 6023-6026.
[39] R.C. Rollings, A.T. Kuan, J.A. Golovchenko, Ion selectivity of graphene nanopores, Nat. Commun. 7 (2016).
[40] J.Z. Ji, Q. Kang, Y. Zhou, Y.P. Feng, X. Chen, J.Y. Yuan, W. Guo, Y. Wei, L. Jiang, Osmotic power generation with positively and negatively charged 2D nanofluidic membrane pairs, Adv. Funct. Mater. 27 (2017).
[41] W. Lee, S.J. Park, Porous anodic aluminum oxide: anodization and templated synthesis of functional nanostructures, Chem. Rev. 114 (2014) 7487-7556.
[42] C.Y. Lin, C. Combs, Y.S. Su, L.H. Yeh, Z.S. Siwy, Rectification of concentration polarization in mesopores leads to high conductance ionic diodes and high performance osmotic power, J. Am. Chem. Soc. 141 (2019) 3691-3698.
[43] Z. Zeng, Y. Ai, S. Qian, pH-regulated ionic current rectification in conical nanopores functionalized with polyelectrolyte brushes, Phys. Chem. Chem. Phys. 16 (2014) 2465-2474.
[44] D.H. Lin, C.Y. Lin, S. Tseng, J.P. Hsu, Influence of electroosmotic flow on the ionic current rectification in a pH-regulated, conical nanopore, Nanoscale 7 (2015) 14023-14031.
[45] Z. Zhang, X.Y. Kong, K. Xiao, Q. Liu, G. Xie, P. Li, J. Ma, Y. Tian, L. Wen, L. Jiang, Engineered asymmetric heterogeneous membrane: a concentration-gradient-driven energy harvesting device, J. Am. Chem. Soc. 137 (2015) 14765-14772.
[46] J.J. Su, D.Y. Ji, J.L. Tang, H. Li, Y.P. Feng, L.X. Cao, L. Jiang, W. Guo, Anomalous pore-density dependence in nanofluidic osmotic power generation, Chinese J. Chem. 36 (2018) 417-420.
[47] L.H. Yeh, F. Chen, Y.T. Chiou, Y.S. Su, Anomalous pH-dependent nanofluidic salinity gradient power, Small 13 (2017).
[48] M. Kosmulski, pH-dependent surface charging and points of zero charge II. Update, J. Colloid Interf. Sci. 275 (2004) 214-224.
[49] D. Constantin, Z.S. Siwy, Poisson-Nernst-Planck model of ion current rectification through a nanofluidic diode, Phys. Rev. E. Stat. Nonlin. Soft Matter Phys. 76 (2007) 041202.
[50] L.H. Yeh, J.P. Hsu, Effects of double-layer polarization and counterion condensation on the electrophoresis of polyelectrolytes, Soft Matter 7 (2011) 396-411.
[51] H. Ohshima, Electrophoresis of soft particles, Adv. Colloid Interface Sci. 62 (1995) 189-235.
[52] L.H. Yeh, M. Zhang, S. Qian, Ion transport in a pH-regulated nanopore, Anal. Chem. 85 (2013) 7527-7534.
[53] J.P. Hsu, S.C. Lin, C.Y. Lin, S. Tseng, Power generation by a pH-regulated conical nanopore through reverse electrodialysis, J. Power Sources 366 (2017) 169-177.
[54] J.P. Hsu, S.T. Yang, C.Y. Lin, S. Tseng, Ionic current rectification in a conical nanopore: influences of electroosmotic flow and type of salt, J. Phys. Chem. C 121 (2017) 4576-4582.
[55] M. Elzbieciak, S. Zapotoczny, P. Nowak, R. Krastev, M. Nowakowska, P. Warszynski, Influence of pH on the structure of multilayer films composed of strong and weak polyelectrolytes, Langmuir 25 (2009) 3255-3259.
[56] L.H. Yeh, M. Zhang, S. Qian, J.P. Hsu, S. Tseng, Ion concentration polarization in polyelectrolyte-modified nanopores, J. Phys. Chem. C 116 (2012) 8672-8677.
[57] T. Cosgrove, T.M. Obey, B. Vincent, The configuration of sodium poly(styrene sulfonate) at polystyrene solution interfaces, J. Colloid Interf. Sci. 111 (1986) 409-418.
Chapter 2
[1] H. Kimizuka, K. Koketsu, Ion transport through cell membrane, J. Theor. Biol. 6 (1964) 290-305.
[2] B. Hille, Ionic channels in excitable membranes - current problems and biophysical approaches, Biophys. J. 22 (1978) 283-294.
[3] N. Unwin, The structure of ion channels in membranes of excitable cells, Neuron 3 (1989) 665-676.
[4] Y. Kamiyama, J. Israelachvili, Effect of pH and salt on the adsorption and interactions of an amphoteric polyelectrolyte, Macromolecules 25 (1992) 5081-5088.
[5] H. Grib, L. Bonnal, J. Sandeaux, R. Sandeaux, C. Gavach, N. Mameri, Extraction of amphoteric amino acids by an electromembrane process. pH and electrical state control by electrodialysis with bipolar membranes, J. Chem. Technol. Biot. 73 (1998) 64-70.
[6] J.E. Rothman, J. Lenard, Membrane asymmetry, Science 195 (1977) 743-753.
[7] M.S. Bretscher, Membrane structure - some general principles, Science 181 (1973) 622-629.
[8] C.C. Harrell, Z.S. Siwy, C.R. Martin, Conical nanopore membranes: controlling the nanopore shape, Small 2 (2006) 194-198.
[9] F. Xia, W. Guo, Y. Mao, X. Hou, J. Xue, H. Xia, L. Wang, Y. Song, H. Ji, Q. Ouyang, Y. Wang, L. Jiang, Gating of single synthetic nanopores by proton-driven DNA molecular motors, J. Am. Chem. Soc. 130 (2008) 8345-8350.
[10] M. Ali, P. Ramirez, H.Q. Nguyen, S. Nasir, J. Cervera, S. Mafe, W. Ensinger, Single cigar-shaped nanopores functionalized with amphoteric amino acid chains: experimental and theoretical characterization, ACS Nano 6 (2012) 3631-3640.
[11] J.M. Perry, K. Zhou, Z.D. Harms, S.C. Jacobson, Ion transport in nanofluidic funnels, ACS Nano 4 (2010) 3897-3902.
[12] P.Y. Apel, I.V. Blonskaya, O.L. Orelovitch, P. Ramirez, B.A. Sartowska, Effect of nanopore geometry on ion current rectification, Nanotechnology 22 (2011) 175302.
[13] J.P. Hsu, H.H. Wu, C.Y. Lin, S. Tseng, Ion current rectification behavior of bioinspired nanopores having a pH-tunable zwitterionic surface, Anal. Chem. 89 (2017) 3952-3958.
[14] Y. Kong, X. Fan, M. Zhang, X. Hou, Z. Liu, J. Zhai, L. Jiang, Nanofluidic diode based on branched alumina nanochannels with tunable ionic rectification, ACS Appl. Mater. Interfaces 5 (2013) 7931-7936.
[15] C.Y. Li, Z.Q. Wu, C.G. Yuan, K. Wang, X.H. Xia, Propagation of concentration polarization affecting ions transport in branching nanochannel array, Anal. Chem. 87 (2015) 8194-8202.
[16] L. Zaraska, E. Kurowska, G.D. Sulka, M. Jaskuła, Porous alumina membranes with branched nanopores as templates for fabrication of Y-shaped nanowire arrays, J. Solid State Electrochem. 16 (2012) 3611-3619.
[17] H. Jo, N. Haberkorn, J.A. Pan, M. Vakili, K. Nielsch, P. Theato, Fabrication of chemically tunable, hierarchically branched polymeric nanostructures by multi-branched anodic aluminum oxide templates, Langmuir 32 (2016) 6437-6444.
[18] R.B. Schoch, J. Han, P. Renaud, Transport phenomena in nanofluidics, Rev. Mod. Phys. 80 (2008) 839-883.
[19] M. Miansari, J.R. Friend, L.Y. Yeo, Enhanced ion current rectification in 2D graphene-based nanofluidic devices, Adv. Sci. (Weinh) 2 (2015) 1500062.
[20] M.L. Kovarik, K. Zhou, S.C. Jacobson, Effect of conical nanopore diameter on ion current rectification, J. Phys. Chem. B 113 (2009) 15960-15966.
[21] T. Yamamoto, M. Doi, Electrochemical mechanism of ion current rectification of polyelectrolyte gel diodes, Nat. Commun. 5 (2014) 4162.
[22] H.S. White, A. Bund, Ion current rectification at nanopores in glass membranes, Langmuir 24 (2008) 2212-2218.
[23] W.J. Lan, D.A. Holden, H.S. White, Pressure-dependent ion current rectification in conical-shaped glass nanopores, J. Am. Chem. Soc. 133 (2011) 13300-13303.
[24] Z. Siwy, Y. Gu, H.A. Spohr, D. Baur, A. Wolf-Reber, R. Spohr, P. Apel, Y.E. Korchev, Rectification and voltage gating of ion currents in a nanofabricated pore, Europhys. Lett. 60 (2002) 349-355.
[25] J. Gao, W. Guo, D. Feng, H. Wang, D. Zhao, L. Jiang, High-performance ionic diode membrane for salinity gradient power generation, J. Am. Chem. Soc. 136 (2014) 12265-12272.
[26] M. Ali, S. Mafe, P. Ramirez, R. Neumann, W. Ensinger, Logic gates using nanofluidic diodes based on conical nanopores functionalized with polyprotic acid chains, Langmuir 25 (2009) 11993-11997.
[27] W. Guo, H. Xia, L. Cao, F. Xia, S. Wang, G. Zhang, Y. Song, Y. Wang, L. Jiang, D. Zhu, Integrating ionic gate and rectifier within one solid-state nanopore via modification with dual-responsive copolymer brushes, Adv. Funct. Mater. 20 (2010) 3561-3567.
[28] H. Daiguji, Y. Oka, K. Shirono, Nanofluidic diode and bipolar transistor, Nano Lett. 5 (2005) 2274-2280.
[29] I. Vlassiouk, Z.S. Siwy, Nanofluidic diode, Nano Lett. 7 (2007) 552-556.
[30] R. Karnik, C. Duan, K. Castelino, H. Daiguji, A. Majumdar, Rectification of ionic current in a nanofluidic diode, Nano Lett. 7 (2007) 547-551.
[31] L. Wen, J. Ma, Y. Tian, J. Zhai, L. Jiang, A photo-induced, and chemical-driven, smart-gating nanochannel, Small 8 (2012) 838-842.
[32] K. Xiao, L. Chen, Z. Zhang, G. Xie, P. Li, X.Y. Kong, L. Wen, L. Jiang, A tunable ionic diode based on a biomimetic structure-tailorable nanochannel, Angew. Chem. Int. Ed. Engl. 56 (2017) 8168-8172.
[33] I. Boussouar, Q. Chen, X. Chen, Y. Zhang, F. Zhang, D. Tian, H.S. White, H. Li, Single nanochannel platform for detecting chiral drugs, Anal. Chem. 89 (2017) 1110-1116.
[34] J.H. Yuan, F.Y. He, D.C. Sun, X.H. Xia, A simple method for preparation of through-hole porous anodic alumina membrane, Chem. Mater. 16 (2004) 1841-1844.
[35] S. Wu, F. Wildhaber, O. Vazquez-Mena, A. Bertsch, J. Brugger, P. Renaud, Facile fabrication of nanofluidic diode membranes using anodic aluminium oxide, Nanoscale 4 (2012) 5718-5723.
[36] O. Jessensky, F. Müller, U. Gösele, Self-organized formation of hexagonal pore arrays in anodic alumina, Appl. Phys. Lett. 72 (1998) 1173-1175.
[37] C.Y. Li, F.X. Ma, Z.Q. Wu, H.L. Gao, W.T. Shao, K. Wang, X.H. Xia, Solution-pH-modulated rectification of ionic current in highly ordered nanochannel arrays patterned with chemical functional groups at designed positions, Adv. Funct. Mater. 23 (2013) 3836-3844.
[38] A.P. Li, F. Muller, A. Birner, K. Nielsch, U. Gosele, Hexagonal pore arrays with a 50-420 nm interpore distance formed by self-organization in anodic alumina, J. Appl. Phys. 84 (1998) 6023-6026.
[39] R.C. Rollings, A.T. Kuan, J.A. Golovchenko, Ion selectivity of graphene nanopores, Nat. Commun. 7 (2016).
[40] J.Z. Ji, Q. Kang, Y. Zhou, Y.P. Feng, X. Chen, J.Y. Yuan, W. Guo, Y. Wei, L. Jiang, Osmotic power generation with positively and negatively charged 2D nanofluidic membrane pairs, Adv. Funct. Mater. 27 (2017).
[41] W. Lee, S.J. Park, Porous anodic aluminum oxide: anodization and templated synthesis of functional nanostructures, Chem. Rev. 114 (2014) 7487-7556.
[42] C.Y. Lin, C. Combs, Y.S. Su, L.H. Yeh, Z.S. Siwy, Rectification of concentration polarization in mesopores leads to high conductance ionic diodes and high performance osmotic power, J. Am. Chem. Soc. 141 (2019) 3691-3698.
[43] Z. Zeng, Y. Ai, S. Qian, pH-regulated ionic current rectification in conical nanopores functionalized with polyelectrolyte brushes, Phys. Chem. Chem. Phys. 16 (2014) 2465-2474.
[44] D.H. Lin, C.Y. Lin, S. Tseng, J.P. Hsu, Influence of electroosmotic flow on the ionic current rectification in a pH-regulated, conical nanopore, Nanoscale 7 (2015) 14023-14031.
[45] Z. Zhang, X.Y. Kong, K. Xiao, Q. Liu, G. Xie, P. Li, J. Ma, Y. Tian, L. Wen, L. Jiang, Engineered asymmetric heterogeneous membrane: a concentration-gradient-driven energy harvesting device, J. Am. Chem. Soc. 137 (2015) 14765-14772.
[46] J.J. Su, D.Y. Ji, J.L. Tang, H. Li, Y.P. Feng, L.X. Cao, L. Jiang, W. Guo, Anomalous pore-density dependence in nanofluidic osmotic power generation, Chinese J. Chem. 36 (2018) 417-420.
[47] L.H. Yeh, F. Chen, Y.T. Chiou, Y.S. Su, Anomalous pH-dependent nanofluidic salinity gradient power, Small 13 (2017).
[48] M. Kosmulski, pH-dependent surface charging and points of zero charge II. Update, J. Colloid Interf. Sci. 275 (2004) 214-224.
[49] D. Constantin, Z.S. Siwy, Poisson-Nernst-Planck model of ion current rectification through a nanofluidic diode, Phys. Rev. E. Stat. Nonlin. Soft Matter Phys. 76 (2007) 041202.
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[51] H. Ohshima, Electrophoresis of soft particles, Adv. Colloid Interface Sci. 62 (1995) 189-235.
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