臺灣博碩士論文加值系統

我們以朗日凡分子動力學模擬研究在不同嫁接密度和外加直流電場條件下的高分子電解質刷系統的構形和其反離子的分佈狀態，系統中電場的方向垂直於基板表面。
首先，我們發現當電場強度大於臨界電場值時，高分子電解質刷的構形開始產生明顯的改變。在低嫁接密度系統中，所有高分子鏈都會隨著電場增強而伸展其高度，此時電解質刷是由同質相所組成；然而，在中和高嫁接密度系統裡，電解質刷可以允許兩相同時並存。研究顯示在中嫁接密度系統下，當電場強度在|E**|<|E|<|E***|的區間，由於一部分高分子鏈沒有伸直其構形，所以電解質刷會分裂成疏密兩層結構。而在高嫁接密度系統中，只有很少數的高分子鏈能被電場拉伸，其他未受拉伸的高分子鏈會和反離子形成緊密層；即使在高電場條件下，高分子電解質刷也不會產生如中嫁接密度系統的兩相再合併情形。
再者，在低和中嫁接密度系統中，當電場強度超過臨界電場時，反離子的分佈狀態會出現明顯的變化。電場強度小於臨界電場時，由於反離子吸附於鏈上的效應，其分佈狀態形似高分子單體的分佈狀態。而電場強度大於臨界電場時，大部份的反離子會往基板表面移動，此時，反離子吸附於鏈上的比率也會降低。另外，我們也可經由計算側視密度圖和俯視密度圖，更加清楚了解高分子單體和反離子的分佈細節。
最後，我們發現臨界電場值隨嫁接密度增高而變大，而且遵循尺度關係律 。此外，我們也討論了在不同嫁接密度和電場強度條件下的系統相圖，讓我們對高分子電解質刷系統有更深入的認識。

We use Langevin dynamics simulations to investigate the conformation of polyelectrolyte (PE) brushes and the counterions distribution at different grafting densities in direct-current uniform electric fields |E|. The field direction is perpendicular to the substrate surface.
Firstly, we observe that |E| larger than a critical electric field |E*| can induce large conformational change of PE brushes. At low grafting densities, the height of chains stretch together with |E| and the brush is in a homogeneous phase. However, at intermediate and high grafting densities, two phases can coexist in the brush. For the intermediate grafting density case, the brush separates into dilute and dense, two-layer phases when |E**|<|E|<|E***| because a fraction of the chains are not stretched. For high grafting density, only few chains are stretched by the electric field. The majority of the chains are non-stretched and form a compact layer with the counterions. The bifurcated brush does not merge into a homogeneous phase in strong electric fields as at the intermediate grafting density.
Secondly, the profiles of the counterion distribution change significantly at low and intermediate grafting density when the field strength exceeds |E*|. Below |E*|, the counterion profiles match the monomer distributions due to ion condensation on the chains. Above |E*|, the majority of the ions move toward the substrate surface and the fraction of the condensed counterions decreases. The monomer and ion distributions are studied in detail through calculation of the side-view and top-view densities.
Finally, we find that |E*| increases with grafting density and follows the scaling law. A schematic phase diagram is presented, which gives a thorough picture of the PE brush sys-tem over the parameter space grafting densities and |E|.

Contents
Chinese Abstract........................................i
English Abstract.......................................ii
Acknowledgments.......................................iii
Contents...............................................iv
List of Figures........................................vi
Chapter 1 Introduction..................................1
1.1 Soft matter.........................................1
1.2 Polyelectrolyte.....................................1
1.3 Polyelectrolyte brush...............................1
1.4 Paper review........................................2
1.5 Motivation of this research.........................5
Chapter 2 Model and Method..............................6
2.1 Model...............................................6
2.1.1 System............................................6
2.1.2 Particle interactions.............................6
2.2 Method..............................................8
2.2.1 Molecular dynamics................................8
2.2.2 Langevin dynamics.................................8
2.2.3 Boundary condition................................9
2.2.4 Numerical method.................................10
2.2.5 Verlet list......................................10
2.2.6 Ewald sum........................................10
2.2.7 Lammps...........................................11
Chapter 3 Parameter Settings...........................12
Chapter 4 Results and Discussion.......................13
4.1 Low grafting density...............................13
4.1.1 Structure and height of the tethered chains......13
4.1.2 Distributions of monomer and counterion
concentrations.........................................17
4.1.3 Counterion condensation and bond length..........23
4.2 Intermediate grafting density......................27
4.2.1 Structure and height of the brush chains.........27
4.2.2 Distributions of monomer and counterion
concentrations.........................................32
4.2.3 Counterion condensation and bond length..........38
4.3 High grafting density..............................42
4.3.1 Structure and height of the brush chains.........42
4.3.2 Distributions of monomer and counterion
concentrations.........................................46
4.3.3 Counterion condensation and bond length..........51
4.4 Comparisons and discussions........................54
4.4.1 Critical electric field..........................54
4.4.2 Brush height.....................................58
4.4.3 Schematic state diagram..........................59
Chapter 5 Conclusions..................................61
Bibliography...........................................63

Bibliography
[Ahrens 2004] H. Ahrens, S. Förster, C. A. Helm, N. A. Kumar, A. Naji, R. R. Netz, and C. Seidel, “Nonlinear osmotic brush regime:  Experiments, simulations and scaling theory”, J. Phys. Chem. B 108, 16870 (2004)
[Baeurle 2009] S. A. Baeurle, M. G. Kiselev, E. S. Makarova, E. A. Nogovitsin, “Ef-fect of the counterion behavior on the frictional-compressive properties of chondroitin sulfate solutions”. Polymer 50, 1805 (2009)
[Ballauff 2006] M. Ballauff and O. Borisov, “Polyelectrolyte brushes”, Curr. Opin. Colloid Interface Sci. 11, 316 (2006)
[Baratlo 2009] M. Baratlo and H. Fazli, “Molecular dynamics simulation of semiflexible polyampholyte brushes - The effect of charged monomers sequence”, Eur. Phys. J. E 29, 131 (2009)
[Baratlo 2010] M. Baratlo and H. Fazli, “Brushes of flexible, semiflexible, and rodlike diblock polyampholytes: Molecular dynamics simulation and scaling analysis”, Phys. Rev. E 81, 011801 (2010)
[Bathe 2005] M. Bathe, G. C. Rutledge, A. J. Grodzinsky, B. Tidor, “A Coarse-grained molecular model for glycosaminoglycans: Application to chondroitin, chondroitin sulfate, and hyaluronic acid". Biophys. J. 88, 3870 (2005)
[Biesheuvel 2008] P. M. Biesheuvel, W. M. de Vos, and V. M. Amoskov, “Semianaytical continuum model for nondilute neutral and charged brushes including finite stretching”, Macromolecules 41, 6254 (2008)
[Borisov 1991] O.V. Borisov, T.M. Birshtein, and E. B. Zhulina, “Collapse of grafted polyelectrolyte layer”, J. Phys. II France 1, 521 (1991)
[Borisov 1994] O. V. Borisov, E. B. Zhulina, T. M. Birshtein, “Diagram of the States of a Grafted Polyelectrolyte Layer”, Macromolecules 27, 4795 (1994)
[Bünsow 2010] J. Bünsow, T. S. Kelby, and W. T. S. Huck, “Polymer brushes: Routes toward mechanosensitive surfaces”, Acc. Chem. Res. 43, 466 (2010)
[Cabane 2012] E. Cabane, X.-Y. Zhang, K. Langowska, C. G. Palivan, and W. Meier,” Stimuli-responsive polymers and their applications in nanomedicine”, Biointerphases 7, 9 (2012)
[Cao 2009] Q.-Q. Cao, C.-C. Zuo, H.-W. He and L.-J. Li, “A molecular dynamics study of two apposing polyelectrolyte brushes with mono- and multivalent counterions”, Macromol. Theory Simul. 18, 441 (2009)
[Cao 2011a] Q.-Q. Cao, C.-C. Zuo, L.-J. Li and M.-F. Gao, “Interactions of polye-lectrolyte brushes with oppositely charged surfactants”, Colloid Polym. Sci. 289, 1089 (2011)
[Cao 2011b] Q.-Q. Cao, C.-C. Zuo, L.-J. Li, and G. Yan, “Effects of chain stiffness and salt concentration on responses of polyelectrolyte brushes under external electric field”, Biomicrofluidics 5, 044119 (2011)
[Cao 2012a] Q.-Q. Cao, C.-C. Zuo, L.-J. Li, Y.-H. Zhang, and G. Yan, “Elec-tro-osmotic flow in nanochannels with voltage-controlled polyelectro-lyte brushes: Dependence on grafting density and normal electric field”, J. Polym. Sci. B Polym. Phys. 50, 805 (2012)
[Cao 2012b] Q.-Q. Cao, C.-C. Zuo, L.-J. Li, and Y.-H. Zhang, “Modulation of elec-troosmotic flow by electric field-responsive polyelectrolyte brushes: A molecular dynamics study”, Microfluid. Nanofluid. 12, 649 (2012)
[Chen 1996] H. Chen, R. Zajac, and A. Chakrabarti, “Conformational properties of polyelectrolyte brushes: A Monte Carlo and self-consistent-field study”, J. Chem. Phys. 104, 1579 (1996)
[Chen 2011] L. Chen, H. Merlitz, S.-Z. He, C.-X. Wu, and J.-U. Sommer, “Polyelec-trolyte brushes: Debye approximation and mean-field theory”, Macro-molecules 44, 3109 (2011)
[Coluzza 2008] I. Coluzza and J. P. Hansen, “Transition from highly to fully stretched polymer brushes in good solvent”, Phys. Rev. Lett. 100, 016104 (2008)
[Csajka 2011] F. S. Csajka, R. R. Netz, C. Seidel, and J.-F. Joanny, “Collapse of po-lyelectrolyte brushes: Scaling theory and simulations”, Eur. Phys. J. E 4, 505 (2001)
[de Vos 2010] W. M. de Vos, F. A. M. Leermakers, A. de Keizer, M. A. C. Stuart, and J. M. Kleijn, “Field theoretical analysis of driving forces for the uptake of proteins by like-charged polyelectrolyte brushes: Effects of charge regulation and patchiness, Langmuir 26, 249 (2010)
[Dobrynin 2005] A. V. Dobrynin and M. Rubinstein, “Theory of polyelectrolytes in solu-tions and at surfaces”, Prog. Polym. Sci. 30, 1049 (2005)
[Eward 1921] P. Ewald, “Die berechnung optischer und elektrostatischer gitterpoten-tiale", Ann. Phys. 369, 253 (1921)
[Fazli 2006] H. Fazli, R. Golestanian, P. L. Hansen, and M. R. Kolahchi, “Rod-like polyelectrolyte brushes with mono- and multivalent counterions”, Eu-rophys. Lett. 73, 429 (2006)
[Goujon 2012] F. Goujon, A. Ghoufi, P. Malfreyt, and D. J. Tildesley, “Frictional forces in polyelectrolyte brushes: Effects of sliding velocity, solvent quality and salt”, Soft Matter 8, 4635 (2012)
[Harden 2001] J. L. Harden, D. Long, and A. Ajdari, “Influence of end-grafted polye-lectrolytes on electro-osmosis along charged surfaces, Langmuir 17, 705 (2011)
[He 2010] S.-Z. He, H. Merlitz, L. Chen, J.-U. Sommer, and C.-X. Wu, “Polyelec-trolyte brushes: MD simulation and SCF theory”, Macromolecules 43, 7845 (2010)
[Hehmeyer 2005] O. J. Hehmeyer and M. J. Stevens, “Molecular dynamics simulations of grafted polyelectrolytes on two apposing walls”, J. Chem. Phys. 122, 134909 (2005)
[Hehmeyer 2007] O. J. Hehmeyer, G. Arya, A. Z. Panagiotopoulos, and I. Szleifer, “Monte Carlo simulation and molecular theory of tethered po-lyelectrolytes”, J. Chem. Phys. 126, 244902 (2007)
[Hickey 2009] O. A. Hickey, J. L. Harden, and G. W. Slater, “Molecular dynamics si-mulations of optimal dynamic uncharged polymer coatings for quenching electro-osmotic flow, Phys. Rev. Lett. 102, 108304 (2009)
[Hickey 2012] Owen A. Hickey, James L. Harden and Gary W. Slater, “Computer si-mulations of time-dependent suppression of EOF by polymer coatings”, Microfluid. Nanofluid.1, 1 (2012)
[Hou 2011] Yi Hou, G.-M. Liu, Y. Wua and G.-Z. Zhang, “Reentrant behavior of grafted poly(sodium styrenesulfonate) chains investigated with a quartz crystal microbalance”, Phys. Chem. Chem. Phys. 13, 2880 (2011)
[Hsiao 2006] P.-Y. Hsiao, “Chain morphology, swelling exponent, persistence length, like-charge attraction, and charge distribution around a chain in polye-lectrolyte solutions: effects of salt concentration and ion size studied by molecular dynamics simulations”, Macromolecules 39, 7125 (2006)
[Hu 2009] Y.-Y. Hu and D.-P. Cao, “Adsorption of nonuniformly charged fulle-rene-like nanoparticles on planar polyelectrolyte brushes in aqueous solutions, Langmuir 25, 4965 (2009)
[Huang 2006] J.-H. Huang, Y.-M. Wang, and M. Laradji, “Flow control by smart na-nofluidic channels:  A dissipative particle dynamics simulation, Ma-cromolecules 39, 5546 (2006)
[Ibergay 2009] C. Ibergay, P. Malfreyt, and D. J. Tildesley, “Electrostatic interactions in dissipative particle dynamics: Toward a mesoscale modeling of the polyelectrolyte brushes”, J. Chem. Theory Comput. 5, 3245 (2009)
[Ibergay 2010] C. Ibergay, P. Malfreyt, and D. J. Tildesley, “Mesoscale modeling of polyelectrolyte brushes with salt”, J. Phys. Chem. B 114, 7274 (2010)
[Ibergay 2011] C. Ibergay, P. Malfreyt and D. J. Tildesley, “Interaction between two polyelectrolyte brushes: A mesoscale modelling of the compression”, Soft Matter 7, 4900 (2011)
[Jiang 2008] T. Jiang and J.-Z. Wu, “Self-organization of multivalent counterions in polyelectrolyte brushes”, J. Chem. Phys. 129, 084903 (2008)
[Kumar 2005] N. A. Kumar and C. Seidel, “Polyelectrolyte brushes with added salt”, Macromolecules 38, 9341 (2005)
[Kumar 2007] N. A. Kumar and C. Seidel, “Interaction between two polyelectrolyte brushes”, Phys. Rev. E. 76, 020801(R) (2007)
[Lammps] http://lammps.sandia.gov/doc/kspace_modify.html
[Leermakers 2007] F. A. M. Leermakers, M. Ballauff, and O. V. Borisov, “On the mechan-ism of uptake of globular proteins by polyelectrolyte brushes:  A two-gradient self-consistent field analysis”, Langmuir 23, 3937 (2007)
[Manning 1969] G. S. Manning, “Limiting laws and counterion condensation in polye-lectrolyte solutions I. colligative properties”, J. Chem. Phys. 51, 924 (1969)
[Mercurieva 2002] A. A. Mercurieva, T. M. Birshtein, E. B. Zhulina, P. Iakovlev, J. van Male, and F. A. M. Leermakers, “An annealed polyelectrolyte brush in a polar-nonpolar binary solvent:  Effect of pH and ionic strength”, Ma-cromolecules 35, 4739 (2002)
[Merlitz 2008] H. Merlitz, G.-L. He, C.-X. Wu, and J.-U. “Sommer, Surface Instabili-ties of Monodisperse and Densely Grafted Polymer Brushes”, Macro-molecules 41, 5070 (2008)
[Merlitz 2009] H. Merlitz, G.-L. He, C.-X. Wu, and J.-U. Sommer, “Nanoscale Brushes: How to Build a Smart Surface Coating”, Phys. Rev. Lett. 102, 115702 (2009)
[Minko 2006] S. Minko, “Responsive Polymer Brushes”, J. Macromol. Sci. Part C 46, 397 (2006)
[Naji 2003] A. Naji, R. R. Netz and C. Seidel, Non-linear osmotic brush regime: Simulations and mean-field theory, Eur. Phys. J. E 12, 223 (2003)
[Netz 2003] R. R. Netz and D. Andelman, “Neutral and charged polymers at inter-faces”, Physics Reports 380 , 1-95 (2003)
[Ouyang 2009] H. Ouyang, Z.-H. Xia, and J. Zhe, “Static and dynamic responses of polyelectrolyte brushes under external electric field”, Nanotechnology 20, 195703 (2009)
[Ouyang 2010] H. Ouyang, Z.-H. Xia, and J. Zhe, “Voltage-controlled flow regulating in nanofluidic channels with charged polymer brushes”, Microfluid. Nanofluid. 9, 915 (2010)
[Pathria 2011] R. K. Pathria, Statistical Mechanics, 3rd Ed, Elsevier, (2011)
[Pincus 1991] P. Pincus, “Colloid stabilization with grafted polyelectrolytes”, Ma-cromolecules 24, 2912 (1991)
[Pryamitsyn 1996] V. A. Pryamitsyn, F. A. M. Leermakers, G. J. Fleer, and E. B. Zhulina, “Theory of the Collapse of the Polyelectrolyte Brush”, Macromolecules 29, 8260 (1996)
[Rapaport 2004] D. C. Rapaport, "The Art of Molecular Dynamics Simulation", 2nd ed., Cambridge (2004)
[Romet-Lemonne 2004]
G. Romet-Lemonne, J. Daillant, P. Guenoun, J. Yang, and J. W. Mays, “Thickness and density profiles of polyelectrolyte brushes: De-pendence on grafting density and salt concentration”, Phys. Rev. Lett. 93, 148301 (2004)
[Rühe 2004] J. Rühe, M. Ballauff, M. Biesalski, P. Dziezok, F. Gröhn, D. Jo-hannsmann, N. Houbenov, N. Hugenberg, R. Konradi, S. Minko, M. Motornov, R. R. Netz, M. Schmidt, C. Seidel, M. Stamm, T. Stephan, D. Usov, and H. Zhang, “Polyelectrolyte Brushes”, Adv. Polym. Sci. 165, 189 (2004)
[Seidel 2003] C. Seidel, “Strongly stretched polyelectrolyte brushes”, Macromole-cules 36, 2536 (2003)
[Sirchabesan 2007] M. Sirchabesan and S. Giasson, “Mesoscale simulations of the behavior of charged polymer brushes under normal compression and lateral shear forces”, Langmuir 23, 9713 (2007)
[Slater 2009] G. W. Slater, C. Holm, M. V. Chubynsky, H. W. de Haan, A. Dubé, K. Grass, O. A. Hickey, C. Kingsburry, D. Sean, T. N. Shendruk, and L.-X. Zhan, “Modeling the separation of macromolecules: A review of cur-rent computer simulation methods”, Electrophoresis 30, 792 (2009)
[Stevens 1995] M. J. Stevens, K. Kremer, “The nature of flexible linear polyelectro-lytes in salt free solution: A molecular dynamics study”, J. Chem. Phys. 103, 1669 (1995)
[Verlet 1967] L. Verlet, “Computer "experiments" on classical fluids. I. thermody-namical properties of Lennard-Jones molecules. Phys. Rev. 159, 98 (1967)
[Verlet 1968] L. Verlet, “Computer "experiments" on classical Fluids. II. equilibrium correlation functions. Phys. Rev. 165, 201 (1968)
[Weeks 1971] J. D. Weeks, D. Chandler, and H. C. Andersen, “Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys. 54, 5237 (1971)
[Weir 2011] M. P. Weir, S. Y. Heriot, S. J. Martin, A. J. Parnell, S. A. Holt, J. R. P. Webster, and R. A. L. Jones, “Voltage-induced swelling and deswelling of weak polybase brushes, Langmuir 27, 11000 (2011)
[Yang 2009] J. Yang and D.-P. Cao, “Counterion valence-induced tunnel formation in a system of polyelectrolyte brushes grafted on two apposing walls”, J. Phys. Chem. B. 113, 11625 (2009)
[Yeh 1999] I.-C. Yeh and M. L. Berkowitz, “Ewald summation for systems with slab geometry”, J. Chem. Phys. 111, 3155 (1999)
[Zhulina 1992] E. B. Zhulina, O. V. Borisov, and T. Birshtein, “Structure of grafted polyelectrolyte layer”, J. Phys. II France 2, 63 (1992)
[Zhulina 1997] E. B. Zhulina and O. V. Borisov, “Structure and interaction of weakly charged polyelectrolyte brushes: Self-consistent field theory”, J. Chem. Phys. 107, 5952 (1997)
[Zhulina 2000] E. B. Zhulina, J. Klein Wolterink, and O. V. Borisov, “Screening effects in a polyelectrolyte brush:  Self-consistent-field theory”, Macromolecules 33, 4945 (2000)