博碩士論文 87242002 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:110 、訪客IP:54.174.43.27
姓名 王冠斐(Guan-Fei Wang)  查詢紙本館藏   畢業系所 物理學系
論文名稱 帶電膠體懸浮液的相圖與液態-玻璃相變研究
(Phase-diagram study and liquid-glass transition phenomenon for chargedcolloidal dispersions)
相關論文
★ 金屬叢集的融化現象★ 帶電膠體系統之液態-液態/固態相變研究
★ 低濃度電解質在奈米管內異常的擴散和導電性★ 一價和多價叢集原子的熱穩定現象
★ 金屬與合金分子叢集的結構★ 物理系統之能量與焓分佈之統計力學研究
★ 膠體系統平衡相域與動態凝聚之研究★ 合金金屬叢集的溫度效應
★ 介面膠體叢聚現象的理論研究★ 膠體相圖之理論計算
★ 膠體、棒狀粒子混合系統之相圖的理論分析★ 利用時間序列的統計方法研究金屬叢集的動力學
★ 由分子動力學模擬探討層狀石墨烯的成長與碳化矽基板上多層石墨烯的熱穩定性★ 金銅合金金屬叢集(N=38)的磁性性質研究
★ 膠體、盤狀粒子混合系統的兩階段動態相變區域★ 由超快速形狀辨識、時間序列分割、時間序列交互相關分析以及擴散理論方法研究蛋白質Transthyretin片斷與金屬叢集的分子動力學模擬
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 本論文主要包含兩部分的研究工作,第一部份的研究工作,主要進行相平衡 (phase equilibrium )現象的計算與分析,第二部分的工作,則針對液態--玻璃相變(liquid-glass transition)的現象進行研究。我們所研究的對象雖然都是帶電膠體系統(charged colloidal dispersion),但是從統計力學的角度來看,第一部份的工作與第二部分的工作兩者極為不同,這兩部分各別涉及了「平衡統計」與「非平衡統計」兩個領域。
摘要(英) This thesis embodies two parts. The …rst part concerns with calculations of phase
equilibrium phenomena and the methodology and analysis we proposed for a thorough un-
derstanding of phase transition. The second part aims at liquid-glass transition phenomena
applying the microscopic mode coupling theory to study the dynamical behaviors and ex-
ploiting the factors leading to glass transition. Although the physical system of interest in
both parts is the charge-colloidal dispersion, the physical process is, however, fundamentally
di¤erent from the viewpoint of statistical mechanics. The …rst part describes equilibrium
scenario. In this part, we revisited the present status of thermodynamic theories applied
to phase-diagram calculations. We put forth in this thesis a novel means of phase-diagram
calculations and introduce free energy landscape analysis to gain insight into phase separa-
tion phenomena. The second part, on the other hand, deals with nonequilibrium processes.
Here we investigate how the colloidal particles embedded in disperse medium can be driven
to a glassy or non-ergodic state. The mechanism of glass transition and how the mode
coupling theory was used to predict and analyze its occurrence are tersely covered in the
present work. We describe below the essential problems that we have touched on in these
two parts.
論文目次 List of Figures v
List of Tables vii
I Phase-diagram of a charged colloidal dispersion 1
1 Introduction: 3
1.1 Free Energy minimization method . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.1 Derivation of FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Thermodynamic basis for FEM Method . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Euler Theory: Criteria for understanding the interaction in subsys-
tems and the size of subsystems . . . . . . . . . . . . . . . . . . . . . 7
1.2.2 Thermodynamic basis for the mixed free energy . . . . . . . . . . . . 8
1.3 Phase rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 What is the phase rule? . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Which is more stable: i-phases or (i+1)-phases in coexistence? . . . . . . . 9
1.5 Free energy landscape method: an alternative analysis for understanding
phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.1 Mixed free energy in the free energy landscape . . . . . . . . . . . . 10
1.5.2 Proof of 2-phases in coexistence . . . . . . . . . . . . . . . . . . . . . 11
1.5.3 Proof of 3-phases in coexistence . . . . . . . . . . . . . . . . . . . . . 13
1.6 Free energy landscape analysis . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Understanding phase diagrams by FEL analysis 19
2.1 van-der Waals-like theory . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.1 Gibbs-Bogoliubov inequality . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.2 Helmholtz free energies of a liquid and a solid . . . . . . . . . . . . . 21
2.2 Numerical result and FEL analysis . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Paradox between FEL and phase rule . . . . . . . . . . . . . . . . . . . . . 28
3 Triple point problem by FEM method 29
3.1 Volume proportions in phase separation at triple point . . . . . . . . . . . . 29
3.2 Problem of coexisting 3-phases . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Puzzle of phase equilibrium equations of three coexisting phases . . . . . . 34
4 Charge-colloidal dispersion induced at moderate and very low salt con-
centration: FEM method 38
4.1 Charge-colloidal dispersion induced at very low electrolyte concentrations:
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Model Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.1 Minimization of F0hc . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.2 Minimization of F0el . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 E¤ective colloid interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5 Total free energy of the colloidal suspension . . . . . . . . . . . . . . . . . . 47
5 Domains of phase separation in a charged colloidal dispersion driven by
electrolytes 50
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.1 Helmholtz free energy: general . . . . . . . . . . . . . . . . . . . . . 54
5.2.2 Helmholtz free energy: (s)
0 . M . . . . . . . . . . . . . . . . . . . . 56
5.3 Numerical results and discussion . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6 Charge-colloidal dispersion at very low salt concentration 65
6.1 Free energy-landscape analysis for a two-component system . . . . . . . . . 65
6.2 The free energy landscape analysis of a real two component system . . . . . 71
6.2.1 Information hidden in the free energy curve . . . . . . . . . . . . . . 71
6.2.2 Di¤erence between ‡uid and solid free energies in a phase equilibrium
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.3 Comparison between di¤erent physical parameters (ns,Z) . . . . . . . . . . . 75
Bibliography 82
II Liquid-glass transition: Mode Coupling Theory 87
7 Introduction 88
7.1 Summary of works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2.1 Mean spherical approximation . . . . . . . . . . . . . . . . . . . . . 91
7.2.2 Mode coupling theory . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8 Rescaled mean spherical approximation for concentrated charge-stabilized
colloids 95
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.2 Numerical results and discussion . . . . . . . . . . . . . . . . . . . . . . . . 97
8.2.1 Rescaling of S(q): numerical method . . . . . . . . . . . . . . . . . . 97
8.2.2 Rescaling of S(q): analytical method . . . . . . . . . . . . . . . . . . 102
8.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9 Liquid-glass reentrant behavior in a charge-stabilized colloidal dispersion105
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
9.2 Numerical results and discussion . . . . . . . . . . . . . . . . . . . . . . . . 106
10 Liquid-glass transition phase boundary for a monodisperse charge-stabilized
colloids in the presence of an electrolyte 112
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
10.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
10.3 Theoretical predictions and experiments . . . . . . . . . . . . . . . . . . . . 117
10.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Bibliography 120
參考文獻 [1] L. Belloni, J. Chem. Phys. 85, 519 (1986).
[2] S. Khan, T.L. Morton, D. Ronis, Phys. Rev. A 35, 4295 (1987).
[3] S.A. Adelman, J. Chem. Phys. 64, 724 (1976).
[4] S.A. Adelman, Chem. Phys. Lett. 38, 567 (1976).
[5] K. Hiroike, J. Phys. Soc. Japan 27, 1415 (1969).
[6] K. Hiroike, Mol. Phys. 33, 1195 (1977).
[7] J.B. Hayter and J. Penfold, Mol. Phys. 42, 109 (1981).
[8] E.J. Verwey and J.G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier,
Amsterdam, 1948).
[9] P. Baur, G. Nägele and R. Klein, Phys. Rev. E 53, 6224 (1996); Physica A 245, 297
(1997).
[10] G. Szamel and H. Löwen, Phys. Rev. A 44, 8215 (1991).
[11] B. Cichocki and W. Hess, Physica A 141, 475 (1987).
[12] E.B. Sirota, H.D. Ou-Yang, S.K. Sinha and P.M. Chaikin, Phys. Rev. Lett. 62, 1524
(1989).
[13] S.K. Lai, J.L. Wang, and G.F. Wang, J. Chem. Phys. 110, 7433 (1999).
[14] W. Härtl, H. Versmold and X. Zhang-Heider, J. Chem. Phys. 102, 6613 (1995).
[15] G.F. Wang, and S.K. Lai, Phys. Rev. Lett. 82, 3645 (1999).
[16] W. Götze, in: J.P. Hansen, D. Levesque, J. Zinn-Justin (Eds.), Liquids, Freezing and
the Glass Transition, Elsevier, Amsterdam, 1991, p. 287.
[17] S.K. Lai and H.C. Chen, J. Phys.: Condens. Matter 5, 4325 (1993); 7, 1499 (1995);
Phys. Rev. B 51, R12869 (1995); Phys. Rev. E 55, 2026 (1997).
[18] J.P. Hansen and J.B. Hayter, Mol. Phys. 46, 651 (1982).
[19] G. Nägele, R. Klein, M. Medina-Noyola, J. Chem. Phys. 83, 2560 (1980)
[20] G. Senatore, L. Blum, J. Phys. Chem. 89, 2676 (1985).
[21] M.J. Gillan, J. Phys. C 7, (1974) L1.
[22] E.Y. Sheu, C.F. Wu, S.H. Chen, Phys. Rev. A 32, 3807 (1985).
[23] D. Bratco, E.Y. Sheu, S.H. Chen, Phys. Rev. A 35, 4359 (1987).
[24] S.K. Lai and G.F. Wang, Phys. Rev. E 58, 3072 (1998)
[25] W. Götze, L. Sjögren, Rep. Prog. Phys. 55, 241 (1992).
[26] Y. Monovoukas, and A.P. Gast, J. Colloid Interface Sci. 128, 533 (1989).
[27] W. Götze, in: J.P. Hansen, D. Levesque, and J. Zinn-Justin, (Eds.), Liquids, Freezing
and the Glass Transition, North-Holland, Amsterdam, 1991, p. 287.
[28] S.D. Wilke and J. Bosse, Phys. Rev. E 59, 1968 (1999).
[29] S.K. Lai, and G.F. Wang, Phys. Rev. E 58, 3072 (1998).
[30] S.K. Lai, G.F. Wang and W.P. Peng, in: F. Tokuyama and H.E. Stanley (Eds.), The
3rd Tohwa University International Conference on Statistical Physics, AIP, vol. CP519,
99 (2000).
[31] S.K. Lai, and H.C. Chen, J. Phys.: Condens. Matter 5, 4325 (1993); S.K. Lai, and
H.C. Chen, J. Phys.: Condens. Matter 7, 1499 (1995); S.K. Lai, and S.Y. Chang, Phys.
Rev. B 51, R12869 (1995).
[32] We are currently looking into the possibility of understanding it analytically following
along the line of Ref. [28] in the lowest region.
[33] W. Götze in Liquids, Freezing and the Glass Transition, edited by J.P. Hansen, D.
Levesque, and J. Zinn-Justin (North-Holland, Amsterdam, 1991).
[34] W. Hess and R. Klein, Adv. Phys. 32, 173 (1983).
[35] P.N. Pusey and W. van Megen, Phys. Rev. Lett. 59, 2083 (1987); W. van Megen and
P.N. Pusey, Phys. Rev. A 43, 5429 (1991).
[36] A. Meller and J. Stavans, Phys. Rev. Lett. 68, 3646 (1992).
[37] H. Matsuoka, T. Harada and H. Yamaoka, Langmuir 10, 4423 (1994); 12, 5588 (1996).
[38] Y. Monovoukas and A.P. Gast, J. Colloid Interface Sci. 128, 533 (1989).
[39] R. Kesavamoorthy, A.K. Sood, B.V.R. Tata and Akhilesh K. Arora, J. Phys. C 21,
4737 (1988).
[40] S. Sengupta and A.K. Sood, Phys. Rev. A 44, 1233 (1991).
[41] P. Salgi and R. Rajagopalan, Langmuir 7, 1383 (1991).
[42] N. Choudhury and S. K. Ghosh, Phys. Rev. E 51, 4503 (1995).
[43] D.A. McQuarrie, Statistical Mechanics ( Harper and Row, New York, 1976), pp. 266.
[44] S.K. Lai, W.J. Ma, W. van Megen and I.K. Snook, Phys. Rev. E 56, 766 (1997).
[45] We have not considered the indirect hydrodynamic interaction since an accurate ac-
count of its in‡uence on the dynamic properties will require knowledge of irreducible
many-body contributions to the di¤usion tensor whose exact expression is, a priori, not
known. Within the MCT, Nägele and Baur [9] have derived an approximate formula
for . 0:08 which falls o¤ the mark of the present work.
[46] Here we follow the work of Baur et al. [9] in our de…nition of the bM(q; z). The di¤erence
between the latter and the one used by others [10, 11] is a factor q2D0 which can easily
be identi…ed.
[47] K. Kawasaki, Physica A 208, 35 (1994).
[48] U. Bengtzelius, W. Götze and A. Sjölander, J. Phys. C 17, 5915 (1984).
[49] L. Sjögren, Phys. Rev. A 22, 2883 (1980).
[50] We should point out that the e¤ective one component model of Belloni [1] is “con-
tracted”from the multicomponent Ornstein-Zernike equations [S.A. Adelman, J. Chem.
Phys. 64, 724 (1976)]. Within the theoretical framework of Belloni, it was shown there
that this one component model S(q) and that S00(q) in the primitive model (which
places equal footing on a collection of charged hard spheres with di¤erent species i and
j interacting via pure Coulomb forces ZiZj= jare exactly equal if the Z0 in both
models is taken to be the same nominal macroion charge. Accordingly, this Z0 should
not be treated as an e¤ective or renormalized macroion charge [51]. Note further that
this Z0 is determined self-consistently with the screening constant 2=4 LB( 0Z0Z1
+Pi=2 iZ2
i ) by the charge neutrality [24].
[51] K.S. Schmitz, Macroions in Solution and Colloidal Suspension (VCH, New York, 1993).
指導教授 賴山強(San-Kiong Lai) 審核日期 2006-1-24
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明