臺灣博碩士論文加值系統

一個真實的統計力學模型 [L. Belloni, J. Chem. Phys. 85, 519 (1986)]，被用來描述帶電膠體間的交互作用力，並應用於探討帶電膠體的相平衡問題。這個模型適用於有限膠體濃度的變化，從η→0(即Derjaguin-Landau-Verwey-Overbeek(DLVO)模型)至η＜0.5，此η範圍適用於討論帶電膠體之液態─液態相分離的物理。
訴諸於Week-Chandler-Andersen [J.D. Weeks, D. Chandler and H.C. Andersen, J. Chem. Phys. 54,5237(1971)] 微擾理論，此膠體系統的自由能是由一階微擾項所貢獻的。而所計算的系統壓力、化學勢和相關熱力學函數，將可以用來求解膠體系統的臨界點，如溫度、濃度和電解值濃度。
與DLVO 模型比較下，我們發現介於鞍點分離線和共存線區域內的面積，Belloni 模型在κ＜200 時，比DLVO模型來的寬，此外其臨界點κ值也比較低；當 κ＞300時，兩者的差異則變小。
同時我們運用相同的熱力學理論，來研究微弱的可逆凝聚現象，這個現象的根源是歸因於膠體作用力間位能屏障與第二極小位能井之間，其微妙的互補作用而形成的。
我們同時探討了不同的帶電膠體特性參數，以分析膠體的穩定性條件對結構所產生的影響。並和聚本乙稀與水的凝聚現象實驗做一比較，發現理論與實驗間兩者是相符且一致的。因此這增強了這個理論的可信度特別是給予Belloni模型一個很好的驗證。

A realistic statistical-mechanics model [L. Belloni, J. Chem. Phys. 85, 519 (1986)] for describing the inter-colloidal particle interaction is applied to study phase equilibria in charged colloidal dispersions. This model which is valid at any finite concentration is appropriate for investigating the liquid-liquid phase separation since the macro-ion volume
fraction η varies continuously from a low η→0
(the usual Derjaguin-Landau-Verwey-Overbeek (DLVO) model) to any finite η＜ 0.5 that characterizes a typical liquid phase. By
appealing to the Weeks-Chandler-Andersen [J.D. Weeks, D.Chandler
and H.C.Andersen, J. Chem. Phys. 54, 5237 (1971)] perturbation theory, the Helmholtz free energy is constructed to first order correction. Calculated pressure, chemical potential and related thermodynamic functions afford a determination of the critical temperature, η and electrolyte concentration. Compared with the DLVO model, we find the areas enclosed within the spinodal decomposition and also the liquid-liquid coexistence curves broader for the present model for κ< 200,sigma0 being the macro-ion diameter, in addition to exhibiting a shift in critical point κ to lower values for κ> 300, the disparities between the two models reduce. The same thermodynamic perturbation theory has been applied to study the weak
reversible coagulation whose physical origin is attributed to subtleties in the inter-colloidal particle interaction in connection with the compensation between the main potential barrier and the second potential minimum. We examine the various colloidal parameters that affect the structure of the latter and deduce from our analysis the conditions of colloidal stability.
In comparison with measured flocculation data for a binary mixture of polystyrene latices and water, we find our calculated results generally reasonable, thus lending great credence to the present theory particularly the proposed model of Belloni.

壹、 簡介 1
貳、 理論 2
一、 總位能 2
二、 WCA 微擾理論 3
參、 數值討論與分析 4
一、 鞍點分離 4
二、 液態─液態共存線 5
三、 可逆與不可逆凝聚現象 6
肆、 結論 9
I. Introduction 1
II. Theory 3
A. Total potential energy 4
B. Week-Chandler-Andersen perturbation theory 6
III. Numerical results and discussion 11
A. Spinodal decomposition 11
B. Liquid-liquid co-existence 13
C. Irreversible and reversible coagulation 13
IV. Conclusion 18
Reference 19
Figure caption

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{22} Contrary to the remark made by Victor and Hansen {12},
we find the stipulation of the potential barrier V(x$_
{\text{M}}$) sensitive to the results predicted. For
example, by choosing V(x$_{\text{M}}$)$% \lesssim $10k$_
{\text{B}}$T, we will obtain a $\sigma _{0}^{\text{min}}$
(see the discussion below) lower by about 500 $\stackrel
{\rm o}{\rm A}$.( In order to clearify the difference
between V(x$_{\text{M}}$)=15 k$_{%\text{B}}$T and V(x$_
{\text{M}}$)=10 k$_{\text{B}}$T. Interesting reader
may consult Appendix A and Appendix B.)
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{25} This x$_{\text{m}}$ is compatible with the experimental
data of Watillon and Joseph-Petit \cite{WJP}. Employing
their measured data ($%\sigma _{0}$=1760$\stackrel{\rm o}
{\rm A},$ A=0.5$\times 10^{-20}$ J,18 mV $% <\Psi <30$ mV
and 150 $<\kappa <$ 303) for the aqueous polystyrene
latices, we have checked that the average x$_{\text{m}}$
for different concentrations of NaClO$_{4}$ is located
approximately at x$_{\text{m}}\approx 1.024$ which is
reasonably close to the value expected for the $\sigma _
{0}$ range. ( For details, interesting reader may see
Appendix H.) \text{B}}$T.
[26] We base our argument on setting V(x$_{\text{M}}$)=15 k$_{%
T. One should bear in mind an order of approximately 500
$\stackrel%{\rm o}{\rm A}$ for a change in setting of
(x$_{\text{M}}$) by about 5k$_{%\text{B}}$T (see the
comment in {22}).