Title page for 86222007


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Student Number 86222007
Author Wen-Ping Peng(彭文平)
Author's Email Address No Public.
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Department Physics
Year 1998
Semester 2
Degree Master
Type of Document Master's Thesis
Language English
Title liquid-liquid phase diagrams in charged colloidal dispersions
Date of Defense
Page Count 52
Keyword
  • Belloni model
  • phase separation
  • potential of mean force
  • reversible and irreversible coagulation
  • secondary minimum
  • WCA perturbation theory
  • Abstract 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.
    Table of Content 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
    Reference {1} L. Belloni, J. Chem. Phys. 85, 519 (1986).
    {2} S. Khan, T.L. Morton and D. Ronis, Phys. Rev. A 35,
    4295 (1987).
    {3} E.J. Verwey and J.G. Overbeek, { Theory of the Stability of
    Lyophobic Colloids} (Elsevier, Amsterdam, 1948) .
    {4} S.K. Lai and G.F. Wang, Phys. Rev. E 58, 3072 (1998).
    {5} S.K. Lai, J.L. Wang and G.F. Wang, J. Chem. Phys., in press
    (1999).
    {6} G.F. Wang and S.K. Lai, Phys. Rev. Lett., May issue (1999).
    {7} J.H. Schenkel and J.A. Kitchener, Trans. Faraday Soc. 56,
    161 (1960).
    {8} J.A. Long, D.W.J. Osmond and B. Vincent, J. Colloid
    Interface Sci. 42, 545 (1973).
    {9} A. Kotera, K. Furusawa and K. Kubo, Kolloid Z. Z. Polym.
    240, 837 (1970).
    {10} K. Gotoh, R. Kohsaka, K. Abe and M. Tagawa, J. Adhesion
    Sci.Technol. 10, 1359 (1996).
    {11} M.J. Grimson, J. Chem. Soc. Faraday Trans. 2 79, 817
    (1983).
    {12} J.M. Victor and J.P. Hansen, J. Physique Lett. 45,
    L307(1984); J. Chem. Soc. Faraday Trans. 2 81, 43 (1985).
    {13} J. Kaldasch, J. Laven and H.N. Stein, Langmuir 12, 6197
    (1996).
    {14} Here we are concerned with the second minimum of V(r)
    whose interaction strength comes solely from the London-
    van der Waals attraction. The physical origin and the
    range of the latter attraction are somewhat different
    from many other mechanisms (see Lowen [Physica A, 235,
    129 (1997)] for a general description) giving rise to
    different range of attractive forces. Since the mechanism
    leading to the attraction varies with the physical system
    and is still not fully understood or may be even
    controversial, we confine our calculations to only the van
    der Waals kind of attraction. Note that, depending on the
    colloidal conditions, the range of the London-van der
    Waals attraction for charged colloids may be short-ranged
    but it is of a somewhat different nature from those
    extremely short-ranged attractions that are shown
    theoretically [J.M. Kincaid, G. Stell and E. Goldmark, J.
    Chem. Phys. 65, 2172 (1976); C.F. Tejero et al., Phys.
    Rev. Lett. 73, 752 (1994)] and in computer simulation
    studies [B. Alder and D. Young, J. Chem. Phys. 70, 473
    (1979); P. Bolhuis and D. Frenkel, Phys. Rev. Lett. 72,
    2211 (1994)] to lead to a different type of phase
    transition---the isostructual solid-solid transition.
    {15} J.D. Weeks, D. Chandler and H.C. Andersen, J. Chem. Phys.
    54, 5237 (1971).
    {16} A. Adelman, Chem. Phys. Lett. 38, 567 (1976); J. Chem.
    Phys. 64, 724 (1976).
    {17} D.A. McQuarrie, Statistical Mechanics (}Harper and Row,
    New York, 1976), pp. 266.
    {18} L. Verlet and J.J. Weis, Mol. Phys. 24, 1013 (1972).
    {19} J.P. Hansen, L. Reatto, M. Tau and J.M. Victor, Mol. Phys.
    56, 385 (1985).
    {20} A. Watillon and A.M. Joseph-Petit, Disc. Faraday Soc. 42,
    143 (1966).
    {21} J. Th. G. Overbeek, Colloid Science, edited by H.R.
    Kruyt, (Elsevier, Amsterdam, 1948)
    {22} Contrary to the remark made by Victor and Hansen {12},
    we find the stipulation of the potential barrier V(x$_
    {ext{M}}$) sensitive to the results predicted. For
    example, by choosing V(x$_{ext{M}}$)$% lesssim $10k$_
    {ext{B}}$T, we will obtain a $sigma _{0}^{ext{min}}$
    (see the discussion below) lower by about 500 $stackrel
    {
    m o}{
    m A}$.( In order to clearify the difference
    between V(x$_{ext{M}}$)=15 k$_{%ext{B}}$T and V(x$_
    {ext{M}}$)=10 k$_{ext{B}}$T. Interesting reader
    may consult Appendix A and Appendix B.)
    {23} B. Vincent, J. Colloid Interface Sci. 42, 270 (1973).
    {24} R.H. Ottewill and J.N. Shaw, Discs. Faraday Soc. 42, 154
    (1966).
    {25} This x$_{ext{m}}$ is compatible with the experimental
    data of Watillon and Joseph-Petit cite{WJP}. Employing
    their measured data ($%sigma _{0}$=1760$stackrel{
    m o}
    {
    m A},$ A=0.5$imes 10^{-20}$ J,18 mV $% <Psi <30$ mV
    and 150 $<kappa <$ 303) for the aqueous polystyrene
    latices, we have checked that the average x$_{ext{m}}$
    for different concentrations of NaClO$_{4}$ is located
    approximately at x$_{ext{m}}approx 1.024$ which is
    reasonably close to the value expected for the $sigma _
    {0}$ range. ( For details, interesting reader may see
    Appendix H.) ext{B}}$T.
    [26] We base our argument on setting V(x$_{ext{M}}$)=15 k$_{%
    T. One should bear in mind an order of approximately 500
    $stackrel%{
    m o}{
    m A}$ for a change in setting of
    (x$_{ext{M}}$) by about 5k$_{%ext{B}}$T (see the
    comment in {22}).
    Advisor
  • S. K. Lai(賴山強)
  • Files No Any Full Text File.
    Date of Submission

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