-
2
-
-
0004144080
-
-
ed. S. Petrucci Academic Press, New York, but note slips in Eqs. (49) and (51)
-
H. Falkenhagen and W. Ebeling, in: Ionic Interactions, ed. S. Petrucci (Academic Press, New York, 1971), Vol. 1; but note slips in Eqs. (49) and (51).
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(1971)
Ionic Interactions
, vol.1
-
-
Falkenhagen, H.1
Ebeling, W.2
-
5
-
-
0001394832
-
-
(b) J. Chem. Phys. 97 (1992) 2609. To our knowledge, these are the first authors to clearly state that the full DH theory (without further supplement) predicts phase separation and a critical point. See also, however,
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J. Chem. Phys.
, vol.97
, pp. 2609
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-
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6
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2942698800
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Leipzig
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(c) W. Ebeling, Z. Phys. Chem. (Leipzig) 247 (1971) 340;
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Z. Phys. Chem.
, vol.247
, pp. 340
-
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Ebeling, W.1
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7
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0003589247
-
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Akademie Verlag, Berlin
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(d) W. Ebeling, W.D. Kraeft and D. Kremp, Theory of Bound States and Ionization Equilibrium in Plasmas and Solids (Akademie Verlag, Berlin, 1976) Sections 6.2,6.4, in relation to the "plasma phase transition" of
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(1976)
Theory of Bound States and Ionization Equilibrium in Plasmas and Solids
-
-
Ebeling, W.1
Kraeft, W.D.2
Kremp, D.3
-
9
-
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0007333041
-
-
(e) G.É. Norman and A.N. Starostin, Teplofiz. Vys. Temp. 6 (1968) 410; 8 (1970) 413; and
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Teplofiz. Vys. Temp.
, vol.8
, pp. 413
-
-
-
10
-
-
0042819973
-
-
but note that the peculiar "schematic" phase diagrams presented, with two types of critical point, do not appear to follow from the theory set out. For comments on the theoretical discussion of McGahay and Tomozawa see Refs. [37, 45, 60] below
-
(f) M. Gitterman and V. Steinberg, Phys. Rev. A 20 (1979) 1236; but note that the peculiar "schematic" phase diagrams presented, with two types of critical point, do not appear to follow from the theory set out. For comments on the theoretical discussion of McGahay and Tomozawa see Refs. [37, 45, 60] below.
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(1979)
Phys. Rev. A
, vol.20
, pp. 1236
-
-
Gitterman, M.1
Steinberg, V.2
-
16
-
-
85030004056
-
-
note
-
c, so that both liquid and vapor branches always lie above the critical density. Friedman and Larsen commented that such a shape "is not realistic". These remarks and observations were a prime stimulus for our own studies but, as we find (see Refs. [5, 6] and Fig. 2 here) the sharp marlin-spike feature is not correct: it seems to have resulted from numerical inadequacies in computing the coexistence curve. (Private communication from Professor H.L. Friedman.) In retrospect it is perhaps surprising that Friedman and Larsen did not also examine the original DH theory which, as we find (Refs. [5, 6]), has a coexistence curve of perfectly acceptable shape.
-
-
-
-
18
-
-
33845470617
-
-
concisely reviews the statistical mechanics and thermodynamics of real ionic fluids and critically discusses the conceptual aspects of ion pairing, etc.
-
K.S. Pitzer, J. Phys. Chem. 88 (1984) 2689, concisely reviews the statistical mechanics and thermodynamics of real ionic fluids and critically discusses the conceptual aspects of ion pairing, etc.
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J. Phys. Chem.
, vol.88
, pp. 2689
-
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Pitzer, K.S.1
-
21
-
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85088670772
-
-
A.Z. Panagiotopoulos, Fluid Phase Equil. 76 (1992) 97; 92 (1994) 313.
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(1994)
Fluid Phase Equil.
, vol.92
, pp. 313
-
-
-
24
-
-
0642355969
-
Melting, Localization and Chaos
-
eds. R. Kalia and P. Vashishta North-Holland, New York
-
c ≳ 0.057 should not be accepted since it is based on an assumption (about the finite-size, canonical density distributions near criticality) which is not trustworthy. This may be seen from the exact finite-size canonical distribution function for a soluble lattice model reported by (a) D.A. Huse and M.E. Fisher in: Melting, Localization and Chaos, Proc. 9th Midwest Solid State Theory Symp., eds. R. Kalia and P. Vashishta (North-Holland, New York, 1982) p. 259:
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(1982)
Proc. 9th Midwest Solid State Theory Symp.
, pp. 259
-
-
Huse, D.A.1
Fisher, M.E.2
-
26
-
-
0001393032
-
-
See also the review Ref. [6]
-
(c) M.J. Gillan, Molec. Phys. 49 (1983) 421; See also the review Ref. [6].
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Molec. Phys.
, vol.49
, pp. 421
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Gillan, M.J.1
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33
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0001324069
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T. Narayanan and K.S. Pitzer, J. Phys. Chem. 98 (1994) 9170; Phys. Rev. Lett. 73 (1994) 3002.
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(1994)
Phys. Rev. Lett.
, vol.73
, pp. 3002
-
-
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34
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0001138141
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H. Weingärtner, T. Merkel, U. Maurer, J.-P. Conzen, H. Glasbrenner and S. Käshammer, Ber. Buns. Phys. Chem. 95 (1991) 1579.
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Ber. Buns. Phys. Chem.
, vol.95
, pp. 1579
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Weingärtner, H.1
Merkel, T.2
Maurer, U.3
Conzen, J.-P.4
Glasbrenner, H.5
Käshammer, S.6
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36
-
-
0000490118
-
-
See, particularly: (a) G. Stell, Phys. Rev. A 45 (1992) 7628;
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(1992)
Phys. Rev. A
, vol.45
, pp. 7628
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Stell, G.1
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38
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0000412853
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(b) A. Kholodenko and A.L. Beyerlein, Phys. Lett. A 132 (1988) 347; J. Chem. Phys. 93 (1990) 8405;
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J. Chem. Phys.
, vol.93
, pp. 8405
-
-
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41
-
-
5544310050
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See also (a) G. Stell, J. Stat. Phys. 78 (1994) 197; Some more recent theoretical studies which tend to discredit one possible source of near-classical critical behavior are reported in
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(1994)
J. Stat. Phys.
, vol.78
, pp. 197
-
-
Stell, G.1
-
45
-
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3843085011
-
-
M.E. Fisher, Phys. Rev. Lett. 57 (1986) 1911; but note, as regards the experimental data stimulating this work, the later experiments by G. Dietler and D.S. Cannell, Phys. Rev. Lett. 60 (1988) 1852.
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(1986)
Phys. Rev. Lett.
, vol.57
, pp. 1911
-
-
Fisher, M.E.1
-
46
-
-
0000439351
-
-
M.E. Fisher, Phys. Rev. Lett. 57 (1986) 1911; but note, as regards the experimental data stimulating this work, the later experiments by G. Dietler and D.S. Cannell, Phys. Rev. Lett. 60 (1988) 1852.
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(1988)
Phys. Rev. Lett.
, vol.60
, pp. 1852
-
-
Dietler, G.1
Cannell, D.S.2
-
48
-
-
35949031669
-
-
See, e.g., M.E. Fisher, Rev. Mod. Phys. 46 (1974) 597; and, as a particular example not unrelated to the present problem, consider the question of the effects of long-range dipolar interactions on the critical behavior of ferromagnets and antiferromagnets with short-range exchange couplings: M.E. Fisher and A. Aharony, Phys. Rev. Lett. 30 (1973) 559; A. Aharony and M.E. Fisher, Phys. Rev. 8 (1973) 3323; A. Aharony, Phys. Rev. B 8 (1973) 3342, 3349, 3358, 3363.
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(1974)
Rev. Mod. Phys.
, vol.46
, pp. 597
-
-
Fisher, M.E.1
-
49
-
-
4243667363
-
-
See, e.g., M.E. Fisher, Rev. Mod. Phys. 46 (1974) 597; and, as a particular example not unrelated to the present problem, consider the question of the effects of long-range dipolar interactions on the critical behavior of ferromagnets and antiferromagnets with short-range exchange couplings: M.E. Fisher and A. Aharony, Phys. Rev. Lett. 30 (1973) 559; A. Aharony and M.E. Fisher, Phys. Rev. 8 (1973) 3323; A. Aharony, Phys. Rev. B 8 (1973) 3342, 3349, 3358, 3363.
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(1973)
Phys. Rev. Lett.
, vol.30
, pp. 559
-
-
Fisher, M.E.1
Aharony, A.2
-
50
-
-
0000829272
-
-
See, e.g., M.E. Fisher, Rev. Mod. Phys. 46 (1974) 597; and, as a particular example not unrelated to the present problem, consider the question of the effects of long-range dipolar interactions on the critical behavior of ferromagnets and antiferromagnets with short-range exchange couplings: M.E. Fisher and A. Aharony, Phys. Rev. Lett. 30 (1973) 559; A. Aharony and M.E. Fisher, Phys. Rev. 8 (1973) 3323; A. Aharony, Phys. Rev. B 8 (1973) 3342, 3349, 3358, 3363.
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(1973)
Phys. Rev.
, vol.8
, pp. 3323
-
-
Aharony, A.1
Fisher, M.E.2
-
51
-
-
0000303061
-
-
See, e.g., M.E. Fisher, Rev. Mod. Phys. 46 (1974) 597; and, as a particular example not unrelated to the present problem, consider the question of the effects of long-range dipolar interactions on the critical behavior of ferromagnets and antiferromagnets with short-range exchange couplings: M.E. Fisher and A. Aharony, Phys. Rev. Lett. 30 (1973) 559; A. Aharony and M.E. Fisher, Phys. Rev. 8 (1973) 3323; A. Aharony, Phys. Rev. B 8 (1973) 3342, 3349, 3358, 3363.
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(1973)
Phys. Rev. b
, vol.8
, pp. 3342
-
-
Aharony, A.1
-
52
-
-
4243150975
-
-
An interesting case of possible conceptual relevance here, in which the derivation of an adequate LGW effective Hamiltonian poses a more difficult problem, is the critical wetting transition in bulk, three-dimensional fluid systems with short-range forces: see M.E. Fisher and A.J. Jin, Phys. Rev. Lett. 69 (1992) 792; A.J. Jin and M.E. Fisher, Phys. Rev. B 48 (1993) 2642.
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(1992)
Phys. Rev. Lett.
, vol.69
, pp. 792
-
-
Fisher, M.E.1
Jin, A.J.2
-
53
-
-
0001635783
-
-
An interesting case of possible conceptual relevance here, in which the derivation of an adequate LGW effective Hamiltonian poses a more difficult problem, is the critical wetting transition in bulk, three-dimensional fluid systems with short-range forces: see M.E. Fisher and A.J. Jin, Phys. Rev. Lett. 69 (1992) 792; A.J. Jin and M.E. Fisher, Phys. Rev. B 48 (1993) 2642.
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(1993)
Phys. Rev. B
, vol.48
, pp. 2642
-
-
Jin, A.J.1
Fisher, M.E.2
-
58
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3743088961
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Coulombic criticality in general dimensions
-
See, e.g., Y. Levin, X.-J. Li and M.E. Fisher, Coulombic criticality in general dimensions, Phys. Rev. Lett. 73 (1994) 2716.
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Phys. Rev. Lett.
, vol.73
, pp. 2716
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Levin, Y.1
Li, X.-J.2
Fisher, M.E.3
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59
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0000299213
-
-
See M.E. Fisher, J. Chem. Phys. 42 (1965) 3852 for the validity of the free-volume form near close packing: few approximate analytic forms embody this.
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(1965)
J. Chem. Phys.
, vol.42
, pp. 3852
-
-
Fisher, M.E.1
-
60
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33644529011
-
-
For differential and partial differential approximant techniques that might be used to extend virial series, etc., see, e.g., M.E. Fisher and H. Au-Yang, J. Phys. A 12 (1979) 1677; 13 (1980) 1517; A.J. Guttmann, in: Phase Transitions and Critical Phenomena, Vol. 13, eds. C. Domb and J.L. Lebowitz (Academic Press, New York, 1989) p. 1.
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(1979)
J. Phys. A
, vol.12
, pp. 1677
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Fisher, M.E.1
Au-Yang, H.2
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61
-
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33644529011
-
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For differential and partial differential approximant techniques that might be used to extend virial series, etc., see, e.g., M.E. Fisher and H. Au-Yang, J. Phys. A 12 (1979) 1677; 13 (1980) 1517; A.J. Guttmann, in: Phase Transitions and Critical Phenomena, Vol. 13, eds. C. Domb and J.L. Lebowitz (Academic Press, New York, 1989) p. 1.
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(1980)
J. Phys. A
, vol.13
, pp. 1517
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62
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33644529011
-
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eds. C. Domb and J.L. Lebowitz Academic Press, New York
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For differential and partial differential approximant techniques that might be used to extend virial series, etc., see, e.g., M.E. Fisher and H. Au-Yang, J. Phys. A 12 (1979) 1677; 13 (1980) 1517; A.J. Guttmann, in: Phase Transitions and Critical Phenomena, Vol. 13, eds. C. Domb and J.L. Lebowitz (Academic Press, New York, 1989) p. 1.
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(1989)
Phase Transitions and Critical Phenomena
, vol.13
, pp. 1
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Guttmann, A.J.1
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63
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85030007718
-
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note
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c for the RPM.
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65
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0346437379
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S.F. Edwards, Philos. Mag. 4 (1959) 1171; and see: P. Minnhagen, Rev. Mod. Phys. 59 (1987) 1001.
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Philos. Mag.
, vol.4
, pp. 1171
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Edwards, S.F.1
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66
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35949013580
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S.F. Edwards, Philos. Mag. 4 (1959) 1171; and see: P. Minnhagen, Rev. Mod. Phys. 59 (1987) 1001.
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Rev. Mod. Phys.
, vol.59
, pp. 1001
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Minnhagen, P.1
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67
-
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85030005337
-
-
note
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4 = 1, takes the value √3 [but note the different prefactors defining p† here and in (4.6)].
-
-
-
-
68
-
-
85030006758
-
-
note
-
It was for this reason that the apparent finding of a "marlin spike", β= 1 coexistence curve by Friedman and Larsen [9, 10] was so startling,
-
-
-
-
69
-
-
0004607567
-
-
Unfortunately, various slips and deficiencies of presentation make this interesting paper, like Ref. [11], hard to assess
-
M. Grigo and W. Ebeling, J. Soln. Chem. 13 (1984) 321. Unfortunately, various slips and deficiencies of presentation make this interesting paper, like Ref. [11], hard to assess.
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J. Soln. Chem.
, vol.13
, pp. 321
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Grigo, M.1
Ebeling, W.2
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70
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0003851731
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National Bureau of Standards, U.S. Govt. Printing Office, Washington, Section 5
-
See, e.g., Handbook of Mathematical Functions, eds. M. Abramowitz and I.A. Stegun (National Bureau of Standards, U.S. Govt. Printing Office, Washington, 1964) Section 5.
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(1964)
Handbook of Mathematical Functions
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Abramowitz, M.1
Stegun, I.A.2
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71
-
-
85030007113
-
-
note
-
1 ≃ 23. However, that seems likely to be an overestimate for the critical region since the densities of charged ions rise increasingly rapidly with temperature above T* ≃ 0.05 and the total vapor pressure on the phase boundary is increasingly uncertain.
-
-
-
-
72
-
-
85030022438
-
-
note
-
It should be mentioned that although McGahay and Tomozawa [4] considered simple Bjerrum theory, they did not notice the unphysical banana effect of Fig. 1 since they did not compute the coexistence curves.
-
-
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73
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0742274036
-
-
(a) R.M. Fuoss, J. Am. Chem. Soc. 80 (1958) 5059. See also J. E. Prue in: Chemical Physics of Ionic Solutions, eds. B.E. Conway and R.G. Barrados (Wiley, New York, 1966).
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J. Am. Chem. Soc.
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, pp. 5059
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Fuoss, R.M.1
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74
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0742274036
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eds. B.E. Conway and R.G. Barrados Wiley, New York
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(a) R.M. Fuoss, J. Am. Chem. Soc. 80 (1958) 5059. See also J. E. Prue in: Chemical Physics of Ionic Solutions, eds. B.E. Conway and R.G. Barrados (Wiley, New York, 1966).
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Chemical Physics of Ionic Solutions
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Prue, J.E.1
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76
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33751399211
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M.-C. Justice and J.-C. Justice, J. Soln. Chem. 5 (1976) 543; 6 (1977) 819.
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79
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0000322775
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H. Weingärtner, T. Merkel, S. Käshammer, W. Schröer, and S. Wiegand, Ber. Buns. Phys. Chem. 97 (1993) 970; W. Schröer, S. Wiegand and H. Weingärtner; Ber. Buns. Phys. Chem. 97 (1993) 975.
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Ber. Buns. Phys. Chem.
, vol.97
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Weingärtner, H.1
Merkel, T.2
Käshammer, S.3
Schröer, W.4
Wiegand, S.5
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80
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0000173576
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H. Weingärtner, T. Merkel, S. Käshammer, W. Schröer, and S. Wiegand, Ber. Buns. Phys. Chem. 97 (1993) 970; W. Schröer, S. Wiegand and H. Weingärtner; Ber. Buns. Phys. Chem. 97 (1993) 975.
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Ber. Buns. Phys. Chem.
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Schröer, W.1
Wiegand, S.2
Weingärtner, H.3
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82
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85030002542
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note
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-4: see (4.6) and (4.7).
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84
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0000399664
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H. Yokoyama and H. Yamatera, Chem. Lett. 1973 (1973) 337; Bull. Chem. Soc. Jpn. 48, (1975) 1770.
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Bull. Chem. Soc. Jpn.
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86
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0000591606
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See, e.g., (a) M.E. Fisher, Physics 3 (1967) 255;
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Physics
, vol.3
, pp. 255
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Fisher, M.E.1
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89
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85030021550
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19th Meeting of the Société de Chimie Physique Montpellier, September
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L. Onsager, J. Chim. Phys. Special Issue, 19th Meeting of the Société de Chimie Physique (Montpellier, September 1968) p. 86.
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J. Chim. Phys. Special Issue
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Onsager, L.1
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90
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85030004538
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See also Ref. [2] p. 47
-
See also Ref. [2] p. 47.
-
-
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91
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85030016249
-
-
note
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2. See Ebeling and Grigo [11] and the discussion of the MSA below in Section 9.
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92
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0003864467
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Interscience, New York, Sections 13, 15
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H.L. Friedman, Ionic Solution Theory (Interscience, New York, 1962) Sections 13, 15.
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Ionic Solution Theory
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Friedman, H.L.1
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93
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85030014363
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-
note
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In their application of Bjerrum's theory, McGahay and Tomozawa [4] employed Fuoss' [46] expression for the association constant being unaware of its unsatisfactory nature [2, 47, 53].
-
-
-
-
94
-
-
85030019422
-
-
note
-
BjT*(1 + 8T*). Used with (5.11) this is around ±10% accurate up to T * ≃ 0.07.
-
-
-
-
95
-
-
0003864328
-
-
Bateman Manuscript Project McGraw-Hill, New York, Chap. 7
-
For the necessary properties of the spherical Bessel functions and other technicalities see Ref. [27(c)]; and e.g., A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, eds., Higher Transcendental Functions, Bateman Manuscript Project (McGraw-Hill, New York, 1953), Vol. II, Chap. 7.
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Erdélyi, A.1
Magnus, W.2
Oberhettinger, F.3
Tricomi, F.G.4
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97
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0000959678
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See also the GMSA proposed by (a) J.S. Høye, J.L. Lebowitz and G. Stell, J. Chem. Phys. 61 (1974) 3253; For earlier work showing coexistence curves and spinodals graphically,
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Høye, J.S.1
Lebowitz, J.L.2
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0001255054
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(a) A.P. Levanyuk, Zh. Eks. Teor. Phys. 36 (1959) 810 [Sov. Phys. JETP 36 (1959) 571] ;
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Sov. Phys. JETP
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102
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0001017405
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(b) V.L. Ginzburg, Fiz. Tverd. Tela 2 (1960) 2031 [Sov. Phys. Solid State 2 (1960) 1824];
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Ginzburg, V.L.1
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103
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0000016599
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(b) V.L. Ginzburg, Fiz. Tverd. Tela 2 (1960) 2031 [Sov. Phys. Solid State 2 (1960) 1824];
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Sov. Phys. Solid State
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, pp. 1824
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107
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0039588263
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eds. W.S. Goree and F. Chilton Stanford Research Inst., Menlo Park, Section IV; and also see: e.g.
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(f) P.C. Hohenberg in: Fluctuations in Superconductors, eds. W.S. Goree and F. Chilton (Stanford Research Inst., Menlo Park, 1968) p. 305, Section IV; and also see: e.g.
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Fluctuations in Superconductors
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Hohenberg, P.C.1
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109
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0001805648
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Critical Phenomena
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ed. F.J.W. Hahne, Springer-Verlag, Berlin
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(h) M.E. Fisher, in: Critical Phenomena, ed. F.J.W. Hahne, Lect. Notes Phys. 186 (Springer-Verlag, Berlin, 1983) pp. 106-107;
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Lect. Notes Phys.
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Fisher, M.E.1
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R.J.F. Leote de Carvalho and R. Evans, Molec. Phys. 83 (1994) 619; J. Phys. Cond. Matt. 7 (1995) L 575.
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B.P. Lee and M.E. Fisher, to be published
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B.P. Lee and M.E. Fisher, to be published.
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114
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J.L. Lebowitz, Phys. Rev. 133 (1964) A 895; R.J. Baxter, J. Chem. Phys. 52 (1970) 4559.
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