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23
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84927486332
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This expression for α derived from a theory of the fluid state should not, in principle, be used for working out the free volume fraction for any state with long range order. The inaccuracies involved in using this expression for the hard sphere solid, as in the work of Lekkerkerker et al., Ref. 22, have been discussed recently in, Ref. 35
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30
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84927466830
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It is not clear that the variable φ3 in, Ref. 24, is equal to our ηp(R). The most natural interpretation of that paper suggests that φ3 = (4/3)π rg3 np = ηp in our notation, in which case the phase diagrams should have looked more like the ones shown in Figs. 2(d), 2(e), and 2(f). This certainly is how subsequent authors have interpreted, Ref. 24, leading to the use of Πp = np kBT in calculating the depletion potential, which is wrong.
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34
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84927500017
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Compare M. Planck, Treatise on Thermodynamics, 3rd ed. (Dover, New York, 1926), Sec. 189, where it is shown that the triple point of the conventional p T phase diagram of a simple substance becomes a triple region in the specific volume specific energy representation. See the very illuminating discussion on the topology of phase diagrams plotted using different kinds of thermodynamic variables by Robert T. De Hoff, Thermodynamics in Material Science (McGraw Hill, New York, 1993), Sec. 7.6 and 9.4.
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42
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84927496716
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see also Robert T. De Hoff, Thermodynamics in Material Science, Ref. 34
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43
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84927462951
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We did not attempt to determine the concentrations of polymer in the various phases, although this could, in principle, be done using the method outlined in the Appendix in, Ref. 14
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44
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4243463085
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A very dramatic illustration of the effect of ``nonideality'' is provided by the recent work on the phase diagram of a mixture of hard spheres with a size ratio of 0.58:, (experiment);
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(1992)
Phys. Rev. Lett.
, vol.68
, pp. 3801
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Bartlett, P.1
Ottewill, R.H.2
Pusey, P.N.3
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45
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85038277011
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fairly nonideal, Nature 365, 35 (1993) (simulation). This size ratio is almost exactly the same as that given by polymer C in this work. At 23°C, the Fixman parameter for this polymer in cis decalin, Ref. 38, is 1.25, but very far from being hard sphere like. The phase diagram for this case, Fig. 2(i), is very different from those obtained for the hard sphere mixture at practically an identical size ratio in the two references quot, also W.
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(1994)
Europhys. Lett.
, vol.28
, pp. 513
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Eldridge, M.D.1
Madden, P.A.2
Frenkel, D.3
Compare4
Poon, C.K.5
Warren, P.B.6
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50
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84927464072
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The possibility of such a situation, of which many investigators seem unaware, has already been pointed out by Cahn in 1968;
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52
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84927497318
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Figure 6 of this review referred to ``a miscibility gap that is entirely metastable.''
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