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27
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0001435573
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See Ref. 23 for further analysis.
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28
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0342449267
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For example, K. E. Starling, Soc. Pet. Eng. J. 6, 363 (1966); D. L. Katz and A. J. Firoozahadi, J. Pet. Technol. 30, 1649 (1978), and references therein.
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Starling, K.E.1
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and references therein
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For example, K. E. Starling, Soc. Pet. Eng. J. 6, 363 (1966); D. L. Katz and A. J. Firoozahadi, J. Pet. Technol. 30, 1649 (1978), and references therein.
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36
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0342883775
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note
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i + 2) terms. On the other hand, for a strongly asymmetric parent, by Eq. (18), the daughters have very different second moments. Thus the skew of the parent is highly influential, contrary to the impression given in Ref. 31.
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37
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0342449257
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note
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In this case, the external fields may be provided by an admixture of other conserved species, in whose presence our slightly polydisperse component exists.
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38
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0342883776
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note
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p and operands of Δ̂).
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39
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0342883773
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note
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This expansion of the equations of the phase boundaries is in some ways equivalent (though in a quite different formalism) to the Clausius-Clapeyron-type equation derived by Bolhuis and Kofke (Ref. 6) for the P - ν phase diagram, where ν parametrizes the variance of a Gaussian distribution of activities of polydisperse hard spheres. The present analysis, though restricted to narrow distributions, is more general.
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40
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0034300186
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N. Clarke, J. A. Cuesta, R. Sear, P. Sollich, and A. Speranza, J. Chem. Phys. 113, 5817 (2000).
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Speranza, A.5
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43
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0343754552
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note
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Greek subscripts were used to denote generic phases, whereas c and s indicate cloud and shadow phases, respectively, for which the relative numbers of constituent particles are specified.
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44
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0342883770
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note
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-1 - P 1)/4 found by comparison with the exact calculation here.
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45
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0000489946
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T. Boublik, J. Chem. Phys. 53, 471 (1970); G. A. Mansoori, N. F. Carnahan, K. E. Starling, and T. W. Leland, ibid. 54, 1523 (1971).
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Boublik, T.1
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T. Boublik, J. Chem. Phys. 53, 471 (1970); G. A. Mansoori, N. F. Carnahan, K. E. Starling, and T. W. Leland, ibid. 54, 1523 (1971).
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Mansoori, G.A.1
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47
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0343754551
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note
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In a monodisperse system, the distribution is a delta function. It is therefore not possible to vary the mean while holding the other moments constant. Nevertheless, being of higher order in the small quantity ∈, the higher moments are stationary, so the partial derivative is well defined.
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48
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0343318697
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note
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An equivalent result appears in Ref. 7.
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51
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0343754549
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(private communication). These data appear implicitly in Ref. 6
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P. G. Bolhuis (private communication). These data appear implicitly in Ref. 6.
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P. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, New York, 1971); M. Huggins, J. Phys. Chem. 46, 151 (1942). See also M. Doi, Introduction to Polymer Physics (Oxford University Press, Oxford, England, 1997).
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Introduction to Polymer Physics
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55
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0343318695
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private communication
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Reproduced by kind permission of P. Sollich (private communication).
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33646068673
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61
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33645914676
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In particular, the second virial coefficient of the polymeric osmotic pressure can be made to vanish, though higher virial coefficients remain; G. C. Berry, J. Chem. Phys. 44, 4550 (1966).
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64
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0342449253
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note
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A more accurate description would include corrections to the pairwise attraction, since three or four latices in close proximity exclude polymer coils from a region with nontrivial geometry.
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68
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0000566969
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0343318692
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note
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Plus terms of the order of the (i + 2)th moment, which become important in a near-symmetric distribution if i is even (Rets. 31 and 32).
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72
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0342449250
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private communication
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R. Sear (private communication).
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Sear, R.1
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