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D)!) because exchanging all particles within their domains and between domains at constant energetic levels as formulated in Equation (12) already involves this entropic contribution.
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D)!) because exchanging all particles within their domains and between domains at constant energetic levels as formulated in Equation (12) already involves this entropic contribution.
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Dislocations separating subdomains have necessarily a width. Hence their creation into an initially perfect 2D supracrystal necessarily increases the surface area of the supracrystal. and hence modifies the base substrate surface tension. However, on the one hand this may be included into the edge enthalpy considered here. On the other hand, as we are interested in systems such as ND-→1 and with non-fractal boundaries, the resulting variation. ΔA0, in the surface area of the 2D supracrystal is proportional to rpd√N0, in which d is the average width of a boundary while the surface area, A0, of the crystal is proportional to rp2N0. Thus, provided that N0 is large enough and d is at most in the same range as the nanoparticle size, r p, one has ΔA0/A0 α 1/√N 0→0. These conditions correspond perfectly to the sy
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[2-4] Hence the ensuing variations in substrate surface tension may be neglected in our analysis.
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Note that the very crystallographic nature of a supracrystal will intervene in our analysis only by specifying the numerical factors which give the exact relationships between N0, N0 and Np, on the one hand and a0 aD. and rp, on the other hand. As evidenced in the Appendix, adapting the present analysis to different supracrystals requires that N0, ND, Np and ωa, are specific parameters close to unity, as evidenced in the Appendix for squared centered or hexagonal arrays
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a, are specific parameters close to unity, as evidenced in the Appendix for squared centered or hexagonal arrays.
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0. However since q > 1 for the systems of practical interest the exact values of the lower limits of the q range are irrelevant to our analyses.
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0. However since q > 1 for the systems of practical interest the exact values of the lower limits of the q range are irrelevant to our analyses.
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55
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One possible approach to overcome the dual constraint between i) strong enthalpic interactions with the array lattice nodes and ii weak enthalpic interactions between the elements of the array is to uncouple chemically both constraints. For example, the nanoparticles may be linked to the 2D surface through strong covalent bonds quantically uncoupled from the nanoparticles. See, e.g.: K. Bandyopadhyay, V. Patil, K. Vijayamohanan, M. Sastry, Langmuir 1997, 13, 5244-5248.
-
One possible approach to overcome the dual constraint between i) strong enthalpic interactions with the array lattice nodes and ii) weak enthalpic interactions between the elements of the array is to uncouple chemically both constraints. For example, the nanoparticles may be linked to the 2D surface through strong covalent bonds quantically uncoupled from the nanoparticles. See, e.g.: K. Bandyopadhyay, V. Patil, K. Vijayamohanan, M. Sastry, Langmuir 1997, 13, 5244-5248.
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