2-D phase transitions

Milchev, A.

doi:10.1016/0013-4686(83)85170-6

Cited by 12 publications

(7 citation statements)

References 11 publications

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“…A rather surprising finding of numerical (Monte Carlo) calculations is that a single type of trio interaction need not necessarily lead to a large asymmetry in the phase boundary about half-coverage. 56 This result, illustrated in Figure 2 for the case of a c(2X2) overlayer described in eq 2, is in sharp contrast to the observation in 2-d calculations that treat fluctuations approximately-mean field and quasi-chemical approximation-that trios must produce such asymmetries. 56 We also see that a linear trio Elt alone does not produce an asymmetry, but when it and Ert are present, the expected notable asymmetry does appear.…”

Section: Effects Of Trio Interactions On Statistical Mechanicsmentioning

confidence: 71%

“…56 This result, illustrated in Figure 2 for the case of a c(2X2) overlayer described in eq 2, is in sharp contrast to the observation in 2-d calculations that treat fluctuations approximately-mean field and quasi-chemical approximation-that trios must produce such asymmetries. 56 We also see that a linear trio Elt alone does not produce an asymmetry, but when it and Ert are present, the expected notable asymmetry does appear. To make some sense of this effect of trios on the phase boundary, we need some way to assess the difference in the way the trio interactions affect the lowtemperature ordered phase compared to the high-temperature disordered phase.…”

Section: Effects Of Trio Interactions On Statistical Mechanicsmentioning

confidence: 71%

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Multisite lateral interactions and their consequences

Einstein¹

1991

Langmuir

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Section: Effects Of Trio Interactions On Statistical Mechanicsmentioning

confidence: 71%

Section: Effects Of Trio Interactions On Statistical Mechanicsmentioning

confidence: 71%

Multisite lateral interactions and their consequences

Einstein¹

1991

Langmuir

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“…In the present investigation we have harnessed the coarse-grained bead-spring algorithm for polymer chains 19 already applied successfully for systems of GM in ref. 17 . Our description can therefore be brief.…”

Section: Model and Methodsmentioning

confidence: 99%

“…We stress that the equilibration kinetics is rather slow compared to similar systems of GM in the bulk 15 which are allowed to break and where the dynamics is not limited to end monomer adsorption and desorption. This forced us to simulate relatively short chains compared to our previous study 17 .…”

Section: Model and Methodsmentioning

confidence: 99%

Formation and equilibrium properties of living polymer brushes

Milchev

Wittmer

Landau

2000

The Journal of Chemical Physics

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Polydisperse brushes obtained by reversible radical chain polymerization reaction onto a solid substrate with surface-attached initiators, are studied by means of an off-lattice Monte Carlo algorithm of living polymers (LP). Various properties of such brushes, like the average chain length and the conformational orientation of the polymers, or the force exerted by the brush on the opposite container wall, reveal power-law dependence on the relevant parameters. The observed molecular weight distribution (MWD) of the grafted LP decays much more slowly than the corresponding LP bulk system due to the gradient of the monomer density within the dense pseudo-brush which favors longer chains. Both MWD and the density profiles of grafted polymers and chain ends are well fitted by effective power laws whereby the different exponents turn out to be mutually self-consistent for a pseudo-brush in the strong-stretching regime. The specific values are, however, inconsistent with a standard self-consistent field theory of pseudo-brushes which predicts a much softer mushroom-like layer.

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“…From a theoretical point of view, the consequences of considering nonadditive interactions in the adsorption thermodynamics have been studied for a long time. In fact, statistical mechanics of adsorbed monolayers has been the subject of analytical treatment by means of the Bragg-Williams approximation (BWA) [35][36][37], the quasichemical approximation (QCA) [38], and Monte Carlo simulations [39][40][41]. In all cases, one fundamental feature is preserved.…”

Section: Introductionmentioning

confidence: 99%

Statistical thermodynamics of straight rigid rods with nonadditive lateral interactions: Theory and Monte Carlo simulations

2011

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The statistical thermodynamics of straight rigid rods of length k (k-mers) with nonadditive lateral interactions was developed on a generalization in the spirit of the lattice-gas model and the classical Bragg-Williams approximation (BWA) and the quasichemical approximation (QCA). The new theoretical framework is obtained by combining (i) the exact analytical expression for the partition function of noninteracting linear k-mers adsorbed in one dimension and its extension to higher dimensions, and (ii) a generalization of BWA and QCA in which the adsorbate can occupy more than one adsorption site. The traditional assumption of a strictly pairwise additive nearest-neighbors interaction is replaced by a more general one, namely that the bond linking a certain atom with any of its neighbors depends considerably on how many of them are actually present (or absent) on the sites in the first coordination shell of the atom. The coverage and temperature dependence of the Helmholtz free energy, chemical potential, configurational entropy, and differential heat of adsorption are given. The formalism (i) reproduces the classical results for monomers, (ii) leads to the exact statistical thermodynamics of nonadditive interacting k-mers adsorbed in one dimension, and (iii) provides a close approximation for two-dimensional systems, taking into account multisite occupancy and nonadditive lateral interactions. Comparisons with Monte Carlo simulations are performed in order to test the validity of the theoretical model. Significant quantitative differences are shown and discussed. In all cases, the QCA appears to be the more accurate approach.

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2-D phase transitions

Cited by 12 publications

References 11 publications

Multisite lateral interactions and their consequences

Multisite lateral interactions and their consequences

Formation and equilibrium properties of living polymer brushes

Statistical thermodynamics of straight rigid rods with nonadditive lateral interactions: Theory and Monte Carlo simulations

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