Monomer Adsorption on Terraces and Nanotubes

Phares, Alain J.; Grumbine, David; Wunderlich, Francis J.

doi:10.1021/la0620354

Cited by 13 publications

(42 citation statements)

References 75 publications

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“…In a number of very special cases, a method for computing the degeneracy relied on solving a number of linearly coupled recursion relations. − Subsequently, we have shown that it is possible, in these special cases, to bypass the degeneracy problem and go directly to the partition function, replacing the problem of solving linearly coupled recursion relations by that of solving an equal number of linear equations among a set of generating functions. − The linear equations are then solved using the standard matrix method, exhibiting the T matrix, whose eigenvalues provide the partition function, thus completely circumventing the degeneracy problem. Section 3 presents the generating function technique, which is now generalized to the coadsorption of n monomer species on terrace or nanotube surfaces of periodic geometry.…”

Section: General Formulation Of the Adsorption Problemmentioning

confidence: 99%

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Coadsorption of n Monomer Species on Terraces and Nanotubes

Phares

2011

Langmuir

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The knowledge of the partition function, Z, of a system of particles adsorbed on a surface is all that is required to determine the occupational characteristics of the adsorbates and the thermodynamic properties of the system. The surface considered is a terrace or a nanotube of arbitrary periodic lattice geometry, L atomic sites in length, and M' sites in the width of the terrace or in the normal cross section of the nanotube. The matrix method introduced in 2007 to obtain Z for the adsorption study of one species of monomers is now generalized to the study of the coadsorption of any number, n, of monomer species. We provide proof that Z can be related to the eigenvalues of a real and non-negative matrix (T matrix) of rank (n + 1)(M), where M is an integer multiple of M'. In the infinite-L limit, we also prove that Z is the largest eigenvalue of the T matrix, raised to the power of (1)/(M). Because the rank of this matrix increases exponentially with M, we develop a technique for its recursive construction applicable to any lattice geometry, which is easily programmed and efficiently adaptable for supercomputing and multiparallel processing. As examples, we consider the coadsorption on square, equilateral triangular, and honeycomb surfaces. This general formulation can now be applied to model a whole new set of experiments involving the coadsorption of two or more monomer species, on terrace or nanotube surfaces with various periodic lattice structures.

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Section: General Formulation Of the Adsorption Problemmentioning

confidence: 99%

“…We follow an alternate path that does not rely on any approximation beyond that of the precision in conducting the numerical computations. This path is based on introducing generating functions. − …”

Section: Partition Function and T Matrixmentioning

confidence: 99%

Coadsorption of n Monomer Species on Terraces and Nanotubes

Phares

2011

Langmuir

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“…In addition, there is another reason why honeycomb lattices might be particularly interesting. From an experimental point of view, honeycomb lattices are intriguing systems, forming the structure of many natural and artificial objects [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Honeycomb lattices composed of carbon atoms form graphene sheets and carbon nanotubes [31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

“…From an experimental point of view, honeycomb lattices are intriguing systems, forming the structure of many natural and artificial objects [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Honeycomb lattices composed of carbon atoms form graphene sheets and carbon nanotubes [31][32][33][34][35][36][37]. The spontaneous formation of honeycomb structures has been observed in self-assembled layers of anthraquinone molecules on a Cu(111) surface [38,39].…”

Section: Introductionmentioning

confidence: 99%

Jamming and percolation of linear k -mers on honeycomb lattices

2020

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Numerical simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of elongated objects deposited on two-dimensional honeycomb lattices. The depositing particle is modeled as a linear array of length k (so-called k-mer), maximizing the distance between first and last monomers in the chain. The separation between k-mer units is equal to the lattice constant. Hence, k sites are occupied by a k-mer when adsorbed onto the surface. The adsorption process starts with an initial configuration, where all lattice sites are empty. Then, the sites are occupied following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be deposited due to the absence of empty site clusters of appropriate size and shape. Jamming coverage θ j,k and percolation threshold θ c,k were determined for a wide range of values of k (2 k 128). The obtained results shows that (i) θ j,k is a decreasing function with increasing k, being θ j,k→∞ = 0.6007( 6) the limit value for infinitely long k-mers; and (ii) θ c,k has a strong dependence on k. It decreases in the range 2 k < 48, goes through a minimum around k = 48, and increases smoothly from k = 48 up to the largest studied value of k = 128. Finally, the precise determination of the critical exponents ν, β, and γ indicates that the model belongs to the same universality class as 2D standard percolation regardless of the value of k considered.

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“…The problem is not only of theoretical interest, but also has practical importance. A complete summary about adsorption on triangular lattices can be found in [12][13][14][15] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Statistical Thermodynamics of Long Straight Rigid Rods on Triangular Lattices: Nematic Order and Adsorption Thermodynamic Functions

2012

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The statistical thermodynamics of straight rigid rods of length k on triangular lattices was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtz free energy and its derivatives were written in terms of the order parameter δ , which characterizes the nematic phase occurring in the system at intermediate densities. Then, using the principle of minimum free energy with δ as a parameter, the main adsorption properties were calculated. Comparisons with Monte Carlo simulations and experimental data were performed in order to evaluate the reaches and limitations of the theoretical model.

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Monomer Adsorption on Terraces and Nanotubes

Cited by 13 publications

References 75 publications

Coadsorption of n Monomer Species on Terraces and Nanotubes

Coadsorption of n Monomer Species on Terraces and Nanotubes

Jamming and percolation of linear k -mers on honeycomb lattices

Statistical Thermodynamics of Long Straight Rigid Rods on Triangular Lattices: Nematic Order and Adsorption Thermodynamic Functions

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