A new lattice density functional theory for polymer adsorption at solid-liquid interface

Chen, Xueqian; Sun, Lin; Liu, Honglai; Hu, Ying; Jiang, Jianwen

doi:10.1063/1.3191783

Cited by 12 publications

(10 citation statements)

References 45 publications

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“…Scaling considerations concerning adsorbed chains were pioneered by de Gennes4 while a mean‐field approximation (an extension of the Flory‐Huggins treatment of polymer solutions) was introduced by Scheutjens and Fleer 5, 6. Recently, lattice density functional theory has been extended to study polymer adsorption 7. Computer simulations of such systems8 have been mainly devoted to the transition from a weak to strong adsorption regime, the scaling properties, the dynamics,9, 10 the influence of the internal macromolecular architecture11 and phase transitions 12–16.…”

Section: Introductionmentioning

confidence: 99%

Adsorption of Copolymers on Solid Surfaces

Rybicka¹,

Sikorski²

2010

Macro Theory & Simulations

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Monte Carlo simulations of idealized models of polymer chains at interfaces were carried out. The models chains consisted of hydrophobic and hydrophilic united atoms (beads) and were embedded in a [310] hybrid lattice. The polymer beads interacted through a long‐distance contact potential and were placed near an impenetrable and attractive surface. The properties of the model system were determined using the replica‐exchange Monte Carlo algorithm. The influence of temperature, adsorption strength and bead sequence on the properties of model chains were studied. It was shown that weak chain adsorption did not change alter the process of chain collapse significantly. For strong adsorption, the chain rearrangements were found to be more complicated, especially for alternating copolymers.

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Section: Introductionmentioning

confidence: 99%

Adsorption of Copolymers on Solid Surfaces

Rybicka¹,

Sikorski²

2010

Macro Theory & Simulations

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“…The extension of density functional theory from continuum to lattice fluids [1] has proven to be useful for treating problems like ordering transitions [1][2][3], properties of interfaces separating different phases [4][5][6], phase separation in mixtures [7], or polymer adsorption at solidliquid interfaces [8]. Time-dependent density functional theory [9] furthermore allows one to describe the kinetics of lattice fluids [10], as emerging in phase ordering phenomena [11], relaxation processes [12], and particle transport in driven lattice gases [13][14][15].…”

mentioning

confidence: 99%

Exact density functional for hard-rod mixtures derived from Markov chain approach

2012

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Using a Markov chain approach we rederive the exact density functional for hard rod mixtures on a one-dimensional lattice, which forms the basis of the lattice fundamental measure theory. The transition probability in the Markov chain depends on a set of occupation numbers, which reflects the property of a zero-dimensional cavity to hold at most one particle. For given mean occupation numbers (density profile), an exact expression for the equilibrium distribution of microstates is obtained, that means an expression for the unique external potential that generates the density profile in equilibrium. By considering the rod ends to fall onto lattice sites, the mixture is always additive. In 2002 Lafuente and Cuesta extended Rosenfeld's fundamental measure theory to lattice models based on a derivation of an exact density functional for hard rod mixtures in one dimension [16,17]. This derivation was carried out following a procedure developed by Vanderlick et al.[18] for continuum fluids. Since the excess free energy part of the functional could be expressed in terms of differences between parts that agree in their functional form with the excess free energy functional of a zerodimensional cavity, approximate functionals in higher dimensions were obtained by dimensional expansion of the corresponding difference operator. By construction these fundamental measure functionals have the property to become exact under dimensional reduction and their impressive power was first shown by determining phase diagrams of hard squares [17,19] and hard cube mixtures [16,17,20] with good quality. The fundamental measure functionals moreover allow one to apply the method of dimensional crossover and the merit of this was demonstrated by deriving functionals for lattice gases with nearest neighbor exclusion for different lattice types (square, triangular, face-and body-centered cubic) from the functional for cubes in (d + 1) dimensions [21]. The structure of the corresponding results led to a suggestion how to construct fundamental measure functionals for hard core lattice gases for any type of lattice, shape of the particles, and arbitrary dimension [22].In this report we rederive the exact density functional for hard rod mixtures in one dimension, that means the * philipp.maass@uni-osnabrueck.de

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“…For the details of the numerical procedure of solving the above equations, please refer to our previous work . And the average thickness of the polymer brushes can be described by

⟨H⟩

, twice the first moment of the density distribution

⟨H⟩ = \frac{2 \int z ρ false(z false) normald z}{\int ρ false(z false) normald z}

…”

Section: Theorymentioning

confidence: 99%

“…Although this approach is known to give only coarse‐grained information about the thermodynamic behavior of a system, it provides important insights on the mechanisms of various complex phenomena. In our previous work, a LDFT for polymer solutions is constructed by adopting the close‐packed molecular thermodynamic model for polymer solutions with local density approximation (LDA) and weighted density approximation (WDA). We also used LDFT to investigate the temperature‐thickness relationship for different types of polymer brushes, and the thermoresponsive behavior of a polymer brush is found to be characterized by the bulk phase behaviors of its corresponding polymer solution …”

Section: Introductionmentioning

confidence: 99%

Substrate Effect on the Phase Behavior of Polymer Brushes with Lattice Density Functional Theory

Lian

Chen

Zhao

et al. 2014

Macromol. Theory Simul.

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The lattice density functional theory (LDFT) is used to describe the substrate effect on the phase behavior of polymer brush grafted on different substrates. The LDFT predicts that: both attractive and repulsive interactions between the substrate and the polymer chains have effects on the thickness of brushes; when the short‐range monomer–substrate interaction is larger than a certain value, the thickness and density profiles of polymer brushes almost do not change. And also an attractive substrate can increase the critical grafting density of pancake to brush transition. For temperature responsive polymer brushes, the temperature transition points are almost the same with different substrates, however, an attractive substrate can increase the swelling ratio and a repulsive substrate can decrease the swelling ratio. We also find that an increasing grafting density can decrease the substrate effect on the swelling behavior of temperature responsive polymer brushes.

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A new lattice density functional theory for polymer adsorption at solid-liquid interface

Cited by 12 publications

References 45 publications

Adsorption of Copolymers on Solid Surfaces

Adsorption of Copolymers on Solid Surfaces

Exact density functional for hard-rod mixtures derived from Markov chain approach

Substrate Effect on the Phase Behavior of Polymer Brushes with Lattice Density Functional Theory

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