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Journal ArticleDOI

Molecular Thermodynamics of Polymer Chains Confined between Planar Surfaces Bearing End-Tethered Flexible Molecules

01 Jan 2012-Journal of Macromolecular Science, Part B (Taylor & Francis Group)-Vol. 51, Iss: 1, pp 164-183
TL;DR: In this article, a lattice-based model of the confinement of homopolymer free chains between two flat solid surfaces, each covered with end-tethered flexible chains, is developed.
Abstract: A lattice-based model of the confinement of homopolymer free chains between two flat solid surfaces, each covered with end-tethered flexible chains, is developed. The free energy and free energy change for the formation of the confined state from reference states of the different components are calculated based on lattice and scaling theory concepts. Entropic and energetic factors determine the free energy of the system. The dependency of free energy and free energy change on the chain lengths (molecular weights) of free polymers and tethered polymers, the density of end-tethered chains on the surfaces, the distance between the surfaces, and the various intersegment interaction energy parameters for various component species, were studied. The phase diagrams obtained in this work provide ways for designing thermodynamically stable systems in various regimes. The results are qualitatively in agreement with those from earlier models based on self-consistent field theory and experiments.
Citations
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01 Mar 2000
TL;DR: In this paper, a simulation of the flow of a symmetric diblock copolymer from a bulk melt into a slit whose surfaces are modified by grafted surfactant chains, and whose walls are maintained at a constant pressure to permit the slit to open as polymer intercalates, is presented.
Abstract: Polymer-layered silicate nanocomposites may be formed by annealing layered silicate particles with a polymer melt. Polymer molecules flow from a bulk melt into the galleries between silicate sheets, swelling the silicate structure. The use of an amphiphilic intercalant raises possibilities of forming novel structures and enhancing the intercalation kinetics relative to the case of homopolymer intercalants. We perform molecular dynamics simulations of the flow of a symmetric diblock copolymer from a bulk melt into a slit whose surfaces are modified by grafted surfactant chains, and whose walls are maintained at a constant pressure to permit the slit to open as polymer intercalates. Intercalation kinetics are examined for a variety of polymer–surface and interblock interactions and for thermodynamic states in which the bulk polymer occupies either a lamellar or disordered phase. Comparison to previous simulations of homopolymer intercalation demonstrates that diblock copolymers may be used to intercalate a block that would not spontaneously intercalate as a homopolymer.

34 citations

Journal ArticleDOI
TL;DR: In this article, a molecular model for the free energy of a confined system of diblock copolymer chains within a 2D slit with the interior surfaces having end-tethered chains is presented, based on a combined lattice and scaling theory approach.
Abstract: A molecular model for the free energy of a confined system of diblock copolymer chains within a 2D slit with the interior surfaces having end-tethered chains is presented, based on a combined lattice and scaling theory approach. The thermodynamics of a model system, based on a constrained minimization of free energy, is explored as a function of the intermolecular energy parameters for interaction between the segments of block copolymer chains, end-tethered chains, and the surfaces. The effects of chain length and the block length ratio are investigated over a wide range of values. The results obtained are qualitative in nature; however, the model can be implemented to real systems provided appropriate parameterization of the model parameters to real systems can be performed. The phase diagrams obtained here provide ways for designing thermodynamically stable systems within the physical parametric variable space.

1 citations


Cites background or methods from "Molecular Thermodynamics of Polymer..."

  • ...We had previously presented a formulation based on these aforementioned concepts, that provides a description of confinement of homopolymer chains between surfaces bearing end-tethered homopolymer chains.[47] Here, we extend that approach to describe the confinement thermodynamics for diblock copolymer chains between flat surfaces bearing end-tethered chains....

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  • ...The present model not only takes into account the elastic stretching effects for the end-tethered chains without any restrictions posed to their length or molecular weight, but also, for the diblock chains, in a manner similar to the formulation which included this effect (term) in the case of confined homopolymer free chains as in our previous work.[47] In the limiting condition in the absence of the tethered chains in the system, we have φf = 1, and this means that the copolymer chains in the confined space in this limit will have interactions only with each other and with the confining surfaces....

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  • ...This minimization is performed under the constraints posed by the mass balances of the free and tethered chain segments in the confined space.[47] In order to prove that the free energy calculated using eq....

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  • ...The details of the numerical solution procedure are similar to those provided in our earlier work for solving the equations for the homopolymer free chains system.[47] The equations given in the present section of this paper are for the total energy components and these respective expressions were divided by Nf in order to obtain the “reduced” free energy per diblock (free-chain) copolymer chain, the results of which are provided in the next section....

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References
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Book
01 Jan 1953

16,827 citations

Book
15 Dec 1979

10,942 citations


"Molecular Thermodynamics of Polymer..." refers methods in this paper

  • ...[6] Early studies on the scaling description of the adsorption of polymers at impenetrable surfaces have been provided by Alexander[7] and de Gennes....

    [...]

  • ...[6] Early studies on the scaling description of the adsorption of polymers at impenetrable surfaces have been provided by Alexander[7] and de Gennes.[8,9] Polymers in confinement have been studied for structure and thermodynamic properties by different theoretical methods, such as scaling theory, Monte Carlo (MC) simulations, and self-consistent field theory....

    [...]

Book
01 Jan 1995
TL;DR: In this paper, Free-Radical Chain-Growth Polymerization (FRCG) and Ionic chain-growth polymers (Ionic chain growth polymers) are discussed.
Abstract: Physical Properties and Physical Chemistry of Polymers.- Free-Radical Chain-Growth Polymerization.- Ionic Chain-Growth Polymerization.- Ring-Opening Polymerizations.- Common Chain-Growth Polymers.- Step-Growth Polymerization and Step-Growth Polymers.- Naturally Occurring Polymers.- Reactivity and Chemical Modifications of Polymers.- Polymeric Materials for Special Applications.

2,239 citations


"Molecular Thermodynamics of Polymer..." refers background in this paper

  • ...The entropy for the melt of free chains[26] is given by...

    [...]

  • ...The enthalpy part for the amorphous melt[26] of the system is...

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  • ...The total Gibbs free energy[26] of the system combines various terms including the pressure-derived internal energy, and can be given as...

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Journal ArticleDOI

2,082 citations


"Molecular Thermodynamics of Polymer..." refers background or methods in this paper

  • ...(13c) is obtained from the segment balance on grafted molecules.[8] Upon solving the minimum free energy equation and with use of eqs....

    [...]

  • ...[6] Early studies on the scaling description of the adsorption of polymers at impenetrable surfaces have been provided by Alexander[7] and de Gennes.[8,9] Polymers in confinement have been studied for structure and thermodynamic properties by different theoretical methods, such as scaling theory, Monte Carlo (MC) simulations, and self-consistent field theory....

    [...]

  • ...[6] Early studies on the scaling description of the adsorption of polymers at impenetrable surfaces have been provided by Alexander[7] and de Gennes....

    [...]

  • ...The entropic free energy additionally also contains an elastic contribution[8] for the tethered chains,...

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  • ...The separation distance is considered to be greater than the radius of gyration[8] Rg of the end-tethered chains, where Rg scales as n 3/5 g a, with “a” as the monomer size (“a” is also taken as the mesh size in the lattice model)....

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Book
01 Jan 1983

1,869 citations


"Molecular Thermodynamics of Polymer..." refers background in this paper

  • ...Polymers tethered to impenetrable solid surfaces are of importance in many applications involving physicochemical phenomena, such as wetting and adhesion, 1a a chromatography, 2 stabilization of colloidal dispersions, 3a a, and for biocompatibility....

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