Molecular Thermodynamics of Polymer Chains Confined between Planar Surfaces Bearing End-Tethered Flexible Molecules
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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
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....
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...[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....
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2,239 citations
"Molecular Thermodynamics of Polymer..." refers background in this paper
...The entropy for the melt of free chains[26] is given by...
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...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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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....
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...[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....
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...[6] Early studies on the scaling description of the adsorption of polymers at impenetrable surfaces have been provided by Alexander[7] and de Gennes....
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...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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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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