# Thermodynamic Free Energy Behavior of Diblock Copolymer Chains Confined Between Planar Surfaces Having End-Tethered Flexible Polymer Molecules

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.

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### "Thermodynamic Free Energy Behavior ..." refers background in this paper

...This stretching effect can be appropriately represented in the present model by the elastic properties of the diblock chains[8,9] as given by,...

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...The entropic contribution to the free energy additionally also contains an elastic contribution[8,9] for the tethered chains which is given by,...

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2,019 citations

### "Thermodynamic Free Energy Behavior ..." refers background or methods in this paper

...The combinatorial entropy[49] therefore, for the free diblock chains, can be...

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...Intermolecular interaction energy between various constituents can be calculated by the Flory–Huggins χ Parameters....

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...Which, with the incorporation of the number of arrangements[49] given as per the Flory theory,...

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...Intermolecular interaction energy between various constituents can be calculated by the Flory–Huggins χ Parameters.[49] The interaction energy for the present system can be cast in the following form,...

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1,994 citations

### "Thermodynamic Free Energy Behavior ..." refers background in this paper

...(14c) is obtained from the segment species volume conservation on grafted molecules.[8] After solving the minimum free energy equation and using eqs....

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...This stretching effect can be appropriately represented in the present model by the elastic properties of the diblock chains[8,9] as given by,...

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...The entropic contribution to the free energy additionally also contains an elastic contribution[8,9] for the tethered chains which is given by,...

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

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1,851 citations

### Additional excerpts

...Polymers tethered onto impenetrable surfaces are of significance in many applications such as wetting and adhesion, [ 1 ] stabilization of colloidal dispersions, [ 2 ] transport through narrow pores, [ 3 ] chromatography, [ 4 ] for steric stabilization of drug particles, [ 5 ] and for in vivo biocompatibility....

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