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Journal ArticleDOI

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

10 May 2012-Journal of Macromolecular Science, Part B (Taylor & Francis Group)-Vol. 51, Iss: 7, pp 1282-1302
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.
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

References
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Journal ArticleDOI
TL;DR: In this article, the authors analyzed the structure of long worm-like polymers sterically confined between two parallel, structureless walls separated by a distance W. They determined the induced attractive force acting on the walls, mediated by the Onsager excluded-volume interaction between polymer segments.
Abstract: On the basis of a mean-field treatment of semiflexible polymer chains, we analyze the structure of long wormlike polymers sterically confined between two parallel, structureless walls separated by a distance W. With the Onsager excluded-volume interaction between polymer segments, the system displays three phases, uniaxial, biaxial, and condensed, depending on the polymer density and W. We have also determined the induced attractive force acting on the walls, mediated by the Onsager excluded-volume interaction between polymer segments.

30 citations

Journal ArticleDOI
TL;DR: In this paper, the lamellar/cylinder and cylinder/sphere phase boundaries for strongly segregated diblock copolymer melts using selfconsistent field theory (SCFT) and the standard Gaussian chain model were examined.
Abstract: We examine the lamellar/cylinder and cylinder/sphere phase boundaries for strongly segregated diblock copolymer melts using self‐consistent‐field theory (SCFT) and the standard Gaussian chain model. Calculations are performed with and without the conventional unit‐cell approximation (UCA). We find that for strongly segregated melts, the UCA simply produces a small constant shift in each of the phase boundaries. Furthermore, the boundaries are found to be linear at strong segregations when plotted versus (χN)−1, which allows for accurate extrapolations to χN=∞. Our calculations using the UCA allow direct comparisons to strong‐segregation theory (SST), which is accepted as the χN=∞ limit of SCFT. A significant discrepancy between the SST and SCFT results indicate otherwise, suggesting that the present formulation of SST is incomplete.

26 citations

Journal ArticleDOI
TL;DR: In this article, the kinetics of intercalation of a series of poly(styrene-b-isoprene) block copolymers into a layered silicate were examined via X-ray diffraction.
Abstract: In addition to phase morphology, diffusion, and dynamics in the bulk, the behavior of block copolymers in the confined state has been of great interest. Although random and graft copolymers have been used in polymer-layered silicate nanocomposites, well-defined block copolymers have received relatively little attention. In this study, the kinetics of intercalation of a series of poly(styrene-b-isoprene) block copolymers into a layered silicate were examined via X-ray diffraction. Intercalation was observed even when the copolymer was in the ordered state, with no discontinuity around the order-disorder transition of the copolymer. As the size of the polystyrene block was increased, slower intercalation kinetics were observed, possibly because of the increased glass-transition temperature of the polystyrene segment. Finally, the clearing temperature of the copolymer in the nanocomposites as measured by small-angle X-ray scattering showed a large heating-rate dependence suggesting that the nanoparticles act as kinetics barriers to the disordering of the copolymer.

21 citations


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

  • ...This confined state,[40] that is present even with significant variations in block lengths of the PSPI chains (20%–60% PS fraction), was found to be quite persistent, especially so without a disruption of the equilibrium ordered morphology of the block copolymer bulk matrix phase (in lamellar and cylindrical as well as gyroid phases) and no discontinuity around the order–disorder transition....

    [...]

  • ...The intercalation of poly(styrene-b-isoprene) (PSPI) between clay (layered silicates) platelets provides a classic system[34,40] in which the confining flat surfaces (clay platelets) contain end-tethered organic hydrophobic molecules that can interact favorably with one of the blocks and also one of the blocks (PS) interacts favorably with the clay surface itself via dipolar interactions (due to the phenyl rings in PS chains)....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the exact scaling functions for the self-avoiding walks were derived by considering the two variable asymptotics of the partition function for simultaneous large length and large width.
Abstract: The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been recently calculated. The walks can be considered to model the polymerinduced steric stabilization and sensitized flocculation of colloidal dispersions. Thelarge-widthasymptoticsledtoaphasediagramdifferenttothatofapolymer attached to, and attracted to, a single wall. The question that arises is: Can one interpolate between the single wall and two wall cases? In this paper, we calculate the exact scaling functions for the partition function by considering the two variable asymptotics of the partition function for simultaneous large length and large width. Consequently, we find the scaling functions for the force induced by the polymer on the walls. We find that these scaling functions are given by elliptic ϑ functions. In some parts of the phase diagram there is more a complex crossover between the single wall and two wall cases and we elucidate how this happens.

13 citations

Journal ArticleDOI
TL;DR: In this article, the exact scaling functions for the partition function were derived by considering the two variable asymptotics of the partition functions for simultaneous large length and large width, and these scaling functions were given by elliptic theta-functions.
Abstract: The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been calculated recently. The walks can be considered to model the polymer-induced steric stabilisation and sensitised floculation of colloidal dispersions. The large width asymptotics led to a phase diagram different to that of a polymer attached to, and attracted to, a single wall. The question that arises is: can one interpolate between the single wall and two wall cases? In this paper we calculate the exact scaling functions for the partition function by considering the two variable asymptotics of the partition function for simultaneous large length and large width. Consequently, we find the scaling functions for the force induced by the polymer on the walls. We find that these scaling functions are given by elliptic theta-functions. In some parts of the phase diagram there is more a complex crossover between the single wall and two wall cases and we elucidate how this happens.

12 citations