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.
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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
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TL;DR: In this paper, a scaling description of the chain configurations and interactions is used, and it is shown that the presence of a uniform surface attraction changes the phase diagram drastically, and the transition between the two phases is first order.
Abstract: The adsorption of chain molecules at an interface is investigated assuming that the molecule has both a polar head type of attraction localized on the chain and a uniform interaction of the chain monomers with the surface. A scaling description of the chain configurations and interactions is used. It is shown that the presence of a uniform surface attraction changes the phase diagram drastically. Both a low density two-dimensional regime and a high density phase with the chains confined in narrow cylinders can occur. The transition between the two phases is first order. Power laws for the surface density, layer thickness and surface pressure are derived. The qualitative similarity with the behaviour observed for short chain lipids and surfactants is also noted and it is suggested that a uniform surface interaction may also play an important role there.
1,360 citations
TL;DR: In this article, a general theory for polymer adsorption using a quasi-crystalline lattice model is presented, where the Bragg-Williams approximation of random mixing within each layer parallel to the surface is adopted.
Abstract: We present a general theory for polymer adsorption using a quasi-crystalline lattice model. The partition function for a mixture of polymer chains and solvent molecules near an interface is evaluated by adopting the Bragg-Williams approximation of random mixing within each layer parallel to the surface. The interaction between segments and solvent molecules is taken into account by use of the Flory-Huggins parameter x; that between segments and the interface is described in terms of the differential adsorption energy parameter xs. No approximation was made about an equal contribution of all the segments of a chain to the segment density in each layer. By differentiating the partition function with respect to the number of chains having a particular conformation an expression is obtained that gives the numbers of chains in each conformation in equilibrium. Thus also the train, loop, and tail size distribution can be computed. Calculations are carried out numerically by a modified matrix procedure as introduced by DiMarzio and Rubin. Computations for chains containing up to lo00 segments are possible. Data for the adsorbed amount r, the surface coverage 0, and the bound fraction p = O/r are given as a function of xs, the bulk solution volume fraction c#J,, and the chain length r for two x values. The results are in broad agreement with earlier theories, although typical differences occur. Close to the surface the segment density decays roughly exponentially with increasing distance from the surface, but at larger distances the decay is much slower. This is related to the fact that a considerable fraction of the adsorbed segments is present in the form of long dangling tails, even for chains as long as r = 1000. In previous theories the effect of tails was usually neglected. Yet the occurrence of tails is important for many practical applications. Our theory can be easily extended to polymer in a gap between two plates (relevant for colloidal stability) and to copolymers.
1,180 citations
TL;DR: In this article, a mean-field, lattice-based model of polymer melt intercalation in organically-modified mica-type silicates (OLS) has been developed.
Abstract: A mean-field, lattice-based model of polymer melt intercalation in organically-modified mica-type silicates (OLS) has been developed. In general, an interplay of entropic and energetic factors determines the outcome of polymer intercalation. Free energy curves and their dependence on energetic and entropic factors suggest three possible equilibrium statesimmiscible, intercalated, and exfoliatedall of which have been experimentally observed. The entropic penalty of polymer confinement may be compensated for by the increased conformational freedom of the surfactant chain as the layers separate. When the total entropy change is small, small changes in the system's internal energy will determine if intercalation is thermodynamically possible. Complete layer separation, though, depends on the establishment of very favorable polymer−OLS interactions to overcome the penalty of polymer confinement. For alkylammonium-modified layered silicates, a favorable energy change is accentuated by maximizing the magnitude a...
782 citations
"Thermodynamic Free Energy Behavior ..." refers background in this paper
...The earlier lattice model[52] specifically does not take into account the elastic free energy of stretching of the tethered molecules due to the short length of the tethered chains....
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TL;DR: In this paper, the melt-state linear viscoelastic properties for a series of intercalated nanocomposites are examined and the linear dynamic oscillatory moduli and the stress relaxation moduli are in quantitative agreement and suggest that at short times the relaxation of the nanocom composites is essentially unaffected by the presence of layered-silicate.
Abstract: The melt-state linear viscoelastic properties for a series of intercalated nanocomposites are examined. The nanocomposites are based on a short disordered polystyrene−polyisoprene diblock copolymer and varying amounts of dimethyldioctadecylammonium modified montmorillonite. The linear dynamic oscillatory moduli and the stress relaxation moduli are in quantitative agreement and suggest that at short times the relaxation of the nanocomposites is essentially unaffected by the presence of the layered-silicate. However, at long times (or equivalently low frequency), the hybrids exhibit dramatically altered viscoelastic behavior. Hybrids with silicate loadings in excess of 6.7 wt % exhibit pseudo-solidlike behavior, similar to that observed in previous studies of exfoliated end-tethered nanocomposites. On the basis of simple phenomenological arguments, the long time behavior is attributed to the presence of anisotropic stacks of silicate sheets randomly oriented and forming a percolated network structure that i...
566 citations
"Thermodynamic Free Energy Behavior ..." refers background in this paper
...Based on a linear viscoelasticity[34] study of the intercalated PSPI-silicate nanocomposite, it was concluded that the viscoelastic moduli are strongly correlated to the mesoscale structure of such a composite and that the interaction strengths between the different chemical species as well as the molecular weight of the block copolymer chain (of highly...
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...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)....
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512 citations