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The parabolic approximation for self‐consistent molecular potential is widely used for theoretical analysis of conformational and thermodynamic properties of polymer brushes formed by linear or branched macromolecules. The architecture‐dependent parameter of the potential (topological coefficient) can be calculated for arbitrary branched polymer architecture from the condition of elastic stress balance in all the branching points. However, the calculation routine for the topological coefficient does not allow unambiguously identifying the range of applicability and the accuracy of the parabolic approximation. Here the limits of applicability of parabolic approximation are explored by means of numerical self‐consistent field method for brushes formed by Y‐shaped and comb‐like polymers. It is demonstrated that violation of the potential parabolic shape can be evidenced by appearance of multimodal distribution of the end monomer unit in the longest elastic path of the macromolecule. The asymmetry of branching of Y‐shaped polymers does not disturb the parabolic shape of the potential as long as the degree of polymerization of the root segment remains sufficiently large. The same applies to comb‐shape polymers with sufficiently long main chain and large number of branching points. For short comb‐like polymers multiple modes in the distribution of the end monomer unit of the main chain are observed and related to deviation from the parabolic shape of the potential. [ABSTRACT FROM AUTHOR]

The self-consistent field theory of brushes of neutral water-soluble polymers described by two-state models is formulated in terms of the effective Flory interaction parameter χ[sub eff](T,[lowercase_phi_synonym]) that depends on both temperature, T, and the monomer volume fraction, [lowercase_phi_synonym]. The concentration profiles, distribution of free ends and compression force profiles are obtained in the presence and in the absence of a vertical phase separation. A vertical phase separation within the layer leads to a distinctive compression force profile and a minimum in the plot of the moments of the concentration profile versus the grafting density. The analysis is applied explicitly to the Karalstrom model. The relevance to brushes of Poly(N-isopropylacrylamide)(PNIPAM) is discussed. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Using analytical and numerical self-consistent field (SCF) methods we analyze equilibrium structure of dry (solvent-free) brush of branched polymers in wide range of chain grafting densities. A detailed analysis is performed for starlike polymers end-tethered to planar surface by terminal monomer of one of their branches. At moderate grafting densities ensuring Gaussian elasticity of tethered stars the brush structure is described by strong stretching SS-SCF theory employing parabolic molecular potential. At high grafting densities an approximate analytical AA-SCF theory is used to describe stratification of dry brush. Analytical predictions are supplemented by results of numerical Scheutjens-Fleer SF-SCF model. Interpenetration between dry brushes is analyzed as a function of grafting density and degree of branching of tethered chains. Comparison of interpenetration and friction between dry brushes with varied chain architectures pointed at optimal lubrication by macrocycles tethered to the surface by branching point. It is demonstrated that shear stress in sliding brushes of starlike macromolecules sharply decreases at high grafting densities corresponding to almost full stretching of the longest elastic path in the polymers. [ABSTRACT FROM AUTHOR]

We present a theory describing structural properties of brushes formed by cycled macromolecules tethered to planar surface. Diverse architectures of macromolecules that differ with respect to position and number of subchains in macrocycle are considered. We use the self-consistent field analytical approach based on strong stretching approximation and assumption of Gaussian elasticity of brush-forming molecules. Predictions of the analytical theory are systematically compared to the results of numerical SF-SCF modeling. Similarity of the effects of cyclization and branching on large-scale properties of polymer brush is demonstrated. It is also predicted that weaker interpenetration of sliding brushes formed by cyclic macromolecules might enhance their performance as lubricants. [ABSTRACT FROM AUTHOR]

A planar polymer brush of arm-grafted polymer stars subjected to external deformation is studied theoretically We propose a simple mean-field model of the star brush that takes into account segregation of the brush-forming stars in two populations: (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended towards brush periphery. The polymer density profile in the brush is assumed to have a 'two-step' shape. Stars in the extended population are assumed to be equally stretched, the position of extended stars' branching points sets the boundary between two parts of the brush. We show that the theory quantitatively accurately describes earlier numerical results obtained with Scheutjens-Fleer numerical self-consistent field (SF-SCF) approach for free (non-deformed) star brush. We study compression of a star brush by an impenetrable plane by using two complementary models, the SF- SCF approach and the developed mean-field theory, and demonstrate a very good quantitative agreement between the two models. It is shown than depending on the grafting density of the stars, compression could affect the two-population brush structure in opposite ways. In sparsely grafted brushes the fraction of stars in the stretched population increases while in densely grafted brushes it decreases with deformation. [ABSTRACT FROM AUTHOR]

To study conformational transition occuring upon inferior solvent strength in a brush formed by linear or dendritically branched macromolecules tethered to the inner surface of cylindrical or planar (slit-like) pore, a self-consistent field analytical approach is employed. Variations in the internal brush structure as a function of variable solvent strength and pore radius, and the onset of formation of a hollow channel in the pore center are analysed. The predictions of analytical theory are supported and complemented by numerical modelling by a self-consistent field Scheutjens–Fleer method. Scaling arguments are used to study microphase segregation under poor solvent conditions leading to formation of a laterally and longitudinally patterned structure in planar and cylindrical pores, respectively, and the effects of confinement on "octopus-like" clusters in the pores of different geometries. [ABSTRACT FROM AUTHOR]

End-grafting of polyelectrolyte chains to conducting substrates offers an opportunity to fabricate electro-responsive surfaces capable of changing their physical/chemical properties (adhesion, wettability) in response to applied electrical voltage. We use a self-consistent field numerical approach to compare the equilibrium properties of tethered strong and weak (pH-sensitive) polyelectrolytes to applied electrical field in both salt-free and salt-containing solutions. We demonstrate that both strong and weak polyelectrolyte brushes exhibit segregation of polyions in two populations if the surface is oppositely charged with respect to the brush. This segregation gives rise to complex patterns in the dependence of the brush thickness on salt concentration. We demonstrate that adjustable ionization of weak polyelectrolytes weakens their conformational response in terms of the dependence of brush thickness on the amplitude of the applied voltage. [ABSTRACT FROM AUTHOR]

Nanomechanical properties of natural and artificial nanomembranes can be strongly affected by anchored or tethered macromolecules. The intermolecular interactions in polymeric layers give rise to so-called induced bending rigidity which complements the bare rigidity of the membrane. Using analytical mean-field theory, we explore how macromolecular architecture of tethered polymers affects the bending rigidities of the polymer-decorated membranes. The developed theory enables us to consider explicitly various polymer architectures including regular dendrons, Ψ-shaped, star- and comblike macromolecules as well as macrocycles. Numerical self-consistent field computations for selected (regular dendritic) topology complement the analytical theory and support its predictions. We consider both cases of (i) quenched symmetric distribution of tethered molecules on both sides of the membrane and (ii) annealing distribution in which the tethered polymers can relocate from the concave to the convex side of the membrane upon bending. We demonstrate that at a given surface coverage an increase in the degree of branching or cyclization leads to the decrease in the induced bending rigidity. Relocation of the tethered molecules from concave to convex surfaces leads to the additional decrease in polymer contribution to the membrane bending rigidity. In the latter case, a decrease in configurational entropy due to this redistributions substantially contributes to the bending rigidity. [ABSTRACT FROM AUTHOR]