Dendron Brushes in Polymer Medium: Interpenetration and Depletion
Kazakov, Alexander D. ; Polotsky, Alexey A. ; Zhulina, Ekaterina B. ; Birshtein, Tatiana M. ; Leermakers, Frans A.M. ; Borisov, Oleg V. - \ 2019
Macromolecules 53 (2019)1. - ISSN 0024-9297 - p. 387 - 397.
Structural properties of polymer brushes formed by branched tree-like macromolecules (dendrons) attached to a surface and immersed into a melt of linear polymer chains are studied by means of self-consistent field theory. The conformational swelling-to-collapse transition provoked in the brush by an increase in the degree of polymerization of mobile polymer chains is analyzed. It is demonstrated that the sharpness of this transition decreases upon branching of tethered polymers. The effect of architecture of the brush-forming macromolecules on penetration and exclusion of mobile polymers is considered. The regimes of full, partial, and peripheral penetration of mobile chains into the brush are distinguished. The depth of penetration of mobile polymers into the brush is calculated as a function of molecular masses of mobile chains and tethered dendrons, grafting density, and topological parameters of the brush-forming macromolecules. It is demonstrated that the penetration length decreases upon branching of tethered macromolecules. For sufficiently long mobile chains, the penetration length is controlled by the number of monomer units in the longest elastic path of the dendrons. The predictions of the analytical self-consistent field theory are in excellent agreement with the results of numerical modeling based on the Scheutjens-Fleer approach.
Impact of Macromolecular Architecture on Bending Rigidity of Dendronized Surfaces
Mikhailov, Ivan V. ; Leermakers, Frans A.M. ; Borisov, Oleg V. ; Zhulina, Ekaterina B. ; Darinskii, Anatoly A. ; Birshtein, Tatiana M. - \ 2018
Macromolecules 51 (2018)9. - ISSN 0024-9297 - p. 3315 - 3329.
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, φ-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.
Unfolding of a comb-like polymer in a poor solvent : Translation of macromolecular architecture in the force-deformation spectra
Polotsky, Alexey A. ; Birshtein, Tatiana M. ; Mercurieva, Anna A. ; Leermakers, Frans A.M. ; Borisov, Oleg V. - \ 2017
Soft Matter 13 (2017)48. - ISSN 1744-683X - p. 9147 - 9161.
A numerical self-consistent field modeling approach was employed to study the mechanical unfolding of a globule made by comb-like polymers in a poor solvent with the aim of unraveling how the macromolecular architecture affects the shape of the single-molecule force-deformation curves. We demonstrate that the dependence of the restoring force on the imposed extension of the main chain of the comb-like polymer exhibits a characteristic oscillatory shape in the intermediate deformation range. Theoretical arguments are developed that enable us to relate the shape of the patterns on the force-deformation curves to the molecular architecture (grafting density and length of the side chains) and interaction parameters. Thus, the results of our study suggest a new approach for the determination of macromolecular topology from single-molecule mechanical unfolding experiments.
Bending moduli of dendritic polymer brushes in a good solvent
Mikhaylov, I.V. ; Borisov, Oleg V. ; Darinskii, A.A. ; Leermakers, F.A.M. ; Birshtein, T.M. - \ 2017
Polymer Science Series. A: Polymer physics 59 (2017)5. - ISSN 0965-545X - p. 772 - 783.
The effect of branching on the Helfrich mean kC and Gaussian kG bending moduli of polymer brushes consisting of dendrons grafted to both sides of a thin impermeable surface (membrane) is studied theoretically. The case of an athermal solvent is considered. The moduli are calculated from a change in the free energy of a brush upon cylindrical and spherical bending of the grafting surface, respectively. The grafting density σ, the total number of monomer units N, and the number of generations g in tethered dendrons are varied. Two variants of the self-consistent field method are applied: the analytical approach and the numerical Scheutjens-Fleer method. The first method is applied at small values of σ, when the density profile of monomer units of grafted chains is parabolic in shape. The second method is free of these restrictions. The universal ratio between moduli is found: kG =−64/105kC. Both methods predict that the values of moduli decrease with increasing g at constant N and σ. The scaling dependence N3 remains valid for the moduli of dendritic brushes with different generation numbers g at all of the considered values of σ. The analytical approach also gives the universal scaling dependence kC ∼ kG ∼ σ7/3; however, the numerical method predicts that the dependences of moduli on σ become stronger with increasing degree of branching of tethered dendrons.
Structure of mixed brushes made of arm-grafted polymer stars and linear chains
Polotsky, A.A. ; Leermakers, F.A.M. ; Birshtein, T.M. - \ 2015
Macromolecules 48 (2015)7. - ISSN 0024-9297 - p. 2263 - 2276.
polydisperse block copolymers - symmetric diblock copolymers - supercrystalline structures - supermolecular structures - abc-triblock - neutron reflectivity - bicomponent mixtures - lamellar structures - blend composition - parameter space
The structure of a mixed brush made of arm-grafted polymer stars and grafted linear chains is investigated using the Scheutjens–Fleer self-consistent field method. It is shown that the mixing of stars and chains is thermodynamically favorable with respect to their lateral segregation in the brush. On the other hand, a segregation of linear and starlike macromolecules in the direction perpendicular to the grafting surface is observed. Conformations of stars and linear chains in the brush are determined by the overall molecular weight and the longest path length of linear and starlike macromolecules. Short linear chains occupy the space adjacent to the grafting surface and push the stars toward the brush periphery. In the case of long chains the interior of the brush is filled by the stars while the chains pass through the layer of the stars and expose their ends at the brush periphery. The most interesting is the intermediate situation where the linear chains have larger longest path but lower molecular weight than the stars. In this case, conformations of stars and linear chains depend essentially on the brush composition. When the amount of linear chains is small, they behave as effectively long, but larger fractions behave as short ones. The transition between two regimes is characterized by a bimodal distribution of linear chains and large fluctuation in the position of their free ends.
Interaction of a hydophobic weak polyelectrolyte star with an apolar surface
Rudd, O.V. ; Leermakers, F.A.M. ; Birshtein, T.M. - \ 2014
Langmuir 30 (2014)1. - ISSN 0743-7463 - p. 48 - 54.
block-copolymer micelles - amphiphilic multiarm - aqueous-solutions - drug-delivery - brushes - collapse - solvent - ph
We consider star-like polymers with weak, that is, pH-dependent, hydrophobic polyelectrolyte arms. For low ionic strength conditions, a microphase-segregated quasimicellar structure is found, for which the star features a compact apolar core and a charged and swollen corona. This state is jump-like lost when the ionic strength is increased, i.e., at some intermediate ionic strength value. Using numerical self-consistent field modeling, we focus on the adsorption characteristics of these objects onto hydrophobic surfaces as a function of the ionic strength. In the quasimicellar state, the stars are attracted to the surface, albeit that, typically, an adsorption barrier is present. The strongest repulsion is found at intermediate ionic strength, where the star-like molecule is in a single-phase state and the barrier remains modest at both low and high ionic strength cases. Remarkably, it is possible that a star in a single swollen phase state is pushed into the quasimicellar state.
Interaction between brushes of root-tethered dendrons
Borisov, O.V. ; Zhulina, E.B. ; Polotsky, A.A. ; Leermakers, F.A.M. ; Birshtein, T.M. - \ 2014
Macromolecules 47 (2014)19. - ISSN 0024-9297 - p. 6932 - 6945.
starlike polymer brushes - consistent-field-theory - monte-carlo - scaling theory - good solvent - dendrimers - model - core - conformations - simulation
Polymer molecules densely tethered to surfaces (polymer brushes) can improve the colloidal stability of dispersion by protecting particles against aggregation. We use mean field and self-consistent field theoretical models to consider repulsive interactions between brushes of branched (dendritic) macromolecules tethered to planar and spherical surfaces. It is demonstrated that compared to planar brushes of linear chains, the brushes composed of dendritic macromolecules provide a sharper repulsive force when pushed to overlap. The sharp increase in force is found also for dendron brush-decorated spherical particles. At the same distance between surfaces, apposing dendron brushes interpenetrate less than brushes of linear chains with the same mass per unit area. Hence the colloidal stability of dendron brush-decorated particles will go hand in hand with improved tribological properties of dispersions.
Dendron brushes and dendronized polymers: a theoretical outlook
Borisov, O.V. ; Polotsky, A.A. ; Rud, V. ; Zhulina, E.B. ; Leermakers, F.A.M. ; Birshtein, T.M. - \ 2014
Soft Matter 10 (2014)13. - ISSN 1744-683X - p. 2093 - 2101.
mean-field model - monte-carlo - persistence length - scaling theory - good solvent - dendrimers - macromolecules - conformations - simulation - core
Dendron brushes are molecular structures built up of treelike macromolecules, with multiple generations of branches, grafted with a root segment to a surface (particle) or to a backbone chain (dendronized polymer) with a sufficiently high grafting density so that the dendrons interact laterally. Recent advances in the theory of dendron brushes are highlighted and complemented by insights from numerical self-consistent field modelling. Our focus is on controversial issues, which are still under debate, such as, the strain distribution in individual dendrons and the appearance of distinct populations with a different extent of stretching for dendrons in planar brushes. We anticipate that dendritic brushes (i) show a strong resistance against bending, which may manifest in a high apparent persistence length of dendronized polymers, and (ii) have an unusually large beneficial effect on the colloidal stability due to the sharp steric repulsive interaction observed when these surface layers are pushed towards the overlap.
Dendritic spherical polymer brushes: Theory and self-consistent field modeling
Rud, O.V. ; Polotsky, A.A. ; Gillich, T. ; Borisov, O.V. ; Leermakers, F.A.M. ; Textor, M. ; Birshtein, T.M. - \ 2013
Macromolecules 46 (2013)11. - ISSN 0024-9297 - p. 4651 - 4662.
polyelectrolyte brushes - scaling theory - conformations - macromolecules - dendrimers
Equilibrium structural properties of polymer brushes formed by dendrons grafted via the root segment onto spherical surfaces (dendritic spherical polymer brushes, DSPB) are studied by means of the Scheutjens–Fleer self-consistent field (SF-SCF) numerical approach and scaling analysis. In particular, we focus on the effects of the variable curvature of the surface on the polymer volume fraction distribution and extension of the individual dendrons in DSPB. A systematic comparison with spherical polymer brushes formed by linear polymer chains (LSPB) end-grafted to the surfaces of the same curvature radii is performed. We demonstrate that the difference in internal structural organization of DSPB and LSPB is most pronounced at small curvature radius of the grafting surface. In particular, the radial distribution of polymer volume fraction in DSPB is close to uniform, whereas in LSPB it decays in the radial direction following a power law. The quasi-plateau polymer volume fraction distribution in DSPB is ensured by wide radial distribution of the end segments. In contrast, in LSPB the end segments of the chains are localized preferentially close to the periphery of the brush. An increase in the curvature radius of the surface is accompanied by emerging segregation into two (or more, for larger number of generations) populations of dendrons: the less extended and the more extended ones. The former ones fill the space in the central region of the DSPB, and the latter bring the majority of the monomer units closer to the periphery of the DSPB. The theoretical results are in line with experimental findings on hydrodynamic radii of linear and dendritic poly(ethylene glycol) brushes end-grafted onto Fe3O4 nanoparticles.
On the two-population structure of brushes made of arm-grafted polymer stars
Polotsky, A.A. ; Leermakers, F.A.M. ; Zhulina, E.B. ; Birshtein, T.M. - \ 2012
Macromolecules 45 (2012)17. - ISSN 0024-9297 - p. 7260 - 7273.
scaling theory - dendrimers - monolayers
The structure of a brush made of arm-grafted polymer stars is investigated using the Scheutjens–Fleer self-consistent field method. By using the “probe macromolecule” approach, conditional distributions of end- and branching points were obtained, which allowed for a detailed analysis of intramolecular correlations in the brush. Results strongly support a previously suggested “two population” picture of the star structure: stars in the brush are divided into two populations (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended toward the solvent. The stars in the “stretched” population have no arms that fold back toward the grafting surface and their free arms form a new sub-brush with effective grafting density determined solely by the total surface loading: molecular mass of polymer grafted onto unit area. With increasing grafting density or/and number of star arms the fraction of stars in the “stretched” population grows. The degree of backfolding of arms is estimated, the total fraction of backfolded arms is invariably small and decreases with increasing grafting density; only stars of the weakly extended population contribute to backfolding. The free ends within a given star are correlated: the ends of different arms are located approximately at the same distance from the grafting plane. Comparison of conditional ends distributions at fixed position of the branching points at different grafting densities reveals a conformational universality of grafted stars belonging to the weakly stretched population: the shape of the ends distribution does not depend on the grafting density but is determined solely by the position of the branching point. We also present analytical arguments showing that this effect is due to universal parabolic self-consistent potential acting on monomer units in the star brush, this potential is independent of the grafting density and the number of star arms.
Collapse of polyelectrolyte star. Theory and modelling
Rud, O.V. ; Mercurieva, A.A. ; Leermakers, F.A.M. ; Birshtein, T.M. - \ 2012
Macromolecules 45 (2012)4. - ISSN 0024-9297 - p. 2145 - 2160.
branched polyelectrolytes - homopolymer globule - copolymer micelles - block-copolymers - polymer brushes - conformations - layer - macromolecules - surfaces - solvent
The collapse of hydrophobic polyelectrolyte stars in aqueous solutions is studied using the Scheutjens–Fleer self-consistent field (SF-SCF) approach. The hydrophobic property of the segments tends to compact the stars, whereas the presence of charges has the opposite effect. As a result, star conformations can be switched from an extended, strongly hydrated, and swollen state to a collapsed state via semicollapsed, quasi-micellar state using control parameters such as the solvent quality, specified by the Flory–Huggins parameter, the pH value or the ionic strength. More specifically, there exists a range of parameters wherein the stars have an inhomogeneous radial structure with a collapsed region, referred to as the core, and a swollen region forming the corona. In such microphase segregated state the fraction of arms of the star that form the core, or alternatively escape into the swollen corona, can be controlled. The SF-SCF analysis is complemented with analytical models to rationalize the complex phase behavior.
Dendritic versus linear polymer brushes: Self-consistent field modeling, scaling theory, and experiments
Polotsky, A.A. ; Gilich, T. ; Borisov, O.V. ; Leermakers, F.A.M. ; Textor, M. ; Birshtein, T.M. - \ 2010
Macromolecules 43 (2010)22. - ISSN 0024-9297 - p. 9555 - 9566.
neurofilament brush - ionic-strength - monte-carlo - chains - macromolecules - stabilization - conformation - simulation - surfaces - collapse
Equilibrium structural properties of polymer brushes formed by dendritic polymer chains (dendrons) are studied by means of Scheutjens-Fleer self-consistent field (SF-SCF) modeling and scaling analysis. Limiting cases of minimal and maximal possible losses of conformational entropy corresponding to different assumptions concerning distribution of elastic tension in the end-grafted dendrons are analyzed on the basis of the Flory-type scaling approach. The numerical SCF modeling indicates that the effective exponent of the power-law dependence for the height of dendritic brush on the grafting density differs from that derived within the Flory-type approximation. This is explained by changing of the intramolecular elastic tension distribution upon an increase in grafting density. The distributions of end and branching points are wide and exhibit multiple maxima, pointing to a broad distribution in the chain stretching. This distribution leads to monotonically decreasing overall density profiles. The theoretical results are in line with experimental findings on linear and dendritic poly(ethylene glycol) layers end-grafted onto TiO2 surfaces
Modeling of charged amphiphilic copolymer stars near hydrophobic surfaces
Mercurieva, A.A. ; Birshtein, T.M. ; Leermakers, F.A.M. - \ 2009
Langmuir 25 (2009)19. - ISSN 0743-7463 - p. 11516 - 11527.
poly(vinylidene fluoride) membranes - interacting chain molecules - branched polyelectrolytes - block-copolymers - protein resistance - statistical-theory - adsorption - polymers - hydrophilicity - micelles
Numerical self-consistent field theory has been applied to amphiphilic copolyelectrolyte stars in the solution and at interfaces both in one- and two-gradient coordinate systems. Our focus is on polymer stars for which the solvent is poor for the short blocks in the center and good for the longer charged chain parts at the periphery of the star. Both in solution as well as near an interface, the structure of the core is influenced by the hydrophobic interactions that tend to form a compact globule with size Rc and the forces exerted by the charged peripheral chain parts that like to expand the core. When the distance H of the center of the star to the surface becomes smaller than the total size R, the interaction force becomes significant; it is positive for Rc
Mechanical unfolding of a homopolymer globule studied by self-consistent field modeling
Polotsky, A.A. ; Charlaganov, M. ; Leermakers, F.A.M. ; Daoud, M. ; Borisov, O.V. ; Birshtein, T.M. - \ 2009
Macromolecules 42 (2009)14. - ISSN 0024-9297 - p. 5360 - 5371.
microphase coexistence - polymeric brushes - poor solvents - afm - deformation - transitions - molecules - chains
We present results of numerical self-consistent field (SCF) calculations for the equilibrium mechanical unfolding of a globule formed by a single flexible polymer chain collapsed in a poor solvent. In accordance with earlier scaling theory and stochastic dynamics simulations findings we have identified three regimes of extensional deformation: (i) a linear response regime characterized by a weakly elongated (ellipsoidal) shape of the globule at small deformations, (ii) a tadpole structure with a globular "head" coexisting with a stretched "tail" at intermediate ranges of deformations, and (iii) an uniformly stretched chain at strong extensions. The conformational transition from the tadpole to the stretched chain is accompanied by an abrupt unfolding of the depleted globular head and a corresponding jump-wise drop in the intrachain tension. The unfolding-refolding cycle demonstrates a hysteresis loop in the vicinity of the transition point. These three regimes of deformation, as well as the first-order like transition between the tadpole and the stretched chain conformations, can be experimentally observable provided that the number of monomer units in the chain is large and/or the solvent quality is sufficiently poor. For short chains, on the other hand, under moderately poor solvent strength conditions, the unfolding transition is continuous. Upon an increase in the imposed end-to-end distance the extended globule retains a longitudinally uniform shape at any degree of deformation. In all cases the system exhibits a negative extensional modulus in the intermediate range of deformations. We anticipate that predicted patterns in force-deformation curves for polymer molecules in poor solvent can be observed in single molecule atomic spectroscopy experiments.
Conformations of polymer and polyelectrolyte stars
Birshtein, T.M. ; Mercurieva, A.A. ; Leermakers, F.A.M. ; Rud, O.V. - \ 2008
Polymer Science Series. A: Polymer physics 50 (2008)9. - ISSN 0965-545X - p. 992 - 1007.
branched polyelectrolytes - starburst dendrimer - chain molecules - drug-delivery - field theory - model - nanoparticles - adsorption - micelles - dynamics
The structure of polymer and polyelectrolyte stars in solution was studied by means of joint analysis of the results of analytical consideration, allowing for nonlocal effects, and numerical simulation based on the Scheutjens-Fleer self-consistent field approach. A limitation of the theoretical treatment is the assumption that all ends of polymer chains are fixed onto the external surface and its benefit is the possibility of obtaining compact and interpretable results. The Scheutjens-Fleer approach makes it possible to study conformations without introduction of additional limitations. The combination of analytical methods and direct numerical calculation turns out to be especially informative.
On the curvature energy of a thin membrane decorated by polymer brushes
Birshtein, T.M. ; Iakovlev, P.A. ; Arnoskov, V.M. ; Leermakers, F.A.M. ; Zhulina, E.B. ; Borisov, O.V. - \ 2008
Macromolecules 41 (2008)2. - ISSN 0024-9297 - p. 478 - 488.
molecular bottle-brushes - interacting chain molecules - repulsive interactions - cylindrical brushes - lyotropic behavior - statistical-theory - elastic properties - grafted polymers - bending rigidity - lipid-membranes
In this work, we present approximate analytical predictions for the contribution to the free energy of curvature of a thin (flexible) membrane rising from a polymer brush, which is grafted to both sides of the membrane. The influence of the approximations is revealed by a detailed comparison with numerically exact self-consistent field (SCF) calculations. We consider both the quenched case, i.e., when the grafting density is the same on both sides, and the annealed case, i.e., when the polymer chains can translocate upon bending from one side of the membrane to the other. It is found that the analytical predictions give the correct sign for the brush contribution to the free energy of curvature. Moreover, for spherically curved membranes, a reasonably accurate scaling with the grafting density ¿ and the chain length N is obtained. However, in the case of a cylindrical curvature, the analytical models overestimate the dependence on the polymer chain length. It is shown that the mean bending modulus is positive, which implies that the grafting of polymers onto membranes makes these stiffer. The Gaussian bending modulus is negative and scales with the chain length in the power three, whereas the mean bending modulus scales with the chain length with a power two. This is in contrast with the analytical predictions which point to the same power-law dependence of three. Our results imply that for sufficiently long polymers the flat conformation becomes unstable in favor of bending.
Wetting phase diagrams of polyacid brush with a triple point.
Mercurieva, A.A. ; Iakovlev, P.A. ; Zhulina, E.B. ; Birshtein, T.M. ; Leermakers, F.A.M. - \ 2006
Physical Review. E, Statistical nonlinear, and soft matter physics 74 (2006)3. - ISSN 1539-3755 - 10 p.
interacting chain molecules - polymer brush - statistical-theory - adsorption - transitions - block - size
The (pre)wetting behavior of an annealed polyelectrolyte (PE) brush by an electrolyte solution that is strongly segregated from an apolar phase is analyzed. In this complex interface, there are interactions on various length scales. There are short-range interactions with the (uncharged) surface, and there are interactions on the length scale of the brush height. Using either the ionic strength or the water-surface interaction strength as the control parameters, it is possible to approach and induce a wetting transition in this system. The first-order wetting transition, promoted by favorable short-range substrate interactions with the surface, is in competition with the wetting transition controlled by the detachment of the fluid interface from the periphery of the PE brush. The electric double layer on top of the PE brush contributes with a repulsive forces to the disjoining pressure that tends to thicken the wetting film, and therefore, the transition in all cases is first order. Various phase portraits of the wetting phase diagram are envisioned. One of these features the crossing of two prewetting lines. At the crossing point three surface states coexist. This triple point is analyzed in some detail with the help of a molecular-level self-consistent field model
An annealed polyelectrolyte brush in a polar-nonpolar binary solvent : effect of pH and ionic strength
Mercurieva, A.A. ; Birshtein, T.M. ; Zhulina, E.B. ; Iakovlev, P. ; Male, J. van; Leermakers, F.A.M. - \ 2002
Macromolecules 35 (2002). - ISSN 0024-9297 - p. 4739 - 4752.
A weakly charged polyelectrolyte brush in a polar-nonpolar solvent mixture is studied using a boxlike model and by numerical self-consistent-field theory. The work is a continuation of a similar study of a neutral polymer brush in a solvent mixture with a pronounced solubility gap. We study both the structure and structural transitions of the brush in particular in the one-phase region of the solvent mixture in the bulk. With respect to the neutral system, the polyelectrolyte system is even richer in its behavior. Starting from a nonpolar main solvent, upon increasing the chemical potential of water, we find the development of a mesoscopic water film inside the brush. The polymer takes up this thin film as it finds an environment that allows for the dissociation of its groups energetically attractive. The phase transition can be accompanied by an anomalous collapse of the ionizable brush and tuned by the pH of the solution and the ionic strength in the system. Another brush transition can occur when nonpolar solvent is added to a brush immersed in water. Finally, it is feasible that systems exist that feature three successive brush transitions upon changing the bulk composition from pre-binodal, to biphasic, and then to post-binodal compositions, where a forward, a reentry, and again a forward transition are found, respectively.
Effect of a polymer brush on capillary condensation
Leermakers, F.A.M. ; Zhulina, E.B. ; Male, J. van; Mercurieva, A.A. ; Fleer, G.J. ; Birshtein, T.M. - \ 2001
Langmuir 17 (2001). - ISSN 0743-7463 - p. 4459 - 4466.
Amphiphilic polymer brush in a mixture of incompatible liquids. Numerical self-consistent-field calculations
Mercurieva, A.A. ; Leermakers, F.A.M. ; Birshtein, T.M. ; Fleer, G.J. ; Zhulina, E.B. - \ 2000
Macromolecules 33 (2000). - ISSN 0024-9297 - p. 1072 - 1081.
We studied a polymer brush composed of homodisperse end-grafted chains in a binary A-B solvent mixture by means of numerical self-consistent-field calculations. The focus is on the case that the solvents have a solubility gap in the bulk phase behavior, and we investigated the system near the bulk binodal. We assume that both solvents are good solvents for the polymer: the monomers of the chains have amphiphilic properties. When the minority solvent B is the better solvent, it is possible to find a preferential uptake of the solvent B. This solvent uptake can either occur in a continuous manner or in a first-order transition. From a wetting perspective, such a stepwise increase in B uptake may be identified as a prewetting step. In this case, however, the step is not necessarily caused by specific interactions with the solid substrate, but it results from an instability in the structure of the polymer brush at intermediate compositions of A and B in the brush. It is not always true that at coexistence the substrate is completely wet by the minority solvent, even when there is a prewetting step. We examine the post-transition solvent uptake up to and beyond the bulk binodal (in the case of partial wetting). The numerical SCF results complement a recent analysis of the same problem by a model of the Alexander-de Gennes type. Both in the numerical and in the analytical models, it is observed that the first-order phase transition is unusual: the polymer chains absorb the better solvent and then suddenly collapse to a very dense sublayer when there is only a small amount of the wetting component.