Search

A scaling theory of adsorption of polyampholyte chains at charged spherical particles from dilute low salt solutions is developed. The expressions for the surface coverage and the thickness of adsorbed layer are derived as functions of bulk polymer concentration, particle size, and surface charge density.

The equilibrium structure of an interpolyelectrolyte complex (IPEC) coacervate consisting of weakly charged flexible polyanions and polycations with equal degree of ionization is considered. We study effects of salt concentration cs and solvent quality defined by second virial coefficient v on polymer density, surface tension, salt absorption, and correlations of charges and monomer units in equilibrium IPEC. Five different scaling regimes of IPEC are revealed, and a salt-solvent quality (cs-v) diagram of coacervate states is constructed. Boundaries between different regimes correspond to crossovers between low/high salt concentrations and poor/Θ-/good solvent conditions. Derived scaling laws for coacervate physical properties in each of regimes are in agreement with analysis based on the random phase approximation (RPA). This study summarizes and complements current theoretical comprehension of symmetrical IPEC of weakly charged polyions. [ABSTRACT FROM AUTHOR]

We present a theory of conformational transition triggered by inferior solvent strength in brushes formed by dendritically branched macromolecules tethered to planar, concave, or convex cylindrical and spherical surfaces. In the regime of linear elasticity for brush-forming dendrons, an analytical strong stretching self-consistent field (SS-SCF) approach provides brush conformational properties as a function of solvent strength. A boxlike model is applied to describe the collapse transition in brushes formed by macromolecules with arbitrary treelike topology, including hyperbranched polymers. We demonstrate that an increase in the degree of branching, that is, an increase in the number of generations or/and functionality of branching points in tethered macromolecules, makes the swelling-to-collapse transition less sharp. A decrease in surface curvature has a similar effect. The numerical Scheutjens-Fleer self-consistent field approach is used to analyze the collapse transition in dendron brushes in the nonlinear stretching regime. It is demonstrated that inferior solvent strength suppresses stratification that is exhibited under good solvent conditions by densely grafted dendron brushes. [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]

We develop a scaling model relating the friction forces between two polyelectrolyte brushes sliding over each other to the separation between grafted surfaces, number of monomers and charges per chain, grafting density of chains, and solvent quality. We demonstrate that the lateral force between brushes increases upon compression, but to a lesser extent than the normal force. The shear stress at larger separations is due to solvent slip layer friction. The thickness of this slip layer sharply decreases at distances on the order of undeformed brush thickness. The corresponding effective viscosity of the layer sharply increases from the solvent viscosity to a much higher value, but this increase is smaller than the jump of the normal force resulting in the drop of the friction coefficient. At stronger compression we predict the second sharp increase of the shear stress corresponding to interpenetration of the chains from the opposite brushes. In this regime the velocity-dependent friction coefficient between two partially interpenetrating polyelectrolyte brushes does not depend on the distance between substrates because both normal and shear forces are reciprocally proportional to the plate separation. Although lateral forces between polyelectrolyte brushes are larger than between bare surfaces, the enhancement of normal forces between opposing polyelectrolyte brushes with respect to normal forces between bare charged surfaces is much stronger resulting in lower friction coefficient. The model quantitatively demonstrates how polyelectrolyte brushes provide more effective lubrication than bare charged surfaces or neutral brushes. [ABSTRACT FROM AUTHOR]

The self-assembly of synthetic diblockcopolymers has been extensivelystudied experimentally and theoretically. In contrast, self-assemblyof polypeptide diblock copolymers has so far been mostly studied experimentally.We discovered that the theory developed for synthetic diblock copolymerdoes not fully explain the self-assembly of elastin-like polypeptidediblock copolymers, leading us to generalize the theory to make itapplicable for these polypeptides. We demonstrated that elastin-likepolypeptide diblocks self-assemble into weak micelles with dense coresand almost unstretched coronas, a state not previously observed forsynthetic diblock copolymers. Weak micelles form if the surface tensionat the core–corona interface is low compared to that expectedof a micelle with a dense core. The predictions of the theory of weakmicelles for the critical micelle temperature, hydrodynamic radius,and aggregation number of elastin-like polypeptide diblocks are inreasonable agreement with the experimentally measured values. Theunique and unprecedented control of amphiphilicity in these recombinantpeptide polymers reveals a new micellar state that has not been previouslyobserved in synthetic diblock copolymer systems. [ABSTRACT FROM AUTHOR]

Weak polyampholytes and globular proteins among them can be efficiently absorbed from solutions by polyelectrolyte brushes or microgels even if the net charge of the polyampholyte is of the same sign as that of the brush/microgel. We use a mean-field approach for calculating the free energy of insertion of a probe polyampholyte molecule into a polyelectrolyte brush/microgel. We anticipate that the insertion of the polyampholyte into similarly charged brush/microgel may be thermodynamically favorable due to the gain in the cumulative re-ionization free energy of the pH-sensitive acidic and basic residues. Importantly, we demonstrate that the polyampholyte (protein) charge sign inversion upon transfer from the bulk of the solution to the brush/microgel does not provide sufficient conditions to assure negative re-ionization free energy balance. Thus (in the absence of other driving or stopping mechanisms), charge sign inversion does not necessarily provoke spontaneous absorption of the polyampholyte into the brush/microgel.

Nanoparticles (NPs) decorated with topographically or chemically distinct surface patches are an emerging class of colloidal building blocks of functional hierarchical materials. Surface segregation of polymer ligands into pinned micelles offers a strategy for the generation of patchy NPs with controlled spatial distribution and number of patches. The thermodynamic nature of this approach poses a question about the stability of multiple patches on the NP surface, as the lowest energy state is expected for NPs carrying a single patch. In the present work, for gold NPs end-grafted with thiol-terminated polymer molecules, we show that the patchy surface morphology is preserved under conditions of strong grafting of the thiol groups to the NP surface ( i . e ., up to a temperature of 40 °C), although the patch shape changes over time. At higher temperatures ( e . g ., at 80 °C), the number of patches per NP decreases, due to the increased lateral mobility and coalescence of the patches as well as the ultimate loss of the polymer ligands due to desorption at enhanced solvent quality. The experimental results were rationalized theoretically, using a scaling approach. The results of this work offer insight into the surface science of patchy nanocolloids and specify the time and temperature ranges of the applications of patchy NPs.

The spatial distribution of polymer ligands on the surface of nanoparticles (NPs) is of great importance because it determines their interactions with each other and with the surrounding environment. Phase separation in mixtures of polymer brushes has been studied for spherical NPs; however, the role of local surface curvature of nonspherical NPs in the surface phase separation of end-grafted polymer ligands remains an open question. Here, we examined phase separation in mixed monolayers of incompatible polystyrene and poly(ethylene glycol) brushes end-capping the surface of gold nanorods in a good solvent. By varying the molar ratio between these polymers, we generated a range of surface patterns, including uniform and nonuniform polystyrene shells, randomly distributed polystyrene surface patches, and, most interestingly, a helicoidal pattern of polystyrene patches wrapping around the nanorods. The helicoidally patterned nanorods exhibited long-term colloidal stability in a good solvent. The helicoidal wrapping of the nanorods was achieved for the mixtures of polymers with different molecular weights and preserved when the quality of the solvent for the polymers was reduced. The helicoidal organization of polymer patches on the surface of nanorods can be used for templating the synthesis or self-assembly of helicoidal multicomponent nanomaterials.

Using a combination of a mean-field theoretical method and the numerical Scheutjens-Fleer self-consistent field approach, we predict that it is possible to have re-entrant morphological transitions in nanostructures of diblock copolymers upon variation in temperature-mediated solubility of the associating blocks. This peculiar effect is explained by the different rates in variation of the density of the collapsed core domains and the corresponding interfacial energy as a function of the temperature. The theoretical findings are supported by existing experimental observations of reversed sequences of the morphological transitions occurring upon temperature variation in solutions of amphiphilic block copolymers.

We propose scaling theory of complex coacervate core micelles (C3Ms). Such micelles arise upon electrostatically driven coassembly of bis-hydrophilic ionic/nonionic diblock copolymers with oppositely charged ionic blocks or bis-hydrophilic diblock copolymers with oppositely charged macroions. Structural properties of the C3Ms are studied as a function of the copolymer composition, degree of ionization of the ionic blocks, and ionic strength of the solution. It is demonstrated that at sufficiently large length of the polyelectrolyte blocks the C3Ms may exhibit polymorphism; that is, morphological transitions from spherical to cylindrical micelles and further to lamellar structure or polymersomes may be triggered by increasing salt concentration. A diagram of states of micellar aggregates in the salt concentration/ionization degree coordinates is constructed, and scaling laws for experimentally measurable properties, e.g., micelle aggregation number and core and corona sizes, are found.

A self-consistent field theory is applied to study structural properties of micelles formed upon spontaneous assembly of diblock copolymers comprising soluble dendron block covalently linked to insoluble linear block in selective solvent. The structure of spherical micelles is analyzed as a function of degrees of polymerization of the blocks and number of generations and branching functionality of the dendron block. We demonstrate that for a given molecular mass of blocks both the hydrodynamic dimensions of the micelles and the aggregation number decrease as a function of the degree of branching of the dendron block. However, the number of potentially functionalizable terminal segments of dendrons in the corona exposed to the solution increases compared to the number of terminal groups in the corona of linear diblock copolymer micelle. This result may have important implications for construction of linear-dendritic block copolymer micelles with smart functionalities for targeted drug and gene delivery.

Chemically and topographically patterned nanoparticles (NPs) with dimensions on the order of tens of nanometers have a diverse range of applications and are a valuable system for fundamental research. Recently, thermodynamically controlled segregation of a smooth layer of polymer ligands into pinned micelles (patches) offered an approach to nanopatterning of polymer-functionalized NPs. Control of the patch number, size, and spatial distribution on the surface of spherical NPs has been achieved, however, the role of NP shape remained elusive. In the present work, we report the role of NP shape, namely, the effect of the local surface curvature, on polymer segregation into surface patches. For polymer-functionalized metal nanocubes, we show experimentally and theoretically that the patches form preferentially on the high-curvature regions such as vertices and edges. An in situ transformation of the nanocubes into nanospheres leads to the change in the number and distribution of patches; a process that is dominated by the balance between the surface energy and the stretching energy of the polymer ligands. The experimental and theoretical results presented in this work are applicable to surface patterning of polymer-capped NPs with different shapes, thus enabling the exploration of patch-directed self-assembly, as colloidal surfactants, and as templates for the synthesis of hybrid nanomaterials.

We present a theoretical analysis targeted to describe the structural properties of brushes formed by Ψ-shaped macromolecules tethered by terminal segment of stem to planar surface while exposing multiple free branches to the surrounding solution. We use an analytical self-consistent field approach based on the strong stretching approximation, and the assumption of Gaussian elasticity for linear chain fragments of the tethered macromolecules. The effect of weak and strong polydispersity of branches is analyzed. In the case of weakly polydisperse macromolecules, variations in length of branches lead to a more uniform polymer density distribution with slight increase in the brush thickness compared to the case of monodisperse chains with the same degree of polymerization. We demonstrate that in contrast to linear chains, strong polydispersity of Ψ-shaped macromolecules does not necessarily lead to strong perturbations in polymer density distribution. In particular, mixed brushes of the so-called "mirror" dendrons (in which number of stem monomers in one component coincides with number of monomers in a branch of the other component, and vice versa) give rise to a unified polymer density distribution with shape independent of the brush composition. The predictions of analytical theory are systematically compared to the results of numerical self-consistent field modeling based on the Scheutjens-Fleer approach.

We develop a scaling model relating the friction forces between two polyelectrolyte brushes sliding over each other to the separation between grafted surfaces, number of monomers and charges per chain, grafting density of chains, and solvent quality. We demonstrate that the lateral force between brushes increases upon compression, but to a lesser extent than the normal force. The shear stress at larger separations is due to solvent slip layer friction. The thickness of this slip layer sharply decreases at distances on the order of undeformed brush thickness. The corresponding effective viscosity of the layer sharply increases from the solvent viscosity to a much higher value, but this increase is smaller than the jump of the normal force resulting in the drop of the friction coefficient. At stronger compression we predict the second sharp increase of the shear stress corresponding to interpenetration of the chains from the opposite brushes. In this regime the velocity-dependent friction coefficient between two partially interpenetrating polyelectrolyte brushes does not depend on the distance between substrates because both normal and shear forces are reciprocally proportional to the plate separation. Although lateral forces between polyelectrolyte brushes are larger than between bare surfaces, the enhancement of normal forces between opposing polyelectrolyte brushes with respect to normal forces between bare charged surfaces is much stronger resulting in lower friction coefficient. The model quantitatively demonstrates how polyelectrolyte brushes provide more effective lubrication than bare charged surfaces or neutral brushes.

Molecular bottle-brushes are highly branched macromolecules with side chains densely grafted to a long polymer backbone. The brush-like architecture allows focusing of the side-chain tension to the backbone and its amplification from the pico-Newton to nano-Newton range. The backbone tension depends on the overall molecular conformation and the surrounding environment. Here we study the relation between the tension and conformation of the molecular brushes in solutions, melts, and on substrates. In solutions, we find that the backbone tension in dense brushes with side chains attached to every backbone monomer is on the order of f(0)N(3/8) in athermal solvents, f(0)N(1/3) in theta solvents, and f(0) in poor solvents and melts, where N is the degree of polymerization of side chains, f(0) approximately equal k(B)T/b is the maximum tension in side chains, b is the Kuhn length, k(B) is Boltzmann's constant, and T is the absolute temperature. Depending on the side chain length and solvent quality, molecular brushes develop tension on the order of 10-100 pN, which is sufficient to break hydrogen bonds. Significant amplification of tension occurs upon adsorption of brushes onto a substrate. On a strongly attractive substrate, maximum tension in the brush backbone is approximately f(0)N, reaching values on the order of several nano-Newtons, which exceeds the strength of a typical covalent bond. At low grafting density and high spreading parameter, the cross-sectional profile of an adsorbed molecular brush is approximately rectangular with a thickness approximately b (A/S)1/2, where A is the Hamaker constant, and S is the spreading parameter. At a very high spreading parameter (S > A), the brush thickness saturates at monolayer approximately b. At a low spreading parameter, the cross-sectional profile of adsorbed molecular brush has a triangular tent-like shape. In the cross-over between these two opposite cases, covering a wide range of parameter space, the adsorbed molecular brush consists of two layers. Side chains in the lower layer gain surface energy due to the direct interaction with the substrate, while the second layer spreads on the top of the first layer. Scaling theory predicts that this second layer has a triangular cross-section with width R approximately N(3/5) and height h approximately N(2/5). Using self-consistent field theory we calculate the cap profile y(x) = h(1 - x2/R2)2, where x is the transverse distance from the backbone. The predicted cap shape is in excellent agreement with both computer simulation and experiment.

Molecular dynamics simulations are used to probe the structural organization of nonstoichiometric interpolyelectrolyte complexes (IPECs) formed by oppositely charged starlike and linear polyelectrolytes (PEs) in dilute aqueous solution. We demonstrate that undercompensated star-IPEC consists of a denser coacervate core and a charged starlike corona. Two distinctive populations of star branches completely embedded in a coacervate core and stretched in a lyophilizing corona are found. The scaling arguments support the stability of IPEC with partitioned star branches.