Effect of polymer architecture on the adsorption behaviour of amphiphilic copolymers: A theoretical study.

HYPOTHESIS: Polymer architecture is known to have significant impact on its adsorption behaviour. Most studies have been concerned with the more concentrated, "close to surface saturation" regime of the isotherm, where complications such as lateral interactions and crowding also additionally affect the adsorption. We compare a variety of amphiphilic polymer architectures by determining their Henry's adsorption constant (kH), which, as with other surface active molecules, is the proportionality constant between surface coverage and bulk polymer concentration in a sufficiently dilute regime. It is speculated that not only the number of arms or branches, but also the position of adsorbing hydrophobes influence the adsorption, and that by controlling the latter the two can counteract each other. METHODOLOGY: The Self-consistent field calculation of Scheutjens and Fleer was implemented to calculate the adsorbed amount of polymer for many different polymer architectures including linear, star and dendritic. Using the adsorption isotherms at very low bulk concentrations, we determined the value of kH for these. FINDINGS: It is found that the branched structures (star polymers and dendrimers) can be viewed as analogues of linear block polymers based on the location of their adsorbing units. Polymers containing consecutive trains of adsorbing hydrophobes in all cases showed higher level of adsorption compared to their counterparts, where the hydrophobes were more uniformly distributed on the chains. While increasing the number of branches (or arms for star polymers) also confirmed the known result that the adsorption decreased with the number of arms, this trend can be partially offset by the appropriate choice of the location of anchoring groups.

Hybrid Molecules Consisting of Lysine Dendrons with Several Hydrophobic Tails: A SCF Study of Self-Assembling.

In this article, we used the numerical self-consistent field method of Scheutjens-Fleer to study the micellization of hybrid molecules consisting of one polylysine dendron with charged end groups and several linear hydrophobic tails attached to its root. The main attention was paid to spherical micelles and the determination of the range of parameters at which they can appear. A relationship has been established between the size and internal structure of the resulting spherical micelles and the length and number of hydrophobic tails, as well as the number of dendron generations. It is shown that the splitting of the same number of hydrophobic monomers from one long tail into several short tails leads to a decrease in the aggregation number and, accordingly, the number of terminal charges in micelles. At the same time, it was shown that the surface area per dendron does not depend on the number of hydrophobic monomers or tails in the hybrid molecule. The relationship between the structure of hybrid molecules and the electrostatic properties of the resulting micelles has also been studied. It is found that the charge distribution in the corona depends on the number of dendron generations G in the hybrid molecule. For a small number of generations (up to G=3), a standard double electric layer is observed. For a larger number of generations (G=4), the charges of dendrons in the corona are divided into two populations: in the first population, the charges are in the spherical layer near the boundary between the micelle core and shell, and in the second population, the charges are near the periphery of the spherical shell. As a result, a part of the counterions is localized in the wide region between them. These results are of potential interest for the use of spherical dendromicelles as nanocontainers for drug delivery.

Colloidal particles interacting with a polymer brush: a self-consistent field theory.

The interaction of colloidal particles with a planar polymer brush immersed in a solvent of variable thermodynamic quality is studied by a numerical self-consistent field method combined with analytical mean-field theory. The effect of embedded particle on the distribution of polymer density in the brush is analyzed and the particle insertion free energy profiles are calculated for variable size and shape of the particles and sets of polymer-particle and polymer-solvent interaction parameters. In particular, both cases of repulsive and attractive interactions between particles and brush-forming chains are considered. It is demonstrated that for large particles the insertion free energy is dominated by repulsive (osmotic) contribution and is approximately proportional to the particle volume in accordance with earlier theoretical predictions [Halperin et al., Macromolecules, 2011, 44, 3622]. For the particles of smaller size or/and large shape asymmetry the adsorption or depletion of a polymer from the particle surface essentially contributes to the insertion free energy balance. As a result, depending on the set of polymer-solvent and polymer-particle interaction parameters and brush grafting density the insertion free energy profile may exhibit complex patterns, i.e., from a pure repulsive effective potential barrier to an attractive well. The results of our study allow for predicting equilibrium partitioning and controlling diffusive transport of (bio)nanocolloids across (bio)polymer brushes of arbitrary geometry including polymer-modified membranes or nanopores.

Computer modeling of polymer stars in variable solvent conditions: a comparison of MD simulations, self-consistent field (SCF) modeling and novel hybrid Monte Carlo SCF approach.

Computer-aided modeling is a systematic approach to grasp the physics of macromolecules, but it remains essential to know when to trust the results and when not. For a polymer star, we consider three approaches: (i) Molecular Dynamics (MD) simulations and implementing a coarse-grained model, (ii) the self-consistent field approach based on a mean-field approximation and implementing the lattice model due to Scheutjens and Fleer (SF-SCF) and (iii) novel hybrid Monte Carlo self-consistent field (MC-SCF) method, which combines a coarse-grained model driven by a Monte Carlo method and a mean-field representation driven by SF-SCF. We compare the performance of these approaches under a wide range of solvent qualities. The MD approach is formally the most exact but suffers from reasonable convergence. The mean-field approach works similarly in all solvent qualities but is quantitatively least accurate. The MC-SCF hybrid allows us to combine the benefits of the simulation route and the effective performance of SCF. We consider the center-to-end distance Rce, the radius of gyration Rg2 of the star and the polymer density profiles φ(r) of polymer-segments in it. All three methods show a good qualitative agreement one to another. The MC-SCF method is in good agreement with the scaling predictions in the whole range of solvent quality values showing that it grasps the essential physics while remaining computationally in bounds.

Long Tails with Flower-like Conformations Undergo an Escape Transition in Homopolymer Adsorption Layers.

De Gennes predicted that homopolymer adsorption on a solid-liquid interface results in an adsorption profile with a proximal, a central, and a distal region, wherein, for a good solvent, the central region has a self-similar structure with a density profile that decays as a power law with a coefficient of -4/3. Recent numerical self-consistent field (SCF) predictions for the long-chain length (N) limit revealed a more complex central region with an inner part, where the loops dominate the layer, with a (mean-field) power-law coefficient of -2 and an outer part, where tails dominate, with a "de Gennes" scaling of -4/3. The tails with length t < t* contribute to the inner part of the central region, and these have similar conformations as the loops. The outer part is populated by tails with a length t > t*, and these behave differently. With the increasing length of the tails, there exists a weak escape transition at t = t escape ≈ N/10. Long tails in the adsorption profile (t ≳ t* ∝ N 0.733) show enhanced fluctuations due to this nearby escape transition, and this explains the excluded volume scaling for the outer part of the central region in SCF. With this interpretation, the -2 scaling found by SCF for the inner part should be classified as a mean-field result.

Turning autophobic wetting on biomimetic surfaces into complete wetting by wetting additives.

Autophobicity or pseudo partial wetting, a phenomenon of a liquid not spreading on its own monolayer, is characterized by an energy barrier that prevents the growth of a wetting film beyond the monolayer thickness. Applying a molecularly detailed self-consistent field theory we illustrate how autophobic wetting can be overcome by wetting additives. More specifically we use an emulsifier which keeps the interfacial tension between the wetting component and the majority solvent low, and a co-solvent additive which partitions inside the film and then destroys the molecular order in it so that the barrier for film growth is cleared. An application wherein it is believed that autophobic wetting is counteracted by such a set of wetting additives is found in an antidandruff shampoo formulation. We have experimental results that show thick deposits onto hydrophobic hair surfaces by administration of the antidandruff shampoo. The complementary modeling of such a system suggests that the active ingredient plays the role of the co-solvent additive. As significant amounts of the co-solvent additives are needed to approach the completely wet state, the formulation naturally brings large amounts of active ingredient to the root of the hair where its presence is required.

Electroresponsive Polyelectrolyte Brushes Studied by Self-Consistent Field Theory.

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.

(Homo)polymer-mediated colloidal stability of micellar solutions.

Despite their wide range of applications, there is a remarkable lack of fundamental understanding about how micelles respond to other components in solution. The colloidal stability of micellar solutions in presence of (homo)polymers is investigated here following a theoretical bottom-up approach. A polymer-mediated micelle-micelle interaction is extracted from changes in the micelle-unimer equilibrium as a function of the inter-micelle distance. The homopolymer-mediated diblock copolymer micelle-micelle interaction is studied both for depletion and adsorption of the homopolymer. The fluffy nature of the solvophilic domain (corona) of the micelle weakens the depletion-induced destabilization. Accumulation of polymers into the corona induces bridging attraction between micelles. In fact, both depletion and adsorption phenomena are regulated by the coronal thickness relative to the size of the added polymer. Penetration of guest compounds into the coronal domain of crew-cut micelles, with a narrower yet denser corona, is less pronounced as for starlike micelles (with a more diffuse corona). Therefore, crew-cut micelles are less sensitive to the effect of added compounds, and hence more suitable for applications in multicomponent systems, such as industrial formulations or biological fluids. The trends observed for the colloidal stability of crew-cut micelles qualitatively match with our experimental observations on aqueous dispersions of polycaprolactone-polyethylene glycol (PCL-PEO) micellar suspensions with added PEO chains.

The physics of microemulsions extracted from modeling balanced tensionless surfactant-loaded liquid-liquid interfaces.

Microemulsions are explored using the self-consistent field approach. We consider a balanced model that features two solvents of similar size and a symmetric surfactant. Interaction parameter χ and surfactant concentration φs b complement the model definition. The phase diagram in χ-φs b coordinates is known to feature two lines of critical points, the Scott and Leibler lines. Only upon imposing a finite distance between the interfaces, we observe that the Scott line meets the Leibler line. We refer to this as a Lifshitz point (LP) for real systems. We add regions that are relevant for microemulsions to this phase diagram by considering the saturation line, which connects (χ, φs b)-points for which the interface becomes tensionless. Crossing this line implies a first-order phase transition as internal interfaces develop, characteristic for one-phase microemulsions. The saturation line ends at the so-called microemulsion point (MP). The MP is shown to connect with the LP by a line of MP-like critical points, found by searching for a "MP" while the distance between interfaces is fixed. A pair of binodal lines that envelop the three-phase (Winsor III) microemulsion region is shown to connect to the MP. The cohesiveness of the middle phase in Winsor III is related to non-monotonic, inverse DLVO-type interaction curves between the surfactant-loaded tensionless interfaces. The mean and Gaussian bending modulus, relevant for the shape fluctuations and the topology of interfaces, respectively, are evaluated along the saturation line. Near the MP, both rigidities are positive and vanish in a power-law fashion with coefficient unity at the MP. Overseeing these results proves that the MP has a pivoting role in the physics of microemulsions.

Non-linear elasticity effects and stratification in brushes of branched polyelectrolytes.

Brushes formed by arm-tethered starlike polyelectrolytes may exhibit internal segregation into weakly and strongly extended populations (stratified two-layer structure) when strong ionic intermolecular repulsions induce stretching of the tethers up to the limit of their extensibility. We propose an approximate Poisson-Boltzmann theory for analysis of the structure of the stratified brush and compare it with results of numerical self-consistent field modeling. Both analytical and numerical models point to the formation of a narrow cloud of counterions (internal double electrical layer) localized inside a stratified brush at the boundary between the layers.

Plasticity in colloidal gel strands.

Colloidal gels are space-spanning networks of aggregated particles. The mechanical response of colloidal gels is governed, to a large extent, by the properties of the individual gel strands. To study how colloidal gels respond to repeated deformations, we perform Brownian dynamics simulations on single strands of aggregated colloidal particles. While current models assume that gel failure is due to the brittle rupture of gel strands, our simulations show that gel strands undergo large plastic deformations prior to breaking. Rearrangement of particles within the strands leads to plastic lengthening and softening of the strands, which may ultimately lead to strand necking and ductile failure. This failure mechanism occurs irrespective of the thickness and length of the strands and the range and strength of the interaction potential. Rupture of gel strands is more likely for long and thin strands and for a long-ranged interaction potential.

Temperature-Induced Re-Entrant Morphological Transitions in Block-Copolymer Micelles.

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.

Elastic properties of symmetric liquid-liquid interfaces.

The mean (κ) and Gaussian (κ[over ¯]) bending rigidities of liquid-liquid interfaces, of importance for shape fluctuations and topology of interfaces, respectively, are not yet established: Even their signs are debated. Using the Scheutjens Fleer variant of the self-consistent field theory, we implemented a model for a symmetric L-L interface and obtained high-precision (mean-field) results in the grand-canonical (µ,V,T) ensemble. We report positive values for both moduli when the system is close to critical where the rigidities show the same scaling behavior as the interfacial tension γ. At strong segregation, when the interfacial width becomes of the order of the segment size, κ[over ¯] turns negative. The length scale λ≡sqrt[κ/γ] remains of the order of segment size for all strengths of interaction; yet the 1/sqrt[N] chain length correction reduces λ significantly when the chain length N is small.

Structure and properties of polydisperse polyelectrolyte brushes studied by self-consistent field theory.

Two complementary self-consistent field theoretical approaches are used to analyze the equilibrium structure of binary and ternary brushes of polyions with different degrees of polymerization. Stratification in binary brushes is predicted: the shorter chains are entirely embedded in the proximal sublayer depleted of end-points of longer chains while the peripheral sublayer contains exclusively terminal segments of longer chains. The boundary between sublayers is enriched with counterions that neutralize the residual charge of the proximal sublayer. These analytical predictions for binary brushes are confirmed and extended to ternary brushes using the numerical Scheutjens-Fleer approach.

Electrostatic stiffening and induced persistence length for coassembled molecular bottlebrushes.

A self-consistent field analysis for tunable contributions to the persistence length of isolated semiflexible polymer chains including electrostatically driven coassembled deoxyribonucleic acid (DNA) bottlebrushes is presented. When a chain is charged, i.e., for polyelectrolytes, there is, in addition to an intrinsic rigidity, an electrostatic stiffening effect, because the electric double layer resists bending. For molecular bottlebrushes, there is an induced contribution due to the grafts. We explore cases beyond the classical phantom main-chain approximation and elaborate molecularly more realistic models where the backbone has a finite volume, which is necessary for treating coassembled bottlebrushes. We find that the way in which the linear charge density or the grafting density is regulated is important. Typically, the stiffening effect is reduced when there is freedom for these quantities to adapt to the curvature stresses. Electrostatically driven coassembled bottlebrushes, however, are relatively stiff because the chains have a low tendency to escape from the compressed regions and the electrostatic binding force is largest in the convex part. For coassembled bottlebrushes, the induced persistence length is a nonmonotonic function of the polymer concentration: For low polymer concentrations, the stiffening grows quadratically with coverage; for semidilute polymer concentrations, the brush chains retract and regain their Gaussian size. When doing so, they lose their induced persistence length contribution. Our results correlate well with observed physical characteristics of electrostatically driven coassembled DNA-bioengineered protein-polymer bottlebrushes.

Behavior of Weak Polyelectrolyte Brushes in Mixed Salt Solutions.

Hydrophilic and hydrophobic weak polybasic brushes immersed in aqueous solutions of mixed salt counterions are considered using a mean-field numerical self-consistent field approach. On top of the solvent quality of the polymer, the counterion-solvent interactions are accounted for by implementing Flory-Huggins interaction parameters. We show that ion specificity within the brush can bring about large changes in conformation. It is found that the collapse transition of hydrophobic, weak polyelectrolyte brushes features an intermediate two-phase state wherein a subset of chains are collapsed in a dense layer at the substrate, while the remainder of chains are well-solvated and strongly stretched away from the it. Besides pH and ionic strength, solvent quality of counterions and the composition of ions in the solvent are important control parameters for the behavior of polyelectrolyte brushes. Increasingly hydrophobic counterions penetrate deeper within the brush and stabilize the collapsed region, while hydrophilic counterions do the opposite.

Sign Switch of Gaussian Bending Modulus for Microemulsions: A Self-Consistent Field Analysis Exploring Scale Invariant Curvature Energies.

Bending rigidities of tensionless balanced liquid-liquid interfaces as occurring in microemulsions are predicted using self-consistent field theory for molecularly inhomogeneous systems. Considering geometries with scale invariant curvature energies gives unambiguous bending rigidities for systems with fixed chemical potentials: the minimal surface Im3m cubic phase is used to find the Gaussian bending rigidity κ[over ¯], and a torus with Willmore energy W=2π^{2} allows for direct evaluation of the mean bending modulus κ. Consistent with this, the spherical droplet gives access to 2κ+κ[over ¯]. We observe that κ[over ¯] tends to be negative for strong segregation and positive for weak segregation, a finding which is instrumental for understanding phase transitions from a lamellar to a spongelike microemulsion. Invariably, κ remains positive and increases with increasing strength of segregation.

Microphase Segregation of Diblock Copolymers Studied by the Self-Consistent Field Theory of Scheutjens and Fleer.

We used the self-consistent field (SCF) formalism of Scheutjens and Fleer (SF-SCF) to complement existing theoretical investigations on the phase behavior of block copolymer melts. This method employs the freely jointed chain (FJC) model for finite chain length and systematic differences exist compared to the classical SCF predictions. We focus on the critical and hexagonal (HEX) to lamellar (LAM) phase transition region at intermediate and strong segregations. Chain length (N) dependence of the critical point ( χ c r ) was found to be χ c r N = 10.495 ( 1 + 4 / N ) . The characteristic spacing (D) of LAM was found as D = 4 / 3 N at the critical conditions. We present SF-SCF predictions for the phases single gyroid (SG), double gyroid (DG) and hexagonally perforated lamellar (HPL), in the region where HEX and LAM compete. At χ N = 30 , N = 300 ; we found SG and HPL were metastable with respect to LAM or HEX, DG was stable in a narrow region of the asymmetry ratio. In contrast to the latest predictions, at strong segregation χ N = 120 , DG was found to be metastable. From the structural evolution of HPL, we speculate that this may be an intermediate phase that allows the system to go through various connectivity regimes between minority and majority blocks.

Unfolding of a comb-like polymer in a poor solvent: translation of macromolecular architecture in the force-deformation spectra.

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.

Modeling of Polyelectrolyte Adsorption from Micellar Solutions onto Biomimetic Substrates.

Depositing cationic polyelectrolytes (PEs) from micellar solutions that include surfactants (SU) onto surfaces is a rich, complex, highly relevant, and challenging topic that covers a broad field of practical applications (e.g., from industrial to personal care). The role of the molecular architecture of the constituents of the PEs are often overruled, or at least and either, underestimated in regard to the surface properties. In this work, we aim to evaluate the effect of a model biomimetic surface that shares the key characteristics of the extreme surface of hair and its concomitant chemo- and physisorbed properties onto the deposition of a complex PEs:SU system. To tackle out the effect of the molecular architecture of the PEs, we consider (i) a purely linear and hydrophilic PE (P100) and (ii) a PE with lateral amphiphilic chains (PegPE). Using numerical self-consistent field calculations, we show that the architecture of the constituents interfere with the surface properties in a nonintuitive way such that, depending on the amphiphilicity and hydrophilicity of the PEs and the hydrophobicity of the surface, a re-entrant adsorbing transition can be observed, the lipid coverage of the model hair surface being the unique control parameter. Such a behavior is rationalized by the anticooperative associative properties of the coacervate micelles in solution, which is also controlled by the architecture of the PEs and SU. We now expect that PEs adsorption, as a rule, is governed by the molecular details of the species in solution as well as the surface specificities. We emphasize that molecular realistic modeling is essential to rationalize and optimize the adsorption process of, for example, polymer conditioning agents in water-rinsed cosmetic or textile applications.