On the Curvature Energy of a Thin Membrane Decorated by Polymer Brushes

Entropy-Enhanced Mechanochemical Activation for Thermal Degrafting of Surface-Tethered Dry Polystyrene Brushes

Dry polymer brushes have attracted great attention because of their potential utility in regulating interface properties. However, it is still unknown whether dry polymer brushes will exhibit degrafting behavior as a result of thermal annealing. Herein, a study of the conformational entropy effect on thermal degrafting of dry polystyrene (PS) brushes is presented. For PS brushes with an initial grafting density (σ_pⁱⁿⁱ) of 0.61 nm^-2, degrafting behavior was observed at 393 K, and the equilibrium σ_p was approximately 0.14 nm^-2 at 413 K. However, for brushes with σ_pⁱⁿⁱ ≤ 0.14 nm^-2, thermal degrafting was not observed even if the temperature was increased to 453 K. Furthermore, we found that the degrafting rate was faster for PS brushes with higher σ_pⁱⁿⁱ and higher molecular weights when σ_pⁱⁿⁱ > 0.14 nm^-2. Our findings confirmed that degrafting is a mechanochemical activation process driven by tension imposed on bonds that anchor the chains to the surface, and the process is amplified by conformational entropy.

End-exclusion zones in strongly stretched, molten polymer brushes of arbitrary shape

Theories of strongly stretched polymer brushes, particularly the parabolic brush theory, are valuable for providing analytically tractable predictions for the thermodynamic behavior of surface-grafted polymers in a wide range of settings. However, the parabolic brush limit fails to describe polymers grafted to convex curved substrates, such as the surfaces of spherical nanoparticles or the interfaces of strongly segregated block copolymers. It has previously been shown that strongly stretched curved brushes require a boundary layer devoid of free chain ends, requiring modifications of the theoretical analysis. While this "end-exclusion zone" has been successfully incorporated into the descriptions of brushes grafted onto the outer surfaces of cylinders and spheres, the behavior of brushes on surfaces of arbitrary curvature has not yet been studied. We present a formulation of the strong-stretching theory for molten brushes on the surfaces of arbitrary curvature and identify four distinct regimes of interest for which brushes are predicted to possess end-exclusion zones, notably including regimes of positive mean curvature but negative Gaussian curvature. Through numerical solutions of the strong-stretching brush equations, we report predicted scaling of the size of the end-exclusion zone, the chain end distribution, the chain polarization, and the free energy of stretching with mean and Gaussian surface curvatures. Through these results, we present a comprehensive picture of how the brush geometry influences the end-exclusion zones and exact strong-stretching free energies, which can be applied, for example, to model the full spectrum of brush geometries encountered in block copolymer melt assembly.

The effect of artificial light at night on the biomass of caterpillars feeding in urban tree canopies

Alternation of day and night is the oldest cycle on Earth, which is increasingly disturbed by the accelerating rate of urbanization and technological development. Despite the ubiquity of light pollution in cities, many aspects of its influence on urban ecosystems are still poorly understood. Here we studied the effect of artificial light at night (ALAN) on the biomass of arboreal caterpillar populations, which are a major component of the diet of many insectivorous animals. We predicted that increasing ALAN intensity is associated with reduced caterpillar biomass, because ALAN may increase predation risk for both caterpillars and adult lepidopterans (i.e. moths), and can also hinder the moths’ reproductive rate. We estimated caterpillar biomass from frass samples (n = 3061) collected from 36 focal trees in two cities in Hungary during four consecutive years. To quantify ALAN we measured light intensity during night at each focal tree (range of illumination: 0.69–3.18 lx). We found that caterpillar biomass of individual trees was repeatable over the four years. This temporal consistency in prey biomass production may be important for birds because it can help predict territory quality, especially in cities where caterpillar abundance is generally low. Our results did not support the negative effect of ALAN on urban caterpillar populations, because ALAN intensity was not related to caterpillar biomass, and this lack of effect was consistent between study sites and tree species. We suggest that the effect of ALAN on urban caterpillar biomass is either weak and thus can be masked by other, local environmental factors, or light pollution may have antagonistic effects acting during different stages of the lepidopteran life cycle. Another explanation could be that even the lower levels of our sites’ public lighting are strong enough to cause serious detrimental effects for caterpillars, resulting in their uniformly low biomass.

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 φ_s ^b complement the model definition. The phase diagram in χ-φ_s ^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, φ_s ^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.

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.

Chain Length and Grafting Density Dependent Enhancement in the Hydrolysis of Ester-Linked Polymer Brushes

Poly(N,N-dimethylacrylamide) (PDMA) brushes with different grafting density and chain length were grown from an ester group-containing initiator using surface-initiated polymerization. Hydrolysis of the PDMA chains from the surface was monitored by measuring thickness of the polymer layer by ellipsometry and extension length by atomic force microscopy. It was found that the initial rate of cleavage of one end-tethered PDMA chains was dependent on the grafting density and chain length; the hydrolysis rate was faster for high grafting density brushes and brushes with higher molecular weights. Additionally, the rate of cleavage of polymer chains during a given experiment changed by up to 1 order of magnitude as the reaction progressed, with a distinct transition to a lower rate as the grafting density decreased. Also, polymer chains undergo selective cleavage, with longer chains in a polydisperse brush being preferentially cleaved at one stage of the hydrolysis reaction. We suggest that the enhanced initial hydrolysis rates seen at high grafting densities and high chain lengths are due to mechanical activation of the ester bond connecting the polymer chains to the surface in association with high lateral pressure within the brush. These results have implications for the preparation of polymers brushes, their stability under harsh conditions, and the analysis of polymer brushes from partial hydrolysates.

Curvature elasticity of a grafted polyelectrolyte brush

The curvature elasticity of a polyelectrolyte brush monolayer attached to curved surface is investigated theoretically. An analytical method based on the strong-stretching theory for a Gaussian chain is developed to calculate the elastic modulus induced by a polyelectrolyte brush. In particular, the scaling relations for the bending or Gaussian modulus with respect to system parameters related to the electrostatic interaction (degree of ionization and salt concentration) are derived. Using the numerical self-consistent-field theory, the inner structural, free-energy, and elastic moduli are computed for the polyelectrolyte brush with excluded-volume interactions. Compared to the analytical result, the curvature elasticity has a weaker dependence on the system parameters, which is attributed to the linearization for the Poisson-Boltzmann equation in the analytical treatment. Furthermore, our results are compared to the curvature elasticity of a bare charged surface, wherefrom the unique polyelectrolyte brush effect on the surface elasticity is clarified clearly. The scaling relations derived in our paper can serve as a guide to experimental studies on the related systems.

Membrane rigidity induced by grafted polymer brush

The contribution of neutral polymer brush to the curvature elasticity of the grafting surface is investigated theoretically. Using self-consistent field theory, we accurately evaluate the dependence of bending modulus on parameters including chain length, Flory-Huggins parameter and grafting density and reveal the importance of solvent. The results show that the brush-induced bending modulus follows a complex dependence on grafting density and Flory-Huggins parameter, while it obeys a simple power law with chain length as N(3). The method is further applied to calculate the polymer brush's contribution to the elastic properties of PEG-grafted lipid monolayers.

Surface induced self-organization of comb-like macromolecules

We present a review of the theoretical and experimental evidence for the peculiar properties of comb copolymers, demonstrating the uniqueness of these materials among other polymer architectures. These special properties include an increase in stiffness upon increasing side-chain length, the spontaneous curvature of adsorbed combs, rod-globule transition, and specific intramolecular self-assembly. We also propose a theory of chemically heterogeneous surface nanopattern formation in ultrathin films of comblike macromolecules containing two different types (A and B) of incompatible side chains (so-called binary combs). Side chains of the binary combs are strongly adsorbed on a surface and segregated with respect to the backbone. The thickness of surface domains formed by the B side chains is controlled by the interaction with the substrate. We predict the stability of direct and inverse disc-, torus- and stripelike nanostructures. Phase diagrams of the film are constructed.

A closer look at the structure of sterically stabilized liposomes: a small-angle X-ray scattering study

The evaluation of the radial electron density profile of a drug containing a sterically stabilized liposomal system is described. Using synchrotron small-angle X-ray scattering, we were able to characterize the hydrophilic shell of the polyethylene glycol chains. Using a Gaussian model for describing the electron density profile along the normal of the bilayer, we got an asymmetric distribution of PEGylated lipids in accordance with theoretical considerations. Moreover, we used anomalous X-ray scattering to study the localization of a hydrophobic drug (a kinase inhibitor), which revealed that these molecules are mainly located in the hydrocarbon chain region of the phospholipid bilayer.

Polymer-decorated tethered membranes under good- and poor-solvent conditions

We study tethered membranes grafted by polymer chains on one side. Mean-field and scaling arguments predicting a spontaneous curvature are compared to the results of lattice-based Monte Carlo simulations using the Bond Fluctuation Model, which are carried out for various grafting densities and chain lengths. We show that already slightly overlapping chains bend the membrane significantly. This proves the entropic origin for the bending stiffness, which is of order kT. To understand the membrane curvature under conditions of very small bending stiffness we apply a geometrical model which takes into account the state of chains at the overlap threshold. Applying a thermal solvent model for the grafted chains, we demonstrate that the bending direction of the membrane can be triggered by variation of the solvent quality. This indicates that polymer-decorated membranes may serve as switchable nanoscale devices.

Solid-state scrolls from hierarchical self-assembly of T-shaped rod-coil molecules

On a roll: Attachment of flexible coils to the middle of a rigid rod generates T-shaped rod-coil molecules that self-assemble into layers that roll up to form filled cylindrical and hollow tubular scrolls, depending on the coil length, in the solid state (see picture); the rods are arranged parallel to the layer plane.