Planar Brushes Research Articles

Telechelic associative polymers: Interaction potential and high frequency modulus

Previous studies establish that adsorbed layers of telechelic polymers can exchange ends, increasing the entropy and allowing the loops to relax. The resulting entropic attraction amounts to approximately 1kT per bridging chain for ideal chains but decreases with increasing degree of stretching. From the interactions between planar brushes of highly stretched chains, we calculate the pair potential between spheres via the Derjaguin approximation. The softness of the repulsion and the depth of the attraction depend on the degree of stretching of the chains, the aggregation number or adsorption density, and the ratio of the overall size to the layer thickness. From the interaction potential, second virial coefficients in the osmotic pressure and the high-frequency modulus, characterizing dilute micellar solutions, follow directly. The second virial coefficient in the osmotic pressure is very negative with modest stretching but approaches the hard sphere limit as the chains become very strongly stretched. Th...

Characterization of a Planar Poly(acrylic acid) Brush as a Materials Coating for Controlled Protein Immobilization

The adsorption of two different proteins at a planar poly(acrylic acid) (PAA) brush was studied as a function of the ionic strength of the protein solutions applying total internal reflection fluorescence (TIRF) spectroscopy. Planar PAA brushes were prepared with a grafting density of 0.11 nm(-2) and were characterized using X-ray reflectometry. Hen egg-white lysozyme and bovine serum albumin (BSA) were used as model proteins, which have a net positive and negative charge at neutral pH-values, respectively. It has been found that both proteins adsorb strongly at a planar PAA brush at low ionic strength. Whereas lysozyme interacts with a PAA brush under electrostatic attraction at neutral pH-values, BSA binds under electrostatic repulsion at pH > 5. Even at pH = 8, significant amounts of BSA are adsorbed to a planar PAA brush. In addition, the reversibility of BSA adsorption has been characterized. Dilution of a BSA solution leads to an almost complete desorption of BSA from a PAA brush at short contact times. When the ionic strength of the protein solutions is increased to about 100-200 mM, a planar PAA brush appears largely protein-resistant, regardless of the protein net charge. The results of this study indicate that the salt-dependent protein affinity of a PAA brush represents a unique effect that must be explained by a novel protein-binding mechanism. On the basis of a recent model, it is suggested that a release of counterions is the most probable driving force for protein adsorption at a PAA brush. In a general view, this study characterizes a planar PAA brush as a new materials coating for the controlled immobilization of proteins whose use in biotechnological applications appears to be rewarding.

Salt-induced contraction of polyelectrolyte brushes

We present an experimental study dedicated to understanding the behaviour ofpolyelectrolyte chains when salt goes into a polyelectrolyte brush. We use theability of asymmetric neutral-charged diblock copolymers to anchor to a selectiveinterface or to self-assemble in water, to examine polyelectrolyte brushes bothin planar and in spherical geometries. Using neutron reflectivity, the monomerprofile of planar brushes has been found to switch from a Gaussian profile to aparabolic profile, showing that at large spatial scale a salted planar brush behaveslike a neutral one in good solvent. Using small angle neutron scattering, it isfound that spherical brushes exhibit the same behaviour at a large spatial scalealthough polyelectrolyte chains remain rod-like at a small spatial scale whatever thesalinity is. The charged chains inside a polyelectrolyte brush could be viewedas ‘surveyor’s chains’, which fold their rod-like segments of persistence lengthlp. In the last part, spherical polyelectrolyte brushes in contact have been examined. Theirbehaviour is discussed in terms of interdigitation or contraction of the brushes.

Salt-induced protein resistance of polyelectrolyte brushes studied using fluorescence correlation spectroscopy and neutron reflectometry

We used two-photon excitation fluorescence correlation spectroscopy (FCS) and neutron reflectometry to study in situ the effect of salt concentration on the degree of protein binding to polyelectrolyte brushes. The binding of bovine serum albumin (BSA) to poly(acrylic acid) (PAA) brushes was characterized at neutral pH values where both the protein and the brushes carry a negative charge. Spherical PAA brush particles were used in the FCS experiments, whereas a planar PAA brush served as protein substrate in the neutron reflectometry experiments. It has been found that BSA binds strongly to both the spherical and the planar PAA brushes under electrostatic repulsion at low ionic strength. The BSA volume fraction profile, as determined from the neutron reflectivities, indicates a deep penetration of the BSA molecules into the PAA brush. However, the analysis of the FCS data reveals that the protein affinity of the spherical PAA brush particles decreases drastically when increasing the concentration of sodium chloride to a few 100 mM. This observation is in line with the measured neutron reflectivities of the planar PAA brush. The reflectivity curve obtained in the absence of protein is virtually overlapping with that measured when the PAA brush is in contact with a BSA solution but containing 500 mM sodium chloride which suggests protein resistance of the planar PAA brush at this elevated salt concentration. The results of this study provide evidence for a new kind of protein-resistant interfaces. Whereas protein binding to the PAA brush is likely to be dominated by the release of counterions, this driving force vanishes as the ionic strength of the solution is raised and protein molecules are repelled from the interface by steric interactions. In a general view, the “switching” of the protein affinity of a PAA brush by varying the ionic strength of the protein solution over a relatively small range may appear to be useful for biotechnological applications.

Telechelic Associative Polymers: Interactions between Strongly Stretched Planar Adsorbed Layers

The interactions between planar brushes of adsorbed telechelic polymers are investigated via a self-consistent mean-field calculation via the strong stretching approximation. By allowing the relaxation of the loops upon the initiation of bridging, we obtain a stronger attraction than from Milner and Witten's analysis that excludes this effect. The entropy of ends is the origin of the attraction, but excluded-volume interactions play a role. The interaction potential in kT per chain is determined by the dimensionless separation and a single dimensionless parameter, the extent of stretching normalized by the size of a Gaussian coil.

Signatures of a Concentration‐Dependent Flory χ Parameter: Swelling and Collapse of Coils and Brushes

AbstractThe quality of solvents of polymers is often described in terms of the Flory χ parameter typically assumed to depend only on the temperature, T. In certain polymer‐solvent systems fitting the experimental data enforces the replacement of (χT) by a concentration‐dependent χeff. In turn, this modifies the swelling and collapse behavior. These effects are studied, in the framework of a mean‐field theory, for isolated coils and for planar brushes. The ϕ dependence of χeff gives rise to three main consequences: (i) shift in the cross‐over between Gaussian and self‐avoidance regimes; (ii) a possibility of first‐order collapse transition for isolated flexible coils; (iii) the possibility of a first‐order phase transition leading to a vertical phase separation within the brush. The discussion relates these effects directly to thermodynamic measurements and does not involve a specific microscopic model. The implementation for the case of poly(N‐isopropylamide) (PNIPAM) brushes is discussed.ϕ vs. z plots, for brushes with N = 300, σ/a2 = 18 (σ/R = 0.019) characterized by different χeff.magnified imageϕ vs. z plots, for brushes with N = 300, σ/a2 = 18 (σ/R = 0.019) characterized by different χeff.

Tethered polymer chains: surface chemistry and their impact on colloidal and surface properties

In this review the grafting of polymer chains to solid supports or interfaces and the subsequent impact on colloidal properties is examined. We start by examining theoretical models for densely grafted polymers (brushes), experimental techniques for their preparation and the properties of the ensuing structures. Our aim is to present a broad overview of the state of the art in this field, rather than an in-depth study. In the second section the interactions of surfaces with tethered polymers with the surrounding environment and the impact on colloidal properties are considered. Various theoretical models for such interactions are discussed. We then review the properties of colloids with tethered polymer chains, interactions between planar brushes and nanocolloids, interactions between brushes and biocolloids and the impact of grafted polymers on wetting properties of surfaces, using the ideas presented in the first section. The review closes with an outlook to possible new directions of research.

Experimental investigation of three-dimensional flame-front structure in premixed turbulent combustion—I: hydrocarbon/air bunsen flames

OH concentrations and three-dimensional gradients of the reaction progress variable have been measured in turbulent liquefied petroleum gas/air and compressed natural gas/air premixed flames stabilized on a Bunsen-type burner with a combined two-sheet Rayleigh scattering and planar LIF-OH imaging technique. The progress variable is observed to undergo a transition from lamella-like to non-flamelet front structure with increasing turbulence. This is consistent with the recently proposed change of the combustion regimes from complex-strain to turbulent flame front regime on a recently proposed premixed combustion diagram. The anisotropy of local flame-front orientation in three-dimensional space is explained by the forward propagation ability of the planar turbulent flame brush. Weighting functions have thus been derived for the isotropic pdf distributions of the in-plane and out-of-plane orientation angles to agree better with the experimental data. A linear scaling is found between the overall flame surface area and the turbulence intensity normalized by the laminar burning velocity. However, flames with excess backward-facing flame fronts do not comply with this linear relationship, showing enhanced flame surface folding. The thin-flame assumption breaks down when non-flamelet broadening effects become important, although the pdf’s of the progress variable are still bimodal-like. Non-unity Lewis-number combined curvature effects are evident for LPG/air flames of weak turbulence, in that the conditional mean scalar dissipation increases steadily from the unburnt to burnt side across the flame brush. A consistent correlation exists between the Favre-averaged scalar dissipation and progress variable variance. This implies that small-scale scalar dissipation of local flame-fronts is linked to large-scale scalar fluctuations. Sub- or super-flamelet OH concentration is found in lean LPG/air or CNG/air premixed flames, respectively, and occurs in line with a positive or negative correlation between OH concentrations and magnitudes of the progress variable gradient.

Annealed Star-Branched Polyelectrolytes in Solution

Equilibrium conformations of annealed star-branched polyelectrolytes (polyacids) are calculated with a numerical self-consistent-field (SCF) model. From the calculations we obtain also the size and charge of annealed polyelectrolyte stars as a function of the number of arms, pH, and the ionic strength. The results are compared with predictions from analytical theory. Upon varying the number of branches or the ionic strength of the solution, the star size changes nonmonotonically, which is in agreement with the analytical predictions. The salt concentration at this maximum is directly related to the charge density of the star. The internal structural properties of the star corona (the polymer density, the ionization profiles, and the distribution of the end points) are analyzed. The shape of the density profiles indicates increasing local stretching of the branches as a function of the distance from the star center. Furthermore, a bimodal end-point distribution is found and interpreted in analogy to that predicted earlier by analytical SCF theory for planar polyelectrolyte brushes. Results of recent experiments with annealed star-shaped micelles are discussed on the basis of our numerical model calculations.

Polymer Brushes: From Self-Consistent Field Theory to Classical Theory.

We consider planar brushes formed by end-grafted polymers with moderate to strong excluded-volume interactions. We first rederive the mean-field theory and solve the resulting self-consistent equations numerically. In the continuum limit, the results depend sensitively on a single parameter, beta, whose square is the ratio of the scaling prediction for the brush height to the unperturbed polymer radius of gyration, and which measures therefore the degree to which the polymers are stretched. For large values of beta, the density profile is close to parabolic, as predicted by the infinite-stretching theory of Zhulina et al. and of Milner et al. As beta decreases, the profile deviates strongly from a parabolic one. By calculating the most probable paths and comparing their contribution to various properties with those obtained from the full self-consistent theory, we determine the effect of the fluctuations about such paths. At large values of beta, these effects are very small everywhere. As beta decreases, fluctuation effects on the density profile become increasingly important near the grafting surface, but remain small far from it. For all values of beta, we find that polymer paths which begin far from the grafting surface are strongly, and almost uniformly, stretched throughout their length, including their free end points. Paths which begin close to the grafting surface are also stretched, but they initially move away from the grafting surface before reaching a maximum height and then returning to it. The classical theory is then derived from the self-consistent field equations by retaining, for each end point location, only that single trajectory which minimizes the free energy of the system. This free energy contains an entropy, of relative weight beta-1, which arises from the distribution of end points. Even for brushes which are only moderately stretched, the results of the classical theory for the brush profile and polymer end point distribution agree well with those of the full self-consistent theory except near the grafting surface itself. There the density profile as calculated in the self-consistent theory shows a characteristic decrease which is not captured by the classical theory. However it does capture the fact that the individual polymer paths are stretched in general throughout their length, including the end points, and yields nonmonotonic paths for polymers whose end points are close to the grafting surface. In addition, it reproduces extremely well the form of the density distribution far from the grafting surface, which is essentially Gaussian. This results from the fact that the stretching energy dominates the interaction energy of those polymers which extend far from the grafting surface, so that their behavior is nearly ideal. In the limit of infinite stretching, beta --> infinity, the theory reduces to that of Zhulina et al. and of Milner et al.

Structure in Tethered Chains: Polymeric Micelles and Chains Anchored on Polystyrene Latex Spheres

The star models are briefly summarized and used to explain the layer thickness of the soluble block of polystyrene-poly(ethylene oxide) (PS-PEO) diblock copolymer micelles in water and cyclopentane. Both the discrete blob model (DB) and the distribution density (DD) model describe well the tethered layer of the soluble block. The structure and thickness of the adlayer formed by adsorption of the PS -PEO diblock copolymer micelles onto PS lattices is strongly dependent on the radius of the latex particle and the length of the PEO block. The star model is adequate for a latex of 32 nm radius and long PEO blocks (N = 445 and 480), but deviates for smaller PEO chains (N = 148), where the adlayer thickness is well predicted by the planar brush model. This planar brush model is still valid for a latex of 54 nm radius and the same PEO chain. For longer chains and/or larger lattices, neither model correctly predicts the adlayer thickness because of the disruption of the micelles during their adsorption process. This disruption results in the formation of loops and trains on the PS surface that make the subsequent adsorption of more micelles and the formation of a dense adlayer difficult.

Liquid-crystalline polymer brushes: deformation and microphase segregation

A statistical theory of the structure and thermodynamics of a planar brush (‘accordion’) formed by bridged polymer chains containing mesogenic segments and immersed in a solvent is developed. It is shown that deformation of an accordion can lead to the formation of a two-phase structure with coexisting liquid-crystalline (LC) and swollen microphases. Phase diagrams for accordions with different grafting densities are obtained. The influence of anisotropic interaction between mesogenic segments on the structure of phase diagrams is investigated.

Structure of Weakly Charged Polyelectrolyte Brushes: Monomer Density Profiles

The internal structure (the monomer density profiles) of weakly charged polyelectrolyte brushes of different morphologies has been analyzed on the basis of the self-consistent-field approach. In contrast to previous studies based on the local electroneutrality approximation valid for sufficiently strongly charged or densely grafted (osmotic) brushes we consider the opposite limit of sparse brushes which are unable to retain the counterions inside the brush. We have shown that an exact analytical solution of the SCF-equations is available in the case of a planar brush. In contrast to Gaussian monomer density profile known for osmotic polyelectrolyte brushes we have found that weakly charged brushes are characterized by constant monomer density. At the same time free ends of grafted polyions are distributed throughout the brush. Thus, the structural cross-over between polyelectrolyte mushrooms and dense brush regimes is established.

Long and Short Chains in a Polymeric Brush: A Conformational Transition

End-anchored macromolecules admixed to a homogeneous monodisperse planar brush and differing from the majority brush-forming chains only by molecular mass take three different types of conformation, depending on its polymerization index, K, relative to that of the majority chains, N. The fraction of the admixed macromolecules is taken to be small. Shorter minority chains form slightly deformed random coils with both the average end height and its fluctuation proportional to K1/2. A longer minority chain with K > N acquires an inhomogeneous flower-like conformation: an N-segment stem of height H equal to the thickness of the brush and a randomly coiled crown outside the brush. The stem is strongly stretched and fluctuates only weakly. The transition from one type of conformation to another occurs as the number of segments of the minority chain, K, changes within a narrow range around N, where the chain is simultaneously strongly stretched and strongly fluctuating. We show that the coil-to-flower transitio...

Phase transitions in polymer brushes

AbstractLiquid crystalline ordering in planar polymer brushes is investigated theoretically by numerical calculations within a self‐consistent field approximation. The brushes are formed by macromolecules with mesogenic groups in main chain and immersed in a solvent. Existence of a microphase segregated brush (MSB) regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At small grafting density, the transition from a conventional brush state to the microphase segregated state is a jump‐wise first order phase transition for a finite chain length (N). The magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N → ∞ since this transition occurs only in a vanishingly small part (∝ N−1/2) of the brush. High compressibility of MSB brush is demonstrated. The origin of phase transition in planar brushes is discussed.

Shear Swelling of Polymer Brushes Grafted onto Convex and Concave Surfaces

The shear response of polymer brushes is explored as a function of grafting surface curvature using the Alexander-deGennes ansatz, where the free ends of the chains are localized at the tip of the brush and all tethered chains in the brush are stretched equally. Brushes adsorbed onto the concave and convex surfaces of a cylinder are found to swell to a maximum of 35% of their nonsheared brush height in good solvent, larger than the predicted maximum shear swelling of planar brushes of the same grafting density. For significantly convex surfaces, increased surface curvature increases the maximum amount of shear swelling. In contrast, brushes grafted onto concave surfaces with the same grafting density show diminished shear swelling as the grafting surface becomes more concave. The shear response of nonplanar brushes is important in a variety of possible applications, including the fabrication of pressure-sensitive microvalves and dynamic membranes and an understanding of the rheological behavior of hairy-rod polymers or molecular bottlebrushes.

Inhomogeneous Structure of Collapsed Polymer Brushes Under Deformation

The theory of the equilibrium structure and properties of a planar brush under poor solvent conditions subjected to normal deformations (stretching or compression) is presented. Using a scaling type analysis, we demonstrate that at moderate grafting densities the brush loses its lateral homogeneity and the grafted chains form aggregates (pinned micelles) with globular cores and extended legs connecting the core with the grafting surface. These micelles are stable in a rather wide range of grafting densities provided that the chains are long and the solvent is poor enough so that τ N1/2 >> 1. Scaling relations as well as diagrams of states are obtained. It is shown that the normal deformation of the brush alters boundaries of the micelle stability regime and leads to the rearrangement of the equilibrium micelle structure. Stretching leads to an increase in both the width of the stability region and the number of chains in a micelle whereas compression causes a decrease in these values. Different scenarios of brush deformation are predicted. Hysteresis effects in the processes of interaction between brushes are discussed.

Dynamics of polymer brushes — What can neutron spin-echo spectroscopy contribute?

Polymer brushes forming the outer shells of micellar aggregates of A–B diblock copolymers in a selective solvent allow for the observation of collective relaxational motions via neutron spin-echo spectroscopy. New neutron spin-echo investigations on planar PEB-brushes on the surface of crystalline PE-cores of platelet-like aggregates are reported. The data are discussed in comparison to a continuum model of the brush assuming a parabolic density profile, semidilute solution scaling relations for the elastic properties and friction coefficient. For the planar brush a full 3D solution of the model is accessible. The observed scattering from an isotropic sample is compatible with the continuum model with an added static fluctuation contribution.

Theory of planar polyelectrolyte brush immersed in solution of asymmetric salt

The analytical self-consistent field theory of polymer brushes and the Scheutjens–Fleer numerical theory are applied in a study of the equilibrium behaviour of a planar polyelectrolyte brush immersed in a solution of an asymmetric salt. A scaling-type diagram comprising various regimes of brush behaviour is constructed and verified by numerical calculations. It is shown that for a highly asymmetric salt with multivalent coions there are two different salt-controlled regimes of brush behaviour. At large salt contents, highly charged coions penetrate into the brush and dominate the screening of the electrostatic repulsion between grafted polyions (salted brush; SB). In this regime the brush thickness H scales as H ∼ I − 1 3 , where I is the ionic strength of the outer solution (made up of coion and counterion contributions). At relatively small salt contents, highly charged coions are excluded from the brush whereas counterions equal out their concentrations in the brush and outer solution (counterion brush; CB). In this regime the screening of electrostatic repulsion in the brush is performed by mobile counterions and the brush thickness scales as H ∼ φ −1 s, where φ s is the concentration of salt counterions only in the outer solution. Possible experiments to verify these theoretical predictions are discussed.

Moduli of polymer brushes, contact mechanics, and atomic force microscope experiments

We present two new simple derivations of the elastic moduli of planar polymer brushes in the melt regime. We find moduli which are somewhat deformation dependent. We also examine the problem of the penetration of such a brush by the tip of an atomic force microscope for the case of weak deformations