New approach to oligonucleotide microarrays using zirconium phosphonate-modified surfaces

A new approach to oligonucleotide arrays is demonstrated that utilizes zirconium phosphonate-derivatized glass slides. The active slides are prepared by binding Zr(4+) to surfaces terminated with organophosphonate groups previously deposited using either Langmuir-Blodgett or self-assembled monolayer methods. Oligonucleotide probes modified with a terminal phosphate bind strongly to the active zirconium phosphonate monolayer, and arrays for detecting fluorescent targets have been prepared using commercial spotting and scanning instruments. Preferred binding to the surface of the terminal phosphate of the modified probes instead of the internal phosphate diester groups is demonstrated and shown to yield increased fluorescence intensity after hybridization with labeled targets. A significant decrease in background signal is achieved by treating the slides with bovine serum albumin after spotting and before hybridization. A further increase in fluorescence after hybridization is observed when using a poly-guanine spacer between the probe oligomer and the terminal phosphate. Combining these modifications, an intensity ratio of nearly 1000 is achieved when comparing 5'-phosphate-modified 33-mer probes with unmodified probes upon hybridization with fluorescent targets.     

Mean‐field theoretical analysis of brush‐coated nanoparticle dispersion in polymer matrices

The equilibrium dispersion of nanoparticles with grafted polymer chains into polymer matrices, of the same chemical structure as the brush, is studied through the device of mean‐field theory. Our results show that the disperion of brush‐coated nanoparticles into a matrix polymer is improved with (i) decreasing particle radius and (ii) increasing brush chain length. Both of these aspects can be understood based on the fact that, unlike the case of planar surfaces, homopolymer chains end‐grafted to spherical nanoparticle surfaces tangentially spread away from the surface thus alleviating the packing frustration that is created by the relatively high grafting densities. This permits significant brush/matrix overlap, even at high grafting densities, a regime that has only recently become experimentally available due to advances in polymer synthesis (i.e., the “grafting‐to” methods). © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 351–358, 2008     

Molecular dynamics simulations of grafted layers of bottle-brush polyelectrolytes

Using molecular dynamics simulations, we study the effect of the brush grafting density and degree of polymerization of the side chains on conformations of brush layers made of charged bottle-brush macromolecules. The thickness of the brush layer first decreases with increasing brush grafting density; then, it saturates and remains constant in the wide interval of the brush grafting densities. The brush layers consisting of the bottle-brush macromolecules with longer side chains have a larger layer thickness. The elongation of the side chains of the bottle-brush macromolecules decreases with increasing brush grafting density. This contraction of the side chains is due to counterion condensation inside the volume occupied by bottle-brushes. Our simulations showed that counterion condensation is a multiscale process reflecting different symmetries of the bottle-brush layer.     

Interaction of bovine serum albumin and human blood plasma with PEO-tethered surfaces: influence of PEO chain length, grafting density, and temperature

Solid surfaces are modified by grafting poly(ethylene oxide), PEO, to influence their interaction with indwelling particles, in particular molecules of bovine serum albumin and human plasma proteins. As a rule, the grafted PEO layers suppress protein adsorption. The suppression is most effective when the PEO layer is in a molecular brush conformation having a reciprocal grafting density (area per grafted PEO chain) less than the dimensions of the protein molecules. Nevertheless, the protein molecules may penetrate the PEO brush to some extent. For a given grafting density, the penetration is facilitated by increasing thickness of the brush. Tenuous brushes of reciprocal grafting densities exceeding the protein molecular dimensions enhance protein adsorption. The results point to a weak attractive interaction between PEO and protein. The protein repellency of a densely PEO-brushed surface is ascribed to a high activation energy for the protein molecules to enter the brush. Varying the temperature between 22 and 38 degrees C does not significantly affect the range of grafting density over which the brush changes from protein-attractive to protein-repellent.     

Stochastic dynamics simulation of grafted polymer brushes under shear deformation

We present results of computer simulations of polymer brushes (layers of polymer chains attached at one end onto an impermeable planar surface) under shear deformation at constant shear rate. As the first stage of calculations the behavior of a single brush was studied. The monomer density profile, the distribution of the chain ends, the positions and orientations of different monomers along the chain were calculated. Dimensions of the polymer chains as functions of the shear rate were obtained for different grafting densities. An increase in the brush thickness over the grafting plane with an increase in the shear rate as predicted by the theory of Barrat was observed. However, the magnitude of the effect appears to be small. We explain this by finite extensibility of the grafted chains.     

Poly(dG) spacers lead to increased surface coverage of DNA probes: an XPS study of oligonucleotide binding to zirconium phosphonate modified surfaces

A spacer is often employed between the surface linking group and the probe sequence to improve the performance of DNA microarrays. Previous work demonstrated that a consecutive stretch of guanines as a spacer increased target capture during hybridization relative to probes with either no spacer or a similar stretch of one of the other nucleotides. Using zirconium phosphonate modified surfaces with 5'-phosphorylated ssDNA probes, the present study compares the surface coverage of ssDNA probes containing either a poly(dG) spacer or a poly(dA) spacer. Surface coverages are quantified by XPS using a modified overlayer model. The results show that after treatment to mimic conditions of the passivation and hybridization steps the probe with the poly(dG) spacer has about twice the surface coverage as the probe with the poly(dA) spacer, indicating that increased target capture is due to higher probe coverage. When monitoring the surface coverage after each rinsing step, it is observed that the probe with the poly(dA) spacer is more susceptible to rinsing, suggesting the interaction with the surface is different for the two probes. It is suggested that the formation of G quadruplexes causes an increased avidity of the probe for the zirconium phosphonate surface.     

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.     

Hydrogen-bonded layer-by-layer films of block copolymer micelles with pH-responsive cores

The structure of grafted adsorbing polymers on surfaces is described as a statistical ensemble of loops generated by an one-dimensional random walk perpendicular to the surface. The configuration of each chain is considered as a succession of closed loops ended by an open loop (a tail). The probability of formation of each individual loop is the product between the probability of first return to the surface and a Boltzmann factor containing the free energy of the Flory-Huggins kind, which is approximated by the minimum free energy of all possible configurations of that loop. At high grafting densities, the attractive interactions between monomers and surface control the fraction of polymer belonging to either closed loops or tails, hence the formation of a stretched grafted brush. At low grafting densities, the increase of that interaction above a critical value generates an abrupt collapse of the brush on the surface. Whereas for long polymers (with more than about 100 Kuhn segments), the structure of the brush can be determined, in general, only via Monte-Carlo sampling, it is argued that the two structural transitions indicated above can be well predicted by simple approximations.     

An experimental-theoretical analysis of protein adsorption on peptidomimetic polymer brushes

Surface-grafted water-soluble polymer brushes are being intensely investigated for preventing protein adsorption to improve biomedical device function, prevent marine fouling, and enable applications in biosensing and tissue engineering. In this contribution, we present an experimental-theoretical analysis of a peptidomimetic polymer brush system with regard to the critical brush density required for preventing protein adsorption at varying chain lengths. A mussel adhesive-inspired DOPA-Lys (DOPA = 3,4-dihydroxy-phenylalanine; Lys = lysine) pentapeptide surface grafting motif enabled aqueous deposition of our peptidomimetic polypeptoid brushes over a wide range of chain densities. Critical densities of 0.88 nm(-2) for a relatively short polypeptoid 10-mer to 0.42 nm(-2) for a 50-mer were identified from measurements of protein adsorption. The experiments were also compared with the protein adsorption isotherms predicted by a molecular theory. Excellent agreements in terms of both the polymer brush structure and the critical chain density were obtained. Furthermore, atomic force microscopy (AFM) imaging is shown to be useful in verifying the critical brush density for preventing protein adsorption. The present coanalysis of experimental and theoretical results demonstrates the significance of characterizing the critical brush density in evaluating the performance of an antifouling polymer brush system. The high fidelity of the agreement between the experiments and molecular theory also indicate that the theoretical approach presented can aid in the practical design of antifouling polymer brush systems.     

Molecular dynamics simulations of polyelectrolyte brushes: from single chains to bundles of chains

Using molecular dynamics simulations in combination with scaling analysis, we have studied the effects of the solvent quality and the strength of the electrostatic interactions on the conformations of spherical polyelectrolyte brushes in salt-free solutions. The spherical polyelectrolyte brush could be in one of four conformations: (1) a star-like conformation, (2) a "star of bundles" conformation in which the polyelectrolyte chains self-assemble into pinned cylindrical micelles, (3) a micelle-like conformation with a dense core and charged corona, or (4) a conformation in which there is a thin polymeric layer uniformly covering the particle surface. These different brush conformations appear as a result of the fine interplay between electrostatic and monomer-monomer interactions. The brush thickness depends nonmonotonically on the value of the Bjerrum length. This dependence of the brush thickness is due to counterion condensation inside the brush volume. We have also established that bundle formation in poor solvent conditions for the polymer backbone can also occur in a planar polyelectrolyte brush. In this case, the grafted polyelectrolyte chains form hemispherical aggregates at low polymer grafting densities, cylindrical aggregates at an intermediate range of the grafting densities, and vertically oriented ribbon-like aggregates at high grafting densities.     

Interfacial properties of statistical copolymer brushes in contact with homopolymer melts

We use polymer self-consistent field theory to quantify the interfacial properties of random copolymer brushes (AB) in contact with a homopolymer melt chemically identical to one of the blocks (A). We calculate the interfacial widths and interfacial energies between the melt and the brush as a function of the relative chain sizes, grafting densities, compositions of the random copolymer in the brush, and degree of chemical incompatibility between the A and B species. Our results indicate that the interfacial energies between the melt and the brush increase (signifying expulsion of the free chains from the brush) with increasing grafting density, chemical incompatibility between A and B components, and size of the free chains relative to the grafted chains. We also compare the interfacial energies of random copolymers of different sequence characteristics and find that, except for the case of very blocky or proteinlike chains, blockiness of the copolymer has only little effect on interfacial properties. Our results for interfacial energies are rationalized based on the concept of an "effective volume fraction" of the brush copolymers, f(eff), which quantifies the chemical composition of the brush segments in the interfacial zone between the brush and melt copolymers. Using this concept, we modify the strong-stretching theory of brush-melt interfaces to arrive at a simple model whose results qualitatively agree with our results from self-consistent field theory. We discuss the ramifications of our results for the design of neutral surfaces.     

Properties of star-branched polymer brushes

A simple model of a polymer brush was constructed. The star polymers with three arms were terminally attached with one arm (the stem) to an impenetrable surface with the other two arms (branches) free. The excluded volume effect was included into the model as the only interaction. Therefore, the system was studied in good solvent conditions. The simulations were carried out by means of the dynamic Monte Carlo method using the local changes of chain conformations to sample efficiently the conformational space. The influence of both the number of chains (the grafting density) and the length of chains on the static properties of the polymer brush was studied. The internal and local structure of a formed polymer layer was determined. It was shown that the size of the stems increased rapidly with the increase of the grafting density, while the size of the branches diminished. The changes of the spatial orientations of the stems and the branches for different grafting densities were shown and discussed.     

Metalization of polypropylene. I. Synthesis and melt free‐radical grafting of novel maleimides and methacrylates containing chelating moieties

Several chelating monomers with methacrylate and maleimide residues as polymerizable groups and diketone and aspartic acid residues as metal‐bonding groups were synthesized. A long‐chain aliphatic spacer was introduced to increase the solubility of the monomers in the polymer melt and to enhance the compatibility of grafted side chains and homopolymers with polypropylene (PP). PP was functionalized by melt free‐radical grafting, and some properties of the modified polymer were investigated. The grafting of a chelating methacrylic ester by injection molding afforded grafting yields of 30–50%. A comparison with products obtained by the grafting of commercially available acetoacetoxy methyl methacrylate showed the beneficial effect of the aliphatic spacer with respect to the grafting yield as well as the tensile strength and flexural modulus. The grafting of an aspartic acid based maleimide in an extruder afforded grafting yields of 80–95% and a significant increase in the surface wettability, as shown by contact‐angle measurements. A comparative study using samples obtained by the grafting of maleimidobenzoic acid indicated that the homogeneity‐increasing effect of the spacer was neutralized by the detrimental effect of the dicarboxylic chelating group. Nevertheless, the results showed that the maleimides were well suited for grafting by reactive extrusion because of their low susceptibility to homopolymerization under melt‐processing conditions. Preliminary metalization experiments showed the feasibility of plating without the use of corrosive etchants. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3400–3413, 2003     

Electrostatic binding of oppositely charged surfactants to spherical polyelectrolyte brushes

We use Brownian dynamics (BD) simulations to investigate the formation and structural characteristics of the complex between a spherical polyelectrolyte brush (SPB) and oppositely charged surfactants. Increasing the amount of added surfactants leads to a collapsed conformation of the SPB and the number of adsorbed surfactants exhibits a linear dependence. Nevertheless, the surfactant uptake into the SPB does not increase with further addition of surfactants. It is found that the surfactant length has a strong influence on the SPB conformation and the adsorption properties of surfactant. Upon changing the surfactant length from 3 to 11, the SPB undergoes a swelling-deswelling-reswelling conformational transition. The brush deswelling is due to the increase in the surfactant uptake. The increasing size of adsorbed aggregates is a main reason for reswelling of the SPB. A non-linear relationship between the brush thickness and the grafting density is observed. Especially at intermediate grafting densities, increasing the number of grafted chains has a weak effect on the brush thickness. We also find that a completely collapsed brush conformation occurs at high surfactant/SPB charge ratios or large surfactant lengths, while the brush layer is in a partly collapsed or extended state at an intermediate charge ratio and surfactant length.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

Molecular dynamics studies of anchored polyelectrolytes

We study polyelectrolytes end-grafted to a surface in a model which includes counterions explicitly and treats the full long-range Coulomb interaction. For strongly charged polyelectrolytes the counterions are localized inside the brush and electroneutrality is satisfied locally. Under these conditions, we find that the brush thickness is linearly proportional to the chain length and the grafting density. The counterion distribution is strongly inhomogeneous, and counterion condensation can be observed although the Bjerrum length is smaller than the average bond length. Varying the Bjerrum length we find a non-monotonic behaviour of the brush height. Counterion diffusion is anisotropic, and is enhanced at higher grafting densities. For partially charged polyelectrolytes we obtain a crossover from quasi-neutral behaviour to the strongly charged behaviour reported above.     

Conformations of molecular brushes based on polyimide and poly(methyl methacrylate) in selective solvents: Experiment and computer simulation

The effect of solvent quality with respect to main and side chains on the conformations of molecular brushes is investigated by the methods of molecular hydrodynamics and optics as well as by computer simulation. Copolymers with a polyimide backbone and poly(methyl methacrylate) side chains are studied in solvents featuring strongly different thermodynamic qualities (chloroform, ethyl acetate, and 3-heptanone). The studied samples have close total molecular masses and backbone lengths but differ in grafting densities and lengths of side chains: a brush with densely grafted and relatively short side chains versus a brush with loosely grafted but very long side chains. For both types of brushes, similar changes in hydrodynamic behavior with improvement in the solvent quality are found experimentally. Computer simulation shows that these changes have different origins. In the former case, macromolecules are elongated, and their volumes grow simultaneously, while in the latter case, the shape of the macromolecules remains close to spherical and the changes in hydrodynamic parameters are mainly due to an increase in the volume of macromolecules.     

Diblock polyampholytes grafted onto spherical particles: effect of stiffness, charge density, and grafting density

The structure of spherical brushes formed by symmetric diblock polyampholytes end-grafted onto small spherical particles in aqueous solution is examined within the framework of the so-called primitive model using Monte Carlo simulations. The properties of the two blocks are identical except for the sign of their charges. Three different chain flexibilities corresponding to flexible, semiflexible, and stiff blocks are considered at various polyampholyte linear charge densities and grafting densities. The link between the two blocks is flexible at all conditions, and the grafted segments are laterally mobile. Radial and lateral spatial distribution functions of different types and single-chain properties are analyzed. The brush structure strongly depends on the chain flexibility. With flexible chains, a disordered polyelectrolyte complex is formed at the surface of the particle, the complex becoming more compact at increasing linear charge density. With stiff blocks, the inner blocks are radially oriented. At low linear charged density, the outer blocks are orientationally disordered, whereas at increasing electrostatic interaction the two blocks of a polyampholyte are parallel and close to each other, leading to an ordered structure referred to as a polyampholyte star. As the grafting density is increased, the brush thickness responds differently for flexible and nonflexible chains, depending on a different balance between electrostatic interactions and excluded volume effects.     

Electro‐osmotic flow in nanochannels with voltage‐controlled polyelectrolyte brushes: Dependence on grafting density and normal electric field

Molecular dynamics simulations were performed for electro‐osmotic flow (EOF) confined in a polyelectrolyte‐grafted nanochannel under variable grafting density and normal electric field. With decreasing the value of the normal electric field, the brush undergoes a collapse transition, and the ion distribution is changed significantly. The brush thickness increases on increasing the grafting density at positive and weak negative electric fields, whereas a reduced brush thickness is observed at strong negative electric field. Our results further reveal that the flow velocity is not only dependent on conformational transition of the brush but also related to the cation and anion distributions. At low grafting density, the EOF is almost completely quenched at high electric field strength due to strong surface friction between ions and walls. For the case of very dense grafting, the flow velocity is influenced weakly within the brush when varying the grafting density. Additionally, a bidirectional flow occurs at an intermediate electric field. The investigation on fluid flux indicates that the fluid flux is insensitive to the grafting density, when the normal electric field is removed. For nonzero normal electric fields, a significant change in the fluid flux is observed at low grafting densities. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

On the monomer density of grafted polyelectrolyte brushes and their interactions

Most of the modern theories of grafted polyelectrolyte brushes are valid only for moderate stretching of the polyelectrolyte. However, particularly at low ionic strength and high grafting densities, even a moderate charge of the polyelectrolyte can generate a strong stretching. A simple mean field model for strongly stretched grafted polyelectrolyte brushes is suggested, based on an approximate calculation of the partition function of a polyelectrolyte chain. It is shown that the average Boltzmann factor of a possible chain configuration can be approximated by the Boltzmann factor of a configuration with a constant monomer distribution, for which the free energy can be readily obtained. The monomer density in the brush and the interaction between two surfaces with grafted polyelectrolyte brushes could be calculated as a statistical average over all possible configurations. Some simple analytical results are derived, and their accuracy is examined. The dependence of the brush thickness on the electrolyte concentration is investigated, and it is shown that the trapping of a fraction of counterions in the brush influences strongly the thickness of the brush. When two surfaces with grafted polyelectrolyte brushes approach each other more rapidly than the ion diffusion parallel to the surface, the trapping of the counterions between the brushes can affect the interactions by orders of magnitude.