Simple model for grafted polymer brushes

The first theories of grafted polymer brushes assumed a step profile for the monomer density. Later, the real density profile was obtained from Monte Carlo or molecular dynamics simulations and calculated numerically using a self-consistent field theory. The analytical approximations of the solutions of the self-consistent field equations provided a parabolic dependence of the self-consistent field, which in turn led to a parabolic distribution for the monomer density in neutral brushes. As shown by numerical simulations, this model is not accurate for dense polymer brushes, with highly stretched polymers. In addition, the scaling laws obtained from the analytical approximations of the self-consistent field theory are identical to those derived from the earlier step-profile-approximation and predict a vanishing thickness of the brush at low graft densities, and a thickness exceeding the length of the polymer chains at high graft densities. Here a simple model is suggested to calculate the monomer density and the interaction between surfaces with grafted polymer brushes, based on an approximate calculation of the partition function of the polymer chains. The present model can be employed for both good and poor solvents, is compatible with a parabolic-like profile at moderate graft densities, and leads to an almost steplike density for highly stretched brushes. While the thickness of the brush depends strongly on solvent quality, it is a continuous function in the vicinity of the temperature. In good and moderately poor solvents, the interactions between surfaces with grafted polymer brushes are always repulsive, whereas in poor solvents the interactions are repulsive at small separations and become attractive at intermediate separation distances, in agreement with experiment. At large separations, a very weak repulsion is predicted.     

Interaction forces between polyethylene oxide-polypropylene oxide ABA copolymers adsorbed to hydrophobic surfaces

Block and graft copolymers are frequently used as stabilizing agents in colloidal dispersions. One common material is the range of polymers known as "Pluronics," which is a BASF trade name for ABA block copolymers composed of a propylene oxide anchoring block (B block) and two ethylene oxide buoy or stabilizing blocks (A block); the equivalent ICI (Uneqima) trade name is Synperonic. In the work presented here the interactions between adsorbed layers of these materials immersed in 10(-2) M sodium sulfate solutions are presented. The block copolymers investigated had an approximately fixed molecular weight of around 3250 Da for the anchoring B block, whilst the molecular weight of the stabilizing polyethylene oxide chains varies around 800-6500 Da. Hydrophobic glass surfaces were used as the test substrate. It was found that in the absence of polymer a long ranged attractive interaction is observed, typical for the interaction between hydrophobic surfaces in aqueous media, but that in the presence of the polymers a repulsion was observed. The repulsion became longer ranged as the molecular weight of the ethylene oxide chain increased. On separation of the surfaces, the interaction was slightly longer ranged, suggesting that the two polymer layers intertwine and stretch each other on separation. This effect was more noticeable for the higher molecular weight polymers. The compression data were well described using a scaling analysis for the interaction between polymer brushes.     

Structure of short polymers at interfaces: a combined simulation and theoretical study

The structure of polymers confined between surfaces is studied using computer simulation and a density functional approach. The simple model system considers the polymer molecule as a pearl necklace of freely jointed hard spheres, having attractions among the beads, confined between attractive surfaces. This approach uses the universality of the free-energy functional to obtain the self-consistent field required in the single chain simulation. The second-order direct correlation function for the uniform bulk fluid required as input has been calculated from the reference interaction site model integral equation theory using mean spherical approximation. The theoretical results are shown to compare well with the Monte Carlo simulation results for varying densities, chain lengths, and with different attractive interaction parameters. The simulation results on the conformational properties give important indications regarding the behavior of chains as they approach the surfaces.     

The Nano-threading of Polymers

When guest polymers are threaded by host cyclodextrins (CDs) to form crystalline inclusion compounds (ICs), the included polymer chains are highly extended and separated from neighboring chains. This is a consequence of the stacking of the cyclic oligosaccharides, α-, β-, or γ-CD containing 6, 7, or 8 glucose units, respectively, which produces continuous narrow channels (~0.5–1.0 nm diameters), where the guest polymers are included and confined. Observations that illuminate several important aspects of the nano-threading of polymers to form polymer-CD-ICs are described. These include (i) the competitive CD threading of polymers with different chemical structures and molecular weights from their solutions containing suspended solid or dissolved CDs, (ii) the threading and insertion of undiluted liquid polymers into solid CDs, and (iii) suspension of polymer A or B-CD-IC crystals in a solution of polymer B or A and observation of the transfer of polymer B or A from solution to displace polymer A or B and form polymer B or A-CD-ICs, without dissolution of the CD-ICs. In addition, we report observations of polyolefins adsorbed on zeolites, where we believe the adsorbed polyolefin chains are actually threaded and absorbed into the interiors of the zeolite nano-pores, rather than adsorbed on the zeolite surfaces. All of the above observations were made to assist in answering the question “Why do randomly-coiling polymer chains in solution or the melt become threaded or thread into the nano-pores of dissolved or solid CDs and solid zeolites, where they are highly extended and segregated from other polymer chains?” Though still not fully able to answer this question, we are able to assess the importance of several factors that have been previously suggested to be important in the formation of CD-ICs with both polymer and small-molecule guests and to the nano-threading of polymers in general. In particular, the value in observations of the inclusion of guest polymers, as well as small-molecule guests, into solid CDs suspended in their solutions and in neat guest liquids were made apparent, because interactions between host CDs, between CDs and solvents, and between quests and solvents, which complicate and make understanding the formation of polymer-CD-ICs difficult, are either eliminated or can be independently varied in these experiments.     

Surface forces,supramolecular polymers,and inversion symmetry

The effects of supramolecular equilibrium polymers on surface forces are studied by both a phenomenological Landau type analysis and a molecular model based on a Bethe-Guggenheim approximation. We point out that surface forces brought about by equilibrium polymers may be completely different from what can be found with "ordinary" polymers. The new feature is the role of inversion (a)symmetry or "directionality" of the associating unit molecules ("monomers"). Symmetric B-B monomers (where B denotes a self-complementary binding group) give rise to nondirectional chains and lead to attractive forces between similar surfaces. Asymmetric A-D monomers (where A and D denote complementary acceptor and donor groups, respectively) produce directional chains and can cause strong repulsion. The range of the attractive force has a maximum at intermediate concentration, while the range of the repulsive force increases over the whole concentration range.     

Simple models of adsorbed polymers: Vibrational properties

The vibrational properties of polymers adsorbed on surfaces are investigated within the frame of two simple models. First the surface is modelled as a one-dimensional infinite harmonic chain. Polymeric “ molecules ” are represented as harmonic chains of finite length. The coupling between the polymers and the surface is treated within the frame of the Interface Response Theory. Upon adsorption of polymers, resonant vibrational modes appear as well defined peaks in the variation of the density of states of the system. The effect of the interaction between adsorbed polymers via phonons is investigated and shown to lead to antiresonances in the spectral density of states and the formation of gaps in the density of states as the surface coverage is increased. A second more realistic model is introduced where the same finite harmonic chains (polymers) are grafted on a two dimensional [001] surface cut through a cubic harmonic crystal. Again the variation in density of states exhibits resonant modes between the polymers and the substrate. However, in this case, the interaction between polymers is short range. Adsorption of a film of polymers produces resonant modes which remain well-defined features within the substrate bulk band.     

Nonadditivity of polymeric and charged surface interactions: consequences for doped lamellar phases

We explore theoretically the modifications to the interactions between charged surfaces across an ionic solution caused by the presence of dielectric polymers. Although the chains are neutral, the polymer physics and the electrostatics are coupled; the intrasurface electric fields polarize any low-permittivity species (e.g., polymer) dissolved in a high-permittivity solvent (e.g., water). This coupling enhances the polymer depletion from the surfaces and increases the screening of electrostatic interactions with respect to a model which treats polymeric and electrostatic effects as independent. As a result, the range of the ionic contribution to the osmotic interaction between surfaces is decreased while that of the polymeric contribution is increased. These changes modify the total interaction in a nonadditive manner. Building on the results for parallel surfaces, we investigate the effect of this coupling on the phase behavior of polymer-doped smectics.     

Polymer-tethered ligand-receptor interactions between surfaces II

In this paper, we analyze the thermodynamics of interactions between surfaces mediated by polymer-tethered ligand-receptor binding. From statistical thermodynamics calculations, we obtain an effective two-dimensional binding constant reflecting contributions from the microscopic binding affinity as well as from the conformation entropy of the polymer tethers. The total interaction is a result of the interplay between attractive binding and repulsion due to confinement of the polymer chains. We illustrate the differences between three scenarios when the binding molecules are (1) immobile, (2) mobile with a fixed density, and (3) mobile with a fixed chemical potential (connected to a reservoir), which correspond to different biological or experimental situations. The key features of interactions, including the range of adhesion (onset of binding) and the equilibrium separation, can be obtained from scaling analysis and are verified by numerical solutions. In addition, we also extend our method of treating the quenched case with immobile ligands and receptors developed in a previous paper [Martin, J. I.; Zhang, C.-Z.; Wang, Z.-G. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 2621-2637] as a density expansion in terms of both ligand and receptor densities. Finally, we examine several cases having ligand-receptor pairs with different tether lengths and binding affinities, and/or nonbinding linear polymers as steric repellers. Such systems can exhibit complex interactions such as a double-well potential, or a bound state with an adjustable barrier (due to the repellers), which have both biological and bioengineering relevance.     

Polymer depletion profiles around nonspherical colloidal particles

We study the effect of chain self-avoidance on the polymer density profiles that are induced by a single colloidal particle of nonspherical shape such as an ellipsoid, a dumbbell, or a lens in a solution of nonadsorbing polymers. For colloid sizes sigma much smaller than the size R(x) of the polymers, we observe a pronounced difference between ideal and self-avoiding chains. In the case of ideal polymers, the surfaces of constant density always have the same character as the surface of the particle, e.g., are oblate for an oblate ellipsoid. In the self-avoiding case, however, the character changes with increasing distance r from the particle, and an oblate particle induces prolate surfaces of constant density if sigma相似文献   

Hydrophobic forces, electrostatic steering, and acid-base bridging between atomically smooth self-assembled monolayers and end-functionalized PEGolated lipid bilayers

A molecular level understanding of interaction forces and dynamics between asymmetric apposing surfaces (including end-functionalized polymers) in water plays a key role in the utilization of molecular structures for smart and functional surfaces in biological, medical, and materials applications. To quantify interaction forces and binding dynamics between asymmetric apposing surfaces in terms of their chemical structure and molecular design we developed a novel surface forces apparatus experiment, using self-assembled monolayers (SAMs) on atomically smooth gold substrates. Varying the SAM head group functionality allowed us to quantitatively identify, rationalize, and therefore control which interaction forces dominated between the SAM surfaces and a surface coated with short-chain, amine end-functionalized polyethylene glycol (PEG) polymers extending from a lipid bilayer. Three different SAM-terminations were chosen for this study: (a) carboxylic acid, (b) alcohol, and (c) methyl head group terminations. These three functionalities allowed for the quantification of (a) specific acid-base bindings, (b) steric effects of PEG chains, and (c) adhesion of hydrophobic segments of the polymer backbone, all as a function of the solution pH. The pH-dependent acid-base binding appears to be a specific and charge mediated hydrogen bonding interaction between oppositely charged carboxylic acid and amine functionalities, at pH values above the acid pK(A) and below the amine pK(A). The long-range electrostatic "steering" of acid and base pairs leads to remarkably rapid binding formation and high binding probability of this specific binding even at distances close to full extension of the PEG tethers, a result which has potentially important implications for protein folding processes and enzymatic catalysis.     

Confinement free energy of surfaces bearing end-grafted polymers in the mushroom regime and local measurement of the polymer density

End-tethered polymer chains usually adopt mushroomlike structures on the surface when their density is low. The behaviors of these surface-attached hemicoils are described by existing polymer theory. Dolan and Edwards derived the free energy of a single polymer chain confined between two planar surfaces. Their theory was used to approximate the steric interaction free energy, E, of two identical surfaces bearing polymers in the mushroom regime and to compare with experimental data obtained from surface force measurements. However, because of a mislabeled plot in the original paper, experimental force profiles did not seem to fit the free energy approximation satisfactorily. We have correctly relabeled the involved plot and derived a new simple expression for E. In order to verify this expression, we have performed experiments on PEG45 polymers incorporated in lipid bilayers using a surface force apparatus. The measured force profiles are in perfect agreement with the prediction. We show that such measurements can be used to determine the local density of grafted polymer with good precision.     

Atomic force microscopy study of the interaction between adsorbed poly(ethylene oxide) layers: effects of surface modification and approach velocity

The interaction forces between layers of the triblock copolymer Pluronic F108 adsorbed onto hydrophobic radio frequency glow discharge (RFGD) thin film surfaces and hydrophilic silica, in polymer-free 0.15 M NaCl solution, have been measured using the atomic force microscope (AFM) colloid probe technique. Compression of Pluronic F108 layers adsorbed on the hydrophobic RFGD surfaces results in a purely repulsive force due to the steric overlap of the layers, the form of which suggests that the PEO chains adopt a brush conformation. Subsequent fitting of these data to the polymer brush models of Alexander-de Gennes and Milner, Witten, and Cates confirms that the adsorbed Pluronic F108 adsorbs onto hydrophobic surfaces as a polymer brush with a parabolic segment density profile. In comparison, the interaction between Pluronic F108 layers adsorbed on silica exhibits a long ranged shallow attractive force and a weaker steric repulsion. The attractive component is reasonably well described by van der Waals forces, but polymer bridging cannot be ruled out. The weaker steric component of the force suggests that the polymer is less densely packed on the surface and is less extended into solution, existing as polymeric isolated mushrooms. When the surfaces are driven together at high piezo ramp velocities, an additional repulsive force is measured, attributable to hydrodynamic drainage forces between the surfaces. In comparing theoretical predictions of the hydrodynamic force to the experimentally obtained data, agreement could only be obtained if the flow profile of the aqueous solution penetrated significantly into the polymer brush. This finding is in line with the theoretical predictions of Milner and provides further evidence that the segment density profile of the adsorbed polymer brush is parabolic. A velocity dependent additional stepped repulsive force, reminiscent of a solvation oscillatory force, is also observed when the adsorbed layers are compressed under high loads. This additional force is presumably a result of hindered drainage of water due to the presence of a high volume fraction of polymer chains between the surfaces.     

Choose sides: differential polymer adhesion

AFM-based single molecule desorption measurements were performed on surface end-grafted poly(acrylic acid) monolayers as a function of the pH of the aqueous buffer to study the adhesion properties of polymers that bridge two surfaces. These properties were found to depend on the adhesion forces of both surfaces in a differential manner, which is explained with a simple model in analogy to the Bell-Evans formalism used in dynamic force spectroscopy. The measured interaction forces between the poly(acrylic acid) chains and silicon nitride AFM tips depend on the grafting density of the polymer monolayers as well as on the contour length of the polymer chains. This study demonstrates that the stability of polymer bridges is determined by the adhesion strengths on both surfaces, which can be tuned by using pH-dependent polyelectrolyte monolayers.     

Mean field theory for a reversibly crosslinked polymer network

We present a mean field theory for melts and solutions of reversibly crosslinked polymers. In our model, crosslinks are considered as local bonds between two monomers. For a blend of A+B+AB polymers, we assume reversible crosslinks between the copolymers AB with a crosslink strength z and interaction weights ω(A) and ω(B) for monomers of type A and B, respectively. The usual mean field model for polymer blends without reversible crosslinks is recovered if z vanishes. With or without crosslinks, the A+B+AB blend can form a lamellar phase with A and B rich regions. If reversible crosslinks are enabled and ω(A) differs strongly from ω(B), the lamellar nanophase separation of A and B monomers is accompanied by a similar segregation of crosslinked and noncrosslinked polymers. If ω(A) and ω(B) are equal, crosslinked copolymers are well mixed with the homopolymers. For a homopolymer solution with reversible crosslinks between the polymers, our calculations show that polymers and solvent molecules are separated macroscopically if the Flory-Huggins interaction parameter and the crosslink strength are suitably high or if the volume fraction of polymers or the chain length are suitably low.     

Spherical polymer brushes under good solvent conditions: molecular dynamics results compared to density functional theory

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions by molecular dynamics methods and density functional theory. With increasing chain length, the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Finally, a brief discussion of the experiment is given.     

Effect of attractive interactions on the structure of polymer melts confined between surfaces: a density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.     

Poly(L-lysine) containing azobenzene units in the side chains: influence of the degree of substitution on liquid crystalline structure and thermotropic behaviour

The structure of poly(L-lysine)s containing between 20% and 100% of azobenzene units in the side chains has been studied by X-ray diffraction, between room temperature and 250 C. Except for samples having very low contents of azobenzene, the polymers are found to exhibit mesomorphic structures of the smectic A1 type deriving from the beta -structure of polypeptides. For polymers in which all lysine residues were substituted, the polypeptide main chains are arranged in layers corresponding to the sheets of a polypeptide 'antiparallel' beta -structure, and the side chains are perpendicular to the smectic layers. For polymers containing both substituted and free lysine side chains, each smectic layer results from the superposition of two layers: one layer contains the free lysine side chains; the other contains the azobenzenemodified lysine side chains and the polypeptide main chains that are arranged in 'antiparallel' beta -structures. All polymers exhibit only one smectic A mesophase as a function of temperature. The thickness of the smectic layers increases with increasing temperature until a thickness is reached that corresponds to the maximum interaction between the azobenzene mesogens in their trans -configuration.     

Star-branched polymers in an adsorbing slit: a Monte Carlo study

A coarse-grained model of star-branched polymer chains confined in a slit was studied. The slit was formed by two parallel impenetrable surfaces, which were attractive for polymer beads. The polymer chains were flexible homopolymers built of identical united atoms whose positions in space were restricted to the vertices of a simple cubic lattice. The chains were regular star polymers consisted of f = 3 branches of equal length. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between the polymer beads-only the excluded volume was present. Monte Carlo simulations were carried out using the algorithm based on a chain's local changes of conformation. The influence of the chain length, the distances between the confining surfaces, and the strength of the adsorption on the properties of the star-branched polymers was studied. It was shown that the universal behavior found previously for the dimension of chains was not valid for some dynamic properties. The strongly adsorbed chains can change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the temperature only.     

Adsorption Mechanism of Comb Polymer Dispersants at the Cement/Water Interface

Comb polymers are commonly used as dispersants to stabilize highly concentrated cement suspensions. The effectiveness of such polymeric additives to stabilize these suspensions is determined to a large extent by the amount adsorbed. In this study we investigated the adsorption characteristics of various comb dispersant containing different graft densities on surfaces of cement particle. The effect of inorganic salts on their adsorption was also examined in order to elucidate their adsorption mechanism. The results show that the adsorption of comb polymer dispersants on cement surface conforms approximately to Langmuir's adsorption isotherm and the characteristic plateau A _s and adsorption free energy ΔG_ads are largely dependent on the anionic group content of the comb polymers. The A _s and ΔG_ads increase with increasing anionic group content. This information suggests that the adsorption of comb polymers on cement surfaces is dominated by electrostatic interaction between COO-groups on the comb polymers and the positive surface of the cement. This conclusion is supported by effects of inorganics such as calcium and sulfate ions, and diffuse reflectance FTIR spectroscopy. The implication of results for tuning polymers for the required performance in cement manufacture should be noted.