Probing chain ends in adsorbed polymer layers

We study theoretically the pull-out of polymer chains from an adsorbed polymer layer by sticking of the chain ends on an opposing surface using scaling arguments and a mean field theory. When only one chain is pulled out from the layer, we extend previous results obtained for a single adsorbed chain and calculate the force necessary to extract the chain from the layer. We then discuss end adsorption from an adsorbed layer of polymers bearing specific end groups onto a second surface. Two bridging regimes are predicted: a diffuse layer regime at weak separations (or/and weak interaction) and a large separation strong interaction regime where the bridges stretch into a brush like structure. Bridging fractions and force profiles are displayed that could be compared to atomic force microscope or surface force apparatus experiments.     

Effect of end-group sticking energy on the properties of polymer brushes: comparing experiment and theory

Using surface force balance measurements we have established that polystyrene chains bearing three zwitterionic groups have a higher end-group sticking energy than equivalent chains bearing a single zwitterionic group. In a good solvent, polystyrene chains end-functionalized with three zwitterionic groups form brushes of a higher surface coverage than those bearing a single zwitterion. The increase in surface coverage is slow compared with the initial formation of the brush. Measurements of the refractive index allow us to directly quantify the variation of surface coverage, permitting comparison with models for the kinetics of brush formation based on scaling theory and an analytical self-consistent field. We find qualitative support for associating the kinetic barrier with the energy required for an incoming chain to stretch as it penetrates the existing brush.     

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.     

Scaling behavior of a brush-homopolymer interface in the limit of high grafting density

The interface between a polymer brush and a chemically equivalent homopolymer is examined using self-consistent field theory (SCFT). Focusing on ultrahigh grafting densities, we extract how the properties scale with the brush thickness, L, and compare with predictions based on strong-stretching theory (SST). Although the scaling exponents are consistent, the overall agreement is poor. We attribute this to the inaccurate way the SST-based calculation treats chain fluctuations at the extremity of the brush. This accounts for a previous disagreement between SCFT and SST in regards to autophobic dewetting, and brings into question a number of other SST predictions. Our conclusion is that SST requires a more sophisticated treatment of finite-stretching corrections, along the lines of that proposed by Likhtman and Semenov [Europhys. Lett. 51, 307 (2000)].     

Grafted polymers under strong shear: Scaling and non-equilibrium Monte Carlo studies

End-grafted polymer chains exposed to strong shear solvent flow in the x-direction are investigated by a non-equilibrium Monte Carlo method using the bond-fluctuating model. The solvent flow is modelled by an enhanced jump rate of monomers in the flow direction. Under strong enough shear flow, the shear force is non-linear with the blob size ζ depending on the shear force and not on the monomer volume fraction ϕ. For the case of a grafted single chain, our data on the end-to-end distance of the polymer for a wide range of shear rate γ agree well with the proposed scaling form and compare reasonably well with the Langevin force law in the extreme strong shear case. Also the scaling for the blob size is derived with ζ = aN^vK(γN^2+v) for some scaling function K, and verified by our simulation data. For the case of a polymer brush, we derive the crossover force scale F^* separating the weak and strong shear regime with F^*a/(kT) = ϕ^v/(3v−1) where v is the usual self-avoiding walk exponent. For the case of a polymer brush under strong shear, the velocity profile, v(z), inside and above the brush is calculated analytically by treating the flow as in a porous medium and solving the Brinkman equation. The solution of the velocity profile is then combined with non-equilibrium Monte Carlo simulation data which allow a self-consistent determination of the chain end-to-end length and the incline angle of the chain. Also we derive the scaling form for the positions x(n) of the nth monomer and verify it by our simulation data. We further obtain an analytical expression for x(n) in terms of the effective viscosity η of the model, given by F = ηav(z). The effective viscosity is also found from our simulation to be ηa²/(kT) ≃ 0.02 ± 0.005.     

Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献   

Polymer translocation in solid-state nanopores: dependence of scaling behavior on pore dimensions and applied voltage

We investigate unforced and forced translocation of a Rouse polymer (in the absence of hydrodynamic interactions) through a silicon nitride nanopore by three-dimensional Langevin dynamics simulations, as a function of pore dimensions and applied voltage. Our nanopore model consists of an atomistically detailed nanopore constructed using the crystal structure of β-Si(3)N(4). We also use realistic parameters in our simulation models rather than traditional dimensionless quantities. When the polymer length is much larger than the pore length, we find the translocation time versus chain length scales as τ ～ N(2+ν) for the unforced case and as τ ～ N((1+2ν)/(1+ν)) for the forced case. Our results agree with theoretical predictions which indicate that memory effects and tension on the polymer chain play an important role during the translocation process. We also find that the scaling exponents are highly dependent on the applied voltage (force). When the length of the polymer is on the order of the length of the pore, we do not find a continuous scaling law, but rather scaling exponents that increase as the length of the polymer increases. Finally, we investigate the scaling behavior of translocation time versus applied voltage for different polymer and pore lengths. For long pores, we obtain the theoretical scaling law of τ ～ 1/V(α), where α ? 1 for all voltages and polymer lengths. For short pores, we find that α decreases for very large voltages and/or small polymer lengths, indicating that the value of α = 1 is not universal. The results of our simulations are discussed in the context of experimental measurements made under different conditions and with differing pore geometries.     

Polyelectrolyte brushes

The simple scaling theory of weakly-charged polyelectrolyte brush (the layer of polyelectrolyte chains grafted at one end onto an impermeable surface) immersed into a good solvent has been developed.The asymptotic scaling dependences of the free layer thickness on charge density and solvent strength are obtained. The behavior of polyelectrolyte brush subjected to normal and tangential external forces is considered. New “polyelectrolyte effect” is predicted: shear of a free polyelectrolyte brush leads to a decrease in brush thickness in contrast to the case of a free neutral brush. Such behavior is equivalent to that of a neutral brush subjected to external normal stretching force. This force in the case of polyelectrolyte brush is created by the osmotic pressure of mobile counterions neutralizing grafted chain charges.     

Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.     

Solvent quality effects on scaling behavior of poly(methyl methacrylate) brushes in the moderate- and high-density regimes

Herein, we give a detailed experimental analysis for scaling law behavior in the "moderately dense" and "high-density" brush regimes for poly(methyl methacrylate) brushes swollen in a range of solvent conditions. This expansive experimental analysis aims to validate decades of mean field theory predictions on power law scaling behavior of grafted polymer chains. Brushes with grafting densities (σ) ranging from 0.1 to 0.8 nm(-2) are prepared by atom-transfer radical polymerization. The swollen thickness (h) is characterized using liquid cell ellipsometry, and the solvent quality is varied using mixtures of acetone and methanol. In a good solvent, the exponential scaling behavior (h ∝ σ(n)) has the typical n = 1/3 dependency for grafting densities of σ ≤ 0.4 nm(-2). For grafting densities of >0.4 nm(-2), n increases, indicating the transition from the moderately dense to the high-density brush regime. However, in a poor solvent, the scaling behavior is independent of σ and scales as h ∝ σ(0.80), approaching the theoretical expectations of h ∝ σ(1). An abrupt transition between these scaling law behaviors occurs at the Θ-solvent condition of ～45% (v/v) methanol in acetone. While our experimental results parallel trends predicted by mean field theory, differences are observed and appear to be attributed to self-solvation of the polymer, polydispersity in the molecular weight, and chain termination.     

Prediction of conformational characteristics and micellar solution properties of fluorocarbon surfactants

A molecular-thermodynamic theory is developed to model the micellization of fluorocarbon surfactants in aqueous solutions, by combining a molecular model that evaluates the free energy of micellization of fluorocarbon surfactant micelles with a previously developed thermodynamic framework describing the free energy of the micellar solution. In the molecular model of micellization developed, a single-chain mean-field theory is combined with an appropriate rotational isomeric state model of fluorocarbon chains to describe the packing of the fluorocarbon surfactant tails inside the micelle core. Utilizing this single-chain mean-field theory, the packing free energies of fluorocarbon surfactants are evaluated and compared with those of their hydrocarbon analogues. We find that the greater rigidity of the fluorocarbon chain promotes its packing in micellar aggregates of low curvatures, such as bilayers. In addition, the mean-field approach is utilized to predict the average conformational characteristics (specifically, the bond order parameters) of fluorocarbon and hydrocarbon surfactant tails within the micelle core, and the predictions are found to agree well with the available experimental results. The electrostatic effects in fluorocarbon ionic surfactant micelles are modeled by allowing for counterion binding onto the charged micelle surface, which accounts explicitly for the effect of the counterion type on the micellar solution properties. In addition, a theoretical formulation is developed to evaluate the free energy of micellization and the size distribution of finite disklike micelles, which often form in the case of fluorocarbon surfactants. We find that, compared to their hydrocarbon analogues, fluorocarbon surfactants exhibit a greater tendency to form cylindrical or disklike micelles, as a result of their larger molecular volume as well as due to the greater conformational rigidity of the fluorocarbon tails. The molecular-thermodynamic theory developed is then applied to several ionic fluorocarbon surfactant-electrolyte systems, including perfluoroalkanoates and perfluorosulfonates with added LiCl or NH(4)Cl, and various micellar solution properties, including critical micelle concentrations (cmc's), optimal micelle shapes, and average micelle aggregation numbers, are predicted. The predicted micellar solution properties agree reasonably well with the available experimental results.     

Primary versus ternary adsorption of proteins onto PEG brushes

Polyethylene glycol (PEG) brushes are used to reduce protein adsorption at surfaces. Their design needs to allow for two leading adsorption modes at the brush-coated surface. One is primary adsorption at the surface itself. The second is ternary adsorption within the brush as a result of weak PEG-protein attraction. We present a scaling theory of the equilibrium adsorption isotherms allowing for concurrent primary and ternary adsorption. The analysis concerns the weak adsorption limit when individual PEG chains do not bind proteins. It also addresses two issues of special relevance to brushes of short PEGs: the consequences of large proteins at the surface protruding out of a shallow brush and the possibility of marginal solvent conditions leading to mean-field behavior. The simple expressions for the adsorption isotherms are in semiquantitative agreement with experiments.     

Modified interfacial statistical associating fluid theory: application to tethered polymer chains

Modified interfacial statistical associating fluid theory density functional theory is extended to tethered polymer chains in the absence or presence of free polymer chains. The structures of the "dry" and "wet" polymer brushes have been calculated and compared with simulation results available in the literature. The comparisons show that the theory accurately predicts the structure of the tethered polymer brush. The average brush heights calculated from the theory agree with well-established scaling theories for tethered polymers. However, these scaling theories cannot predict the detailed structure, accurately. The effects of the segment-segment interactions of the tethered polymer and the free polymer have been effectively captured by the theory.     

Compression of Polymer Brushes Under a Lateral Force

Summary: The influence of a lateral force (or lateral shear) acting on chains in a polymer brush is investigated theoretically. Brushes consisting of chains with temperature dependent anisotropic interactions between monomers (main‐chain mesogenic groups) are considered. It is shown that a lateral force applied to polymer brush induces its compression. In contrast to a conventional brush, the compression of brush, capable of forming a liquid crystalline (LC) state, can be caused by comparatively small shear forces. Moreover, such shear forces can induce a phase transition of a brush into the tilted LC state with a several‐fold decrease in brush thickness. These results allow us to predict a possibility to observe a decrease in brush thickness in a real experiment with reasonably values of shear rate.

Model of a chain in a polymer brush under an influence of lateral force p.     

Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte

A statistical mechanical model is presented which explicitly accounts for the fluctuations, the electrostatic, and the excluded volume correlations for ions bound to a polyelectrolyte such as DNA. The method can be employed to treat a wide range of ionic conditions including multivalent ions. The microscopic framework of the theory permits the use of realistic finite length and grooved structural model for the polyelectrolyte and modeling of the finite size of the bound ions. Test against Monte Carlo simulations suggests that the theory can give accurate predictions for the ion distribution and the thermodynamic properties. For multivalent ions, the theory makes improved predictions as compared with the mean-field approach. Moreover, for long polyelectrolyte and dilute salt concentration, the theory predicts ion binding properties that agree with the counterion condensation theory.     

Localization of a multiblock copolymer at a selective interface: scaling predictions and Monte Carlo verification

We investigate the localization of a hydrophobic-polar regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length M on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copolymer chain perpendicular and parallel to the interface in terms of chain length N and block size M, as well as the selectivity parameter chi. The scaling relations differ for the case of weak and strong localization. In the strong localization limit a scaling relation for the lateral diffusion coefficient D( parallel) is also derived. We implement a dynamic off-lattice Monte Carlo model to verify these scaling predictions. For chain lengths in a wide range (32相似文献   

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.     

Ionizable polyelectrolyte brushes: brush height and electrosteric interaction

Semi-analytical scaling theory is used to describe quenched and annealed (weakly charged, ionizable, charge-regulating) polyelectrolyte brushes in electrolyte solutions of arbitrary salt concentration. An Alexander-De Gennes box model with homogeneous distribution of polymer segments and the free ends located at the edge of the brush is assumed, as is local electroneutrality in the brush. For annealed polyelectrolyte and in the low-salt regime, the theory predicts that for sufficiently dense brushes, the salt concentration has a small influence on brush height, while the brush expands with increasing grafting density, in agreement with experiment. Expressions are presented for the interaction free energy of compressed ionizable and quenched polyelectrolyte brushes (proportional to the force between particles or curved surfaces). In all cases, the required prefactors are explicitly stated. The theory is compared directly with published experiments on the influence of salt concentration, pH, and grafting density on the thickness and interaction force of polystyrene sulfonate (quenched) and poly(meth)acrylic acid (annealed) brushes. In general, trends are well reproduced but significant deviations remain.     

Deformation,Stretching, and Relaxation of Single‐Polymer Chains: Fundamentals and Examples#

Abstract

We review the basic theory for the static and dynamic properties of ideal and real chains. We describe the stretching of single ideal chains in both the strain and the stress ensembles, give scaling arguments for the deformation of real chains, and also consider the impact of chain rigidity by discussing the stretching of worm-like chains. We complement this theoretical outlook with specific examples that highlight the relevance of the single-molecule deformation in a practical perspective: the translocation of a macromolecule over a potential barrier, the collision of a single chain with fixed obstacles or other chains, the dynamics of a thethered chain in a strong shear flow, and some remarkable predictions concerning the deformation of composite chain molecules during free-solution electrophoresis.     

Specific ion effects in solutions of globular proteins: comparison between analytical models and simulation

Monte Carlo simulations have been performed for ion distributions outside a single globular macroion and for a pair of macroions, in different salt solutions. The model that we use includes both electrostatic and van der Waals interactions between ions and between ions and macroions. Simulation results are compared with the predictions of the Ornstein-Zernike equation with the hypernetted chain closure approximation and the nonlinear Poisson-Boltzmann equation, both augmented by pertinent van der Waals terms. Ion distributions from analytical approximations are generally very close to the simulation results. This demonstrates that properties that are related to ion distributions in the double layer outside a single interface can to a good approximation be obtained from the Poisson-Boltzmann equation. We also present simulation and integral equation results for the mean force between two globular macroions (with properties corresponding to those of hen-egg-white lysozyme protein at pH 4.3) in different salt solutions. The mean force and potential of mean force between the macroions become more attractive upon increasing the polarizability of the counterions (anions), in qualitative agreement with experiments. We finally show that the deduced second virial coefficients agree quite well with experimental results.