Adsorption of Multiblock and Random Copolymer on a Solid Surface: Critical Behavior and Phase Diagram

Influence of Selected Factors on the Adsorption Layer Structure of Polyamino Acids and Their Block Copolymers at the Solid-Aqueous Solution Interface

The adsorption mechanism of different polymers containing ionic polyamino acids monomers in the chain structure at the solid-liquid interface was investigated. Initially, the influence of molecular weight and solution pH on simple polyamino acids (poly(L-aspartic acid) and poly(L-lysine) binding was determined. Considering the obtained dependencies, the polymer adsorption layer conformation was proposed in the systems containing block copolymers (both diblock and symmetrical triblock) consisting of polypeptide as well as poly(ethylene glycol) fragments. The presented studies focused on the application of two experimental methods. The polymer adsorption was carried out using the batch method and the adsorbate concentration was determined spectrophotometrically. Then, the turbidimetric measurements were taken. The analysis of the obtained results showed that the adsorption process of block copolymers depends on two factors. Firstly, the solution pH determines both the nature of the interactions of the copolymer structural units with the solid surface and the conformation of the polypeptide chains. The second parameter influencing the adsorption layer structure is the ratio of the lengths of both blocks. Introducing a short PEG fragment into the polymer main chain may improve the polymer adsorption properties by increasing the number of interactions with the adsorbent surface.

Interactions of complex polymers with nanoporous substrate

With the advance of polymer synthesis, polymers that possess unique architectures such as stars or cyclic chains, and unique chemical composition distributions such as block copolymers or statistical copolymers have become frequently encountered. Characterization of these complex polymer systems drives the development of interactive chromatography where the adsorption of polymers on the porous substrate in chromatography columns is finely tuned. Liquid Chromatography at the Critical Condition (LCCC) in particular makes use of the existence of the Critical Adsorption Point (CAP) of polymers on solid surfaces and has been successfully applied to characterization of complex polymer systems. Interpretation and understanding of chromatography behaviour of complex polymers in interactive chromatography motivates theoretical/computational studies on the CAP of polymers and partitioning of these complex polymers near the CAP. This review article covers the theoretical questions encountered in chromatographic studies of complex polymers.

Critical adsorption of copolymer tethered on selective surfaces

Critical adsorption behaviors of flexible copolymer chains tethered to a flat homogeneous surface are studied by using Monte Carlo simulations. We have compared the critical adsorption temperature Tc, estimated by a finite-size scaling method, for different AB copolymer sequences with A the attractive monomer and B the inert monomer. We find that Tc increases with an increase in the fraction of monomers A, fA, in copolymers, and it increases with an increase in the length of block A for the same fA. In particular, Tc of copolymer (AnBn)r can be expressed as a function of the block length, n, and Tc of copolymer (AnB)r and (ABm)r can be expressed as a linear function of fA. Tc of random copolymer chains also can be expressed as a linear function of fA and it can be estimated by using weight-average of Tc of different diblocks in the random copolymer. However, the crossover exponent is roughly independent of AB sequence distributions either for block copolymers or for random copolymers.

PNIPAmx–PPO36–PNIPAmx thermo-sensitive triblock copolymers: chain conformation and adsorption behavior on a hydrophobic gold surface

The presence of the PNIPAm block is not a sufficient condition for the complex adsorption behavior of PNIPAm_x–PPO₃₆–PNIPAm_x triblock copolymers.

Monte Carlo simulations of lattice models for single polymer systems

Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length N~O(10(4)). Based on the standard simple cubic lattice model (SCLM) with fixed bond length and the bond fluctuation model (BFM) with bond lengths in a range between 2 and √10, we investigate the conformations of polymer chains described by self-avoiding walks on the simple cubic lattice, and by random walks and non-reversible random walks in the absence of excluded volume interactions. In addition to flexible chains, we also extend our study to semiflexible chains for different stiffness controlled by a bending potential. The persistence lengths of chains extracted from the orientational correlations are estimated for all cases. We show that chains based on the BFM are more flexible than those based on the SCLM for a fixed bending energy. The microscopic differences between these two lattice models are discussed and the theoretical predictions of scaling laws given in the literature are checked and verified. Our simulations clarify that a different mapping ratio between the coarse-grained models and the atomistically realistic description of polymers is required in a coarse-graining approach due to the different crossovers to the asymptotic behavior.

Critical adsorption of a flexible polymer on a stripe-patterned surface

The adsorption and dynamics of a polymer chain on a stripe-patterned surface composed of periodical attractive and neutral stripes are studied by using Monte Carlo simulation. The critical adsorption temperature Tc and pattern-recognition temperature Tr are estimated from the desorption probability, surface contact number, and bridge number. A phase diagram presenting three polymer states, including a desorbed state above Tc, a multi-stripe adsorbed state at an intermediate temperature Tr < T < Tc, and a single-stripe adsorbed state below Tr, is provided for infinitely long chains. Normal diffusion is always observed for a polymer in the direction parallel to the stripe even at low temperature. But in the direction perpendicular to the stripe, the polymer can freely diffuse above Tc, whereas the polymer is confined to one attractive stripe below Tr. However, the adsorbed polymer can hop from one attractive stripe to another at the intermediate temperature Tr < T < Tc.

Multiblock copolymer solutions in contact with a surface: self-assembly, adsorption, and percolation

Amphiphilic copolymers are often used as compatibilizing or stabilizing agents, either in solution or at surfaces. In the special case of multiblock copolymers the connectivity of the blocks combines with the antagonistic behavior of the different types of blocks. Here we report on the behavior of solutions of amphiphilic multiblock copolymers with a large number of blocks and a low fraction of solvophobic monomers in contact with an attractive surface. Using lattice Monte Carlo simulations, the influence on the structures of the solvent quality and the type of surface from noninteracting to strongly attractive to the solvophobic monomers can be assessed. In the presence of a surface bulk micelles are formed that are not different in size and shape from the micelles observed in the absence of a surface. When increasing the surface attraction, solvophobic monomers tend to adsorb either as isolated blocks or forming surface micelles. Evidence is given of a surface concentration threshold above which surface micelles can form due to microphase separation. These surface micelles are in equilibrium with bulk micelles, some of which are connected to the surface through a path of either hydrophobic and/or hydrophilic blocks or hydrophobic cross-links, or both. The size distributions of bulk and connected micelles are similar. With increasing surface concentration surface micelles get organized due to the steric repulsion between core-shell surface micelles. Moreover, these organized surface micelles percolate. The connected micelles form a concentrated layer parallel to the attractive surface. In addition, these systems are governed by two very different time scales: The fast one leads to micellar self-assembly in the bulk and at the surface while the slow one prevents the system from reaching equilibrium in the course of the simulations and corresponds to the transfer of copolymers from the bulk to the attractive surface.

Simulation of conformational properties of end-grafted diblock copolymers

The conformational properties of end-grafted diblock copolymers XA_nB_n and XB_nA_n are dependent on the position of the grafted end X.

Adsorption of a single polymer chain on a surface: effects of the potential range

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value U(c) corresponding to the adsorption transition scales as W(-1/ν), where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory U(c)≈(π(2)/24)(W+1/2)(-2) and in the best-fit equation for the MC simulation data U(c)=0.585(W+1/2)(-5/3). Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NU(c),U/U(c)). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value <R(g[perpendicular])(2)>/<R(g[parallel])(2)>=0.320±0.003 only at N~5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent φ(eff)(N). Strong corrections to scaling of order N(-0.5) are observed, and the extrapolated value φ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of φ(eff)(N) were identified as the asymptotic value for the crossover exponent.

Mechanical desorption of a single chain: unusual aspects of phase coexistence at a first-order transition

The phase transition occurring when a single polymer chain adsorbed at a planar solid surface is mechanically desorbed is analyzed in two statistical ensembles. In the force ensemble, a constant force applied to the nongrafted end of the chain (that is grafted at its other end) is used as a given external control variable. In the z-ensemble, the displacement z of this nongrafted end from the surface is taken as the externally controlled variable. Basic thermodynamic parameters, such as the adsorption energy, exhibit a very different behavior as a function of these control parameters. In the thermodynamic limit of infinite chain length the desorption transition with the force as a control parameter clearly is discontinuous, while in the z-ensemble continuous variations are found. However, one should not be misled by a too-naive application of the Ehrenfest criterion to consider the transition as a continuous transition: rather, one traverses a two-phase coexistence region, where part of the chain is still adsorbed and the other part desorbed and stretched. Similarities with and differences from two-phase coexistence at vapor-liquid transitions are pointed out. The rounding of the singularities due to finite chain length is illustrated by exact calculations for the nonreversal random walk model on the simple cubic lattice. A new concept of local order parameter profiles for the description of the mechanical desorption of adsorbed polymers is suggested. This concept give evidence for both the existence of two-phase coexistence within single polymer chains for this transition and the anomalous character of this two-phase coexistence. Consequences for the proper interpretation of experiments performed in different ensembles are briefly mentioned.

Pulling an adsorbed polymer chain off a solid surface

The thermally assisted detachment of a self-avoiding polymer chain from an adhesive surface by an external force applied to one of the chain-ends is investigated. We perform our study in the "fixed height" statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain-end is kept fixed at height h over the solid plane at different adsorption strength [Formula: see text]. The phase diagram in the h-[Formula: see text] plane is calculated both analytically and by Monte Carlo simulations. We demonstrate that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than f is used as an independent control parameter.