The adsorption of materials on surfaces is critical to many industries for preparing surfaces that are protective against toxins, resistant to corrosion and wear, and multifunctional for numerous applications. Polymers are frequently used in these situations not only because they are economical but also because they are easily processable and allow for unique control over composition and architecture on the nanoscale. Because they undergo self-assembly, a process in which supramolecular hierarchical organization is established without external intervention, synthetic copolymers, i.e., macromolecules made of covalently connected sequences of chemically different synthetic units, also represent the simplest structural blocks capable of mimicking biomolecule behavior.
Adsorption of polymers at interfaces between the polymer solution and a solid non-polymeric substrate has been a subject of long-standing theoretical and experimental interest. It has now been well established that the driving force for polymer adsorption involves an interplay between: i) the gain in energy due to the adsorption of the binding monomers of the macromolecule to the attractive surface, and ii) the loss in chain entropy associated with the reduction in the number of possible configurations of the adsorbed chain in comparison with that of a free chain. The topic of polymer adsorption on chemically heterogeneous substrates has been recently addressed in several theoretical models and computer simulations. These early studies revealed that the fundamental parameters, which govern the adsorption of polymers in such systems are: i) the interactions between polymer segments and the substrate, ii) the shape, size and spatial distribution of the chemical heterogeneities on the substrate, iii) the polymer microstructure, and iv) the chain length. For example, it was found that when the area of adsorption on the surface is randomly diluted, the macromolecule has a tendency to be localized at regions of high concentrations of adsorptive sites, which may cause a shrinkage or an extension of the chain parallel to the surface depending on the relationship between the chain length and the spatial distribution of the adsorptive sites on the substrate. While providing the first glimpse at the heterogeneous adsorption phenomena, these studies were limited to just a few specific systems involving homopolymers, random copolymers and polymers with statistically correlated disordered sequences, and block copolymers. The techniques used to study the adsorption on heterogeneous surfaces were based on the density functional theory and field-theoretic methods, Monte Carlo simulations, and two-dimensional self-consistent field (SCF) approaches.
We have recently developed and presented a three-dimensional self-consistent field (3D SCF) lattice model of polymer adsorption and used it to study the adsorption of copolymers with ordered sequence distributions on flat chemically heterogeneous substrates composed of ordered checkerboard patterns. Our model is derived from the one-dimensional version of the self-consistent field scheme introduced by Scheutjens and Fleer (SF SCF). Unlike the original SF SCF model, the polymer segment density in our system is not only a function of z, the coordinate perpendicular to the mixture/substrate interface, but also x and y, the coordinates parallel with the surface plane. In contrast to 1D and 2D SCF approaches that consider plane and line averages, respectively, we apply a mean-field approximation only at a (x,y,z) site. Specifically, the segment density at a site (x,y,z) is derived from the weighted contributions of the site’s nearest-neighbors (see figure below). We note that this nearest-neighbor averaging provides quantitatively accurate results for systems with relatively modest concentration gradients only, however. For systems with larger polymer concentration gradients, the nearest-neighbor averaging is expected to be just qualitatively correct. A simple way to circumvent these limitations would be to determine the average segment density at a site (x,y,z) by simultaneously considering appropriately weighted contributions of both the nearest-neighbors and the next-nearest-neighbors of the (x,y,z) site.
We consider a mixture of a homopolymer A (number of segments NhA) and a copolymer A-B (number of segments NC) placed onto a cubic lattice in contact with a planar chemically heterogeneous substrate. The substrate is composed of two kinds of sites (C and D) that experience different chemical affinities towards A and B. The results presented in this work have been calculated for a lattice composed of 24x24x24 sites with periodic boundary conditions applied in each (x,y) plane. During each calculation we keep the following parameters constant: NhA=200, NC=40, and the A-B volume fraction in the mixture ϕc=0.01. We investigate the adsorption characteristics of A-B copolymers with the volume fractions of B, fB, in the copolymer equal to 0.125 (NCA=35, NCB=5), 0.25 (NCA=30, NCB=10), and 0.50 (NCA=20, NCB=20).
The interaction between the A and B segments is characterized by a positive value of χAB. By assigning the A/C, B/C, and A/D interactions to be athermal (=0) and those between D and B to be attractive (<0), the B segments of the A-B copolymer are expected to adsorb preferentially on the D regions of the substrate while there is no preference for either A or B to occupy the C surface sites. To address the interplay between the A-B repulsion and the B-D attraction, we carried out our calculations for various combinations of χABNCB and χBDNCB. Specifically, taking χABNCB=5.0 and χBDNCB=-2.0 as a benchmark (set-0), we increased the B-D attraction by 100% to χBDNCB=-4.0 while keeping χABNCB constant (set-1). Finally, we probed the effect of the A-B repulsion by keeping the B-D attraction unchanged and increased χABNCB from 5.0 to 6.0 (set-2).
The results show that in contrast to the block copolymers that can be applied as “amplifiers” of surface chemical patterns, copolymers with alternating (or random) sequence distribution can be used to “mask” (or suppress) chemical “roughness” of the substrate. Compositionally asymmetric diblock copolymers can be used to detect and amplify small chemical non-uniformities on substrates; the pattern character and the distance to which it can be transferred from the substrate are dictated by the compositional asymmetry of the macromolecule.
Similar calculations have also been carried out for substrates with ordered chemical patterns comprising checkerboards of C and D sites with various repeating patterns ranging from [1×1] to [6×6]. The results in the figure below show the in-plane volume fraction profiles of A and B segments at the interface between the substarte and the A-B copolymer/A homopolymer mixture (results for [1×1], [3×3], and [6×6] substrates are shown). As previously shown the amount of B and A adsrobed at the interface depends intimetely on the interplay between the sequence distribution in the copolymer and the spatial distribution of the adsorption sites.
We are now complementing the results of the 3D SCF model with Monte Carlo simulations.
Snapshots from Monte Carlo simulations illustrating the conformations of A/B copolymers adsorbing on C/D substrates [Semler & Genzer, unpublished]. The results show the adsorption of: a) A15-b-B15 diblock on [15×15] substrate with χBD=-0.1; b) A15-b-B15 diblock on [15×15] substrate with χBD=-1.0; c) A15-alt-B15 alternating on [15×15] substrate with χBD=-1.0; and d) A20-b-B20 diblock on [1×1] substrate with χBD=-1.0. In all simulations χAB=0.1. The blue and red colors denotes the adsorbing (B) and non-adsorbing (A) segments of the A-B copolymer.