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

Unsynchronous conformational transitions induced by the asymmetric adsorption-response of an active diblock copolymer in an inert brush

To exploit the chemical asymmetry of diblock copolymer chains on the design of high-performance switch sensors, we propose an analytically tractable model system which contains an adsorption-responsive diblock copolymer in an otherwise inert brush, and study its phase transitions by using both analytical theory and self-consistent field calculations. The copolymer chain is chemically asymmetric in the sense that the two blocks assume different adsorption strengths, which is characterized by the defined adsorption ratio. We found that the conformation states, the number of stable phases, and transition types are mainly controlled by the length of each block and the adsorption ratio. In particular, when the length of the ungrafted block is longer than the brush chains, and the adsorption ratio is smaller than a critical value, the copolymer chain shows three thermodynamically stable states, and undergoes two unsynchronous transitions, where the two blocks respond to the adsorption in a different manner, when the adsorption changes from weak to sufficiently strong. For this kind of three-state transition, the transition point, transition barrier, and transition width are evaluated by using the self-consistent field method, and their scaling relationship with respect to the system parameters is extracted, which matches reasonably well with the predictions from the analytical theory. The self-consistent field calculations also indicate that the conformational transitions involved in the three-state transition process are sharp with a low energy barrier, and interestingly, barrier-free transitions are observed. Our finding shows that the three-state transitions not only specify a region where high performance unsynchronous switch sensors can be exploited, but may also provide a useful model understanding the unsynchronous biological processes.

Anomalous Diffusion of Polyelectrolyte Segments on Supported Charged Lipid Bilayers

This work provides mesoscale models for the anomalous diffusion of a polymer chain on a heterogeneous surface with rearranging randomly distributed adsorption sites. Both the "bead-spring" model and oxDNA model were simulated on supported lipid bilayer membranes with various molar fractions of charged lipids, using Brownian dynamics method. Our simulation results demonstrate that "bead-spring" chains exhibit sub-diffusion on charged lipid bilayers which agrees with previous experimental observations for short-time dynamics of DNA segments on membranes. In addition, the non-Gaussian diffusive behaviors of DNA segments have not been observed in our simulations. However, a simulated 17 base pairs double stranded DNA, using oxDNA model, performs normal diffusion on supported cationic lipid bilayers. Due to the number of positively charged lipids attracted by short DNA is small, the energy landscape that the short DNA experiences during diffusion is not as heterogeneous as that experienced by long DNA chains, which results in normal diffusion rather than sub-diffusion for short DNA.

Partition-function-zero analysis of polymer adsorption for a continuum chain model

Polymer chains undergoing adsorption are expected to show universal critical behavior which may be investigated using partition function zeros. The focus of this work is the adsorption transition for a continuum chain, allowing for investigation of a continuous range of the attractive interaction and comparison with recent high-precision lattice model studies. The partition function (Fisher) zeros for a tangent-hard-sphere N-mer chain (monomer diameter σ) tethered to a flat wall with an attractive square-well potential (range λσ, depth ε) have been computed for chains up to N=1280 with 0.01≤λ≤2.0. In the complex-Boltzmann-factor plane these zeros are concentrated in an annular region, centered on the origin and open about the real axis. With increasing N, the leading zeros, w_{1}(N), approach the positive real axis as described by the asymptotic scaling law w_{1}(N)-y_{c}∼N^{-ϕ}, where y_{c}=e^{ε/k_{B}T_{c}} is the critical point and T_{c} is the critical temperature. In this work, we study the polymer adsorption transition by analyzing the trajectory of the leading zeros as they approach y_{c} in the complex plane. We use finite-size scaling (including corrections to scaling) to determine the critical point and the scaling exponent ϕ as well as the approach angle θ_{c}, between the real axis and the leading-zero trajectory. Variation of the interaction range λ moves the critical point, such that T_{c} decreases with λ, while the results for ϕ and θ_{c} are approximately independent of λ. Our values of ϕ=0.479(9) and θ_{c}=56.8(1.4)^{∘} are in agreement with the best lattice model results for polymer adsorption, further demonstrating the universality of these constants across both lattice and continuum models.

Adsorption of Semiflexible Polymers in Cylindrical Tubes

Conformations of wormlike chains in cylindrical pores with attractive walls are explored for varying pore radius and strength of the attractive wall potential by molecular dynamics simulations of a coarse-grained model. Local quantities such as the fraction of monomeric units bound to the surface and the bond-orientational order parameter as well as the radial density distribution are studied, as well as the global chain extensions parallel to the cylinder axis and perpendicular to the cylinder surface. A nonmonotonic convergence of these properties to their counterparts for adsorption on a planar substrate is observed due to the conflict between pore surface curvature and chain stiffness. Also the interpretation of partially adsorbed chains in terms of trains, loops, and tails is discussed.

Polymer brushes with reversibly tunable grafting density

We propose a novel class of responsive polymer brushes, where the effective grafting density can be controlled by external stimuli. This is achieved by using end-grafted polymer chains that have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly and in a controlled way as a response to changes in environmental parameters. The effect is demonstrated by numerical self-consistent field calculations and analyzed by scaling arguments. Since the thickness of the denser layer is about a few monomer sizes, its capacity to form a microphase is limited by the product of the brush chain length and the grafting density. We explore the range of chain lengths and grafting densities where the effect is most pronounced. In this range, the SCF studies suggest that individual chains inside the brush show large rapid fluctuations between two states that are separated by only a small free energy barrier. The behavior of the brush as a whole, however, does not reflect these large fluctuations, and the effective grafting density varies smoothly as a function of the control parameters.

Semiflexible Polymers Interacting With Planar Surfaces: Weak versus Strong Adsorption

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness κ as well as the strength of the adsorption potential ϵwall are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter η) and the mean square gyration radius parallel, 〈Rg2〉||, and perpendicular, 〈Rg2〉⊥, to the wall. While for strongly adsorbed chains EV has negligible effect on f and η, we find that 〈Rg2〉|| is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that f,η, and 〈Rg2〉⊥ converge to their asymptotic values with 1/N corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.

Adsorption of two-dimensional polymers with two- and three-body self-interactions

Using extensive Monte Carlo simulations, we investigate the surface adsorption of self-avoiding trails on the triangular lattice with two- and three-body on-site monomer-monomer interactions. In the parameter space of two-body, three-body, and surface interaction strengths, the phase diagram displays four phases: swollen (coil), globule, crystal, and adsorbed. For small values of the surface interaction, we confirm the presence of swollen, globule, and crystal bulk phases. For sufficiently large values of the surface interaction, the system is in an adsorbed state, and the adsorption transition can be continuous or discontinuous, depending on the bulk phase. As such, the phase diagram contains a rich phase structure with transition surfaces that meet in multicritical lines joining in a single special multicritical point. The adsorbed phase displays two distinct regions with different characteristics, dominated by either single- or double-layer adsorbed ground states. Interestingly, we find that there is no finite-temperature phase transition between these two regions though rather a smooth crossover.

Linear Dimensions of Adsorbed Semiflexible Polymers: What Can Be Learned about Their Persistence Length?

Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length L, chain stiffness, κ, and the strength of the adsorption potential over a wide range. Molecular dynamics simulations show that partially adsorbed chains (with "tails," surface attached "trains," and "loops") are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value (ℓ_{p}) to the enhanced value in two dimensions (2ℓ_{p}) is analyzed, and excluded volume effects are identified for L≫ℓ_{p}. Consequences for the interpretation of experiments are suggested. We verify the prediction that the adsorption threshold scales as ℓ_{p}^{-1/3}.

Adsorption of interacting self-avoiding trails in two dimensions

We investigate the surface adsorption transition of interacting self-avoiding square lattice trails onto a straight boundary line. The character of this adsorption transition depends on the strength of the bulk interaction, which induces a collapse transition of the trails from a swollen to a collapsed phase, separated by a critical state. If the trail is in the critical state, the universality class of the adsorption transition changes; this is known as the special adsorption point. Using flatPERM, a stochastic growth Monte Carlo algorithm, we simulate the adsorption of self-avoiding interacting trails on the square lattice using three different boundary scenarios which differ with respect to the orientation of the boundary and the type of surface interaction. We confirm the expected phase diagram, showing swollen, collapsed, and adsorbed phases in all three scenarios, and confirm universality of the normal adsorption transition at low values of the bulk interaction strength. Intriguingly, we cannot confirm universality of the special adsorption transition. We find different values for the exponents; the most likely explanation is that this is due to the presence of strong corrections to scaling at this point.

Phase transitions in solvent-dependent polymer adsorption in three dimensions

We consider the phase diagram of self-avoiding walks (SAWs) on the simple cubic lattice subject to surface and bulk interactions, modeling an adsorbing surface and variable solvent quality for a polymer in dilute solution, respectively. We simulate SAWs at specific interaction strengths to focus on locating certain transitions and their critical behavior. By collating these new results with previous results we sketch the complete phase diagram and show how the adsorption transition is affected by changing the bulk interaction strength. This expands on recent work considering how adsorption is affected by solvent quality. We demonstrate that changes in the adsorption crossover exponent coincide with phase boundaries.

Relaxation processes and glass transition of confined polymer melts: A molecular dynamics simulation of 1,4-polybutadiene between graphite walls

Molecular dynamics simulations of a chemically realistic model for 1,4-polybutadiene in a thin film geometry confined by two graphite walls are presented. Previous work on melts in the bulk has shown that the model faithfully reproduces static and dynamic properties of the real material over a wide temperature range. The present work studies how these properties change due to nano-confinement. The focus is on orientational correlations observable in nuclear magnetic resonance experiments and on the local intermediate incoherent neutron scattering function, F_s(q_z, z, t), for distances z from the graphite walls in the range of a few nanometers. Temperatures from about 2T_g down to about 1.15T_g, where T_g is the glass transition temperature in the bulk, are studied. It is shown that weakly attractive forces between the wall atoms and the monomers suffice to effectively bind a polymer coil that is near the wall. For a wide regime of temperatures, the Arrhenius-like adsorption/desorption kinetics of the monomers is the slowest process, while very close to T_g the Vogel-Fulcher-Tammann-like α-relaxation takes over. The α-process is modified only for z≤1.2 nm due to the density changes near the walls, less than expected from studies of coarse-grained (bead-spring-type) models. The weakness of the surface effects on the glass transition in this case is attributed to the interplay of density changes near the wall with the torsional potential. A brief discussion of pertinent experiments is given.

Universality of crossover scaling for the adsorption transition of lattice polymers

Recently, it has been proposed that the adsorption transition for a single polymer in dilute solution, modeled by lattice walks in three dimensions, is not universal with respect to intermonomer interactions. Moreover, it has been conjectured that key critical exponents ϕ, measuring the growth of the contacts with the surface at the adsorption point, and 1/δ, which measures the finite-size shift of the critical temperature, are not the same. However, applying standard scaling arguments the two key critical exponents should rather be identical, hence pointing to a potential breakdown of these standard scaling arguments. Both of these conjectures are in contrast to the well-studied situation in two dimensions, where there are exact results from conformal field theory: these exponents are both accepted to be 1/2 and universal. We use the flatPERM algorithm to simulate self-avoiding walks and trails on the hexagonal, square, and simple cubic lattices up to length 1024 to investigate these claims. Walks can be seen as a repulsive limit of intermonomer interaction for trails, allowing us to probe the universality of adsorption. For each lattice model we analyze several thermodynamic properties to produce different methods of estimating the critical temperature and the key exponents. We test our methodology on the two-dimensional cases, and the resulting spread in values for ϕ and 1/δ indicates that there is a systematic error which can far exceed the statistical error usually reported. We further suggest a methodology for consistent estimation of the key adsorption exponents which gives ϕ=1/δ=0.484(4) in three dimensions. Hence, we conclude that in three dimensions these critical exponents indeed differ from the mean-field value of 1/2, as had previously been calculated, but cannot find evidence that they differ from each other. Importantly, we also find no substantive evidence of any nonuniversality in the polymer adsorption transition.

Conformational properties and the entropic barrier in the "head-on" adsorption of a single polymer chain towards a flat surface

This work investigates the change in conformations and the entropic free energy barrier in the "head-on" adsorption process of a flexible polymer chain towards a flat surface in the framework of the Gaussian chain model. Analytical expressions are reported for the distribution of chain end, the mean square end-to-end distance, the entropic free energy barrier and the adsorption equilibrium constant at low surface coverage (the "mushroom" regime). Theoretical results are discussed in the context of polyoxyethylene-phosphonate-type polymer dispersants, possessing a non-adsorbing polyoxyethylene chain and an adsorbing head-group.

Phase transitions in single macromolecules: Loop-stretch transition versus loop adsorption transition in end-grafted polymer chains

We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter ε and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force F applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static behavior and the dynamic behavior of chains with different length N are very well described by a scaling ansatz with the scaling parameters (ε - ε*)N^ϕ (adsorption transition) and (F - F^*)N^ν (loop-stretch transition), respectively, where ϕ is the crossover exponent of the adsorption transition and ν is the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes. This is attributed to the fact that the surface contact dynamics in a strongly adsorbed chain is governed by local processes, whereas the end height relaxation of a strongly stretched chain involves the full spectrum of Rouse modes.

Solvent-dependent critical properties of polymer adsorption

Advanced chain-growth computer simulation methodologies have been employed for a systematic statistical analysis of the critical behavior of a polymer adsorbing at a substrate. We use finite-size scaling techniques to investigate the solvent-quality dependence of critical exponents, critical temperature, and the structure of the phase diagram. Our study covers all solvent effects from the limit of super-self-avoiding walks, characterized by effective monomer-monomer repulsion, to poor solvent conditions that enable the formation of compact polymer structures. The results significantly benefit from taking into account corrections to scaling.

Characterization and optimization of pH-responsive polymer nanoparticles for drug delivery to oral biofilms

We previously reported on cationic, pH-responsive p(DMAEMA)-b-p(DMAEMA-co-BMA-co-PAA) block copolymer micelles with high affinity for dental and biofilm surfaces and efficient anti-bacterial drug release in response to acidic pH, characteristic of cariogenic (tooth-decay causing) biofilm microenvironments. Here, we show that micelle pH-responsive behaviors can be enhanced through alterations in corona:core molecular weight ratios (CCR). Although similarly stable at physiological pH, upon exposure to acidic pH, micelles with CCR of 4.1 were less stable than other CCR examined. Specifically, a ~1.5-fold increase in critical micelle concentration (CMC) and ~50% decrease in micelle diameters were observed for micelles with CCR of 4.1, compared to no changes in micelles with CCR of 0.8. While high CCR was shown to enhance pH-responsive drug release, it did not alter drug loading and dental surface binding of micelles. Diblocks were shown to encapsulate the antibacterial drug, farnesol, at maximal loading capacities of up to ~27 wt% and at >94% efficiencies, independent of CCR or core size, resulting in micelle diameter increases due to contributions of drug volume. Additionally, micelles with small diameters (~17 nm) show high binding capacity to hydroxyapatite and dental pellicle emulating surfaces based on Langmuir fit analyses of binding data. Finally, micelles with high CCR that have enhanced pH-responsive drug release and binding were shown to exhibit greater antibiofilm efficacy in situ. Overall, these data demonstrate how factors essential for nanoparticle carrier (NPC)-mediated drug deliverycan be enhanced via modification of diblock characteristics, resulting in greater antibiofilm efficacy in situ.

Trains, tails and loops of partially adsorbed semi-flexible filaments

Polymer adsorption is a fundamental problem in statistical mechanics that has direct relevance to diverse disciplines ranging from biological lubrication to stability of colloidal suspensions. We combine experiments with computer simulations to investigate depletion induced adsorption of semi-flexible polymers onto a hard-wall. Three dimensional filament configurations of partially adsorbed F-actin polymers are visualized with total internal reflection fluorescence microscopy. This information is used to determine the location of the adsorption/desorption transition and extract the statistics of trains, tails and loops of partially adsorbed filament configurations. In contrast to long flexible filaments which primarily desorb by the formation of loops, the desorption of stiff, finite-sized filaments is largely driven by fluctuating filament tails. Simulations quantitatively reproduce our experimental data and allow us to extract universal laws that explain scaling of the adsorption-desorption transition with relevant microscopic parameters. Our results demonstrate how the adhesion strength, filament stiffness, length, as well as the configurational space accessible to the desorbed filament can be used to design the characteristics of filament adsorption and thus engineer properties of composite biopolymeric materials.

Effects of surface affinity on the ordering dynamics of self-assembled monolayers of chain molecules: Transition from a parallel to a perpendicular structure

The effects of surface interactions on the ordering dynamics of self-assembled monolayers (SAM) of chain molecules were studied using molecular dynamics simulations. When the strength of surface-chain interactions was equal to or less than that of chain-chain interactions, domains of chain molecules adsorbed perpendicular to the surface ("upright" chains) formed on the surface. Although chain molecules adsorbed parallel to the surface ("lying" chains) were initially observed on the surface, they did not develop into two-dimensionally aligned structures. In contrast, when the strength of surface-chain interactions was at least twice that of chain-chain interactions, the proportion of upright chain molecules was initially small, and the reorientation of lying chains was observed shortly afterwards. In this case, the reorientation from lying to upright configuration developed slowly from the domain boundaries of two-dimensionally aligned structures late in the calculation period. Although the orientation processes of chain molecules on surfaces were strongly influenced by the strength of surface-chain interactions, the total adsorption rate on the surface was not. We also analyzed the maximum area of domains formed by lying chains. The development of two-dimensionally aligned domains required strong surface-chain interactions to prevent the spontaneous formation of nuclei of upright domains.

Accuracy of the blob model for single flexible polymers inside nanoslits that are a few monomer sizes wide

The de Gennes' blob model is extensively used in different problems of polymer physics. This model is theoretically applicable when the number of monomers inside each blob is large enough. For confined flexible polymers, this requires the confining geometry to be much larger than the monomer size. In this paper, the opposite limit of polymer in nanoslits with one to several monomers width is studied, using molecular dynamics simulations. Extension of the polymer inside nanoslits, confinement force on the plates, and the effective spring constant of the confined polymer are investigated. Despite the theoretical limitations of the blob model, the simulation results are explained with the blob model very well. The agreement is observed for the static properties and the dynamic spring constant of the polymer. A theoretical description of the conditions under which the dynamic spring constant of the polymer is independent of the small number of monomers inside blobs is given. Our results on the limit of applicability of the blob model can be useful in the design of nanotechnology devices.

Critical adsorption of a single macromolecule in polymer brushes

The adsorption of long flexible macromolecules by polymer brush-coated surfaces is studied by molecular dynamics simulations and by calculations using density functional and self-consistent field theories. The case of repulsive interactions between the substrate surface and the monomers of both the brush polymers and the extra chains that can get absorbed into the brush is considered. Under good solvent conditions, critical absorption can occur, if the interaction between the monomers of the brush polymers and the extra chain is (weakly) attractive. It is shown that it is possible to map out the details of the critical absorption transition, if the chain length and/or the grafting density of the brush polymers are varied. In this way both the strength and the range of the effective adsorption potential of the substrate surface can be controlled. However, it is found that in the general case there is no straightforward mapping of the present problem to the simpler problem of polymer adsorption in a square well potential, in contrast to suggestions in the literature. In particular, it is found that the fraction of monomers of the long free chain that is absorbed in the brush shows a nonmonotonic variation with the grafting density; i.e. from dense brushes free chains are again expelled from their interior. For strong attraction the free chain then gets adsorbed at the brush-solution interface.

Coil-bridge transition in a single polymer chain as an unconventional phase transition: theory and simulation

The coil-bridge transition in a self-avoiding lattice chain with one end fixed at height H above the attractive planar surface is investigated by theory and Monte Carlo simulation. We focus on the details of the first-order phase transition between the coil state at large height H ⩾ Htr and a bridge state at H ⩽ Htr, where Htr corresponds to the coil-bridge transition point. The equilibrium properties of the chain were calculated using the Monte Carlo pruned-enriched Rosenbluth method in the moderate adsorption regime at (H/Na)tr ⩽ 0.27 where N is the number of monomer units of linear size a. An analytical theory of the coil-bridge transition for lattice chains with excluded volume interactions is presented in this regime. The theory provides an excellent quantitative description of numerical results at all heights, 10 ⩽ H/a ⩽ 320 and all chain lengths 40 < N < 2560 without free fitting parameters. A simple theory taking into account the effect of finite extensibility of the lattice chain in the strong adsorption regime at (H/Na)tr ⩾ 0.5 is presented. We discuss some unconventional properties of the coil-bridge transition: the absence of phase coexistence, two micro-phases involved in the bridge state, and abnormal behavior in the microcanonical ensemble.

Exact solution of the thermodynamics and size parameters of a polymer confined to a lattice of finite size: large chain limit

We extend the exact solutions of the Di Marzio-Rubin matrix method for the thermodynamic properties, including chain density, of a linear polymer molecule confined to walk on a lattice of finite size. Our extensions enable (a) the use of higher dimensions (explicit 2D and 3D lattices), (b) lattice boundaries of arbitrary shape, and (c) the flexibility to allow each monomer to have its own energy of attraction for each lattice site. In the case of the large chain limit, we demonstrate how periodic boundary conditions can also be employed to reduce computation time. Advantages to this method include easy definition of chemical and physical structure (or surface roughness) of the lattice and site-specific monomer-specific energetics, and straightforward relatively fast computations. We show the usefulness and ease of implementation of this extension by examining the effect of energy variation along the lattice walls of an infinite rectangular cylinder with the idea of studying the changes in properties caused by chemical inhomogeneities on the surface of the box. Herein, we look particularly at the polymer density profile as a function of temperature in the confined region for very long polymers. One particularly striking result is the shift in the critical condition for adsorption due to surface energy inhomogeneities and the length scale of the inhomogeneities; an observation that could have important implications for polymer chromatography. Our method should have applications to both copolymers and biopolymers of arbitrary molar mass.