DNA on Fluid Membranes: A Model Polymer in Two Dimensions

Adsorption of polyelectrolytes in the presence of varying dielectric discontinuity between solution and substrate

We examine the interactions between polyelectrolytes (PEs) and uncharged substrates under conditions corresponding to a dielectric discontinuity between the aqueous solution and the substrate. To this end, we vary the relevant system characteristics, in particular the substrate dielectric constant ɛs under different salt conditions. We employ coarse-grained molecular dynamics simulations with rodlike PEs in salt solutions with explicit ions and implicit water solvent with dielectric constant ɛw = 80. As expected, at low salt concentrations, PEs are repelled from the substrates with ɛs < ɛw but are attracted to substrates with a high dielectric constant due to image charges. This attraction considerably weakens for high salt and multivalent counterions due to enhanced screening. Furthermore, for monovalent salt, screening enhances adsorption for weakly charged PEs, but weakens it for strongly charged ones. Meanwhile, multivalent counterions have little effect on weakly charged PEs, but prevent adsorption of highly charged PEs, even at low salt concentrations. We also find that correlation-induced charge inversion of a PE is enhanced close to the low dielectric constant substrates, but suppressed when the dielectric constant is high. To explore the possibility of a PE monolayer formation, we examine the interaction of a pair of like-charged PEs aligned parallel to a high dielectric constant substrate with ɛs = 8000. Our main conclusion is that monolayer formation is possible only for weakly charged PEs at high salt concentrations of both monovalent and multivalent counterions. Finally, we also consider the energetics of a PE approaching the substrate perpendicular to it, in analogy to polymer translocation. Our results highlight the complex interplay between electrostatic and steric interactions and contribute to a deeper understanding of PE-substrate interactions and adsorption at substrate interfaces with varying dielectric discontinuities from solution, ubiquitous in biointerfaces, PE coating applications, and designing adsorption setups.

Structure of Strongly Adsorbed Polymer Systems: A Computer Simulation Study

The structure of very thin polymer films formed by strongly adsorbed macromolecules was studied by computer simulation. A coarse-grained model of strictly two-dimensional polymer systems was built, and its properties determined by an efficient Monte Carlo simulation algorithm. Properties of the model system were determined by means of Monte Carlo simulations with a sampling algorithm that combines Verdier-Stockmayer, pivot and reputation moves. The effects of temperature, chain length and polymer concentration on the macromolecular structure were investigated. It was shown that at low temperatures, the chain size increases with the concentration, that is, inversely with high temperatures. This behavior should be explained by the influence of inter-chain interactions.

Equilibrium Conformation of Catenated DNA Networks in Slitlike Confinement

A kinetoplast is a planar network of catenated DNA rings with topology that resembles that of chain mail armor. In this work, we use single-molecule experiments to probe the conformation of kinetoplasts confined to slits. We find that the in-plane size of kinetoplasts increases with degree of confinement, akin to the slitlike confinement of linear DNA. The change in kinetoplast size with channel height is consistent with the scaling prediction from a Flory-type approach for a 2D polymer. With an increase in extent of confinement, the kinetoplasts appear to unfold and take on more uniform circular shapes, in contrast to the broad range of conformations observed for kinetoplasts in bulk.

Modeling hydration-mediated ion-ion interactions in electrolytes through oscillating Yukawa potentials

Classical Poisson-Boltzmann theory represents a mean-field description of the electric double layer in the presence of only Coulomb interactions. However, aqueous solvents hydrate ions, which gives rise to additional hydration-mediated ion-ion interactions. Experimental and computational studies suggest damped oscillations to be a characteristic feature of these hydration-mediated interactions. We have therefore incorporated oscillating Yukawa potentials into the mean-field description of the electric double layer. This is accomplished by allowing the decay length of the Yukawa potential to be complex valued. Ion specificity emerges from assigning individual strengths and phases to the Yukawa potential for anion-anion, anion-cation, and cation-cation pairs as well as for anions and cations interacting with an electrode or macroion. Excluded volume interactions between ions are approximated by replacing the ideal gas entropy by that of a lattice gas. We derive mean-field equations for the Coulomb and Yukawa potentials and use their solutions to compute the differential capacitance for an isolated planar electrode and the pressure that acts between two planar, like-charged macroion surfaces. Attractive interactions appear if the surface charge density of the macroions is sufficiently small.

Lateral diffusion of single polymer molecules at interfaces between water and oil

Lateral diffusion of polymer molecules at the interfaces between immiscible oil and water is investigated at the single molecular level. The interfaces between water and alkanes are chosen as the model systems and polyethylene oxide (PEO) is the model polymer. Fluorescence correlation spectroscopy is used to measure the interfacial diffusion of fluorescence-labeled PEO with its molecular weight ranging over more than an order of magnitude. It is discovered that the interfacial diffusion coefficient scales with the molecular weight by the exponent of -0.5. Detailed analysis shows that the PEO chain takes an ideal two-dimensional random coil conformation at these fluidic interfaces and the bigger contribution from water's hydrodynamic friction is discovered.

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.

Inconsistency of Diffusion and Relaxation of Ring Polymers Adsorbed on Rough Surfaces

We explore the diffusion and relaxation dynamics of a single ring polymer strongly adsorbed on rough surfaces with different roughnesses by means of molecular dynamics simulations. Our simulations demonstrate that on rough surfaces the intrachain topological constraint deriving from the closed architecture induces the inconsistency of diffusion and relaxation of ring polymers. When the lateral chain size is larger than the obstacle distance (2R_g∥,r > d), the ring closure induces the polymers to anchor on a single obstacle and dramatically reduces their diffusivity, where R_g∥,r and d are the lateral components of the mean-square radius of gyration and the obstacle distance, respectively. However, the single obstacle anchoring has no effect on the relaxation of ring polymers, which implies a deviation between the diffusion and the relaxation. With the lateral chain size beyond twice of the obstacle distance (R_g∥,r > d), the ring polymers are totally confined in the array of obstacles and can only diffuse through hopping over the obstacles, resulting in an exponential reduction of their diffusion coefficient. However, the relaxation of ring polymers mainly depends on their rotating reptation and satisfies the reptation-like dynamics, which means that the diffusion and the relaxation are nearly irrelevant. This inconsistency between the diffusion and relaxation is a unique property of adsorbed ring polymers, which would be meaningful to understand the physical nature of polymers with ring closure and significant to develop the corresponding applications.

Long-Lived Self-Entanglements in Ring Polymers

The entanglement of ring polymers remains mysterious in many aspects. In this Letter, we use electric fields to induce self-entanglements in circular DNA molecules, which serve as a minimal system for studying chain entanglements. We show that self-threadings give rise to entanglements in ring polymers and can slow down polymer dynamics significantly. We find that strongly entangled circular molecules remain kinetically arrested in a compact state for very long times, thereby providing experimental evidence for the severe topological constraints imposed by threadings.

Free Energy Landscape and Dynamics of Supercoiled DNA by High-Speed Atomic Force Microscopy

DNA supercoiling fundamentally constrains and regulates the storage and use of genetic information. While the equilibrium properties of supercoiled DNA are relatively well understood, the dynamics of supercoils are much harder to probe. Here we use atomic force microscopy (AFM) imaging to demonstrate that positively supercoiled DNA plasmids, in contrast to their negatively supercoiled counterparts, preserve their plectonemic geometry upon adsorption under conditions that allow for dynamics and equilibration on the surface. Our results are in quantitative agreement with a physical polymer model for supercoiled plasmids that takes into account the known mechanical properties and torque-induced melting of DNA. We directly probe supercoil dynamics using high-speed AFM imaging with subsecond time and ∼nanometer spatial resolution. From our recordings we quantify self-diffusion, branch point flexibility, and slithering dynamics and demonstrate that reconfiguration of molecular extensions is predominantly governed by the bending flexibility of plectoneme arms. We expect that our methodology can be an asset to probe protein-DNA interactions and topochemical reactions on physiological relevant DNA length and supercoiling scales by high-resolution AFM imaging.

Control of Membrane Binding and Diffusion of Cholesteryl-Modified DNA Origami Nanostructures by DNA Spacers

DNA origami nanotechnology is being increasingly used to mimic membrane-associated biophysical phenomena. Although a variety of DNA origami nanostructures has already been produced to target lipid membranes, the requirements for membrane binding have so far not been systematically assessed. Here, we used a set of elongated DNA origami structures with varying placement and number of cholesteryl-based membrane anchors to compare different strategies for their incorporation. Single and multiple cholesteryl anchors were attached to DNA nanostructures using single- and double-stranded DNA spacers of varying length. The produced DNA nanostructures were studied in terms of their membrane binding and diffusion. Our results show that the location and number of anchoring moieties play a crucial role for membrane binding of DNA nanostructures mainly if the cholesteryl anchors are in close proximity to the bulky DNA nanostructures. Moreover, the use of DNA spacers largely overcomes local steric hindrances and thus enhances membrane binding. Fluorescence correlation spectroscopy measurements demonstrate that the distinct physical properties of single- and double-stranded DNA spacers control the interaction of the amphipathic DNA nanostructures with lipid membranes. Thus, we provide a rational basis for the design of amphipathic DNA origami nanostructures to efficiently bind lipid membranes in various environments.

Microscale Objects via Restructuring of Large, Double-Stranded DNA Molecules

As the interest in DNA nanotechnology increases, so does the need for larger and more complex DNA structures. In this work, we describe two methods of using large, double-stranded (ds) DNA to self-assemble sequence-specific, nonrepetitive microscale structures. A model system restructures T7 DNA (40 kb) through sequence-specific biotinylation followed by intramolecular binding to a 40 nm diameter neutravidin bead to create T7 "rosettes". This model system informed the creation of "nodal DNA" where "nodes" with single-stranded DNA flaps are attached to a large dsDNA insert so that a complementary oligonucleotide "strap" bridges the two nodes for restructuring to form a DNA "bolo". To do this in high yield, several methodologies were developed, including a protection/deprotection scheme using RNA/RNase H and dialysis chambers, which remove excess straps while retaining large DNA molecules. To assess these restructuring processes, the DNA was adsorbed onto supported lipid bilayers, allowing for a visual assay of their structure using single-molecule fluorescence microscopy. Good agreement between the expected and observed fluorescence intensity measurements of the individual features of restructured DNA for both the DNA rosettes and bolos gives us a high degree of confidence that both processes give sequence-specific restructuring of large, dsDNA molecules to create microscale objects.

Investigation of nematic to smectic phase transition and dynamical properties of strongly confined semiflexible polymers using Langevin dynamics

We investigated the nematic to smectic phase transition for strongly confined semiflexible polymer solutions in slit-like confinements using GPU-accelerated Langevin dynamics. We characterized the phase transitions from the nematic to smectic phases for semi-flexible polymer solutions as the polymer density increased. The dependence for the lyotropic nematic to smectic transition can be collapsed by scaling exponents between 0.2 and 0.3. The smectic C phase is found for all the cases with the polymer orientation director tilted with respect to smectic layer lateral alignment. As the chain rigidity increases, the transition density decreases for systems in which the polymer persistence length (P) to slit height (H) ratios are 1.25, 2.5, 3.75, 5 and 25. We also characterized the polymer dynamics for the isotropic-nematic-smectic transitions. The overall polymer diffusivity decreased steadily as the polymer density increased. We observed anomalous polymer diffusion along the nematic director near the isotropic-nematic transition, similar to previously reported behavior for nematic-forming ellipsoids. Polymer diffusivity decreased sharply by two orders of magnitude upon the nematic-smectic transition.

Effects of surface roughness on the self-diffusion dynamics of a single polymer

We employ molecular dynamics simulations to simulate the diffusion dynamics of a single polymer adsorbed on surfaces with different roughnesses, which are characterized by the separation distance between obstacles and the height of obstacles. Our simulations demonstrate that for strong adsorption and when the confinement of obstacles is strong enough for all chains, the scaling exponent α of the diffusion coefficient on the chain length exhibits three cases with increase of the height of obstacles: a Rouse plateau with α ≈ -1 (the lateral motion of the polymer chains is free), a reptationlike plateau with α ≈ -1.5 (the polymer chains can hardly stride over the obstacles in the perpendicular direction) and a transition from the Rouse plateau to the reptationlike plateau with -1.5 < α < -1 (the obstacles hinder the lateral motion of the polymer chains). However, with increase of the separation distance between obstacles, the confinement from the obstacles exhibits a decrease (more lateral motions of the polymer chains are allowed), which results in a higher plateau (no longer separate reptationlike dynamics). Our results clarify the effects of surface roughness on the diffusion mechanism of polymer chains strongly adsorbed on solid surfaces in dilute solutions and the resulting transition mechanism from the Rouse scaling to the reptationlike scaling, which is significant for the understanding of the physical nature and the development of the corresponding applications.

Adsorption of charged macromolecules upon multicomponent responsive surfaces

A predictive model for polyelectrolyte adsorption upon responsive surfaces is presented, decoupling the effect of surface charges and crowders.

Smectic C and Nematic Phases in Strongly Adsorbed Layers of Semiflexible Polymers

Molecular dynamics simulations of semiflexible polymers in a good solvent reveal a dense adsorbed layer when the solution is exposed to an attractive planar wall. This layer exhibits both a nematic and a smectic phase (smA for short and smC for longer chains) with bond vectors aligned strictly parallel to the wall. The tilt angle of the smC phase increases strongly with the contour length of the polymers. The isotropic-nematic transition is a Kosterlitz-Thouless transition and also the nematic-smectic transition is continuous. Our finding demonstrates thus a two-dimensional realization of different liquid crystalline phases, ubiquitous in three dimensions, that occurs in a single monomolecular layer ordered at least over mesoscopic scales.

Monte Carlo studies of two-dimensional polymer-solvent systems

The static properties of two-dimensional athermal polymer solutions were studied by performing Monte Carlo lattice simulations using the cooperative motion algorithm (CMA) and taking into account the presence of explicit solvent molecules. The simulations were performed for a wide range of polymer chain lengths N (16–1024) and concentrations φ (0.0156–1). The results obtained for short chains (N < 256) were in good agreement with those given by previous simulations. For the longest chains (512 or 1024 beads), some unexpected behavior was observed in the dilute and semidilute regimes. A pronounced change in the concentration dependence of chain size and shape was observed below a certain critical concentration (0.6 for the longest chains under consideration, consisting of 1024 beads). Longer chains became more extended below this concentration. The behavior of the single-chain structure factor confirmed these changes in the fractal dimension of the chain as a function of the concentration. The observed phenomena are related to the excluded volume of solvent molecules, which causes the chain statistics to be modified in the vicinity of other chains; this effect is important in strictly 2D systems.

Graphical abstract

Kinetics of polymer collapse: effect of temperature on cluster growth and aging

Using state of the art Monte Carlo simulations of a bead-spring model we investigate both the equilibrium and the nonequilibrium behavior of the homopolymer collapse. The equilibrium properties obtained via multicanonical sampling recover the well-known finite-size scaling behavior of collapse for our model polymer. For the nonequilibrium dynamics we study the collapse by quenching the homopolymer from an expanded coiled state into the globular phase. The sequence of events observed during the collapse is independent of the quench depth. In particular, we focus on finding out universal scaling behaviors related to the growth or coarsening of clusters of monomers, by drawing phenomenological analogies with ordering kinetics. We distinguish the cluster coarsening stage from the initial stage of primary cluster formation. By successful application of a nonequilibrium finite-size scaling analysis we show that at all quench temperatures, during the coarsening stage, the cluster growth is roughly linear and can be characterised by a universal finite-size scaling function. In addition, we provide evidence of aging by constructing a suitable autocorrelation function and its corresponding dynamical power-law scaling with respect to the growing cluster sizes. The predicted theoretical bound for the exponent governing such scaling is strictly obeyed by the numerical data irrespective of the quench temperature. The results and methods presented here in general should find application in similar phenomena such as the collapse of a protein molecule preceding its folding.

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.

Nanoscale topography influences polymer surface diffusion

Using high-throughput single-molecule tracking, we studied the diffusion of poly(ethylene glycol) chains at the interface between water and a hydrophobic surface patterned with an array of hexagonally arranged nanopillars. Polymer molecules displayed anomalous diffusion; in particular, they exhibited intermittent motion (i.e., immobilization and "hopping") suggestive of continuous-time random walk (CTRW) behavior associated with desorption-mediated surface diffusion. The statistics of the molecular trajectories changed systematically on surfaces with pillars of increasing height, exhibiting motion that was increasingly subdiffusive and with longer waiting times between diffusive steps. The trajectories were well-described by kinetic Monte Carlo simulations of CTRW motion in the presence of randomly distributed permeable obstacles, where the permeability (the main undetermined parameter) was conceptually related to the obstacle height. These findings provide new insights into the mechanisms of interfacial transport in the presence of obstacles and on nanotopographically patterned surfaces.

Modeling DNA condensation on freestanding cationic lipid membranes

Motivated by recent experimental observations of a rapid spontaneous DNA coil-globule transition on freestanding cationic lipid bilayers, we propose simple theoretical models for DNA condensation on cationic lipid membranes. First, for a single DNA rod, we examine the conditions of full wrapping of a cylindrical DNA-like semi-flexible polyelectrolyte by an oppositely charged membrane. Then, for two parallel DNA rods, we self-consistently analyze the shape and the extent of the membrane enveloping them, focusing on membrane elastic deformations and the membrane-DNA embracing angle, which enables us to compute the membrane-mediated DNA-DNA interactions. We examine the effects of the membrane composition and its charge density, which are the experimentally tunable parameters. We show that membrane-driven rod-rod attraction is more pronounced for higher charge densities and for smaller surface tensions of the membrane. Thus, we demonstrate that for a long DNA chain adhered to a cationic lipid membrane, such membrane-induced DNA-DNA attraction can trigger compaction of DNA.

Localization and stretching of polymer chains at the junction of two surfaces

We present a molecular dynamics study on the stretching of a linear polymer chain that is adsorbed at the junction of two intersecting flat surfaces of varying alignments. We observe a transition from a two-dimensional to one-dimensional (1D) structure of the adsorbed polymer when the alignment, i.e., the angle between the two surfaces that form a groove, θ, is below 135°. We show that the radius of gyration of the polymer chain Rg scales as Rg ∼ N(3/4) with the degree of polymerization N for θ = 180° (planer substrate), and the scaling changes to Rg ∼ N(1.0) for θ < 135° in good solvents. At the crossover point, θ = 135°, the exponent becomes 1.15. The 1D stretching of the polymer chain is found to be 84% of its contour length for θ ⩽ 90°. The center of mass diffusion coefficient D decreases sharply with θ. However, the diffusion coefficient scales with N as D ∼ N(-1), and is independent of θ. The relaxation time τ, for the diffusive motion, scales as τ ∼ N(2.5) for θ = 180° (planar substrate), which changes to τ ∼ N(3.0) for θ ⩽ 90°. At the crossover point, the exponent is 3.4, which is slightly higher than the 1D value of 3.0. Further, a signature of reptation-like dynamics of the polymer chain is observed at the junction for θ ⩽ 90° due to its strong 1D localization and stretching.

Concerted spatio-temporal dynamics of imported DNA and ComE DNA uptake protein during gonococcal transformation

Competence for transformation is widespread among bacterial species. In the case of Gram-negative systems, a key step to transformation is the import of DNA across the outer membrane. Although multiple factors are known to affect DNA transport, little is known about the dynamics of DNA import. Here, we characterized the spatio-temporal dynamics of DNA import into the periplasm of Neisseria gonorrhoeae. DNA was imported into the periplasm at random locations around the cell contour. Subsequently, it was recruited at the septum of diplococci at a time scale that increased with DNA length. We found using fluorescent DNA that the periplasm was saturable within minutes with ∼40 kbp DNA. The DNA-binding protein ComE quantitatively governed the carrying capacity of the periplasm in a gene-dosage-dependent fashion. As seen using a fluorescent-tagged derivative protein, ComE was homogeneously distributed in the periplasm in the absence of external DNA. Upon addition of external DNA, ComE was relocalized to form discrete foci colocalized with imported DNA. We conclude that the periplasm can act as a considerable reservoir for imported DNA with ComE governing the amount of DNA stored potentially for transport through the inner membrane.

Bacterial transformation is the import and inheritable integration of external DNA. As such, it is believed to be a major evolutionary force. A key step is the import of DNA through the outer membrane. Here, we have characterized the spatio-temporal dynamics of DNA during import and residence in the periplasm of the Gram-negative pathogen Neisseria gonorrhoeae. We found that the periplasm can serve as a reservoir for imported DNA that can fill within five minutes by importing DNA from the environment. The amount of imported DNA roughly corresponds to the size of a phage genome. The periplasmic DNA-binding protein ComE is homogeneously distributed in the periplasm in the absence of extracellular DNA. It relocates rapidly to imported DNA when external DNA is added to competent gonococci. As ComE governs the carrying capacity of the periplasm, we propose that it might condense DNA, thus linking DNA uptake to its compaction. Although the import through the outer membrane was localized all around the cell contour, the major part of the imported DNA relocated to the septum at the center of diplococci. Our findings strongly support the idea that the periplasm masses DNA independently of transport through the inner membrane.

Methods for modeling cytoskeletal and DNA filaments

This review summarizes the models that researchers use to represent the conformations and dynamics of cytoskeletal and DNA filaments. It focuses on models that address individual filaments in continuous space. Conformation models include the freely jointed, Gaussian, angle-biased chain (ABC), and wormlike chain (WLC) models, of which the first three bend at discrete joints and the last bends continuously. Predictions from the WLC model generally agree well with experiment. Dynamics models include the Rouse, Zimm, stiff rod, dynamic WLC, and reptation models, of which the first four apply to isolated filaments and the last to entangled filaments. Experiments show that the dynamic WLC and reptation models are most accurate. They also show that biological filaments typically experience strong hydrodynamic coupling and/or constrained motion. Computer simulation methods that address filament dynamics typically compute filament segment velocities from local forces using the Langevin equation and then integrate these velocities with explicit or implicit methods; the former are more versatile and the latter are more efficient. Much remains to be discovered in biological filament modeling. In particular, filament dynamics in living cells are not well understood, and current computational methods are too slow and not sufficiently versatile. Although primarily a review, this paper also presents new statistical calculations for the ABC and WLC models. Additionally, it corrects several discrepancies in the literature about bending and torsional persistence length definitions, and their relations to flexural and torsional rigidities.

Strictly two-dimensional self-avoiding walks: thermodynamic properties revisited

The density crossover scaling of various thermodynamic properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse-grained bead-spring model. In the semidilute regime we confirm over an order of magnitude of the monomer density ρ the expected power law scaling for the interaction energy between different chains e(int) ~ ρ(21/8), the total pressure P ~ ρ(3) and the dimensionless compressibility g(T) = lim(q→0)S(q) ~ 1/ρ(2). Various elastic contributions associated to the affine and non-affine response to an infinitesimal strain are analyzed as functions of density and sampling time. We show how the size ξ(ρ) of the semidilute blob may be determined experimentally from the total monomer structure factor S(q) characterizing the compressibility of the solution at a given wave vector q. We comment briefly on finite persistence length effects.

MOLECULAR DYNAMICS SIMULATION OF THE ADSORPTION AND DIFFUSION OF A SINGLE POLYDIMETHYLSILOXANE POLYMER CHAIN ON A SILICON (111) SURFACE

The adsorption of polydimethylsiloxane (PDMS) single chain with different chain lengths on a silicon (111) surface were studied by molecular dynamics simulations. The relative dielectric constant was selected to be 1 and 78.0 to mimic in vacuum and in solution environment, respectively. The chains were all present as two-dimensional (2D) adsorption conformation on the surface but different conformations and dynamic properties were found in the two absolutely different environments. The relationship between the adsorption energy of the different chain lengths and the degree of polymerization follows a linear function and the average adsorption energy per segment is -0.42 kcal/mol. In addition, the diffusion coefficient (D) of such chains scales with the degree of polymerization (N) as N-3/2.

Visualization of two-dimensional single chain conformations solubilized in a miscible polymer blend monolayer by atomic force microscopy

Polymer Langmuir monolayers spread on a water surface are one of the best models for two-dimensional (2D) polymer and have been extensively studied. However, the most fundamental issue in understanding a 2D film, the polymer chain packing in the film, is still not well-understood, especially from the experimental point of view. Direct observation of the chain packing by microscopy at a molecular level, such as by atomic force microscopy (AFM), might be one of the most promising ways to study this issue; however, because of the limited resolution of the method, the chain packing of polymer cannot be resolved by AFM, except for especially large polymers. Here, we show that a mixed monolayer of vinyl polymers, poly(methyl methacrylate) (PMMA) and poly(n-nonyl acrylate) (PNA), was miscible at a low surface pressure, and if a small amount of PMMA chains was solubilized in a PNA monolayer, the isolated PMMA chains in the PNA monolayer were, for the first time, successfully visualized by AFM with a clear contrast, which originated from a difference of rigidities of the polymers due to their different glass transition temperatures (105 °C(PMMA) and -89 °C(PNA)). The PMMA chains were found to strongly interpenetrate into the PNA monolayer, with a radius of gyration (R(g(PMMA))) that was several times larger than that of the 2D ideal chain (segregated-chain). Furthermore, the radius scaled with the molecular weight of the PMMA (M(PMMA)) as R(g(PMMA)) ∝ M(PMMA)(0.63), which was between the scaling of the 2D ideal chain (segregated chain), R(g) ∝ M(0.5), and the 2D chain in good solvent, R(g) ∝ M(0.75). On the other hand, R(g(PMMA)) was independent of the molecular weight of the PNA matrix over a wide range. These results indicate that the PNA/PMMA monolayer is a strongly miscible system, although the R(g(PMMA)) scaling with M(PMMA) (0.63) is somewhat smaller than that expected for a 2D chain in good solvent systems (0.75). The generation of molecular level information by direct observation of polymer chains in 2D blend films should improve our understanding of polymer 2D films.

ADSORPTION AND DIFFUSION PROCESSES OF POLYETHYLENE ON SILICON (111) SURFACE STUDIED BY MOLECULAR DYNAMICS SIMULATION

The adsorption of polyethylene with different chain lengths on a silicon (111) surface is studied via molecular dynamics simulations. The relative dielectric constant is selected to be 1 and 78.0 to mimic in vacuum and in solution environment, respectively. Different configurations and dynamic properties are found in the two absolutely different environments, showing that the solvent condition plays an obvious role in the process of chain adsorption and diffusion on the hydrophobic surface. The chain all present as two-dimensional (2D) adsorption configuration on the surface. The adsorption energy of different chain lengths follows a linear function, and the average adsorption energy per segment is -1.58 kcal/mol. In addition, the diffusion coefficient (D) of such chains scales with the degree of polymerization (N) as N-3/2.

Conformation of ring polymers in 2D constrained environments

The combination of ring closure and spatial constraints has a fundamental effect on the statistics of semiflexible polymers such as DNA. However, studies of the interplay between circularity and constraints are scarce and single-molecule experimental data concerning polymer conformations are missing. By means of atomic force microscopy we probe the conformation of circular DNA molecules in two dimensions and in the concentrated regime (above the overlap concentration c*). Molecules in this regime experience a collapse, and their statistical properties agree very well with those of simulated vesicles under pressure. Some circular molecules also create confining regions in which other molecules are trapped. Thus we show further that spatially confined molecules fold into specific conformations close to those found for linear chains, and strongly dependent on the size of the confining box.

Dynamics of a polymer chain confined in a membrane

We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free-membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical structure factor. For large polymer size, both quantities show Zimm-like behavior in the free-membrane case, whereas they are Rouse-like for the sandwiched membrane geometry. We use the scaling argument to discuss the effect of excluded-volume interactions on the polymer relaxation time.

Polyelectrolyte condensation in bulk, at surfaces, and under confinement

In this review we discuss recent results from computer simulations based on coarse-grained polyion models representing aqueous solutions of polyelectrolytes. The focus will be directed to the conformation of the polyions and, in particular, their condensation in bulk, induced by multivalent ions and oppositely charged polyelectrolytes, at responsive surfaces and under confinement.