Adsorption study on the formation of interfacial layers based on birch glucuronoxylans

Glucuronoxylans (GX), particularly crude fractions obtained by pressurized hot water extraction of birch wood, act as potent emulsifiers and stabilizers against physical separation and lipid oxidation. Herein, we studied the adsorption of GX on hydrophobic interfaces to correlate their multicomponent character towards the formation of interfacial layers in emulsions. Dynamic interfacial tension (DIFT) and quartz crystal microgravimetry with dissipation monitoring (QCM-D) were applied to various GX fractions and the results compared with those from cellulose-based emulsifiers. The roles of residual lignin and polysaccharides are discussed considering the formation of interfacial layers during emulsification. The DIFT of the different GXs reached quasi-equilibrium faster as the lignin concentration increased, implying a correlation between the rate of adsorption and the residual lignin content. The effect of NaCl addition was more pronounced in polysaccharide-rich fractions, indicating that the polysaccharide fraction modulated the effect of ionic strength. QCM-D showed that despite the fast adsorption exhibited by the lignin-rich GX extract in the DIFT curves, the adsorbed materials were lightweight, suggesting that the polysaccharide fraction built the bulk of the interfacial layer. These results provide a foundation towards understanding the role of GX in interfacial stabilization beyond traditional plant-based counterparts.

Nanoscopic Interfacial Hydrogel Viscoelasticity Revealed from Comparison of Macroscopic and Microscopic Rheology

Deviations between macrorheological and particle-based microrheological measurements are often considered to be a nuisance and neglected. We study aqueous poly(ethylene oxide) (PEO) hydrogels for varying PEO concentrations and chain lengths that contain microscopic tracer particles and show that these deviations reveal the nanoscopic viscoelastic properties of the particle-hydrogel interface. Based on the transient Stokes equation, we first demonstrate that the deviations are not due to finite particle radius, compressibility, or surface-slip effects. Small-angle neutron scattering rules out hydrogel heterogeneities. Instead, we show that a generalized Stokes-Einstein relation, accounting for an interfacial shell around tracers with viscoelastic properties that deviate from bulk, consistently explains our macrorheological and microrheological measurements. The extracted shell diameter is comparable to the PEO end-to-end distance, indicating the importance of dangling chain ends. Our methodology reveals the nanoscopic interfacial rheology of hydrogels and is applicable to different kinds of viscoelastic fluids and particles.

Influence of Polymer Molecular Weight on Chain Conformation at the Polystyrene/Silver Interface

The dependence between the conformation of polystyrene (PS) and its molecular weight (Mw) in the vicinity of a metal interface was investigated by sum frequency generation (SFG) spectroscopy. Tilt angles θ ≥ 50^° (the angle between the C₂ axis of the pendant phenyl ring and the surface normal) were observed for all samples because of the interaction between the aromatic rings and the metal surface. Furthermore, it was found that θ decreases with increasing Mw for PS samples ranging from 20 × 10³ g/mol to 400 × 10³ g/mol. The intensity of the backbone SFG signal was higher for high Mw PS, compared to low Mw PS, indicating a greater number of backbone interactions with the silver substrate surface for the high Mw sample. These structural differences are driven by different entropic and enthalpic contributions to the free energy of adsorption for different polymer molecular weights. Differences in the polymer free volume and in the relative amount of chain ends with higher mobility may also influence the chain conformation. These results suggest that important interfacial properties of polymeric thin films, such as adhesion and wettability, could be tailored by modifying the polymer Mw to achieve the desired interfacial conformation.

Modeling the Protective Role of Bacterial Lipopolysaccharides against Membrane-Rupturing Peptides

Lipopolysaccharide (LPS) is a key surface component of Gram-negative bacteria, populating the outer layer of their outer membrane. A number of experimental studies highlight its protective role against harmful molecules such as antibiotics and antimicrobial peptides (AMPs). In this work, we present a theoretical model for describing the interaction between LPS and cationic antimicrobial peptides, which combines the following two key features. The polysaccharide part is viewed as forming a polymer brush, exerting an osmotic pressure on inclusions such as antimicrobial peptides. The charged groups on LPS (those in lipid A and the two Kdo groups in the inner core) form electrostatic binding sites for cationic AMPs or cations. Using the resulting model, we offer a quantitative picture of how the brush component enhances the protective role of LPS against magainin-like peptides, in the presence of divalent cations such as Mg²⁺. The LPS brush tends to diminish the interfacial binding of the peptides, at the lipid headgroup region, by about 30%. In the presence of 5 mM of Mg²⁺, the interfacial binding does not reach a threshold value for wild-type LPS, beyond which the LPS layer is ruptured, even though it does for LPS Re (the simplest form of LPS, lacking the brush part), as long as [AMP] ≤ 20 μM, where [AMP] is the concentration of AMPs. At a low concentration of Mg²⁺ (≈1 mM), however, a smaller [AMP] value (≳2 μM) is needed to reach the threshold coverage for wild-type LPS. Our results also suggest that the interfacial binding of peptides is insensitive to their possible weak interaction with the surrounding brush chains.

Effect of surface properties and polymer chain length on polymer adsorption in solution

In polymer nanoparticle composites (PNCs) with attractive interactions between nanoparticles (NPs) and polymers, a bound layer of the polymer forms on the NP surface, with significant effects on the macroscopic properties of the PNCs. The adsorption and wetting behaviors of polymer solutions in the presence of a solid surface are critical to the fabrication process of PNCs. In this study, we use both classical density functional theory (cDFT) and molecular dynamics (MD) simulations to study dilute and semi-dilute solutions of short polymer chains near a solid surface. Using cDFT, we calculate the equilibrium properties of polymer solutions near a flat surface while varying the solvent quality, surface-fluid interactions, and the polymer chain lengths to investigate their effects on the polymer adsorption and wetting transitions. Using MD simulations, we simulate polymer solutions near solid surfaces with three different curvatures (a flat surface and NPs with two radii) to study the static conformation of the polymer bound layer near the surface and the dynamic chain adsorption process. We find that the bulk polymer concentration at which the wetting transition in the poor solvent system occurs is not affected by the difference in surface-fluid interactions; however, a threshold value of surface-fluid interaction is needed to observe the wetting transition. We also find that with good solvent, increasing the chain length or the difference in the surface-polymer interaction relative to the surface-solvent interaction increases the surface coverage of polymer segments and independent chains for all surface curvatures. Finally, we demonstrate that the polymer segmental adsorption times are heavily influenced only by the surface-fluid interactions, although polymers desorb more quickly from highly curved surfaces.

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.

Multichain adsorption at fluid interfaces: Amphiphilic homopolymers vs copolymers

HYPOTHESIS

At selective liquid-liquid interface, amphiphilic homopolymers, having groups with different affinity for the liquids in each monomer unit, would demonstrate higher occupation of the interfacial layer than copolymers with various distributions of groups and be advantageous as interface stabilizers.

EXPERIMENTS

By means of Langevin dynamics computer simulation, conformations of multiple chains of amphiphilic macromolecules adsorbed at the liquid-liquid interface were studied. Monomer units having different affinity for the liquids were distributed variously along the polymer chains. Homopolymers, amphiphilic at the level of an individual monomer unit, and copolymers with random, altermating and multiblock distribution of groups were considered. The surface coverage, structure of the layer, and spatial distribution of monomer units were investigated depending on the polymer concentration.

FINDINGS

Compared to copolymers with random, alternating and multiblock distributions of the groups, the interfacial layer concentration of amphiphilic homopolymer is about 1.5 times higher, the adsorbed layer is remarkably thinner, has membrane-like structure and is asymmetric with respect to interface boundary. Also, the adsorbed amphiphilic homopolymers form fewer loops and tails, most located on one side of the interface. This combination of properties is promising for practical application in modern self-assembling molecular devices.

Adsorption of polypropylene oxide-polyethylene oxide type surfactants at surfaces of pharmaceutical relevant materials: effect of surface energetics and surfactant structures

Protein therapeutics are exposed to various surfaces during product development, where their adsorption possibly causes unfolding, denaturation, and aggregation. In this paper, we aim to characterize four types of typical surfaces used in the development of biologics: polycarbonate, polyethersulfone, borosilicate glass, and cellulose. Contact angles of these surfaces were measured using three probing liquids: water, formamide, and diidomethane, from which acid/base (AB) and Lifshitz-van der Waals (LW) interaction components were derived. To explore the interactions of surfactants of Pluronics/Poloxamers (PEO-PPO-PEO copolymers) with these surfaces, the adsorption of three Pluronics (F68, F127, and L44) at these surfaces was determined using a quartz crystal microbalance with dissipation technique (QCM-D). For hydrophobic surfaces without AB component (polycarbonate and polyethersulfone), these copolymers exhibited significant adsorption with a little dissipation at low concentrations. For hydrophilic surfaces with AB component (cellulose and borosilicate), the adsorption at low-surfactant concentration is low while dissipation is relatively high. Additionally, the chemical properties of Pluronics such as the ratio of PPO to PEO, along with the interaction of PPO with surfaces were observed to play a critical role in adsorption. Furthermore, the interfacial structure of the adsorbed layer was affected by both AB interaction and the presence of PEO block.

Drastic Swelling of Lipid Oligobilayers by Polyelectrolytes: A Potential Molecular Model for the Internal Structure of Lubricating Films in Mammalian Joints

Osteoarthritis is the most common arthropathy in western civilization. It is primarily caused by the degeneration of lipid-coated cartilage, leading to increased friction in joints. Hyaluronic acid (HA), a negatively charged polysaccharide and the main component of the synovial fluid, is held responsible for joint lubrication. It is believed that HA, adsorbed to the lipid-coated cartilage, forms a protective layer against wear. Studies have shown that the concentration and molecular weight (MW) of HA are reduced in joints suffering from osteoarthritis. On the basis of these observations, local joint injections of HA or mixtures of HA and surface-active phospholipids (SAPLs) have been applied as medical cures to restore the functionality of the joints in a procedure called viscosupplementation. However, this cure is still disputed, and no consensus has been reached with respect to optimum HA concentration and MW. To provide detailed insight in the structural rearrangement of lipid films upon contact with HA or polymeric analogues, we studied the interaction of the polyelectrolyte poly(allylamine hydrochloride) (PAH) with surface-bound oligobilayers of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) by neutron reflectivity (NR) and ellipsometry. Using this model system, we found a drastic swelling of the lipid films as a function of PAH concentration, whose strength compares to that in previous studies on HA incubation. In contrast, no significant dependence of film thickness on PAH MW was observed. A detailed picture of the film architecture was developed which inter alia shows that charged PAH is adsorbed to the lipid headgroups, leading to electrostatic repulsion. The swelling behavior is well explained by the equilibrium of Coulomb and van der Waals interactions in a DLVO-based model. Our detailed structural analysis of the PAH/lipid interfacial layer may help to elucidate the mechanisms of viscosupplementation and derive a structure-function relationship for the lubricating interface in mammalian joints.

Tuning Adsorption Duration To Control the Diffusion of a Nanoparticle in Adsorbing Polymers

Controlling the nanoparticle (NP) diffusion in polymers is a prerequisite to obtain polymer nanocomposites (PNCs) with desired dynamical and rheological properties and to achieve targeted delivery of nanomedicine in biological systems. Here we determine the suppression mechanism of direct NP-polymer attraction to hamper the NP mobility in adsorbing polymers and then quantify the dependence of the effective viscosity η_eff felt by the NP on the adsorption duration τ_ads of polymers on the NP using scaling theory analysis and molecular dynamics simulations. We propose and confirm that participation of adsorbed chains in the NP motion break up at time intervals beyond τ_ads due to the rearrangement of polymer segments at the NP surface, which accounts for the onset of Fickian NP diffusion on a time scale of t ≈ τ_ads. We develop a power law, η_eff ∼ (τ_ads)^ν, where ν is the scaling exponent of the dependence of polymer coil size on the chain length, which leads to a theoretical basis for the design of PNCs and nanomedicine with desired applications through tuning the polymer adsorption duration.

A theoretical study of dispersion-to-aggregation of nanoparticles in adsorbing polymers using molecular dynamics simulations

The properties of polymer-nanoparticle (NP) mixtures significantly depend on the dispersion of the NPs. Using molecular dynamics simulations, we demonstrate that, in the presence of polymer-NP attraction, the dispersion of NPs in semidilute and concentrated polymers can be stabilized by increasing the polymer concentration. A lower polymer concentration facilitates the aggregation of NPs bridged by polymer chains, as well as a further increase of the polymer-NP attraction. Evaluating the binding of NPs through shared polymer segments in an adsorption blob, we derive a linear relationship between the polymer concentration and the polymer-NP attraction at the phase boundary between dispersed and aggregated NPs. Our theoretical findings are directly relevant for understanding and controlling many self-assembly processes that use either dispersion or aggregation of NPs to yield the desired materials.

Chelating effect in short polymers for the design of bidentate binders of increased affinity and selectivity

The design of new strong and selective binders is a key step towards the development of new sensing devices and effective drugs. Both affinity and selectivity can be increased through chelation and here we theoretically explore the possibility of coupling two binders through a flexible linker. We prove the enhanced ability of double binders of keeping their target with a simple model where a polymer composed by hard spheres interacts with a spherical macromolecule, such as a protein, through two sticky spots. By Monte Carlo simulations and thermodynamic integration we show the chelating effect to hold for coupling polymers whose radius of gyration is comparable to size of the chelated particle. We show the binding free energy of flexible double binders to be higher than that of two single binders and to be maximized when the binding sites are at distances comparable to the mean free polymer end-to-end distance. The affinity of two coupled binders is therefore predicted to increase non linearly and in turn, by targeting two non-equivalent binding sites, this will lead to higher selectivity.

Strong Selective Adsorption of Polymers

A scaling theory is developed for selective adsorption of polymers induced by the strong binding between specific monomers and complementary surface adsorption sites. By "selective" we mean specific attraction between a subset of all monomers, called "sticky", and a subset of surface sites, called "adsorption sites". We demonstrate that, in addition to the expected dependence on the polymer volume fraction ϕ_bulk in the bulk solution, selective adsorption strongly depends on the ratio between two characteristic length scales, the root-mean-square distance l between neighboring sticky monomers along the polymer, and the average distance d between neighboring surface adsorption sites. The role of the ratio l/d arises from the fact that a polymer needs to deform to enable the spatial commensurability between its sticky monomers and the surface adsorption sites for selective adsorption. We study strong selective adsorption of both telechelic polymers with two end monomers being sticky and multisticker polymers with many sticky monomers between sticky ends. For telechelic polymers, we identify four adsorption regimes at l/d < 1 that are characterized by the fraction of occupied adsorption sites and whether the dominant conformation of adsorbed chains is a single-end-adsorbed "mushroom" or double-end-adsorbed loop. For l/d > 1, we expect that the adsorption layer at exponentially low ϕ_bulk consists of separated unstretched loops, while as ϕ_bulk increases the layer crosses over to a brush of extended loops with a second layer of weakly overlapping tails. For multisticker chains, in the limit of exponentially low ϕ_bulk, adsorbed polymers are well separated from each other. As l/d increases, the conformation of an individual polymer changes from a single-end-adsorbed "mushroom" to a random walk of loops. For high ϕ_bulk, adsorbed polymers at small l/d are mushrooms that cover all the adsorption sites. At sufficiently large l/d, adsorbed multisticker polymers strongly overlap. We anticipate the formation of a self-similar carpet and with increasing l/d a two-layer structure with a brush of loops covered by a self-similar carpet. As l/d exceeds the threshold determined by the adsorption energy, the brush of loops under the carpet reaches a saturated state, resulting in a l/d-independent brush-under-carpet structure, which can also be applied to describe adsorbed multisticker polymers in nonselective adsorption where a sticker can strongly bind to any place on the adsorption surface. We examine the adsorbed amount Γ of multisticker polymers in different regimes for selective adsorption. If the adsorbed multisticker polymers are nonoverlapping mushrooms, the adsorbed amount Γ increases linearly with the surface density of adsorption sites Σ ≈ 1/d². In the self-similar carpet regime, Γ increases sublinearly as Σ^0.15 in a good solvent, while only logarithmically in a theta solvent. Formation of a brush layer under the carpet contributes an additional adsorbed amount. This additional amount increases linearly with Σ and eventually dominates the overall adsorbed amount Γ before saturating at a plateau value controlled by the adsorption energy.

Adsorption of branched and dendritic polymers onto flat surfaces: a Monte Carlo study

Using Monte Carlo simulations based on the bond fluctuation model we study the adsorption of starburst dendrimers with flexible spacers onto a flat surface. The calculations are performed for various generation number G and spacer length S in a wide range of the reduced temperature τ as the measure of the interaction strength between the monomers and the surface. Our simulations indicate a two-step adsorption scenario. Below the critical point of adsorption, τc, a weakly adsorbed state of the dendrimer is found. Here, the dendrimer retains its shape but sticks to the surface by adsorbed spacers. By lowering the temperature below a spacer-length dependent value, τ*(S) < τc, a step-like transition into a strongly adsorbed state takes place. In the flatly adsorbed state the shape of the dendrimer is well described by a mean field model of a dendrimer in two dimensions. We also performed simulations of star-polymers which display a simple crossover-behavior in full analogy to linear chains. By analyzing the order parameter of the adsorption transition, we determine the critical point of adsorption of the dendrimers which is located close to the critical point of adsorption for star-polymers. While the order parameter for the adsorbed spacers displays a critical crossover scaling, the overall order parameter, which combines both critical and discontinuous transition effects, does not display simple scaling. The step-like transition from the weak into the strong adsorbed regime is confirmed by analyzing the shape-anisotropy of the dendrimers. We present a mean-field model based on the concept of spacer adsorption which predicts a discontinuous transition of dendrimers due to an excluded volume barrier. The latter results from an increased density of the dendrimer in the flatly adsorbed state which has to be overcome before this state is thermodynamically stable.

Polymer-induced inverse-temperature crystallization of nanoparticles on a substrate

Using molecular dynamics simulations, we study the properties of liquid state polymer-nanoparticle composites confined between two parallel substrates, with an attractive polymer-substrate interaction. Polymers are in the semidilute regime at concentrations far above the overlap point, and nanoparticles are in good solvent and without enthalpic attraction to the substrates. An increase of temperature then triggers the crystallization of nanoparticles on one of the two substrate surfaces-a surprising phenomenon, which is explained in terms of scaling theory, such as through competing effects of adsorption-and correlation blobs. Moreover, we show that the first, closely packed layer of nanoparticles on the substrate increases the depletion attraction of additional nanoparticles from the bulk, thereby enhancing and stabilizing the formation of a crystalline phase on the substrate. Within the time frame accessible to our numerical simulations, the crystallization of nanoparticles was irreversible; that is, their crystalline phase, once created, remained undamaged after a decrease of the temperature. Our study leads to a class of thermoreactive nanomaterials, in which the transition between a homogeneous state with dissolved nanoparticles and a surface-crystallized state is triggered by a temperature jump.

Nanostructured ultrathin films obtained by the spreading of diblock copolymers on a surface

We propose a theory of nanopattern formation in ultrathin films obtained by the spreading of A-B diblock copolymers on a surface. A blocks are strongly adsorbed (spread) on the substrate, and the strength of the adsorption can be varied. B blocks are incompatible with the substrate, but they can spread atop the layer of the A blocks. We predict disk-shaped micelles ordered with hexagonal symmetry and parallel stripe-shaped micelles and bilayers to be stable. The type of resulting structure and its geometrical parameters depend on the composition of the copolymer and interaction parameters. We interrelate these results with those obtained for the case of the spreading of both blocks on the substrate, and we construct a unified phase diagram.

Mean-field treatment of polymer chains trapped between surfaces and penetrable interfaces

We study the exact solutions for the problem of adsorption of polymers in a system containing two interfaces within the mean-field ground-state dominance approximation both for penetrable and nonpenetrable interfaces. We discuss the case of saturation of the polymer double layer for the limiting case of zero bulk concentration. Here, the exact solution is controlled by a single scaling variable which describes the coupling between the interfaces due to the polymer chains. For the case of penetrable interfaces we obtain a nonmonotonous behavior of the amount of adsorbed polymers as a function of the distance between the interfaces. This leads to a high- and a low-energy phase for the double layer with respect to the amount of polymers localized. At the saturation point, the force acting between the interfaces is strictly attractive and monotonously decaying toward zero for increasing interface distance for both types of interfaces. The exact solution for the chemical equilibrium state of the polymer double layer with a semidilute bulk state is governed by two scaling variables and explicit concentration dependence can be removed. The scaling variables describe the ratio between the interface distance and the bulk correlation length and the ratio between the localization length of the interfaces and the bulk correlation length, respectively. Using the exact solution on intervals of constant potentials opens the possibility to treat various localization problems for polymer chains using the appropriate boundary conditions.

Concentration and saturation effects of tethered polymer chains on adsorbing surfaces

We consider end-grafted chains at an adsorbing surface under good solvent conditions using Monte Carlo simulations and scaling arguments. Grafting of chains allows us to fix the surface concentration and to study a wide range of surface concentrations from the undersaturated state of the surface up to the brushlike regime. The average extension of single chains in the direction parallel and perpendicular to the surface is analyzed using scaling arguments for the two-dimensional semidilute surface state according to Bouchaud and Daoud [J. Phys. (Paris) 48, 1991 (1987)]. We find good agreement with the scaling predictions for the scaling in the direction parallel to the surface and for surface concentrations much below the saturation concentration (dense packing of adsorption blobs). Increasing the grafting density we study the saturation effects and the oversaturation of the adsorption layer. In order to account for the effect of excluded volume on the adsorption free energy we introduce a new scaling variable related with the saturation concentration of the adsorption layer (saturation scaling). We show that the decrease of the single chain order parameter (the fraction of adsorbed monomers on the surface) with increasing concentration, being constant in the ideal semidilute surface state, is properly described by saturation scaling only. Furthermore, the simulation results for the chains' extension from higher surface concentrations up to the oversaturated state support the new scaling approach. The oversaturated state can be understood using a geometrical model which assumes a brushlike layer on top of a saturated adsorption layer. We provide evidence that adsorbed polymer layers are very sensitive to saturation effects, which start to influence the semidilute surface scaling even much below the saturation threshold.

Dynamical scaling of single chains on adsorbing substrates: Diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.

Static and dynamic properties of tethered chains at adsorbing surfaces: A Monte Carlo study

We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain's extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength epsilon(c) one has M(c) approximately N(phi), and we find (using the above results) as best candidate phi to equal 0.59. However, slight changes in the estimation of epsilon(c) lead to large deviations in the resulting phi; this might be a possible reason for the difference in the phi values reported in the literature. We also investigate the dynamical scaling behavior at epsilon(c), by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at epsilon(c) the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum.

Irreversible adsorption from dilute polymer solutions

We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two broad cases are considered, distinguished by the magnitude of the local monomer-surface sticking rate Q: chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single-chain adsorption. While single-chain physisorption times tau ads are typically micro- to milli-seconds, for chemisorbing chains of N units we find experimentally accessible times tau ads=Q(-1)N(3/5), ranging from seconds to hours. We establish 3 chemisorption universality classes, determined by a critical contact exponent: zipping, accelerated zipping and homogeneous collapse. For dilute solutions, the mechanism is accelerated zipping: zipping propagates outwards from the first attachment, accelerated by occasional formation of large loops which nucleate further zipping. This leads to a transient distribution omega(s) approximately s(-7/5) of loop lengths s up to a maximum size smax approximately (Qt)(5/3) after time t. By times of order tau ads the entire chain is adsorbed. The outcome of the single-chain adsorption episode is a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb onto, late-arriving chains form a diffuse outer layer. In a simple picture we find for both chemisorption and physisorption a final loop distribution Omega(s) approximately s(-11/5) and density profile c(z) approximately z(-4/3) whose forms are the same as for equilibrium layers. In contrast to equilibrium layers, however, the statistical properties of a given chain depend on its adsorption time; the outer layer contains many classes of chain, each characterized by a different fraction of adsorbed monomers f. Consistent with strong physisorption experiments, we find the f values follow a distribution P(f) approximately f(-4/5).

Nuclear magnetic relaxation without spin diffusion in polymers at interfaces

We consider theoretically the possibility of solid state NMR experiments with frozen linear polymer chains at interfaces. Three different cases are studied, namely, when the macromolecules are grafted on the surface, when they are adsorbed, and when they are very strongly adsorbed from a melt that is subsequently washed by a good solvent. The latter case is somewhat intermediate between the two former ones. For each case, we consider the relaxation when paramagnetic centers are located on the surface. We show that the shape of the relaxation curves depends critically on the monomer concentration profile, and exhibits characteristic power-law variations.