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.     

Adsorption of random copolymers by a selective layer: Monte Carlo studies

We use scaling arguments and computer simulations to investigate the adsorption of symmetric AB-random copolymers (RC) from a diluted solution onto a selective ABA layer. Depending on the ratio between the layer thickness and the size of excess blobs, d/xi, three regimes of RC adsorption are predicted. For large values of the layer thickness RC adsorption can be understood as adsorption on two selective interfaces where sequences of RC chains form bridges. When the layer thickness is of the order of xi, excess blobs are trapped in the layer and localize the copolymer chain strongly. If the layer thickness is very small a weak adsorption scenario is predicted where large loops are formed outside the layer. Our simulations using the bond fluctuation model are in good agreement with the scaling predictions. We show that chain properties display non-monotonous behavior with respect to the layer thickness with optimal values for d approximately xi. In particular, we discuss simulation results for density profiles, statistics of bridges, loops and tails formed by the adsorbed chains, as well as for the adsorption order parameter and free energy.     

Adsorption of semiflexible block copolymers on homogeneous surfaces

We present the results of extensive numerical off-lattice Monte Carlo simulations of semiflexible block-copolymer chains adsorbed onto flat homogeneous surfaces. We have compared the behavior of several chain structures, such as homopolymers, diblocks, (A(alpha)B(alpha)) block copolymers, and random heteropolymers. In all the cases studied, we have found the adsorption process to be favored with an increase of the chain rigidity. Particularly, the adsorption of diblock structures becomes a two-step process characterized by two different adsorbing temperatures that depend on the chain stiffness kappa, the chain length N, and the adsorbing energies epsilon(A) and epsilon(B). This twofold adsorbing process changes to a single one for copolymers of reduced block size alpha. Each block of the stiff copolymer chain is found to satisfy the classical scaling laws for flexible chains, however, we found the scaling exponent phi to depend on the chain stiffness. The measurement of the radius of gyration exhibits a typical behavior of a polymer chain composed of Nl(p) blobs whose persistence length follows l(p) approximately (kappa/k(B)T)(0.5) for large stiff chains.     

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.     

THE ADSORPTION OF LINEAR POLY(N-ISOPROPYLACRYLAMIDE)CHAINS ON SURFACTANT-FREE POLYSTYRENE NANOPARTICLES

The adsorption of linear poly(N-isopropylacrylamide) (PNIPAM) chains on surfactant-freepolystyrene (PS) nanoparticles was used as a model system to study the hydrophobic adsorption of polymeron the surface, because the hydrophobility of PNIPAM can be continuously varied by a small temperaturechange. The adsorption was investigated by a combination of static and dynamic laser light scattering (LLS)measurements, In static LLS, the absolute excess scattered light intensity led to the amount of PNIPAMadsorbed on the surface. In dynamic LLS, the hydrodynamic thickness of the adsorbed PNIPAM layer wasaccurately measured. For a given particle concentration, the adsorption increases as thc PNIPAMconcentration and the incubation temperature increase. The average density of the adsorbed PNIPAM layer isreciprocally proportional to the number of the PNIPAM chains on the surface, revealing a simple scaling ofthe chain density distribution. The adsorption follows the Langmuir's isotherm. The enthalpy changeestimated from the adsorption at 25℃and 30℃is slightly positive, indicating that the adsorption involvesthe coil-to-globule transition of the chains on the surface.     

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.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

Short chains at solid surfaces: wetting transition from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the wetting transition changes with the change of the chain length and with the relative strength of the fluid-solid interaction. End segments adsorb preferentially in the first adsorbed layer whereas the concentration of the middle segments is enhanced in the second layer. We observe that the wetting temperature rescaled by the bulk critical temperature decreases with an increase of the chain length. For longer chains this temperature reaches a plateau. For the surface critical temperature an inverse effect is observed, i.e., the surface critical temperature increases with the chain length and then attains a plateau. These findings may serve as a quick estimate of the wetting and surface critical temperatures for fluids of longer chain lengths.     

Irreversible adsorption of tethered chains at substrates: Monte Carlo study

The irreversible adsorption of single chains grafted with one end to the surface is studied using scaling arguments and computer simulations. We introduce a two-phase model, in which the chain is described by an adsorbate portion and a corona portion formed by nonadsorbed monomers. The adsorption process can be viewed as consisting of a main stage, during which monomers join by "zipping" (along their order in the chain) the surface, and a late stage, in which the remaining corona collapses on the surface. Based on our model we derive a scaling relation for the time of adsorption t(M) as a function of the number M of adsorbed monomers; t(M) follows a power law, M(alpha), with alpha > 1. We find that alpha is related to the Flory exponent nu by alpha = 1 + nu. Using further scaling arguments we derive relations between the overall time of adsorption, the characteristic time of adsorption (given by the crossover time between the main and the last stage of adsorption), and the chain length. To support our analysis we perform Monte Carlo simulations using the bond fluctuation model. In particular, the sequence of adsorption events is very well reproduced by the simulations, and an analysis of the various density profiles supports our theoretical model. Especially the loop formation during adsorption clearly shows that the growth of the adsorbate is dominated by zipping. The simulations are also in almost quantitative agreement with our theoretical scaling analysis, showing that here the assumption of a linear relation between Monte Carlo steps and time is well obeyed. We conclude by also discussing the geometrical shape of the adsorbate.     

Structure of Adsorbed Polymer Chains: A Monte Carlo Study

The structure of adsorbed polymer chains was studied using simplified lattice models. The model chains were adsorbed on an impenetrable surface with an attractive potential. The dynamic Monte Carlo simulations based in the Metropolis scheme were carried out using these models. The influence of the internal chain architecture (linear, star‐branched and ring chains) and the degree of adsorption on the chain's structure was studied. It was shown that for weakly adsorbed chain regime the ring polymers which exhibit an almost twice as high degree of adsorption compared to linear and star chains have a higher number of adsorbed parts of chain (trains). But the length of such train remains almost the same for all types of a polymer chain. Star‐branched chains exhibit a slightly different change in number and the mean length of trains, loops and tails with the temperature and the chain total length compared to two other types of chain.     

A physico-chemical investigation of poly(ethylene oxide)-block-poly(L-lysine) copolymer adsorption onto silica nanoparticles

The adsorption behavior of poly(ethylene oxide)-b-poly(L-lysine) (PEO(113)-b-PLL(10)) copolymer onto silica nanoparticles was investigated in phosphate buffer at pH 7.4 by means of dynamic light scattering, zeta potential, adsorption isotherms and microcalorimetry measurements. Both blocks have an affinity for the silica surface through hydrogen bonding (PEO and PLL) or electrostatic interactions (PLL). Competitive adsorption experiments from a mixture of PEO and PLL homopolymers evidenced greater interactions of PLL with silica while displacement experiments even revealed that free PLL chains could desorb PEO chains from the particle surface. This allowed us to better understand the adsorption mechanism of PEO-b-PLL copolymer at the silica surface. At low surface coverage, both blocks adsorbed in flat conformation leading to the flocculation of the particles as neither steric nor electrostatic forces could take place at the silica surface. The addition of a large excess of copolymer favoured the dispersion of flocs according to a presumed mechanism where PLL blocks of incoming copolymer chains preferentially adsorbed to the surface by displacing already adsorbed PEO blocks. The gradual addition of silica particles to an excess of PEO-b-PLL copolymer solution was the preferred method for particle coating as it favoured equilibrium conditions where the copolymer formed an anchor-buoy (PLL-PEO) structure with stabilizing properties at the silica-water interface.     

Differences between tethered polyelectrolyte chains on bare mica and hydrophobically modified mica

This study investigates the structures of layers of amphiphilic diblock copolymers of poly(t-butyl styrene)-poly(styrene sulfonate) (PtBS-PSS) adsorbed on both the bare mica surface (hydrophilic) and an octadecyltriethoxysilane (OTE)-modified mica surface (hydrophobic). When the surface is rendered hydrophobic, the nonsoluble block exhibits stronger interaction with the surface and higher adsorbed masses are achieved. Interaction forces between two such adsorbed layers on both substrates were measured using the surface forces apparatus. The effect of salt concentration (Cs) and molecular weight (N) on the height of the self-assembled layers (L0) was examined in each case. The resulting scaling relationship is in good agreement with predictions of the brush model, L0 proportional to N(1.0) in the low-salt limit and L0N(-1) proportional to (Cs/sigma)(-0.32) in the salted regime, when adsorption takes place onto the hydrophobized mica surface. For adsorption on the bare mica surface, L0N(-0.7) proportional, variant Cs(-0.17) agrees with the scaling prediction of the sparse tethering model. The results suggest that, on the hydrophilic bare mica surface, the adsorbed amount is not high enough to form a brush structure and only very little intermolecular stretching of the tethered chains occurs; in contrast, the presence of the hydrophobic OTE layer increases the tethering density such that the polyelectrolyte chains adopt a brush conformation.     

Adsorption of bituminous components at oil/water interfaces investigated by quartz crystal microbalance: implications to the stability of water-in-oil emulsions

Silica-gel-coated QCM crystals oscillating in a thickness shear mode are used to measure adsorption of bituminous components in water-saturated heptol (1/1 vol ratio of a heptane/toluene mixture) at the oil/water interface. In addition to the viscoelasticity of the adsorbed film, the effects of the bulk liquid density and viscosity as well as the liquid trapped in interfacial cavities are taken into account for the calculation of adsorbed mass. Asphaltenes in heptol adsorb continuously at the oil/water interface, while resins (the surface-active species in maltenes) show adsorption saturation in the same solvent. For Athabasca bitumen in heptol, two adsorption regimes are observed depending on concentration. At low concentrations, a slow, non-steady-state, and irreversible adsorption takes place. At high concentrations, a steady-state adsorption with limited reversibility results in a quick adsorption saturation. The threshold concentration between these adsorption regimes is 1.5 wt % and 8 wt % for oil/water and oil/gold interfaces, respectively. The threshold concentration, the total adsorbed amount, and the flux of non-steady-state adsorption depend on the resin-to-asphaltene ratio. The threshold concentration is related to the earlier reported critical bitumen concentration characterizing the rigid-to-flexible transition of the interfacial film. We propose a new mechanism based on the change of the effective resin-to-asphaltene ratio with dilution to explain both the adsorption behavior and emulsion stability.     

Dynamics of amphiphilic diblock copolymers at the air-water interface

Two polyisoprene-polyethyleneoxide diblock copolymers with different block length ratios adsorbed to the water surface were investigated by multiple angle of incidence ellipsometry, evanescent wave light scattering, and surface tension experiments. In a semidilute interfacial regime, the transition from a two-dimensional to a "mushroom" regime, in which polymer chains form loops and tails in the subphase, was discussed. A diffusion mechanism parallel to the interface was probed by evanescent wave dynamic light scattering. At intermediate concentrations, the interfacial diffusion coefficient D(∥) scales with the surface concentration Γ, as D(∥) ~ Γ(0.77) in agreement with the scaling observed for polymer solutions in a semidilute regime. At relatively high concentrations a decreasing of D(∥) is discussed in terms of increasing friction due to interactions between polyisoprene chains.     

The effect of the amphiprotic nature of human hair keratin on the adsorption of high charge density cationic polyelectrolytes

Adsorption of the cationic polymers poly(methacrylamidopropyltrimethyl ammonium chloride) (PMAPTAC) and poly(1,1-dimethylpiperidinium-3,5-diallylmethylene chloride) (PDMPDAMC) on human hair was studied by measurements of the amount of polymer adsorbed and by the streaming potential method. Results reflect the amphoteric nature of the keratin surface and show that the excess of anionic sites at pH values above 4 is the main driving force for the adsorption of cationic polyelectrolytes. Lowering the pH below 4 or addition of neutral salt (KCl) reduces the amount of adsorbed polymer. It was shown that the adsorption of cationic polymer in the concentration range 0.01 to 0.1 % and at neutral pH reverses the overall character of the surface from anionic to cationic. Keratin fibers modified in this manner do not exhibit amphoteric character and bear excess positive charge in the pH range 2–9.5. The value of the amount of the polymer adsorbed at saturation concentration (2 mg/g) as well as the lack of molecular weight effect in the range (5 · 10⁴ – 10⁶) on the amount of polymer adsorbed suggest that polymer chains adopt a rather extended conformation on the fiber surface. Some data concerning the formation of a complex between adsorbed cationic polymer and anionic detergents or polyelectrolytes are also presented.     

Surface and aggregation behavior of aqueous solutions of Ru(II) metallosurfactants. 3. Effect of chain number and orientation on the structure of adsorbed films of [Ru(bipy)2(bipy')]Cl2 complexes

The surface behavior of a range of surfactant [Ru(bipy)(2)(p,p'-dialkyl-2,2'-bipy)]Cl(2) complexes, which we express as Ru(q)(p)C(n) where n is the alkyl chain length, p refers to the substitution position on the bipyridine ligand (=4 or 5), and q (=1 or 2) is the number of substituted alkyl chains, has been examined using neutron reflectometry. The adsorption of the single-chain Ru(1)(4)C(19) and Ru(1)(5)C(19) surfactants is strongly time-dependent, taking in excess of 10 h to form an equilibrium film. It is suggested that the slow adsorption rate is related to the alkyl chain length rather than the low monomer concentration present in the solutions. At concentrations below the critical micelle concentration (cmc) of Ru(1)(4)C(19), the film of Ru(1)(5)C(19) is denser than that of Ru(1)(4)C(19) at comparable concentration, consistent with the mass densities of the bulk solids, whereas at concentrations close to and greater than this cmc the converse pertains. Close to the cmc, the adsorbed films possess an average area per molecule significantly less than the nominal headgroup area of the surfactants (approximately 30 angstroms(2) compared with approximately 100 angstroms(2)). This fact together with consideration of the thickness and density of the adsorbed films leads to the conjecture that surface aggregates may be the adsorbing units. The adsorption of the double-chain surfactant Ru(1)(p)C(19), in contrast to the behavior of the Ru(1)(p)C(19) surfactants, is weak and independent of time. This behavior is attributed to the alkyl chain orientation. The adsorption behavior of a racemic mixture of the Delta and Lambda isomers of Ru(2)(4)C(19) has been compared with that of the Delta isomer. It is found that the film of racemic material is more closely packed than that of the resolved complex.     

Computer Simulation of Adsorbed Polymer Chains with a Different Molecular Architecture

Simulations of simple models of polymer chains were carried out by the means of the dynamic Monte Carlo method. The model chains were confined to a simple cubic lattice. Three different chain architectures were studied: linear, star‐branched and ring chains. The polymer model chain interacted with an impenetrable surface with a simple contact attractive potential. It was found that size parameters of all these polymers obey scaling laws. The temperatures of the transitions from weakly to strongly adsorbed chain were determined. It was shown for weakly adsorbed chains that ring polymers are always ca. 50% more adsorbed than linear and star‐branched ones. The properties of adsorbed linear and star‐branched polymers are very similar in the length of chain and the strength of adsorption studied. Strongly adsorbed ring polymers are still more adsorbed but differences between all kinds of chains become less pronounced.     

Supramolecular structures in nanocomposite multilayered films

We investigate the multilayered structures of poly(ethylene)oxide/montmorillonite nanocomposite films made from solution. The shear orientation of a polymer-clay network in solution combined with simultaneous solvent evaporation leads to supramolecular multilayer formation in the film. The resulting films have highly ordered structures with sheet-like multilayers on the micrometer length scale. The polymer covered clay platelets were found to orient in interconnected blob-like chains and layers on the nanometer length scale. Inside the blobs, scattering experiments indicate the polymer covered and stacked clay platelets oriented in the plane of the film. The polymer is found to be partially crystalline although this is not visible by optical microscopy. Atomic force microscopy suggests that the excess polymer, which is not directly adsorbed to the clay, is wrapped around the stacked platelets building blobs and the polymer also interconnects the polymer-clay layers. Overall our results suggest the re-intercalation of clay platelets in films made from exfoliated polymer-clay solutions as well as the supramolecular order and hierarchical structuring on the nanometer, via micrometer to the centimeter length scale.     

Development of equations for differential and integral enthalpy change of adsorption for simulation studies

We present equations to calculate the differential and integral enthalpy changes of adsorption for their use in Monte Carlo simulation. Adsorption of a system of N molecules, subject to an external potential energy, is viewed as one of transferring these molecules from a reference gas phase (state 1) to the adsorption system (state 2) at the same temperature and equilibrium pressure (same chemical potential). The excess amount adsorbed is the difference between N and the hypothetical amount of gas occupying the accessible volume of the system at the same density as the reference gas. The enthalpy change is a state function, which is defined as the difference between the enthalpies of state 2 and state 1, and the isosteric heat is defined as the negative of the derivative of this enthalpy change with respect to the excess amount of adsorption. It is suitable to determine how the system behaves for a differential increment in the excess phase adsorbed under subcritical conditions. For supercritical conditions, use of the integral enthalpy of adsorption per particle is recommended since the isosteric heat becomes infinite at the maximum excess concentration. With these unambiguous definitions we derive equations which are applicable for a general case of adsorption and demonstrate how they can be used in a Monte Carlo simulation. We apply the new equations to argon adsorption at various temperatures on a graphite surface to illustrate the need to use the correct equation to describe isosteric heat of adsorption.