Computer simulation study of pattern transfer in AB diblock copolymer film adsorbed on a heterogeneous surface

In this work we investigate how a pattern imposed in a copolymer film at a certain distance from the surface propagates through the film onto an adsorbing heterogeneous surface. We bias the copolymer film to adopt a specified target pattern and then use simulation to design a surface pattern that helps the adsorbed film to maintain that target pattern. We examine the effect of varying the copolymer chain length, the size of the target pattern, and the distance from the surface where the target pattern is applied, z', on the extent of pattern transfer. For each chain length, target pattern, and z' we compare the energy of the system when a pattern is applied in the bulk to the energy when no pattern is applied in order to understand why a certain pattern size is transferred to the surface with higher fidelity than the others. At constant chain length, pattern transfer is best when the pattern size brings the energy of the system close to the energy when no pattern is applied. At constant pattern size, pattern transfer is best in the systems with longer chains. This is because longer chains are more likely to adsorb as brushes and loops which then helps transfer the pattern through the adsorbed film down to the surface.     

Phase transition of short linear molecules adsorbed on solid surfaces from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on strongly attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the layering transitions change with the change of the chain length and with relative strength of the fluid-solid interaction. The critical temperature of the first layering transition, rescaled by the bulk critical temperature, increases slightly with an increase of the chain length. We have found that for longer chains the layering transitions within consecutive layers are shifted toward very low temperatures and that their sequence is finally replaced by a single transition.     

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.     

Transition from Incomplete to Complete Wetting of Solid Surface in Polymer–Solvent System: 3. The Regime of Weak Adsorption

The transition from incomplete to complete wetting occurring near the critical temperature of a two-phase polymer–solvent system at the substrate surface that weakly adsorbs macromolecules was studied using the Cahn–de Gennes model. It was shown that, depending on the force of attraction between the segments and the wall, the energy of interaction between the segments in the surface layer, as well as on the length of chain, the wetting transition can occur as the first- or second-order phase transitions, or as the tricritical wetting transition. Near the temperatures of these transitions, we determined the character of the variations in the difference of the surface concentrations that are established at the boundaries between the substrate and semidilute or dilute polymer solutions, as well as in the difference between the interfacial tensions and of the cosine of contact angles. It was shown that the temperature of each transition varies inversely to the square root of the molecular mass of polymer, and its deviation from the critical temperature is determined by the type of transition. At the first-order transitions at the SP-regime, the deviation is proportional to the energy of attraction between the chain units and the wall and is independent of polymer chain length, whereas at the critical wetting it is proportional to the squared energy of attraction between the segments and the substrate and increases with polymer chain length according to the N ^1/2law. At the considered asymptotic regime, which corresponds to the substrates that weakly attract polymer chain units, the type of the wetting transition can be regulated by varying only the length of polymer chain at the same energy characteristics of a substrate. The possibility of observing the critical wetting transitions using the solutions of high-molecular-mass compounds is discussed.     

Monte Carlo simulation for the adsorption of symmetric triblock copolymers II. Adsorption layer information

By using Monte Carlo simulation, adsorption of both end-adsorbed and middle-adsorbed symmetric triblock copolymers from a non-selective solvent on an impenetrable surface has been studied. Influences of the adsorption energy, the bulk concentration, the chain composition and the chain length on the adsorption behavior including the surface coverage, the adsorption amount and the layer thickness are presented. It is shown that the total surface coverage for both end-adsorbed and middle-adsorbed copolymers increases monotonically as the bulk concentration increases. The higher the adsorption energy and the more the attractive segments, the higher the total surface coverage is exhibited. Surface coverage θ decreases with increasing the length of the non-attractive segments, but the product of θ and the proportion of the non-attractive segments in a triblock copolymer chain is nearly independent of the chain length. The adsorption amount increases almost monotonically with the bulk concentration. The logarithm of the adsorption amount is a linear function of the reciprocal of the reduced temperature. When the adsorption energy is large, the adsorption amount exhibits a maximum as the composition of the attractive segment increases. The adsorption isotherms of copolymers with different length of the non-attractive segments can be mapped onto a single curve under certain energy indicating that copolymers with different chain length have the same adsorption amount. The adsorption layer thickness for the end-adsorbed copolymers decreases as the energy and the number of adsorbing segments increases. The longer non-attractive segments, the larger adsorbed layer thickness is found. The tails mainly governs the adsorption layer thickness.     

Statistics of stiff polymer chains near an adsorbing surface

The exact solution of the problem of adsorption of a long ideal polymer chain with variable degree of stiffness on a plane surface is presented. It is shown that the adsorption of stiff polymer chains is a second-order phase transition; in the adsorbed state “train” (i.e. adsorbed) sections are relatively longer and loop sections relatively shorter than for flexible chains. This effect is very pronounced: already for moderately stiff chains the number of Kuhn segment lengths in one “train” section at the temperature T = T_cr/2 (T_cr is the critical temperature for adsorption transition) can reach several thousands, and deviation from the surface occurs only in the form of small “hairpins”. The maximum length of the chain, which at the given conditions would flatten completely on the surface, is estimated.     

Elastic behavior of adsorbed polymer chains

Elastic behaviors of single polymer chains adsorbed on the attractive surface are first investigated using Monte Carlo simulation method based on the bond fluctuation model. We investigate the chain size and shape of adsorbed chains, such as mean-square radius of gyration S2, mean-square bond length b2, shape factors sf(i) and delta*, and the orientation of chain segments P2, to illuminate how the shape of polymer chains changes during the process of tensile elongation. There are some special behaviors of the chain size and shape at the beginning of elongation, especially for strong attraction interaction. For example, mean fraction of adsorbed segments decreases abruptly in the region of small elongation ratio and then decreases slowly with increasing elongation ratio. In fact, the chain size and shape also changes abruptly for small elongation ratio with strong attraction interaction. Some thermodynamics properties are also investigated here. Average Helmholtz free energy increases fast for elongation ratio lambda<1.15, especially with strong attraction, and increases slowly for lambda>1.15. Similar behaviors are obtained for average energy per bond. Elastic force (f ) and energy contribution to force (f(U)) are also studied, and we find that elastic force decreases abruptly for lambda<1.15, and there is a minimum of elastic force for strong attraction interaction, then increases very slowly with increasing elongation ratio. However, there are different behaviors for weak attraction interaction. For energy contribution to force (f(U)), there is a maximum value for strong attraction interaction in the region of lambda<1.15. Some comparisons with the atomic force microscopy experiments are also made. These investigations may provide some insights into the elastic behaviors of adsorbed polymer chains.     

方阱链状分子临界性质的Monte Carlo模拟

在巨正则系综下对阱宽为λ=1.5,链长分别为4、8、16的方阱链状流体实施Monte Carlo模拟,采用建立在完整标度基础上的无偏的Q-参数方法,通过histogram reweighting技术以及有限尺寸标度理论得到了热力学极限下该系列流体的临界温度和临界密度.模拟结果表明,方阱链流体的临界温度随着链长的增加而升高.并且不同链长方阱流体的临界温度均低于已报道的结果.由于本文所采用的完整标度的无偏性,我们估计的临界点更加准确.并且流体的临界温度与链长之间的关系与Flory-Huggins理论相一致.我们还预测了无限链长方阱流体的临界温度,比已有结果略高.     

Adsorption of Ethyl(hydroxyethyl)cellulose onto Silica Particles: The Role of Surface Chemistry and Temperature

The adsorption characteristics of an ethyl(hydroxyethyl)cellulose (EHEC) polymer onto colloidal silica particles from aqueous solution have been investigated. The influence of solution temperature and the silica surface chemistry on EHEC adsorption isotherms and adsorbed layer thicknesses have been determined in an attempt to elucidate the mechanisms of adsorption. As the hydrophobicity of the silica particles are increased by physical and chemical treatment, the plateau EHEC adsorbed amount increased, while the corresponding adsorbed layer thickness decreased. The estimated free energy of adsorption (DeltaG(o)(ads)) was shown to be dependent on the silica surface chemistry, but did not correlate directly with silica's advancing water contact angle and suggests that EHEC adsorption is not directly controlled by hydrophobicity alone. As the solution temperature increased from 18 to 37 degrees C, the plateau coverage of EHEC increased while the layer thickness generally decreased, this concurred with a reduction in the solvency. For hydrophilic and dehydrated silica particles, DeltaG(o)(ads) decreased in magnitude with increasing temperature, whereas for chemically treated silica, DeltaG(o)(ads) increased with temperature. These findings are discussed with respect to the specific interactions between EHEC segments and surface sites, which control the adsorption mechanisms of cellulose polymers. Copyright 2000 Academic Press.     

Surface properties of bottle-brush polyelectrolytes on mica: effects of side chain and charge densities

Surface properties of a series of cationic bottle-brush polyelectrolytes with 45-unit-long poly(ethylene oxide) side chains were investigated by phase modulated ellipsometry and surface force measurements. The evaluation of the adsorbed mass of polymer on mica by means of ellipsometry is complex due to the transparency of mica and its birefringence and low dielectric constant. We therefore employed a new method to overcome these difficulties. The charge and the poly(ethylene oxide) side chain density of the bottle-brush polymers were varied from zero charge density and one side chain per segment to one charge per segment and no side chains, thus spanning the realm from a neutral bottle-brush polymer, via a partly charged brush polyelectrolyte, to a linear fully charged polyelectrolyte. The adsorption properties depend crucially on the polymer architecture. A minimum charge density of the polymer is required to facilitate adsorption to the oppositely charged surface. The maximum adsorbed amount and the maximum side chain density at the surface are obtained for the polymer with 50% charged segments and the remaining 50% of the segments carrying poly(ethylene oxide) side chains. It is found that brushlike layers are formed when 25-50% of the segments carry poly(ethylene oxide) side chains. In this paper, we argue that the repulsion between the side chains results in an adsorbed layer that is non-homogeneous on the molecular level. As a result, not all side chains will contribute equally to the steric repulsion but some will be stretched along the surface rather than perpendicular to it. By comparison with linear polyelectrolytes, it will be shown that the presence of the side chains counteracts adsorption. This is due to the entropic penalty of confining the side chains to the surface region.     

Protein adsorption and wetting of the protein adsorbed surfaces studied by a new type of laser reflectometer

We have devised a new type of laser reflectometer that can measure adsorption behavior of (bio)-polymers, such as proteins, on the substrate surface and also the wetting for the surface of adsorbed layer of such (bio)-polymers. The adsorption and the wetting experiments can be conducted in a sequential manner using the same sample by this apparatus. So, the wetting of the surface of protein-adsorbed layer can be measured in virtually intact state. The reflectometry is based on the traditional optical polarimetry and the wetting measurement is due to the dropping time method (DTM) that has been reported before by the authors. The two methods are combined in an apparatus and hence we can correlate the wetting of protein layer adsorbed on the substrate surfaces with the amounts of protein molecules on the surface. As a model case we demonstrate the adsorption of several typical water soluble globular proteins on stainless steel surfaces. For this combination of the adsorbent with adsorbates, it is found that the water wetting of the protein adsorbed surface is closely related with the adsorbed amounts of proteins not depending on species.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Adsorption of interacting oligomers and polymers at an interface

We discuss in a qualitative way the physical background of a recently developed polymer adsorption theory, in which all the possible chain conformations for interacting chain molecules near an adsorbing interface are taken into account. Any conformation is described as a step-weighted random walk in a lattice. Each step is weighted according to a segmental weighting factor that contains the adsorption energy (for segments in contact with the surface), the entropy of mixing, and the attraction or repulsion between segments and solvent molecules. A suitable computing method is used to calculate the contribution of all chain conformations to the concentration profile, to the adsorbed amount, to the fraction of trains, loops and tails, to the layer thickness, etc. The theory is valid for any chain length and any concentration in the solution.Results for various chain lengths are given. Oligomers have a low affinity for the surface, whereas polymer adsorption isotherms are of the well known high affinity type. Three concentration regimes can be distinguished. In (extremely) dilute solutions the molecules on the surface adsorb as isolated chains (the Henry region).     

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.     

Structure of poly(methyl methacrylate) chains adsorbed on sapphire probed using infrared-visible sum frequency generation spectroscopy

We have studied the orientation of the train segments of a poly(methyl methacrylate) (PMMA) adsorbed layer at the CCl4-sapphire interface using surface-sensitive IR-visible sum frequency generation (SFG) spectroscopy. The SFG spectra of PMMA chains adsorbed on sapphire indicate ordered ester methyl groups. In comparison, we did not observe any significant contributions from the backbone methylene and alpha methyl groups, suggesting that these groups are disordered. No change in the structure of the adsorbed layer is observed upon cooling the solvent below the theta temperature; this is consistent with the picture of flat adsorbed chains on the surface. Interestingly, the orientation of the ester methyl groups of a spin-coated PMMA film at the PMMA-sapphire interface is similar to that of the same groups in the chains adsorbed from solution.     

Adsorption of alkyl polyglucosides on the solid/water interface: equilibrium effects of alkyl chain length and head group polymerization

The equilibrium adsorption behavior of two n-alkyl-beta-D-glucosides (octyl (C8G1) and decyl (C10G1)) and four n-alkyl-beta-D-maltosides (octyl (C8G2), decyl (C10G2), dodecyl (C12G2), and tetradecyl (C14G2)) from aqueous solution on a titania surface, as measured by ellipsometry, has been investigated. The main focus has been on the effect of changes in the alkyl chain length and headgroup polymerization, but a comparison with their adsorption on the silica/water and air/water interfaces is also presented. Some comparison with the corresponding adsorption of ethylene oxide surfactants, in particular C10E6 and C12E6, is given as well. For all alkyl polyglucosides, the maximum adsorbed amount on titania is reached slightly below the critical micelle concentration (cmc), where it levels off to a plateau and the amount adsorbed corresponds roughly to a bilayer. However, there is no evidence that this is the actual conformation of the surfactant assemblies on the surface, but the surfactants could also be arranged in a micellar network. On hydrophilic silica, the adsorbed amount is a magnitude lower than on titania, corresponding roughly to a layer of surfactants lying flat on the surface. A change in the alkyl chain length does not result in any change in the plateau molar adsorbed amount at equilibrium; however, the isotherm slope for the alkyl maltosides increases with increasing chain length. Headgroup polymerization on the other hand affects the adsorbed amount. The alkyl glucosides start adsorbing at lower bulk concentrations than the maltosides and equilibrate at higher adsorbed amounts above the cmc. When compared with the ethylene oxide (EO) surfactants, it is confirmed that the EO surfactants hardly adsorb on titania, since the measured changes in the ellipsometric angles are within the noise level. They do, however, adsorb strongly on silica.     

Random copolymers at a selective interface: saturation effects

Combining scaling arguments and Monte Carlo simulations using the bond fluctuation method we have studied concentration effects for the adsorption of symmetric AB-random copolymers at selective, symmetric interfaces. For the scaling analysis we consider a hierarchy of two length scales given by the excess (adsorption) blobs and by two dimensional thermal blobs in the semidilute surface regime. When both length scales match, a densely packed array of adsorption blobs is formed (saturation). We show that for random copolymer adsorption the interface concentration can be further increased (oversaturation) due to reorganization of excess blobs. Crossing over this threshold results in a qualitative change in the behavior of the adsorption layer which involves a change in the average shape of the adsorbed chains towards a hairpinlike form. We have analyzed the distribution of loops and tails of adsorbed chains in the various concentration regimes as well as the chain order parameter, concentration profiles, and the exchange rate of individual chains. We emphasized the role of saturation scaling which dominates the behavior of static and dynamic quantities at higher surface concentration.     

Diverse spreading behavior of binary polymer nanodroplets

Molecular dynamics simulations are used to study the spreading of binary polymer nanodroplets in a cylindrical geometry. The polymers, described by the bead-spring model, spread on a flat surface with a surface-coupled Langevin thermostat to mimic the effects of a corrugated surface. Each droplet consists of chains of length 10 or 100 monomers with approximately 350,000 monomers total. The qualitative features of the spreading dynamics are presented for differences in chain length, surface interaction strength, and composition. When the components of the droplet differ only in the surface interaction strength, the more strongly wetting component forms a monolayer film on the surface even when both materials are above or below the wetting transition. In the case where the only difference is the polymer chain length, the monolayer film beneath the droplet is composed of an equal amount of short chain and long chain monomers even when one component (the shorter chain length) is above the wetting transition and the other is not. The fraction of short and long chains in the precursor foot depends on whether both the short and the long chains are in the wetting regime. Diluting the concentration of the strongly wetting component in a mixture with a weakly wetting component decreases the rate of diffusion of the wetting material from the bulk to the surface and limits the spreading rate of the precursor foot, but the bulk spreading rate actually increases when both components are present. This may be due to the strongly wetting material pushing out the weakly wetting material as it moves toward the precursor foot.     

Layering, condensation, and evaporation of short chains in narrow slit pores

The phase behavior of short-chain fluids in slit pores is investigated by using a nonlocal-density-functional theory that takes into account the effects of segment size, chain connectivity, and van der Waals attractions explicitly. The layering and capillary condensation/evaporation transitions are examined at different chain length, temperature, pore width, and surface energy. It is found that longer chains are more likely to show hysteresis loops and multilayer adsorptions along with the capillary condensation and evaporation. Decreasing temperature favors the inclusion of layering transitions into the condensation/evaporation hysteresis loops. For large pores, the surface energy has relatively small effect on the pressures of the capillary condensation and evaporation but affects significantly on the layering pressures. It is also observed that all phase transitions within the pore take place at pressures lower than the corresponding bulk saturation pressure. The critical temperature of condensation/evaporation is always smaller than that of the bulk fluid. All coexistence curves for confined phase transitions are contained within the corresponding bulk vapor-liquid coexistence curve. As in the bulk phase, the longer the chain length, the higher are the critical temperatures of phase transitions in the pore.     

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.