Critical Adsorption Energy Research Articles

Interfacial adhesion properties of graphene sheet on nanoscale corrugated surface: a molecular dynamics simulation study

Adhesive contacts between graphene sheet (GS) and corrugated substrates made of an ordered array of atomic pillars with variable geometries were investigated by molecular dynamics simulations. Depending on the height and interval distance of the pillars, GS can conformably coat the surface, partially adhere, or remain flat on top of the pillars. The relationship between the geometries of the pillar and the final adhesion configurations of GS was partially established. A critical adsorption energy was determined to achieve stable adsorption configuration of GS on corrugated substrates made of ordered pillar arrays. Besides the geometries of pillars, the effects of initial coating angle of GS were also considered as an important factor that affects the final adsorption configuration. We observed two interesting morphologies of GS, ‘I shape’ and ‘L shape’, which were determined by the initial coating angles.

Macrophase and Microphase Separations for Surfactants Adsorbed on Solid Surfaces: A Gauge Cell Monte Carlo Study in the Lattice Model

By combining the gauge cell method and lattice model, we study the surface phase transition and adsorption behaviors of surfactants on a solid surface. Two different cases are considered in this work: macrophase transition and adsorption in a single-phase region. For the case of macrophase transition, where two phases coexist, we investigate the shape and size of the critical nuclei and determine the height of the nucleation barrier. It is found that the nucleation depends on the bulk surfactant concentration. Our simulations show that there exist a critical temperature and critical adsorption energy, below which the transition from low-affinity adsorption to the bilayer structure shows the characteristic of a typical first-order phase transition. Such a surface phase transition in the adsorption isotherm is featured by a hysteresis loop. The hysteresis loop becomes narrower at higher temperature and weaker adsorption energy and finally disappears at the critical value. For the case where no macrophase transition occurs, we study the adsorption isotherm and microphase separation in a single-phase region. The simulation results indicate that the adsorption isotherm in adsorption processes is divided into four regions in a log-log plot, being in agreement with experimental observations. In this work, the four regions are called the low-affinity adsorption region, the hemimicelle region, the morphological transition region, and the plateau region. Simulation results reveal that in the second region the adsorbed monomers aggregate and nucleate hemimicelles, while adsorption in the third region is accompanied by morphological transitions.

Adsorption of Multiblock and Random Copolymer on a Solid Surface: Critical Behavior and Phase Diagram

The adsorption of a single multiblock AB copolymer on a solid planar substrate is investigated by means of computer simulations and scaling analysis. It is shown that the problem can be mapped onto an effective homopolymer adsorption problem. In particular, we discuss how the critical adsorption energy and the fraction of adsorbed monomers depend on the block length M of sticking monomers A, and on the total length N of the polymer chains. Also the adsorption of the random copolymers is considered and found to be well described within the framework of the annealed approximation. For a better test of our theoretical prediction, two different Monte Carlo (MC) simulation methods were employed: (a) off-lattice dynamic bead-spring model, based on the standard Metropolis algorithm (MA), and (b) coarse-grained lattice model using the pruned-enriched Rosenbluth method (PERM) which enables tests for very long chains. The findings of both methods are fully consistent and in good agreement with theoretical predictions.

Simulation of Gradient Copolymers Synthesis via Conformation-Dependent Graft Copolymerization near a Uniform Adsorbing Surface

A statistical model is developed for radical graft copolymerization in a solution of monomers A and B in the vicinity of a surface selectively absorbing the monomers of type A and corresponding copolymer sections. The influence of the monomer concentrations and the short-range monomer A−surface attraction on the copolymer sequence is investigated. It is shown that under certain conditions, the adsorption copolymerization can yield gradient copolymers. We find three copolymerization regimes corresponding to different values of dimensionless adsorption energy u. When the growing macroradical is weakly or nonadsorbed, u < uc (uc is the critical adsorption energy), the statistical properties of graft copolymers approach asymptotically, in the long-chain limit, to those of a random copolymer. If u ≳ uc, the statistics of designed and random copolymers is very different. In the vicinity of uc, the adsorption copolymerization leads to copolymers with the largest compositional nonuniformity and well-pronounced gr...

Separating Surface and Solvent Effects and the Notion of Critical Adsorption Energy in the Adsorption of Phenolic Compounds by Activated Carbons

A modified form of the Freundlich equation in which the solute equilibrium concentration is normalized with respect to the solute solubility is analyzed and applied to adsorption isotherms of phenol, 4-nitrophenol, 4-chlorophenol, and 2-chlorophenol at different values of pH on commercial activated carbon before and after oxidation. The analysis confirms the importance of normalizing the solute equilibrium concentration when analyzing the adsorption isotherms, and it is suggested that a parameter, K(F10), obtained by taking 10% solubility as the reference point when applying the Freundlich equation, is probably the best comparative estimate of the relative adsorption capacity of the carbon for different phenolic compounds. In combination with the Freundlich exponent, n(F), estimates of the adsorption capacity at any other reference point can then be obtained. Analysis of the experimental results also indicates a need to distinguish between two regimes of adsorption, characterized by an adsorption energy, E(ads), greater than or less than a critical value, E(ca). When E(ads) > E(ca), the shape of the adsorption isotherm is determined by solute-solid interactions. On the other hand, when E(ads) < E(ca), solute-solution interactions become more important.

Monte Carlo Calculations of Polymer Adsorption at the Entrance of Cylindrical Pores in Flat Adsorbing Surfaces

The influence of surface interactions on the conformation of flexible polymers partially confined inside narrow cylindrical pores in a flat surface is studied above the critical adsorption energy in a good solvent. We use a static configurational bias computational sampling method to calculate the adsorption free energy and the radius of gyration components parallel and perpendicular to the pore axis as a function of the polymer center of mass position at different degrees of confinement. We find strong free‐energy minima just in front of the pore entry for all degrees of confinement studied. At the location of the free‐energy minimum, polymers are partially adsorbed inside the pore and on the outer solid surface and adopt drawing pin‐like conformations. A distinct maximum in the average loop length at the pore entry indicates that the polymer bridges the pore entry of small pores.

Concentration Effects in Partitioning of Macromolecules into Pores with Attractive Walls

The influence of polymer concentration on the partitioning of flexible macromolecules into adsorptive pores was examined by simulations in an open system under good solvent conditions. In dilute solutions, the partition coefficient K(ε,φ) is sensitive to small variations of both polymer−pore attraction strength ε and concentration φ, whereas in semidilute solutions both influences level off. At weak attraction below critical adsorption energy εc, the coefficient K increases with φ in a fashion that resembles the weak-to-strong penetration transition found for purely steric exclusion (ε = 0) but modified as if the width of pores effectively increased. At moderate attraction above the critical condition the increasing concentration brings about a dramatic drop in the value of K. Additionally, the K(φ) dependences in attractive pores were calculated by an approximate method based on expressions for chemical potentials, and the results were in good agreement with the simulation data. The critical adsorption energy εc for excluded volume chains was found to depend on concentration; the compensation point K = 1 was located at about φ = 0.012 irrespective of the pore width. The energy and entropy contributions to the free energy of confinement were calculated and the compensation of their values at the critical condition was demonstrated. Furthermore, it was shown that the effect of concentration in polymer partitioning with adsorptive pores can alternatively be regarded as a confined adsorption and two alternatives of the adsorbed amount Γ were calculated. The adsorption and depletion concentration profiles φI(x) in the pore in equilibrium with the bulk solution were presented and their variation with concentration φ and attraction ε was analyzed.

Properties ofABcopolymers with a special adsorption-tuned primary structure

As one of the realizations of our recently proposed idea of conformation-dependent sequence design (engineering) of $\mathrm{AB}$ copolymers, here we introduce the notion of adsorption-tuned copolymers (ATC's). Such copolymers are prepared by adsorbing a homopolymer chain onto a flat surface, after which its adsorbed segments are called type A ones, and its unadsorbed segments type B ones. Next, for the primary structure generated in this way, we study the adsorption of ATC's on (some other) surface for the case when only the type A segments are attracted to this surface. The properties of the ATC copolymers are compared with those of random copolymers (RC's) with the same content of type A segments, and random-block copolymers (RBC's) with the same content of type A segments and the same number of blocks. It is shown that the specific features of the ATC primary structure promote adsorption of the ATC chains, leading to an increase of their (negative) critical adsorption energy and the number of adsorbed segments as compared to that of RC and RBC chains. Some characteristics of the adsorbed single chains (statistics of trains, loops, and tails) are studied. The difference between the ATC, RBC, and RC ensembles in these characteristics is explained by the difference in the primary structures of the copolymers. The results obtained support the general idea of conformation-dependent sequence design of $\mathrm{AB}$ copolymers, and are probably connected with the theory of the early stages of macromolecular prebiological evolution.

A Continuum Model for Polymer Adsorption at the Solid−Liquid Interface

A continuum version of self-consistent field model for polymer adsorption at the solid−liquid interface has been formulated and solved to obtain configurational statistics of an adsorbed polymer chain. The solid surface is viewed as a singular phase (having zero thickness but finite adsorption capacity) in equilibrium with the solution. Chain configuration is described by the random flight model. The surface boundary condition accounts for both the configurational constraint and the adsorption equilibrium. The potential field is described by a modified form of the Flory−Huggins theory, which incorporates the effect of unequal partial volumes of the species (chain segment and solvent molecule) in the solution and their unequal partial areas in the surface phase. The model predictions are in qualitative agreement with the Scheutjens and Fleer model, except that the model predicts a negative value of , the critical adsorption energy parameter. The model has been validated using experimental data reported in the literature. The present model has advantages over the Scheutjens and Fleer model both in terms of ease of computation and the ability of the model to account for the difference in the packing densities between the solution and the surface.

Polymer chain binding with a flat adsorbent in the case of selective adsorption of segments: Monte Carlo simulation

Adsorption of a single regular AB copolymer chain on a flat impenetrable surface is studied by Monte Carlo simulation. Type A segments, which are regularly distributed over the chain length, are attracted to the surface with the energy ε, whereas for type B segments the surface serves only as an impenetrable obstacle. The critical adsorption energy is found as a function of fraction of type A segments φ. The dependencies of the average numbers of adsorbed sections (i.e., trains), loops, and tails and the average numbers of segments in these sections on ε are obtained. These dependencies are qualitatively different for homogeneous (φ=1) and heterogeneous (φ&amp;lt;1) chains. At φ⩽0.25, the lengths of train and loop sections become independent of the parameters φ and ε and determined solely by geometric peculiarities of the chain model under consideration. The average number and length of tails are always independent of the chain length. In the strong adsorption regime, the average numbers of loops and trains are proportional to the chain length for both heterogeneous and homogeneous chains. The segment density distribution for the adsorbed chain near the surface is different for homogeneous and heterogeneous chains in both weak and strong adsorption regimes.

Brush Theory of Tethered Chains with a Charged Group at the Free End

We consider the problem of end-grafted polymer molecules with a charged group attached to the free end both by an analytical and a numerical method. In the analytical approach the Gaussian model for the polymer chains is used. In this model volume interactions are ignored and analytical solutions for special type of boundary conditions are found. We consider both a repulsive surface, and a critical adsorption energy surface. The complete Poisson-Boltzmann equation is used and deviations from local electroneutrality are considered in a perturbation methd scheme. It is found that deviations of local electroneutrality both scale inversely with the chain length (N -1 and inversely with the ionic strength (Φ s -1 ). In the numerical method we apply a self-consistent-field scheme of freely jointed chains in Θ conditions. Results of the analytical model compare favorably to those obtained by the numerical method.

Effect of an adsorbing surface on the phase behavior of a confined semiflexible liquid crystal

Results of a study of the nematic to isotropic transition of a liquid crystal near an adsorbing surface in a thin film using Monte Carlo simulation are presented. The order parameter profile, heat capacity and overall order parameter are calculated to characterize the system as it undergoes the transition. We show that the strength of the adsorption energy has a large influence on the phase behavior of the system. At low adsorption energies a boundary layer is present which undergoes a transition from a nematic to a partially ordered phase at the reduced temperature τ1 and then undergoes a transition to an isotropic orientation at the reduced temperature τ2 which is separate from the bulk. The bulk undergoes an order–disorder transition at a temperature τ3 between the two orientation transitions τ1 and τ2 of the boundary layer. For strong adsorption energies, the boundary layer increases to the thickness of the sample. In this regime, the complete system undergoes the nematic–isotropic transition simultaneously and the temperature of this transition increases linearly with the adsorption energy. The case of intermediate adsorption energies corresponds to a crossover between the above two limiting situations. Here, the boundary layer is more disordered than the bulk and, yet, the entire sample undergoes the nematic–isotropic transition simultaneously. The observed phase behavior is explained in terms of the influence of the boundary layer on the order of the system. The present situations suggest the existence of a critical adsorption energy above which there is only one transition but below which several transitions occur due to the intervention of the boundary layer.

Separation Mechanism of Copolymers from Styrene and Methyl Methacrylate According to Composition by Liquid Adsorption Chromatography

Abstract Silica gel and a mixture of chloroform and ethanol were used as the stationary and the mobile phases, respectively. At the isocratic elution mode, the copolymers tended to adsorb on the column with increasing MMA content in the copolymers, with increasing column temperature, and with decreasing ethanol content in the mobile phase. The copolymers appeared always at the position proportional to the interstitial volume in the column, otherwise they adsorbed on the column. The equilibrium distribution of the copolymers between the mobile phase and the stationary phase cannot be considered in this system. Hydrogen bonding of carbonyl groups in MMA units of the copolymers to silanol groups on the surface of silica gel was considered to be the main interaction between the copolymers and the adsorbent. The hydrogen bonding increases with increasing the number of carbonyl groups per unit surface of copolymer coil in solution and with increasing free silanol groups on the silica surface. Ethanol in the stationary phase controls the content of the free silanol groups on the surface and is controlled by the content of ethanol in the mobile phase in addition to column temperature. This phenomena can be explained by introducing the term of the adsorption energy of a copolymer segment with the silica surface. The adsorption energy is proportional to the strength of the hydrogen bonding. Above the critical adsorption energy which is defined to be equal to the dissolution energy of the copolymer to the mobile pahse, the copolymers adsorb on the surface of silica gel and the desorption of the copolymers advances when the adsorption energy approaches to the critical adsorption energy. No adsorption of the copolymers is possible when the adsorption energy is equal or below the critical adsorption energy.

Imaging of layered semiconductor clusters by scanning tunneling microscopy: Bi2S3 on graphite and gold substrates

We present scanning tunneling microscope images of Bi2S3 clusters deposited on the surfaces of graphite and gold. We observed similar images on both substrates, discerning the disk-like structures expected for clusters having layered symmetry. The images of highest quality were obtained for 600-atom clusters roughly 100 Å in lateral extent and 25 Å thick. The difficulty in characterizing clusters with smaller lateral dimension suggests that clusters must be bound to the surface with a critical adsorption energy in order to obtain stable images.

Phase transitions on adsorption of macromolecules

The general theory of the conformational transition on adsorption of the individual macromolecule on a solid surface is developed. The statistical sum of the macromolecule on the surface is constructed by the method of generating functions. It is shown that change in the equilibrium state of the chain from the free to adsorbed on a rigid adsorbent comes about for a certain critical adsorption energy of the units, i.e. has the character of a phase transition (for N → ∞). An equation is constructed relating the critical adsorption energy to the characteristics of the chain and adsorbent. The order of the phase transition is analyzed and it is shown that it is determined by the distribution function of the lengths of the loops formed by the free chain relative to the virtual surface drawn through it, the geometric equivalent of the adsorbent. An expression is obtained for the order of the phase transition including the dimensionality of the free volume and adsorbent (the number of measurements according to which the extent of the adsorbent is infinite) and the exponent in the dependence of the size of the free chain on the degree of polymerization. The possibility of diverse phase transitions on adsorption of the macromolecules is shown.

Adsorption of polypeptides on solid surfaces. I. Effect of chain stiffness

AbstractThe general method of obtaining the partition function and thermodynamic characteristics of polymer chains near an adsorbing surface, simulated by random walks on a lattice, is developed. The method takes into account the effect of short‐range interactions in polymer chains, in particular, the chain stiffness and secondary structure. The theory of adsorption of chains of different stiffness is developed, and the process of adsorption which occurs when the external conditions change is shown to be always a second‐order phase transition. The critical adsorption energy decreases and the sharpness of transition grows when the chain stiffness increases. A simple model of a chain with “virtual” steps is proposed which simplifies the treatment; the results obtained are in good agreement with exact theories. A general scheme of analysis of adsorption of chains with a given secondary structure is set forth and the analogy between the stiffness of a noncooperative chain and the presence of helical segments in a polypeptide chain is discussed.

Thin-layer chromatography of oligomers

The mechanism of the thin-layer chromatography of oligomers based on the different adsorption activities of the end groups and the central units, characterized by adsorption energies −ϵ e and −ϵ c , is discussed. It is shown that the application of the concept of the critical adsorption energy, −ϵ o , to the central oligomer units makes it possible to distinguish three cases of the molecular weight dependence of R F values: at −ϵ o > −ϵ c and −ϵ o < −ϵ c we have a negative and positive molecular weight dependence of R F values, respectively, while at −ϵ o = −ϵ c the R F values do not depend on molecular weight. In the last instance, thin-layer chromatography can be used for the separation of oligomers on the basis of functional groups and degree of branching independent of their molecular weights. For the separation of oligomers on the basis of molecular weight thin-layer chromatography, hydroxyl end groups should be blocked in the case of poor adsorption activity of the central units. In this instance the second type of molecular weight dependence of R F values is observed. A quantitative method for the determination of low-functionality impurities monools and poly(propylene oxide)diols in oligomers based on the chromatographic spot length is suggested.

Conformation of Adsorbed Polymeric Chain. IV

Abstract In order to develop further the theoretical treatment of a polymeric chain adsorbed at an interface, a random walk model, in which each step has the same probability except that no step can retrace the preceding one on a simple cubic lattice, has been used. The average number of adsorbed segments \barν, the average number of trains \barm, and the mean square end-to-end distance \barr2 are calculated as functions of the adsorption energy of segment ε and the number of segments n when n is infinitely large. The average numbers of segments in a train and a loop, \bark′ and \bark′, are also calculated. Through the increment in the value of critical adsorption energy εc, prohibition of immediate reversal for the random walk fairly influences the average properties of adsorbed polymeric ,chain. The decrease in \barm and the increase in \bark′ with ε⁄kT at its large values are remarkable in comparison with those of the symmetric random walk, which may be accounted for by the diminution of the chance of making loops. It is shown that \barr2 is equivalent to the mean square two-dimensional end-to-end distance of a restricted random walk without immediate reversals on a simple cubic lattice at εc⁄kT and approaches that on a simple square lattice in the limit ε⁄kT→∞.