Monte Carlo(MC) simulations produce evidence that annealed copolymers incorporating two interconverting monomers, P and H, adsorb as homopolymers with an effective adsorption energy per monomer, $ε_{eff}$, that depends on the PH equilibrium constants in the bulk and at the surface. The cross-over exponent, $Φ,$ is unmodified. The MC results on the overall PH ratio, the PH ratio at the surface and in the bulk as well as the number of adsorbed monomers are in quantitative agreement with this hypothesis and the theoretically derived $ε_{eff}$. The evidence suggests that the form of surface potential does not affect $Φ$ but does influence the PH equilibrium.
We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple equations for the adsorption-desorption transition line. We show that the adsorption threshold is the same for systems with quenched and annealed disorder. The results are discussed with respect to their implications for the physics of molecular recognition.
We study the translocation of a flexible polymer through a pore in a membrane induced by its adsorption on \trans side of the membrane. When temperature $T$ is higher than $T_c$, the adsorption-desorption transition temperature, attractive interaction between polymer and membrane plays little role in affecting polymer conformation, leading to translocation time that scales as $τ\sim L^3$ where $L$ is the polymer contour length. When $T < T_c$, however, the translocation time undergoes a sharp crossover to $τ\sim L^2$ for sufficiently long polymers, following the second order conformational (ad…
The structural properties of polymers adsorbed onto a surface have been widely investigated using self-consistent mean-field theories. Recently, analytical mean-field theories have been applied to study polymer adsorption on curved surfaces but all in the context of the ground state dominance approximation in which the polymer chain length (N) is essentially infinite. Using an expression for the free energy by Semenov, we determine leading order (in 1/N) corrections due to the finiteness of the polymer chain length on surface tension, spontaneous curvature, and rigidity constants.
Low-energy structures of a hybrid system consisting of a polymer and an attractive nanowire substrate as well as the thermodynamics of the adsorption transition are studied by means of Monte Carlo computer simulations. Depending on structural and energetic properties of the substrate, we find different adsorbed polymer conformations, amongst which are spherical droplets attached to the wire and monolayer tubes surrounding it. We identify adsorption temperatures and the type of the transition between adsorbed and desorbed structures depending on the substrate attraction strength.
The adsorption of a single polymer to a flat surface in shear is investigated using Brownian hydrodynamics simulations and scaling arguments. Competing effects are disentangled: in the absence of hydrodynamic interactions, shear drag flattens the chain and thus enhances adsorption. Hydrodynamic lift on the other hand gives rise to long-ranged repulsion from the surface which preempts the surface-adsorbed state via a discontinuous desorption transition, in agreement with theoretical arguments. Chain flattening is dominated by hydrodynamic lift, so overall, shear flow weakens the adsorption of f…
We have performed chain-growth simulations of minimalistic hybrid lattice models for polymers interacting with interfaces of attractive solid substrates in order to gain insights into the conformational transitions of the polymers in the adsorption process. Primarily focusing on the dependence of the conformational behavior on temperature and solubility we obtained pseudophase diagrams with a detailed structure of conformational subphases. In the study of hydrophobic-polar peptides in the vicinity of different types of substrates, we found a noticeable substrate specificity of the assembly of …
We discuss the adsorption of semiflexible polymers to a planar attractive wall and focus on the questions of the adsorption threshold for polymers of {\it finite} length and their loop and tail distributions using both Monte-Carlo simulations and analytical arguments. For the adsorption threshold, we find three regimes: (i) a flexible or Gaussian regime if the persistence length is smaller than the adsorption potential range, (ii) a semiflexible regime if the persistence length is larger than the potential range, and (iii) for finite polymers, a novel crossover to a rigid rod regime if the def…
Generalized-ensemble simulations enable the study of complex adsorption scenarios of a coarse-grained model polymer near an attractive nanostring, representing an ultrathin nanowire. We perform canonical and microcanonical statistical analyses to investigate structural transitions of the polymer and discuss their dependence on the temperature and on model parameters such as effective wire thickness and attraction strength. The result is a complete hyperphase diagram of the polymer phases, whose locations and stability are influenced by the effective material properties of the nanowire and the …
Monte Carlo simulations using an explicit solvent model indicate a new pathway for translocation of a polymer chain through a lipid bilayer. We consider a polymer chain composed of repeat units with a given hydrophobicity and a coarse-grained model of a lipid bilayer in the self-organized liquid state. By varying the degree of hydrophobicity the chain undergoes an adsorption transition with respect to the lipid bilayer. Close to the transition point, at a properly balanced hydrophobicity of the chain, the membrane becomes transparent with respect to the chain. At the same time the solvent perm…
The selective solute partitioning within a polymeric network is of key importance to applications in which controlled release or uptake of solutes in a responsive hydrogel is required. In this work we investigate the impact of cross-links on solute adsorption in a swollen polymer network by means of all-atom, explicit-water molecular dynamics simulations. We focus on a representative network subunit consisting of poly($N$-isopropylacrylamide) (PNIPAM) and $N$,$N'$-methylenebisacrylamide (BIS/MBA) cross-linker types. Our studied system consists of one BIS-linker with four atactic PNIPAM chains …
Single-molecule fluorescence imaging of adsorption onto initially-bare surfaces shows that polymer chains need not localize immediately after arrival. In a system optimized to present limited adsorption sites (quartz surface to which polyethylene glycol (PEG) is exposed in aqueous solution at pH = 8.2) we find that some chains diffuse back into bulk solution and re-adsorb at some distance away, sometimes multiple times before either they localize at a stable position or else diffuse away into bulk solution. This mechanism of surface diffusion is considerably more rapid than the classical model…
We propose a theoretical investigation of the physical adsorption of neutral comb-polymers with an adsorbing skeleton and non-adsorbing side-chains on a flat surface. Such polymers are particularly interesting as "dynamic coating" matrices for bio-separations, especially for DNA sequencing, capillary electrophoresis and lab-on-chips. Separation performances are increased by coating the inner surface of the capillaries with neutral polymers. This method allows to screen the surface charges, thus to prevent electro-osmosis flow and adhesion of charged macromolecules (e.g. proteins) on the capill…
Advanced chain-growth computer simulation methodologies have been employed for a systematic statistical analysis of the critical behavior of a polymer adsorbing at a substrate. We use finitesize scaling techniques to investigate the solvent-quality dependence of critical exponents, critical temperature, and the structure of the phase diagram. Our study covers all solvent effects from the limit of super-self-avoiding walks, characterized by effective monomer-monomer repulsion, to poor solvent conditions that enable the formation of compact polymer structures. The results significantly benefit f…
The study of competitive and cooperative adsorption of functionalized molecules such as polymers, rheology modifiers and surfactant molecules on colloidal particles immersed in a solvent is undertaken using coarse grained, dissipative particle dynamics simulations. The results show that a complex picture emerges from the simulations, one where dispersants and surfactants adsorb cooperatively up to certain concentrations, on colloidal particles, but as the surfactant concentration increases it leads to dispersant desorption. The presence of rheology modifying agents in the colloidal dispersion …
The process of adsorption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions is investigated. The performed scaling analysis is based on formal analogy between the polymer adsorption problem and the equivalent problem of critical phenomena in the semi-infinite $|ϕ|^4$ n-vector model (in the limit $n\to 0$) with a planar boundary. The whole set of surface critical exponents characterizing the process of adsorption of long-flexible polymer chains at the surface is obtained. The polymer linear dimensions parallel and perpendicul…
A liquid droplet impacting on a solvophobic surface normally rebounds. The rebound is suppressed by a small amount of dissolved polymer. In this work, using multi-body dissipative particle dynamics simulations, two anti-rebound mechanisms, the slow-retraction and the slow-hopping mechanisms, are identified. Which of them dominates depends on the polymer-surface attraction strength. However, these two mechanisms are not excluding each other but may coexist. During the droplet rebound, the surface-adsorbed polymer acts in two ways: the adsorbed beads mediate solvent-surface interactions, and hig…
We analyse the conformational behaviour of a linear semiflexible homo-polymer chain confined by two geometrical constraints under a good solvent condition in two dimensions. The constraints are stair shaped impenetrable surfaces. The impenetrable surfaces are lines in a two dimensional space. The infinitely long polymer chain is confined in between such two (A and B) surfaces. A lattice model of a fully directed self-avoiding walk is used to calculate the exact expression of the partition function, when the chain has attractive interaction with one or both the constraints. It has been found th…
We analyze the free energy for translocation of a polymer from the outside of a spherical vesicle to the inside. The process is assumed to be driven by the adsorption of the polymer on the inner surface of the vesicle. We argue that in the case where the polymer is adsorbed on the outer surface too, the entropic barrier for translocation is absent. We analyze the adsorption energy and find the free energy profile for the process. We argue that the motion corresponds to a polymer crossing a region with a change in free energy per segment. Based upon our earlier analsis of the behaviour of kinks…
The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data over a wide range of sphere radius and temperature, we have constructed entire phase diagrams both for non-grafted and end-grafted polymers. For the identification of the conformational phases, we have calculated several energetic and structural observables such as gyration tensor based shape parameters and their fluctuations by canonical statistical analysis. …
Adsorption of polymers to surfaces is crucial for understanding many fundamental processes in nature. Recent experimental studies indicate that the adsorption dynamics is dominated by non-equilibrium effects. We investigate the adsorption of a single polymer of length $N$ to a planar solid surface in the absence of hydrodynamic interactions. We find that for weak adsorption energies the adsorption time scales $ \sim N^{(1+2ν)/(1+ν)}$, where $ν$ is the Flory exponent for the polymer. We argue that in this regime the single chain adsorption is closely related to a field-driven polymer translocat…
Thermoresponsive polymer architectures have become integral building blocks of 'smart' functional materials in modern applications. For a large range of developments, e.g., for drug delivery or nanocatalytic carrier systems, the selective adsorption and partitioning of molecules (ligands or reactants) inside the polymeric matrix are key processes that have to be controlled and tuned for the desired material function. In order to gain insights into the nanoscale structure and binding details in such systems, we here employ molecular dynamics simulations of the popular poly(N-isopropylacrylamide…
Using non-equilibrium Brownian dynamics computer simulations, we have investigated the steady state statistics of a polymer chain under three different shear environments: i) linear shear flow in the bulk (no walls), ii) shear vorticity normal to the adsorbing wall, iii) shear gradient normal to the adsorbing wall. The statistical distribution of the chain end-to-end distance and its orientational angles are calculated within our monomer-resolved computer simulations. Over a wide range of shear rates, this distribution can be mapped onto a simple theoretical finite-extensible-nonlinear-elastic…
We present a lattice model for helicity induction on an optically inactive polymer due to the adsorption of exogenous chiral amine molecules. The system is mapped onto a one-dimensional Ising model characterized by an on-site polymer helicity variable and an amine occupancy one. The equilibrium properties are analyzed at the limit of strong coupling between helicity induction and amine adsorption and that of non-interacting adsorbant molecules. We discuss our results in view of recent experimental results.
We probe the electrostatic mechanism driving adsorption of polyelectrolytes onto like-charged membranes upon the addition of tri- and tetravalent counterions to a bathing monovalent salt solution. We develop a one-loop-dressed strong coupling theory that treats the monovalent salt at the electrostatic one-loop level and the multivalent counterions within a strong-coupling approach. It is shown that the adhesive force of the multivalent counterions mediating the like-charge adsorption arises from their strong condensation at the charged membrane. The resulting interfacial counterion excess loca…
Random sequential adsorption (RSA) of polymer, modeled as a chain of identical spheres, is systematically studied. In order to control precisely anisotropy and number of degrees of freedom, two different kinds of polymers are used. In the first one, monomers are placed along a straight line, whereas in the second, relative orientations of particles are random. Such polymers fill a flat homogeneous surface randomly. The paper focuses on maximal random coverage ratio and adsorption kinetics dependence on polymer size, shape anisotropy, and numbers of degrees of freedom. Obtained results were dis…
The adsorption of polymer and surfactant molecules onto colloidal particles or droplets in solution can be characterized non-destructively by scattering techniques. In a first part, the general framework of Dynamic Light Scattering, Small Angle Neutron and X-ray Scattering for the determination of the structure of adsorbed layers, and namely of the density profile, is presented. We then review recent studies of layers of the model polymer poly(ethylene oxide), as homopolymer or part of a block copolymer. In this field, scattering with contrast variation has been shown to be a powerful tool to …
The adsorption of polydisperse ideal polymer chains is shown to be sensitive to the large N tail of the distribution of chains. If and only if the number of chains decays more slowly than exponentially then there is an adsorption transition like that of monodisperse infinite chains. If the number decays exponentially the adsorption density diverges continuously at a temperature which is a function of the mean chain length. At low coverages, chains with repulsive monomer--monomer interactions show the same qualitative behaviour
Taking into account the well known correspondence between the field theoretical O(n)-vector model in the limit $n\to 0$ and the behavior of long-flexible polymer chains in a good solvent the investigation of ideal polymer chains adsorption onto structured surface like as a chemical step (where one part of a surface is repulsive for polymers and other part is at the adsorption threshold) was performed. The two-point correlation function of ideal polymer chain in the half - space bounded by structured surface with different adsorption energies $c_{1}$ and $c_{2}$ (with $c_{1}\neq c_{2}$) and the…
We construct the complete structural phase diagram of polymer adsorption at substrates with attractive stripe-like patterns in the parameter space spanned by the adsorption affinity of the stripes and temperature. Results were obtained by extensive generalized-ensemble Monte Carlo simulations of a generic model for the hybrid organic-inorganic system. By comparing with adhesion properties at homogeneous substrates, we find substantial differences in the formation of adsorbed polymer structures if translational invariance at the surface is broken by a regular pattern. Beside a more specific und…
Modification of surface properties by polymer adsorption is a widely used technique to tune interactions in molecular experiments such as nanopore sensing. Here, we investigate how the ionic current noise through solid-state nanopores reflects the adsorption of short, neutral polymers to the pore surface. The power spectral density of the noise shows a characteristic change upon adsorption of polymer, the magnitude of which is strongly dependent on both polymer length and salt concentration. In particular, for short polymers at low salt concentrations no change is observed, despite verificatio…
The adsorption of a single ideal polymer chain on energetically heterogeneous and rough surfaces is investigated using a variational procedure introduced by Garel and Orland (Phys. Rev. B 55 (1997), 226). The mean polymer size is calculated perpendicular and parallel to the surface and is compared to the Gaussian conformation and to the results for polymers at flat and energetically homogeneous surfaces. The disorder-induced enhancement of adsorption is confirmed and is shown to be much more significant for a heterogeneous interaction strength than for spatial roughness. This difference also a…
We consider the adsorption of a semiflexible polymer chain onto interfaces and surfaces by using the differential equation of the distribution function $G(R,L)$ of the end-to-end distance $R$, which is associated with the moment expansion of the latter. We present the results of the approximative treatment consisting of taking into account the 2nd and 4th moments in the differential equation for $G(R,L)$. The essential features of adsorption of the semiflexible polymer are: {\it i}) the existence of a new local length scale, which results in two-exponential decay of the monomer density of adso…
We investigate the cooperative effects of a single finite chain of monomers near an attractive substrate by first constructing a conformational pseudo-phase diagram based on the thermal fluctuations of energetic and structural quantities. Then, the adsorption transition is analyzed in more detail. This is conveniently done by a microcanonical analysis of densities of states obtained by extensive multicanonical Monte Carlo simulations. For short chains and strong surface attraction, the microcanonical entropy turns out to be a convex function of energy in the transition regime. This is a charac…
Physico-chemical study of polymer mixtures formed by a polycation and a zwitterionic copolymer in aqueous solution and upon adsorption onto negatively charged surfaces
Polymer adsorption on fractally rough walls of varying dimensionality is studied by renormalization group methods on hierarchical lattices. Exact results are obtained for deterministic walls. The adsorption transition is found continuous for low dimension $d_w$ of the adsorbing wall and the corresponding crossover exponent $ϕ$ monotonically increases with $d_w$, eventually overcoming previously conjectured bounds. For $d_w$ exceeding a threshold value $d_w^*$, $ϕ$ becomes 1 and the transition turns first--order. $d_w^*>d_{saw}$, the fractal dimension of the polymer in the bulk. An accurate num…
We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of …
We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p_c of attractive sites. The percolation cluster is characterized by a fractal dimension d_s^{p_c}=91/49. The conformational properties of polymer chains grafted to such a fractal substrate are studied by means of the pruned-enriched Rosenbluth method (PERM). We find estimates for the surface crossover exponent governing the scaling of the adsorption energy in the vicinity of the transition point, ϕ_s^{p_c}=0.425\pm0.009, and for …
We study the adsorption of semiflexible polymers such as polyelectrolytes or DNA on planar and curved substrates, e.g., spheres or washboard substrates via short-range potentials using extensive Monte-Carlo simulations, scaling arguments, and analytical transfer matrix techniques. We show that the adsorption threshold of stiff or semiflexible polymers on a planar substrate can be controlled by polymer stiffness: adsorption requires the highest potential strength if the persistence length of the polymer matches the range of the adsorption potential. On curved substrates, i.e., an adsorbing sphe…
We compare the thermodynamic behavior of a finite single nongrafted polymer near an attractive substrate with that of a polymer grafted to that substrate. After we recently found first-order-like signatures in the microcanonical entropy at the adsorption transition in the nongrafted case, and given the fact that many studies on polymer adsorption in the past have been performed for grafted polymers, the question arises, to what extent and in what way does grafting change the nature of the adsorption transition? This question is tackled here using a coarse-grained off-lattice polymer model and …
In many biological processes highly charged biomolecules are adsorbed into oppositely charged surfaces of macroions and membranes. They form strongly correlated structures close to the surface which can not be explained by the conventional Poisson-Boltzmann theory. Many of the flexible biomolecules can be described by Gaussian polymers. In this work strong coupling theory is used to study the adsorption of highly charged Gaussian polyelectrolytes. Two cases of adsorptions are considered, when the Gaussian polyelectrolytes are confined a) by one charged wall, and b) between two charged walls. T…
We consider the phase diagram of self-avoiding walks (SAW) on the simple cubic lattice subject to surface and bulk interactions, modeling an adsorbing surface and variable solvent quality for a polymer in dilute solution, respectively. We simulate SAWs at specific interaction strengths to focus on locating certain transitions and their critical behavior. By collating these new results with previous results we sketch the complete phase diagram and show how the adsorption transition is affected by changing the bulk interaction strength. This expands on recent work considering how adsorption is a…
The evolution over time of the non-linear slip behavior of a polydimethylsiloxane (PDMS) polymer melt on a weakly adsorbing surface made of short non-entangled PDMS chains densely end-grafted to the surface of a fused silica prism has been measured. The critical shear rate at which the melt enters the nonlinear slip regime has been shown to increase with time. The adsorption kinetics of the melt on the same surface has been determined independently using ellipsometry. We show that the evolution of slip can be explained by the slow adsorption of melt chains using the Brochard-de Gennes's model.
Adsorption of the low density lipoproteins on the micropatterned polymer brush: computer simulations
Yukhnovskii Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院尤赫诺夫斯基凝聚态物理研究所）；Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University（利沃夫国立理工大学应用数学与基础科学研究所）；Department of Internal Medicine No. 2, Danylo Halytskyi Lviv Medical University（丹尼尔·加利茨基利沃夫医科大学第二内科）
The subject of this work is the adsorption transition of a long flexible self-avoiding polymer chain onto a rigid thin rod. The rod is represented by a cylinder of radius R with a short-ranged attractive surface potential for the chain monomers. General scaling results are obtained by using renormalization group arguments in conjunction with available results for quantum field theories with curved boundaries [McAvity and Osborn 1993 Nucl. Phys. B 394, 728]. Relevant critical exponents are identified and estimated using geometric arguments.
We have explored a model for adsorption of water into slit-like nanochannels with two walls chemically modified by grafted polymer layers forming brushes. A version of density functional method is used as theoretical tools. The water-like fluid model adopted from the work of Clark et al. [Mol. Phys., 2006, 104, 3561] adequately reproduces the bulk vapour-liquid coexistence envelope. The polymer layer consists of chain molecules in the framework of pearl-necklace model. Each chain molecule is chemically bonded to the pore walls by a single terminating segment. Our principal focus is in the stud…
In their tubelike phase, nanowire-adsorbed polymers exhibit strong structural similarities to morphologies known from single-walled carbon (hexagonal) and boron (triangular) nanotubes. Since boron/boron nitride tubes require some disorder for stability the triangular polymer tubes provide a closer analog to the carbon tubes. By means of computer simulations of both two and three dimensional versions of a coarse-grained bead-spring model for the polymers, we investigate their structural properties and make a detailed comparison with structures of carbon nanotubes.
We propose a design for polymer-based sensors and switches with sharp switching transition and fast response time. The switching mechanism involves a radical change in the conformations of adsorption-active minority chains in a brush. Such transitions can be induced by a temperature change of only about ten degrees, and the characteristic time of the conformational change is less than a second. We present an analytical theory for these switches and support it by self-consistent field calculations and Brownian dynamics simulations.
Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the non-equilibrium layers which result. While the density profile and loop distribution are the same as for equilibrium layers, the final layer comprises a tightly bound inner part plus an outer part whose chains make only fN surface contacts where N is chain length. The contact fractions f follow a broad distribution, P(f) ~ f^{-4/5}, in rather close agreement with strong physisorption experiments [H. M. Schneider et al, Langmuir v.12, p.994 (1996)].
We study by Monte Carlo simulations a model of knotted polymer ring adsorbing onto an impenetrable, attractive wall. The polymer is described by a self-avoiding polygon (SAP) on the cubic lattice. We find that the adsorption transition temperature, the crossover exponent $ϕ$ and the metric exponent $ν$, are the same as in the model where the topology of the ring is unrestricted. By measuring the average length of the knotted portion of the ring we are able to show that adsorbed knots are localized. This knot localization transition is triggered by the adsorption transition but is accompanied b…
We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter $\varepsilon$, and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force $F$ applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption…
We examine the phase transition of polymer adsorption as well as the underlying kinetics of polymer binding from dilute solutions on a structureless solid surface. The emphasis is put on the properties of regular multiblock copolymers, characterized by block size M and total length N as well as on random copolymers with quenched composition p of sticky and neutral segments. The macromolecules are modeled as coarse-grained bead-spring chains subject to a short-ranged surface adhesive potential. Phase diagrams, showing the variation of the critical threshold for single chain adsorption in terms …
The force-assisted desorption kinetics of a macromolecule from adhesive surface is studied theoretically, using the notion of tensile (Pincus) blobs, as well as by means of Monte-Carlo (MC) and Molecular Dynamics (MD) simulations. We show that the change of detached monomers with time is governed by a differential equation which is equivalent to the nonlinear porous medium equation (PME), employed widely in transport modeling of hydrogeological systems. Depending on the pulling force and the strength of adsorption, three kinetic regimes can be distinguished: (i) "trumpet" (weak adsorption and …
The behavior of annealed branched polymers near adsorbing surfaces plays a fundamental role in many biological and industrial processes. Most importantly single stranded RNA in solution tends to fold up and self-bind to form a highly branched structure. Using a mean field theory, we both perturbatively and numerically examine the adsorption of branched polymers on surfaces of several different geometries in a good solvent. Independent of the geometry of the wall, we observe that as branching density increases, surface tension decreases. However, we find a coupling between the branching density…
We investigated the influence of short- and long-range correlated quenched disorder introduced into the medium on the process of adsorption of long-flexible polymer chains on a wall by using the field theoretical approach in $d=4-ε$ and the directly in d=3 dimensions up to one-loop order for the semi-infinite $|ϕ^4|$ m-vector model (in the limit $m \to 0$) with a boundary. This allows us to describe the critical behaviour of long-flexible polymer chains in the vicinity of the surface and to obtain the whole set of surface critical exponents at the special surface transition ($c=c_{ads}$), whic…
We study analytically a model of a two dimensional, partially directed, flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an externally applied force. We find that the wall has a dramatic effect on the polymer. For wall attraction smaller than the non-sequential nearest neighbor attraction, the fraction of monomers at the wall is zero and the model is the same as that of a polymer without a wall. However, for greater than, the fraction of monomers at the wall undergoes a first order trans…
