In detailed microcanonical analyses of densities of states obtained by extensive multicanonical Monte Carlo computer simulations, we investigate the caloric properties of conformational transitions adsorbing polymers experience near attractive substrates. For short chains and strong surface attraction, the microcanonical entropy turns out to be a convex function of energy in the transition regime, indicating that surface-entropic effects are relevant. Albeit known to be a continuous transition in the thermodynamic limit of infinitely long chains, the adsorption transition of nongrafted finite-length polymers thus exhibits a clear signature of a first-order-like transition, with coexisting phases of adsorbed and desorbed conformations. Another remarkable consequence of the convexity of the microcanonical entropy is that the transition is accompanied by a decrease of the microcanonical temperature with increasing energy. Since this is a characteristic physical effect it might not be ignored in analyses of cooperative macrostate transitions in finite systems.
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.
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
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…
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…
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 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…
For the estimation of transition points of finite elastic, flexible polymers with chain lengths from $13$ to $309$ monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification o…
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 address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that si…
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 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 …
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 …
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…
We study the problem of adsorption and collapse transition of a linear polymer chain situated in a fractal container represented by a 4-simplex lattice and interacting with a surface adsorbed linear polymer chain. The adsorbed chain monomers act as pinning sites for the polymer chain. This problem has been solved exactly using real space renormalization group transformation. The resulting phase diagram and critical exponents are given.
We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying notion of a ``stem-flower'' polymer conformation, and the related mechanism of ``zipping'' during the adsorption process are shown to lead to a Fokker-Planck equation with reflecting boundary conditions for the time-dependent probability distribution function (PDF) of the number of adsorbed monomers. The theoretical treatment predicts that the mean fraction …
This chapter deals with various aspects related to the adsorption of long chain-like macromolecules (polymers) onto solid surfaces. Physical aspects of the adsorption mechanism are elaborated mainly at thermodynamical equilibrium. The basic features needed in modeling of this adsorption are discussed. We first discuss the adsorption of a single and long polymer chain to the surface. The surface interaction is modeled by a potential well with a long-ranged attractive tail. A simple mean-field theory description is presented and the concept of polymer "blobs" is used to describe the conformation…
The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.
Using extensive Monte Carlo simulations, we investigate the surface adsorption of self-avoiding trails on the triangular lattice with two- and three-body on-site monomer-monomer interactions. In the parameter space of two-body, three-body, and surface interaction strengths, the phase diagram displays four phases: swollen (coil), globule, crystal, and adsorbed. For small values of the surface interaction, we confirm the presence of swollen, globule, and crystal bulk phases. For sufficiently large values of the surface interaction, the system is in an adsorbed state, and the adsorption transitio…
The problem of charged polymer chains (polyelectrolytes) as they adsorb on a planar surface is addressed theoretically. We review the basic mechanisms and theory underlying polyelectrolyte adsorption on a single surface in two situations: adsorption of a single charged chain, and adsorption from a bulk solution in $θ$ solvent conditions. The behavior of flexible and semi-rigid chains is discussed separately and is expressed as function of the polymer and surface charges, ionic strength of the solution and polymer bulk concentration. We mainly review mean-field results and briefly comment about…
We employ the recently introduced generalized microcanonical inflection point method for the statistical analysis of phase transitions in flexible and semiflexible polymers and study the impact of the bending stiffness upon the character and order of transitions between random-coil, globules, and pseudocrystalline conformations. The high-accuracy estimates of the microcanonical entropy and its derivatives required for this study were obtained by extensive replica-exchange Monte Carlo simulations. We observe that the transition behavior into the compact phases changes qualitatively with increas…
We analyze the structural behavior of a single polymer chain grafted to an attractive, flexible surface. Our model is composed of a coarse-grained bead-and-spring polymer and a tethered membrane. By means of extensive parallel tempering Monte Carlo simulations it is shown that the system exhibits a rich phase behavior ranging from highly ordered, compact to extended random coil structures and from desorbed to completely adsorbed or even partially embedded conformations. These findings are summarized in a pseudophase diagram indicating the predominant class of conformations as a function of the…
By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of systematically identifying and locating independent and dependent phase transitions of any order is proposed. The power of the generalized method is demonstrated in applications to the ferromagnetic Ising model and a coarse-grained model for polymer adsorption onto a substrate. The results shed new light on the intrinsic phase structure of systems with cooperative beha…
We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two cases are considered, distinguished by the value of the local monomer-surface sticking rate Q: chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single chain adsorption. While single chain physisorption times tau_ads are typically microsecs, for chemisorbing chains of N units we find experimentally accessible times tau_ads = Q^{-1} N^{3/5}, ranging from secs to hrs. We establish 3 chemisorption…
Recent experiments have demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk, the amplitude and the sign of this effect depending on the interaction between the polymer and the substrate. A model has been proposed recently for explaining these effects in two limiting cases: suspended films and strongly adsorbed films. We extend here this model for describing the cross-over between these two situations. We show here how, by adjusting the strength of the adsorption, one can control the glass transition temperature of …
Lattice model of directed self avoiding walk is used to investigate adsorption properties of a semiflexible sequential copolymer chain on an impenetrable curved surface on a hexagonal lattice in two dimensions. Walks of the copolymer chains are directed in a direction away from the surface at a suitable value of monomer surface attraction, the copolymer chain gets adsorbed on the surface. To calculate exact value of monomer surface attraction, the directed walk model have been solved analytically using generating function method to discuss results when one type monomer of the copolymer chain h…
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically from series expansion up to 19 sites of a self-attracting self avoiding walk in three dimensions. In two dimensions, we calculate analytically phase boundaries in some cases for a partially directed model. Both the numerical as well as analytical results corroborate the proposed qualitative phase diagram.
Counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. {\bf 120}, 9343 (2004)] that considers Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self consistent calculations of effective charge and size of polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions, polymer charge is compensated and reversed with…
Polymer chains undergoing a continuous adsorption-desorption transition are studied through extensive computer simulations. A three-dimensional self-avoiding walk lattice model of a polymer chain grafted onto a surface has been treated for different solvent conditions. We have used an advanced contact-density chain-growth algorithm, in which the density of contacts can be directly obtained. From this quantity, the order parameter and its fourth-order Binder cumulant are computed, as well as the corresponding critical exponents and the adsorption-desorption transition temperature. As the number…
Using molecular dynamic simulation, we study the stretching of an adsorbed homopolymer in a poor solvent with one end held at a distance $z_e$ from the substrate. We measure the vertical force $f$ on the end of the chain as a function of the extension $z_e$ and the substrate interaction energy $w$. The force reaches a plateau value at large extensions. In the strong adsorption limit, we show that the plateau value increase linearly in $w$ in good agreement with a theoretical model. In the weak adsorption limit, a polymer globule with a layered structure is formed and elastically deformed when …
In a mixed suspension of rods and small polymer coils, the rods adsorb onto a hard wall in contact with the suspension. This adsorption is studied in the low density of rods limit. It is driven by depletion forces and is much stronger for long rods than for spheres. This is shown by means of exact, numerical, calculations and an approximate theory.
Adsorption of charged polymers (polyelectrolytes) from a semi-dilute solution to a charged surface is investigated theoretically. We obtain simple scaling laws for (i) the amount of polymer adsorbed to the surface, Gamma, and (ii) the width of the adsorbed layer D, as function of the fractional charge per monomer p and the salt concentration c_b. For strongly charged polyelectrolytes (p<1) in a low-salt solution, both Gamma and D scale as p^{-1/2}. In salt-rich solutions D~c_b^{1/2}/p whereas the scaling behavior of Gamma depends on the strength of the polymer charge. For weak polyelectrolytes…
Prudent walks are self-avoiding walks which cannot step towards an already occupied vertex. We introduce a new model of adsorbing prudent walks on the square lattice, which start on an impenetrable surface and accrue a fugacity $a$ with each step along the surface. These are different to other exactly solved models of polymer adsorption, like Dyck paths, Motzkin paths and partially-directed walks, in that they are not trivially directed - they are able to step in all lattice directions. We calculate the generating functions, free energies and surface densities for this model and observe a firs…
We analyze the recently proposed "pattern-matching" phase of a Gaussian random heteropolymer adsorbed on a disordered substrate [S. Srebnik, A.K. Chakraborty and E.I. Shakhnovich, Phys. Rev. Lett. 77, 3157 (1996)]. By mapping the problem to that of a directed homopolymer in higher-dimensional random media, we show that the pattern-matching phase is asymptotically weakly unstable, and the large scale properties of the system are given by that of an adsorbed homopolymer.
We investigate the binding transition of two flexible polymers grafted to a steric surface with closeby end points. While free polymers show a discontinuous transition, grafting to a steric flat surface leads to a continuous binding transition. This is supported by results from Metropolis and parallel multicanonical simulations. A combination of canonical and microcanonical analyses reveals that the change in transition order can be understood in terms of the reduced translational entropy of the unbound high-temperature phase upon grafting.
We analyze equilibrium properties and adsorption desorption phase transition behaviour of a linear semiflexible copolymer chain under constrained geometrical situation on square lattice in a good solvent. One dimensional stair shaped line imposes geometrical constrain on the chain. Lattice model of fully directed self avoiding walk is used to model the chain, semiflexibility of the chain is accounted by introducing energy barrier for each bend of the chain. Exact expression of the partition function of the chain is obtained using generating function technique for the cases, viz. (i) constraine…
This chapter deals with charged polymers (polyelectrolytes) in solution and at surfaces. The behavior of polyelectrolytes is markedly different from that of neutral polymers. In bulk solutions, i.e. disregarding the surface effect, there are two unique features to charged polymers: first, due to the presence of long-ranged electrostatic repulsion between charged monomers, the polymer conformations are much more extended, giving rise to a very small overlap concentration and high solution viscosity. Second, the presence of a large number of counter-ions increases the osmotic pressure of polyele…
Recently, it has been proposed that the adsorption transition for a single polymer in dilute solution, modeled by lattice walks in three dimensions, is not universal with respect to inter-monomer interactions. It has also been conjectured that key critical exponents $ϕ$, measuring the growth of the contacts with the surface at the adsorption point, and $1/δ$, which measures the finite-size shift of the critical temperature, are not the same. However, applying standard scaling arguments the two key critical exponents should be identical, thus pointing to a potential breakdown of these standard …
We show that the structural properties and phase behavior of a self-avoiding polymer chain on adhesive substrate, subject to pulling at the chain end, can be obtained by means of a Grand Canonical Ensemble (GCE) approach. We derive analytical expressions for the mean length of the basic structural units of adsorbed polymer, such as loops and tails, in terms of the adhesive potential and detachment force, and determine values of the universal exponents which govern their probability distributions. Most notably, the hitherto controversial value of the critical adsorption exponent $ϕ$ is found to…
By means of contact-density chain-growth simulations, we investigate a simple lattice model of a flexible polymer interacting with an attractive substrate. The contact density is a function of the numbers of monomer-substrate and monomer-monomer contacts. These contact numbers represent natural order parameters and allow for a comprising statistical study of the conformational space accessible to the polymer in dependence of external parameters such as the attraction strength of the substrate and the temperature. Since the contact density is independent of the energy scales associated to the i…
We study the problem of adsorption of self-interacting linear polymers situated in fractal containers that belong to the three-dimensional (3d) Sierpinski gasket (SG) family of fractals. Each member of the 3d SG fractal family has a fractal impenetrable 2d adsorbing surface (which is, in fact, 2d SG fractal) and can be labelled by an integer $b$ ($2\le b\le\infty$). By applying the exact and Monte Carlo renormalization group (MCRG) method, we calculate the critical exponents $ν$ (associated with the mean squared end-to-end distance of polymers) and $ϕ$ (associated with the number of adsorbed m…
We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles, but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or con…
The microcanonical analysis is shown to be a powerful tool to characterize the protein folding transition and to neatly distinguish between good and bad folders. An off-lattice model with parameter chosen to represent polymers of these two types is used to illustrate this approach. Both canonical and microcanonical ensembles are employed. The required calculations were performed using parallel tempering Monte Carlo simulations. The most revealing features of the folding transition are related to its first-order-like character, namely, the S-bend pattern in the caloric curve, which gives rise t…
A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge. The well-known mapping between the statistical mechanics of an ideal polymer and the quantum problem of a particle in a potential is then used to analyze the singular behavior of the unbinding transition of the polymer. The divergence of the localization length is found to be governed by an exponent that varies continuously with the angle (wh…
We present a dissipative particle dynamics (DPD) simulation study on the surface modification of initiator embedded microparticles (MPs) of different shapes via atom transfer radical polymerization (ATRP) brush growth. The surface-initiated ATRP-brush growth leads to the formation of a more globular MP shape. We perform the comparative analysis of ATRP-brush growth on three different forms of particle surfaces: cup surface, spherical surface, and flat surface (rectangular/disk-shaped). First, we establish the chemical kinetics of the brush growth: the monomer conversion and the reaction rates.…
Using the results of the recently studied problem of adsorption of a Gaussian polymer in a weak periodic surface potential we study the influence of a single rod like defect on the polymer being localized in the periodic surface potential. We have found that the polymer will be localized at the defect under condition u>u_c, where u_c is the localization threshold in the periodic potential, for any infinitesimal strength of the interaction with defect. We predict that the concentration of monomers of the localized polymer decays exponentially as a function of the distance to the defect and is m…
The adsorption of a single multi-block $AB$-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 …
We use the lattice model of directed walks to investigate the conformational as well as the adsorption properties of a semiflexible homopolymer chain immersed in a good solvent in two and three dimensions. To account for the stiffness in the chain we have introduced energy barrier for each bend in the walk and have calculated the persistent length as a function of this energy. For the adsorption on an impenetrable surface perpendicular to the preferred direction of the walk we have solved the model exactly and have found the critical value of the surface attractions for the adsorption in both …
Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks interacting with (alternate) sites on the surface of the honeycomb lattice is $1+\sqrt{2}$. A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks interacting with a surface on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed for the honeycomb lattice persist ir…
We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. Using a ($n=0$ component) spin representation for these paths, we show the existence of a phase transition for strong coupling (i.e. at low temperature) towards a ``frozen'' phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between …
The critical adsorption point (CAP) of self-avoiding walks (SAW) interacting with a planar surface with surface disorder or sequence disorder has been studied. We present theoretical equations, based on ones previously developed by Soteros and Whittington (J. Phys. A.: Math. Gen. 2004, 37, R279-R325), that describe the dependence of CAP on the disorders along with Monte Carlo simulation data that are in agreement with the equations. We also show simulation results that deviate from the equations when the approximations used in the theory break down. Such knowledge is the first step toward unde…
A phase diagram for a surface-interacting long flexible polymer chain in a two-dimensional poor solvent where the possibility of collapse exists is determined using exact enumeration method. A model of a self-attracting self avoiding walk (SASAW) on a square lattice was considered and up to 28 steps in series were evaluated. A new adsorbed state having the conformation of a surface attached globule is found. Four phases (i) desorbed expanded, (ii) desorbed collapsed, (iii) adsorbed expanded and (iv) surface attached globule are found to meet at a point on the adsorption line.
We study the adsorption-desorption phase transition of directed branched polymer in $d+1$ dimensions in contact with a line by mapping it to a $d$ dimensional hard core lattice gas at negative activity. We solve the model exactly in 1+1 dimensions, and calculate the crossover exponent related to fraction of monomers adsorbed at the critical point of surface transition, and we also determine the density profile of the polymer in different phases. We also obtain the value of crossover exponent in 2+1 dimensions and give the scaling function of the sticking fraction for 1+1 and 2+1 dimensional di…
We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point. The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walks on regular lattices and gaussian walks. The adsorption transition, which is discontinuous, and its influence on the pressure are also studied.
Forced desorption of a semiflexible polymer chain on a solid substrate is theoretically investigated. The pulling force versus displacement is studied for different adsorption energy and persistence length P. It is found that the relationships between pulling force and cantilever displacement show a series of characteristic force spikes at different persistence length P. These force spikes becomes more pronounced but the average magnitude of this force decrease as P grows. Our results are of relevance to forced desorption of DNA on an attractive wall in single-molecule pulling experiments.
