On the location of the surface-attached globule phase in collapsing polymers

We investigate the existence and location of the surface phase known as the "Surface-Attached Globule" (SAG) conjectured previously to exist in lattice models of three-dimensional polymers when they are attached to a wall that has a short range potential. The bulk phase, where the attractive intra-polymer interactions are strong enough to cause a collapse of the polymer into a liquid-like globule and the wall either has weak attractive or repulsive interactions, is usually denoted Desorbed-Collapsed or DC. Recently this DC phase was conjectured to harbour two surface phases separated by a boundary where the bulk free energy is analytic while the surface free energy is singular. The surface phase for more attractive values of the wall interaction is the SAG phase. We discuss more fully the properties of this proposed surface phase and provide Monte Carlo evidence for self-avoiding walks up to length 256 that this surface phase most likely does exist. Importantly, we discuss alternatives for the surface phase boundary. In particular, we conclude that this boundary may lie along the zero wall interaction line and the bulk phase boundaries rather than any new phase boundary curve.Comment: slightly extended versio

Layering transitions for adsorbing polymers in poor solvents

An infinite hierarchy of layering transitions exists for model polymers in solution under poor solvent or low temperatures and near an attractive surface. A flat histogram stochastic growth algorithm known as FlatPERM has been used on a self- and surface interacting self-avoiding walk model for lengths up to 256. The associated phases exist as stable equilibria for large though not infinite length polymers and break the conjectured Surface Attached Globule phase into a series of phases where a polymer exists in specified layer close to a surface. We provide a scaling theory for these phases and the first-order transitions between them.Comment: 4 pages, 4 figure

Pulling absorbing and collapsing polymers from a surface

A self-interacting polymer with one end attached to a sticky surface has been studied by means of a flat-histogram stochastic growth algorithm known as FlatPERM. We examined the four-dimensional parameter space of the number of monomers up to 91, self-attraction, surface attraction and force applied to an end of the polymer. Using this powerful algorithm the \emph{complete} parameter space of interactions and force has been considered. Recently it has been conjectured that a hierarchy of states appears at low temperature/poor solvent conditions where a polymer exists in a finite number of layers close to a surface. We find re-entrant behaviour from a stretched phase into these layering phases when an appropriate force is applied to the polymer. We also find that, contrary to what may be expected, the polymer desorbs from the surface when a sufficiently strong critical force is applied and does \emph{not} transcend through either a series of de-layering transitions or monomer-by-monomer transitions.Comment: 4 pages, 4 figure

Surface critical behaviour of the Interacting Self-Avoiding Trail on the square lattice

The surface critical behaviour of the interacting self-avoiding trail is examined using transfer matrix methods coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points along the collapse transition line. The phase diagram is also presented.Comment: Journal of Physics A (accepted

Conformational Mechanics of Polymer Adsorption Transitions at Attractive Substrates

Conformational phases of a semiflexible off-lattice homopolymer model near an attractive substrate are investigated by means of multicanonical computer simulations. In our polymer-substrate model, nonbonded pairs of monomers as well as monomers and the substrate interact via attractive van der Waals forces. To characterize conformational phases of this hybrid system, we analyze thermal fluctuations of energetic and structural quantities, as well as adequate docking parameters. Introducing a solvent parameter related to the strength of the surface attraction, we construct and discuss the solubility-temperature phase diagram. Apart from the main phases of adsorbed and desorbed conformations, we identify several other phase transitions such as the freezing transition between energy-dominated crystalline low-temperature structures and globular entropy-dominated conformations.Comment: 13 pages, 15 figure

Influence of long-range correlated surface and near the surface disorder on the process of adsorption of long-flexible polymer chains

The influence of long-range correlated surface and decaying near surface disorder with quenched defects is studied. We consider a correlation function for the defects of the form $\frac{e^{-z/\xi}}{r^{a}}$, where $a<d-1$ and $z$ being the coordinate in the direction perpendicular to the surface and $r$ denotes the distance parallel to the surface. We investigate the process of adsorption of long-flexible polymer chains with excluded volume interactions on a "marginal" and attractive wall in the framework of renormalization group field theoretical approach up to first order of perturbation theory in a double ($\epsilon$,$\delta$)- expansion ($\epsilon=4-d$, $\delta=3-a$) for the semi-infinite $|\phi|^4$ $O(m,n)$ model with the above mentioned type of surface and near the surface disorder in the limit $m,n\to 0$. In particular we study two limiting cases. First, we investigate the scenario where the chain's extension it much larger then $\xi$. Second, we consider the case where the chain's extension is of the order of $\xi$. For both cases we obtained series for bulk and the whole set of surface critical exponents, characterizing the process of adsorption of long-flexible polymer chains at the surface. The polymer linear dimensions parallel and perpendicular to the surface and the corresponding partition functions as well as the behavior of monomer density profiles and the fraction of adsorbed monomers at the surface and in the volume are studied.Comment: 31 pages, 5 figures, 2 table