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 sphere or an adsorbing washboard surface, the adsorption can be additionally controlled by the curvature of the surface structure. The additional bending energy in the adsorbed state leads to an increase of the critical adsorption strength, which depends on the curvature radii of the substrate structure. For an adsorbing sphere, this gives rise to an optimal polymer stiffness for adsorption, i.e., a local minimum in the critical potential strength for adsorption, which can be controlled by curvature. For two- and three-dimensional washboard substrates, we identify the range of persistence lengths and the mechanisms for an effective control of the adsorption threshold by the substrate curvature.
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 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…
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…
Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length $L$, chain stiffness, $κ$, and the strength of the adsorption potential over a wide range. Molecular Dynamics simulations show that partially adsorbed chains (with "tails", surface attached "trains" and "loops") are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value $(\ell_p)$ to the enhanced value in two dimensions $(2\ell_p)$ is analyzed, and excluded volume effects are identified for $L \gg \ell_p$. Con…
A systematic fieldtheoretic description of critical adsorption on curved objects such as spherical or rodlike colloidal particles immersed in a fluid near criticality is presented. The temperature dependence of the corresponding order parameter profiles and of the excess adsorption are calculated explicitly. Critical adsorption on elongated rods is substantially more pronounced than on spherical particles. It turns out that, within the context of critical phenomena in confined geometries, critical adsorption on a microscopically thin `needle' represents a distinct universality class of its own…
We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum mechanical propagator method. The expressions and relations existing for flexible polymers can be generalized to semiflexible ones, if one replaces the Fourier-Laplace transform of the end-to-end polymer distance, $1/(k^{2}/3+p)$, through the matrix $\tilde{P}(k,p)=(I+ikDM)^{-1}D$, where $D$ and $M$ are related to the spectrum of the quantum rigid rotator, and co…
Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influence the conformational statistics of such polymers. We give exact results for the tangent-tangent spatial correlation function C(r) = t(s).t(s + r), both in two and three dimensions. Contrary to expectation, C(r) does not show any oscillatory behavior, rather decays exponentially and the effective persistence length has strong length dependence for short polymers. We …
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.
We develop a theory describing density profile of the semi-flexible polymers absorbed onto a planar surface. The theoretical analysis consists of two parts. As a first part, we calculate a density profile of the adsorbed polymers by developing an extension of the Bethe-Peierls approximation to the case of nonhomogeneous systems. This approach relies on the combination of the single chain adsorption theory and the lattice version of the self-consistent field theory. Semi-flexibility of a chain is described by incorporating a finite coordination number of the lattice into the consideration, in t…
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…
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 solubi…
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. …
In manuscript arXiv:1703.08719 [cond-mat.soft], it was claimed that the well-known deduction of Tolman's law is not rigorous, since Tolman's argument implies that two different definitions of the surface tension, called $γ$ and $\barγ$ in the manuscript, coincide. This claim is retracted as it can be shown by free-energy minimization that $γ= \barγ$ indeed holds for the Laplace radius. Joachim Groß, Philipp Rehner, Carlos Vega, Øivind Wilhelmsen, and the anonymous reviewers of The Journal of Chemical Physics contributed to finding the mistake in the manuscript.
A recurring motif in the organization of biological tissues are networks of long, fibrillar protein strands effectively confined to cylindrical surfaces. Often, the fibers in such curved, quasi-2D geometries adopt a characteristic order: the fibers wrap around the central axis at an angle which varies with radius and, in several cases, is strongly bimodally distributed. In this Letter, we investigate the general problem of a 2D crosslinked network of semiflexible fibers confined to a cylindrical substrate, and demonstrate that in such systems the trade-off between bending and stretching energi…
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…
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.
Protein fibril accumulation at interfaces is an important step in many physiological processes and neurodegenerative diseases as well as in designing materials. Here we show, using $β$-lactoglobulin fibrils as a model, that semiflexible fibrils exposed to a surface do not possess the Gaussian distribution of curvatures characteristic for wormlike chains, but instead exhibit a spontaneous curvature, which can even lead to ring-like conformations. The long-lived presence of such rings is confirmed by atomic force microscopy, cryogenic scanning electron microscopy and passive probe particle track…
We explore the pressure of active particles on curved surfaces and its relation to other interfacial properties. We use both direct simulations of the active systems as well as simulations of an equilibrium system with effective (pair) interactions designed to capture the effects of activity. Comparing the active and effective passive systems in terms of their bulk pressure, we elaborate that the most useful theoretical route to this quantity is via the density profile at a flat wall. This is corroborated by extending the study to curved surfaces and establishing a connection to the particle a…
