Leonid I. Klushin

Kinetics of a homopolymer collapse: Beyond the Rouse–Zimm scaling

We present a phenomenological theory describing the self-similar coarsening stage in the collapse of a long flexible homopolymer chain in a dilute solution upon a sudden quench. The approach is based on the “necklace” picture of the collapsing chain being composed of clusters separated by strands as demonstrated by computer simulations. The model represents a special class in the cluster growth problem where aggregation is driven by tension in the connecting strands. The mean cluster size in the free-draining limit is predicted to grow with time as s(t)∼t6/7(1+ν) where ν is the exponent characterizing the initial conformation of the coil. The characteristic collapse time scales as τc∼N1+ν∼N1.6 in agreement with the Langevin dynamics simulations. Incorporation of hydrodynamic effects leads to τc∼N1/3+ν∼N0.93. For a realistic experimental situation the theory presented thus predicts a much faster collapse than suggested by self-consistent field calculations.

Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations.

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.

Dragging a polymer chain into a nanotube and subsequent release

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method (PERM). The nanotube is a long channel opened at one end and its diameter D is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position x inside the tube: the free energy of confinement, the average end-to-end distance, the average number of segments imprisoned in the tube, and the average stretching of the confined part of the chain for various values of D and for the number of repeat units in the chain, N. We show that when the chain end is dragged by a certain critical distance x* into the tube, the polymer undergoes a first-order phase tr...

Sharp and fast: sensors and switches based on polymer brushes with adsorption-active minority chains.

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.

Flow and transport in brush-coated capillaries: A molecular dynamics simulation

We apply an efficient method of forced imbibition to (nano-)capillaries, coated internally with a polymer brush, to derive the change in permeability and suction force, corresponding to different grafting densities and lengths of the polymer chains. While the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers, which form the brush coating, are described by a standard bead-spring model. Our computer experiments reveal a significant increase in the suction force (by a factor of 4, as compared to the case of a capillary with bare walls) when the brush width approaches the tube radius. A similar growth in the suction force is found when the grafting density of the brush is systematically increased. Even though the permeability of the tube is found to decline with both growing brush width and grafting density, the combined effect on the overall fluid influx into the capillary turns out to be weak, i.e., the total fluid uptake under spont...

Structural properties of concave cylindrical brushes interacting with free chains

We present a self-consistent field theoretical study of the microstructure of concave cylindrical brushes as a function of the cylinder radius, grafting density, grafted chain length, and the solvent quality. We show that the results for the radial monomer density profile and the distribution of the free ends are in good agreement with the corresponding molecular dynamics results. Part of the investigation is focused on the conformational behavior of a free macromolecule in a cylindrical brush. A central result is the observed non-monotonous variation of the size of a free chain in a brush-coated tube when the tube radius is systematically changed. An interpretation of this behavior which differs qualitatively from that of a polymer in cylindric confinement is suggested in terms of scaling theory and rationalized by considering the overlap between the free polymer and the grafted chains as a function of the tube radius.

Stimuli-Responsive Brushes with Active Minority Components: Monte Carlo Study and Analytical Theory

Using a combination of analytical theory, Monte Carlo simulations, and three-dimensional self-consistent field calculations, we study the equilibrium properties and the switching behavior of adsorption-active polymer chains included in a homopolymer brush. The switching transition is driven by a conformational change of a small fraction of minority chains, which are attracted by the substrate. Depending on the strength of the attractive interaction, the minority chains assume one of two states: an exposed state characterized by a stem-crown-like conformation and an adsorbed state characterized by a flat two-dimensional structure. Comparing the Monte Carlo simulations, which use an Edwards-type Hamiltonian with density-dependent interactions, with the predictions from self-consistent-field theory based on the same Hamiltonian, we find that thermal density fluctuations affect the system in two different ways. First, they renormalize the excluded volume interaction parameter vbare inside the brush. The prope...

Polydisperse Polymer Brushes: Internal Structure, Critical Behavior, and Interaction with Flow

We study the effect of polydispersity on the structure of polymer brushes by analytical theory, a numerical self-consistent field approach, and Monte Carlo simulations. The polydispersity is represented by the Schulz–Zimm chain-length distribution. We specifically focus on three different polydispersities representing sharp, moderate, and extremely wide chain length distributions and derive explicit analytical expressions for the chain end distributions in these brushes. The results are in very good agreement with numerical data obtained with self-consistent field calculations and Monte Carlo simulations. With increasing polydispersity, the brush density profile changes from convex to concave, and for given average chain length Nn and grafting density σ, the brush height H is found to scale as (H/Hmono – 1) ∝ (Nw/Nn – 1)1/2 over a wide range of polydispersity indices Nw/Nn (here Hmono is the height of the corresponding monodisperse brush). Chain end fluctuations are found to be strongly suppressed already...

Stretching and compression of a macromolecule under different modes of mechanical manupulations

This review is concerned with the response of an isolated polymer chain subjected to the action of the two different modes of the mechanical impact on the chain ends. In one mode, the end-to-end distance is changed in a controlled fashion and the fluctuating response force is measured; in the second case, an external stress field is applied to the chain end, and the measured response of the system is the fluctuating end-to-end distance. The main attention is focused on the results of the computer-aided simulation experiments and theoretical results. Upon stretching of an ideal chain, a real chain in a good solvent, or a globule, the resultant strain-force and force-strain dependences are shown to be different for chains with finite length L; however, this difference diminishes with an increase in the length of a molecule. When the anchored Gaussian chain is separated from the adsorbing surface, this difference disappears in the limit of high L; however, in the neighborhood of the phase transition, some characteristics (fluctuations, distribution functions) appear to be critically different under different impact modes even in the thermodynamic limit. The example of an abnormal system is discussed: The behavior of a polymer chain compressed by a small piston is different in the conjugated ensembles, and, as the system increases in size, this difference becomes even more pronounced.

ADSORPTION-STRETCHING ANALOGY FOR A POLYMER CHAIN ON A PLANE. SYMMETRY PROPERTY OF THE PHASE DIAGRAM

We consider a Gaussian chain of finite length adsorbing on a planar surface with the stretching force applied to its free end. The model is exactly solvable and appears to have an unexpectedly rich behavior, exhibiting in the thermodynamic limit N→∞ phase transitions of both the first and the second order. A closed analytical form for the partition function at arbitrary N is obtained. The phase diagram is completely symmetrical with respect to stretching force and adsorption strength parameters. Thus, a rigorous analogy is established between the adsorption of a chain onto a plane in the absence of external force and the stretching of a nonadsorbed chain attached to a plane by one end, both being the second‐order transitions. Competition of simultaneous stretching and adsorption leads to a first‐order transition. Adsorption of ring polymers is discussed as a natural by‐product of this scheme. Nonequilibrium free energy is obtained as a function of the order parameter and compared with the Landau theory of...