arXiv subjects

Alexei V. Tkachenko

Publications and source records attributed to Alexei V. Tkachenko.

51 records · Page 3Linked to original sources

arXiv2007

Error-proof programmable self-assembly of DNA-nanoparticle clusters

We study theoretically a new generic scheme of programmable self-assembly of nanoparticles into clusters of desired geometry. The problem is motivated by the feasibility of highly selective DNA-mediated interactions between colloidal particles. By analyzing both a simple generic model and a more realistic description of a DNA-colloidal system, we demonstrate that it is possible to suppress the glassy behavior of the system, and to make the self-assembly nearly error-proof. This regime requires a combination of stretchable interparticle linkers (e.g. sufficiently long DNA), and a soft repulsive potential. The jamming phase diagram and the error probability are computed for several types of clusters. The prospects for the experimental implementation of our scheme are also discussed. PACS numbers: 81.16.Dn, 87.14.Gg, 36.40.Ei

cond-mat.soft↗

arXiv2007

Statistical Mechanics of DNA-Mediated Colloidal Aggregation

We present a statistical mechanical model of aggregation in colloidal systems with DNA mediated interactions. We obtain a general result for the two-particle binding energy in terms of the hybridization free energy $ΔG$ of DNA and two model dependent properties: the average number of available DNA bridges $\left< N\right>$ and the effective DNA conccentration $c_{eff}$. We calculate these parameters for a particular DNA bridging scheme. The fraction of all the $n$-mers, including the infinite aggregate, are shown to be universal functions of a single parameter directly related to the two-particle binding energy. We explicitly take into account the partial ergodicity of the problem resulting from the slow DNA binding-unbinding dynamics, and introduce the concept of angular localization of DNA linkers. In this way, we obtain a direct link between DNA thermodynamics and the global aggregation and melting properties in DNA-colloidal systems. The results of the theory are shown to be in quantitative agreement with two recent experiments with particles of micron and nanometer size. PACS numbers: 81.16.Dn, 82.20.Db, 68.65.-k, 87.14.Gg

cond-mat.stat-mech↗

arXiv2006

Dynamics of particles with "key-lock" interactions

The dynamics of particles interacting by key-lock binding of attached biomolecules are studied theoretically. Examples of such systems include DNA-functionalized colloids as well as nanoparticles grafted with antibodies to cell membrane proteins. Depending on the coverage of the functional groups, we predict two distinct regimes separated by a percolation transition. In the localized regime at low coverage, the system exhibits a broad, power law like distribution of particle departure times. At higher coverage, there is an interplay between departure dynamics and particle diffusion. This interplay leads to a sharp increase of the departure times, a phenomenon qualitatively similar to aging in glassy systems. This diffusive regime is analogous to dispersive transport in disordered semiconductors: depending on the interaction parameters, the diffusion behavior ranges from standard diffusion to anomalous, subdiffusive behavior. The connection to recent experiments and implications for future studies are discussed.

cond-mat.soft↗

arXiv2006

Electrostatic effects in DNA stretching

The response of a semiflexible polyelectrolyte chain to stretching in the regimes of moderate and weak screening is studied theoretically, with a special focus on DNA experiments. By using the nonlinear Poisson--Boltzmann description of electrostatic self--interactions of the chain, we explicitly demonstrate the applicability of the concept of effective charge to certain aspects of the problem. This charge can be extracted from the far--field asymptotic behavior of electrostatic potential of the fully aligned chain. Surprisingly, in terms of the effective charge, the electrostatically renormalized persistence length can be formally described by the classical Odijk-Skolnick-Fixman (OSF) formula, whose domain of applicability is limited to linearized Debye Huckel (DH) approximation. However, the short--length behavior of the chain in the nonlinear regime deviates from the of DH--based result, even upon the charge renormalization. This difference is revealed in calculated stretching curves of strongly charged DNA, and our results are in good agreement with the recent experiments. In the limit of weak screening we predict the elastic response to have a distinctive two-stage character, with a peculiar intermediate "unstretchable" regime.

cond-mat.soft↗

arXiv2005

Effects of Kinks on DNA Elasticity

We study the elastic response of a worm-like polymer chain with reversible kink-like structural defects. This is a generic model for (a) the double-stranded DNA with sharp bends induced by binding of certain proteins, and (b) effects of trans-gauche rotations in the backbone of the single-stranded DNA. The problem is solved both analytically and numerically by generalizing the well-known analogy to the Quantum Rotator. In the small stretching force regime, we find that the persistence length is renormalized due to the presence of the kinks. In the opposite regime, the response to the strong stretching is determined solely by the bare persistence length with exponential corrections due to the ``ideal gas of kinks''. This high-force behavior changes significantly in the limit of high bending rigidity of the chain. In that case, the leading corrections to the mechanical response are likely to be due to the formation of multi-kink structures, such as kink pairs.

cond-mat.soft↗

arXiv2004

Unfolding and unzipping of single-stranded DNA by stretching

We present a theoretical study of single-stranded DNA under stretching. Within the proposed framework, the effects of basepairing on the mechanical response of the molecule can be studied in combination with an arbitrary underlying model of chain elasticity. In a generic case, we show that the stretching curve of ssDNA exhibits two distinct features: the second-order "unfolding" phase transition, and a sharp crossover, reminiscent of the first-order "unzipping" transition in dsDNA. We apply the theory to the particular cases of Worm-like Chain (WLC) and Freely-Joint Chain (FJC) models, and discuss the universal and model--dependent features of the mechanical response of ssDNA. In particular, we show that variation of the width of the unzipping crossover with interaction strength is very sensitive to the energetics of hairpin loops. This opens a new way of testing the elastic properties of ssDNA.

cond-mat.soft↗

arXiv2004

Kinetic pinning and biological antifreezes

Biological antifreezes protect cold-water organisms from freezing. An example are the antifreeze proteins (AFPs) that attach to the surface of ice crystals and arrest growth. The mechanism for growth arrest has not been heretofore understood in a quantitative way. We present a complete theory based on a kinetic model. We use the `stones on a pillow' picture. Our theory of the suppression of the freezing point as a function of the concentration of the AFP is quantitatively accurate. It gives a correct description of the dependence of the freezing point suppression on the geometry of the protein, and might lead to advances in design of synthetic AFPs.

cond-mat.mtrl-sci↗

arXiv2003

Entropically-Stabilized Self-Compactification in Model Colloidal Systems

We discuss the phenomenon of spontaneous self-compactification in a model colloidal system, proposed in a recent work on DNA-mediated self-assembly. We focus on the effect of thermal fluctuations on the stability of membrane-like self-assembled phase with in-plane square order. Surprisingly, the fluctuations are shown to enhance the stability of this quasi-2D phase with respect to transition to alternative 3D structures.

cond-mat.soft↗

arXiv2001

With a little help of DNA: Morphological diversity of colloidal self-assembly

We study theoretically a binary system in which an attraction of unlike particles is combined with a type-independent soft core repulsion. The possible experimental implementation of the system is a mixture of DNA-covered colloids, in which both the repulsion and the attraction may be induced by DNA solution. The system is shown to exhibit surprisingly diverse and unusual morphologies. Among them are the diamond lattice and the membrane phase with in-plane square order, a striking example of spontaneous compactification.

cond-mat.soft↗

arXiv2000

Generalized Entropy approach to far-from-equilibrium statistical mechanics

We present a new approach to far-from-equilibrium statistical mechanics, based on the concept of generalized entropy, which is a microscopically-defined generalization of Onsager-Machlup functional. In the case when a set of slow (adiabatic) variables can be chosen, our formalism yields a general form of the macroscopic evolution law (Generalized Langevin Equation) and extends Fluctuation Dissipative Theorem. It also provides for a simple understanding of recently-discovered Fluctuation Theorem

cond-mat.stat-mech↗

arXiv1999

Mesoscopic Physics of Granular Flows

We present a description of granular dynamics based on the idea of differentiation between fluid and solid components. First, we construct a model of completely fluidized phase. Then we discuss a shear surface motion on the boundary of the bulk solid phase, induced by a moving wall. Our results include the thickness dependence of the velocity of a developed avalanche, density and velocity profiles in granular Couette flow experiment.

cond-mat.soft↗

arXiv1999

Stress in frictionless granular material: Adaptive Network Simulations

We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces. The procedure works by sequentially removing and adding individual contacts between adjacent beads, while the bead positions are not modified. In a series of two-dimensional realizations, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent theories. The coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about .6 of the normal loading. The spatial distribution of contact forces shows strong concentration along ``force chains". The probability of contact forces of magnitude f shows an exponential falloff with f. The response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally.

cond-mat.soft↗

arXiv1999

Stress Propagation through Frictionless Granular Material

We examine the network of forces to be expected in a static assembly of hard, frictionless spherical beads of random sizes, such as a colloidal glass. Such an assembly is minimally connected: the ratio of constraint equations to contact forces approaches unity for a large assembly. However, the bead positions in a finite subregion of the assembly are underdetermined. Thus to maintain equilibrium, half of the exterior contact forces are determined by the other half. We argue that the transmission of force may be regarded as unidirectional, in contrast to the transmission of force in an elastic material. Specializing to sequentially deposited beads, we show that forces on a given buried bead can be uniquely specified in terms of forces involving more recently added beads. We derive equations for the transmission of stress averaged over scales much larger than a single bead. This derivation requires the Ansatz that statistical fluctuations of the forces are independent of fluctuations of the contact geometry. Under this Ansatz, the $d(d+1)/2$-component stress field can be expressed in terms of a d-component vector field. The procedure may be generalized to non-sequential packings. In two dimensions, the stress propagates according to a wave equation, as postulated in recent work elsewhere. We demonstrate similar wave-like propagation in higher dimensions, assuming that the packing geometry has uniaxial symmetry. In macroscopic granular materials we argue that our approach may be useful even though grains have friction and are not packed sequentially.=17

cond-mat.soft↗

arXiv1998

Effect of Chain Flexibility on Nematic-Smectic Transition

The theory of nematic-smectic phase transition in the system of uniform semi-flexible chains with hard-core repulsion is presented. Both the general density-functional formalism the tube-model calculation show that the flexibility of the chains results in a strong first-order transition, in contrast to the common weak-cristallization scenario of the nematic-smectic transition in rigid rods. The calculated spinodal volume fraction of the uniform nematic phase and the period of the modulation instability are consistent with recent experimental results.

cond-mat.soft↗

arXiv1998

On the Glassy Behavior of Parking Lot Model

We present a theoretical discussion of the reversible parking problem, which appears to be one of the simplest systems exhibiting glassy behavior. The existence of slow relaxation, nontrivial fluctuations, and an annealing effect can all be understood by recognizing that two different time scales are present in the problem. One of these scales corresponds to the fast filling of existing voids, the other is associated with collective processes that overcome partial ergodicity breaking. The results of the theory are in a good agreement with simulation data; they provide a simple qualitative picture for understanding recent granular compaction experiments and other glassy systems.

cond-mat.stat-mech↗