E. I. Kats

Long range correlations in DNA : scaling properties and charge transfer efficiency

We address the relation between long-range correlations and charge transfer efficiency in aperiodic artificial or genomic DNA sequences. Coherent charge transfer through the highest occupied molecular orbital states of the guanine nucleotide is studied using the transmission approach, and the focus is on how the sequence-dependent backscattering profile can be inferred from correlations between base pairs.

Weak crystallization theory

Abstract We discuss the weak crystallization of a liquid or a liquid crystal which is a first-order phase transition close to a continuous one. Such a phase transition is accompanied by the softening of the order parameter, describing the short-wavelength density modulation. The softening occurring in the vicinity of certain lines or surfaces in the reciprocal space induces a number of characteristic peculiarities of the transition. Quantitatively the softening may be characterized by the value of the gap, figuring in the expression for the pair correlator of fluctuations of the order parameter. The value of the gap is small near the phase transition temperature and possesses a complex behaviour. A peculiarity of the weak crystallization is the important role of fluctuations of the order parameter accounted for by a large phase volume of the fluctuations. We investigate the behaviour of the gap both in the framework of mean field approximation and with the effects of fluctuations taken into account. The theory enables us to construct the phase diagram of the system which appears to be rather reach for all the considered cases. In this diagram there arise (depending on the strength of the anisotropy and fluctuations) both crystalline phases of different symmetry and smectic, columnar and quasicrystalline phases. The dynamics of the order parameter is pure relaxational and the respective kinetic coefficient proves to be insensitive to the phase transition, therefore the relaxation time is inversely proportional to the gap. All physical characteristics of the system in some degree depend on the proximity to the transition point. For example the heat capacity and the compressibility of the system have singular contributions which may be expressed explicitly through the value of the gap. The most singular behaviour near the phase transition is inherent in the bulk viscosity coefficients determining the sound attenuation.

Observation of new states of liquid crystal 8CB under nonlinear shear conditions as observed via a novel and unique rheology/small-angle X-ray scattering combination.

New stable states of liquid crystal 8CB could be induced by nonlinear shear conditions and observed by a newly developed rheology/X-ray scattering setup using synchrotron X-ray radiation. Nonlinear oscillatory shear created a distorted sixth order orientational structure. Even when oscillatory shear is switched off, the induced structure remains stable and can be removed only by heating the system into the isotropic state. We assume the structure to be stabilized by defects that pin the new 6-fold phase.

Surface anchoring and temperature variations of the pitch in thin cholesteric layers

The temperature variations of the cholesteric pitch in thin planar layers of cholesterics and their dependence on the surface anchoring force are investigated theoretically. It is shown that the temperature variations of the pitch in a layer are of a universal character. This is manifested in the fact that they depend not separately on the parameters of the sample but only on one dimensionless parameter Sd=K22/dW, where K22 is the torsional modulus in the Frank elastic energy, W is the height of the surface-anchoring potential, and d is the thickness of the layer. The investigation is performed the parameter Sd in a range where the change per unit number of cholesteric half-turns within the thickness of the layer accompanying a change in the temperature is due to the slipping of the director on the surface of the layer through the potential barrier for surface anchoring. The critical values of the parameter Sd (which are most easily attained experimentally by varying the thickness of the layer), determining the region of applicability of the approach employed, are presented. The temperature variations of the free energy of the layer and the pitch of the cholesteric helix in the layer as well as the temperature hysteresis in the variations of the pitch with increasing and decreasing temperature are investigated for the corresponding values of Sd. Numerical calculations of the quantities mentioned above are performed using the Rapini anchoring potential.

Landau theory for helical nematic phases

We propose Landau phenomenology for the phase transition from the conventional nematic into the conical helical orientationally non-uniform structure recently identified in liquid crystals formed by “banana”-shaped molecules. The mean field predictions are mostly in agreement with experimental data. Based on the analogy with de Gennes model, we argue that fluctuations of the order parameter turn the transition to the first order phase transition rather than continuous one predicted by the mean-field theory. This conclusion is in agreement with experimental observations. We discuss the new Goldstone mode to be observed in the low-temperature phase.

Base pair dynamic assisted charge transport in DNA

A one-dimensional model with time-dependent random hopping is proposed to describe charge transport in DNA. It permits the investigation of both diffusion of electrons and their tunneling between different sites in DNA. The tunneling appears to be strongly temperature-dependent. Observations of a strong (exponential) as well as a weak distance dependence of the charge transfer in DNA can be explained in the framework of our model.

Propagating vibrational excitations in molecular chains

We investigate quantum dynamics of vibrational excitations in one-dimensional (1D) molecular chain. Our model includes nearest neighbor interaction between identical molecular sites and one impurity atom placed in the middle (n = 0). We show that upon exciting the impurity site, its excess energy for relatively long for molecular scales time up to 100 ps is not redistributed uniformly among all other degrees of freedom. On the contrary an excitation propagates along the chain, reflected from the chain ends, and quantum interference of these waves yields to recurrence cycles and echo phenomena. For a critical cycle number kc, echo components of the neighboring cycles start to overlap, and eventually for k ≫ kc dynamics looks like chaotic one. The critical cycle number kc depends on the coupling strength 0 ≤ C ≤ 1 of the impurity site with its neighbors n = ±1. kc achieves the maximum for C2 = 1/2. Our results are in qualitative agreement with experimental data on vibrational excitations in various (CH2)n molecular chains, and besides offer a way for loss-free energy transfer between separated in space reaction centers.

Bubble Relaxation Dynamics in Double-Stranded DNA

This paper deals with the two-state (opening-closing of base pairs) model used to describe the fluctuation dynamics of a single bubble formation. We present an exact solution for the discrete and finite size version of the model that includes end effects and derive analytic expressions of the correlation function, survival probability, and lifetimes for the bubble relaxation dynamics. It is shown that the continuous and semi-infinite limit of the model becomes a good approximation to an exact result when aN <<1, where N is bubble size and a, the ratio of opening to closing rates of base pairs, is the control parameter of DNA melting.

Temperature pitch variations in planar cholesteric layers: The role of fluctuations and surface anchoring

The influence of thermodynamic fluctuations on temperature pitch variations in planar cholesteric samples with a finite surface anchoring energy is theoretically investigated in the framework of the continuum theory of liquid crystals. It is shown that taking fluctuations into account allows explanation of experimental observations, namely, the absence of a temperature pitch jump hysteresis in sufficiently thick samples and its existence in thin ones. A description of fluctuations, including two phenomenological parameters, is proposed. It allows us to predict temperature points at which the pitch jumps in the sample between two configurations, with the numbers of director half-turns differing by one, as a function of the anchoring energy, Frank elastic modulus, sample thickness, and temperature (or fluctuation energy). It is shown that performing precise measurements of the pitch versus the temperature in well-controlled samples should allow determination of the phenomenological constants and then prediction the influence of fluctuations on pitch jump parameters in samples of an arbitrary thickness and/or surface anchoring energy. The corresponding calculations are performed using the Rapini-Papoular anchoring potential. It is shown that the influence of fluctuations on the pitch variation is only negligible in sufficiently thin layers. It is also noted that the results obtained could be useful for investigating pitch jump dynamics in the future.

Quadrupolar forces and aggregation of nematic droplets

The electrostatic quadrupolar interaction between spherical nematic droplets in an isotropic (and nonconducting) liquid is calculated. It is found to have an anisotropic form Uq∝1/R5, where R is the distance between droplets, with repulsion for droplets having parallel orientation of the quadrupole moments and attraction at oblique angles around the orthogonal orientation. In an external magnetic field aligning the orientations of the quadrupole moments, a competition of the quadrupolar repulsion and van der Waals attraction (UvdW∝ 1/R6) leads to a specific spatial organization of droplets which is in fact often reported in experimental observations (see the monograph by P. Drzaic, Liquid Crystal Dispersions, World Scientific, Singapore (1995) and references cited therein).