Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

The dynamics of weakly bending polymers is analyzed on the basis of a Gaussian semiflexible chain model and the fluorescence correlation spectroscopy (FCS) correlation function is determined. Particular attention is paid to the influence of the rotational motion on the decay of the FCS correlation function. An analytical expression for the correlation function is derived, from which the averaged segmental mean square displacement can be determined independent of any specific model for the polymer dynamics. The theoretical analysis exhibits a strong dependence of the correlation function on the rotational motion for semiflexible polymers with typical lengths and persistence lengths of actin filaments or fd viruses. Hence, FCS allows for a measurement of the rotational motion of such semiflexible polymers. The theoretical results agree well with experimental measurements on actin filaments and confirm the importance of large relaxation times.     

The effect of restricted rotational diffusion on the dynamics of rodlike molecules in concentrated solution

The model of Doi for the rotational dynamics of rodlike molecules in solution is compared with that of Warchol and Vaughan and Wang and Pecora. The similarities in the results for dielectric relaxation are discussed and the application of the models to the behaviour of isotropic solutions, anisotropic (lyotropic-nematic) solutions, and mixtures of small molecules with polymers is briefly discussed.     

The role of the torsional potential in relaxation dynamics: a molecular dynamics study of polyethylene

The role of the torsional potential in bulk polymer chain dynamics is investigated via molecular dynamics simulation using polyethylene as a model system. A number of three-fold barrier values, both greater and less than the standard one, were invoked. The one-fold potential that determines the gauche vs trans energy difference was also varied. For each of the selected torsional potentials, the MD volumetric glass transition temperature, T_g, was located. It was found that T_g is quite sensitive to the three-fold barrier magnitude, moving from below 100 K to nearly 400 K as the barrier goes from zero to twice the standard value. However T_g was found to be quite insensitive to the gauche trans energy difference. Details of the conformational dynamics were studied for the case of a zero torsional potential. This included the rate and location of conformational transitions, the decay of the torsional angle autocorrelation function (ACF) and the cooperativity of conformational transitions, all as a function of temperature. The temperature dependence of the conformational transition rate remains Arrhenius at all temperatures. The relaxation time characterizing the torsional angle ACF decay exhibits WLF temperature behavior. The conformational transitions are randomly distributed over the bonds at high temperature, but near T_g they become spatially heterogeneous and localized. The transitions show next-neighbor correlation as well as self-correlated forward-backward transitions. All of these features are similar to those found in previous simulations under the standard torsional potential.     

A study of DNA tethered to a surface by an all-atom molecular dynamics simulation

 In order to understand the structure of DNAs and their interactions when on microarray surfaces, we performed the first all-atom molecular dynamics simulation of DNA tethered to a surface. On the surface, the binding of the DNA was enhanced, and its average equilibrium conformation was the B form. The DNA duplex spontaneously tilted towards its nearest neighbor and settled in a leaning position with a interaxial distance of 2.2 nm. This close packing of the DNAs, which affects both in situ synthesis and deposition of probes on microarray surfaces, can thus be explained by salted-induced colloidlike DNA–DNA attractions. Received: 30 November 2000 / Accepted: 7 February 2001 / Published online: 22 May 2001     

Brownian dynamics simulations of simplified cytochrome c molecules in the presence of a charged surface

Simulations were performed for up to 150 simplified spherical horse heart cytochrome c molecules in the presence of a charged surface, which serves as an approximate model for a lipid membrane. Screened electrostatic and short-ranged attractive as well as repulsive van der Waals forces for interparticle and particle-membrane interactions are utilized in the simulations. At a distance from the membrane, where particle-membrane interactions are negligible, the simulation is coupled to a noninteraction continuum analogous to a heat bath [Geyer et al., J. Chem. Phys. 120, 4573 (2004)]. From the particles' density profiles perpendicular to the planar surface binding isotherms are derived and compared to experimental results [Heimburg et al. (1999)]. Using a negatively charged structureless membrane surface a saturation effect was found for relatively large particle concentrations. Since biological membranes often contain membrane proteins, we also studied the influence of additional charges on our model membrane mimicking bacterial reaction centers. We find that the onset of the saturation occurs for much lower concentrations and is sensitive to the detailed implementation. Therefore we suggest that local distortion of membrane planarity (undulation), or lipid demixing, or the presence of charged integral membrane proteins create preferential binding sites on the membrane. Only then do we observe saturation at physiological concentrations.     

Rotational viscosity of fluids composed of linear molecules: an equilibrium molecular dynamics study

In this paper, we investigate the rotational viscosity for a chlorine fluid and for a fluid composed of small linear molecules by using equilibrium molecular dynamics simulations. The rotational viscosity is calculated over a large range of state points. It is found that the rotational viscosity is almost independent of temperature in the range studied here but exhibits a power-law dependency on density. The rotational viscosity also shows a power-law relationship with the molecular length, and the ratio between the shear and rotational viscosities approaches 0.5 for the longest molecule studied here. By changing the number of atoms or united atomic units per molecule and by keeping the molecule length fixed, we show that fluids composed of molecules which have a rodlike shape have a lower rotational viscosity. We argue that this phenomenon is due to the reduction in intermolecular connectivity, which leads to larger fluctuations around the values possessed by the fluid on average. The conclusions here can be extended to fluids composed of uniaxial molecules of arbitrary length.     

A molecular dynamics study of structural relaxation in tetrahedrally coordinated nanocrystals

The reorganisation of nanocrystals in order to reduce their surface energies has been examined in computer simulations. The relaxation takes a qualitatively different path for sphalerite- and wurtzite-structured particles. The surfaces of the sphalerite particles reconstruct into hexagonal nets, but the interior remains identifiable as sphalerite-like, whereas wurtzite particles form facetted, hexagonal nanorods by virtue of a reorganisation of the whole particle which involves the creation of a low energy internal interface between oppositely oriented domains. Despite the reorganisation, the diffraction patterns remain compatible with a wurtzite structure with some internal strain. The dipole moments of thermalized wurtzite particles are compared with experimental results for CdSe.     

Ordering transition and demixing of a binary mixture of thick and thin rodlike molecules in the presence of an external field

The effect of an external field (electric/magnetic) on the phase behavior of the binary mixture of very long thick and thin rodlike particles is studied. Both the thick and thin particles possess positive but different susceptibility anisotropics (Delta alpha). The difference in the extent of interaction between the external field and the two species is varied by means of a coupling parameter (l = Delta alpha(thick)/Delta alpha(thin)). Isotropic-nematic phase transition and demixing phase transitions taking place both in the isotropic and nematic phases are examined as a function of field strength on the level of the second virial theory of Onsager in the range of 0 < l <1. The approximate sixth order Legendre polynomial expansion method is used to represent the excluded volume interaction between the rodlike particles. It is found that the isotropic phase becomes weakly nematic (paranematic) in the presence of external field and the field orients both components in the direction of the field even if the field does not have direct interaction with the thick component (l = 0). Analytical expressions are derived for the external field induced order parameters and birefringence. The increasing field destabilizes both types of demixing transitions (isotropic-isotropic and nematic-nematic) and the paranematic-nematic phase transition. Moreover it induces closed loop immiscibility, and upper and lower critical points terminating the paranematic-nematic phase coexistence may occur for low values of the coupling parameter. It is interesting that while the phase boundaries of the paranematic-paranematic demixing and the paranematic-nematic transitions are very sensitive to the value of the coupling parameter at low pressures, the paranematic-nematic and nematic-nematic phase boundaries are practically independent of the coupling parameter at high pressures.     

The Ehrenfest method with quantum corrections to simulate the relaxation of molecules in solution: equilibrium and dynamics

The use of the Ehrenfest method to simulate the relaxation of molecules in solution is explored. Using the cyanide ion dissolved in water as a test model, the independent trajectory (IT) and the bundle of trajectories (BT) approximations are shown to provide very different results for the time evolution of the vibrational populations of the solute. None of these approximations reproduce the Boltzmann equilibrium vibrational populations accurately. A modification of the Ehrenfest method based on the use of quantum correction factors is thus proposed to solve this problem. The simulations carried out using the modified Ehrenfest method provide IT and BT relaxation times which are closer to each other and which agree quite well with previous hybrid perturbative results.     

Confinement and surface effects on the molecular dynamics of a nematic mixture investigated by dielectric relaxation spectroscopy

Broadband dielectric spectroscopy (10(-2)-10(9) Hz) was employed to investigate the molecular dynamics of the liquid crystalline mixture E7 confined in both untreated and lecithin-treated 20 nm Anopore membranes. Because E7 does not crystallize, it was possible to cover a temperature range of more than 200 K, providing an exhaustive dielectric characterization of a liquid crystal confined to Anopore membranes for the first time. In the nematic state, the tumbling (alpha-) and the delta-relaxation are observed, also under confinement conditions. The analysis of their relative intensities give that the orientation of the E7 molecules is preferentially axial in untreated but opposite radial in lecithin-treated pores. The radial alignment of the liquid crystals in the modified membrane is understood as a tail-to-tail conformation of E7 molecules imposed by the adsorbed lecithin molecules. The relaxation rate of the alpha-process is enhanced for E7 confined in native Anopore compared with the bulk and E7 in treated pores. This is interpreted as resulting from a less dense molecular packing of E7 in the middle of the pore compared to the bulk. In both untreated and treated membranes, the relaxation rate of the delta-process is higher than in the bulk, and the values of the respective Vogel-Fulcher-Tammann temperatures depend on the actual surface treatment. Additionally, a surface process, due to molecular fluctuations of molecules within an adsorbed layer at the pore wall, was detected.     

Anomalous dielectric relaxation of water molecules at the surface of an aqueous micelle

Dielectric relaxation of aqueous solutions of micelles, proteins, and many complex systems shows an anomalous dispersion at frequencies intermediate between those corresponding to the rotational motion of bulk water and that of the organized assembly or macromolecule. The precise origin of this anomalous dispersion is not well-understood. In this work we employ large scale atomistic molecular dynamics simulations to investigate the dielectric relaxation (DR) of water molecules in an aqueous micellar solution of cesium pentadecafluorooctanoate. The simulations clearly show the presence of a slow component in the moment-moment time correlation function [PhiMW(t)] of water molecules, with a time constant of about 40 ps, in contrast to only 9 ps for bulk water. Interestingly, the orientational time correlation function [Cmu(t)] of individual water molecules at the surface exhibits a component with a time constant of about 19 ps. We show that these two time constants can be related by the well-known micro-macrorelations of statistical mechanics. In addition, the reorientation of surface water molecules exhibits a very slow component that decays with a time constant of about 500 ps. An analysis of hydrogen bond lifetime and of the rotational relaxation in the coordinate frame fixed on the micellar body seems to suggest that the 500 ps component owes its origin to the existence of an extended hydrogen bond network of water molecules at the surface. However, this ultraslow component is not found in the total moment-moment time correlation function of water molecules in the solution. The slow DR of hydration water is found to be well correlated with the slow solvation dynamics of cesium ions at the water-micelle interface.     

Nuclear-spin relaxation in nonrigid molecules: discrete multisite local dynamics combined with anisotropic molecular reorientation

Nuclear-spin relaxation is considered in a molecular system undergoing two types of dynamic processes: asymmetric-top small-step rotational diffusion and discrete multisite local jumps. The two processes are assumed to be uncorrelated. Time correlation functions for relevant rank-two interactions and corresponding spectral density functions are derived for a general relation between the characteristic rate constants. In addition, limiting cases of fast and slow local motions and of some specific jump conditions are also investigated.     

Time-reversible always stable predictor-corrector method for molecular dynamics of polarizable molecules

An improved method for classic molecular dynamics of polarizable molecules is proposed. The method uses a predictor, one evaluation of the electrostatic field per integration step, and relaxation (damping). The self-consistent solution is approximated with error of the second order (with respect to the timestep). The time reversibility (long-time energy conservation) error is of the (2n - 1)th order, where n is the predictor length. The method is easy to implement, efficient, accurate, and suitable for any model of polarizability.     

Extended rotational diffusion and orientational relaxation of symmetric top molecules in a strong dc electric field: second-rank orientational correlation functions

Second-rank orientational correlation functions (pertaining to Kerr effect relaxation and Raman scattering) are obtained using the extended rotational diffusion (J-diffusion) model of symmetric top polar molecules in a strong constant external field. It is shown that the shape of the molecule noticeably affects all second-rank correlation functions and relaxation times in the rare collision limit. In the opposite limit of frequent collisions, the quantities of interest are shown to be shape independent as a consequence of vanishingly small inertial effects. An interpolation formula for the orientation relaxation times in the intermediate regime between the rare and frequent collision limits is also given.     

Laser-induced orientational change of nematic liquid crystalline molecules mediated by photochromic reactions of surface azobenzenes

The alignment of nematic liquid crystalline (LC) molecules with respect to the LC cell surface was regulated between the homeotropic (H) state and the parallel (P) state by the photochromic trans—cis isomerization of surface-attached azobenzene (Az) moieties. By bringing the angular-selective photoreaction into the system, the orientational order in the P state was significantly improved to attain a universal orientational axis over the entire irradiated area, which was rotatable and erasable photochemically. Laser pulse experiments revealed that the allignment relaxation time τ was reduced from 1000 to 30 ms by increasing the pulse intensity from 10 to 20 mJ cm⁻². Strong coupling between the LC and Az molecules was indicated.     

Simultaneous measurement of orientational and spectral dynamics of single molecules in nanostructured host-guest materials

Nanostructured host-guest materials are important for various applications in nanoscience, and therefore, a thorough understanding of the dynamics of the guest molecules within the host matrix is needed. To this aim we used single-molecule fluorescence techniques to simultaneously examine the spectral and the orientational behavior of single molecules in nanostructured porous host materials. Two types of host-guest systems have been investigated. First, oxazine-1 dye molecules were fixed rigidly in the channels of microporous AlPO4-5 crystals. Second, it was shown that terrylenediimide (TDI) dye molecules move in the mesoporous network of an uncalcined M41S thin film. In the first sample both spectral fluctuations ( approximately 5 nm) and rare spectral jumps (>10 nm) of the emission maximum were observed. However, the orientation of the emission dipole of the dye molecules remained constant. In contrast, the second system showed orientational dynamics as well as substantially more spectral dynamics. In this system the molecules were found to move between different regions in the host. The typical motion of the TDI molecules in the pores of M41S was not continuous but characterized by jumps between specific sites. Moreover, the spectral and orientational dynamics were correlated and arose directly from the different environments that were being explored by the mobile molecule.     

A study of the potential surface of LiOB by the method of diatomic fragments in molecules

Conclusion The results of the calculations by the DFM method provide evidence that the minimum on the potential surface of LiOB in the state¹A corresponds to the linear structure Li–O–B. Estimates of the dissociation energy with respect to various decomposition channels show that the molecule is stable. The qualitative behavior of the section of the potential surface corresponding to the minimum energy path for the intramolecular rearrangement Li–O–BO–B–Li is independent of the adjustable parameters of the method—the coefficients of the mixing of the diatomic states of identical symmetry. The lack of agreement between the difference in the energies of the linear forms Li–O–B and O–B–Li and the results of nonempirical calculations indicates that the model of the molecule chosen within the framework of the DFM approach requires further refinement. In particular, the addition to the set of MBF of functions constructed with allowance for the excited state⁴P of the boron atom will make it possible to decrease this energy difference. It will then be necessary, however, to take into account the much larger number of states from the fragments BO and BLi.M. V. Lomonosov Moscow State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 24, No. 3, pp. 13–17, May–June, 1983.     

Kinetics of surface enrichment: A molecular dynamics study

We use molecular dynamics to study the kinetics of surface enrichment (SE) in a stable homogeneous mixture (AB), placed in contact with a surface which preferentially attracts A. The SE profiles show a characteristic double-exponential behavior with two length scales: ξ(-), which rapidly saturates to its equilibrium value, and ξ(+), which diverges as a power-law with time (ξ(+)～t(θ)). We find that hydrodynamic effects result in a crossover of the growth exponent from θ?0.5 to θ?1.0. There is also a corresponding crossover in the growth dynamics of the SE layer thickness.     

Gear formalism of the always stable predictor-corrector method for molecular dynamics of polarizable molecules

The recently proposed always stable predictor-corrector method for molecular dynamics of polarizable molecules [J. Kolafa, J. Comput. Chem. 25, 335 (2004)] is rewritten in the Gear formalism. This equivalent form simplifies an implementation if the Newton equations of motion are integrated by the Gear method and also enables a variable integration step. Algorithms are presented for both the original and new versions and tested on a pair of polarizable ions exhibiting anharmonic vibrations.