A comprehensive molecular dynamics study of a single polystyrene chain in a good solvent

In this study, molecular characteristics of polystyrene (PS) was calculated measuring its dilute-solution properties in toluene at 288.15 K via molecular dynamics (MD) simulations. The solution models consisted of PS chains with different number of repeating units all of which were in a dilute regime. In order to investigate the compatibility between the polymer and the solvent molecules, interaction energy and Flory-Huggins (FH) interaction parameter were estimated. The simulation results indicate that increasing the chain repeating units enhanced the interaction between the solute and the solvent. Additionally, the chain dimensions were evaluated calculating the radius of gyration (R_g) and end-to-end distance, r0. To determine the dynamic behavior of the chains in the solutions, mean square displacement (MSD) and diffusivity coefficient were calculated. The simulation results indicated that the chain rigidity at low molecular weight and chain flexibility with increasing the molecular weight influenced chains dynamic behavior and diffusivity. Moreover, radial distribution function (RDF) illustrated the effect of steric hindrance of the chains in dilute solution on capturing the solvent molecules. In addition, solution viscosity was calculated by performing non-equilibrium molecular dynamics simulation (NEMD). The obtained results of chain characteristics and viscosity showed a good agreement with experimental results published previously. This agreement confirms the accuracy of the applied simulation method to characterize the dilute solutions and the chains characteristics.     

拉伸取向聚合物2H NMR谱的键涨落模型Monte Carlo模拟

采用三维键涨落模型（BFM）的Monte Carlo计算机模拟方法,模拟了两种分别具有高取向和低取向链微观结构的拉伸取向聚合物²H NMR谱. 讨论了排除体积效应与链的均方末端距分布对²H NMR谱线的影响. 结果表明,排除体积效应对高取向和低取向聚合物²H谱劈裂的影响是不同的,较小均方末端距的链决定²H谱劈裂,而较大均方末端距的链使²H谱产生长的拖尾. 采用BFM计算机模拟与²H NMR实验的结合是研究拉伸取向聚合物网络微观结构的有力手段.     

On Continuous-Time Self-Avoiding Random Walk in Dimension Four

We study the distribution of the end-to-end distance of continuous-time self-avoiding random walks (CTRW) in dimension four from two viewpoints. From a real-space renormalization-group map on probabilities, we conjecture the asymptotic behavior of the end-to-end distance of a weakly self-avoiding random walk (SARW) that penalizes two-body interactions of random walks in dimension four on a hierarchical lattice. Then we perform the Monte Carlo computer simulations of CTRW on the four-dimensional integer lattice, paying special attention to the difference in statistical behavior of the CTRW compared with the discrete-time random walks. In this framework, we verify the result already predicted by the renormalization-group method and provide new results related to enumeration of self-avoiding random walks and calculation of the mean square end-to-end distance and gyration radius of continous-time self-avoiding random walks.     

End-to-end Distance Distribution in Fluorescent Derivatives of Bradykinin in Interaction with Lipid Vesicles

Cellular membranes have relevant roles in processes related to proteases like human kallikreins and cathepsins. As enzyme and substrate may interact with cell membranes and associated co-factors, it is important to take into account the behavior of peptide substrates in the lipid environment. In this paper we report an study based on energy transfer in two bradykinin derived peptides labeled with the donor-acceptor pair Abz/Eddnp (ortho-aminobenzoic acid/N-[2,4-dinitrophenyl]-ethylenediamine). Time-resolved fluorescence experiments were performed in phosphate buffer and in the presence of large unilamelar vesicles of phospholipids, and of micelles of sodium dodecyl sulphate (SDS). The decay kinetics were analyzed using the program CONTIN to obtain end-to-end distance distribution functions f(r). Despite of the large difference in the number of residues the end-to-end distance of the longer peptide (9 amino acid residues) is only 20?% larger than the values obtained for the shorter peptide (5 amino acid residues). The proline residue, in position 4 of the bradykinin sequence promotes a turn in the longer peptide chain, shortening its end-to-end distance. The surfactant SDS has a strong disorganizing effect, substantially broadening the distance distributions, while temperature increase has mild effects in the flexibility of the chains, causing small increase in the distribution width. The interaction with phospholipid vesicles stabilizes more compact conformations, decreasing end-to-end distances in the peptides. Anisotropy experiments showed that rotational diffusion was not severely affected by the interaction with the vesicles, suggesting a location for the peptides in the surface region of the bilayer, a result consistent with small effect of lipid phase transition on the peptides conformations.     

Effective temperature scaled dynamics of a flexible polymer in an active bath

Langevin dynamics simulations are employed to study the dynamical properties of a flexible polymer in an active bath. The diffusion of the centre of mass and end-to-end distance fluctuation are particularly analysed. We modulate both active force and active particle size to probe the activity-induced facilitation of polymer dynamics. Results indicate diffusivity and chain relaxation time can be well scaled by the effective temperature of the active bath. In addition, diffusion dynamics demonstrates an anomalous superdiffusive behaviour in short time scales, which becomes more prominent with increasing active particle size. Lastly, we extract the effective viscosity experienced by the probed chain, showing a sharp decrease with increment of effective temperature. The attenuation of effective viscosity due to activity might be responsible for the facilitated polymer dynamics.     

A new paradigm for the molecular basis of rubber elasticity

The molecular basis for rubber elasticity is arguably the oldest and one of the most important questions in the field of polymer physics. The theoretical investigation of rubber elasticity began in earnest almost a century ago with the development of analytic thermodynamic models, based on simple, highly-symmetric configurations of so-called Gaussian chains, i.e. polymer chains that obey Markov statistics. Numerous theories have been proposed over the past 90 years based on the ansatz that the elastic force for individual network chains arises from the entropy change associated with the distribution of end-to-end distances of a free polymer chain. There are serious conceptual objections to this assumption and others, such as the assumption that all network nodes undergo a simple volume-preserving linear motion and that all of the network chains have the same length. Recently, a new paradigm for elasticity in rubber networks has been proposed that is based on mechanisms that originate at the molecular level. Using conventional statistical mechanics analyses, Quantum Chemistry, and Molecular Dynamics simulations, the fundamental entropic and enthalpic chain extension forces for polyisoprene (natural rubber) have been determined, along with estimates for the basic force constants. Concurrently, the complex morphology of natural rubber networks (the joint probability density distributions that relate the chain end-to-end distance to its contour length) has also been captured in a numerical model (EPnet). When molecular chain forces are merged with the network structure in this model, it is possible to study the mechanical response to tensile and compressive strains of a representative volume element of a polymer network. As strain is imposed on a network, pathways of connected taut chains, that completely span the network along strain axis, emerge. Although these chains represent only a few percent of the total, they account for nearly all of the elastic stress at high strain. Here we provide a brief review of previous elasticity theories and their deficiencies, and present a new paradigm with an emphasis on experimental comparisons.     

Lennard-Jones chain mixtures: radial distribution functions from Monte Carlo simulation

Radial distribution functions are calculated for binary Lennard-Jones chain mixtures from Monte Carlo simulation. Average and end-to-end inter- and intrachain radial distribution functions are calculated, ten for a binary mixture and four for a pure component. The effects of density, concentration, temperature, chain length, Lennard-Jones size and energy parameters are investigated. It is found that intrachain radial distribution functions are largely independent of density except at very high densities, where they start to take on a structure tending towards that of a crystal lattice. In addition, the effect of using different distribution functions to calculate the associating contribution in statistical associating fluid theory (SAFT) is examined. Further, the effect of using short chain fluids rather than the monomer unit as the reference system in the calculation of the pressure and free energy of chain fluids in first-order thermodynamic perturbation theory (TPT) is examined. It is found that the choice of reference radial distribution function has a marked effect on the calculation of thermodynamic properties through the use of SAFT and TPT.     

Spatial disorder in a smectic A mesophase

Starting with the equations of motion for a stiff chain, a projection operator approach is utilized to develop diffusional equations for the dynamics of the end-to-end distance. The diffusion equation resulting has a spatial-dependent diffusion coefficient calculable from equilibrium properties of the chain, and a frequency-dependent part which requires dynamical information. The analysis is applied, in so far as the spatial dependence of D is determined, for three and four bond chains. A critique of this procedure is provided.     

On the interpretation of fluorescence anisotropy decays from probe molecules in lipid vesicle systems

Measurements of fluorescence depolarization decays are widely used to obtain information about the molecular order and rotational dynamics of fluorescent probe molecules in membrane systems. This information is obtained by least-squares fits of the experimental data to the predictions of physical models for motion. Here we present a critical review of the ways and means of the data analysis and address the question how and why totally different models such as Brownian rotational diffusion and wobble-in-cone provide such convincing fits to the fluorescence anistropy decay curves. We show that while these models are useful for investigating the general trends in the behavior of the probe molecules, they fail to describe the underlying motional processes. We propose to remedy this situation with a model in which the probe molecules undergo fast, though restricted local motions within a slowly rotating cage in the lipid bilayer structure. The cage may be envisaged as a free volume cavity between the lipid molecules, so that its position and orientation change with the internal conformational motions of the lipid chains. This approach may be considered to be a synthesis of the wobble-in-cone and Brownian rotational diffusion models. Importantly, this compound motion model appears to provide a consistent picture of fluorescent probe behavior in both oriented lipid bilayers and lipid vesicle systems.     

Theoretical study of quantum dots distribution function and the process of nucleation during Ostwald ripening in InAsSbP system

Experimental results on distribution of quantum dots versus sizes in InAsSbP system at different growth times are analyzed theoretically. It is shown that depending on growth time the process of nucleation and ripening of QDs is controlled either by transition kinetics in the grain-matrix boundary (Wagner distribution) or by the volume diffusion (Lifshitz-Slyozov distribution). Comparing theoretically calculated results with experimental data, numerical value of the reaction rate on the grain surface and the volume diffusion coefficient at nucleation temperature T = 550°C were estimated.     

Free volume and density and temperature dependence of diffusion coefficients of liquid mixtures

A simple formula for the diffusion coefficient of liquid mixtures, expressed in terms of the work necessary to create a characteristic free volume in the liquid, is presented in the spirit of the Arrhenius activation theory and tested in comparison with available experimental data. If use is made of the generic van der Waals equation of state, the free volume appearing in the formula for the diffusion coefficient can be expressed in terms of the equilibrium pair correlation functions. The theoretical values for diffusion coefficients agree excellently with experimental values with regard to the density and temperature dependence of the diffusion coefficients of argon and krypton.     

Sub-persistence-length complex scaling behavior in lysozyme amyloid fibrils

We combine atomic force microscopy single-molecule analysis with polymer physics concepts to study molecular conformations of lysozyme amyloid fibrils. We resolve a wavy structure of the fibrils in which the scaling behavior varies at multiple length scales. Bond and pair correlation functions, end-to-end distribution, and wormlike chain model identify three characteristic length scales. At short length scales (≈150 nm), there is a first bending transition of the fibrils corresponding to a bending length L(b). At larger length scales (>2L(b)), fibrils become pseudoperiodic and start to undulate. Finally, at length scales larger than the persistence length (~ μm), the fibrils become flexible and follow a 2D self-avoiding random walk. We interpret these results in terms of the twisting of the fibrils and the impact this has on the area moment of inertia and the propensity of the fibril to bend.     

Dynamical properties of colloidal systems: II. Correlation- and response functions

For systems of interacting Brownian particles a Fokker-Planck equation is derived for the probability distribution function of the concentration fluctuations, using assumption of a Gaussian static distribution function. The drift- and the diffusion term are determined by static correlation functions. By this approach specific properties of different systems as e.g., suspensions of charged spherical particles or chain polymers are taken into account. Although the diffusion term is fluctuation dependent the properties of detailed balance and both fluctuation dissipation theorems are satisfied. Using the formalism of Martin, Siggia and Rose, Dyson- and vertex-equations for the two-particle correlation functions are derived. An explicit calculation of these functions, together with related quantities as the dynamic structure factor, and of the diffusion coefficients, is given in a mean-field approximation. The results are compared with several earlier theories, which were developed for specific systems.     

Excluded-volume polymer-induced depletion interaction between parallel flat plates

The interaction between two parallel plates due to non-adsorbing polymer chains with excluded volume is calculated using the adsorption method. The adsorption is calculated from the profile of the polymer segment concentration between the plates, which is obtained from the product function of the concentration profile near a single wall, involving the correlation length. The renormalization group theory provides expressions for the osmotic pressure and consequently for the osmotic compressibility, chemical potential and correlation length of a polymer solution. Both the local polymer concentration profiles as well as the minimum of the interaction potential between the plates agree with recently published self-avoiding random walk computer simulations. Received 9 August 2001     

Fluorescence Depolarization Due to Excitation Energy Migration in Polymeric Micelles: A Monte Carlo Study

Cores of block copolymer micelles have been studied by Monte Carlo simulation. Core-forming chains have been modeled as self-avoiding chains enclosed in a spherical cavity and tethered to its surface. A fraction of the untethered end segments of chains (18–53%) has been treated as fluorescent probes. The time-dependent solution of the Pauli master equation that describes excitation energy migration among probes has been averaged in an ensemble of 10⁴ simulated cores. We have studied the dependence of the depolarization function G ^S(t), i.e., the probability that the originally excited probe is still excited at time t, on the chain length and on the energy migration critical radius of the probe. Cores with randomly solubilized probes and with clusters of probes have been also studied for comparison.     

Luminescence quenching kinetics upon diffusion-accelerated dipole-dipole energy transfer for a realistic condensed-matter model

The hard-sphere model is considered as a more realistic condensed-matter model. In this model, the radial distribution function of molecules in a medium, used for calculations of luminescence decay kinetics, takes into account the short-range order in fluids and has the shape of damped oscillations. It is assumed that the motion of donor and acceptor molecules in a solution for the lifetime of the excited state of the donor is described by the diffusion equation, while the luminescence quenching occurs due to the long-range dipole-dipole energy transfer. It is shown that, if diffusion coefficients are small, the kinetics determined in this study hardly differs at all from the traditional kinetics. At intermediate and large diffusion coefficients, this difference becomes significant and should be taken into account in estimating the Förster energy transfer radius and diffusion coefficients from experimental luminescence decay curves.     

Depletion effects and loop formation in self-avoiding polymers

Langevin dynamics is employed to study the looping kinetics of self-avoiding polymers both in ideal and crowded solutions. A rich kinetics results from the competition of two crowding-induced effects: the depletion attraction and the enhanced viscous friction. For short chains, the enhanced friction slows down looping, while for longer chains, the depletion attraction renders it more frequent and persistent. We discuss the possible relevance of the findings for chromatin looping in living cells.     

Deformation of a tethered polymer in uniform flow

Static properties of a single polymer fixed at one end and subjected to a uniform flow field are investigated for several polymer models: the Gaussian chain, the freely jointed chain, and the FENE (Finitely Extensible Nonlinear Elastic) chain. By taking into account first the excluded-volume interaction and subsequently also the hydrodynamic interaction, the polymer models are gradually completed and the relevance of each effect for the polymer deformation can be identified. Results from computer simulations of these bead spring chains are compared with analytical calculations using either the conformational distribution function or blob models. To this end, in contrast to the blob model with non-draining blobs introduced for a tethered polymer by Brochard-Wyart, we here develop also a model with free-draining blobs. It turns out that a limited extensibility of the polymer – described by nonlinear spring forces in the model – leads to a flow velocity dependence of the end-to-end distance, segment density, etc. which agrees with the power law predictions of the blob model only for very long chains and in a narrow range of flow velocities. This result is important for comparison with recent experiments on DNA molecules which turn out to be still rather short in this respect. The relative importance of finite extensibility, the excluded-volume effect, and hydrodynamic interactions for polymers in flow is not fully understood at present. The simulation of reasonably long chains becomes possible even when fluctuating hydrodynamic interactions are taken into account without employing averaging procedures by introducing efficient numerical approximation schemes. At medium velocity of the uniform flow the polymer is partially uncoiled and simulations show that the effects of excluded-volume and hydrodynamic interactions are position-dependent. Both are stronger near the free end than near the tethered end of the polymer. A crossover from a nearly non-draining polymer at small flow velocities to a free-draining almost uncoiled chain at large velocities is found in the simulations. Accordingly, models assuming the polymer to be composed of either free- or non-draining subunits, like the two blob models, cannot correctly describe the extension and shape of a tethered polymer in flow, and simple power laws for the polymer extension, etc. cannot be expected. Received 21 June 1999     

Analytical solutions of the simplified spherical harmonics equations

We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared to solutions of the diffusion equation, especially for large absorption coefficients, short time values, and small distances from the source.