Elasticity of strongly stretched ssDNA

We present a simple model which describes elastic response of single-stranded DNA (ssDNA) to stretching, including the regime of very high force (up to 1000 pN). ssDNA is modelled as a discrete persistent chain, whose ground state is a zigzag rather than a straight line configuration. This mimics the underlying molecular architecture and helps to explain the experimentally observed saturation of the stretching curve at very high force.     

Force-extension behavior of folding polymers

The elastic response of flexible polymers made of elements which can be either folded or unfolded, having different lengths in these two states, is discussed. These situations are common for biopolymers as a result of folding interactions intrinsic to the monomers, or as a result of binding of other smaller molecules along the polymer length. Using simple flexible-chain models, we show that even when the energy ε associated with maintaining the folded state is comparable to k _B T, the elastic response of such a chain can mimic usual polymer linear elasticity, but with a force scale enhanced above that expected from the flexibility of the chain backbone. We discuss recent experiments on single-stranded DNA, chromatin fiber and double-stranded DNA with proteins weakly absorbed along its length which show this effect. Effects of polymer semiflexiblity and torsional stiffness relevant to experiments on proteins binding to dsDNA are analyzed. We finally discuss the competition between electrostatic self-repulsion and folding interactions responsible for the complex elastic response of single-stranded DNA. Received 7 August 2002 and Received in final form 7 March 2003 / Published online: 15 April 2003 RID="a" ID="a"e-mail: jmarko@uic.edu     

Stretching of homopolymeric RNA reveals single-stranded helices and base-stacking

We have found strong supporting evidence for the helical structures of single-stranded nucleic acids by stretching individual molecules of polyadenylic acid [poly(A)] and polycytidylic acid [poly(C)]. Analyzing the force versus extension data using a two-state elastic model in which random-coil domains alternate with rigid helical domains allows one to extract the thermodynamic and structural properties. In addition, it also yields moderate to low cooperativity of the helix-coil transition for poly(A) and poly(C), respectively.     

Stretching single stranded DNA,a model polyelectrolyte

The elastic properties of single stranded (ss)DNA, studied by pulling on an isolated molecule, are shown to agree with a recent model of ssDNA that takes into account base pairings and screened electrostatic repulsion of the phosphodiester backbone. By an appropriate physicochemical treatment, the pairing interactions were suppressed and ssDNA used as an experimental model for a generic polyelectrolyte. The elastic behavior of such an altered ssDNA deviates strongly from the behavior of an ideal polymer. This deviation is shown to result from the elasticity of the chain and its electrostatic self-avoiding interactions.     

Rheological evidence for a dynamical crossover in polymer melts via nonequilibrium molecular dynamics

A certain "critical" molecular weight controls rheological properties of the multibead finitely extensible nonlinear elastic (FENE) chain model polymer melt. The rheological crossover manifests itself in a change of power law behavior for the viscous properties at a critical number of beads per chain N(c) = 100+/-10. This finding confirms a newly proposed relationship between dimensionless critical weight, characteristic length, and flexibility which we obtain as a side result. Results further suggest that the entanglement molecular weight N(e) for the flexible FENE chain model could be comparable in size or even larger than its critical molecular weight N(c).     

Ferroelectricity in a diatomic Ising chain as investigated by the elastic Ising model

An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca₃CoMnO₆, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca₃Co_2-xMn_xO₆ (x ≈0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.     

The elastic theory of a single DNA molecule

We study the elastic responses of double-(ds) and single-stranded (ss) DNA at external force fields. A double-strand-polymer elastic model is constructed and solved by path integral methods and Monte Carlo simulations to understand the entropic elasticity, cooperative extensibility, and supercoiling property of dsDNA. The good agreement with experiments indicates that short-ranged base-pair stacking interaction is crucial for the stability and the high deformability of dsDNA. Hairpin-coil transition in ssDNA is studied with generating function method. A threshold force is needed to pull the ssDNA hairpin patterns, stabilized by base pairing and base-pair stacking, into random coils. This phase transition is predicted to be of first order for stacking potential higher than some critical level, in accordance with experimental observations.     

Dissipation and dispersion properties of microinhomogeneous media

The propagation of a harmonic elastic wave in a microinhomogeneous (defect-containing) medium is considered in the framework of the rheological model that reperesents the medium in the form of a one-dimensional chain of masses connected by purely elastic elements and by Kelvin-Voigt viscoelastic elements. Analytical expressions are derived for the dissipation and dispersion characteristics of this medium for various distributions of the parameters of the viscoelastic elements. The dissipation and dispersion properties are found to obey the Kramers-Kronig relations. It is also shown that the damping decrement of the wave is almost constant, and the phase velocity monotonically increases in a sufficiently wide range of parameters of the viscoelastic elements in a wide frequency band. The derived expressions for the dispersion and dissipation are used to simulate the propagation of broadband pulses in this kind of medium.     

Nonlinear elastic properties of a model one-dimensional granular unconsolidated structure

The characteristic features of the propagation of finite-amplitude elastic waves in a model one-dimensional unconsolidated granular medium are investigated. The model medium is represented by a linear chain of 80 steel balls with a diameter of 6.5 mm each, this chain being preliminarily loaded with an external static force F. The elastic properties of the model are analyzed. The theoretical dependences of the coefficients of elasticity of the second, third, and fourth orders on the force F are obtained. The experimental setup is described. The results of studying the nonlinear effects, namely, the higher harmonic generation and the wave generation at combination frequencies, which accompany the acoustic wave propagation in the chain, are presented. For the chain of balls under study, a structural phase transition from the 1D structure to a 2D one is observed with an increase in the external compression force F applied to the balls. The results of the study are analyzed using the Hertz theory of contact interactions.     

Hairpin rubber elasticity

We model the elastic properties of main chain liquid crystalline elastomers, formed by cross linking chains in a strongly nematic state, when they have hairpin defects. We study the response of the elastomer to imposed uniaxial extension along the nematic direction, and employ a microscopic model of how the deformation is distributed non-affinely amongst the hairpin and straight chain populations. The rubber shows a plateau in the stress as a function of the elongation imposed along the director. It is a consequence of the depletion of the actively stretching population of hairpin chains and should not be confused with soft elasticity effects associated with director rotation.     

Ferroelectricity in diatomic Ising chain as investigated by elastic Ising model

An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca₃CoMnO₆, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca₃Co_2-xMn_xO₆ (x ≈0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.     

Elastic Behavior of Polymer Chains

在三维非格子模型中研究了高分子链的弹性行为. 使用蒙特卡罗方法在构相空间中对高分子链抽样,每种链都得到了超过109个样本,然后使用类橡胶弹力的非高斯理论对这些样本进行数值分析并进行统计分析. 通过观测链柔性以及伸长量对高分子链的均方末端距、平均能量、平均赫尔姆霍兹自由能、弹力、能量对弹力的贡献和熵对弹力的贡献等性质的影响,发现刚性链比柔性链更加容易被拉伸. 而由于熵的作用,当拉伸长度大到一定程度时,刚性链的拉伸难度会大大增加.     

玻璃-橡胶混合颗粒体系的弹性行为研究

废旧橡胶制品颗粒与砂土颗粒混合物作为建筑填充材料具有环保、轻质、减震效果好等特点.软硬组分的混合比例可以调制体系力学性能从而实现兼顾材料柔韧性与强度的需求,但细观层面上材料性能改变的原因尚不明确.本文主要研究玻璃-橡胶混合颗粒体系的弹性行为及其微观机制.利用飞行时间法测量混合材料等效动弹性模量,发现随着橡胶颗粒增加,体系逐渐从类玻璃刚性行为转变为类橡胶柔性行为.离散元模拟结果与实验结果类似.此外,模拟显示低橡胶颗粒占比样品内主要由玻璃颗粒构成主力链结构,而橡胶颗粒基本不参与强力链的构成.当橡胶颗粒占比较大时,玻璃颗粒和橡胶颗粒共同构成主力链网络结构,但颗粒间法向接触力分布相对更为均匀,可视为玻璃颗粒悬浮于橡胶颗粒中.基于上述结果,提出了改进的等效介质理论,用于描述混合颗粒体系的弹性行为.研究认为:橡胶颗粒占比较小时内部颗粒的变形相对均匀,材料近似满足等应变假设,视为并联弹簧模型;橡胶颗粒占比较大时混合材料近似满足等应力假设,视为串联弹簧模型.两种模型得到的结果与模拟结果一致.上述结果有利于从微观角度揭示混合颗粒材料弹性行为的变化机制.     

On the theory of the condensed states of heteropolymers

The collapse (globulization) of an ideal heteropolymer chain under the action of an external attractive field is considered. The problem of the collapse of different types of primary structures, including mobile, periodic, large-block, and statistical structures, is formulated. It is shown that for a random heteropolymer, the mathematical image of the globular state is the chain-length independence of the probability distribution of a random thermal distribution function of the end monomer coordinates. The free energy per monomer of a chain in a globular state and local densities of monomers of all types are shown to be a self-averaging quantities. An exactly solvable model is proposed for a globule formed by a statistical heteropolymer chain. In this model, different types of monomers are attracted to different centers by linear elastic forces with identical elastic constants. The modulus of elasticity is obtained for a heteropolymer globule with respect to the attraction of different types of monomers in different directions. It is shown that this modulus is higher for a short-periodic polymer than for a statistical one.     

Relaxation dynamics of a crumpled globule

The relaxation dynamics of elastic networks of crumpled (fractal) globules obtained by computer simulation of the collapse of a polymer chain in different modes is studied. It is shown that, in their dynamic properties, folded globules are similar to proteins, molecular machines.     

Characteristic features of elastic wave propagation in a one-dimensional model of an unconsolidated medium

The characteristic features of elastic wave propagation in a one-dimensional model of a discrete inhomogeneous unconsolidated medium are investigated. The model is represented by a linear chain of 80 uncoupled steel spheres with a diameter of 6.5 mm. Nonlinear effects that may arise in such systems are reviewed. The experimental setup is described. Results of studying the dispersion of elastic waves in the system and the dependence of the elastic wave velocity on the wave amplitude under increasing compression are presented. The results are analyzed using the Hertz contact theory.     

Scaling theory of mixed amphiphilic monolayers

We predict the elastic properties of mixed amphiphilic monolayers in the swollen state within the blob model using scaling arguments. First the elastic moduli and the spontaneous curvature of a bimodal brush are determined as a function of the composition and the relative chain length. We obtain simple and useful scaling functions which interpolate between the elastic moduli of a pure short-chain brush and a pure long-chain brush. By using the analogy between block copolymer interfaces and polymeric brushes, the effect of mixing on self-assembled diblock copolymer monolayers is investigated in the swollen state. We calculate various interfacial properties, such as the equilibrium surface coverage, interface curvature, and the mixing free energy as a function of the composition. In general, we find a nonlinear dependence on the composition, which deviates from the simple linear averaging of the properties of pure components. Our results are used to discuss a recent experiment on the effect of amphiphilic block copolymers on the efficiency of microemulsions. Received 29 December 2000 and Received in final form 19 March 2001     

Highly stretched single polymers: atomic-force-microscope experiments versus ab-initio theory

Experimental single-molecule stretching curves for three backbone architectures (single-stranded DNA, various types of peptides, polyvinylamine) are quantitatively compared with corresponding quantum-chemical (zero-temperature) ab-initio calculations in the high-force range of up to two nanonewtons. For high forces, quantitative agreement is obtained with the contour length of the polymers as the only fitting parameter. For smaller forces, the effects of chain fluctuations are accounted for by using recent theoretical results for the stretching response of a freely-rotating-chain model.     

Cracks and crazes: on calculating the macroscopic fracture energy of glassy polymers from molecular simulations

We combine molecular dynamics simulations of deformation at the submicron scale with a simple continuum fracture mechanics model for the onset of crack propagation to calculate the macroscopic fracture energy of amorphous glassy polymers. Key ingredients in this multiscale approach are the elastic properties of polymer crazes and the stress at which craze fibrils fail through chain pullout or scission. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length, and polymer rigidity.