Finite Chain Length Effects Research Articles

Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA.

We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality to the numerical evaluation of Marko and Siggia's variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests that our analytical finite chain length corrections achieve a comparable accuracy. As an application of our results, we discuss the possibility of inferring the time-dependent number of nicks in single-molecule stretching experiments on double-stranded DNA from the accompanying changes in the effective chain length.

Macroscopic Strain-Induced Transition from Quasi-infinite Gold Nanoparticle Chains to Defined Plasmonic Oligomers.

We investigate the formation of chains of few plasmonic nanoparticles-so-called plasmonic oligomers-by strain-induced fragmentation of linear particle assemblies. Detailed investigations of the fragmentation process are conducted by in situ atomic force microscopy and UV-vis-NIR spectroscopy. Based on these experimental results and mechanical simulations computed by the lattice spring model, we propose a formation mechanism that explains the observed decrease of chain polydispersity upon increasing strain and provides experimental guidelines for tailoring chain length distribution. By evaluation of the strain-dependent optical properties, we find a reversible, nonlinear shift of the dominant plasmonic resonance. We could quantitatively explain this feature based on simulations using generalized multiparticle Mie theory (GMMT). Both optical and morphological characterization show that the unstrained sample is dominated by chains with a length above the so-called infinite chain limit-above which optical properties show no dependency on chain length-while during deformation, the average chain length decrease below this limit and chain length distribution becomes more narrow. Since the formation mechanism results in a well-defined, parallel orientation of the oligomers on macroscopic areas, the effect of finite chain length can be studied even using conventional UV-vis-NIR spectroscopy. The scalable fabrication of oriented, linear plasmonic oligomers opens up additional opportunities for strain-dependent optical devices and mechanoplasmonic sensing.

Conformation transitions of a single polyelectrolyte chain in a poor solvent: a replica-exchange lattice Monte-Carlo study.

The thermodynamic behaviors of a strongly charged polyelectrolyte chain in a poor solvent are studied using replica-exchange Monte-Carlo simulations on a lattice model, focusing on the effects of finite chain length and the solvent quality on the chain conformation and conformation transitions. The neutralizing counterions and solvent molecules are considered explicitly. The thermodynamic quantities that vary continuously with temperature over a wide range are computed using the multiple histogram reweighting method. Our results suggest that the strength of the short-range hydrophobic interaction, the chain length, and the temperature of the system, characterized by ε, N, and T, respectively, are important parameters that control the conformations of a charged chain. When ε is moderate, the competition between the electrostatic energy and the short-range hydrophobic interaction leads to rich conformations and conformation transitions for a longer chain with a fixed length. Our results have unambiguously demonstrated the stability of the n-pearl-necklace structures, where n has a maximum value and decreases with decreasing temperature. The maximum n value increases with increasing chain length. Our results have also demonstrated the first-order nature of the conformation transitions between the m-pearl and the (m-1)-pearl necklaces. With the increase of ε, the transition temperature increases and the first-order feature becomes more pronounced. It is deduced that at the thermodynamic limit of infinitely long chain length, the conformational transitions between the m-pearl and the (m-1)-pearl necklaces may remain first order when ε > 0 and m = 2 or 3. Pearl-necklace conformations cannot be observed when either ε is too large or N is too small. To observe a pearl-necklace conformation, the T value needs to be carefully chosen for simulations performed at only a single temperature.

Loop formation and stability of self-avoiding polymer chains

Using 3-dimensional Langevin dynamics simulations, we investigated the dynamics of loop formation of chains with excluded volume interactions, and the stability of the formed loop. The mean looping time τl scales with chain length N and corresponding scaling exponent α increases linearly with the capture radius scaled by the Kuhn length a/l due to the effect of finite chain length. We also showed that the probability density function of the looping time is well fitted by a single exponential. Finally, we found that the mean unlooping time τu hardly depends on chain length N for a given a/l and that the stability of a formed loop is enhanced with increasing a/l.

Finite-length effects on the coil-globule transition of a strongly charged polyelectrolyte chain in a salt-free solvent

The nature of coil-globule transition and scaling behavior of a strongly charged polyelectrolyte chain in a solution system with explicit neutralizing counterions and solvent molecules are studied using replica-exchange Monte Carlo simulations, focusing on the effects of finite chain length. The results reveal that at the thermodynamic limit of infinitely long chain length, the coil-globule transition may remain first order. Phase transition temperatures at various ion concentrations are obtained by extrapolating the values obtained at finite chain lengths. Furthermore, it is found that the exponent ν of the radius of gyration, <R(g)(2)> ~ N(2ν), can be slightly larger than 1 under some conditions.

Influence of non-universal effects on dynamical scaling in driven polymer translocation

We study the dynamics of driven polymer translocation using both molecular dynamics (MD) simulations and a theoretical model based on the non-equilibrium tension propagation on the cis side subchain. We present theoretical and numerical evidence that the non-universal behavior observed in experiments and simulations are due to finite chain length effects that persist well beyond the relevant experimental and simulation regimes. In particular, we consider the influence of the pore-polymer interactions and show that they give a major contribution to the non-universal effects. In addition, we present comparisons between the theory and MD simulations for several quantities, showing extremely good agreement in the relevant parameter regimes. Finally, we discuss the potential limitations of the present theories.

Unifying model of driven polymer translocation

We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by solving the model for chain lengths up to 10^{10} monomers, we show that the chain lengths probed by experiments and simulations are typically orders of magnitude below the asymptotic limit. This explains both the considerable scatter in the observed scaling of translocation time with respect to chain length, and some of the shortcomings of present theories. Our study shows that for a quantitative theory of polymer translocation, explicit consideration of finite chain length effects is required.

On the phase behavior and structural properties of polyelectrolyte solutions

Correlations between structural properties and phase behavior of polyelectrolyte solutions were discussed along the line of the work reported by Châtellier and Joanny [Joanny JF, Châtellier X. J Phys France II 1996;6:1669]. A multicomponent system made of polyions, salt ions and counterions was considered under poor solvent conditions. Unlike this reference, partial structure factors were derived from the celebrated Zimm’s formula written in the matrix form including the effects of finite chain length. These effects were found to generate significant shifts in phase diagrams and qualitative changes in structural properties. The presence of a charged solid surface was briefly discussed. Here also, the phase diagram was found to shift with an increasing amount as the polyion chain length decreased.

Developments in Wang-Landau simulations of a simple continuous homopolymer

The Wang-Landau method is used to study thermodynamic properties of a three-dimensional flexible homopolymer chain with continuous monomer positions. Results describing the coil-globule and solid-liquid transitions are presented for chain lengths up to N = 100. In order to elucidate the thermodynamic behavior, finite chain length effects and the influence of the energy range over which the density of states is determined are carefully analyzed. Simulation efficiency is also studied and it is shown that setting the natural logarithm of the final modification factor equal to 10-6 is an appropriate choice for this model.

Phase behavior of a single polyethylene chain confined between two adsorption walls

AbstractThe phase behavior of a single polyethylene chain confined between two adsorption walls is investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, that is, the coil‐to‐globule transition, and the finite chain length effects are considered since the critical region depends on chain lengths. When the chain is confined between two attractive walls, however, the equilibrium properties not only depend on the chain length but also depend on the adsorption energy and the confinement. Mainly, we focus on the influence of polymer chain length, confinement, and adsorption interaction on the equilibrium thermodynamic properties of the polyethylene chains. Chain lengths of N = 40, 80, and 120 beads, distances between the two walls of D = 10, 20, 30, 50, and 90 Å, and adsorption energies of w = 1.5, 2.5, 3.5, 6.5, and 8.5 kcal/mol are considered here. By considering the confinement–adsorption interactions, some new folding structures are found, that is, the hairpin structure for short chain of N = 40 beads, and the enhanced hairpin or crystal like structures for long chains of N = 80 and 120 beads. The results obtained in our simulations may provide some insights into the phase behaviors of confined polymers, which can not be obtained by previous studies without considering confinement–adsorption interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 370–387, 2008

The phase behaviors of adsorbed polymethylene chains

The phase behaviors of a single adsorbed polymethylene chain are investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, i.e., the coil-to-globule transition, and finite chain length effects are considered since the critical region may depend on the chain length. When the chain is adsorbed on an attractive surface, however, the equilibrium properties may not only depend on chain length but also depend on the adsorption energy. For short chain of N=40 monomers, a coil-to-globule transition is found for weak adsorption energy of w=2.5kcal/mol, but the critical temperature is lower than the free chain, and for strong adsorptions of w=3.5 and 4.5kcal/mol, the structures at low temperatures are adsorbed hairpin like, so we may call the transition process coil-to-hairpin transition. For long chains of N=80 monomers and N=120 monomers, the critical regions are the same for the free chains both at T=265K, and for the adsorption energies of w=2.5, 3.5, and 4.5kcal/mol, the curves of the heat capacities are smooth when T>200K, and while T<200K, the values of the heat capacities decrease as the temperatures decreasing, so the transition may be from loose globular structures to compact globular structures, and for more stronger adsorption energy of w=6.5 and 8.5kcal/mol, the critical regions are obvious and they are coil-to-crystal like transitions.

Intramolecular long-range correlations in polymer melts: The segmental size distribution and its moments

We present theoretical arguments and numerical results to demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers, which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion u(s) approximately s/rho R3(s) approximately c(e)/sqrt[s] when connecting two segments together where s denotes the curvilinear length of a segment, R(s) its typical size, c(e) approximately 1/rho b(e)3 the "swelling coefficient," b(e) the effective bond length, and rho the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to u(s). The analysis of different moments of this distribution allows for a precise determination of the effective bond length b(e) and the swelling coefficient c(e) of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's ideality hypothesis the bond-bond correlation function of two bonds separated by s monomers along the chain is found to decay algebraically as 1/s(3/2). Effects of finite chain length are briefly considered.

Dynamics of polyethylene melts studied by Monte Carlo simulations on a high coordination lattice

AbstractA detailed comparison is made between the experiment, prior simulations by other groups, and our simulation based on a newly designed dynamic Monte Carlo algorithm, on the dynamics of polyethylene (PE) melts. The new algorithm, namely, noncross random two‐bead move has been developed on a high coordination lattice (the 2nnd lattice) for studying the dynamics of realistic polymers. The chain length (molecular weight) in our simulation ranges from C40 (562 Da) to C324 (4538 Da). The effects of finite chain length have been confirmed and significant non‐Gaussian statistics evidently results in nonstandard static and dynamic properties of short PE chains. The diffusion coefficients scale with molecular weight (M) to the −1.7 power for short chains and −2.2 for longer chains, which coincides very well with experimental results. No pure Rouse scaling in diffusion has been observed. The transitional molecular weight to the entanglement regime is around 1500 Da. The detailed mean square displacements of middle bead (g1) are presented for several chain lengths. The reptation‐like slowdown can be clearly observed only above M ∼ 2400 Da. The slope 0.25 predicted by the theory for the intermediate regime is missing; instead a slope close to 0.4 appears, indicating that additional relaxation mechanism exists in this transitional region. The relaxation times extracted by fitting the autocorrelation function of end‐to‐end vectors with reptation model scale with M to 2.5 for long chains, which seemingly conflicts with the scaling of diffusion. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2556–2571, 2006

Pure shear deformation of physical and chemical gels of poly(vinyl alcohol)

Pure shear deformation reveals the significant differences in elastic properties of the poly(vinyl alcohol) (PVA) gels with almost identical initial modulus, but with different types of crosslinks, physical crosslinks formed by microcrystallites and chemical crosslinks made of covalent bonds. The ratio of the two principal stresses steeply increases with elongation in the physical gels, while that remains almost constant independently of stretching in the chemical gels. The marked growth of the stress ratio with elongation in the physical gels leads to the negative values of the derivative of the elastic free energy ( W 2) with respect to the second invariant of the deformation tensor in the whole range of deformation, which is firstly observed for elastomeric materials. By contrast, the chemical gels exhibit the positive values of W 2 like most chemically crosslinked rubbers. Among the existing theories of rubber elasticity, the classical non-Gaussian three-chain model considering the effect of finite chain-length is qualitatively successful in accounting for the steep increase of the stress ratio and the negative values of W 2 in the physical gels, although it fails to reproduce the large difference in the stress–strain behavior among uniaxial, pure shear and equi-biaxial deformations. These features of the physical gels are expected to stem from the structural characteristics such as fewer amounts of slippery-trapped entanglement along network strands compared to the chemical PVA gels.

The electrostatic persistence length of polymers beyond the OSF limit.

We use large-scale Monte Carlo simulations to test scaling theories for the electrostatic persistence length l(e) of isolated, uniformly charged polymers with Debye-Hückel intrachain interactions in the limit where the screening length kappa(-1) exceeds the intrinsic persistence length of the chains. Our simulations cover a significantly larger part of the parameter space than previous studies. We observe no significant deviations from the prediction l(e) proportional to kappa(-2) by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity and electrostatically excluded volume to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. A linear or sublinear dependence of the persistence length on the screening length can be ruled out. We show that previous results pointing into this direction are due to a combination of excluded-volume and finite chain length effects. The paper emphasizes the role of scaling arguments in the development of useful representations for experimental and simulation data.

Finite chain-length effects in rubber elasticity

We present a finite chain-length calculation of the rubber elasticity of an isotropic crosslinked network of freely jointed chains under affine deformation. Whilst this is a classical calculation, the result is derived in its full tensorial structure for the first time, and new predictions of non-Gaussian elasticity for general biaxial deformations are presented. The full tensorial rubber-elasticity derivation allows any deformation regime to be treated, to facilitate validation with experimental data. Even though more complex many-chain effects are neglected, this theory appears to be the only one to offer a physical explanation for negative values of W 2 observed experimentally at small strains.

Finite chain length effects on the coil–globule transition of stiff-chain macromolecules: A Monte Carlo simulation

We study the effect of finite chain length on the collapse transition of stiff-chain macromolecules by means of a Monte Carlo simulation within the framework of the bond fluctuation lattice model. Variable stiffness of the chains was modeled by introducing a potential depending on the angle between successive bonds and we introduced an additional quasi-Lennard-Jones potential between monomer units which are not nearest neighbors along the chain to model the quality of the solvent. Chains of length up to 200 monomer units were simulated. For the flexible case these chains are long enough to determine the θ-temperature, but for higher stiffnesses we show systematic effects in the dependence of the apparent transition temperature on the stiffness. For fixed chain lengths we determine apparent phase diagrams and give the apparent transition points and points of ideal chain size as a function of stiffness. We report on the occurrence of a toroidal structure in our model and characterize this structure by local and global packing and orientational ordering.

Chain-end effects in Su-Schrieffer-Heeger-type models of alternating trans-polyacetylene

Finite chain-length effects on soliton dynamics in Su-Schrieffer-Heeger-type models for trans-polyacetylene are reported, indicating that for the frequently used value of 0.1 Å for the dimerization constant, the results depend strongly on the chain length. The ansatz for the potential due to σ-electron is reformulated so that no additional linear terms to avoid chain shrinking are necessary. Second-neighbour resonance integrals of a magnitude suggested by experimental findings are shown to have no influence on soliton dynamics.

Effect of finite chain length on the helix/coil coexistence behavior of polymers: poly(oxymethylene)

Effect of finite chain length on the helix/coil coexistence behavior of polymers: poly(oxymethylene)

Mean configurational relaxation rates in finite length polypeptides

Expressions for the mean relaxation rate &amp;lt;r≳ and the time correlation function &amp;lt;ϑ (0) ϑ (t) ≳ of the helix fraction are derived for polypeptides in the helix–random coil transition region. The resulting equations are based upon a general description of the time rate of change of the configurational probabilities in the form of a set of coupled differential equations. Quantities are expressed in terms of the Zimm–Bragg equilibrium statistics and the neighbor dependent transition rates for an individual peptide unit. Both &amp;lt;r≳ and &amp;lt;ϑ (0) ϑ (t) ≳ exhibit strong chain length dependent behavior throughout the transition region. The quantities 1/&amp;lt;r≳ show maxima at some ϑ?0.5 within the range of the transition. As chain length increases, these curves sharpen and their maxima shift toward ϑ = 0.5, asymptotically. Results for &amp;lt;r≳ are identical to those calculated by an alternative method which follows from a theory developed by Schwarz. Effects of finite chain length can persist to greater than 1000 peptide units.