Semiflexible Polymer Chains Research Articles

Mixing and demixing arising from compression of two semiflexible polymer chains in nanochannels.

We use molecular dynamics simulation to probe the non-equilibrium physics of two nanochannel-confined semiflexible polymers in a homogeneous flow field. We find that for sufficiently stiff chains the internal organization of the two chains takes the form of interwoven folds and circular coils. This organization can lead to mixing or demixing depending on chain stiffness and flow speed. At low and intermediate flow, the two chains adopt a folded configuration, which favours mixing. At high flow, the two chains adopt a predominantly coiled configuration. The coiled configuration results in demixing when the chains are compressed from an initially demixed condition and mixing when the chains are compressed from an initially mixed condition. We find that the mixing/demixing behaviour is governed by the ratio of the number of folded segments of one chain relative to the other at low flow and by the degree of coiling in both chains at high flow. For decreasing stiffness, the chains start to aggregate locally instead of mixing smoothly at low and intermediate flow. In the limit of completely flexible chains, the two chains either completely segregate at low flow, or adopt a locally demixed configuration consisting of large aggregates of one chain relative to the other that undergo complex stochastic dynamics, diffusing, disintegrating, and reforming at intermediate flow. The transition from complete segregation to the aggregate-dominated configuration occurs when the linear intra-chain ordering breaks down.

Compression of a confined semiflexible polymer under direct and oscillating fields.

The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.

Kinetic models for semiflexible polymers in a half-plane

Based on a general discrete model for a semiflexible polymer chain, we introduce a formal derivation of a kinetic equation for semiflexible polymers in the half-plane via a continuum limit. It turns out that the resulting equation is the kinetic Fokker-Planck-type equation with the Laplace-Beltrami operator under a non-local trapping boundary condition. We then study the well-posedness and the long-chain asymptotics of the solutions of the resulting equation. In particular, we prove that there exists a unique measure-valued solution for the corresponding boundary value problem. In addition, we prove that the equation is hypoelliptic and the solutions are locally H\"older continuous near the singular boundary. Finally, we provide the asymptotic behaviors of the solutions for large polymer chains.

Removal of highly concentrated methylene blue dye by cellulose nanofiber biocomposites

The contamination of water by dyes in high concentrations is a worldwide concern, and it has prompted the development of efficient, economical, and environmentally friendly materials and technologies for water purification. The hydration and adsorption capacity for methylene blue (MB) in biocomposites (BCs) based on cellulose nanofiber (CNF) (0 to 2 wt%) were studied. BCs were synthesized through a simple and straightforward route and characterized by spectroscopy, microscopic techniques and thermogravimetric analysis, among others. Hydration studies showed that BCs prepared with 2 wt% of CNF can absorb large volumes of water, approximately 2274 % in the case of poly 2-acrylamide-2-methyl-1-propanesulfonic acid (PAMPS)-CNF and 2408 % in poly sodium 4-styrene sulfonate (PSSNa)-CNF. These BCs showed outstanding adsorption capacity for highly concentrated MB solutions (4536 mg g−1 PAMPS-CNF and 11,930 mg g−1 PSSNa-CNF). It was confirmed that the adsorption mechanism is through electrostatic interactions. Finally, BCs showed high MB adsorption efficiency after several sorption-desorption cycles and on a simulated textile effluent. Furthermore, the theoretical results showed a preferential interaction between MB and the semiflexible polymer chains at the lowest energy setting. The development and study of a new adsorbent material with high MB removal performance that is easy to prepare, economical and reusable for potential use in water purification treatments was successfully achieved.

Conformation and dynamics of a tethered active polymer chain.

The conformational and dynamical properties of a tethered semiflexible polymer chain under tangential active force (f_{a}) are studied by using the Langevin dynamics simulation method. The head of the polymer is fixed near an infinite flat surface at z=0. The polymer is equilibrated first at f_{a}=0 and then subjected to the active force. Under the influence of the active force, the polymer is gradually compressed. Specially, for large f_{a} and large bending rigidity (k_{b}), the polymer is buckled into a quasihelical structure rotating around the z axis at the steady state. It is found that both the radius of the quasihelical structure (R) and the angular velocity of the rotation (ω) are nearly independent of the polymer length (N), but show scaling relations with f_{a} and k_{b}, i.e., R∝f_{a}^{-1/3}k_{b}^{1/3} and ω∝f_{a}^{4/3}k_{b}^{-1/3}, which are explained by simple dynamical models. Before reaching the steady state, it is further found that the buckling velocity of the polymer is proportional to f_{a} but roughly independent of k_{b} and N, then the buckling time (t_{b}) can be described by a scaling relation t_{b}∝Nf_{a}^{-1}. The underlying mechanism of the buckling process is revealed.

Theory of the Effects of Specific Attractions and Chain Connectivity on the Activated Dynamics and Selective Transport of Penetrants in Polymer Melts

We generalize and apply a microscopic force level statistical mechanical theory of activated spherical penetrant dynamics in glass-forming liquids to study the influence of semiflexible polymer connectivity and penetrant–polymer attractive interactions on the penetrant hopping rate. The detailed manner that attractions of highly variable strength and spatial range modify the penetrant size and polymer melt density (from the rubbery state to slightly beyond the kinetic glass transition) dependences of penetrant activation barriers is established. Of special interest are possible nonadditive consequences of physical bonding and steric caging, the degree of coupling of penetrant hopping and the Kuhn segment scale alpha relaxation process, the relative importance of local caging and long-range matrix collective elasticity as a function of penetrant size, and implications for optimizing transport selectivity. With increasing attraction strength, the repulsive caging-restriction effect on penetrant mobility is predicted to grow, in contrast to the effect of the equilibrium penetrant–matrix solvation shell size, which decreases. The former dynamical effect results in a significant enhancement of the importance of the local cage barrier, while the latter effect results in a decrease of the importance of the nonlocal collective elastic barrier. These two competing effects have a very strong influence on selective penetrant transport for different sized penetrants: selectivity varies nonmonotonically with attraction strength in the deeply supercooled state but decreases monotonically in the rubbery state and at fixed attraction strength, exhibits a nonmonotonic variation with the matrix packing fraction. By comparing results based on modeling the matrix as semiflexible polymer chains with analogous calculations using the same dynamical theory but for a disconnected hard sphere matrix, the effect of chain connectivity is revealed and found to have quantitative, but not qualitative, consequences on penetrant-activated dynamics.

Persistence length of semi-flexible polymer chains on Euclidean lattices

We have studied the persistence length behavior of semi-flexible linear polymers, represented by self-avoiding random walks (SAWs) on the square (d=2) and simple cubic (d=3) lattice. By employing the PERM Monte Carlo algorithm we have generated SAWs, changing the chain stiffness (characterized by the parameter s, related to each bend of a SAW). We have examined two quantities that measure persistence length of N-step SAWs: (1) ℓN, which is defined as an average length of straight parts of polymer chains, and (2) λN, defined as the mean projection of the end-to-end distance vector on the SAW’s first step. For each particular s, we have found that ℓN is a linear function of 1/N in both dimensions, d=2 and d=3, while λN is a linear function of 1/NΦeff, where Φeff≈0.3 in d=2 and Φeff≈0.82 in d=3. Sequences of ℓN and λN have been extrapolated in the range of very long chains, and we have established that, for each examined s, they converge to s dependent constants ℓp=ℓN→∞ and λp=λN→∞. We analyze dependence of ℓp and λp on the polymer stiffness s, and make a comparison between our findings and former results for studied quantities.

Organized states arising from compression of single semiflexible polymer chains in nanochannels.

We use molecular dynamics simulation to probe the nonequilibrium physics of single nanochannel-confined semiflexible polymers in a homogeneous flow field. The flow field compresses the polymer against the end of the nanochannel, simulating an experiment of a nanochannel confined chain compressed against a slit barrier. The flow-based compression gives rise to a packing of the chain against the channel end that possesses a striking organization, consisting of interweaving of folds and circular coils. For stiff chains at low flow, we find that the organization is dominated by repeated hairpin folds. For stiff chains at higher flow, we observe that circular coils arise along with the folds, with folding and coiling domains becoming interwoven at the highest flow speeds. Chain organization is retained even when the chain persistence length is on order of the channel width. We show that the global polymer organization, consisting of a number of defined folds and coiled loops, arises from the minimization of the total chain free energy.

RNA Secondary Structures Regulate Adsorption of Fragments onto Flat Substrates.

RNA is a functionally rich molecule with multilevel, hierarchical structures whose role in the adsorption to molecular substrates is only beginning to be elucidated. Here, we introduce a multiscale simulation approach that combines a tractable coarse-grained RNA structural model with an interaction potential of a structureless flat adsorbing substrate. Within this approach, we study the specific role of stem-hairpin and multibranch RNA secondary structure motifs on its adsorption phenomenology. Our findings identify a dual regime of adsorption for short RNA fragments with and without the secondary structure and underline the adsorption efficiency in both cases as a function of the surface interaction strength. The observed behavior results from an interplay between the number of contacts formed at the surface and the conformational entropy of the RNA molecule. The adsorption phenomenology of RNA seems to persist also for much longer RNAs as qualitatively observed by comparing the trends of our simulations with a theoretical approach based on an ideal semiflexible polymer chain.

Diffusion of Short Semiflexible DNA Polymer Chains in Strong and Moderate Confinement.

In many technological applications, DNA is confined within nanoenvironments that are smaller than the size of the unconfined polymer in solution. However, the dependence of the diffusion coefficient on molecular weight and characteristic confinement dimension remains poorly understood in this regime. Here, convex lens-induced confinement (CLiC) was leveraged to examine how the diffusion of short DNA fragments varied as a function of slit height by using single-molecule fluorescence tracking microscopy. The diffusion coefficient followed approximate power law behavior versus confinement height, with exponents of 0.27 ± 0.01, 0.32 ± 0.02, and 0.42 ± 0.06 for 692, 1343, and 2686 base pair chains, respectively. The weak dependence on slit height suggests that shorter semiflexible chains may adopt increasingly rodlike conformations and therefore experience weaker excluded-volume interactions as the confinement dimension is reduced. The diffusion coefficient versus molecular weight also exhibited apparent power law behavior, with exponents that varied slightly (from -0.89 to -0.85) with slit height, consistent with hydrodynamic interactions intermediate between Rouse and Zimm model predictions.

Influence of chain stiffness on semiflexible polymer melts in two dimensions via molecular dynamics simulation

ABSTRACT Two-dimensional (2D) semiflexible polymers exhibit distinctive conformational and dynamical behaviour compared to the corresponding bulk polymers. Understanding the microscopic origins of this characteristic behaviour of 2D semiflexible polymers is critical for the practical applications of nanoscale polymer systems such as monolayer polymer films, polymer nanocomposites, and biological membranes. To this end, we used coarse-grained molecular dynamics simulation to investigate the behaviour of two-dimensional (2D) semiflexible polymers in a melt by varying the chain stiffness and chain length. Interestingly, the conformational and dynamical behaviour of semiflexible polymer chains was observed to depend on the chain stiffness.

Viscoelasticity of a Stretched Semiflexible Polymer Chain with Fixed Ends

Regularities of the decay of time correlation functions of fluctuations of the microscopic stress tensor characterizing viscoelastic properties for statically stretched chains composed of elastic units with bending stiffness are studied by molecular dynamics and analytically. Chains with the persistent length smaller than the contour length at degrees of extension up to break are considered. In the region of high extensions, where distortions of the local structure of a chain appear, the decay of correlation functions can be described by the modified Rouse model consisting of subchains with anisotropic rigidities depending on the equilibrium chain extension. This makes it possible to determine the relaxation times and moduli of strongly stretched chains, which is necessary in studying the strength of polymer networks. For correlation functions, the analytical relation is formulated that takes into account the contribution of transverse bending fluctuations and agrees with the results of computer simulation at low extensions. A change in the correlation functions with the extension of long semiflexible chains is qualitatively similar to that for flexible chains, but quantitatively is appreciably different.

Stretching a Polymer Chain in a Confined Space

The quantitative characterization of micromechanical properties of polymer biomaterials and the development of advanced biological micro-/nano- technology and devices need to quantitatively analyze the statistical thermodynamic properties and behaviors of polymer chains such as biological macromolecules in complex microenvironment. In the process of achieving this goal, the cross research of continuum mechanics and statistical thermodynamics plays a very important role. Aiming at the mechanics problems in this field, starting from the force stretching of DNA molecules, and by introducing several theoretical models describing the statistical thermodynamic properties of polymer chains, it is pointed out that the wormlike chain model has more significant advantages in describing the relationship between force and configuration change of semi-flexible polymer chains than other ideal random chain models, so that the qualitative and quantitative understanding of the statistical thermodynamic properties and behavior of polymers in complex microenvironment has become largely dependent on the relevant research progresses based on the wormlike chain model. Based on this fact, by reviewing the research on the influence of geometric constraints on the random conformation distribution of polymer chains, the research on the statistical thermodynamic model of polymer chains under the simultaneous action of tension and constraints, and the simulation research on the statistical physical properties of polymer chains based on high-performance computers, the latest progress and challenging problems in the research of statistical thermodynamic properties and behavior of worm chains under different constraints and stress microenvironments are summarized. Finally, through summary and analysis, it is pointed out that the study of statistical thermodynamics of worm chain in complex microenvironment is an important basis for understanding life phenomena from the molecular and cell scale, developing advanced micro- and nano- technology and constructing the constitutive relationship of soft matter. At present, it has become a very challenging frontier topic in the interdisciplinary of mechanics.

Crystallization of semiflexible polymers in melts and solutions.

We studied the crystallization of semiflexible polymer chains in melts and poor-solvent solutions with different concentrations using dissipative particle dynamics (DPD) computer simulation techniques. We used the coarse-grained polymer model to reveal the general principles and microscopic scenario of crystallization in such systems at large time and length scales. It covers both primary and secondary nucleation as well as crystallites' merging. The parameters of the DPD model were chosen appropriately to reproduce the entanglements of polymer chains. We started from an initial homogeneous disordered solution of Gaussian chains and observed the initial stages of crystallization process caused in our model by orientational ordering of polymer chains and polymer-solvent phase separation. We found that the overall crystalline fraction at the end of the crystallization process decreases with the increasing polymer volume fraction while the steady-state crystallization speed at later stages does not depend on the polymer volume fraction. The average crystallite size has a maximal value in the systems with a polymer volume fraction from 0.7 to 0.95. In our model, these polymer concentrations represent an optimal value in the sense of balance between the amount of polymer material available to increase the crystallite size and chain entanglements, that prevent crystallites' growth and merging. On large time scales, our model allows us to observe lamellar thickening linear in logarithmic time scale.

Aggregation of a macromolecule in a nano cube

We model a macromolecule as an infinitely long Gaussian semi-flexible polymer chain and the conformations of the chain were realized in the nano cube using a cubic lattice. A modified version of the recursion relations is used to calculate the grand canonical partition function of the chain to investigate distinct thermo-dynamical properties of the nano polymer aggregate than corresponding bulk behaviour of the macromolecule. Our analytical estimates on the thermo-dynamical properties of the macromolecule clearly show that the nano aggregate of the polymer chain has interesting and distinct conformational statistics than its corresponding bulk state, and the method described in the present report can be easily extend to investigate the thermodynamics of the self-avoiding polymer chain in the nano dimensions.

Transient helix formation in charged semiflexible polymers without confinement effects

Switching on generic interactions e.g. the Coulomb potential or other long ranged spherically symmetric repulsive interactions between monomers of bead-spring model of a semi-flexible polymer induce instabilities in a semiflexible polymer chain to form transient helical structures. Our proposed mechanism could explain the spontaneous emergence of helical order in stiff (bio-) polymers as a chain gets charged from a neutral state. But since the obtained helical structures dissolve away with time, hydrogen bonding (or other additional mechanisms), would be required to form stabilized helical structures as observed in nature (such as in biological macro-molecules). The emergence of the helix is independent of the molecular details of the monomer constituent. The key factors which control the emergence of the helical structure is the persistence length and the charge density. We have avoided using torsional potentials to obtain the transient helical structures. Moreover, we can drive the semiflexible polymer to form helices in a recurring manner by periodically increasing and decreasing the effective charge of the monomers. If the two polymer ends are tethered to two surfaces separated by a distance equal to the contour length of the polymeric chain, which could be in the range 10 nm–μ, the life time of the helical structures formed is increased.

A nano polymer aggregate on a substrate: A Theoretical study

We use lattice model to investigate the thermodynamics of an ideal semi-flexible polymer chain at the nano scale. The polymer chain is assumed to polymerize on the nano size substrate and the conformations of the chain were realized on the substrate using a square lattice. Our analytical estimates show clear distinctions in the thermodynamics of the polymer chain from its corresponding bulk . The persistent length versus stiffness curve varies linearly at the possible small length scale but in the bulk this variation is gradual. The polymer chain is confined from each direction and therefore, the nature of the force of confinement on a flexible and a semi-flexible chains has also been discussed for the proposed nano scale confinement.

Nonmonotonic adsorption behavior of semiflexible polymers

We study the adsorption behavior of semiflexible polymer chains with finite concentrations onto a structureless, planar, and impenetrable surface using polymer density functional theory based on a discretization of the Kratky-Porod wormlike chain model. Adsorption characteristics are investigated at different attractive interactions between the surface and polymers of various intrinsic stiffnesses. We analyze the density distributions in the vicinity of the surface and find, in the adsorption regime (when the surface attraction is strong: ϵw≳ϵw c, where ϵw c is the critical surface potential of adsorption transition), a nonmonotonic adsorption behavior for polymer chains with various intrinsic stiffnesses: the adsorption amount first decreases and then increases with the intrinsic stiffness, and the minimum adsorption amount (as well as the maximum critical surface potential of adsorption transition) occurs at lp ∼ Δ (Δ and lp are the attractive range of surface potential and persistence length, respectively), while in the depletion regime (ϵw≪ϵw c), the depletion depth and range are increased monotonically with the intrinsic stiffness. Furthermore, we find βϵw c∼lp/Δ-0.185 for lp ⋗ Δ and βϵw c∼lp/Δ0.366 for lp < Δ.

Critical properties of semi-flexible polymer chains situated within the simple cubic lattice

We have studied the critical properties of semi-flexible polymer chains whose elastic properties are brought out by the stiffness parameter s, and which are modelled by self-avoiding random walks (SAWs) in three-dimensional space. By applying the PERM Monte Carlo method, we have simulated the polymer chains by SAWs along the bonds of the simple cubic lattice, for a set of specific values for the stiffness parameter s. More precisely, we have examined behaviour of critical exponent νN, associated with the mean squared end-to-end distance of polymer chains of length N, as a function of s. Thus, we have established that νN monotonically decreases with N for s ⩾ 0.6, whereas the critical exponent νN displays a non-monotonic behaviour for s < 0.6. Values of νN, obtained for various s, have been extrapolated in the range of very long chains, and we have shown that obtained values ν = limN→∞νN do not depend on the polymer flexibility. Besides, we have calculated approximately the partition function for SAWs of length N, and examined its asymptotic behaviour, which turns out to be governed by the entropic critical exponent γ (associated with the total number of different polymer configurations), and the growth constant μ. We demonstrate that μ is a linear function of s, while γ does not depend on the polymer flexibility. Finally, we discuss and compare our results to those obtained previously for polymers on Euclidean lattices.

Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent.

This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provides a consistent characterization of the domain growth. Our results indicate that the coarsening kinetics presents a scaling behaviour that is independent of the solvent quality parameter, in analogy to the time–temperature superposition principle. Interestingly, the domain growth in time follows a power-law behaviour that is approximately independent of the architecture for all the flexible systems; while it is steeper for the semiflexible chains. Nevertheless, the fractal nature of the dense regions emerging during the collapse exhibits the same scaling behaviour for all the macromolecules. This suggests that the faster growing length scale in the semiflexible chains originates just from a faster mass diffusion along the chain contour, induced by the local stiffness. The decay of the dynamic correlations displays scaling behavior with the growing length scale of the system, which is a characteristic signature in coarsening phenomena.