Persistence Length Of Polymers Research Articles

The local persistence length of semi-flexible self-avoiding walks on the square lattice

By applying the pruned-enriched Rosenbluth Monte Carlo simulation method, we have studied the local persistence length of semi-flexible linear polymers presented by self-avoiding walks (SAWs) on the square lattice, where the stiffness property is characterised by the weight s assigned to each bend of the walk. In this model, the local persistence length λN(k) of N-step SAWs is formulated as an ensemble average of the projection of the end-to-end position vector onto the oriented kth step of the SAW path. We have found that the persistence length λN(k)(s) decreases with s and increases with k and N. Regarding the chain position parameter k, we have scrutinised two particular cases: the first case is when k has a constant (fixed) value, independent of the chain length, and the second one is the situation when k is comparable with the SAW length k∼N . For fixed k, we have learnt that in the limit N→∞ , the persistence length λN(k)(s) tends towards a constant value λp(k)(s) behaving as k1/2 . In the other analysed case k∼N , in the same limit, λN(k)(s) diverges as N ϕ , with φ=1/2 . We have also examined the dependence of the studied quantity on s and discussed our results in the context of previous findings and predictions related to the persistence length behaviour of SAWs in Euclidean spaces.

Effects of inertia on conformation and dynamics of tangentially driven active filaments.

Active filamentlike systems propelling along their backbone exist across scales ranging from motor-driven biofilaments to worms and robotic chains. In macroscopic active filaments such as a chain of robots, in contrast to their microscopic counterparts, inertial effects on their motion cannot be ignored. Nonetheless, the consequences of the interplay between inertia and flexibility on the shape and dynamics of active filaments remain unexplored. Here we examine inertial effects on a flexible tangentially driven active polymer model pertinent to the above examples and we determine the conditions under which inertia becomes important. Performing Langevin dynamics simulations of active polymers with underdamped and overdamped dynamics for a wide range of contour lengths and activities, we uncover striking inertial effects on conformation and dynamics for high levels of activities. Inertial collisions increase the persistence length of active polymers and remarkably alter their scaling behavior. In stark contrast to passive polymers, inertia leaves its fingerprint at long times by an enhanced diffusion of the center of mass. We rationalize inertia-induced enhanced dynamics by analytical calculations of center-of-mass velocity correlations, applicable to any active polymer model, which reveal significant contributions from active force fluctuations convoluted by inertial relaxation.

Phase stability of colloidal spheres mixed with semiflexible supramolecular polymers

HypothesisMixtures of colloids and supramolecular polymers may exhibit stimuli-responsive phase behaviour. However, in theoretical descriptions of such systems, the polymers are commonly described either as flexible chains or as rigid rods, while in experimental systems supramolecular polymers usually fall in between these two limits. We expect the flexibility of the polymers to have a profound effect on the stimuli-responsive phase behaviour. TheoryWe propose a general approach to predict the phase behaviour of colloidal hard spheres mixed with covalent or supramolecular polymers of arbitrary persistence length using free volume theory and an interpolation between flexible and rigid chains. FindingsThe binodals are predicted to shift to lower monomer concentrations as the persistence length is increased, making the polymers more efficient depletants. The persistence length is therefore an additional degree of freedom for manipulating the phase behaviour of colloid–polymer mixtures. We show that by manipulating the persistence length of temperature responsive supramolecular polymers, a wide range of phase diagrams with various topologies can be obtained. For example, we find phase diagrams with a critical point but no triple point or displaying two triple points for temperature-sensitive supramolecular polymers mixed with hard spheres.

Modeling of Branched Thickening Polymers under Poiseuille Flow Gives Clues as to How to Increase a Solvent's Viscosity.

The viscosity enhancement of a solvent produced by the addition of thickening branched polymers is predicted as a function of polymer concentration, branch length and persistence length, and strength of the covalent bonding interactions. Nonequilibrium, stationary-state Poiseuille numerical simulations are performed using the dissipative particle dynamics model to obtain the viscosity of the fluid. It is found that the clustering of the polymers into aggregates increases the viscosity and that it is more strongly affected by the strength of the bonding interactions. General scaling relationships are found for the viscosity as a function of the variables studied, which are expected to be useful for the design and synthesis of new viscosifying polymers. It is argued that our results can be applied to aqueous thickeners, of importance for colloidal fluids such as paints and coatings and also for nonpolar fluids such as supercritical CO2, which is a promising nonhydraulic fracking fluid also useful in enhanced oil recovery.

Statistical properties of a tangentially driven active filament

Active polymers play a central role in many biological systems, from bacterial flagella to cellular cytoskeletons. Minimal models of semiflexible active filaments have been used to study a variety of interesting phenomena in active systems, such as defect dynamics in active nematics, clustering and laning in motility assays, and conformational properties of chromatin in eukaryotic cells. In this paper, we map a semiflexible polymer to an exactly solvable active Rouse chain, which enables us to analytically compute configurational and dynamical properties of active polymers with arbitrary rigidity. Upon mapping back to the semiflexible filament, we see that the center of mass diffusion coefficient grows linearly with an activity parameter that is renormalized by the polymer persistence length. These results closely agree with numerical data obtained from microscopic simulations.

Molecular dynamics study of polymeric chemical gels: Effect of persistence length and crosslinker density

ABSTRACTUsing molecular dynamics, we study the formation of chemical gels from an initial solution of reactive polymers that undergo a crosslinking reaction. We study the effect of the polymer persistence length and different densities of crosslinkers along the chains. As the reaction progresses, different structural features are identified in the system leading to the development of a percolated cluster. These features are (a) single strands, (b) double strands, and (c) bridges. We found that the total numbers of these three kinds of features are roughly independent of the persistence length; however, the average lengths of single and double strands grow with this variable. The average length of double strands strongly increases with increasing crosslinker density and the amount of single strands sharply falls as crosslinker density grows. We also found that general structural features of polymer networks are highly dependent on chain persistence length and crosslinker density. Fully flexible chains with high density of crosslinkers result in inhomogeneous network structures with large voids. In contrast, precursor chains with high rigidity and scarce number of crosslinkers result in homogeneous networks having small cavities. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1343–1350

Semi-flexible compact polymers in two dimensional nonhomogeneous confinement

We have studied the compact phase conformations of semi-flexible polymer chains confined in two dimensional nonhomogeneous media, modelled by fractals that belong to the family of modified rectangular (MR) lattices. Members of the MR family are enumerated by an integer p and fractal dimension of each member of the family is equal to 2. The polymer flexibility is described by the stiffness parameter s, while the polymer conformations are modelled by weighted Hamiltonian walks (HWs). Applying an exact recurrence equations method, we have found that partition function ZN for closed HWs consisting of N steps scales as , where constants and depend on both p and s. We have calculated numerically the stiffness dependence of the polymer persistence length, as well as various thermodynamic quantities (such as free and internal energy, specific heat and entropy) for a large set of members of the MR family. Analysis of these quantities has shown that semi-flexible compact polymers on MR lattices can exist only in the liquid-like (disordered) phase, whereas the crystal (ordered) phase has not appeared. Finally, behavior of the examined system at zero temperature has been discussed.

The Persistence Length of Semiflexible Polymers in Lattice Monte Carlo Simulations.

While applying computer simulations to study semiflexible polymers, it is a primary task to determine the persistence length that characterizes the chain stiffness. One frequently asked question concerns the relationship between persistence length and the bending constant of applied bending potential. In this paper, theoretical persistence lengths of polymers with two different bending potentials were analyzed and examined by using lattice Monte Carlo simulations. We found that the persistence length was consistent with theoretical predictions only in bond fluctuation model with cosine squared angle potential. The reason for this is that the theoretical persistence length is calculated according to a continuous bond angle, which is discrete in lattice simulations. In lattice simulations, the theoretical persistence length is larger than that in continuous simulations.

Persistence Length, End-to-End Distance, and Structure of Coarse-Grained Polymers.

Coarse-grained (CG) polymer simulations can access longer times and larger lengths than all-atom (AA) molecular dynamics simulations; however, not all CG models correctly reproduce polymer properties on all length scales. Here we coarse-grain atomistic position data from polyethylene (PE) and polytetrafluoroethylene (PTFE) melt simulations by combining λ backbone carbon atoms in a single CG bead. Resulting CG variables have correlations along the chain backbone that depend on the coarse-graining scale λ and are generally not reproduced by independent bond-length, bond-angle and torsion-angle distributions. By constructing distributions of CG variables equivalent to those from simulated CG potentials we are able to evaluate the bond-orientation correlation for different CG models at reduced computational cost. CG models and potentials that include only nonbonded, bond-length, and bond-angle interactions computed by Boltzmann inversion correctly reproduce the CG variable distributions but do not necessarily reproduce the chain stiffness, overestimating the persistence length Lp and end-to-end distance ⟨ R2⟩1/2 with increasing λ. While CG models that include an independent torsion angle match the bond-orientation correlation and ⟨ R2⟩1/2 better, only approximate models that include correlations between bond and torsion angles match the true bond-orientation correlation.

Investigation of nematic to smectic phase transition and dynamical properties of strongly confined semiflexible polymers using Langevin dynamics.

We investigated the nematic to smectic phase transition for strongly confined semiflexible polymer solutions in slit-like confinements using GPU-accelerated Langevin dynamics. We characterized the phase transitions from the nematic to smectic phases for semi-flexible polymer solutions as the polymer density increased. The dependence for the lyotropic nematic to smectic transition can be collapsed by scaling exponents between 0.2 and 0.3. The smectic C phase is found for all the cases with the polymer orientation director tilted with respect to smectic layer lateral alignment. As the chain rigidity increases, the transition density decreases for systems in which the polymer persistence length (P) to slit height (H) ratios are 1.25, 2.5, 3.75, 5 and 25. We also characterized the polymer dynamics for the isotropic-nematic-smectic transitions. The overall polymer diffusivity decreased steadily as the polymer density increased. We observed anomalous polymer diffusion along the nematic director near the isotropic-nematic transition, similar to previously reported behavior for nematic-forming ellipsoids. Polymer diffusivity decreased sharply by two orders of magnitude upon the nematic-smectic transition.

Polymer translocation through a nanopore in the presence of chaperones: A three dimensional MD simulation study

The chaperone assisted polymer translocation through a nanopore is studied using Langevin dynamics simulations in three dimensions. We investigate the effects of the polymer persistence length, the binding energy between the polymer and the chaperones and the chaperone concentration on the translocation. The results show that the probability of translocation increases and the mean translocation time decreases by increasing the chaperone concentration and the binding energy for all persistence lengths. The translocation probability also increases as the polymer persistence length increases, but the translocation process of stiffer polymers takes longer time compared with the flexible ones. Also, it is found that the strength of chaperone binding differently affects the translocation probabilities of flexible and stiff polymers. Dynamics of the translocation is described using the waiting time distribution of monomers for different persistence lengths. The obtained results can be exploited to understand some biological chaperone assisted translocations in which different conditions such as a variation in the value of temperature, pH or salt concentration change the chain flexibility.

Highly absorbing multispectral near-infrared polymer nanoparticles from one conjugated backbone for photoacoustic imaging and photothermal therapy.

Semiconducting polymers with specific absorption are useful in various applications, including organic optoelectronics, optical imaging, and nanomedicine. However, the optical absorption of a semiconducting polymer with a determined structure is hardly tunable when compared with that of inorganic semiconductors. In this work, we show that the optical absorption of polymer nanoparticles from one conjugated backbone can be effectively tuned through judicious design of the particle morphology and the persistence length of polymers. Highly absorbing near-infrared (NIR) polymers based on diketopyrrolopyrrole-dithiophene (DPP-DT) are synthesized to have different molecular weights (MWs). The DPP-DT polymer with a large molecular weight and high persistence length exhibited remarkably high optical absorption with a peak mass extinction coefficient of 81.7Lg-1cm-1, which is one of the highest value among various photothermal agents reported to date. Particularly, the polymer nanoparticles with different sizes exhibit broadly tunable NIR absorption peaks from 630 to 811nm. The PEGylated small polymer dots (Pdots) show good NIR light-harvesting efficiency and high non-radiative decay rates, resulting in a relatively high photothermal conversion efficiency in excess of 50%. Thus, this Pdot-based platform can serve as promising photothermal agents and photoacoustic probes for cancer theranostics.

Compressive response and helix formation of a semiflexible polymer confined in a nanochannel.

Configurations of a single semiflexible polymer is studied when it is pushed into a nanochannel in the case where the polymer persistence length l_{p} is much longer than the channel diameter D:l_{p}/D≫1. Using numerical simulations, we show that the polymer undergoes a sequence of recurring structural transitions upon longitudinal compression: random deflection along the channel, a helix going around the channel wall, double-fold random deflection, double-fold helix, etc. We find that the helix transition can be understood as buckling of deflection segments, and the initial helix formation takes place at very small compression with no appreciable weak compression regime of the random deflection polymer.

Reduction of the effective shear viscosity in polymer solutions due to crossflow migration in microchannels: Effective viscosity models based on DPD simulations

ABSTRACTMolecular dynamics simulations (dissipative particle dynamics–DPD) were developed and used to quantify wall-normal migration of polymer chains in microchannel Poseuille flow. Crossflow migration due to viscous interaction with the walls results in lowered polymer concentration near the channel walls. A larger fraction of the total flow volume becomes depleted of polymer when the channel width h decreases into the submicron range, significantly reducing the effective viscosity. The effective viscosity was quantified in terms of channel width and Weissenberg number Wi, for 5% polymer volume fraction in water. Algebraic models for the depletion width δ(Wi, h) and effective viscosity μe(δ/h, Wi) were developed, based on the hydrodynamic theory of Ma and Graham and our simulation results. The depletion width model can be applied to longer polymer chains after a retuning of the polymer persistence length and the corresponding potential/thermal energy ratio.

Toward a better understanding of conjugated polymer blends with non-spherical small molecules: coupling of molecular structure to polymer chain microstructure

Abstract

Shifting the Isotropic–Nematic Transition in Very Strongly Confined Semiflexible Polymer Solutions

We investigated how very strong confinement, smaller than the polymer persistence length lp, affects the isotropic–nematic transition for semiflexible polymer solutions using GPU-accelerated Langevin dynamics. Walls facilitate polymer alignment, and under strong quasi-two-dimensional slitlike confinement, the I–N transition is found to be a continuous transition occurring via capillary nematization. We found that the I–N transition in the slit is a second-order transition, and the transition volume fraction ϕcr decreases with decrease of the slit height H. For H < lp, the critical exponent of the order parameter is found to be β ≈ 0.3–0.5. β sharply increases for H higher than a critical height, indicating the onset of a different wall-induced phase transition. Higher ϕcr are found for larger H, which is associated with increased monomer packing near the walls and correspond to the partial wetting transition predicted by self-consistent field theory.

Mechanical properties of single supramolecular polymers from correlative AFM and fluorescence microscopy

We characterize the structure and mechanical properties of 1,3,5-benzenetricarboxamide (BTA) supramolecular polymers using correlative AFM and fluorescence imaging.

Lattice models of directed and semiflexible polymers in anisotropic environment

We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along direction of the external stretching field and semiflexible polymers. We are working within the frames of lattice models: partially directed self-avoiding walks (PDSAWs) and biased self-avoiding walks (BSAWs). Our numerical analysis of PDSAWs reveals, that competition between the stretching field and anisotropy caused by presence of extended defects leads to existing of three characteristic length scales in the system. At each fixed concentration of disorder we found a transition point, where the influence of extended defects is exactly counterbalanced by the stretching field. Numerical simulations of BSAWs in anisotropic environment reveal an increase of polymer stiffness. In particular, the persistence length of semiflexible polymers increases in presence of disorder.

Structure of Microgels with Debye–Hückel Interactions

The structural properties of model microgel particles are investigated by molecular dynamics simulations applying a coarse-grained model. A microgel is comprised of a regular network of polymers internally connected by tetra-functional cross-links and with dangling ends at its surface. The self-avoiding polymers are modeled as bead-spring linear chains. Electrostatic interactions are taken into account by the Debye–Hückel potential. The microgels exhibit a quite uniform density under bad solvent conditions with a rather sharp surface. With increasing Debye length, structural inhomogeneities appear, their surface becomes fuzzy and, at very large Debye lengths, well defined again. Similarly, the polymer conformations change from a self-avoiding walk to a rod-like behavior. Thereby, the average polymer radius of gyration follows a scaling curve in terms of polymer length and persistence length, with an asymptotic rod-like behavior for swollen microgels and self-avoiding walk behavior for weakly swollen gel particles.

Mechanism of Crystallization and Implications for Charge Transport in Poly(3‐ethylhexylthiophene) Thin Films

In this work, crystallization kinetics and aggregate growth of poly(3‐ethylhexylthiophene) (P3EHT) thin films are studied as a function of film thickness. X‐ray diffraction and optical absorption show that individual aggregates and crystallites grow anisotropically and mostly along only two packing directions: the alkyl stacking and the polymer chain backbone direction. Further, it is also determined that crystallization kinetics is limited by the reorganization of polymer chains and depends strongly on the film thickness and average molecular weight. Time‐dependent, field‐effect hole mobilities in thin films reveal a percolation threshold for both low and high molecular weight P3EHT. Structural analysis reveals that charge percolation requires bridged aggregates separated by a distance of ≈2–3 nm, which is on the order of the polymer persistence length. These results thus highlight the importance of tie molecules and inter‐aggregate distance in supporting charge percolation in semiconducting polymer thin films. The study as a whole also demonstrates that P3EHT is an ideal model system for polythiophenes and should prove to be useful for future investigations into crystallization kinetics.