Chain Contour Research Articles

Conformation and Dynamics along the Chain Contours of Polymer-Grafted Nanoparticles.

Densely grafted polymer chains onto spherical nanoparticles produce a diverse range of conformations. At high grafting densities, the corona region near the nanoparticle surface undergoes intense confinement due to a high concentration of chains in the concentrated polymer brush (CPB) region, which results in strong stretching for portions of the chains located within. In contrast, a semi-dilute polymer brush (SDPB) forms farther away from the core and offers reduced confinement for the polymer and more ideal conformations. However, conventional experimental methods are limited in their ability to provide detailed information on individual segments of grafted polymers in these regions; hence, molecular dynamics (MD) simulations are essential for gaining comprehensive insights into the behavior of the grafted chains. This study aims to explore the variations in polymer structure and dynamics that occur along the contour of the grafted chains as influenced by spatial confinement. We focus on the motions and relative positions of each bead along grafted polymers. Our results show that only the initial few grafted beads near the nanoparticle surface exhibit the strong stretching attributed segments in the CPB region of the brush. Increased grafting density or decreased chain flexibility leads to more stretched grafted chains and more aligned bond vectors. As a result, the relaxation dynamics of local regions of the polymer are also strongly influenced by these parameters. Although the grafted beads in the interior of the CPB region are highly sensitive to these parameters, those farther from the nanoparticle core experience significantly diminished effects. In comparison to the Daoud-Cotton (DC) model's predictions of CPB size, beads near the nanoparticle surface show slower dynamic decay, especially in high grafting densities, aligning with the DC model's estimates. Finally, we compare our simulations to previous works for additional insight into polymer-grafted nanoparticles.

Diffusion of knots in nanochannel-confined DNA molecules.

We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an "opening up process," wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.

Single-chain and condensed-state behavior of hnRNPA1 from molecular simulations.

Intrinsically disordered proteins (IDPs) are essential components for the formation of membraneless organelles, which play key functional and regulatory roles within biological systems. These complex assemblies form and dissolve spontaneously over time via liquid-liquid phase separation of IDPs. Mutations in their amino acid sequence can alter their phase behavior, which has been linked to the emergence of severe diseases. We study the conformation and phase behavior of a low-complexity domain of heterogeneous nuclear ribonucleoprotein A1 (hnRNPA1), using coarse-grained implicit solvent molecular dynamics simulations. We systematically analyze how these properties are affected by the number of aromatic residues within the examined sequences. We find a significant compaction of the chains and an increase in the critical temperature with increasing number of aromatic residues. The local persistence length is determined in single-chain simulations, revealing strong sequence-specific variations along the chain contour. Comparing single-chain and condensed state simulations, we find much more collapsed polymer conformations in the dilute systems, even at temperatures near the estimated theta temperature of the solution. These observations strongly support the hypothesis that aromatic residues play a dominant role for condensation, which is further corroborated by a detailed analysis of the intermolecular contacts, and conversely that important properties of condensates are captured in coarse-grained simulations. Interestingly, we observe density inhomogeneities within the condensates near criticality, which are driven by electrostatic interactions. Finally, we find that the relatively small fraction of hydrophobic residues in the IDPs results in interfacial tensions which are significantly lower compared to typical combinations of immiscible simple liquids.

Can Polymer Helicity Affect Topological Chirality of Polymer Knots?

We investigate the effect of helicity in isolated polymers on the topological chirality of their knots with computer simulations. Polymers are described by generic worm-like chains (WLC), where helical conformations are promoted by chiral coupling between segments that are neighbors along the chain contour. The sign and magnitude of the coupling coefficient u determine the sense and strength of helicity. The corrugation of the helix is adjusted via the radius R of a spherical, hard excluded volume around each WLC segment. Open and compact helices are, respectively, obtained for R that is either zero or smaller than the length of the WLC bond, and R that is a few times larger than the bond length. We use a Monte Carlo algorithm to sample polymer conformations for different values of u, spanning the range from achiral polymers to chains with well-developed helices. Monitoring the average helix torsion and fluctuations of chiral order as a function of u, for two very different chain lengths, demonstrates that the coil-helix transition in this model is not a phase transition but a crossover. Statistical analysis of conformations forming the simplest chiral knots, 31, 51, and 52, demonstrates that topological mirror symmetry is broken─knots formed by helices with a given sense prefer one handedness over the other. For the 31 and 51 knots, positive helical sense favors positive handedness. Intriguingly, an opposite trend is observed for 52 knots, where positive helical sense promotes negative handedness. We argue that this special coupling between helicity and topological chirality stems from a generic mechanism: conformations where some of the knot crossings are found in "braids" formed by two tightly interwoven sections of the polymer.

Depletion Interactions between Nanoparticles: The Effect of the Polymeric Depletant Stiffness.

A Density Functional Theory is employed to study depletion interactions between nanoparticles mediated by semiflexible polymers. The four key parameters are the chain contour length and the persistence length of the polymeric depletant, its radius of gyration, and the nanoparticle radius. In the Density Functional Theory calculation of the depletion interaction between the nanoparticles mediated by semiflexible polymers, the polymer gyration radius is kept constant by varying the contour length and the persistence length simultaneously. This makes it possible to study the effect of the chain stiffness on the depletion potential of mean force between the nanoparticles for a given depletant size. It is found that the depletion attraction becomes stronger for stiffer polymer chains and larger colloids. The depletion potential of mean force is used as input to compute the phase diagram for an effective one-component colloidal system.

Single-chain and condensed-state behavior of hnRNPA1 from molecular simulations.

Intrinsically disordered proteins (IDPs) are essential components for the formation of membraneless organelles, which play key functional and regulatory roles within biological systems. These complex assemblies form and dissolve spontaneously over time via liquid-liquid phase separation of IDPs. Mutations in their amino acid sequence can alter their phase behavior, which has been linked to the emergence of severe diseases. We study the conformation and phase behavior of a low-complexity domain of heterogeneous nuclear ribonucleoprotein A1 (hnRNPA1) using coarse-grained implicit solvent molecular dynamics simulations. We systematically analyze how these properties are affected by the number of aromatic residues within the examined sequences. We find a significant compaction of the chains and an increase in the critical temperature with an increasing number of aromatic residues. The local persistence length is determined in single-chain simulations, revealing strong sequence-specific variations along the chain contour. Comparing single-chain and condensed-state simulations, we find many more collapsed polymer conformations in the dilute systems, even at temperatures near the estimated θ-temperature of the solution. These observations strongly support the hypothesis that aromatic residues play a dominant role in condensation, which is further corroborated by a detailed analysis of the intermolecular contacts, and conversely that important properties of condensates are captured in coarse-grained simulations. Interestingly, we observe density inhomogeneities within the condensates near criticality, which are driven by electrostatic interactions. Finally, we find that the relatively small fraction of hydrophobic residues in the IDPs results in interfacial tensions, which are significantly lower compared to typical combinations of immiscible simple liquids.

Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush.

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).

Complementary assessment of γ-irradiated polyurethane-POSS hybrids by chemiluminescence and differential scanning calorimetry

A series of segmental polyurethane organic inorganic hybrids with polyhedral oligomeric silsesquioxanes (POSS) incorporated along the chain contour on the hard segments is irradiated by γ radiation at doses up to 100 kGy. The effects of this treatment on the morphology of the materials and the low temperature stability to oxidation are assessed complementary by non-isothermal and isothermal chemiluminescence experiments as well as with differential scanning calorimetry. From the methodological point of view, it was found that both physical and chemical processes have a footprint on both methods, but the physical ones manifest themselves more intensely in the thermal method, whereas chemical ones in chemiluminescence. Due to γ-exposure the onset oxidation temperatures decrease by several degrees, but POSS seems to protect the material to some extent. γ-Irradiation damage has also a negative effect on the development of phase separation, which is further enhanced by the presence of POSS. The crystallinity of the soft segments in the matrix is completely suppressed by irradiation, however, even a small amount of POSS preserves the phenomenon.

Controlling the Chain Folding for the Synthesis of Single-Chain Polymer Nanoparticles Using Thermoresponsive Polymers

Synthetic polymer single-chain nanoparticles (SCNPs) are an emerging new class of nanomaterials that possess similar folded structures as natural proteins. However, most SCNPs reported so far are p...

A Polymer with Mechanochemically Active Hidden Length.

Incorporating hidden length into polymer chains can improve their mechanical properties, because release of the hidden length under mechanical loads enables localized strain relief without chain fracture. To date, the design of hidden length has focused primarily on the choice of the sacrificial bonds holding the hidden length together. Here we demonstrate the advantages of adding mechanochemical reactivity to hidden length itself, using a new mechanophore that integrates (Z)-2,3-diphenylcyclobutene-1,4-dicarboxylate, with hitherto unknown mechanochemistry, into macrocyclic cinnamate dimers. Stretching a polymer of this mechanophore more than doubles the chain contour length without fracture. DFT calculations indicate that the sequential dissociation of the dimer, followed by cyclobutene isomerization at higher forces yields a chain fracture energy 11 times that of a simple polyester of the same initial contour length and preserves high energy-dissipating capacity up to ∼3 nN. In sonicated solutions cyclobutene isomerizes to two distinct products by competing reaction paths, validating the computed mechanochemical mechanism and suggesting an experimental approach to quantifying the distribution of single-chain forces under diverse loading scenarios.

Sequence effects on internal structure of droplets of associative polymers

Intrinsically disordered proteins (IDPs) can form liquid-like membraneless organelles, gels, and fibers in cells and in vitro. In this study, we propose a simple model of IDPs as associative polymers in poor solvent and explore the formation of transient liquid droplets and their transformation into solid-like aggregates. We use Langevin dynamics simulations of short polymers with two stickers placed symmetrically along their contour to study the effect of the primary sequence of these polymers on their organization inside condensed droplets. We observe that the shape, size, and number of sticker clusters inside the droplet change from a long cylindrical fiber to many compact clusters as one varies the location of stickers along the chain contour. Aging caused by the conversion of intramoleclular to intermolecular associations is observed in droplets of telechelic polymers but not for other sequences of associating polymers. The relevance of our results to condensates of IDPs is discussed.

Rigidification of Poly(p-phenylene)s through ortho-Phenyl Substitution.

A sterically π-congested ortho-phenylated poly(p-phenylene) (PPP) has been synthesized with unprecedentedly high molecular weights up to 29 kDa after fractionation, as confirmed by gel permeation chromatography coupled with a multiangle laser light scattering detector. The chain translation diffusion coefficient obtained from dynamic light scattering experiments displayed strong scaling (∼Lw–0.8) to the chain contour length, indicating a rodlike shape with remarkably high rigidity of this novel PPP. These results provide an interesting insight into the relationship between the structure and the chain stiffness of PPP-based polymers and challenge the validity of the existing diffusion models in polymer physics.

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.

How does stiffness of polymer chains affect their adsorption transition?

The adsorption transition and the structure of semiflexible adsorbed macromolecules are studied by a molecular dynamics simulation of a coarse-grained, bead-spring type model. Varying chain length N and stiffness κ (which is proportional to the persistence length ℓp in d = 3 dimensions) as well as the strength ϵwall of the adsorption potential, the adsorbed monomer fraction, orientational bond order parameter, and chain linear dimensions are studied. In the simulations, excluded volume interactions normally are included but can be "switched off," and thus, the influence of excluded volume (leading to deviations from predictions of the wormlike chain model) can be identified. It is shown that the variation in the adsorption threshold ϵwall cr with ℓp is compatible with the predicted law ϵwall cr∝ℓp -1/3. In the vicinity of the adsorption threshold, the coils are still three-dimensional, and for large ℓp, the effect of the excluded volume is almost negligible, while for strongly adsorbed chains it is always felt. Near the transition, the decay length of orientational correlations along the chain contour increases gradually from ℓp to 2ℓp. While the latter value is expected for strictly two-dimensional chains from the Kratky-Porod model, this model is inaccurate for the description of lateral chain dimensions of long, strongly adsorbed, semiflexible polymers due to its neglect of excluded volume. The significance of these findings for the interpretation of pertinent experiments is briefly discussed.

Semiflexible Polymers Interacting With Planar Surfaces: Weak versus Strong Adsorption.

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness as well as the strength of the adsorption potential are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter ) and the mean square gyration radius parallel, , and perpendicular, , to the wall. While for strongly adsorbed chains EV has negligible effect on f and , we find that is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that , and converge to their asymptotic values with corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.

Methylcellulose fibrils: a mini review

AbstractThis review covers the recently discovered methylcellulose (MC) fibrils and their impact on MC thermogelation and overall gel strength. The thermogelation of MC aqueous solutions has been studied for nearly 100 years, but it has only recently been attributed to fibril formation at elevated temperatures. The assembly of a fibrillar network explains the general features of MC gels: the unusually high modulus, the turbidity, and the nonlinear rheological behavior at high strains. Recent scattering, atomic force microscopy (AFM) and cryogenic transmission electron microscopy (cryo‐TEM) experimental efforts have led to critical discoveries about the fibril structure. MC fibrils are 60% water by volume when in solution. The length of the fibrils, especially for shorter chains, is closely correlated with the MC chain contour length. On the other hand, the fibril radius does not depend on the temperature, molecular weight or concentration of MC chains but does seem to be correlated with chain stiffness. The discovery of MC fibrils represents a significant departure from the entanglement of polymer chains and localized phase separation based physical model of MC gelation, opens new questions about the mechanism of fibril formation and presents new pathways for stimulus responsive material design. © 2019 Society of Chemical Industry

Nonlinear shear of entangled polymers from nonequilibrium molecular dynamics

ABSTRACTThis study aims to use molecular dynamics (MD) simulations of Kremer–Grest (KG) chains to inform future developments of models of entangled polymer dynamics. We perform nonequilibrium MD simulations, under shear flow, for well‐entangled KG chains. We study chains of 512 and 1000 KG beads, corresponding to 8 and 15 entanglements, respectively. We compute the linear rheological properties from equilibrium simulations of the stress autocorrelation and obtain from these data the tube model parameters. Under nonlinear shear flow, we compute the shear viscosity, the first and second normal stress differences, and chain contour length. For chains of 512 monomers, we obtain agreement with the results of Cao and Likhtman (ACS Macro. Lett. 2015, 4, 1376). We also compare our nonlinear results with the Graham, Likhtman and Milner‐McLeish (GLaMM) model. We identify some systematic disagreement that becomes larger for the longer chains. We made a comparison of the transient shear stress maximum from our simulations, two nonlinear models and experiments on a wide range of melts and solutions, including polystyrene (PS), polybutadiene, and styrene–butadiene rubber. This comparison establishes that the PS melt data show markedly different behavior to all other melts and solutions and KG simulations reproduce the PS data more closely than either the GLaMM or Xie and Schweizer models. We discuss the performance of these models against the data and simulations. Finally, by imposing a rapid reversing flow, we produce a method to extract the recoverable strain from MD simulations, valid for sufficiently entangled monodisperse polymers. We explore how the resulting data can probe the melt state just before the reversing flow. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1692–1704

Effect of γ-substituted poly(ɛ-caprolactone) chain length on its coil-to-globule transition temperature in water: A molecular dynamics simulation study

The influence of chain length on the coil-to-globule transition temperature (Tcg) of poly{γ-2-[2-(2methoxyethoxy)ethoxy]ethoxy-3-caprolactone} (PMEEECL) chains was investigated via full atomistic molecular dynamics (MD) simulation. Chains with different repeating unit numbers (N) of 5, 10, 15, and 20 were simulated over a wide temperature range. It was found that Tcg increased with increasing N of the PMEEECL chain. The simulation results showed that as the chain contour length is of the order of the Kuhn length, the chain bending and chain collapse become more involved. The chains exhibit significant sensitivity to the temperature when the contour length exceeds the Kuhn length. Nonetheless, for the short chains, i.e. pentamer, the oligomer was temperature insensitive in the studied temperature range. Furthermore, aggregation of five PMEEECL chains with N = 20 was clearly observed at the temperatures above Tcg.

Broadband dielectric spectroscopy to validate architectural features in Type-A polymers: Revisiting the poly(glycidyl phenyl ether) case.

Broadband dielectric spectroscopy (BDS) is a powerful technique that allows studying the molecular dynamics of materials containing polar entities. Among a vast set of different applications, BDS can be used as a complementary tool in polymer synthesis. In this work, we will show how BDS can be used to validate architectural features in Type-A polymers, those having a net dipole moment component along the chain contour. Specifically, we will focus on the evaluation of the dielectric relaxation of poly(glycidyl phenyl ether) (PGPE) samples designed and synthesized with a variety of topologies and regio-orders: linear regio-regular chains synthesized from monofunctional and bifunctional initiators, macrocyclic regio-regular chains, and linear and macrocyclic regio-irregular chains. Our study highlights the impact of using BDS as a complementary characterization technique for providing topological details of polymers, which are otherwise not possible with many traditional techniques (e.g., NMR and mass spectrometry).

Bacterial chromosome organization. II. Few special cross-links, cell confinement, and molecular crowders play the pivotal roles.

Using a coarse-grained bead-spring model of bacterial chromosomes of Caulobacter crescentus and Escherichia coli, we show that just 33 and 38 effective cross-links in 4017 and 4642 monomer chains at special positions along the chain contour can lead to the large-scale organization of the DNA polymer, where confinement effects of the cell walls play a key role in the organization. The positions of the 33/38 cross-links along the chain contour are chosen from the Hi-C contact map of bacteria C. crescentus and E. coli. We represent 1000 base pairs as a coarse-grained monomer in our bead-spring flexible ring polymer model of the DNA polymer. Thus, 4017/4642 beads on a flexible ring polymer represent the C. crescentus/E. coli DNA polymer with 4017/4642 kilo-base pairs. Choosing suitable parameters from Paper I, we also incorporate the role of compaction of the polymer coil due to the presence of molecular crowders and the ability of the chain to release topological constraints. We validate our prediction of the organization of the bacterial chromosomes with available experimental data and also give a prediction of the approximate positions of different segments within the cell. In the absence of confinement, the minimal number of effective cross-links required to organize the DNA chains of 4017/4642 monomers was 60/82 [Agarwal et al., Europhys. Lett. 121, 18004 (2018) and Agarwal et al., J. Phys.: Condens. Matter 30, 034003 (2018)].