Effect Of Chain Stiffness Research Articles

Monte Carlo simulation for the effect of chain stiffness on the free surface of polymer melts

The role of chain stiffness on structural and molecular properties for the free surface of polymer melts was examined by Monte Carlo (MC) simulations of the coarse-grained (CG) polyethylene-like chains on the second nearest neighbor diamond (2nnd) lattice. Polyethylene-like model by multiplying the statistical weights with the chain stiffness parameter (k) to represent more flexible (k = 0.0 and 0.5) and stiffer (k = 1.5 and k = 2.0) chains than normal polyethylene (k = 1.0). For the melt-vacuum surfaces of stiffer chains, bulk densities become lower with broader surface profiles. For more flexible chains, monomers at the end/middle position are more segregated/depleted near the surface. Bonds and chains tend to be randomly orientated in the bulk region but exhibit anisotropic orientation near the surface, especially for stiffer chains. For more flexible chains, polymers adopt a larger amount of gauche conformation and chain dimensions become smaller with a more compact shape. The main principal axes of polymer coils are preferably oriented parallelly to the surface and the magnitudes of this anisotropy are larger for stiffer chains. Based on intra- and intermolecular energetics, more flexible chains have a larger amount of gauche conformation with denser bulk structures but they adopt more trans conformation near the surface.

Random close packing of semi-flexible polymers in two dimensions: Emergence of local and global order.

Through extensive Monte Carlo simulations, we systematically study the effect of chain stiffness on the packing ability of linear polymers composed of hard spheres in extremely confined monolayers, corresponding effectively to 2D films. First, we explore the limit of random close packing as a function of the equilibrium bending angle and then quantify the local and global order by the degree of crystallinity and the nematic or tetratic orientational order parameter, respectively. A multi-scale wealth of structural behavior is observed, which is inherently absent in the case of athermal individual monomers and is surprisingly richer than its 3D counterpart under bulk conditions. As a general trend, an isotropic to nematic transition is observed at sufficiently high surface coverages, which is followed by the establishment of the tetratic state, which in turn marks the onset of the random close packing. For chains with right-angle bonds, the incompatibility of the imposed bending angle with the neighbor geometry of the triangular crystal leads to a singular intra- and inter-polymer tiling pattern made of squares and triangles with optimal local filling at high surface concentrations. The present study could serve as a first step toward the design of hard colloidal polymers with a tunable structural behavior for 2D applications.

Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain.

Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.

Molecular simulation for the effect of chain stiffness on polymer crystallization from the melts

The chain stiffness that arises from structural constraints and hindrances to internal rotation is intimately related to the macroscopic properties of polymeric materials. The main goal of this study is to examine the role chain stiffness plays in controlling polymer crystallization. Molecular simulations of the coarse-grained (CG) polymer model were used to determine the effect of chain stiffness on the structural formation upon stepwise cooling from the melts. The polyethylene (PE)-like model with different chain stiffness parameter (k) was proposed to modify the statistical weights in the rotational isomeric state (RIS) chains. The PE-like models with 0.5 < k < 1.0 and 1.0 < k < 1.5, can be regarded as more flexible to stiffer chains than normal PE (k = 1.0). Simulation results indicate that the rate of structural formation and the degree of crystallinity are increased better for normal PE chains (k = 1.0). Highly flexible chains (the case of k = 0.5) adopt larger amount of gauche conformation and have much difficulty to form the ordered structure. On the other hand, much stiffer chains (the case of k = 1.5), can still have some gauche conformation which cannot be converted to the trans state upon cooling from the melts. Our study implies that only polymers with the appropriate chain stiffness can exhibit clear evidence for crystallization.

Semiflexible polymer nanocomposites: Role of stiffness on structure and macrophase separation

Polymer nanocomposites are lighter in weight as compared to the traditionally bigger size filler-loaded composites. Moreover, polymer nanocomposites show enhancement in properties with small fractions of nanoparticles. In certain cases, a high fraction of nanoparticles is needed to incorporate the required properties significantly. In most of the theoretical and simulation studies of polymeric systems, the polymer chain is modeled as ideal freely-jointed chains, thereby neglecting the effects of chain stiffness. We study a system of semiflexible polymers containing 50% volume fraction of nanoparticles using Polymer Reference Interaction Site Model (PRISM) theory. In the absence of chemical anisotropy, these systems undergo a disordered fluid phase to a macrophase-separated state. The phase transition of these systems is favored by an increase in the persistence length of the polymer chain. At lower values of persistence lengths, a slight increase in the persistence length results in a sharp decrease in the critical packing fraction. However, for longer persistence lengths, an increase in the persistence length barely affects the critical packing fraction. Studies of the local structure of these systems show that an increase in persistence length increases the polymer–polymer contacts and polymer-nanoparticle contacts. On the contrary, nanoparticle-nanoparticle contact initially increases suddenly, then decreases slightly at longer persistence lengths.

Glassy dynamics of model colloidal polymers: Effect of controlled chain stiffness* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11804085 and 11847115) and the Doctoral Foundation of Heze University (Grant No. XY18BS13).

Colloidal polymers with tunable chain stiffness have been successfully assembled in experiments recently. Similar to molecular polymers, chain stiffness is an important feature which can distinctly affect the dynamical behaviors of colloidal polymers. Hence, we model colloidal polymers with controlled chain stiffness and study the effect of chain stiffness on glassy behaviors. For stiff chains, there are long-ranged periodic intrachain correlations besides two incompatible local length scales, i.e., monomer size and bond length. The mean square displacement of monomers exhibits sub-diffusion at intermediate time/length scale and the sub-diffusive exponent increases with chain stiffness. The data of localization length of stiff polymers versus rescaled volume fraction for different monomer sizes can gather close to an exponential curve and decay slower than those of flexible polymers. The increase of chain stiffness linearly increases the activation energy of the colloidal-polymer system and thus makes the colloidal polymers vitrify at lower volume fraction. Static and dynamic equivalences between stiff colloidal polymers of different monomer sizes have been checked.

Hierarchical Self-Assembly of Poly(d-glucose carbonate) Amphiphilic Block Copolymers in Mixed Solvents

We report the fibril formation of poly(d-glucose carbonate) (PGC)-based amphiphilic diblock copolymers using solution assembly. Unlike conventional cylindrical micelles constructed from amphiphilic block copolymers (BCPs) with coil-like blocks, the assembled PGC fibrils exhibit thin, ribbon-like features due to significant stiffness and hydrophobicity of the PGC BCP backbone that result in a unique polymer chain packing. A tetrahydrofuran/H2O solvent mixture was used to create a solvent quality gradient during which a hierarchical assembly pathway was observed with fibril precursor nanoparticles that linked together into fibrils. These initial precursors were soft, patchy nanoparticles caused by the phase-segregated hydrophilic block of the PGC diblock copolymer. With aging, the patchy nanoparticles underwent unidirectional attachment through hydrophobic association to transform into uniform fibril structures. Transmission electron microscopy, interpretation of the small-angle neutron scattering measurements fit with analytical models, and genetic algorithm-based reverse engineering of structure confirmed the presence of initial particle precursors, intermediate stages during growth, and the fully matured fibrils. The results suggest that unconventional backbone chemistry-based molecules reveal unique effects of chain stiffness and hydrophobicity on block copolymer solution assembly when using glucose-based polycarbonates.

Effects of chain stiffness and shear flow on nanoparticle dispersion and distribution in ring polymer melts

The dispersion behavior and spatial distribution of nanoparticles (NPs) in ring polymer melts are explored by using molecular dynamics (MD) simulations. As polymer-NP interactions increase, three general categories of polymer-mediated NP organization are observed, namely, contact aggregation, bridging, and steric dispersion, consistent with the results of equivalent linear ones in previous studies. In the case of direct contact aggregation among NPs, the explicit aggregation-dispersion transition of NPs in ring polymer melts can be induced by increasing the chain stiffness or applying a steady shear flow. Results further indicate that NPs can achieve an optimal dispersed state with the appropriate chain stiffness and shear flow. Moreover, shear flow cannot only improve the dispersion of NPs in ring polymer melts but also control the spatial distribution of NPs into a well-ordered structure. This improvement becomes more evident under stronger polymer-NP interactions. The observed induced-dispersion or ordered distribution of NPs may provide efficient access to the design and manufacture of high-performance polymer nanocomposites (PNCs).

Simulation of the Critical Adsorption of Semi-Flexible Polymers**Supported by the National Natural Science Foundation of China under Grant Nos 11674277, 11704210 and 21574117.

The critical adsorption of semi-flexible polymer chains on attractive surfaces is studied using Monte Carlo simulations. The results reveal that the critical adsorption point of a free polymer chain is the same as that of an end-grafted one. For the end-grafted polymer, we find that the finite-size scaling relation and the maximum fluctuation of adsorbed monomers are equivalent in estimating the critical adsorption point. The effect of chain stiffness on the critical adsorption is also investigated. The surface attraction strength for the critical adsorption of semi-flexible polymer chain decreases exponentially with an increase in the chain stiffness; In other words, lower adsorption energy is needed to adsorb a stiffer polymer chain. The result is explained from the viewpoint of the free energy profile for the adsorption.

Effect of chain stiffness on the entropic segregation of chain ends to the surface of a polymer melt.

Entropic segregation of chain ends to the surface of a monodisperse polymer melt and its effect on surface tension are examined using self-consistent field theory (SCFT). In order to assess the dependence on chain stiffness, the SCFT is solved for worm-like chains. Our focus is still on relatively flexible polymers, where the persistence length of the polymer, ℓ p , is comparable to the width of the surface profile, ξ, but still much smaller than the total contour length of the polymer, ℓ c . Even this small degree of rigidity causes a substantial increase in the level of segregation, relative to that of totally flexible Gaussian chains. Nevertheless, the long-range depletion that balances the surface excess still exhibits the same universal shape derived for Gaussian chains. Furthermore, the excess continues to reduce the surface tension by one unit of k B T per chain end, which results in the usual N -1 reduction in surface tension observed by experiments. This enhanced segregation will also extend to polydisperse melts, causing the molecular-weight distribution at the surface to shift towards smaller N n relative to the bulk. This provides a partial explanation for recent quantitative differences between experiments and SCFT calculations for flexible polymers.

Influence of polymer flexibility on nanoparticle dynamics in semidilute solutions.

The hierarchical structure and dynamics of polymer solutions control the transport of nanoparticles (NPs) through them. Here, we perform multi-particle collision dynamics simulations of solutions of semiflexible polymer chains with tunable persistence length lp to investigate the effect of chain stiffness on NP transport. The NPs exhibit two distinct dynamical regimes - subdiffusion on short time scales and diffusion on long time scales. The long-time NP diffusivities are compared with predictions from the Stokes-Einstein relation (SER), mode-coupling theory (MCT), and a recent polymer coupling theory (PCT). Increasing deviations from the SER as the polymer chains become more rigid (i.e. as lp increases) indicate that the NP motions become decoupled from the bulk viscosity of the polymer solution. Likewise, polymer stiffness leads to deviations from PCT, which was developed for fully flexible chains. Independent of lp, however, the long-time diffusion behavior is well-described by MCT, particularly at high polymer concentration. We also observed that the short-time subdiffusive dynamics are strongly dependent on polymer flexibility. As lp is increased, the NP dynamics become more subdiffusive and decouple from the dynamics of the polymer chain center-of-mass. We posit that these effects are due to differences in the segmental mobility of the semiflexible chains.

The effect of chain stiffness and salt on the elastic response of a polyelectrolyte.

We present simulations of the force-extension curves of strong polyelectrolytes with varying intrinsic stiffness as well as specifically treating hyaluronic acid, a polyelectrolyte of intermediate stiffness. Whereas fully flexible polyelectrolytes show a high-force regime where extension increases nearly logarithmically with force, we find that the addition of even a small amount of stiffness alters the short-range structure and removes this logarithmic elastic regime. This further confirms that the logarithmic regime is a consequence of the short-ranged "wrinkles" in the flexible chain. As the stiffness increases, the force-extension curves tend toward and reach the wormlike chain behavior. Using the screened Coulomb potential and a simple bead-spring model, the simulations are able to reproduce the hyaluronic acid experimental force-extension curves for salt concentrations ranging from 1 to 500 mM. Furthermore, the simulation data can be scaled to a universal curve like the experimental data. The scaling analysis is consistent with the interpretation that, in the low-salt limit, the hyaluronic acid chain stiffness scales with salt with an exponent of -0.7, rather than either of the two main theoretical predictions of -0.5 and -1. Furthermore, given the conditions of the simulation, we conclude that this exponent value is not due to counterion condensation effects, as had previously been suggested.

Interfacial and dielectric behavior of polymer nano-composites: Effects of chain stiffness and cohesive energy density

This work discusses dynamics and polarizability of polymer chains in the interfacial layer around nano-particles based on characteristics of the chains: stiffness (C∞) and cohesive energy density (CED). Three polymers differing pairwise in C∞ and CED were selected, and effects of low concentration of nano-titania on glass transition temperature (Tg), thickness of interfacial layers, and dielectric behavior of polymers were investigated. As a result of interfacial loose layers formed around nano-titania, polymethylmethacrylate with high C∞ and CED gained more segmental mobility, resulting in lower Tg, and higher dielectric permittivity than the neat polymer. Similar changes with less magnitude were observed for polystyrene having similar C∞ but less CED. However, due to immobilized dense layers around nano-titania, ethylene propylene rubber with low C∞ and CED lost its segmental mobility, but both Tg and permittivity of nano-composite increased. Broadband dielectric analysis showed that an optimum segmental mobility in the interfacial layer is needed for enhanced chain polarization and dielectric permittivity.

Brownian Dynamics Simulations of Rigid Polyelectrolyte Chains Grafting to Spherical Colloid

Brownian dynamics simulations are employed to explore the effects of chain stiffness and trivalent salt concentration on the conformational behavior of spherical polyelectrolyte brush. The rigid brush adopts bundle-like morphology at a wide range of trivalent salt concentration. The number variation of bundles pinned on the colloid surface shows a non-monotonic profile as a function of the chain stiffness. The radial distributions of monomers and ions and the charge ratio between condensed ions and monomers are calculated. The charge inversion is observed for the high salt concentration regardless of chain rigidity. Furthermore, the pair correlation functions of monomer-monomer and monomer-salt cation are used to elucidate the aggregated mechanism of the bundle-like structure.

Monte Carlo simulation on the dynamics of a semi-flexible polymer in the presence of nanoparticles.

The dynamics of a semi-flexible polymer chain in the presence of periodically distributed nanoparticles is simulated by using off-lattice Monte Carlo simulations. For repulsive or weak attractive nanoparticles, the dynamics are slowed down monotonically by increasing the chain stiffness kθ or decreasing the inter-particle distance d. For strong attractive nanoparticles, however, the dynamics show nonmonotonic behaviors with kθ and d. An interesting result is that a stiff polymer may move faster than a flexible one. The underlying mechanism is that the nanoparticle's attraction is weakened by the chain stiffness. The nonmonotonic behavior of the polymer's dynamics with kθ is explained by the competition between the weakening effect of the chain stiffness on the nanoparticle's attraction and the intrinsic effect of chain stiffness which reduces the dynamics of the polymer. In addition, the nonmonotonic behavior of the polymer's dynamics with d is explained by the competition between the nanoparticle-exchange motion of the polymer dominated at small d and the desorption-and-adsorption motion at large d. The excluded volume effect of the nanoparticles plays a more important role for stiffer polymers as the attraction of the nanoparticles is weakened by the chain stiffness.

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

Polymeric single-chain nanoparticles (SCNPs) are soft nano-objects synthesized by purely intramolecular cross-linking of single polymer chains. By means of computer simulations, we investigate the conformational properties of SCNPs as a function of the bending stiffness of their linear polymer precursors. We investigate a broad range of characteristic ratios from the fully flexible case to those typical of bulky synthetic polymers. Increasing stiffness hinders bonding of groups separated by short contour distances and increases looping over longer distances, leading to more compact nanoparticles with a structure of highly interconnected loops. This feature is reflected in a crossover in the scaling behaviour of several structural observables. The scaling exponents change from those characteristic for Gaussian chains or rings in θ-solvents in the fully flexible limit, to values resembling fractal or ‘crumpled’ globular behaviour for very stiff SCNPs. We characterize domains in the SCNPs. These are weakly deformable regions that can be seen as disordered analogues of domains in disordered proteins. Increasing stiffness leads to bigger and less deformable domains. Surprisingly, the scaling behaviour of the domains is in all cases similar to that of Gaussian chains or rings, irrespective of the stiffness and degree of cross-linking. It is the spatial arrangement of the domains which determines the global structure of the SCNP (sparse Gaussian-like object or crumpled globule). Since intramolecular stiffness can be varied through the specific chemistry of the precursor or by introducing bulky side groups in its backbone, our results propose a new strategy to tune the global structure of SCNPs.

Effect of chain stiffness for semiflexible macromolecules in array of cylindrical nanoposts.

Equilibrium conformation of a semiflexible macromolecule in an array of nanoposts exhibits a non-monotonic behavior both at variation of the chain stiffness and increased crowding imposed by nanoposts. This is a result of the competition between the axial chain extension in channel-like interstitial volumes between nanoposts and the chain partitioning among these volumes. The approximation of a nanopost array as a combination of a quasi-channel and a quasi-slit like geometry semi-qualitatively explains the behavior of a chain in the array. In this approximation, the interstitial spaces are viewed as being of the channel geometry, while the passages between two adjacent posts are viewed as being of the slit geometry. Interestingly, the stiffer chains tend to penetrate more readily through the passage apertures, in the direction perpendicular to the post axes, and thus to occupy more interstitial volumes. This is consistent with the prediction of the free-energy penalty that is lower for a stiffer chain at strong slit-like confinement. These findings can find applications in the control of macromolecular conformations in recent nanotechnological techniques with bio-macromolecules such as a DNA.

Droplet Transport in a Nanochannel Coated by Hydrophobic Semiflexible Polymer Brushes: The Effect of Chain Stiffness.

We study the influence of chain stiffness on droplet flow in a nanochannel, coated with semiflexible hydrophobic polymers by means of nonequilibrium molecular dynamics simulations. The studied system is then a moving droplet in the slit channel, coexisting with its vapor and subjected to periodic boundary conditions in the flow direction. The polymer chains, grafted by the terminal bead to the confining walls, are described by a coarse-grained model that accounts for chain connectivity, excluded volume interactions and local chain stiffness. The rheological, frictional and dynamical properties of the brush are explored over a wide range of persistence lengths. We find a rich behavior of polymer conformations and concomitant changes in the friction properties over the wide range of studied polymer stiffnesses. A rapid decrease in the droplet velocity was observed as the rigidity of the chains is increased for polymers whose persistence length is smaller than their contour length. We find a strong relation between the internal dynamics of the brush and the droplet transport properties, which could be used to tailor flow properties by surface functionalization. The monomers of the brush layer, under the droplet, present a collective "treadmill belt" like dynamics which can only be present due the existence of grafted chains. We describe its changes in spatial extension upon variations of polymer stiffness, with bidimensional velocity and density profiles. The deformation of the polymer brushes due to the presence of the droplet is analyzed in detail. Lastly, the droplet-gas interaction is studied by varying the liquid to gas ratio, observing a 16% speed increase for droplets that flow close to each other, compared to a train of droplets that present a large gap between consecutive droplets.

Physical deposition behavior of stiff amphiphilic polyelectrolytes in an external electric field

Coarse-grained molecular dynamics simulations are conducted to study the physical deposition behavior of stiff amphiphilic polyelectrolytes (APEs) in an external electric field. The effects of chain stiffness, the charge distribution of a hydrophilic block, and electric field strength are investigated. Amphiphilic multilayers, which consist of a monolayer of adsorbed hydrophilic monomers (HLMs), a hydrophobic layer, and another hydrophilic layer, are formed in a selective solvent. All cases exhibit locally ordered hydrophilic monolayers. Two kinds of hydrophobic micelles are distinguished based on local structures. Stripe and network hydrophobic patterns are formed in individual cases. Increasing the chain stiffness decreases the thickness of the deposited layer, the lateral size of the hydrophobic micelles, and the amount of deposition. Increasing the number of positively charged HLMs in a single chain has the same effect as increasing chain stiffness. Moreover, when applied normally to the substrate, the electric field compresses the deposited structures and increases the amount of deposition by pulling more PEs toward the substrate. A stronger electric field also facilitates the formation of a thinner and more ordered hydrophilic adsorption layer. These estimates help us explore how to tailor patterned nano-surfaces, nano-interfaces, or amphiphilic nanostructures by physically depositing semi-flexible APEs which is of crucial importance in physical sciences, life sciences and nanotechnology.

Influence of Chain Stiffness, Grafting Density and Normal Load on the Tribological and Structural Behavior of Polymer Brushes: A Nonequilibrium-Molecular-Dynamics Study.

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equilibrium behavior of the model brushes, we first study the shearing behavior of flexible chains at different grafting densities covering brush and mushroom regimes. Next, we focus on the effect of chain stiffness on the tribological behavior of polymer brushes. The tribological properties are interpreted by means of the simultaneously recorded density profiles. We find that the friction coefficient decreases with increasing persistence length, both in velocity and separation-dependency studies, over the stiffness range explored in this work.