Phantom Chains Research Articles

PHANTOM CHAINS TONTOR OF BIONIC OBJECT'S MOVEMENTS OF AUTOMATED SYSTEMS. Part 1

This presented work results provides an understanding of how phantom life cycle diagrams of abstract objects can be formed based on the conditions of their existence. Thus, an essential feature of the action of these objects is their possibility of application in automated systems, which is an important aspect of the development of technical bionic means and systems. The problem of using a phantom for modeling actions, movements of objects in space, features of the obtained results is quite widely used in various fields of scientific research. However, there remain tasks related to understanding how the main actions of robotic working bodies of automated systems take place. Thus, it becomes possible to create formalized models of the processes of performing actions of experimental objects in medicine, industry, astronomy, based on phantom constituents of chain and step geometric elements. Thus, it is possible to present similar bionic objects in medical automated systems, which refers to the design of bionic prostheses, exoskeleton systems, as well as systems for scientific research of biomechanical properties of objects. At the same time, we analyze the peculiarities of motor movements, for which we create and analyze phantom models of TONTOR steps and their combination into phantom chains. Prospects for further research, which will be presented in the next part of this work, are the creation of analytical models of phantom features of the existence of various bionic technical means in view of their connection between the volume of the abstract object and the phantom. Similar analytical approaches make it possible to determine the phantom matrix model of the life cycle of a bionic abstract object in automated systems.

Excluded volume effects on tangentially driven active ring polymers.

The conformational and dynamical properties of active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain, driven by tangential forces, put in contact with a heat bath described by the Brownian multiparticle collision dynamics. Both phantom polymers and chains comprising excluded volume interactions are considered for different bending rigidities. The size and shape are found to be dependent on persistence length, driving force, and bead mutual exclusion. The lack of excluded volume interactions is responsible for a shrinkage of active rings when increasing driving force in the flexible limit, while the presence induces a moderate swelling of chains. The internal dynamics of flexible phantom active rings shows activity-enhanced diffusive behavior at large activity values while, in the case of self-avoiding active chains, it is characterized by active ballistic motion not depending on stiffness. The long-time dynamics of active rings is marked by rotational motion whose period scales as the inverse of the applied tangential force, irrespective of persistence length and beads' self-exclusion.

Phantom chain simulations for fracture of end-linking networks

Despite numerous studies, the relationship between network structure and fracture remains unclear. In this study, the fracture properties of end-linking networks were compared with those of loop-free analogs made from star prepolymers by performing phantom chain simulations. The networks were created from equilibrated sols of stoichiometric mixtures of linear prepolymers and f-functional linkers through end-linking reactions using Brownian dynamics schemes. The examined networks, with various f values (between 3 and 8) and strand-connection rates (φs), were evaluated in terms of the primary loop fraction and the cycle rank ξ. These structural characteristics were consistent with mean-field theories that assume independent reactions. Energy minimization and uniaxial stretch were applied to the networks until they broke without Brownian motion. The fracture characteristics, including strain at break (εb), stress at break (σb), and work for fracture (Wb), were obtained from stress-strain curves. The end-linking networks exhibited larger εb and smaller σb and Wb than those for star networks due to primary loops, at the same set of f and φs. However, εb, σb/νbr and Wb/νbr (with νbr being the branch point density) lie on the same master curves as those for star networks if they are plotted against ξ. This result implies that the fracture of end-linking networks is essentially the same as that for star analogs, and the effects of primary loops are embedded in ξ.

Phantom Chain Simulations for the Effect of Stoichiometry on the Fracture of Star-Polymer Networks

Phantom Chain Simulations for the Effect of Stoichiometry on the Fracture of Star-Polymer Networks

Phantom chain simulations for the fracture of star polymer networks with various strand densities.

Despite many attempts, the relationship between the fracture and structure of polymer networks is yet to be clarified. For this problem, a recent study on phantom chain simulations [Y. Masubuchi et al., Macromolecules, 2023, 56, 9359-9367.] has demonstrated that the fracture characteristics obtained for polymer networks with various node functionalities and conversion ratios lie on master curves if they are plotted against cycle rank, which is the number of closed loops in the network per network node. In this study, we extended the simulation to the effect of prepolymer concentration c on the relationships between the cycle rank and fracture characteristics within the concentration range of 1 ≲ c/c* ≲ 10, concerning the overlapping concentration c*. We created networks from sols of star-branched phantom bead-spring chains via an end-linking reaction between different chains through Brownian dynamics simulations upon varying the number of branching arms f from 1 to 8, and the conversion ratio φc from 0.6 to 0.95. For the resultant networks, the cycle rank ξ was consistent with the mean-field theory. The networks were uniaxially stretched with energy minimization until break to obtain modulus G, strain at break εb, stress at break σb, and work for fracture Wb. As reported earlier, εb data for various f and φc are located on a master curve if plotted against ξ. The other quantities also draw master curves as functions of ξ if normalized by the branch point density υbr. The master curves depend on c; as c increases, all the mechanical characteristics monotonically increase. If we plot σb/υbr and Wb/υbr against G/υbr, the data for various f and φc lie on master curves but depending on c. Consequently, the fracture characteristics are not solely described by the modulus.

Phantom chain simulations for fracture of polymer networks created from star polymer mixtures of different functionalities

Phantom chain simulations for fracture of polymer networks created from star polymer mixtures of different functionalities

Phantom Chain Simulations for the Fracture of Energy-Minimized Tetra- and Tri-Branched Networks

Effects of branch functionality on mechanical properties of polymer networks are yet to be fully elucidated, although multi-functional approaches have been mainly attempted. For instance, Fujiyabu et al. [Sci. Adv. 2022, 8, abk0010] recently reported that polymer networks made from tri-branch prepolymers exhibit superior mechanical properties to tetra-branch analogues. Although they attribute the difference to stretch-induced crystallization observed in tri-branch poly (ethylene glycol) networks, the mechanism still needs to be clarified. In this study, we performed coarse-grained molecular simulations to extract the effect of branch functionality. The prepolymers were replaced by bead-spring phantom chains, and gelation was simulated by a Brownian dynamics scheme. We subjected the resultant networks to energy minimization and uniaxial stretch by introducing breakage for elongated segments. In the stress–strain relation thus obtained, stress and strain at the break were larger for tri-branch networks than that for tetra-branch analogues, consistent with the experiment. The superiority of tri-branch networks is observed in a wide range of the conversion ratio in gelation, molecular weights of prepolymers, and polymer concentrations. The result implies that the mechanical superiority of tri-branch networks to tetra-branch ones is due to a fundamental structural difference generated during gelation.

Efficient generation of self-avoiding, semiflexible rotational isomeric chain ensembles in bulk, in confined geometries, and on surfaces

We provide an efficient ready-to-run code gensaw that generates single or large ensembles of self-avoiding, flexible, semiflexible, rotationally isometric or helical chains in the bulk or subject to arbitrary confinement and tethering conditions, where we allow for arbitrary intramolecular bending and dihedral energy functions. The resulting configuration files are provided in various common formats and can be immediately used to do molecular simulations or statistical analysis. We work out analytic expressions for the mean squared end-to-end distance and gyration radius of the semiflexible, helical and rotational isomeric state models with a finite number of bonds and arbitrary interaction potentials for direct comparison and testing of the code in the limiting case of unconfined phantom chains. In addition to the graphics-free linux standalone batch version gensaw that creates configuration and other files for high throughput applications from the command line, we provide an interactive online version gensaw-visualization that serves as platform-independent graphical user interface, and animates the resulting conformations using a remote gensaw server. Program summaryProgram title:gensawCPC Library link to program files:https://doi.org/10.17632/8xfgf88f3w.1Licensing provisions: MITProgramming languages: fortran 90, perl (standalone batch version) or java (interactive online version)Required software:ifort 16+ or gfortran 4+, perl 5+ (standalone batch version), jre 1.8.0+ (interactive online version)Nature of problem: Efficient creation of self-avoiding, semiflexible multibead walks/chains of variable contour length, subject to arbitrary confinement and tethering conditions, characterized by a conformational energy that is composed of arbitrary bending and torsion contributions. The code must produce an ensemble of such chains, using a flexible output format. For the limiting case of chains with zero thickness, the code should reproduce analytic results for the ideal chains.Solution method: We use an adapted enrichment procedure that optimizes its parameters on the fly and derive all analytic results for semiflexible chains with arbitrary bending and torsion potentials for comparison with the created ensembles. While gensaw creates configuration and optionally other files from the command line, gensaw-visualization serves as a platform-independent graphical user interface and allows to visualize and animate the conformations.

Role of Charge Regulation and Fluctuations in the Conformational and Mechanical Properties of Weak Flexible Polyelectrolytes.

This work addresses the role of charge regulation (CR) and the associated fluctuations in the conformational and mechanical properties of weak polyelectrolytes. Due to CR, changes in the pH-value modifies the average macromolecular charge and conformational equilibria. A second effect is that, for a given average charge per site, fluctuations can alter the intensity of the interactions by means of correlation between binding sites. We investigate both effects by means of Monte Carlo simulations at constant pH-value, so that the charge is a fluctuating quantity. Once the average charge per site is available, we turn off the fluctuations by assigning the same average charge to every site. A constant charge MC simulation is then performed. We make use of a model which accounts for the main fundamental aspects of a linear flexible polyelectrolyte that is, proton binding, angle internal rotation, bond stretching and bending. Steric excluded volume and differentiated treatment for short-range and long-range interactions are also included. This model can be regarded as a kind of “minimal” in the sense that it contains a minimum number of parameters but still preserving the atomistic detail. It is shown that, if fluctuations are activated, gauche state bond probabilities increase and the persistence length decreases, so that the polymer becomes more folded. Macromolecular stretching is also analyzed in presence of CR (the charge depends on the applied force) and without CR (the charge is fixed to the value at zero force). The analysis of the low force scaling behavior concludes that Pincus exponent becomes pH-dependent. Both, with and without CR, a transition from 1/2 at high pH-values (phantom chain) to 3/5 at low pH-values (Pincus regime) is observed. Finally, the intermediate force stretching regime is investigated. It is found that CR induces a moderate influence in the force-extension curves and persistence length (which in this force regime becomes force-dependent). It is thus concluded that the effect of CR on the stretching curves is mainly due to the changes in the average charge at zero force. It is also found that, for the cases studied, the effect of steric excluded volume is almost irrelevant compared to electrostatic interactions.

Counting Secondary Loops Is Required for Accurate Prediction of End-Linked Polymer Network Elasticity.

To predict and understand the properties of polymer networks, it is necessary to quantify network defects. Of the various possible network defects, loops are perhaps the most pervasive and yet difficult to directly measure. Network disassembly spectrometry (NDS) has previously enabled counting of the simplest loops-primary loops-but higher-order loops, e.g., secondary loops, have remained elusive. Here, we report that the introduction of a nondegradable tracer within the NDS framework enables the simultaneous measurement of primary and secondary loops in end-linked polymer networks for the first time. With this new "NDS2.0" method, the concentration dependences of the primary and secondary loop fractions are measured; the results agree well with a purely topological theory for network formation from phantom chains. In addition, semibatch monomer addition is shown to decrease both primary and secondary loops, though the latter to a much smaller extent. Finally, using the measured primary and secondary loop fractions, we were able to predict the shear storage modulus of end-linked polymer gels via real elastic network theory (RENT).

Complex Interactions with the Surroundings Dictate a Tagged Chain’s Dynamics in Unentangled Polymer Melts

For more than half a century the theoretical landscape for single chain dynamics for dense polymeric solutions and melts below the entanglement threshold has been dominated by the Rouse model for independent phantom chains, supported by ideas of hydrodynamic screening. There exists, however, a large body of literature from experiments, Monte Carlo, and molecular dynamics simulations on the deviations from the Rouse behavior for unentangled homopolymer melts, showcased mostly in the subdiffusive behavior of center-of-mass of tagged chains at intermediate times, with the subdiffusion exponent reported in the range 0.75–0.85. The influence of the surrounding chains of length Ns on the motion of a single tagged chain of length N is a key test, by which, through high-precision numerical simulation of unentangled melts, we show that the Rouse model fails. Our central results are that at intermediate times the tagged chain’s center-of-mass moves subdiffusively, ⟨Δr2cm⟩ ∝ tα with subdiffusion exponent α = 0.87 ± ...

The Ghost in the Machine: Is the Bacterial Chromosome a Phantom Chain?

In the classic picture of bacterial genome organization, the bacterial chromosome is considered to be a disordered polymer, like spaghetti confined in a bag. Progress in high-resolution microscopy radically advanced our understanding of chromosomal organization and completely toppled this classic picture. Many experiments in recent years have revealed intriguing order in chromosomal structure at different length- and timescales (1,2). The questions that arise from these observations include: What is the origin of multiscale order? And what does it mean?

Modelling tie chains and trapped entanglements in polyethylene

A Monte Carlo random walk model was developed to simulate the chain structure of amorphous layers in polyethylene. The chains emerging from the orthorhombic crystal lamellae were either folding back tightly (adjacent re-entry) or performing a random walk (obeying phantom chain statistics) forming statistical loops or tie chains. A correct amorphous density (ca. 85% of the crystalline density) was obtained by controlling the probability of tight folding. Important properties like fracture toughness depend on the number of chains covalently linking together the crystalline regions. The model structure was analysed with a novel numerical topology algorithm for calculating the concentration of tie chains and trapped entanglements. The numerical efficiency of the algorithm allowed molecular cubic systems with a side length of 100 nm to be readily analysed on a modern personal computer. Simulations showed that the concentration of trapped entanglements was larger than the concentration of tie chains and that the thickness of the amorphous layer (La) had a greater impact than the crystal thickness (Lc) on the tie-chain concentration. In several other commonly used models, such as the Huang–Brown model, the influence of trapped entanglements and the effect of the La/Lc ratio are neglected. Simulations using as input the morphology data from Patel generated results in agreement with experimental rubber modulus data.

Stochastic entangled chain dynamics of dense polymer solutions

We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.

Static properties of polymer melts in two dimensions

Self-avoiding polymers in strictly two-dimensional (d=2) melts are investigated by means of molecular dynamics simulation of a standard bead-spring model with chain lengths ranging up to N=2048. The chains adopt compact configurations of typical size R(N)∼Nν with ν=1/d. The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents Θ0=3/8, Θ1=1/2, and Θ2=3/4 predicted by Duplantier. Due to the segregation of the chains the ratio of end-to-end distance Re(N) and gyration radius Rg(N) becomes Re2(N)/Rg2(N)≈5.3<6 for N⪢100 and the chains are more spherical than Gaussian phantom chains. The second Legendre polynomial P2(s) of the bond vectors decays as P2(s)∼1/s1+νΘ2, thus measuring the return probability of the chain after s steps. The irregular chain contours are shown to be characterized by a perimeter length L(N)∼R(N)dp of fractal line dimension dp=d−Θ2=5/4. In agreement with the generalized Porod scattering of compact objects with fractal contour, the Kratky representation of the intramolecular structure factor F(q) reveals a strong nonmonotonous behavior with qdF(q)∼1/(qR(N))Θ2 in the intermediate regime of the wave vector q. This may allow to confirm the predicted contour fractality in a real experiment.

Fluctuation in entanglement positions via elastic slip-links

We consider the spatiotemporal fluctuation of slip-link positions via the implementation of elastic slip-links. The level of description is similar to our previously proposed slip-link model, wherein we use the entanglement position in space as dynamic variables, and the number of Kuhn steps between entanglements. However, since it is a mean-field, single-chain description it has some relevance to the slip-spring simulations of Likhtman, and the phantom chain model for cross-linked networks. It might also provide a connection between slip-links and tubes. Two implementations are possible, depending on whether or not the slip-links are allowed to pass through one another. If a boundary condition on the dynamics preventing such passage is imposed, then the plateau modulus is unchanged from perfectly rigid slip-links. Only the dynamics is changed. On the other hand, for phantom slip-links the distribution of the number of entanglements changes from Poisson. Furthermore, requiring normalization of the distribution function sets a constraint on how loose the virtual springs for the elastic slip-link are. These restrictions appear to be in agreement with parameter values used for the slip-spring simulations, although nonphantom slip-links were used there. The results are completely analogous to what was found by James and Guth for ideal elastic networks, whose derivation is repeated here. Our earlier rigid slip-link model is recovered as a limiting case.

Self-consistent field/density functional study of conformational properties of polymers at interfaces: Role of intramolecular interactions

We study the properties of athermal polymers at hard walls using two different versions of self-consistent field theory (SCFT). We calculate the segment density profiles, center of mass profiles, bond orientation vector profiles, and end-to-end vector distributions and compare with grand canonical Monte Carlo simulations. Using the same excess free energy prescription for both theories, we investigate the role of the excluded volume intramolecular interactions on these properties, show the relation between SCFT and density functional theory, and discuss several numerical implementations of the SCFT method. The phantom chain model gives Gaussian chain statistics independent of the conditions. Including the full intramolecular potential leads to an improved description of the low density regime but it does not produce any significant improvement in the semidiluted and concentrated regimes. We show that a viable compromise is achieved by using the effective field resulting from the phantom chain model and by calculating single chain properties using the full intramolecular potential.

Prediction of solution properties of flexible-chain polymers: a computer simulation undergraduate experiment

This paper describes a computational exercise at undergraduate level that demonstrates the employment of Monte Carlo simulation to study the conformational statistics of flexible polymer chains, and to predict solution properties. Three simple chain models, including excluded volume interactions, have been implemented in a public-domain computer program that is the tool on which this exercise is based. The first stage considers fundamental aspects of polymer chain statistics, such as the distribution of end-to-end distance and the exponents in the power laws that relate properties to chain length, for both ideal, phantom chains and also with excluded volume effects. The numerical results are employed to predict properties of real polymer/solvent systems, such as polystyrene in cyclohexane and toluene, which are then compared to experimental data.

Static Rouse modes and related quantities: Corrections to chain ideality in polymer melts

Following the Flory ideality hypothesis intrachain and interchain excluded-volume interactions are supposed to compensate each other in dense polymer systems. Multichain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume ("hard monomers") to no excluded volume ("phantom chains"). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.

Phantom Chain Simulations of Realistically Sized Polymer‐Based Nanocomposites

AbstractSummary: Phantom chain MC simulations have been performed for realistically sized systems of polymer chains filled with solid nanoparticles. The results of the simulations and simple theoretical considerations are used to rationalize a number of parameters relevant to the characterization of these systems. Even when the average number of nanoparticles in contact with a chain is very small (much less than unity), the nanoparticles are nodes of highly interconnected transient networks bridged by the polymer chains. magnified image