Folding transition of a single semiflexible polyelectrolyte chain through toroidal bundling of loop structures

We consider how the DNA coil-globule transition progresses via the formation of a toroidal ring structure. We formulate a theoretical model of this transition as a phenomenon in which an unstable single loop generated as a result of thermal fluctuation is stabilized through association with other loops along a polyelectrolyte chain. An essential property of the chain under consideration is that it follows a wormlike chain model. A toroidal bundle of loop structures is characterized by a radius and a winding number. The statistical properties of such a chain are discussed in terms of the free energy as a function of the fraction of unfolded segments. We also present an actual experimental observation of the coil-globule transition of single giant DNA molecules, T4 DNA (165.5 kbp), with spermidine (3+), where intrachain phase segregation appears at a NaCl concentration of more than 10 mM. Both the theory and experiments lead to two important points. First, the transition from a partially folded state to a completely folded state has the characteristics of a continuous transition, while the transition from an unfolded state to a folded state has the characteristics of a first-order phase transition. Second, the appearance of a partially folded structure requires a folded structure to be less densely packed than in the fully folded compact state.     

Formation and Reversible Morphological Transition of Bicontinuous Nanospheres and Toroidal Micelles by the Self‐Assembly of a Crystalline‐b‐Coil Diblock Copolymer

We herein report the formation of two complex nanostructures, toroidal micelles and bicontinuous nanospheres, by the self‐assembly of the single structurally simple crystalline‐b‐coil diblock copolymer poly[bis(trifluoroethoxy)phosphazene]‐b‐poly(styrene), PTFEP‐b‐PS, in one solvent (THF) and without additives. The nature of these nanostructures in solution was confirmed by DLS and cryo‐TEM experiments. The two morphologies are related by means of a new type of reversible morphological evolution, bicontinuous‐to‐toroidal, triggered by changes in the polymer concentration. WAXS experiments showed that the degree of crystallinity of the PTFEP chains located at the core of the toroids was higher than that in the bicontinuous nanospheres, thus indicating that the final morphology of the aggregates is mostly determined by the ordering of the PTFEP core‐forming blocks.     

From toroidal to rod‐like nanostructure,a mechanism study for the reversible morphological control on amphiphilic triblock copolymer micelles

Mechanism of the morphological changes between toroidal and rod‐like nanostructures of P4VP‐b‐PS‐b‐P4VP amphiphilic triblock copolymer micelles has been investigated in aqueous solution. This transition is proved to be highly reversible and tunable upon changing temperature. The toroidal structure, evolving from fibers at 20 °C, can transform to rod‐like morphology as the temperature either gradually or directly increases to 80 °C, and vice versa. However, the transition mechanisms are quite different in different temperature‐changing processes. The structure and thickness of the micelles are dependent on the specific temperature, whereas the transition mechanism is related to the method of the temperature change. These morphological changes are considered as a result from the interaction parameter between the solvent and the copolymer blocks, especially the hydrophobic block. Our research complements the external control over the reversible morphological transition of block copolymer micelles without changing the composition of the system or introducing additional influencing factors. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1450–1457     

Low-energy states of a semiflexible polymer chain with attraction and the whip-toroid transitions

We establish a general model for the whip-toroid transitions of a semiflexible homopolymer chain using the path integral method and the O3 nonlinear sigma model on a line segment with the local inextensibility constraint. We exactly solve the energy levels of classical solutions and show that some of its classical configurations exhibit toroidal forms, and the system has phase transitions from a whip to toroidal states with a conformation parameter c = (W2l)(L2pi)2. We also discuss the stability of the toroid states and propose the low-energy effective Green's function. Finally, with the finite size effect on the toroid states, predicted toroidal properties are successfully compared to experimental results of DNA condensation.     

Persistence lengths and structure factors of wormlike polymers under confinement

The behavior of semiflexible chains modeling wormlike polymers such as DNA and actin in confined spaces was explored by coarse-grained Monte Carlo simulations. The persistence length P, mean end-to-end distance R2, mean radius of gyration Rg2, and the size ratio R2/Rg2 were computed for chains in slits, cylinders, and spheres. It was found that the intrinsic persistence length of a free chain undergoes on confinement substantial alteration into the apparent persistence length. The qualitative differences were found in trends of the apparent persistence lengths between slits and cylinders on one side and spheres on the other side. The quantities P, R2, Rg2, and R2/Rg2 display similar dependences upon squeezing the chains in nanopores. The above quantities change nonmonotonically with confinement in slits and cylinders, whereas they drop smoothly with decreasing radius of a sphere. For elongation of a chain in a cylinder, two regimes corresponding to strong and moderate confinements were found and compared to experiments and predictions of the blob and Odijk theories. In a spherical cavity, the toroidal chain structure with a hole in the center was detected under strong confinements. The scattering form factor S(q) computed for semiflexible confined chains revealed three regimes of behavior in a slit and a cylinder that matched up well with the scaling theory. The complex form of the function S(q) computed for a sphere was interpreted as a sign of the toroidal structure. A reasonable agreement was found between the simulations and measurements of DNA and actin filaments, confined in nano- and microfluidic channels and spherical droplets, pertaining to the changes of the persistence lengths, chain elongation, and toroidal structure formation.     

Association-dissociation equilibrium of loop structures in single-chain folding into a toroidal condensate

Recently, it has been revealed that a semiflexible polyelectrolyte chain can form a partially folded conformation stably as a result of an electrostatic interaction. Interestingly, there are cases where the appearance of this structure requires a high-salt condition of a solution. In order to solve this problem, we consider the double equilibrium of the formation of loops and their aggregation on a single-chain polymer. First, an aggregate with a typical surface energy is examined as a test case. The basic nature of the folding transition is discussed with regard to the chemical potential of loop structures. Next, we consider a charged aggregate for which the interior is completely neutralized by counter ions. In this model, a partially folded chain appears with a high-salt condition. Based on this model, screened interactions between surface charges and a toroidal shape of a folded structure are considered essential factors bihind this phenomenon.     

Influence of surface interactions on folding and forced unbinding of semiflexible chains

We have investigated the folding and forced unbinding transitions of adsorbed semiflexible polymer chains using theory and simulations. These processes describe, at an elementary level, a number of biologically relevant phenomena that include adhesive interactions between proteins and tethering of receptors to cell walls. The binding interface is modeled as a solid surface, and the wormlike chain (WLC) is used for the semiflexible chain (SC). Using Langevin simulations, in the overdamped limit we examine the ordering kinetics of racquet-like and toroidal structures in the presence of an attractive interaction between the surface and the polymer chain. For a range of interactions, temperature, and the persistence length, l(p), we obtained the monomer density distribution, n(x), (x is the perpendicular distance of a tagged chain end from the surface) for all of the relevant morphologies. There is a single peak in n(x) inside the range of attractive forces, b, for chains in the extended conformations, whereas in racquet and toroidal structures there is an additional peak at x approximately b. The simulated results for n(x) are in good agreement with theory. The formation of toroids on the surface appears to be a first-order transition as evidenced by the bimodal distribution in n(x). The theoretical result underestimates the simulated n(x) for x < b and follows n(x) closely for x >/= b; the calculated density agrees exactly with n(x) in the range x < b. The chain-surface interaction is probed by subjecting the surface structures to a pulling force, f. The average extension, x( f), as a function of f exhibits a sigmoidal profile with sharp all-or-none transition at the unfolding force threshold f = f(c) which increases for more structured states. Simulated x(f) compare well with the theoretical predictions. The critical force, f(c), is a function of l(s)/l(c) for a fixed temperature, where l(c) and l(s) are the length scales that express the strength of the intramolecular and SC-surface attraction, respectively. For a fixed l(s), f(c) increases as l(p) decreases.     

Carbon nanotori and nanotubes encapsulating carbon atomic-chains

In this paper we investigate toroidal carbon nanotubes (carbon nanotori) encapsulating a single symmetrically located carbon atomic-chain. The interaction energy of the carbon chain is found from the Lennard-Jones potential using the continuous approach which assumes that atoms are uniformly distributed over the surface of the torus and the line of the circular chain with constant atomic surface and line densities, respectively. We assume that the chain is centrally located and that the carbon nanotorus is synthesized from a perfect carbon nanotube. We predict that the carbon chain can be encapsulated inside the carbon nanotorus when the cross-sectional radius \(r\) of the nanotorus is larger than 3.17 Å. At the minimum energy, a value of the toroidal radius \(R\) lies between 3.6 and 3.7 Å corresponding to each value of \(r\) . We also investigate the energy of carbon chains inside carbon nanotubes, which are (4,4), (5,5) and (10,0) tubes. We find that they are energetically favourable in (5,5) and (10,0) tubes, but not in a (4,4) tube, because it is geometrically too small, and these results are in agreement with existing studies. The same results for these three carbon nanotubes can also be obtained from the corresponding nanotori when \(R\) goes to infinity.     

Structures of stiff macromolecules of finite chain length near the coil‐globule transition: A Monte Carlo simulation

Using a coarse‐grained model of a semiflexible macromolecule, the equilibrium shapes of the chain have been studied varying both the temperature and the chain stiffness. We have applied Monte Carlo techniques using the bond fluctuation model for a chain length of N = 80 effective monomers, and two different types of interactions: a potential depending on the angle between successive bonds along the chain to control the chain stiffness, and an attractive interaction between non‐bonded effective monomers to model variable solvent quality. In a diagram of states where chain stiffness and inverse temperature are used as variables, we find regions where the chain exists as coil, as spherical globule, and as toroidal globule, respectively. Some of these regions are not limited by sharply defined boundaries, but rather wide two‐state coexistence regions occur in between them, where also intermediate metastable structures (such as rods and disks) occur. Recording histograms of energy, orientational order parameters, etc., which exhibit a two‐peak structure in the two‐state coexistence regions, we perform a subensemble analysis of the individual structures corresponding to these peaks.     

Single chain distribution analysis near a substrate using a combined method of three-dimensional imaging and SCF simulation

The effect of preferential wetting of one of the constituent block chains and corresponding block copolymer morphologies to a carbon substrate is studied from a molecular level. The single chain distribution of the block copolymer was estimated as a function of the distance from the substrate by a combined method of transmission electron microtomography (TEMT) and self-consistent field (SCF) simulation. The former provides three-dimensional (3D) morphological information of cylindrical microdomains near the surface, while the latter utilizes the 3D morphology to quantitatively determine the interaction between the block chains and substrate, which is further used to estimate the single chain distribution of one of the block chains, i.e., the subchain, of the matrix. It was found that the subchains in the vicinity of the wetting layer are substantially compressed, while the radius of gyration of the subchain at a distance L (L is the interlayer distance of the cylindrical microdomains from the substrate) has already reached the same value as that in the bulk, indicating that the propagation of the surface interaction is limited to one layer. The methodology developed in this study can be used not only to estimate the surface effect on polymer chains for a variety of different surfaces, but also to provide a means to understand complicated block copolymer morphologies from a molecular level.     

Blends of alkylated comb-like polyacrylates with copolymers with a controlled ethylene-vinyl acetate composition

The thermodynamic and morphological behaviors of poly(octadecyl acrylate) (PODA) with flexible ethylene-co-vinyl acetate copolymer (EVA) with a controlled amount of vinyl acetate units in the copolymer were investigated over the entire composition region by thermal analysis, Fourier transform infrared (FTIR) spectroscopy, x-ray diffraction, optical microscopy, and light scattering. Thermal analysis revealed that the EVA portion interferes with the side chain crystallization of PODA, as the number of crystallized methylene units in PODA was calculated from the heat of fusion of the paraffinic side chain crystals. The hexagonal packing of side chains was also confirmed by FTIR and x-ray diffraction. Optical microscope studies showed a homogeneous melt state beyond the melting temperature of EVA, but clearly showed two phases over the whole range of composition in EVA20, EVA40, and EVA50/PODA blends after the side chain crystallization of PODA. Light scattering showed the single circular halo as the evidence of phase separation when the samples were cooled to below the crystallization temperature. The changes in crystallization cannot be accounted for by the miscibility, because liquid-liquid phase separation competes with crystallization. © 1996 John Wiley & Sons, Inc.     

The first {Dy4} single-molecule magnet with a toroidal magnetic moment in the ground state

A toroidal magnetic moment in the absence of a conventional total magnetic moment was first observed in a novel tetranuclear dysprosium cluster with nonmagnetic ground state. The toroidal state is quite robust with respect to variations of the exchange parameters.     

Effect of chain defects on the morphology and thermal behavior of solution-grown single crystals of syndiotactic polypropylene

The morphology of solution-grown single crystals of syndiotactic polypropylene with different degree of stereoregularity is compared. A sector formation phenomenon, found in some monolayer single crystals, is discussed in terms of possible crystallographic fold planes, growth planes, and gemination planes. A correlation between thermodynamic and morphological properties such as apparent enthalpy of fusion, critical long spacing, critical annealing temperature, and the number of configurational chain defects along the macromolecule has been found. Two endothermic peaks are observed in the DSC thermograms of single-crystal aggregates of syndiotactic polypropylene. The low-temperature peak is attributed to melting of crystals or parts of crystals with incorporated chain defects. The high-temperature peak corresponds to the melting endotherm of more regular crystalline zones. The peak-area ratio seems to depend on the degree of stereoregularity.     

Self‐Consistent Integral Equation Theory for Semiflexible Polyelectrolytes in Poor Solvent

Self‐consistent hybrid MC/PRISM method is presented for calculating properties of polyelectrolytes in semidilute and more concentrated regimes in a poor solvent. The static structure and conformational behavior of salt‐free polyelectrolyte solutions composed of semiflexible polyions and monovalent counterions are studied using the approach which combines the traditional Monte‐Carlo (MC) simulation with the numerical solution of the polymer integral PRISM equation. The MC technique is applied to generate the configurations of a single chain molecule and obtain the averaged intrapolymer correlation function. The PRISM equation is then numerically solved for a given monomer density to obtain the various correlation functions and the medium‐induced intrapolymer potential. This is used in a single chain MC simulation, where the polymer sites interact via the bare Coulomb potential together with the short range attractive potential and a self‐consistently determined medium‐induced potential. The monomer‐monomer pair correlation functions and static structure factors are calculated for a large variety of parameters. Conformational properties such as the radius of gyration and visual images are obtained as a function of attractive short‐range interaction, monomer density, Bjerrum length, and chain stiffness. The MC/PRISM study predicts that there is a range of hydrophobicity and monomer density for which polyion chains can form the toroidal structure in a poor solvent. Nonmonotonic dependence of the chain size on monomer density is predicted over the entire range of parameters. Polyion structure factor peak position as a function of density is described. Two concentration regimes in which the polyion structure factors exhibit physically different peaks were found. Over the entire concentration regime considered polyelectrolyte chains undergo strong compression with R_g ∝ lequation/tex2gif-stack-1.gif.

Conformation of a polyion chain for l_B = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.     

Semiflexible grafted polymers in poor solvents: toroidal, archway, and tower micelles

We study a system of grafted semiflexible polymers in a poor solvent which form toroidal or rodlike conformations in the bulk. However, because of the physical constraint of surface grafting, macrophase separation is inhibited and a number of different polymer aggregates (or micelles) form which can be related to the chains' stiffness and their affinity for each other. In contrast to the fully flexible Gaussian case, we observe a number of novel micelle structures, including tower micelles, archway micelles, and spider micelles. We also attempt to develop a phase diagram for the occurrence of these structures with respect to the variables of chain length, chain stiffness, and polymer grafting density.     

Simulation of Chain Organization in Encapsulated Polymers

Summary : The dimensional and structural properties of polymers confined into a cavity are computed by the Monte Carlo method as a function of the chain stiffness. The reduction of the size ratio <R² > / < R> close to 2, distinctive of compact spheres, is observed at squeezing of chains into a capsule. The plots of the static structure factor S(q) computed for stiff chains show characteristic humps attributed to the toroidal structure. The orientation correlation function is found to be a very sensitive indicator of the globule – toroid transition in encapsulated chains. Evidence is presented that the toroidal morphology is formed in stiff polymers when the capsule radius approaches the chain persistence length (D ∼ P).     

单分子磁环最新进展及研究展望

与单分子磁体的定义(SMMs)相类似,单分子磁环(SMTs)定义为具有环形磁双稳态的一类分子。该类配合物的特征在于弱耦合磁矩的"涡旋"空间分布导致总磁矩为零,但是分子仍具有环形磁矩。单分子磁环为量子计算和信息存储提供了广阔的应用前景,也可以作为具有磁电耦合效应的多铁材料。自从在[Dy3]分子中首次观察到典型的单分子磁环行为以来,研究人员在合成单分子磁环方面做出了巨大的努力,致力于合成具有环形磁矩的分子以及设法将环形磁矩增强。本文将对近年报道的新兴单分子磁环配合物进行详细地分析讨论,旨在阐明影响环形磁矩排列的因素以及单分子磁环配合物的综合设计策略,指导探索合成具有增强环形磁矩的单分子磁环配合物。     

Extended‐chain crystals in high‐pressure crystallized poly(ethylene terephthalate)/bisphenol a polycarbonate blends

Morphologies of extended‐chain crystals with different characteristics were observed with scanning electron microscopy (SEM) in the high‐pressure crystallized polyethylene terephthalate/polycarbonate (PET/PC) blends. The crystals memorize their nucleation and growth process, which reveal an involvement of different mechanisms simultaneously. The presence of sliding diffusion during crystal thickening is indicated by a wedge shape of some crystals, while bent crystals suggest the occurrence of transesterification in the formation of the large extended‐chain crystals. The observation of two morphological features on one group of crystals shows that two mechanisms may work simultaneously. The connection between folded‐chain and extended‐chain crystals is demonstrated by the S‐shaped extended‐chain crystals as well as their direct morphological connection observed with SEM. Though transesterification plays the essential role in the formation of the large crystals, which acts in different aspects during the process, the thermodynamic driving force is the enthalpy gain associated with large crystals. This is a high‐pressure self‐assembly with a coupling between crystallization and transesterification, which may be instructive to grow such large crystals in similar polymer systems. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3148–3156, 2006     

Bipolar to toroidal configuration transition in liquid crystal droplets

Liquid crystal (LC) droplets dispersed in isotropic media are of significant interest for scientific community and great importance for industries. The confinement can generate many fascinating LC director configurations and enable important practical applications. With tangential anchoring condition at the droplet surface, theoretically there are several possible configurations: bipolar, twisted bipolar, escaped toroidal, toroidal and so on. Bipolar configuration is usually observed in droplets made from common LCs while the toroidal configuration is rarely observed and it is hard to create especially in thermotropic LCs. Their realisations depend on the splay, bend and twist elastic constants ratio, and anchoring condition of the LC and polymer interface. We constructed thermotropic LCs with abnormally small bend elastic constants, with which stable toroidal configuration were successfully created. We provide a brand new method to create toroidal droplet by simply varying the bend elastic constant. We observed the transition from bipolar configuration to toroidal configuration. We performed a detailed study of the texture of toroidal droplets.     

Gel permeation chromatographic studies of the degradation of polyethylene with fuming nitric acid. II. Bulk polyethylene

Preliminary results are reported on the use of gel permeation chromatography in morphological studies of bulk polymers and fibres. Several samples of bulk isotropic and drawn polyethylene were analyzed by gel permeation chromatography following nitric acid oxidation. In all cases suitable samples showed two peaks in the molecular weight distribution, suggesting a qualitative similarity with results for single crystals. It is concluded that the present data are consistent with chain folding in bulk polymers, both in the isotropic and oriented states, with a less degree of regularity than exists in single crystals.