Effect of orientation in translocation of polymers through nanopores

The motion of polymers with inhomogeneous structure through nanopores is discussed theoretically. Specifically, we consider the translocation dynamics of polymers consisting of double-stranded and single-stranded blocks. Since only the single-stranded chain can go through the nanopore the double-stranded segment has to unzip before the translocation. Utilizing a simple analytical model, translocation times are calculated explicitly for different polymer orientations, i.e., when the single-stranded block enters the pore first and when the double-stranded segment is a leading one. The dependence of the translocation dynamics on external fields, energy of interaction in the double-stranded segment, size of the polymer, and the fraction of double-stranded monomers is analyzed. It is found that the order of entrance into the pore has a significant effect on the translocation dynamics. The theoretical results are discussed using free-energy landscape arguments.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Effect of charge distribution on the translocation of an inhomogeneously charged polymer through a nanopore

We investigate the voltage-driven translocation of an inhomogeneously charged polymer through a nanopore by utilizing discrete and continuous stochastic models. As a simplified illustration of the effect of charge distribution on translocation, we consider the translocation of a polymer with a single charged site in the presence and absence of interactions between the charge and the pore. We find that the position of the charge that minimizes the translocation time in the absence of pore-polymer interactions is determined by the entropic cost of translocation, with the optimum charge position being at the midpoint of the chain for a rodlike polymer and close to the leading chain end for an ideal chain. The presence of attractive and repulsive pore-charge interactions yields a shift in the optimum charge position toward the trailing end and the leading end of the chain, respectively. Moreover, our results show that strong attractive or repulsive interactions between the charge and the pore lengthen the translocation time relative to translocation through an inert pore. We generalize our results to accommodate the presence of multiple charged sites on the polymer. Our results provide insight into the effect of charge inhomogeneity on protein translocation through biological membranes.     

Synthesis of diblock copolymers containing both polydiene and polyalcohol blocks

A wide range of functional diblock copolymers containing both functional polymer and hydrocarbon polymer, have been prepared by the combination of anionic polymerization and borane chemistry. The distinctive hydroboration reactivity between various polydienes enables us to selectively functionalize one polydiene segment in diblock copolymers which contain two different polydiene segments. In turn, the hydroborated polymers are valuable intermediate compounds which can be converted to a whole family of functional polymers with a variety of other functionalities under mild reaction conditions. The hydroxylated diblock copolymer is used as an example to demonstrate the chemistry. The two-phase nature of these copolymers is also shown by the observation of two distinctive glass transition temperatures associated with the individual polymer segments.     

What's so special about polymers? A little known organizing principle gives rise to an abundance of polymer phase transitions

We argue that if an organizing principle exists it must have to do with the linear connectivity of the monomers since this feature is what distinguishes polymers from all other materials. We then compare a linear polymer threading a pore in a membrane (PTM) with an equal number of unconnected monomers which are also allowed to transit through a pore in a membrane. The crucial difference between the two cases is that the connected monomers are distinguishable from one another by virtue of their location along the polymer chain whereas the disconnected monomers are indistinguishable. Because of this, the disconnected monomers obey the ideal gas laws while the connected monomers undergo a first-order thermodynamic phase transition! Four other phase transitions occurring in isolated linear polymer molecules are known. They are the helix to random coil (HR) transitions in biological polymers, surface adsorption (SA), polymer collapse (C), and a model of polymerization (P). These five kinds of transitions can be coupled to one another resulting in a sizable number of exactly solvable minimal models of phase transitions. There are also five classes of phase transitions in many polymers systems. The coupling of these 10 classes of transitions to each-other results in a plethora of phases. These in turn provide the basis for the many polymer structures observed in the world about us. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2612–2620, 2006     

Relaxation properties of some segmented polyurethane-CaCO3 composites. A Dielectric study

Dielectric relaxation in three segmented polyurethane-CaCO₃ composites was investigated between ?70°C and +150°C in the 300 Hz to 100 kHz frequency range. Two of the polymers contained a polyacetal-polyether soft segment, whereas the soft component of the third polymer was polypropylene oxide. The hard segments consisted of 4,4′-diphenyl methane diisocyanate in two cases and toluene-2,4-diisocyanate in the third case. In parallel studies two calorimetric relaxations, designated α and α′, were observed for each sample and were determined to be glass transitions of the soft and hard segments, respectively. In general, the transition temperatures decrease with increasing filler content. High frequency, low temperature permittivities increase while low frequency, high temperature AC conductivities generally decrease with increasing filler content. The shift in the transition temperatures can be explained using the adsorption theory of filler-polymer interactions and the densities of the samples. The interfacial polarization mechanism becomes important only above the α′ transition temperature and below 1 kHz.     

Threading synthetic polyelectrolytes through protein pores

We have measured the ionic current signatures of sodium poly(styrene sulfonate) as its single molecules translocate through an alpha-hemolysin pore embedded into a bilayer in a salty aqueous medium under an externally applied electric field. As in the previous experiments involving DNA and RNA, the pore current, which is a measure of the ionic conductivity of the low molar mass electrolyte ions, is significantly reduced when the polymer molecule translocates through the pore. The magnitude and the duration of the reduction in the pore current are measured for each of the translocation events. By studying thousands of events of reduction in the ionic current, we have constructed distribution functions for the extent of the reduced current and for the translocation time. The details of these distribution functions are significantly different from those for DNA and RNA. By investigating over two orders of magnitude in the molecular weight of the polymer, the average translocation time is found to be proportional to the molecular weight and inversely proportional to the applied voltage. This demonstration of threading a synthetic polyelectrolyte through a protein pore opens up many opportunities to systematically explore the fundamental physical principles behind translocation of single macromolecules, by resorting to the wide variety of synthetically available polymers without the complexities arising from the sequences of biological polymers. In addition, the present experiments suggest yet another experimental protocol for separation of polymer molecules directly in aqueous media.     

毛细管内高分子溶液的浓度分布

采用连续自洽场理论分析了毛细管中发生凝胶化之前的聚合物溶液浓度分布的影响因素及其规律. 结果表明, 体系尺寸有限时, 改变聚合物链段、溶剂与壁面的相互作用参数之差, 聚合物溶液浓度分布会发生贫化/吸附转变; 临界作用参数与聚合物链长的倒数呈线性关系, 且拟合常数与体系尺寸、聚合物溶液平均体积分数有关; 聚合物分子量分布为多分散时, 分子量较低的组分更容易接近容器壁面, 分子量较大的组分则相反. 总之, 增加聚合物溶液浓度、链长, 选择优良溶剂, 减小体系尺寸等都会使浓度分布更加均匀.     

流场驱动高分子链迁移穿过微通道的耗散粒子动力学模拟

利用耗散粒子动力学模拟方法研究了高分子链在流场驱动作用下迁移穿过微通道过程中的链构象变化和动力学行为.在足够大的流场力驱动作用下,高分子链在沿着流场方向逐渐被拉伸,从而能够穿过管径小于其自身尺寸的微通道.耗散粒子动力学模拟结果表明高分子链的迁移过程主要分为3个步骤:(1)在流场驱动作用下,高分子链漂移并逐渐靠近微通道入口;(2)高分子链逐渐调整自身构象,并使其部分进入微通道;(3)高分子链成功穿过微通道.同时,模拟还发现当高分子链尺寸大于微通道细管道管径时,高分子链穿过微通道所需的平均迁移时间随着流量的增加而逐渐减小.此外,为了研究高分子链刚性对高分子链穿过微通道的影响,模型中还引入了蠕虫状高分子链模型.模拟结果发现,高分子链的链刚性越强,其迁移穿过微通道的时间越长.     

Dynamics of polymer translocation into a circular nanocontainer through a nanopore

Using Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a circular nanocontainer through a nanopore under a driving force F. We observe that the translocation probability initially increases and then saturates with increasing F, independent of φ, which is the average density of the whole chain in the nanocontainer. The translocation time distribution undergoes a transition from a Gaussian distribution to an asymmetric distribution with increasing φ. Moreover, we find a nonuniversal scaling exponent of the translocation time as chain length, depending on φ and F. These results are interpreted by the conformation of the translocated chain in the nanocontainer and the time of an individual segment passing through the pore during translocation.     

Numerical and theoretical study on the mechanism of biopolymer translocation process through a nano-pore

We conducted a numerical study on the translocation of a biopolymer from the cis side to the trans side of a membrane through a synthetic nano-pore driven by an external electric field in the presence of hydrodynamic interactions (HIs). The motion of the polymer is simulated by 3D Langevin dynamics technique using a worm-like chain model of N identical beads, while HI between the polymer and fluid are incorporated by the lattice Boltzmann equation. The translocation process is induced by electrophoretic force, which sequentially straightens out the folds of the initial random configuration of the polymer chain on the cis side. Our simulation results on translocation time and velocity are in good quantitative agreement with the corresponding experimental ones when the surface charge on the nano-pore and the HI effect are considered explicitly. We found that the translocation velocity of each bead inside the nano-pore mainly depends upon the length of the straightened portion of the polymer in forced motion near the pore. We confirmed this by a theoretical formula. After performing simulations with different pore lengths, we observed that translocation velocity mainly depends upon the applied potential difference rather than upon the electric field inside the nano-pore.     

The theta-temperature depression caused by topological effect in ring polymers studied by Monte Carlo simulation

We studied equilibrium conformations of linear and ring polymers in dilute solutions over the wide range of segment number N of up to 2048 with Monte Carlo simulation, and evaluated N dependence of the radii of gyration, R(g), of chains. The polymer molecules treated in this study are assumed to be composed of beads and bonds, and they are put in a three-dimensional face-centered cubic (FCC) lattice. The values of Flory's critical exponent, ν, for linear and ring polymers were estimated from the N dependence of R(g), and the temperatures at which ν reach 1/2 were obtained. Here we define those as Θ-temperatures in this report. The simulation result shows that the Θ-temperature for ring polymers is evidently lower than that of the linear polymers, and the origin of the Θ-temperature depression is discussed. Since R(g) of a ring polymer is smaller than that for a linear polymer at the same N and temperature, the segment density for a ring polymer is increased by the topological effect and the repulsive force between segments of a ring polymer at the Θ-temperature for a linear polymer is stronger. Thus, the origin of the Θ-temperature depression for ring polymers is the repulsive force emphasized by the topological effect of rings.     

Dispersions of polymer ionomers: I

The principal subject discussed in the current paper is the effect of ionic functional groups in polymers on the formation of nontraditional polymer materials, polymer blends or polymer dispersions. Ionomers are polymers that have a small amount of ionic groups distributed along a nonionic hydrocarbon chain. Specific interactions between components in a polymer blend can induce miscibility of two or more otherwise immiscible polymers. Such interactions include hydrogen bonding, ion-dipole interactions, acid-base interactions or transition metal complexation. Ion-containing polymers provide a means of modifying properties of polymer dispersions by controlling molecular structure through the utilization of ionic interactions. Ionomers having a relatively small number of ionic groups distributed usually along nonionic organic backbone chains can agglomerate into the following structures: (1) multiplets, consisting of a small number of tightly packed ion pairs; and (2) ionic clusters, larger aggregates than multiplets. Ionomers exhibit unique solid-state properties as a result of strong associations among ionic groups attached to the polymer chains. An important potential application of ionomers is in the area of thermoplastic elastomers, where the associations constitute thermally reversible cross-links. The ionic (anionic, cationic or polar) groups are spaced more or less randomly along the polymer chain. Because in this type of ionomer an anionic group falls along the interior of the chain, it trails two hydrocarbon chain segments, and these must be accommodated sterically within any domain structure into which the ionic group enters. The primary effects of ionic functionalization of a polymer are to increase the glass transition temperature, the melt viscosity and the characteristic relaxation times. The polymer microstructure is also affected, and it is generally agreed that in most ionomers, microphase-separated, ion-rich aggregates form as a result of strong ion-dipole attractions. As a consequence of this new phase, additional relaxation processes are often observed in the viscoelastic behavior of ionomers. Light functionalization of polymers can increase the glass transition temperature and gives rise to two new features in viscoelastic behavior: (1) a rubbery plateau above T(g) and (2) a second loss process at elevated temperatures. The rubbery plateau was due to the formation of a physical network. The major effect of the ionic aggregate was to increase the longer time relaxation processes. This in turn increases the melt viscosity and is responsible for the network-like behavior of ionomers above the glass transition temperature. Ionomers rich in polar groups can fulfill the criteria for the self-assembly formation. The reported phenomenon of surface micelle formation has been found to be very general for these materials.     

高分子链在球内表面上的吸附/排空转变

应用自洽场理论(SCFT)研究了受限于球内的高分子溶液的结构,重点关注高分子链在受限壁附近的行为.根据自洽场理论数值计算结果,讨论了球半径、高分子与球限制壁的相互作用、高分子平均浓度等因素对球内高分子浓度分布的影响.从高分子浓度分布和吸附/排空层厚度可以发现,在一定的条件下,受限的高分子在受限壁上会发生吸附/排空转变.吸附/排空转变与受限球大小、高分子链长和平均浓度,以及高分子链与受限壁之间相互作用都有关系.理论预测发生吸附/排空转变时的高分子与球限制壁的临界相互作用参数与链长的倒数成线性关系,且斜率与球半径有关.限制球越小,要发生吸附/排空转变,需要高分子与球之间有更大的临界吸引能.     

Coupling Effects of Electrostatic Interactions and Salt Concentration Gradient in Polymer Translocation through a Nanopore: A Coarse-Grained Molecular Dynamics Simulations Study

We study the influence of polymer pore interactions and focus on the role played by the concentration gradient of salt in the translocation of polyelectrolytes (PE) through nanopores explicitly using coarse-grained Langevin dynamics simulations. The mean translocation time is calculated by varying the applied voltage, the pH, and the salt concentration gradient. Changing the pH can alter the electrostatic interaction between the protein pore and the polyelectrolyte chain. The polymer pore interaction is weakened by the increase in the strength of the externally applied electric field that drives translocation. Additionally, the screening effect of the salt can reduce the strong charge-charge repulsion between the PE beads which can make translocation faster. The simulation results show there can be antagonistic or synergistic coupling between the salt concentration-induced screening effect and the drift force originating from the salt concentration gradient thereby affecting the translocation time. Our simulation results are explained qualitatively with free energy calculations.     

Interactions of carbon nanotubes with pyrene‐functionalized linear‐dendritic hybrid polymers

A series of linear‐dendritic hybrid polymers, containing pyrene units at the periphery of aliphatic polyester dendrons, were prepared for the purpose of dispersing shortened single‐walled carbon nanotubes (SWNTs) in tetrahydrofuran (THF). The prepared hybrids contained 1, 2, 4, 8, or 16 (G0 through G4) pyrene units and a linear segment composed of polystyrene. It was found that a minimum of four pyrene units was necessary to form a strong enough interaction with SWNTs to enable steric stabilization in solution, when using a linear polymer segment of 11.5 kDa. Increasing either the number of pyrene units per polymer chain or the length of the polymer segment to 18.0 kDa did not improve nanotube solubility, whereas decreasing the polymer length resulted in significantly less effective nanotube dissolution. The G4 dendron alone, without the linear polystyrene segment, was also found to impart solubility to the nanotubes in THF. Interactions between the series of linear‐dendritic hybrids and full‐length multiwalled carbon nanotubes were also investigated, and it was found that the polymers exhibited strong interactions with the multiwalled carbon nanotube surface, resulting in the formation of stable solutions. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1016–1028, 2010     

Cooperative conformational transitions of linear biopolymers

Conformational transitions in proteins, nucleic acids, and other biopolymers evidently play a decisive role in many biological processes, particularly in control processes. They often proceed cooperatively, i.e. the elementary process of the transition of an individual segment of these macromolecules in influenced by the state of other segments via intramolecular interactions. In general, the segments favor the same state as their neighbours. The resulting equilibrium properties of cooperative systems, e.g. the sharpness of the transitions and their dependence on the chain length, can be quantitatively explained for linear systems by the linear Ising model. The molecular causes of the cooperativity can be explained for simple model polymers.     

Supramolecular Porphyrin Copolymer Assembled through Host–Guest Interactions and Metal–Ligand Coordination

Bisporphyrin cleft molecule 1 Zn possessing a guest moiety assembled to form supramolecular polymers through host–guest interactions. Bispyridine cross‐linkers created interchain connections among the supramolecular polymers to form networked polymers in solution. Solution viscometry confirmed that the cross‐linked supramolecular polymers were highly entangled. Frequency‐dependent linear viscoelastic spectroscopy revealed that the supramolecular polymers generated well‐entangled solutions with associating and networking polymers, whereas the solid‐like aggregates moved individually without breaking and reforming structures below the transition temperature of 9.6 °C. Morphological transition of the supramolecular polymers was evidenced by AFM images; the non‐cross‐linked polymer resulted in wide‐spread thin networks, while the cross‐linked networks produced thicker worm‐like nanostructures. The supramolecular networks gelled in 1,1,2,2‐tetrachloroethane, and an elastic free‐standing film was fabricated with a Young’s modulus of 1 GPa.     

Phase transitions of a polymer threading a membrane coupled to coil-globule transitions

We theoretically study phase transitions of a polymer threading through a pore imbedded in a membrane. We focus on the coupling between a partition of the polymer segments through the membrane and a coil-globule transition of the single polymer chain. Based on the Flory model for collapse transitions of a polymer chain, we calculate the fraction of polymer segments and the expansion factor of a polymer coil on each side of the membrane. We predict a first-order phase transition of a polymer threading a membrane; polymer segments in one side are discontinuously translocated into the other side, depending on solvent conditions and molecular weight of the polymer. We also discuss the equilibrium conformation of the polymer chain on each side of the membrane.