Scaling Behaviors of a Polymer Ejected from a Cavity through a Small Pore.

Langevin dynamics simulations are performed to investigate ejection dynamics of spherically confined flexible polymers through a pore. By varying the chain length N and the initial volume fraction ϕ_{0} of the monomers, two scaling behaviors for the ejection velocity v on the monomer number m in the cavity are obtained: v∼m^{1.25}ϕ_{0}^{1.25}/N^{1.6} for large m and v∼m^{-1.4} as m is small. A robust scaling theory is developed by dividing the process into the confined and the nonconfined stages, and the dynamical equation is derived via the study of energy dissipation. After trimming the prior stage related to the escape of the head monomer across the pore, the evolution of m is shown to be well described by the scaling theory. The ejection time exhibits two proper scaling behaviors: N^{(2/3ν)+y_{1}}ϕ_{0}^{-(2/3ν)} and N^{2+y_{2}} under the large and small ϕ_{0} or N conditions, respectively, where y_{1}=1/3, y_{2}=1-ν, and ν is the Flory exponent.

Charged dendrimers under the action of AC electric fields: breathing characteristics of molecular size, polarizations, and ion distributions.

Langevin dynamics simulations are performed to study the response of charged dendrimers in alternating current electric fields in 3:1 salt solutions. Time evolutions of molecular size show breathing characteristics which take saw-tooth-like patterns in square-wave electric fields and undulated sine-function ones in sine-wave fields. Detailed study reveals how the dendrimer and condensed ions oscillate in the electric fields, which result in polarization of the molecule. To effect a significant deformation of the dendrimer, the applied field amplitude must be larger than some critical strength Ecrit and the field frequency smaller than a threshold fcrit. The response behavior is characterized by two relaxation times in square-wave fields, both of which decrease linearly with the strong field strength larger than Ecrit. In sine-wave fields, the molecular size exhibits interesting hysteretic behavior in plotting the curves with the field variation. A Maxwell-Wagner type polarization theory is derived and proved by simulations, which connects fcrit with the strength of the applied electric field.

Expansion Kinetics of Flexible Polymers upon Release from a Disk-Shaped Confinement.

A general theory is developed to explain the expansion kinetics of a polymer released from a confining cavity in a d-dimensional space. At beginning, the decompressed chain undergoes an explosive expansion while keeping the structure resembling a sphere. As the process continues, the chain transitions to a coil conformation, and the expansion significantly slows down. The kinetics are derived by applying Onsager's variational principle. Computer simulations are then conducted in a quasi-two-dimensional space to verify the theory. The average expansion of the chain size exhibits a distinctive sigmoidal variation on a logarithmic scale, characterized by two times and associated exponents that represent the fast and the slow dynamics, respectively. Through an analysis of the kinetic state diagrams, two important universal behaviors are discovered in the two expansion stages. The intersection of the expansion speed curves allows us to define the crossover point between the stages and study its properties. The scaling relations of the characteristic times and exponents are thoroughly investigated under different confining conditions, with the results strongly supporting the theory. Additional calculations conducted in a three-dimensional (3D) space demonstrate the robustness of the proposed theory in describing the kinetics of polymer expansion in both 2D and 3D spaces.

Structure of polyelectrolyte brushes subject to normal electric fields.

Molecular dynamic simulations of salt-free polyelectrolyte brushes subject to external fields applied normal to the grafting substrate reveal the three-dimensional monomer and counterion distributions. It is found that below a critical electric field, local electroneutrality holds for densely grafted brushes and the brush height remains independent of field intensity. Above this critical field (which scales as 1/3 with grafting density) brush height increases smoothly, and the fraction of condensed counterions decreases. The brush bifurcates into two subpopulations of stretched and collapsed chains when the grafting density is not low. At intermediate grafting densities, the majority of chains are stretched and the minority are nonstretched. At high grafting densities bifurcation and brush height growth occur consecutively. The majority of the chains are nonstretched at high grafting densities. Although not observed prior to overstretching of the chain model, it is predicted that the two subpopulations will re-merge to a single highly stretched phase when field intensity reaches a third critical value. The ability to control subpopulations of chains suggests that utilizing electric fields normal to polyelectrolyte brushes holds potential as controllable gates in microfluidic devices.

Expansion of Single Chains Released from a Spherical Cavity.

A two-stage model is developed to explain the phenomena of chain expansion, released from a confining cavity. In the first stage, the chain is assumed to expand as a sphere, while in the second stage it expands like a coil. The kinetic equations for the variation of chain size are derived in the two stages by balancing the rate of the free energy change with the rate of the energy dissipation. Langevin dynamics simulations are then performed to examine the theory. We find that the expansion process is dominated by the second stage and the evolution of chain size follows, mainly, the predicted curve for coil expansion, which depends on the chain length and is not sensitive to the confining volume fraction. It permits to define the expansion time for the process. Further study reveals that the chain does undergo a spherical expansion in the first stage with the characteristic time much shorter than the one for the second stage. As a consequence, the first-stage variation of chain size can be regarded as an add-on to the principal curve of expansion designated by the second stage. The scaling behaviors and the associated scaling exponents are analyzed in details. The simulation results well support the theory.

Polyelectrolytes in multivalent salt solutions.

We study conformational and electrophoretic properties of polyelectrolytes (PEs) in tetravalent salt solutions under the action of electric fields by means of molecular dynamics simulations. Chain conformations are found to have a sensitive dependence on the salt concentration C(s). As C(s) is increased, the chains first shrink to a globular structure and subsequently re-expand above a critical concentration C(s)*. An external electric field can further alter the chain conformation. If the field strength E is larger than a critical value E*, the chains are elongated. E* is shown to be a function of C(s) by using two estimators E(I)* and E(II)* through the study of the polarization energy and the onset point of chain unfolding, respectively. The electrophoretic mobility of the chains depends strongly on C(s), and the magnitude increases significantly, accompanying the chain unfolding, when E>E(II)*. We study the condensed ion distributions modified by electric fields and discuss the connection of the modification with the change of chain morphology and mobility. Finally, E* is studied by varying the chain length N. The inflection point is used as a third estimator E(III)*. E(III)* scales as N(-0.63(4)) and N(-0.76(2)) at C(s) =0.0 and C(s)*, respectively. E(II)* follows a similar scaling law to E(III)* but a crossover appears at C(s) =C(s)* when N is small. The E(I)* estimator fails to predict the critical field, which is due to oversimplifying the critical polarization energy to the thermal energy. Our results provide valuable information to understand the electrokinetics of PE solutions at the molecular level and could be helpful in micro/nanofluidic applications.

Pore-spanning lipid membrane under indentation by a probe tip: a molecular dynamics simulation study.

We study the indentation of a free-standing lipid membrane suspended over a nanopore on a hydrophobic substrate by means of molecular dynamics simulations. We find that in the course of indentation the membrane bends at the point of contact and the fringes of the membrane glide downward intermittently along the pore edges and stop gliding when the fringes reach the edge bottoms. The bending continues afterward, and the large strain eventually induces a phase transition in the membrane, transformed from a bilayered structure to an interdigitated structure. The membrane is finally ruptured when the indentation goes deep enough. Several local physical quantities in the pore regions are calculated, which include the tilt angle of lipid molecules, the nematic order, the included angle, and the distance between neighboring lipids. The variations of these quantities reveal many detailed, not-yet-specified local structural transitions of lipid molecules under indentation. The force-indentation curve is also studied and discussed. The results make a connection between the microscopic structure and the macroscopic properties and provide deep insight into the understanding of the stability of a lipid membrane spanning over nanopore.

Dynamic information for cardiotoxin protein desorption from a methyl-terminated self-assembled monolayer using steered molecular dynamics simulation.

Dynamic information, such as force, structural change, interaction energy, and potential of mean force (PMF), about the desorption of a single cardiotoxin (CTX) protein from a methyl-terminated self-assembled monolayer (SAM) surface was investigated by means of steered molecular dynamics (SMD) simulations. The simulation results indicated that Loop I is the first loop to depart from the SAM surface, which is in good agreement with the results of the nuclear magnetic resonance spectroscopy experiment. The free energy landscape and the thermodynamic force of the CTX desorption process was represented by the PMF and by the derivative of PMF with respect to distance, respectively. By applying Jarzynski's equality, the PMF can be reconstructed from the SMD simulation. The PMFs, calculated by different estimators based upon Jarzynski's equality, were compared with the conventional umbrella sampling method. The best estimation was obtained by using the fluctuation-dissipation estimator with a pulling velocity of v = 0.25 nm/ns for the present study.

Constructing a force interaction model for thermal conductivity computation using molecular dynamics simulation: ethylene glycol as an example.

This study aims to construct a force interaction model for thermal conductivity computation and to analyze the liquid properties in atomic level for liquid ethylene glycol (EG) using molecular dynamic simulation. The microscopic details of the molecular system and the macroscopic properties of experimental interest are connected by Green-Kubo relations. In addition, the major contributions of heat transfer modes for thermal conductivity due to convection, interaction, and torque are obtained quantitatively. This study reveals that the intramolecular interaction force fields result in different conformations of the EG in the liquid and thus the molecular shapes. The trans∕gauche ratio for EG's O-Me-Me-O torsional angle and the number of intermolecular∕intramolecular H-bonds are found to be important parameters affecting the thermal conductivity.

A general theory of polymer ejection tested in a quasi two-dimensional space.

A general ejection theory of polymer is developed in a two- and three-dimensional space. A polymer is confined initially in a cavity and ejects spontaneously to the outer space through a nanopore channel without the help of any external stimulus. A reflective wall boundary is set at the pore entrance to prevent the falling of the head monomer of chain into the cavity. Three stages are distinguished in a process: (1) an entering stage, in which the head monomer enters the pore to search for a way to traverse the pore channel, (2) a main ejection stage, in which the chain body is transported from the cavity to the outer space, (3) a leaving stage, in which the tail monomer passes through and leaves the pore channel. Depending on the number of the monomers remaining in the cavity, the main ejection stage can be divided into the confined and the non-confined stages. The non-confined stage can be further split into the thermal escape and the entropic pulling stages. The Onsager's variational principle is applied to derive the kinetics equation of ejection. The escape time is calculated from the corresponding Kramers' escape problem. Extensive molecular dynamics simulations are then performed in a quasi two-dimensional space to verify the theory. The variation of the ejection speed is carefully examined. The decreasing behavior of the number of monomers in the cavity is studied in details. The scaling properties of the spending time at each processing stage are investigated systematically by varying the chain length, the cavity diameter, and the initial volume fraction of chain. The results of simulation support firmly the predictions of the theory, cross-checked in the studies of various topics. In combining with the previous investigations in the three-dimensional space, the generalized theory is very robust, able to explain the two seemly different phenomena, polymer ejection and polymer translocation, together under the same theoretical framework in the two space dimensions.

Crumpling an elastoplastic thin sphere.

The phenomenon of crumpling is common in nature and our daily life. However, most of its properties, such as the power-law relation for pressure versus density and the ratio of bending and stretching energies, as well as the interesting statistical properties, were obtained by using flat sheets. This is in contrast to the fact that the majority of crumpled objects in the real world are three-dimensional. Notable examples are car wreckage, crushed aluminum cans, and blood cells that move through tissues constantly. In this work, we did a thorough examination of the properties of a crumpled spherical shell, hemisphere, cube, and cylinder via experiments and molecular-dynamics simulations. Physical arguments are provided to understand the discrepancies with those for flat sheets. The root of this disparity is found to lie less in the nonzero curvature, sharp edges and corner, and open boundary than in the dimensionality of the sample.

Effect of chain stiffness on ion distributions around a polyelectrolyte in multivalent salt solutions.

Ion distributions in dilute polyelectrolyte solutions are studied by means of Langevin dynamics simulations. We show that the distributions depend on the conformation of a chain while the conformation is determined by the chain stiffness and the salt concentration. We observe that the monovalent counterions originally condensed on a chain can be replaced by the multivalent ones dissociated from the added salt due to strong electrostatic interaction. These newly condensed ions give an important impact on the chain structure. At low and at high salt concentrations, the conformation of a semiflexible chain is rodlike. The ion distributions show similarity to those for a rigid chain, but difference to those for a flexible chain whose conformation is a coil. In the midsalt region, the flexible chain and the semiflexible chain collapse but the collapsed chain structures are, respectively, disordered and ordered structures. The ion distributions, hence, show different profiles for this three chain stiffness with the curves for the semiflexible chain lying between those for the flexible and the rigid chains. The number of the condensed multivalent counterions, as well as the effective chain charge, also shows similar behavior, demonstrating a direct connection with the chain morphology. Moreover, we find that the condensed multivalent counterions form triplets with two adjacent monomers and are localized on the chain axis at intermediate salt concentration when the chain stiffness is semiflexible or rigid. The microscopic information obtained here provides a valuable insight to the phenomena of DNA condensation and is very useful for researchers to develop new models.

Translocation of a Polyelectrolyte through a Nanopore in the Presence of Trivalent Counterions: A Comparison with the Cases in Monovalent and Divalent Salt Solutions.

A polyelectrolyte threading through a nanopore in a trivalent salt solution is investigated by means of molecular dynamics simulations under a reflective wall boundary. By varying the chain length N and the strength E of the driving electric field applied inside the pore, the translocation time is carefully calculated to get rid of the bouncing effect because of the boundary. The results are analyzed under the scaling form ⟨τ⟩ ∼ N α E -δ and four driving force regimes; namely, the unbiased, the weakly driven, the strongly driven trumpet, and the strongly driven isoflux regime, are distinguished. The exponents are calculated in each regime and compared with the cases in the monovalent and divalent salt solutions. Owing to strong condensation of counter ions, the changes of the exponents in the force regimes are found to be nontrivial. A large increase in translocation time can be, however, achieved as the driving field is weak. The variations of the chain size, the ion condensation, and the effective chain charge show that the process is proceeded in a quasi-equilibrium way in the unbiased regime and deviated to exhibit strong nonequilibrium characteristics as E increases. Several astonishing scaling behaviors of the waiting time function, the translocation velocity, and the diffusion properties are discovered in the study. The results provide deep insights into the phenomena of polyelectrolyte translocation in various salt solutions at different driving forces.

Scaling Theory of a Polymer Ejecting from a Cavity into a Semi-Space.

A two-stage model is developed in order to understand the scaling behaviors of single polymers ejecting from a spherical cavity through a nanopore. The dynamics of ejection is derived by balancing the free energy change with the energy dissipation during a process. The ejection velocity is found to vary with the number of monomers in the cavity, m, as mz1/(Nx1D3z1) at the confined stage, and it turns to be m-z2 at the non-confined stage, where N is the chain length and D the cavity diameter. The exponents are shown to be z1=(3ν-1)-1, z2=2ν and x1=1/3, with ν being the Flory exponent. The profile of the velocity is carefully verified by performing Langevin dynamics simulations. The simulations further reveal that, at the starting point, the decreasing of m can be stalled for a good moment. It suggests the existence of a pre-stage that can be explained by using the concept of a classical nucleation theory. By trimming the pre-stage, the ejection time are properly studied by varying N, D, and ϕ0 (the initial volume fraction). The scaling properties of the nucleation time are also analyzed. The results fully support the predictions of the theory. The physical pictures are given for various ejection conditions that cover the entire parameter space.

Crumpling-origami transition for twisting cylindrical shells.

Origami and crumpling are two processes to reduce the size of a membrane. In the shrink-expand process, the crease pattern of the former is ordered and protected by its topological mechanism, while that of the latter is disordered and generated randomly. We observe a morphological transition between origami and crumpling states in a twisted cylindrical shell. By studying the regularity of the crease pattern, acoustic emission, and energetics from experiments and simulations, we develop a model to explain this transition from frustration of geometry that causes breaking of rotational symmetry. In contrast to solving von Kármán-Donnell equations numerically, our model allows derivations of analytic formulas that successfully describe the origami state. When generalized to truncated cones and polygonal cylinders, we explain why multiple and/or reversed crumpling-origami transitions can occur.

Overcharging, charge inversion, and reentrant condensation: using highly charged polyelectrolytes in tetravalent salt solutions as an example of study.

We study salt-induced charge overcompensation and charge inversion of flexible polyelectrolytes via computer simulations and demonstrate the importance of ion excluded volume. Reentrant condensation takes place when the ion size is comparable to monomer size, and happens in a middle region of salt concentration. In a high-salt region, ions can overcharge a chain near its surface and charge distribution around a chain displays an oscillatory behavior. Unambiguous evidence obtained by electrophoresis shows that charge inversion does not necessarily appear with overcharging and occurs when the ion size is not big. These findings suggest a disconnection of resolubilization of polyelectrolyte condensates at high salt concentration with charge inversion.

Free solution electrophoresis of homopolyelectrolytes.

We investigate the behavior of single polyelectrolytes in multivalent salt solutions under the action of electric fields through computer simulations. The chain is unfolded in a strong electric field and aligned parallel to the field direction, and the chain size shows a sigmoidal transition. The unfolding electric field E* depends on the salt concentration and scales as V (-1/2) with V being the ellipsoidal volume occupied by the chain. The magnitude of the electrophoretic mobility of chain drastically increases during the unfolding. The fact that E* depends on the chain length provides a plausible mechanism to separate long charged homopolymers by size in free solution electrophoresis via the unfolding transition of globule polyelectrolytes condensed by multivalent salt.

Enhanced thermal conductivity of nanofluids diagnosis by molecular dynamics simulations.

Molecular Dynamics simulations are performed to calculate the thermal conductivity of nanofluids, and to understand the fundamental physics of the enhancement of thermal conductivity observed in experiments. Based on the analysis, intermolecular interactions between copper-copper atoms, layer structure surrounding nanoparticles, convection effect induced by the Brownian motion of copper atoms, as well as particle-particle interactions are identified and confirmed on the enhancement using Green-Kubo method in thermal conductivity.

Translocation of Charged Polymers through a Nanopore in Monovalent and Divalent Salt Solutions: A Scaling Study Exploring over the Entire Driving Force Regimes.

Langevin dynamics simulations are performed to study polyelectrolytes driven through a nanopore in monovalent and divalent salt solutions. The driving electric field E is applied inside the pore, and the strength is varied to cover the four characteristic force regimes depicted by a rederived scaling theory, namely the unbiased (UB) regime, the weakly-driven (WD) regime, the strongly-driven trumpet (SD(T)) regime and the strongly-driven isoflux (SD(I)) regime. By changing the chain length N, the mean translocation time is studied under the scaling form 〈 τ 〉 ∼ N α E - δ . The exponents α and δ are calculated in each force regime for the two studied salt cases. Both of them are found to vary with E and N and, hence, are not universal in the parameter's space. We further investigate the diffusion behavior of translocation. The subdiffusion exponent γ p is extracted. The three essential exponents ν s , q, z p are then obtained from the simulations. Together with γ p , the validness of the scaling theory is verified. Through a comparison with experiments, the location of a usual experimental condition on the scaling plot is pinpointed.

Conformation Change, Tension Propagation and Drift-Diffusion Properties of Polyelectrolyte in Nanopore Translocation.

Using Langevin dynamics simulations, conformational, mechanical and dynamical properties of charged polymers threading through a nanopore are investigated. The shape descriptors display different variation behaviors for the cis- and trans-side sub-chains, which reflects a strong cis-trans dynamical asymmetry, especially when the driving field is strong. The calculation of bond stretching shows how the bond tension propagates on the chain backbone, and the chain section straightened by the tension force is determined by the ratio of the direct to the contour distances of the monomer to the pore. With the study of the waiting time function, the threading process is divided into the tension-propagation stage and the tail-retraction stage. At the end, the drift velocity, diffusive property and probability density distribution are explored. Owing to the non-equilibrium nature, translocation is not a simple drift-diffusion process, but exhibits several intermediate behaviors, such as ballistic motion, normal diffusion and super diffusion, before ending with the last, negative-diffusion behavior.