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... minimum radius of the sphere is set to the length of the DNA cylinder for each DNA fragment and the DNA concentration is calculated assuming that N nucleotide residues occupy an effective volume the size of the cell which is varied by increasing the radius. Simulation parameters are listed in Table 1. Three fractions of DNA of molecular weight N bp ) 64, 128, 256 are studied. ...
Context 2
... simulations are easily parallelized by the use of "embarrassingly parallel" programs which sum up and average over trajectories generated on a large number of nodes. In Table 1, total numbers of simulation time steps obtained by double summing over jobs and nodes are also given. Figures 1 and 2 show different views of the counterion distribution for a N bp ) 128 base-pair DNA at a polymer concentration c p ) 1.2 mM nucleotide residues. ...
Citations
... Even in salt-free dilute solutions at C s = 0, the N 8 and N 9 values were substantially greater than N 2 and N 5 (N 8 and N 9 represent diffused counterions; N 2 and N 5 represent condensed counterions), which indicate the prominent presence of free counterions. This behavior agrees with the MC simulations of model DNA fragments in dilute salt-free solution where the diffuse-ion atmosphere was more significant than condensed ions [41]. The work by Chremos and Douglas [32] has already illustrated the counterion distribution around the model polyelectrolyte in explicit solvent using MD simulations. ...
The difference in the structural properties of highly charged polyacrylic acid (PAA) and polymethacrylic acid (PMA) is investigated by atomistic molecular dynamics (MD) simulations in the presence of divalent salt magnesium chloride. A united-atom model approach was used to represent the backbone methylene groups in both the polymers. The salt concentration (Cs) dependence of conformational radius of gyration (Rg) and chain persistence length (Lp) is discussed in detail for PAA and PMA. The Rg showed a decrease with Cs for both PAA and PMA. However, the PMA Rg is greater than PAA at the salt concentration range of 0.1 < Cs < 0.9 M. The chain stiffness calculated by Lp demonstrated a decrease with Cs for both PAA and PMA. However, the Lp of PMA at Cs ≥ 0.7 M is greater than PAA, rendering it stiffer than its counterpart at higher salt concentration. The total number of intermolecular hydrogen bonds between PAA and water is greater compared to PMA–water at all Cs values. This behavior may be attributed to methyl side groups in PMA, rendering it more hydrophobic. The coordination number value for PAA–water is greater than the PMA–water pair across the entire Cs range. However, the number of h-bonds does not change with variations in Cs for both PAA and PMA. The degree of counterion binding to the polyelectrolyte quantified by coordination number shows a decrease with Cs due to an increase in salt concentration and replacement of Na⁺ counterions by divalent Mg²⁺ salt ions for PAA and PMA. The spatial distribution of salt ions shows an increase in PAA-Mg²⁺ and PMA-Mg²⁺ coordination number with Cs. However, the coordination number for PAA-Mg²⁺ is greater than its counterpart at all Cs values indicating a significant electrostatic charge screening in the case of the PAA compared to PMA. Overall, the understanding pertaining to the differences in the microstructure, hydrogen bonding, intermolecular structure, and salt-ion distribution around PAA and PMA in the dilute aqueous divalent salt solution is significantly advanced in the present work.
Graphical abstract
... Special attention is devoted to the effect of the surface charge density, because the counter-ion condensation at the charged surface must have important effects on the response. 32,33 The dependence of the effective electrical conductivity and of the flow rate in a Poiseuille geometry is examined, and the inversion of the streaming current and the electro-osmotic flow 27 is discussed. ...
Electrokinetic flows of an aqueous NaCl solution in nanochannels with
negatively charged surfaces are studied using molecular dynamics (MD)
simulations. The four transport coefficients that characterise the response to
weak electric and pressure fields, namely the coefficients for the electrical
current in response to the electric field ($M^{jj}$) and the pressure field
($M^{jm}$), and those for the mass flow in response to the same fields
($M^{mj}$ and $M^{mm}$), are obtained in the linear regime using a Green-Kubo
approach. Nonequilibrium simulations with explicit external fields are also
carried out, and the current and mass flows are directly obtained. The two
methods exhibit good agreement even for large external field strengths, and
Onsager's reciprocal relation ($M^{jm} = M^{mj}$) is numerically confirmed in
both approaches. The influence of the surface charge density on the flow is
also considered. The values of the trans- port coefficients are found to be
smaller for larger surface charge density, because the counter-ions strongly
bound near the channel surface interfere with the charge and mass flows. A
reversal of the streaming current and of the reciprocal electro-osmotic flow,
with a change of sign of $M^{mj}$ due to the excess co-ions, takes places for
very high surface charge density.
... In the system with added salt, when 4.0 ( Fig. 7(b)), counterions that are apparently tied to the polyion are found. The additional stretching effect beyond the power law found in the ≥ 1.0 system cannot be explained by scaling or mean field theory and it may therefore be due to a dynamic effect called counterion polarization [11,27], which has already been highlighted by Oosawa [24]. The existence of a condensed counterion layer causes a large dipole fluctuation in the longitudinal direction of the polyions and this causes the attractive force between two polyions. ...
As an example of a very low friction system, Monte Carlo Brownian dynamics simulations have been used to calculate equilibrium structures of a polyelectrolyte brush grafted onto planes. The polymers were calculated in a semi-flexible coarse-grain model that is appropriate to treat the charge density of the polyion. The effect of linear charge density on the polyion ξ, the surface negative charge, and added salts were studied. In salt-free solution, scaling theories predicted the structure well in the low — region. In the high ξ region, additional shrinkage was found from the theories due to counterion condensation. The effect of surface charge showed not only the repulsion of the polyion from the surface but also the shrinkage in the high ξ region due to the additional counterions required for electrical neutrality. The addition of salts led to the shrinkage of the brush heights, and in the high ξ region, additional extension was found. The computational strategy for calculating the friction dynamics of the system is also discussed.
... Monte-Carlo simulations conrm this assumption. [33][34][35] Nevertheless, in recent theories developed for a discrete charge line 36 and long cylinders 37 the origin of the induced dipole moment is postulated to be the polarization of the condensed counterions; the possible contribution of the diffuse counterions is neglected. Comparison of the theoretical results with experimental ones shows that the effective diffusion coef-cient of the counterions is equal to that of the free ions in the bulk; 36 this result is interpreted by Manning as evidence for condensed counterion polarization, but in our understanding it reveals that the polarizability of polyelectrolytes in solution is due to the diffuse counterions. ...
When the linear charge density of a polyelectrolyte chain reaches some critically high level, an electrostatic adsorption of part of the counterions appears, that is the so-called counterion condensation. There are contradictory opinions in the literature about the condensed counterion mobility along the polymer chain: the analytical theories predict some mobility, but the experimental research does not give an unequivocal answer. The present experimental investigation aims to verify the reports for the condensed counterion migration in a sinusoidal electric field. By using electric light scattering we investigate an aqueous suspension of γ-alumina particles after the complete adsorption of carboxymethyl cellulose on their surface; the probable migration of condensed counterions must contribute to the electric polarizability (when the frequency is under a given critical value) leading to a higher degree of particle orientation in the applied electric field. We compare the frequency dependences of the polarizability at two polyelectrolyte concentrations in the suspension: under and above the recharging point (appearing due to adsorption of the negatively charged polyelectrolyte on the positively charged surface) where the total polarizability is equal, but the ratio between the quantities of the diffuse and the condensed counterions is different. A procedure for determination of the counterion shares is invented; it uses the measured electrophoretic mobility and the calculated fraction of the condensed ions. The results indicate the absence of the polarizability component caused by the condensed counterions; i.e. they do not manifest their presence when an external electric field is applied. We have concluded that the condensed ions are immobile in a sinusoidal field with moderate intensity in the frequency range of 10 Hz to 1 MHz.
... In this study, coarse-grained Metropolis Monte Carlo Brownian dynamics (MCBD) [12][13][14] simulations are employed to investigate the friction dynamics of the transfer film of multilayered graphene sheets. MCBD was first introduced by Kikuchi et al. 12 in order to calculate the dynamics of colloid suspensions. ...
... As two carbon atoms, which are facing each other on the honeycomb structures, can be geometrically distinguished by the periodicity, the potential between the sheets U sheet-sheet is calculated using U atom-sheet (x, y). U sheet-sheet ¼ (U atom-sheet (Dx,Dy) + U atom-sheet (Dx,Dy À (1/2)l a ))$S(Dx,Dy) (13) where Dx and Dy are the distances between center of two circle shaped sheets in the x and y directions respectively, and S(Dx,Dy) is the number of the carbon atoms in an overlapped area of two circles in a position Dx and Dy. By eqn (13), the end effect which is the effect of the finite size of the graphene sheets is able to be included in the simulation. ...
... U sheet-sheet ¼ (U atom-sheet (Dx,Dy) + U atom-sheet (Dx,Dy À (1/2)l a ))$S(Dx,Dy) (13) where Dx and Dy are the distances between center of two circle shaped sheets in the x and y directions respectively, and S(Dx,Dy) is the number of the carbon atoms in an overlapped area of two circles in a position Dx and Dy. By eqn (13), the end effect which is the effect of the finite size of the graphene sheets is able to be included in the simulation. The potential surface U sheet-sheet of the system is plotted in Fig. 2. Dx ¼ 0 and Dy ¼ 0 correspond to the AB stuck structure and the interaction between the sheets decreases when two sheets are in separated positions. ...
Coarse-grained Metropolis Monte Carlo Brownian Dynamics simulations are used to clarify the ultralow friction mechanism of a transfer film of multilayered graphene sheets. Each circular graphene sheet consists of 400 to 1,000,000 atoms confined between the upper and lower sliders and are allowed to move in 3 translational and 1 rotational directions due to thermal motion at 300 K. The sheet-sheet interaction energy is calculated by the sum of the pair potential of the sp2 carbons. The sliding simulations are done by moving the upper slider at a constant velocity. In the monolayer case, the friction force shows a stick-slip like curve and the average of the force is high. In the multilayer case, the friction force does not show any oscillation and the average of the force is very low. This is because the entire transfer film has an internal degree of freedom in the multilayer case and the lowest sheet of the layer is able to follow the equipotential surface of the lower slider.
... The charge polarization of polyelectrolytes under dc or low-frequency ac fields has been theoretically studied and reviewed. [11][12][13] Yet prior work has mainly focused on "strong" polyelectrolytes whose charges are fixed and neutralized by the localized counterions, known as "condensed counterions". The effect of ac electric fields is thus limited to mobile counterions in the diffusive double layer and not the condensed ones in the Stern layer, resulting in simply modifying the screening ion cloud near a polyelectrolyte without fundamentally changing its charge density. ...
A reversible and gradual ac-field-induced coil-to-globule transition (CGT) of a synthetic weak polyelectrolyte, poly(2-vinylpyridine) (P2VP) by using fluorescence correlation spectroscopy (FCS) at a single molecule resolution was reported. The lower and upper ω were set between 5 kHz and 10MHz, corresponding to the electrode screening frequency to avoid P2VP electrochemical adsorption on electrodes and the inverse charge relaxation frequency, ω C, for a P2VP coil, respectively. The ω-dependent induced dipole term was shown to elevate the energy of the coil minimum relative to the barrier, leading to a shift from a coil radius toward a globule radius. An optimum ac frequency window exists, which was determined by the inverse charge relaxation time and inverse counterion dissociation/association time scales on the polyelectrolyte backbone. The ac-induced local pH variation caused counterion dissociation and migration to modify the P2VP charge density.
... The Monte Carlo (MC) Brownian dynamics method 7-11 enables us to calculate concentrations of small ions and the electrical potential as functions of space and time with hydrodynamic interactions between ionic species taken into account. Recently, we started to determine anisotropy of the static electric polarizability ∆R of model DNA fragments in aqueous solution by MC simulation 12-20 and reproduced characteristics of the electric properties of polyelectrolytes in both salt-free 19,20 and salt solutions. 17 The system has prolate ellipsoidal symmetry with the foci located at both ends of the DNA polyion cylinder. ...
... 17 The system has prolate ellipsoidal symmetry with the foci located at both ends of the DNA polyion cylinder. 21 In saltfree solutions, 19,20 at every simulation step, we numerically sort counterions in increasing order of the sum of their distances from both ends of the polyion. Two kinds of counterions are distinguished from their spatial distributions and identified in the framework of the counterion condensation theory 3,22,23 as condensed counterions and diffuse ion atmospheres. ...
... Although it is seen that counterions apparently comparable to the Manning fraction are located in the immediate vicinity of the polyion, it is hard to find unique points on the curves that single out condensed counterions as in a salt-free solution. 20 Even the composition of counterions in the immediate vicinity of the polyion cannot be accounted for solely by condensed counterions. As Figure 6 shows, Ramanathan-Woodbury distribution and supposed counterion distributions from the PB equation take approximately the same value 0.1 M at r ≈ 1.8 nm. ...
Monte Carlo simulations are performed to determine the anisotropy of the electric polarizability of a model DNA fragment in aqueous salt solution. By taking into consideration the participation of coions in the electroneutrality condition, at every simulation step, we obtain a list of counterions constituting the net charge arranged in increasing order of their distance from the DNA and calculate the contribution to the dipole moment from the first n counterions in the list. We define a partial polarizability tensor due to these n counterions to understand the origin of the polarizability in close relation to the solution structure. The ionic distributions are described by the counterion condensation theory. Characteristic features of the electric properties of polyelectrolytes are reproduced. The anisotropy of the electric polarizability Deltaalpha of DNA decreases with the addition of salt, yielding values comparable to experiment. The effect of electrophoretic motion of the polyion is examined by estimating its upper limit.
... Computer simulations would be helpful in guiding that theoretical effort to better understand the molecular aspects of polarization at different frequencies. Monte Carlo simulations are currently underway [178] but molecular dynamics simulations with an explicit solvent are not quite possible yet [179]. ...
The dielectric and conductometric properties of aqueous polyelectrolyte solutions present a very complex phenomenology, not yet completely understood, differing from the properties of both neutral macromolecular solutions and of simple electrolytes. Three relaxations are evident in dielectric spectroscopy of aqueous polyelectrolyte solutions. Near 17 GHz, water molecules relax and hence this highest frequency relaxation gives information on the state of water in the solution. At lower frequencies in the MHz range, free counterions respond to the applied field and polarize on the scale of the correlation length. This intermediate frequency relaxation thus provides information about the effective charge on the polyelectrolyte chains, and the fraction of condensed counterions. However, the presence of polar side chains adds a further polarization mechanism that also contributes in this intermediate frequency range. At still lower frequencies, the condensed counterions polarize in a non-uniform way along the polyelectrolyte chain backbone and dielectric spectroscopy in the kHz range may determine the effective friction coefficient of condensed counterions. In this review, we analyse in detail the dielectric and conductometric behaviour of aqueous polyelectrolyte solutions in the light of recent scaling theories for polyelectrolyte conformation and summarize the state-of-the-art in this field.
... This difficulty can be circumvented if instead of following physical trajectories of the system a more efficient phase space sampling is done. It was shown [179,190] that the Metropolis Monte Carlo method can be used to describe non-equilibrium stationary systems. But unless cluster algorithms are applied the problem of separated time scales remains [100]. ...
... The dielectric increment at low frequencies is often associated with "bound" counterions [135] where of course the distinction between "free" and "bound" counterions needs some clarification. The explanation of the polarization mechanism is by far not conclusive [17] which can be seen from the great number of recent publications dealing with the subject [39,89,179]. Electric birefringence and dichroism provide another method to determine polarizabilities. ...
... I therefore use finite fields. In the salt-free case, however, it was successfully used in a recent Monte Carlo study [179]. ...
In this study, water / oil / amphiphilic polymer ternary system is analyzed by Monte Carlo (MC) method using a lattice model to determine the thermal equilibrium distribution by component ratio. Particularly the rheological properties such as shear stress and viscosity are evaluated via Monte Carlo Brownian Dynamics (MCBD) simulation, in which the flexibility of polymer movement is considered by the bond fluctuation model and the shear force is expressed by the Kramers potential. Our analysis on the mixed micelle pattern for each concentration ratio shows that, the increase of polymer concentration decreases the solute (water, polymer) mobility, and exponentially increases the viscosity. These results in our simulation reflect general phenomena in concentrated colloid system.
By assuming that the polymer orientation dominates the stress of system by the elasticity between polymer bonds, we newly find that from the polymer placement under the shear field, the shear stress itself exponentially increases while raising the concentration. Even in the category of lattice model, our study indicates the possibility of acquiring new knowledge on Dynamics by using a polymer model with specific consideration on flexible mobility and MCBD method.
