Electrophoresis of a bead-rod chain through a narrow slit: a Brownian dynamics study

We use two-dimensional Brownian dynamics simulations to study the electrophoresis of a bead-rod chain through a narrow slit. A constant electric field is assumed to act inside and outside of the slit, and each bead on the chain is assigned a constant uniform charge. We calculate the dependence of the polymer transit velocity on chain length, slit dimensions (width-to-length ratio), and electric-field strength. For sufficiently narrow slits, the transit velocity increases nonlinearly with the applied field for low-field strengths, whereas it increases linearly for high-field strengths. In the low-field strength region and for sufficiently narrow slits, the transit velocity decreases rapidly for small chain lengths and then decreases slowly beyond a critical chain length. As the slit width increases, the transit velocity decreases with chain length in more continuous manner, and for sufficiently large slits the transit velocity becomes independent of chain length as expected. Distributions of the chain end-to-end distances and the translocation times depend strongly on the relative size of the chain to the slit. These results show the sensitivity of the transit velocity vs chain length relationship to the slit dimensions and applied electric-field strength, and suggest that there may be an optimal slit width for a given field strength and vice versa. The results may be useful for microfluidic separations and for understanding the motion of biological polymers through narrow constrictions.     

Molecular arrangements and conformations of liquid unbranched alkanes in narrow slits

Realistic, atomistic models of liquid tridecane in broad slits (>3 nm) and in narrow slits of thickness 1,2 nm and 1,0 nm have been obtained using the Monte Carlo technique. The setup of the models is such that the molecules in the slits are in equilibrium with the bulk liquid. The surfaces of the plates are modelled as two-dimensional arrays of hexagonally packed units having the same size and interaction parameters of a methylene group. The regions adjacent to the plates in slits with thickness > 3 nm are characterized by a well defined tendency to form partially ordered layer structures, while molecules at a distance from the plates larger than 1,5 nm are unperturbed. The simultaneous presence of two plates increases the tendency to form layer structures when their distance is 1,2 nm, while this tendency is almost totally destroyed when the slit is squeezed down to a thickness of 1,0 nm. This is also associated with a 10% decrease of the density in the latter slit.     

The Structure of Star-Branched Chains in a Confined Space

Summary. We studied the properties of a simplified model of star-branched polymers confined in a slit formed by two parallel and impenetrable surfaces. The chains were built of identical united atoms (segments) whose positions were restricted to vertices of a simple cubic lattice. The polymer excluded volume and polymer segment-surface contact interactions were also introduced into the model. The properties of the model chains were determined by means of Monte Carlo simulations with a Metropolis-type sampling algorithm based on local changes of chain’s conformation. The structure of star-branched chains was investigated and the influence of the confinement and the temperature on the chain dimensions and structure was studied. It was shown that for chains in the adsorbing slits their sizes do not exhibit a universal behavior contrary to confined athermal polymers. The polymers in narrow slits at higher temperatures still exhibited features of a three-dimensional chain. It was also shown that chains in small slits and at low temperatures were fully adsorbed at one of the surfaces but could also switch the surface rapidly.     

Polymer-induced depletion interaction between weakly attractive plates

Lattice Monte Carlo simulations have been employed to calculate depletion interaction of excluded volume chains in a weakly attractive slit, particularly in the region around the critical point of adsorption. The simulations were performed under full equilibrium conditions where a dilute solution in a slit was in contact with the reservoir. The free energy of confinement deltaA, the force f, and the relative pressurepI/pE on the slit walls were calculated as a function of slit width D and the attraction strength epsilon. The depletion region in the pressure profile pI/pE vs D is reduced by an increase in the attraction potential epsilon in a manner resembling the influence of polymer concentration. At the critical point of adsorption epsilonc the depletion interaction vanishes both in the pressure pI/pE and in the intraslit concentration profile phiI(x). The parameters used to assess the stability of colloidal dispersions such as the depletion potential W(D) (an integral of the net pressure deltap) reach a unique value at the critical condition. A monotonic repulsive profilepI vs D was found for chains trapped in the slit at restricted equilibrium. The mean dimensions (R2) of chains compressed in attractive slits feature a distinct minimum at intermediate slit widths.     

Polymolecular adsorption and capillary condensation in narrow slit pores

Capillary condensation and polymolecular adsorption in narrow slits has been calculated, where the fields of surface forces overlap one another. The calculations were carried out on the basis of macroscopic theory of dispersion forces and the isotherms of lone adsorption layers at the free surface. It has been shown that under the effect of mutual attraction through a gap, polymolecular adsorption films lose their stability long before their thickness has approached the half-width of a flat slit. This results in hysteresis of the capillary condensation in an ensemble of plane-parallel slits.

In the case of systems having strong adsorbate-adsorbate interaction, there has been detected the existence of the lower limit of sizes of slit pores, wherein the capillary meniscus can coexist with adsorption films. With a slit width smaller than the critical one, the meniscus is likely to form a finite contact angle with “dry” surfaces of a slit. Thus an explanation has been given of the lower limit of the capillary condensation in an ensemble of flat-surface, slit pores. In the case of strong adsorbate-adsorbent interaction, the coexistence of meniscus with adsorption films within the scope of the approach used is possible in slits of any width.

The value of corrections for the surface forces effect to be entered in the calculations of slit pores dimensions has been analyzed on the basis of the capillary condensation data obtained.

In wedge-shaped slits there also exists, besides lower limit the upper limit of capillary hysteresis.     

Self-assembly behavior of rod-coil-rod triblock copolymers within a planar slit

The self-assembly behavior of sphere-forming R₅C₃₀R₅ triblock copolymers within a planar slit is studied by performing dissipative particle dynamics simulations. A sequence of novel structures which are not observed in bulk are formed within slits, including wetting layers, island-like structure, parallel cylinders, perpendicular cylinders and cross-cylindrical structures. Perpendicular cylinders are always formed before the increase in the layers of parallel cylinders. A phase diagram of the assembled structures with respective to the slit property and height is thus presented. The rod length is found to have a significant impact on the rod alignment, and a disordered-ordered transition of rod orientation occurs with an increase in the length of rod blocks. Some special structures, such as parallel half-cylinders and arrowhead-shaped morphology, are observed when the rod length increases to a certain extent. Our results show that the property and height of the slit and rod length all influence the self-assembly of rod-coil-rod triblock copolymers.     

Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.     

Methane adsorption and diffusion in a model nanoporous carbon: an atomistic simulation study

A constricted slit model was introduced to improve, one step further, the performance of the simple slit model in prediction of the adsorption and diffusion behavior of simple molecules in the nanoporous carbons (NPCs). The grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations are performed to study the adsorption and diffusion behavior of methane within the constricted slit models. The models are called slit-1, 2, and 3 with constriction heights 5, 7, and 9 Å respectively. For comparison, we used the slit-0 name for the simple slit without constriction. Adsorption results show that at low pressures, the constriction increases the adsorbed amount irrespective of its height. Slit-2 with a constriction height as a molecular diameter has the greatest heat of adsorption and has highest loading at pressures up to 3,000 kPa. At high pressures, when all pores are filled, the adsorption trend is in line with the pore volumes of slits where slit-0 with higher pore volume is dominant. The density profiles in the models were calculated and examined. The spatial distribution of adsorbed methane molecules was examined by various radial distribution functions calculated by MD. Also, MD simulation results show that the diffusion coefficient of methane decreases in constricted slits. The calculated diffusion coefficients in slit-2 in the direction of the constriction are one order of magnitude smaller than the calculated one in the simple slit model but it is far from the experimental values in the NPCs.     

Symmetry breaking of the fluid density profiles in closed nanoslits

The density profiles in a fluid interacting with the two identical solid walls of a closed long slit were calculated for wide ranges of the number of fluid molecules in the slit and temperature by employing a nonlocal density functional theory. Using argon as the sample fluid and considering the walls composed of solid carbon dioxide, it is shown that the density profile corresponding to the stable state of the fluid considerably changes its shape with increasing average density rho(av) of the fluid inside the slit. Temperature dependent critical values rho(sb1) and rho(sb2) of rho(av) were identified, such that for rho(sb1)相似文献   

Free energy in vertically aligned liquid crystal mode

Vertical alignment (VA) is a widely applied operation mode for liquid crystal displays. To achieve optimum brightness, the electrode of VA is often patterned with fish-bone fine slits to generate fringe field, so the negative liquid crystal aligns along the fine slits when the electric field is applied. VA is usually simply modelled by the bend geometry along the cell gap. However, defects, domain boundaries and periodical splay induced by the fine slits also exist in real pixels and disturb the liquid crystal alignment. Polymer-stabilised VA test cells with various fine slit pitches which lead to various strength of fringe field were fabricated to observe the deformation of liquid crystal. Then the models of liquid crystal deformation nearby the defects and in the fine slit area were proposed to calculate the electromagnetic (f_EM) and elastic free energy (f_elastic). The results show that the key factor to regulate f_EM and f_elastic is the pitch of the fine slits, and the optimum liquid crystal alignment is obtained when f_EM and f_elastic are equal. The models are useful for further investigation on the dynamics of liquid crystal alignment and applications in industrial products.     

Screening effects on structure and diffusion in confined charged colloids

Using molecular dynamics computer simulations we investigate structural and dynamic (diffusion) properties of charged colloidal suspension confined to narrow slit pores with structureless, uncharged walls. The system is modeled on an effective level involving only the macroions, which interact via a combination of a soft-sphere and a screened Coulomb potential. The aim of our study is to identify the role of the range of the macroion-macroion interaction controlled by the inverse Debye screening length, kappa. We also compare to bulk properties at the same chemical potential as determined in parallel grand canonical Monte Carlo simulations. Our results reveal a significant influence of the interaction range which competes, however, with the influence of density. At liquidlike densities a decrease of range yields a decreasing mobility (and a corresponding enhancement of local structure) in the bulk system, whereas the reverse effect occurs in narrow slits with thickness of a few particle diameter. These differences can be traced back to the confinement-induced, and kappa-dependent, reduction of overall density compared to the bulk reservoir. We also show that an increase of kappa softens the oscillations in the normal pressure as function of the wall separation, which is consistent with experimental observations concerning the influence of addition of salt.     

Programmed placement of gold nanoparticles onto a slit-type DNA origami scaffold

A novel DNA scaffold, called a DNA slit, was designed for the programmed positioning of Au nanoparticles (AuNPs), and various patterns of thiolated DNA slits were constructed. AuNPs were correctly placed at the predesigned positions in the thiolated DNA slits, indicating that the thiolated staples and the slit cavities guide the correct assembly of AuNPs.     

A simple and compact blue diode laser powered excitation source for fluorescence detection in capillary electrochromatographic microchip separation

A simple and compact fluorescence excitation source was prepared using a 405 nm blue laser diode module and characterized in capillary electrochromatographic or capillary electrophoretic microchip separation. An inexpensive blue laser diode module with a tiny focusing lens was simply mounted at the center of an aluminum block on a miniature linear motion guide for heat dissipation and position control. A slit unit has a series of fifteen laser-machined slits with 1 mm space along the direction of the separation channel of the microchip above this unit. The laser beam was focused through a slit with 50 μm width to the separation channel at the position of a desired length. Although the excitation source unit was connected to a simple current controlled power supply, it was stable with 0.1% drift per hour and 1.3% (1σ) fluctuation in intensity. This simple excitation source can be prepared easily with inexpensive minimum optical components and mounted with a microchip on the stage of an ordinary fluorescence microscope for daily separation studies using a CE or CEC microchip. The applicability of the excitation source was evaluated with FITC-amino acid derivative mixtures using a polymer based CEC microchip packed fully with submicron silica beads in its microchannel.     

Study on the coil–globule transition and dynamics of polymer chain confined in slit

The coil–globule transition and dynamics of a lattice self‐avoiding bond fluctuation polymer chain confined in slit are studied by Monte Carlo simulations. The coil–globule transition temperature of polymer chain is increased at intermediate slit height H (H ∼ R_G0 with R_G0 the radius of gyration of polymer in dilute solution) due to the squeeze of the polymer in the repulsive slit, but it is decreased by surface attraction as the polymer is extended along the surface. We have compared the difference between the rotational relaxation time τ_R for the reorientation of end‐to‐end vector and the relaxation time τ for the polymer diffusing over a distance of the size of polymer. We find that τ_R is clearly distinct from τ as they have different scaling exponents in their slit height‐dependent behaviors and for the polymer in the extended coil state, that is, α_R > α. And both exponents increase with an increase in the intrapolymer attraction and surface attraction. However, these scaling relations are destroyed by strong surface attraction when the polymer is adsorbed on surfaces. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1053–1062     

Experimental characterization of straight spectrometer slits

A technique for calibrating slit width for straight spectrometer slits based on the diffraction of laser radiation is described. Related slit properties and calibration apparatus are discussed.     

The asymptotics of distribution functions in fluid-filled finite slits

Asymptotic formulas have been derived for distribution functions in cylindrical slits with finite cross-section radii. The problem has been solved based on the asymptotic principle of interbody interactions within the framework of dispersion forces. Symmetric and asymmetric slits between two identical cylinders and between a cylinder and a planar infinite solid surface have been considered. Calculations have been performed for a symmetric slit with a width equal to two cylinder radii.     

Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

Tangential and nondiagonal components of pressure in a circular slit

Two local tangential and one nondiagonal components of the pressure tensor have been calculated inside circular plane-parallel empty slits with dispersion forces. Symmetric and asymmetric slits have been considered. The spatial dependences have the same character for both tangential components, although their absolute values are somewhat different. It has been shown that, in the symmetric slit, the corrections for its finite size to the tangential pressure appear to be larger than those to the normal pressure. The nondiagonal pressure component becomes noticeable only near the edges of narrow slits.     

Free energy and dimensions of macromolecules under confinement in layered assemblies

The changes in the free energy ΔA accompanying penetration of polymer solutions from bulk into slit-like cavities were determined by lattice simulations. In dilute solutions the thermodynamics of penetration is controlled mainly by the parameter ϵ_w specifying interaction between polymer and walls of repulsive or adsorptive cavities. However, the magnitude of |ΔA| is substantially reduced by increasing concentration ∅︁ in bulk solution. Furthermore, compression of chains by concentration in good solvents and adsorptive cavities was found to be larger in the slit then in the bulk. At intermediate confinement, a region of a minimum coil size was observed at all concentrations and attraction strengths, where molecules are squeezed along all three axes.     

Properties of branched confined polymers

A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain's local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out.