The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h (h is the distance between two plates), until a basin occurs, and a universal h/〈R _g〉₀ dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain’s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.     

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.     

平行板间高分子链构象熵的动力学Monte Carlo模拟

用动力学Monte Carlo方法模拟了受限于两平行板之间的高分子链,并用扫描法计算了链的构象熵S,研究了构象熵相对于自由链的减小量(S0-S)与平行板间距D和高分子链长n的关系.结果证实了de Gennes的自由能标度关系,并给出了标度关系适用的范围.当D非常小时,高分子链受到强烈限制,S0-S与n成正比,表明单链节受到平行板的平均排斥作用力与链长无关.随着D增大,平行板对构象熵的影响越来越弱,单链节受到平行板的平均排斥作用力随链长的增长而增大.当D比较大时,平行板对构象熵的影响近似可以忽略,高分子链构象熵与自由空间中的结果一致.     

Structure of an associating polymer melt in a narrow slit by molecular dynamics simulation

Molecular dynamics simulation has been used to study the equilibrium properties of a generic coarse-grained polymer melt with associating terminal groups, confined in a narrow slit by two atomically smooth walls. Simulations were carried out as a function of wall separation and attracting strength as well as polymer end-end interaction strength. We find that confinement has an important effect on the melt properties. In particular, strongly attracting walls can produce radical changes in chain conformation, the nature of the transient network, and the structure of the aggregates formed by the associating terminals.     

Concentration dependence of the global and anisotropic dimensions of confined macromolecules

The chain dimensions 〈R²〉 of nondilute polymer solutions confined to a slit of the width D were studied using lattice simulations. It was found that the chain compression induced in good solvents by the concentration ϕ is enhanced in a slit relative to the bulk. The global dimensions of chains also change with ϕ in confined and unconfined theta solutions. At intermediate slit widths, a region was noted where coils are squeezed along all three axes. This region is manifested as a channel on the three‐dimensional surface 〈R²〉(D,ϕ) in both good and theta solvents. The coil anisotropy, given by the ratio of the parallel and perpendicular components of the chain dimensions 〈R_y²〉/〈R_x²〉, reaches high values at strong confinements, where coils form quasi‐two‐dimensional pancakes. The concentration‐induced reduction of the global chain dimensions in good solvents is almost fully transmitted to the parallel component 〈R_y²〉. The computed effects of concentration and confinement were compared with the predictions of mean‐field and scaling theories, and implications of the results to ultrathin films and layered nanocomposites were discussed. In addition, the distribution functions of the components of the end‐to‐end distance R perpendicular and parallel to the plates, W (R_x) and W (R_y), were calculated. The function W (R_x) combined with the concentration profile ϕ (x) along the pore provided details of the chain structure close to walls. A marked difference in the pace of the filling up of the depletion layer was noticed between chains in theta and good solvents. From the distribution functions W (R_x) and W (R_y), the highly anisotropic force‐elongation relations imply the deformation of chains in confined solutions and ultrathin bulk films.     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

Applicability of polymer theories to the thermodynamics of proteins at the air/water interface: example of β-lactoglobulin

Knowledge of the equation of state of adsorbed or deposited layers of proteins at the air/water interface is of fundamental interest in the understanding of the surface activity of these molecules. Using scaling laws of current polymer theories, it has been shown that the equation of state of the interfacial layer in the semi-dilute regime should relate the surface pressure to the surface concentration through a power law. The exponent of this power law should reflect the quality of the solvent and the conformation of the adsorbed polypeptide chain. In the case of β-lactoglobulin layers, in the range of surface concentrations that should correspond to the semi-dilute regime, the relationship between surface pressure and surface concentration is expressed as a power law. The exponent of this power law is strongly influenced by the nature of the aqueous substrate and by the net charge of the protein molecule. The use of scaling laws gives a coherent view of the expansion of the polypeptide chain in the interfacial layer and of the relationship between surface concentration and surface pressure in the semi-dilute regime. This result favours a strong similarity between β-lactoglobulin and a polymer chain in the interfacial layer. It is concluded that current theories of polymer adsorption could be applied to interfacial protein layers.     

Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement

We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation time of the chain, tau, with the chain length N and pore diameter D. An earlier scaling analysis based on the de Gennes blob picture led to tau approximately N(2)D(13). Our numerical effort that combines molecular dynamics and Monte Carlo simulations, however, consistently produces different tau results for N up to 2000. We argue that the previous scaling prediction is only asymptotically valid in the limit N"D(53)"1, which is currently inaccessible to computer simulations and, more interestingly, is also difficult to reach in experiments. Our results are thus relevant for the interpretation of recent experiments with DNA in nano- and microchannels.     

Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献   

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.     

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.     

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.     

Structure of flexible and semiflexible polyelectrolyte chains in confined spaces of slit micro/nanochannels

Understanding the behavior of a polyelectrolyte in confined spaces has direct relevance in design and manipulation of microfluidic devices, as well as transport in living organisms. In this paper, a coarse-grained model of anionic semiflexible polyelectrolyte is applied, and its structure and dynamics are fully examined with Brownian dynamics (BD) simulations both in bulk solution and under confinement between two negatively charged parallel plates. The modeling is based on the nonlinear bead-spring discretization of a continuous chain with additional long-range electrostatic, Lennard-Jones, and hydrodynamic interactions between pairs of beads. The authors also consider the steric and electrostatic interactions between the bead and the confining wall. Relevant model parameters are determined from experimental rheology data on the anionic polysaccharide xanthan reported previously. For comparison, both flexible and semiflexible models are developed accompanying zero and finite intrinsic persistence lengths, respectively. The conformational changes of the polyelectrolyte chain induced by confinements and their dependence on the screening effect of the electrolyte solution are faithfully characterized with BD simulations. Depending on the intrinsic rigidity and the medium ionic strength, the polyelectrolyte can be classified as flexible, semiflexible, or rigid. Confined flexible and semiflexible chains exhibit a nonmonotonic variation in size, as measured by the radius of gyration and end-to-end distance, with changing slit width. For the semiflexible chain, this is coupled to the variations in long-range bond vector correlation. The rigid chain, realized at low ionic strength, does not have minima in size but exhibits a sigmoidal transition. The size of confined semiflexible and rigid polyelectrolytes can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at long length scale.     

Equilibrium dynamics of an associating polymer melt in narrow slits by computer simulation

Molecular dynamics simulations have been used to study the dynamics of a coarse-grained model of a melt of polymer chains with associating terminal groups, confined in a narrow slit by two layers of Lennard-Jones sites. Simulations were carried out as a function of wall separation and attracting strength. We found that confinement has an important effect on the overall dynamics of the system. Strongly attracting walls can significantly modify the dynamics of the melt, giving an aggregation structure with extremely long relaxation times. A noticeable degree of anisotropy was found for the dynamics of both the individual chains and the aggregates formed by the associating terminal groups.     

Unmixing of polymer blends confined in ultrathin films: crossover between two-dimensional and three-dimensional behavior

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16 infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.     

Studies on the behavior of nanoconfined homopolymers with cyclic chain architecture

We have performed Monte Carlo simulations to study the effect of cyclic architecture on the behavior of homopolymer chains under several conditions of confinement. The collapse of the rings in two stages, a coil-to-globule and a liquidlike-to-solidlike transition, was observed even at extreme confinement. Both transitions were observed at lower temperatures than for linear chains of the same length, 2%-5% lower for unconfined systems, and 10%-15% lower for wall separations below three bond lengths due to the effect of confinement. When the plates separation approached the two-dimensional regime, the coil-to-globule transition shifted to lower temperatures. The inverse trend was observed when the chain length was increased. In the collapsed state, the average size and conformations of linear and cyclic molecules of same length were similar independently of confinement. At temperatures near the coil-to-globule transition, the radius of gyration of unconfined linear chains, [R(g)(2)](linear), became larger than for the cyclic chains, [R(g)(2)](cyclic), and this difference increased considerably with confinement. The radius of gyration ratio [R(g)(2)](linear)/[R(g)(2)](cyclic) in this region decreased rapidly. The decrease was more pronounced and occurred at lower temperatures for slit width confinements. At higher temperatures, in the coil state, the radius of gyration ratio became nearly constant for a given separation, and varied from 0.56 for unconfined systems to 0.47 when the chain was completely confined between the walls. This reduction was attributed to the higher increase in the average size of linear chains with confinement when compared with cyclic chains, due to architectural restrictions.     

Modulation of ionization and structural properties of weak polyelectrolytes due to 1D, 2D,and 3D confinement

What is the impact of reducing the space available to molecules onto their properties is a fundamental question for capillary systems, molecular biology and transport, protein and material sciences. Possibly influenced by space restriction, ionization degree has rarely been studied for confined polyelectrolytes; Monte Carlo titrations and coarse‐grained models are thus used to investigate structural and ionization changes induced on a single polyelectrolyte chain by confinement into slit (1D), cylindrical (2D), or spherical (3D) cavities. Four polyelectrolyte models differing in chain stiffness and the possible formation of charged hydrogen bonds (c? H? bonds) are studied. Low pH effective ionization constants (pK_a ) of confined chains are lower than for the free species if c? H? bonds can be formed. This is especially evident for 3D‐confined stiff chains, a finding rationalized by the impact of global compression onto chain conformations. If no c? H? bonds are allowed, chain ionization is largely unaffected by 1D or 2D confinement, while it is depressed by 3D. Chain confinement Helmholtz energy (ΔA _conf) was computed as a function of both pH and confining width (W) to gauge the impact of ionization‐induced stiffening onto ΔA _conf versus W behavior, the partition coefficient governing absorption, and the average number of c? H? bond formed. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 1088–1102     

Numerical Simulation of the Distribution Function and Free Energy of a Single Wormlike Polymer Confined between Hard Walls

We focus on the distribution and free energy of a wormlike polymer confined between two parallel hard walls.The variation in the distribution and free energy of the wormlike chain as the spacing between the walls decreases(or as the total contour length of the wormlike chain increases or as the persistence length of the chain increases)is simulated.The main reason for these changes is a degradation of the long wormlike chain into a Gaussian long chain under weak confinement.     

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.     

Bottom-up self-organizing dissipative polymer nanostructures

Based on scaling concepts a methodology of research of non-equilibrium polymer systems has been elaborated. Polymers with flexible chains (melt-crystallized linear high density polyethylene is chosen as an example) are solutions in melt as well as in solid state, the ends of a chain serving as a solvent for it. At critical polymerization degree all phases (melt, solid isotropic or oriented state) are identical. The square of the neck draw ratio is equal to the product of the square of the draw ratio at break and the chain ends collision probability. This probability in its turn is proportional to the average thickness of amorphous layers in the isotropic material. Depending on the type of polymer statistics (Gauss or Lévy–Khinchin) and the number of components of an ordering field for the second case, the melt viscosity and the self-diffusion coefficient vs. the molecular weight of linear flexible-chain polymer follow the power laws with the 3.50, 3.41 or 3.33 and −2.50, −2.05 or −1.65 exponents, respectively, within the reptation model near the critical point. Vibrational–rotational Brownian motions of chain ends about the polymer melt flow direction were taken into account to find better agreement with the experiment. The recent experimental results of dynamic mechanic and dielectric spectroscopy show the value 3.5 ± 0.1 for the viscosity exponent of long chains, while NMR data result in −2.3 ± 0.1 for the self-diffusion coefficient exponent of short chains. Possible reasons are discussed.