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1.
Depletion interactions between colloidal particles in polymer solutions: density functional approach
A density functional theory for colloid–polymer mixtures based on the weighted-density approximation has been developed to investigate the depletion effects acting between two colloids immersed in a bath of polymers and the depletion effects for a colloid near a planar hard wall. The theoretical results for the polymer-induced depletion interactions and the local polymer density distributions are in good agreement with the computer simulations. The calculation shows that the depletion interaction for a colloid near a planar hard wall is much stronger than that between two colloids in a polymer solution because of the strong confinement effect. The behaviour of the depletion interactions has been analysed as a function of the polymer density, the polymer chain length, and the colloid/polymer size ratio. Strong depletion effects appear in short-chain systems and with large colloid/polymer size ratios. 相似文献
2.
Milchev A 《The European physical journal. E, Soft matter》2002,8(5):531-537
An off-lattice bead-spring model of self-assembling equilibrium ("living") polymers is used to study the polymer-induced interaction between parallel walls immersed in polydisperse solutions of different concentration by means of Monte Carlo simulation. The two walls form an open slit in contact with an external reservoir so that the confined system may exchange monomers with the surrounding phase and adapt its polydispersity in order to relax the confinement constraint. We find that the properties of the polymers in the constrained system as well as the net force deltaF acting on the walls depend essentially on the polymer concentration in the reservoir which leads to qualitative differences in their behavior with changing inter-planar distance H: In a dilute polymer solution at concentration phi below the semi-dilute threshold phi* the force between the walls is attractive and decreases steadily with growing wall separation H, so that deltaF approximately 0 at H/ Rg> or =3 if H is measured in gyration radii Rg of the unperturbed polymers. The total monomer concentration within the slit is smaller than the concentration in the reservoir and decreases monotonically with H/Rg-->0. The ratio Nin/Nout of mean chain length Nin in the slit to that in the reservoir, Nout, decreases from unity at H-->infinity, goes through a minimum at H/Rg approximately 1, and then rises again to Nin/Nout>1 for wall separations H/Rg<1. In contrast, in a dense solution of equilibrium polymers at phi>phi* one detects no indirect wall-wall interaction, deltaF approximately 0, for H larger than the monomer size. Thus, earlier speculations about the existence of possible depletion interaction between parallel walls even in a dense polymer system cannot be confirmed. Inside the slit the monomer density is found to be always larger than in the reservoir while Nin/Nout<1 and decreases steadily as H/Rg-->0. The depletion force between parallel plates has been determined also in a monodisperse solution of conventional polymers. Qualitatively the force behavior does not differ from that of living polymers. 相似文献
3.
In present work, using density functional theory and extended restricted orientation model, the one particle density of hard Gaussian overlap fluid near the colloid walls is calculated. The hard needle–wall interaction between molecules and colloids are considered. Using non-linear equation, proposed by Grimson–Rickyazen, the solvation force of hard ellipsoidal molecular fluid with hard Gaussian overlap interaction is calculated. We could not find the exact or simulation results for comparison. The results in the case k = 2.0 are compared with the solvation force of one-dimensional hard rod fluids. The results are corresponded, qualitatively. 相似文献
4.
A. Bringer E. Eisenriegler F. Schlesener A. Hanke 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(1):101-119
The attractive depletion interaction between a spherical particle and a planar wall in a dilute solution of long flexible
nonadsorbing free polymer chains is found to depend crucially on the particle to polymer size ratio . While the polymer-induced force between particle and wall decreases monotonically with increasing distance for large , for small it has a maximum at a distance of the order of the polymer size. For ideal chains we study the crossover from large to small behavior in full quantitative detail. Besides the free energy of interaction and the force, we also discuss the spatial variations
of the densities of chain-ends and chain-monomers near the wall and particle. Two independent procedures, (1) solving directly
the diffusion equation for the density of ends in terms of planar and spherical waves and (2) minimizing the Ginzburg-Landau
functional of the “magnetic analog” of the polymer problem, are used to obtain results numerically for a broad range of ratios of the three lengths particle size, polymer size and distance of particle from the wall. Besides
previously known cases, we find two more interesting limiting regions of the length ratios for which analytical results can be obtained. [2mm]
Received 11 December 1998 相似文献
5.
Shiqi Zhou 《The European physical journal. E, Soft matter》2000,3(4):343-353
A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding
interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation
in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and
the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation
function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick
(PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption
isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous
theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the
most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two
hard walls immersed in polymer melts are consistent with the experimental results available in the literature.
Received 18 April 2000 相似文献
6.
We map dilute or semidilute solutions of nonintersecting polymer chains onto a fluid of "soft" particles interacting via a concentration dependent effective pair potential, by inverting the pair distribution function of the centers of mass of the initial polymer chains. A similar inversion is used to derive an effective wall-polymer potential; these potentials are combined to successfully reproduce the calculated exact depletion interaction induced by nonintersecting polymers between two walls. The mapping opens up the possibility of large-scale simulations of polymer solutions in complex geometries. 相似文献
7.
Stretched polymers will lose their possible configurations if they are mixed with nanoparticles or touch a hard wall,which leads to a strong depletion attraction responsible for the enrichment of nanoparticles near substrates.Moreover,it is found that there exists a sacrifice mechanism in confined pure polymer samples or polymer-nanoparticle mixtures,that part of the polymers,in order to reach a minimum free energy for the total system,are adsorbed on hard walls even though they lose their conformation.The current study provides a simple yet effective approach for the design of thin polymer composites. 相似文献
8.
The depletion potentials between two infinite planes, and between two large spheres, due to polydisperse mixtures of non-interacting polymer coils and of interacting small hard spheres, are calculated over a wide range of polydispersities and of polymer or colloid concentrations. The case of non-interacting polymers can be treated analytically within a generalization of the Asakura-Oosawa model. The more difficult case of a polydisperse bath of hard spheres is treated within Rosenfield's ‘fundamental measure’ formulation of density functional theory. Polydispersity is found to have little effect on the depletion attraction, but to strongly reduce the repulsive barrier due to correlation and to damp the subsequent oscillations in the depletion potential. 相似文献
9.
Joanna Halun Pawel Karbowniczek Piotr Kuterba Zoriana Danel 《Entropy (Basel, Switzerland)》2021,23(2)
The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with arms in a -solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with , 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries. 相似文献
10.
A. Milchev J.P. Wittmer D.P. Landau 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,12(2):241-251
We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means
of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate
in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The
Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute
solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear
rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total
monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length
with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition
into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear
flow on this state is briefly examined.
Received 22 October 1998 and Received in final form 12 April 1999 相似文献
11.
Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance
(
is the Flory exponent). For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. We measure the densities of monomers and of end points as functions of the distance from the walls, the longitudinal extent of the chain, and the forces exerted on the walls. Their scaling with D and the universal ratio between force and monomer density at the wall are compared to theoretical predictions.Received: 14 August 2003, Published online: 8 December 2003PACS:
61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 07.05.Tp Computer modeling and simulation - 61.41. + e Polymers, elastomers, and plastics 相似文献
12.
The structural and thermodynamic properties of a confined hard ellipse fluid are studied using Monte Carlo simulation. The angular, average number densities and order parameters of hard ellipses confined between hard parallel walls are obtained for various bulk densities, aspect ratios and wall separations. The results show that the effect of the existence of the wall on the molecular fluid structure, either on their directions or their locations, with respect to the bulk, especially close to the walls, is significant. For this system the pressure is also obtained and it is shown that the average density at the wall is proportional to the pressure, βP=〈ρw〉. Our simulation results show that the order parameters depend on the number of the particles in the box unless it exceeds thousand. 相似文献
13.
The equilibrium density profiles in a classical multicomponent plasma near a hard wall made with a dielectric material characterized by a relative dielectric constant ∈w are studied from the first Born–Green–Yvon (BGY) equation combined with Poisson equation in a regime where Coulomb coupling is weak inside the fluid. In order to prevent the collapse between charges with opposite signs or between each charge and its dielectric image inside the wall when ∈w>1, hard-core repulsions are added to the Coulomb pair interaction. The charge-image interaction cannot be treated perturbatively and the density profiles vary very fast in the vicinity of the wall when ∈w≠1. The formal solution of the associated inhomogeneous Debye–Hückel equations will be given in Paper II, together with a systematic fugacity expansion which allows to retrieve the results obtained from the truncated BGY hierarchy. In the present paper the exact density profiles are calculated analytically up to first order in the coupling parameter. The expressions show the interplay between three effects: the geometric repulsion from the impenetrable wall; the electrostatic effective attraction (∈w>1) or repulsion (∈w<1) due to its dielectric response; and the Coulomb interaction between each charge and the potential drop created by the electric layer which appears as soon as the system is not symmetric. We exhibit how the charge density profile evolves between a structure with two oppositely-charged layers and a three-layer organization when ∈w varies. (The case of two ideally conducting walls will be displayed elsewhere). 相似文献
14.
ABSTRACT A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found. 相似文献
15.
《中国物理 B》2015,(7)
Structural properties of polymers confined in nanocylinders are investigated by Monte Carlo simulation, which is successfully used to consider the conformational property of constrained polymers. The conformational properties of the polymers close to the walls exhibit different features. The density profiles of polymers are enhanced near the wall of the nanocylinder, which shows that the packing densities differ near the wall and far from the wall. The highest densities near the wall of the nanocylinder decrease with increasing radius of the nanocylinder. Furthermore, the density excess is not only near the wall of the nanocylinder, but also shifts to the center of the nanocylinder at lower temperatures. The radius of gyration and the bond length of polymers in the nanocylinder show that the polymer chains tend to extend along the axis of the nanocylinder in highly confined nanocylinder and contract at lower temperature. Our results are very helpful in understanding the packing induced physical behaviors of polymers in nanocylinders, such as glass transition, crystallization,etc. 相似文献
16.
We investigate critical phenomena in colloids by means of the renormalization-group based hierarchical reference theory of fluids. We focus on three experimentally relevant model systems: namely, the Asakura-Oosawa model of a colloidal dispersion under the influence of polymer-induced attractive depletion forces; fluids with competing short-range attractive and longer-range repulsive interactions; solutions of star polymers whose pair potential presents both an attractive well and an ultrasoft repulsion at shorter distance. Our results show that the ability to tune the effective interactions between colloidal particles allows one to generate a variety of crossovers to the asymptotic critical behavior, which are not observed in atomic fluids. 相似文献
17.
We study the dynamic properties of asymmetric vortex Bloch walls and classical 1D Néel walls controlled by a spin-polarized current in magnetic films with in-plane anisotropy. It is shown that fairly high velocities of domain walls (up to 100 m/s) can be obtained for the current density in the range j = 106–108 A/cm2. The nonlinear dependence of the wall velocity on the film thickness and the linear dependence of the velocity on the current density and inverse damping parameter are found. 相似文献
18.
Star polymers with a high number of arms, f=263, become kinetically trapped when dispersed in an athermal solvent at concentrations above the overlapping one, forming physical gels. We show that the addition of linear chains at different concentrations and molecular weights reduces the modulus of the gel, eventually melting it. We explain this linear polymer-induced gel-liquid transition in terms of effective interactions and star depletion. In the limit of very high linear-chain molecular weight a "reentrant gelation" is detected and attributed to bridging flocculation, analogous to that observed in colloidal dispersions. 相似文献
19.
Nguyen T. Hieu Ha Grainne M. Moran 《Journal of Macromolecular Science: Physics》2013,52(10):1942-1975
Two parameters characterizing the branching features of polymers, branching density (BD), and branching completeness (BC), are proposed. Both have values of zero (0) for linear polymers. Branching density has the values of 1/2, 2/3, and (f – 2)/(f – 1) for the fully and densest branched polymers formed from tri-, tetra-, and f-functional monomers typed AB f –1. Branching completeness will reach the value of one (1) for a completely branched polymer, where all possible branching monomeric units have reacted at least tri-functionally and all units are either terminal or dendritic. Branching density is close to the mole fraction of terminal units, and BC is close to the mole fraction of dendritic and terminal units in the branching polymers. The major advantage of these parameters is their independence of the degree of polymerization (dp). Branching density depends on the functionalities (f) of monomer units; BC does not. The higher the fraction of the dendritic unit monomerically bonded to a higher number of other units (the higher the terminal units fraction), the denser branched the polymer and the higher the BD. The BC and BD can be used in a simple way for describing multicharacter branching systems and for comparing the branching characters among them without any theoretical limitations. Physical quantities (namely, the number of dendritic and terminal units and the degree of polymerization) used for BD and BC evaluation can be determined directly from practical analyses, where NMR is most useful. The BC and BD, however, do not concisely describe branching characteristics for a polymer with cyclization or crosslinking in its structure. 相似文献
20.
I. Y. Erukhimovich A. Johner J. F. Joanny 《The European physical journal. E, Soft matter》2008,27(4):435-445
We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space
to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral
equation for the partition function G
D(r,r′, N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r′ . The expression for G(r,r′, s) is found to be the sum of the commonly accepted Dirichlet result G
D(r,r′, N) = G
0(r,r′, N) - G
0(r,r”, N) , where r” is the mirror image of r′ , and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density
at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall
or contact theorem). A significant correction to the density profile (of magnitude 1/is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems
are discussed. 相似文献