Elastic behavior of single polymer chains adsorbed on rough surfaces

In this paper, elastic behaviors of single polymer chains adsorbed on the rough surfaces with a substrate and some periodically tactic pillars are investigated by the pruned-enriched-Rosenbluth method (PERM). In our simulation, a single polymer chain is firstly adsorbed on the substrate and then pulled along the z-axis direction, which is vertical to the substrate. We investigate the chain size and shape of polymer chains, such as mean-square radii of gyration per bond 〈S²〉_xy/N, 〈S²〉_z/N and shape factor 〈δ^∗〉 in order to show how the size and shape of adsorbed polymer chains change during the desorption process. Due to the occurrences of separation of the chains from the substrate, farther adsorption on the upper surfaces of pillars and complete separation from the whole rough surfaces in the elastic process, the changes of 〈S²〉_xy/N, 〈S²〉_z/N and 〈δ^∗〉 during the process are complicated. On the other hand, some thermodynamic properties such as average energy per bond, average Helmholtz free energy per bond, elastic force f are investigated, and our aim is to study the elastic behaviors of polymer chains adsorbed on the rough surface during the elasticity process. Elastic force f has some plateaus during the desorption process for strong adsorption interaction. If there is no adsorption interaction, the chains can get away from the rough surfaces spontaneously. These investigations can provide some insights into the elastic behaviors of polymer chains adsorbed on the rough surface.     

Elastic behavior of ring polymer chains

In this article, the conformational properties and elastic behaviors of ring polymers in the process of tensile elongation are investigated with the Monte Carlo method and the bond fluctuation model. The ratio of the mean‐square diameter <d²> to the mean‐square radius of gyration <S²> increases with the elongation ratio, λ, and the instantaneous shape of ring polymers is more symmetric than that of linear chains in the process of tensile elongation. Here <d²> for ring polymers rather than the mean‐square end‐to‐end distance <R²> for linear polymers is defined as the average of squared distances between two segments separated by N/2 bonds, where N represents the total number of bonds. Local quantities, that is, the mean‐square bond length <b²> and the mean bond angle <θ> increase with λ, especially for short ring chains. The <d²> and <S²> have the same relationship with the chain length, N, that is, <d²> ～ N^1.130±0.020 and <S²> ～ N^1.160±0.013 for a different λ. Some thermodynamics properties are also addressed here. The average energy per bond <U> decreases with λ and the average Helmholtz free energy and elastic force f increase with λ, especially for short ring chains. Comparisons with linear chains are also made. These investigations may provide insight into the elastic behaviors of ring polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 223–232, 2005     

Elastic behavior of comb-like polymer chains

<正>Three-dimensional Monte Carlo simulations of comb-like polymer chains with various backbone lengths N_b,arm lengths N_a and arm densities m are carried out to study the elastic behavior of comb-like polymer chains.The radius of gyration,the shape factors and bond length in different cases during elastic process are calculated,and it is found that the comb-like polymer molecules with longer backbone or shorter arm are more close to linear chains.But the arm density m affects the chain conformation non-monotonously.Some thermodynamic properties are also studied.Average Helmholtz free energy and elastic force f all increase with elongation ratioλfor all chains.     

Elastic behavior of uniform star polymer chains

Elastic behaviors of uniform star polymer chains with two to seven branches (namely, functionality f = 2-7) are investigated using Monte Carlo simulation and the bond fluctuation model. Here chain dimensions and thermodynamic properties of uniform star polymer chains during the process of tensile elongation are studied, and comparisons with linear chain are also made. Static properties of chains such as chain sizes and asphericities of chains are calculated, and g-value of g = 〈S²〉_star/〈S²〉_linear decreases with elongation ratio increasing for different functionality f. Thermodynamic properties such as average energy 〈U〉, free energy per bond 〈A′〉 and elastic force F are also investigated during the process of tensile elongation. In the meantime, scatting functions P(q) are calculated for star polymer chains with different functionality f. Additionally, we also discuss the influence of elongation ratio on scattering form factor. The impenetrability of the star cores is known to cause a discontinuity in the osmotic pressure showed through a peak in the scattering functions, and some different behaviors in the tensile process for uniform star chain are obtained.     

A steered molecular dynamics simulation on the elastic behavior of adsorbed star polymer chains

<正>Elastic behavior of 4-branched star polymer chain with different chain length N adsorbed on attractive surface is investigated using steered molecular dynamics(SMD) simulation method based on the united-atom(UA) model for branched alkanes.The simulation is realized by pulling up the chain via a linear spring with a constant velocity v = 0.005 nm/ps.At the beginning,the chain lies extensionally on adsorbed surface and suffers continuous deformations during the tensile process.Statistical parameters as mean-square radii of gyration S~2_(xy),S~2_z,shape factor δ,describing the conformational changes,sectional density den which gives the states of the chain,and average surface attractive energy U_a,average total energy U,average force f probed by the spring,which characterize the thermodynamic properties, are calculated in the stimulant process.Remarkably,distinguishing from the case in linear chains that there only exists one long plateau in the curve of f,the force plateau in our study for star chains is multiple,denoting different steps of desorption,and this agrees well with the experimental results in essence.We find during the tensile process,there are three characteristic distances Z_c,Z_t and Z_0 from the attractive surface,and these values vary with N.When Z=Z_c,the chain is stripped from the surface,but due to the form of wall-monomer interaction,the surface retains weak influence on the chain till Z = Z_c.From Z=Z_t,parameters U_a,U and f respectively reach a stable value,while the shape and the size of the chain still need adjustments after Z_t till Z_0 to reach their equilibrium states.Specifically,for short chain of N= 41,Z_t and Z_0 are incorporated.These results may help us to deepen the knowledge about the elastic behavior of adsorbed star polymer chains.     

Elastic behavior of non-Gaussian polymethylene chains

In this paper, elastic behaviors of non-Gaussian polymethylene (PM) chains with chain length N=100 are investigated by rotational isomeric state model. Here the tetrahedral lattice of PM chain and the non-local interaction of Sutherland potential are adopted. In the metropolis movement of PM chain, a four-bond movement model is used. The average energy and average Helmholtz free energy with various elongation ratios λ are calculated by Monte Carlo simulation method. The average energy increases with elongation ratio λ and the average Helmholtz free energy decreases with elongation ratio λ. The elastic force f and the energy contribution to elastic force f_u can be obtained from f=∂〈A〉/∂r and f=∂〈U〉/∂r. We find that the elastic force f increases with elongation ratio λ and the energy contribution f_u decreases with elongation ratio λ, and f_u is less than zero. The ratio f_u/f is close to −0.21 for λ?1.25, and −0.04 to −0.35 for λ>1.25 at T=364 K. In our calculation, the rubber elasticity may be discussed in terms of the chemical structure of polymer chains.     

Phase behavior of semiflexible polymer chains

Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01sigma and 1.05sigma (where sigma is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02sigma and 2.1sigma. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10相似文献   

Elastic behavior of poly(ethylene terephthalate) chains

The Monte Carlo (MC) method based on the rotational-isomeric-state (RIS) model is adopted in studying the elastic behavior of poly(ethylene terephthalate) (PET) chains in this paper. The mean-square end-to-end distance 〈R²〉, the mean-square radius of gyration 〈S²〉, and the ratio of 〈R²〉/〈S²〉 all increase with elongation ratio λ. The interior conformations are also investigated through calculating the a priori probability of rotational state in the process of tensile elongation. The radius of gyration tensor S is introduced here in order to measure the shape of PET chains, and increases with elongation ratio λ, however, some different behaviors are obtained for . Here , and are the eigenvalues of the radius of gyration tensor . The average energy per repeat unit 〈U〉 and the average free energy per repeat unit 〈A〉 are also calculated, and we find that the average energy decreases with elongation ratio λ, however, the average free energy per repeat unit increases with elongation ratio λ. Elastic force f, energy contribution to force f_U, and entropy contribution to force f_S are also investigated. Both elastic force f and entropy contribution to force f_S increases with λ, however, energy contribution to force f_U and the ratio f_U/f decreases with λ. The ratio of f_U/f is less than zero and almost independent of chain length. The results of these microscopic calculations may explain some macroscopic phenomena of rubber elasticity.     

Dynamics of adsorbed polymer chains subjected to flow: The dumbbell model

The dumbbell model of an adsorbed polymer segment is analyzed in order to investigate the response of such segments to a velocity gradient imposed at the solid/liquid interface. It is demonstrated that exact expressions for the time-dependent moments of the distribution function describing the conformation can be obtained. Both a dangling end and an attached loop can be represented and several bulk properties of a polymer film subjected to flow are evaluated.     

Steered molecular dynamics simulation of elastic behavior of adsorbed single polyethylene chains

We investigate the dynamics of the detachment of single polyethylene (PE) chains from a strongly adsorbing surface in vacuum using a united atom model. Various statistical properties, including the mean‐square end‐to‐end distance 〈R²〉, the mean‐square radii of gyration , , the shape factor , the torsion angle distribution, the average surface adsorption energy , the average total energy , and the average force , are analyzed. The relationship between the average force and the pulling velocity v shows two distinctive regions: a weakly dependence region at Å/ps and a strongly dependence region at Å/ps. Remarkably, the PE chain manifests force hysteresis under sequential stretching and releasing. These investigations may provide some insights into the elastic behavior of adsorbed polymer chains. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2322–2332, 2007     

Elastic behavior of short compact chains confined in double parallel boundaries

Adsorption of short two-dimensional compact chains confined in the double attractive parallel planar boundaries is investigated by using enumeration calculation method in this paper. First, we calculate the chain size and shape of adsorbed compact chains, such as mean-square end-to-end distance per bond R²/N, mean-square radii of gyration per bond S²_x/N and S²_y/N, shape factor δ and fraction of adsorbed segments f_a to illuminate that how the size and shape of adsorbed compact chains changes during the process of tensile elongation. There are some special behaviors in the chain size and shape for strong attraction interaction. In the meantime, compact chains can reach to the stable state with large distance between two parallel boundaries D. On the other hand, some thermodynamic properties, such as average energy per bond, Helmholtz free energy per bond, elastic force f and energy contribution to elastic f_U are also investigated in order to study the elastic behavior of compact chains adsorbed on the double attractive parallel planar boundaries. These investigations may provide some insights into the thermodynamic behaviors of adsorbed compact chains.     

Bead–spring model for adsorbed polymer chains in shear flow: Hydrodynamic interaction

We consider the hydrodynamic interaction between two absorbed polymer chains in a simple shear flow, each modeled by a bead connected to the wall by a linear spring. It is concluded that hydrodynamic interaction between the beads or between the beads and the wall cannot be responsible for the experimentally observed increase in hydrodynamic thickness.     

Beyond the born approximation. The case of very long polymer chains adsorbed at an interface

Two experimental evidences are discussed of the reflectance discontinuity associated with very long adsorbed polymer chains. The anomalous low reflectivity is compared to the Ramsauer-Townsend effect in the scattering of slow electrons by rare-gas atoms.     

Crystallization of short aliphatic polymer chains. I. General chain-folding behavior

Short aliphatic polymer chains of different lengths were prepared by degrading polyethylene samples of appropriately chosen initial fold lengths to the chain lengths which correspond to a single chain traverse through the lamella. The resulting dicarboxylic acids were either used as such for further crystallization experiments or were first converted into diiodides to remove polar endgroups. The resulting short polymers all crystallized by chain folding even if the chains (peak of distribution) were only 1.5–4 times the length of a traverse through the lamella. In the diiodides the fold length varied continuously with crystallization temperature, as is usual in high molecular weight material, but with the dicarboxylic acids such variation, while observable, was only small. The effect of the molecular weight on the fold length due to its influence on supercooling at a given crystallization temperature has become apparent. Renewed degradation with nitric acid and subsequent GPC analysis of the degradation products confirmed the folded nature of the chains in the above crystals. This analysis combined with experiments on the reactivity of chain ends has led to the picture that each chain folds completely, once, twice etc. so that both folds and ends are in the surface zone but are located at varying heights, as appropriate to the overall layer thickness for the molecular weight distribution in question. This picture is consistent with other concurrent work.     

Shape instabilities in adsorbed polymer condensates

A polymer chain in a poor solvent collapses to a spherical globule. If this globule is subsequently deformed, either by stretching it or if it has some non-zero net electric charge, it will become unstable to sinusoidal perturbations leading to novel final states. When such globules are imaged by direct methods such as atomic force microscopy the substrate on which they adsorb can affect the final morphological state. We therefore investigate strongly adsorbed polymers in poor solvents. We demonstrate that the real-space, Self-Consistent Field method is an ideal numerical tool in predicting equilibrium morphologies. New structures are predicted, which support previous explicit free energy calculations. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3327–3337, 2007     

Interaction forces between adsorbed polymer layers

The interaction forces between adsorbed polymer layers were investigated. Two types of graft copolymers that were adsorbed on hydrophobic surfaces have been investigated: (i) a graft copolymer consisting of polymethylmethacrylate/polymethacrylic acid back bone (the B chain) on which several poly(ethylene oxide) chains are grafted (to be referred to as PMMA/PEO_n); and (ii) a graft copolymer consisting of inulin (linear polyfructose with degree of polymerization > 23) (the A chain) on which several C₁₂ chains are grafted (INUTEC SP1). In the first case adsorbed layers of the graft copolymer were obtained on mica sheets and the interaction forces were measured using the surface force apparatus. In the second case the interaction forces were measured using Atomic Force Microscopy (AFM). For this purpose a hydrophobically modified glass sphere was attached to the tip of the cantilever of the AFM and the glass plate was also made hydrophobic. Both the sphere and the glass plate contained an adsorbed layer of INUTEC SP1.In the surface forces apparatus one essentially measures the energy E(D)–distance D curves for the graft copolymer of PMMA/PEO_n between mica surfaces bearing the graft copolymer and this could be converted to interaction energy between flat surfaces. Using the de Gennes scaling theory, it is possible to calculate the interaction energy between the polymer layers. The same graft copolymer was used in latex dispersions and the high frequency modulus G′_∝ was measured as a function of the volume fraction ? of the dispersion. This high frequency modulus could be related to the potential of mean force. In this way one could compare the results obtained from rheology and those obtained from direct measurement of interaction forces.In the AFM method, the interaction forces are measured in the contact area between two surfaces, i.e. a spherical glass particle and a glass plate. Both glass spheres and plates were hydrophobized using dichlorodimethylsilane. Results were obtained for adsorbed layers of INUTEC SP1 in water and in the presence of various concentrations of Na₂SO₄ (0.3, 0.8, 1.0 and 1.5 mol dm^{− 3}). All results showed a rapid increase of force with a decrease of separation distance and the forces were still repulsive up to the highest Na₂SO₄ concentration. This explains the high stability of dispersions when using INUTEC SP1 as stabilizer.     

Steady-state properties and dynamic behavior of polymer chains in dilute solution under elongational flow

The behavior of polymer chains in dilute solution under a steady, homogeneous elongational flow has been studied employing Brownian dynamics simulation. We first consider the dependence of polymer properties in steady state on the elongational rate, ϵ. When this rate exceeds some critical value, ϵ_c, the properties show a dramatic change from the values typical of the coil state to those of a stretched conformation. We describe the dependence of ϵ_c on chain length for different polymer/solvent conditions. Following the trajectories of individual molecules, we have characterized dynamic aspects of the coil-stretch transition. Each chain suffer the transition after some time, t_trans, has elapsed after the flow start-up. The values of t_trans vary remarkably from one molecule to another, and we have characterized the statistical distribution of this quantity. We also determine the kinetics of the coil-to-stretch process, which seems to follow a first-order kinetics after some induction time. The dependence of the statistical and kinetic parameters on chain length and elongational rate has been determined.     

MMX polymer chains on surfaces

Fibres of [Ru(2)Br(micro-O(2)CEt)4]n polymer have been isolated on different surfaces under specific conditions, and morphologically characterised by AFM and STM, showing an unexpected helical internal structure.     

Electrostatic sums for polymer chains

A rapidly convergent expression is given for calculating the Madelung energy of infinite linear polymers with small radius.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday