Quantum-Monte-Carlo simulations of polyethylene

The diffusion Quantum-Monte-Carlo method of solving the Schr?dinger equation is applied to the vibrational ground state of a polyethylene molecule. The results for the ground state energy show good agreement with normal mode analysis. In addition to stretching, bending and torsional interaction van-der-Waals interaction is applied to a single chain showing a decrease of the energy of 5%. The decrease for a polyethylene system of 5 chains with 10 atoms per molecule at the positions of a unit cell is determined to be 4.8% per molecule. Finally first steps towards simulating excited states were performed. Received: 9 February 1998 / Revised: 2 April 1998 / Accepted: 23 April 1998     

Theory of gel point in real polymer solutions

We develop a new theory of gelation which takes into account (i) delay of the gel point and (ii) change of functionality due to ring formation. We show that the problem of finding the gel point in real polymer solutions reduces to the problem of calculating the total ring concentration and the extent of reaction of intermolecular reaction at the gel point. In this paper, we solve a special case of this problem, on the basis of the independence assumption between intermolecular reaction and cyclization which takes into account only (i) the delay of the gel point: making use of the asymptotic equality of the total ring concentration, we acquire an approximate solution for the gel point D_c as a function of the inverse concentration , the relative frequency of cyclization and dimension d. Applying the observed values of in linear polyesters, the theoretical result reproduces well the Wile and the Gordon-Scantlebury observations, showing the existence of a critical dilution beyond which gelation can not occur, and an asymptote . As the classical gel point is approached, the present theory reduces to the linear equation, which makes one-to-one correspondence with the real slope , suggesting the inequality which is just what polymer chemists have quested for so far, with the physical meaning having remained unknown. Receveid: 30 December 1997 / Revised: 28 May 1998 / Accepted: 12 June 1998     

Grafted polymers with annealed excluded volume: A model for surfactant association in brushes

We present an analytical self-consistent-field (SCF) theory for a neutral polymer brush (a layer of long polymer chains end-grafted to a surface) with annealed excluded volume interactions between the monomer units. This model mimics the reversible adsorption of solute molecules or aggregates, such as small globular proteins or surfactant micelles, on the grafted chains. The equilibrium structural properties of the brush (the brush thickness, the monomer density profile, the distribution of the end segments of the grafted chains) as well as the overall adsorbed amount and the adsorbate density profile are analyzed as a function of the grafting density, the excluded volume parameters and the chemical potential (the concentration) of the adsorbate in the solution. We demonstrate that, when the grafting density is varied, the overall adsorbed amount always exhibits a maximum, whereas the root-mean-square brush thickness either increases monotonically or passes through a (local) minimum. At high grafting densities the chains are loaded by adsorbed aggregates preferentially in the distal region of the brush, whereas in the region proximal to the grafting surface depletion of aggregates occurs and the polymer brush retains an unperturbed structure. Depending on the relative strength of the excluded volume interactions between unloaded and loaded monomers both the degree of loading of the chains and the polymer density profile are either continuous or they exhibit a discontinuity as a function of the distance from the grafting surface. In the latter case intrinsic phase separation occurs in the brush: the dense phase consists of unloaded and weakly extended chains and occupies the region proximal to the surface, whereas a more dilute phase consisting of highly loaded and strongly extended chains forms the periphery of the brush. Received 26 November 1998 and Received in final form 2 April 1999     

Anomalous adhesion in adsorbed polymer layers

Anomalous adhesion behaviour observed in the polydimethylsiloxane/heptane/silica system is reported. This behaviour is characterised by the infrequent appearance of one or more elastic minima which occur in addition to the ever-present primary adhesion. The resulting elastic force is attributed to loops connecting the tip to the substrate and can be described by two models; a worm-like chain, and a freely jointed chain. Both models give similar values for the characteristic segment length of around 0.24 nm and indicate that the chains have been extended by between 90 to 95% of their chain contour length before desorption. In some cases multiple adhesions were observed between tip and substrate and have been used to suggest a method for determining the distribution of adsorbed polymer loops. Received: 12 November 1997 / Accepted: 6 March 1998     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Calculation of scattering from stretched copolymers using the tube model: a generalisation of the RPA

There are many experimental situations in which polymer chains are constrained or localised into a small region of space (e.g. melt chains confined to a “tube”, network chains pinned by crosslinks). We show that detailed consideration of the quenched variables is vital in these experiments. This paper provides a crucial link between microscopic models with localising constraints and scattering patterns by a generalisation of the Random Phase Approximation (RPA) which allows for quenched translational variables. A method is developed which deals with correlations between the quenched variables brought about by incompressiblity (for example, in a polymer melt there are correlations between tubes because of the interaction between chains). As an example, the generalised RPA is applied to models based on the Warner-Edwards picture of the tube. Theoretical results for a melt of H-shaped copolymers are compared with experimental scattering. Early results suggest that to fit the scattering we may be forced to relax one of the central assumptions of the tube model; that the tube deforms affinely, that all chains retract by the same amount or that the tube diameter does not couple to the strain. Received 26 October 1998 and Received in final form 19 March 1999     

Polymer adsorption on heterogeneous surfaces

The adsorption of a single ideal polymer chain on energetically heterogeneous and rough surfaces is investigated using a variational procedure introduced by Garel and Orland (Phys. Rev. B 55, 226 (1997)). The mean polymer size is calculated perpendicular and parallel to the surface and is compared to the Gaussian conformation and to the results for polymers at flat and energetically homogeneous surfaces. The disorder-induced enhancement of adsorption is confirmed and is shown to be much more significant for a heterogeneous interaction strength than for spatial roughness. This difference also applies to the localization transition, where the polymer size becomes independent of the chain length. The localization criterion can be quantified, depending on an effective interaction strength and the length of the polymer chain. Received: 29 October 1997 / Revised: 19 December 1997 / Accepted: 6 March 1998     

Log-periodic oscillations for biased diffusion of a polymer chain in a porous medium

A coarse-grained off-lattice bead-spring model is used to reveal the complex dynamics of a polymer chain in a quenched porous medium in the presence of an external field B. The behavior of the mean square displacement (MSD) of the center chain bead and that of the center of mass of the chain as a function of time is studied at different values of the barrier concentration C, the field strength B and the chain length N. In a field, important information on the way in which chains move between obstacles and overcome them is gained from the MSD vs. time analysis in the directions parallel and perpendicular to the flow. Instead of a steady approach to uniform drift-like motion at low C, for sufficiently strong field B we observe logarithmic oscillations in the effective exponents describing the time dependence of the MSD along and perpendicular to field. A common nature of this phenomenon with oscillatory behavior, observed earlier for biased diffusion of tracers on random lattices, is suggested. Received 7 August 1998     

On the number of intersections of self-repelling polymer chains

We give a detailed analysis of the intersection properties of polymers. Using the renormalization group we provide a full crossover function for the dependence of the number of intersections in a single polymer on chain length and excluded volume strength. We compare our results with Monte-Carlo data and with exact calculations for a random walk, finding good agreement in all respects. Restricting to the vicinity of the eight ternary fixed points we also calculate the number of intersections between two chains placed at a fixed distance, including the two halves of a block-copolymer. The analysis of these systems confirms the interpretation of the different contributions to the number of intersections in a single chain. Due to the highly nontrivial character of the correlations in a polymer chain the correction exponents in both cases however are different. None of the results can be extracted from any Flory-type estimate. Received: 1 April 1997 / Revised: 24 October 1997 / Accepted: 29 January 1998     

Microgels and fractal structures at interfaces and surfaces

The behavior of microgels near surfaces and their adsorption is studied by simple scaling theory. Two different types of microgels can be studied, i.e., fractal type microgels and randomly crosslinked polymer chains. In the first case the gel can be described mainly by introducing a spectral dimension. The second type requires more attention and uses the number of crosslinks as parameter. The main result is that soft gels with weakly coupled crosslinks and a low number of crosslinks adsorb much better than hard gels, with many crosslinks. Similar results for fractal gels and branched polymer are presented. Fractal gels with low connectivity adsorb easier than gels with a large connectivity dimension. We discuss also consequences on surface protection by microgels. Received: 11 August 1997 / Received in final form: 20 November 1997 / Accepted 22 January 1998     

Electrostatic assembly of protein lysozyme on DNA visualized by atomic force microscopy

In the present work, atomic force microscopy (AFM) has been used to study the assembly of protein lysozyme on DNA molecule. Based on the electrostatic interaction, the positively charged lysozyme can easily bind onto the negatively charged DNA molecule surface. The protein molecules appear as globular objects on the DNA scaffold, which are distinguishable in the AFM images. At the same time, lysozyme molecules can be assembled onto DNA as dense or sporadic pattern by varying the protein concentration. This work may provide fundamental aspects for building protein nanostructures and studying of DNA-protein interaction.     

Boerdijk-Coxeter helix and biological helices

Helices and dense packing of spherical objects are two closely related problems. For instance, the Boerdijk-Coxeter helix, which is obtained as a linear packing of regular tetrahedra, is a very efficient solution to some close-packing problems. The shapes of biological helices result from various kinds of interaction forces, including steric repulsion. Thus, the search for a maximum density can lead to structures related to the Boerdijk-Coxeter helix. Examples are presented for the -helix structure in proteins and for the structure of the protein collagen, but there are other examples of helical packings at different scales in biology. Models based on packing efficiency related to the Boerdijk-Coxeter helix, explain, mainly from topological arguments, why the number of amino acids per turn is close to 3.6 in -helices and 2.7 in collagen. Received 26 November 1998 and Received in final form 12 April 1999     

Collapse transitions of a periodic hydrophilic hydrophobic chain

We study a single self avoiding hydrophilic hydrophobic polymer chain, through Monte-Carlo lattice simulations. The affinity of monomer i for water is characterized by a (scalar) charge , and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs (i,j), proportional to . In this article, we take (resp. ()) for hydrophilic (resp. hydrophobic) monomers and consider a chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a periodic distribution of the along the chain, with periodicity 2p. The simulations are done for various chain lengths N, in d=2 (square lattice) and d=3 (cubic lattice). There is a critical value p _c (d,N) of the periodicity, which distinguishes between different low temperature structures. For p >p _c , the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For p <p _c (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydrophobic droplets, coated by hydrophilic monomers. We restrict our study to two extreme cases, and to illustrate the physics of the various phase transitions. A tentative variational approach is also presented. Received: 10 March 1998 / Received in final form: 25 June 1998 / Accepted: 1st July 1998     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

Magnetic and transport properties of sputtered Fe/Si multilayers

The structural, magnetic and transport properties of sputtered Fe/Si multilayers were studied. The analyses of the data of the X-ray diffraction, resistance and magnetic measurements show that heavy atomic interdiffusion between Fe and Si occurs, resulting in multilayers of different complicated structures according to different sublayer thicknesses. The nominal Fe layers in the multilayers generally consist of Fe layers doped with Si, ferromagnetic Fe-Si silicide layers and nonmagnetic Fe-Si silicide interface layers, while the nominal Si spacers turn out to be Fe-Si compound layers with additional amorphous Si sublayers only under the condition either for the series or for the series multilayers. A strong antiferromagnetic (AFM) coupling and negative magnetoresistance (MR) effect, about 1%, were observed only in multilayers with iron silicide spacers and disappeared when -Si layers appear in the spacers. The dependences of MR on and on bilayer numbers N resemble the dependence of AFM coupling. The increase of MR ratio with increasing N is mainly attributed to the improvement of AFM coupling for multilayers with N. The dependence of MR ratio is similar to that in metal/metal system with predominant bulk spin dependent scattering and is fitted by a phenomenological formula for GMR. At 77 K both the MR effect and saturation field increase. All these facts suggest that the mechanisms of the AFM coupling and MR effect in sputtered Fe/Si multilayers are similar to those in metal/metal system. Received: 11 February 1998 / Revised: 9 March 1998 / Accepted: 9 March 1998     

Towards spectral pattern of spin polarized sodium clusters: The example of Na

We investigate spin modes in the ground state and the polarized first isomer of the Na₁₂ cluster describing the valence electrons in time-dependent local-spin-density approximation (TDLSDA) and the detailed ionic background using local pseudopotentials. The spin modes show a collective redshift compared to the unperturbed particle-hole excitations. They are strongly fragmented and the average energy of the modes along the principal axes are related to the underlying geometry (triaxial or axially symmetric). For the polarized isomer, we find significant cross talk between the spin modes and the dipole plasmon, which hints at a possible spectroscopic identification. Received: 22 June 1998 / Accepted: 29 July 1998     

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t ^-3/8 and t ^-3/4 may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998     

Extensive stretch of polysiloxane network chains with random- and super-coiled conformations

The stress-elongation relations at large deformations for the polymer network chains with randomcoiled and supercoiled conformations are investigated using the polysiloxane networks with high elongations at break far over 10. Supercoil is the conformation of network chains in deswollen polymer networks which are made by removing solvent from the networks crosslinked in solutions at low polymer concentrations. The validity of the scaling concept of Pincus blob for the mechanical response of a polymer chain is experimentally confirmed for the network composed of randomcoiled chains. The analysis of the stress- relations for the deswollen networks comprised of supercoiled chains on the basis of the Pincus blob concept suggests that supercoil is a much more contracted conformation relative to randomcoil. Received: 25 August 1997 / Received in final form: 13 October 1997 / Accepted: 22 January 1998     

The phase behaviour of single polyethylene chains with and without fixing one end

The phase behaviour of a single polyethylene chain is studied by using molecular dynamics simulations. A free chain and a chain with fixing one end are considered here, since the atomic force microscope （AFM） tip can play a significant role in polymer crystallization in experiment. For a free chain, it is confirmed in our calculation that the polymer chain exhibits an extended coil state at high temperatures, collapses into a condensed state at low temperatures, i.e. the coil-to-globule transition that is determined by a high temperature shoulder of the heat capacity curve, and an additional liquid-to-solid transition that is described by a low temperature peak of the same heat curve. These results accord with previous studies of square-well chains and Lennard-Jones homopolymers. However, when one of the end monomers of the same chain is fixed the results become very different, and the chain cannot reach an extended coil-like state as a free chain does at high temperatures, i.e. there exists no coil-to-globule-like transition. These results may provide some insights into the influence of AFM tip when it is used to study the phase behaviour of polymer chains. If the interaction force between AFM tip and polymer monomers is strong, some monomers or one of them can be seen as being fixed by the tip, which is similar to our simulation model, and it is also found that AFM tip could induce polymer crystallization.