Dynamics of selfavoiding tethered membranes. I. Model A dynamics (Rouse model)

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D are studied using model A dynamics. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by . This result applies especially to membranes (D=2) but also to polymers (D=1). Received: 5 September 1997 / Accepted: 17 November 1997     

Dynamics of selfavoiding tethered membranes. II. Inclusion of hydrodynamic interaction (Zimm model)

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D embedded into d dimensions are studied including hydrodynamical interactions. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by z=d. The crossover to the region, where the membrane is crumpled swollen but the hydrodynamic interaction irrelevant is discussed. The results apply as well to polymers (D=1) as to membranes (D=2). Received: 5 September 1997 / Accepted: 17 November 1997     

Effects of finite thickness on interfacial widths in confined thin films of coexisting phases

The capillary broadening of a 2-phase interface is investigated both experimentally and theoretically. When a binary mixture in a thin film with thickness D segregates into two coexisting phases the interface between the two phases may form parallel to the substrate due to preferential surface attraction of one of the components. We show that the interfacial profile (of intrinsic width w₀) is broadened due to capillary waves, which lead to fluctuations, of correlation length of the local interface positions in the directions parallel to the confining walls. We postulate that acts as an upper cutoff for the spectrum of capillary waves on the interface, so that the effective mean square interfacial width w varies as . In the limit of large D this yields or respectively for the case of short- or long-range forces between walls and the interface. We used the Nuclear Reaction Analysis depth profiling technique, to investigate this broadening effect directly in two binary polymer mixtures. Our results reveal that the interfacial width indeed increases with film thickness D, though the observed interfacial width is lower than the predicted w. This is probably due to surface tension effects imposed by the confining surfaces which are not taken into account in our model. Received: 19 February 1998 / Received in final form: 2 September 1998 / Accepted: 8 September 1998     

Static and dynamic properties of supercooled thin polymer films

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular-dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), D, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time α-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT β-process. An analysis of the temperature dependence of the α-relaxation time suggests that the critical temperature, T _c, of MCT decreases with D. If the confinement is not too strong ( D≥10monomer diameter), the static structure factor of the film coincides with that of the bulk when compared for the same distance, T - T _c(D), to the critical temperature. This suggests that T - T _c(D) is an important temperature scale of our model both in the bulk and in the films. Received 12 September 2001     

A Monte-Carlo study of equilibrium polymers in a shear flow

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     

A geometric generalization of field theory to manifolds of arbitrary dimension

We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for , while leads to self-avoiding tethered membranes (as the O(N) model reduces to self-avoiding polymers). The model is studied perturbatively by a 1-loop renormalization group analysis, and exactly as .Freedom to choose the expansion point D, leads to precise estimates of critical exponents of the O(N) model. Insights gained from this generalization include a conjecture on the nature of droplets dominating the 3d-Ising model at criticality; and the fixed point governing the random bond Ising model. Received: 15 October 1998 / Accepted: 4 November 1998     

Multiple conformations in polyampholytes

We study the configurational statistics of a ring polyampholyte chain made of N randomly charged monomers with elementary charge .To a large extent, the overall structure of a polyampholyte is controlled by a total sum Q of all charges. When the total charge is smaller than , the polyampholyte has a compact globular structure. At charges larger than , the configuration has the form of a ring of small globules (beads) connected by strings. Between Q₁ and Q₂ we find a remarkable diversity of meta-stable configurations having the shapes of irregular clusters of small globules connected by the strings. We estimate the number of these configurations and the energy barriers between them. Between Q₁ and Q₂, the minimum energy configurations are completely controlled by randomness in the charge distribution along the chain. There are hysteresis effects in the shapes of the clusters. As the total charge increases, the linearly extended configurations become dynamically more preferable. When the charge decreases, the circular shapes are preferred. We remark on the probable connection with the multiple phase transitions observed in polyampholyte gels. Received: 10 July 1997 / Accepted: 13 October 1997     

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     

Monte carlo studies of phase transitions in polymer blends and block copolymer melts

Summary The unmixing transition of both symmetrical polymer blends AB (i.e. chain lengthsN _A=N _B=N) and asymmetrical ones (N _B/N _A=2,3) is studied by large-scale Monte Carlo simulations of the bond fluctuation model. Combination of semi-grand-canonical simulation techniques, ?histogram reweighting? and finitesize scaling allows an accurate location of the coexistence curve in the critical region. The variation of the critical temperature with chain length (N) is studied and compared to theoretical predictions. For the symmetrical case, use of chain lengths up toN=512 allows a rough estimation of crossover scaling functions for the crossover from Ising to mean-field exponents. The order-disorder transitions in melts of both symmetric (compositionf=N _A/(N _A+N _B)=1/2) and asymmetric (f=3/4) block copolymers is studied for very short chains (16≤N≤60). The interplay between structure and chain configuration is emphasized. Qualitative evidence for ?dumbell formation? of chains and vacancy enrichment in A-B-interfaces and near hard walls is presented. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

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     

Chain radius dependence on concentration in a 2D living polymer system

A living polymer system is used to study the effect of concentration on a broad, polydisperse two-dimensional polymer system. It is found that the mean squared end-to-end radius of a chain of L monomers does not decrease by following a simple power law of the concentration but by a function of the form . An origin for such a behaviour is proposed. Received: 21 November 1997 / Received in final form: 21 April 1998 / Accepted: 24 April 1998     

Water droplets in a spherically confined nematic solvent: A numerical investigation

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998     

Globules of annealed amphiphilic copolymers: Surface structure and interactions

A mean-field theory of globules of random amphiphilic copolymers in selective solvents is developed for the case of an annealed copolymer sequence: each unit can be in one of two states, H (insoluble) or P (soluble or less insoluble). The study is focussed on the regime when H and P units tend to form long blocks, and when P units dominate in the dilute phase, but are rare in the globule core. A first-order coil-to-globule transition is predicted at some T = T _cg. The globule core density at the transition point increases as the affinity of P units to the solvent, ˜, is increased. Two collapse transitions, coil → “loose” globule and “loose” globule → “dense” globule, are predicted if ˜ is high enough and P units are marginally soluble or weakly insoluble. H and P concentration profiles near the globule surface are obtained and analyzed in detail. It is shown that the surface excess of P units rises as ˜ is increased. The surface tension decreases in parallel. Considering the interaction between close enough surfaces of two globules, we show that they always attract each other at a complete equilibrium. It is pointed out, however, that such equilibrium may be difficult to reach, so that partially equilibrium structures (defined by the condition that a chain forming one globule does not penetrate into the core of the other globule) are relevant. It is shown that at such partial equilibrium the interaction is repulsive, so the globules may be stabilized from aggregation. The strongest repulsion is predicted at the coil-to-globule transition point T _cg: the repulsion force decreases with the distance between the surfaces according to a power law. In the general case (apart from T _cg) the force vs. distance decay becomes exponential; the decay length ξ diverges as T → T _cg. The developed theory explains certain anomalous properties observed for globules of amphiphilic homopolymers.     

2-Dimensional polymers confined in a strip

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     

Topology invariance in percolation thresholds

An universal invariant for site and bond percolation thresholds ( and respectively) is proposed. The invariant writes where and are positive constants, and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d. The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6. Received: 7 July 1997 / Accepted: 5 November 1997     

Field-induced winding of chiral polymers

We propose a microscopic model of a chiral polymer chain with permanent transverse dipoles interacting with an external electric field. Its behaviour has been investigated by computer simulation in the limit of weak chirality. Large-scale (tertiary) helical winding induced along the field direction has been found above a threshold field E_c, and the helix parameters have been calculated as functions of the field strength. Below E_c there is no coherent helical structure of the chain conformation. We find a characteristic scaling of the threshold and the winding radius a with the chain bending modulus , and . Received: 15 November 1997 / Accepted: 16 February 1998     

Correlation between the Soret coefficient and the static structure factor in a polymer blend

Mutual mass diffusion and thermal diffusion has been investigated in poly(dimethylsiloxane)/ poly(ethylmethylsiloxane) (PDMS/PEMS) polymer blends of equal weight fractions. Molar masses ranged from below 1 to over 20 kg/mol. Both the mutual mass (D) and the thermal diffusion (D_T) coefficient contain a thermally activated factor with an activation temperature of 1415 K. The molar mass dependence of D_T is due to an end-group effect of the local friction coefficient. The thermal diffusion coefficient in the limit of long chains and infinite temperature is D_T^0, = - 1.69×10^-7cm²(sK)^-1. The Soret coefficient S_T of blends far enough away from a critical point is proportional to the static structure factor S(q = 0).     

The escape transition of a polymer: A unique case of non-equivalence between statistical ensembles

A flexible polymer chain under good solvent conditions, end-grafted on a flat repulsive substrate surface and compressed by a piston of circular cross-section with radius L may undergo the so-called “escape transition” when the height of the piston D above the substrate and the chain length N are in a suitable range. In this transition, the chain conformation changes from a quasi-two-dimensional self-avoiding walk of “blobs” of diameter D to an inhomogeneous “flower” state, consisting of a “stem” (stretched string of blobs extending from the grafting site to the piston border) and a “crown” outside of the confining piston. The theory of this transition is developed using a Landau free-energy approach, based on a suitably defined (global) order parameter and taking also effects due to the finite chain length N into account. The parameters of the theory are determined in terms of known properties of limiting cases (unconfined mushroom, chain confined between infinite parallel walls). Due to the non-existence of a local order parameter density, the transition has very unconventional properties (negative compressibility in equilibrium, non-equivalence between statistical ensembles in the thermodynamic limit, etc.). The reasons for this very unusual behavior are discussed in detail. Using Molecular Dynamics (MD) simulation for a simple bead-spring model, with N in the range 50 N 300 , a comprehensive study of both static and dynamic properties of the polymer chain was performed. Even though for the considered rather short chains the escape transition is still strongly rounded, the order parameter distribution does reveal the emerging transition clearly. Time autocorrelation functions of the order parameter and first passage times and their distribution indicate clearly the strong slowing down associated with the chain escape. The theory developed here is in good agreement with all these simulation results.     

3d D lifetime in laser cooled Ca : Influence of cooling laser power

We have measured the lifetime of the metastable 3D _5/2 level in Ca⁺ using the “quantum jump" technique on a single stored and laser cooled ion in a linear Paul trap. We found a linear dependence of the measured decay rate on the power of the laser which repumps the ions from the long lived 3D _3/2 level. This can be explained by off-resonant depletion of the 3D _5/2 level. The proper lifetime of this level is obtained by a linear extrapolation of the measured lifetime to zero laser power. We obtain 1100(18) ms in agreement with theoretical calculations. The observed systematic change of the decay rate resolves discrepancies between earlier experiments in which this effect had not been considered. Measurements on a linear chain of 10 laser cooled ions showed unexpected frequent coincidences of quantum jumps within our observation time of 20 ms. This indicates a so far unexplained correlation between the ions in the chain at large distances. Received 3 March 1999     

Compression induced phase transitions in PEO brushes: the n-cluster model

The compression of brushes of terminally anchored chain within the de Gennes n-cluster model is analysed. This model was developed for Poly(ethylene oxide) in water but may apply to other systems. Brushes described by this model exhibit discontinuous concentration profile associated with the coexistence of an inner dense “phase” and an outer, dilute, one. The compression induces growth of the dense, weakly compressible region. This, in turn, gives rise to distinctive force profiles associated with changes of slope. When the dilute region disappears, the compression of two brushes can give rise to a transient attraction. Received: 4 November 1997 / Revised: 29 January 1998 / Accepted: 24 March 1998