Visualizing the strain field in semiflexible polymer networks: strain fluctuations and nonlinear rheology of F-actin gels

We image semiflexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 microm. The degree of nonaffine strain depends upon the polymer length and cross-link density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of the networks in the bulk.     

Freezing and microphase separation in random copolymers

Summary A two-letter random copolymer with attraction between similar monomers and repulsion between different ones is investigated using the replica method. This type of interactions favors microphase separation (MPS) in a compact state of a polymer or in a melt. Frustrations between interactions and polymeric bonds may lead to freezing transition in a phase where only a few conformations dominate and replica symmetry is broken. Our analysis reveals that stiff polymers have a frozen phase and do not undergo transition to a phase with microdomain structure. In flexible polymers the microphase transition may occur before freezing. A complete phase diagram showing the interplay between the two phase transitions is constructed for the two-letter random copolymer. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Random Walks and Polymers in the Presence of Quenched Disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both ‘random walk models’, where the random walk is a dynamical process generated by local transition rules, and on ‘polymer models’, where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points: thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures T _c(i,L) over the ensemble of samples (i) of size L. We describe the results of this analysis for the bidimensional wetting and for the Poland–Scheraga model of DNA denaturation.Conference Proceedings “Mathematics and Physics”, I.H.E.S., France, November 2005     

Packing of compressible granular materials

3D computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. In the rigid ball limit, we find a continuous transition in which the stress vanishes as (straight phi-straight phi(c))(beta), where straight phi is the (solid phase) volume density. The value of straight phi(c) depends on whether the grains interact via only normal forces (giving rise to random close packings) or by a combination of normal and friction generated transverse forces (producing random loose packings). In both cases, near the transition, the system's response is controlled by localized force chains.     

Freedericksz transition in polymer-stabilized nematic liquid crystals

We have constructed polymer-stabilized nematic liquid crystals by photopolymerizing diacrylate monomers in the nematic phase. The orientation of the liquid crystal was controlled by the polymer network. We studied the Freedericksz transition in these systems. Experimentally we studied the transition by measuring the capacitance of the liquid crystal cells as a function of applied voltage. The transition was affected profoundly by the dispersed polymer network. The threshold was higher with shorter interpolymer network distance. Theoretically we studied the systems using a two-dimensional model in which the polymer networks were represented by parallel cylinders with random location. The interaction between the liquid crystal and the polymer network was described by the boundary condition imposed by the polymer network. By fitting the experimental data, we found that the polymer cylinders had diameters of a few submicrons, and a substantial amount of liquid crystal was trapped inside the cylinders.     

Phase diagram of magnetic polymers

We consider polymers made of magnetic monomers (Ising or Heisenberg-like) in a good solvent. These polymers are modeled as self-avoiding walks on a cubic lattice, and the ferromagnetic interaction between the spins carried by the monomers is short-ranged in space. At low temperature, these polymers undergo a magnetic induced first order collapse transition, that we study at the mean field level. Contrasting with an ordinary point, there is a strong jump in the polymer density, as well as in its magnetization. In the presence of a magnetic field, the collapse temperature increases, while the discontinuities decrease. Beyond a multicritical point, the transition becomes second order and -like. Monte Carlo simulations for the Ising case are in qualitative agreement with these results. Received 11 February 1999     

一种共轭聚合物单分子发色团吸收和发射特性动态演变过程的实时测量

利用频域信息重构的散焦宽场成像测量了Poly[2,7-(9,9-dioctylfluorene)-alt-4,7-bis(thiophen-2-yl)benzo-2,1,3-thiadiazole](PFO-DBT)共轭聚合物单分子发色团的吸收与发射特性及其动态演变过程.通过调制用于激发共轭聚合物单分子的超短脉冲对的相对相位,对单分子荧光进行傅里叶变换的频域测量,跟踪发色团吸收偶极取向变化;通过测量散焦荧光成像光斑探测发色团发射偶极取向变化.研究发现, PFO-DBT共轭聚合物单分子发色团存在吸收和发射偶极取向均保持不变、其中之一变化以及两者同时变化三种情况.这种对共轭聚合物单分子发色团吸收和发射偶极取向演化过程的实时测量可用于分析共轭聚合物构象变化及其对能量转移过程的影响.     

Arm retraction potential of branched polymers in the absence of dynamic dilution

We study the stress relaxation of model polymer networks containing low contents of star shaped and linear dangling polymers. As compared with their melts, the behavior of star and dangling polymers leads to a dynamic response with unprecedented large relaxation times. By comparing data of star melts with those corresponding to stars and dangling chains residing in polymer networks, we were able to identify the effects of dynamic dilution clearly. Since in polymer networks the dynamic dilution effect is suppressed, we were able by the first time to experimentally test the validity of the potential for arm retraction proposed by Pearson and Helfand.     

The Continuum Directed Random Polymer

Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white noise. The strength of the interaction is determined by an inverse temperature parameter β, and for a given β and realization of the noise the path is a Markov process. The transition probabilities are determined by solutions to the one-dimensional stochastic heat equation. We show that for all β>0 and for almost all realizations of the white noise the path measure has the same Hölder continuity and quadratic variation properties as Brownian motion, but that it is actually singular with respect to the standard Wiener measure on C([0,1]).     

Bio-inspired network optimization in soft materials — Insights from the plant cell wall

The dynamic-mechanical responses of ionotropic gels made from the biopolymer pectin have recently been investigated by microrheological experiments and found to exhibit behaviour indicative of semi-flexible polymer networks. In this work we investigate the gelling behaviour of pectin systems in which an enzyme (pectinmethylesterase, PME) is used to liberate ion-binding sites on initially inert polymers, while in the presence of ions. This is in contrast to the previous work, where it was the release of ions (rather than ion-binding groups) that was controlled and the polymers had pre-existing cross-linkable moieties. In stark contrast to the semi-flexible network paradigm of biological gels and the previous work on pectin, the gels studied herein exhibit the properties of chemically cross-linked networks of flexible polymers.     

Proton spin lattice relaxation in aromatic polymers.

The most striking requirement for the NMR imaging of an object is that this object should be made with components having different NMR parameters. In most cases these parameters are due to the presence of a fluid and to its mobility, thus measurable parameters are proton signal intensity contrasted in T1 or T2. From the glass transition temperature Tg, by decreasing the temperature, all nonaromatic polymers as well as any well degassed polymers, show a continuous increase of their proton spin-lattice relaxation, which at low temperature is usually larger than 10-20 sec. However, due to O2 molecules selectively adsorbed on aromatic rings, non-degassed aromatic polymers show a marked shortening of the proton spin-lattice relaxation. This effect is maximal at rather low temperature, where T1 can be shorter than 1 msec, and in many known cases shorter than 500 msec. Since the amount of sorbed-O2 is a function of the chemical nature of the polymer, the type of crystallinity (polymorphism of semicrystalline polymers), the crystalline-amorphous ratio, and so on, a careful study of T1 relaxation as a function of the temperature can define optimal conditions for T1 contrast. Examples regarding polymorphism in syndiotactic polystyrene, butadiene-styrene block copolymers and blends, and poly(phenylene) oxide, will be discussed.     

"Bending to stretching" transition in disordered networks

From polymer gels to cytoskeletal structures, random networks of elastic material are commonly found in both materials science and biology. We present a three-dimensional micromechanical model of these networks and identify a "bending-to-stretching" transition. We characterize this transition in terms of concentration scaling laws, the stored elastic energy, and affinity measurements. Understanding the relationship between microscopic geometry and macroscopic mechanics will elucidate, for example, the mechanical properties of polymer gel networks or the role of semiflexible network mechanics in cells.     

Thermodynamic behaviour of two-dimensional vesicles revisited

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher (Phys. Rev. Lett. 59, 1989 (1987)). We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure [Formula: see text] , where [Formula: see text] = Np/4[Formula: see text] , with the number of monomers N [Formula: see text] ∞ and the pressure p [Formula: see text] 0 , keeping [Formula: see text] constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N -gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. Away from these limits, we argue that the transition is replaced by a sharp crossover. The area, however, scales with N(2) for all positive p in all such models, consistent with earlier scaling theories.     

EXAFS study on ultrafine Ni-Co-B amorphous catalysts

\chem{\chemvar{A}C_{60}} with , , . From the temperature dependent line shift of we have extracted information about the electron density distribution on the molecules. The data also support the existence of an like bonding type between the molecules. The magnetic phase transition observed at low temperature in and is monitored by an increase of the second moment as well as an increase of the spin lattice relaxation rates of the and alkali nuclei. The results are compared to NMR data of where no signs of a magnetic ordering are found. The magnetically ordered phases are discussed in terms of antiferromagnetic spin density wave. We also report on NMR measurements of orthorhombic one dimensional and rhombohedral two dimensional polymers of obtained under high pressure. By spinning the samples up to , we are able to identify two resonances at and for the orthorhombic polymer and six resonances at , , , , and for the rhombohedral one. The static distortion of the molecules induced by the transformation under pressure must be at the origin of the observed inequivalent carbons in both systems. The NMR lineshape simulations of the obtained spectra are compatible with the suggested polymeric structures where the molecules are connected by cycloadditions. Received: 10 October 1996/Accepted: 13 November 1996     

Diffusive-Ballistic Transition in Random Polymers with Drift and Repulsive Long-Range Interactions

In this note phase transition issues are addressed for random polymers on \(\mathbb {Z}^2\) with long-range self-repulsive interactions. It is shown that, in the absence of drift and with power law interactions, the polymer exhibits transition from diffusive to a ballistic behavior. When non-null drifts are added and positive translation invariant interactions are considered, the polymer presents a ballistic behavior. Our results complement some previous studies on the matter and we also derive a Central Limit Theorem for the model.     

Structural Properties and Phase Behavior of Crosslinked Networks in Polymer Solutions

Structural properties and phase behavior of crosslinked networks embedded in polymer solutions are theoretically investigated. The partial structure factor of the network is calculated using a matrix formulation of the random phase approximation and the forward scattering limit is correlated with the phase behavior. Swelling and deswelling processes are analyzed in terms of the polymer concentration, the mismatch of solvent quality with respect to polymer and network, the polymers incompatibility and their characteristic sizes. Most studies reported so far in the literature have focussed on the swelling of crosslinked networks and gels in pure solvents but the correlation of the structural properties with the phase behavior in the presence of high molecular weight polymers in solution has not been given sufficient attention. The present work is intended to fill this gap in view of the current efforts to develop novel drug encapsulating and targeted delivery devices.     

Manning-Oosawa counterion condensation

Counterion condensation is a basic feature of 2D electrostatics exhibited by highly charged rodlike polymers such as DNA. In the framework of the Poisson Boltzmann equation with salt, we show that such a polymer of radius a attracts a condensate of thickness RM=A(axi)1/2 where xi is the Debye length and A depends weakly on the polymer charge density q0. To leading order in 1/ln(xi/a), we derive the condensate structure and show that free ions follow universal density profiles independent of a and q0. Generalizing this approach we calculate ion profiles for finite concentration solutions.     

The immunity of polymer-microemulsion networks

The concept of network immunity, i.e., the robustness of the network connectivity after a random deletion of edges or vertices, has been investigated in biological or communication networks. We apply this concept to a self-assembling, physical network of microemulsion droplets connected by telechelic polymers, where more than one polymer can connect a pair of droplets. The gel phase of this system has higher immunity if it is more likely to survive (i.e., maintain a macroscopic, connected component) when some of the polymers are randomly degraded. We consider the distribution p(σ) of the number of polymers between a pair of droplets, and show that gel immunity decreases as the variance of p(σ) increases. Repulsive interactions between the polymers decrease the variance, while attractive interactions increase the variance, and may result in a bimodal p(σ).     

Potts model on complex networks

We consider the general p-state Potts model on random networks with a given degree distribution (random Bethe lattices). We find the effect of the suppression of a first order phase transition in this model when the degree distribution of the network is fat-tailed, that is, in more precise terms, when the second moment of the distribution diverges. In this situation the transition is continuous and of infinite order, and size effect is anomalously strong. In particular, in the case of p = 1, we arrive at the exact solution, which coincides with the known solution of the percolation problem on these networks.Received: 3 December 2003, Published online: 17 February 2004PACS: 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 87.18.Sn Neural networks     

Strain-dependent localization, microscopic deformations, and macroscopic normal tensions in model polymer networks

We use molecular dynamics simulations to investigate the microscopic and macroscopic response of model polymer networks to uniaxial elongations. By studying networks with strand lengths ranging from N(s)=20 to 200 we cover the full crossover from cross-link to entanglement dominated behavior. Our results support a recent version of the tube model which accounts for the different strain dependence of chain localization due to chemical cross-links and entanglements.