Self-Healing of Unentangled Polymer Networks with Reversible Bonds.

Self-healing polymeric materials are systems that after damage can revert to their original state with full or partial recovery of mechanical strength. Using scaling theory we study a simple model of autonomic self-healing of unentangled polymer networks. In this model one of the two end monomers of each polymer chain is fixed in space mimicking dangling chains attachment to a polymer network, while the sticky monomer at the other end of each chain can form pairwise reversible bond with the sticky end of another chain. We study the reaction kinetics of reversible bonds in this simple model and analyze the different stages in the self-repair process. The formation of bridges and the recovery of the material strength across the fractured interface during the healing period occur appreciably faster after shorter waiting time, during which the fractured surfaces are kept apart. We observe the slowest formation of bridges for self-adhesion after bringing into contact two bare surfaces with equilibrium (very low) density of open stickers in comparison with self-healing. The primary role of anomalous diffusion in material self-repair for short waiting times is established, while at long waiting times the recovery of bonds across fractured interface is due to hopping diffusion of stickers between different bonded partners. Acceleration in bridge formation for self-healing compared to self-adhesion is due to excess non-equilibrium concentration of open stickers. Full recovery of reversible bonds across fractured interface (formation of bridges) occurs after appreciably longer time than the equilibration time of the concentration of reversible bonds in the bulk.

Age-dependent stochastic models for understanding population fluctuations in continuously cultured cells.

For symmetrically dividing cells, large variations in the cell cycle time are typical, even among clonal cells. The consequence of this variation is important in stem cell differentiation, tissue and organ size control, and cancer development, where cell division rates ultimately determine the cell population. We explore the connection between cell cycle time variation and population-level fluctuations using simple stochastic models. We find that standard population models with constant division and death rates fail to predict the level of population fluctuation. Instead, variations in the cell division time contribute to population fluctuations. An age-dependent birth and death model allows us to compute the mean squared fluctuation or the population dispersion as a function of time. This dispersion grows exponentially with time, but scales with the population. We also find a relationship between the dispersion and the cell cycle time distribution for synchronized cell populations. The model can easily be generalized to study populations involving cell differentiation and competitive growth situations.

General approach to polymer chains confined by interacting boundaries.

Polymer chains, confined to cavities or polymer layers with dimensions less than the chain radius of gyration, appear in many phenomena, such as gel chromatography, rubber elasticity, viscolelasticity of high molar mass polymer melts, the translocation of polymers through nanopores and nanotubes, polymer adsorption, etc. Thus, the description of how the constraints alter polymer thermodynamic properties is a recurrent theoretical problem. A realistic treatment requires the incorporation of impenetrable interacting (attractive or repulsive) boundaries, a process that introduces significant mathematical complications. The standard approach involves developing the generalized diffusion equation description of the interaction of flexible polymers with impenetrable confining surfaces into a discrete eigenfunction expansion, where the solutions are normally truncated at the first mode (the "ground state dominance" approximation). This approximation is mathematically well justified under conditions of strong confinement, i.e., a confinement length scale much smaller than the chain radius of gyration, but becomes unreliable when the polymers are confined to dimensions comparable to their typically nanoscale size. We extend a general approach to describe polymers under conditions of weak to moderate confinement and apply this semianalytic method specifically to determine the thermodynamics and static structure factor for a flexible polymer confined between impenetrable interacting parallel plate boundaries. The method is first illustrated by analyzing chain partitioning between a pore and a large external reservoir, a model system with application to chromatography. Improved agreement is found for the partition coefficients of a polymer chain in the pore geometry. An expression is derived for the structure factor S(k) in a slit geometry to assist in more accurately estimating chain dimensions from scattering measurements for thin polymer films.

Plasticization and antiplasticization of polymer melts diluted by low molar mass species.

An analysis of glass formation for polymer melts that are diluted by structured molecular additives is derived by using the generalized entropy theory, which involves a combination of the Adam-Gibbs model and the direct computation of the configurational entropy based on a lattice model of polymer melts that includes monomer structural effects. Our computations indicate that the plasticization and antiplasticization of polymer melts depend on the molecular properties of the additive. Antiplasticization is accompanied by a "toughening" of the glass mixture relative to the pure polymer, and this effect is found to occur when the diluents are small species with strongly attractive interactions with the polymer matrix. Plasticization leads to a decreased glass transition temperature T(g) and a "softening" of the fragile host polymer in the glass state. Plasticization is prompted by small additives with weakly attractive interactions with the polymer matrix. However, the latter situation can lead to phase separation if the attractive interactions are sufficiently strong. The shifts in T(g) of polystyrene diluted by fully flexible short oligomers (up to 20% mass of diluent) are evaluated from the computations, along with the relative changes in the isothermal compressibility at T(g) (a softening or toughening effect) to characterize the extent to which the additives act as antiplasticizers or plasticizers. The theory predicts that a decreased fragility can accompany both antiplasticization and plasticization of the glass by molecular additives. The general reduction in the T(g) of polymers by molecular additives is rationalized by analyzing the influence of the diluent's properties (cohesive energy, chain length, and stiffness) on glass formation in fluid mixtures and the variation of fragility is discussed in relation to changes in the molecular packing in diluted polymer melts. Our description of constant temperature glass formation upon increasing the diluent concentration directly leads to the Angell equation (tau(alpha) approximately A exp{B/(phi(0,p)-phi(p))}) for the structural relaxation time as function of the polymer concentration, where the extrapolated "zero mobility concentration" phi(0,p) calculated from the theory scales linearly with the inverse polymerization index N.

Application of the entropy theory of glass formation to poly(alpha-olefins).

The entropy theory of glass formation, which has previously been developed to describe general classes of polymeric glass-forming liquids, is extended here to model the thermodynamic and dynamic properties of poly(alpha-olefins). By combining this thermodynamic theory with the Adam-Gibbs model (which relates the configurational entropy to the rate of structural relaxation), we provide systematic computations for all four characteristic temperatures (T(A), T(c), T(g), T(0)), governing the position and breadth of the glass transition, and the fragility parameters (D,m) describing the strength of the temperature dependence of the structural relaxation time, where T(A) is the temperature below which the relaxation is non-Arrhenius, T(c) is the crossover or empirical mode-coupling temperature, T(g) is the glass transition temperature, and T(0) is the temperature at which the extrapolated relaxation time diverges. These temperatures and fragility parameters are evaluated as a function of molar mass, pressure, and the length n of the alpha-olefin side chains. The nearest neighbor interaction energy and local chain rigidities are found to strongly influence the four characteristic temperatures and the low temperature fragility. We also observe an "internal plasticization" of the poly(alpha-olefins) wherein the fragility decreases as the number n of "flexible" side group units increases. Our computations provide solid support for a pressure counterpart of the Vogel-Fulcher-Tammann relation. The entropy theory of glass formation predicts systematic changes in fragility with chain stiffness, cohesive energy, polymerization index, and side chain length, and qualitative trends in these parameters are discussed.

Multistep relaxation in equilibrium polymer solutions: a minimal model of relaxation in "complex" fluids.

We examine the rheological and dielectric properties of solutions of equilibrium self-assembling particles and molecules that form polydisperse chains whose average length depends on temperature and concentration (free association model). Relaxation of the self-assembling clusters proceeds by motions associated either with cluster rotations, with diffusive internal chain dynamics, or with interchain entanglement interactions. A hierarchy of models is used to emphasize different physical effects: Unentangled rodlike clusters, unentangled flexible polymers, and entangled chains. All models yield a multistep relaxation for low polymer scission rates ("persistent polymers"). The short time relaxation is nearly exponential and is dominated by the monomeric species and solvent, and the long time relaxation is approximately a stretched exponential, exp[-(t/tau)(beta)], a behavior that arises from an averaging over the equilibrium chain length distribution and the internal relaxation modes of the assembled structures. Relaxation functions indicate a bifurcation of the relaxation function into fast and slow contributions upon passing through the polymerization transition. The apparent activation energy for the long time relaxation becomes temperature dependent, while the fast monomeric relaxation process remains Arrhenius. The effective exponent beta(T), describing the long time relaxation process, varies monotonically from near unity above the polymerization temperature to a low temperature limit, beta approximately 13, when the self-assembly process is complete. The variation in the relaxation function with temperature is represented as a function of molecular parameters, such as the average chain length, friction coefficient, solvent viscosity, and the reaction rates for particle association and dissociation.

Electrochemical, spectroscopic, and DFT study of C60(CF3)n frontier orbitals (n = 2-18): the link between double bonds in pentagons and reduction potentials.

The frontier orbitals of 22 isolated and characterized C(60)(CF(3))(n) derivatives, including seven reported here for the first time, have been investigated by electronic spectroscopy (n = 2 [1], 4 [1], 6 [2], 8 [5], 10 [6], 12 [3]; the number of isomers for each composition is shown in square brackets) fluorescence spectroscopy (n = 10 [4]), cyclic voltammetry under air-free conditions (all compounds with n

Minimal model of relaxation in an associating fluid: viscoelastic and dielectric relaxations in equilibrium polymer solutions.

Cluster formation and disintegration greatly complicate the description of relaxation processes in complex fluids. We systematically contrast the viscoelastic and dielectric properties for models of equilibrium polymers whose thermodynamic properties have previously been established. In particular, the monomer-mediated model allows chain growth to proceed only by monomer addition, while the scission-recombination model enables all particles to associate democratically, so that chain scission and fusion occur at the interior segments as well as at chain ends. The minimal models neglect hydrodynamic and entanglement interactions and are designed to explore systematically the competition between chemical reaction and internal chain relaxation and how this coupling modifies the dynamics from that of a polydisperse solution of Rouse chains with fixed lengths (i.e., "frozen" chains). As expected, the stress relaxation is nearly single exponential when the assembly-disassembly reaction is fast on the time scale of structural chain rearrangements, while multiexponential or nearly stretched exponential relaxation is obtained when this reaction rate is slow compared to the broad relaxation spectrum of almost unperturbed, nearly "dead" chains of intrinsically polydisperse equilibrium polymer solutions. More generally, a complicated intermediate behavior emerges from the interplay between the chemical kinetic events and internal chain motions.

Transport of single molecules along the periodic parallel lattices with coupling.

General discrete one-dimensional stochastic models to describe the transport of single molecules along coupled parallel lattices with period N are developed. Theoretical analysis that allows to calculate explicitly the steady-state dynamic properties of single molecules, such as mean velocity V and dispersion D, is presented for N=1 and N=2 models. For the systems with N>2 exact analytic expressions for the large-time dynamic properties are obtained in the limit of strong coupling between the lattices that leads to dynamic equilibrium between two parallel kinetic pathways. It is shown that for all systems dispersion is maximal when the coupling between channels is weak.

Dynamic transitions in coupled motor proteins.

The effect of interactions on dynamics of coupled motor proteins is investigated theoretically. A simple stochastic discrete model, which allows one to calculate explicitly the dynamic properties, is developed. It is shown that there are two dynamic regimes, depending on the interaction between the particles. For strong interactions the motor proteins move as one tight cluster, while for weak interactions there is no correlation in the motion of the proteins, and the particle separation increases steadily with time. The boundary between the two regimes is specified by a critical interaction that has a nonzero value only for the coupling of the asymmetric motor proteins, and it depends on the temperature and transition rates. At the critical interaction there is a change in slope for the mean velocities and a discontinuity in the dispersions of the motor proteins as a function of interactions.

ATP hydrolysis stimulates large length fluctuations in single actin filaments.

Polymerization dynamics of single actin filaments is investigated theoretically using a stochastic model that takes into account the hydrolysis of ATP-actin subunits, the geometry of actin filament tips, and the lateral interactions between the monomers as well as the processes at both ends of the polymer. Exact analytical expressions are obtained for the mean growth velocity, for the dispersion in the length fluctuations, and the nucleotide composition of the actin filaments. It is found that the ATP hydrolysis has a strong effect on dynamic properties of single actin filaments. At high concentrations of free actin monomers, the mean size of the unhydrolyzed ATP-cap is very large, and the dynamics is governed by association/dissociation of ATP-actin subunits. However, at low concentrations the size of the cap becomes finite, and the dissociation of ADP-actin subunits makes a significant contribution to overall dynamics. Actin filament length fluctuations reach a sharp maximum at the boundary between two dynamic regimes, and this boundary is always larger than the critical concentration for the actin filament's growth at the barbed end, assuming the sequential release of phosphate. Random and sequential mechanisms of hydrolysis are compared, and it is found that they predict qualitatively similar dynamic properties at low and high concentrations of free actin monomers with some deviations near the critical concentration. The possibility of attachment and detachment of oligomers in actin filament's growth is also discussed. Our theoretical approach is successfully applied to analyze the latest experiments on the growth and length fluctuations of individual actin filaments.

Coupling of two motor proteins: a new motor can move faster.

We study the effect of a coupling between two motor domains in highly processive motor protein complexes. A simple stochastic discrete model, in which the two parts of the protein molecule interact through some energy potential, is presented. The exact analytical solutions for the dynamic properties of the combined motor species, such as the velocity and dispersion, are derived in terms of the properties of free individual motor domains and the interaction potential. It is shown that the coupling between the motor domains can create a more efficient motor protein that can move faster than individual particles. The results are applied to analyze the motion of RecBCD helicase molecules.

Understanding mechanochemical coupling in kinesins using first-passage-time processes.

Kinesins are processive motor proteins that move along microtubules in a stepwise manner, and their motion is powered by the hydrolysis of ATP. Recent experiments have investigated the coupling between the individual steps of single kinesin molecules and ATP hydrolysis, taking explicitly into account forward steps, backward steps, and detachments. A theoretical study of mechanochemical coupling in kinesins, which extends the approach used successfully to describe the dynamics of motor proteins, is presented. The possibility of irreversible detachments of kinesins from the microtubules is explicitly taken into account. Using the method of first-passage times, experimental data on the mechanochemical coupling in kinesins are fully described using the simplest two-state model. It is shown that the dwell times for the kinesin to move one step forward or backward, or to dissociate irreversibly, are the same, although the probabilities of these events are different. It is concluded that the current theoretical view-that only the forward motion of the motor protein molecule is coupled to ATP hydrolysis--is consistent with all available experimental observations for kinesins.

Polymerization dynamics of double-stranded biopolymers: chemical kinetic approach.

The polymerization dynamics of double-stranded polymers, such as actin filaments, is investigated theoretically using simple chemical kinetic models that explicitly take into account some microscopic details of the polymer structure and the lateral interactions between the protofilaments. By considering all possible molecular configurations, the exact analytical expressions for the growth velocity and dispersion for two-stranded polymers are obtained in the case of the growing at only one end, and for the growth from both polymer ends. Exact theoretical calculations are compared with the predictions of approximate multilayer models that consider only a finite number of the most relevant polymer configurations. Our theoretical approach is applied to analyze the experimental data on the growth and fluctuations dynamics of individual single actin filaments.

Simple growth models of rigid multifilament biopolymers.

The growth dynamics of rigid biopolymers, consisting of N parallel protofilaments, is investigated theoretically using simple approximate models. In our approach, the structure of a polymer's growing end and lateral interactions between protofilaments are explicitly taken into account, and it is argued that only few configurations are important for a biopolymer's growth. As a result, exact analytic expressions for growth velocity and dispersion are obtained for any number of protofilaments and arbitrary geometry of the growing end of the biopolymer. Our theoretical predictions are compared with a full description of biopolymer growth dynamics for the simplest N=2 model. It is found that the results from the approximate theory are approaching the exact ones for large lateral interactions between the protofilaments. Our theory is also applied to analyze the experimental data on the growth of microtubules.