Dynamics of strongly entangled polymer systems: activated reptation

The effect of excluded-volume interactions on the reptation dynamics of long polymer chains is considered theoretically. It is shown that interactions give rise to an exponential increase of the reptation time, , if polymer chains are long enough: , where is the number of monomers per entanglement. We propose a novel dynamical mechanism of activated reptation implying that neighboring chains exchange conformations of their terminal fragments. It is shown that the exchange mechanism is compatible with the equilibrium polymer chain statistics and that it provides a bridge between the previous theories. Received: 25 July 1997 / Accepted: 8 October 1997     

Mobility in thin polymer films ranging from local segmental motion, Rouse modes to whole chain motion: A coupling model consideration

Large increases of mobility of local segmental relaxation observed in polymer films as the film thickness is decreased, as evidenced by decreases of the glass temperature, are not found for relaxation mechanisms that have longer length scales including the Rouse relaxation modes and the diffusion of entire polymer chains. We show that the coupling model predictions, when extended to consider polymer thin films, are consistent with a large increase of the mobility of the local segmental motions and the lack of such a change for the Rouse modes and the diffusion of entire polymer chains. There are two effects that can reduce the coupling parameter of the local segmental relaxation in thin films. One is the chain orientation that is induced parallel to the surface when the film thickness h becomes smaller than the end-to-end distance of the chains and the other is a finite-size effect when h is no longer large compared to the cooperative length scale. Extremely thin ( ≈ 1.5 nm) films obtained by intercalating a polymer into layered silicates have thickness significantly less than the cooperative length scale near the bulk polymer glass transition temperature. As a result, the coupling parameter of the local segmental relaxation in such thin films is reduced almost to zero. With this plausible assumption, we show the coupling model can explain quantitatively the large decrease of the local segmental relaxation time found experimentally. Received 1 August 2001 and Received in final form 1 December 2001     

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     

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     

Adsorption of polymer chains by disordered traps

We study the adsorption cross-over of ideal polymer chains in an environment of disordered traps. Starting from the assumption of an optimal cluster size of traps (optimal fluctuation method) we derive a general scaling form of the free energy function for arbitrary spatial dimensions. For small concentrations of traps we find a cross-over from localized (adsorbed) behavior to delocalized behavior depending on the chain's length and on the depth of the traps; this is connected with the non-monotonic behavior of the chain's extension. In terms of the free energy of the chain this cross-over resembles a first order transition scenario, the chain gets localized at many traps at once. Received 18 November 1998     

The effect of stiffness in wormlike micelles

The effect of stiffness in a 2D living polymer system is investigated by Monte-Carlo simulation in a canonical ensemble. As the flexibility decreases, the mean chain contour length decreases and goes through a local maximum. The mean end to end square distance shows a non-monotonic behaviour due to the coil-to-rod transition and the decrease in chain contour length. Near the maximum of chain ordering in the bulk, the chain length distribution adapts itself to increase the configurational entropy. With the parameters used in this simulation, it seems that the effect of the stiffness for high stiffness is to decrease as in the isotropic case, since the ordering decreases again. Received: 16 September 1997 / Revised: 27 June 1998 / Accepted: 29 June 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     

Rheology of nanosized hairy grain suspensions

Suspensions of nanosized hairy grains have been prepared by grafting long polydimethylsiloxane chains (molecular weight ) onto silica particles (radius ), dispersed into a good solvent of PDMS. Depending on the particle volume fraction, different rheological behaviors are observed. In the very dilute regime, the suspensions are perfectly stable and the particles behave almost as hard spheres: flow penetration inside the corona is then very weak. When the particle volume fraction goes to the close packing volume fraction, the suspension viscosity does not diverge as for hard spheres due to the increase of flow penetration inside the corona and to corona entanglements. The particles have then the same behavior as polymer stars having an intermediate number of arms (). Finally, in the concentrated regime (), the suspensions form irreversible gels. We shown that this unexpected gelation phenomenon is related to the presence of the silica cores: grafted PDMS chains can adsorb onto different particles and form irreversible bonds between the cores. The viscosity and elastic modulus evolutions during gelation are well described by the scalar percolation model of sol-gel transition. Received 23 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     

Piezoelectricity of chiral nematic elastomers

A molecular model of freely jointed chains of chiral monomers is developed to describe the piezoelectric effect in chiral nematic elastomers. The model, an extension of the neo-classical theory of nematic polymer networks, takes into account a chiral biasing of molecular alignment under shear which leads to induced polarisation if the monomers contain a transverse dipole moment. The resulting theory is fully non-linear in elastic deformations, in the spirit of ordinary rubber elasticity. The expansion to the highest order in small strains gives the three linear piezoelectric coefficients predicted by phenomenological models. Received 7 September 1998 and Received in final form 19 October 1998     

Adsorption and spreading of polymers at plane interfaces; theory and molecular dynamics simulations

Nonequilibrium processes play a key role in the adsorption kinetics of macromolecules. It is expected that the competition between transport of polymer towards an interface and its subsequent spreading has a significant influence on the adsorbed amount. An increase of the transport rate can lead to an increase of the adsorbed amount, especially when the polymer has too little time to spread at the interface. In this study we present both molecular dynamics simulations and analytical calculations to describe some aspects of the adsorption kinetics. From MD simulations on a poly(ethylene oxide) chain in vacuum near a graphite surface, we conclude that the spreading process can, in first approximation, be described by either a simple exponential function or by first-order reaction kinetics. Combining these spreading models with the transport equations for two different geometries (stagnation-point flow and overflowing cylinder) we are able to derive analytical equations for the adsorption kinetics of polymers at solid-liquid and at liquid-fluid interfaces. Received: 18 July 1997 / Received in final form: 27 October 1997 / Accepted: 6 November 1997     

A minimal model for vorticity and gradient banding in complex fluids

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relation for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions. Received 1 April 2001 and Received in final form 16 June 2001     

Excluded-volume polymer-induced depletion interaction between parallel flat plates

The interaction between two parallel plates due to non-adsorbing polymer chains with excluded volume is calculated using the adsorption method. The adsorption is calculated from the profile of the polymer segment concentration between the plates, which is obtained from the product function of the concentration profile near a single wall, involving the correlation length. The renormalization group theory provides expressions for the osmotic pressure and consequently for the osmotic compressibility, chemical potential and correlation length of a polymer solution. Both the local polymer concentration profiles as well as the minimum of the interaction potential between the plates agree with recently published self-avoiding random walk computer simulations. Received 9 August 2001     

Influence of the nematic order on the rheology and conformation of stretched comb-like liquid crystalline polymers

We have studied the rheology and the conformation of stretched comb-like liquid-crystalline polymers. Both the influence of the comb-like structure and the specific effect of the nematic interaction on the dynamics are investigated. For this purpose, two isomers of a comb-like polymetacrylate polymer, of well-defined molecular weights, were synthesized: one displays a nematic phase over a wide range of temperature, the other one has only an isotropic phase. Even with high degrees of polymerization N, between 40 and 1000, the polymer chains studied were not entangled. The stress-strain curves during the stretching and relaxation processes show differences between the isotropic and nematic comb-like polymers. They suggest that, in the nematic phase, the chain dynamics is more cooperative than for a usual linear polymer. Small-angle neutron scattering has been used in order to determine the evolution of the chain conformation after stretching, as a function of the duration of relaxation t _r. The conformation can be described with two parameters only: , the global deformation of the polymer chain, and p, the number of statistical units of locally relaxed sub-chains. For the comb-like polymer, the chain deformation is pseudo-affine: is always smaller than (the deformation ratio of the whole sample). In the isotropic phase, has a constant value, while pincreases as tr. This latter behavior is not that expected for non-entangled chains, in which p varies as t _r ^1/2 (Rouse model). In the nematic phase, decreases as a stretched exponential function of t _r, while p remains constant. The dynamics of the comb-like polymers is discussed in terms of living clusters from which junctions are produced by interactions between side chains. The nematic interaction increases the lifetime of these junctions and, strikingly, the relaxation is the same at all scales of the whole polymer chain. Received 5 May 1999 and Received in final form 18 October 1999     

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     

Multilayer Markov Chains with Applications to Polymers in Shear Flow

We present an analysis of multilayer Markov chains and apply the results to a model of a tethered polymer chain in shear flow. We find that the stationary probability measure in the direction of the flow is nonmonotonic, and has several maxima and minima for sufficiently high shear rates. This is in agreement with the experimental observation of cyclic dynamics for such polymer systems. Estimates for the stationary variance and expectation value were obtained and showed to be in accordance with our numerical results.     

Frictional properties of confined polymers

We present molecular dynamics friction calculations for confined hydrocarbon solids with molecular lengths from 20 to 1400 carbon atoms. Two cases are considered: a) polymer sliding against a hard substrate, and b) polymer sliding on polymer. In the first setup the shear stresses are relatively independent of molecular length. For polymer sliding on polymer the friction is significantly larger, and dependent on the molecular chain length. In both cases, the shear stresses are proportional to the squeezing pressure and finite at zero load, indicating an adhesional contribution to the friction force. The friction decreases when the sliding distance is of the order of the molecular length indicating a strong influence of molecular alignment during run-in. The results of our calculations show good correlation with experimental work.     

Dynamics of a tethered polymer in shear flow

The dynamics of a single polymer tethered to a solid surface in a shear flow was observed using fluorescently labeled DNA chains. Dramatic shear enhanced temporal fluctuations in the chain extension were observed. The rate of these fluctuations initially decreased for increasing shear rate gamma; and increased above a critical gamma;. Simulations revealed that these anomalous dynamics arise from a continual recirculating motion of the chain or cyclic dynamics. These dynamics arise from a coupling of the chain velocity in the flow direction to thermally driven fluctuations of the chain in the shear gradient direction.