Irreversible adsorption from dilute polymer solutions

We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two broad cases are considered, distinguished by the magnitude of the local monomer-surface sticking rate Q: chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single-chain adsorption. While single-chain physisorption times are typically micro- to milli-seconds, for chemisorbing chains of N units we find experimentally accessible times , ranging from seconds to hours. We establish 3 chemisorption universality classes, determined by a critical contact exponent: zipping, accelerated zipping and homogeneous collapse. For dilute solutions, the mechanism is accelerated zipping: zipping propagates outwards from the first attachment, accelerated by occasional formation of large loops which nucleate further zipping. This leads to a transient distribution of loop lengths s up to a maximum size after time t. By times of order the entire chain is adsorbed. The outcome of the single-chain adsorption episode is a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb onto, late-arriving chains form a diffuse outer layer. In a simple picture we find for both chemisorption and physisorption a final loop distribution and density profile whose forms are the same as for equilibrium layers. In contrast to equilibrium layers, however, the statistical properties of a given chain depend on its adsorption time; the outer layer contains many classes of chain, each characterized by a different fraction of adsorbed monomers f. Consistent with strong physisorption experiments, we find the f values follow a distribution .Received: 13 January 2003, Published online: 8 July 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 68.08.-p Liquid-solid interfaces     

Two-dimensional turbulence of dilute polymer solutions

We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that, at vanishingly small concentrations, such that the polymers are passively transported, the probability distribution of polymer elongation has a power law tail: Its slope is related to the statistics of finite-time Lyapunov exponents of the flow, in quantitative agreement with theoretical predictions. We show that at finite concentrations and sufficiently large elasticity the polymers react on the flow with manifold consequences: Velocity fluctuations are drastically depleted, as observed in soap film experiments; the velocity statistics becomes strongly intermittent; the distribution of finite-time Lyapunov exponents shifts to lower values, signaling the reduction of Lagrangian chaos.     

Hydrodynamics of dilute rouse polymer solutions under flow

Using Langevin method the hydrodynamics of dilute polymer solutions under flow is described by deriving an effective hydrodynamic equation for these solutions. The systematics of the present treatment is demonstrated by considering Rouse chains as a simple example.     

Hydrodynamic interactions of dilute polymer solutions in elongational flow

Dumbbell models are only crude representations of actual polymer molecules, but their simplicity allows for explicit calculations which in many instances have shed light on the connection between molecular properties and rheological behavior. On the other hand, hydrodynamic interactions are known to strongly influence the dynamic response of polymer solutions and this makes the representation of the hydrodynamic drag an important aspect in the calculations. In the present work, the effects of the state of flow are incorporated explicitly in the frictional properties of the FENE model of a dilute polymer solution. Results for the steady elongational viscosity and the mean square end-to-end distance arc presented.     

Calculation of the intrinsic viscosity for dilute polymer solutions undergoing shear flow

Starting from a set of coupled Langevin equations describing the dynamics of flexible (Gaussian) polymer chains in the presence of hydrodynamic interactions and undergoing a weak shear flow, the stress tensor is determined using Kramers formula. With the aid of renormalization group techniques the steady state intrinsic viscosity is extracted toO() (4–d,d being the spatial dimensionality) and to lowest nontrivial order in the flow strength. Within the preaveraging approximation we find a numerically small effect of shear thinning.     

Frictional properties of dilute polymer solutions IV. Intrinsic viscosity

In the framework of our generalization of the Debye-Bueche theory for the frictional properties of dilute polymer solutions we study the intrinsic viscosity. A careful definition of the intrinsic viscosity for polymers with spherically symmetric density distribution is given. The equations are solved explicity for uniform spheres and spherical shells. For the general case a perturbation method is applied and a variational principle of minimum energy dissipation is formulated which is suitable for numerical work.     

Frictional properties of dilute polymer solutions: III. Translational-friction coefficient

In the framework of our generalization of the Debye-Bueche theory for the frictional properties of dilute polymer solutions we study the translational-friction coefficient of polymers with spherically symmetric segment distribution. A variational principle of minimum energy dissipation is formulated which is suitable for numerical work.     

Einstein's equations as constitutive relations

The aim of this article is to present one more possible derivation of the Einstein's equations of general relativity. The new route is based on old concepts of continuum mechanics, extended to four spacetime dimensions. Our main idea is to consider Einstein's equations as the constitutive relations of the spacetime manifold. Moreover, for us, the spacetime manifold is a nonlinear elastic medium with extrinsic defects (extra-matter). This idea dates back to Cauchy's treatment of elasticity. In Cauchy's words: the crucial ingredient in solid mechanics is the equation which expresses how the force intensity at any point in a body is related to the change of shape near that point. We will try to generalize them.     

Pattern formation in Taylor-Couette flow of dilute polymer solutions: dynamical simulations and mechanism

We report spatiotemporal pattern formation in Taylor-Couette flow (i.e., flow between rotating cylinders) of viscoelastic dilute polymer solutions obtained for the first time from first-principles dynamical simulations. Solution structures with varying spatial and temporal symmetries, such as rotating standing waves, flames, disordered oscillations, and solitary vortex solutions which include diwhirls (stationary and axisymmetric) and oscillatory strips (axisymmetric or nonaxisymmetric), are observed, depending on the ratio of fluid relaxation time to the time period of inner cylinder rotation. The flow-microstructure coupling mechanisms underlying the pattern formation process are also discussed.     

On optimal reconstruction of constitutive relations

In this investigation we develop and validate a computational method for reconstructing constitutive relations based on measurement data, applicable to problems arising in nonequilibrium thermodynamics and continuum mechanics. This parameter estimation problem is solved as PDE-constrained optimization using a gradient-based technique in the optimize-then-discretize framework. The principal challenge is that the control variable (i.e., the relation characterizing the constitutive property) is not a function of the independent variables in the problem, but of the state (dependent) variable. The proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable. It relies on three main ingredients: a computationally friendly expression for the cost functional gradient, Sobolev gradients used in lieu of discontinuous L₂ gradients, and a systematic technique for shifting the identifiability region. The performance of this approach is illustrated by the reconstruction of the temperature dependence of the thermal conductivity in a one-dimensional model problem.     

Microscopic calculation of the constitutive relations

Homogenization theory is used to calculate the macroscopic dielectric constant from the quantum microscopic dielectric function in a periodic medium. The method can be used to calculate any macroscopic constitutive relation, but it is illustrated here for the case of electrodynamics of matter. The so-called cell problem of homogenization theory is solved and an explicit expression is given for the macroscopic dielectric constant in a form akin to the Clausius-Mossotti or Lorentz-Lorenz relation. The validity of this expression is checked by showing that the standard formula is recovered for cubic materials and that the average of the microscopic energy density is the macroscopic one. Finally, the general expression is applied to Bloch eigenstates.     

Dielectric studies in dilute solutions

Dielectric studies in dilute solutions of cyclohexane and benzene have been carried out in the temperature range 294–318°K. The observed data have been utilized to evaluate the relaxation times and thermodynamic parameters of these molecules. The high values ofα for 2-acetyl pyridine indicate the occurrence of more than one relaxation time. In the remaining systems, the observed lowα values indicate their rigid behaviour. The variation in the dielectric relaxation time is mostly correlated with the change in the heterocyclic configuration of the system.     

Rheological observation of glassy dynamics of dilute polymer solutions near the coil-stretch transition in elongational flows

It has long been conjectured that the macroscopic dynamics of dilute polymer solutions may exhibit a glasslike slowdown caused by ergodicity breaking, in the vicinity of the coil-stretch transition in elongational flows. We report experimental observations using a filament stretching rheometer that confirm the existence of such glassy states. It is observed that different time-dependent elongational strain-rate profiles lead to a pronounced history dependence and aging effects within a narrow range of strain rates. The results have a direct bearing on the analysis and design of processes employing dilute polymer solutions, such as ink-jet printing, surface coating, and turbulent-drag reduction.     

Exact and approximate solutions for the dilute Ising model

The ground state energy and entropy of the dilute mean field Ising model is computed exactly by a single order parameter as a function of the dilution coefficient. An analogous exact solution is obtained in the presence of a magnetic field with random locations. Results lead to a complete understanding of the geography of the associated random graph. In particular, we give the size of the giant component (continent) and the number of isolated clusters of connected spins of all given size (islands). We also compute the average number of bonds per spin in the continent and in the islands. Then, we tackle the problem of solving the dilute Ising model at strictly positive temperature. In order to obtain the free energy as a function of the dilution coefficient and the temperature, it is necessary to introduce a second order parameter. We are able to find out the exact solution in the paramagnetic region and exactly determine the phase transition line. In the ferromagnetic region we provide a solution in terms of an expansion with respect to the second parameter which can be made as accurate as necessary. All results are reached in the replica frame by a strategy which is not based on multi-overlaps.     

稀薄量子系统中的接触量和普适关系

对接触量和普适关系的发现是超冷原子物理中的一个重大理论突破。自檀时钠于2005年首次指出接触量这个概念以来,对普适关系的研究已经成为冷原子物理中的一个重要课题,并对其他相关的领域产生了重大的影响。文章介绍了什么是接触量和普适关系,以及普适关系的来源,并讨论在这个研究方向上最新的一些进展,包括高分波散射的接触量和接触量谱。     

Critical behavior of dilute electrolyte solutions

A theory of the critical behavior of a dilute ionic solution is constructed. An expression for the susceptibility in a wide temperature range is obtained. It is shown that ionic solutions belong to the universality class of the Ising model. The Ginzburg parameter of the ionic solutions decreases with the increase of the solvent concentration. In the general case, the critical exponent of susceptibility nonmonotonically depends on the temperature in the crossover region from the Ising-like to the mean-field behavior. In the vicinity of the transition point, the Debye-Hückel screening radius is proportional to the correlation length. As T→T _c, the screening radius tends to infinity and the screening disappears. The voltage between the two phases of the ionic solution is proportional to the order parameter and changes as |T/T _c?1|^β in the vicinity of the phase transition point.