Hydrodynamic Chain Research Articles

Mechanical reinforcement by bridging chains in polymer nanocomposites

The adsorption-induced bridging of polymer chains between adjacent nanoparticles was studied in poly(vinyl acetate)/silica nanocomposites with different polymer molecular weights, interaction strengths, nanoparticle sizes, and silica loading fractions. The polymer bridging contribution is successfully decoupled from the apparent rubbery plateau modulus by subtracting the hydrodynamic and trapped chain entanglement contributions. The bridging modulus depends on the nearest interparticle surface distance through a power-law relation with a universal exponent −3. Polymer molecular weight can enhance the bridging modulus only when nanoparticles have a high density of adsorption sites due to the emergence of direct bridging of multiple particles by one chain in addition to the regular bridging through self-similar carpets. Our results illustrate that bridging chains can dominate modulus enhancement at nanoparticle's loading at about 10 vol% in polymer nanocomposites with long polymer chains and high surface silanol density.

Symmetric matrix ensemble and integrable hydrodynamic chains

The partition function of the Symmetric Matrix Ensemble is identified with the tau -function of a particular solution of the Pfaff Lattice. We show that, in the case of even power interactions, in the thermodynamic limit, the tau -function corresponds to the solution of an integrable chain of hydrodynamic type. We prove that the hydrodynamic chain so obtained is diagonalisable and admits hydrodynamic reductions in Riemann invariants in an arbitrary number of components.

Design, synthesis, MTT assay, DNA interaction studies of platinum(II) complexes

The square planar Pt(II) complexes of the type [Pt(Ln)(Cl2)] (where Ln = L1−3 = thiophene-2-carboxamide derivatives and L4−6 = thiophene-2-carbothioamide derivatives) have been synthesized and characterized by physicochemical and various spectroscopic studies. MIC method was employed to inference the antibacterial potency of complexes in reference to free ligands and metal salt. Characteristic binding constant (Kb) and binding mode of complexes with calf thymus DNA (CT-DNA) were determined using absorption titration (0.76–1.61 × 105 M−1), hydrodynamic chain length assay and fluorescence quenching analysis, deducing the partial intercalative mode of binding. Molecular docking calculation displayed free energy of binding in the range of –260.06 to –219.63 kJmol−1. The nuclease profile of complexes towards pUC19 DNA shows that the complexes cleave DNA more efficiently compared to their respective metal salt. Cytotoxicity profile of the complexes on the brine shrimp shows that all the complex exhibit noteworthy cytotoxic activity with LC50 values ranging from 7.87 to 15.94 μg/mL. The complexes have been evaluated for cell proliferation potential in human colon carcinoma cells (HCT 116) and IC50 value of complexes by MTT assay (IC50 = 125–1000 μg/mL).

A method for the computation of turbulent polymeric liquids including hydrodynamic interactions and chain entanglements

An asymptotically exact method for the direct computation of turbulent polymeric liquids that includes (a) fully resolved, creeping microflow fields due to hydrodynamic interactions between chains, (b) exact account of (subfilter) residual stresses, (c) polymer Brownian motion, and (d) direct calculation of chain entanglements, is formulated. Although developed in the context of polymeric fluids, the method is equally applicable to turbulent colloidal dispersions and aerosols.

Numerical energy balance analysis for an onshore oscillating water column–wave energy converter

The hydrodynamic performance of Oscillating Water Column (OWC) wave energy converters depends mainly on the behaviour of the wave–OWC interaction. In this paper, a fully nonlinear 2D RANS–based computational fluid dynamics (CFD) model was used to carry out an energy balance analysis of an onshore OWC. Chamber differential air pressure and free surface elevation from published physical measurements were used to validate the CFD model. Additional validation was carried out via PIV data from available model–scale experiments to validate the CFD model's capability in capturing the flow field and the turbulent kinetic energy. The validated CFD model was then used in an extensive campaign of numerical tests to quantify the relevance of different design parameters such as incoming wave height and turbine pneumatic damping to characterise the hydrodynamic performance and wave energy conversion chain of the OWC. To capture the flow field inside the OWC in good agreement, additional refinement was required at the field of view together with utilizing either SST or RSM turbulence models rather than k-ɛ. It is found that the applied damping has crucial impacts on the energy conversion process. Also, increasing the wave height can lead to a massive drop in the system efficiency. Furthermore, both power take–off (PTO) damping and wave height play an important role in vortex formation around the upper and lower chamber's lips during the in–flow and out–flow stages.

Thin films of homopolymers and cylinder-forming diblock copolymers under shear.

We study thin films of homopolymers (PS) and monolayers of cylinder-forming diblock copolymers (PS–PHMA) under shear. To this end, we employed both experiments and computer simulations that correctly take into account hydrodynamic interactions and chain entanglements. Excellent quantitative agreement for static as well as dynamic properties in both the homopolymer and diblock copolymer cases was achieved. In particular, we found that the homopolymer thin films exhibit a distinct shear thinning behavior, which is strongly correlated with the disentanglement and shear alignment of the constituent polymer chains. For the PS–PHMA films, we show that shear can be employed to induce long-range ordering to the spontaneously self-assembled microdomains, which is required for many applications such as the fabrication of nanowire arrays. We found that the impact of chemical incompatibility on the viscosity is only minor in shear-aligned films. Once the domains were aligned, the films exhibited an almost Newtonian response to shear because the cylindrical microdomains acted as guide rails, along which the constituent copolymer chains could simply slide. Furthermore, we developed a model for predicting the onset of shear alignment based on equilibrium dynamics data, and found good agreement with our shear simulations. The employed computational method holds promise for a faster and more cost-effective route for developing custom tailored materials.

The potential of coordinated reservoir operation for flood mitigation in large basins – A case study on the Bavarian Danube using coupled hydrological–hydrodynamic models

Summary The coordinated operation of reservoirs in large-scale river basins has great potential to improve flood mitigation. However, this requires large scale hydrological models to translate the effect of reservoir operation to downstream points of interest, in a quality sufficient for the iterative development of optimized operation strategies. And, of course, it requires reservoirs large enough to make a noticeable impact. In this paper, we present and discuss several methods dealing with these prerequisites for reservoir operation using the example of three major floods in the Bavarian Danube basin (45,000 km2) and nine reservoirs therein: We start by presenting an approach for multi-criteria evaluation of model performance during floods, including aspects of local sensitivity to simulation quality. Then we investigate the potential of joint hydrologic-2d-hydrodynamic modeling to improve model performance. Based on this, we evaluate upper limits of reservoir impact under idealized conditions (perfect knowledge of future rainfall) with two methods: Detailed simulations and statistical analysis of the reservoirs’ specific retention volume. Finally, we investigate to what degree reservoir operation strategies optimized for local (downstream vicinity to the reservoir) and regional (at the Danube) points of interest are compatible. With respect to model evaluation, we found that the consideration of local sensitivities to simulation quality added valuable information not included in the other evaluation criteria (Nash–Sutcliffe efficiency and Peak timing). With respect to the second question, adding hydrodynamic models to the model chain did, contrary to our expectations, not improve simulations, despite the fact that under idealized conditions (using observed instead of simulated lateral inflow) the hydrodynamic models clearly outperformed the routing schemes of the hydrological models. Apparently, the advantages of hydrodynamic models could not be fully exploited when fed by output from hydrological models afflicted with systematic errors in volume and timing. This effect could potentially be reduced by joint calibration of the hydrological–hydrodynamic model chain. Finally, based on the combination of the simulation-based and statistical impact assessment, we identified one reservoir potentially useful for coordinated, regional flood mitigation for the Danube. While this finding is specific to our test basin, the more interesting and generally valid finding is that operation strategies optimized for local and regional flood mitigation are not necessarily mutually exclusive, sometimes they are identical, sometimes they can, due to temporal offsets, be pursued simultaneously.

Collapse Dynamics of Copolymers in a Poor Solvent: Influence of Hydrodynamic Interactions and Chain Sequence

We investigate the dynamics of the collapse of a single copolymer chain, when the solvent quality is suddenly quenched from good to poor. We employ Brownian dynamics simulations of a bead-spring chain model and incorporate fluctuating hydrodynamic interactions via the Rotne-Prager-Yamakawa tensor. Various copolymer architectures are studied within the framework of a two-letter HP model, where monomers of type H (hydrophobic) attract each other, while all interactions involving P (polar or hydrophilic) monomers are purely repulsive. The hydrodynamic interactions are found to assist the collapse. Furthermore, the chain sequence has a strong influence on the kinetics and on the compactness and energy of the final state. The dynamics is typically characterised by initial rapid cluster formation, followed by coalescence and final rearrangement to form the compact globule. The coalescence stage takes most of the collapse time, and its duration is particularly sensitive to the details of the architecture. Long blocks of type P are identified as the main bottlenecks to find the globular state rapidly.

Revisiting of dimensional scaling of linear chains in dilute solutions

The dimensions of linear polymer chains are scaled to their molar mass ( M) as R = kM α with α = 1/2 and 3/5 in a theta and an athermal solvent, respectively. In a good solvent, both k and α are a function of the solvent quality and chain length range. A high-temperature laser light-scattering spectrometer was used to measure the average radius of gyration (〈 R g〉) and hydrodynamic radius (〈 R h〉) of a set of narrowly distributed linear polystyrene chains in decalin over a wide temperature range. k and α in the scaling experimentally varying with T over a chain length range was analyzed. The results reveal that for 〈 R g〉, α = 0.59 − 0.09exp(− τ/0.066) and k = 0.60 τ 2 α−1 , reasonably agreeing with the thermal blob theory. For 〈 R h〉, α = 0.59 − 0.09exp(− τ/0.106), but k deviates from the relationship of k ∝ τ 2 α−1 , reflecting that the hydrodynamic interaction and chain draining are not considered in the thermal blob theory.

Single flexible and semiflexible polymers at high shear: Non-monotonic and non-universal stretching response

Using Brownian hydrodynamic simulation techniques, we study single polymers in shear. We investigate the effects of hydrodynamic interactions, excluded volume, chain extensibility, chain length and semiflexibility. The well-known stretching behavior with increasing shear rate [Formula: see text] is only observed for low shear [Formula: see text] < [Formula: see text] , where [Formula: see text] is the shear rate at maximum polymer extension. For intermediate shear rates [Formula: see text] < [Formula: see text] < [Formula: see text] the radius of gyration decreases with increasing shear with minimum chain extension at [Formula: see text] . For even higher shear [Formula: see text] < [Formula: see text] the chain exhibits again shear stretching. This non-monotonic stretching behavior is obtained in the presence of excluded-volume and hydrodynamic interactions for sufficiently long and inextensible flexible polymers, while it is completely absent for Gaussian extensible chains. We establish the heuristic scaling laws [Formula: see text] approximately N (-1.4) and [Formula: see text] approximately N (0.7) as a function of chain length N , which implies that the regime of shear-induced chain compression widens with increasing chain length. These scaling laws also imply that the chain response at high shear rates is not a universal function of the Weissenberg number Wi = [Formula: see text] [Formula: see text] anymore, where [Formula: see text] is the equilibrium relaxation time. For semiflexible polymers a similar non-monotonic stretching response is obtained. By extrapolating the simulation results to lengths corresponding to experimentally studied DNA molecules, we find that the shear rate [Formula: see text] to reach the compression regime is experimentally realizable.

Soluble Polymer Carriers for the Treatment of Cancer: The Importance of Molecular Architecture

Chemotherapy can destroy tumors and arrest cancer progress. Unfortunately, severe side effects (treatment is usually a series of injections of highly toxic drugs) often restrict the frequency and size of dosages, much to the detriment of tumor inhibition. Most chemotherapeutic drugs have pharmacokinetic profiles with tremendous potential for improvement. Water-soluble polymers offer the potential to increase drug circulation time, improve drug solubility, prolong drug residence time in a tumor, and reduce toxicity. Cytotoxic drugs that are covalently attached to water-soluble polymers via reversible linkages more effectively target tumor tissue than the drugs alone. Macromolecules passively target solid tumor tissue through a combination of reduced renal clearance and exploitation of the enhanced permeation and retention (EPR) effect, which prevails for fast-growing tumors. Effective drug delivery involves a balance between (i) elimination of the polymeric drug conjugate from the bloodstream by the kidneys, liver, and other organs and (ii) movement of the drug out of the blood vasculature and into the tumor (that is, extravasation). Polymers are eliminated in the kidney by filtration through pores with a size comparable to the hydrodynamic diameter of the polymer; in contrast, the openings in the blood vessel structures that traverse tumors are an order of magnitude greater than the diameter of the polymer. Thus, features that may broadly be grouped as the "molecular architecture" of the polymer, such as its hydrodynamic volume (or molecular weight), molecular conformation, chain flexibility, branching, and location of the attached drug, can greatly impact elimination of the polymer from the body through the kidney but have a much smaller effect on the extravasation of the polymer into the tumor. Molecular architecture can in theory be adjusted to assert essentially independent control over elimination and extravasation. Understanding how molecular architecture affects passage of a polymer through a pore is therefore essential for designing polymer drug carriers that are effective in passively delivering a drug payload while conforming to the requirement that the polymers must eventually be eliminated from the body. In this Account, we discuss examples from in vivo studies that demonstrate how polymer architectural features impact the renal filtration of a polymer as well as tumor penetration and tumor accumulation. In brief, features that inhibit passage of a polymer through a pore, such as higher molecular weight, decreased flexibility, and an increased number of polymer chain ends, help prevent elimination of the polymer by the kidneys and can improve blood circulation times and tumor accumulation, thus improving therapeutic effectiveness.

Transformations of integrable hydrodynamic chains and their hydrodynamic reductions

Hydrodynamic reductions of the hydrodynamic chain associated with the dispersionless limit of the 2+1-dimensional Harry-Dym equation are found by using the Miura type and reciprocal transformations applied to the Benney hydrodynamic chain.

Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor

The integrability of an m-component system of hydrodynamic type, u t = V(u)u x , by the generalized hodograph method requires the diagonalizability of the m × m matrix V(u). This condition is known to be equivalent to the vanishing of the corresponding Haantjes tensor. We generalize this approach to hydrodynamic chains—infinite-component systems of hydrodynamic type for which the ∞ × ∞ matrix V(u) is ‘sufficiently sparse’. For such systems the Haantjes tensor is well-defined, and the calculation of its components involves finite summations only. We illustrate our approach by classifying broad classes of conservative and Hamiltonian hydrodynamic chains with the zero Haantjes tensor. We prove that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition for the integrability.

Noncommutative Integrable Systems of Hydrodynamic Type

On noncommutative spaces, integrable hierarchies of hydrodynamic type systems (1\(^{st}\)-order quasilinear PDE’s) do not, in general, exist. Nevertheless, an infinite-component hydrodynamic chain defined below is shown to be integrable. Its modified version is also constructed and it exhibits a new purely noncommutative phenomenon: the number of modified variables is either \(2\) or \(\infty\).

Left-Symmetric Algebras in Hydrodynamics

Left-Symmetric algebras are shown to appear naturally in integrable hydrodynamical systems. First, to a data a Left-Symmetric algebra and an operator of strong deformation on it is attached an infinite commuting hierarchy of integrable systems of hydrodynamical type in 1+1−d. Second, this picture (without deformation) is embedded into an infinite-component integrable hydrodynamic chain.

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

AbstractWe report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 105 ≤ Mw ≤ 3.0 × 106 Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (Mw ≥ 2.0 × 106 Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006

Extensions of 1-Dimensional Polytropic Gas Dynamics

1-dimensional polytropic gas dynamics is integrable for trivial reasons, having 2 < 3 components. It is realized as a subsystem of two different integrable systems: an infinite-component hydrodynamic chain of Lax type, and a 3-component system not of Lax type.

Quasi-equilibrium closure hierarchies for the Boltzmann equation

In this paper, explicit method of constructing approximations (the triangle entropy method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a problem (such as, for example, rates of processes) as new independent variables. The work of the method is demonstrated on the Boltzmann's-type kinetics. New macroscopic variables are introduced (moments of the Boltzmann collision integral, or scattering rates). They are treated as independent variables rather than as infinite moment series. This approach gives the complete account of rates of scattering processes. Transport equations for scattering rates are obtained (the second hydrodynamic chain), similar to the usual moment chain (the first hydrodynamic chain). Various examples of the closure of the first, of the second, and of the mixed hydrodynamic chains are considered for the hard sphere model. It is shown, in particular, that the complete account of scattering processes leads to a renormalization of transport coefficients. The method gives the explicit solution for the closure problem, provides thermodynamic properties of reduced models, and can be applied to any kinetic equation with a thermodynamic Lyapunov function.

Viscosity- and Hydrodynamic-Radius Expansion Factors of Oligo- and Poly(α-methylstyrene)s in Dilute Solution

The intrinsic viscosity [η] was determined for 23 samples of atactic oligo- and poly(α-methylstyrene)s (a-PαMS), each with the fraction of racemic diads fr = 0.72, in the range of weight-average molecular weight Mw from 4.12 × 102 to 5.46 × 106 in three good solvents, toluene, 4-tert-butyltoluene, and n-butyl chloride, at 25.0 °C. The translational diffusion coefficient D was also determined from dynamic light-scattering measurements for 17 a-PαMS samples in the range of Mw from 1.04 × 103 to 3.22 × 106 under the same solvent conditions. It was found that the values of [η] in toluene and n-butyl chloride are appreciably smaller than the previous ones of [η]ϑ in cyclohexane at 30.5 °C (ϑ) in the oligomer region in which the intramolecular excluded-volume effect may be ignored, while those of [η] in 4-tert-butyltoluene are only slightly larger than the latter there because of the dependence on solvent of the hydrodynamic chain (bead) diameter. The disagreement in toluene and n-butyl chloride may be regarded as arising from the so-called specific interaction between polymer and solvent molecules, and therefore the viscosity-radius expansion factor αη in these solvents was calculated after removing its contribution. On the other hand, the values of the hydrodynamic radius RH defined from D in the three good solvents were found to agree well with the previous ones of RH,ϑ in cyclohexane at ϑ in the oligomer region, and therefore the hydrodynamic-radius expansion factor αH could be calculated straightforwardly. It was then found that both plots of αη and αH against the scaled excluded-volume parameter z̃ for a-PαMS in the three good solvents along with those for atactic polystyrene and atactic and isotactic poly(methyl methacrylate)s previously studied form their respective single-composite curves, confirming the validity of the quasi-two-parameter scheme that all expansion factors are functions only of z̃ irrespective of the differences in polymer species (chain stiffness and local chain conformation) and solvent condition.

First and Second Concentration-Dependent Coefficients of Translational Diffusion and Sedimentation for Poly(α-methylstyrene) in a Good Solvent

The first and second concentration-dependent coefficients of translational diffusion, kD and kD2, and of sedimentation, ks and ks2, for poly(α-methylstyrene) fractions of high molecular weight in benzene at 30 °C were determined by dynamic light scattering and sedimentation velocity measurements. In the molecular weight, Mw, range of 3.76 × 105 ≤ Mw ≤ 6.85 × 106, the first coefficients are positive, as reported previously, but the second are negative, which has not been previously observed. These molecular weight dependences are described by power laws (k ∝ Mwa), but the exponents for kD (0.769) and ks (0.663) and for kD2 (1.54) and ks2 (1.48) are smaller than the predicted values in the good-solvent limit, 0.80 and 1.60, respectively. Expressed in the volume-fraction frame of reference, the coefficients are not constant, which contradicts the hard sphere approximation for swollen chains, and are represented well by universal functions of X, the ratio of the thermodynamic interaction radius derived from the second virial coefficient, A2, and the hydrodynamic chain radius derived from the diffusion coefficient; the functions are as predicted by Akcasu and Benmouna with a Mw-independent thermodynamic g factor (=A3/A22Mw) = 0.22−0.23. The hydrodynamic g factors defined by kD2/kD2 and ks2/ks2 are constant, −0.14 and −0.05, respectively, for higher Mw. The two- and three-body effective hydrodynamic interaction radii deduced from ks and ks2 are larger than those from kD and kD2, indicating the long-range nature of the purely hydrodynamic interactions. The swollen chain dynamics in good solvents cannot be described by the hard sphere approximation but require a more detailed treatment of hydrodynamic interactions.