Maximum Chain Length Research Articles

Multiscale simulations of viscoelastic fluids in complex geometries using a finitely extensible nonlinear elastic transient network model

This paper presents a novel implementation of a numerical scheme for predicting complex flows of viscoelastic fluids using a finitely extensible nonlinear elastic (FENE) transient network model. This model extends the FENE model by incorporating chain interactions and accounting for the way in which the maximum chain length, drag, and relaxation time are influenced by entanglement and disentanglement processes. Three different initial networks are considered (disentanglement, entanglement, and aleatory), and the influence of variables such as the kinetic rate constants, elasticity, and chain length on the microstate concentration, stresses, and drag force is investigated. It is shown that although the concentrations of the microstates are independent of the Weissenberg number and the maximum extension length, the stresses and hence the drag are influenced by them.

The Ramsey indexes of paths and cycles

Let G be a graph of size m and let c be a red-blue colouring of the edges of G. A Ramsey chain in G with respect to c is a sequence G 1 , G 2 , … , G ℓ of pairwise edge-disjoint subgraphs of G such that each subgraph G i ( 1 ≤ i ≤ ℓ ) is monochromatic of size i and G i is isomorphic to a subgraph of G i + 1 ( 1 ≤ i ≤ ℓ − 1 ). The Ramsey index A R c ( G ) of G with respect to c is the maximum length of a Ramsey chain in G with respect to c. The Ramsey index AR ( G ) of G is the minimum value of A R c ( G ) among all red-blue colourings c of G. Consequently, if G is a graph of size m where ( k + 1 2 ) ≤ m < ( k + 2 2 ) , then AR ( G ) ≤ k . It was proved that if G = m K 2 is a matching of size m or G = K 1 , m is a star of size m, then AR ( G ) = k if and only if ( k + 1 2 ) ≤ m < ( k + 2 2 ) . A question was posed as to whether there are other classes S of graphs with the property that for every sufficiently large integer m, every graph G of size m in S has the property that AR ( G ) = k if and only if ( k + 1 2 ) ≤ m < ( k + 2 2 ) . We show that all paths have this property and, as a consequence, all cycles have this property as well.

Ramsey Chains in Linear Forests

Every red–blue coloring of the edges of a graph G results in a sequence G1, G2, …, Gℓ of pairwise edge-disjoint monochromatic subgraphs Gi (1≤i≤ℓ) of size i, such that Gi is isomorphic to a subgraph of Gi+1 for 1≤i≤ℓ−1. Such a sequence is called a Ramsey chain in G, and ARc(G) is the maximum length of a Ramsey chain in G, with respect to a red–blue coloring c. The Ramsey index AR(G) of G is the minimum value of ARc(G) among all the red–blue colorings c of G. If G has size m, then k+12≤m&lt;k+22 for some positive integer k. It has been shown that there are infinite classes S of graphs, such that for every graph G of size m in S, AR(G)=k if and only if k+12≤m&lt;k+22. Two of these classes are the matchings mK2 and paths Pm+1 of size m. These are both subclasses of linear forests (a forest of which each of the components is a path). It is shown that if F is any linear forest of size m with k+12&lt;m&lt;k+22, then AR(F)=k. Furthermore, if F is a linear forest of size k+12, where k≥4, that has at most k−12 components, then AR(F)=k, while for each integer t with k−12&lt;t&lt;k+12 there is a linear forest F of size k+12 with t components, such that AR(F)=k−1.

Conformational Parameters and Hydrodynamic Behavior of Poly(2-Methyl-2-Oxazoline) in a Broad Molar Mass Range.

In this work, we report our results on the hydrodynamic behavior of poly(2-methyl-2-oxazoline) (PMeOx). PMeOx is gaining significant attention for use as hydrophilic polymer in pharmaceutical carriers as an alternative for the commonly used poly(ethylene glycol) (PEG), for which antibodies are found in a significant fraction of the human population. The main focus of the current study is to determine the hydrodynamic characteristics of PMeOx under physiological conditions, which serves as basis for better understanding of the use of PMeOx in pharmaceutical applications. This goal was achieved by studying PMeOx solutions in phosphate-buffered saline (PBS) as a solvent at 37 °C. This study was performed based on two series of PMeOx samples; one series is synthesized by conventional living cationic ring-opening polymerization, which is limited by the maximum chain length that can be achieved, and a second series is obtained by an alternative synthesis strategy based on acetylation of well-defined linear poly(ethylene imine) (PEI) prepared by controlled side-chain hydrolysis of a defined high molar mass of poly(2-ethyl-2-oxazoline). The combination of these two series of PMeOx allowed the determination of the Kuhn-Mark-Houwink-Sakurada equations in a broad molar mass range. For intrinsic viscosity, sedimentation and diffusion coefficients, the following expressions were obtained: η=0.015M0.77, s0=0.019M0.42 and D0=2600M-0.58, respectively. As a result, it can be concluded that the phosphate-buffered saline buffer at 37 °C represents a thermodynamically good solvent for PMeOx, based on the scaling indices of the equations. The conformational parameters for PMeOx chains were also determined, revealing an equilibrium rigidity or Kuhn segment length, (A) of 1.7 nm and a polymer chain diameter (d) of 0.4 nm. The obtained value for the equilibrium rigidity is very similar to the reported values for other hydrophilic polymers, such as PEG, poly(vinylpyrrolidone) and poly(2-ethyl-2-oxazoline), making PMeOx a relevant alternative to PEG.

A theory for the coexistence of coiled and stretched configurational phases in the extensional flow of entangled polymer melts.

It has recently been demonstrated via nonequilibrium molecular dynamics (NEMD) simulation [M. H. Nafar Sefiddashti, B. J. Edwards, and B. Khomami, J. Chem. Phys. 148, 141103 (2018); Phys. Rev. Lett. 121, 247802 (2018)] that the extensional flow of entangled polymer melts can engender, within a definite strain-rate regime [expressed in terms of the Deborah number (De) based on the Rouse time], the coexistence of separate domains consisting primarily of either coiled or stretched chain-like macromolecules. This flow-induced phase separation results in bimodal configurational distributions, where transitions of individual molecules between the coiled and stretched states occur very slowly by hopping over an apparent energy activation barrier. We demonstrate that the qualitative aspects of this phenomenon can be described via the single-mode Rolie-Poly model including Convective Constraint Release (CCR) and finite extensibility of the chain-like macromolecules. This analysis reveals the physical mechanism for the configurational coexistence, namely, the nonlinear rate of change of the average entropic restoring force of a given entangled chain with extension. Under conditions of significant flow-induced disentanglement, the rate of change of the effective restoring force initially decreases with extension (effective spring softening) and then increases (hardens) as the maximum chain length is approached. When balanced by flow-induced chain stretching, we find that there can be two configuration states within the same De regime, as covered by the NEMD simulations; therefore, a region of conformational coexistence can indeed exist. However, we demonstrate that this coexistence of configurational microstates is only possible when the magnitude of the CCR parameters is consistent with the rate of flow-induced disentanglement, as observed in the NEMD simulations.

Purification, characterization, and in vitro antitumor activity of a novel glucan from the purple sweet potato Ipomoea Batatas (L.) Lam

A novel glucan PSPP-1 (18.3 kDa) was purified from the foot tuber of purple sweet potato Ipomoea Batatas (L.) Lam. Its backbone was composed of →4)-α-d-Glcp(1→ glycosyl, and branching at the O-2, O-3, and O-6 positions with α-d-Glcp(1→ residues. X-ray diffraction experiment showed that PSPP-1 existed as an amorphous form. Its microstructure was detected via scanning electron microscopy. Its particle size was mainly concentrated at 230 nm in water. Congo red and circular dichroism experiments showed there was no triple-helix conformation. Atomic force microscopy data suggested that its height and width ranged from 1.0 to 6.1 nm and 65 to 210 nm, respectively; its maximum ring diameter and chain length was ∼800 nm and ∼7.0 μm, respectively. Furthermore, it exhibited inhibitory activities on HepG2, LOVO, and MCF-7 cells. Collectively, our data are useful for understanding the structural characteristics of sweet potato polysaccharides, and their application in foods and pharmaceutical areas.

Polymerization-Induced Microphase Separation with Long-Range Order in Melts of Gradient Copolymers.

In this work, we studied the question of whether it is possible to develop a one-step approach for the creation of microphase-separated materials with long-range order with the help of spontaneous gradient copolymers, i.e., formed during controlled copolymerization solely due to the large difference in the reactivity ratios. To that end, we studied the polymerization-induced microphase separation in bulk on the example of a monomer pair with realistic parameters based on styrene (S) and vinylpirrolydone (VP) by means of computer simulation. We showed that for experimentally reasonable chain lengths, the structures with long-range order start to appear at the conversion degree as low as 76%; a full phase diagram in coordinates (fraction of VP—conversion degree) was constructed. Rather rich phase behavior was obtained; moreover, at some VP fractions, order–order transitions were observed. Finally, we studied how the conversion degree at which the order–disorder transition occurs changes upon varying the maximum average chain length in the system.

Forest conversion to oil palm compresses food chain length in tropical streams.

In Southeast Asia, biodiversity-rich forests are being extensively logged and converted to oil palm monocultures. Although the impacts of these changes on biodiversity are largely well documented, we know addition to samples we collected in 201 little about how these large-scale impacts affect freshwater trophic ecology. We used stable isotope analyses (SIA) to determine the impacts of land-use changes on the relative contribution of allochthonous and autochthonous basal resources in 19 stream food webs. We also applied compound-specific SIA and bulk-SIA to determine the trophic position of fish apex predators and meso-predators (invertivores and omnivores). There was no difference in the contribution of autochthonous resources in either consumer group (70-82%) among streams with different land-use type. There was no change in trophic position for meso-predators, but trophic position decreased significantly for apex predators in oil palm plantation streams compared to forest streams. This change in maximum food chain length was due to turnover in identity of the apex predator among land-use types. Disruption of aquatic trophic ecology, through reduction in food chain length and shift in basal resources, may cause significant changes in biodiversity as well as ecosystem functions and services. Understanding this change can help develop more focused priorities for mediating the negative impacts of human activities on freshwater ecosystems.

Lessons learned from using respondent-driven sampling (RDS) to assess sexual risk behaviors among Kenyan young adults living in urban slum settlements: A process evaluation.

BackgroundRespondent-driven sampling (RDS) is a peer-referral sampling methodology used to estimate characteristics of underserved groups that cannot be randomly sampled. RDS has been implemented in several settings to identify hidden populations at risk for HIV, but few studies have reported the methodological lessons learned on RDS design and implementation for assessing sexual risk behaviors in marginalized youth.MethodsWe used RDS to recruit N = 350 young adults, aged 18 to 22, who were living in urban slum settlements in Nairobi, Kenya. A structured survey was used to assess sexual risk behaviors. Twenty seeds were selected and asked to recruit up to three eligible peers. We used small monetary incentives and a three-day recruitment coupon with sequential numbers linking recruiters to their recruits.ResultsData collection was completed in 8 days with a maximum chain length of 6 waves. Each seed yielded 16 to 21 eligible recruits. Three (15%) seeds were unproductive and were replaced. RDS benefits were high identification rates (90% coupons returned per coupons given), high eligibility rates (100% eligible recruits per coupons returned), and high efficiency (~39 eligible recruits per day). 44% of the sample was female. Most recruits (74%) reported being “friends” for 7+ years with their recruiter. RDS overcame feasibility concerns of household-, clinic-, and school-based sampling methodologies in that underserved youth who were unemployed (68%), out of school (48%), ethnic minorities (26%), and having prior residential instability (≥2 moves in the past year) (20%) were successfully recruited, based on weighted analyses. Youth reporting HIV risk behaviors, including unprotected sex (38%), sex while high/drunk (35%), and sex exchange for pay (14%), were also enrolled. However, 28% were not sexually active within the last 6 months. Challenges included managing wait times during peaks and participant referral expectations. Community engagement, use of study-stamped coupons, broad inclusion criteria, incentives, and study sites within walking distances all contributed to the successful implementation of the sampling methodology.ConclusionRDS is an important tool in reaching a diverse sample of underserved and at-risk young adults for study participation. Implications for optimizing RDS for behavioral studies in this population are discussed.

Introducing electrical conductivity to metal-organic framework thin films by templated polymerization of methyl propiolate.

We herein present a case study on the templated, Pd-catalyzed polymerization reaction of methyl propiolate in the confined pore space of three different surface anchored metal-organic framework (SURMOF) systems in order to introduce electrical conductivity to MOF thin films and provide predictions for potential device integrations. To gain comprehensive insight into the influence of the template on polymerization, we chose Cu(bpdc), Cu2(bdc)2(dabco) and HKUST-1 because of their different types of pore channels, 1D, quasi-1D and 3D, and their free pore volumes. Well-defined MOF thin films were prepared using layer-by-layer deposition, which allows for the application of several characterization techniques not applicable for conventional powder MOFs. With SEM, AFM, XRD, MALDI-ToF/MS, ToF-SIMS and QCM, we were able to investigate the behaviour of the polymer formation. For lower dimensional pore channels, we find a depot-like release of monomeric units leading to top-layer formation determined by desorption kinetics, whereas for the 3D channels, quick release of an excess amount of monomers was observed and polymerization proceeds perfectly. Despite polymerization issues, control over the maximum chain lengths and the molecular weight distribution was achieved depending on the dimensionality of the pore systems. For the HKUST-1 system, polymerization was optimized and we were able to measure the electrical conductivity introduced by the conjugated polymer inside the channels.

Determination of the Structural Integrity and Stability of Polysialic Acid during Alkaline and Thermal Treatment.

Polysialic acid (polySia) is a linear homopolymer of varying chain lengths that exists mostly on the outer cell membrane surface of certain bacteria, such as Escherichia coli (E. coli) K1. PolySia, with an average degree of polymerization of 20 (polySia avDP20), possesses material properties that can be used for therapeutic applications to treat inflammatory neurodegenerative diseases. The fermentation of E. coli K1 enables the large-scale production of endogenous long-chain polySia (DP ≈ 130) (LC polySia), from which polySia avDP20 can be manufactured using thermal hydrolysis. To ensure adequate biopharmaceutical quality of the product, the removal of byproducts and contaminants, such as endotoxins, is essential. Recent studies have revealed that the long-term incubation in alkaline sodium hydroxide (NaOH) solutions reduces the endotoxin content down to 3 EU (endotoxin units) per mg, which is in the range of pharmaceutical applications. In this study, we analyzed interferences in the intramolecular structure of polySia caused by harsh NaOH treatment or thermal hydrolysis. Nuclear magnetic resonance (NMR) spectroscopy revealed that neither the incubation in an alkaline solution nor the thermal hydrolysis induced any chemical modification. In addition, HPLC analysis with a preceding 1,2-diamino-4,5-methylenedioxybenzene (DMB) derivatization demonstrated that the alkaline treatment did not induce any hydrolytic effects to reduce the maximum polymer length and that the controlled thermal hydrolysis reduced the maximum chain length effectively, while cost-effective incubation in alkaline solutions had no adverse effects on LC polySia. Therefore, both methods guarantee the production of high-purity, low-molecular-weight polySia without alterations in the structure, which is a prerequisite for the submission of a marketing authorization application as a medicinal product. However, a specific synthesis of low-molecular-weight polySia with defined chain lengths is only possible to a limited extent.

Effects of polymer/surfactant additives on forced convective heat transfer in vortex shedding flow past a circular cylinder

The unsteady incompressible flow of dilute polymer/surfactant solutions past an unconfined heated circular cylinder is studied to reveal the effects of these additives on convective heat transfer properties in the laminar and transitional vortex shedding regime. Both inelastic and elastic non-Newtonian features are considered and compared using two-dimensional numerical simulations. Inelastic power-law and purely viscoelastic Oldroyd-B as well as Giesekus and FENE-P constitutive models, exhibiting both shear thinning and elastic effects are adopted in the formulation. A finite element based software is used in simulations for the Reynolds number range 80≤Re≤300, power-law index range 0.6≤n≤1 and Weissenberg number Wi=1 for weakly elastic solutions. Heat transfer enhancement is observed under inelastic shear thinning effects through an increase of the local and average Nusselt numbers, however purely viscoelastic effects lead to a decrease in the rate of convective heat transfer for the studied range of parameters. The increase in the Giesekus model mobility factor which is associated with anisotropic Brownian motion effects on polymer/surfactant molecules increases the heat transfer rate, and shifts the location of the maximum local Nusselt number to the front of the cylinder. However, increasing the FENE-P model finite extensibility parameter related to the maximum polymer chain length, decreases the local Nusselt number while the maximum heat transfer rate location moves towards the rear region on the cylinder surface. Temperature gradients decrease in the wake region under elasticity whereas shear thinning leads to an increase in the gradients and to the formation of clustered isotherms.

Impact of defect-driven surface inhomogeneity and minimal island formation on temperature-programmed desorption spectra: A kinetic Monte Carlo study

Inhomogeneity often manifests itself on surfaces with pre-adsorbed adsorbates in which islands have widely-disparate sizes due to the presence of distinct morphological features or perhaps even impurities, or defects. In this kinetic Monte Carlo study, we developed a model in which these defects are in the form of vacancy clusters or chains and grow progressively longer with each repeated adsorption-desorption cycle owing to repeated stress that a substrate is subjected to with each cycle. We then explored different simulation-imposed conditions – vacancy or defect concentration as well as maximum vacancy chain length – and noted their impact on the resulting temperature-programmed desorption spectra. We found that growing chains can induce single desorption peak to progressively shift, then split into two closely-overlapping ones over a course of several such cycles. Interestingly, such evolving peaks may hide the true desorption kinetics since calculation of desorption order may yield unconventional, non-integer values – neither zero, first or second-order. We also observed that for the same vacancy concentration, peak-splitting becomes more pronounced with increasing maximum chain length. Analysis of simulation data also revealed that unlike bigger and more compact islands, small ones follow first-order desorption kinetics rather than half-order kinetics.

Use of THM-PY-GC/MS technique to characterize complex, multilayered Chinese lacquer

Use of micro-destructive analytical techniques to explore the complex matrix composition, structure and lacquering techniques of multilayer lacquered objects has been the focus of many researchers. This work presents the results of a comprehensive investigation of the “Tixi” carved lacquer micro-sample excavated from Zhejiang province in China (Song Dynasty, A.D. 960-A.D. 1279). Stereomicroscopy, EPMA-EDS, FTIR, μ-RS and THM-Py-GC/MS were used in a comprehensive study of the object. The results show that the structure of the lacquer body consists of one wooden body layer, one lacquer ash layer, one ground lacquer layer and four lacquer film pigment layers, which indicates that it has been lacquered for several times. The chemical composition analysis results show that the lacquer stucco layer was made from the ashes by“Wan lacquering” craft. The lacquer film was made up of pigment (soot (black layer), orpiment (yellow layer), cinnabar (red layer)), lacquer sap, heat-bodied tung oil and tannins (partial layer); the presence of the series of catechols, acid catechols, phenols, alkyl benzenes, and hydrocarbons in which each has a maximum side chain length of 17 carbons and the most abundant member has nine carbons clearly indicate the species of the lacquer tree was Rhus succedanea that produces laccol. “Tixi” carved craft was used to make different lacquer film pigment veins layers appear simultaneously to emerge its unique characteristics like “drifting clouds and flowing water”.

Characterization of oxidized oligomers from polyethylene films by mass spectrometry and NMR spectroscopy before and after biodegradation by a Rhodococcus rhodochrous strain

The objective of this work was to develop a new approach to assess the specificity and the efficiency of biodegradation of oxidized oligomers extracted from aged HDPE polyethylene films and to bring insight on the mechanisms occurring during biodegradation. 1H NMR spectroscopy and LC Orbitrap™ mass spectrometry were combined together with data processing using Kendrick mass defect calculation and Van Krevelen Diagram.We showed that the molecular weight of extracted oligomers was lower than 850 Da with maximum chain length of 55 carbon atoms. The oligomers were divided into 11 classes of molecules with different oxidation state ranging from 0 to 10. All classes included series of chemically related compounds including up to 19 molecules.95% of the soluble oligomers were assimilated by a strain of Rhodococcus rhodocchrous after 240 days of incubation. Large highly oxidized molecules completely disappeared while the other classes of molecules were still represented. Molecules containing 0–1 oxygen atom were less degraded. A strong shift to smaller molecules (<450 Da, 25 carbon atoms) was observed suggesting that longer molecules disappeared more rapidly than the smaller ones. It opens new perspectives on biodegradation processes as not only intracellular β-oxidation must be considered but also extracellular mechanisms leading to chain cleavages.

Variation of surface area of silica monoliths by controlling ionic character/chain length of surfactants and polymers

To achieve maximum pore diameter and surface area of porous silica monoliths different structure directing agents (SDAs) (Cationic/anionic/neutral/mixture) were used. BET study showed alteration of SDA’s chain length, composition or concentration have a cumulative effect on controlling the surface area and pore size. PEG in combination with other SDAs like CTAB, SDS, BTMAC, Triton-X100 etc. controlled internal agglomeration along with particles size. The maximum amount of surface area was observed by using maximum chain length of PEG and CTAB.

Oscillating collision of the granular chain on static wall

Collision of the granular chain on static wall is investigated by discrete element method. Collision time and traveling time are proposed on the basis of the characteristics of the collision of a single grain with a wall and the propagation of interaction force wave in a granular chain to explain the collision process. Simulation results show that an oscillating collision force is generated when the force waves successively arrive at the wall. For the collision of a mono-dispersed chain, the simulation data are in good agreement with the predicted relationship between the maximum chain length of nmax and the first maximum collision force FA. Rigid wall and soft wall are defined as nmax=1 and nmax≥2, respectively. Two similar processes of oscillating collisions occur when a light or a heavy impure grain is introduced. In these processes, two maximum collision forces, namely, FA and FB, are observed, respectively. The simulation results about the influence of the mass and position of light impure grain on the collision force FB further confirm our theoretical predictions.

Complex reaction network generation for Steady State Isotopic Transient Kinetic Analysis: Fischer-Tropsch Synthesis

A versatile modeling strategy for Steady State Isotopic Transient Kinetic Analysis (SSITKA) data, acquired in a plug flow reactor, is elaborated with particular attention to complex reaction networks and Fischer-Tropsch Synthesis as example. A spatial discretization scheme optimizing accuracy and CPU time is developed. For low switch time constants, the van Leer and van Albada flux limiter functions used in conjunction with the DASPK solver yields the lowest CPU time for the integration of the resulting ordinary differential equations. For larger switch time constants, conventional central differencing can be applied. A network generation methodology is implemented accounting for the isotopic labeling. It reduces the exponential dependence of the number of considered species on the carbon number to a quadratic dependence. For a reaction network allowing a maximum chain length of 5 carbon atoms a gain in CPU time up to a factor of 10 can be achieved.

A Note on a Mixed Routing and Scheduling Problem on a Grid Graph

In this paper we study a particular case of the Fleet Quickest Routing Problem (FQRP) on a grid graph, i.e., a Manhattan graph of m×n nodes: nodes are placed in m lines (which we shall call levels) and n columns. FQRP is a particular Multi-commodity Flow Problem in which we must find the routes n vehicles have to perform from an initial position, at the lowest level, to a final position at the highest level. Vehicles must respect capacity constraints on the arcs and on the nodes of the grid. The objective consists in the minimization of the sum of times needed to route every vehicle. The problem arises when we must manage at the same time and automatically the movements of a fleet of vehicles. In this setting, the number of levels has a strong impact both on the existence of routes which do not use the same resource at the same time, and on the time needed to reach the final position. In the paper we prove that the minimum number of levels which guarantees a feasible solution is linked to a parameter defined as the maximum length of a C-type conflict chain we can build in a problem involving n vehicles. In the paper we also propose a strategy which allows to find the optimal route for each vehicle.

Polymer adsorption on reconstructed Au(001): a statistical description of P3HT by scanning tunneling microscopy and coarse-grained Monte Carlo simulations.

We report on a combined theoretical and experimental characterization of isolated Poly(3-hexylthiophene) (P3HT) chains weakly adsorbed on a reconstructed Au(001) surface. The local chain conformations of in situ deposited P3HT molecules were investigated by means of scanning tunneling microscopy. For comparison, Monte Carlo simulations of the system were performed up to a maximum chain length of 60 monomer units. The dependence of the end-to-end distance and the radius of gyration on the polymer chain length shows a good agreement between experiment and Monte Carlo simulations using simple updates for short chains.