Effect Of Polydispersity Research Articles

Discussion about the use of the volume specific surface area (VSSA) as a criterion to identify nanomaterials according to the EU definition. Part two: experimental approach.

The first part of this study was dedicated to the modelling of the influence of particle shape, porosity and particle size distribution on the volume specific surface area (VSSA) values in order to check the applicability of this concept to the identification of nanomaterials according to the European Commission Recommendation. In this second part, experimental VSSA values are obtained for various samples from nitrogen adsorption isotherms and these values were used as a screening tool to identify and classify nanomaterials. These identification results are compared to the identification based on the 50% of particles with a size below 100 nm criterion applied to the experimental particle size distributions obtained by analysis of electron microscopy images on the same materials. It is concluded that the experimental VSSA values are able to identify nanomaterials, without false negative identification, if they have a mono-modal particle size, if the adsorption data cover the relative pressure range from 0.001 to 0.65 and if a simple, qualitative image of the particles by transmission or scanning electron microscopy is available to define their shape. The experimental conditions to obtain reliable adsorption data as well as the way to analyze the adsorption isotherms are described and discussed in some detail in order to help the reader in using the experimental VSSA criterion. To obtain the experimental VSSA values, the BET surface area can be used for non-porous particles, but for porous, nanostructured or coated nanoparticles, only the external surface of the particles, obtained by a modified t-plot approach, should be considered to determine the experimental VSSA and to avoid false positive identification of nanomaterials, only the external surface area being related to the particle size. Finally, the availability of experimental VSSA values together with particle size distributions obtained by electron microscopy gave the opportunity to check the representativeness of the two models described in the first part of this study. They were also used to calculate the VSSA values and these calculated values were compared to the experimental results. For narrow particle size distributions, both models give similar VSSA values quite comparable to the experimental ones. But when the particle size distribution broadens or is of multi-bimodal shape, as theoretically predicted, one model leads to VSSA values higher than the experimental ones while the other most often leads to VSSA values lower than the experimental ones. The experimental VSSA approach then appears as a reliable, simple screening tool to identify nano and non-nano-materials. The modelling approach cannot be used as a formal identification tool but could be useful to screen for potential effects of shape, polydispersity and size, for example to compare various possible nanoforms.

Reduced Ensemble Plasmon Line Widths and Enhanced Two-Photon Luminescence in Anodically Formed High Surface Area Au-TiO2 3D Nanocomposites.

Localized surface plasmon resonances (LSPR) in TiO2 nanorod and nanotube arrays decorated by gold nanoparticles can be exploited to improve photocatalytic activity, enhance nonlinear optical coefficients, and increase light harvesting in solar cells. However, the LSPR typically has a low quality factor, and the resonance is often obscured by the Urbach tail of the TiO2 band gap absorption. Attempts to increase the LSPR extinction intensity by increasing the density of gold nanoparticles on the surface of the TiO2 nanostructures invariably produce peak broadening due to the effects of either agglomeration or polydispersity. We present a new class of hybrid nanostructures containing gold nanoparticles (NPs) partially embedded in nanoporous/nanotubular TiO2 by performing the anodization of cosputtered Ti-Au thin films containing a relatively high ratio of Au:Ti. Our method of anodizing thin film stacks containing alternate layers of Ti and TiAu results in very distinctive LSPR peaks with quality factors as high as 6.9 and ensemble line widths as small as 0.33 eV even in the presence of an Urbach tail. Unusual features in the anodization of such films are observed and explained, including oscillatory current transients and the observation of coherent heterointerfaces between the Au NPs and anatase TiO2. We further show that such a plasmonic NP-embedded nanotube structure dramatically outperforms a plasmonic NP-decorated anodic nanotube structure in terms of the extinction coefficient, and achieves a strongly enhanced two-photon fluorescence due to the high density of gold nanoparticles in the composite film and the plasmonic local field enhancement.

Polydisperse Polymer Brushes: Internal Structure, Critical Behavior, and Interaction with Flow

We study the effect of polydispersity on the structure of polymer brushes by analytical theory, a numerical self-consistent field approach, and Monte Carlo simulations. The polydispersity is represented by the Schulz-Zimm chain-length distribution. We specifically focus on three different polydispersities representing sharp, moderate and extremely wide chain length distributions and derive explicit analytical expressions for the chain end distributions in these brushes. The results are in very good agreement with numerical data obtained with self-consistent field calculations and Monte Carlo simulations. With increasing polydispersity, the brush density profile changes from convex to concave, and for given average chain length $N_n$ and grafting density $\sigma$, the brush height $H$ is found to scale as $(H/H_{\mathrm{mono}}-1)\propto(N_w/N_n-1)^{1/2}$ over a wide range of polydispersity indices $N_w/N_n$ (here $H_{\mathrm{mono}}$ is the height of the corresponding monodisperse brush. Chain end fluctuations are found to be strongly suppressed already at very small polydispersity. Based on this observation, we introduce the concept of the brush as a near-critical system with two parameters (scaling variables), $(N_{n}\sigma^{2/3})^{-1}$ and $(N_w/N_n-1)^{1/2}$, controlling the distance from the critical point. This approach provides a good description of the simulation data. Finally we study the hydrodynamic penetration length $l_\mathrm{p}$ for brush-coated surfaces in flow. We find that it generally increases with polydispersity. The scaling behavior crosses over from $l_\mathrm{p}\sim N_\mathrm{n}^{1/2}\sigma^{-1/6}$ for monodisperse and weakly polydisperse brushes to $l_\mathrm{p}\sim N_{n}^{2/3}$ for strongly polydisperse brushes.

Contaminated particle characteristics influence on membrane fouling

AbstractThe goal of the current research study was to critically examine the role of the shape of contaminated particles for an accurate prediction of membrane fouling phenomenon. Polycarbonate flat membranes with uniform pore sizes of 0.05 µm and 0.1 µm, in addition to Polysulfone membranes with molecular weight cut of 60,000, were used under a constant feed flow rate and a cross‐flow mode in ultrafiltration of a latex paint solution featuring a wide range of particle size distribution. The current mathematical model was developed to illustrate the effect of irregularity and polydispersity of latex particles on the mass of fouling and irreversible fouling on membranes. The results obtained indicate that the sphericity of contaminated particles had a significant influence on fouling potential at different aggregation levels.

The effect of polydispersity on the magnetostatic properties of concentrated ferrofluids

A statistical model of highly concentrated polydisperse ferrocolloids is proposed. The study approach is based on the second-order modified mean-field theory (MMF2) [A.O. Ivanov, O.B. Kuznetsova, Magnetic properties of dense ferrofluids: an influence of interparticle correlations, Phys. Rev. E 64 (2001) 041405-1–12]. To increase the accuracy of the analytical expression of the magnetization we calculate the contribution of the dipole–dipole interaction energy up to the 2nd order in the pair distribution function for ferroparticles system. The obtained expression of magnetization corresponds to the theoretical expression of initial magnetic susceptibility proposed by the new polydisperse theory [A.O. Ivanov, E.A. Elfimova, Low-temperature magnetic susceptibility of concentrated ferrofluids: the influence of polydispersity, J. Magn. Magn. Matter. 374 (2015) 327–332] exactly. In conjunction it can be applied for magnetogranulometric analysis of polydisperse concentrated ferrofluids.

Effects of Blockiness and Polydispersity on the Phase Behavior of Random Block Copolymers

The effects of blockiness and compositional/sequential polydispersity on the order–disorder transition of random block copolymers are studied using a segment model of random block copolymers. Specifically, the copolymers are randomly assembled from a collection of equal‐length “segments,” while the characteristics of the segments are chosen according to the nature of the polydispersity. The phase behavior of the model system is examined using the random phase approximation. The critical points of the system are calculated over a range of blockiness and polydispersity for a variety of segment models. It is observed that the critical value of the Flory–Huggins parameter χ, above which the homogeneous phase becomes unstable, is inversely proportional to the blockiness. Furthermore, it is found that sequential and compositional dispersity decreases the critical value of χ, but that the effect of sequential dispersity is much weaker. At sufficiently large compositional dispersity, the random block copolymers can undergo macrophase separation. In this region of phase space, the critical point is entirely determined by the compositional polydispersity.image

Effect of Energy Polydispersity on the Nature of Lennard-Jones Liquids.

In the companion paper [ Ingebrigtsen , T. S. ; Tanaka , H. J. Phys. Chem. B 2015 , 119 , 11052 ] the effect of size polydispersity on the nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, was studied. More specifically, it was shown that even highly size polydisperse LJ liquids are Roskilde-simple (RS) liquids. RS liquids are liquids with strong correlation between constant volume equilibrium fluctuations of virial and potential energy and are simpler than other types of liquids. Moreover, it was shown that size polydisperse LJ liquids have isomorphs to a good approximation. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless (reduced) units. In this paper, we study the effect of energy polydispersity on the nature of LJ liquids. We show that energy polydisperse LJ liquids are RS liquids. However, a tendency of particle segregation, which increases with the degree of polydispersity, leads to a loss of strong virial-potential energy correlation but is mitigated by increasing temperature and/or density. Isomorphs are a good approximation also for energy polydisperse LJ liquids, although particle-resolved quantities display a somewhat poorer scaling compared to the mean quantities along the isomorph.

Effect of Polydispersity of Clay Platelets on the Aggregation and Mechanical Properties of Clay at the Mesoscale

AbstractThe results from mesoscale simulations of the formation and evolution of microstructure for assemblies of Na-smectite particles based on assumed size distributions of individual clay platelets are presented here. The analyses predicted particle arrangements and aggregation (i.e. platelets linked in face—face configurations) and are used to link geometric properties of the microstructure and mechanical properties of the particle assemblies. Interactions between individual ellipsoidal clay platelets are represented using the Gay-Berne potential based on atomistic simulations of the free energy between two Na-smectite clay-platelets in liquid water, following a novel coarse-graining method developed previously. The current study describes the geometric (aggregate thickness, orientation, and porosity) and elastic properties in the ‘jammed states’ from the mesoscale simulations for selected ranges of clay particle sizes and confining pressures. The thickness of clay aggregates for monodisperse assemblies increases (with average stack thickness consisting of n = 3–8 platelets) with the diameter of the individualclay platelets and with the level of confining pressure. Aggregates break down at high confining pressures (50–300 atm) due to slippage between the platelets. Polydisperse simulations generate smaller aggregates (n = 2) and show much smaller effects of confining pressure. All assemblies show increased order with confining pressure, implying more anisotropic microstructure. The mesoscale simulations are also in good agreement with macroscopic compression behavior measured in conventional 1-D laboratory compression tests. The mesoscale assemblies exhibit cubic symmetry in elastic properties. The results for larger platelets (D = 1000 Å) are in good agreement with nano-indentation measurements on natural clays and shale samples.

Effects of polydispersity, additives, impurities and surfaces on the crystallization of poly(ethylene oxide)(PEO) confined to nanoporous alumina

Abstract The effects of polydispersity, additives, impurities, free top layer and of surface roughness on the nucleation are studied for poly(ethylene oxide) located inside self-ordered nanoporous aluminum oxide (AAO). AAO pore diameters ranged from 400 nm to 25 nm. With the exception of a surface layer, none of the above factors is able to induce heterogeneous nucleation under confinement. Homogeneous nucleation remains the sole mechanism in pores having diameters below 65 nm. The internal pore surface roughness is small, which explains the minor effects of AAO surfaces on inducing heterogeneous nucleation especially within the smaller pores. The presence of oligomers shifts the homogeneous nucleation temperature to lower temperatures, reflecting the plasticizing effect of the oligomers on the liquid-to-glass temperature.

Numerical study of the multi-flame structure in spray combustion

We investigate the multi-flame phenomenon often seen in spray combustion. To do so, simulations are made of two cases from the Delft Spray in Hot Coflow (DSHC) database. These two cases have the same fuel (ethanol) but differ in the type of coflow: room temperature air (case AII) or products of lean premixed combustion (case HII), and they exhibit remarkably different flame structure, respectively with a ‘double flame’ and a ‘single flame’. The two-phase flow was handled with an Eulerian–Lagrangian approach. Large Eddy Simulation (LES) with Flamelet Generated Manifolds (FGM) method was used to account for the turbulence and combustion. Validation was done by using available experimental data as well as information on similar systems reported in literature. Major features of these two cases were correctly reproduced. Simulation results revealed that four spatially separated reaction regions exist in the flame AII and two in the flame HII. These regions are of different types, premixed or non-premixed, and are formed by different species, major fuel (ethanol) or intermediate species, e.g. carbon monoxide. The mechanism underlying the multi-flame structure was investigated and explained in terms of the relative magnitude of different time scales, namely of droplet evaporation, dispersion, convection and reaction. Parametric studies on the effect of spray polydispersity and coflowing air temperature were carried out, demonstrating an even wider range of flame structures. An important observation is that the ‘single flame’ structure usually present in the hot-diluted coflow case (HII), is also generated in a case of room temperature air coflow, provided the injected droplets are small. This is attributed to the fact that representative droplets in all cases with single flame have similar evaporation time scale. Or stated more generally, by matching important time scales, similar flame structure can be created under considerably different conditions.

Investigation of bubble swarm drag at elevated pressure in a contaminated system

Improved estimates of bubble dynamics in industrial gas-liquid fluid systems are important for accurately modeling multiphase flow. In many gas-liquid industrial systems at elevated pressure, bubbles exist in a polydisperse size population. This work experimentally characterizes the effects of bubble swarm polydispersity and gas holdup on drag using a monofibre optical probe in an ethanol contaminated aqueous system, providing an evaluation of current swarm drag models under industrially relevant pressures and high gas holdup conditions (up to 37% gas fraction). At atmospheric pressure, the rise velocity and swarm-corrected drag of individual bubbles within a polydisperse distribution of bubbles was found to be well-predicted by the swarm correction model of Lockett and Kirkpatrick (1975). An improved fit to the reported data was found using a piecewise isolated single bubble drag coefficient correlation. At elevated pressures (6.5MPa), swarm hindrance effects were not observed for detected bubbles and the rise velocity and drag coefficient of individual bubbles within a polydisperse distribution were well predicted without the use of a swarm correction model.

Effect of the Polydispersity of a Colloidal Drop on Drying Induced Stress as Measured by the Buckling of a Floating Sheet.

We study the stress developed during the drying of a colloidal drop of silica nanoparticles. In particular, we use the wrinkling instability of a thin floating sheet to measure the net stress applied by the deposit on the substrate and we focus on the effect of the particle polydispersity. In the case of a bidisperse suspension, we show that a small number of large particles substantially decreases the expected stress, which we interpret as the formation of lower hydrodynamic resistance paths in the porous material. As colloidal suspensions are usually polydisperse, we show for different average particle sizes that the stress is effectively dominated by the larger particles of the distribution and not by the average particle size.

Modeling the viscosity of polydisperse suspensions: Improvements in prediction of limiting behavior

The present study develops a fully consistent extension of the approach pioneered by Farris [“Prediction of the viscosity of multimodal suspensions from unimodal viscosity data,” Trans. Soc. Rheol. 12, 281–301 (1968)] to describe the viscosity of polydisperse suspensions significantly improving upon our previous model [P. M. Mwasame, N. J. Wagner, and A. N. Beris, “Modeling the effects of polydispersity on the viscosity of noncolloidal hard sphere suspensions,” J. Rheol. 60, 225-240 (2016)]. The new model captures the Farris limit of large size differences between consecutive particle size classes in a suspension. Moreover, the new model includes a further generalization that enables its application to real, complex suspensions that deviate from ideal non-colloidal suspension behavior. The capability of the new model to predict the viscosity of complex suspensions is illustrated by comparison against experimental data.

An analytical investigation of the effect of non-uniformity on the elastic moduli of granular media

• The effect of polydispersity on the small strain elastic moduli is considered. • For their evaluation an upscaling technique based on the elastic energy is used. • Two different types of granulometric curves are considered. • The elastic moduli show a strong dependence of the coefficient of uniformity. • The model captures well the laboratory results. The present work is concerned with the analytical investigation of the effect of polydispersity on the elastic moduli of granular media. Empirical formulas are available for the estimation of elastic parameters of sands, especially for the shear modulus, usually as a function of the void ratio and the effective mean pressure. These relationships do not reflect the dependence of the small strain shear modulus on the granulometric material properties and especially on the non-uniformity index. This dependence is however strong as shown by experimental results. In the present work it is attempted to derive this qualitative dependence analytically, so as to provide a better understanding of the observations. Two different forms of granulometric curves are considered and the small strain moduli derived for isotropic and triaxial compression. In spite of the purely theoretical nature of the approach, the results are in good agreement with the experiments. A simplified formula is suggested, to facilitate application.

Effect of Molecular Weight, Polydispersity, and Monomer of Linear Homopolymer Melts on the Intrinsic Mechanical Nonlinearity 3Q0(ω) in MAOS

Linear mono- and polydisperse homopolymer melts have been investigated with Fourier transformation rheology (FT rheology) to quantify their nonlinear behavior under oscillatory shear via mechanical higher harmonics, i.e., I3/1(ω,γ0). Master curves of the zero-strain nonlinearity, 3Q0(ω) ≡ limγ0→0 I3/1/γ02, have been created for these linear homopolymer melts, applying the time–temperature superposition (TTS) principle. The quantity 3Q0(ω) is examined for its dependence on molecular weight, molecular weight distribution, and monomer. The investigated nonlinear master curves of 3Q0(ω) for polymer melts with a polydispersity index (PDI) of about 1.07 or smaller display the expected scaling exponent of 3Q0(ω) ∝ ω2 at low frequencies until a maximum, 3Q0,max, is reached. This maximum 3Q0,max was found to be in the magnitude of the longest relaxation time τ0 and the value of 3Q0,max to be weakly dependent on molecular weight, or the number of entanglements Z, with 3Q0,max ∝ Z0.35. Within the measured experiment...

Computer simulation study of polydispersity effect on the phase behavior of short diblock copolymers

Recent progress in producing short chain length diblock copolymers facilitates the fabrication of block copolymer nanostructures with extremely small feature sizes. In this work, phase diagrams for monodisperse, one-sided and two-sided polydisperse short diblock copolymer melts are constructed using dissipative particle dynamics (DPD) simulations. Detailed comparisons are carried out between these systems to elucidate the influence of chain length polydispersity on the phase behavior of short diblock copolymers. In particular, we find an unexpected stability of a bicontinuous structure over a wide composition range between 0.7 < f ≤ 0.8 in one-sided polydisperse system, where f is the volume fraction of the polydisperse component. In the case of the two-sided polydisperse system, due to the presence of highly asymmetrical block copolymers and the pulling-away of short blocks of these molecules into opposite domain, an up-shift is found in the order–disorder transition boundary to larger χN values over the composition range we investigated.

Effects of polydispersity on liquid–liquid equilibrium of polymeric fluids

The effects of polymer polydispersity on the liquid–liquid equilibrium (LLE) of polymer solutions were investigated for the simple case of polydisperse polymer solutions: mixtures composed of a solvent and two monodisperse polymers of different molecular weights. Various quasi-binary cloud point curves including the upper critical solution temperature (UCST), lower critical solution temperature (LCST), both UCST and LCST, and closed loop miscibility were determined from thermal optical analysis (TOA). To describe the phase equilibrium of polydisperse polymer solutions, we extended the chain length contribution term in the modified double lattice chain length dependent model (extended MDL-CL). Phase equilibrium calculations were conducted for several ternary systems including hypothetical hourglass type LLE. The extended MDL-CL model appropriately described the effect of polymer polydispersity on the LLE of polymer solutions and the calculated results were in satisfactory agreement with the experimental data.

Modeling the effects of polydispersity on the viscosity of noncolloidal hard sphere suspensions

The present study develops an extension of the approach pioneered by Farris [Trans. Soc. Rheol. 12, 281–301 (1968)] to model the viscosity in polydisperse suspensions. Each smaller particle size class is assumed to contribute to the suspension viscosity through a weighting function in two ways: first, indirectly, by altering the background viscosity, and second, directly, by increasing the contribution of the larger particles to the suspension viscosity. The weighting functions are developed in a consistent fashion as a power law with the exponent, h, a function of the relative volume fraction ratio and the base, g, a function of the solid particle size ratio. The model is fit to available theoretical and experimental results for the viscosity of several binary suspensions and shows good to excellent agreement depending on the functions g and h chosen. Once parameterized using binary suspension viscosity data, the predictive capability to model the viscosity of arbitrary continuous size distributions is realized by representing such distributions with equivalent ternary approximations selected to match the first six moments of the actual size distribution. Model predictions of the viscosity of polydisperse suspensions are presented and compared against experimental data.

Start-up rheometry of highly polydisperse magnetorheological fluids: experiments and simulations

An extensive experimental and simulation study is carried out in conventional magnetorheological fluids formulated by dispersion of mixtures of carbonyl iron particles having different sizes in Newtonian carriers. Apparent yield stress data are reported for a wide range of polydispersity indexes (PDI) from PDI = 1.63 to PDI = 3.31, which for a log-normal distribution corresponds to the standard deviation ranging from ν = 0.38 to ν = 0.76. These results demonstrate that the effect of polydispersity is negligible in this range in spite of exhibiting very different microstructures. Experimental data in the magnetic saturation regime are in quantitative good agreement with particle-level simulations under the assumption of dipolar magnetostatic forces. The insensitivity of the yield stresses to the polydispersity can be understood from the interplay between the particle cluster size distribution and the packing density of particles inside the clusters.

Effect of Polydispersity in Oil-droplet Size on Lipid Oxidation in Oil-in-water Emulsions

Effect of Polydispersity in Oil-droplet Size on Lipid Oxidation in Oil-in-water Emulsions