Effect Of Size Polydispersity Research Articles

Effects of Size Polydispersity and Dense Media on Quantitative Ultrasound Estimates.

Quantitative ultrasound (QUS) techniques based on the backscatter coefficient (BSC) aim to characterize the scattering properties of biological tissues. A scattering model is fit to the measured BSC, and the fitted QUS parameters can provide local tissue microstructure, namely, scatterer size and acoustic concentration. However, these techniques may fail to provide a correct description of tissue microstructure when the medium is polydisperse and/or dense. The objective of this study is to investigate the effects of scatterer size polydispersity in sparse or dense media on the QUS estimates. Four scattering models (i.e., the monodisperse and polydisperse sparse models, and the monodisperse and polydisperse concentrated models based on the structure factor) are compared to assess their accuracy and reliability in quantifying the QUS estimates. Simulations are conducted with different scatterer size distributions for sparse, moderately dense, and dense media (volume fractions of 1%, 20%, and 73%, respectively). The QUS parameters are estimated by using model-based inverse methods at different center frequencies between 8 and 50 MHz. Experimental data are also analyzed using colon adenocarcinoma HT29 cell pellet biophantoms to further validate the results obtained from simulations at the volume fraction of 73%. Our findings reveal that the choice of scattering model has a significant impact on the accuracy of QUS estimates. For sufficiently high frequencies and dense media, the polydisperse concentrated model outperforms the other models and enables more accurate quantification. Furthermore, our results contribute to advancing our understanding of the complexities associated with scatterer size polydispersity and dense media in spectral-based QUS techniques.

Effects of size polydispersity on segregation of spherical particles in rotating drum.

To get insight into the segregation process of a polydisperse granular materials flow, we numerically investigated the migration process of particles in a rotating drum operating in the rolling regime by means of the discrete element method. Particle migration is analyzed through the variation of the proportion of particles in different zones where the flow property is characterized. The proportion of particles in different zones of the drum shows to increase in the center of the flow radially and axially where a higher concentration of small particles is observed, while its decreases in other zones with a higher concentration of larger particles. Interestingly, we find that the migration process of particles leads to radial and axial segregation which is caused by a combination between the exerted fluctuation forces on particles and its surrounding pressure gradient.

Monte Carlo simulations of patch models with applications to soft matter.

Patch models have been employed to describe anisotropic interactions in disparate soft matter systems. In this work, we present a unified study of a patch model to explore particle self-assembly in both monodisperse and polydisperse systems, with applications to both proteins and colloids. In the first case, we obtained a temperature-density phase diagram for a model of the protein polyglutamine from Monte Carlo simulations. These simulations evinced clusters in the gas phase and, via a comparison with the corresponding coarse-grained PLUM model for this system, we verified that dense clustering in the gas phase falls into the supersaturation region of the saturation curve. In the second case, we have investigated the effect of size polydispersity on the phase behavior of binary colloidal mixtures. It was found that the width of gas-liquid phase coexistence increases with increasing polydispersity and that, in addition to the aforementioned particle clustering, small particles decorate patches on large particles, thereby creating large-particle bridges. Our aim is to compare and contrast self-assembly in these two prototypical systems.

Analytical strong-stretching theory of polyelectrolyte brushes loaded with charged nanoparticles

Nanoparticles can be used to tune the properties of polyelectrolyte brushes, and polyelectrolyte brushes can be used to control the interaction between nanoparticles and substrates. In the present paper, we investigate the polyelectrolyte brushes immersed in a nanoparticle solution within the analytical strong-stretching theoretical framework. The theoretical model does not take the excluded volume interaction between any two components into account. When there is no nanoparticle loaded, the polyelectrolyte brush is assumed to be an osmotic brush. Local electroneutral approximation is assumed to be still valid after the nanoparticles have been loaded. The loaded nanoparticles are not big enough to deform the grafted polyelectrolyte chains laterally. Analytical formulae for density profiles of each component and brush thickness are derived. The loaded nanoparticles always compress the polyelectrolyte brush. By analyzing the limiting case, a scaling-type diagram for behaviors of the nanoparticle-loading polyelectrolyte brush is constructed. Two characteristic nanoparticle controlling regimes are shown. When the charge of the nanoparticle, <i>Z</i>, is not very large, charged nanoparticles penetrate into the brush and the brush thickness is scaled by <inline-formula><tex-math id="M5">\begin{document}$H \sim (Z\varPhi)^{-1/3}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M5.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$\varPhi$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M6.png"/></alternatives></inline-formula> is the nanoparticle volume fraction. When the nanoparticle charge <i>Z</i> is large enough, nanoparticles are mainly distributed outside the brush and the brush thickness is scaled by <inline-formula><tex-math id="M7">\begin{document}$H \sim (Z\varPhi)^{-1}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M7.png"/></alternatives></inline-formula>. In the former case, the Coulombic repulsion between the grafted polyelectrolyte chains is screened by the counterions and the nanoparticles, and the brush behavior is determined by the balance between the chain elasticity and the osmotic pressure of the counterions and the nanoparticles. In the latter case, the electrostatic screening is executed by the counterions, and the chain elasticity is balanced by the osmotic pressure of the counterions. The two regimes are divided into subregimes which are dominated respectively by electrostatic or non-electrostatic interaction. The effects of size polydispersity of the nanoparticles are also investigated. It is found that the behaviors of the grafted polyelectrolyte chains are mainly determined by the ratio between the first two moments of the nanoparticle size distribution function. The polyelectrolyte brush is compressed more by the polydispere nanoparticles than by the monodisperse ones. Possible improvement in the present theory is discussed in the conclusion section.

Effects of size polydispersity on random close-packed configurations of spherical particles.

We analyze the packing properties of simulated three-dimensional polydisperse samples of spherical particles assembled by mechanical compaction with zero interparticle friction, leading to random close-packed configurations of the highest packing fraction. The particle size distributions are generated from the incomplete beta distribution with three parameters: A size span and two shape parameters that control the curvature of the distribution function. For each size distribution, the number of particles is determined by accounting for the statistical representativity of all particle size classes in terms of both the numbers and volumes of particles. Remarkably, the packing fraction increases, up to a small variability, with an effective size span, known as the coefficient of uniformity, that combines the three control parameters of the distribution. The local particle environments are characterized by the particle connectivities and anisotropies, which unveil the class of particles with four contact neighbors as the largest class with an increasing population as a function of size span, indicating the higher stability of particles trapped by four larger particles. As a result of increasing topological inhomogeneity of the packings, the force distributions get increasingly broader with increasing effective size span. Finally, we find that larger particles do not always carry stronger average stresses, in particular when the particle size distribution allows for a sufficiently large number of small particles.

Effect of Size Polydispersity on the Pitch of Nanorod Cholesterics

Many nanoparticle-based chiral liquid crystals are composed of polydisperse rod-shaped particles with considerable spread in size or shape, affecting the mesoscale chiral properties in, as yet, unknown ways. Using an algebraic interpretation of Onsager-Straley theory for twisted nematics, we investigate the role of length polydispersity on the pitch of nanorod-based cholesterics with a continuous length polydispersity, and find that polydispersity enhances the twist elastic modulus, K 2 , of the cholesteric material without affecting the effective helical amplitude, K t . In addition, for the infinitely large average aspect ratios considered here, the dependence of the pitch on the overall rod concentration is completely unaffected by polydispersity. For a given concentration, the increase in twist elastic modulus (and reduction of the helical twist) may be up to 50% for strong size polydispersity, irrespective of the shape of the unimodal length distribution. We also demonstrate that the twist reduction is reinforced in bimodal distributions, obtained by doping a polydisperse cholesteric with very long rods. Finally, we identify a subtle, non-monotonic change of the pitch across the isotropic-cholesteric biphasic region.

Auxeticity enhancement due to size polydispersity in fcc crystals of hard-core repulsive Yukawa particles.

The Poisson's ratio of the fcc hard-core repulsive Yukawa crystals with size polydispersity was determined by Monte Carlo simulations in the isothermal-isobaric ensemble. The effect of size polydispersity on the auxetic properties of Yukawa crystals has been studied. It has been found that an increase of particle size polydispersity causes a decrease of the Poisson's ratio in auxetic directions as well as appearance of a negative Poisson's ratio in formerly non-auxetic directions. A measure of auxeticity was introduced to estimate quantitatively an enhancement of auxetic properties in polydisperse Yukawa crystals. The proposed measure of auxeticity can be applied to appraise the auxeticity of any studied system.

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 Size Polydispersity on the Nature of Lennard-Jones Liquids.

Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. We study here the effect of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to size polydisperse fluids and can be used to improve even further the understanding of these intriguing systems.

Effect of charge polydispersity and charge residence time on the dynamics of a micellar system.

We use dynamic light scattering to investigate the effects of charge polydispersity and charge residence time on the dynamics of a micellar system. While in the corresponding uncharged system only one exponential relaxation is observed, two relaxation modes are seen when charging the micelles by adding charged co-surfactant molecules with a long residence time. We attribute the existence of these two relaxation modes to the combined effect of size polydispersity and charge polydispersity, i.e. frozen fluctuations of the number of charges per micelle. Further support to this scenario is provided by control experiments on a similar charged system, but where the charge residence time is short compared to the time scales probed by dynamic light scattering. Here, charge polydispersity is effectively suppressed due to the rapid exchange of charged molecules between micelles and only one single relaxation mode is seen, thereby demonstrating the key role of frozen charge fluctuations in the complex dynamics of our micellar system.

Effects of size polydispersity on electron mobility in a two-dimensional quantum-dot superlattice

We found that the transitions between delocalized electronic states in quantum-dot superlattices with smaller size dispersion can account for higher electron mobility. In particular, we solved for the quantum states of a two-dimensional quantum-dot (QD) superlattice using a one-electron approximation. Electron transport properties were studied by considering hopping transitions among coupled delocalized electronic states. Molecular dynamics simulations were employed to introduce disorders in superlattice configurations as a function of QD size and size dispersion for calculation of electron mobility. The interparticle spacing, size, and temperature dependence of the electron mobility can be well explained within the framework of our analysis.

Effect of size polydispersity on the structural and vibrational characteristics of two-dimensional granular assemblies

Two-dimensional disordered granular assemblies composed of 2048 polydispersed frictionless disks are simulated using the discrete element method. The height of the first peak of the pair correlation function, g1, the local and global bond orientational parameters ψ6l and ψ6g, and the fluctuations of these parameters decrease with increasing polydispersity s, implying the transition from a polycrystalline state to an amorphous state in the system. As s increases, the peak position of the boson peak ωBP shifts towards a lower frequency and the intensity of the boson peak D(ωBP)/ωBP increases, indicating that the position and the strength of the boson peak are controlled by the polydispersity of the system. Moreover, the inverse of the boson peak intensity ωBP/D(ωBP), the shear modulus G, and the basin curvature SIS all have a similar dependence on s, implying that the s dependence of the vibrational density of states at low frequencies likely originates from the s dependence of the basin curvature.

Effects of size polydispersity on mechanical and geometrical properties of granular system

In this paper, the multi-disperse systems composed of 2048 frictionless particles with different size polydispersities are simulated by using the distinct element method, and effects of size polydispersity on mechanical and geometrical properties of these systems are studied under isotropic confining. The result shows that changing polydispersity can qualitatively affect the coordination number, shear modulus, static structure factor and orientational order correlation function, but it does not influence the cumulative force distribution. At small wave number k, static structure factor of mono-disperse systems shows the power scaling law S(k)∝0.2k-4/3. Moreover, the peak of orientational order correlation function exhibits an exponent scaling law g6 (r)∝ae-r/ξ6, and the scaling exponent ξ6 decreases with polydispersity increasing.

Effects of size polydispersity on the extinction spectra of colloidal nanoparticle aggregates

We investigate the effect of particle polydispersity on the optical extinction spectra of colloidal aggregates of spherical metallic (silver) nanoparticles, taking into account the realistic interparticle gaps caused by layers of stabilizing polymer adsorbed on the metal surface (adlayers). The spectra of computer-generated aggregates are computed using two different methods. The coupled-multipole method is used in the quasistatic approximation and the coupled-dipole method beyond the quasistatics. The latter approach is applicable if the interparticle gaps are sufficiently wide relative to the particle radii. Simulations are performed for two different particle size distribution functions (bimodal and Gaussian), varying the number of particles per aggregate, and different distribution functions of the interparticle gap width. The strong influence of the latter factor on the spectra is demonstrated and investigated in detail.

Structure of Polydisperse Inverse Ferrofluids: Theory and Computer Simulation

By using theoretical analysis and molecular dynamics simulations, we investigate the structure of colloidal crystals formed by nonmagnetic microparticles (or magnetic holes) suspended in ferrofluids (called inverse ferrofluids), by taking into account the effect of polydispersity in size of the nonmagnetic microparticles. Such polydispersity often exists in real situations. We obtain an analytical expression for the interaction energy of monodisperse, bidisperse, and polydisperse inverse ferrofluids. Body-centered tetragonal (bct) lattices are shown to possess the lowest energy when compared with other sorts of lattices and thus serve as the ground state of the systems. Also, the effect of microparticle size distributions (namely, polydispersity in size) plays an important role in the formation of various kinds of structural configurations. Thus, it seems possible to fabricate colloidal crystals by choosing appropriate polydispersity in size.

Toner Transfer: Effects of Size Polydispersity

Toned images comprised of monodisperse, spherical toner particles, having diameters of either 2 μm or 5 μm or of blends thereof were electrostatically transferred from an organic photoreceptor to either paper or film receivers. It was found that the transfer efficiency of the images made with the monodisperse toners was quite high and the image quality quite good. However, even small amounts of the 5 μm toner significantly impeded the transfer of the 2 μm, resulting in much poorer transfer efficiency and a large increase in mottle and granularity. Mathematical analysis shows that the maximum electrostatic field that can be applied prior to the onset of ionization is too small to remove the toner particles from the photoreceptor. Rather, the adhesive forces holding the toner to the photoreceptor must be partially offset by comparable adhesive forces between the toner particles and the receiver for transfer to occur.

Effects of size polydispersity on depletion interactions

The depletion potentials between two infinite planes, and between two large spheres, due to polydisperse mixtures of non-interacting polymer coils and of interacting small hard spheres, are calculated over a wide range of polydispersities and of polymer or colloid concentrations. The case of non-interacting polymers can be treated analytically within a generalization of the Asakura-Oosawa model. The more difficult case of a polydisperse bath of hard spheres is treated within Rosenfield's ‘fundamental measure’ formulation of density functional theory. Polydispersity is found to have little effect on the depletion attraction, but to strongly reduce the repulsive barrier due to correlation and to damp the subsequent oscillations in the depletion potential.

Effect of Size Polydispersity on the Dielectric Relaxation of Colloidal Suspensions: A Numerical Study in the Frequency and Time Domains

In this article, a systematic numerical study is described of the effect of the polydispersity of suspensions of spherical particles on their dielectric behavior, in both the frequency and time domains, starting from the model proposed by DeLacey and White (J. Chem. Soc., Faraday Trans. 277, 2007 (1981)) for monodisperse suspensions. The distribution function of relaxation times, characterizing the dielectric response of the systems, is also calculated. It is found that in both the frequency and time domains the predicted behavior does not differ in any essential way from the one obtained for a monodisperse suspension with particle radius close to the volume-averaged mean radius of the polydisperse system. Hence, no arguments related to polydispersity seem to be useful for explaining the discrepancies frequently found between measured and calculated dielectric increments in suspensions, namely, those concerning the magnitude of the dielectric constant of the suspension (its low-frequency value), the value of the characteristic or relaxation frequency, or the overall shape of the relaxation pattern.

Electrophoretic Mobility of a Semi-dilute Suspension of Spherical Particles with Thick Double Layers and Low Zeta Potentials

The electrophoretic mobilities of two spherical particles are analyzed for the case where the electrical double layer is no longer thin with respect to the particle sizes, but the zeta potentials on the particles are low. Using a method of reflections, we obtain the mobilities as a power series in 1/r12up toO(r−1012) (wherer12is the center-to-center separation of the spheres), with the proviso that the double layers on the two particles do not overlap. Unlike the case of thin double layers, there is now a nonzero interaction between identical particles. The first term in the interaction isO(r−312), but the coefficient becomes large for thick double layers. An expression for the average mobility of a mildly polydisperse suspension of spheres with thick double layers is then derived correct to first order in the volume fraction of the spheres. The results of the reflection calculation are then used to obtain an approximate evaluation of this expression. It is found that the first order effect for thick double layers is significantly larger than it is for thin double layers, and that the average effect of polydispersity in size or surface potential is weak unless the double layers are quite thick. For a monodisperse suspension, an expression is obtained for the mean square deviation of the particle velocity from the mean velocity. An approximate evaluation of this expression using the reflection results shows that the magnitude of the mean square fluctuations in the direction of the applied field can be significantly larger than that in the transverse direction.

Effect of size polydispersity on granular materials.

We present particle dynamics simulations on fluidization of vertically vibrated granular beds where solidlike and fluidlike domains appear spontaneously. The existence of polydispersity in granular size significantly alters where the boundary between solidlike and fluidlike regions appears. A threshold value of polydispersity ${\mathrm{\ensuremath{\sigma}}}_{\mathit{th}}$ exists above which the system becomes insensitive to the change in the degree of polydispersity. The value of ${\mathrm{\ensuremath{\sigma}}}_{\mathit{th}}$ shows good agreement with the critical polydispersity reported on the solid-fluid phase transition in thermodynamic hard-core systems. The present result implies that the existence of polydispersity is crucial in some granular systems. \textcopyright{} 1996 The American Physical Society.