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We study the liquid phase behavior of ternary mixtures of monodisperse hard spheres in solution. The interactions are modeled in terms of the second virial coefficient and can be additive hard sphere (HS) or non-additive hard sphere (NAHS) interactions. We give the set of equations that defines the phase diagram for mixtures of three components. We calculate the theoretical liquid–liquid phase separation boundary for two-phase separation (the binodal) and, if applicable, the three-phase boundary, as well as the plait points and the spinodal. The sizes of the three components are fixed. The first component (A) is the smallest one, the second component (B) is four times the size of the smallest component, and the third (C) component is three times the size of the smallest one. The interaction between the first two components is fixed, and this AB sub-mixture shows phase separation. The interactions of component C with the other two components are varied. Component C can be compatible or incompatible with components A and B. Depending on the compatibility of the components, the phase diagram is altered. The addition of the third component has an influence on the phase boundary, plait points, stability region, fractionation, and volume ratio between the different phases. When all sub-mixtures (AB, AC, and BC) show phase separation, a three-phase system becomes possible when the incompatibility among all components is high enough. The position and size of the three-phase region is dependent on the interactions between the different sub-mixtures. We study the fractionation off all components depending on specific parent concentrations.

Eudragit® polymers have proven their potential as a means to control the release of aqueous insoluble drugs in various delivery systems as polymer nanoparticles (PNPs). The size (S) and polydispersity index (PDI) of PNPs are crucial factors for their interaction with biological systems from a pharmaceutical standpoint. This study aimed to determine the impact of the volumes of the organic phase (OP) and aqueous phase (AP), as well as the polymer amount (PA), on the size and PDI of PNPs prepared using the nanoprecipitation method for encapsulating quercetin (Qr). The study also evaluated the toxic effects of PNPs on human erythrocytes. The PNPs were prepared using preformed polymers derived from methacrylic acid and polyvinyl alcohol (PVA) as a surfactant. The nanoprecipitation technique enabled the production of particles smaller than 200 nm with a PDI lower than 0.2, and the study established the significant impact (p < 0.05) of the three variables related to the polymers and solvents. The selected PNPs contained 5 mg of Qr and 50 mg of Eudragit polymers (1:10 w/w Eudragit® EPO, E100, L100, and Eudragit L100-55) and diverse concentrations of PVA. The study found that including PVA in the AP increased the Qr encapsulation by up to 98%. The hemolytic potential of Eudragit® PNPs and Qr was assessed in human erythrocytes, with no significant cytotoxic activity observed (p < 0.001) compared with the control. In conclusion, via the nanoprecipitation technique, preparing PNPs with defined and homogeneous S to entrap the flavonol Qr efficiently is possible.

Size and zeta potential are critical physicochemical properties of nanoparticles (NPs), influencing their biological activity and safety profile. These are essential for further industrial upscale and clinical success. However, the characterization of polydisperse, non-spherical NPs is a challenge for traditional characterization techniques (ex., dynamic light scattering (DLS)). In this paper, superparamagnetic iron oxide nanoparticles (SPIONs) were coated with polyvinyl alcohol (PVAL) exhibiting different terminal groups at their surface, either hydroxyl (OH), carboxyl (COOH) or amino (NH2) end groups. Size, zeta potential and concentration were characterized by orthogonal methods, namely, batch DLS, nanoparticle tracking analysis (NTA), tunable resistive pulse sensing (TRPS), transmission electron microscopy (TEM), asymmetric flow field flow fractionation (AF4) coupled to multi-angle light scattering (MALS), UV–Visible and online DLS. Finally, coated SPIONs were incubated with albumin, and size changes were monitored by AF4-MALS-UV-DLS. NTA showed the biggest mean sizes, even though DLS PVAL-COOH SPION graphs presented aggregates in the micrometer range. TRPS detected more NPs in suspension than NTA. Finally, AF4-MALS-UV-DLS could successfully resolve the different sizes of the coated SPION suspensions. The results highlight the importance of combining techniques with different principles for NPs characterization. The advantages and limitations of each method are discussed here.

Acoustic droplet vaporization is the ultrasound-mediated phase change of liquid droplets into gas microbubbles. Following the phase change, oxygen diffuses from the surrounding fluid into the microbubble. An in vitro model was used to study the effects of droplet diameter, the presence of an ultrasound contrast agent, ultrasound duty cycle, and droplet concentration on the magnitude of oxygen scavenging in oxygenated deionized water. Perfluoropentane droplets were manufactured through a microfluidic approach at nominal diameters of 1, 3, 5, 7, 9, and 12 µm and studied at concentrations varying from 5.1 × 10−5 to 6.3 × 10−3 mL/mL. Droplets were exposed to an ultrasound transduced by an EkoSonicTM catheter (2.35 MHz, 47 W, and duty cycles of 1.70%, 2.34%, or 3.79%). Oxygen scavenging and the total volume of perfluoropentane that phase-transitioned increased with droplet concentration. The ADV transition efficiency decreased with increasing droplet concentration. The increasing duty cycle resulted in statistically significant increases in oxygen scavenging for 1, 3, 5, and 7 µm droplets, although the increase was smaller than when the droplet diameter or concentration were increased. Under the ultrasound conditions tested, droplet diameter and concentration had the greatest impact on the amount of ADV and subsequent oxygen scavenging occurred, which should be considered when using ADV-mediated oxygen scavenging in therapeutic ultrasounds.

The ability to separate enzymes, or cells or viruses, from a mixture is important and can be realized by the incorporation of the mixture into a macromolecular solution. This incorporation may lead to a spontaneous phase separation, with one phase containing the majority of one of the species of interest. Inspired by this phenomenon, we studied the theoretical phase behavior of a model system composed of an asymmetric binary mixture of hard spheres, of which the smaller component was monodisperse and the larger component was polydisperse. The interactions were modeled in terms of the second virial coefficient and could be additive hard sphere (HS) or nonadditive hard sphere (NAHS) interactions. The polydisperse component was subdivided into two subcomponents and had an average size ten or three times the size of the monodisperse component. We gave the set of equations that defined the phase diagram for mixtures with more than two components in a solvent. We calculated the theoretical liquid–liquid phase separation boundary for the two-phase separation (the binodal) and three-phase separation, the plait point, and the spinodal. We varied the distribution of the polydisperse component in skewness and polydispersity, and we varied the nonadditivity between the subcomponents as well as between the main components. We compared the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We found that when the compatibility between the polydisperse subcomponents decreased, the three-phase separation became possible. The shape and position of the phase boundary was dependent on the nonadditivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the subcomponents increases.

Nanoparticle aggregation has been found to be crucial for the thermal properties of nanofluids and their performance as heating or cooling agents. Most relevant studies in the literature consider particles of uniform size with point contact only. A number of forces and mechanisms are expected to lead to deviation from this ideal description. In fact, size uniformity is difficult to achieve in practice; also, overlapping of particles within aggregates may occur. In the present study, the effects of polydispersity and sintering on the effective thermal conductivity of particle aggregates are investigated. A simulation method has been developed that is capable of producing aggregates made up of polydispersed particles with tailored morphological properties. Modelling of the sintering process is implemented in a fashion that is dictated by mass conservation and the desired degree of overlapping. A noticeable decrease in the thermal conductivity is observed for elevated polydispersity levels compared to that of aggregates of monodisperse particles with the same morphological properties. Sintered nanoaggregates offer wider conduction paths through the coalescence of neighbouring particles. It was found that there exists a certain sintering degree of monomers that offers the largest improvement in heat performance.

Novel vaccine platforms for delivery of nucleic acids based on viral and non-viral vectors, such as recombinant adeno associated viruses (rAAV) and lipid-based nanoparticles (LNPs), hold great promise. However, they pose significant manufacturing and analytical challenges due to their intrinsic structural complexity. During product development and process control, their design, characterization, and quality control require the combination of fit-for-purpose complementary analytical tools. Moreover, an in-depth methodological expertise and holistic approach to data analysis are required for robust measurements and to enable an adequate interpretation of experimental findings. Here the combination of complementary label-free biophysical techniques, including dynamic light scattering (DLS), multiangle-DLS (MADLS), Electrophoretic Light Scattering (ELS), nanoparticle tracking analysis (NTA), multiple detection SEC and differential scanning calorimetry (DSC), have been successfully used for the characterization of physical and chemical attributes of rAAV and LNPs encapsulating mRNA. Methods’ performance, applicability, dynamic range of detection and method optimization are discussed for the measurements of multiple critical physical−chemical quality attributes, including particle size distribution, aggregation propensity, polydispersity, particle concentration, particle structural properties and nucleic acid payload.

The equilibrium concentration distribution of magnetic nanoparticles in a nonuniform magnetic field is studied theoretically. A linear current-carrying wire is used as a source of a nonuniform field. An exact solution for the concentration profile of a dilute monodisperse suspension is obtained within the framework of the continuous mass transfer theory. The applicability of this solution in a broad range of amperage values is tested using Langevin dynamics simulations. Obtained solution is also generalized for polydisperse suspensions. It is demonstrated that the particle size distribution in a polydisperse system strongly depends on the distance from the wire and in general does not coincide with the original distribution of a uniform suspension.

Phosphate ore slurry is a suspension of insoluble particles of phosphate rock, the primary raw material for fertilizer and phosphoric acid, in a continuous phase of water. This suspension has a non-Newtonian flow behavior and exhibits yield stress as the shear rate tends toward zero. The suspended particles in the present study were assumed to be noncolloidal. Various grades and phosphate ore concentrations were chosen for this rheological investigation. We created some experimental protocols to determine the main characteristics of these complex fluids and established relevant rheological models with a view to simulate the numerical flow in a cylindrical pipeline. Rheograms of these slurries were obtained using a rotational rheometer and were accurately modeled with commonly used yield-pseudoplastic models. The results show that the concentration of solids in a solid–liquid mixture could be increased while maintaining a desired apparent viscosity. Finally, the design equations for the laminar pipe flow of yield pseudoplastics were investigated to highlight the role of rheological studies in this context.

Magnetic inductive heating (MIH) has been a topic of great interest because of its potential applications, especially in biomedicine. In this paper, the parameters characteristic for magnetic inductive heating power including maximum specific loss power (SLPmax), optimal nanoparticle diameter (Dc) and its width (ΔDc) are considered as being dependent on magnetic nanoparticle anisotropy (K). The calculated results suggest 3 different Néel-domination (N), overlapped Néel/Brownian (NB), and Brownian-domination (B) regions. The transition from NB- to B-region changes abruptly around critical anisotropy Kc. For magnetic nanoparticles with low K (K < Kc), the feature of SLP peaks is determined by a high value of Dc and small ΔDc while those of the high K (K > Kc) are opposite. The decreases of the SLPmax when increasing polydispersity and viscosity are characterized by different rates of d(SLPmax)/dσ and d(SLPmax)/dη depending on each domination region. The critical anisotropy Kc varies with the frequency of an alternating magnetic field. A possibility to improve heating power via increasing anisotropy is analyzed and deduced for Fe3O4 magnetic nanoparticles. For MIH application, the monodispersity requirement for magnetic nanoparticles in the B-region is less stringent, while materials in the N- and/or NB-regions are much more favorable in high viscous media. Experimental results on viscosity dependence of SLP for CoFe2O4 and MnFe2O4 ferrofluids are in good agreement with the calculations. These results indicated that magnetic nanoparticles in the N- and/or NB-regions are in general better for application in elevated viscosity media.

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.

The copolymerization of styrene (St) with a bioderived monomer, pentadecylphenyl methacrylate (PDPMA), via atom transfer radical polymerization (ATRP) was studied in this work. The copolymerization reactivity ratio was calculated using the composition data obtained from 1H NMR spectroscopy, applying Kelen-Tudos and Finemann-Ross methods. The reactivity ratio of styrene (r1 = 0.93) and PDPMA (r2 = 0.05) suggested random copolymerization of the two monomers with alternation. The copolymerization conversion increased with increasing PDPMA concentration of the feed, upto 70 wt % PDPMA, but decreased thereafter. The molecular weight determined by gel permeation chromatography was lower than the theoretical values and the polydispersity increased from 1.32 to 2.19, with increasing PDPMA content in the feed. The influence of styrene content on the glass transition and thermal decomposition behavior of the copolymers was studied by differential scanning calorimetry (DSC) and thermogravimetric analysis, respectively. Morphological characterization by transmission electron microscopy (TEM) revealed a phase separated soft core-hard shell type structure. The complex viscosity and adhesion properties like peel strength and lap shear strength of the copolymer on different substrates increased with increasing styrene content.

Most undergraduate students who have followed a thermodynamics course would have been asked to evaluate the volume occupied by one mole of air under standard conditions of pressure and temperature. However, what is this task exactly referring to? If air is to be regarded as a mixture, under what circumstances can this mixture be considered as comprising only one component called “air” in classical statistical mechanics? Furthermore, following the paradigmatic Gibbs’ mixing thought experiment, if one mixes air from a container with air from another container, all other things being equal, should there be a change in entropy? The present paper addresses these questions by developing a prior-based statistical mechanics framework to characterise binary mixtures’ composition realisations and their effect on thermodynamic free energies and entropies. It is found that (a) there exist circumstances for which an ideal binary mixture is thermodynamically equivalent to a single component ideal gas and (b) even when mixing two substances identical in their underlying composition, entropy increase does occur for finite size systems. The nature of the contributions to this increase is then discussed.

We estimated source-based aerosol optical properties for polydisperse aerosols according to a chemical-species-resolved mass contribution method based on source apportionment. We investigated the sensitivity of aerosol optical properties based on PM2.5 (particulate matter that have a diameter of less than 2.5 micrometers) monitoring results. These aerosols were composed of ions, metals, elemental carbon, and water-soluble organic carbon which includes humic-like carbon substances and water-soluble organic carbon. We calculated aerosols’ extinction coefficients based on the PM2.5 composition data and the results of a multivariate receptor model (Solver for Mixture Problem model, SMP). Based on the mass concentration of chemical composition and nine sources calculated with the SMP receptor model, we estimated the size-resolved mass extinction efficiencies for each aerosol source using a multilinear regression model. Consequently, this study quantitatively determined the size resolved sources contributing to the apportionment-based aerosol optical properties and calculated their respective contributions. The results show that source-resolved mass concentrations and extinction coefficients had varying contributions. This discrepancy between the source-based mass concentration and extinction coefficient was mainly due to differences between the source-dependent aerosol size distribution and the aerosol optical properties from different sources.

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.

Although substantial progress has been made in recent years in research onsheared granular matter, relatively few studies concentrate on the behavior of materials withvery strong polydispersity. In this paper, shear deformation of a two-dimensional granularmaterial composed of frictional disk-shaped grains with power-law size distribution isanalyzed numerically with a finite-difference model. The analysis of the results concentrateson those aspects of the behavior of the modeled system that are related to its polydispersity. Itis demonstrated that many important global material properties are dependent on the behaviorof the largest grains from the tail of the size distribution. In particular, they are responsiblefor global correlation of velocity anomalies emerging at the jamming transition. They alsobuild a skeleton of the global contact and force networks in shear-jammed systems, leadingto the very open, “sparse” structure of those networks, consisting of only ~ 35% of all grains.The details of the model are formulated so that it represents fragmented sea ice moving ona two-dimensional sea surface; however, the results are relevant for other types of stronglypolydisperse granular materials, as well.

Understanding magnetic interparticle interactions within a single hydrodynamic volume of polydispersed magnetic nanoparticles and the resulting nonlinear magnetization properties is critical for their implementation in magnetic theranostics. However, in general, the field-dependent static and dynamic magnetization measurements may only highlight polydispersity effects including magnetic moment and size distributions. Therefore, as a complement to such typical analysis of hysteretic magnetization curves, we spectroscopically examined the complex magnetization harmonics of magnetic nanoclusters either dispersed in a liquid medium or immobilized by a hydrocolloid polymer, later to emphasize the harmonic characteristics for different core sizes. In the case of superparamagnetic nanoclusters with a 4-nm primary size, particularly, we correlated the negative quadrature components of the third-harmonic susceptibility with an insignificant cluster rotation induced by the oscillatory field. Moreover, the field-dependent in-phase components appear to be frequency-independent, suggesting a weak damping effect on the moment dynamics. The characteristic of the Néel time constant further supports this argument by showing a smaller dependence on the applied dc bias field, in comparison to that of larger cores. These findings show that the complex harmonic components of the magnetization are important attributes to the interacting cores of a magnetic nanocluster.

We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature.

Novel vaccine platforms for delivery of nucleic acids based on viral and non-viral vectors, such as recombinant adeno associated viruses (rAAV) and lipid-based nanoparticles (LNPs), hold great promise. However, they pose significant manufacturing and analytical challenges due to their intrinsic structural complexity. During product development and process control, their design, characterization, and quality control require the combination of fit-for-purpose complementary analytical tools. Moreover, an in-depth methodological expertise and holistic approach to data analysis are required for robust measurements and to enable an adequate interpretation of experimental findings. Here the combination of complementary label-free biophysical techniques, including dynamic light scattering (DLS), multiangle-DLS (MADLS), Electrophoretic Light Scattering (ELS), nanoparticle tracking analysis (NTA), multiple detection SEC and differential scanning calorimetry (DSC), have been successfully used for the characterization of physical and chemical attributes of rAAV and LNPs encapsulating mRNA. Methods' performance, applicability, dynamic range of detection and method optimization are discussed for the measurements of multiple critical physical-chemical quality attributes, including particle size distribution, aggregation propensity, polydispersity, particle concentration, particle structural properties and nucleic acid payload.

Nanoparticle aggregation has been found to be crucial for the thermal properties of nanofluids and their performance as heating or cooling agents. Most relevant studies in the literature consider particles of uniform size with point contact only. A number of forces and mechanisms are expected to lead to deviation from this ideal description. In fact, size uniformity is difficult to achieve in practice; also, overlapping of particles within aggregates may occur. In the present study, the effects of polydispersity and sintering on the effective thermal conductivity of particle aggregates are investigated. A simulation method has been developed that is capable of producing aggregates made up of polydispersed particles with tailored morphological properties. Modelling of the sintering process is implemented in a fashion that is dictated by mass conservation and the desired degree of overlapping. A noticeable decrease in the thermal conductivity is observed for elevated polydispersity levels compared to that of aggregates of monodisperse particles with the same morphological properties. Sintered nanoaggregates offer wider conduction paths through the coalescence of neighbouring particles. It was found that there exists a certain sintering degree of monomers that offers the largest improvement in heat performance.

The equilibrium concentration distribution of magnetic nanoparticles in a nonuniform magnetic field is studied theoretically. A linear current-carrying wire is used as a source of a nonuniform field. An exact solution for the concentration profile of a dilute monodisperse suspension is obtained within the framework of the continuous mass transfer theory. The applicability of this solution in a broad range of amperage values is tested using Langevin dynamics simulations. Obtained solution is also generalized for polydisperse suspensions. It is demonstrated that the particle size distribution in a polydisperse system strongly depends on the distance from the wire and in general does not coincide with the original distribution of a uniform suspension.

Understanding magnetic interparticle interactions within a single hydrodynamic volume of polydispersed magnetic nanoparticles and the resulting nonlinear magnetization properties is critical for their implementation in magnetic theranostics. However, in general, the field-dependent static and dynamic magnetization measurements may only highlight polydispersity effects including magnetic moment and size distributions. Therefore, as a complement to such typical analysis of hysteretic magnetization curves, we spectroscopically examined the complex magnetization harmonics of magnetic nanoclusters either dispersed in a liquid medium or immobilized by a hydrocolloid polymer, later to emphasize the harmonic characteristics for different core sizes. In the case of superparamagnetic nanoclusters with a 4-nm primary size, particularly, we correlated the negative quadrature components of the third-harmonic susceptibility with an insignificant cluster rotation induced by the oscillatory field. Moreover, the field-dependent in-phase components appear to be frequency-independent, suggesting a weak damping effect on the moment dynamics. The characteristic of the N&eacute;el time constant further supports this argument by showing a smaller dependence on the applied dc bias field, in comparison to that of larger cores. These findings show that the complex harmonic components of the magnetization are important attributes to the interacting cores of a magnetic nanocluster.