Wide Size Distribution Research Articles

Facile Preparation of Dense Polysulfone UF Membranes with Enhanced Salt Rejection by Post-Heating.

Polysulfone (PSf) membranes typically have a negligible rejection of salts due to the intrinsic larger pore size and wide pore size distribution. In this work, a facile and scalable heat treatment was proposed to increase the salt rejection. The influence of heat treatment on the structure and performance of PSf membranes was systematically investigated. The average pore size decreased from 9.94 ± 5.5 nm for pristine membranes to 1.18 ± 0.19 nm with the increase in temperature to 50 °C, while the corresponding porosity decreased from 2.07% to 0.13%. Meanwhile, the thickness of the sponge structure decreased from 20.20 to 11.5 μm as the heat treatment temperature increased to 50 °C. The MWCO of PSf decreased from 290,000 Da to 120 Da, whereas the membrane pore size decreased from 5.5 to 0.19 nm. Correspondingly, the water flux decreased from 1545 to 27.24 L·m-2·h-1, while the rejection ratio increased from 3.1% to 74.0% for Na2SO4, from 1.3% to 48.2% for MgSO4, and from 0.6% to 23.8% for NaCl. Meanwhile, mechanism analysis indicated that the water evaporation in the membranes resulted in the shrinkage of the membrane pores and decrease in the average pore size, thus improving the separation performance. In addition, the desalting performance of the heat-treated membranes for real actual industrial wastewater was improved. This provides a facile and scalable route for PSf membrane applications for enhanced desalination.

Numerical investigation of wide continuous particle size distribution on the supersonic powder loading oxygen jet

Supersonic oxygen-powder jet injection has spanned wide range of operations in chemical engineering. However, the ubiquitous polydispersity of solid powder known to exert different flow behavior than the monodisperse counterpart has not been revealed. In this work, numerical simulation of the supersonic oxygen-powder jet injection via the Laval nozzle is performed under the Eulerian-Lagrangian framework to explore the impact of wide continuous size distribution of solid phase on the gas-solid hydrodynamics. Specifically, the gas phase is solved using the Eulerian method, while the particle motion is tracked under the Lagrangian framework. The numerical model is well validated with the experimental measurements. The results reveal that the blending of particles restricts the gas phase expansion, leading to the obvious reduction of gas velocity and increase of gas temperature. Additionally, a narrow particle size distribution (PSD) width corresponds to a higher proportion of large particles, inducing stronger vortices and hindering gas phase expansion. With regard to solid phase, the penetration ability of particles is significantly enhanced within the supersonic gas flow by accelerating the particle velocity to about 300 m/s. Furthermore, particles with wider PSD exhibit increased sensitivity to interphase interaction, particle-particle collisions and lift forces, resulting in higher velocities, lower temperatures along the axial direction and greater dispersion along the radial direction. Lastly, the interphase heat transfer mainly occurs in the convergent section, divergent section, and one nozzle length downstream from the nozzle exit. The findings obtained in this study offer valuable insights for industrial applications.

Three-dimensional angular scattering simulations inform analysis of scattering from single cells.

Organelle sizes, which are indicative of cellular status, have implications for drug development and immunology research. At the single cell level, such information could be used to study the heterogeneity of cell response to drugs or pathogens. Angularly resolved elastic light scattering is known to be sensitive to changes in organelle size distribution. We developed a Mie theory-based simulation of angular scattering from single cells to quantify the effects of noise on scattering and size estimates. We simulated randomly sampled organelle sizes (drawn from a log normal distribution), interference between different organelles' scattering, and detector noise. We quantified each noise source's effect upon the estimated mean and standard deviation of organelle size distributions. The results demonstrate that signal-to-noise ratio in the angular scattering increased with the number of scatterers, cell area, and exposure time and decreased with the size distribution width. The error in estimating the mean of the size distributions remained below 5% for nearly all experimental parameters tested, but the widest size distribution tested (standard deviation of 600nm) reached 20%. The simulator revealed that sparse sampling of a broad size distribution can dominate the mismatch between actual and predicted size parameters. Alternative estimation strategies could reduce the discrepancy.

Local anesthetics effects of lidocaine-loaded chitosan nanoparticles in a rat model: An in vitro and in vivo study

Due to low molecular weight, locally administered anesthetic drugs are drained or absorbed. In the current study, lidocaine was loaded into chitosan nanoparticles using ionotropic gelation method in order to develop a potential anesthetic formulation to improve the drug’s long term effects. in vitro experiments including scanning electron microscopy assay, cell viability assay, hemocompatibility assay, and release assay were used to characterize the delivery system in vitro. in vivo anesthetic function of the developed delivery system was investigated in a rat model. in vitro studies showed that the developed nanoparticles had a submicron size and a wide size distribution. Lidocaine-loaded and lidocaine-free nanoparticles had mean particle size around 301.92±67.92 nm and 313.73±73.97 nm, respectively. The prepared nanoparticles were not toxic against L929 cells and promoted their viability. in vivo studies showed that the anesthetic effects of lidocaine-loaded nanoparticles were longer-lasting than free lidocaine. This study suggests potential applicability of the developed delivery system for anesthetic applications in the clinic.

The Influence of Powder Particle Size Distributions on Mechanical Properties of Alloy 718 by Laser Powder Bed Fusion

Currently, metallic powders for laser powder bed fusion (LPBF) primarily come in two commercially available powder size distributions (PSDs): 15+/45− for non-reactive powders and 15+/63− for reactive powders. These powders are generally produced via gas atomization processes that create highly spherical particles with a Gaussian PSD. Because of the standard deviation within a Gaussian distribution, only small portions of the total product are used for LPBF applications. This screening process makes the other particle sizes a waste product and, thus, increases processing costs. The non-reactive 718 powder was printed with both the typical PSD of 15+/45− and a wider bimodal experimental PSD. Compared to conventional 718, the 718 alloys with bimodal PSD shows less than a 0.2% difference in density, and insignificant change in mechanical behavior. Electron backscattered diffraction studies revealed that grain sizes and morphology were similar between the two sample sets, but bimodal 718 alloy has a slightly greater degree of large grains. The study suggests that particles with wide or bimodal size distributions show promise in producing equivalent high-quality products without sacrificing mechanical properties.

Influence of bed surface structure on bedload transport in mountain rivers

AbstractMountain rivers are characterized by wide grain size distributions and complex bed surface structures, which significantly affect bedload transport. Owing to the lack of a clear understanding of the quantitative influence of the bed surface structure on the bedload transport rate, existing methods for estimating the bedload transport rate in mountain rivers produce large errors. Based on theoretical analysis and flume experiments, this study reveals the influence of bed surface structure on nonuniform bedload transport and proposes a method for estimating bedload transport rate considering the quantitative influence of bed surface structure. The findings of the present study provide theoretical methodological support for predicting the sediment transport and bed evolution in mountain rivers.

TWO-STEP SYNTHESIS AND FORMATION MECHANISM FOR LACUOS NANO-SIZED AGGLOMERATES

We have developed a two-step synthesis method to obtain pure LaCuOS nano-sized agglomerates using La(NO3)3·6H2O, CuSO4·5H2O and NH3·H2O as the starting materials. The result shows that the precursor can be converted into La2O2SO4, La2(SO4)3 and CuO phases at 800 °C for 2 h in air, which was then converted into a pure LaCuOS phase by a reduction at 800 °C for 5 h in a flowing argon and hydrogen atmosphere. The as prepared LaCuOS nano-aggregates have poor dispersion and a wide size distribution range (50–100 nm).

Manufacture of mirco-meso-macroporous ACNF/PANI/MIL-101(Cr)-NH2 composites with exceptional adsorption phenomenon for indomethacin

Exploiting advanced adsorbents for the elimination of the alarming level of nonsteroidal anti-inflammatory drugs (NSAIDs) pollution has sparked extensive research attention. Herein, taking acid-treated carbon nanofiber (ACNF) as composite skeleton, a unique ACNF/polyaniline/MIL-101(Cr)-NH2 (ACNF/PANI/MIL-101(Cr)-NH2) with robust 3D-supporting framework and tertiary pore structure was synthesized to remove indomethacin (IDM). Considering the large BET surface area (SBET), wide pore size distribution, highly-exposed active sites and affluent functional groups, ACNF/PANI/MIL-101(Cr)-NH2 depicted a standout adsorption capacity of 400.1 mg/g for IDM, which was far superior to most reported adsorbents. Moreover, ACNF/PANI/MIL-101(Cr)-NH2 acquired rapid adsorption kinetics, wonderful reusability and stability. Ulteriorly, inspired by the electrode fabrication craft, one easy-to-recyclable ACNF/PANI/MIL-101(Cr)-NH2 taking graphite felt (GF) as carrier was manufactured and achieved superior adsorption capacity as well as satisfactory reusability. The adsorption mechanism was appraised via Fourier-transformed infrared spectroscopy (FT-IR) and X-ray photoelectron spectroscopy (XPS). The experimental data disclosed that the superior adsorption capability mainly depended on the electrostatic interaction, hydrogen bonding and π-π interaction. Overall, this work sheds light on one feasible strategy to develop advanced adsorbents in practical wastewater treatment.

Characteristics and Factors Influencing Pore Structure in Shale Oil Reservoirs of Different Lithologies in the Jurassic Lianggaoshan Formation of the Yingshan Gas Field in Central Sichuan Basin

Shale in the Jurassic Lianggaoshan Formation in central Sichuan exhibits strong heterogeneity. The study of the pore structure characteristics of different lithologies is crucial to the selection of the target interval. Shale samples of the Lianggaoshan Formation from well YS5 in the central part of the Sichuan Basin were analyzed using scanning electron microscopy, low-temperature nitrogen adsorption, high-pressure mercury injection (HPMI), and large -field splicing method -based scanning electron microscopy (LFS-SEM) to elucidate the pore structure characteristics of shale and their influencing factors. The mineral composition of the reservoir in the study area was diverse, primarily consisting of clay minerals, followed by quartz and calcite. The reservoir space comprised intergranular, granular, and organic matter pores, and oil was observed to fill the reservoir space. Reservoir characteristics varied with the lithological properties. In clayey shale, intergranular pores located in clay mineral particles and pores between pyrite and natural fractures were mainly observed, with a bimodal distribution of pore size and peak distribution of 10–50 nm and >100 nm. The storage space of ash-bearing shale mainly consisted of intragranular pores and intergranular (crystalline) micropores, with pore sizes primarily concentrated in the 10–50 nm range. The storage space in silty shale mainly developed in clastic mineral particles such as quartz, followed by clay mineral intergranular pores with a relatively wide distribution of sizes. Pores were mainly inkbottle-shaped and slit-type/plate-type pores, with an average specific surface area of approximately 6.9046 m2·g−1 and an average pore volume of approximately 0.0150 cm3·g−1. The full-pore capillary pressure curve was established using a combination of gas adsorption–desorption tests and HPMI. The fractal dimension of the sample pore structure was calculated, and a significant linear correlation was found between clay mineral content and the fractal dimension. Thus, the pore structure characteristics were mainly controlled by the content and distribution of clay minerals.

Mechanism of heel build-up on adsorbents through oxygen induced reactions

Oxygen induced reactions during the desorption of volatile organic compounds (VOCs) from adsorbents (such as activated carbon) promote heel buildup and reduce the adsorbent’s lifetime. This study aims to improve the understanding of heel build-up mechanisms in the presence of oxygen in the desorption purge gas. Three activated carbons (ACs) and one zeolite adsorbent were exposed to an extreme condition of 1,2,4-trimethylbenzene (TMB) and high oxygen concentration at three temperatures (150, 200, and 250 °C). Thermogravimetric analysis and gas chromatography-mass spectrometry (GC–MS) were used to assess the thermal stability and chemical structure of the formed heel, respectively. Additionally, nitrogen adsorption was performed to evaluate the effect of heel formation on the adsorbent’s pore properties. Increasing the desorption temperature in the presence of oxygen was found to reduce the BET surface area and increase the oxygen-induced reactions on the adsorbents. Among the three tested temperatures, minimum heel formation was obtained at the intermediate temperature, 200 °C. Compared to zeolite, ACs were more susceptible to oxygen induced reactions at elevated temperatures due to their wide pore size distribution. Further analysis using GC–MS revealed that oxygen presence during the desorption process can form a broad range of organic species in terms of molecular weight, chemical structure, and functional group.

The performance and mechanism for photocatalytic degradation of methylene blue catalyzed by ultrathin NiAl-layered double hydroxides

Ultrathin materials are widely used in various photocatalytic reactions due to their large specific surface area, multi-surface active sites, easy carrier separation and transport. In this work, ultrathin NiAl-layered double hydroxides (U-LDHs) nanosheets were prepared by a urea-assisted strategy for photocatalytic degradation of methylene blue. Atomic force microscopy (AFM) measurements show that the thickness of U-LDHs nanosheet is generally between 3 and 8 nm, with a wide pore size distribution and a high specific surface area (109 m2/g). U-LDHs nanosheets can remove 92.42% of methylene blue after 90 min light irradiation, which is nearly 40% higher than that of bulk NiAl-LDHs (B-LDHs). In addition, combined with photoelectric performance characterization and density functional theory calculation, it is confirmed that the U-LDHs nanosheets are much better to the separation and transfer of photogenerated carriers compared with the bulk LDHs. Besides, U-LDHs is conducive to adsorb oxygen to generate superoxide radicals, promoting the progress of photocatalytic reactions and significantly improving photodegradation performance.

Uniaxial dynamic behavior of foam glass aggregate under oedometric (fully side restrained) condition at different compaction ratios

Foam glass aggregate (FGA) is considered as a lightweight and thermal insulation material. It has a wide granular size distribution nature that can influence the material's dynamic response when subjected to moving loads. Therefore, it is crucial to investigate the impact of different compaction ratios on the material's dynamic behavior. This study focused on examining the effects of varying compaction ratios (10%, 20%, 30%, and 40%) on dynamic parameters such as resilient stiffness (Mr) and accumulated plastic strains (ɛacc) of FGA. Uniaxial deviatoric stresses were applied to the material samples in a series to assess their influence on the material's behavior over multiple cycles. The results revealed the significant influence of increasing the compaction ratio to 40% on the material's behavior. At this compaction ratio, the ɛacc decreased to approximately 71%, 69%, and 86% for deviatoric stresses of 25 kPa, 100 kPa, and 200 kPa, respectively, after subjecting the material to 40,000 cycles. The increase in recoverable strains resulting from the material's fragile property under higher compaction energy led to a decrease in the Mr values of FGA samples as the compaction ratios increased. The lower boundary of Mr values for FGA ranged from 102 MPa to 189 MPa, while the upper boundary ranged from 150 MPa to 219 MPa under the selected deviatoric stresses. Although the interpretation of the shakedown criterion limitations yielded varying ranges for the colocation of FGA samples, it was found that FGA samples compacted at 40% exhibited robust characteristics suitable for constructing road embankments. This can be beneficial for infrastructure applications due to their excellent lightweight and thermal insulation properties.

Study of the properties of Multi-walled carbon nanotubes/ Carbon Quantum Dots Nanocomposites

In recent years, there has been a growing interest in the synthesis and characterization of nanomaterials for various applications. Carbon nanotubes (CNTs) and quantum dots (QDs) are among the promising nanomaterials due to their unique properties. This study aims to synthesize and characterize multi-walled CNTs and QDs using the hydrothermal method. MWCNTs were synthesized at a temperature of 200°C using Ferrocene and Sulfur as precursors, while QDs were prepared at a temperature of 160°C using Polyethylene glycol (PEG). To fabricate the nanocomposite films, MWCNTs and QDs were mixed at different weight ratios (3:1, 2:2, and 1:3) through ultrasonic dispersion. The resulting mixture was then used to form films on glass surfaces. Characterization of the composites was carried out using a series of analyses including Fourier-transform infrared spectroscopy (FT-IR), field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD), and electrical conductivity measurements. From the FESEM measurements, spherical particles of various sizes were observed, with a wide size distribution of less than 10nm. XRD analysis revealed d-spacing values of 0.34nm, 0.39nm, and 0.46nm for all the mentioned weight ratios. Additionally, the diameter of the particles ranged from 32.48nm to 31.96nm, with a length of approximately 1µm. The electrical conductivity of the films was also measured, and the obtained results indicated activation energies of 0.155eV, 0.14eV, and 0.25eV for the respective weight ratios. The resulting nanocomposite films exhibited unique properties as characterized by various techniques. These findings contribute to the understanding and potential applications of nanomaterials in diverse

Microfluidic ultrasonic cavitation enables versatile and scalable synthesis of monodisperse nanoparticles for biomedical application

Controllable and scalable synthesis of biomedical organic nanoparticles (NPs) with tailored properties is critical for their clinical translation. However, the existing microfluidics-based synthesis is challenged by clogging and limited throughput, while the traditional ultrasound-assisted synthesis suffers from inhomogeneous cavitation activity, leading to wide particle size distribution. Herein, a series of biomedical organic NPs were successfully synthesized in a controlled, clog-free and scalable manner via a versatile microfluidic ultrasonic cavitation (MUC) approach. First, the effects of microchannel dimension and operating conditions on ultrasonic cavitation behavior and mixing performance was systematically studied. Cavitation pattern maps were developed for different operating conditions. By adjusting microchannel dimension and operating parameters, rapid mixing on a millisecond scale can be accomplished across an extensive range of conditions, including flow rates between 4 and 24 mL/min and flow rate ratios from 5:1 to 1:1. Then, the MUC approach was utilized to synthesize polymeric NPs, lipopolymeric NPs and lipid NPs encapsulating mRNA (mRNA-LNP). Compared to traditional microfluidics and ultrasound-based methods, NPs synthesized by MUC approach showed smaller sizes and more uniform distributions. The ability of MUC approach for clog-free and scalable production was demonstrated by the continuous synthesis of lipopolymeric NPs at a throughput of 1.6 g/h with desired properties. The successful synthesis of soft and fragile mRNA-LNPs has been accomplished by tailoring the cavitation pattern of MUC approach. The resultant mRNA-LNPs showed a mRNA encapsulation rate as high as 98.3%, over 99% transfection efficiency of cell with 0.5 μg dosage, and robust luciferase expression with 10 μg dosage at the injection site of BALB/c mice 24 h after injection.

Zero-Oil-Fouling Membrane With High Coverage of Grafted Zwitterionic Polymer for Separation of Oil-in-Water Emulsions.

Current hydrophilic modification strategies improve the antifouling ability of membranes but fail to completely eliminate the fouling of emulsified oil droplets with a wide size distribution. Constructing membranes with superior anti-oil-fouling ability to resist various oil droplets especially at high permeation fluxes is challenging. Here, the fabrication of a zero-oil-fouling membrane by grafting considerably high coverage of zwitterionic polymer and building defect-free hydration defense barrier on the surface is reported. A uniform layer of protocatechuic acid with COOH as abundant as existing in every molecule is stably deposited on the membrane so as to provide sufficient reactive sites and achieve dense grafting of the zwitterionic polymer. The coverage of zwitterionic polymer on the membrane plays a crucial role in promoting the antifouling ability to emulsified oil droplets. The poly(vinylidene fluoride) membrane with 93% coverage of the zwitterionic polymer exhibits zero oil fouling when separating multitudinous oil-in-water emulsions with ≈0% flux decline, ≈100% flux recovery, and a high water flux of ≈800 L m-2 h-1 bar-1. This membrane outperforms almost all of the reported membranes in terms of the comprehensive antifouling performance. This work provides a feasible route for manufacturing super-antifouling membranes toward oil/water separation application.

Linear relationship between lateral size of reduced graphene oxide (RGO) and water vapor barrier property in RGO/PEI composite membrane

The wide distribution of the lateral size of lab-prepared graphene oxide (GO) sheets often complicates the measurement of accurate average size. Herein, a series of reduced-GO/polyethyleneimine (RGO/PEI) composite membranes with compact brick-wall structures were successfully prepared. The large lateral size of RGO sheets in the membrane benefited gas barrier properties, including oxygen, nitrogen, and water vapor. The RGO sheets acted as impermeable inorganic filler to prolong the diffusion path, forcing gas molecules to wiggle through the permeable and tortuous channels of the PEI/water mixture. The water vapor transmission rate of RGO/PEI composite membranes was relatively high, and a linear correlation was established between the length of PEI/water channels and the water vapor barrier property. The length of PEI/water channels under the same membrane thickness was determined by the lateral size of RGO sheets. Therefore, the statistic averages of lateral size of RGO sheets (from 2.48μm to 44.35μm) showed a linear correlation with the water vapor barrier property, as confirmed by the positron annihilation technique and molecular dynamics simulations. In sum, the linear correlation could be used to practicably measure the statistic averages of lateral size of GO sheets according to water vapor permeability measurements.

Hydrodynamics of expanded bed adsorption studied through CFD-DEM

The hydrodynamics of the Expanded Bed Adsorption process is studied through simulations combining Computational Fluid Dynamics and the Discrete Element Method. A representative base case is defined, based on process design parameters commonly encountered in literature. Then, 19 other cases are defined, each representing a singular adjustment to the column design, material properties, or operating conditions. The parameters that are varied are the expansion factor, liquid viscosity, bed aspect ratio, mean particle density, width of the particle density distribution, width of the particle size distribution, column taper angle, and column alignment angle. The impact of each adjustment on the bed behaviour is discussed, using the local particle size distribution and solids dispersion coefficient as main indicators of bed stability. Optimal performance was found for an expansion factor of two to three, and the combination of particle size distribution and particle density distribution was found to greatly improve bed stability. The mixing process of the liquid and solid phases is concluded to be of highly complex nature, and cannot simply be predicted from the liquid flow velocity.

Development of a particle packed bed model for homogeneity evaluation of liquid chromatography column

Particle packed columns used for liquid chromatography (LC) can suppress a column internal band broadening (hereinafter referred to as band broadening) by packing monodisperse particles homogenously. However, a quantitative evaluation for the effects of particle shape and packed state on band broadening needs to be more investigated. In this study, we fabricated a model of particle packed bed using microfluid LC columns that have pillar array structure prepared by microfabrication technology, evaluating how structural factors inside of a column affect its band broadening. At first, microfluid LC columns was prepared using Si-quartz glass (Si-Q column) for the optimization of LC measurement system. Through the evaluation, it showed 11.6 times higher pressure tolerance compared to that of PDMS-soda lime glass (PDMS-g column).Then, an optimized LC measurement system was constructed using a microfluidic LC column made of Si-Q column, and it was confirmed that the measurement error was small enough and the LC measurement could be performed with high repeatability.Additionally, the effect of a distribution of structural size on band broadening was evaluated. It was confirmed that wide distribution of the structural size provided large band broadening in actual measurements. Comparing two columns having different structural log-normal distributions of 0 and 0.22 showed approximately 1.8 times difference in both real LC measurement.Lastly, the relationship between packed state and band broadening was evaluated.As packed state, we employed void arrangement and structural arrangement in the columns.Different location arrangements of 50 and 100 µm pillar sizes afforded different band broadening. Well-homogenized array showed approximately two times worse band broadening compared to that of delocalized array. Based on these results, the developed packed bed of particles model was able to evaluate the relation between structural factors and band broadening.

Densification of the eggshell powder by spark plasma sintering

Chicken eggshells (eggshells) are the bio-waste produced during day-to-day egg consumption by humans. The eggshell contains calcium carbonate (CaCO3) along with several other elements such as Si, Mg, K, P, Na, etc., which enables its application for human bio-implants. Our research work aims to practically implement the eggshell powder as the bio-implant, for which, the study of the densification behavior of the eggshell powder is required. Hence, the present paper represents the densification behavior of the crystalline eggshell powder by spark plasma sintering. The eggshell powders were irregular in shape with a wide particle size distribution. The eggshell powder was sintered at six varying temperatures, i.e., 250 °C, 500 °C, 750 °C, 850 °C, 900 °C, and 1000 °C. The consolidated samples were characterized through SEM, FTIR, and XRD analysis, and the optimum spark plasma sintering temperature was determined. The consolidation of eggshells at 850 °C not only avoids the calcination process (due to the application of pressure) but gives optimum density and hardness making it an optimum condition for consolidating eggshells into compacts.

Investigation of the Quartz Distribution in Electro-Porcelain Materials

Analysis of the microstructure of electro-porcelain is important to better understand its influence on mechanical, electrical and aging behavior. The microstructures of two electro-porcelain materials with low and high quartz contents were analyzed with respect to the distribution of quartz. Using an adequate evaluation of EDS (energy dispersive spectroscopy) mapping data, a reproducible analysis of the size distribution and quantity of quartz was achieved. The method allows the analysis of large areas (12.5 mm2). Therefore, the probability of occurrence for a few large quartz grains could be determined. Independent of the overall amount of quartz in the materials, a wide distribution of the grain size was observed. The size of the large detected quartz grains in both materials was very similar. Around the large quartz particles, microcrack systems with lengths of several 100 µm were observed. They are linearly correlated with the equivalent circle diameter of the quartz grains. The evaluation of the cracks allowed us to determine the critical size below which no cracks around the quartz particles are formed. This size is approximately 10 µm.