Elasticity of colloidal gels: structural heterogeneity, floppy modes, and rigidity

Soft Matter ◽  
2021 ◽  
Author(s):  
D. Zeb Rocklin ◽  
Lilian C Hsiao ◽  
Megan E Szakasits ◽  
Michael J Solomon ◽  
Xiaoming Mao
Keyword(s):  
Coordination Number ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Structural Heterogeneity ◽  
Colloidal Gels ◽  
Shear Moduli ◽  
Rheological Measurements

Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number,...

scholarly journals Predictions of the shear modulus of cheese, a soft matter approach

2019 ◽  
Vol 29 (1) ◽  
pp. 58-68 ◽  
Author(s):  
Graeme Gillies
Keyword(s):  
Shear Modulus ◽  
Soft Matter ◽  
Volume Fraction ◽  
Quantitative Model ◽  
Nano Particles ◽  
Core Shell ◽  
Two Dimensional ◽  
Shear Moduli ◽  
Numerical Predictions ◽  
The Many

Abstract The rheological and structural properties of cheese govern many physical processes associated with cheese such as slumping, slicing and melting. To date there is no quantitative model that predicts shear modulus, viscosity or any other rheological property across the entire range of cheeses; only empirical fits that interpolate existing data. A lack of a comprehensive model is in part due to the many variables that can affect rheology such as salt, pH, calcium levels, protein to moisture ratio, age and temperature. By modelling the casein matrix as a series core-shell nano particles assembled from calcium and protein these variables can be reduced onto a simpler two-dimensional format consisting of attraction and equivalent hard sphere volume fraction. Approximating the interaction between core-shell nano particles with a Mie potential enables numerical predictions of shear moduli. More qualitatively, this two-dimensional picture can be applied quite broadly and captures the viscoelastic behaviour of soft and hard cheeses as well as their melting phenomena.

scholarly journals Effect of the Free Volume on the Electronic Structure of Cu70Zr30 Metallic Glasses

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4911
Author(s):  
Simon Evertz ◽  
Jochen M. Schneider
Keyword(s):  
Electronic Structure ◽  
Bond Strength ◽  
Coordination Number ◽  
Free Volume ◽  
Metallic Glasses ◽  
Volume Content ◽  
Short Distance ◽  
Volume Fraction ◽  
Plastic Behavior ◽  
Local Bonding

While it is accepted that the plastic behavior of metallic glasses is affected by their free volume content, the effect on chemical bonding has not been investigated systematically. According to electronic structure analysis, the overall bond strength is not significantly affected by the free volume content. However, with an increasing free volume content, the average coordination number decreases. Furthermore, the volume fraction of regions containing atoms with a lower coordination number increases. As the local bonding character changes from bonding to anti-bonding with a decreasing coordination number, bonding is weakened in the volume fraction of a lower coordination number. During deformation, the number of strong, short-distance bonds decreases more for free volume-containing samples than for samples without free volume, resulting in additional bond weakening. Therefore, we show that the introduction of free volume causes the formation of volume fractions of a lower coordination number, resulting in weaker bonding, and propose that this is the electronic structure origin of the enhanced plastic behavior reported for glasses containing free volume.

Computation of Electron Delocalization for Extended Cyclic Conjugated Molecules

2016 ◽  
Vol 69 (9) ◽  
pp. 999 ◽  
Author(s):  
Suhwan Song ◽  
Minwoo Han ◽  
Eunji Sim
Keyword(s):  
Structural Parameters ◽  
Quantitative Relationship ◽  
Structural Heterogeneity ◽  
Electron Delocalization ◽  
Strongly Correlated ◽  
Conjugated Molecules ◽  
Alkyl Groups ◽  
Out Of Plane ◽  
Two Parameters ◽  
Torsional Angles

Cyclic conjugated molecules have relatively planar conformations due to overlap of adjacent π-orbitals of delocalized electrons and which is strongly correlated with the degree of electron delocalization. We first demonstrate the quantitative relationship between structural heterogeneity and two structural parameters: out-of-plane distances of atoms and torsional angles between neighbouring aromatic moieties. The molecular characteristic-dependent trend of planarity is presented in terms of these two parameters for the number of unit moieties, type and distribution of linkers, and substituting alkyl groups. The method presented may provide a simple yet systematic guide for determining the degree of delocalization of cyclic conjugated molecules.

scholarly journals The Off-Axis IBII Test for Composites

2020 ◽  
Author(s):  
S. Parry ◽  
L. Fletcher ◽  
F. Pierron
Keyword(s):  
Shear Modulus ◽  
Strain Rate ◽  
High Strain ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Fibre Volume ◽  
Published Data ◽  
Shear Moduli ◽  
Test Methodology ◽  
Split Hopkinson

Abstract Composite components regularly experience dynamic loads in service. Despite this, it is still difficult to obtain accurate mechanical properties of composite materials under high strain rate conditions. In this study, a new application of the Image-Based Inertial Impact (IBII) test methodology was developed, to generate an accurate in-plane transverse and shear moduli dataset from unidirectional (UD) off-axis composite specimens. The obtained dataset was consistent across different sample configurations, where results from the UD45$$^{\circ }$$ ∘ off-axis specimens agreed well with the UD90$$^{\circ }$$ ∘ values. Validation of the shear modulus identification was also undertaken by comparing the results from the UD90$$^{\circ }$$ ∘ and UD45$$^{\circ }$$ ∘ specimens with a multi-directional (MD) configuration. Here, it was found that MD±45$$^{\circ }$$ ∘ specimen shear modulus values where marginally lower than that from the UD specimens, in accordance with the lower fibre volume fraction of the MD laminate. Low strain rate sensitivities in the $$0.5-2\times$$ 0.5 - 2 × 10$$^{3}$$ 3  $$\hbox {s}^{-1}$$ s - 1 regime evidenced in this work suggest previously published data (often from split-Hopkinson bar tests) may include both a material and system i.e. testing apparatus response.

Structural and Mechanical Properties of Mandibular Condylar Bone

2006 ◽  
Vol 85 (1) ◽  
pp. 33-37 ◽  
Author(s):  
T.M.G.J. van Eijden ◽  
P.N. van der Helm ◽  
L.J. van Ruijven ◽  
L. Mulder
Keyword(s):  
Mechanical Properties ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Sagittal Plane ◽  
Mandibular Condyle ◽  
Mechanical Anisotropy ◽  
Bone Volume Fraction ◽  
Shear Moduli ◽  
Trabecular Density ◽  
Ct System

The trabecular bone of the mandibular condyle is structurally anisotropic and heterogeneous. We hypothesized that its apparent elastic moduli are also anisotropic and heterogeneous, and depend on trabecular density and orientation. Eleven condyles were scanned with a micro-CT system. Volumes of interest were selected for the construction of finite element models. We simulated compressive and shear tests to determine the principal mechanical directions and the apparent elastic moduli. Compressive moduli were relatively large in directions acting in the sagittal plane, and small in the mediolateral direction. The degree of mechanical anisotropy ranged from 4.7 to 10.8. Shear moduli were largest in the sagittal plane and smallest in the transverse plane. The magnitudes of the moduli varied with the condylar region and were proportional to the bone volume fraction. Furthermore, principal mechanical direction correlated significantly with principal structural direction. It was concluded that variation in trabecular structure coincides with variation in apparent mechanical properties.

A Versatile Micromechanical Model for Estimating the Effective Properties of Isotropic Composite Materials

2009 ◽  
Vol 614 ◽  
pp. 255-260
Author(s):  
Qi Chang He ◽  
H. Le Quang
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Micromechanical Model ◽  
Characteristic Parameter ◽  
Effective Medium ◽  
Inclusion Type ◽  
Composite Sphere ◽  
Host Matrix ◽  
Shear Moduli ◽  
Isotropic Composite

This work is concerned with a versatile and efficient model for estimating the effective moduli of isotropic composites consisting of isotropic phases whose microstructure may be of matrix-inclusion type, disordered or intermediate. This extended version of generalized self-consistent model (GSCM) is built by inserting a composite sphere embedded in an infinite unknown effective medium has the core made of the unknown effective medium and coated by the constituent phases. The volume fraction of the constituent phases in this composite sphere is the characteristic parameter of the relevant microstructure. By imposing the an energy equivalency condition, the equations thus obtained to estimate the effective bulk and shear moduli involve the microstructural parameter which turns out to be capable of describing in some sense how far a microstructure is from the host matrix/inclusion morphology

Characterizing Tensile Strength Properties in an E-Glass Composite With Fiber Waviness

2011 ◽  
Author(s):  
Cory Kendall ◽  
Greg R. Doud
Keyword(s):  
Finite Element ◽  
Tensile Strength ◽  
Volume Fraction ◽  
Strength Properties ◽  
Resin Matrix ◽  
Fiber Waviness ◽  
Bending Tests ◽  
Shear Moduli ◽  
Helicopter Blades ◽  
Failure Properties

This report investigates failure properties of a unidirectional fiber-reinforced E-glass epoxy resin matrix (CYCOM 5216). This material is used in military and commercial helicopter blades and structures and is commonly used in engine nacelles. Testing and failure analysis is critical for these structures, which undergo vibratory and complex aerodynamic loading. Defined manufacturing methods were modified to produce thick samples containing wrinkle defects. Wrinkles were added to simulate realistic marcelling, which commonly occurs within complex structures. All samples were validated using volume fraction experiments. Static uniaxial tension and five-point bending testing was performed as strain was measured using a multi-axis strain gage or an axial extensometer. Tensile and shear moduli, tensile strength, and shear strength were all determined. Shear modulus was determined through the use of a reinforced five point bending apparatus. The effects of fiber waviness on static strength were observed by testing samples with wrinkles of varying amplitude in both shear and tension. Fatigue analysis in this study differs from previous finite element crack growth studies due to the introduction of fiber waviness. For this reason, previous mixed mode bending tests and analytical methods were used with finite element techniques to improve failure prediction methods.

Small Angle Scattering from Nanocrystalline Pd

1988 ◽  
Vol 132 ◽  
Author(s):  
G. Wallner ◽  
E. Jorra ◽  
H. Franz ◽  
J. Peisl ◽  
R. Birringer ◽  
...  
Keyword(s):  
Crystallite Size ◽  
Size Distribution ◽  
Small Angle ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Spatial Arrangement ◽  
Small Angle Scattering ◽  
X Rays ◽  
Angle Scattering ◽  
Log Normal

ABSTRACTThe microstructure of nanocrystalline Pd was investigated by small angle scattering of neutrons and X-rays. The samples were prepared by compacting small crystallites produced by evaporation and condensation in an inert gas atmosphere. The strong scattering signal is interpreted to arise from crystallites embedded in a matrix of incoherent interfaces. Size distributions were deduced from the scattering curves. They consist of two parts: the crystallite size distribution dictated by the production process, and a structureless contribution due to the correlation in the spatial arrangement of the crystallites. The crystallite size distribution may be described by a log-normal distribution centred at R=2nm. The characteristic form of the correlation contribution arises from the dense packing of non-spherical crystallites. From the scattering cross-section in absolute units the volume fraction vc of crystallites was obtained as vc≈0.3, and the mean atomic density ρi in the interfaces as ρi≈0.52. The change of structural parameters during thermal annealing of the samples was studied. Up to high temperatures an appreciable volume fraction of crystallites with nearly unchanged size remains along with large particles.

A multivariate approach to structural heterogeneity of retinal ganglion cells

2011 ◽  
Vol 28 (6) ◽  
pp. 499-512 ◽  
Author(s):  
I.I. PUSHCHIN ◽  
T.A. PODUGOLNIKOVA ◽  
S.L. KONDRASHEV
Keyword(s):  
Functional Organization ◽  
Ganglion Cells ◽  
Structural Parameters ◽  
Clustering Algorithms ◽  
Cluster Structure ◽  
Structural Heterogeneity ◽  
Multivariate Techniques ◽  
Accessory Optic System ◽  
Neuronal Types

AbstractKnowing neuronal types is essential for understanding the structural and functional organization of the nervous system. It has long been recognized that neuronal types should be discovered and not defined. This can be done using cluster analysis (CA). Despite there being many studies using CA to classify neurons, only a few of them meet its formal prerequisites. In the present study, we provide an example of using CA in combination with other multivariate techniques for examining neuronal diversity. A special emphasis is put on formal prerequisites to the data and procedure. The data under scrutiny are a sample of ganglion cells projecting to the basal optic nucleus [accessory optic system-projecting ganglion cells (AOS GCs)] in the common frog. There is physiological evidence that these cells comprise at least two functional types but their structural heterogeneity has not been addressed. Cells were labeled with horseradish peroxidasein vivoand examined in whole-mounted retinae using light microscopy. A sample of well-stained cells was obtained and used to estimate 18 structural parameters. A variety of clustering algorithms were used to classify the cells. The joint polar distribution of dendrite mass was monomodal. CA did not reveal a statistically reliable cluster structure in the sample. The clusters were not cohesive and well isolated. ANOVA-on-Ranks revealed no significant between-cluster differences. Our formal conclusion is that functionally distinct frog AOS GCs do not differ in morphology or dendritic arbor orientation. The advantages and limitations of the adopted approach are discussed.

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