Random Networks,Graphs, and Matrices

Summary: The theory of elasticity based on the distribution function of the gyration tensor is reviewed. It is shown that the James-Guth potential for a network is a model potential of mean force, derivable in principle from the true many-body potential for the elastic body. The determination of the modulus of elasticity is resolved in the calculation of the statistical mechanical average of the smallest, non-zero, eigenvalue of the connectivity matrix that describes the network. The mathematical problem to determine the spectrum of eigenvalues of the random network can be couched in both the language of random graphs and of random matrices.     

Particulate and continuum mechanics of microgel pastes: effect and non-effect of compositional heterogeneity

Microgels are deformable colloids that can be packed by external compression; such packing transforms a suspension of loose microgels into a viscoelastic paste with mechanical properties controlled by the elasticity of the constituent particles. We aim to understand how the presence of microgel particles with different individual elastic moduli affects this interplay in heterogeneous microgel packings. We do this by preparing microgel pastes that contain both soft, loosely cross-linked and stiff, densely cross-linked microgel particles and probe their shear elasticity. We consider particle packing fractions that cover the range from particles at the onset of contact to particles that are strongly packed, deformed, and deswollen to investigate the transition from a particulate suspension to a macrogel-type system. These studies reveal that the elasticity of heterogeneous microgel suspensions at low packing is due to the response of the soft, easily deformable microgel particles alone, whereas at high packing both soft and stiff microgels linearly add to the paste elasticity. This fundamental difference is due to the fundamentally different origin of elasticity at different microgel packing; whereas the soft particle interaction potential dominates the suspension mechanics at low microgel packing, rubber-like elasticity that equally reflects both soft and stiff contributions governs the mechanics of the same samples at high microgel packing.     

Electrostriction of supported lipid films at presence of cationic surfactants,surfactant-DNA and DNA-Mg(2+) complexes

The method of electrostriction has been applied to study the physical properties of supported lipid membranes (sBLM) during membrane formation at application of negative potential. Application of negative potential -350 mV to the sBLM during its formation resulted in more compact membrane structure as revealed by higher elastic modulus in comparison with sBLM formed without application of this potential. We also studied interaction with sBLM cationic surfactant hexadecylamine (HDA), HDA-DNA and DNA-Mg(2+) complexes. Interaction of HDA with sBLM resulted in decrease of membrane capacitance and two-directional effect on elasticity modulus (increase or decrease), which can be caused by different aggregation state of surfactant at the surface of sBLM. In contrast with effect of HDA, the complexes of HDA-DNA resulted, in most cases, increase of elasticity modulus and increase of membrane capacitance, which can be caused by incorporation of these complexes into the hydrophobic interior of the membrane. Certain part of these complexes can, however, be adsorbed on the sBLM surface. DNA itself does not cause substantial changes of physical properties of sBLM; however, addition of bivalent cations Mg(2+) to the electrolyte-contained DNA caused substantial increase of elasticity modulus and surface potential. These changes are, however, much slower than that observed for HDA-DNA complexes, which can be caused by slow competitive exchange between Na(+) and Mg(2+) ions.     

Changes of conductance and compressibility of bilayer lipid membranes induced by oligonucleotide-cationic polyene antibiotic complexes

The positively charged polyene molecule amphotericin B 3-dimethylaminopropylamide (AMA) is an efficient agent for the delivery of antisense oligodeoxyribonucleotides (ODN) into target cells. In the present study, bilayer lipid membrane (BLM) conductance, elasticity modulus perpendicular to the membrane plane, surface potential and electrical capacitance were measured by conductance and electrostriction methods in the presence of AMA, pure or complexed to 20-mer single stranded ODN at different ratios. Pure AMA did not induce changes in conductance of cholesterol-containing BLM, but did induce an increase in elasticity modulus and surface potential. ODN/AMA complexes changed BLM properties depending on the charge ratio. The most pronounced effect on membrane conductance was observed for positively charged ODN/AMA complexes (charge ratio rho-/+=0.1), while for negatively charged complexes these changes were less marked/apparent, correlating to substantially lower binding constants. The effect of ODN/AMA complexes on elasticity modulus and charge potential was biphasic. After an increase in both values, a decrease was observed for higher incubation times and ODN/AMA concentrations. These results are interpreted as indicating that the membrane property changes result from the large AMA aggregates induced by the presence of the negatively charged ODN, which condensate on these aggregates. It is suggested that the decrease of elasticity modulus and surface potential in the presence of increasing incubation time and AMA concentration result from desorption of the complexes in the complex-free compartment of the BLM cell, or appearance of a non-linear conductance of the lipid bilayer. The first alternative would explain the AMA-induced transmembrane transfer of ODN.     

Expressions for the stress and elasticity tensors for angle-dependent potentials

The stress and elasticity tensors for interatomic potentials that depend explicitly on bond bending and dihedral angles are derived by taking strain derivatives of the free energy. The resulting expressions can be used in Monte Carlo and molecular dynamics simulations in the canonical and microcanonical ensembles. These expressions are particularly useful at low temperatures where it is difficult to obtain results using the fluctuation formula of Parrinello and Rahman [J. Chem. Phys. 76, 2662 (1982)]. Local elastic constants within heterogeneous and composite materials can also be calculated as a function of temperature using this method. As an example, the stress and elasticity tensors are derived for the second-generation reactive empirical bond-order potential. This potential energy function was used because it has been used extensively in computer simulations of hydrocarbon materials, including carbon nanotubes, and because it is one of the few potential energy functions that can model chemical reactions. To validate the accuracy of the derived expressions, the elastic constants for diamond and graphite and the Young's Modulus of a (10,10) single-wall carbon nanotube are all calculated at T = 0 K using this potential and compared with previously published data and results obtained using other potentials.     

An Organic Crystal with High Elasticity at an Ultra‐Low Temperature (77 K) and Shapeability at High Temperatures

Organic single crystals with elastic bending capability and potential applications in flexible devices and sensors have been elucidated. Exploring the temperature compatibility of elasticity is essential for defining application boundaries of elastic materials. However, related studies have rarely been reported for elastic organic crystals. Now, an organic crystal displays elasticity even in liquid nitrogen (77 K). The elasticity can be maintained below ca. 150 °C. At higher temperatures, the heat setting property enables us to make various shapes of crystalline fibers based on this single kind of crystal. Through detailed crystallographic analyses and contrast experiments, the mechanisms behind the unusual low‐temperature elasticity and high‐temperature heat setting are disclosed.     

Towards a microscopic theory of the modulus of elasticity in crystalline covalent materials and a survey of potential superhard materials

The present report is an account of the generalization of the dynamic elasticity theory earlier proposed by Bucknum et al. and applied to the cubic diamond and tetragonal glitter lattices. It describes a theory of elasticity in which the elasticity moduli are based upon the microscopic constants of the various structure-types. Such microscopic constants include the force constants of the chemical bonds in the unit of pattern of the material, its associated lattice parameters, and the elastic chemical bond deformation parameters of the material. In developing the outward features of the dynamic elasticity model, it is shown that an integral over the force density in the unit cell of a given material; where the force is modeled based upon the elastic deformation forces of the chemical bonds in the unit of pattern of the material, and the volume is written as a function of the deformations taking place inside the unit cell of the material; generates the terms for calculating its modulus of elasticity at pressure, in components, that are directed along the principal axes of the unit cell. Several potential solutions to the problem of superhardness are discussed and illustrated.     

Peculiarities of the DNA hybridization on the surface of bilayer lipid membranes

The method of electrostriction was applied to study the peculiarities of interaction of short oligonucleotides with free standing (BLM) and supported lipid membranes (sBLM) and of the duplex formation between complementary oligonucleotides on a membrane surface. The 15-mer single stranded DNA (pentadecathymidylate-(dT)(15)) was modified either with cholesterol (CH(dT)(15)) or by palmitoyl chain (C16(dT)(15)). The interaction of CH(dT)(15) with free standing BLM or with BLM formed on an agar or gold support was accompanied by sharp increase of elasticity modulus in direction perpendicular to the membrane plane ,E( perpendicular), and by increase of surface potential. In contrast, C16(dT)(15) did not induce substantial changes of elasticity modulus, however, the surface potential was changed in a similar manner as for CH(dT)(15). Hybridization of DNA following addition of complementary chain (dA)(15) has been accompanied by a small decrease of elasticity modulus and by a slight increase of surface potential. Both the incorporation of chemically modified oligonucleotides into the lipid bilayer as well as hybridization of DNA are not cooperative processes as has been demonstrated by analysis using Scatchard plot of corresponding values.     

Dynamic elastic modulus in bending: A new determination technique in impact and rebound conditions

The potential of a new technique for the determination of the dynamic elastic modulus under impact conditions and thus at high strain rates is described. Determination at high strain rate is found to be indispensable when evaluation of a material according to the rules of fracture mechanics at high test speeds is desired.

Although the modulus of elasticity is a property of the material itself, it is dependent on the strain rate. Tests carried out with those techniques normally used have shown their inadequacy in determining the modulus of elasticity as the same strain rate as an impact. On the other hand, the technique presented here, which better simulates the actual technological application conditions of the materials, permits wider study of the physical-mechanical properties of the material.

The apparatus used, which is characterized by its simplicity, can be constructed and used with considerable economic advantage by any laboratory and in particular by those which use instrumented equipment.     

Extremes of some foam properties and elasticity of thin foam films near the critical micelle concentration

The elasticity of open and closed thin foam films is analyzed. The elasticity modulus of a closed film is shown to be additive with respect to contributions from Gibbs elasticity and disjoining pressure. A detailed expression for the film elasticity modulus explains the pronounced maxima of foaminess and foam stability near the critical micelle concentration observed earlier in many experiments. A theory of transversal elasticity of thin foam films is formulated under conditions excluding the action of Gibbs elasticity. Near the critical micelle concentration, the theory predicts maxima of the transversal elasticity modulus and of the films thickness as functions of concentration at a given disjoining pressure. The prediction has been verified experimentally by measuring the film thickness in equilibrium foam as a function of height.     

Properties of cellulose acetate in solution. II. Light scattering and elasticity measurements on gels in benzyl alcohol

Kinetic studies are reported for the light scattering and elasticity of thermally reversible gels of cellulose acetate in benzyl alcohol over a range of temperature and polymer concentration. The small-angle light scattering data are found to be described by exponential correlation functions, and it is concluded that the scattering has its origin in the nonrandom character of the crosslinking in the gels studied. The elasticity is discussed in terms of the density of crosslinks in the gels. Thus, the kinetics studied by light scattering and elasticity measurements are independently related to temperature and polymer concentration.     

Thermodynamic and structural characterization of a mixed perfluorocarbon-phospholipid ternary monolayer surfactant system

Pulmonary lung surfactant is a mixture of surfactants that reduces surface tension during respiration. Perfluorinated surfactants have potential applications for artificial lung surfactant formulations, but the interactions that exist between these compounds and phospholipids in surfactant monolayer mixtures are poorly understood. We report here, for the first time, a detailed thermodynamic and structural characterization of a minimal pulmonary lung surfactant model system that is based on a ternary phospholipid-perfluorocarbon mixture. Langmuir and Langmuir-Blodgett monolayers of binary and ternary mixtures of the surfactants 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dipalmitoyl-sn-glycero-3-phosphoglycerol (DPPG) and perfluorooctadecanoic acid (C18F) have been studied in terms of miscibility, elasticity and film structure. The extent of surfactant miscibility and elasticity has been evaluated via Gibbs excess free energies of mixing and isothermal compressibilities. Film structure has been studied by a combination of atomic force microscopy and fluorescence microscopy. Combined thermodynamic and microscopy data indicate that the ternary monolayer films were fully miscible, with the mixed films being more stable than their pure individual components alone, and that film compressibility is minimally improved by the addition of perfluorocarbons to the phospholipids. The importance of these results is discussed in context of these mixtures' potential applications in pulmonary lung surfactant formulations.     

The interfacial dilational properties of hydrophobically modified associating polyacrylamide studied by the interfacial tension relaxation method at an oil-water interface

The interfacial dilational viscoelastic properties of hydrophobically associating block copolymer composed of acrylamide (AM) and a low amount of 2-phenoxylethyl acrylate (POEA) (<1.0 mol%) at the octane-water interfaces were studied by means of the interfacial tension relaxation method. The dependencies of interfacial dilational elasticity and viscous component on the dilational frequency were investigated. The interaction of hydrophobically associating block copolymer [P(AM/POEA)] with sodium dodecyl sulfate (SDS) has been explored. The results show that at lower frequency, the dilational elasticity for different concentration copolymer is close to zero; at higher frequency, the dilational elasticity shows no change with increased frequency; At moderate frequency (10(-3)-1 Hz), the dilational elasticity decreased with a decrease in the dilational frequency. The results show that the hydrophobic groups of [P(AM/POEA)] chains can be associated by inter- or intrachain liaisons in water solution. The dilational viscous component for P(AM/POEA) comes forth a different maximum value at different frequencies when the polymer concentration is different. It is generally believed that the dilational viscous component reflects the summation of the various microscopic relaxation processes at and near the interface and different relaxation processes have different characteristic frequencies. The spectrum of dilational viscous component may appear more than once maximum values at different frequencies. The influence of SDS on the limiting dilational elasticity and viscous component for polymer solution was elucidated. For 5000 ppm polymer solution, the limiting dilational elasticity decreased with an increase in SDS concentration. The dilational viscous component passed through a maximum value with a rise in the dilational frequency, which appeared at different frequency when SDS concentration is different; and the higher is the concentration, the lower is the dilational frequency. It can be explained that macromolecules may be substituted by SDS molecules in the interface and the interaction of molecules decrease, which makes the limiting dilational elasticity decrease. For 200 ppm polymer solution, the limiting dilational elasticity increased firstly and then decreased with SDS concentration increasing. This may be explained that the interfacial polymer concentration is so low that SDS molecules absorbed in the interface dominate dilational properties of the interfacial film even at very low SDS concentration. However, SDS molecules can gradually substitute the polymer molecules in the interface with a rise in SDS concentration, which results in the decrease in the limiting dilational elasticity.     

Effect of Matrix Elasticity on the Continuous Foaming of Food Models

The aim is to understand the effect of matrix elasticity on continuous foaming using food models based on glucose syrup. This was modified by adding polyacrylamide (PAA) with 2% whey protein isolate (WPI) or Tween 80 as foaming agents. Foaming was conducted in a stirred column. Rotation speed N and gas-to-liquid flow ratio (G/L) were varied. Overrun, average bubble size d (32), texture and stability were measured using densimetry, image analysis, and rheometry, respectively. Experimental results showed that 0.01% PAA did not modify the viscosity of 2% WPI models, but conferred low elastic behavior. PAA (0.05%) doubled matrix viscosity and drastically increased elasticity. The increase of elasticity became slower for further PAA addition. Foaming experiments demonstrated that theoretical overrun could not be achieved for inelastic WPI models in two cases: for high viscosity and low N, as dispersion effectiveness was reduced; for high G/L and N because of enhanced coalescence. Matrix elasticity was shown to increase overrun at constant viscosity for high G/L by enhancing interface stabilization. However, in elastic models, gas dispersion was more difficult and d (32) was higher than in inelastic fluids of similar viscosity. Finally, when the limiting step was dispersion, foaming was shown to be negatively affected by matrix elasticity.     

Elasticity of cardiac cells on the polymer substrates with different stiffness: an atomic force microscopy study

Influences of substrate stiffness on mechanical properties of cardiac myocytes and fibroblasts were investigated by cell elasticity measurement with atomic force microscopy. The cells were cultured on collagen-coated polyacrylamide substrates with gradient rigidity. While cardiac myocytes showed no evident change in cell elasticity on different substrates, cardiac fibroblasts displayed the non-monotonic dependence on substrate stiffness with a maximum elastic modulus. Moreover, the elasticity change of cardiac fibroblasts with substrates stiffness was found to be regulated by actin filaments. Study of the effect of substrate stiffness on cell elasticity for different cardiac cells provides new information for the better understanding of cardiac physiology and pathology.     

A Flexible Organic Single Crystal with Plastic-Twisting and Elastic-Bending Capabilities and Polarization-Rotation Function

Flexible organic single crystals capable of plastic or elastic deformations have a variety of potential applications. Although the integration of plasticity and elasticity in a crystal is theoretically possible and it may cause rich and complex deformations which are highly demanded for potential applications, the integration is hard to realize in practice. Here, we show that through utilizing different modes of external forces for influencing molecular packing in different crystallographic directions, plastic helical twisting and elastic bending can both be achieved for a crystal, and they can even be realized simultaneously. Detailed crystallographic analyses and contrast experiments disclose the mechanisms behind these two kinds of distinct deformations and their mutual compatibility. Based on the plastically twistable nature of the crystal, a new application field of flexible organic single crystals, namely polarization rotators, is successfully opened up.     

A Flexible Organic Single Crystal with Plastic‐Twisting and Elastic‐Bending Capabilities and Polarization‐Rotation Function

Flexible organic single crystals capable of plastic or elastic deformations have a variety of potential applications. Although the integration of plasticity and elasticity in a crystal is theoretically possible and it may cause rich and complex deformations which are highly demanded for potential applications, the integration is hard to realize in practice. Here, we show that through utilizing different modes of external forces for influencing molecular packing in different crystallographic directions, plastic helical twisting and elastic bending can both be achieved for a crystal, and they can even be realized simultaneously. Detailed crystallographic analyses and contrast experiments disclose the mechanisms behind these two kinds of distinct deformations and their mutual compatibility. Based on the plastically twistable nature of the crystal, a new application field of flexible organic single crystals, namely polarization rotators, is successfully opened up.     

Quantitative evaluation of mechanosensing of cells on dynamically tunable hydrogels

Thin hydrogel films based on an ABA triblock copolymer gelator [where A is pH-sensitive poly(2-(diisopropylamino)ethyl methacrylate) (PDPA) and B is biocompatible poly(2-(methacryloyloxy)ethyl phosphorylcholine) (PMPC)] were used as a stimulus-responsive substrate that allows fine adjustment of the mechanical environment experienced by mouse myoblast cells. The hydrogel film elasticity could be reversibly modulated by a factor of 40 via careful pH adjustment without adversely affecting cell viability. Myoblast cells exhibited pronounced stress fiber formation and flattening on increasing the hydrogel elasticity. As a new tool to evaluate the strength of cell adhesion, we combined a picosecond laser with an inverted microscope and utilized the strong shock wave created by the laser pulse to determine the critical pressure required for cell detachment. Furthermore, we demonstrate that an abrupt jump in the hydrogel elasticity can be utilized to monitor how cells adapt their morphology to changes in their mechanical environment.     

一种古老而又年轻的天然高分子—杜仲胶

本文简述了杜仲胶的开发史及资源情况。指出,杜仲胶高弹性体的出现,是其研究开发进入新阶段的标志。指出临界交联度是杜仲胶获得高弹性的关键概念。这种由有序柔性链组成的大分子网络,其高弹性不宜用分子链无规线团的贡献来解释,而是由于大分子网络的整体无序性。     

Morphological and mechanical properties of tannic acid/PAAm semi-IPN hydrogels for cell adhesion

A series of hydrogels were fabricated from tannic acid (TA), a typical plant polyphenol widely present in wood, and polyacrylamide (PAAm) by semi-IPN and cryogelation techniques. The introduction of TA into the PAAm network endows the system with enhanced cell adhesion properties. The cryogels with open interconnected macropores had a superfast swelling rate and a high swelling ratio, as well as high elasticity in response to compression. The degradation of the hydrogels can be tuned by modulating the content of cross-linker poly(ethylene glycol) diacrylate (PEGDA). Cytotoxicity results revealed that the hydrogels were non-toxic to COS-7 cells. All these results suggested that TA/PAAm semi-IPN hydrogels have great potential for applications in tissue engineering.