Corresponding-States Laws for Protein Solutions

The monomers or aggregates of protein molecules in protein crystallization solution at the initial stage of crystallization process are the basis of subsequent nucleation process. Tanaka et al (Tanaka S., et al, J. Cryst. Growth, 1996) concluded that there are units and clusters of lysozyme molecules in solution at the beginning of lysozyme crystallization process, and the decrease of clusters' amount showed the nucleation process comes up. Therefore, cluster of protein molecules in solution is one of important parameters, by which we can judge the crystallization process, in particular, nucleation process. However, the formation process of lysozyme clusters was not reported up to now. In this paper, we studied the aggregates of lysozyme molecules in solution 1 hr and 12 hrs after the mixture of lysozyme and NaCl (precipitant) solution, by atomic force microscopy (AFM) and dynamic light scattering (DLS). Moreover, we studied the effect of solution temperature on the aggregates in solution. Our results showed that, 1 hr after the mixture of lysozyme and NaCl solution, the mean size of aggregates in solution first increased and then decreased. Our results also showed that the aggregates of lysozyme molecules in solution gradually disassembled and clusters of lysozyme molecules appeared within 12 hrs after the mixture of lysozyme and NaCl solution. The decrease of solution temperature decreased the period for appearance of clusters of lysozyme molecules in solution.

The paper is concerned with the nucleation, growth and coalescence of microdefects in the form of voids in S235JR steel. The material is known to be one of the basic steel grades commonly used in the construction industry. The theory and methods of damage mechanics were applied to determine and describe the failure mechanisms that occur when the material undergoes deformation. Until now, engineers have generally employed the Gurson-Tvergaard- Needleman model. This material model based on damage mechanics is well suited to define and analyze failure processes taking place in the microstructure of S235JR steel. It is particularly important to determine the critical void volume fraction fc, which is one of the basic parameters of the Gurson-Tvergaard-Needleman material model. As the critical void volume fraction fc refers to the failure stage, it is determined from the data collected for the void coalescence phase. A case of multi-axial stresses is considered taking into account the effects of spatial stress state. In this study, the parameter of stress triaxiality η was used to describe the failure phenomena. Cylindrical tensile specimens with a circumferential notch were analysed to obtain low values of initial stress triaxiality (η = 0.556 of the range) in order to determine the critical void volume fraction fc. It is essential to emphasize how unique the method applied is and how different it is from the other more common methods involving parameter calibration, i.e. curve-fitting methods. The critical void volume fraction fc at void coalescence was established through digital image analysis of surfaces of S235JR steel, which involved studying real, physical results obtained directly from the material tested.

The characterization and interpretation of ductile fracture mechanisms in AL2024-T351 using X-ray and focused ion beam tomography

Particle number fluctuations are considered within the van der Waals (VDW) equation, which contains both attractive (mean-field) and repulsive (eigenvolume) interactions.The VDW equation is used to calculate the scaled variance of particle number fluctuations in generic Boltzmann VDW system and in nuclear matter.The strongly intensive measures ∆[E * , N ] and Σ[E * , N ] of the particle number and excitation energy fluctuations are also considered, and, similarly, show singular behavior near the critical point.The ∆[E * , N ] measure is shown to attain both positive and negative values in the vicinity of critical point.Based on universality argument, similar behavior is expected to occur in the vicinity of the QCD critical point.

Complex phase transition of DNA condensation under crowding confinement conditions

Journal of Cellular and Comparative PhysiologyVolume 49, Issue S1 p. 59-62 Article The forces between protein molecules in solution: A summary† John G. Kirkwood, John G. Kirkwood Sterling Chemistry Laboratory, Yale University, New Haven, ConnecticutSearch for more papers by this author John G. Kirkwood, John G. Kirkwood Sterling Chemistry Laboratory, Yale University, New Haven, ConnecticutSearch for more papers by this author First published: May 1957 https://doi.org/10.1002/jcp.1030490406Citations: 7 † Summary of lecture given also at a Symposium on “Molecular Structure and Biological Specificity,” Washington, D. C., October 1955; sponsored by the American Institute of Biological Sciences and supported by the Office of Naval Research. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume49, IssueS1May 1957Pages 59-62 RelatedInformation

Two-phase vapor-liquid equilibrium (VLE) isochores for binary mixtures are defined as the thermodynamic paths along which the overall density and composition are fixed. Data along such isochores are generated from a modified Leung-Griffiths model fit to experimental data for the binary system nitrogen-methane. The behavior of the liquid volume fraction along these isochores is found to be similar to that for pure fluids. Rectilinear diameters for varying overall densities (fixed composition) are seen to be nearly coincident. Straight-line diameters and the critical liquid volume fraction method are utilized to predict critical densities using data near and removed from the critical point. Both methods give acceptable results but the critical liquid volume fraction method is more accurate. A critical literature review of the need for binary mixture critical densities is presented and a proposed experimental procedure is given for the determination of mixture critical densities.

The behavior of ductile crack initiation from a notch and a crack under mode I loading has been investigated on a structural steel, SM 41 A. Experiments and large deformation finite element analyses based on Gurson's yield function were carried out for three-point-bending specimens with a notch or a crack. In the notched specimens, void growth behavior around the notch tip is described by the void volume fraction obtained by the finite element analysis, and the ductile crack initiation can be predicted based on the concept of critical void volume fraction. In the finite element analysis of the cracked specimen, a large strain field - process zone- around the crack tip is characterized by the void volume fraction. From the comparison of experimental results with analytical results, it is suggested that, in order to predict the ductile crack initiation from a crack based on the concept of critical void volume fraction, the correlation between the size of large strain field and the spatial distribution of inclusions should be taken into consideration.

Examination of different lattice structures in porous electrodes using a three-dimensional conductivity model

A generic experimental procedure is presented in this work to enhance the electrical responses of polydimethylsiloxane (PDMS) through incorporation of conducting polymer nanowires, while maintaining the desirable mechanical flexibility of PDMS. The conducting polypyrrole (PPy) nanowires are synthesized using a template method. The dielectric constants of the composites are characterized by impedance measurements, and the effect of nanowire concentration is investigated by the percolation theory. Using a continuous hyperbolic tangent function, critical volume fraction is estimated to be 9.6 vol%, at which an 85-fold enhancement in the dielectric constants is achieved. The viscoelastic properties of the composites are characterized by the stress relaxation nanoindentation tests, and the effect of nanowire concentration on the elastic modulus of composites is found to deviate significantly from the Wang–Pyrz model at the critical volume fraction. The tunable multifunctionality of PDMS composites that possess significantly enhanced electrical and moderate viscoelastic responses is desirable for many sensing and actuation applications.

Cellulosic derivatives form an interesting range of polymer liquid crystals. They belong to a class of mesophases in which the polymer chain is stiff or semiflexible and is chemically homogeneous. The cellulose backbone, a single-stranded homopolymer of β-linked 1,4-anhydroglucose units, contains three hydroxy groups per anhydroglucose unit which provide convenient sites for substitution reactions, leading to a wide variety of cellulose ethers and esters. Many of these derivatives form cholesteric liquid-crystalline phases in suitable solvents, and some derivatives with relatively large (but non-mesogenic) side chains form both lytropic and thermotropic liquid crystals.Published observations on the phase separation of cellulose-based polymers indicate that the mesophases form at critical volume fractions of polymer ranging from 0.3 to 0.5 for high molar mass samples at room temperature. The critical volume fractions for a given polymer and solvent decrease with increasing molar mass to approach these asymptotic values. The critical volume fraction increases with temperature. The nature of the solvent is also important; highly polar or acidic solvents generally favour mesophase separation at lower critical concentrations than simple organic solvents. Furthermore, whereas heavily substituted derivatives with long flexible side-chains form mesophases easily in a wide range of solvents, the more familiar derivatives with smaller substituents seem to form mesophases with specific solvents, but not with others.We have measured the critical concentrations of fractions of (acetoxypropyl)cellulose in dialkyl phthalate solvents over a large temperature range and compared the results with predictions of theories for the phase separation of freely jointed and worm-like chains. The results indicate that chain geometry and stiffness are the major factors controlling liquid-crystalline phase formation and that anisotropic inter-chain interactions play a minor role. Thus the chemical structure of polymer and solvent govern the phase separation indirectly in these systems, primarily through effects on the chain conformation.

Measurements of the storage modulus of suspensions of marble particles in a surfactant-based lyotropic liquid-crystalline medium (lamellar, smectic B) are reported. The suspension is a model system for several food and consumer products. The storage modulus is found to remain nearly constant with an increase in the particle volume fraction until a critical value is reached, beyond which a sharp increase in the storage modulus is obtained. The critical volume fraction is found to increase with an increase in particle size. The storage modulus of the suspensions exhibits a power law dependence on the oscillation frequency, and the power law exponent decreases sharply near the critical volume fraction. The experimental data indicate a transition from a multidomain lamellar liquid-crystalline structure to a structure with a rigid sample spanning network. A network model for the suspension is proposed in which a large number of parallel lamellae bridge randomly placed particles with surfaces closer than a specified distance, the maximum layer size (sm). The network formation is essentially a continuum percolation problem, for which the dimensionless critical number density is found by numerical simulations to be alpha(c) = rho(c)(1/3)L(m) approximate to 0.87 where L-m is the maximum distance between the centers of bonded particles and rho(c) is the critical number density. The modulus (G(c)) of the percolation network is obtained computationally as the stress required for a small tensile deformation of the network. The computed modulus is found to be of the form G(c) proportional to rho(2/3)(alpha - alpha(c))(2.5), which is in good agreement with experimental data.

In the classical ideal gas there are no interparticular forces. The Dutch scientist Johannes Diderik van der Waals derived a correction leading to the van der Waals equation. The interparticular forces in the van der Waals equation can not be explained by covalent bonds (characterized by the sharing of electron pairs) of the particles (atoms and molecules) in the gas. Those forces can only be explained via weak interactions and can be attractive or repulsive. The weak interactions between atoms and molecules have later been named after Johannes Diderik van der Waals. Weak interactions are not restricted to intermolecular interactions but can also occur intramolecular. In both cases the weak interactions can be responsible for the shape of molecules, supersystems and clusters. A famous example for this is the protein folding in RiboNucleic Acid (RNA) and DeoxyriboNucleic Acid (DNA). The effect of medical compounds often is founded on weak interactions with something in the human body. Unfortunately, the calculation of weak interactions is a challenging task. Very accurate ab initio quantum mechanical methods and a good description of the molecular orbitals are needed. Both requirements lead to high computational demands (calculation time and storage usage for main memory and hard disc). In ab initio quantum chemistry one normally only calculates the (total) energy E of a system. This is done with an accuracy of approximately 99% (when compared to the exact result) if the Hartree-Fock method (HF) is used. For many cases this accuracy is not sufficient to achieve the chemical accuracy of 1 kcal/mol. In contrast to thermochemistry where (reaction) enthalpies are typically calculated from standard enthalpies of formation (which are of the same order of magnitude as the reaction enthalpies and a certain accuracy of the formation enthalpies leads to a result of similar quality of the relative energies) in ab initio quantum chemistry calculations, the calculated total energies are larger by orders of magnitude than the energy of the desired property. For weak interactions the ratio of calculated values and the desired property is even larger and dynamic electron correlation, which is not covered at all by HF, plays a larger role or is sometimes responsible for the complete interaction energy. In particular the dispersion energy is a pure electron correlation effect. Methods that give a correction to HF to include dynamic electron correlation in the calculated energy need larger basis sets for the description of the molecular orbitals than HF itself. In the example of the interaction energy of the benzene dimer, the total electronic energy of the dimer is approximately 300000 kcal/mol, whereas the interaction energy is approximately 3 kcal/mol. This ratio of 105 illustrates why an accuracy of more than 99% and hence methods that cover dynamic electron correlation are necessary. The Coupled Cluster method with single and double excitations and triple excitations at perturbation theory level (CCSD(T)) (see Section 3.10) is considered to be highly accurate for most weak interactions. The convergence of the total energy with the basis set size can be greatly improved by the introduction of explicit correlation. Unfortunately CCSD(T) is rather expensive and systems with more than 30 atoms are very hard to calculate. Many systems of interest with weak interactions are larger, and therefore CCSD(T) is not feasible for their calculation. The MP2 method is much cheaper[c] than the CCSD(T) method, but unfortunately not as accurate. Earlier attempts to improve MP2 like SCS-MP2 have been successful to some extent but were never totally satisfying. Other attempts such as MP2.5 are more expensive and therefore also restricted to smaller systems. The goal of this work was to test the effects of explicit correlation in the CCSD(T) method and to develop a new method for the calculation of weak interactions that is able to improve on MP2 and SCS-MP2 towards CCSD(T). A new method - Dispersion-Weighted-MP2[d] (DW-MP2) has been developed in this work. It combines MP2 and SCS-MP2 and will be shown to achieve the accuracy needed for chemical accuracy.

The exact measurements of the isotherms of gases have proved extremely valuable in the determination of interatomic forces. For this purpose it has been found necessary to express the pv values of a gas as a finite power series in the density or in the pressure, and the coefficients so obtained have been compared with theoretical expressions in terms of interatomic fields. Many accounts of the method have been given and it is not necessary to give further details here (cf. Lennard-Jones 1931). While these methods are valid for gases at low densities where binary encounters are predominant, they fail for gases at high densities such as obtain in the neighbourhood of the critical point. Michels and his collaborators (Michels and others 1937) have recently studied the isotherms of gases at pressures as high as 3000 atm., and they find that the usual method of representing isotherms as simple functions of density or pressure ceases to be useful. The equation of state of van der Waals was astonishingly successful in accounting for the critical phenomena of gases and the form of the isotherms for temperatures below the critical temperature. Other empirical equations of state, for example that of Dieterici, were even more successful in reproducing the observed relations between the critical pressure, volume and temperature, and their very success has often obscured the fact that they were not logical theories of critical phenomena in gases, based as they were on arguments which were valid only for gases of low concentration. Thus the van der Waals equation, valuable as it has been and useful as it still is, implies that the internal energy of a vapour and its liquid phase is proportional only to the first power of the density, and this cannot be true for gases or vapours at densities comparable with those of liquids. The problem still remains of explaining why gases exhibit critical properties and of correlating the observed values of the critical temperature with the forces which atoms or molecules exert on each other.

Statistical complexity, virial expansion, and van der Waals equation