Molecular weight dependence of phase Behavior of PEO/P(EO-b-DMS) blends: Application of Sanchez-Lacombe lattice fluid theory

Molecular weight dependence of phase separation behavior of the Poly (ethylene oxide) (PEO)/Poly(ethylene oxide-block-dimethylsiloxane) (P(EO-b-DMS)) blends was investigated by both experimental and theoretical methods. The cloud point curves of PEO/P(EO-b-DMS) blends were obtained by turbidity method. Based on Sanchez-Lacombe lattice fluid theory (SLLFT), the adjustable parameter, epsilon*(12)/k (quantifying the interaction energy between different components), was evaluated by fitting the experimental data in phase diagrams. To calculate the spinodals, binodals, and the volume changes of mixing for these blends, three modified combining rules of the scaling parameters for the block copolymer were introduced.

Simulations of Mechanical Behavior of Polycrystalline Copper with Nano-Twins

Mechanical behavior and microstructure evolution of polycrystalline copper with nano-twins were investigated in the present work by finite element simulations. The fracture of grain boundaries are described by a cohesive interface constitutive model based on the strain gradient plasticity theory. A systematic study of the strength and ductility for different grain sizes and twin lamellae distributions is performed. The results show that the material strength and ductility strongly depend on the grain size and the distribution of twin lamellae microstructures in the polycrystalline copper.

Theory Of Phase Transformation And Reorientation In Single Crystalline Shape Memory Alloys

A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

The study of the behavior of exciton and photon within semiconductor microcavity under hydrostatic pressure

We studied, for the first time, the strong coupling between exciton and cavity mode within semiconductor microcavity under hydrostatic pressure, and measured the Rabi splitting. The strong coupling between exciton and cavity mode, and so Rabi splitting appear clearly as the applied pressure reaches 0.37-0.41 GPa. The experiment result shows that hydrostatic pressure not only can tune the coupling between exciton and cavity mode effectively, but also can keep exciton property almost unchanged during the whole tuning procedure in contrast to other tuning method (temperature field et al). Our result agrees with the related theory very well. The Rabi splitting, extracted from fitting the measured mode-energy vs pressure curves with correspanding theoretical model, is equal to 6 meV.

Pressure effects on thermodynamics of phase behavior in polystyrene/methylcyclohexane solutions

The calculations presented in this paper are based on the Sanchez-Lacombe (SL) lattice fluid theory. The interaction energy parameter, g*(12)/k, required in this approach was obtained by fitting the cloud points of polystyrene (PS) /methyleyclohexane (MCH) polymer solutions under pressure. The SL lattice fluid theory was used to calculate the spinodals, the binodals, and the Flory-Huggins (FH) interaction parameter of the solutions. The calculated results show that the SL lattice fluid theory can describe the dependences of thermodynamics of PS/MCH solutions on temperature and pressure very well. However, the calculated enthalpy and the excess volume changes indicate that the Clausius-Clapeyron equation cannot be suitable to describe pressure effect on PS/MCH solutions. Further analysis on the thermodynamics of this system under pressure shows that the role of entropy is more important than the excess volume in the present case.

Thermodynamics of phase behavior in PEO/P(EO-b-DMS) homopolymer and block co-oligomer mixtures under pressure

The cloud-point temperatures (T-cl's) of poly(ethylene oxide) (PEO) and poly(ethylene oxide)-block-polydimethylsiloxane (P(EO-b-DMS)) homopolymer and block-oligomer mixtures were determined by turbidity measurements over a range of temperatures (105 to 130degrees), pressures (1 to 800 bar), and compositions (10-40 wt.-% PEO). The system phase separates upon cooling and T-cl was found to decrease with an increase in pressure for a constant composition. In the absence of special effects, this finding indicates negative excess volumes. Special attention was paid to the demixing temperatures as a function of the pressure for the different polymer mixtures and the plots in the T-phi plane (where phi signifies volume fractions). The cloud-point curves of the polymer mixture under pressures were observed for different compositions. The Sanchez-Lacombe (SL) lattice fluid theory was used to calculate the spinodals, the binodals, the Flory-Huggins (FH) interaction parameter, the enthalphy of mixing, and the volume changes of mixing. The calculated results show that modified P(EO-b-DMS) scaling parameters with the new combining rules can describe the thermodynamics of the PEO/P(EO-b-DMS) system well with the SL theory.

Monte Carlo simulation of phase behavior of polymer blends with special interactions

Full Paper: The phase, behavior of A-B-random copolymer/C-homopolymer, blends with special interaction was studied by a. Monte, Carlo simulation in two dimensions. The interaction between I segment A and segment C was repulsive, whereas it was attractive between segment B and segment C. The simulation results showed that the blend became two large co-continuous phase domains at lower segment-B component compositions, indicating that the blend showed spinodal decomposition. With an increase of the segment-B component, the miscibility between the copolymer,and the polymer was gradually improved up to being miscible. In addition, it was found that segment B tended to move to the surface of the copolymer phase in the case of a lower component of segment B. On the other hand, if was observed that the average, end-to-end distances ((h) over bar) for both copolymer and polymer changed slowly with increasing segment-B component of the copolymer up to 40%, thereafter they increased considerably with increasing segment B component. Moreover, it was found that the (h) over bar of the copolymer was obviously shorter than that of the homopolymer for the segment-B composition, region from 0% to 80%. Finally, a, phase diagram showing I phase and - II phase regions under the condition of constant-temperature is presented.

Dislocation theory of the fracture criterion for anisotropic solids

A dislocation theory of fracture criterion for the mixed dislocation emission and cleavage process in an anisotropic solid is developed in this paper. The complicated cases involving mixed-mode loading are considered here. The explicit formula for dislocations interaction with a semi-infinite crack is obtained. The governing equation for the critical condition of crack cleavage in an anisotropic solid after a number dislocation emissions is established. The effects of elastic anisotropy, crack geometry and load phase angle on the critical energy release rate and the total number of the emitted dislocations at the onset of cleavage are analysed in detail. The analyses revealed that the critical energy release rates can increase to one or two magnitudes larger than the surface energy because of the dislocation emission. It is also found elastic anisotropy and crystal orientation have significant effects on the critical energy release rates. The anisotropic values can be several times the isotropic value in one crack orientation. The values may be as much as 40% less than the isotropic value in another crack orientation and another anisotropy parameter. Then the theory is applied to a fee single crystal. An edge dislocation can emit from the crack tip along the most highly shear stressed slip plane. Crack cleavage can occur along the most highly stressed slip plane after a number of dislocation emissions. Calculation is carried out step by step. Each step we should judge by which slip system is the most highly shear stressed slip system and which slip system has the largest energy release rate. The calculation clearly shows that the crack orientation and the load phase angle have significant effects on the crystal brittle-ductile behaviours.

The Flow Theory of Mechanism-Based Strain Gradient Plasticity

The flow theory of mechanism-based strain gradient (MSG) plasticity is established in this paper following the same multiscale, hierarchical framework for the deformation theory of MSG plasticity in order to connect with the Taylor model in dislocation mechanics. We have used the flow theory of MSG plasticity to study micro-indentation hardness experiments. The difference between deformation and flow theories is vanishingly small, and both agree well with experimental hardness data. We have also used the flow theory of MSG plasticity to investigate stress fields around a stationary mode-I crack tip as well as around a steady state, quasi-statically growing crack tip. At a distance to crack tip much larger than dislocation spacings such that continuum plasticity still applies, the stress level around a stationary crack tip in MSG plasticity is significantly higher than that in classical plasticity. The same conclusion is also established for a steady state, quasi-statically growing crack tip, though only the flow theory can be used because of unloading during crack propagation. This significant stress increase due to strain gradient effect provides a means to explain the experimentally observed cleavage fracture in ductile materials [J. Mater. Res. 9 (1994) 1734, Scripta Metall. Mater. 31 (1994) 1037; Interface Sci. 3(1996) 169].

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

Approximate theory of natural-convection with small grashof number

To gain some insight into the behaviour of low-gravity flows in the material processing in space, an approximate theory has been developed for the convective motion of fluids with a small Grashof number Gr. The expansion of the variables into a series of Gr reduces the Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.

Theory of local mode excitation in polyatomics by frequency-modulated lasers

that the Stokes-interaction relation is reasonable qualitatively but not correct

Statistical-theory of multiphoton excitation of polyatomic-molecules based on the wigner function

This paper is aimed at establishing a statistical theory of rotational and vibrational excitation of polyatomic molecules by an intense IR laser. Starting from the Wigner function of quantum statistical mechanics, we treat the rotational motion in the classical approximation; the vibrational modes are classified into active ones which are coupled directly with the laser and the background modes which are not coupled with the laser. The reduced Wigner function, i.e., the Wigner function integrated over all background coordinates should satisfy an integro-differential equation. We introduce the idea of ``viscous damping'' to handle the interaction between the active modes and the background. The damping coefficient can be calculated with the aid of the well-known Schwartz–Slawsky–Herzfeld theory. The resulting equation is solved by the method of moment equations. There is only one adjustable parameter in our scheme; it is introduced due to the lack of precise knowledge about the molecular potential. The theory developed in this paper explains satisfactorily the recent absorption experiments of SF6 irradiated by a short pulse CO2 laser, which are in sharp contradiction with the prevailing quasi-continuum theory. We also refined the density of energy levels which is responsible for the muliphoton excitation of polyatomic molecules.

A closure theory of intermittency of turbulence

The variational approach to the closure problem of turbulence theory, proposed in an earlier article [Phys. Fluids 26, 2098 (1983); 27, 2229 (1984)], is extended to evaluate the flatness factor, which indicates the degree of intermittency of turbulence. Since the flatness factor is related to the fourth moment of a turbulent velocity field, the corresponding higher-order terms in the perturbation solution of the Liouville equation have to be considered. Most closure methods discard these higher-order terms and fail to explain the intermittency phenomenon. The computed flatness factor of the idealized model of infinite isotropic turbulence ranges from 9 to 15 and has the same order of magnitude as the experimental data of real turbulent flows. The intermittency phenomenon does not necessarily negate the Kolmogorov k−5/3 inertial range spectrum. The Kolmogorov k−5/3 law and the high degree of intermittency can coexist as two consistent consequences of the closure theory of turbulence. The Kolmogorov 1941 theory [J. Fluid Mech. 62, 305 (1974)] cannot be disqualified merely because the energy dissipation rate fluctuates.

Some comments on the stability theory of mhd shock waves

The stability (evolutionarity) problem for a kind of MHD shock waves is discussed in this paper. That is to solve the interaction problem of MHD shock waves with (2-dimensional) oblique incident disturbances. In other words, the result of gasdynamic shocks is generalized to the case of MHD shocks. The previous conclusion of stability theory of MHD shock waves obtained from the solution of interaction problem of MHD shock wave with (one-dimensional) normal shock wave is that only fast and slow shocks are stable, and intermediate shocks are unstable. However, the results of this paper show that when the small disturbances are the Alfven waves a new stability condition which is related to the parameters in front of and behind the shock wave is derived. When the disturbances are entropy wave and fast and slow magneto acoustic waves the stability condition is related to the frequency of small disturbances. As the limiting ease, i. e. when a normal incident (reflection, refraction) is consid...更多ered, the fast and slow shocks are unstable. The results also show that the conclusion drawn by Kontorovich is invalid for the stability theory of shock waves.