Regularity of strain distribution in short-fiber/whisker reinforced composites

Based on studies on the strain distribution in short-fiber/whisker reinforced metal matrix composites, a deformation characteristic parameter, lambda is defined as a ratio of root-mean-square strain of the reinforcers identically oriented to the macro-linear strain along the same direction. Quantitative relation between lambda and microstructure parameters of composites is obtained. By using lambda, the stiffness moduli of composites with arbitrary reinforcer orientation density function and under arbitrary loading condition are derived. The upper-bound and lower-bound of the present prediction are the same as those from the equal-strain theory and equal-stress theory, respectively. The present theory provides a physical explanation and theoretical base for the present commonly-used empirical formulae. Compared with the microscopic mechanical theories, the present theory is competent for stiffness modulus prediction of practical engineering composites in accuracy and simplicity.

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range. A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.

An Instrumented Indentation Method for Young's Modulus Measurement with Accuracy Estimation

The relationships between indentation responses and Young's modulus of an indented material were investigated by employing dimensional analysis and finite element method. Three representative tip bluntness geometries were introduced to describe the shape of a real Berkovich indenter. It was demonstrated that for each of these bluntness geometries, a set of approximate indentation relationships correlating the ratio of nominal hardness/reduced Young's modulus H (n) /E (r) and the ratio of elastic work/total work W (e)/W can be derived. Consequently, a method for Young's modulus measurement combined with its accuracy estimation was established on basis of these relationships. The effectiveness of this approach was verified by performing nanoindentation tests on S45C carbon steel and 6061 aluminum alloy and microindentation tests on aluminum single crystal, GCr15 bearing steel and fused silica.

Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q(B circle A(-1)) for the Hadamard product of A(-1) and B, and a lower bound on the minimum eigenvalue q(A star B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius rho(A circle B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B. (C) 2009 Elsevier Inc. All rights reserved.

Weak measurement of qubit oscillations with strong response detectors: Violation of the fundamental bound imposed on linear detectors

Qubit measurement by mesoscopic charge detectors has received great interest in the community of mesoscopic transport and solid-state quantum computation, and some controversial issues still remain unresolved. In this work, we revisit the continuous weak measurement of a solid-state qubit by single electron transistors (SETs) in nonlinear-response regime. For two SET models typically used in the literature, we find that the signal-to-noise ratio can violate the universal upper bound "4," which is imposed quantum mechanically on linear-response detectors. This different result can be understood by means of the cross correlation of the detector currents by viewing the two junctions of the single SET as two detectors. Possible limitation of the potential-scattering approach to this result is also discussed.

Stability shear stress and equilibrium cross-sectional geometry of sheltered tidal channels

This study relates tidal channel cross-sectional area (A) to peak spring discharge (Q) via a physical mechanism, namely the stability shear stress ( tau sub(S)) just necessary to maintain a zero gradient in net along-channel sediment transport. It is assumed that if bed shear stress ( tau ) is greater than tau sub(S), net erosion will occur, increasing A, and reducing tau similar to (Q/A) super(2) back toward tau sub(S). If tau < tau sub(S) there will be net deposition, reducing A and increasing tau toward tau sub(S). A survey of the literature allows estimates of Q and A at 242 sections in 26 separate sheltered tidal systems. Assuming a single value of tau sub(S) characterizes the entire length of a given tidal channel, it is predicted that along-channel geometry will follow the relation Ah sub(R) super(1) super(/) super(6) similar to Q. Along-channel regressions of the form Ah sub(R) super(1) super(/) super(6) similar to Q super( beta ) give a mean observed value for beta of 1.00 plus or minus 0.06, which is consistent with this concept. Results indicate that a lower bound on tau sub(S) (and an upper bound on A) for stable channels is provided by the critical shear stress ( tau sub(C)) just capable of initiating sediment motion. Observed tau sub(S) is found to vary among all systems as a function of spring tidal range (R sub(sp)) according to the relation tau sub(S) approximately 2.3 R sub(sp) super(0.79) tau sub(C). Observed deviations from uniform tau sub(S) along individual channels are associated with along-channel variation in the direction of maximum discharge (i.e., flood-versus ebb-dominance).

边坡工程的极限分析上限法

Theory of limit analysis include upper bound theorem and lower bound theorem. To deal with slope stability analysis by limit analysis is to approximate the real solution from upper limit and lower limit. The most used method of limit analysis is upper bound theorem, therefore it is often applied to slope engineering in many cases. Although upper bound approach of limit analysis can keep away from vague constitutive relation and complex stress analyses, it also can obtain rigorous result. Assuming the critical surface is circular slip surface, two kinematically admissible velocity fields for perpendicular slice method and radial slice method can be established according to the limit analysis of upper bound theorem. By means of virtual work rate equation and strength reduction method, the upper-bound solution of limit analysis for homogeneous soil slope can be obtained. A log-spiral rotational failure mechanism for homogeneous slope is discussed from two different conditions which represent the position of shear crack passing the toe and below the toe. In the dissertition, the author also establishes a rotational failure mechanics with combination of different logarithmic spiral arcs. Furthermore, the calculation formula of upper bound solution for inhomogeneous soil slope stability problem can be deduced based on the upper bound approach of rigid elements. Through calculating the external work rate caused by soil nail, anti-slide pile, geotechnological grid and retaining wall, the upper bound solution of safety factor of soil nail structure slope, slip resistance of anti-slide pile, critical height of reinforced soil slope and active earth pressure of retaining wall can be obtained by upper bound limit analysis method. Taking accumulated body slope as subject investigated, with study on the limit analysis method to calculate slope safety factor, the kinematically admissible velocity fields of perpendicular slice method for slope with broken slip surface is proposed. Through calculating not only the energy dissipation rate produced in the broken slip surfaces and the vertical velocity discontinuity, but also the work rate produced by self-weight and external load, the upper bound solution of slope with broken slip surface is deduced. As a case study, the slope stability of the Sanmashan landslide in the area of the Three Gorges reservoir is analyzed. Based on the theory of limit analysis, the upper bound solution for rock slope with planar failure surface is obtained. By means of virtual work-rate equation, energy dissipation caused by dislocation of thin-layer and terrane can be calculated; furthermore, the formulas of safety factor for upper bound approach of limit analysis can be deduced. In the end, a new computational model of stability analysis for anchored rock slope is presented after taking into consideration the supporting effect of rock-bolts, the action of seismic force and fissure water pressure. By using the model, not only the external woke-rate done by self-weight, seismic force, fissure water pressure and anchorage force but also the internal energy dissipation produced in the slip surface and structural planes can be totally calculated. According to the condition of virtual work rate equation in limit state, the formula of safety factor for upper bound limit analysis can be deduced.

基于精细结构描述及数值试验的断续节理岩体力学参数智能选取

Evaluating the mechanical properties of rock masses is the base of rock engineering design and construction. It has great influence on the safety and cost of rock project. The recognition is inevitable consequence of new engineering activities in rock, including high-rise building, super bridge, complex underground installations, hydraulic project and etc. During the constructions, lots of engineering accidents happened, which bring great damage to people. According to the investigation, many failures are due to choosing improper mechanical properties. ‘Can’t give the proper properties’ becomes one of big problems for theoretic analysis and numerical simulation. Selecting the properties reasonably and effectively is very significant for the planning, design and construction of rock engineering works. A multiple method based on site investigation, theoretic analysis, model test, numerical test and back analysis by artificial neural network is conducted to determine and optimize the mechanical properties for engineering design. The following outcomes are obtained: (1) Mapping of the rock mass structure Detailed geological investigation is the soul of the fine structure description. Based on statistical window，geological sketch and digital photography，a new method for rock mass fine structure in-situ mapping is developed. It has already been taken into practice and received good comments in Baihetan Hydropower Station. (2) Theoretic analysis of rock mass containing intermittent joints The shear strength mechanisms of joint and rock bridge are analyzed respectively. And the multiple modes of failure on different stress condition are summarized and supplied. Then, through introducing deformation compatibility equation in normal direction, the direct shear strength formulation and compression shear strength formulation for coplanar intermittent joints, as well as compression shear strength formulation for ladderlike intermittent joints are deducted respectively. In order to apply the deducted formulation conveniently in the real projects, a relationship between these formulations and Mohr-Coulomb hypothesis is built up. (3) Model test of rock mass containing intermittent joints Model tests are adopted to study the mechanical mechanism of joints to rock masses. The failure modes of rock mass containing intermittent joints are summarized from the model test. Six typical failure modes are found in the test, and brittle failures are the main failure mode. The evolvement processes of shear stress, shear displacement, normal stress and normal displacement are monitored by using rigid servo test machine. And the deformation and failure character during the loading process is analyzed. According to the model test, the failure modes quite depend on the joint distribution, connectivity and stress states. According to the contrastive analysis of complete stress strain curve, different failure developing stages are found in the intact rock, across jointed rock mass and intermittent jointed rock mass. There are four typical stages in the stress strain curve of intact rock, namely shear contraction stage, linear elastic stage, failure stage and residual strength stage. There are three typical stages in the across jointed rock mass, namely linear elastic stage, transition zone and sliding failure stage. Correspondingly, five typical stages are found in the intermittent jointed rock mass, namely linear elastic stage, sliding of joint, steady growth of post-crack, joint coalescence failure, and residual strength. According to strength analysis, the failure envelopes of intact rock and across jointed rock mass are the upper bound and lower bound separately. The strength of intermittent jointed rock mass can be evaluated by reducing the bandwidth of the failure envelope with geo-mechanics analysis. (4) Numerical test of rock mass Two sets of methods, i.e. the distinct element method (DEC) based on in-situ geology mapping and the realistic failure process analysis (RFPA) based on high-definition digital imaging, are developed and introduced. The operation process and analysis results are demonstrated detailedly from the research on parameters of rock mass based on numerical test in the Jinping First Stage Hydropower Station and Baihetan Hydropower Station. By comparison，the advantages and disadvantages are discussed. Then the applicable fields are figured out respectively. (5) Intelligent evaluation based on artificial neural network (ANN) The characters of both ANN and parameter evaluation of rock mass are discussed and summarized. According to the investigations, ANN has a bright application future in the field of parameter evaluation of rock mass. Intelligent evaluation of mechanical parameters in the Jinping First Stage Hydropower Station is taken as an example to demonstrate the analysis process. The problems in five aspects, i. e. sample selection, network design, initial value selection, learning rate and expected error, are discussed detailedly.

东喜马拉雅构造结新生代碰撞变形与岩石圈演化

The Eastern Himalayan Syntaxis (EHS) is one of the strongest deformation area along the Himalayan belt resulted from the collision between Indian plate and the Eurasian Plate since the 50～60Ma, and has sensitivity tracked and preserved the whole collisional processes. It should depend on the detail geological investigations to establish the deformational accommodate mode, and the uplift history, to elucidate the deep structure and the crust-mantle interaction of the Tibet Plateau of the EHS. The deep-seated (Main Mantle Thrusts) structures were exhumed in the EHS. The MMT juxtapose the Gangdese metamorphic basement and some relic of Gangdese mantle on the high Himalayan crystalline series. The Namjagbawa group which is 1200～1500Ma dated by U/Pb age of zircon and the Namla group which is 550Ma dated by U/Pb age of zircon is belong to High Himalayan crystalline series and Gangdese basement respectively. There is some ophiolitic relic along the MMT, such as metamorphic ocean mantle peridotite and metamorphic tholeiite of the upper part of ocean-crust. The metamorphic ocean mantle peridotites (spinel-orthopyroxene peridotite) show U type REE patterns. The ~(87)Sr/~(86)Sr ratios were, 0.709314～0.720788, and the ~(143)Nd/~(144)Nd ratios were 0.512073～0.512395, plotting in the forth quadrant on the ~(87)Sr/~(86)Sr-~(143)Nd/~(144)Nd isotope diagram. Some metamorphic basalt (garnet amphibolite) enclosures have been found in the HP garnet-kynite granulite. The garnet amphibolites can be divided two groups, the first group is deplete of LREE, and the second group is flat or rich LREE, and their ~(87)Sr/~(86)Sr, ~(143)Nd/~(144)Nd ratios were 0.70563～0.705381 and 0.512468～0.51263 respectively. Trace element and isotopic characteristics of the garnet amphibolites display that they formed in the E-MORB environment. Some phlogolite amphibole harzburgites, which exhibit extensive replacement by Phl, Amp, Tc and Dol etc, were exhumed along the MMT. The Phl-Amp harzburgites are rich in LREE and LILE, such as Rb, K etc, and depletes Eu (Eu~* = 0.36 ～ 0.68) and HFSE, such as Nb, Ta, Zr, Hf, P, Ti etc. The trace element indicate that the Phl-Amp harzburgites have island arc signature. Their ~(87)Sr/~(86)Sr are varied from 0.708912 to 0.879839, ~(143)Nd/~(144)Nd from 0.511993 to 0.512164, ε Nd from- 9.2 to - 12.6. Rb/Sr isochrone age of the phlogolite amphibole harzburgite shows the metasomatism took place at 41Ma, and the Amp ~(40)Ar/~(39)Ar cooling age indcate the Phl-Amp harzburgite raising at 16Ma. There is an intense crust shortening resulted from the thrust faults and folds in the Cayu block which is shortened more 120km than that of the Lasha block in 35～90Ma. With the NE corner of the India plate squash into the Gangdese arc, the sinistral Pai shear fault and the dextral Aniqiao shear fault on the both sides of the Great bent of Yalun Zangbu river come into active in 21～26Ma. On the other hand, the right-lateral Gongrigabu strike-slip faults come into activity at the same period, a lower age bound for the Gongrigabu strike-slip fault is estimated to be 23～24Ma from zircon of ion-probe U/Pb thermochronology. The Gongrigabu strike-slip faults connect with the Lhari strike-slip fault in the northwestern direction and with the Saganing strike-slip at the southeastern direction. Another important structure in the EHS is the Gangdese detachment fault system (GDS) which occurs between the sedimental cover and the metamorphic basement. The lower age of the GDS is to be 16Ma from the preliminary 40Ar/39Ar thermochronology of white mica. The GDS is thought to be related to the reverse of the subducted Indian crust and the fast uplift of the EHS. Structural and thermochronology investigation of the EHS suggest that the eastern Tibet and the western Yunnan rotated clockwise around the EHS in the period of 35～60Ma. Later, the large-scale strike-slip faults (RRD, Gaoligong and Saganing fault) prolongate into the EHS, and connect with the Guyu fault and Gongrigabu fault, which suggest that the Indianchia block escape along these faults. Two kind of magmatic rocks in the EHS have been investigated, one is the mantle-derived amphibole gabbro, dioposide diorite and amphibole diorite, another is crust origin biotit-garnet adamellite, biotit-garnet granodiorite and garnet-amphibole-biotite granite. The amphibole gabbro dioposite diorite and amphibole diorite are rich in LREE, and LILE, such as Ba, Rb, Th, K, Sr etc, depleted in HFSE, such as Nb, Ta, Zr, Hf, Ti etc. The ratio of ~(87)Sr/~(86)Sr are from 0.7044 to 0.7048, ~(143)Nd/~(144)Nd are from 0.5126 to 0.5127. The age of the mantle origin magamatic rocks, which result from the partial melt of the raising and decompression anthenosphere, is 8Ma by ~(40)Ar/~(39)Ar dating of amphibole from the diorite. The later crust origin biotite-garnet adamellite, biotite-garnet granodiorite and garnet-amphibole-biotite granite are characterized by aboudance in LREE, and strong depletion of Eu. The ratios of ~(87)Sr-~(86)Sr are from 0.795035 to 0.812028, ~(143)Nd/~(144)Nd from 0.51187 to 0.511901. The ~(40)Ar/~(39)Ar plateau age of the amphibole from the garnet-amphibole-biotite granite is 17.5±0.3Ma, and the isochrone age is 16.8±0.6Ma. Their geochemical characteristics show that the crust-derived magmatic rocks formed from partial melting of the lower curst in the post-collisional environment. A group of high-pressure kaynite-garnet granulites and enclave of high-pressure garnet-clinopyroxene grnulites and calc-silicate grnulites are outcroped along the MMT. The peak metamorphic condition of the high-pressure granulites yields T=800～960 ℃, P=1.4～1.8Gpa, corresponding the condition of 60km depth. The retrograde assemblages of the high-pressure grnulites occur at the condition of T=772.3～803.3 ℃, P=0.63～0.64Gpa. The age of the peak metamorphic assemblages are 45 ～ 69Ma indicated by the zircon U/Pb ion-plobe thermochronology, and the retrograde assemblage ages are 13～26Ma by U/Pb, ~(40)Ar/~(39)Ar thermochronology. The ITD paths of the high-pressure granulites show that they were generated during the tectonic thickening and more rapid tectonic exhumation caused by the subducting of the Indian plate and subsequent break-off of the subducted slab. A great deal of apatite, zircon and sphene fission-track ages, isotopic thermochronology of the rocks in the EHS show that its rapid raising processes of the EHS can be divided into three main periods. There are 35～60Ma, 13～25Ma, 0～3Ma. 3Ma is a turn in the course of raising in the EHS which is characterized by abruptly acceleration of uplifting. The uplift ratios are lower than 1mm .a~(-1) before 3Ma, and higher than 1mm .a~(-1) with a maximum ratio of 30mm .a~(-1) since 3Ma. The bottom (knick point) of the partial anneal belt is 3.8km above sea level in the EHS, and correspond to age of 3Ma determined by fission-track age of apatite. The average uplift ratio is about 1.4 mm .a~(-1) below the knick point. The EHS has raised 4.3km from the surface of 2.36km above sea level since 3Ma estimated by the fossil partial anneal belt of the EHS. We propose a two-stage subduction model (B+A model) basing on Structural, thermochronological, magmatical, metamorphic and geophysical investigations of the EHS. The first stage is the subduction of the Indian continental margin following after the subduction of the Tethys Ocean crust and subsequent collision with the Gangdese arc, and the second stage is the Indian crust injecting into the lower crust and upper mantle of the Tibet plateau. Slab break-off seems to be occurred between these two stages.

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

拟压缩性方法在非定常球形Couette-Taylor流模拟中的应用

本文以拟压缩性法和物理时间/伪时间双重时间推进,数值求解非定常不可压缩流N=S方程。拟压缩性项是对伪时间的导数项,在每一物理时间层,进行对伪时间的推进使拟压缩性项趋于零,从而使连续方程得到满足。用Lower-Upper Symmetric Gaus-—Seidel(LU-SGS)恪式求解离散所得的方程。针对前人LU-SGS格式未计及隐式物理粘性,在计算中低Re数流动时容易发散或造成收敛率低的问题,利用简化的隐式粘性项改善了格式的稳定性,并用三阶迎风紧致差分逼近无粘通量,提高了伪时间推进的收敛率。模拟了间隙比σ=0.18的两同心旋转球之间轴对称Couette-Taylor流的0-、1-和2-涡三种流态和它们之间的转变过程。

Numerical Analyses of Transonic Fluid/Structure interaction in Aircraft Engineering

Through the coupling between aerodynamic and structural governing equations, a fully implicit multiblock aeroelastic solver was developed for transonic fluid/stricture interaction. The Navier-Stokes fluid equations are solved based on LU-SGS (lower-upper symmetric Gauss-Seidel) Time-marching subiteration scheme and HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) spacing discretization scheme and the same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Transfinite interpolation (TFI) is used for the grid deformation of blocks neighboring the flexible surfaces. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between fluid and structure. The developed code was fort validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. In the subsonic and transonic range, the calculated flutter speeds and frequencies agree well with experimental data, however, in the supersonic range, the present calculation overpredicts the experimental flutter points similar to other computations. Then the flutter character of a complete aircraft configuration is analyzed through the calculation of the change of structural stiffness. Finally, the phenomenon of aileron buzz is simulated for the weakened model of a supersonic transport wing/body model at Mach numbers of 0.98 and l.05. The calculated unsteady flow shows, on the upper surface, the shock wave becomes stronger as the aileron deflects downward, and the flow behaves just contrary on the lower surface of the wing. Corresponding to general theoretical analysis, the flow instability referred to as aileron buzz is induced by a stronger shock alternately moving on the upper and lower surfaces of wing. For the rigid structural model, the flow is stable at all calculated Mach numbers as observed in experiment

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

Solid-state qubit measurement with single electron transistors

In this paper we consider the continuous weak measurement of a solid-state qubit by single electron transistors (SET). For single-dot SET, we find that in nonlinear response regime the signal-to-noise ratio can violate the universal upper bound imposed quantum mechanically on any linear response detectors. We understand the violation by means of the cross-correlation of the detector currents. For double-dot SET, we discuss its robustness against wider range of temperatures, quantum efficiency, and the relevant open issues unresolved.

Gas permeability and permselectivity of polyimides prepared from phenylenediamines with methyl substitution at the ortho position

Polyimides were prepared from diamines: 2,4,6-trimethyl-1,3-phenylenediamine (3MPDA) and 2,3,4,5-tetramethyl-1,4-phenylenediamine (4MPDA). 1,4-Bis(3,4-dicarboxyphenoxy)benzene dianhydride (HQDPA), 3,3',4,4'-benzophenone tetracarboxylic dianhydride (BTDA), 3,3'-4,4'-diphenylsulphone tetracarboxylic dianhydride (SO(2)PDA), 3,3',4,4'-diphenylsulphide tetracarboxylic dianhydride (SPDA), pyromellitic dianhydride (PMDA), and 2,2'-bis(3,4-dicarboxyphenyl)hexa-fluoroisopropane dianhydride (6FDA) were used as dianhydride. The gas permeabilities of H-2, O-2 and N-2 through the polyimides were measured at temperatures from 30 degrees C to 90 degrees C. The results show that as methyl and trifluoromethyl substitution groups densities increase from 7.73 x 10(-3) molcm(-3) to 13.50 x 10(-3)molcm(-3), the peameability of H-2 increases 10-fold at 60% loss of permselectivity of H-2/N-2 however, the permeability of O-2 increases 20-fold at 20% loss of permselectivity of O-2/N-2. For O-2/N-2 separation, PMDA-3MPDA has similar performance to 6FDA-3MPDA and 6FDA-4MPDA; all have higher permeabilities for O-2 than normal polyimides, and the P(O-2)/alpha(O-2/N-2) trade-off relationships lie on the upper bound line for polymers. (C) 1999 Society of Chemical Industry.