Self-diffusion Coefficient Model Based on Activation Energy and Free Volume

A new model for self-diffusion coefficients was proposed based oil both the concepts of molecular free volume and activation energy. The unknown parameters of this model were clearly defined and compared with the Chapman-Enskog model. At the same time a new method for calculating activation energy was devised and applied to the new model. In addition, the free volume was defined by implementing the generic van der Waals equation of state, the radial distribution function of which was obtained by using the Morsali- Goharshadi empirical formula. Under the same conditions, the new model was better than the original free volume model.

Comparison of the Free Volume of LiCl-Added SPPO Membrane and SPPO-PES Blend Membrane by Positron Annihilation Method

Positron annihilation lifetime spectroscopy （PALS） is a powerful technique for the study of free volume in polymers. The lifetime of ortho-positronium （o-Ps）, a bound state of an electron and a positron, can be used to assess the pore size, while the intensity can be used to characterize the number of pores. Based on the values of the long-lived o-Ps components in the lifetime spectra, the radii and fractional free volumes of sulfonated poly （2,6-dimethyl-1,4- phenyleneoxide） （SPPO） membranes with added LiCl and SPPO-PES （Polyethersulfone） blend were compared. Free volume radii in both kinds of membranes are discussed.

Investigation of the free volume and ionic conducting mechanism of poly(ethylene oxide)-LiClO_4 polymeric electrolyte by positron annihilating lifetime spectroscopy

The positron annihilation lifetime and ionic conductivity are each measured as a function of organophilic rectorite（OREC） content and temperature in a range from 160 K to 300 K.According to the variation of ortho-positronium（o-Ps） lifetime with temperature,the glassy transition temperature is determined.The continuous maximum entropy lifetime（MELT） analysis clearly shows that the OREC and temperature have important effects on o-Ps lifetime and free volume distribution.The experimental results show that the temperature dependence of ionic conductivity obeys the Vogel-Tammann-Fulcher（VTF） and Williams-Landel-Ferry（WLF） equations,implying a free-volume transport mechanism.A linear least-squares procedure is used to evaluate the apparent activation energy related to the ionic transport in the VTF equation and several important parameters in the WLF equation.It is worthwhile to notice that a direct linear relationship between the ionic conductivity and free volume fraction is established using the WLF equation based on the free volume theory for nanocomposite electrolyte,which indicates that the segmental chain migration and ionic migration and diffusion could be explained by the free volume theory.

Free Volume Properties of Interpenetrating Polymer Networks Probed by Positron Annihilation

Positron annihilation lifetime (PAL) spectroscopy was applied to investigate the free volume properties of two types of simultaneous interpenetrating polymer networks (SINs), stoichiometric SINs and non--stoichiometric SINs. PU/VER SINs are all composed of polyurethane(PU) and vinyl ester resin (VER)with different compositions. Mean free volume size in PU/VER deceased with the increase of VER weight percentage, and the relative intensity, relevant to free volume content, increased with VER contents. The effect of chemical bonds between PU networks and VER networks to free volume properties was observed. Results revealed that chemical bonds between the two networks led to molecular denser packing, free volume contraction and made stoichoimetric PU/VER SINs a miscible system.

A new model for electromigration grain boundary noise based on free volume

Grain boundary plays a key role in electromigration process of polycrystal interconnection. We take a free volume to represent a ＇vacancy-ion complex＇ as a function of grain boundary specific resistivity, and develop a new characterisation model for grain boundary noise. This model reveals the internal relation between the boundary scattering section and electromigration noise. Comparing the simulation result with our experimental result, we find the source as well as the form of noise change in the electromigration process. In order to describe the noise enhancement at grain boundary quantitatively, we propose a new parameter--grain boundary noise enhancement factor, which reflects that the grain boundary noise can characterise the electromigration damage sensitively.

Gas Permeability and Free Volume Hole Properties of Interpenetrating Polymer Network Studied by Positrons

A series of polyurethane/epoxy resin interpenetrating polymer networks （PU/ER IPN） were studied by positron annihilation lifetime spectroscopy （PALS）. The effects of epoxy resin type and content on the free volume properties in IPN were investigated. We found that in PU/ER IPN, the free volume hole size and fractional free volume showed a negative deviation due to closer segmental chain packing through some chemical bonding between PU and epoxy resin. Direct relationship between the gas permeability and the free volume has been established based on the free volume theory. Experimental results revealed that the free volume plays an important role in determining the gas diffusion and permeability.

BIOLOGICAL INVASION PROBLEM WITH FREE BOUNDARY NONLOCAL DIFFUSION EQUATION

In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.

How does the initial free volume distribution affect shear band formation in metallic glass?

Introducing heterogeneities into the structure is an effective way to enhance the plasticity in metallic glasses (MGs). As natural heterogeneity, the original randomly distributed free volume in MGs has been found to be in favor of plasticity. However, the exact correlation between the free volume distribution and mechanical response is still unclear. In this paper, we investigate the shear banding in MGs with different structural disorders, characterized by both the free volume concentration (FVC) and the free volume dispersion (FVD). It is found that, either high FVC or wide FVD leads to low activation stress of shear band; wide FVD promotes the multiplication of shear bands but high FVC restricts it. It reveals that the yield strength in MGs is dependent on the amount of free volume while the plasticity mainly relies on the distribution. An optimum combination of the two aspects probably helps to design a MG of both good plasticity and high strength.

Effect of Conductive Fillers on the Cyclic Stress-Strain and Nano-Scale Free Volume Properties of Silicone Rubber

The effect of carbon black （CB） and graphite （G） powders on the macroscopic and nano-scale free volume properties of silicone rubber based on poly（di-methylsiloxane） （PDMS） was studied through thermal and cyclic mechanical measurements, as well as with positron annihilation lifetime spectroscopy （PALS）. The melting temperature of the composites （Tm） and the endothermic enthalpy of melting （ΔHm） were estimated by differential scanning calorimetry （DSC）. Tm and the degree of crystallinity （χc） of PDMS composites were found to decrease with increasing the CB content. This can be explained due to the increase in physical cross-linking which results in a decrease in the crystallite thickness. Besides, χc was found to be dependent on the filler type. Cyclic stress-strain behavior of PDMS loaded with different contents of filler has been studied. Mullins ratio （RM） was found to be dependent on the filler type and content. It was found that, RM increases with increasing the filler content due to the increase in physical cross-linking which results in a decrease in the size of free volume, as observed through a decrease of the o-Ps lifetime τ3 measured by PALS. Moreover, the hysteresis in PDMS-CB composites was more pronounced than in PDMS-G composites. Furthermore, a correlation was established between the free volume Vf and the mechanical properties of PDMS composites containing different fillers. A negative correlation was observed between Vf and RM.

Integration of molecular dynamic simulation and free volume theory for modeling membrane VOC/gas separation

Gas membrane separation process is highly unpredictable due to interacting non-ideal factors, such as composition/pressure-dependent permeabilities and real gas behavior. Although molecular dynamic （MD） simulation can mimic those complex effects, it cannot precisely predict bulk properties due to scale limitations of calculation algorithm. This work proposes a method for modeling a membrane separation process for volatile organic compounds by combining the MD simulation with the free volume theory. This method can avoid the scale-up problems of the MD method and accurately simulate the performance of membranes. Small scale MD simulation and pure gas permeation data are employed to correlate pressure-irrelevant parameters for the free volume theory; by this approach, the microscopic effects can be directly linked to bulk properties （non-ideal permeability）, instead of being fitted by a statistical approach. A lab-scale hollow fiber membrane module was prepared for the model validation and evaluation. The comparison of model predictions with experimental results shows that the deviations of product purity are reduced from 10% to less than 1%, and the deviations of the permeate and residue flow rates are significantly reduced from 40% to 4%, indicating the reliability of the model. The proposed method provides an efficient tool for process engineering to simulate the membrane recovery process.

Prediction of the viscosity of natural gas at high temperature and high pressure using free-volume theory and entropy scaling

Eighteen models based on two equations of state(EoS),three viscosity models,and four mixing rules were constructed to predict the viscosities of natural gases at high temperature and high pressure(HTHP)conditions.For pure substances,the parameters of free volume(FV)and entropy scaling(ES)models were found to scale with molecular weight,which indicates that the ordered behavior of parameters of Peng-Robinson(PR)and Perturbed-Chain Statistical Associating Fluid Theory(PC-SAFT)propagates to the behavior of parameters of viscosity model.Predicting the viscosities of natural gases showed that the FV and ES models respectively combined with MIX4 and MIX2 mixing rules produced the best accuracy.Moreover,the FV models were more accurate for predicting the viscosities of natural gases than ES models at HTHP conditions,while the ES models were superior to PRFT models.The average absolute relative deviations of the best accurate three models,i.e.,PC-SAFT-FV-MIX4,tPR-FVMIX4,and PC-SAFT-ES-MIX2,were 5.66%,6.27%,and 6.50%,respectively,which was available for industrial production.Compared with the existing industrial models(corresponding states theory and LBC),the proposed three models were more accurate for modeling the viscosity of natural gas,including gas condensate.

Study of the Synergistic Effect Between Corrosion Inhibitors by Using Fractional Free Volume

The fractional free volumes(FFVs)of the adsorption films formed with different ratios of dipropargyl methoxythiourea imidazoline(DPFTAI)and pyridine quaternary ammonium salt(16BD)were calculated by simulation to determine their synergistic corrosion inhibition effect.The results suggest that the composite corrosion inhibitor at the molar ratio between DPFTAI and 16BD of 4:1 gives the best corrosion inhibition effect.This simulation method to predict the synergistic effect between corrosion inhibitors was further validated by mass loss and electrochemical experiments.This finding delivers valuable understandings of inhibition mechanism of corrosion inhibitors.

Understanding the Li diffusion mechanism and positive effect of current collector volume expansion in anode free batteries

In anode free batteries(AFBs), the current collector acts as anode simultaneously and has large volume expansion which is generally considered as a negative effect decreasing the structural stability of a battery. Moreover, despite many studies on the fast lithium diffusion in the current collector materials of AFB such as copper and aluminum, the involved Li diffusion mechanism in these materials remains poorly understood. Through first-principles calculation and stress-assisted diffusion equations, here we study the Li diffusion mechanism in several current collectors and related alloys and clarify the effect of volume expansion on Li diffusion respectively. It is suggested that due to the lower Li migration barriers in aluminum and tin, they should be more suitable to be used as AFB anodes, compared to copper, silver, and lead. The Li diffusion facilitation in copper with a certain number of vacancies is proposed to explain why the use of copper with a thickness≤100 nm as the protective coating on the anode improves the lifetime of the batteries. We show that the volume expansion has a positive effect on Li diffusion via mechanical–electrochemical coupling. Namely, the volume expansion caused by Li diffusion will further induce stress which in turn affects the diffusion. These findings not only provide in-depth insight into the operating principle of AFBs, but also open a new route toward design of improved anode through utilizing the positive effect of mechanical–electrochemical coupling.

Effects of transection of cervical sympathetic trunk on cerebral infarct volume and oxygen free radical levels in rats with focal cerebral ischemia/reperfusion injury

BACKGROUND： Stellate ganglion block （SGB） plays a protective role on the brain, but the precise mechanism of action is not clear. OBJECTIVE： To simulate SGB by transection of the cervical sympathetic trunk （TCST） and to investigate the TCST effects on changes in cerebral infarct volume and oxygen free radical levels in rats with focal cerebral ischemia/reperfusion injury. DESIGN, TIME AND SETTING： A complete randomized control animal experiment was performed at the Institute of Neurological Diseases of Taihe Hospital, Yunyang Medical College from February to December 2005. MATERIALS： A total of 101 healthy Wistar rats, weighing 280-320 g, of both genders, aged 17-18 weeks, were used in this study. 2, 3, 5-triphenyltetrazolium chloride （TTC） was purchased from Changsha Hongyuan Biological Company. Superoxide dismutase （SOD）, malondialdehyde （MDA） and nitric oxide （NO） assay kits were provided by Nanjing Jiancheng Bioengineering Institute. METHODS： Rats were randomly divided into a TCST group, a model group and a sham operation group. Successful models were included in the final analysis, with at least 20 rats in each group. After TCST, rat models of focal cerebral ischemia/reperfusion injury were established in the TCST group by receiving middle cerebral artery occlusion （MCAO） by the intraluminal suture method for 2 hours, followed by 24 hours of reperfusion. Rat models of focal cerebral ischemia/reperfusion injury were made in the model group. Rats in the sham operation group underwent experimental procedures as for the model group, threading depth of 10 mm, and middle cerebral artery was not ligated. MAIN OUTCOME MEASURES： Brain tissue sections of ten rats from each group were used to measure cerebral infarct volume by TTC staining. Brain tissue homogenate of another ten rats from each group was used to detect SOD activities, MDA contents and NO levels. Rat neurological function was assessed by neurobehavioral measures. RESULTS： Cerebral infarct volume was bigger in the model group than in the TCST group （P 〈 0.05）. Twenty four hours after cerebral ischemia/reperfusion, SOD activities were lower, whereas MDA contents and NO levels were higher in the TCST and model groups, compared with the sham operation group （P 〈 0.05 or P 〈 0.01）. Compared with the model group, SOD activities were higher, whereas MDA contents and NO levels were lower in the TCST group （P 〈 0.05）. CONCLUSION： After TCST, cerebral infarct volume is reduced, SOD activities are increased, and MDA contents and NO levels are decreased compared to the model group in rats with focal cerebral ischemia/reperfusion injury. These changes may be associated with TCST.

A Higher-Efficient Non-Hydrostatic Finite Volume Model for Strong Three-Dimensional Free Surface Flows and Sediment Transport

In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.

Thermodynamic Equilibrium of the Saturated Fluid with a Free Surface Area and the Internal Energy as a Function of the Phase-Specific Volumes and Vapor Pressure

This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimate of the ratio of the respective free energies of systems with and without A show that the system variables given by Gibbs suffice to describe the volumetric properties of the fluid. The well-known Gibbsian expressions for the internal energies of the two-phase fluid, namely for the vapor and for the condensate (liquid or solid), only differ with respect to the phase-specific volumes and . The saturation temperature T, vapor presssure p, and chemical potential are intensive parameters, each of which has the same value everywhere within the fluid, and hence are phase-independent quantities. If one succeeds in representing as a function of and , then the internal energies can also be described by expressions that only differ from one another with respect to their dependence on and . Here it is shown that can be uniquely expressed by the volume function . Therefore, the internal energies can be represented explicitly as functions of the vapor pressure and volumes of the saturated vapor and condensate and are absolutely determined. The hitherto existing problem of applied thermodynamics, calculating the internal energy from the measurable quantities T, p, , and , is thus solved. The same method applies to the calculation of the entropy, chemical potential, and heat capacity.

Constraints on Characteristics and Distribution of Gas Hydrate and Free Gas Using Broad-Band Processing of Three-Dimensional Seismic Data

Gas hydrate drilling expeditions in the Pearl River Mouth Basin,South China Sea,have identified concentrated gas hydrates with variable thickness.Moreover,free gas and the coexistence of gas hydrate and free gas have been confirmed by logging,coring,and production tests in the foraminifera-rich silty sediments with complex bottom-simulating reflectors(BSRs).The broad-band processing is conducted on conventional three-dimensional(3D)seismic data to improve the image and detection accuracy of gas hydratebearing layers and delineate the saturation and thickness of gas hydrate-and free gas-bearing sediments.Several geophysical attributes extracted along the base of the gas hydrate stability zone are used to demonstrate the variable distribution and the controlling factors for the differential enrichment of gas hydrate.The inverted gas hydrate saturation at the production zone is over 40% with a thickness of 90 m,showing the interbedded distribution with different boundaries between gas hydrate-and free gas-bearing layers.However,the gas hydrate saturation value at the adjacent canyon is 70%,with 30-m-thick patches and linear features.The lithological and fault controls on gas hydrate and free gas distributions are demonstrated by tracing each gas hydrate-bearing layer.Moreover,the BSR depths based on broad-band reprocessed 3D seismic data not only exhibit variations due to small-scale topographic changes caused by seafloor sedimentation and erosion but also show the upward shift of BSR and the blocky distribution of the coexistence of gas hydrate and free gas in the Pearl River Mouth Basin.

Friction effect on free volume in amorphous-crystal region of PTFE

POSITRON annihilation technique (PAT) is a sensitive probe to detect the size and concentrationof free volume holes. In recent years, it has been used to study the correlation between mi-crostructure and macroscopic properties of crystal polymers. Experimental results show thatthe polymers’ macroscopic properties, such as mechanical properties, thermal properties andstructural phase transition, can be reflected by the change of free volume. It

GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Free radicals trigger the closure of open pores in lignin-derived hard carbons toward improved sodium-storage capacity

The chemical activation of various precursors is effective for creating additional closed pores in hard carbons for sodium storage.However,the formation mechanism of closed pores under the influence of pore-forming agents is not well understood.Herein,an effective chemical activation followed by a high-temperature self-healing strategy is employed to generate interconnected closed pores in lignin-derived hard carbon(HCs).By systematic experimental design combined with electron paramagnetic res-onance spectroscopy,it can be found that the content of free radicals in the carbon matrix influences the closure of open pores at high temperatures.Excessively high activation temperature(>700 C)leads to a low free radical concentration,making it difficult to achieve self-healing of open pores at high tempera-tures.By activation at 700°C,a balance between pore making and self-healing is achieved in the final hard carbon.A large number of free radicals triggers rapid growth and aggregation of carbon microcrys-tals,blocking pre-formed open micropores and creating additional interconnected closed pores in as-obtained hard carbons.As a result,the optimized carbon anode(LK-700-1300)delivers a high reversible capacity of 330.8 mA h g^(-1) at 0.03 A g^(-1),which is an increase of 86 mA h g^(-1) compared to the pristine lignin-derived carbon anode(L-700-1300),and exhibits a good rate performance(202.1 mA h g^(-1) at 1 A g^(-1)).This work provides a universal and effective guidance for tuning closed pores of hard carbons from otherprecursors.