三嵌段共聚物SEBS中自由体积行为的温度及e+辐照时间依赖性的研究

利用正电子湮没寿命谱实验手段研究了²²Na放射源的e⁺自辐射对三 嵌段共聚物SEBS的正电子湮没参数的影响，而后结合Eldrup的经典模型，研究了SEBS的自由体积孔尺寸和自由体积分数随着温度的变化关系，给出了自由体积分数在T_g以上和在Tg以下各自区域内分别与温度呈线性关系，最后结合Williams-Landel-Ferry(WLF)自由体积理论和Eldrup的经典模型讨论了热膨胀系数和自由体积分数中的A常数. 关键词： 正电子湮没技术 嵌段共聚物 自辐射 热膨胀     

Time-temperature superposition and relaxational behavior in polymeric glasses

It is shown that a free-volume treatment of the relaxational behavior of a polymer can be extended into the glassy region. A modified form of the WLF equation is derived in which the temperature is replaced by T_e, a parameter related to the “frozen” free volume in the glass and defined such that Te = T at equilibrium. Measurements of the isothermal volume contraction of polystyrene and poly(methyl methacrylate) between ?20 and + 95°C are used to estimate the “frozen” free volume and to calculate the temperature dependence of log(a_T) below Tg. The calculated shift factors are compared to experimental values for the glassy state, and good agreement is obtained by selecting an arbitrary, but reasonable, equilibrium glass volume-temperature curve. The slope of this equilibrium glass curve is smaller than the experimental volume curve at some finite cooling rate. The data indicate that the glass is not an “iso-free volume” state and that the relaxation mechanisms in the glass are controlled primarily by the free volume, at least in the vicinity of Tg. A quantitative definition of the role of free volume in the glassy state requires evaluation of the quantities ? log a_T/?V)_T,P and (? log a_T/?T)_v,p; sufficient data of this type are not presently available.     

On the nature of the liquid-to-glass transition equation

Within the model of delocalized atoms, it is shown that the parameter δT_g, which enters the glasstransition equation qτ_g = δT_g and characterizes the temperature interval in which the structure of a liquid is frozen, is determined by the fluctuation volume fraction \({f_g} = {\left( {{{\Delta {V_e}} \mathord{\left/ {\vphantom {{\Delta {V_e}} V}} \right. \kern-\nulldelimiterspace} V}} \right)_{T = {T_g}}}\) frozen at the glass-transition temperature T_g and the temperature T_g itself. The parameter δT_g is estimated by data on f_g and T_g. The results obtained are in agreement with the values of δT_g calculated by the Williams–Landel–Ferry (WLF) equation, as well as with the product qτ_g—the left-hand side of the glass-transition equation (q is the cooling rate of the melt, and τ_g is the structural relaxation time at the glass-transition temperature). Glasses of the same class with f_g ≈ const exhibit a linear correlation between δT_g and T_g. It is established that the currently used methods of Bartenev and Nemilov for calculating δT_g yield overestimated values, which is associated with the assumption, made during deriving the calculation formulas, that the activation energy of the glass-transition process is constant. A generalized Bartenev equation is derived for the dependence of the glass-transition temperature on the cooling rate of the melt with regard to the temperature dependence of the activation energy of the glasstransition process. A modified version of the kinetic glass-transition criterion is proposed. A conception is developed that the fluctuation volume fraction f = ΔV_e/V can be interpreted as an internal structural parameter analogous to the parameter ξ in the Mandelstam–Leontovich theory, and a conjecture is put forward that the delocalization of an active atom—its critical displacement from the equilibrium position—can be considered as one of possible variants of excitation of a particle in the Vol’kenshtein–Ptitsyn theory. The experimental data used in the study refer to a constant cooling rate of q = 0.05 K/s (3 K/min).     

Application of a new structural theory to polymers. ii. transition states for amorphous polymers and copolymers

A recently developed nonequilibrium thermodynamic theory of continuum rheology is combined with a generalized definition of thermomechanical transitions, to produce a single equation for interrelating the basic variables (stress o, strain rate ε, pressure p, temperature T, and structure ?) at a transition. Specialization of ? to represent uncrosslinked polymers leads to incorporation of molecular weight M as a variable. New predictions are thus made for the glass transition [T_g(M), T_g(p), T_g(ε) and others] and compared successfully with data. Particularly remarkable are the results that 1/T_g is a piecewise linear function of In M, and T is piecewise linear with p. Comparable results and confirmation with data arise when applying the theory to the liquid-liquid transition, T _ll (M). For random copolymers, application of a single mixing rule to the transition equation leads to a prediction of T_g as a function of composition and the T_gi for the homopolymers (components i). This relationship reduces, in various cases, to several familiar equations in which the parameters were simply empirical, thus providing an interpretation of those parameters and defining restrictions applicable to each case. Finally, an alternative interpretation of ? in terms of free volume allows the theory to be extended to other systems, including those with small molecules.     

Geometric study of the connection between the Lagrangian and Hamiltonian constraints

The second order differential equation character of the solutions of the dynamical equation i(Γ)ω_L = dE_L for a singular Lagrangian L, as well as the conditions for the existence of such a solution, are studied. We also introduce a couple of maps R (L)_v : T _FL(v)(T¹Q) → T_v(TQ) and T(L)_v : T_FL(v)(T¹Q) → T_FL(v)(T¹Q), with v ϵ TQ, which are shown to be very useful for establishing the connection between the constraints arising in the Lagrangian and Hamiltonian formulations.     

Phase transitions in poly(ethylene oxide) and polystyrene at high pressure

Abstract

The temperature and enthalpy of melting for poly(ethy1ene oxide) have, for the first time, been studied as a fuction of pressure up to 1 GPa by means of differential scanning calorimetry. The initial increase of the temperature of melting with increasing pressure is 64 K/GPa, whereas the enthalpy decreases by 40% in the 1 GPa pressure range. Using Clausius-Clapeyrons equation the volume change on melting is estimated to be 1.5 cm³/mol. The glass transition temperature T_g for polystyrene has also been studied by the same technique for pressures up to 0.1 GPa. The measurements show that T_g increases with increasing pressure by 250 K/GPa.     

Concerning free volume quantities and the glass temperature

Free volume quantities proposed earlier by Boyer and Simha in connection with the glass transition are reformulated by taking into account the temperature dependence of the thermal expansivities α _l and α_g for the liquid and the glass, respectively. This necessitates an extrapolation of the liquid to temperatures below Tg which is performed by means of the reduced volume-temperature function established and given a theoretical foundation previously. For the glass, low temperature experimental data, encompassing all relaxations occuring below T_g, are required.

Two polymer series are examined in detail, namely, poly(methacrylates) and poly(vinyl) alkyl ethers, where α_g has been measured between at least 30°K and T_g. Results for poly(methylacrylate) and poly(styrene) are also given. The systematic decrease in the product (αl - αg) · T|_T=Tg with increasing length of the side chain noted previously is considerably reduced but not eliminated when the appropriately corrected expression is substituted instead. However, the free volume fraction related to the quantity αlT|_T=Tg remains more nearly invariant in the polymers analyzed.

An alternative treatment is discussed which considers an occupied volume expanding below T_g by a mechanism of thermal vibrations solely. Experimental and theoretical means of obtaining this quantity arc suggested.     

Rotational and Vibrational Temperature Measurements in a High‐Pressure Cylindrical Dielectric Barrier Discharge (C‐DBD)

The rotational (T_R) and vibrational (T_v) temperatures of N₂ molecules were measured in a high‐pressure cylindrical dielectric barrier discharge (C‐DBD) source in Ne with trace amounts (0.02 %) of N₂ and dry air excited by radio‐frequency (rf) power. Both T_R and T_v of the N₂ molecules in the C ³Π_u state were determined from an emission spectroscopic analysis the 2^nd positive system (C ³Π_u → B³Π_g). Gas temperatures were inferred from the measured rotational temperatures. As a function of pressure, the rotational temperature is essentially constant at about 360 K in the range from 200 Torr to 600 Torr (at 30W rf power) and increases slightly with increasing rf power at constant pressure. As one would expect, vibrational temperature measurements revealed significantly higher temperatures. The vibrational temperature decreases with pressure from 3030 K at 200 Torr to 2270 K at 600 Torr (at 30 W rf power). As a function of rf power, the vibrational temperature increases from 2520 K at 20 W to 2940 K at 60 W (at 400 Torr). Both T_R and T_v also show a dependence on the excitation frequency at the two frequencies that we studied, 400 kHz and 13.56 MHz. Adding trace amounts of air instead of N₂ to the Ne in the discharge resulted in higher T_R and T_v values and in a different pressure dependence of the rotational and vibrational temperatures. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Glass and β transitions of atactic polystyrenes monitored by volume dilatometry

Volume recovery in the temperature range of above T_g to below T _β has been studied for two atactic polystyrene specimens (M _w = 210,000 and 300,000 g/mol). Observations clearly disclose the collapse of free volume even at temperatures well below T_β. In an excess free volume sufficient environment, as the aging temperature is lowered through T_β, the retardation of the initial volume recovery becomes progressively longer, forming a variation in the nonlinearity of the isotherms. Indeed, it is this variation that leads to the observation of the β transition in the V-T plot. The β transition is time dependent, but molecular weight independent. On the other hand, in addition to well-known molecular weight and time dependence, the glass transition has another important feature: The difference in thermal expansion coefficients above and below T_g increases slightly with aging time. Thus, time cannot alter the existence of Tg. Consequently, this study favors thermodynamic theories for the formation of T_g.     

Electron-vibration effects in Cs2SiF6 : Mn4+

We report a study of the ⁴ A _2g →² T _1g absorption band of Mn⁴⁺ in Cs₂SiF₆. The band shows several lines or groups of lines associated with transitions from the ⁴ A _2g ground state to the spin-orbit components (² T _1g )Γ₈ and (² T _1g )Γ₆ coupled to the three odd-parity vibrations v ₆(t _2u ), v ₄(t _1u ) and v ₃(t _1u ). The absorptions associated with the (² T _1g )Γ₈ electronic state have structure whereas those associated with the (² T _1g )Γ₆ do not. It is shown that the structure is a consequence of splitting of the Γ₈ × v vibronic multiplets by electron-vibration interaction. The intensity of the ⁴ A _2g →(² T _1g )Γ _i + v_j vibronic transitions are expressed in terms of a small number of parameters; two parameters for v(t _1u ) modes and three for v(t _2u ) modes. Plausible but not good fits to the low temperature Zeeman data and vibronic splitting patterns are obtained. The excitation spectrum of the Cs₂SiF₆ : Mn⁴⁺ in the region of the ⁴ A _2g →² E_g and ⁴ A _2g →² T _1g is recorded using a c.w. dye laser. This reveals numerous weaker lines involving combinational modes and even-parity modes v₅ (t _2g ), v ₂(e_g ) and v ₁(a _1g ). Several interesting electron-vibrational effects are observed. These are illustrated and discussed qualitatively.     

On linear dynamical equations of state for isotropic media II: Some cases of special interest

In a previous paper we have investigated the relation (dynamical equation of state) among the hydrostatic pressure P, the volume v and the temperature T of an isotropic medium with an arbitrary number, say n, of scalar internal degress of freedom. It has been shown that linearization of the theory leads to a dynamical equation of state which has the form of a linear relation among P, v, T, the first n derivatives with respect to time of P and T and the first n+1 derivatives with respect to time of v. In this paper we give a more detailed investigation of the coefficients of P, v and T in the linear dynamical equation of state. Furthermore, we consider the case of media without volume viscosity. It is shown that for these media the derivative with respect to time of order n+1 of the volume does not occur in the dynamical equation of state. Finally, we pay special attention to media with one and with two scalar internal variables.     

Effects of thermal and mechanical history on the viscoelastic properties of rigid poly(vinyl Chloride)

The effects of processing variables on the solid state properties of rigid PVC were studied by evaluating dynamic mechanical and tensile properties for thin film specimens of two different resins. The dynamic measurements were performed over the temperature range ?1]60 to 85°C, encompassing both the low temperature β transition and above ambient a transition (T_g). Engineering tensile strengths and energies to fracture were obtained at ambient conditions for several rates of elongation. Test specimens were prepared by solvent casting and compression molding techniques and subsequently were subjected to various thermal-mechanical histories. The results obtained were similar for both types of specimens and are described below. The various thermal histories considered include: (1) quick quenching from 225°C (samples referred to as “untreated”); (2) very slow (equilibrium) cooling after annealing at T_g; (3) quick quenching from T_g. In addition, the effects of frozen stresses were examined by systematically varying the stresses imposed on samples during the cooling processes 2 and 3. Increasing the load level imposed on specimens during equilibrium cooling resulted in enhancements of the β transition loss dispersion and tensile yield strength. Changes in loading during process 3, however, had little effect on the cooled specimens. But process 3 does alter the relaxation spectrum below T_g so that additional molecular relaxation is induced between T_β and T_α as much as 45°C below the a transition. The anomalous tan δ dispersions thus produced are accompanied by diminished tensile yield strengths and greatly increased energies to fracture. The most extreme case was encountered for the “untreated” specimens which were rapidly quenched from 225°C. The loss tangent data indicate remarkable differences in the region between T_β and T_α. When comparing the dynamic mechanical data with the fracture energy results for the same samples we note that increases in the intensity of the T < T_g anomalous dispersion correlate with increasing energies to fracture. On the other hand, the β transition intensity does not directly correlate. One molecular model which is consistent with these observations assumes that elongation induces a dilation of the polymer. Since most polymers possess Poisson ratios less than 0.5, the dilation will create extra internal volume (including free volume) in the polymer network. The increase in internal volume as elongation proceeds has the net effect of shifting the conditions of testing toward higher temperatures on a molecular relaxation scale permitting a higher level of molecular mobility at ambient conditions. As a sample continues to elongate one of two consequences is encountered: the imposed deformation cannot be accommodated by the available molecular mobility and the specimen fractures; or the deformation results in dilation to the extent that the response properties are shifted into a region of the relaxation spectrum where molecular mobility is sufficient for the specimen to accommodate the imposed deformation and yielding occurs. Yielding is expected if the effective temperature shifts as far as T_g before the sample fractures. In a case where there are additional molecular relaxation possibilities prior to the a transition, such as those in the anomalous dispersion region between T_β and T_α, sufficient dilation for yielding will be encountered before the normal T_g is reached. The anomalous T < T_g relaxation process thus tends to promote increased elongation and higher energies to fracture in PVC.     

Yielding behavior of glassy polymers. III. Relative influences of free volume and kinetic energy

The free-volume model for interpreting the initial yielding behavior of glassy polymers is extended to include kinetic energy influences. Molecular mobility is assumed to be determined by the product of the probabilities of attaining sufficient local free volume to allow molecular rearrangement, and kinetic energy to overcome restraining forces. Yielding then is initiated at the point where the free-volume increase resulting from the dilational component of the applied stress is sufficient to bring the local molecular mobility to that characteristic of the unstressed polymer at T_g.

Expressions are derived for the temperature and strain-rate dependences of the initial yield strain (defined as the proportional limit on the tensile stress-strain curve) and compared with experimental data for poly(methyl methacrylate). The extended model is found to afford no substantial improvement over a simple free-volume model, indicating that relaxational processes in the glassy state-at least in the range T_g to (T_g - 100°C)-are governed principally by freevolume changes.     

金属玻璃Ni30Zr70的动态粘度和稳态粘度

本文测量了金属玻璃Ni₃₀Zr₇₀的动态粘度和稳态粘度,结果表明,由于结构弛豫的影响,动态粘度随升温速率的减小而线性增加,在玻璃转变温度T_g以下,动态粘度与温度的关系可以用Arrhenius方程进行描述,稳态粘度与温度的依赖关系满足Fulcher-Vogel方程。从4种不同升温速率的高温(结晶开始温度T_x)动态粘度值,给出金属玻璃Ni₃₀Zr₇₀的平衡粘度。在630—670K     

Effect of Alkyl Side Chain Length on Relaxation Behaviors in Poly(n-alkyl Acrylates) and Poly(n-alkyl Methacrylates)

Dynamic mechanical analysis (DMA) is used to investigate the effect of alkyl side chain length on the relaxation behavior of poly(n-alkyl acrylates) (PnAA) and poly(n-alkyl methacrylates) (PnAMA) above the glass transition temperature (T_g). Master curves and shift factors (log a_T) were obtained using the time–temperature superposition (TTS) principle. The log a_T curves of PnAA and PnAMA exhibit a dynamic crossover from one Vogel–Fulcher–Tammann–Hesse (VFTH) equation to another above T_g. The corresponding temperature was designated as the dynamic crossover temperature (T_c). It is found that T_c/T_g and the apparent activation energy (E_g) increases, e whereas the fragility index (m) decreases with increasing alkyl side chain length. Further analysis shows that m ∝ T_g, E_g∝ , and E_g∝ m² for both PnAA and PnAMA.     

Temperature range of the liquid–glass transition

It has been shown that the currently used method for calculating the temperature range of δT_g in the glass transition equation qτ_g = δT_g as the difference δT_g = (T₁₂–T₁₃) results in overestimated values, which is explained by the assumption of a constant activation energy of glass transition in deriving the calculation equation (T₁₂ and T₁₃ are the temperatures corresponding to the logarithmic viscosity values of logη = 12 and logη = 13). The methods for the evaluation of δT_g using the Williams–Landel–Ferry equation and the model of delocalized atoms are considered, the results of which are in satisfactory agreement with the product qτ_g (q is the cooling rate of the melt and τ_g is the structural relaxation time at the glass transition temperature). The calculation of τ_g for inorganic glasses and amorphous organic polymers is proposed.     

Theory of melting,vacancy model

A theory of melting based on vacancy model is formulated. The polymer solution theory is used for derivation of the melting equation for a two-species model of melting solid. Under simplifying assumptions the analysis leads to a simple correlation betweenT _m and 〈v〉, the average energy of interaction between the vibrating atoms. Pseudopotential method is used for calculating 〈v〉 for the alkali metals lithium, sodium, potassium and rubidium at temperatureT _m. The calculated values ofT _m〈v〉 are in accord with those expected from our model. Application to the high pressure melting curves of solids is also discussed.     

Dynamic light scattering in solid polymers

The viscosity of an amorphous polymeric solid above its glass transition [T _g (T,P)] increases as the temperature of the solid is decreased or the pressure is increased. Under changes in temperature or pressure, molecular subunits in the polymeric solid undergo configurational changes. Such changes or relaxations have a distribution of relaxation strengths and times. As the solid is cooled or as the hydrostatic pressure on the solid is increased, the relaxation strengths increase and the relaxation times increase. These changes in relaxation or dynamic properties are very dramatic as the empirical T _g is approached. Near T _g the polymeric solid is no longer in volume equilibrium; continued cooling or pressuring at a time rate faster than the average relaxation time will produce a polymeric glass. This glass is a nonequilibrium, amorphous solid. If the glass is held at a fixed temperature and pressure very close to, but below, T _g , the volume of the glass will be observed to relax to its equilibrium value. For temperatures and pressures well below T _g , equilibrium is a much more conjectural concept since the relaxation times become extremely long. It has been proposed^1,2 that there is a characteristic temperature T _g at which an amorphous polymer undergoes a second-order transition to an equilibrium glass with zero configurational entropy (i.e., a noncrystallizable solid).     

Dependence of Tg and T ll on tacticity of PMMA by differential scanning calorimetry

A differential scanning calorimeter (DSC) investigation (heating rate 10 K/min) is presented on the multiple transition (relaxation) spectra of PMMA: T_β < T_g; T_g, T_ll > T_g; and T_lρ > T_ll, as a function of tacticity. Specimens are characterized by fractional triad content: isotactic (it-), Xii; syndiotactic (st-), Xss; and atactic (at-), Xis. Values for the seven specimens are it-, 1.0;, at-, 0.495 to 0.750; st-, 0.958. Results on T_β were inconclusive. Our T_g results clarify some discrepancies in the prior literature.

Linear least squares regression analyses give: T_g (°C) = 56.6 + 76.6 Xss (our data) T_g (°C) = 49.1 + 87.3 Xss (our data plus selected literature data)

Extrapolated T_g 's for Xss = 1 are 133.2°C and 136.1°C, respectively, in contrast to Thompson's extrapolated value of 160°C. Similarly T_g(°C) = 99.5 + 71.6 (1?Xii) for our DSC data. The extrapolated T_ll for Xss = 1 is 171.1°C. The intensity of T_ll is high for st-and it-, with a broad minimum over the at-region. A second liquid state process, T_lρ > T_ll, occurs at 149°C for it-, but is above the measured range for at-and st-. T_ll (at-) from DSC compares favorably with reported literature values by a variety of techniques. T_ll and T_lρ at all tacticities agree well with those from a companion study by the thermally stimulated current (TSC) technique on the same group of specimens, as reported elsewhere. This includes the influence of tacticity on intensity. These cross-comparisons by a variety of methods indicate that neither T_ll nor T_lρ is an artifact of our DSC technique. The Frenkel segment-segment contact hypothesis is favored to explain the molecular origin of T_ll Sequences longer than triads may be needed for improved correlations of T_g and T_lρ with tacticity.     

Comparison of tumor histology to dynamic contrast enhanced magnetic resonance imaging-based physiological estimates

Purpose

The purpose of this study was to compare histologically determined cellularity and extracellular space to dynamic contrast-enhanced magnetic resonance imaging (DCE MRI)-based maps of a two-compartment model's parameters describing tumor contrast agent extravasation, specifically tumor extravascular extracellular space (EES) volume fraction (v_e), tumor plasma volume fraction (v_p) and volume-normalized contrast agent transfer rate between tumor plasma and interstitium (K_TRANS/V_T).

Materials and Methods

Obtained v_e, v_p and K_TRANS/V_T maps were estimated from gadolinium diethylenetriamine penta-acetic acid DCE T₁-weighted gradient-echo images at resolutions of 469, 938 and 2500 μm. These parameter maps were compared at each resolution to histologically determined tumor type, and the high-resolution 469-μm maps were compared with automated cell counting using Otsu's method and a color-thresholding method for estimated intracellular (V_{intracellular}) and extracellular (V_{extracellular}) space fractions.

Results

The top five K_TRANS/V_T values obtained from each tumor at 469 and 938 μm resolutions are significantly different from those obtained at 2500 μm (P<.0001) and from one another (P=.0014). Using these top five K_TRANS/V_T values and the corresponding tumor EES volume fractions v_e, we can statistically differentiate invasive ductal carcinomas from noninvasive papillary carcinomas for the 469- and 938-μm resolutions (P=.0017 and P=.0047, respectively), but not for the 2500-μm resolution (P=.9008). The color-thresholding method demonstrated that v_e measured by DCE MRI is statistically similar to histologically determined EES. The V_{extracellular} obtained from the color-thresholding method was statistically similar to the v_e measured with DCE MRI for the top 10 K_TRANS/V_T values (P>.05). DCE MRI-based K_TRANS/V_T estimates are not statistically correlated with histologically determined cellularity.

Conclusion

DCE MRI estimates of tumor physiology are a limited representation of tumor histological features. Extracellular spaces measured by both DCE MRI and microscopic analysis are statistically similar. Tumor typing by DCE MRI is spatial resolution dependent, as lower resolutions average out contributions to voxel-based estimates of K_TRANS/V_T. Thus, an appropriate resolution window is essential for DCE MRI tumor diagnosis. Within this resolution window, the top K_TRANS/V_T values with corresponding v_e are diagnostic for the tumor types analyzed in this study.