Temperature dependence of liquid viscosity

Least squares programs were used to evaluate the correlation between recent experimental results and theoretical, semi-theoretical, or empirical relations between liquid viscosity and temperature. It was found that none of these describes the experimental dependence in the whole range of temperature. A new dependence based on the free volume concept and cell-hole liquid theory is proposed. The theory permits linearization of the viscosity-temperature data in the range (T_i, T_i+1), where the T_i's are the liquid-liquid transition temperatures. It was demonstrated that these transitions, both in small molecular and in polymeric liquids, occur in discrete steps: T_i = a_iT_g, where T_g is the glass transition temperature and the a_i's are numerical parameters. Not all the transitions T_i were apparent in all liquids. Transition T₂ = 1.26T_g was observed for most polymeric liquids. On the basis of thermal analysis it was demonstrated that the T_i's coincide with the temperatures at which small changes in the apparent specific heat were detected. These temperatures can be assigned to the maximum rate of crystallization and melting temperatures of the metastable and stable crystalline forms.     

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     

Rheological Characterization of in situ Compatibilized Binary Polymer Blends With Variable Steady Shear Viscosities of Components

Zero shear viscosities of binary polymer blends, η_0,bc, of polypropylene (PP)/polystyrene (PS), in situ compatibilized by anhydrous aluminum chloride (AlCl₃) catalyst, were obtained by fitting their shear rate sweep curves according to the modified Carreau model. The results showed that the dependence of η_0,bc on AlCl₃ content was complicated and obviously influenced by viscosity variations of the components as well as the interfacial compatibilization effect of the in situ formed PP-g-PS copolymer. For further investigation, η_0,bc was divided into three parts: contribution of the viscosity of components, contribution of phase geometry, and contribution of the interfacial compatibilization effect. The results showed that when the apparent value of the third part was experimentally determined, the significant influence of viscosity variations of the components had to be considered, while the influence of phase morphology geometry resulting from viscosity variations of the components could be ignored experimentally and reasonably within the whole experimental range of AlCl₃ content. The contribution of the interfacial compatibilization effect to η_0,bc could be used as the rheological parameter to characterize the interfacial character and could be used to interpret the variations of η_0,bc of the in situ compatibilized polymer blend successfully. In addition, η_0,bc is more sensitive to the shear viscosity variations of the components than the phase structure geometry evolution of the reactive blends.     

Effect of nanoparticle dispersion on glass transition in thin films of polymer nanocomposites

We present spectroscopic ellipsometry measurements on thin films of polymer nanocomposites consisting of gold nanoparticles embedded in poly(styrene). The temperature dependence of thickness variation is used to estimate the glass transition temperature, T _g . In these thin films we find a significant dependence of T _g on the nature of dispersion of the embedded nanoparticles. Our work thus highlights the crucial role played by the particle polymer interface morphology in determining the glass transition in particular and thermo-mechanical properties of such nanocomposite films.     

Viscosity and thermal conductivity from non-conformal potentials. I Theory and application to noble gases

The approximate non-conformal (ANC) theory provides effective spherical potentials for more than 40 pure real gases and predicts many of their binary mixtures in the case of the second volumetric virial coefficients B(T). Each substance is characterized by only three parameters; besides the usual minimum energy ε and its corresponding position r _m, a softness parameter s is proposed to take account of the form of a particular potential. In this work the ANC theory is extended to take account of viscosity η(T) and thermal conductivity λ(T) coefficients in dilute gases. Very simple expressions are derived to calculate the appropriate collision integral Ω as a function of temperature and in terms of the parameters ε, r _m and s, using a reference collision integral Ω₀(T). The theory is successfully applied to the noble gases Ne, Ar, Kr and Xe, with deviations from experiment for η(T) and λ(T) within experimental uncertainties. In the case of Ne, the ANC potential obtained here reproduces simultaneously η(T) and λ(T) as well as B(T) within experimental uncertainty, using a single set of parameters. A prediction for the radon gas is proposed.     

Simulated glass-forming polymer melts: Glass transition temperature and elastic constants of the glassy state

By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature T _g and for the elastic properties of the glassy state are presented. We find that T _g increases with chain length N and is for all N larger for the semiflexible model. The N dependence of T _g is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below T _g via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching T _g from below, the shear modulus μ displays a much stronger decrease near T _g. From the present simulation data it is not possible to decide whether μ takes a finite value at T _g, as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.     

The Newtonian viscosity of polymer solutions: Scaling relationships

Scaling in terms of temperature, composition, and molecular weight variables has practical and fundamental significance. The viscosity of polymer solutions deviates from that predicted by the Huggins equation when the concentration is higher than a characteristic concentration c_ch. The value of c_ch depends on the molecular weight of the polymer and the thermodynamic conditions of the system. It is also a known fact that the deviations are due to the entanglements and interactions of polymer molecules. Therefore, we believe cch can be used as a concentration-reducing parameter to get the superposition curves. It can be shown that the concentration corresponding to a minimum value of η_sp/ch² (in the case of η_sp/c² vs concentration curves) is the value of c_ch of that system. Moreover, this c_ch is related to the intrinsic viscosity and molecular weight through the Huggins and Mark-Hauwink-Sakurada equations (c_ch = k′M^?a′). Using c_ch values for different systems and plotting log η_r versus C/C_ch, the superposition curves are obtained. In each case these curves are found to be linear, at least when concentrations approach zero. Master curves may be plotted by making use of the initial slopes of the curve (log η_r vs Bc/c_ch) and it is found that the data obtained at different thermodynamic conditions fit these (log η_r vs Bc/c_ch, B being the initial slope of log η vs c/c_ch) curves very well. The slopes are also compared to k′, a′, and the expansion coefficient of the system and the relationships are found to be linear. It is concluded that c_ch is a better parameter for the superposition of viscosity data, as well as being easy to obtain experimentally.     

Rapid viscous flow of a nematic liquid crystal in the vicinity of the nematic-smectic <Emphasis Type="Italic">A</Emphasis> transition

The resistance to shear flow is investigated theoretically for polar liquid crystals, such as 4-n-octyl-4′-and 4-n-octyloxy-4′-cyanobiphenyls. It is established that the lowest resistance to shear flow at temperatures in the vicinity of the nematic-smectic A phase transition point T _NA is observed when the nematic director is oriented perpendicular to both the flow velocity vector and the flow velocity gradient. The three Miesowicz shear viscosity coefficients η_i (i=1–3) at temperatures close to the phase transition temperature (tens of millikelvins from T _NA ) and far from this transition are calculated in the framework of the Ericksen-Leslie theory. The decrease in the viscosity coefficients in the order η₂>η₁>η ₃ is explained by the fact that fluctuations of the local smectic order in the nematic phase lead to a singular behavior of the viscosity coefficient η₂, whereas the other two viscosity coefficients η₁ and η₃ are not affected by order parameter fluctuations.     

Confinement and processing effects on glass transition temperature and physical aging in ultrathin polymer films: Novel fluorescence measurements

Fluorescence intensity measurements of chromophore-doped or -labeled polymers have been used for the first time to determine the effects of decreasing film thickness on glass transition temperature, T _g, the relative strength of the glass transition, and the relative rate of physical aging below T _g in supported, ultrathin polymer films. The temperature dependence of fluorescence intensity measured in the glassy state of thin and ultrathin films of pyrene-doped polystyrene (PS), poly(isobutyl methacrylate) (PiBMA), and poly(2-vinylpyridine) (P2VP) differs from that in the rubbery state with a transition at T _g. Positive deviations from bulk T _g are observed in ultrathin PiBMA and P2VP films on silica substrates while substantial negative deviations from bulk T _g are observed in ultrathin PS films on silica substrates. The relative difference in the temperature dependences of fluorescence intensity in the rubbery and glassy states is usually reduced with decreasing film thickness, indicating that the strength of the glass transition is reduced in thinner films. The temperature dependence of fluorescence intensity also provides useful information on effects of processing history as well as on the degree of polymer-substrate interaction. In addition, when used as a polymer label, a mobility-sensitive rotor chromophore is demonstrated to be useful in measuring relative rates of physical aging in films as thin as 10 nm. Received 21 August 2001     

Spin-Probe ESR Studies on Nanocomposite Polymer Electrolytes

The possibility of using spin-probe electron spin resonance (ESR) as a tool to study glass transition temperature, T _g, of polymer electrolytes is explored in 4-hydroxy-2,2,6,6-tetramethylpiperidine-N-oxyl (TEMPOL)-doped composite polymer electrolyte (PEG)₄₆LiClO₄ dispersed with nanoparticles of hydrotalcite. The T _g is estimated from the measured values of T _50G, the temperature at which the extrema separation 2A _zz of the broad powder spectrum decreases to 50 G. In another method, the correlation time τ_c for the spin probe dynamics was determined by computer simulation of the ESR spectra and T _g has been identified as the temperature at which τ_c begins to show temperature dependence. While both methods give values of T _g close to those obtained from differential scanning calorimetry, it is concluded that more work is required to establish spin-probe ESR as a reliable technique for the determination of T _g.     

Transport coefficients of hard sphere fluids

New calculations have been made of the self-diffusion coefficient D, the shear viscosity η_s, the bulk viscosity η_b and thermal conductivity λ of the hard sphere fluid, using molecular dynamics (MD) computer simulation. A newly developed hard sphere MD scheme was used to model the hard sphere fluid over a wide range up to the glass transition (～0.57 packing fraction). System sizes of up to 32 000 hard spheres were considered. This set of transport coefficient data was combined with others taken from the literature to test a number of previously proposed analytical formulae for these quantities together with some new ones given here. Only the self-diffusion coefficient showed any substantial N dependence for N < 500 at equilibrium fluid densities (ε 0.494). D increased with N, especially at intermediate densities in the range ε ～ 0.3–0.35. The expression for the packing fraction dependence of D proposed by Speedy, R. J., 1987, Molec. Phys., 62, 509 was shown to fit these data well for N ～ 500 particle systems. We found that the packing fraction ε dependence of the two viscosities and thermal conductivity, generically denoted by X, were represented well by the simple formula X/X ₀ = 1/[1 ? (ε/ε₁)]^m within the equilibrium fluid range 0 > ε > 0.493. This formula has two disposable parameters, ε and m, and X ₀ is the value of the property X in the limit of zero density. This expression has the same form as the Krieger-Dougherty formula (Kreiger, I. M., 1972, Adv. Colloid. Interface Sci., 3, 111) which is used widely in the colloid literature to represent the packing fraction dependence of the Newtonian shear viscosity of monodisperse colloidal near-hard spheres. Of course, in the present case, X _o was the dilute gas transport coefficient of the pure liquid rather than the solvent viscosity. It was not possible to fit the transport coefficient normalized by their Enskog values with such a simple expression because these ratios are typically of order unity until quite high packing fractions and then diverge rapidly at higher values over a relatively narrow density range. At the maximum equilibrium fluid packing fraction ε = 0.494 for both the hard sphere fluid and the corresponding colloidal case a very similar value was found for η_s/η_o ?30–40, suggesting that the ‘crowding’ effects and their consequences for the dynamics in this region of the phase diagram in the two types of liquid have much in common. For the hard sphere by MD, D_o/D ～ 11 at the same packing fraction, possibly indicating the contribution from ‘hydrodynamic enhancement’ of this transport coefficient, which is largely absent for the shear viscosity. Interestingly the comparable ratio for hard sphere colloids is the same.     

Thermal Cross‐Linking of Poly(Vinyl Methyl Ether). I. Effect of Cross‐Linking Process on the Viscoelastic Properties

Abstract

Thermal cross‐linking of poly(vinyl methyl ether) (PVME) in the absence of cross‐linking agent, was detected rheologically. The linear viscoelastic properties of PVME were found to be greatly changed by the onset of the cross‐linking process. The viscoelastic material functions, such as dynamic shear moduli, G′ and G″, complex shear viscosity, η*, and loss tangent, tan δ, were found to be sensitive to the structure changes during the cross‐linking process and the formation of a three‐dimensional polymer network. At the onset temperature of the cross‐linking process, an abrupt increase in G′, G″, and η* (several orders of magnitude) during dynamic temperature ramps (2°C/min heating rate) was observed with some frequency dependence. The temperature dependence of tan δ was found to be frequency independent at the gel‐point, T _gel, that is, the crossover in tan δ regardless of the value of frequency can be taken as an accurate method for determination of T _gel. The coincidence of G′ and G″ at the gel‐point cannot be considered a general method for evaluation of T _gel due to its high frequency dependence, that is, T _gel determined from the crossover of G′ and G″ in the dynamic temperature ramp at 1 rad/sec is about 20°C less than at 100 rad/sec. Furthermore, a dramatic increase in η₀ above the minimum (“v” shape) was observed at T = T _gel in agreement with the value obtained from tan δ vs. T (190°C). The time–temperature‐superposition principle was found to be valid only for temperatures lower than the T _gel (190°C); the principle failed at T ≥ 190°C. This was clearly seen in the low‐frequency region as a deviation from the terminal slope in the G′ curve. Similar behavior was observed in the modified Cole–Cole analyses (G″ vs. G′) that is, the curves start to deviate at 190°C.     

Temperature behavior of the Kohlrausch exponent for a series of vinylic polymers modelled by an all-atomistic approach

The Kohlrausch-Williams-Watt (KWW) function, or stretched exponential function, is usually employed to reveal the time dependence of the polymer backbone relaxation process, the so-called α relaxation, at different temperatures. In order to gain insight into polymer dynamics at temperatures higher than the glass transition temperature T _g , the behavior of the Kohlrausch exponent, which is a component of the KWW function, is studied for a series of vinylic polymers, using an all-atomistic simulation approach. Our data show very good agreement with published experimental results and can be described by existing phenomenological models. The Kohlrausch exponent exhibits a linear dependence with temperature until it reaches a constant value of 0.44, at 1.26T _g , revealing the existence of two regimes. These results suggest that, as the temperature increases, the dynamics progressively change until it reaches a plateau. The non-exponential character then describes subdiffusive motion characteristic of polymer melts.     

SMMA/SMA共聚物共混物的自由体积的热动态特性与相分离行为的PALS研究

基于自由体积理论，利用正电子湮灭寿命谱仪(PALS)分别研究在不同升温速率条件下，聚苯乙烯-甲基丙烯酸甲酯共聚物(SMMA)和聚苯乙烯-马来酸酐共聚物(SMA)混合物(30/70)的自由体积参数的温度依赖性，探索相容共混物相行为的热动态特性.在PALS实验中，在玻璃化转变温度T_g以上，当结构松弛的弛豫时间与等温停留时间相当，发现在某一段温度范围内，共混物的自由体积参数随着温度的变化明显地偏离线性关系.从自由体积孔的浓度I₃值在该段的变化趋势，初步推断共混物在该温 关键词： 正电子湮没 正电子素 聚合物共混物 相分离     

A model for viscosity coefficients of gases with potentials differing in form

A recent theory of non-conformal interactions has been very succesful in providing effective spherical potentials for the pressure of more than 40 real gases and many of their binary mixtures. Here, this theory is applied to deal with low-density viscosity coefficients. In its simplest form, the approximate non-conformal (ANC) theory introduces, besides the usual corresponding states parameters-energy ? and distance r_m-a softness parameter s to account for the form of a particular potential function. We investigate the effects of the potential form on the temperature behaviour of the viscosisty coefficient η. It is shown that the softer potentials, with wider attractive wells, have larger viscosities and an explicit expression for η (T, ?, r_m, s) is obtained. The ANC potentials are tested in their capacity to reproduce the temperature dependence of η for the heavier noble gases (Ar, Kr and Xe), diatomics (H₂, N₂, O₂ and CI₂) and a dozen small polyatomics. It is found that the ANC model η (T, ?, r_m, s), with only three substance-dependent parameters, reproduces experimental 7 data within their estimated error.     

Rheological Characterization of Poly(3,3′-Diaminodiphenylsulfone Terephthaloylchloride) Solutions in Dimethylsulfoxide

Steadyshear and oscillatory shear rheological measurements were performed to characterize the solution rheological behavior of poly(3,3′-diaminodiphenylsulfone terephthaloylchloride) (P(3,3′-DDS-TPC)) in dimethyl sulfoxide (DMSO). The effects of temperature, concentration, and weight-average molar mass () on the rheological properties were investigated. From the temperature dependence of zero-shear viscosity, the flow activation energies, E_η, of P(3,3′-DDS-TPC)/DMSO solutions were calculated. Both the overlap concentration, C*, and the entanglement concentration, C_e, were determined from the concentration dependence of the specific viscosity η_sp. All the P(3,3′-DDS-TPC) solutions, we studied, can be separated into three regimes: the dilute, semidilute-unentangled, and entangled regime with slopes of 1, 1.3, and 3.9, of concentration versus η_sp plots, respectively, which are consistent with scaling predictions for flexible polymers in a good solvent.     

Freezing Temperature in Dilute Ising Spin Glasses with Long-Range Interactions

The onset of spin-glass freezing in dilute Ising systems with long-range interactions is investigated with the use of numerical simulations. We show that taking pair correlations explicitly into account results in the renormalization of the interaction matrix and suppression of the density of localized states compared with conventional mean field theory. Application of the theory to the RKKY interaction in the dilute limit raises the question of the appropriate boundary eigenvalue of the effective interaction matrix that separates localized and extended states. We identify the onset of spin-glass freezing with the temperature T _g at which this boundary eigenvalue is equal to one. Numerical simulations reproduces the linear concentration dependence of T _g in the very dilute limit, in agreement with scaling relations, and show a significant improvement over the conventional mean-field theory in the value obtained for the freezing temperature.     

μ+SR in amorphous spin glasses Pd75Fe5Si20 and Pd75Fe5P20

The zero-field muon spin relaxation functionG _zz (t) has been measured as a function of reduced temperaturet=T/T _g in the amorphous metallic spin glasses Pd₇₅Fe₅Si₂₀ and Pd₇₅Fe₅P₂₀. The results are in qualitative agreement with earlier measurements on dilute alloy spin glasses, including an onset of static order belowT _g and a [t/(t-1)]² dependence of the correlation time τ_c aboveT _g. Both samples have the same τ_c (t) aboveT _g and almost identical static width Δ_S→Δ_o?43 μS^?1) asT»0, but thet-dependence of Δ_s nearT _g differs markedly.     

Viscosity of strong and fragile glass-forming liquids investigated by means of principal component analysis

The Vogel—Fulcher-Tammann-Hesse (VFTH) equation has been the most widespread tool for describing the temperature dependence with viscosity for strong, moderate and fragile glass-forming liquids. In this work, the VFTH equation was applied over a wide temperature range (between the glass transition temperature, T_g, and the melting point, T_m) for 38 oxide glasses, considering simple, binary and ternary compositions of silicate and borate systems. The Levenberg-Marquart non-linear fitting procedure was used to assess VFTH viscosity parameters B and T₀, maintaining A=−5 fixed (in Pa·s) to reduce the number of adjustable parameters. Regarding this restriction, the VFTH formula has shown to adjust very well to experimental data in a wide temperature range. Previous assertions revealed that there is statistical correlation between B and T₀. Principal component analysis (PCA) was used in the present study to verify the correlation between the B and T₀ parameters [J. F. Mano, E. Pereira, J. Phys. Chem. A 108 (2004) 10824], as well as between T_g and T_m. In brief, PCA is a mathematical method aimed at reorganizing information from data sets. The results have shown that it is possible to map either borate (and almost fragile) or silicate (usually strong up to near fragile) systems. As a statistical tool, PCA justifies the use of B, T₀ and T_g as the main parameters for the fragility indexes m=d(log₁₀η)/d(T_g/T)|_T=Tg and D=B/T₀, where η is the viscosity and T the absolute temperature.