Effect of crosslink density on the pressure relaxation response of polycyanurate networks

The effect of crosslink density on the pressure-volume-temperature (PVT) behavior and on the pressure relaxation response for two polycyanurate networks is investigated using a custom-built pressurizable dilatometer. Isobaric cooling measurements were made to obtain the pressure-dependent glass transition temperature (T_g). The pressure relaxation studies were carried out as a function of time after volume jumps at temperatures in the vicinity of the pressure-dependent T_g, and the pressure relaxation curves obtained were shifted to construct master curves by time-temperature superposition. The reduced pressure relaxation curves are found to be identical in shape and placement, independent of crosslink density, when T_g is used as the reference temperature. The horizontal shift factors used to create the master curves are plotted as a function of the temperature departure from T_g (T − T_g), and they agree well with their counterparts obtained from the shear response. Moreover, the retardation spectra are derived from bulk compliance and compared to those from the shear. The results, similar to our previous work on polystyrene, indicate that at short times, the bulk and shear responses have similar underlying molecular mechanisms; however, the long-time mechanisms available to the shear response, which increase with decreasing crosslink density, are unavailable to the bulk response. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2477–2486, 2009     

Bulk and shear rheology of a symmetric three‐arm star polystyrene

The bulk and shear rheological properties of a symmetric three‐arm star polystyrene were measured using a self‐built pressurizable dilatometer and a commercial rheometer, respectively. The bulk properties investigated include the pressure–volume–temperature behavior, the pressure‐dependent glass transition temperature (T_g), and the viscoelastic bulk modulus and Poisson's ratio. Comparison with data for a linear polystyrene indicates that the star behaves similarly but with slightly higher T_gs at elevated pressures and slightly higher limiting bulk moduli in glass and rubbery states. The Poisson's ratio shows a minimum at short times similar to what is observed for the linear chain. The horizontal shift factors above T_g obtained from reducing the bulk and shear viscoelastic responses are found to have similar temperature dependence when plotted using T ? T_g scaling; in addition, the shift factors also exhibit a similar temperature dependence to linear polystyrene. The retardation spectra for the bulk and shear responses are compared and show that the long time molecular mechanisms available to the shear response are unavailable to the bulk. At short times, the two spectra have similar slopes, but the short‐time retardation spectrum for the shear response is significantly higher than that for the bulk, a finding that is, as yet, unexplained. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Mechanical relaxation spectroscopy of three triepoxide-based polymers

Three network structure polymers formed by the chemical reactions of a triepoxide with aniline, 3-chloroaniline,and 4-chloroaniline were prepared and their shear modulus relaxation spectra studied over the 10⁻³- to 1-Hz range and temperatures up to their rubber modulus region. The decrease in the unrelaxed modulus with increase in temperature is found to be a reflection of both an increase in volume, and a decrease in the relaxed modulus of the sub-T_g relaxations process. It is quantitatively shown that the increase in the rubber modulus with increase in temperature above T_g is predominantly due to an increase in the entropy and not to a decrease in the number of cross-links density on thermal expansion. The unrelaxed modulus remained unaffected by the change in the overall size of the phenyl groups of the amines and of the steric hindrance to their rotations caused by the proximity of the chlorine atom to the cross-linking N-atom in the network structure, but the rubber modulus was effected. The shear modulus spectra could be fitted to a stretched exponential decay function with a temperature-independent stretch parameter of 0.25 for two polymers and 0.22 for one. The time–temperature superposition of the spectra did not yield a master curve, and a vertical displacement of the data also failed to produce it. This was more clearly demonstrated by the spectra of the mechanical loss tangent. After considering the various contributions to the shear modulus, it was concluded that deviations from the time–temperature superposition of the spectra are intrinsic to these polymers and arise from the change in the viscoelastic functions for segmental dynamics on change in the temperature such that the overall distribution of relaxation times remains unaffected. The mechanical loss tangent of the three polymers is found to be higher than that of polycarbonate at ambient temperature, implying a higher loss of mechanical energy before these polymers may fracture. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3071–3083, 1999     

Acrylic acid level and adhesive performance and peel master‐curves of acrylic pressure‐sensitive adhesives

Three series of pressure‐sensitive adhesives were prepared with constant glass‐transition temperature, using emulsion polymerization. The monomers chosen were butyl acrylate, 2‐ethylhexyl acrylate (EHA), methyl methacrylate (MMA), and acrylic acid (AA). Within each polymer series, the proportion of AA monomer was held constant for each polymer preparation but acrylic ester monomer levels were varied. Adhesion performance was assessed by measurement of loop tack, static shear resistance, and through the construction of peel master‐curves. Peel master‐curves were generated through peel tests conducted over a range of temperatures and peel rates and through application of the time–temperature superposition principle. Bulk effects dominated by polymer zero shear viscosity change as AA and EHA levels were varied were attributed to the observed effect on static shear resistance and the horizontal displacements of peel master‐curves. Static shear resistance was found to strongly correlate with log(a_C), a parameter introduced to horizontally shift peel master‐curves to form a superposed, “super master‐curve”. An interfacial interaction was proposed to account for deviations observed when loop tack was correlated with log(a_C). Surface rearrangements via hydrogen bonding with the test substrate were suggested as responsible for the interfacial interaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1237–1252, 2006     

Creep behavior of amorphous ethylene–styrene interpolymers in the glass transition region

The viscoelastic behavior of amorphous ethylene–styrene interpolymers (ESIs) was studied in the glass transition region. The creep behavior at temperatures from 15°C below the glass transition temperature (T_g) to T_g was determined for three amorphous ESIs. These three copolymers with 62, 69, and 72 wt % styrene had glass transition temperatures of 11, 23, and 33°C, respectively, as determined by DMTA at 1 Hz. Time–temperature superposition master curves were constructed from creep curves for each polymer. The temperature dependence of the shift factors was well described by the WLF equation. Using the T_g determined by DMTA at 1 Hz as a reference temperature, C₁ and C₂ constants for the Williams, Landel, and Ferry (WLF) equation were calculated as approximately 7 and 40 K, respectively. The master curves were used to obtain the retardation time spectrum and the plateau compliance. The entanglement molecular weight obtained from the plateau compliance increased with increasing styrene content as 1,600, 1,870, and 2,040, respectively. The entanglement molecular weight of the ESIs was much closer to that of polyethylene (1,390) than to that of polystyrene (18,700); this was attributed to the unique chain microstructure of these ESIs with no styrene–styrene dyads. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2373–2382, 1999     

Interpretation of the TSDC fractional polarization experiments on the α‐relaxation of polymers

We report on the interpretation of the thermally stimulated depolarization current (TSDC) experiments, with partial polarization methods, on the dielectric α‐relaxation. The results obtained on polyvinyl acetate are rationalized on the basis of the Boltzmann superposition principle in combination with a Kohlrausch–Williams–Watts (KWW) time decay of the polarization (with the β exponent essentially temperature independent and equal to the value determined by conventional dielectric methods at T_g). From this analysis of the global TSDC spectrum we found a complex temperature dependence of the KWW relaxation time, which is Arrhenius‐like at the lowest temperatures but crosses over to the Vogel–Fulcher behavior observed above T_g in the temperature range of the TSDC peak. On the basis of these results, we found the way of predicting the TSDC spectra measured after partial polarization procedures. We found that, the distribution of activation energies and compensation behavior deduced by following the standard way of analysis are associated to the assumption of an Arrhenius‐like temperature dependence of the α‐relaxation time in the temperature range explored by TSDC. Therefore we conclude that both the distribution of activation energies and compensation behavior obtained by following the standard way of analysis do not give a proper physical picture of the α‐relaxation of glassy polymers around the glass‐transition temperature. Our results also show that the partial polarization TSDC methods are not able to give insight about the actual existence or not of a distribution of relaxation times at the origin of the nonexponentiality of the α‐relaxation of polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2105–2113, 2000     

Measurement of high frequency linear viscoelastic functions of a nitrile‐butadiene rubber compound by ultrasound spectroscopy

The storage and loss components of the complex wave modulus, M*(ω), measured on a nitrile‐butadiene rubber compound (NBR‐DIN 53538) by ultrasound spectroscopy at a temperature of 293.2 K, were combined with the components of the complex shear modulus, G*(ω), measured on the same sample in a commercial Rheometric Scientific ARES instrument with torsion geometry at different frequencies and temperatures, and superposed in a master plot using the time–temperature superposition principle. From the combined measurements the components of the complex bulk modulus, K*(ω), were obtained by means of the exact formula M*(ω) = K*(ω) + (4/3)G*(ω). Some of the features of the complex bulk modulus reported in the literature for polymeric materials are confirmed for the NBR‐DIN mixture. The maxima in G″(ω) and K″(ω) are separated by more than one order of magnitude in the frequency scale and furthermore, the shapes of the peaks are different. The simple idea, that, for many polymers, the mechanisms for relaxation in shear and in bulk are of the same basic nature appears not to be supported by the present data. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 91–102, 2007     

Physical aging of an amorphous polyimide: Enthalpy relaxation and mechanical property changes

The physical aging behavior of an isotropic amorphous polyimide possessing a glass transition temperature of approximately 239°C was investigated for aging temperatures ranging from 174 to 224°C. Enthalpy recovery was evaluated as a function of aging time following sub‐T_g annealing in order to assess enthalpy relaxation rates, and time‐aging time superposition was employed in order to quantify mechanical aging rates from creep compliance measurements. With the exception of aging rates obtained for aging temperatures close to T_g, the enthalpy relaxation rates exhibited a significant decline with decreasing aging temperature while the creep compliance aging rates remained relatively unchanged with respect to aging temperature. Evidence suggests distinctly different relaxation time responses for enthalpy relaxation and mechanical creep changes during aging. The frequency dependence of dynamic mechanical response was probed as a function of time during isothermal aging, and failure of time‐aging time superposition was evident from the resulting data. Compared to the creep compliance testing, the dynamic mechanical analysis probed the shorter time portion of the relaxation response which involved the additional contribution of a secondary relaxation, thus leading to failure of superposition. Room temperature stress‐strain behavior was also monitored after aging at 204°C, with the result that no discernible embrittlement due to physical aging was detected despite aging‐induced increases in yield stress and modulus. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1931–1946, 1999     

Correlation between dipolar TSDC and AC dielectric spectroscopy at the PVDF glass transition

The α_a-mode (associated to the dynamic glass transition) in PVDF-α has been studied by Thermally Stimulated Depolarization Currents (TSDC) and Dielectric Spectroscopy (DS) techniques. The distribution of relaxation parameters, reorientation energies, characteristic temperature, and preexponential factors of the Vogel–Tammann–Fulcher relaxation times have been precisely determined by using the Simulated Annealing Direct Signal Analysis applied to a partially discharged TSDC α_a peak. This distribution has been used to predict the variation of the dielectric loss, ε″(ω, T), in the temperature and frequency range where the DS measurements were made on the same material. The simulated ε′(T, ω) for various ω, are compared to the experimental values. The width of the peak is always too low, due to the restricted distribution used for the generation of the curves. A relaxation map including the TSDC results is used to determine the relaxation time variation. In the limited frequency range where the AC DS experiments are performed (10² ≤ f ≤ 10⁵ Hz) a master curve is drawn and the exponents of the frequency dependence are found at low and high frequency; also, a fitting to the Havriliak–Negami distribution is successfully performed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2483–2493, 1997     

Comparison of ultrasonic shear wave and dynamic-mechanical measurements in acrylic-type copolymers

An ultrasonic shear wave reflection method was applied to study film formation and temperature dependence of the complex shear modulus (G^*G′ + iG″) in different amorphous films made of aqueous dispersions of acrylic-type copolymers. The data are compared with dynamic-mechanical measurements in the low frequency range. It is shown that the temperature dependence of the storage (G′) and the loss modulus (G″) for both methods can be fitted by the same set of parameters using the Havriliak–Negami function incorporating the Vogel–Fulcher–Tamman–Hesse equation for the temperature dependence of relaxation times. The temperature dependence of the relaxation times obtained from the fits to the ultrasonic shear modulus is compared to the shift factors of the dynamic-mechanical measurements. The agreement between both methods is good. This suggests an almost thermorheological simplicity of the samples for the main glass–rubber relaxation and demonstrates the capacity of the ultrasonic rheometer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1703–1711, 1998     

以时温等效方法研究尼龙1010应力松弛行为及使用寿命预测

以尼龙材料的应力松弛行为作为研究对象, 考察初始应变为1.0%, 2.8%和5.1%的尼龙1010样品在温度区间293353 K的松弛曲线, 采用时间-温度等效叠加方法得到了松弛模量主曲线, 计算出叠加过程中的表观活化能、 松弛过程中的活化体积和应力辅助功. 结果表明, 整个松弛过程中的表观活化能和应力辅助功表现出相同的变化趋势, 体现出松弛过程中克服运动单元位垒的过程. 当293323 K区间的松弛曲线叠加时, 随着初始应变的增加, 表观活化能和应力辅助功均逐渐降低, 有助于聚合物内部的运动单元越过能垒发生松弛, 与松弛过程中的应力辅助热活化理论相一致; 当333353 K区间的松弛曲线叠加时, 不同初始应变样品的表观活化能均为260 kJ/mol, 应力辅助功均为60 MPa·nm³, 说明松弛过程中克服运动单元的能垒与应力作用无关. 根据松弛主曲线, 计算出了尼龙1010在1.0%, 2.8%和5.1% 3种形变下, 长时间范围内应力衰减与时间的关系, 为预测实际使用过程中的应力松弛行为提供了依据.     

Viscoelastic characteristics of UV polymerized poly(ethylene glycol) diacrylate networks with varying extents of crosslinking

The viscoelastic relaxation characteristics of ultraviolet crosslinked networks based on poly(ethylene glycol) diacrylate [PEGDA] have been investigated by dynamic mechanical methods. Effective crosslink density in the networks was varied via the use of PEGDA prepolymers of different molecular weight, or by the introduction of controlled amounts of water in the reaction mixture. In all cases examined, fully amorphous networks were obtained. Time–temperature superposition was applied to obtain master curves of storage modulus versus frequency across the glass transition, and these could be satisfactorily described using the Kohlrausch–Williams–Watts relaxation function. The glass transition temperature (T_g), relaxation breadth, and fragility of the segmental relaxation were correlated with the effective crosslink density obtained in the networks. Gas permeation measurements on the PEGDA/water networks indicated only a very modest variation in gas transport properties, despite the sizeable variation in apparent crosslink density achieved in these materials. This result suggests that the controlling structural factor for gas transport in the networks is not simply crosslink density, and that attempts to correlate gas transport to network structure must necessarily consider the broader relationships between crosslink density, segmental mobility, and fractional free volume. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2058–2070, 2006     

Effect of endgroup modification on dynamic viscoelastic relaxation and motion of hyperbranched poly(ether ketone)s

Fluoro‐terminated hyperbranched poly(ether ketone) (FHPEK) was synthesized and its end groups were modified with alkyl compounds of different chain lengths, i.e., hexyloxy (C6), dodecyloxy (C12), and octadecyloxy, (C18), to produce alkyl‐modified HPEKs (HPEK‐C6, HPEK‐C12, and HPEK‐C18, respectively). Master curves were constructed by using the time‐temperature superposition principle. The horizontal shift factors, a_T, used for the construction of the master curves were fit using the William‐Landel‐Ferry (WLF) equation. From the fitting parameters, the apparent activation energy, E_a, was estimated. With increasing alkyl chain length, the E_a values were found to decrease in the order FHPEK > HPEK‐C6 > HPEK‐C12, and then increase for HPEK‐C18. The average relaxation time, τ_HN, was determined by fitting of the dynamic moduli G′(ω) and G″(ω) to the empirical Havriliak‐Negami equation. Similarly, the τ_HN values decreased in the order of FHPEK > HPEK‐C6 > HPEK‐C12, and then increased for HPEK‐C18. This indicates that the endgroup modification with short alkyl chains (C6, C12) increased the molecular mobility due to the internal plasticization effect of these alkyl chains. Modification with the longer alkyl chain (C18) retarded the molecular motion through an antiplasticization effect caused by summation of nonpolar hydrophobic interactions between long hydrocarbon chains. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2079–2089, 2008     

Anomalous aging in two-phase systems: Creep and stress relaxation differences in rubber-toughened epoxies

From time–aging time superposition principles, similar to time–temperature superposition, one would expect similar shifting or superposition behaviors for both creep and stress relaxation responses. In particular, for isotropic homogeneous systems, in the linear viscoelastic regime, consideration of superposition in rheology by Markowitz¹ or the discussion by Ferry² from the Kramers–Kronig relation would seem to demand that creep and stress relaxation shift in the same way. Here we report on results from creep and stress relaxation measurements in two-phase, rubber-toughened epoxies that exhibit Boltzman additivity of creep or relaxation behaviors and follow the time–aging time superposition behavior in creep, but not in stress relaxation. While the lack of superposition in stress relaxation is, perhaps, not surprising, the finding that the creep responses at different aging times superimpose while the stress relaxation responses do not, presents an anomalous behavior that has not been previously reported. In addition, our findings show that the stress relaxation responses show short time “softening” upon aging. Possible reasons for the anomalous behaviors are briefly considered. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1167–1174, 1997     

Confirmation of universality of time–humidity superposition principle for various water‐absorbable polymers through dynamic viscoelastic measurements under controlled conditions of relative humidity and temperature

Dynamic viscoelastic measurements were made for storage (E′) and loss (E″) tensile moduli of water‐absorbable polymers such as nylon‐6, nylon‐66, poly(vinyl alcohol), ethylene–vinyl alcohol copolymers, and regenerated cellulose under the control of stepwise scanned relative humidity at constant temperature by changes in the strain frequency over a wide range. Smooth master curves of log(E′) and log(E″) plotted against log(frequency) were successfully obtained for all samples. The evaluated shift factors changed with the relative humidity and could be interpreted well on the basis of a concept of free volume in the amorphous region. The free volume was affected sensitively, depending on the heat‐treatment condition and the types of polymers used. For nylon‐66 film, the dynamic viscoelastic measurements were made at different humidities and temperatures, from which one smooth master curve was obtained. This experimental result is important in realizing the similar effect of relative humidity and temperature on the expansion of free volume of the amorphous phase: the shift factor change induced by the relative humidity change of about 30% was equivalent to the shift factor change induced by the temperature change of about 30 °C. That is, the time–humidity superposition principle and the time–temperature superposition principle were applicable as equivalent contributors to the mechanical property of water‐absorbable polymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1638–1650, 2001     

Volume-dependent rate processes in an epoxy resin

Results for four different volume-dependent rate processes of an epoxy resin, Epon 1001F, fully cured with a stoichiometric amount of 4,4′-diamino diphenyl sulfone are presented: (1) specific volume measurements at constant rates of cooling; (2) time-dependent volume measurements after rapid temperature changes; (3) elongational creep compliance measurements; and (4) shear creep compliance measurements. Voluminal and shear retardation spectra are compared as are the temperature time scale shift factors, a_T obtained from the four processes. Volume–temperature cooling curves show the decreasing glass temperature with decreasing rate of cooling, but appear to reach the glass line at a constant temperature regardless of the rate of cooling. This narrowing of the “transition range” is not predicted by the Kovacs, Aklonis, Hutchinson, and Ramos (KAHR) multiparameter model, which assumes thermorheological simplicity.     

Linear thermoviscoelasticity and characterization of noncrystalline EPDM rubber networks

An experimental study has been made to specify how the time-temperature superposition and the linear viscoelastic characteristics vary with the degree of crosslinking for a broad class of noncrystalline peroxide-cured EPDM networks. A new, very sensitive method is applied to determine the horizontal and vertical shift functions in an independent way. All uncrosslinked samples are thermoelasticoviscously simple with horizontal shift functions a_T of the WLF type and vertical shift functions almost independent of temperature, in agreement with recent theoretical understanding. Upon crosslinking, these materials become thermoviscoelastically complex networks, but superposition can still be accomplished by assuming different temperature dependences for the relaxational strength and the equilibrium modulus. The a_T functions can be taken independent of the degree of crosslinking. The vertical shift functions b_T for the relaxational strength vary with the degree of crosslinking between theoretical predictions for uncrosslinked and perfectly crosslinked EPDM networks. The equilibrium moduli of the lightly cured networks decreases with increasing temperature, which is ascribed to the presence of interchain associations between ethylene sequences in the trans state. Upon further crosslinking, these effects gradually vanish and eventually the networks can be described as viscoelastically simple with an energy elastic contribution due to the ethylene trans-gauche transitions. The linear viscoelastic characteristics, namely the storage and loss moduli and compliances and phase-angle master curves and the relaxation and retardation spectra are discussed as a function of the degree of crosslinking. A sol/gel analysis and equilibrium swelling measurements complete the experimental characterization of three familes of five EPDM networks each.     

Measurements of the relaxation spectra of unplasticized poly(vinyl chloride) melts

We have measured the relaxation modulus in the temperature range 150–220°C of two samples of poly(vinyl chloride) resin with different molecular weights. The data were treated by the principle of reduced variables to yield composite curves. The shift factors (a_T) when plotted against reciprocal temperature gave good straight lines from which apparent activation energies were obtained. An apparent activation energy of 50 kcal/mole was obtained for both samples. A relaxation spectrum for each resin was calculated from the relaxation modulus data. These spectra showed a marked molecular weight dependence. The spectra were in the range characteristic of the terminal zone of the entanglement plateau. Zero-shear-rate viscosities were obtained from the integration of relaxation modulus plots. From extrapolation of capillary viscosity data it is shown that the viscosity of the higher molecular weight resin used in this study does not approach its zero-shear value until shear rates less than 10^?3 sec^?1 are reached. The effect of supermolecular flow units is briefly discussed.     

Dynamic master curves from the stretched exponential relaxation modulus

The stretched exponential relaxation modulus of regular and polymer modified asphalts is studied. It is shown that this relaxation function can generate the dynamic functions of these materials very well on any finite interval of the reduced frequencies (master curves). By continuation one can, in principle, cover the whole region of master curves of G′ and G″. The dispersive defect diffusion mechanism, which leads to the stretched exponential law, points to the stronger three-dimensional structure of modified asphalt at low temperatures. The method of calculating G′ and G″ from the stretched exponential relaxation modulus is proposed and tested on one regular and one modified asphalt. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1225–1232, 1997     

Rheology of polydimethylsiloxane swollen with supercritical carbon dioxide

Viscosity curves were measured for polydimethyl siloxane (PDMS) melts swollen with dissolved carbon dioxide at 50 and 80°C for shear rates ranging from 40 to 2300 s⁻¹, and for carbon dioxide contents ranging from 0 to 21 wt %. The measurements were performed with a capillary extrusion rheometer modified for sealed, high-pressure operation to prevent degassing of the melt during extrusion. The concentration-dependent viscosity curves for these systems are self-similar in shape, exhibiting low-shear rate Newtonian plateau regions followed by shear-thinning “power-law” regions. Considerable reduction of viscosity is observed as the carbon dioxide content is increased. Classical viscoelastic scaling methods, employing a composition-dependent shift factor to scale both viscosity and shear rate, were used to reduce the viscosity data to a master curve at each temperature. The dependence of the shift factors on polymer chain density and free volume were investigated by comparing the shift factors for PDMS-CO₂ systems to those obtained by iso-free volume dilutions of high molecular weight PDMS. This comparison suggests that the free volume added to PDMS upon swelling with dissolved carbon dioxide is the predominant mechanism for viscosity reduction in those systems. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 523–534, 1997