Expansion Coefficient Of Free Volume Research Articles

Mechanism and quantitative study of specific heat change during glass transition of amorphous polystyrene and Pd<sub>40</sub>Ni<sub>10</sub>Cu<sub>30</sub>P<sub>20</sub>

<sec>The nature of glass transition is one of the most interesting problems in modern condensed matter physics. There is a theory that shows that when the particle's diffusion motion probability <i>P</i> is less than <inline-formula><tex-math id="M2">\begin{document}$ {{\rm{e}}^{ - 2{{\rm{e}}^3}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200331_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200331_M2.png"/></alternatives></inline-formula>, the proportion of particles whose diffusion motion is frozen is not less than 1 + 2e<sup>3</sup>/ln<i>P</i>. Based on the modulus temperature formula of this theory and the experimental modulus-temperature curve of polystyrene in the literature, the free volume expansion coefficient of polystyrene is determined to be in a range of 0.00045－0.00052. </sec><sec>In this paper, we first quantitatively study the specific heat temperature relationship in the glass transition of polystyrene. Based on this theory, the specific heat-temperature formula in the glass transition region is derived. The material in the glass transition region is a mixture of rubber and glass, and this two-component (rubber and glass) system’s total specific heat is the product of the specific heat of the rubber and the percentage of rubber in the two-component system plus the product of the specific heat of the glass and the percentage of glass in the two-component system. Let <i>b</i> be the number of atoms in the main chain of the segment, then the proportion of rubber will be the <i>b</i>-th power of free volume fraction. This specific heat-temperature formula with polystyrene is tested. By substituting the obtained free volume expansion coefficient of the polystyrene into the specific heat-temperature formula, the resulting formula can accurately and quantitatively describe the specific heat-temperature relationship in the glass transition of polystyrene without fitting any parameters. </sec><sec>In this paper, we also study the change of motion in the glass transition of polystyrene. According to the analysis, the glass transition process of polystyrene is a process in which the diffusion movement of the main chain atoms is activated or frozen, which is consistent with the conclusions of relevant research on amorphous alloys. When the main chain atom is used as the molar unit of measurement, the specific heat change in the glass transition of polystyrene is 1.61<i>R</i> (<i>R</i> is the gas constant), which is consistent with the law, i.e. “the specific heat change in the glass transition of the amorphous alloy is about 1.5<i>R</i>”. These consistent conclusions predict that the glass transitions of amorphous alloys and glass transitions of polystyrene have the same essence. Based on this idea, the specific heat temperature formulas of the amorphous alloy Pd<sub>40</sub>Ni<sub>10</sub>Cu<sub>30</sub>P<sub>20</sub> and polystyrene are verified and prove to be consistent.</sec>

Effect of the degree of cure on the viscoelastic properties of vinyl ester resins

Dynamic mechanical thermal analysis (DMTA) was performed on model vinyl ester resin (VER) samples prepared from bisGMA and styrene, partially cured using either benzoin ethyl ether (BEE) as a conventional photoinitiator or p-xylylene bis-( N, N-diethyldithiocarbamate) (XDT) as a photoiniferter, and on fully cured samples using benzoyl peroxide as a thermal initiator. Thermogravimetric studies showed that minimal styrene monomer was lost during the DMTA experiments. The DMTA experiments for the samples partially cured using BEE revealed two plateaus in the storage modulus and two peaks in the tan δ curves, attributed to trapped radicals gaining mobility and continuing polymerization after the samples were heated beyond their initial T g. Only a single transition was observed for samples cured using XDT because this system did not contain trapped radicals. Performing photopolymerizations with XDT thus allowed us to probe the effect of cure conditions on the glass transition temperature, rubber modulus and relaxational behaviour of partially cured resins. The breadth of the glass transition was characterized in the temperature and frequency domains (obtained by time–temperature superposition). Partially cured bisGMA/styrene blends showed a narrowing of the transition in the frequency domain with increased cure but the bisGMA system showed no variation. When partially and fully cured bisGMA/styrene blends were studied, the breadths of the frequency domains showed opposite trends as the styrene concentration was varied. Thus, the breadth of the transition could not be interpreted as a simple measure of the network heterogeneity but is believed to be related to the distribution of mobilities in the network structure which determine the distribution of relaxation times. Time–temperature superposition yielded shift factors which, when fitted to the WLF equation, indicated that the free volume at the glass transition temperature ( T g) and the free volume expansion coefficient depended on both crosslink density and also the ability of the monomer units to pack into the network.

High‐pressure rheology of eight synthetic lubricants based on phase diagrams

AbstractNew sets of equations have been constructed from the density‐pressure‐temperature and viscosity‐pressure‐temperature relationships to determine the rheology of synthetic lubricants at high pressure. A phase diagram was first plotted for the oils up to a pressure of 1.2 GPa and temperatures from 303 to 353 K using high‐pressure density experimental results and others. For the oils at temperatures of 313, 333, and 353 K, the high‐pressure viscosity experiment was done up to a viscosity of 104 Pa s and up to a pressure of 0.4 GPa. A relationship, based on free volume theory, between pressure and temperature with varying density and viscosity was proposed. It was found that the new equations from these relationships could predict the high‐pressure rheology more closely than those of previous researchers. Moreover, it was shown that the Ehrenfest equation or the gradient of the phase diagram is closely related to the expansion coefficient of free volume.

Melt rheology and structure of silicone resins

Rheological investigation and X-ray analysis of silicone resins have been performed to get a fundamental understanding of the relationship between melt rheology and structure. Rheological properties of the melts of silicone resins were characterized by dynamic shear measurements. Samples were a series of silicone resins having different side groups, such as methyl, phenyl, methylphenyl, and propylphenyl. A time-temperature superposition based on the WLF rule was successfully applicable. The free volume fraction at the glass transition temperature and the free volume expansion coefficient were estimated from the C1 and C2 values of the WLF-equation. The loss modulus G′′ was found to be proportional to the angular frequency in a double-logarithmic plot over a wide frequency range. However, the storage modulus G′ exhibited a bending in a intermediate frequency region for all silicone resins. The shape of the G′ curve is unexpected from the results of gel permeation chromatography (GPC) and differential scanning calorimeter (DSC), which demonstrate that the silicone resins are amorphous polymers of relatively low molecular weight. To get more insight into the rheological properties of the silicone resins which indicate a heterogeneous structure, X-ray analysis was carried out. The X-ray measurement displayed two peaks, one broad peak around 4.5 A of d-spacing which corresponds to a random amorphous structure, and the other higher intensity peak from 8.5 A to 12 A. This peak strongly depends on the size of organic side groups. From the rheological characterization and the X-ray analysis, it can be concluded that the silicone resins consist of two components; one of them shows a random amorphous and the other a regular structure even in the molten stage.

Relationship between molecular structure and zero-shear viscosity of polymers

The relationship between molecular structure and zero-shear viscosity of polymers was studied. In this study we propose a new equation, which is based on Berry and Fox's equation. This new equation is constructed from some molecular parameters, such as mean square length and average molecular weight of statistical skeletal unit, characteristic ratio, entanglement molecular weight, glass-transition temperature, free volume fraction at glass-transition temperature, and thermal expansion coefficient of free volume. It is proposed that some of these molecular parameters could be predicted by group contribution methods, except for the free volume parameters. We also propose new empirical relations between free volume parameters and molecular structures of polymers, which make it possible for free volume parameters to be obtained from molecular structure. Using these relationships, it is possible that the zero-shear viscosity and its temperature dependence are obtainable from the molecular structure of polymers. We applied this formula to some polymers, including both amorphous and semicrystalline polymers. Comparison between the measured and calculated zero-shear viscosity showed quite good agreement. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1609–1618, 2001

Modeling the principal amorphous halo in quiescent melts of polyethylene and ethylene copolymers using wide-angle X-ray scattering and its implications

Wide-angle X-ray scattering (WAXS) studies of the melts of polyethylenes indicate that the low-angle amorphous halo (LAH) retains sensible information regarding the liquid state, which can be used to model the amorphous fraction in the semicrystalline state. The LAH was found to consist of a temperature-independent and a temperature-dependent region. A linear relationship was observed for the temperature dependence of the LAH peak value below 135 °C in branched ethylene copolymers, and was found dependent on comonomer concentration. When combined with group contribution theory, a simple model of average intermolecular separation determined from the WAXS-LAH peak value is consistent with free volume considerations, both with respect to predicting T g (∞) and the free volume expansion coefficient. The polyethylene, without branches, shows a different behavior in the region 131-160 °C. A semiquantitative method is proposed to model the scattering from the LAH for use in the phase analysis of the copolymers through the separation of the temperature-dependent (intermolecular) and temperature-independent (intramolecular) fractions.

Viscoelastic and Dielectric Relaxation Behavior of Substituted Poly(p-phenylenes)

The thermal, dynamic mechanical, and dielectric relaxation behavior of poly(p-phenylenes) substituted with benzoyl and 4-phenoxybenzoyl groups and of a copolymer of benzoyl-1,4-phenylene and 1,3-phenylene were investigated. These amorphous materials were found to have flexural moduli higher than any other reported unoriented thermoplastic. Benzoyl-substituted poly(p-phenylene) which possesses the greatest rigid-rod character also displayed the highest modulus. The temperature dependence of viscoelastic and dielectric relaxation times were well described by the Williams-Landel-Ferry and Vogel-Fulcher equations, respectively. The temperature sensitivity or «fragility» of viscoelastic shift factors α T and apparent dielectric relaxation times τ * was greatest for the copolymer. The glass transition temperature of these polymers varied as a function of the total free volume. The polymer containing the 4-phenoxybenzoyl side group exhibited the lowest T g due to internal plasticization, but the highest Vogel energy attributable to the large intramolecular bond rotational barrier associated with the bulky pendant group. The shape of frequency plane dielectric relaxation spectra of the substituted polyphenylenes could be accurately fitted to the Kolrausch-Williams-Watts (KWW) correlation function. The KWW stretched exponential term β displayed a very weak dependence on molecular structure and remained constant within experimental error for each material over the temperature range studied. Since β should be proportional to the degree of intermolecular coupling, the structural variation in «fragility», albeit small, of the substituted polyphenylenes may not be fully described by the coupling model for relaxation. Assuming the macroscopic expansion coefficient is proportional to the free volume expansion coefficient, the temperature dependence of τ * and α T may be explained more simply from free volume considerations. The 4-phenoxybenzoyl-substituted polymer displayed the highest expansion coefficient and largest total free volume, but the benzoyl-1,4-phenylene/1,3-phenylene copolymer exhibited the largest relative change in free volume with temperature, which explained the greater «fragility» of the copolymer compared to either homopolymer

Molecular analysis of the viscoelastic properties of epoxy networks as deduced from the study of model systems

Various model systems were built from a diepoxide and different amines (or mixtures of amines) in order to investigate the dependence of molecular motions on the cross-link density and network chain flexibility. Dynamic mechanical experiments were performed over the frequency range 0.01–85 Hz at temperatures covering the β-relaxation process and the glass transition region. The glass transition temperature, T g, markedly depends on both the cross-link density and chain flexibility. The frequency-temperature superposition principle (WLF equation) was used to determine the viscoelastic coefficients C 1 g and C 2 g. C 1 g, related to the free volume fraction available at T g, mostly depends on cross-link density, whereas the product C 1 g C 1 g, related to the free volume expansion coefficient, is a function of both the chain flexibility and the cross-link density. Motions responsible for the β-process begin to develop at the same temperature, whatever the cross-link density and chain flexibility may be. However, an increase in cross-link density is accompanied by an increase in amplitude and a broadening towards high temperatures of both damping, tan δ, and loss modulus, E′. This effect is responsible for the decrease of the elastic modulus, E′, at room temperature with increasing cross-link density.

Viscoelastic response of model epoxy networks in the glass transition region

AbstractSix epoxy networks with various structures built up from a diepoxy prepolymer, DGEBA, and three different diamines or mixtures of a monoamine and a diamine were studied by dynamic mechanical analysis in the glass transition region. The systems were designed in order to investigate the dependence of glass transition Tg on both crosslink density and network chain flexibility. The time (frequency)—temperature superposition principle (WLF equation) was used to determine the viscoelastic coefficients Cg1 and C which are related to some free volume characteristics on the molecular scale. Cg1, related to the free volume fraction available at Tg depends mainly on crosslink density, even though the product Cg1C, related to the free volume expansion coefficient, is dependent on both chain flexibility and crosslink density. Thus, viscoelastic properties determined over large temperature and frequency ranges are shown to yield more precise information on epoxy network structure than the simple analysis of glass transition temperature.

Molecular weight dependence of some rheological and thermal properties of perfluoropolyethers

The glass transition temperatures and the viscosities (over a very large temperature range) have been measured as a function of molecular weight, for two different series of perfluoropolyethers. The results have been interpreted according to well-known free-volume models. The Williams-Landel and Ferry equation describes the viscosity data with values of f g (the fractional free volume at T g ) close to 0.04 and with values of α f (the free-volume expansion coefficient) close to 7 × 10 −4° C −1. The critical molecular weight, M c , is approximately 5000–6000 for perfluoropolyethers from hexafluoropropene and 7800 for perfluoropolyethers from tetrafluoroethene.

Viscosity and relaxation times temperature behaviour above the glass transition in some glassy polymers

We have performed mechanical and dielectric dynamic measurements above the glass-transition temperature range of two glassy-polymers: Poly(Hydroxyether of Bisphenol-A) and Poly(Carbonate of Bisphenol-A). From these measurements the temperature dependence of mechanical and dielectric mean relaxation times has been calculated. Results obtained have been compared with the viscosity temperature behaviour of the same polymers, which has been reported elsewhere. Both, relaxation times and viscosity temperature behaviour can well be described by Doolittle functional forms, exp{1/[αf(T-To)]}, with the same values of To but different values of the apparent free-volume expansion coefficient, αf. This difference in the experimental behaviour has been addresed in the framework of the free-volume model ideas. In this context, the different values of αf obtained from viscosity and relaxation times temperature behaviour can be understood assuming different values of critical volume controlling the molecular motions associated to viscosity and relaxation processes. Similar conclusions have also been obtained by means of a fine revision of the viscosity and relaxation times data of another two glassy-polymers: Poly(Arylate) and Poly(Sulfone of Bisphenol-A), reported previously.

Stress relaxation of oriented nylon 6 fibers

The stress relaxation of oriented and dried nylon 6 fibers was measured at temperatures ranging from room temperature to 423 K using a simple tensile method. After the reduction for temperature and crystallinity by Nagamatsu et al.'s procedure,2 the relaxation modulus curves were shifted along a time axis, and master curves were obtained. The Arrhenius plots of shift factor was represented by two straight lines having a break point, the temperature of which was in approximate agreement with those of the breakdown of hydrogen bonds in the amorphous region. The relationship between the breakdown of hydrogen bonds and the values of apparent activation energies for relaxation is discussed. It was found that the effects of hydrogen bonds on the relaxation behavior are similar to those of crosslinking points in crosslinked polymers. Moreover, from the constants C1 and C2 of the WLF equation, the free volume fraction at Tg(fg) and the expansion coefficient of free volume at Tg(fg) were estimated to be 0.013 and 4.2 × 10−5, respectively. Finally, through the use of the usual primary approximation method, the relaxation time spectra were obtained from the relaxation master curves. The obtained spectra showed two distributions of wedge type and box type. When the draw ratio increases, the height of distribution of the box type becomes higher and its position shifts to a longer time side, whereas those of the wedge type remain virtually unchanged.

Some viscoelastic properties of ABS polymer

AbstractThe discrete relaxation spectrum of an ABS (acrylonitrile–butadiene–styrene) polymer at 190°C. was calculated by using results from tensile relaxation moduli and the principle of reduced variables. The shift factor was found to conform well to the WLF equation, and the free volume fraction at Tg was calculated to be 0.026 in good agreement with the universal value. The values of the thermal expansion coefficient of free volume were calculated to be 9.8 X 10‐4 deg.−1 and 7.0 × 10−4 deg.−1, respectively, from the WLF coefficients and from dilatometric results. The width of the entanglement plateau of the relaxation spectrum was observed to be a factor of approximately 2 larger than that calculated from molecular weights between entanglement couplings determined either from rubber elasticity theory or from an assumed molecular model which discounts the presence of the butadiene in the ABS system. By using Pao's theory, flow curves at 190°C. were calculated both from the discrete relaxation spectrum and from the dynamic modulus. These curves were essentially identical. However, the stress values of these curves were found to be about a decade higher than those experimentally determined from capillary flow measurements. Nevertheless, the shapes of the curves are in good agreement, and an explanation is suggested for existing discrepancies. Flow instability, processing variables, and residual strains are discussed in light of the flow curves and the calculated recoverable shear strains.

Volume–temperature relation of epoxy resin–acid anhydride mixtures with different degrees of crosslinking

AbstractVolume‐temperature relations of six kinds of epoxy resin‐acid anhydride composite and different curing times are discussed on the basis of free‐volume and occupied‐volume concepts. The specific volume Va at a fixed temperature above Tg decreases linearly with increasing Tg, but the specific volume Vb below Tg increases linearly. The specific volume Vg at Tg increases linearly with increasing Tg. The relation between Tg and log crosslinkage is linear except in the final stage of the curing process. The slope B of the Vg‐Tg relation is obtained from the iso‐free‐volume theory of glass‐transition phenomena as B = Voαb(1 – ΔVo/Vf · Vf/Vo · αa – αb/αb), where Vo is the occupied volume, Vf the free volume, αa – αb the thermal expansion coefficient of free volume, αb the thermal expansion coefficient of occupied volume; Vo is the sum of the two components Vo and Vo, where Vo is the occupied volume in the strict sense and ve is the empty volume into which polymer chains cannot flow. The equation predicts qualitatively the observed value of B.

Non-Linear Flow and its Temperature Dependence of Paving Straight Asphalt

In order to investigate non-Newtonian flow of asphalt and its temperature dependence, viscosity and variation of specific volume with temperature were measured with a short tube type viscometer and dilatometer respectively.The results were as follows; 1) Calculated thermal expansion coefficient of free volume was quite similar to the difference of measured macroscopic expansion coefficient at the glass transition point. 2) The upper limit of the glass transition region, the width of its region and the standard temperature were -9°C, 22.5°C and 41°C respectively. 3) Extruding pressure to give the same rate of shear was in proportion with the ratio of the length to radius of short tubes. 4) The time-temperature superposition principle applied to the nonlinear flow and the experimental values of the shift factor aT0=(φ'T0/φ'T)σ checked well with the WLF equation. 5) Apparent flow curves checked with the de Waele-Ostwald's equation φ'=Kσn. The flow curve and the viscosity-rate of shear curve at arbitrary temperature were represented by the equations φaT0=(3+n) K0σn/4 and η(φ)={(3+n)K0/4}-1/nγ(1/n)-1aT01/n respectively. 6) Another shift factor was defined as bT=(σT/σT0)φ and the relation bT={η(T)/η(T0)}φ=aT01/n was observed. 7) Temperature susceptibility was expressed as equation dη(φ)/dT=(1/n){η(γ)/aT0}daT0/dT etc. 8) The apparent activation energy of flow observed at the stated values of rate of shear was represented by the equation ΔHa, φ=Rd ln bT/d(1/T) and the one at the stated values of shear stress coincided with the apparent activation energy for viscoelastic relaxation time.

Viscoelastic Properties of Glucose Glass near Its Transition Temperature

Storage (G′) and loss (G″) shear moduli of supercooled glucose have been measured at thirteen temperatures from 27.4 to 41.1°C in the frequency range from 0.3 to 1.8 cps. Shear creep has been measured at four temperatures from 41.1 to 47.6°C. The temperature dependence of the storage moduli and the creep compliance was described by reducing the time and frequency scales with shift factors calculated from the WLF equation, the constants corresponding to a fractional free volume of 0.026 at 41.1°C and a free volume expansion coefficient of 3.6×10−4 deg−1. The loss moduli plotted against reduced frequency did not give a single composite curve, however. Conversion of the dynamic measurements to creep compliance by approximation methods provided the latter function over ten decades of logarithmic time except for a gap of three decades in the middle of the range. At long times, the creep was indistinguishable from viscous flow; the viscosity at 41.1°C was 1.82×1010 poise. At short times, the limiting creep compliance appeared to be 0.32×10−16 cm2/dyne, and there was an additional time-dependent compliance of at least this magnitude with a broad distribution of retardation times. The relaxation and retardation spectra were calculated for this region.

Effect of crosslinking density on the viscoelastic properties of unsaturated polyesters

AbstractViscoelastic properties of unsaturated polyesters were investigated in the glass‐rubber transition region in relation to the temperature dependence of specific volume. Polyesters which are homologous with respect to crosslinking density were prepared by using mixtures of succinic and fumaric acid as the dibasic acid component. The temperature dependence of the specific volume was determined by refractive index measurement, the specific refractivity being assumed to be independent of temperature. The temperature dispersion of dynamic viscoelasticity was measured at a constant frequency. Results are summarized as follows. Specific volume and glass temperature are linearly related to the logarithm of crosslinking density. The thermal expansion coefficient and steepness of viscoelastic dispersion decrease with increasing crosslinking density. Fractional free volume and expansion coefficient of free volume, both of which were calculated by WLF equation, are in good agreement with the temperature dependence of specific volume. The results indicate that the effect of crosslinking is largely attributable to the change in amount and distribution of free volume in polymer networks.

The mechanical properties of films. III. Dilato‐metric observations of multiple transitions

AbstractEvaluation of dilatometric data on cast films by the normal graphical method indicated the presence of multiple transitions. An alternative method is developed in which the coefficients of the polynomial which approximates to the given set of point data have been calculated using a least‐squares criterion and a programme written for a Ferranti Mercury computer. The peak values of the second derivative of this curve corroborated the transition temperatures obtained by the graphical method. Preliminary experiments suggested that the highest transition is associated with oxidative ageing conditions; this transition is absent in specimens prepared in non‐oxidising atmospheres.The free volume expansion coefficient αF approximates very closely to the Williams, Landel & Ferry predicted value of 4.8 × 10−4 c.c./°c/c.c. provided the contributions from all transitions are included. Experimental values less than this have invariably led to the detection of a further transition or transitions when the temperature range has been extended.

Viscosity of amorphous polymers

AbstractAn amorphous polymer is characterized as a homogeneous array of N identical, n‐center polymer segments which can be described in terms of four molecular constants. A mechanism for viscous flow (or self diffusion) is visualized as a positional exchange of two adjacent polymer segments in a hole the size of a segment‐pair. The activation energy for the viscous flow is the energy required to overcome the cohesive bonding to neighboring segments plus the work of compression required to form a hole of molecular dimensions. The effect of chain entanglement is estimated by using the theories of Bueche. An equation is derived for the viscosity in terms of a characteristic temperature, T0, a free volume expansion coefficient, β′, a fractional free volume for the glassy state fg0, an average segmental length, 2λn, and the four measurable molecular constants. This equation describes the lower limiting viscosity of polyisobutylene, polystyrene, and poly(vinyl acetate) over a viscosity range of up to a factor of 108 and for the whole temperature range of available data. It is shown that the characteristic temperature, T0, is close to the measured glass transition temperature, the free volume expansion coefficient, β′, is about 0.4 of the thermal expansion coefficient of the rubber and the fractional free volume fg0, is 0.1 for all the polymers. The size of the jumping unit in viscous flow is calculated to be about 0.1–0.3 of the size of an equivalent freely orienting segment.

Dynamic mechanical properties and creep of poly- n-dodecyl methacrylate

The real ( J′) and imaginary ( J″) components of the complex compliance have been measured between 24 and 3600 cycles/sec. in the temperature range from −40° to 45° C. for a fractionated poly- n-dodecyl methacrylate with molecular weight 0.95 × 10 6. The creep compliance, J( t), was measured from −30° to 30°C. The method of reduced variables gave superposed curves for J′ and J″ against frequency and for J( t) against time except for an anomaly at and below −28°, interpreted as due to crystallization of the side groups. The temperature dependence of relaxation times followed the WLF form with α f (thermal expansion coefficient of free volume) = 3.7 × 10 −4 deg. −1. The retardation and relaxation spectra, combining dynamic and creep data, show a rudimentary plateau region from which the average spacing between entanglement points is estimated to correspond to a degree of polymerization of 650. The logarithm of the monomeric friction coefficient (in dynes-sec./cm.) is −6.57 extrapolated to 100°C. The dependence of friction coefficient on side group length in the methacrylate series, using revised data including now those for the dodecyl polymer, can be rather satisfactorily attributed to differences in free volume by either the treatment of Dannhauser, Child, and Ferry or that of Fujita and Kishimoto.