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Miscibility in blends of liquid crystalline copolyester and semicrystalline poly(ethylene-2,6-naphthalene dicarboxylate)

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Miscibility in blends of liquid crystalline copolyester and semicrystalline

poly(ethylene-2,6-naphthalene dicarboxylate)

Jia-Chong Ho, Tai-Ching Lin, Kung-Hwa Wei*

Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu 30049, Taiwan, ROC Received 7 December 1999; received in revised form 18 February 2000; accepted 29 February 2000

Abstract

The miscibility in blends of random liquid crystalline copoly(oxybenzoate-ethylene terephthalate) at a molar ratio of 60:40 (P64) and semicrystalline poly(ethylene-2,6-naphthalene dicarboxylate) (PEN) were investigated with differential scanning calorimetry, wide angle X-ray diffraction and polarized optical micrography. It was found that P64 and PEN were partially miscible as evidenced from the appearance of a single glass transition temperature for each blend at different compositions. Furthermore, the Flory–Huggins interaction parameter,x12, for P64 and PEN was determined to be21.13 through the melting point depression analysis, indicating miscibility in blends of P64 and PEN at the melt state. The coherence lengths of PEN in the presence of a small amount of P64, around 3%, were larger than that in pure PEN, implying the regularity of PEN crystals in the blends with low P64 content being more perfect than that of the pure PEN.q 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Liquid crystalline copolyester; Miscibility; Semicrystalline copolyester

1. Introduction

Thermotropic liquid crystalline polymers (TLCPs) exhi-bit low melt viscosity and high modulus in the oriented direction in the solid form. Blending TLCPs with amor-phous or crystalline polymers to form in-situ organic poly-mer composites appeared to be very attractive because of advantages in lowering the viscosity of amorphous or crys-talline polymers during processing and in reinforcing the final mechanical properties of the matrix polymer [1–4]. However, liquid crystalline polymer chains are very stiff, and the enthalpy of mixing a rigid-rod polymer with a flex-ible-chain polymer was mostly positive; thus the entropy gained in the mixing was usually too small to compensate for the enthalpy gained. This generally led to phase-sepa-rated systems. To our knowledge, there were only several cases of miscibility in liquid crystalline polymer blends reported. They are blends of copoly(oxybenzoate-ethylene terephthalate) (POB–PET)/polycarbonate (PC) [5–7], POB–PET/poly(ether imide) (PEI) [8], POB–PET/poly (butylene terephthalate) (PBT) [9], POB–PET/poly(hexa-methylene terephthalate) (PHMT) [10], POB–PET/poly (ethylene terephthalate) (PET) [11,12] and POB–PET/poly-amide 6 [13]. The miscibility in the cases of POB–PET/PC, POB–PET/PBT and POB–PET/PHMT were found to

increase with the extent of transesterification between POB–PET and PC, PBT or PHMT.

Poly(ethylene-2,6-naphthalene dicarboxylate) (PEN) is a new aromatic polyester that differs from poly(ethylene terephthalate) (PET) in the double aromatic rings of the naphthalate group instead of a single one present in PET. The naphthalene moiety in PEN provides stiffness to the linear polymer backbone. The glass transition temperature (Tg), the crystallization temperature (Tc) and the melting

temperature (Tm) were 120, 190 and 2608C, respectively.

The oxygen permeability of PEN is approximately one-quarter to one-fifth of that of PET. PEN can be a good candidate for hot-fill and high barrier packaging applica-tions [14–16]. There are two known crystal modificaapplica-tions of PEN. The first one was thea-form crystal, and the unit cell of thea-form crystal was a triclinic unit cell with the unit-cell parameters aˆ 0:651 nm; b ˆ 0:575 nm; c ˆ 1:32 nm; aˆ 81:338; bˆ 1448; gˆ 1008 as determined by Mencik [17]. The density of the a-form is 1.407 g cm23, with one chain passing through each unit cell of thea-form. The naphthalene planes are nearly paral-lel to the… 110† plane. The second one was the b-form crys-tal. Theb-form is also a triclinic unit cell with the unit-cell parameters [18] of aˆ 0:926 nm; b ˆ 1:559 nm; c ˆ 1:273 nm; aˆ 121:68; bˆ 95:578; gˆ 122:528: The density of the b-form is 1.439 g cm23, with four chains passing through each unit cell of the b-form. The chains

0032-3861/00/$ - see front matterq 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 2 - 3 8 6 1 ( 0 0 ) 0 0 3 0 2 - 5

* Corresponding author. Tel.:1886-3-5731871; fax: 1886-3-5724727.

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are not completely extended, and every naphthalene is twisted by 1808. At crystallization temperatures up to 2008C only the a-form crystal of PEN is formed. As the crystallization temperatures increased from 2408C up to melting temperature, the b-crystal of PEN formed mainly [18]. Additionally, the amorphous form can be induced to the a-form of the PEN film with N,N-dimethylformamide and the b-form with dioxane [19].

Copoly(oxybenzoate-ethylene) at a molar ratio 60:40 (P64) is a random liquid crystalline copolyester having Tg,

Tc, and Tmat 59.8, 103.3 and 194.68C, respectively [20,21].

In this study, we would like to investigate the miscibility and the induced crystal size changes in the binary blend of liquid crystalline P64 and semicrystalline PEN by using differential scanning calorimetry, wide angle X-ray diffrac-tion and polarized optical micrography.

2. Experimental

Liquid crystalline POB–PET at a mole ratio of 60:40 was obtained from Unitika Ltd, Japan, and it was termed P64. Poly(ethylene-2,6-naphthalene dicarboxylate) was purchased from Aldrich, and it was termed PEN. The chemical struc-tures of P64 and PEN are shown in Fig. 1. The solution blending of P64 and PEN was carried out by dissolving both polymers in 100 ml of dichloroacetic acid. The concen-tration of the solution containing P64 and PEN was 2% by weight. The weight ratios of P64 to PEN in the solution were 15:85, 30:70, 50:50, 70:30 and 80:20. The polymer solu-tions were then cast onto glass slides and were dried under vacuum at 1008C for 72 h in an oven for removing the solvent. The thermal gravimetric analysis of the dried blends showed no appreciable weight loss up to 3508C, indicating a complete removal of the solvent. The thermal

analysis of the blends was carried out with a DuPont 2910 differential scanning calorimetry (d.s.c.). The d.s.c. samples were heated from 25 to 3208C at a heating rate of 408C/min under nitrogen. Then, the samples were quenched to 258C. The samples were heated again from 0 to 3208C at a heating rate of 208C/min. The d.s.c. curves of the samples were taken during the second heating. The midpoints in glass transitions of the d.s.c. curves were taken as the glass transi-tion temperatures (Tg). The peak temperatures of the melting

endothermic of the annealed blends from d.s.c. were deter-mined as the melting temperatures. In the equilibrium melt-ing temperature measurement, the samples were heated from 25 to 3208C at a heating rate of 408C/min under nitro-gen. Subsequently, the samples were quenched to the crys-tallization temperature, and were maintained at the crystallization temperature for 4 h. For the polarized optical micrography and the wide angle X-ray diffraction analyses, the specimens were heated from room temperature to 3208C, and were maintained at 3208C for 1 min for wiping out the previous thermal history of these samples. The speci-mens were then quenched to 2008C (crystallization tempera-ture) and were annealed at 2008C for 4 h. After the annealing, the samples were quenched in liquid nitrogen again. The birefringence of these samples was obtained using a Carl Zeiss Axiophot microscope equipped with a Mettler FP82HT hot stage. Wide angle X-ray diffraction of these samples were performed with a MAC Science MXT-3 X-ray diffractometer using Cu Ka radiation with a voltage of 50 kV and a current of 200 mA. The diffraction patterns were recorded with a step size of 0.028 from 2uˆ 5 to 358.

3. Results and discussion

The d.s.c. curves of P64/PEN blends at various composi-tions are shown in Fig. 2, and the obtained Tg, Tc, Tm, the

crystallization exothermic enthalpy (DHc) and the melting

endothermic enthalpy (DHm) are given in Table 1. In Fig. 2,

a composition-dependent Tgappeared in each of the d.s.c.

curves of the P64/PEN blends. The Tg of the P64/PEN

blends increased slightly with P64 content in the blends. The Fox equation [22] and the Gordon–Taylor equation [23] were used to predict the glass transition temperatures of the P64/PEN binary blends, and they are given in Eqs. (1) and (2), respectively 1 Tg ˆ w1 Tg1 1 w2 Tg2 ; …1† 1 Tg ˆ w11 kw2 w1Tg11 kw2Tg2 …2†

where Tgiand wi(iˆ 1, 2) are the glass transition tempera-ture and the weight fraction of polymer component i, respectively, and Tgthe glass transition temperature of the

blend. In the Gordon–Taylor equation, the adjustable para-meter k is related to the intensity of the interaction forces

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between the constituents in the blend. The single Tgof the

P64/PEN blends at various compositions agreed well with the predicted values by the Gordon–Taylor equation with kˆ 0.30 as shown in Fig. 3. This indicated a medium inter-action between the amorphous phases of P64 and PEN. In Table 1, the Tcs of P64 and PEN were 103.3 and 194.98C,

respectively, and the TcandDHcdecreased with the

concen-tration of P64 in the P64/PEN blends. In the cases of the 40:60 and the 50:50 P64/PEN blends, there were two crys-tallization peaks in their d.s.c. curves. This indicated that the crystalline phases of the 40:60 and the 50:50 P64/PEN blend were not miscible. The miscibility in crystalline polymer blends can also be studied through the melting depression analysis. The Tms of P64 and PEN were 194.6 and 265.38C,

respectively, and the Tms are 257.5, 246.2, 234.0 and

206.38C for the 15:85, 30:70, 50:50 and 70:30 P64/PEN blends, respectively, as given in Table 1. The equilibrium melting point depression of semicrystalline polymers can be predicted by the Hoffman–Weeks equation from the equili-brium thermodynamics [24,25], as given in the following [26]: T0mˆ Tc g 1 1 2 1 g   T8m …3†

where T0m and T8m are the measured melting temperature and the equilibrium melting temperature, respectively, Tc

the crystallization temperature, g the proportional factor between the initial lamellar thickness, lp, and the final lamel-lar thickness, l

gˆ l=lp: …4†

A number of polymer crystals thicken either isothermally at Tcor upon heating to the melting temperature, the lamellar

thickness at the time of melting, l, may be greater than the initial lamellar thickness, lp. g is generally related to the crystallization temperature, the time and the heating condi-tions up to the melting temperature. Atgˆ 1; the polymers do not exhibit isothermal lamellar thickening. If T0mis equal to Tc, the crystal is an inherently unstable one.g is

deter-mined by the slope of the T0mvs. Tcline, and T8mis obtained as the intersection points between the T0m ˆ Tcline and the T0m vs. Tcline. The Hoffman–Weeks plots of PEN and the

P64/PEN blends are shown in Fig. 4, and the obtainedgand T8m are given in Table 2. In Table 2, the values ofg are found to vary from 1.34 to 1.71 for the pure PEN and the P64/PEN blends. This phenomenon can be interpreted in terms of PEN’s relaxation behavior. Thea-relaxation beha-vior of PEN is similar to that of PEEK, PPS, PET, Nylons and it-PS [27–31], where they did not display a distinctive crystalline a-relaxation in the temperature range investi-gated. PEN, PEEK, PPS, PET, Nylons and it-PS are there-fore not expected to exhibit lamellar thickening under isothermal crystallization condition that resulted in a small

g value. Theg value for the P64/PEN blends being larger than that for pure PEN indicated that the crystal thickening during isothermal crystallization formed a more stable crys-tal of PEN in the P64/PEN blends, and it was similar to that

Table 1

Thermal analysis results of the P64/PEN blends

P64/PEN Tg(8C) Tc(8C) DHc(J/g) Tm(8C) DHm(J/g) 0:100 120.7 194.9 44.5 265.3 46.9 15:85 119.3 169.1 34.6 257.5 44.8 30:70 112.6 166.2 25.8 246.2 32.3 40:60 111.2 144.8, 166.4a 19.7 241.6 28.6 50:50 107.0 139.6, 166.1a 13.5 234.0 20.8 70:30 94.4 125.6 2.8 206.3 11.4 80:20 88.7 113.5 2.1 199.5 8.6 100:0 59.8 103.3 1.6 194.6 3.1 a

40:60 and 50:50 P64/PEN blends exhibit two crystallization peaks.

Fig. 3. The glass transition temperatures of the P64/PEN blends: (B) experi-mental data; (· · ·) predicted by Fox equation; (—) predicted by Gordon– Taylor equation.

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of the PBT/PETG blend [32]. The equilibrium melting point of the pure PEN is 349.58C, and the equilibrium melting point for the 70:30 P64/PEN blend is 279.38C as given in Table 2. The Flory–Huggins interaction parameter in a miscible semicrystalline polymer blend can be determined by the extent of the equilibrium melting point depression through an equation derived by Nishi and Wang [33]

1 T80m 2 1 T8m ˆ 2RV2 DH2V1 lnf2 m2 1 1 m2 2 1 m1   …1 2f2†   2 RV2 DH2V1 x12…1 2f2†2: …5†

The subscripts 1 and 2 denoted the amorphous and the crys-talline components, respectively. In Eq. (5), T8m and T80m are the equilibrium melting points of the pure polymer and the blend, respectively, V the molar volume of the polymer repeating unit,f2the volume fraction of the component in

the blend, DH2 the enthalpy of fusion of the crystalline

polymer, mi(iˆ 1,2) the degree of polymerization, R the universal gas constant, andx12the Flory–Huggins

interac-tion parameter. When m1and m2are very large, Eq. (5) can

be reduced to the following form: 1 T80m 2 1 T8m ˆ RV2 DH2V1 x12…1 2f2†2: …6†

In Eq. (6), the parameters used were V1ˆ 106:29 cm3=mol [34], V2ˆ 182:82 cm3=mol [35], and DH2ˆ 25 kJ=mol [36]. T8mˆ 349:58C was used as the equilibrium melting point of PEN in Eq. (6) for these calculations. Eq. (6) was used to fit the equilibrium melting points of the P64/PEN blends, and the results are shown in Fig. 5. In Fig. 5, the slope of this line was 2…RV2=DH2V1†x12; and the Flory– Huggins interaction parameter for the P64/PEN blends obtained is 21.13. The negative value of x12 indicated

that P64 and PEN were miscible in the melt state.

For the X-ray diffraction study, the P64/PEN blends were treated by first quenching from the melt state and then being annealed at 2008C for 4 h. In Fig. 6, the annealed PEN exhibited three strong diffraction peaks at 2uˆ 15:6; 23.3 and 27.08, respectively, and these peaks are attributed to the (010), (100) and… 110† planes of the a-form crystal of PEN. Moreover, the two weak peaks at 2uˆ 19:4 and 20.38 are

Fig. 4. The Hoffman–Weeks plots for PEN and the P64/PEN blends.

Table 2

The equilibrium melting points and thegof the P64/PEN blends

P64/PEN T8m(8C) g 0:100 349.5 1.34 15:85 336.2 1.38 30:70 326.8 1.39 40:60 307.2 1.50 50:50 294.5 1.56 70:30 279.3 1.71

Fig. 5. The plots for determining the Flory–Huggins interaction parameter from the equilibrium melting point measurements of PEN and the P64/PEN blends.

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caused by the… 1 11† and (020) planes of the b-form of PEN. P64 displayed a broad diffraction peak at 2uˆ 19:68: The portion of the a-form of PEN in the P64/PEN blends decreased with the increasing amount of P64. The positions of the X-ray diffraction peaks of the P64/PEN blends were not shifted as compared to that of pure PEN, indicating that the pure PEN crystal structure remained in the P64/PEN blend. The crystal size of the semicrystalline polymer can be estimated by using the Scherrer equation from the broad-ening of the diffraction peak. The Scherrer equation is given as follows [37]:

thklˆ

Kl bhklcosuhkl

…7†

where thklis the crystal size in the crystallographic directions or defined as the coherence length. K andl are the Scherrer constant and X-ray wavelength and their values are 0.9 and 1.54 A˚ , respectively.bhklis the half-width of the diffraction peak of the Miller indices (hkl) anduhklis the Bragg angle. In order to carry out the calculation, the individual peak caused by the different crystal form of PEN must be resolved first. The X-ray diffraction curves of pure PEN and the 30:70 P64/PEN blend were deconvoluted into five and six components, respectively, by approximating peaks

with Gaussian curves as shown in Fig. 7(a) and (b). Since the crystallization of P64 become dominant when the amount of P64 is more than 50%, we only estimated the crystal sizes of the pure PEN and P64/PEN blends with P64 as the minor components. In Table 3, the coherence lengths t(100), t(010) and t… 110† of the pure PEN were 7.9, 6.6 and

5.8 nm, respectively. For the 3:97 and 6:94 P64/PEN blends, the t(100), t(010)and t… 110†are larger than that of pure PEN. As

the amount of P64 is equal to or larger than 12% in the blend, the coherence lengths decreased with the P64 content, as given in Table 3. From these results, we can conclude that the PEN crystals in the P64/PEN blends with low P64 content appeared to be more regular than that of the pure PEN. This phenomenon is similar to that of the PBT/LCP blend [38].

The polarized micrographs of PEN, P64 and P64/PEN blends are shown in Fig. 8. In Fig. 8(a), the pure P64 exhib-ited strong birefringence. The dark region and the light region represented the amorphous phase and the crystalline phase of PEN, respectively, as shown in Fig. 8(b), and the spherulites in the light region had a mean size about 2mm. In the cases of the 3:97 and 6:94 P64/PEN blends, the sizes of spherulites are 3.5 and 2.5mm, respectively, which are greater than that of pure PEN, as shown in Fig. 8(c) and (d). When the amount of P64 increased to 12%, the size of the spherulite became smaller than that of pure PEN as shown in Fig. 8(e). For the 30:70 P64/PEN blend, the light region actually contained both the birefringence of P64 and the crystalline phase of PEN, as shown in Fig. 8(f). The close coexistence of these two phases revealed that there was no strong phase separation present for P64 and PEN at this composition. When the amount of P64 increased to 50% and then to 70%, the birefringence of P64 became more intensive as shown in Fig. 8(g) and (h).

4. Conclusions

The amorphous phases in blends of random liquid crystal-line copoly(oxybenzoate-ethylene terephthalate) (P64) and semicrystalline poly(ethylene-2,6-naphthalene dicarboxy-late) (PEN) were found to be miscible as evidenced by a

Fig. 7. The deconvolution curves of the X-ray diffraction curve: (a) pure PEN; and (b) the 30:70 P64/PEN blend.

Table 3

The coherence lengths of the P64/PEN blends in the (100), (010) and… 110† planes P64/PEN (100) (010) … 110† b(100)a t(100)(nm) b(010)a t(010)(nm) b… 110†a t… 110†(nm) 0:100 1.05 7.9 1.32 6.6 1.54 5.8 3:97 0.99 8.3 1.11 7.8 1.29 6.9 6:94 1.02 8.1 1.21 7.1 1.40 6.4 12:88 1.22 6.8 1.62 5.3 2.12 4.2 30:70 1.45 5.7 2.4 3.6 2.96 3.0

a The half-width of the diffraction peak of the Miller indices (hkl) in degrees.

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composition-dependent single Tg. The

composition-depen-dent Tgcan be predicted by the Gordon–Taylor equation

with kˆ 0.30. Moreover, the P64/PEN blends were confirmed to be thermodynamically miscible at the melt state by having a Flory–Huggins interaction parameter,

x12, of21.13, through the equilibrium melting-depression

analysis. The coherence length of PEN in the P64/PEN blends was larger than that of pure PEN when a small amount of P64, around 3%, was present, indicating that the regularity of PEN crystals in the blends was more perfect than that of pure PEN.

Acknowledgements

The authors appreciate the financial support provided by the National Science Council through Project NSC88-2216-E-009-008.

References

[1] Kiss G. Polym Engng Sci 1987;27:410.

[2] Kolhi A, Chung N, Weiss RA. Polym Engng Sci 1989;29:573. [3] Brostow W. Polymer 1990;31:979.

[4] Wei KH, Kiss G. Polym Engng Sci 1996;36:713. [5] Wei KH, Hwang WJ, Tyan HL. Polymer 1996;37:2087. [6] Wei KH, Jang HC, Ho JC. Polymer 1997;38:3521. [7] Wei KH, Ho JC. Macromolecules 1997;30:1587. [8] Wei KH, Tyan HL. Polymer 1998;39:2103.

[9] Kimura M, Porter RS. J Polym Sci, Polym Phys Ed 1983;21:367. [10] Laivins GV. Macromolecules 1989;29:3974.

[11] Nakai A, Shiwaku T, Wang W, Hasegawa H, Hashimoto T. Macro-molecules 1996;29:2259.

[12] Nakai A, Wang W, Ogasawa S, Hasegawa H, Hashimoto T. Macro-molecules 1998;31:5391.

[13] Meng YZ, Tjong SC. Polymer 1998;39:99.

[14] Ishiharada M, Hayashi S, Saito S. Polymer 1989;30:349.

[15] Murakami S, Nishikawa Y, Tsuji M, Kawaguchi A, Kohjiya S, Cakmak M. Polymer 1995;36:291.

[16] Zhang H, Ward IM. Macromolecules 1995;28:7622. [17] Mencik Z. Chem Prum 1976;17(2):78.

[18] Zachmann HG, Wiswe D, Gehrke R, Riekel C. Makromol Chem Suppl 1985;12:175.

[19] Kim SJ, Nam JY, Lee YM, Im SS. Polymer 1999;40:5623. [20] Nicely VA, Dougherty JT, Renfro LW. Macromolecules

1987;20:578.

[21] Ho JC, Lin YS, Wei KH. Polymer 1999;40:3843. [22] Fox TG. Bull Am Phys Soc 1956;1:123. [23] Gordon M, Taylor J. J Appl Chem 1952;2:493.

[24] Kimura M, Porter RS. J Polym Sci, Polym Phys Ed 1983;21:367. [25] Xing P, Ai X, Dong L, Feng Z. Macromolecules 1998;31:6898. [26] Hoffman JD, Weeks JJ. J Res Natl Bur Stand 1962;66:13. [27] Boyd R. Polymer 1985;26:323.

[28] Boyd R. Polymer 1985;26:1123.

[29] Marand H, Xu J, Srinivas S. Macromolecules 1998;31:8219. [30] Canadas JC, Diego JA, Mudarra M, Belana J, Diaz-Calleja R, Sanchis

MJ, Jaimes C. Polymer 1999;40:1181.

[31] Aoki Y, Li L, Amari T, Nishimura K, Arashiro Y. Macromolecules 1999;32:1923.

[32] Nabi Saheb D, Jog JP. J Polym Sci, Polym Phys Ed 1999;37:2439. [33] Nishi T, Wang TT. Macromolecules 1975;8:909.

[34] Jung HC, Lee HS, Chun YS, Kim SB, Kim WN. Polym Bull 1998;41:387.

[35] Bicakci S, Cakmak M. Polymer 1998;39:4001.

[36] Cheng SZD, Wunderlich B. Macromolecules 1988;21:789. [37] Cullity BD. Elements of X-ray diffraction. 2nd ed. Reading, MA:

Addison-Wesley, 1978 (p. 102).

[38] Yan H, Xu J, Mai K, Zeng H. Polymer 1999;40:4865.

Fig. 8. The room-temperature birefringence pictures of pure polymers and the P64/PEN blends after annealing at 2008C for 4 h: (a) P64; (b) PEN; (c) 3:97 P64/ PEN; (d) 6:94 P64/PEN; (e) 12:88 P64/PEN; (f) 30:70 P64/PEN; (g) 50:50 P64/PEN; (h) 70:30 P64/PEN.

數據

Fig. 1. The chemical structures of P64 and PEN.
Fig. 2. The d.s.c. curves of the P64/PEN blends at various compositions.
Fig. 4. The Hoffman–Weeks plots for PEN and the P64/PEN blends.
Fig. 7. The deconvolution curves of the X-ray diffraction curve: (a) pure PEN; and (b) the 30:70 P64/PEN blend.
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