Crystalline forms of cellulose in the silver tree fern Cyathea dealbata

Solid-state ¹³C NMR spectroscopy was used to characterize fibrous material cut from the midrib of a fern frond. Signals associated with cellulose crystallites were separated from those associated with the lignin--hemicellulosic matrix by exploiting differences in proton rotating-frame relaxation time constants. Heights of signals at 90.2 and 88.5 ppm, assigned to C-4 in cellulose I_α and I_β, indicated similar proportions of the two crystalline forms. This observation conflicts with a suggestion that plant celluloses can be grouped into the two categories of I_α-rich and I_β-rich. This revised version was published online in August 2006 with corrections to the Cover Date.     

Structural investigation of cellulose Iα and Iβ by 2D RFDR NMR spectroscopy: determination of sequence of magnetically inequivalent d-glucose units along cellulose chain

In our previous studies of the crystal structure of native cellulose (cellulose I) by solid-state two-dimensional (2D) ¹³C–¹³C INADEQUATE, it was revealed that cellulose I_α contains two kinds of β-d-glucose residues (A and A′) in the unit cell and that cellulose I_β contains another two kinds of residues (B and B′). In the present study, the sequence of residues A and A′ along the same chains in cellulose I_α and that of residues B and B′ in I_β were investigated by 2D ¹³C–¹³C rotor-synchronized radiofrequency-driven recoupling (RFDR) experiments using, respectively, uniformly ¹³C₆-labeled (U−¹³C₆) bacterial cellulose and the same [U−¹³C₆] cellulose sample after thermal treatment at 260 °C. The RFDR spectra recorded with a short mixing time (1.0 ms) showed dipolar-coupled ¹³C spin pairs of only the neighboring carbon of the both phases, while those recorded with a longer mixing time (3.0–15 ms) provided correlations between weakly coupled ¹³C spin pairs as well as strongly coupled ¹³C spin pairs such as neighboring carbon nuclei. In the RFDR spectrum of the [U−¹³C₆] cellulose recorded with a mixing time of 15 ms, the inter-residue ¹³C–¹³C correlation between C4 of residue A and C2 of residue A′ and that between C3 of residue A and C4 of residue A′ were clearly observed. In the case of cellulose I_β, however, inter-residue ¹³C–¹³C correlations between residues B and B′ could not be detected in the series of RFDR spectra recorded with different mixing times of annealed [U−¹³C₆] cellulose. From these findings, that cellulose I_α was revealed to have the –A–A′– repeating units along the cellulose chain. For cellulose I_β, it was revealed that the respective residues B and B′ are composed of independent chains (–B–B– and –B′–B′– repeating units) and that there are no –B–B′– repeating units in the chain.     

Lateral thermal expansion of cellulose Iβ and IIII polymorphs

Measurements of the thermal expansion coefficients (TECs) of cellulose crystals in the lateral direction are reported. Oriented films of highly crystalline cellulose I_β and III_I were prepared and then investigated with X‐ray diffraction at specific temperatures from room temperature to 250 °C during the heating process. Cellulose I_β underwent a transition into the high‐temperature phase with the temperature increasing above 220–230 °C; cellulose III_I was transformed into cellulose I_β when the sample was heated above 200 °C. Therefore, the TECs of I_β and III_I below 200 °C were measured. For cellulose I_β, the TEC of the a axis increased linearly from room temperature at α_a = 4.3 × 10^?5 °C^?1 to 200 °C at α_a = 17.0 × 10^?5 °C^?1, but the TEC of the b axis was constant at α_b = 0.5 × 10^?5 °C^?1. Like cellulose I_β, cellulose III_I also showed an anisotropic thermal expansion in the lateral direction. The TECs of the a and b axes were α_a = 7.6 × 10^?5 °C^?1 and α_b = 0.8 × 10^?5 °C^?1. The anisotropic thermal expansion behaviors in the lateral direction for I_β and III_I were closely related to the intermolecular hydrogen‐bonding systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1095–1102, 2002     

In situ crystallization of bacterial cellulose II. Influences of different polymeric additives on the formation of celluloses Iα and Iβ at the early stage of incubation

Effects of polymeric additives with different degrees of polymerization (DP) or substitution (DS) on the crystallization of celluloses I and I have been examined at an early stage of the incubation of Acetobactor xylinum by using newly developed FT-IR spectroscopy. It was found that the mass fraction of cellulose I is greatly decreased with increasing concentrations of carboxymethyl cellulose sodium salt (CMC) or xyloglucan (XG) in the incubation medium. Such a decrease in the mass fraction of cellulose I, which corresponds to the enhanced crystallization of cellulose I, is more prominent for CMC or XG with lower DPs, but the additives with too low DPs are not so effective probably due to higher solubility and the lower adhesion on the surface of microfibrils. Moreover, the mass fractions of celluloses I and I are highly correlated with the crystallite size of microfibrils, indicating that I is crystallized in larger-size microfibrils while I is produced in smaller-size microfibrils. On the basis of these experimental results, the mechanism of the crystallization of celluloses I and I is discussed in the Acetobactor xylinum system.     

Thermal characterization of bacterial cellulose–phosphate composite membranes

Cellulose–phosphate composite membranes have been prepared from bacterial cellulose membranes (BC) and sodium polyphosphate solution. The structure and thermal behavior of the new composites were evaluated by X-ray diffraction (XRD), ³¹P-nuclear magnetic resonance (NMR), scanning electron microscopy (SEM), differential scanning calorimetry (DSC), thermogravimetry (TG) and thermomechanical analysis (TMA). From XRD analyses the Iα and Iβ cellulose crystalline phases were identified together with crystalline sodium phosphate that covers the cellulose microfibrils as revealed by SEM. ³¹P NMR spectra show peaks assigned to Q⁰ and Q¹ phosphate structures to be compared to the Q² units that characterize the precursor polyphosphate. Glass transition temperature, T _g, obtained from TMA curves and thermal stability obtained from TG and DSC measurements, were observed to be dependent on the phosphate content.     

In Situ Crystallization of Bacterial Cellulose III. Influences of Different Polymeric Additives on the Formation of Microfibrils as Revealed by Transmission Electron Microscopy

Effects of polymer additives on the formation of microfibrils of bacterial cellulose have been examined by transmission electron microscopy. Among additives with different degrees of polymerization (DP) or substitution (DS), carboxymethyl cellulose sodium salt (CMC) with DP = 80 and DS = 0.57 is the most effective in producing separate, smaller-size microfibrils. By increasing the concentration of this CMC from 0.1 to 1.5%, the percentage of microfibrils measuring 3–7 nm wide is increased and levels off at around 1.0%. Other polymer additives such as xyloglucan are less effective than CMC in producing microfibrils with smaller sizes and the resulting microfibrils still tend to aggregate. The number of charged substituents and the molecular weight seem to be important factors in the production of highly separate smaller-size microfibrils. The reduction in average microfibril size is well correlated to the decrease in mass fraction of cellulose I in bacterial cellulose crystals. On the basis of these results, the mechanism of the crystallization of celluloses I and I is discussed. The effect of colony types, smooth and rough, on the formation of microfibrils in the presence of CMC is also described.     

In Situ crystallization of bacterial cellulose I. Influences of polymeric additives,stirring and temperature on the formation celluloses I α and I β as revealed by cross polarization/magic angle spinning (CP/MAS)13C NMR spectroscopy

To obtain further information about the formation of cellulose I and I, cross polarization/magic angle spinning (CP/MAS)¹³C NMR spectroscopy was used to study the effects of polymeric additives, stirring and culture temperature on the I When xyloglucan (XG) or carboxymethyl cellulose sodium salt (CMC) was added to the incubation medium, the amount of cellulose I decreased markedly, from a normal level of 64% to as low as 30%, with the most additive giving the lowest levels of I. Moreover, stirring causes mixtures containing even small amounts of XG to have a large effect. These results suggest that CMC or XG interferes with the aggregation of fibrillar units into the normal ribbon assemblies. It may be that there is a strain associated with this aggregation that results in the higher-energy I form. Thus, cellulose I may grow preferentially when the strain caused by aggregation is not present. Lower temperatures (36–10 °C) gave an increase in I (from 56 to 72%).     

Localization of Iα and Iβ phases in algal cellulose revealed by acid treatments

Highly crystalline I-rich type Cladophora cellulose, which had been kept in never-dried condition, was treated in 60wt% sulfuric acid at 100°C, for 1–48h. The cellulose microcrystals thus obtained were analysed by X-ray diffractometry, FT-IR, and transmission electron microscopy. The I component was found to be more degraded than the I component. The cellulose I/I ratios of the samples acid-treated for 0, 24, and 48 h were about 8:2, 6:4, and 4:6, respectively. After the acid treatment, the microcrystals became narrower in width, and very sharp at their ends. These results indicate that the I phase is mostly located at the surface of the microcrystals, which is morphologically more susceptible to the acid treatment.     

The cellulose system in viscin from mistletoe berries

The cellulose system of the viscous fibrous cellulosic polysaccharide (viscan) in the viscin tissue of the European mistletoe, Viscum album L., was analyzed by chemical and physicochemical techniques including sugar analysis, optical and transmission electron microscopy, X-ray and electron diffraction together with solid state CP/MAS ¹³C-NMR spectroscopy. The results confirmed that in the elongated thin viscin cells, the cellulose microfibrils (having a diameter of around 3 nm) were tightly coiled with their axes perpendicular to the long axis of the cell. Upon stretching these cells became deformed by more than a hundred fold. In such a deformation, the cellulose microfibrils became unwound to be perfectly aligned along the stretching direction. Based on solid-state CP/MAS ¹³C-NMR spectroscopic analysis of the viscin tissue, it was found that its cellulose consisted of I and I polymorphs in the ratio 1:1.     

Simulation of X-ray diffractograms relevant to the purported polymorphs cellulose IV<Subscript>I</Subscript> and IV<Subscript>II</Subscript>

Diffractograms were simulated for model nanocrystals of cellulose I_β, using numerical summation of radiation scattered from all carbon and oxygen atoms in the nanocrystal. Diffractogram peaks were sometimes displaced by a few degrees from positions calculated by the Bragg equation, as predicted in a published study based on a different mathematical approach. Simulated diffractograms showed 2 or 3 peaks, depending on the cross-sectional size and shape of the model nanocrystal. Some of the 2-peak diffractograms resembled published results for the purported polymorph cellulose IV_I, or for cell-wall cellulose, supporting suggestions that cellulose IV_I is simply cellulose I fragmented into nanocrystals with relatively small cross-sectional dimensions. A published diffractogram for cellulose IV_II could not be simulated with acceptable precision, suggesting that this polymorph might have a crystal structure distinctly different from that of cellulose I_β.     

The Thermal Expansion of Wood Cellulose Crystals

We have investigated tension wood cellulose obtained from Populus maximowiczii using X-ray diffraction at temperatures from room temperature to 250 °C. Three equatorial and one meridional d-spacings showed a gradual linear increase with increasing temperature. For temperatures above 180 °C, however, the equatorial d-spacing increased dramatically. Thus, the linear and volume thermal expansion coefficients (TECs) below 180 °C were determined from the d-spacings. The linear TECs of the a-, b-, and c-axes were: α _a = 13.6 × 10⁻⁵ °C⁻¹, α _b = −3.0× 10⁻⁵ °C⁻¹, and α _c =0.6× 10⁻⁵ °C⁻¹, respectively, and the volume TEC was β = 11.1× 10⁻⁵ °C⁻¹. The anisotropic thermal expansion in the three coordinate directions was closely related to the crystal structure of the wood cellulose, and it governed the macroscopic thermal behavior of solid wood.     

Analysis of vitamin E in food and phytopharmaceutical preparations by HPLC and HPLC-APCI-MS-MS

Summary The analysis of α, β, γ, δ-tocopherols, trienols, α-tocopheryl acetate and nicotinate (vitamin E) in complex matrices was carried out using a new liquid chromatographic (HPLC) method giving better separation efficiency, selectivity and sensitivity than that described in the literature. The use of normal-phase (NP)-HPLC on silica gel with issoctane-diisopropylether-1,4-dioxane as optimized mobilepphase yielded higher resolution than conventional reversed-phase (RP)-HPLC using methanol mobile phase. Identification of peaks was by UV-absorbance at 295 nm, diode array, or fluorescence detection (λ _ex = 295 nm,λ _ex = 330 nm). The latter was found to be more selective and ten times more sensitive than UV-absorbance detection. A quadrupole, ion-trap mass spectrometer with an atmospheric-pressure ionization (APCl) interface was used to detect vitamin E constituents in the femtomole range. With collision-induced dissociation (CID) in the ion source, which gave characteristic fragmentation, the identity of the investigated compounds could be confirmed. Plots of peak area versus amount injected allowed quantitation of α, β, γ, δ-tocopherols and-trienols, α-tocopheryl acetate and nicotinate in real samples such as peanut, almond, spinach, spelt grain bran, latex and tablets. The method described offers fast identification and quantitation of vitamin E constituents of complex biological origin. Dedicated to Professor Dr. Heinz Engelhardt on the occasion of his 65^th birthday.     

Synthesis, crystal structure and forming mechanism of two novel copper (II) α-methacrylate complexes with benzimidazole

Two copper (II) α-Methacrylate complexes with benzimidazole, Cu[CH₂ = C(CH₃)-COO]₂ (C₃H₆N₂)₂(1) and Cu₂[CH₂ = C(CH₁)-COO]₂(C₃H₆N₂)₂(2), have been prepared and characterized by elemental analyses, IR and electronic reflectance spectroscopies. ’The single crystal X-ray diffraction study of the two complexes shows that complex 1 has a square planar configuration, while complex 2 has a binuclear cage structure. The crystal structural analyses show that both complexes 1 and 2 are monoclinic. with space group p2₁/c,a = 0.924 16(8) nm,b = 1.233 02(13) nm,c = 0.989 1(3) nm,β = 91.912 (13),D _c = 1.386 g/cm³,Z=2,R = 0.033 9 for the former; anda = 0.905 7(2) nm,b = 2.252 1(5) nm,c = 1.623 5(4) nm,β = 90.11 (2),D _c = 1.411 g/cm³,Z = 4,R = 0.056 8, Cu-Cu = 0.266 21 nm for tin latter. Different structural types of complexes 1 and 2 were produced simultaneously in the reaction of copper (II) α-methacrylate with benzimidazole in methanol solution. ’The forming mechanism of the complexes has been summanzed. Project supported by the national natural Science Foundation of China (Grant No. 29831010) and the Foundation of the State Key Laboratory of Coordination Chemistry of Nanjing university.     

Crystal structures of seven-coordinate (NH4)2[MnII(edta)(H2O)]·3H2O, (NH4)2[MnII(cydta)(H2O)]·4H2O and K2[MNII(hdtpa)]·3.5H2O complexes

The title compounds, (NH₄)₂[Mn^II(edta)(H₂O)]·3H₂O (H₄edta = ethylenediamine-N,N,N′,N′-tetraacetic acid), (NH₄)₂[Mn^II(cydta)(H₂O)]·4H₂O (H₄cydta = trans-1,2-cyclohexanediamine-N,N,N′,N′-tetraacetic acid) and K₂[Mn^II(Hdtpa)]·3.5H₂O (H₅dtpa = diethylenetriamine-N,N,N′,N″,N″-pentaacetic acid), were prepared; their compositions and structures were determined by elemental analysis and single-crystal X-ray diffraction technique. In these three complexes, the Mn²⁺ ions are all seven-coordinated and have a pseudomonocapped trigonal prismatic configuration. All the three complexes crystallize in triclinic system in P-1 space group. Crystal data: (NH₄)₂[Mn^II(edta)(H₂O)]·3H₂O complex, a = 8.774(3) ?, b = 9.007(3) ?, c = 13.483(4) ?, α = 80.095(4)°, β = 80.708(4)°, γ = 68.770(4)°, V = 972.6(5) ?³, Z = 2, D _c = 1.541 g/cm³, μ = 0.745 mm⁻¹, R = 0.033 and wR = 0.099 for 3406 observed reflections with I ≥ 2σ(I); (NH₄)₂[Mn^II(cydta)(H₂O)]·4H₂O complex, a = 8.9720(18) ?, b = 9.4380(19) ?, c = 14.931(3) ?, α = 76.99(3)°, β = 83.27(3)°, γ = 75.62(3)°, V = 1190.8(4)?³, Z = 2, D _c = 1.426 g/cm³, μ = 0.625 mm⁻¹, R = 0.061 and wR = 0.197 for 3240 observed reflections with I ≥ 2σ(I); K₂[Mn^II(Hdtpa)]·3.5H₂O complex, a = 8.672(3) ?, b = 9.059(3) ?, c = 15.074(6) ?, α = 95.813(6)°, β = 96.665(6)°, γ = 99.212(6)°, V = 1152.4(7) ?³, Z = 2, D _c = 1.687 g/cm³, μ = 1.006 mm⁻¹, R = 0.037 and wR = 0.090 for 4654 observed reflections with I ≥ 2σ(I). Original Russian Text Copyright ? 2008 by X. F. Wang, J. Gao, J. Wang, Zh. H. Zhang, Y. F. Wang, L. J. Chen, W. Sun, and X. D. Zhang The text was submitted by the authors in English. Zhurnal Strukturnoi Khimii, Vol. 49, No. 4, pp. 753–759, July–August, 2008.     

Characterization of tension and normally lignified wood cellulose inPopulus maximowiczii

We have investigated unlignified tension wood and normally lignified wood celluloses inPopulus maximowiczii with particular reference to the composition of two crystalline phases I/I (triclinic/ monoclinic). Four independent techniques, which enable us to detect the two phases, CP/MAS¹³C NMR, Fourier transform infrared microscopy, selected-area electron diffraction, and X-ray diffraction were applied. Because of the low crystallinity of wood celluloses, particularly in the case of celluloses in the lignified cell wall, no single method was decisive enough to be able to determine the composition of the two phases as one can with highly crystalline materials. The I dominant structure (monoclinic crystal type) was, however, preferred for both tension and normal wood celluloses.     

Mixed-ligand complex compounds [Pb(Phen)×{(iso-C4H9)2PS2}2] and [Pb(2,2′-Bipy){(iso-C4H9)2PS2}2] and formation of supramolecular assemblies in their crystal structures

Mixed-ligand complex compounds [Pb(Phen)(i-Bu₂PS₂)]₂ (I) and [Pb(2,2′-Bipy)(i-Bu₂PS₂)]₂ (II) were synthesized. Their structures were determined from X-ray diffraction data (X8 APEX diffractometer, MoK _α radiation, 6392 _Fhkl , R = 0.0233 for I and 3937 F _hkl , R = 0.0252 for II). Crystals I are triclinic: a = 10.2662(3) Å, b = 12.3037(2) Å, c = 14.8444(4) Å; α = 92.054(1)°, β = 103.473(1)°, γ = 105.561(1)°, V = 1746.89(8) ų, Z = 2, ρ_calc = 1.532 g/cm³, space group P . Crystals II are monoclinic: a = 9.3462(3) Å, b = 26.3310(12) Å, c = 28.5345(13) Å; β = 96.436(1)°, V = 6977.9(5) ų, Z = 8, ρ_calc = 1.489 g/cm³, space group P2₁/n. The structures are built from mononuclear molecules. In both structures, the intermolecular contacts between the Pb and S atoms of the neighboring mononuclear molecules form supramolecular assemblies involving two molecules. The environment of the Pb atoms in the assemblies is a pentagonal bipyramid, N₂S₄₊₁. The assemblies are joined into ribbons by π-π interactions of the Phen rings in I and C…C short contacts between the pyridine rings in II. Original Russian Text Copyright ? 2008 by R. F. Klevtsova, E. A. Sankova, T. E. Kokina, L. A. Glinskaya, and S. V. Larionov __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 49, No. 1, pp. 123–131, January–February, 2008.     

Synthesis of diblock copolymers with cellulose derivatives. 3. Cellulose derivatives carrying a single pyrene group at the reducing-end and fluorescent studies of their self-assembly systems in aqueous NaOH solutions

Novel cellobiose and cellulose (DP _n =ca. 30) derivatives, N-(1-pyrenebutyloyl)-4-O-(β-d-glucopyranosyl)-β-d-glucopyranosylamine (6), N-(15-(1-pyrenebutyloylamino)-pentadecanoyl)-4-O-(β-d-glucopyranosyl)-β-d-glucopyranosylamine (7), N-(1-pyrenebutyloyl)-β-cellulosylamine (13), N-(15-(1-pyrenebutyloylamino)-pentadecanoyl)-β-cellulosylamine (14) carrying a pyrene group as a single fluorescent probe at the reducing end, were prepared in order to investigate their self-assembly systems in solutions. The relative intensity of the excimer emission at ca. 480 nm due to dimerized pyrenes (intensity I _E) to the monomer emission at ca. 380 nm due to isolated pyrene (intensity I _M), i.e., I _E/I _M, was monitored in various solutions. In water/dimethyl sulfoxide (DMSO) mixed solvent (0–98%, v/v), the ratio I _E/I _M remained low (0.04) for compound 6 over the range of water concentrations, indicating that pyrenes at C-1 position of compound 6 were diffused. On the other hand, the ratio I _E/I _M increased (0.04–4.96) for compound 7 with the increase in water concentration, indicating that pyrenes at C-1 position were associated. In aqueous NaOH solutions (4.4–17.5%, w/w), compound 14 showed a large increase in the ratio I _E/I _M (0.84–8.14) with the increase in NaOH concentration, compared to compound 13 (0.06–0.41). It was found that the association of hydrophobic groups at the reducing-end of cellulose could be controlled by the hydrophilic–hydrophobic balance of compounds and the solvent polarity.     

Crystal structure of [Mn(1,10-C12H8N2)3](B6H7)2

A new compound [MN^II(Phen)₃]²⁺(B₆H₇)₂⁻ is synthesized; its crystal structure is studied by XRD at 100 K. Crystallographic data: C₃₆H₃₈B₁₂N₆Mn, M = 739.39, triclinic symmetry, space group P , unit cell parameters: a = 10.3131(3) ?, b = 13.4839(4) ?, c = 15.1132(4) ?; α = 97.696(1)°, β = 108.324(1)°, γ = 102.211(1)°; V = 1903.9(1) ?³, Z = 2, d _calc = 1.290 g/cm³. The structure is solved by direct and Fourier methods and refined by full-matrix LSM in the anisotropic (isotropic for hydrogen atoms) approximation to the final factor R ₁ = 0.036 for 10169 I _hkl ≥ 2σ _I (Bruker-Nonius X8 APEX CCD diffractometer, λMoK _α). The structure contains two crystallographically different anions. Original Russian Text Copyright ? 2009 by T. M. Polyanskaya, M. K. Drozdova, V. V. Volkov, and K. G. Myakishev __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 50, No. 2, pp. 381–385, March–April, 2009.     

Thermal behavior of isotactic polypropylene in different content of β-nucleating agent

The effects of non-isothermal and isothermal crystallization on the formation of α- and β-phase in isotactic polypropylene (iPP) with different content of β-nucleating agent are investigated by differential scanning calorimetry (DSC). On non-isothermal crystallization, the content of β-phase and regularity of its crystals are depended on both cooling rate and the content of β-nucleating agent. The faster cooling rate is, the lower of melting peak temperature (T_mp) and crystallization peak temperature (T_cp) of α- and β-phase are. The enthalpy of fusion (∆H) of β-phase increases with cooling rate in a certain range for the sample with 0.1 wt% β-nucleating agent (G₁) and decreases for that with 0.3 wt% β-nucleating agent (G₃). On isothermal crystallization, the enthalpy of fusion of β-phase in G₁ is higher than in G₃ which is related to the efficiency of nucleation in different concentration of nucleating center in two samples.     

An electroconductivity study on degree of counterion binding or dissociation of a-sulfonatomyristic acid methyl ester micelles in water as a function of temperature

 For a sodium salt of α-sulfonatomyristic acid methyl ester (14SFNa), one of the α-SFMe series surfactants, the differential conductivity (∂κ/∂C) _T , _P vs. square root of concentration (√C) was employed in order to determine not only CMC but also the limiting molar conductance (Λ⁰) and the molar conductance of micellar species (Λ^M). Based on the data of the degree of counterion binding to micelles (β) determined previously at different temperatures ranging 15–50 °C at every 5 °C, the experimental values of the degree of dissociation (ionization) of a micelle (α_EX) were calculated by regarding as α_EX=1−β. The ratio Λ^M/Λ⁰ corresponding to the ratio of slopes below and above CMC in the curve of specific conductivity (κ) vs. concentration (C), which has been often assumed to be the degree of ionization of micelles (α), was compared with the present α_EX. However, the ratio Λ^M/Λ⁰ (=α) was found to have a correlationship with α_EX (=1−β) as α_EX≈0.40×(Λ^M/Λ⁰), or strictly, α_EX=0.40 (Λ^M/Λ⁰)+0.08, indicating that the simple ratio of the slopes below and above CMC in κ vs. C curve is not true for α_EX=1−β. On the other hand, the method proposed by Evans gave a value closer to α_EX compared with the simple ratio. Received: 17 September 1996 Accepted: 8 April 1997