Derivation of a general mixed interpolation formula

A general procedure is developed to derive a mixed interpolation formula for approximating any (n + 1) times differentiable function ?(x), for x&isin;[0,nh], by a function ss="imgLazyJSB inlineImage" height="20" width="40" alt=" title=" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-0377042796001458-si2.gif">script>style="vertical-align:bottom" width="40" alt=" title=" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-0377042796001458-si2.gif">script> of the type ss="imgLazyJSB inlineImage" height="24" width="227" alt=" title=" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-0377042796001458-si3.gif">script>style="vertical-align:bottom" width="227" alt=" title=" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-0377042796001458-si3.gif">script>, the interpolating points being the ones given by x<sub>jsub> = jh,(h>0),j = 0,1,…,n, where U<sub>1sub>(kx) and U<sub>2sub>(kx) are the two linearly independent solutions of a suitable second order Ordinary Differential Equation (ODE) and k > 0 is an appropriately chosen parameter. The results for the particular case when U<sub>1sub>(kx) and U<sub>2sub>(kx) represent the trigonometric functions follow easily. An analysis of the error is also discussed and specific numerical examples are included for the sake of comparison with the known interpolation formulae. Tables showing the comparison of the maximum errors occuring in the use of the various interpolation formulae has also been presented for some specially chosen functions.     

Description of the turbidity measurements near the phase transition temperature of poly(N-isopropyl acrylamide) copolymers: the effect of pH, concentration, hydrophilic and hydrophobic content on the turbidity

Absorbance values between 300 and 800 nm of aqueous solutions of poly(N-isopropyl acrylamide-co-itaconic acid-9.80), poly(N-isopropyl acrylamide-co-itaconic acid-52.05) and poly(N-isopropyl acrylamide)s containing Tegomer H-Si 2111 end groups and/or blocks were measured using a Shimadzu 160-A UV-visible spectrometer. Turbidities obtained from these absorbance values were used to interpret the macromolecular phase transition from a hydrophilic to a hydrophobic structure of the polymers. The effects of comonomer type and content, concentration of the solutions, pH and temperature on the coil-globule transition were discussed in terms of turbidity form factor, β related to size and shapes of particles and calculated by using the simplified form of Debye equation.The results presented in this work show that the presence of Tegomer H-Si 2111 (Si containing end groups and/or blocks) or high amount of itaconic acid (IA) in the chains prevent a collapse transition from hydrated extended coils to hydrophobic globules, which aggregate and form a separate phase (β<2). Furthermore, it was observed that in the case of concentrated solutions intermolecular hydrophobic interactions between isopropyl groups overcame the repulsive forces resulting from the ionized carboxylic acid groups of IA or surface active nature of Si containing hydrophobic groups (β>2). This stage of the transition corresponds to macroscopic phase separation after an intramolecular process.     

纳米级NiTiO3粉体的合成

以Ｈ２ＴｉＯ３，Ｈ２Ｏ２及ＮｉＣｌ２为主要原料，用化学共沉淀法制备了纳米级ＮｉＴｉＯ３。确定了反应物Ｈ２ＴｉＯ３，Ｈ２Ｏ２，ＮＨ３的最佳摩尔比为１：８：２，用不同的退火温度和退火时间对样品处理得到相应粒径的纳米级粉体。     

Low detection limit spectrophotometry

An efficient, more sensitive and accurate spectrophotometric process is possible and can be used to obtain qualitative or quantitative results for analytes at limiting concentrations lower than usual. Transmission measurements (incident light power, P<sub>0sub>, or transmitted, P) are performed with a fluorescence spectrometer. One cell only is used to measure standards or unknown solutions, placed between the standard holder cuvette and the emission monochromator of the instrument. The source of the radiant power (P<sub>0sub>) is not the xenon lamp but the fluorescence or scattered radiation from the holder cuvette filled with an appropriate solution. The analyte concentration is found from a calibration graph, based upon Beer&rsquo;s law or the approximate formula P<sub>0sub>&minus;P=2.303P<sub>0sub>εbc, which is valid for dilute solutions. Determination of iron in a reference material, using 1,10-phenanthroline as the chromogenic reagent, was chosen as an example to demonstrate the suitability of the proposed method and clarify several important statistical questions. Also discussed is why and to what extent molecular fluorescence methods are more sensitive than molecular absorption methods.     

Acetylenic/cyanoacetylenic complexes: simulation of the Titan’s atmosphere chemistry

The structures and energies of the 1:1 acetylene/cyanoacetylene, acetylene/dicyanoacetylene and cyanoacetylene/dicyanoacetylene complexes in solid argon matrices have been investigated using FT-IR spectroscopy and ab initio calculations, at the B3LYP/6-31G** level of theory. For the three complexes, predicted frequency shifts for the L shaped structures, characterized by a hydrogen bond between the nitrogen of the cyano group and the acetylenic proton, were found to be in good agreement with those experimental. Only in the case of acetylene/cyanoacetylene complex, we obtained a second minimum with a T shaped structure characterized by an interaction between the proton of cyanoacetylene and the Π system of acetylene. It appears clearly that HC<sub>3sub>N acts as an electrophile or as a nucleophile in these complexes.     

STABILITY OF POLY（N,N＇-METHYLENEBISACRYLAMIDE-co-4-VINYLPYRIDINE） MICROGEL DISPERSION AND ADJUSTMENT OF THE HYDROPHOBICITY IN THE MICROGELS

In the UV-Vis spectra of pure light-scattering systems, there is an exponential relationship between absorbance and wavelength （A = Kλ^-n）. Here, the exponent n is named as flocculation-coagulation parameter. In the present paper, the effects of different additives on the stability of poly（N,N＇-methylenebisacrylamide-co-4-vinylpyridine） （poly（Bis-co-4-VP）） microgel dispersion were studied in detail via this parameter. The results showed that the stability of the dispersion mainly comes from the ionization of pyridine groups, making the microgel positively charged on its surface. This was confirmed by the measurement of Zeta potential and the result of conductometric titration. The result of fluorescence analysis indicated that the hydrophobicity in the microgels is enhanced with the increase in total 4-VP unit content.     

The Legacy of Raimond Castaing

 In April 1998 Raimond Castaing left the world of electrons, of ions and others particles, his wife and his family, his numerous students, for the world of stars. Raimond Castaing (Fig. 1) had a very strong personality. No one will forget their first meeting with him and all his students remember how brilliant he was as a teacher. A lot of anecdotes about his famous hot temper are still circulating among his friends and his former students. But in this paper, we would like to evoke Castaing’s memory through his achievements in Instrumental Physics, from the time of his doctoral thesis to later developments with his students, which were all centred on the imaging of the microstructures of materials and their quantitative chemical analysis.     

Equations describing lamellar structure parameters and melting points of polyethylene-<Emphasis Type="Italic">co</Emphasis>-(butene/octene)s

Time- and temperature-dependent SAXS-experiments were used to determine the effect of octene and butene co-units on the lamellar structure and the melting properties of polyethylene. As expected, melting points decrease with increasing co-unit content, but crystal thicknesses are not affected and depend on the crystallization temperature only. Results can be cast into some simple equations which describe the dependence:ss="OrderedList">

Synthesis and properties of novel poly(amide-imide)s containing pendent diphenylamino groups

A new dicarboxylic acid, 2,4-bis(N-trimellitoyl)triphenylamine, bearing two preformed imide rings was synthesized from the condensation of 2,4-diaminotriphenylamine and trimellitic anhydride at 1:2 molar ratio. A series of poly(amide-imide)s (PAIs) with inherent viscosities of 0.38-0.66 dl/g were prepared by triphenyl phosphite-activated polycondensation from the diimide-dicarboxylic acid with various aromatic diamines. All the resulting PAIs were readily soluble in a variety of organic solvents and formed strong and tough films via solution casting. These PAIs have useful levels of thermal stability associated with moderately high glass-transition temperatures (259-314 °C) and 10% weight loss temperatures in excess of 530 °C in nitrogen or in air.