解初值问题y″=g(x，y)的含参数块方法

1引言对于二阶常微分方程的初值问题y″=g(x,y),y(x_0)=y_0,y′(x_0)=y_0′,x_0(?)x(?)T(1)的数值解法的研究引起人们的广泛兴趣．对于直接积分(1),自从1976年J．D．Lambert和I．A．Waston提出二阶P-稳定方法和1978年G．Dahlquist证明P-稳定常系数线性多步方法的最高相容阶不超过2的重要结论以来,截止目前,已积累了许多高于2阶的P-稳定方法．例如,修正的Numerov方法,混合法(特殊形式RK的方法),多导法,Obrechkoff方法,显式RKN方法,单隐方法和对角隐式RKN方法等(顺便指出,文献[5,16]中所说的高阶方法的相容阶均不超过4)．所有这些方法,有些相     

Functionalized poly(oxanorbornene)‐block‐copolymers: Preparation via ROMP/click‐methodology

Block copolymers on basis of poly(oxanorbornenes) bearing functional moieties in their side‐chains are prepared via a combination of ROMP‐methods and 1,3‐dipolar‐“click”‐reactions. Starting from N‐substituted‐ω‐bromoalkyl‐oxanorbornenes and alkyl‐/perfluoroalkyl‐oxanorbornenes, block copolymers with molecular weights up to 25,000 g mol^?1 were generated. Subsequent nucleophilic exchange‐reactions yielded the block‐copolymers functionalized with ω‐azidoalkyl‐moieties in one block. The 1,3‐azide/alkine‐“click” reactions with a variety of terminal alkynes in the presence of a catalyst system consisting of tetrakis(acetonitrile)hexafluorophosphate copper(I) and tris(1‐benzyl‐5‐methyl‐1H‐ [1,2,3]triazol‐4‐ylmethyl)‐amine furnished the substituted block copolymers in high yields, as proven by NMR‐spectroscopy. The resulting polymers were investigated via temperature‐dependent SAXS‐methods, revealing their microphase separated structure as well as their temperature‐dependent behavior. The presented method offers the generation of a large set of different block‐copolymers from only a small set of starting materials because of the high versatility of the “click” reaction, thus enabling a simple and complete functionalization after the initial polymerization reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 485–499, 2007     

Facile syntheses of surface-functionalized micelles and shell cross-linked nanoparticles

Block copolymer micelles and shell cross-linked nanoparticles (SCKs) presenting Click-reactive functional groups on their surfaces were prepared using two separate synthetic strategies, each employing functionalized initiators for the controlled radical polymerization of acrylate and styrenic monomers to afford amphiphilic block copolymers bearing an alkynyl or azido group at the α-terminus. The first route for the synthesis of the azide-functionalized nanostructures was achieved via sequential nitroxide-mediated radical polymerization (NMP) of tert-butyl acrylate and styrene, originating from a benzylic chloride-functionalized initiator, followed by deprotection of the acrylic acids, supramolecular assembly of the block copolymer in water and conversion of the benzylic chloride to a benzylic azide. In contrast, the second strategy utilized an alkynyl-functionalized reversible addition fragmentation transfer (RAFT) agent directly for the RAFT-based sequential polymerization of tetrahydropyran acrylate and styrene, followed by selective cleavage of the tetrahydropyran esters to give the α-alkynyl-functionalized block copolymers. These Click-functionalized polymers, with the functionality located at the hydrophilic polymer termini, were then self-assembled using a mixed-micelle methodology to afford surface-functionalized “Clickable” micelles in aqueous solutions. The optimum degree of incorporation of the Click-functionalized polymers was investigated and determined to be ca. 25%, which allowed for the synthesis of well-defined surface-functionalized nanoparticles after cross-linking selectively throughout the shell layer using established amidation chemistry. Functionalization of the chain ends was shown to be an efficient process under standard Click conditions and the resulting functional groups revealed a more “solution-like” environment when compared to the functional group randomly inserted into the hydrophilic shell layer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5203–5217, 2006     

Nitroxide‐mediated radical polymerization of 2‐(dimethylamino)ethyl acrylate and its sequential block copolymerization with styrene and N‐butyl acrylate

Nitroxide‐mediated radical polymerization (NMRP) of 2‐(dimethylamino)ethyl acrylate (DMAEA) was carried out at 100–120 °C, initiated by MONAMS, an alkoxyamine based on N‐tert‐butyl‐N‐(1‐diethyl phosphono‐2,2‐dimethylpropyl)nitroxide, SG1. Controlled polymerization can be achieved by the addition of free SG1 (the initial molar ratio of SG1 to MONAMS ranged from 0.06 to 0.12), giving a linear first‐order kinetic plot up to 55–70% conversion depending on the reaction conditions. The molecular weights show a near linear increase with conversion; however, they deviate to some extent with theoretical values. SG1‐mediated polymerization of DMAEA at 112 °C is also controlled in organic solvents (N,N‐dimethylformide, anisole, xylene). Polymerization rate increases with increasing solvent polarity. Chain transfer to polymer produces ～1 mol % branches in bulk and 1.2–1.9 mol % in organic solvents, typical of those for acrylates. From poly(styrene) (pS) and poly(n‐butyl acrylate) (pBA) macroinitiators, amphiphilic di‐ and triblock copolymers p(S‐b‐DMAEA), p(DMAEA‐b‐S‐b‐DMAEA), p(BA‐b‐DMAEA), and p(DMAEA‐b‐BA‐b‐DMAEA) were synthesized via NMRP at 110 °C. Polymers were characterized by GPC, NMR, surface tension measurements, and DSC. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 414–426, 2006     

Synthesis and application as polymer electrolyte of hyperbranched polyether made by cationic ring‐opening polymerization of 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxymethyl}‐3′‐methyl‐oxetane

A novel cyclic ether monomer 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxy‐methyl}‐3′‐methyloxetane (HEMO) was prepared from the reaction of 3‐hydroxymethyl‐3′‐methyloxetane tosylate with triethylene glycol. The corresponding hyperbranched polyether (PHEMO) was synthesized using BF₃·Et₂O as initiator through cationic ring‐opening polymerization. The evidence from ¹H and ¹³C NMR analyses revealed that the hyperbranched structure is constructed by the competition between two chain propagation mechanisms, i.e. active chain end and activated monomer mechanism. The terminal structure of PHEMO with a cyclic fragment was definitely detected by MALDI‐TOF measurement. A DSC test implied that the resulting polyether has excellent segment motion performance potentially beneficial for the ion transport of polymer electrolytes. Moreover, a TGA assay showed that this hyperbranched polymer possesses high thermostability as compared to its liquid counterpart. The ion conductivity was measured to reach 5.6 × 10^?5 S/cm at room temperature and 6.3 × 10^?4 S/cm at 80 °C after doped with LiTFSI at a ratio of Li:O = 0.05, presenting the promise to meet the practical requirement of lithium ion batteries for polymer electrolytes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3650–3665, 2006     

Synthesis and micellization of amphiphilic poly(sebacic anhydride)–poly(ethylene glycol)–poly(sebacic anhydride) block copolymers

Amphiphilic biodegradable block copolymers [poly(sebacic anhydride)–poly(ethylene glycol)–poly(sebacic anhydride)] were synthesized by the melt polycondensation of poly(ethylene glycol) and sebacic anhydride prepolymers. The chemical structure, crystalline nature, and phase behavior of the resulting copolymers were characterized with ¹H NMR, Fourier transform infrared, gel permeation chromatography, and differential scanning calorimetry. Microphase separation of the copolymers occurred, and the crystallinity of the poly(sebacic anhydride) (PSA) blocks diminished when the sebacic anhydride unit content in the copolymer was only 21.6%. ¹H NMR spectra carried out in CDCl₃ and D₂O were used to demonstrate the existence of hydrophobic PSA domains as the core of the micelle. In aqueous media, the copolymers formed micelles after precipitation from water‐miscible solvents. The effects on the micelle sizes due to the micelle preparation conditions, such as the organic phase, dropping rate of the polymer organic solution into the aqueous phase, and copolymer concentrations in the organic phase, were studied. There was an increase in the micelle size as the molecular weight of the PSA block was increased. The diameters of the copolymer micelles were also found to increase as the concentration of the copolymer dissolved in the organic phase was increased, and the dependence of the micelle diameters on the concentration of the copolymer varied with the copolymer composition. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1271–1278, 2006     

Synthesis and characterization of multiblock copolymers composed of poly(5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one) outer blocks and poly(L‐lactide) inner blocks

Ethylene glycol (EG) initiated, hydroxyl‐telechelic poly(L ‐lactide) (PLLA) was employed as a macroinitiator in the presence of a stannous octoate catalyst in the ring‐opening polymerization of 5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one (MBC) with the goal of creating A–B–A‐type block copolymers having polycarbonate outer blocks and a polyester center block. Because of transesterification reactions involving the PLLA block, multiblock copolymers of the A–(B–A)_n–B–A type were actually obtained, where A is poly(5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one), B is PLLA, and n is greater than 0. ¹H and ¹³C NMR spectroscopy of the product copolymers yielded evidence of the multiblock structure and provided the lactide sequence length. For a PLLA macroinitiator with a number‐average molecular weight of 2500 g/mol, the product block copolymer had an n value of 0.8 and an average lactide sequence length (consecutive C₆H₈O₄ units uninterrupted by either an EG or MBC unit) of 6.1. For a PLLA macroinitiator with a number‐average molecular weight of 14,400 g/mol, n was 18, and the average lactide sequence length was 5.0. Additional evidence of the block copolymer architecture was revealed through the retention of PLLA crystallinity as measured by differential scanning calorimetry and wide‐angle X‐ray diffraction. Multiblock copolymers with PLLA crystallinity could be achieved only with isolated PLLA macroinitiators; sequential addition of MBC to high‐conversion L ‐lactide polymerizations resulted in excessive randomization, presumably because of residual L ‐lactide monomer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6817–6835, 2006     

Synthesis of A2B star block copolymers from a heterotrifunctional initiator

We described the obtention of A₂B star block copolymers through the use of a new heterotrifunctional initiator. That way, well‐defined (PCL)₂‐arm‐PtBuMA and (PCL)₂‐arm‐PS star block copolymers have been synthesized from a heterotrifunctional initiator bearing two hydroxyl groups able to initiate ROP of CL (with AlEt₃ or Sn(Oct)₂ as coinitiator) and a bromide function able to initiate ATRP of tBuMA or styrene. Firstly, we have proceeded using a sequential process (two‐steps), leading to an intermediate macroinitiator. Secondly, attempt to polymerize these two monomers in a simultaneous process (one‐step), that is directly from the mixture of monomers, initiator, coinitiators, and solvent, has been realized and has shown that some interferences between the two polymerizations occurred, leading to an inhibition of ATRP when Sn(Oct)₂ was used and an unexpected increase in control when AlEt₃ was used as catalyst for the ROP (obtention of well‐defined (PCL)₂‐arm‐PtBuMA with pdi of 1.18). © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1796–1806, 2006     

Double‐hydrophilic block copolymer for encapsulation and two‐way pH change‐induced release of metalloporphyrins

A double hydrophilic block copolymer composed of poly(acrylic acid) (PAA) and poly(4‐vinyl pyridine) (P4VP) was obtained through hydrolysis of diblock copolymer of poly(tert‐butyl acrylate) (PtBA) and P4VP synthesized using atom transfer radical polymerization. Water‐soluble micelles with PAA core and P4VP corona were observed at low (acidic) pH, while micelles with P4VP core and PAA corona were formed at high (basic) pH. Two metalloporphyrins, zinc tetraphenylporphyrin (ZnTPP) and cobalt tetraphenylporphyrin (CoTPP), were used as model compounds to investigate the encapsulation of hydrophobic molecules by both types of micelles. UV–vis spectroscopic measurements indicate that micelles with P4VP core are able to entrap more ZnTPP and CoTPP as a result of the axial coordination between the transition metals and the pyridine groups. The study found that metalloporphyrins encapsulated by the micelles with PAA core could be released on pH increase, while those entrapped by the micelles with P4VP core could be released on pH decrease. This behavior originates from the two‐way pH change‐induced disruption of PAA‐b‐P4VP micelles. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1734–1744, 2006