Highly Segregated Lamello‐Columnar Mesophase Organizations and Fast Charge Carrier Mobility in New Discotic Donor–Acceptor Triads

Four new donor–acceptor triads (D–A–D) based on discotic and arylene mesogens have been synthesized by using Sonogashira coupling and cyclization reactions. This family of triads consists of two side‐on pending triphenylene mesogens, acting as the electron‐donating groups (D), laterally connected through short lipophilic spacers to a central perylenediimide (PI), benzo[ghi]perylenediimide (BI), or coronenediimide (CI) molecular unit, respectively, playing the role of the electron acceptor (A). All D–A–D triads self‐organize to form a lamello‐columnar oblique mesophase, with a highly segregated donor–acceptor (D–A) heterojunction organization, consequent to efficient molecular self‐sorting. The structure consists in the regular alternation of two disrupted rows of triphenylene columns and a continuous row of diimine species. High‐resolution STM images demonstrate that PI‐TP2 forms stable 2D self‐assembly nanostructures with some various degrees of regularity, whereas the other triads do not self‐organize into ordered architectures. The electron‐transport mobility of CI‐TP2, measured by time‐of‐flight at 200 °C in the mesophase, is one order of magnitude higher than the hole mobility. By means of this specific molecular designing idea, we realized and demonstrated for the first time the so‐called p–n heterojunction at the molecular level in which the electron‐rich triphenylene columns act as the hole transient pathways, and the coronenediimide stacks form the electron‐transport channels.     

Charge Transfer Properties of Organic Semiconductor Molecules of Perylene Derivatives

The charge transfer rates of perylene and its four derivatives were studied at the level of B3LYP/6-31G** by density functional theory. The results showed that the perylene and its four derivatives belonged to the semiconductor molecules, which released energy when electron was injected. Therefore, they were suitable to be used as the electron injection material. The introduction of OH group can improve the electron transfer rate significantly. The formations of intramolecular hydrogen bonds were unfavorable to the hole transfer, but conducive to the electron transfer. The perylene derivatives, 2,5-3,4,5-(trifluorophenyl)ethynyl-8,11-3,4,5-trihydroxyphenyl ethynyl, designed in this article had the hole transfer rate of 1.57 cm2/V·s-1. Therefore, this kind of material will be potential hole transfer material with high transfer efficiency.     

一种新的求非线性方程组的数值延拓法

针对迭代过程中的Jacobi奇异问题,本文提出了一种新的数值延拓法.通过构造双参数同伦算子,采用可控条件和适当选取参数的方式克服Jacobi奇异性,并分析了方法的收敛性.最后,通过数值实验对比,验证了方法的可行性和优越性.特别是具有可调控越过Jacobi奇异(点、线、面)的优势,从而也在某种程度上解决了数值延拓法严重依赖于初值的问题.     

Davey-Stewartson系统粗糙爆破解的极限行为

研究了Davey-Stewartson系统(简记为D-S系统)粗糙爆破解的动力学性质.所谓粗糙爆破解即为正则性为H~s(s1)的爆破解,此时D-S系统粗糙解不再满足能量守恒率.利用I-方法与Profile分解理论,得到了D-S系统粗糙爆破解在H~s(R~2)(其中ss_0,且s_0≤(1+11~(1/2))/5≈0.8633)中的极限行为,包括L~2强极限的不存在性与L~2集中性质以及极限图景.     

苯并䓛盘状液晶: 合成、柱状相和光物理性质

盘状液晶分子由稠环芳核和围绕的多条柔性链构成, 具有独特的自组装有序超分子结构、半导体性质和光学性质. 其可通过溶液或喷墨打印技术加工成为光电子薄膜器件, 具有低成本优势. 通过Suzuki-Miyaura交叉偶联和Scholl氧化环化策略, 合成了一系列新的具有苯并䓛结构的非对称酸酐、羧酸酯、酰亚胺和苯并咪唑稠环衍生物, 并对其液晶性和光物理性质进行了详细研究. 通过偏振光学显微镜(POM), 差示扫描量热法(DSC)和小角度X射线散射(SAXS)测试表明, 这些极性盘状化合物自组装堆积呈六方柱状(Col_hex)液晶相, 其中, 最宽的液晶温度范围达206 ℃. 官能团和共轭体系大小决定了相变温度和液晶范围. 荧光测试结果表明, 化合物溶液中绝对量子产率高达34%, 根据官能团不同, 这些化合物发蓝、绿和红光. 借助密度泛函理论(DFT)计算, 解释了该系列极性盘状液晶分子发光性质的差异. 基于本工作的合成方法, 从萘酸酐原料出发为构建结构多变、性质丰富的π-共轭(杂环)芳烃盘状液晶化合物提供了新途径.     

三唑环修饰的苯并菲二羧酸酯和酰亚胺: 合成、液晶及凝胶性

在盘状液晶分子外围柔性链中引入功能不同的基团, 是设计和合成具有良好液晶性能化合物的常用策略. 本工作从苯并菲2,3-二甲酸和酸酐出发, 通过亲核取代和点击反应, 分别合成了两类三唑环修饰的苯并菲二羧酸酯和苯并菲酰亚胺化合物. 热重分析仪(TGA)测试表明, 新制备的主要中间产物与目标化合物失重为5%时的温度在274~389 ℃之间, 均表现出良好的热稳定性. 我们通过差示扫描量热法(DSC)、偏光显微镜(POM)和变温X射线衍射(XRD)实验对这些化合物的热力学行为和介晶性进行了研究. 除三唑环修饰的酯3a和3b无液晶性外, 主要中间产物(2和5)与三唑环修饰的酰亚胺产物(6a和6b)均有一个六方柱状液晶相. 此外, 制备的以三唑为桥联基团的酰亚胺二聚体10为室温液晶, 具有173 ℃的液晶范围. XRD证实了该二聚体中存在有序度不同的两种柱状液晶相(Col_h1和Col_h2). 另外, 由于三唑环的引入, 三唑环修饰的酯类和酰亚胺两类化合物在某些有机溶剂中都能形成有机凝胶. 其中, 二聚体10在1,2-二氯乙烷和1,4-二氧六环中表现出优异的凝胶能力, 其临界凝胶浓度(CGC)可低至1 mg/mL. 相比之下, 不含三唑环的中间产物2和5则不能形成凝胶, 表明三唑环之间的偶极-偶极作用和液晶刚性核π-π堆积的协同作用对于超分子凝胶的形成起着重要的作用. 因此, 同时表现出液晶和凝胶性质的三唑环修饰的苯并菲2,3-二酰亚胺分子具有成为一种多功能材料的潜在应用价值.     

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.     

MAXIMAL ELEMENTS OF A FAMILY OF GB-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.