Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Free boundary viscous flows at micro and mesolevel during liquid composites moulding process

Numerical simulation aspects, related to low Reynolds number free boundary viscous flows at micro and mesolevel during the resin impregnation stage of the liquid composite moulding process (LCM), are presented in this article. A free boundary program (FBP), developed by the authors, is used to track the movement of the resin front accurately by accounting for the surface tension effects at the boundary. Issues related to the global and local mass conservation (GMC and LMC) are identified and discussed. Unsuitable conditions for LMC and consequently GMC are uncovered at low capillary numbers, and hence a strategy for the numerical simulation of such flows is suggested. FBP encompasses a set of subroutines that are linked to modules in ANSYS. FBP can capture the void formation dynamics based on the analysis developed. We present resin impregnation dynamics in two dimensions. Extension to three dimensions is a subject for further research. Several examples are shown and efficiency of different stabilization techniques are compared. Copyright © 2004 John Wiley & Sons, Ltd.     

Photochemical attachment of polymers on planar surfaces with a covalently anchored monolayer of a novel naphthyl ketone photochemical radical generator

A monolayer of covalently anchored, novel, binaphthyl ketone is used as a surface‐confined photochemical radical generator (PRG) for anchoring a variety of polymers to silicon surfaces. The precursor PRG is synthesized by the application of a facile and novel method for the oxidation of sterically hindered benzylic hydrocarbons to carbonyl compounds. Oxidation was carried out with a stoichiometric amount of potassium peroxydisulfate, in the presence of a catalytic amount of copper sulfate in an acetonitrile/water mixture. The PRG synthesized is characterized by ¹H NMR, UV, and Fourier transform infrared (FTIR). The covalently attached monolayers are characterized by X‐ray photoelectron spectroscopy, ellipsometry, and water contact angle measurements. The method developed is applicable to the preparation of a monolayer of a variety of polymers on a wide range of substrates carrying surface hydroxyl groups. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5413–5423, 2004     

Stereological simulations of asymmetric polymerization in channels of bile acid inclusion compounds: A detailed analysis of the monomer arrangements in the channels

We studied simulations by computer graphics to estimate the steric mechanism of the asymmetric polymerization of prochiral diene monomers in channels of inclusion compounds of steroidal bile acids, such as deoxycholic acid (DCA) and cholic acid. We applied a hierarchization method to interpret the crystal structures of bile acids, clarifying that the chiral host molecules associated to form characteristic 2₁-helical assemblies with uneven surfaces. A detailed analysis of the uneven channels in a close-packing state indicated that there were many possible arrangements of the monomers in the channels. The plausible arrangements in the channel could explain a previous study, which showed that the polymerization in the DCA channel yielded chiral polymers with a predominant configuration from prochiral diene monomers, such as 2-methyl-trans-1,3-pentadiene. On the basis of such simulation studies of the arrangements of guest monomers in the channel, we examined a plausible steric mechanism for asymmetric inclusion polymerization. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4648–4655, 2004     

Viscoelastic behavior of polypropylene/nitrile rubber thermoplastic elastomer blends: Application of Kerner's models for reactively compatibilized and dynamically vulcanized systems

The viscoelastic properties of binary blends of nitrile rubber (NBR) and isotactic polypropylene (PP) of different compositions have been calculated with mean‐field theories developed by Kerner. The phase morphology and geometry have been assumed, and experimental data for the component polymers over a wide temperature range have been used. Hashin's elastic–viscoelastic analogy principle is used in applying Kerner's theory of elastic systems for viscoelastic materials, namely, polymer blends. The two theoretical models used are the discrete particle model (which assumes one component as dispersed inclusions in the matrix of the other) and the polyaggregate model (in which no matrix phase but a cocontinuous structure of the two is postulated). A solution method for the coupled equations of the polyaggregate model, considering Poisson's ratio as a complex parameter, is deduced. The viscoelastic properties are determined in terms of the small‐strain dynamic storage modulus and loss tangent with a Rheovibron DDV viscoelastometer for the blends and the component polymers. Theoretical calculations are compared with the experimental small‐strain dynamic mechanical properties of the blends and their morphological characterizations. Predictions are also compared with the experimental mechanical properties of compatibilized and dynamically cured 70/30 PP/NBR blends. The results computed with the discrete particle model with PP as the matrix compare well with the experimental results for 30/70, 70/30, and 50/50 PP/NBR blends. For 70/30 and 50/50 blends, these predictions are supported by scanning electron microscopy (SEM) investigations. However, for 30/70 blends, the predictions are not in agreement with SEM results, which reveal a cocontinuous blend of the two. Predictions of the discrete particle model are poor with NBR as the matrix for all three volume fractions. A closer agreement of the predicted results for a 70/30 PP/NBR blend and the properties of a 1% maleic anhydride modified PP or 3% phenolic‐modified PP compatibilized 70/30 PP/NBR blend in the lower temperature zone has been observed. This may be explained by improved interfacial adhesion and stable phase morphology. A mixed‐cure dynamically vulcanized system gave a better agreement with the predictions with PP as the matrix than the peroxide, sulfur, and unvulcanized systems. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1417–1432, 2004     

Behavior and surface energies of polybenzoxazines formed by polymerization with argon,oxygen, and hydrogen plasmas

Polybenzoxazine (PBZZ) thin films can be fabricated by the plasma‐polymerization technique with, as the energy source, plasmas of argon, oxygen, or hydrogen atoms and ions. When benzoxazine (BZZ) films are polymerized through the use of high‐energy argon atoms, electronegative oxygen atoms, or excited hydrogen atoms, the PBZZ films that form possess different properties and morphologies in their surfaces. High‐energy argon atoms provide a thermodynamic factor to initiate the ring‐opening polymerization of BZZ and result in the polymer surface having a grid‐like structure. The ring‐opening polymerization of the BZZ film that is initiated by cationic species such as oxygen atoms in plasma, is propagated around nodule structures to form the PBZZ. The excited hydrogen atom plasma initiates both polymerization and decomposition reactions simultaneously in the BZZ film and results in the formation of a porous structure on the PBZZ surface. We evaluated the surface energies of the PBZZ films polymerized by the action of these three plasmas by measuring the contact angles of diiodomethane and water droplets. The surface roughness of the films range from 0.5 to 26 nm, depending on the type of carrier gas and the plasma‐polymerization time. By estimating changes in thickness, we found that the PBZZ film synthesized by the oxygen plasma‐polymerization process undergoes the slowest rate of etching in CF₄ plasma. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4063–4074, 2004     

Control of self‐organized low‐dimensional morphology in poly(styrene‐b‐4vinylpyridine)/polystyrene blend thin films

The surface morphologies of poly(styrene‐b‐4vinylpyridine) (PS‐b‐P4VP) diblock copolymer and homopolystyrene (hPS) binary blend thin films were investigated by atomic force microscopy as a function of total volume fraction of PS (?_PS) in the mixture. It was found that when hPS was added into symmetric PS‐b‐P4VP diblock copolymers, the surface morphology of this diblock copolymer was changed to a certain degree. With ?_PS increasing at first, hPS was solubilized into the corresponding domains of block copolymer and formed cylinders. Moreover, the more solubilized the hPS, the more cylinders exist. However, when the limit was reached, excessive hPS tended to separate from the domains independently instead of solubilizing into the corresponding domains any longer, that is, a macrophase separation occurred. A model describing transitions of these morphologies with an increase in ?_PS is proposed. The effect of composition on the phase morphology of blend films when graphite is used as a substrate is also investigated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3496–3504, 2004     

喷气Z箍缩内爆等离子体的雪铲模型

 在喷气Z pinch内爆等离子体研究中，雪铲模型是一种常用的、比较简单的物理模型。根据实验中提供的电流波形，负载线质量和初始半径，可以通过雪铲模型来估算内爆到心的时刻。根据一维运动方程和不同构形下的解析解以及部分实验结果相结合，讨论了雪铲模型的适用范围。数值计算的内爆时间和实验（Gamble II, Double EAGLE, BLACKJACK 5）测量值符合得较好。结果表明，雪铲模型在喷气Z pinch实验的负载优化设计研究中是很有参考价值的方法。     

Shell effects in the symmetric-modal fission of pre-actinide nuclei

Mass distributions of fragments in the low-energy fission of nuclei from ¹⁸⁷Ir to ²¹³At have been analysed. This analysis has shown that shell effects in symmetric-mode fragment mass yields from the fission of pre-actinide nuclei could be described if one assumes the existence of two strongly deformed neutron shells in the arising fragments with neutron numbers N₁ ≈ 52 and N₂ ≈ 68. A new method has been proposed for quantitatively describing the mass distributions of the symmetric fission mode for pre-actinides with A ≈ 180–220.     

On a Question of Phillips

In [5] Phillips proved that one can obtain the additive group of any nonstandard model *? of the ring ? of integers by using a linear mod 1 function h : F ?, where F is the α-dimensional vector space over ? when α is the cardinality of *?. In this connection it arises the question whether there are linear mod 1 functions which are neither addition nor quasi-linear. We prove that this is the case.