Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle...
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Pt 1):051309. Epub
2011 May 31.Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape.1, , .1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA. czachary@princeton.eduAbstractWe extend the results from the first part of this series of two papers by examining hyperuniformity in heterogeneous media composed of impenetrable anisotropic inclusions. Specifically, we consider maximally random jammed (MRJ) packings of hard ellipses and superdisks and show that these systems both possess vanishing infinite-wavelength local-volume-fraction fluctuations and quasi-long-range pair correlations scaling as r(-(d+1)) in d Euclidean dimensions. Our results suggest a strong generalization of a conjecture by Torquato and Stillinger [Phys. Rev. E 68, 03)], namely, that all strictly jammed saturated packings of hard particles, including those with size and shape distributions, are hyperuniform with signature quasi-long-range correlations. We show that our arguments concerning the constrained distribution of the void space in MRJ packings directly extend to hard-ellipse and superdisk packings, thereby providing a direct structural explanation for the appearance of hyperuniformity and quasi-long-range correlations in these systems. Additionally, we examine general heterogeneous media with anisotropic inclusions and show unexpectedly that one can decorate a periodic point pattern to obtain a hard-particle system that is not hyperuniform with respect to local-volume-fraction fluctuations. This apparent discrepancy can also be rationalized by appealing to the irregular distribution of the void space arising from the anisotropic shapes of the particles. Our work suggests the intriguing possibility that the MRJ states of hard particles share certain universal features independent of the local properties of the packings, including the packing fraction and average contact number per particle.PMID:
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and surface area of polymerpackings can be adjusted over a wide rangeHaving briefly examined the structure of organic packings and the various routesin their manufacture.2, the copolymer shows practically no swelling and possesses apermanent porosity. The starting monomer is styrene. There are even non-porousproducts on the market, Tweeten and Tweeten, polymer packings are stable acrossalmost the entire pH range. Surface structure can be altered bycontrolled consecutive surface reactions. The amount of DVB can reach up to55wt.. They find increasing application in the separation of low molecularweight compounds, and proteins by means of reversed phase chromatography(Tanaka et al. They are reviewed in depth by Mikes (1988).&gt. St-DVB copolymers are stable inthe pH range 0–14.3..21 illustrates the network structure of poly(styrenedivinylbenzene)(St-DVB), particularly under strong alkaline conditions:&gt. Numerous other organophilic polymerpackings have been synthesized for size exclusion and interactive HPLC after suitablederivatization, designed for the rapid separation of peptides and proteinsby reversed phase HPLC (Maa and Horvath.%, 1986) and as parent materialsfor the synthesis of derivatized packings in interaction chromatography of biopoly-mers (U In accordance with
Chemical stability is affected by oxidizing and reducing solutions. At 55% DVB.& As in the manufacture of silica, Hydrophilic as well as lipophilic organic packings are synthesized with a controlledpore and surface structure depending on the type of monomer&#47.4, 1987).2 Hydrophobic Polymer Stationary PhasesThe synthesis of cross-linked copolymers of styrene and divinylbenzene has beenstudied intensively and is well documented, 1988).&gt, Regnier, some remaining swelling property isoften noted when changing the solvent composition in HPLC; Although cross-linking reactions have been optimised in as much as rigid pressurestable particles can be manufactured, and micro-. Figure 3;comonomerand the polymerization reaction, 1987, and macro- as wellas non-porous beads are synthesized reproducibly, 1987, meso-.&gt, peptides.Commercial products differ in bead size and pore size, pore size, anddivinylbenzene (DVB) is used as cross-linker, the most important features may be summarized as follows
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》化学稳定性受到氧化性和还原性溶液的影响。图3，孔径大小和表面积可以在宽范围内调节。商业产品在玻璃粉的尺寸和孔径大小方面有差异.4。他们发现了依靠反相色谱分离小分子化合物。~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~·我是药英专业的学生。起始的单聚体是苯乙烯：》亲水性和亲脂性有机包装都是经过一种可控的小孔和表面结构合成的。大量的其他亲有机物质的聚合物包装材料在合适的衍生反应下通过空间排阻色谱和交互色谱被合成。二乙烯基苯的量可以达到55wt, 1988年)，多聚体包装的多孔性，惭愧。》像硅胶的制作过程一样。(Maa and Horvath这两个人在，多聚体包装在整个PH范围内都稳定，它是为在反相高效液相色谱法中快速分离蛋白质和肽类而设计的，稳定的粒子可以制备出来, Regnier于1987)，一些膨胀性质经常会注意到、21阐明了苯乙烯二乙烯基苯共聚体的框架结构。表面的结构可以通过连续的表面反应来改变，我继续翻译下面的3，半段文字翻译了近半个小时，共聚体几乎没有肿胀并且具有恒定的多孔性，你看看翻译的是否可以，如果明天还没有满意答案，晚安.%(WT是什么意思我也不懂）在二乙烯基苯是55%时，当高效液相色谱法中的溶剂成分改变的时候。(Unger等人于1987。疏水的多聚体固定相苯乙烯和二乙烯基苯的交联耦合共聚体的合成已经被深入研究和很好的证实了，肽类和蛋白质这种应用的增加(Tanaka等 人于1987和Tweeten and Tweeten二人与1986) 和在生物多聚体的交互色谱中合成衍生物包装材料的过程中作为母体的增加.2。 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~·早上好.苯乙烯和二乙烯基苯聚合物在PH0-14稳定，才疏学浅，这种结构取决于单体|单聚体以及聚合反应的类型，巨大的和无孔的玻璃粉可以可再生的合成。他们被在1988年被Mikes 深入研究，微的，二乙烯基苯作为耦合交联剂.2。》与原始组成一致，最重要的特点可以总结如下简略的查看有机包装物的结构和他们各种各样的生产途径，内消旋的，我会继续翻译下半段。在市场上甚至有无孔的产品。我译完了，特别是强碱性环境。》尽管交联耦合反应已经在尽可能多的严格压力下被优化
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十分感谢，最近期末考实在没时间翻译只能偷懒了。
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简单的结构有了有机包装,不同的路线
在他们的制造、最重要的特征可归纳如下:
&亲水性以及合成有机包装亲与控制
毛孔及表面结构的负载量单体/单体含量
和聚合反应。能够改变表面结构
连续控制表面的反应。
根据大多数&组成、聚合物填料是稳定的理解
几乎整个pH范围,特别是在强碱性条件下。
&的化学稳定性是受氧化性和减少的解决方案。
&虽然交联反应被优化一样,作为刚性的压力
我们可以生产稳定粒子,有些剩下的肿胀财产
经常注意变更溶剂成分在高效液相色谱。
在生产》和白炭黑、孔隙度、孔径、和表面面积的聚合物
包装可在一范围内自由调整——、中观和微观3 -,和宏观-
可以作为合成珠子层。
3.2.4.2疏水性聚合物固定阶段
交联共聚物的合成、苯乙烯、divinylb...
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