Berry number

Experimental findings show that the diameter of electrospun fibers is dependent on the solution concentration and the polymer chain conformation in solution. Thus, the Berry number is defined by the following equation as indicated in Section 1.6. 

The capacity of a polymer solution to from a network under extension may be judged by the Berry number or the number of entanglements per chain in the solution. 

In the case of evaporation of the solvent, the extruded polymer solution properties inside the spinning zone would vary in relation to the original properties of the solutions taken and would, therefore, correlate with the original concentration and molecular weight of the original polymer solution. Figure 1.8 shows the relationship of nanofiber diameter against the Berry number, which is the product of... 

It was observed that the electrospinning of polymer solution below the Berry number of 10 yielded droplets or fibers with droplets and the nanofiber diameter increased with an increase in the Berry number from 65 nm to above submicron and micron size when the Berry number increased above 10. The data can be fitted using a set of straight lines with different slopes in two different regions (Fig. 1.8]. The correlation coefficient for the first trendline improved from 0.891 for the Berry number plot to 0.974 for the number of entanglements plot. ... 

For PLA electrospun fibers beadless at 1 5e 2.7, entanglement probability increases and favorable conditions for fiber production takes place. This Berry number range is convenient for nanofiber production of PLA. 

Plot of nanofiber diameter agalnstthe Berry number. Reprinted with permission from Ref. 35. Copyright 2013, The Korean Fiber Society+Business Media Dordrecht. 

Experimental results indicate that the diameter of the fiber produced by electrospinning is influenced by the polymer concentration and molecular conformation,such influence is, described by the Berry number, B, on an electrospun poly (L-lactic acid]/chloroform system gives the following equation ... 

In Simha s early model (Simha and Zakin 1962), transition from a dilute to a concentrated polymer solution was envisioned as being due to interpenetration of polymer chains that occurs when concentration lies somewhere in the region 1 < [ryjc < 10. This transition is evident from the change in the concentration dependence of viscosity in polymer solutions. The quantity [r ]c, the Simha-Frisch parameter (Frisch and Simha 1956), also sometimes called the Berry number (Gupta et al. 2005), is therefore a reasonable measure of chain overiap in solution. As Shenoy et al. (2005b), however, correctly point out, the dependency, being ultimately based on the equivalent hard sphere hydrodynamic model, is strictly applicable only at low polymer concentrations. 

Well, now that the thermodynamics have been covered, we know how to get the polymer into solution, but how the polymer chains are organized in the solution is also important. Let us initially assume that the polymer is in a fairly dilute solution, therefore we can assume that there are very few entanglements between the polymer chains. Entanglements begin to set in when the dimensionless Berry number (Be), the product of intrinsic viscosity and concentration, exceeds unity [18] ... 

Equation 14.13a quantitatively holds for just about all polymer melts. The addition of a low molecular weight solvent, of course, cuts down the entanglements and raises M c-Equation 7.15 suggests that entanglements set in when the dimensionless product of intrinsic viscosity and concentration (the Berry number) exceeds one, [tj]c >1. Thus, if you know [rj] for your polymer in the solvent, you can get an idea of the concentration above which Equation XAA ib should be used (and the viscosity rises much more sharply ). In practice, even moderately concentrated (say 25% or more) polymer solutions have viscosities proportional to provided that M , is in the range of commercial... 

Solution. First, we assume that entanglements begin when the Berry number, [tj]c, equals 1. Because all we are after here is a rough estimate, we can assume that M= M (see Example 5.4). Thus,... 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

To see that this phase has no relation to the number of ci s encircled (if this statement is not already obvious), we note that this last result is true no matter what the values of the coefficients k, X, and so on are provided only that the latter is nonzero. In contrast, the number of ci s depends on their values for example, for some values of the parameters the vanishing of the off-diagonal matrix elements occurs for complex values of q, and these do not represent physical ci s. The model used in [270] represents a special case, in which it was possible to derive a relation between the number of ci s and the Berry phase acquired upon circling about them. We are concerned with more general situations. For these it is not warranted, for example, to count up the total number of ci s by circling with a large radius. 

Oxalic acid is poisonous and occurs naturally in a number of plants including sorrel and begonia It is a good idea to keep houseplants out of the reach of small children who might be tempted to eat the leaves or berries... 

Japan Wax. Japan wax [8001-39-6] is a fat and is derived from the berries of a small tree native to Japan and China cultivated for its wax. Japan wax is composed of triglycerides, primarily tripalmitin. Japan wax typically has a melting point of 53°C, an acid number of 18, and a saponification number of 217. Principal markets include the formulation of candles, poHshes, lubricants, and as an additive to thermoplastic resins. The product has some food-related apphcations. 

Bayberry Wax. Bayberry wax [8038-77-5] is removed from the surface of the berry of the bayberry (myrtle) shmb by boiling the berries in water and skimming the wax from the surface of the water. The wax is green and made up primarily of lauric, myristic, and palmitic acid esters. The wax has a melting point of 45°C, an acid number of 15, a saponification number of 220, and an iodine number of 6. The wax has an aromatic odor and is used primarily in the manufacture of candles and other products where the distinctive odor is desirable. 

The pentacoordinate molecules of trigonal bipyramidal form, like PF5, are a very nice example for the study of the formal properties of stereoisomerizations. They are characterized by an appreciable nonrigidity and they permit the description of kinetics among a reasonable number of isomers, at least in particular cases (see below). Therefore the physical and chemical properties of these molecules have been thoroughly investigated in relation to stereoisomerization. Recent reviews may be found in the literature on some aspects of this problem. Mislow has described the role of Berry pseudorotation on nucleophilic addition-elimination reactions and Muetterties has reviewed the stereochemical consequences of non-rigidity, especially for five- and six-atom families as far as their nmr spectra are concerned. 

Pi the Berry step is seen as a double bending of an equatorial and an apical angle. The two apical ligands become equatorial and two equatorial ones go to apical positions. One of the equatorial ligands, the so-called pivot, is on the fourfold axis of the tetragonal pyramidal intermediate state. The connectivity i.e. the number of isomers reached from a given one in one step, is three. 

The five processes are not really independent. This is well illustrated in Fig. 2. The symbols I, II, III, IV, V under each group of isomers give the number of Berry steps needed to reach them from 12, considered as the starting isomer. However, if one performs one P2 step, it is easy to convince oneself that one reaches also the six isomers of group 11 For this reason the symbols I, III,... etc., refer also to the index of the process needed to reach the corresponding groups in one step. The only difference is that multiple steps allow for a wider variety of paths, because one can come back to the starting point. 

Zeaxanthin is the abundant xanthophyll in only a small number of food sources and is the dominant xanthophyll in orange peppers and Gou Zi Qi or lycium mill (Lycium chinense) berries, probably the richest sources. - ... 

More than 20% of insects are pollinators. Bees alone pollinate more than 50 agricultural crops [111]. When fully pollinated, fruit and berry plants grow 30-40% more, and melons and squash twice as much, or more. Bees increase harvest size 3-4 times in feed grass like alfalfa, red clover, and vetch [111]. However, the number of bees and other plant pollinators sharply and universally decreased in regions of the USSR where chemicals were used in agriculture in the middle of the 1980s. Because of this decrease, harvest size of some plants has noticeably decreased (for example, buckwheat and melons). 

A number of yellow dyes were known in antiquity weld and saffron seem to have been the most widely used, but barberry root, turmeric, Persian berries, and safflower have also been identified in ancient fibers. Weld, probably the oldest European-known yellow dye, is derived from the herbaceous plant Roseda luteola, which is indigenous to central Europe. The dye is distributed throughout the entire plant, although it is concentrated in the upper... 

---