Bimodal distributions branch

On the other hand, the parts of each crosslinking molecule between two adjacent branch points can be taken as short network chains. In this case the junctions are trifunctional (f = 3) and the chains have a bimodal distribution. The total number of network chains,, is threefold the number of former a,u-divinyl chains, because two short chains and one long chain proceed from each crosslink. Vj is also tabulated in Table II. 

The average branch chain length of amylopectin has a bimodal distribution that differs from the single modal distribution of that of glycogen.257 The average branch chain... 

Microscopic branching refers to the observation of a bimodal product energy distribution from one reaction channel (HX) and a normal product energy distribution from the other reaction channel. It appears that the bimodal distribution occurs for the product, HX, containing the most electronegative atom. Figure 9 shows the triangle plots for the detailed vibrational state distributions for the HBr and HC1 products from H + BrCl. Bimodality is seen in the HC1 distribution. The HBr distribution from H + BrCl closely resembles the HBr distribution from H + Br2 and results from a direct reaction with the Br end of BrCl. 

Note that the molecular weight distributions of high-conversion polymers made under conditions where the growth of macromolecules is limited primarily by chain transfer will be random, as described in Section 6.14.1 for low-conversion ca.ses. Then M /M will be 2. An exception to this rule occurs when the chain transfer reactions which determine the polymer molecular weight are to monomer and can result in branching [as in reactions (6-79) or (6-84)]. Tlie molecular weight distributions of the branched polymers that are produced will be broader than the random one, and bimodal distributions may also be observed. 

Figure 8.28 shows the pore size distributions for the PS formed on highly doped / -Si at different current densities." For the PS formed on heavily doped silicon, the pores at a given HF concentration have a narrower distribution at lower current at a given current density, the distribution is narrower at lower HF concentrations. A bimodal distribution of pore diameter is gena-ally associated with two-layer PS on lowly doped / -Si and iUmninated n-Si. The PS formed on p-Si has also been found to have a bimodal distribution of particles sizes small spherically shaped particles with a diameter of a few nanometers and large cylindrically shaped particles oriented with their axis perpendicular to the surface.The distribution of pore size with multiple peaks may be attributed to the fact that PS may have a surface micropore layer and smaller branched pores. Due to the hierarchical structure of the branched pores, the distribution of pore diameters for highly branched PS is found to be fractal-like. ° ... 

Bimodal distribution of branches, similar to the above two, except that the melting shows two endotherms. Usually a broad lower temperature melting and a sharp higher temperature melting, the latter for crystals of molecules with few branches. This is caused by uneven reactivity giving two phases in the reactor. 

Within a BPE with a distribution of branches, there will be a distribution of lamella thickness. This will result in a broad melting range. BPE with a bimodal distribution of branches will have a bimodal distribution of lamella thickness and a corresponding melting temperature range. When two polyethylenes are blended, assuming they are miscible, they will cocrystallize only where they have common MSL. Some molecular segments in each BPE will crystallize independently of... 

By using two or more polymerization catalysts simultaneously, polymer chemists can produce copolymers tvith a bimodal composition distribution. This is made possible by the fact that no two catalysts incorporate monomers at exactly the same rate. The net result is that short chain branches may be preferentially incorporated into either the higher or lower molecular weight fractions. Polymer manufacturers can obtain a similar result by operating two polymerization reactors in series. Each reactor produces a resin with a different copolymer distribution, which are combined to form a bimodal product. Copolymers with a bimodal composition distribution provide enhanced toughness when extruded into films. 

Whereas in the example just described the sample amount was about 50 mg, a similar procedure developed by another group 129) started with 4 g polyethylene copolymer. The sample was applied as a dilute solution in xylene and precipitated by very slow cooling (1.5 K/h) onto the Chromosorb P packing of a 500 x 127 mm column. The first separation was temperature-rising elution fractionation at a flow-rate of 20 ml/min and a Unear temperature increase by 8 K/h. The MMD of the fractions was measured by SEC at 145 °C in o-dichlorobenzene at 0.7 ml/min flow rate. The column set included a pair of bimodal columns 100 A and 1000 A plus a 4000 A column. The apparatus was equipped with an IR detector. The experimental data is computed to show the distribution of short-chain branching and of molar mass simultaneously. 

An important group of surface-active nonionic synthetic polymers (nonionic emulsifiers) are ethylene oxide (block) (co)polymers. They have been widely researched and some interesting results on their behavior in water have been obtained [33]. Amphiphilic PEO copolymers are currently of interest in such applications as polymer emulsifiers, rheology modifiers, drug carriers, polymer blend compatibilizers, and phase transfer catalysts. Examples are block copolymers of EO and styrene, graft or block copolymers with PEO branches anchored to a hydrophilic backbone, and star-shaped macromolecules with PEO arms attached to a hydrophobic core. One of the most interesting findings is that some block micelle systems in fact exists in two populations, i.e., a bimodal size distribution. 

Figure 12.9 depicts a comparison between classical trajectory results and exact close-coupling calculations for He--Cl2 and Ne- -Cl2, respectively. In both cases, the classical procedure reproduces the overall behavior of the final state distributions satisfactorily. Subtle details such as the weak undulations particularly for He are not reproduced, however. As shown by Gray and Wozny (1991), who treated the dissociation of van der Waals molecules in the time-dependent framework, the bimodality for He CI2 is the result of a quantum mechanical interference between two branches of the evolving wavepacket and therefore cannot be obtained in purely classical calculations. 

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