Limiting polymer size

Vinylidene Chloride Copolymer Foams. Low density, fine-celled VDC copolymer foams can be made by extmsion of a mixture of vinylidene chloride copolymer and a blowing agent at 120—150°C (190). The formulation must contain heat stabilizers, and the extmsion equipment must be made of noncatalytic metals to prevent accelerated decomposition of the polymer. The low melt viscosity of the VDC copolymer formulation limits the size of the foam sheet that can be extmded. 

A number of matrices have also been used for the preparation of semiconductor nanoparticles, whereby the particulate material is grown within and subsequently fills the cavities of the host material. These includes zeolites,361 glasses,362 and molecular sieves,363-365 and can be viewed as nanochambers which limit the size to which crystallites can grow. Other synthetic methods include micelles/microemulsions,366-369 sol-gels,370,371 polymers,372-377 and layered solids.378... 

Flocculation rate limitation. The adsorption step was rate limiting for the overall flocculation process in this system. Polymer adsorption rate measurements for dispersed systems reported in the literature (2,26) do not lend themselves to direct comparisons with the present work due to lack of information on shear rates, flocculation rates, and particle and polymer sizes. Gregory (12) proposed that the adsorption and coagulation halftimes, tA and t, respectively, should be good indications of whether or not the adsorption step is expected to be rate limiting. The halftimes, tA and t, are defined as the times required to halve the initial concentrations of polymer and particles, respectively. Adsorption should not limit the flocculation rate if... 

Both methyl acrylate and butyl acrylate have been used to prepare vinylidene chloride copolymers with sufficient stability to permit thermal processing. The presence of alkyl acrylate units in the polymer mainchain limits the size of vinylidene chloride sequences and thus the propagation of degradative dehydrochlorination. More importantly it lowers the melt... 

The presence of crosslinks, which, especially in both polymers, limits domain sizes. 

In any polymerization process one must be concerned with removal of the coproduct (typically H2O or HCl) so that equilibrium limitations do not limit the polymer size. The removal of the product in condensation polymerization to attain higher polymer lengths is a major consideration in polymerization reactor design. This can be done by withdrawing water vapor or by using two phases so that the water and polymer migrate to different phases. 

Intraparticle diffusion limits rates in triphase catalysis whenever the reaction is fast enough to prevent attaiment of an equilibrium distribution of reactant throughout the gel catalyst. Numerous experimental parameters affect intraparticle diffusion. If mass transfer is not rate-limiting, particle size effects on observed rates can be attributed entirely to intraparticle diffusion. Polymer % cross-linking (% CL), % ring substitution (% RS), swelling solvent, and the size of reactant molecule all can affect both intrinsic reactivity and intraparticle diffusion. Typical particle size effects on the... 

Inserted L-rhamnopyranosyl units may provide the necessary irregularities (kinks) in the structure required to limit the size of the junction zones and produce a gel. The presence of side chains composed of D-xylosyl units may also be a factor that limits the extent of chain association. Junction zones are formed between regular, unbranched pectin chains when the negative charges on the carboxylate groups are removed (addition of acid), hydration of the molecules is reduced (addition of a cosolute to a solution of HM pectin), and/or pectinic acid polymer chains are bridged by multivalent, eg, calcium, cations. 

Equation 1.3 represents a system of usually several thousand coupled differential equations of second order. It can be solved only numerically in small time steps At via finite-difference methods [16]. There always the situation at t + At is calculated from the situation at t. Considering the very fast oscillations of covalent bonds, At must not be longer than about 1 fs to avoid numerical breakdown connected with problems with energy conservation. This condition imposes a limit of the typical maximum simulation time that for the above-mentioned system sizes is of the order of several ns. The limited possible size of atomistic polymer packing models (cf. above) together with this simulation time limitation also set certain limits for the structures and processes that can be reasonably simulated. Furthermore, the limited model size demands the application of periodic boundary conditions to avoid extreme surface effects. 

We have already seen that photoactive clusters, e.g. CdS, can be introduced into vesicles and BLMs (Sect. 5.2 and 5.3). Similar support interactions are possible with both inorganic and organic polymeric supports. Photoactive colloidal semiconductor clusters can be introduced, for example, into cellulose [164], porous Vycor [165], zeolites [166], or ion exchange resins [167]. The polymer matrix can thus influence the efficiencies of photoinduced electron transfer by controlling access to the included photocatalyst or by limiting the size of the catalytic particle in parallel to the effects observed in polymerized vesicles. As in bilayer systems,... 

Experimental studies show, however, that these limiting approximations must be used with caution. For example, with some emulsion polymerization systems the mean number of radicals per particle may run from one-half to several depending on the size of the particle (I). Assuming that the polymerization process is stationary with known rates of radical arrival and termination, Stockmayer (6) and O Toole (3) have shown how to calculate not only the mean number of radicals but the entire number distribution as well. Until now, no methods of the same generality seem to exist for calculating the polymer size distribution. 

A method is presented here which yields the polymer size distribution for arbitrary rates of radical arrival and termination. Furthermore, from this analysis one can see when each of the limiting cases is applicable. The computations are all carried out under stationary conditions with the rates of radical arrival, propagation, and termination constant. Under transient conditions the computations would be much more difficult. For the limiting cases, however, the moments of the polymer size distributions under transient conditions can be found (4). 

Following Ref. 4, the polymer size distribution in the Smith-Ewart limit D/B f oo can be developed from the probability equations ... 

To find the polymer size distribution in the opposite limiting case, where D/B 0, we start with phenomenological equation... 

Linear and branched polymer structures were defined in Section 1.6. Branched polymers differ from their linear counterparts in several important aspects. Branches in crystallizable polymers limit the size of ordered domains because... 

We have already mentioned in Sect. 6.2, 6.3 that the physicochemical conditions of the foaming process and the foam stability criteria determine the upper and lower limits of cell sizes so that, depending on the polymer type, composition, and foaming process conditions, the upper limit of size may be as large as a few millimeters 36,83-85) recently, it was believed that the minimum size of a plastic foam cell cannot be less than several dozens of microns (Table 2). However, by the application of scanning electron microscopy and the mercury penetration method, plastic foam structures were found to incorporate gas voids whose minimum dimensions were fractions of a micron, i.e. 2 or 3 orders of magnitude smaller than could be observed earlier in cellular polymers... 

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