Conversion histories

Polyfvinyl acetate) (PVAc) latexes produced by batch and continuous emulsion polymerization were used in this study. Details for the apparatus and the polymerization procedure can be found in Penlidis et al. (6,12,K3). Samples taken during the reaction were subsequently analyzed to follow conversion- and particle growth-time histories. The batch experimental runs were designed to yield similar conversion-time histories but different particle sizes. Conversion was measured both off-line, by gravimetric analysis, and on-line using an on-line densitometer (a U-tube DPR-YWE model with a Y-mode oscillator with a PTE-98 excitation cell and a DPR-2000 electronic board by Anton Paar, Austria). A number of runs were repeated to check for reproducibility of the results. Four batch runs are described in Table I below and their conversion histories are plotted in Figure 1. 

Figure 1. Conversion histories of the batch vinyl acetate emulsion polymerizations (similar recipes only the emulsifier concentration is different).

In Figure 1 are shown experimental conversion histories from bulk polymerization of styrene, methyl methacrylate, and vinyl acetate. It appears that with any of these monomers the rate of polymerization increases substantially during reaction, i.e. gel-effect is important in bulk polymerization of these monomers. The effect is particularly pronoimced with methyl methacrylate. 

Figure 1. Conversion histories in bulk polymerization of methyl methacrylate, styrene, and vinyl acetate...

Since the polymerization conditions for styrene and methyl methacrylate often are chosen such that a in the early stages of polymerization (after N has become constant) lies between 10 2 and 1, it is understandable that gel-effect usually is important in emulsion polymerization of these monomers and therefore must be accounted for since it completely dominates the shape of the conversion history. 

Rp is then calculated from Equation (3). The conversion history is obtained by repeating this calculation stepwise at successively higher conversions and simultaneous integration of Equation (3). 

Systems Where Radical Desorption is Negligible. Styrene and methyl methacrylate emulsion polymerization are examples of systems where radical desorption can be neglected. In Figures 4 and 5 are shown comparisons between experimental and theoretical conversion histories in methyl methacrylate and styrene polymerization. The solid curves represent the model, and it appears that there is excellent agreement between theory and experiment. The values of the rate constants used for the theoretical simulations are reported in previous publications (, 3). The dashed curves represent the corresponding theoretical curves in the calculation of which gel-effect has been neglected, that is, ktp is kept constant at a value for low viscosity solutions. It appears that neglecting gel-effect in the simulation of styrene... 

Figures 4, 5, 6. Comparison between experimental and theoretical conversion histories in emulsion polymerization of methyl methacrylate, styrene, and vinyl acetate. (—), model with gel-effect (—), model without gel-effect.

By employing an object oriented approach, the numerical treatment of particle processes for a finite number of particles is facilitated. Furthermore, it allows tracking of the conversion history of each particle and easy extension of the model for further material and kinetic data. 

Copolymer Analysis. Even though the overall copolymer composition can be determined by residual monomer analysis, it still is necessary to have reliable quantitative techniques for copolymer composition measurements on the actual copolymer, mainly because concentration detectors for SEC or HPLC are sensitive to composition and because the conversion histories are not always available. Some of the techniques used to determine copolymer composition are melt viscometry (46), chemical analysis, elemental analysis, infrared spectroscopy (IR), Nuclear Magnetic Resonance (NMR), ultra-violet spectroscopy (UV), etc. Melt viscometry, chemical and elemental analysis are general techniques that can be applied to almost any polymer. The spectroscopic techniques can be applied depending on the ability of the functional groups present to absorb at specific wavelengths. 

Indeed, it can be shown that if concentration changes are not considered, the remaining temperature dependent portion of Eqs. 2 and 3 are numerically equivalent. Under isothermal conditions th conversion histories match provided that one of the comonomers is not exhausted prior to the completion of the reaction. Under non-Isothermal conditions, composition drift influences the agreement between the two forms. When drift is towards the more reactive comonomer, the approximate form underestimates the thermal trajectory (See Fig. A). Conversely, when drift is towards the less reactive of the pair, the approximate form overestimates the trajectory. Similar behavior is noted in the RA boundaries of Fig. 1. Points for the SAN system lie above the homopolymer boundary, and drift is towards high AN content compositions. Points for the ANMMA boundary lie below the homopolymer boundary, and drift is towards the less reactive of the pair, MMA. As conditions become either more adiabatic or more isotherm, spread between the forms narrows. The poorest agreement of the forms occurs at the para-metr i ca lly sensitive point of the RA transition. 

Figure 5.9 Experimental monomer conversion histories for the bulk polymeri2ation of methyl methacrylate using AIBN, for two near-isothermal (NI) temperature histories. [I]o = 25.8 mol/m. Solid curves are model predictions. (Data from Refs. 6-10.)...

Even if all of the elements described so far have been present within a sedimentary basin an accumulation will not necessarily be encountered. One of the crucial questions in prospect evaluation is about the timing of events. The deformation of strata into a suitable trap has to precede the maturation and migration of petroleum. The reservoir seal must have been intact throughout geologic time. If a leak occurred sometime in the past, the exploration well will only encounter small amounts of residual hydrocarbons. Conversely, a seal such as a fault may have developed early on in the field s history and prevented the migration of hydrocarbons into the structure. 

In a given motion, a particular material particle will experience a strain history The stress rate relation (5.4) and flow rule (5.11), together with suitable initial conditions, may be integrated to obtain the eorresponding stress history for the particle. Conversely, using (5.16) instead of (5.4), may be obtained from by an analogous ealeulation. As before, may be represented by a continuous curve, parametrized by time, in six-dimensional symmetric stress spaee. 

A substantial portion ( 15%) of the magnetite was found to be converted to hematite. As prior work showed small conversion (1%) of hematite to magnetite, the data indicate that the conversion can proceed in either direction depending upon the local microscopic deformation history of the powder particles. 

A chronological examination of the steroid literature regarding the conversion of pregnanes to androstanes, androstanes to pregnanes, and the side-chain polyoxygenation of pregnanes reveals, in microcosm, the history of the development of steroid chemistry over the past three decades. 

In 1919, he made history with yet another of his inventions when his multiple-tuned antenna, antistatic receiver, and magnetic amplifier were used to transmit the first two-way radio conversation. This great event took place 900 miles out to sea, between the Trans-Atlantic Marconi Company station at New Brunswick and the steamship George Washington, with President Woodrow Wilson on board as a witness. 

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The thermal polymerization of S has a long history.310 The process was first reported in 1839, though the involvement of radicals was only proved in the 1930s. Carefully purified S undergoes spontaneous polymerization at a rate of ca 0.1% per hour at 60 C and 2% per hour at 100 °C. At 180 aC, 80% conversion of monomer to polymer occurs in approximately 40 minutes. Polymer production is accompanied by the formation of S dimers and trimers which comprise ca 2% by weight of total products. The dimer fraction consists largely of cis- and trans-1,2-diphenylcyclobutanes (90 and 91) while the stereoisomeric tetrahydronaphthalenes (92 a nd 93) are the main constituents of the trinier fraction.313... 

The conversion-time history is obtained by simxiltaneous solution of equations (ij) and (19) ... 

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Figure 1 shows conversion-time histories for batch emulsion VCM reactors from (70). The recipes used consisted of 1.0 liter of water, 0.47 liters of VCM and varying amounts of soap and initiator, as indicated on the figure. For the cases of Figure lb, Berens (70) measured 0.68 x 101 particles per liter of latex for the upper curve (I = 1.0 gr, S = 3.0 gr) and 0.34 x 1017 for the lower one corresponding to I = 1.0 gr and S = 1.15 gr. Our model s predictions were 0.2 x 1018 and 0.14 x 1017, respectively. In Figure la, the same amount of emulsifier was used for both runs. Berens (70) estimated 0.38 x 1017 particles per liter of latex for both cases, while our model s prediction was close to 0.22 x... 

Figure 1. Conversion-time histories in batch PVC emulsion polymerization for different initiator and emulsifier concentrations.

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