Monomer composition, calculation

The composition of the increment of polymer formed at a monomer composition specified by /i(= 1 —/2) is readily calculated from Eq. (8) if the monomer reactivity ratios ri and V2 are known. Again it is apparent that the mole fraction Fi in general will not equal /i hence both /i and Fi will change as the polymerization progresses. The polymer obtained over a finite range of conversion will consist of the summation of increments of polymer differing progressively in their mole fractions F. ... 

To calculate monomer composition, these chemical shift assignments must follow peak area relationships deduced from isolated, paired, and > paired structures. 

Using these area relationships the equations in Table II were written to use the measured peak areas from a copolymer of vinyl chloride to calculate monomer compositions. The equations also provide checks on internal consistency of the spectra. 

Equations to Calculate Monomer Composition of Vinyl Chloride-Vinylidene Chloride Copolymers from 13C NMR Areas... 

The above-mentioned regularity was found to be useful (201] to predict the transparency of terpolymer mixtures (acrylonitrile + styrene + a-methyl styrene) of various compositions, which had been studied by Slocombe [128]. He studied the turbidity of sixteen binary and one tetranary blends, prepared via mixing of eight samples corresponding to the particular points of the Gibbs-Roozeboom triangle taken in various combinations. The calculations showed that dispersion erf of all transparent blends was less than its critical value of c meanwhile for all turbid mixtures erf > erfcr. To calulate the dispersion of i-th monomer composition distribution f(t,j) of n-component mixture the following equation was used [201] ... 

When the polymerization mechanism is known, peak intensities in the spectra of polymers with different monomer compositions can be compared with calculated intensities based on various polymerization models [e.g., first order Bernoullian (B) or first order Markovian model]. For example, if polymerization mechanism of a vinyl monomer fits a Bernoullian model, then the fractions of triads will be given by ... 

The conventional [Eq. (7.77)] and simplified [eq. (7.81)] terpolymeriza-tion equations can be used to predict the composition of a terpolymer from the reactivity ratios in the two-component systems M1/M2, M1/M3, and Ms/Ms- The compositions calculated by either of the terpolymerization equations show good agreement with the experimentally observed compositions. Neither equation is found superior to the other in predicting terpolymer compositions. Both equations have been successfully extended to multicomponent copolymerizations of four or more monomers [30,31]. 

Ttp 4 Chain microstructure and propagation reactions. Propagation reactions are mainly responsible for the development of polymer chain microstructure (and control chain composition and sequence length distribution in copolymerizations). In free radical polymerization, the stereoregularity of a high molecular weight homopolymer chain depends on polymerization temperature almost exclusively. It is usually independent of initiator type and monomer concentration. Calculations on stereoregularity... 

X-ray diffraction patterns of fibers spun from liquid crystalline melts of p-hydroxybenzoic acid (HBA) and 2-hydroxy-6-naphthoic acid (HNA) show a high degree of axial orientation. Several meridional maxima are detected which are aperiodic and also change in position and number with the monomer composition. The positions of these maxima can be predicted by calculating the theoretical scattering of random copolymer chains, in which the residues are represented by points separated by the monomer lengths. Both peak positions and intensities are reproduced when intraresidue interferences are allowed for in an atomic model for the random chains. This procedure also allows determination of the stiff-chain persistence (or correlation) length from the breadth of the maximum at d=2.lA which increases from 9 to 13 residues as the HBA content is increased from 25 to 75%. 

Figure 8.5 shows an example of the performance of this type of estimation scheme for a semibatch emulsion copolymerization of VAc/BA carried out at 70°C with 33 wt% solids content. It can be seen that the estimated overall monomer conversions and copolymer composition calculated from the estimated amoimts of unreacted monomer compared well with the off-line measurements. 

The prediction of polymer composition often involves the measurement of a bulk property of the entire reaction mass which changes as the degree of polymerization progresses. Assumption of an initial condition, such as monomer composition, is usually required to allow for the calculation of conversion. This asumption can be a source of significant measurement error. 

The fifth column in Table 1 shows an estimation of the percentage of MA consumed at the end of the induction period in the initiation reaction this quantity is relevant since the calculation of ltdsma assumes constant MA concentration. This estimation is based on the assumption of 1 molecule of MA consumed for each two molecules of nitroxide, since the radical 4 is trapped by a second nitroxide molecule during the induction period. Experiments 4 and 5 are not analyzed in this table because their consumption of MA does not justify to approximate constant concentration of this monomer during the induction period. A second source of deviation for the assumption of constant MA concentration is the fact that some of the reactions show an induction period which is not clean that is, they exhibit some limited conversion before the polymerization starts at full rate. Such a behavior is rather a retardation period in which inhibition presumably competes with limited propagation. This phenomenon especially affects experiment 6 and, to a lesser extent, experiment 1. Since the conversion at the end of the retardation period is known from the experimental data, it is possible to estimate the total amount of MA that was copolymerized during the retardation period if the composition of the copolymer formed is also known. From measurements of the polymer composition by NMR under different reaction conditions and monomer composition, we consistently obtained copolymer of 50% molar composition of MA, as long as the M A was not completely consumed. This... 

HEMA content in the polymer composite (squares) and HEMA content in the copolymer (dots) as function of the HEMA content in the monomer feed. The copolymer composition calculated from rs = o.44 and rHEMA = 0-54 is given as reference (solid curve). 

Considering that Narke receptor monomer has a subunit composition of (Ji28Ya [26], the protein moiety of the receptor monomer Is calculated to 219.000 from the values of the four kinds of subunits. This value agree well with the value 220,000 obtained for the protein moiety of the receptor monomer. 

The binary interaction model was applied to a system of copolymer-copolymer binary blend with common monomers in Section 3.3. The SAN/SAN blend, the compositional mismatch that can be tolerated to stay miscible, was calculated. A method to calculate the compositional window of miscibility for a terpolymer-terpolymer blend with common monomers was illustrated in Section 3.4. The RAND key can be used in an MS Excel spreadsheet to arrive at the compositional window of miscibility in computational time. The miscible regions for terpolymer-terpolymer binary blends with common monomers are shown in Figure 3.2. The compositional window of miscibility for terpolymer-homopolymer miscibility without any common monomers was calculated using a binary interaction model in Section 3.5. The system chosen for the illustration was TMPC/AMS-AN-MMA. 

Copolymer composition can be calculated as a function of monomer composition when the polymer is formed by free radical polymerization in a CSTR (continuous stirred tank reactor). Consider two monomers 1 and 2 as starting materials for forming a copolymer with repeat units of 1 and 2. The initiation can be effected by thermal means or by using a peroxy initiator. 

Equation (10.27) can be used to calculate the copolymer composition given the monomer compositions. The inverse problem of finding the monomer composition for a desired polymer composition would require rearranging Equation (10.26) and expressing A in terms of Fj. It appears that the expression would be quadratic in/i. Does this mean that there would be multiple or two roots to a desired polymer composition for some set of reactivity ratios The monomer and copolymer composition for the system of diethyl fumarate and acrylonitrile is shown in Figure 10.3. 

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