Polymer calculation

Taking the length per repeat unit (i.e., bond angles already considered) as 0.78 nm in each instance, evaluate the factors (1 + cos 0)/(l - cos (p) and cos (p for each polymer. Ignoring the difference between 130 and 140°C, do you find the difference in steric hindrance between the tributyrate and tri-caprylate to be what you expected Is the effect of temperature on the 1q value of cellulose tributyrate what you expected Briefly explain each answer. For each polymer, calculate r if n = 10 also do this for the hypothetical chain with no restrictions to rotation and having the same repeat length. 

The kind of chromatographic information generated on these polymers as a function of reaction time is illustrated in Figure 9. Polymerization to soluble polymer, calculated as 7o solids. 

High polymer calculations can be performed on polysaccharides. Calculation of unit cell translation vectors (15), heats of polymerization (15), and elastic moduli (16) can readily be done. The accuracy of such calculations is the same as that of equivalent molecular species. A limitation of elastic moduli calculations is that the polymer is assumed to be 100% ordered, a state not commonly found in polysaccharides. 

A heat-resistant polymer Nomex has a number-average molecular weight of 24,116. Hydrolysis of the polymer yields 39.31% by weight m-aminoaniline, 59.81% terephthalic acid, and 0.88% benzoic acid. Write the formula for this polymer. Calculate the degree of polymerization and the extent of reaction. Calculate the effect on the degree of polymerization if the polymerization had been carried out with twice the amount of benzoic acid. 

Table 2. Values of the diameters of liquid-crystalline polymers calculated by different methods...

In conjunction with a study on the reactivity of dimeric quinone me-thides, Elder et al. (56) examined the physical and electronic structure of guaiacylglycerol-/ -coniferyl ether, which is substituted in a manner representative of the lignin polymer. Calculations were performed using AMBER (Assisted Model Building with Energy Refinement) (24), which is a force-field method, and the energetic minimum was determined to be a folded structure similar to that reported by Gravitis and Erins (55). 

EXAMPLE 1.3 Polydispersity of a Synthetic Polymer. Columns (1) and (2) of Table 1.7 list the number of moles and the jpolecular weight, respectively, for eight fractions of a synthetic polymer. Calculate Mn and Mw from these data and evaluate [Pg.37]

The product was completely functionalized at the terminal primary amine sites as 13C NMR signals from these groups (at ca. 41 ppm in D20) were absent in the product. Elemental analysis suggests the presence of approximately 10% residual water in the polymer calculated for C2y58H4064N50601148 C 46.7, H 7.38, N 12.78, O 33.11 found (Huffman Laboratories, Golden, CO) C 42.68, H 7.77, N 11.59, O 39.41. 

Table 1. Apparent activation energies for relaxation processes in crossEnked polymers calculated from broad line NMR...

Table 2. Apparent Activation energies for relaxation processes in crosstinked polymers calculated from T, relaxation...

A survey of calculated Ea for relaxation processes in crosslinked polymers calculated from Tj measurements assuming a single tc is given in Table 2. 

Figure 2.26 Average sorption coefficients of simple gases in a family of 18 related polyimides plotted against the expected sorption in an ideal polymer calculated using Equation (2.97). Data from Tanaka el al. [23]...

Polarity of Vinyl Acrylic Latex and Surfactant Adsorption Contact angle measurements, dispersion and polar contribution to latex film surface tension and polarity of polymer calculated according to the method of Kaelble (10) of the three latex films are whown in Table V. It is seen that the polarity of the latex film decreases with increase in butyl acrylate content of the vinyl acrylic co-polymer. The polarity of the 70/30 (VA/BA) latex is very similar to that of the polybutyl acrylate homopolymer estimated to be about 0.21 (1). ... 

Weight of crude copolymer (gram) Weight of extracted polymer (gram) Theoretical % butyla Percent chlorine in polymer Calculated % butyl6 Polymer melting point, °C. 

In Fig. 15.27, the transient extensional viscosity of a low-density polyethylene, measured at 150 °C for various extensional rates of strain, is plotted against time (Munstedt and Laun, 1979). Qualitatively this figure resembles the results of the Lodge model for a Maxwell model in Fig. 15.26. For small extensional rates of strain (qe < 0.001 s ) 77+(f) is almost three times rj+ t). For qe > 0. 01 s 1 r/+ (f) increases fast, but not to infinite values, as is the case in the Lodge model. The drawn line was estimated by substitution of a spectrum of relaxation times of the polymer (calculated from the dynamic shear moduli, G and G") in Lodge s constitutive equation. The resulting viscosities are shown in Fig. 15.28 after a constant value at small extensional rates of strain the viscosity increases to a maximum value, followed by a decrease to values below the zero extension viscosity. 

Assay Not less than 90.0% polymer, calculated on the anhydrous, ash-free basis. 

Calculation of the infinite lattice sums remains the most difficult step in ab initio polymer calculations. They can be evaluated in configuration space as well as in momentum space (or the two procedures can be also combined). There is not enough experience accumulated in the literature to decide which approach... 

Wavefunctions and Charge Distributions. Though the quality of the wavefunction obtained in a crystal orbital study cannot be assessed by direct comparison with experiment it is of decisive importance from the point of view of prospective transport calculations on conducting polymers (calculation of electron-phonon interaction matrix elements, optical properties, etc.). Of course, the wavefunction also plays a fundamental role when properties related to the many-electron energy are calculated, and therefore the quality of these quantities partially characterizes that of the wavefunction. 

The composition of a vinylidene chloride (VDC)/vinyl chloride (VC) co-polymer, calculated as a function of conversion using such a program, is shown in Figure 6-22. 

A Floating Spherical Gaussian Orbital (FSGO) model for polymers calculation of X-ray diffraction structure factors. They have evaluated electron densities and related X-ray structure factors for polyethylene. 

The kinetics of butadiene polymerized by bis(7T-allyl nickel trifluoro-acetate) has been studied by Teyssie et al. [173]. Equilibrium constants for the formation of the complex (with aromatic compounds which give the equibinary polymer), calculated from cryoscopic measurements or polymer micro-structure, are 6—7 and 26—35 respectively for benzene and nitrobenzene. The higher concentration of active centres compared with... 

Accordingly, the molecular weight of cationic polymers calculated from viscosity measurements corresponds to one basic group per macromolecule [184]. The number of polymer molecules (as well as of basic groups) is very close to the initial initiator concentration and remains constant over a long period, except the very beginning of polymerization [176, 177, 180, 188]. 

Viscosity of linear polymer calculated from Monte Carlo simulations. Filled circles are repton model data from M. Rubinstein, Phys. Rev. Lett. 59,1946 (1987), with data range extended by D. Shirvanyants and open squares are Evans-Edwards model data from J. M. Deutsch and T. L. Madden,... 

Figure 5.2 shows the influence of filler concentration on the density of polymer calculated from the following equation dr... 

Clearly the Edmonds-Ogston and King et aL equations are not valid if the proteins are treated as hard spheres since in that case A44M42/Na = 4v4. If the proteins are treated as flexible coils (without excluded volume) then A44M42/Na 4v4- The validity of Equation 29 depends on the relative size of the protein and polymer. Calculations not shown here indicate that for the cases considered here. Equation 29 is generally valid. 

Figure 3.7. Reduced density as a function of reduced temperature and reduced pressure for polymers, calculated by using the Sanchez-Lacombe equation-of-state in the limit of infinite molecular weight where it becomes a corresponding states theory. Each curve is labeled by the value of the reduced pressure that was used in its calculation.

The solubility parameters of polymers, calculated by utilizing Equation 5.4 in combination with ECOhi and ECOh2 and the molar volumes computed from equations 3.13 and 3.14, are listed in Table 5.2. As mentioned earlier, it is not possible to measure the solubility parameter of a polymer directly, and this property is deduced indirectly from the results of various types of experiments, so that its value is subject to great uncertainty. Experimental" 5 values deduced in this manner for the polymers and tabulated by van Krevelen [2], are also listed in Table 5.2. 

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