Calculated versus measured molecular

The measured NMR signal amplitude is directly proportional to the mass of adsorbate present, and the NMR signal versus pressure (measured at a fixed temperature) is then equivalent to the adsorption isotherm (mass of adsorbate versus pressure) [24-25]. As in conventional BET measurements, this assumes that the proportion of fluid in the adsorbed phase is significantly higher than the gaseous phase. It is therefore possible to correlate each relaxation time measurement with the calculated number of molecular layers of adsorbate, N (where N = 1 is monolayer coverage), also known as fractional surface coverage. 

Dutta [27] provided a comparison between experimental and calculated zero-shear viscosities from Eq. (4.12) for 35 different polymer grades covering several polymeric species of widely varying melt flow indices. However, the given plot of % (calculated) versus 110 (measured) on log-log scales of 3 X 3 cycles masks a lot of error in the estimate. MFI is rather insensitive to changes in molecular-weight distribution (MWD) as can be seen from Fig. 4.3 (from Hanson [9]). However, MWD has profound effects on low-shear viscosity behavior. 

Rheological methods of measuring the interphase thickness have become very popular in science [50, 62-71]. Usually they use the viscosity versus concentration relationships in the form proposed by Einstein for the purpose [62-66], The factor K0 in Einstein s equation typical of particles of a given shape is evaluated from measurements of dispersion of the filler in question in a low-molecular liquid [61, 62], e.g., in transformer oil [61], Then the viscosity of a suspension of the same filler in a polymer melt or solution is determined, the value of Keff is obtained, and the adsorbed layer thickness is calculated by this formula [61,63,64] ... 

Figure 8 Compressibility factor P/fiksT versus density p = pa3 of the hard-sphere system as calculated from both free-volume information (Eq. [8]) and the collision rate measured in molecular dynamics simulations. The empirically successful Camahan-Starling84 equation of state for the hard-sphere fluid is also shown for comparison. (Adapted from Ref. 71).

Viscometry The specific viscosity of each polymer from the bulk polymerization was measured in acetone at 30°C using an Ubbelohde dilution viscometer. Five concentrations in the range of 1.120 to 0.242 g/d poly(vinyl acetate) and polyvinyl trideuteroacetate) and 0.385 to 0.084 g/dl (poly(trideu-terovinyl acetate)) were run. Intrinsic viscosity was calculated by extrapolation of the Tlsp/c versus c plot to zero concentration. Number average molecular weights were calculated using the equation(20) [q] =1,0 x 10 1 [Mn] 0 72 which is in the mid range of the equations listed. 

Another issue under investigation is the evolution of the second-order hyperpolarizability upon elongation of the 7r-electron path in a molecular backbone. Measurements and quantum-chemical calculations provide an empirical power law of the second-order hyperpolarizability y versus conjugation length (or the number of monomer units n) in short oligomers. 

Fig. 3. Stoichiometric DGEBA/DDS network M, versus prepolymer resin molecular weight. M . (M, calculated from equilibrium rubbery moduli at T = T, -h 45 K). O M, from equihbrium tensile experiments M, from 0.16 hz dynamic mechanical storage modulus measurements (After LeMay >)...

Smaller molecules and inert gas atoms have been extensively studied using EFISH in the gas phase (see for example Miller and Ward, Ward and Miller, Shelton ). Shelton and Rice provide a comprehensive list of gaseous EFISH measurements on small molecules up to 1994. The only such result reported for molecules with donor/ acceptor substitution on a benzene ring appears to be that obtained by Kaatz et alP for pNA in 1998. In this experiment a gas mixture containing 0.075 mole fraction of pNA was used to obtain an EFISH measurement at 1064 nm at one temperature. The y (—2(B (B,a),0) of eqn (4.15) was estimated from a THG experiment and taken as the intercept on a two point plot of y versus /T. The value of was calculated from the slope. The linearity of such plots has been confirmed in the work on smaller molecules. The gas phase method differs from that used for solutions in that the extrapolation to infinite dilution is not made since the molecular density in the gas is very much smaller. Also the internal field factors are close to unity. It is usually possible to make measurements over a sufficiently wide range of temperatures to obtain the quantity (jifi/k) from the plot of F versus l/F. In the case of pNA the value of the dipole was chosen as 6.87 D. 

In order to calculate the molecular weight M) or molecular-weight distribution (MWD) of the polymer, the dependence of the Soret coefficient on M must be known. Because is virtually independent of M, at least for random coil polymers, the dependence of retention on M reduces to the dependence of D on M. The separation of molecular-weight components by D (or hydrodynamic volume, which scales directly with D) is a feature that thermal FFF shares with size-exclusion chromatography (SEC). In the latter technique, the dependence of retention on D forms the basis for universal calibration, as D scales directly with the product [rjjM, where [17] is the intrinsic viscosity. Thus, a single calibration plot prepared in terms of log([i7]M) versus retention volume (F,) can be used to measure M for different polymer compositions, provided an independent measure of [17] is available. In thermal FFF, a single calibration plot can only be used for multiple polymers when the values of for each polymer-solvent system of interest are known. However, a single calibration plot can be used with multiple channels. In... 

If the values of A, 6, and Dj are available, the molecular weight of a polymer can be directly determined from its retention time using Eq. (3). If Dj is not available, one may use a calibration curve [log DlDj) versus log M] constructed with a series of narrow polystyrene standards of known molecular weights. For the molecular-weight analysis of an unknown, the DlDj value of the sample is first calculated from its measured retention time, and then the molecular weight is determined from the calibration curve. 

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