Polymers average measures

Figure 3. Porosity measurements on a microscopic scale for a small (2 cm X 2 cm X 30 urn) thin section of sandstone impregnated with fluorophor-doped polymer. Average porosity - 16.3% range of porosities - 1.8-42%.

Elemental analyses were performed by Galbraith Laboratories, Inc., of Knoxville, TN. The compositions of the HS-MOTSS copolymers were derived from the average of the values calculated from the reported halogen and silicon content. The molecular weight and dispersity of the polymers were measured in tetrahydrofuran by size... 

A fictitious example illustrates the large potential value of even small improvements in the control of a manufacturing process. Suppose one has a continuous process in which the final product (a polymer) is sampled and analyzed to be sure the copolymer composition is within specifications. A sample is taken from the process once every 2 hours, and it takes about 2 hours for the lab to dissolve the polymer and measure its composition. This process produces a number of different copolymer compositions, and it transitions from one product to another about twice a month on average. The 2-hour wait for lab results means that during a transition the new product has been within specification limits for 2 hours before the operators receive lab confirmation and are able to send the product to the in-spec silo. Consequently, on every transition, 2-hours worth of in-spec polymers are sent to the off-spec silo. 

For a polydisperse polymer, experimental measurements of M for the chromatogram at high Tr may not be accurate. When average molecular weights are computed from the distribution w(M) derived fromdata obtained with concentration and molecular weight detectors, the value of Mw is likely to be more valuable than M , which could be substantially in error [25,26]. 

As a result, the site-dependent nonradiative process of individual C molecules is responsible to biexponential fluorescence decay curves of CV observed in the ensemble-averaged measurement. Our single-molecule study presented in this section will open new possibilities in the experimental study of dynamic response of condensed matter, such as polymers and liquid. We further expect that dye molecules with flexible molecular structures like CV are useful to sensitive local probes for microscopic dynamics of various host mediums. 

Synthetic polymers are often produced with a range of degree of polymerization and molecular weight. As shown next, a molecular weight determined for such a polymer by measurement of osmotic pressure is a number-average molecular weight. 

The data of column 4 show the apparently paradoxical result that the mass of polymer alone (measured in air) is greater than that of the polymer plus liquid modulation layer. This is clear evidence that the oxidized PVF-co-PVP film is non-rigid in CH2C12. For this particular film, the dry mass of oxidised copolymer (including counter ion required by electroneutrality) corresponds to deposition of 29 nmol of ferrocene sites. The deposition process involved passage of 3.32 mC of charge, i.e. 34 nmol of ferrocene sites were oxidized in total. This implies an (average) deposition efficiency for this experiment of 85%. 

The number average molecular weight of the degraded polymers was measured on an ebulliometer, using toluene as a solvent and a tristearin standard. Intrinsic viscosities of the polymers were determined using a Desreux dilution viscometer. 

Since the numerator of Eq. 20.7 represents the mass of the polymer sample measured, and the denominator the total number of polymer molecules present, the result of this calculation is simply the average molecular weight per polymer molecule in the sample. 

Carbon 13 nuclear magnetic resonance can be used quantitatively in analyses of polymers to measure conveniently comonomer concentrations, average sequence lengths, run numbers and comonomer triad distributions. 

Traditionally, solutions have been used to characterize the polymer — to measure its molecular weight averages, e.g., number, weight and z-average M, M, and M, or the size of its macromolecular coil. The latter maybe expressed as the unperturbed end-to-end distance (six times larger) or the radius of gyration, viz. ... 

Mark-Kuhn-Houwink equation, derived on the basis of large experimental material analysis, obtained wide spreading for polymers average viscosity molecular weight determination by their solutions intrinsic viscosity [r ] measured values [1]. This equation has a look like ... 

Oxygen permeability coefficients for each polymer were measured at least 3 times and the deviations were 5-15%. The permeability coefficients listed in Tables 1 and II are the average values. 

Montaudo, G., Scamporrino, E., Vitalini, D., and Mineo, P., Novel Procedure for Molecular Weight Averages Measurements of Polydisperse Polymers Directly from Matrix-assisted Laser Desorption/Ionization Time-of-flight Mass Spectra, Rapid Comm. Mass Spectrom., 10,1551,1996. 

Refractive Index. The refractive indices of the bulk polymers were measured by using an Abbe s refractometer at room temperature. In order to measure the refractive indices at several wavelengths, an interference filter was inserted in the refractometer. Two or three measurements were made at each wavelength and averaged. Usually, the refractive-index data were fit to a three-term Sellmeier dispersion equation of the form (P) ... 

The number average molecular weight determines the colligative properties (i.e., those which depend only on the number of dissolved molecules) of polymer solutions. Measurements of freezing point depression (cryoscopy) or... 

The viscosity of polymer solutions depends on both the concentration and the molecular weight of the polymer. Thus, measurement of the viscosity of a solution of polymer can be a way to determine the molecular weight of the dissolved polymer. This can actually be the case providing that the coefficients K and a of the Mark-Houwink-Sakurada equation (Equation 2.5) giving the relationship between the intrinsic viscosity of the polymer, [tj], and the viscosity average molecular weight, M, are known. 

Because the amount of polymer samples available is usually not limited, it is possible to underestimate the sensitivity issue in MALDI polymer characterization. In reality, the use of a MS instrument that provides high sensitivity and a wide dynamic range of ion detection is pivotal to the success of polymer analysis. This is true not only for the measurement of polymer average mass, but also for the determination of polymer composition [110, 113-121]. With limited detection... 

Here the index i refers to a retention volume slice, C, is the polymer concentration measured by SEC for the slice i, Mi is MW determined by light-scattering analysis at retention volume slice i, and [77, ] is the intrinsic viscosity determined by viscometry of slice i. The constants k and a are the Mark-Houwink coefficients for a linear polymer of the same chemical composition My is the viscosity-average MW (Lue and Kwalk 2005). 

Polydispersity n. The breadth of the molecular-weight distribution of a polymer. Two measures of polydispersity are in common use (1) the ratio of the weight-average and number-average molecular weights MJM y and (2) the g-index. 

When c —> 0 (where f) D-i Do) the experimenter s main trouble is to eliminate the contribution of intramolecular motion modes by means of extrapolation q —> 0. At finite polymer concentrations, measurements of the first cumulant ACi, o 6 ve an average diffusion coefficient (see Kquation 3.3-8.5 and curve 3 in Figure 3.41). 

Because the osmotic pressure of a polydisperse polymer solution in which polymers of the same chemical species but different molecular weight are dissolved is related to the average molecular weight of the polymers, we can infer the molecular weight of the polymers by measuring the osmotic pressure of their solutions. 

Average molecular weights of the polymers were measured by means of gel-permeation- chromatography using universal calibration. 

---