Intrinsic viscosity parameter

V 14. Molar intrinsic viscosity J K -M - 4.2Z Intrinsic viscosity parameter K1/2 Ae... 

SEC data for the unknown polydisperse sample can then be obtained on the same instrument using the same solvent and temperature in other words we measure V. and determine Jr Then, as long as we know the values of the intrinsic viscosity parameters K and a for the unknown sample, the molecular weight distribution (the s) and the number... 

Anomalous changes are frequently noted for fractions across the broad molecular weight distribution(s). For example, k + k" / 0.5 —see references (3) and (4). Intrinsic viscosity parameters as a function of percent acetone in E2 solvent are plotted in figure 3 of reference (3) for several PNF fractions. Many other values are tabulated by Hagnauer and Schneider in this reference along with many other solution parameters. Recently, the solution properties of polyphosphazenes have been critically reviewed. Besides polymer quality, there have been problems with tailing" in the fractionation of fluorinated polyphosphazenes as pointed out in reference (15). The quality polymers s)mthesized since the should... 

Comment on the variability of the intrinsic viscosity parameters in the Table X. 

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

Both the intrinsic viscosity and GPC behavior of random coils are related to the radius of gyration as the appropriate size parameter. We shall see how the radius of gyration can be determined from solution viscosity data for these... 

Experiments based on the Poiseuille equation make intrinsic viscosity an easily measured parameter to characterize a polymer. In the next section we consider how this property can be related to the molecular weight of a polymer. 

SAN resins show considerable resistance to solvents and are insoluble in carbon tetrachloride, ethyl alcohol, gasoline, and hydrocarbon solvents. They are swelled by solvents such as ben2ene, ether, and toluene. Polar solvents such as acetone, chloroform, dioxane, methyl ethyl ketone, and pyridine will dissolve SAN (14). The interactions of various solvents and SAN copolymers containing up to 52% acrylonitrile have been studied along with their thermodynamic parameters, ie, the second virial coefficient, free-energy parameter, expansion factor, and intrinsic viscosity (15). 

Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

The solubiHty parameter of a polymer is a measure of its iatermolecular forces, and provides an estimate of the compatibiHty of a polymer with another polymer or a polymer with a solvent. Two components are compatible if they have similar solubiHty parameters. The solubiHty parameter can be determined by various methods, such as intrinsic viscosity and swelling measurements. The solubiHty parameters of various polymers and solvents are tabulated ia refereace handbooks (146,147). It also can be estimated from the stmcture of the polymer (148). 

When viscometric measurements of ECH homopolymer fractions were obtained in benzene, the nonperturbed dimensions and the steric hindrance parameter were calculated (24). Erom experimental data collected on polymer solubiUty in 39 solvents and intrinsic viscosity measurements in 19 solvents, Hansen (30) model parameters, 5 and 5 could be deterrnined (24). The notation 5 symbolizes the dispersion forces or nonpolar interactions 5 a representation of the sum of 8 (polar interactions) and 8 (hydrogen bonding interactions). The homopolymer is soluble in solvents that have solubility parameters 6 > 7.9, 6 > 5.5, and 0.2 < <5.0 (31). SolubiUty was also determined using a method (32) in which 8 represents the solubiUty parameter... 

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

Intrinsic viscosity measurements revealed a conformational transition upon heating from 26 to 40 °C, while the UV absorbance of the solution was insensitive to the change. The entropy parameters for PA were also discussed in light of the Flory-Krigbaum correlation between the second virial coefficient and theta temper-... 

Table 3. Data obtained of intrinsic viscosity and Marck-Houwink parameters of gelatin B at different temperatures.

The classical size-independent combinations are the Floiy parameters that combine the intrinsic viscosity, [rj], and the radius of gyration, Rg. 

Noting the influence of temperature on the intrinsic viscosity is given by the parameter of chain flexibility (dln[ j]/d7), which gives information about the conformation of the macromolecule chain in solution (Kasaii 2007, Chen and Tsaih 1998). The chain flexibility parameter in the temperature range of 20-29°C is dln[t]]/dT = 4,404.11K-i, 0.9993 and in... 

The Mark-Houwink parameters allow to relate the intrinsic viscosity [q] with the viscometric average molecular weight Mv through the relation ... 

Table XLI.—Thermodynamic Parameters Calculated from Intrinsic Viscosities and Their Temperature Coefficients...

Theory presented earlier in this chapter led to the expectation that the frictional coefficient /o for a polymer molecule at infinite dilution should be proportional to its linear dimension. This result, embodied in Eq. (18) where P is regarded as a universal parameter which is the analog of of the viscosity treatment, is reminiscent of Stokes law for spheres. Recasting this equation by analogy with the formulation of Eqs. (26) and (27) for the intrinsic viscosity, we obtain ... 

Parameter relating the intrinsic viscosity to the molecular dimension /r2 (Chaps. VII and XIV). 

Since our indirect method produces both the linear (b=0) and branched intrinsic viscosities across the chromatogram, it is possible to estimate several LCB parameters as a function of elution volume or number average molecular weight. The branching factor G(V) can be written as... 

The rheological behaviour of polymeric solutions is strongly influenced by the conformation of the polymer. In principle one has to deal with three different conformations, namely (1) random coil polymers (2) semi-flexible rod-like macromolecules and (2) rigid rods. It is easily understood that the hydrody-namically effective volume increases in the sequence mentioned, i.e. molecules with an equal degree of polymerisation exhibit drastically larger viscosities in a rod-like conformation than as statistical coil molecules. An experimental parameter, easily determined, for the conformation of a polymer is the exponent a of the Mark-Houwink relationship [25,26]. In the case of coiled polymers a is between 0.5 and 0.9,semi-flexible rods exhibit values between 1 and 1.3, whereas for an ideal rod the intrinsic viscosity is found to be proportional to M2. 

In their seminal work in 1949, Zimm and Stockmayer [69] defined the ratio of the mean square radii of gyration of a branched and a linear polymer of equal molecular weight as the parameter g and is related to the parameter g, which is the ratio of the intrinsic viscosities of a branched and a linear polymer [65-69]. 

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