Intrinsic Viscosity of Polymers

2 Intrinsic Viscosity of Polymers In the absence of flow, the solution is isotropic. Each component (x, y, z) of q, is independent. Then, = (, a) 

In the presence of flow, the bead at r has an additional velocity kt , as we learned in Section 3.3.4 The equation of motion for the nth bead, given by 

Note that kf is a linear function of r . With the preaveraging approximation for and conversion to the normal coordinates, it is straightforward to see the equation of motion for the ith normal mode acquire an additional term  

Although we have used the Zimm model here, this equation is apparently valid for the Rouse model as well. The off-diagonal elements of the tensor k couple different components (jc, y, and z) of q as we will see below, but q, of different i are still independent of each other. 

Now we consider a steady shear flow Bvjdy = k = k, other elements are zero, as given by Eq. 3. 107. This tensor couples and q/y-. 

Owing to the coiled configurations of molecular chains, the viscosity r of dilute polymer solutions increases with respect to that of the solvent, rj. The difference q — is proportional to the radius of the coil and the number of coils per unit of volume is C/M)N, where C is the concentration of polymer in the solution, M is the molecular weight of the polymer, and is Avogadro s number. Since the radius of the coil can be expressed in terms of the mean square end-to-end distance, (r ), the specific increment of the viscosity of the solution due to the polymer can be written as 

Since AP 0, 0. The shear stress is related to the shear rate by the 

Considering the boundary condition v = 0 for y = h/2, the integration of Eq. (13.55) gives the velocity profile along the y axis  

For Newtonian and non-Newtonian liquids, the shear stress at the wall is given by Eq. (13.54). The shear rate at the wall for Newtonian hquids can be expressed in terms of the volumetric flow, making = 1 in Eqs. (13.57) and (13.58). In this case, this quantity can be written as 

In the case of a non-Newtonian fluid, the true wall shear rate Yww can be calculated by using a procedure similar to the Rabinowitsch equation for capillary flow, obtaining 

---

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. 

Table III. Measured Relative Molecular Weight, Passed Through GPC and Reduced Viscosities. Estimated Intrinsic Viscosities of Polymers Columns in Benzene ...

A continuous capillary viscosity detector has been developed for use in High Performance Gel Permeation Chromatography (HPGPC). This detector has been used in conjunction with a concentration detector (DRI) to provide information on the absolute molecular weight, Mark-Houwink parameters and bulk intrinsic viscosity of polymers down to a molecular weight of about 4000. The detector was tested and used with a Waters Associates Model 150 C ALC/GPC. The combined GPC/Viscometer instrumentation was automated by means of a micro/mini-computer system which permits data acquisition/reduction for each analysis. 

In order to determine g as a function of molecular weight, one approach is to use universal calibration with SEC analysis of molecular-weight polydisperse samples (31-33). For a multiarm (MA) branched material, the intrinsic viscosity of polymer eluting in v is ... 

Temperature (°C) Intrinsic Viscosity of Polymer (dL g-1) Ultimate Conversion of Monomer (%) Proportion of Tetramer (%)... 

In some cases, the selection of SEC for the particular application seems to be illogical. A typical example is the determination of the intrinsic viscosities of polymer samples by SEC. Here a simple and cheap glass viscometer is substituted by a rather expensive sophisticated SEC instrument. However, the advantage of SEC is evident when value of manpower, as well as speed and precision of determinations is taken into account. 

On the other hand, the slope of the lines plotted in Fig, 38, from the value of which the mean life of the chains is calculated, may be greatly effected even by small errors in the determination of the intrinsic viscosity of polymers obtained by shorter time tests. The resulting data are mostly concerned by eventual errors. 

The intrinsic viscosities of polymers, including branched ones, have been reviewed by Berry and Casassa (32). 

An important empirical generalization about the intrinsic viscosity of polymer solutions is given by... 

Pyun,C.W Fixman,M. Intrinsic viscosity of polymer chains. J. Chem. Phys. 42, 3838-3844 (1965). 

Fig. 12. Intrinsic viscosities of polymers prepared in nitrobenzene at 25° as a function of [M 0...

Degradation in bulk. Davis and Golden (85) have studied the degradation of PTHF in bulk at various temperatures. The polymers that they studied were prepared using a THF/PF5 complex either in an open flask (polymer A) or in vacuum with exposure to air during the work up (polymer V). The intrinsic viscosity of polymer A. heated at fixed temperatures up to 150° C in a sealed system, fell rapidly to a constant value. Polymer V behaved similarly but the decrease was considerably smaller. When heated in air at a fixed temperature the viscosity of both polymers decreased continuously with eventual destruction of the polymer. Temperatures well in excess of 150° C were required for complete degradation of polymer A or V in vacuum. 

Curves 2-4 in Fig. 5 give the dependence of Tcl on intrinsic viscosity of polymer solutions, which is in a first approximation proportional to the degree of polymerization. 

Another unusual temperature effect is observed in comparing the intrinsic viscosity of polymer prepared with chemical initiators at a series of temperatures from 25° to 100° (7, 126). A distinct maximum appears at a temperature of preparation in the 50° to 60° range, whereas one expects a monotonic decline with temperature. 

In view of experimental simplicity and accuracy, viscosity measurements are extremely useful for routine relative molecular mass determinations on a particular polymer-solvent system. K and a for the system are determined by measuring the intrinsic viscosities of polymer fractions for which the relative molecular masses have been determined independently - e.g. by osmotic pressure, sedimentation or light scattering. 

K 12 — L. Mandelkern and P. J. Flory Molecular weight dependence of intrinsic viscosity of polymer solutions. J. Polymer Sci. 9,381 (1952). 

Figure 5. Yield and intrinsic viscosity of polymer in the peroxide-initiated condensation of sodium 2,6-dichloro-4-bromophenolate...

Intrinsic Viscosity of Polymers Determination by GPC Yefim Brun... 

The intrinsic viscosity of polymers in dilute solutions is an extremely important measure of the coil size, owing to its simplicity and precision. The Zimm model leads directly to the Fox-Flory equation for intrinsic... 

The distinction between poor and good solvent was introduced in the 1950s by Fox and Flory after experimental studies of the intrinsic viscosity of polymer solutions. These authors recognized that the viscosity varies in relation to the dependence of the chain sizes on temperature the poor solvent state is the state of a solution in which the chains have quasi-Brownian configurations. Systematic experiments have been made in this domain, for instance to determine the Flory temperature, but they have never given very precise results. Physicists are just now beginning to overcome the experimental and theoretical difficulties. Experiments have been made to show the existence of a collapse of the polymer chain, and certain authors have been prone to compare it with the coil-globule transition in proteins. 

A measurement of the intrinsic viscosities of polymer solutions containing fractions of polyisobutylene with known molar masses dissolved in diisobutylene yielded the data ... 

Nowadays, the new GPC hardware can have different detectors coupled, such as viscosity detectors, which allow measurements in situ of the intrinsic viscosity of polymers as well as the constants K and a. Using this advanced equipment, one can obtain the MW and intrinsic viscosities of polymers in a very short time. 

The decrease is due to the incompatibility existing between polymer A and polymer B. The quantity A[t7]b = ([t ] B [t ] BA)/[t ]B similarly gives the decrease of the intrinsic viscosity of polymer B due to the presence of polymer A in the solvent. The constant quantity of the polymer A or B in the mixture, solvent plus polymer, is always the same (typically 0.125 X10 g/cm ). Then the quantity A[i7]ab given by Equation (4.4) expresses a measure of the incompatibility existing between polymer A and polymer B. A high value of AjtjjAB for a polymer pair indicates a high value of incompatibility and vice versa. 

In its turn, the value a is linked with intrinsic viscosities of polymer in arbitrary [r ] and 0-solvent [rjjg according to the Eq. (6). The bulk interactions (which result in deviation of coil shape from ideal Gaussian one) parameter e is determined as follows [22] ... 

Lee J, Tripathi A (2005) Intrinsic viscosity of polymers and biopolymers measured by microchip. Anal Chem 77 7137-7147... 

FIGURE 1 The intrinsic viscosity of polymer blend solutions versus composition of blend in mass fraction W, solvent-chloroform, polymer blend of poly(hydroxy butyrate) (PHB), and poly(ethylene oxide), the solid curve represents the linear regression curve. 

Here [t ] and [ti/ aie limiting viscosity numbers (intrinsic viscosities) of polymer in the given and in the theta solvents, respectively. 

FIG U RE 12 Schematic representation of construction of the SEC calibration dependence. M is the peak molar mass (most abundant in the sample), [t]] is the limiting viscosity number (intrinsic viscosity) of polymer, [t]] = (for linear, coiled macromolecules)... 

---