Inverse intrinsic viscosity

The experimental determination of polymer intrinsic viscosity is done through the measurement of polymer solution viscosity. The connotation of intrinsic viscosity [hi/ however, is very different from the usual sense of fluid viscosity. Intrinsic viscosity, or sometimes called the limiting viscosity number, carries a far more reaching significance of providing the size and MW information of the polymer molecule. Unlike the fluid viscosity, vdiich is commonly reported in the poise or centipoise units, the [h] value is reported in the dimension of inverse concentration xinits of dl/g, for exanple. The value of [hi for a linear polymer in a specific solvent is related to the polymer molecular weight (M) through the Mark-Houwink equation ... 

Other models are based upon the immiscibility of polymer blends described above, and they model the system as Newtonian drops of the dispersed polymer with concentration (pi in a Newtonian medium of the second polymer with concentration (p2 = — (pi. There exists some concentration, cpu = cp2i — 1, at which phase inversion takes place that is, at snfficiently high concentration, the droplet phase suddenly becomes continuous, and the second phase forms droplets. The phase inversion concentration has been shown to correlate with the viscosity ratio, A. = r i/r 2, and the intrinsic viscosity for at least a dozen polymer alloys and blends ... 

Another interesting contribution to the study of viscosity behavior in the helix-coil Jransition region is the one due to Hayashi et al. (22) on a PBLA sample (Mw = 23.2 x 104) in m-cresol and a mixture of chloroform and DCA (5.7 voL-% DCA). As mentioned in Chapter B, PBLA undergoes an inverse transition in the chloroform-DCA mixture, while it undergoes a normal transition in m-cresol. Furthermore, its cooperativity parameter is distinctly smaller in the former solvent than in the latter. Thus we may expect that, when compared at the same helical fraction and chain length, the PBLA molecule in the chloroform-DCA mixture assumes a more extended shape and hence a larger intrinsic viscosity than in m-cresol, provided these two solvents have comparable solvent powers for the polymer. The experimental results shown in Fig. 32 are taken to substantiate this prediction, because the approximate agreement of the data points atfN=0 indicates that the two solvents have nearly equal solvent powers for the solute. 

In ordinary vinyl polymerizations, molecular weight varies inversely with the square root of the initiator concentration. In the case of acrylonitrile at 40°, intrinsic viscosity varies as /-°-2 which implies that molecular weight varies as 7-°-3 (126). 

The enzymic activity was proportional to the change of the inverse of the numerical average molecular weight per time unit. The linear relationship between Mv and Mn allowed a simple calculation of the activity from the knowledge of the intrinsic viscosity at zero shear rate as a function of the reaction time. A practical example is given. 

While steric hindrance may play a role in decreasing rates and molecular weights in dimethyl itaconate polymerization, the limited effect of initiator concentration on molecular weights as measured by the intrinsic viscosity suggests other factors must be present. Pol5unethyl methacrylate formed at 60° with benzoyl peroxide initiator shows an inverse proportionality of degree of polymerization with polymerization rate as ifrould be expected kinetically for bimolecular termination. 

The term dn/dc refers to the change in RI of a polymer relative to its concentration. The LS detector responds to M, the VISC detector responds to the intrinsic viscosity ([t]]), which is inversely proportional to molecular density, and the RI detector monitors concentration (C). A single narrow standard is used to determine the offset constants related to the interdetector volume for a given three-detector system [5]. Either C or dn/dc of a polymer sample must be known a priori in order to calculate the other variable using the RI detector [Eq. (3)]. Once both dn/dc and C are known, the LS and VISC [Eqs. (1) and (2)] can be solved to determine M and [77], respectively, for a polymer sample [3]. Structural information, such as chain flexibility, branching, and intramolecular interactions are all related to [7]]. Several key polymer properties related to [iq] are as follows ... 

HEMA, MMA, and MAA or DMAEMA (66, 67). Polymer molecular weight control was attempted by adjustment of initiator concentrator through the presumed inverse square root relationship between initiator level and kinetic chain length, (63) and this was reflected in measured intrinsic viscosities. Comparisons across a series are made difficult by changing Mark-Houwink-Sakurada coefficients. However direct comparisons may be made between polymers of similar composition, for example lc, 2c, and 3c, to show an expected increase in hydrodynamic volume from series 1 through series 3. 

In Eq 7.8 ( ) is the maximum packing volume fraction, and [q] is the intrinsic viscosity. The computed curves are shown in Figure 7.2. To calculate these dependencies ( ) = 0.8 and [rj] = 2 were assumed. The six points of intersection represent the iso-viscous conditions for the dispersions of liquid 1 in 2 and liquid 2 in 1, or in other words, the conditions for phase inversion. 

Eor anisometric particles it is useful to use the particle aspect ratio, p, defined as a ratio of two orthogonal axes. For prolate ellipsoids (fibers) p > 1 is the length-to-diameter ratio, whereas for oblate ellipsoids (plates) p < 1 is the thickness divided by the largest dimension of the plate. It was observed that both, the intrinsic viscosity, [T ], and the inverse of the maximum packing... 

Measurement of the Intrinsic Viscosity The principle behind capillary viscometry is the Poiseuille s law, which states that the time of flow of a polymer solution (ps) through a thin capillary is proportional to the viscosity of the solution. The latter increases with increasing solution concentration. From Equation 17.6, the time of flow of the solvent (solv) or of the polymer solution will be proportional to the viscosity, and inversely proportional to the density ... 

Figure 12.2.13. Dependence of the intrinsic viscosity [tj] of hyaluionic acid ( =0.72) and its benzyl derivatives with decreasing linear charge density, on the inverse square root of ionic strength, 1, at 25 C.

In these equations f/,p is defined as the specific viscosity, is the relative viscosity, is the reduced viscosity and [> ] is the intrinsic viscosity. The relative and specific viscosities are dimensionless and the intrinsic viscosity is either expressed in decilitres per gram or millilitres per gram, i.e. the inverse of concentration. 

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