Macromolecules intrinsic viscosity

Mourey, T.H., Turner, S.R., Rubenstein, M., Frechet, J.M.J., Hawker, C.J., and Wooley, K.L. (1992) Unique behavior of dendritic macromolecules Intrinsic viscosity of polyether dendrimers. Macromolecules 25, 2401-2406. 

Mouiey TH, Turner SR, Rubinstein M, Fiechet JMJ, Hawker CJ, Wooley KL. Unique behavior of dendritic macromolecules intrinsic viscosity of polyether dendrimers. Macromolecules 1992 25 2401-2406. 

Relative methods, on the other hand, measure properties that depend on the chemical and physical structure of the macromolecule. Intrinsic viscosity fractionation and SEC methods are examples of this category in which the measurements are functions of the constitution and configuration of the macromolecule in solution. Relative methods must always be calibrated against an absolute method. 

The intrinsic viscosity (or limiting viscosity number) can be obtained by measuring the relative viscosity at different concentrations and then taking the limit of the specific viscosity when the concentration is extrapolated to zero (Fig. 17.7). The behavior of the intrinsic viscosity with concentration depends on the nature of both the specific polymer molecule and the solvent. Since the intrinsic viscosity of linear polymers is related to the MW, for linear macromolecules intrinsic viscosity measurements provide a simple method for the determination of MW when the relationship between viscosity and MW is known. 

Viscometric contribution of isolated macromolecules intrinsic viscosity... 

VISCOMETRIC CONTRIBUTION OF ISOLATED MACROMOLECULES INTRINSIC VISCOSITY... 

T.H. Mourey, S.R. Turner, M. Rubenstein, J.M.J. Frechet, C.I. Hawker, K.L. Wooley, Unique behavior of dendritic macromolecules intrinsic viscosity of polyetho" dendrimers. Macromolecules 25 (1992)2401-2406. 

However, dendrimeric and hyperbranched polyesters are more soluble than the linear ones (respectively 1.05, 0.70, and 0.02 g/mL in acetone). The solution behavior has been investigated, and in the case of aromatic hyperbranched polyesters,84 a very low a-value of the Mark-Houvink-Sakurada equation 0/ = KMa) and low intrinsic viscosity were observed. Frechet presented a description of the intrinsic viscosity as a function of the molar mass85 for different architectures The hyperbranched macromolecules show a nonlinear variation for low molecular weight and a bell-shaped curve is observed in the case of dendrimers (Fig. 5.18). 

Figure 5.18 Variation of intrinsic viscosity as function of molar mass for linear, hyper-branched, and dendritic macromolecules.

The ionic strength dependence of intrinsic viscosity is function of molecular structure and protein folding, ft is well known that the conformational and rheological properties of charged biopolymer solutions are dependent not only upon electrostatic interactions between macromolecules but also upon interactions between biopolymer chains and mobile ions. Due electrostatic interactions the specific viscosity of extremely dilute solutions seems to increase infinitely with decreasing ionic concentration. Variations of the intrinsic viscosity of a charged polyampholite with ionic strength have problems of characterization. 

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... 

Antonietti M., Briel A., Fosrster S. Quantitative Description of the Intrinsic Viscosity of Branched. Polyelectrolytes. Macromolecules 1997, 30, 2700-2704. 

Chen R.H., Tsaih M.L. 1998. Effect of temperature on the intrinsic viscosity and conformation of chitosans in dilute HCl solution. International Journal of Biological Macromolecules 23,135-141. 

Curvale, R. Masuelli, M. Perez Padilla, A. 2008. Intrinsic viscosity of bovine serum albumin conformers. International Journal of Biological Macromolecules 42, 133-137. 

Multiple Linear Least-Squares Fits with a Common Intercept Determination of the Intrinsic Viscosity of Macromolecules in Solution. Journal of Chemical Education 80(9), 1036-1038. 

Stigter, D, Ionic Charge Effects on the Sedimentation Rate and Intrinsic Viscosity of Polyelectrolytes. T7 DNA, Macromolecules 18, 1619, 1985. 

Another investigation involved the SC VP of a macroinimer 8 via ATRP [46]. GPC/viscosity measurements indicated that the intrinsic viscosity of the branched polymer is less than 40% of that of the linear one at highest MW area (Fig. 6). A significantly lower value for the Mark-Houwink exponent (a=0.47 compared to a=0.80 for linear Pf-BuA) was also observed, indicating the compact nature of the branched macromolecules. 

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. 

Viscosimetric studies of organotin copolymer solutions allow the changes in the shape of the macromolecules to be followed as a function of the electrostatic charge. From the plot of the intrinsic viscosity of copolymers in DMFA solution against the degree of dilution it is seen that increasing dilution results in a rise of viscosity, probably due to an extension of macromolecular chains accompanied by conformational transformations. Naturally, this rise in viscosity with dilution cannot proceed infinitely since a coiled chain cannot be extended more than a completely extended chain conformation, due to intramolecular repulsion. 

JG Kirkwood, J Riseman. The intrinsic viscosities and diffusion constants of flexible macromolecules in solution. J Chem Phys 16 565-573, 1948. 

The next step consists of the determination of the size of the macromolecules in space. Two equivalent sphere radii can be measured directly by means of static and dynamic LS. Another one can be determined from a combination of the molar mass and the second virial coefficient A2. Similarly, an equivalent sphere radius is obtained from a combination of the molar mass with the intrinsic viscosity. This is outlined in the following sections. 

The viscosity of the solution is significantly increased when macromolecules are dissolved in a solvent. The specific viscosity of a solution t sp=(ri-r o)lr o expected to increase proportionally to the concentration c. The reduced viscosity rjgp/c still increases with increasing concentration. The data, however, can be extrapolated to zero concentration and results in the intrinsic viscosity, or the viscosity number [77], sometimes also called the Staudinger index... 

All measurements, of course, have to be made at a finite concentration. This implies that interparticle interactions cannot be fully neglected. However, in very dilute solutions we can safely assume that more than two particles have only an extremely small chance to meet [72]. Thus only the interaction between two particles has to be considered. There are two types of interaction between particles in solution. One results from thermodynamic interactions (repulsion or attraction), and the other is caused by the distortion of the laminar fiow due to the presence of the macromolecules. If the particles are isolated only the laminar flow field is perturbed, and this determines the intrinsic viscosity but when the particles come closer together the distorted flow fields start to overlap and cause a further increase of the viscosity. The latter is called the hydrodynamic interaction and was calculated by Oseen to various approximations [3,73]. Figure 7 elucidates the effect. 

The shift in the intrinsic viscosity is easily understood in qualitative terms. Assuming validity of the Fox-Flory relationship also for branched macromolecules one can write... 

The observed decrease in [ri] (see Fig. 16) can be understood when recalling that due to Marriman and Hermans [98] the intrinsic viscosity of polydisperse macromolecules is given by the ratio of two number averages... 

Fig. 23. The intrinsic viscosity of several end-linked PS star molecules as a function ofM [95]. In the limit of low and high molar masses asymptotic power law behavior may be derived. That at low molar masses is widely controlled by the presence of non-reacted star molecules, that at high molar masses is expected from theory for randomly branched macromolecules. The exponents of the two asymptotic lines are a =0.49 0.08 for M <0.8x10 g/mol and a =0.18 0.05 for M >2.0xl0 g/mol. Reprinted with permission from [95]. Copyright [1997] American Society...

Keywords. Dendrimers, Hyperbranched macromolecules. Block copolymers. Surface functionalization, Solvatochromism, Intrinsic viscosity... 

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