Dimensions, from viscosity

Flory s viscosity theory also furnishes confirmation of the w temperature as that in which a=V.2, and it permits the determination of the unperturbed dimensions of the Polymer chain. Even if a Q solvent is not available, several extrapolation techniques can be used for the estimating the unperturbed dimensions from viscosity data in good solvents. The simplest of these techniques seems to be that of Stockmayer. 

Determination of Polymer Molecular Dimensions from Viscosity... 

Molecular Dimensions from Viscosity Measurements. According to Equation (9-148), the intrinsic viscosity is related to the radius of gyration. Furthermore, in very dilute solutions, [ry] rj p/c, and, consequently,... 

Pxampk 2. A smooth spherical body of projected area Al moves through a fluid of density p and viscosity p with speed O. The total drag 8 encountered by the sphere is to be determined. Clearly, the total drag 8 is a function of O, Al, p, and p. As before, mass length /, and time t are chosen as the reference dimensions. From Table 1 the dimensional matrix is (eq. 23) ... 

Deb P.C., Chatterjee S.R. Unperturbed dimension of polymer molecules from viscosity measurements. Die Makromolekulare Chemie 120,1 (1968) 49-57. 

In Section II.B of Chapter 3, the tube flow viscometer was described in which the viscosity of any fluid with unknown viscous properties could be determined from measurements of the total pressure gradient (— A4>/L) and the volumetric flow rate (Q) in a tube of known dimensions. The viscosity is given by... 

We have omitted a great deal of detail in this discussion of polymer viscosity. The interested reader will find some of the missing information supplied in Flory (1953). In particular, we have omitted all numerical coefficients, which limits us to ratios as far as computational capability is concerned. Numerical coefficients are available for Equation (92), for example, and this allows coil dimensions to be evaluated from viscosity measurements. A general conclusion that unifies all of this section is that any factor that causes a polymer chain to be more extended in space —whether by coil unfolding or swelling by solvent —tends to increase [77]. This is exactly what we expect in terms of the purely qualitative picture provided by Figure 4.8. Example 4.6 illustrates this for some actual polymers. 

Rankine and Smith 3 have employed the method of determination of the molecular dimensions of gaseous molecules from viscosity measurements to decide the constitution of the sulphur dioxide molecule. From... 

There are presently two main difficulties which handicap attempts at exact calculation. The first concerns the intermolecular potential, and the hazards of extrapolation from models derived from viscosity measurements have been discussed. Furthermore, such a method is of dubious validity for polyatomic molecules, because the intermolecular repulsive potential will generally appear to become progressively shallower with increasing molecular dimensions if the viscosity data are cast, for example, in the Lennard-Jones form. Energy transfer depends... 

B 17 Bxjeche, A. M. Dimensions of coiling polymer molecules from viscosity and light scattering. J. Am. Chem. Soc. 71, 1452 (1949). 

This point has been debated by many authors, and we shall briefly discuss it later. Let us first review some data, attention of course being focused on macroion coils and the evaluation of imperturbed dimensions from intrinsic viscosity-molecular weight data determined at T >. ... 

Before becoming too optimistic about the possibility of evaluatii unperturbed macroion dimensions from the procedure outlined above, we must recall two serious objections advancal by Flory 49), First of all. extrapolations of intrinsic viscosity data for the graphical evaluation of K, as required by equations (2) and (3), as well as by the equation of Flory and Fox [50), are extrapolations into a region in which approximate theories of pol5nner solutions are no longer tenable. Secondly, Flory indicates that there is at least one case which clearly shows that the application of equation (3) leads to physically irrational conclusions, namely the case of hydroxyethylcellulose in aqueous solution. Flory s original paper must be consulted for a clearer appreciation of the two important objections indicated above. The first objection is of basic importance and it is perhaps worthwhile to digress briefly and to try... 

More recently Lapanje and Tanford (59) have reported osmotic pressure measurements for reduced protein polypeptide chains in 6M guanidine hydrochloride. Second virial coefficient data and intrinsic viscosity data are combined by these authors to yield unperturbed dimensions of randomly coiled proteins. The result is assentially identical with that obtained earlier from viscosity data alone. 

Deriving molecular dimensions in solution from viscosities depends on the model assumed for the conformations of the free molecules. Since any a- or - triple helical sections of our gelatins vrc>uld be melted at 30 C. we assume near randomness for the chains, and a lew ellipticity for the molecular envelopes. Further, the success of Flory s viscosity theory (17) has shown that the hydrodynamically effective volume of randomly coiled (and of many other) chain molecules is not very different from the volume encompassed by the meandering segments. Thus we treated our data as if they pertained to random coil molecules. The measured layer thicknesses then describe the level within the adsorbed interphase below v ich the segmental density is equal to, or larger, than the effective coil density of the free molecules. 

In [11], a theoretical value of is estimated from column dimensions, gas viscosity, and pressure drop. Calculation is easy, and possible errors in variables related to column geometry (such as column length and diameter) can be... 

Source From Viscosity-molecular weight relationships and unperturbed dimensions of linear chain molecules, in Polymer Handbook. ... 

The calculated dimensions of the polymers are reported in Table n. The radii of gyration (R s) were calculated from viscosity/molecular weight relationships in a good solvent (7). 

Rotational viscometer n. An instrument for measuring the viscosity of pourable liquids, slurries, plastisols, and solutions. Most are of the bob-and-cup type. In these, the bob is a polished, accurate cylinder that is immersed in the liquid contained in the cup. Either the bob or cup is rotated and the torque on one or the other is measured, as is the rotational velocity. From these and the dimensions, the viscosity can be inferred, either directly by calculation from principles or indirectly by calibration with standards of known viscosity. An instrument widely used in the plastics industry is the Brookfield viscometer. 

Determination of the Polymer Coil Dimensions from the Intrinsic Viscosity... 

The assumption in Determination of the polymer coil dimensions from the intrinsic viscosity in Chap. 7 that the polymer coils in solution behave like hard spheres with a constant density inside the coil and a fixed boundary to the solvent is only a simple approximation. In reality, a polymer chain shows a dynamic behavior with fast and statistically changing conformations. 

Adapted from the technology implemented in scanning near field optical microscopy, SECM with shear-force detection involves vibrating the SECM tip with a piezoelectric acmator and recording variations in resonance frequency when the tip is within a few hundred nanometers from the sample surface [124,125]. This is a fast method when operated in real time during the scan, but it is tricky to implement in practice. The tip must be long and narrow to be appropriately flexible but, more importantly, the control loop parameters need to be frequently adjusted as the resonance and shear force properties vary with the tip dimensions, solution viscosity, and sometimes with the elasticity of the sample surface. Moreover, the parameters need to be readjusted if the tip is removed for polishing. 

From Equation 10.21, the dimensions of viscosity are stress multiplied by time, and in the SI system viscosity is measured in units of pascal-seconds (Pas). For polymer melts and solutions, the fluid behavior is non-Newtonian and Equation 10.21 must be modified to allow the viscosity to become a material function of the shear rate. Similarly, material elements may be deformed by pulling on opposite sides of the cube with an equal force this constitutes an extensional deformation that may be characterized by an extensional viscosity. 

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