Dilute Solutions Of High Polymers Research Articles

An Unreasonable Universality of the Thermophoretic Velocity.

Thermophoresis is the migration of dispersed molecules or particles in an inhomogeneous temperature field. It has been associated with various nonequilibrium phenomena ranging from stratified oil reservoirs to prebiotic evolution and the origin of life. The thermophoretic velocity is difficult to predict and appears almost random. We show that, in the case of strongly asymmetric mixtures with high molecular mass ratios of the solute to the solvent, it unexpectedly assumes a universal value once the trivial influence of the viscosity has been factored out. This asymptotic behavior is surprisingly universal and a general property of many highly asymmetric molecular mixtures ranging from organic molecules in n-alkanes to dilute solutions of high polymers. A quantitative explanation is provided on the basis of the asymmetric limit of the pseudoisotopic Soret effect.

Communication: A coil-stretch transition in planar elongational flow of an entangled polymeric melt.

Virtual experimentation of atomistic entangled polyethylene melts undergoing planar elongational flow revealed an amazingly detailed depiction of individual macromolecular dynamics and the resulting effect on bistable configurational states. A clear coil-stretch transition was evident, in much the same form as first envisioned by de Gennes for dilute solutions of high polymers, resulting in an associated hysteresis in the configurational flow profile over the range of strain rates predicted by theory. Simulations conducted at steady state revealed bimodal distribution functions, in which equilibrium configurational states were simultaneously populated by relatively coiled and stretched molecules which could transition from one conformational mode to the other over a relatively long time scale at critical values of strain rates. The implication of such behavior points to a double-well conformational free energy potential with an activation barrier between the two configurational minima.

Mechanical degradation of dilute solutions of high polymers in capillary tube flow

AbstractExperimental results on mechanical degradation in capillary tubes of polyisobutylene polymers in dilute solution are described. In laminar flow, degradation is independent of tube length, indicating that entrance effects are dominant. This shows that capillary experiments do not yield explicit information on the effect of shear stress on mechanical degradation. In turbulent flow, large entrance effects are also observed, but some degradation does take place in the fully developed flow region.

Mathematical properties of polydisperse systems, 1. General relations

AbstractIn the present paper the connection between an arbitrary polydisperse property and the molecular weight distribution is investigated using exact mathematical methods. On the basis of the superposition principle a general equation is derived which can be applied e.g. to the polydispersity problems connected with the Gel Permeation Chromatography, to the light scattering from dilute solutions of high polymers, or the ultracentrifuge. From this point of view, each of these phenomena is described by help of a linear operator with a special kernel, the analytical or numerical inversion of the operator yielding the molecular weight distribution of the system by help of an uniform algorithm.

Drag of Spheres in Dilute High Polymer Solutions

WHITE1 showed that the drag on spheres in water, at Reynolds numbers exceeding the critical value (vd/ν > about 2 × 105), could be increased by dissolving a very small quantity of polyethylene oxide (Union Carbide ‘Polyox WSR301’) in the water, and suggested that this effect resulted from suppression of turbulence in the boundary layer by the additive, which caused earlier separation and a corresponding increase in the wake size.

Drag coefficients for sphers in high reynolds number flow of dilute solutions of high polymers : D. A. White, Nature, 212 (5059) (1966) 277–278; 1 fig., 1 table, 5 refs.

Drag coefficients for sphers in high reynolds number flow of dilute solutions of high polymers : D. A. White, Nature, 212 (5059) (1966) 277–278; 1 fig., 1 table, 5 refs.

Drag Coefficients for Spheres in High Reynolds Number Flow of Dilute Solutions of High Polymers

DILUTE polymer solutions show substantial reduction of drag in turbulent pipe flow1 and a 28 per cent reduction has been reported for sphere drag coefficients in a 0.5 per cent solution of Guar gum for a 1 in. diameter steel ball2. These drag coefficients were measured by timing balls falling down a 3 in. tube. Greater reductions of sphere friction factors were noted in my recent experiments. Balls were dropped by hand in a glass fronted tank, 1 ft. square and 6 ft. deep. The terminal velocity was found using a photographic technique3 in which the position of the ball every 0.04 sec was recorded on a 35 mm negative.

On the computation of viscosity measurements data of dilute solutions of high polymers

On the computation of viscosity measurements data of dilute solutions of high polymers

Entropy of Activation of Viscous Flow in Dilute Solutions of High Polymers

IT has been previously shown1,2 that the entropy of activation of viscous flow, ΔS, of dilute solutions of flexible chain high polymers decreases with increasing concentration c and molecular weight M of the polymer. In contrast, ΔS for dilute solutions of cellulose derivatives, the chains of which are stiffer and more extended in solution3, generally increases with increase of c and M (refs. 1, 2 and 4). An interpretation in terms of positive and negative contributions to ΔS was tentatively advanced2. The positive contribution was assumed to be proportional to Q/T, where Q is the apparent activation energy of viscous flow of the solution and T the absolute temperature. The negative contribution was assumed to be not primarily dependent on Q and to result from synchronization between movements necessary for a successful unit act of flow5. The effects of variation in c and M on Q are relatively small for dilute solutions of flexible chain high polymers and it was suggested that the negative contribution was the greater. The marked increases in Q with increase of C or M, observed with dilute solutions of cellulose derivatives, led to the suggestion that in such cases increases in the positive contribution outweighed any increases in the negative one.

Viscosity/temperature relationships for dilute solutions of high polymers

Values of Q and A in the expression η = Ae Q RT have been obtained for dilute solutions of polyisobutylene, polyvinyl acetate, polymethyl methacrylate, cellulose trinitrate and cellulose triacetate in representative solvents. The apparent activation energy of viscous flow Q is given by Q= Q o + K e Mc where Q 0 is the value for the solvent, M and c are the molecular weight and concentration of polymer and K e depends on polymer and solvent. Values of K e for the cellulose triesters are much larger than for the other polymers and it is suggested that this is due to their greater chain stiffness and extension. For the polymers with flexible chains A= A o + K a Mβc over a limited molecular weight range but with the cellulose triesters A= A o exp (- K a ′ Mλc where A 0 is the value for the solvent and K a, K′ a, α and β depend on polymer and solvent. Application of rate theory suggests that the entropy of activation of viscous flow decreases with increasing c and M for solutions of flexible chain polymers but that the reverse is true for solutions of stiff, extended cellulose derivative chains. Equations are derived relating the intrinsic viscosity to K e, K a or K′ a, α or β, M and T.

Absorption Correction in the Viscometry of Dilute Solutions of High Polymers

IN a private communication, Drs. S. Gundiah and S. L. Kapur (of the National Chemical Laboratories, Poona, India) have pointed out to us that the derivation of the principal equation in our earlier communication1 is in error, and that there is, because of this, a term missing from the equation. We acknowledge the error and are grateful to them for detecting it; but we wish to make it clear that the missing term should be negligible not only for the system we used as an example, but also for all systems of the type we specified, namely, “dilute solutions of high polymers”. In this communication, then, we provide (a) a correction for the record and (b) additional evidence that the method we proposed is both sound and useful, and applicable to a wide variety of systems.

Elimination of the Absorption Correction in the Viscometry of Dilute Solutions of High Polymers

Elimination of the Absorption Correction in the Viscometry of Dilute Solutions of High Polymers

Viscosity-Temperature Relationships for Dilute Solutions of High Polymers

INVESTIGATIONS of the viscosities of dilute solutions of cellulose derivatives1,2 over a range of temperature have shown that the pre-exponential term A and the apparent activation energy of viscous flow Q in the viscosity-temperature relationship: where η is the viscosity, depend on both the concentration c of the polymer and its molecular weight M. (Q − Q0), where Q0 is the value for the solvent, is generally a linear function of c in the range 0.1–0.4 gm./dl. and is a function of M. The value of A generally decreases with increase of both c and M and − log A is a linear function of c and a more complex one of M.

Experimental Study of Thermal Diffusion in Dilute Solutions of High Polymers

Ham [J. Appl. Phys. 31, 1853 (1960) (preceding paper)] has derived a simplified theory for thermal diffusion in dilute solutions of high polymers. It is of interest to apply this theory to two different types of polymer solutions: (a) dilute solutions in a good solvent, and (b) dilute solutions in a poor solvent. By studies of the concentration, temperature, and molecular weight dependence of the thermal diffusion ratio in these two different types of polymer solutions, it has been possible to obtain a detailed test of the theory.

Theory of Dilute High Polymer Solutions. II

The second virial coefficient is calculated according to the smoothed distribution method. Our treatment differs from those of Flory-Krigbaum and Isihara-Koyama through inclusion of the numerous short-range intramolecular contacts arising by virtue of the connected nature of the chain. The result is to replace the previous F(X) by F(X, ρ), where the parameter ρ depends upon the ratio of the total number of intramolecular contacts to the number of long-range contacts counted using a radial segment distribution. The number of intermolecular contacts created when two molecules overlap is estimated by the use of an additional smoothed radial segment distribution which is assumed to be uniformly expanded by intramolecular excluded volume effects. Comparison with experiment reveals that both the temperature and molecular weight dependences of A2 in the vicinity of the theta temperature are described in a reasonably quantitative fashion by the present treatment. In this case there are no adjustable parameters. Furthermore, satisfactory agreement is observed for good solvents using values for the thermodynamic interaction parameter deduced from intrinsic viscosity. In the limit ρ=1 the present treatment yields a result equivalent to those of FK and IK. We conclude that the latter underestimate the number of intramolecular contacts through neglect of the connected nature of the chain. In the other limit, ρ=0, a result approximating that of the Casassa-Markovitz treatment is obtained. We believe that their assumption of a spherical segment distribution about the initial point of contact results in an over-estimation of the number of intermolecular contacts.

Design Problems in Ebulliometry of Polymers

There are two fundamental problems in ebulliometry. The first is to find a detector with sufficient sensitivity to measure the very small boiling point elevations obtained with dilute solutions of high polymers. This problem is solved easily with thermistor bridges and modern high gain amplifiers. The second problem is that of random thermal fluctuations or background noise in the ebulliometer itself. When this study began, it was considered that there were three probable sources of noise, viz., (1) superheated liquid from the Cottrell pump, (2) pressure fluctuations and differences within the ebulliometer, and (3) the presence of foam which usually appears when a polymer solution is maintained at the boil. However, the tests carried out with the ebulliometers described here seem to indicate that the difficulties may be inherently associated with the polymer solutions themselves.

EBULLIOMETRY AND THE DETERMINATION OF THE MOLECULAR WEIGHTS OF POLYMERS: PART II. BACKGROUND NOISE IN THE SMALL EBULLIOMETER

It is shown that the usual form of ebulliometer is subject to at least three sources of noise. Those discussed here are (1) pressure fluctuations over the boiling liquid surface, (2) the Cottrell pump, and (3) the foam which appears on many polymer solutions when maintained at the boiling point. Background noise in this, and other ebulliometers commonly employed, may be large compared to the size of the signals expected for dilute high polymer solutions. Consequently further progress in ebulliometry is dependent on the development of a new ebulliometer with a much lower background noise.

Theory of Dilute High-Polymer Solutions

Theory of Dilute High-Polymer Solutions

Entropy of Mixing of Dilute Polymer Solutions

The entropy of mixing of dilute solutions of high polymers has been calculated. The expression obtained employs a molecular dimension obtained from the intrinsic viscosity, contains no arbitrary constants, and appears to be valid from zero to about two percent polymer, the limit of the osmotic pressure data used.

Non-Newtonian Viscosity of Dilute High Polymer Solutions. III. On the Method of Measuring Zero Shear Viscosity

Non-Newtonian Viscosity of Dilute High Polymer Solutions. III. On the Method of Measuring Zero Shear Viscosity