Intrinsic viscosity of rigid macromolecules in dilute solution in steady shear flow

A rigid linear array of beads in a Newtonian fluid is used to model a rod-like macromolecule in a dilute solution. Following the work of Kotaka, an expression is obtained relating the intrinsic viscosity to the velocity gradient. Computed results are compared with the experimental results of Strömberg.     

Intrinsic viscosity of solutions of rigid particles at high shear rates

The results of a numerical calculation which extends Scheraga's calculation on the non-Newtonian behavior of the viscosity factor v of rigid ellipsoid solutions are given here and compared to experimental data obtained on different poly(γ-benzyl L -glutamate) samples in helical configuration, over a wide range of molecular weight, up to 980,000. Relations for the axial ratio p, the rotary diffusion constant D, and a test of the deformability of the polymer under shear, are given as functions of the shear-rate dependence of the intrinsic viscosity. The experimental behavior under shear shows that PBLG becomes somewhat flexible in dichloroethane, but not in m-cresol. The dimensions calculated from the viscometric results suggest discrete changes in the length per monomeric unit of the helix at different well defined molecular weights.     

Conformation of polyisobutylene in dilute solution subjected to a hydrodynamic shear field

A new light-scattering experiment which allows a direct determination of the conformation of macromolecules deformed in flow is described. Light-scattering relationships based on the interference function are developed, and results of an experimental study are detailed. The deformed conformation of high molecular weight polyisobutylene was determined in a Couette-type shear field. Decalin was the solvent. Variables investigated were the shear rate (0 to 600 sec^?1), the polymer molecular weight (1.0 × 10⁷ to 1.6 × 10⁷), and the polymer concentration (2.0 × 10^?4 to 8.0 × 10^?4 g/cc). Conformation variables determined were the orientation of the molecule in the shear field and its maximum and minimum extension ratios in the plane defined by the direction of flow and the direction of the shear rate. The deformation of the macromolecule was found to be markedly discrepant when compared to the dynamic macromolecular models which assume complete coil flexibility, and more closely in agreement with the recent theories of Cerf, developed for nonfree-draining coils which exhibit a finite internal viscosity.     

Intrinsic viscosity in branched free-radical polymers

The intrinsic viscosity ratio [η]_B/[η]_L was calculated as a function of average branching density for trifunctionally branched, free-radical polymers. Calculations were made for the g^1/2, g^3/2, and h³ rules, using realistic distributions of molecular weights and branches. Experimental data on branched poly(vinyl acetate) lay between the curves obtained from the g^1/2 and h³ relations.     

Intrinsic viscosity of polystyrene in mixed solvents

The intrinsic viscosity of a single sample of polystyrene was measured as a function of the composition of solvent in three mixed solvent pairs. The parameter Y introduced by Shultz and Flory was useful for prediction of trends, but severely overestimated the effect of solvent (1)–solvent (2) interaction on the expansion of polymer coils. The system polystyrene–cyclohexane–ethyl acetate was studied in detail for five samples of polystyrene. The analysis of the data provided strong experimental proof of a strict validity of the Mark–Houwink–Sakurada relation. The dependence of the Mark–Houwink–Sakurada exponent α on the composition of the solvent mixture was unexpectedly unsymmetrical. The unperturbed dimentions of the polystyrene chain are reduced by specific interaction of polystyrene with carbonyl groups in the solvent mixture.     

Intrinsic viscosity of polyelectrolytes in salt solutions

The dependence of the intrinsic viscosity of polyelectrolytes on the concentration of added salt is given satisfactorily by a formula obtained recently. A new viscosity—molecular weight relation gives satisfactory agreement with experiments.     

Frequency dependence of intrinsic viscosity of macromolecules with finite internal viscosity

In order to explain the observed nonvanishing limiting value of dynamic intrinsic viscosity of polymer solutions at ω = ∞ one has considered the necklace model with finite resistance to the rate of coil deformation introduced long ago by Cerf for the study of gradient dependence of intrinsic viscosity and streaming birefringence. The calculation need not take into account change of hydrodynamic interaction as a consequence of coil deformation because the experimental data are always either obtained at very low gradient or extrapolated to zero gradient so that in the experiment the macromolecule has the same conformation as in the solution at rest. The model indeed yields a finite [η]′_{ω = ∞} in good agreement with experiments on polystyrene in Aroclor. According to the theory [η]′_{ω = ∞}/[η]₀ decreases with increasing molecular weight as M^?1 and M^?1/2 for the free-draining and impermeable coil, respectively. The absolute limiting value [η]_∞′, therefore turns out to be nearly independent of M, at least for small values of internal viscosity. From the observed value [η]_∞′/[η₀] one can obtain the coefficient of internal viscosity of the macromolecule. The value for polystyrene in Aroclor calculated from dynamic experiments on rather concentrated solutions is close to that derived by Cerf from streaming birefringence observations of polystyrene in a series of solvents of widely differing viscosity.     

Intrinsic viscosity of flexible ring polymers

The intrinsic viscosity of flexible ring polymers with a finite number of segments is computed with both exact and approximate eigenvalues λk, in the frame of the elastic necklace model. It is shown that exact and approximate calculations of the Flory constant and the Kuhn-Mark-Houwink exponent of the non-free-draining limit are compatible with h^* ? 0.25 and N ≥ 100.     

Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.     

Basic theory and some applications concerning the ratio of shear viscosity to entropy density in dense fluids

Much interest continues relating to the conjecture from string theory of an inequality satisfied by the ratio η/s in dense fluids, where η is the shear viscosity and s the entropy density. First, we summarise the models which have prompted the proposal of the inequality. Second, we consider a model equation of state which may be appropriate for the dense fluids NH₃ and H₂O, both of which satisfy the inequality.     

Viscoelastic and relaxation properties of a polystyrene melt in axial extension

On axial extension of polymer melts at constant deformation rates, the development of high-elastic deformation is of predominant importance during the initial period. High-elastic deformation is accompanied by a rise in viscosity and in the modulus of high-elasticity and by retardation of the relaxation processes in the region of large relaxation times. At relatively low deformation rates, the rise in viscosity and high-elasticity modulus and the retardation of relaxation processes may give way to a decrease in viscosity and high-elasticity modulus and acceleration of relaxation processes, so that stationary flow regimes are attained. The transition from strain regimes with increasing viscosity and modulus of high elasticity to those with a decrease of these quantities corresponds to an increase in the rate of accumulation of irreversible deformation. Accordingly, a competing influence due to the orientation effect and to destruction of the network of intermolecular bonds becomes evident while stationary flow is being attained. The orientation effect must be responsible for the retardation of the relaxation processes, whereas rupture of the intermolecular network bonds results in structural relaxation accelerating relaxation processes. In contrast to shearing, during extension the orientation effect is of predominant importance. Hence in stationary flow regimes the viscosity may not only remain independent of the rate of strain, but even increase with it. In this case the contribution of the large relaxation times to the relaxation spectrum increases with increasing stress in stationary flow regimes. The fact that the longitudinal viscosity and the modulus of high elasticity are independent of the stress in stationary flow regimes does not guarantee linearity of the mechanical properties of the polymer in the prestationary stage of deformation when complex changes occur in its relaxation characteristics. At high deformation rates the viscosity and the modulus of high elasticity keep rising with increasing deformation until rupture occurs. Determination of the strength of polystyrene samples vitrified after extension showed that it is due not to the entire degree of extension, but only to the value of accumulated high-elastic deformation. The strength of the vitrified samples is to a first approximation independent of the rate at which the melt was extended.     

Aggregation of paramagnetic particles in the presence of a hydrodynamic shear

We present an experimental study of the aggregation of paramagnetic particles, in the presence of controlled laminar shear flow, conducted in microchannels subjected to an external magnetic field. The microfluidic channels are made of either glass/silicon or polydimethylsiloxane. In ranges of time up to hundreds of seconds, the growth mechanism of the linear chain consists of the accumulation of isolated particles or small clusters onto existing chains, which are all moving at different speeds. In this time regime the chain length increases linearly and has a growth rate that increases as a power law with the shear. At longer times the chain lengths saturate. The Smoluchovski model, which assumes single particle-chain interactions only, closely reproduces the observations both qualitatively and quantitatively. In particular, the evolution of the growth rate of the mean chain length with respect to the shear rate S, predicted as S1/4, is found to be consistent with the experiments.     

Study on laminar viscosity and zero shear viscosity of latex systems

The flowing nature and rheological properties of polymethyl methacrylate latex systems in a coaxial cylinder viscometer were studied on the basis of laminar shear flow model and rheological experimental data. The physical meaning of laminar viscosity (eta(i,j)) and zero shear viscosity (eta(0)) were described. We assumed that laminar shear flows depended on position and shear time, so microrheological parameters were the function of position and shear time. eta(i,j) was the viscosity of any shear sheet i between two neighboring laminar shear flows at time t; j was denoted as j=t/Deltat; and Deltat was the interacting time of two particles or two laminar shear flows. tau(i,j) and gamma(i,j) were shear stress and shear rate of any shear sheet i at j moment. According to Newton regulation tau(i,j)=eta(i,j)gamma(i,j), apparent viscosity eta(a) should be a statistically mean value of j shear sheets laminar viscosity at j moment, i.e., eta(a)= summation operator(i=j)eta(i,j)gamma(i,j)/ summation operator(i=j)gamma(i,j). eta(0) was defined as shear viscosity between a laminar shear flow and a still fluid surface, i.e., eta(0)=(tau(i,j)/gamma(i,j))(j-i-->0). These new ideas described above may be helpful in the study of the micromechanisms of latex particle systems and worthy of more research.     

Alternative view of self-diffusion and shear viscosity

By performing an elementary transformation, the conventional velocity autocorrelation function expression for the temperature and density dependent self-diffusion constant D(T,rho) has been reformulated to emphasize how initial particle momentum biases final mean displacement. Using collective flow variables, an analogous expression has been derived for 1/eta(T,rho), the inverse of shear viscosity. The Stokes-Einstein relation for liquids declares that D and T/eta should have a fixed ratio as T and rho vary, but experiment reveals substantial violations for deeply supercooled liquids. Upon analyzing the self-diffusion and viscous flow processes in terms of configuration space inherent structures and kinetic transitions between their basins, one possible mechanism for this violation emerges. This stems from the fact that interbasin transitions become increasingly Markovian as T declines, and though self-diffusion is possible in a purely Markovian regime, shear viscosity in the present formulation intrinsically relies on successive correlated transitions.     

Intrinsic viscosity of polymers of low molecular weight

Experimental evidence concerning the dependence of the intrinsic viscosity [η] on molecular weight M in the low molecular weight range (from oligomers to M = 5 × 10⁴) has been collected in a variety of solvents for about ten polymers, i.e., polyethylene, poly(ethylene oxide), poly(propylene oxide), polydimethylsiloxane, polyisobutylene, poly(vinylacetate), poly(methyl methacrylate), polystyrene, poly-α-methylstyrene, and some cellulose derivatives. In theta solvents, the constancy of the ratio [η]Θ/M^0.5 extends down to values of M much lower than those predicted by current hydrodynamic theories. In good solvents, and on decreasing M, the polymers examined, with the exception of polyethylene and some cellulose derivatives, show a decrease in the exponent a of the Mark-Houwink equation [η] = KM^a. This upward curvature gives rise to the existence of a more or less extended linear region where the equation [η] = K₀M^0.5 is obeyed. Below the linear range, i.e., for even shorter chains, the exponent a can increase, i.e., polydimethylsiloxane, or decrease below 0.5, i.e., poly(ethylene oxide), depending on the particular chain properties. These different dependences have been discussed in terms of: (a) variations of thermodynamic interactions with molecular weight; (b) variations of conformational characteristics (as for instance the ratio) 〈r0²/nl²〉, where 〈r0²〉 is the unperturbed mean square end-to-end distance and n is the number of bonds each of length l; (c) hydrodynamic properties of short chains.     

Intrinsic viscosity of aqueous suspensions of cellulose nanofibrils

Cellulose nanofibrils (CNF) from wood fibers are of increasing interest to industry because they are from renewable sources and are biodegradable. Owing to their high aspect ratio, they produce viscous suspensions and stiff gels that are strengthened by interfibrillar hydrogen bonds. In this study, the viscosity of aqueous CNF suspensions, at dilute concentrations ( \(nL^{3}<1\) ), was measured at various pH values by addition of HCl, and at various ionic strengths by addition of NaCl and \(\hbox {CaCl}_{2}\) . The results show that the primary electroviscous effect significantly increases the intrinsic viscosity. The intrinsic viscosity under conditions where the surface charge of nanofibrils is fully screened is in good agreement with the predictions of classical theory for dispersions of rodlike particles at low shear rates. Increasing the ionic strength up to \(\kappa d\approx 1\) decreases the intrinsic viscosity; at \(\kappa d>1\) , the intrinsic viscosity increases because of fibril aggregation and increase of the effective volume fraction.