In a previous paper, it was found that the shearing stress of suspensions under a constant rate of shear increases sigmoidally with increasing time and a structural model assuming two-step formation can explain the complex rheological behavior of suspensions. In the present paper, the analysis of the model has further been developed to predict the effect of rate constants on the variation with time of the structural parameters characteristic of the model. The model assumes two-step formation and breaking of two kinds of structure: An unbranched chain structure is formed by suspended elementary particles in the first process, and the unbranched chains develop into a complex three-dimensional network structure in the second process. Assuming a simple function of exponential type for the time dependence of the length of unbranched chains, an equation for the variation of the structural parameters with time for the network structure can be derived. The analysis of the equation shows that a ratio of the rate constant of the first process to that for breaking of the second process plays a significant role in determining the tendency of the variation of the structural parameter with time. The larger the ratio is, the more the sigmoidal increase of structural parameter becomes remarkable.
The steady flow properties and rheopexy of suspensions have been calculated on the basis of the two-step structural model. In doing so, the following two assumptions have been adopted; (1) the structural parameter of the model is proportional to the viscosity of the system, and (2) the rate constants for the breaking of structure increase with increasing shear rate, while the rate constants for the structure formation are independent of shear rate. A viscosity equation finally obtained is described by two characteristic rates of shear. These characteristic rates of shear correspond to the boundaries or transition points of the three typical regions found by us before. The rheopexy of suspensions strongly depends on a factor u, a function of rate constants of the kinetic model. The shear rate dependence of u is also characterized by the two characteristic rates of shear. Shearing stress at a constant rate of shear increases with increasing time either exponentially or sigmoidally depending upon shear rate showing a good agreement with experimental results obtained for suspensions of titanate fibers in polymer solutions.
Shear storage (G′) and loss moduli (G″), and steady shear (σ) and first normal stress difference (N1) of a commercial high density polyethylene (HDPE) melts and the fractions have been measured with a Weissenberg Rheogoniometer. Pseudo-equilibrium modulus (GeN0) and average molecular weight between entanglement points (Me) were found to be 1.32 × 106 Pa and 2.18 × 103, respectively. The value of Me is approximately half of the literature value reported for Mc, the critical molecular weight for entanglement coupling estimated from molecular weight dependence of viscosity. The value of zero shear viscosity (η0) obtained from both dynamic and steady shear measurements are in good agreement and found to be proportional to 3.8 power of the weight- average molecular weight. Cox- Merz rule does not hold so well at high rate of shear for both the whole polymer and its fraction. Steady state compliance (Je0) of the fractions is much higher than expected value and is remarkably dependent on molecular weight. Storage compliance (J′) obtained from dynamic measurement and steady shear compliance (Js) from steady flow measurement agree with each other in the value and the behavior for each fraction. It was found that J′ (and JS) of the fractions at low frequencies (low shear stresses) increase as increasing molecular weight and molecular weight distribution. On the contrary, J′ at higher angular frequencies decreases with increasing molecular weight and molecular weight distribution. It is suggested that Js, at high rates of shear decreases with increasing molecular weight and molecular weight distribution supporting Mendelson's results.
The behavior of block copolymer solutions may be highly different from that of homopolymer solutions, because of the microdomain structures formed in the systems. The behavior of decalin solutions of a PS-PB-PS and a PS-PB block copolymers were similar to that of homopolymer solutions corresponding to the homogeneity of the systems. However, in the decane solutions, the PS-blocks aggregated to form precipitated domains, then a quasi-network structure was formed in the former while a micelle structure in the latter. Corresponding to such structures, the former showed a behavior similar to crosslinked rubbers and the latter a plateau region in G″ in the lower frequency range. For SB/SBS blend systems dissolved in n-tetradecane, the difference between the micelle and quasi-network systems became more prominant when the nonlinearity of the systems was compared. While the quasi-network system showed the rubberlike linear viscoelasticity, the micelle system showed nonlinear behavior, in which odd harmonics appeared in shear stress, the fundamental harmonics had a plateau region, and the nonlinearity of the system decreased as the frequency increased. These characteristic behavior of the micelle system can be understood as a Bingham-type viscoelastic behavior. The difference between the micelle and the quasi-network systems seems to be caused by the restriction from the microdomain structures that the shear flow occurs in the former by slipping aggregated PS domains with each other, while it does not in the latter without breaking the PS domains.
The degree of flocculation in suspensions depends on particle size and the variation is measured by centrifugal sedimentation. The effect of particle size on the rheological properties of suspensions was studied using a coaxial cylinder rheometer. The apparent viscosity, ηa, the amplitude ratio of stress-to-strain, δ0/γ0, and the imaginary part of Fourier transform, Im, for the Raised-Cosine-Pulse increase with decreasing particle size. This may be attributed to the variation of the degree of flocculation because the sedimentation volume of suspensions increases with the decrease of particle size at a fixed particle concentration.
A Balance Rheometer has the characteristics similar to an orthogonal rheometer such that dynamic measurements can be carried out without converting a rotational motion of a drive to a reciprocating motion by a device such as a cam. The results of dynamic measurements on a polystyrene melt and a silicone oil by a Balance Rheometer were in good agreement with those obtained by a conventional coaxial-type rheometer. The use of a Balance Rheometer has the following advantages: (i) A wide frequency range can be covered. (ii) Materials with high moduli can be measured easily. (iii) Dynamic measurements with a large amplitude of strain can be carried out easily. When the material is a nonlinear viscoelastic body, however, it should be noticed that only apparent moduli can be obtained.
The shear viscosity η of a solution of polyvinylacetate (MW=6.7×104, Mw/Mn=2.2) in 3-heptanone was measured at the critical concentration 20.325g/100cm3 with varying temperature T in the vicinity of the critical solution temperature Tc(=284.52K). The measurements were made at various low shear rates by using a modified Ubbelohde viscometer with variable inclination angle. The critical anomaly in viscosity was observed. The temperature dependence of the anomalous component of viscosity Δη was expressed in the form, Δη/η=A ln[1-(Tc/T)]+B, with A=-0.034 at finite shear rates and A =-0.069 at zero shear rate. Both of these A values, if they are analysed by Oxtoby's and Kawasaki's theories, respectively, yield ν=0.64 for the critical exponent ν of the correlation length. This result is in good agreement with the result of light scattering measurements due to Kuwahara and indicates that the viscosity analysis is useful for the study of the critical behavior of polymer solutions.