Complex modulus concentrated solutions

Osaki,K., Tamura,M Kurata,M Kotaka,T. Complex modulus of concentrated polymer solutions in steady shear. J. Phys. Chem. 69,4183-4191 (1965). 

The SC solutions appear to run into difficulties when there is a large elastic mismatch between the constituent phases, for example, at high concentrations of a rigid phase in a compliant matrix or of a porous phase in a stiff matrix. The latter situation will be discussed in Section 3.6. One approach to this problem is known as the Generalized Self-Consistent Approach, the concept behind which is illustrated in Fig. 3.14. Instead of a single inclusion in an effective medium, a composite sphere is introduced into the medium. As in the composite sphere assemblage discussed in the last section, the relative size of the spheres reflects the volume fraction, i.e., V = a bf as before. Interestingly, this approach leads to the HS bounds for the bulk modulus. The solution for the shear modulus is complex but can be written in a closed form. 

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

Figure 7.10 Effect of the thermodynamic incompatibility of otsi/p-casein + high-methoxy pectin (pH = 7.0, / = 0.01 M) on phase diagram of the mixed solutions and elastic modulus of corresponding casein-stabilized emulsions (40 vol% oil, 2 wt% protein), (a) (O) Binodal line for p-casein + pectin solution with critical point ( ) ( ) binodal line for asi-casein + pectin solution with critical point ( ). (b) Complex shear modulus G (1 Hz) is plotted against the pectin concentration (O) p-casein ( ) o i -casein. Dotted lines indicate the range of pectin concentration for phase separation in the mixed solutions. The pectin was added to the protein solution before emulsion preparation. Data are taken front Semenova et al. (1999a).

The main factors, which determine the foam formation ability and physical stability of the foams in mixed Lys-MR solutions, are surface activity and complex dilatation modulus. With increase of MR concentration in certain range a surface activity and complex dilatation modulus of interfacial layers increased and phase angle decreased. It means that viscoelasticity of interfacial layers became higher. In these conditions the foam volume and mutiplicity as well as stability of foams were growing. This effect may be used for creation of mixed protein-MR system foam type for pharmaceutical applications with improved physical stability and wide range of antibacterial actions. 

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