3D-rheology

For the step from the 3D-rheology to the 2D-state, to the surface rheology, it is best to use the vector treatment for describing the complex variables of strain s , stress complex viscosity T , complex shear modulus G , respectively, ri and G are viscoelastic vectors. The relating vector treatment for strain in a shear deformation is shown in Fig. 3.7. 

In reality we find a superposition of elastic and viscous effects in the strain-stress relationship. In 3D-rheology properties of a given system turned out to be described by the combination of... 

In the cube shown in Fig. 3.5. the tensor components for the strain-stress relationship of a 3D-body can be seen. Neglecting the z-coordinate, the tensor reduces from a 3x4 to a 2x2 matrix. The use of the 3D-rheology for related surface problems is only valid if a 3D-analogue for the relaxation is introduced. This is the only way to learn about the surface state in the absence of ideally elastic behaviour of the adsorption layer. 

All these phenomena are contributions to the surface loss angle in the strain-stress relationship. 3D-rheology deals with a closed system. There is no mass transfer across the limits of this system. In contrast, the so-called surface phase with an adsorption layers can exchange matter with the bulk phase depending on the boundary conditions, such as adsorption after formation of a fresh surface or periodic adsorption and desorption due to periodic changes of the surface area. 

Fig. 1 A schematic comparison between polymer melt rheology and colloid rheology, (a) In a polymer melt, atypical chain (dashed curve) is constrained by many (in reality, 10 ) other chains, here represented by small circles. This gives rise to the fruitful mean-field concept of a tube in which the chain has to move, (b) In a concentrated colloidal suspension, a typical particle (hatched) is surrounded (in 3D) by 10 neighbours. This number is too small for mean-field averaging to be meaningful, (c) Large deformations in polymer melts, such as the process (i) -(ii), involves breaking covalent bonds, and so do not ordinarily occur, (d) There are no covalent constraints on order unity deformations, such as (i)—>(ii), in a colloidal suspension...

In respect of the classical mechanics, E is an "ideal" coefficient, like the elasticity modulus in Hooke s model. Most of the practical compressions/dilatation experiments carried out with adsorption layers are comparable to the screening of elastic properties in material science. In analogy to the coefficients of the 3D-elasticity theory, we have to consider complex coefficients in surface rheology. The surface elasticity coefficient written as a complex modulus therefore has the form... 

Macroscopic properties, in particular, the rheological properties of supramolecular functional materials are determined by the micro/nanostructure of fiber networks. These materials have continuous 3D entangled networks in the liquid, thereby preventing the liquid from flowing owing to the capillary force. 

The implication of Fig. 8 is that the micro/nanostructure can be modified by changing supersaturation according to Eq. 21. The decrease of the mesh size of the 3D interconnecting networks of the materials will lead to an increase of G, G, etc. Therefore, the change of supersaturation should enable us to alter the rheological or other physical properties of the materials. 

The direct ink writing of three-dimensional ceramic structures has been reviewed (20). Both droplet- and filament-based direct ink writing techniques have been detailed. Various ink designs and their corresponding rheological behavior, ink deposition mechanics, potential shapes and the toolpaths required, and representative examples of 3D ceramic structures have been presented. 

Polymers used in bioprinting must be characterized well to analyze batch-to-batch variations that could have a big impact on the properties of a prospective bioink for 3D printing. Both the chemical and physical characteristics of the polymers can have a large influence on the rheological and mechanical behavior as well as on how cells will interact with the material. To assess the chemical composition of the polymers, infrared (IR), NMR, mass spectroscopy (MS), and gel permeation chromatography (GPC) are the most commonly used techniques. 

Abstract This chapter describes the influence of three-dimensional nanofillers used in elastomers on the nonlinear viscoelastic properties. In particular, this part focuses and investigates the most important three-dimensional nanoparticles, which are used to produce rubber nanocomposites. The rheological and the dynamic mechanical properties of elastomeric polymers, reinforced with spherical nanoparticles, like POSS, titanium dioxide and nanosdica, were described. These (3D) nanofillers in are used polymeric matrices, to create new, improved rubber nanocomposites, and these affect many of the system s parameters (mechanical, chemical, physical) in comparison with conventional composites. The distribution of the nanosized fillers and interaction between nanofUler-nanofiUer and nanofiller-matrix, in nanocomposite systems, is crucial for understanding their behavior under dynamic-mechanical conditions. 

The following sections of this chapter describe the design of different inks for the direct-write assembly of 3D microperiodic architectures composed of filamentary arrays, their rheological properties, and potential applications. Future... 

Nematic liquid crystals are 3D anisotropic fluids, and as such they have no translational order, i.e., they do not support extensional or shear strains. For this reason, the rheology of nematic liquid crystals is similar to conventional organic liquids with similar size of molecules. The main difference is due to the anisotropic nature of the materials the director distortion results in elastic responses, and the magnitude of the viscosity depend on the relative orientation of the director with respect to the velocity gradient. 

---