Fractal colloidal aggregates: Consolidation and elasticity
Abstract
The assumption that colloidal aggregates are rigid must break down beyond a critical size; thermal flexibility then leads to internal contacts which under flocculating conditions become new permanent bonds in the structure. It is argued that these self-consistently raise the spectral dimension and the fractal dimension should also be expected to increase. This may explain the unexpectedly high values of both observed by Courtens and Vacher in Brillouin scattering from alcogels.
References (12)
- P. Meakin
Phys. Rev. Lett.
(1983) - M. Kolb et al.
Phys. Rev. Lett.
(1983) - R. Jullien et al.
J. Phys. A
(1984) - W.D. Brown et al.
J. Phys. A
(1985) - Y. Kantor et al.
Phys. Rev. Lett.
(1984) - W.D. Brown
Cited by (28)
Colloidal networks of fat crystals
2019, Advances in Colloid and Interface ScienceThe following paper traces the development of the study of colloidal networks of fat crystals. The work starts with traditional pre-fractal particle network models of fat crystal networks. Due to its central importance in the study of colloidal networks of fat crystals (and other colloidal aggregates), a short exposition of fractal geometry is provided. The development of fractal aggregation models as well as models that describe the rheology of networks of these fractal aggregates is introduced. Later sections of the paper show the application of these aggregation and mechanical models specifically to fats. Finally, recent work in elucidating the nanostructural elements of fat crystal networks and aggregates of these nanostructures is provided.
Peculiar frequency dependence of the storage modulus in a plastic disperse system
2004, Food Research InternationalThe frequency dependence of the storage modulus in a plastic fat was determined from stress sweeps at different frequencies, using a fresh sample at each frequency, rather than from the standard frequency sweeps at a fixed stress or strain. Using this method, a peculiar frequency dependence of the storage modulus was observed, with maxima displayed at 2–3 and 5–6 Hz. The material also displayed work-hardening upon small deformation mechanical working. These effects could be explained using fractal-scaling theories.
Effects of water on the rheological properties of calcite suspensions in dioctylphthalate
2002, Colloids and Surfaces A: Physicochemical and Engineering AspectsYield stress, storage and loss modulus of dispersions of colloidal particles of calcium carbonate in dioctylphthalate have been measured. They depend strongly on small amounts of water present in the suspension. The water thermodynamic activity has been used to characterise the water content of the suspension. There is an increase of more than an order of magnitude of the yield stress and storage modulus over the range 0.1–0.3 of water activity, and a smaller increase of the loss modulus. Beyond an activity of 0.3, these quantities are constant within experimental scatter. The effect of volume fraction has been investigated in this latter range of water activity. The results are discussed in term of interactions between particles.
Structure and mechanical properties of fat crystal networks
2002, Advances in Food and Nutrition ResearchThis chapter discusses structural and mechanical properties of fat crystal networks. Lipids used as food are either in the form of constituents in foods such as milk, cheese, spreads, etc. or in the form of "visible" fats such as butter, lard, ghee, etc. Dietary lipids assume an important role in human nutrition. They can supply a number of essential functions, such as providing calories and essential fatty acids and acting as vitamin carriers. The macroscopic rheological properties of networks formed by lipids are of extreme importance in food products that contain significant amounts of fats. Such products include butter, margarine, chocolate, peanut butter, many spreads such as cream cheese, and ice cream. Many of the sensory attributes such as spreadability, mouth feel, snap and texture are dependent on the mechanical strength of the underlying fat crystal network. However, it must not be inferred from this that knowledge of the mechanical properties of the fat network provides complete knowledge of the food product within which it is formed. In addition to this obvious industrial importance, fat crystal networks form a particular class of soft materials, which demonstrate a yield stress and viscoelastic properties, rendering these materials plastic. The chapter reviews the development of techniques and models which attempt to relate the microstructural structural organization of fat crystal networks to their mechanical properties.
On the structure of particulate gels - The case of salt-induced cold gelation of heat-denatured whey protein isolate
2000, Food HydrocolloidsIn this work we attempted to define the structure of particulate colloidal protein gels using salt-induced cold gelation of heat-denatured whey protein isolate (WPI) as a model. WPI loses its tertiary structure and forms soluble protein aggregates during heat denaturation as evidenced by near-UV circular dichroism and fluorescence spectroscopy, as well as size-exclusion HPLC. Sodium chloride and calcium chloride induced the aggregation of these particles by dispersing charge, and in the case of calcium, also by crosslinking. Light microscopy revealed that these gels were composed of flocs of aggregated primary particles. Flocs are termed microstructures, while primary particles are termed microstructural elements. The size of the microstructures ranges from 10 to 20 μm, while the size of the microstructural elements ranges from 0.5 to 1.0 μm. These gels were structured and behaved rheologically as stochastic mass fractals, where the elastic constant of the gels (K) was related to the volume fraction (φ) of protein in a power law fashion, namely K=γφm. The gel network was found to be in a weak-link regime [Shih, Shih, Kim, Liu & Aksay, 1990. Physical Review A, 42, 4772–4779]. For this case, m=1/(3−D), where D is the fractal dimension for the packing of primary particles within fractal flocs. The constant γ contains information about the particles that make up the network. The mass fractal dimension increased as a function of increasing calcium chloride concentration in the range 5–150 mM, while it remained unchanged as a function of increasing sodium chloride concentration in the range 225–400 mM. The mass fractal dimension determined rheologically in the weak-link regime agreed very well with the spatial mass fractal dimension determined from image analysis of TEM micrographs of the gels. The constant γ decreased in both cases as a function of increasing salt concentration. Internal-L-value measurements suggested that particle size decreased as a function of increasing protein concentration and increased as a function of increasing salt concentration, as expected from decreases in the constant γ. A mechanical and structural model for particulate gels in the weak-link regime was also developed in this work, providing insight into the nature of the constant γ, where γ is proportional to the force constant of the springs, or bonds, between primary particles (kp), proportional to the interfloc distance (d0) and the number of particle–particle interactions at the interface between two fractal flocs (m), inversely proportional to the square of the fractal floc diameter (ξ), and inversely proportional to the diameter of primary particles (a), namely γ∼(mkpd0/aξ2).
Relating structure of fat crystal networks to mechanical properties: A review
1999, Food Research InternationalThis paper reviews the identification of the various levels of structure present in fat crystal networks, and the development of analytical techniques to quantify these levels. The relationship of the various levels of structure to macroscopic physical indicators of the mechanical strength of the network is discussed. The analysis of the microstructural level of the network via fractal geometrical methods is discussed, as well as mechanical models relating the structure to mechanical properties. A method developed to quantify the fractality of fat crystal networks is also presented. The effect of processing conditions on microstructural indicators of the elastic modulus of the network is also discussed. This paper summarizes some 50 years of endeavor to relate the structure of fat crystal networks to their macroscopic rheological properties.