Anisometric particle shape

Due to their strongly anisometric particle shape, triglyceride SLN tend to self-aggregate and build-up stacked lamellae at higher concentrations. The formation of such stacked lamellae was found to be reversible upon dilution and did not lead to an accelerated physical instability of the dispersions. The anisometric particle shape also determines the flow properties of SLN dispersions and high lipid contents (up to 40%) led to the formation of an elastic gel with viscoelastic properties comparable to standard dermal preparations. ... 

Diffusion and sedimentation measurements on dilute solutions of flexible chain molecules could be used to determine the molecular extension or the expansion factor a. However, the same information may be obtained with greater precision and with far less labor from viscosity measurements alone. For anisometric particles such as are common among proteins, on the other hand, sedimentation velocity measurements used in conjunction with the intrinsic viscosity may yield important information on the effective particle size and shape. ... 

Table 6.2 Theoretical multiplication factors for anisometric particles with an aspect ratio r 1. (Note For a disc-shaped particle the aspect ratio is the ratio of disc diameter disk thickness and for a rod-shaped particle it is the ratio of rod length rod diameter). (Source R. Bown, Physical and Chemical Aspects of the Use of Fillers in Paper , in Paper Chemistry , ed. J.C. Roberts, Blackie, Glasgow, 1992, pp. 162-196).

For anisometric particles (e.g., needle- or platelet-shaped particles) mathematical statistics may likewise be applied [1.10]. The two-dimensional logarithmic normal distribution of the length L and breadth B of the particles also allows the representation and calculation of the characteristic parameters and mean values. The eccentricity of the calculated standard deviation ellipse (Fig. 2) is a measure of the correlation between the length and breadth of the particle. By using more than two... 

The particles may be anisometric, i.e., deviate from the spherical form. Moreover, the particles may have a rough surface. The two cases cannot be fully separated because intermediates occur, but a sphere can have a rough surface and a platelet can be smooth. One parameter now is insufficient to characterize a particle. If all particles have approximately congruent shapes (think of a collection of screws of various sizes), it may be possible to use just one size parameter, e.g., length. For irregularly shaped but not very anisometric particles, as found in several powders, one often defines an equivalent sphere diameter. This can be defined in various ways, such as... 

I. 2. If the width is considerable, the shape of the distribution may vary significantly. For anisometric particles, characterization of size poses additional problems. 

Particle shape can also have a large effect. Anisometric particles have an increased collision radius as compared to spheres see the discussion in relation to Figure 5.3. Moreover, capture efficiency is affected, but prediction of the effect is far from easy. 

Particle shape. Anisometric particles tend to give a higher Gm value than spherical ones at the same value of cp, although the effect may be small. Large deformation properties are greatly affected by particle anisometry, but published results appear to be conflicting. 

Rotational Brownian motion results in the disordering of anisometric particles previously oriented in some particular way owing to the flow of the dispersion medium (see Chapter IX) or the application of an electric field. From the time of the disordering one can determine the rotational diffusion coefficient, and, for known particle size and shape, also Avogadro s number. If the particles are able to undergo co-orientation, they usually are of substantially anisometric shape, and their translational and rotational diffusion coefficients differ from those obtained for spherical particles. For example, for prolate ellipsoids of revolution with a ratio of their main diameters d] d2-= 1 10, the diffusion coefficient, D, is about 2/3 of the value obtained for spherical particles of the same volume. 

From all this one may judge that viscosity measurement is an important tool for determining the structure of aggregates in solution, in particular the shape and elongation of anisometric particles. 

According to Eq. (2.8) or (2.10) the concentration dependence of has two parameters, [rj and 0m- Both are measures of a specific physical quantity (respectively, shape and packing) and may be independently determined, for example, [rj] from viscosity of diluted suspensions and 0m from dry packing of solid particles. For anisometric particles, the magnitude of these parameters may also be theoretically predicted see the rheological summary in a quite recent monograph [64]. Once [rj] and 0m are known, Eq. (2.8) will correctly describe the rjr versus 0 dependence for complex industrial systems, for example, PVC (poly(vinyl chloride)) emulsions and plastisols, mica-reinforced polyolefins, and sealant formulations [44,65]. However, in some suspensions and blends, r] and 0m may vary with composition [66]. 

Making a polysiloxane electrically conductive is best carried out using anisometric particles such as films and fibers, because of their low values of the percolation threshold for conducting pathways.Nonetheless, roughly spherical particles of carbon black have also been used for this purpose.2 2 The use of layer-like particles is illustrated by functionalized graphene sheets, while needle shapes are illustrated by unmodified or... 

For all shapes of scattering objects, the equation of Guinier and Foumet (1955) yields the low-Q behavior of the SANS F(Q) for a set of monodisperse, spherical (or at least, not too anisometric) particles ... 

In practice, clays are highly anisometric, often having irregular particle shapes and broad particle size distribution. The distribution of cation exchange capacity... 

Here, [t)] is the shape-dependent intrinsic viscosity, viz. [t ] = 2.5 for spheres and is the maximum packing volume fraction. Owing to < )-dependent rotation and orientation of particles, the flow of suspensions with anisometric particles is more complex. Here also Simha s equation is applicable, but experimental values of the two parameters, [t ] and < ) should be used. 

Asymmetrical flow field-flow fractionation was used for size determinations of SLN in comparison to an emulsion and oil-loaded SLN. The differences found in the sizes and elution profiles were attributed to differences in the particle shapes. Due to their anisometric, platelet-like shape it is likely that SLN are more retained by the cross flow applied compared to spherical emulsion droplets. This method appears very promising as additional size determination method particularly with regard to separation and detection of different colloidal structures. 

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