By Linda S. Hirst
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Extra info for Fundamentals of Soft Matter Science
In this simple case, we have looked at a polymer over just a limited length scale; however, one of the most fascinating aspects of fractal objects is their tendency toward scale invariance. In other words, if you were to look at an object, observing its shape and structure, then zoom in on a particular spot, you would observe exactly the same shapes and structure. This sounds confusing, but actually we observe objects with these properties every day. Look closely at plants and trees, and you will observe a characteristic branching geometry.
These coefficients are determined experimentally for a particular system. , two particles cannot be in the same place at the same time). 5 HYDROPHOBIC EFFECTS AND THE HYDROGEN BOND A large number of soft matter systems exist in aqueous solution, and one of the most common driving forces for assembly in such systems is the hydrophobic effect. 6 The hydrogen bond and molecular structures for water, the polar solvent methanol, and the nonpolar solvent hexane. on Earth and vital to biological processes.
Can you tell how large a cloud is with no frame of r eference? These examples demonstrate scale invariance, and there are also many examples of this kind of structure in soft materials, particularly in colloidal and polymer aggregates. Now, imagine a tree-like branching motif that fills space by constantly branching from smaller and smaller limbs; as we go to higher and higher generations of branching, the space between the largest limbs will be gradually filled. Simple fractals can be easily generated by this kind of repeating algorithm.