Crystallization which occurs randomly could be considered as a way to increase the substrate thickness despite the fact that the tethering density is getting reduced.
Through mentioned method, the tethering density of grafted chains on the substrate could be reduced without altering the molecular weights and crystallization temperature.
During the course of filament elongation analysis as a function of side-binding protein density on the surface, we noticed that filaments appeared more bent as the tether density increased.
Because the chain conformation is dependent on the molecular weight and surrounding environmental conditions such as temperature, solvent quality and other factors, the reduced tethering density ((tilde{sigma })) is more generally used instead of tethering density, σ.
Based on the reduced tethering density, there are three regimes for polymer brushes which are divided in non-interaction regime, crossover regime, and highly stretched regime [7, 16].
Mentioned approaches are not able to control the uniformity of tethering density [6] and chain length of the tethered polymers.
Where the folding spaces are constant, the grafted chains on the substrate surface approach together, and this is the very meaning of tethering density enhancement via rising the substrate thickness.
Besides, with elevation of crystallization temperature, the thickness and, subsequently, tethering density of different phase regions were on the rise.
It is of interests that in conventional homo-brush single-crystal growth systems, the trend of substrate thickness and tethering density is the same.
Tethering density is defined as the number of tethering points in a unit area, and it is an important parameter to describe polymer brushes.
