A thermodynamic analysis of the spider silk and the importance of complexity

The spider silk is one of the most interesting bio-materials investigated in the last years. One of the main reasons that brought scientists to study this organized system is its high level of resistance if compared to other artificial materials characterized by higher density. Subsequently, researchers discovered that the spider silk is a complex system formed by different kinds of proteins, organized (or disorganized) to guarantee the required resistance, which is function of the final application and of the environmental conditions. Some spider species are able to make different silks, up to twelve, having a composition that seems to be function of the final use (i.e. dragline web, capture web, etc). The aim of this paper is to analyze the properties of the spider silk by means of a thermodynamic approach, taking advantage of the well-known theories applied to polymers, and to try to underline and develop some intriguing considerations. Moreover, this study can be taken as an example to introduce and discuss the importance of the concept of optionality and of the anti-fragile systems proposed by N. N. Thaleb in his book “Antifragile: Things that gain from disorder”. 1 General Introduction The present work can be divided in three sections. In the first one, a general description of the silk using the olog approach[1] is proposed. This part is useful to schematize the possible behaviour of the spider silk. In the second section, the 1 ar X iv :1 70 3. 06 49 7v 1 [ nl in . A O ] 1 9 M ar 2 01 7 hierarchical nature of the spider silk is investigated through a thermodynamic approach. The right side of Figure 2.1 shows two examples of the spider web, while in the left side of the picture a scheme of the hierarchical spider silk structure is depicted. It was the starting point to build up the description proposed. Finally, Figure 1: On the left, a spider web; on the right, a schematic picture of the spider silk structure [3]. in the third section, it has been discussed how the interpretation proposed can be taken as an example to explain the importance of the antifragile theory of N. N. Thaleb[2], where the antifragility should not be interpreted only as a toughness anymore. From another point of view, the interpretation proposed suggests that the nature follows the ideas of complexity and optionality: maybe the most important keys to survive. The olog approach was considered necessary to create an initial and general scheme of the structure of the spider silk (see Figure 2), putting in evidence important aspects necessary to build up the proposed interpretation. In order to approach the problem from a thermodynamic point of view, the starting point taken into the account was the equation of free energy proposed by Helmholtz (2.1): dA = −TdS + μdN + σd (1) The equation (2.1) collects all the terms that describe “where” the energy is stored in a system. The free energy (F) represents the work that the system is able to do on the environment or, from another point of view, the energy that the system can provide when it is stressed by an external force. In order to use the equation of the free energy, it was necessary to identify all possible actors that play a role in the “energy storage”. Referring to the general scheme of the internal structure of the spider silk (see Figure 1) and starting from the internal structure deeply studied in literature at the level of protein composition [4,5], different responses can occur at the microscopic level when a spider web is stressed. Upon the occurrence of an external stress, the following phenomena were considered at the microscopic level: