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Dissipative Self-Assembly: a Novel Self-Healing Mechanism for Functional Materials

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Dissipative Self-Assembly: a Novel Self-Healing Mechanism for Functional Materials DISSIPATIVE SELF-ASSEMBLY: A NOVEL SELF-HEALING MECHANISM FOR FUNCTIONAL MATERIALS G. J. M. Koper 1, J. Boekhoven 1,2, W.E. Hendriksen 1, R. Eelkema 1, J.H. van Esch 1 1 Department of Chemical Engineering, TU-Delft, Julianalaan 136, 2628 BL Delft, the Netherlands – e-mail: [email protected] 2 Currently at: Inst. for BioNanotechnology in Medicine, Northwestern University, Chicago, Il, USA. Keywords: self-assembly, dissipation, self-healing, functional materials ABSTRACT Self-assembled systems formed of micelles or vesicles have frequently been discussed as model systems for self-healing materials because their structure is dictated by thermodynamics and hence they quickly restore upon perturbation. In this aspect, they mimic many natural systems such as biological cells. However, in contrast to most synthetic self-assembling systems the natural systems are not equilibrium processes. Attention is therefore now focusing on dissipative self- assembling systems where energy input is required to sustain the self-assembled state. These systems have the potential to adapt themselves and enter into different self-assembled states depending on the rates of environmental reactions whereas their equilibrium counterparts can only assemble or disassemble depending on the environmental equilibrium condition. Recently, we have constructed some dissipative self-assembling systems using chemical fuels and presently more examples are being worked on. During this presentation some important aspects of these systems will be discussed in relation to their capabilities of being self-healing. 1. INTRODUCTION Many functional self-healing materials are synthesized by means of a self-assembly process. Examples are the self-healing rubber of Ludwik Leibler [1], the supramolecular polymers of Bert Meijer [2], the nanofiber forming peptide- amphiphiles of Sam Stupp [3], and the self-healing hydrogels of Takuzo Aida [4]. From a physical point of view, the linear self-assembly process of Stupp’s peptide- amphiphiles is the simplest and we shall use it to illustrate some of the important aspects; a cartoon is given in Figure 1a. In addition, it also represents the simplest class of supramolecular polymerizations as reviewed by Alberto Ciferri [5]. The rate of formation of an aggregate of N monomers is given by N rf k11 x (1) where x1 is the mole fraction of monomers and k1 the forward rate constant. The break-up rate of such an aggregate back into monomers is given by _________________________________________________________________________________ ICSHM2013 450 Figure 1: Linear self-assembly of units with binding sites on either side (a), size distribution for total monomer mole fractions 1, 10 and 100 times the cgc (b), and average size (c) as a function of total monomer mole fraction. _________________________________________________________________________________ ICSHM2013 451 x rk N (2) bNN where xN is the mole fraction of monomers aggregated into aggregates consisting of monomers, so called -aggregates. When we assume equilibrium, the associated equilibrium constant K – per monomer – is defined as N kN K (3) k1 With a total monomer mole fraction xt one finds the characteristic, exponentially- tailed size distribution, see Figure 1b, as predicted using the simple mean field model by Cates and Candau [6] with an average degree of polymerization, see Figure 1c, scaling as [7] 1/2 Nx t (4) The network structures of Leibler [1] are from a physical point of view much more complex, see Figure 2, as they do not only consist of di-functional units, that are responsible for linear aggregation, but also of tri-functional units with which branching junctions are formed. With these building blocks the resulting structure becomes cross-linked as sketched in Figure 2. A geometrical analysis, not surprisingly, yields a length distribution of the mesh size L that is again exponentially tailed and an average mesh size that scales also algebraically with total mole fraction albeit with an exponent of 0.56 which is slightly larger than the 0.5 for the above described linear case [8]. The case of threefold junctions – as present in Leibler’s system – is interesting because the predictions both by Drye and Cates [8] and later by Zilman and Safran [9] indicate the possibility of a phase transition. Experimentally it is indeed found, that crystallization is hampering the synthesis of such systems [1]. Aida’s system of clay particles that are interconnected by dendritic binders are – from a physical point of view – a variation of Leibler’s system where the average functionality of the branch points is typically larger than 3 and hence the behaviour is less interesting as no phase transitions are to be expected. N Figure 2: Network assembled from di-functional and tri-functional units. _________________________________________________________________________________ ICSHM2013 452 A crucial aspect of the above described processes is that it is in equilibrium which means that the forward rate rf (eq.(1)) and the backward rate rb (eq.(2)) are balanced and this indeed is the condition from which the relation for the equilibrium constant emerges, see eq.(3). It is important to realize that this condition is to be taken literally, meaning that indeed there is a constant exchange of monomers between the aggregates themselves and with their environment where there are only isolated monomers. It is generally accepted, that there are two time scales associated with these aggregates. One is associated with the exchange of single monomers with the aggregates. It is relatively short and fully determined by the diffusion coefficient of the monomer. The slow time scale is associated with the formation process of one complete aggregate and roughly equal to the fast time scale times the average aggregation number. Hence, self-assembly processes are dynamic by nature and not static as sometimes suggested [10]. This dynamic aspect is what makes self- assembling systems an interesting option for self-healing materials. The only disadvantage is that when the system consists of more bulky monomers, the time scales become inherently longer. Therefore, even though self-assembling systems can be tuned by environmental conditions, the response times are relatively long to the extent that some systems do not reach equilibrium at all. 2. A SYNTHETIC DISSIPATIVE SELF-ASSEMBLING SYSTEM The equilibrium self-assembling systems described above are much less dynamic than their natural counterparts and it is interesting to see why this actually is the case. It is clear that the natural systems are not in equilibrium and require transfer of energy to operate: in biological systems it is often the ATP hydrolysis that conveys the necessary energy [11]. Examples from Nature are networks built from for instance microtubules or compartments such as mitochondria. To investigate this idea, we chose a synthetic system that has recently been put forward by our group [12,13], see Figure 3. The self-assembly utilizes a low molecular mass hydrogelator, dibenzoyl-(L)-cystine (DBC) in aqueous solution at a pH above its pKa value of 4.5. Under these conditions DBC remains isotropically in solution. Methylation of one of the carboxylic groups results in the formation of fibres and this process can be detected mechanically and optically, using for instance rheometry and turbidity measurements respectively. Crucially, the methylated DBC molecules are chemically unstable and hydrolyse at a pH-dependent rate. Hence, by tuning the pH and the methylation reaction rate the self-assembly dynamics of the gel can be controlled. The methylation reaction is not spontaneous and therefore it is coupled to a reaction that is spontaneous which in the present case is the conversion of dimethyl sulphate (DMS) into monomethyl sulphate (MMS-). In actual fact, also the hydrolysis reaction is a coupled reaction that turns the methylated DBC back into DBC itself, see Figure 3a. Let us now describe the phenomenology of dissipative self-assembly for this system. As soon as fuel is added to the system and the methylation reaction starts, the concentration of self-assembling monomers, the methylated DBC molecules, increases, see Figure 3b. When the critical gelation concentration (cgc) is exceeded the storage modulus starts to increase, see Figure 3c, which indicates that gel formation has started. As soon as the total concentration of monomers – free as well as aggregated – increases, their destruction also sets in by means of the hydrolysis _________________________________________________________________________________ ICSHM2013 453 a) b) c) d) Figure 3: Dissipative self-assembly, schematic of the process (a), total concentration of monomer, the methylated DBC (b), storage modulus of the gelled system (c), and relative recovery after perturbation (d). _________________________________________________________________________________ ICSHM2013 454 reaction. Initially, the formation rate exceeds the destruction rate and the monomer concentration increases resulting in an increasing storage modulus. At the end of the experiment, the destruction rate dominates and the gel breaks down leading to a decreasing storage modulus. In the intermediate regime, where formation and destruction roughly balance, the storage modulus remains reasonably constant. A closer look at the dynamical behaviour of this system reveals, that the maximum in the total monomer concentration occurs before the maximum storage modulus is reached. This most likely is due
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