Errors and Error Tolerance in Irreversible Multistep Growth of Nanostructures

Abstract

Error correction is one of the main features allowing self-assembly and other reversible growth processes to create giant, ordered molecular structures at the nanometer scale and above. On the other hand, in irreversible growth processes, such as chemical synthesis, errors (defects) are usually not removable and, as a result, growth is limited to a small number of synthetic steps and formation of relatively small structures. In this work, we develop a general model and theory to describe the behavior of errors in multistep, irreversible growth processes. Simulations of the model show that despite the large number of ways in which errors may occur in the growth, the average effect of errors seems to obey a universal pattern controlled by only a few parameters, regardless of the exact type of errors that occur. Furthermore, we show that errors that disturb growth cause damage that increases exponentially with the number of growth steps, thus leading to randomly disordered structures after a relatively small number of growth steps. If, however, growth is cooperative, the exponential increase of defects can be suppressed, suggesting that it is possible to create irreversible growth processes with error tolerance similar to that of reversible self-assembly (although without error correction). This may allow growth of ordered superstructures that exceed the limits of current systems.

Porous covalent–organic materials: synthesis, clean energy application and design

“…Alkynyl-based monomers have been widely employed for constructing CMP materials. 45,[128][129][130] Here, we mainly summarize four typical coupling shown in Scheme 3. A series of CMP materials have been prepared by using Pd(II)/Cu(I)-catalyzed homocoupling polymerization (route "a" in Scheme 3), such as HCMP-1 (TEB), 131,132 HCMP-2 (DEB), 131 PPN-1 (TEPM), 133 PPN-2 (TKEPA), 133 5 (TEPM).…”

Out of Equilibrium Self-Assembly of Janus Nanoparticles: Steering It from Disordered Amorphous to 2D Patterned Aggregates

“…Despite the vast amount of work so far presented, our perusal of the literature has evidenced that only a few articles discuss the effect of coupling Janus self-assembly with processes or fields (e.g., evaporation, flows, etc.) compared to near-thermodynamics studies; this contrasts sharply with the attention paid toward the self-assembling under various solvent evaporation conditions of mono- or poly-dispersed NPs with homogeneous interactions. − Noticeably, the latter studies have shown how a wide set of final aggregation patterns can be induced upon varying specific details such as the evaporation regime or ratio between diffusion and evaporation rates. Thus, coverage patterns such as disks, worm-like aggregates, , networks, ,,− , rings ,,, and hexagons, , fingers, − ,, linear or bridged wires, stalagmites, , and check or stripe , patterned aggregates have been shown and interpreted with the help of simulation approaches.…”

Reversible Multistep Synthesis with Equilibrium Properties Based on a Selection-Oriented Process with a Repetitive Sequence of Steps

“…However, it is limited by its lack of reversibility and error correction, which often results in reduced overall yield. 1,4 The second method is based on using reversible equilibrium reactions, which by themselves could be inaccurate and could lead to a large number of products. Yet the reversibility of the reaction can cause the majority of the products to be transformed back into the starting materials while leaving only specific stable structures.…”

“…The first method involves the synthesis of a structure by using an irreversible sequence of mostly accurate reactions that leads to a target structure. − This method is used in the majority of syntheses of organic molecules. However, it is limited by its lack of reversibility and error correction, which often results in reduced overall yield. , The second method is based on using reversible equilibrium reactions, which by themselves could be inaccurate and could lead to a large number of products. Yet the reversibility of the reaction can cause the majority of the products to be transformed back into the starting materials while leaving only specific stable structures.…”

“…Yet the reversibility of the reaction can cause the majority of the products to be transformed back into the starting materials while leaving only specific stable structures. Consequently, reversible system can selectively increase the fraction of some of the products concurrent with the reduction of the fraction of the others. , As a result, reversible processes exhibit many interesting properties, such as equilibrium and error correction, that allow them to surpass the limits of irreversible ones. − However, reversible systems are limited by the need for completely reversible reactions and the use of one-pot, one-step processes. Multistep processes are, on the other hand, mostly irreversible due to a nonrepetitive sequence of steps and the use of one-directional reactions.…”