Errors and Error Tolerance in Irreversible Multistep Growth of Nanostructures

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.