Modeling is the development of a mathematical representation of an actual or proposed set (group) of interactions that can be employed to predict the functioning of the set (group) under possible conditions. Interest in modeling has grown since the late 1970 and early 1980s coincident with the development of more and more powerful computers. The size of models has grown and the additional sophistication of the evaluation has increased.
What does this have to do with nanotechnology? It has been demonstrated that physical material properties change as the size of the material decreases into the low double-digit nanometers. The application of gold nanoparticles to produce the color of red in stained glass windows is an example of usage that is hundred of years old. The effect of sliver nanoparticles on bacteria in another example. Is it possible to develop a model that will predict the behavior of materials for any size or shape? The answer is: “Yes, BUT”.
One instance that raises a question about modeling goes back to the early 1960s. Professor Edward Lorenz (MIT) employed a computer simulation of weather patterns. Supposedly, he left to get a cup of coffee and when he returned, he was very surprised. He was rerunning a simulation he had previously made. Except, this time he rounded 0.506127 to 0.506. This small change in value changed the entire pattern of the projected two months of weather results. [Ref. #1] This result has become know as the butterfly effect, which is used to refer to a very tiny occurrence can change the course of what follows. This terminology as used in chaos theory, represents the dependence sensitivity of the initial modeling conditions that can produce significant changes in the resultant projections. [Ref. #2]
In a quote I attribute to Professor Robert Shannon of Texas A&M University, he said: “All models are wrong! Some are useful.” Once the natural occurring probability impacts the occurrence of the data employed, the results are uncertain. The interesting thought is that complex models run on 16-bit computers could have completely different results from the same model run on a 64-bit computer. In addition to this difference in precision, the initial starting conditions are important. In many models, the initial conditions are left empty or zero and the model is run to take remove the “initialization” bias. Obviously, models, like weather forecasting, need initialization data. In the weather example, there are a number of tropical storm forecasting models that are compared. Each of the model’s projection is actually based on a number of runs of that data to determine an average or best fit. In comparisons, the European model, which has more sensors than the US model, tends to be a bit more accurate. Trying to predict smaller effects is more difficult because the minor change in variables can cause greater effects when trying to restrict the weather impact to smaller regions.
So, the question is what kind of results can be anticipated with modeling on nanotechnology. One example is the recently identified Schwarzite carbon structure. [Ref. #3] Material with these properties was predicted as early as the 1880s, but no one was able to create it to validate the theoretical (modeling) results. Now that it has been created, the predicted properties can be tested and evaluated. Once the material is in hand, then actual testing can be done. Predictions can point out directions to follow, but do not guarantee that the material will have the specific, predicted properties.
These was recent article [Ref. #4] that implies computer simulation will be used to develop the laws of nature and end much work being done in theoretical physics. While there might be benefits gained and some people are indicating that artificial intelligence (AI) will provide interesting breakthroughs, these “discoveries” will still need to be proven.
One thing that modeling can not do is to find surprises. University of Wisconsin physicists constructed a 2-D form of tungsten-ditelluride [Ref. #5] that has unanticipated properties, including “spontaneous electrical polarization” from combining two mono-layers of the material. Until models can be constructed that contain all the variables and correct relationships among particles, models will be “wrong” but useful.