Types of Models

Let's discuss some different types of models with examples.

Structural models

All of the chemistry examples on the previous page are structural models. They tell you something about how atoms and electrons are structurally arranged.

A map is another example of a structural model. It represents the structure of a place so you can navigate it. Maps make it easy to understand an important aspect of models that we will return to again: the scale of a model needs to match its purpose. The map of the globe in Figure 2.4.1 is not useful if you are trying to navigate through Chicago, even though Chicago is technically on the map. It is useful if you want to identify the world's large mountain ranges.

Structural models can be three dimensional. For example, a model car is a structural model of a real car. Looking at a model car, you can learn some things about the design and geometry of a real car, but probably not everything. Likewise, we saw a 3D ball-and-stick model of a molecule in the previous section.

Structural models can be more abstract. For example, the network below represents a social network. Each circle represents a person and links represent friendships. The grey circles identify close friend groups. (How do you think they model "close friend groups" here?) The network represents the "structure" of the social network, but it doesn't represent any sort of physical distance or structure the way a map does. Instead, it represents something less physically tangible, like how often the people interact, or how close they report feeling to one another.

In MSE, we will encounter many structural models - crystal structures that represent the arrangement of atoms in an ideal crystal or chain-type drawings representing long polymer molecules. They have some similarities to models you have seen in chemistry, but also some differences. In Figure 2.4.3 here is one example of a crystal structure model of magnesium silicide, $\ce{Mg2Si}$:

Categories as Models

Categories can be seen as a type of model. When you say two things are in the same category, you are saying that they are similar in some way. The category represents something about its members. As with all models, categories don't always perfectly represent their members. There are usually exceptions or differences of perspective. Consider the example from Section 1.7.1, in which tomatoes are strictly taxonomically a fruit because they are the seed-bearing fruit of an angiosperm, but in culinary practice it is a vegetable.

In this course, we will learn various categories or classifications for materials. Remember that these classifications are useful for some purposes, but they are a kind of model and therefore only approximations. We often find the classification scheme for materials classes in Section 1.7 very useful in organizing materials knowledge, but it has its shortcomings.

Equation-based models

Equations can be used as models. Imagine a car is traveling at a speed of 30 km/h and we want to predict how far will it have travelled in time (t). We can write an equation:

$d(t)=30t$

This equation serves as a good first model of how far the car will go, but the equation is not reality. First, the speed of the car will certainly vary, even if the driver is trying to stay exactly at 30 km/h. But more than this, something could happen that isn't included in the model at all. Maybe the car will get a flat. Or maybe the driver will get hungry and stop at a drive-through. Still, the model represents an approximation of reality and can be used to predict how far the car will travel. If the implicit assumptions of the model are true, its prediction will be pretty good.

Computational models

A computational model uses computer-based rules to represent a phenomenon. We will use many computational models in this course using a software platform called NetLogo. NetLogo model 2.4.1 shows is a simple computational model of a forest fire. In this model the agents (the things that act) are trees that are either on fire or not. The simple rules of the model can be summarized as: a tree that is on fire lights its neighbors on fire and then burns out. This is repeated until there is no fire left. You can click setup and go and watch the fire spread. It will be a bit different each time, because the forest is initialized randomly based on the density slider. Each spot in the forest has a probability equal to density of starting with a tree and is empty otherwise. We will use this model again shortly in our discussion of how models are used in science. We'll explore this model more in Section 2.6, but play around with it now if you like.