Sunday, September 19, 2010

Phenomenological Parameters

The discussion in this chapter compared many theoretical models to experimental data. It reminded me of section 8.5 from last chapter, which I made a post about last week. This chapter gave us a name for some of the constants which we can fit to a model, the phenomenological parameters. The subtle difference between the constants needed to fit a model and phenomenological parameters are that constants involved in a model can be definite traditional variables, like the length of a bond, or the number of particles in a situation. The phenomenological parameters only describe a bulk behaviour of a model; they only make sense in the large scale, and they break down when applied to individual constituents of the bulk substance. In other words, the constants in a model can exist outside the model, but the phenomenological parameters only make sense when the model is used, such as the co-operativity parameter γ in the helix-coil transition model.

This distinction comes back to the two methods for creating scientific models discussed in section 8.5. When a model is built from the theory up, and then compared to experimental data, constants that exist independently of the model are being used. When the model is created after analysing experimental data, constants which describe the observations are discovered, and are named phenomenological constants.

This distinction was also obvious in the way this chapter was constructed. When discussing simpler topics and models, the chapter would discuss the theory that lead to the model, and only after the model had been made would the experimental data be shown, to verify that the model is sound. This chapter however was different; we saw the data very early (p351, figure 9.4) and didn’t finish discussing it until p362. This approach is quite necessary for the analysis of the extension profile for the stretching of DNA, as it has a very complicated behaviour, and it would be very unlikely that a model which predicts this behaviour would have been developed before the data was discovered.

I like that this textbook demonstrates both methods of model development. I can see strengths and flaws in both approaches, and I am glad that as scientists we have both models available to us.

1 comment:

  1. This is explained well in idea 9.1 - "When we study a system with a large number of locally interacting, identical constituents on a far bigger scale than the size of the constituents, then we reap a huge simplicifcation: Just a few effective degrees of freedom describe the system's behaviour, with just a few phenomenological parameters."

    In terms of polymers and DNA the important parameter is the bend persistence length A. Polymers with a bend persistence length less than it's contour length will be bent by thermal motion. Some structural polymers have a large bend persistence length and therefore can be considered rigid, DNA however has a small bend persistence length compared to its contour length.

    This section of the book also describes a polymer for which using this particular simplified model does not work - proteins. In proteins each monomer has different properties. So knowing when to apply simplified models is also important.