Restrictions on the size of prokaryote molecules

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This question was a lecture discussion topic during my Biophysics course at university. I missed the lecture and the question is bothering me.

"Eukaryotes (multi-cell organisms) evolved into very large sizes whereas prokaryotes (single-cell organisms) remained quite small (about 1 micrometer). What has prevented prokaryotes from growing to larger sizes?"
I think the answer may be grounded in statistical mechanics but since I don't know the answer, that could be rubbish. Any help is appreciated!
 
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I would first note that the distinction between eukaryotes and prokaryotes is rooted in the presence or absence of a cell nucleus - there are unicellular eukaryotes like yeast, after all.

The answer likely involves consideration of the surface area to volume ratio, diffusion of gases through said volume, and that unicellular organisms need to be able to "do everything" - contrast this to multicellular organisms which possesses features which enable them to circulate necessary nutrients and chemicals through their bodies.
 
Here is the answer I got:

From a survival/evolutionary standpoint, for single celled organisms to survive (such as a bacteria in a pond), it needs to be able to identify a potential source of danger (by some sensing mechanism) and transmit that information to the CPU of that cell in order to take action and propel the cell away (using the flagellum). So there has to be a 'sensing of danger' stage and a 'signal processing' stage.

Because prokaryotes are single-celled organisms there are no specialised cells like neurons that can transmit signals. The only way that information can be transmitted between the cell's sensors and its 'CPU' is by chemical diffusion within the cell. Typical values of diffusion coefficients for a cell's cytoplasm is on the order of D = 10^-9 m^2/s which is very slow.

As a result, prokaryotes with a very small cell size are able to identify danger in order to survive.

Pretty interesting...