136 BIG MOLECULES 



tribution shown in Figure 6-6 clearly shows this. Number-average, or 

 weight-average molecular weights are obtained, depending upon whether 

 the number of particles or their size is reflected by the measurement. (2) The 

 configurations which the macromolecule can take in solution can vary, de- 

 pending upon hydrogen ion concentration (pH), cation content, and other 

 factors which imply strong electrical effects. (3) Many macromolecules are 

 themselves polymers, and in turn may polymerize further in solution. 



From this discussion it is easy to see that the elucidation of the exact size 

 and shape, or structure, of a particular macromolecule in a particular solu- 

 tion is probably still a long way off. Some physicochemical experiments 

 which throw light on this vexing but important problem will now be outlined. 

 We follow, in part, Paul Doty in this outline, and recommend highly his 

 clearly written reviews 5 of 1956 and 1960 to the reader who wishes to pursue 

 the subject beyond the bare outline given here. The methods are divided 

 conveniently into static (or equilibrium) and dynamic methods. All give 

 molecular weight and/or dimensions. 



Static Methods 



Osmotic Pressure. This is the most sensitive property of dilute solutions of 

 macromolecules, but since it is a colligative property it is strongly influenced 

 by the presence of any molecules or ions other than the macromolecule being 

 studied. The osmotic pressure, ir, as a function of concentration, c, can be 

 expressed 



7T \ B C 



= — h c + c 2 + ■■■ 



cRT Ad M 2 M 3 



where M is the number-average molecular weight, B and C are constants 

 related to molecular size and interactions, R is the gas constant, and T the 

 absolute temperature. Measurements* of osmotic pressure at several concen- 

 trations can be plotted as tt/cRTvs c, as is shown in Figure 6-7, Doty's 1960 

 data on collagen at 2°C. Extrapolation to zero concentration, where the 

 polymer molecules have no influence on one another no matter how uncoiled 

 they may be, gives the first term, \/M, the reciprocal of which is the num- 

 ber-average molecular weight, M„, in this case 300,000. The parameters 

 B and Care not zero because the macromolecules can physically coil around 

 each other and, furthermore, interact with each other's electrically charged 

 groups of atoms. 



Light Scattering. We saw in Chapter 4 that light is scattered and absorbed 

 by molecules in solution (Rayleigh scattering of light, and the Beer-Lambert 

 law of light absorption). For macromolecules the loss is explicitly stated 



*Referback to Figure 2-3 and the discussion on page 36. If c is expressed in g/1, it in 

 atm, and R as 0.082 1 atm/deg. mol, M has units of g/mole. 



