Polydispersity Notation and basic features

P(n) gives Ihe probability that a diain, randomly chosen from our solution, has length n. We will often use a reduced distribution p y) defined ns 

In explicit perturbative expressions, p y) often occurs in terms of its Laplace transform 

Since any physically reasonable form of p y) for small y is bounded, i ( r) for z — cxD hUvS to vanish at least as const/x For small x the iiormalizatioTi conditions (5.38) imply 

Grand Canonical Description of Solutions at Finite Concentration 

All our results will hold for general p y), subject only to the condition that the Laplace transform exists. Experimentally p y) in general is not very well known, but is characterized by some low order moments. An often used ansatz is the so-called Schultz distribution 

A physical solution of long chains always contains some distribution of chain lengths, and to control the resulting polydispersity effects1 is an important, but experimentally quite difficult issue. In the theory, as we have formulated it up to now. polydispersity is contained in the function cp(n). giving the concentration of chains of length n. Introducing the total chain concentration 

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