Blob concept

For the blob concept to make sense physically, a chain clearly must be larger than an " b -blob n > n B. We may then look at these blobs also from a different point of view. The concentration of -blobs in the solution is... 

For s 1. the Tit blob is smaller than the whole chain and the blob-concept starts to make sense. For large overlap in view of screening the number of concentration blobs per chain should not be important. Thus iJ should reduce to a function of the blob concentration only. In view of Eq. (9-11) we therefore expect U to become a function of c independent of n. With this assumption the scaling law (9.2) yields... 

The blob concept is very successful in describing qualitative features of the concentration crossover5 from dilute to semidilute solutions. This has led to a discussion of the temperature crossover5 among the 0- or excluded... 

Sec Fig. 9.L We now restrict ourselves to d = 3.) Deep in these regimes, the blob concept predicts characteristic power laws. Now the line cannot extend down to i = 0 since for fixed n wc kiave the region 2 1. We should thus draw another line t separating a f9-regioii F from the excluded... 

The mean field theory seems to be helpful in explaining the behavior of semidilute solutions, but it fails in explaining various experimental results [35]. Alternative theories such as the blob concept and the scaling theory, both introduced in the 1970s, have been successfully applied to determine the thermodynamic behavior of these solutions [15]. 

The consonance noted above between the predictions of scaling law theories and the results of experiments suggests that the assumptions underlying the theories are correct. Mattice (1981), however, has criticized the basic assumptions of the blob concept because they are not verified by rotational isomeric state calculations that incorporate the excluded volume term, admittedly in a somewhat empirical fashion. A major difficulty envisaged by Mattice in the simple application of the blob concept lies in its failure to account for the consequences of the repulsive interaction of the subchain with atoms elsewhere in the main chain. 

In Section 1.4, we explained that the blob concept enables us to derive expressions for the concentration dependence of static properties of concentrated polymer solutions. In the following, we show that the same results can be derived by a simple argument called the scaling theory. First, we consider (5 )(c), which, as before, denotes the mean-square radius of gyration of a test polymer (modeled by a spring-bead chain) in a solution of concentration c. Basic assumptions of the scaling theory are that a dimensionless factor Hs defined by... 

We note, however, that this choice of is established neither theoretically nor experimentally. For example, a well-documented QELS study of Adam and Delsanti [10] on polystyrene in benzene yielded fx = 0.55 0.02. Equation 2.34 with fx equated to u was derived by Brochard and de Gennes [11] using the blob concept. 

Gaussian chain with df = 2. We also note here that the blob concept obviously only applies to systems with excluded volume effects, i.e., where df < 2. 

The osmotic pressure and the time scale of motion depend heavily on concentration and molecular weight. The dependence is universal for a certain class of solutions each class, however, exhibits a characteristic dependence. For many years, we had not had a good understanding of those characteristics until the blob concept, the scaling theory, and the reptation model were introduced in 1970s. With simple ideas and simple mathematics, these concepts elegantly explained the observed complicated dependence. 

---