Viscometric study of aggregation phenomena in polymer dilute solutions and determination of the critical concentration c**t Anastasios Dondos, Constantinos Tsitsilianis and George Staikos Department of Chemical Engineering, University of Patras, 26110 Patras, Greece (Received 17 October 1988; accepted20 December 1988) A crossover is observed in the variation of the reduced viscosity, qsp/c, as a function of the concentration, c, for the systems poly(methyl methyacrylate)/nitromethane and poly(vinyl-2 pyridine)/benzene. This crossover is correlated with the critical concentration of the polymer c** in which the macromolecular coils start their contacts. The critical concentration c** is related with the molecular weight and the intrinsic viscosity of the polymer through the scaling laws: c**ocM-= and c**oc[q]-l. (Keywords: critical concentration; incipient overlap; aggregation; scaling laws) INTRODUCTION In recent years experimental and theoretical works have established the existence of three concentration regimes of macromolecular solutions t-3 namely dilute, semidilute and concentrated. The transition, in general, from one region to another does not occur abruptly. Instead it occurs rather gradually and it is not always possible to establish a well defined transition concentration separating the different concentration regimes. In dilute solutions the macromolecules behave as individual units and a characteristic length scale is the radius of gyration of the molecule. At a certain concentration, c*, the domains of the polymer molecule begin to overlap and the molecules lose their individuality (formation of infinitely large networks of overlapping molecules). We have suggested 4 the existence of a new critical concentration, c**, which separates the dilute solution in extremely dilute solutions and dilute solutions. At the concentration c** (c** <c*) the macromolecular chains start contacts and occupy the entire volume of the solution. In other words, c** corresponds to the incipient overlap of the macromolecular coils. However, in the region between c** and c*, the macromolecular chains conserve their individuality. The critical concentration c** has been studied using ternary systems polymer A/polymer B/solvent4-6. When a macromolecular chain of polymer A contacts a macromolecular chain of polymer B, in the concentration c**, a decrease of their hydrodynamic volumes occurs because incompatibility acts strongly against overlapping. This decrease of the hydrodynamic volume of the macromolecules yields a change in the slope of the curve relating the variation of the reduced viscosity, qsp/C, with the concentration, c, of the polymers. This critical concentration was related to the molecular weight and the intrinsic viscosity of the two polymers¢-6. t Dedicatedto Dr P. Remppon his 60th birthday 0032-3861/89/091690--05503.00 © 1989Butterworth& Co. (Publishers)Ltd. 1690 POLYMER,1989, Vol 30, September In this work we determine by viscometry the critical concentration c** using binary polymer/solvent systems, in which the polymer forms aggregates. The viscometric study of the binary systems was used until now only for the determination of the critical concentration c* (refs. 5, 7). Also in this work we correlate the critical concentration c** with the molecular weight and the intrinsic viscosity of the polymer for a given polymer/ solvent system. EXPERIMENTAL The poly(methyl methacrylate) (PMMA) and poly(vinyl- 2 pyridine) (PV2P) samples were prepared by anionic polymerization. The ratio of the weight-average mol- ecular weight to the number-average molecular weight, Mw/M,, of the samples never exceeds the value of 1.2. The samples of PMMA and PV2P are not isotactic because of their preparation by anionic polymerization. A very highly branched PV2P sample (Mw = 575 000) is also used in this work. Its preparation has been described elsewhere s. The viscosity measurements were conducted with an automatic viscometer (AVS, Schott-Gerate). The repro- ducibility was of the order of _ 1%. RESULTS It is well known that the atactic poly(methyl meth- acrylate) (PMMA) presents the phenomenon of aggre- gation via intermolecular interactions and that this phenomenon is influenced by the molecular weight of the polymer sample 9-11. In this work we use the nitromethane as a solvent for PMMA because such a marginal solvent of the polymer favours the interactions between polar groups of the polymer which will lead to the formation of polymolecular micelles. In Figure l we display the variation of reduced viscosity, rlsp/c, as a function of concentration, c, of two samples of PMMA in nitromethane solution at two