di-lute solutions. It thus neglects the interaction between macromolecules in solu-tions and on the surface. Study of adsorption from semi-diluted and concentrated solutions is much more complex. It is necessary to account for the existence of a definite structure of solution, which has a pronounced effect on the adsorption. By increasing concentration of polymer solution, statistical coils be-gin to overlap, and as a result, the compression and decrease in coil size oc-curs.101 In this region of concentration, two regimes exist, according to de Gennes:52 semi-dilute and concentrated solutions. In semi-dilute solutions macromolecular coils begin to overlap, however the volume fraction of polymer, Φ, in solution is still low:Φ << Φ <<* 1.
C=C* (or in volume fractions,Φ=Φ*), the coils begin to touch each other at the concentration corresponding to the threshold of overlapping. This threshold is not sharp and a region of crossover exists. Concentration C*should be compa-rable with the local concentration inside the coil.
A generalized approach gives the possibility to consider the transition con-ditions from semi-dilute to concentrated solutions.102For statistical coils, the critical concentration of overlapping (cross-over concentration) is expressed as
C*= (Φ/NA)(23/[η]) [1.30]
where NAis the Avogadro number andΦis the volume fraction of polymer in so-lution, and [η] the intrinsic viscosity. C*is inversely proportional to the intrinsic viscosity, related to radius of gyration. The transition from semi-dilute to centrated solution means that entangled coils, dissolved in a good solvent, con-tinue to contract towards an unperturbed size limit. The convergence of the hydrodynamic volume is a measure of the crossover between semi-diluted and concentrated regimes. In this case
C**= 1/[η]** [1.31]
where [η]**is the intrinsic viscosity corresponding to the limit molecular mass M**, at which [η] = [η]θ~ (h**/2)3. Here, h**is the distance between chain ends at molecular mass M**and C**.
Adsorption of polymers on adsorbing particles of varying sizes is concentra-tion specific. The analysis of such adsorpconcentra-tion is very difficult, and to describe the experimental data, the first crossover concentration, where macromolecular coils begin to overlap and interact, can be used. Therefore we can use the simple criterion of transition from dilute to semi-dilute solutions:103,104
1 < C[η] < 10 [1.32]
orΦ*= 0.12/[η]. It is worth noting that these criteria have not been taken into ac-count in all preceding investigations of adsorption.
In equilibrium solutions, together with isolated macromolecular level of dispersity), there exist structures of various types formed as a result of aggrega-tion or associaaggrega-tion of macromolecules. These processes proceed in the concentra-tion region both below and above C*, which is connected with the dependence of the thermodynamic parameter of interaction polymer-solvent on concentration.
The interaction between coils leads to the appearance of molecular aggregates, which are unstable structures formed by interactions of coils, having a definite lifetime. The type of aggregates and the number of coils depend on the intermolecular interaction between macromolecules, concentration and nature of a solvent. The thermodynamic reason for the formation of macromolecular ag-gregates is probably incomplete miscibility of polymer fractions of different mo-lecular mass.49 Therefore, by formation of aggregates some fractionating according to molecular mass may proceed. This idea, put forward by S.
M. Lipatov in the early thirties,105assumes the dependence of the aggregation degree on molecular mass, connected with higher solubility of low molecular mass fractions. The aggregates of macromolecules are not colloid particles in a true sense of the word, but they may be considered as some kind of micelles, be-cause their size is comparable with the size of colloid particles. Aggregates are not phase particles and they do not have a sharp phase border with the solvent.
At the same time, the formation of aggregates is determined by the appearance of essential differences in local density in various parts of the system. The den-sity fluctuations, as they are determined by the aggregate formation, may be
considered as the regions of higher concentration of polymer in a given solution as compared with an average density. It is important that these fluctuations of density exceed fluctuations typical for liquids, which can be described by the Boltzmann distribution.
It is worth noting that the size of aggregates strongly depends on solution concentration, temperature, and temperature dependence of the solvent proper-ties. In polymer solutions, there exist equilibria between isolated and aggre-gated macromolecules. In definite conditions, the aggregates may serve as a nuclei of a new phase.106,107 The system which contains aggregates is a one-phase stable system. The transition to a two-phase system proceeds only when the system happens to be in a metastable or unstable region of the phase diagram. There are many experimental results on the formation of aggregates in polymer solutions and methods of estimation of their size, number of mole-cules in an aggregate and size distribution.108-114
To prove experimentally the adsorption of aggregates, we have used the method of turbidity spectra,115-119which allow us to estimate the aggregate size and their number in solution. The comparison of these data with adsorbance shows that aggregates are transferred onto the adsorbent surface (their number
Figure 1.3. Isotherm of adsorption of oligoethylene glycoladipinate on carbon black (1) and fumed silica (2) from ace-tone solutions.
Figure 1.4. Isotherm of adsorption of poly-styrene from toluene (1), cyclohexane (2), and polycarbonate from chloroform (3).
in the equilibrium solution diminishes after adsorption). The preferential ad-sorption of aggregates was explained by their lesser solubility as compared with isolated macromolecules and by analogy with decreasing solubility with grow-ing molecular mass. The transition of aggregates onto the surface assumes weak bonding with the surface because only some molecules, forming an aggregate, interact directly with the surface (see Figure 1.2).
In this case, during desorption, adsorbed polymer is almost fully removed from the surface, which is different in adsorption from dilute solutions. The amount of the adsorbed polymer, which after aggregation is adsorbed on the sur-face, is much higher, compared with dilute solutions. Figures 1.3 and 1.4 show the adsorption isotherms for various systems. High amounts of adsorbed poly-mer are explained by simultaneous transition onto the surface both of aggre-gated and isolated macromolecules. The aggregate size increases with increased
Figure 1.5. Isotherm of adsorption of polycarbonate (a) and polystyrene (b) by various amounts of adsorbent (fumed silica), (mg/ml of solution):1-5, 2-10, 3-20, 4-30, 5-40.
solution concentration. Correspondingly, the value of adsorption begins to in-crease at the same concentration, if marked aggregation proceeds. In some cases, isotherms have no saturation region or adsorption passes through a maxi-mum.It was established120that adsorption from aggregated solutions is charac-terized by the dependence of the adsorption value on the amount of the adsor-bent in the system (Figure 1.5). The adsorption isotherms are situated lower, with increase in the amount of adsorbent due to decreasing adsorption. Maxima observed on the isotherms in formation of aggregates become less pronounced.
Such behavior is explained by preferential adsorption of aggregates and, at the same time, by simultaneous adsorption of aggregates and isolated molecules.
After establishing adsorption equilibria, a new equilibrium between aggregated and isolated molecules is established.
The number of aggregates in solution is considerably lower than that of iso-lated macromolecules. When all the aggregates are adsorbed, the higher the amount of adsorbent, the more pronounced is the adsorption of single molecules.
As a result, the total value of adsorption diminishes.118The maximum on iso-therms with the onset of strong structure formation in solution disappears, which may indicate the change in the equilibrium between aggregated and iso-lated macromolecules under the influence of adsorbent surface. The influence of temperature is determined by its effect on the equilibria between aggregated and isolated molecules, which, in turn, also depends on concentration.118With increasing temperature, due to thermal movement, the aggregates dissociate and their size diminishes. Increasing temperature leads to a shift of the onset of aggregate formation to higher concentrations, and their size diminishes. The concentration dependence of the aggregate size is more pronounced with in-crease in temperature. Thus, when considering the temperature dependence of adsorption, one should have in mind the change in the aggregation degree with temperature, which may result in diminishing adsorption.
It is also necessary to account for the influence of temperature on the inter-action between various aggregates. Its diminishing facilitates the transit of ag-gregates to the adsorbent surface and as a result in some cases the aggregative adsorption increases with temperature. There are many factors influencing ad-sorption from semi-dilute and concentrated solutions, which may be explained now only on the qualitative level.