Reaction-limited cluster aggregation mechanism

Figure AA Dependence of the mean square radius of gyration on the aggregate mass for a collection of reaction-limited cluster aggregation mechanism (RLCA) aggregates. Here, the scaling relationship Rl is verified.

The formation of a particulate network with fractal structure has been reported, which suggests a reaction-limited cluster aggregation (RLCA) mechanism [34]. RLCA requires moderate repulsions to exist between the partides (Le., an energy barrier has to be overcome to permit a cluster-forming collision between particles). Since in ILs the classical electrostatic repukion should be annihilated, the alternate cation-anion layers patterning at the surface of the particles, which is induced by solvation, is thought to provide an effective repulsive barrier. 

In Fig. 29, the dependences of D on reaction duration t for DMDAACh polymerization at both indicated above conditions are adduced. As one can see, the two dependences Dj(t) are similar qualitatively and their distinction consists of only in more slow reaction realization for DMDAACh-1 (the kinetic parameters for DMDAACh synthesis adduced conditions differ on about two orders [1]). Let us note, that for DMDAACh-2 the aggregation mechanism change is observed twice within the range of t < 2 min mechanism particle-cluster is changed by diffusion-limited mechanism cluster-cluster and within the range of t = 5-10 min opposite change occurs [21]. It is important to note, that the last mechanisms change occitrs at constant initial monomers concentration c and practically constant value MM [1]. 

Monomer-cluster or cluster-cluster growth can be limited by diffusion or by reaction. In diffusion-limited monomer-cluster aggregation (DLMCA), simulated by the Witten and Sander model (25) in Fig. 5.11, it is assumed that monomers are released one by one from sites arbitrarily far from a central cluster. The monomers travel by a random walk diffusion mechanism and stick irreversibly at first contact with the growing cluster. Because of this trajectory, the monomers cannot penetrate deeply into a cluster without intercepting a cluster arm and the arms effectively screen the interior of the cluster from incoming monomers. Growth occurs preferentially at exterior sites, resulting in objects in which the density decreases radially from the center of mass (in three dimensions dm = 2.45). 

In Fig. 13, a kinetic curve conversion degree — reaction duration Q, is shown schematically, on which the technique of estimation of the characteristic times t, and tj, corresponding to termination of initial section and autoacceleration section of curve Q, are indicated. The calculated according to the Eq. (4) of Chapter 1 D value, which is equal to 1.65, defines unequivocally polymer formation mechanism as diffusion-limited aggregation cluster-cluster. However, as it was indicated above, in polymerization process beginning at t = 0 monomers (particles) solution was the initial reactive mixture, where macromolecular coils were absent. Let us remind that for such coil formation a macromolecule should consist of, as a minimum, 20 monomer links [35], Therefore, it is obvious, that on the first stage of polymerization mechanism particle-clrrster should be realized and this mechanism will act until in solution macromolecirlar coils (clusters) sufficient number is not formed for mechanism cluster-clrrster realization [36], Hence it follows that... 

The determined according to the Eq. (4) of Chapter 1 value for DMD AACh is equal to approx. 1.65. Such value simply defines the formation mechanism of a macromolecular coil DMD AACh in solution as diffiision-limited aggregation of a cluster-cluster mechanism [21]. Within the framewoiks of this model the dependence of a coil gyration radius on a reaction duration t is determined by the... 

The main conclusion of the present paper is that, what reaction cessation in polycondensation process is limited by purely physical factor, namely, the achievement of macromolecular coil density of solution density in which reaction proceeds. The possibility of such treatment is due fully to macromolecular coil fractality. The indicated processes are simulated within the framework of an irreversible aggregation models over mechanism cluster-cluster. The critical values of molecular weight and reaction duration, above which a S5mthesis reaction ceases, exist. 

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