Macromolecular coils fractal dimension

Chapter 13 - It was shown, that limiting conversion (in the given case - imidization) degree is defined by purely structural parameter - macromolecular coil fraction, subjected evolution (transformation) in chemical reaction course. This fraction can be correctly estimated within the framework of fractal analysis. For this purpose were offered two methods of macromolecular coil fractal dimension calculation, which gave coordinated results. 

TABLE 4 The comparison of macromolecular coil fractal dimensions calculated by different methods, for polyarylates. 

FIGURE 3 The dependences of macromolecular coil fractal dimension on polymer and solvent solubility parameters difference A5 for copolymers SAN-MMA. The solvents 1— toluene, 2—ethyl benzene, 3— benzene, 4—chlorobenzene, 5—chloroform, 6—tetrahydrofuran, 7—pyridine, 8—methyl ethyl ketone, 9-1,4-dioxane, 10—N, N-dimethylformamide. The same conventional signs are used in Figs. 4-11. 

FICURE 6 The dependence of macromolecular coil fractal dimension Z) on corrected... 

TABLE 7 The comparison of calculated according to the Eqs. (4) and (29) values of macromolecular coil fractal dimension... 

Hence, the increase of TMAC contents in copolymers PAA-TMAC has two consequences for macromolecular coil stmcture the chain rigidity increase and macromolecular coil fractal dimension reduction is observed. These changes influence essentially on both synthesis processes and flocculation of low-molecular admixtures processes of the considered copolymers [36]. 

FIGURE 14 The dependence of interaction parameter e on macromolecular coil fractal dimension Dj. A hnear macromolecule characteristic states according to the classification [10] are indicated by points. 

Hence, the results stated above have shown that the macromolecular coil fractal dimension D can serve as volume effects measure. The value D for coil in 0-solvent characterizes such effects absence (D=2.0, e=0). Dj.<2.0 means repulsive interactions availability, >2.0—attractive interactions between randomly drawing closer to one another chain links and also between chain links and solvent molecules. The repulsive interactions weakening and, respectively, attractive interactions intensification means macromolecular coil coimectivity degree enhancement, characterized by the spectral dimension d. Thus, the dimensions D, and d variation (at fixed d) characterizes completely enough biopol5miers (and polymers at all) macromolecular coil behavior in diluted solutions [39]. 

FIGURE 25 The dependence of Kuhn segment length on macromolecular coil fractal dimension for rigid-chain polymers. The straight line—calculation according to the Eq. 

FIGURE 26 The dependence of macromolecular coil fractal dimension on Flory-Huggins interaction parameter x, for solutions ofpolystirene (1), polyfmethyl methacrylate) (2), polysulfone (3) and poly(vinyl acetate) (4). 

FIGURE 30 The dependences of macromolecular coil fractal dimension on formal blocks contents for PESF solutions in tetrachloroethane (1, 3) and chloroform (2,4). Calculations were performed according to the Eqs. (11) (1,2) and (58) (3,4). 

FIGURE 32 The dependences of macromolecular coil fractal dimension on difference of polymer and solvent solubility parameters A8 for polyarylates with metha-( 1) and para-connections in the main chain. 

FIGURE 34 The dependences of macromolecular coil fractal dimension on combined parameter (Ad/CJ for PC (1), PAr with para-connections (2), PAr with metha-connections (3), PMMA (4), PS (5), PDMS (6) and SKN-18 (7). 

As it has been shown above, the solvent change in diluted polymer solution leads to a macromolecular coil fractal dimension change. This effect is due to variation of the interactions polymer-solvent and within the framework of fractal analysis the indicated effect is described by the following equation [25] ... 

FIGURE 57 The dependence of mean-viscous molecular weight A/ on macromolecular coil fractal dimensions (1) and Dj (2) for polyarylate F-2. 

FIGURE 60 The dependences of macromolecular coil fractal dimension Dj, calculated according to the Eq. (13), on formal contents for PESF (1), CP-OPD-lO/OSP-10 (2) andCP-OPD-lO/P-1. 

FIGURE 67 The dependences of adaptability measure/1 on macromolecular coil fractal dimension D ior DMDAAC. The autoacceleration (1) and finish polymerization (2) stages. 

It is obvious, that the macromolecular coil fractal dimension D, which can be changed, for example, by solvent, type of pol mier variation, so forth, is one more factor, influencing on flocculation process effectiveness. Thus, from the Eq. (142) it follows, that the value c can be maintained on previous level by A4Mvariation atZ) change. The authors [181] compared this possibility for PDMDAAC in two solvents water and NaCl water solutions (the value D= AA and 1.65, respectively) and obtained coefficient k, which shows, in how many times a polymer MVf should be reduced at transition from Z) =1.65 to D=IA4 for the previous value preservation. The dependence of on MV/is adduced in Fig. 78, from which the strong dependence of c on a macromolecular coil fractal dimension follows or, in other words, on coil accessibility degree to particles penetration. Thus, at... 

Hence, the stated above results have shown that the molecular weight, macromolecular coil stmcture, characterized by its fractal dimension, and medium, in which flocculation occurs, are included in a factors number, influencing on adsorption of admixtures (flocculation) effectiveness by a pol mier flocculator PDMDAAC. The medium cans influence on flocculation process by two ways by a macromolecular coil fractal dimension change and viscosity variation. The latter factor can influence on diffusive processes intensity. The sole from the enumerated above factors, which will influence equally on fractal and compact objects properties, is a... 

FIGURE 100 The dependences of macromolecular coil fractal dimension on beams number/for PS-Cj without flexible junction (1) and with flexible junctions -Si(CHj)- (2), -(CHj/- (3). The horizontal stroked lines indicate values for coil in good solvent (4), 9-solvent (5) and compact globule (6) in a branched polymers case. 

Kozlov, G. V. Dolbin, I. V. Mashukov, N. 1. Burmistr, M. V Korenyako, V. A. Prediction of the macromolecular coils fractal dimension in diluted solution on the basis of two-dimensional solubUity parameter model. Problems of Chemistry and Chemical Technology, 2001, 6, 71-77. 

Temiraev, K. B. Kozlov, G. V. Sozaev, V. A. The prediction of macromolecular coil fractal dimension by polymer molecular characteristics. Bulletin of Kabardino-Balkarian State University, series physical sciences, 1998, 3, 24-28. 

TABLE 5 The polycondensation mode and macromolecular coil fractal dimensions for PAASO. 

The simplest and most reliable method of confirmation of the fact, that the macromolecular coil fractal dimension A is unequivocal structural characteristics of polymer melt, is proposed in Ref [48]. It has been shown earlier [50], that the dependences (where is the... 

Thus, the results stated above have shown that the macromolecular coil fractal dimension is a parameter, unequivocally characterizing polymer melt structure. The steric hindrances in polymer chain can play the role of the traps for free radicals, creating the effect, similar to the effect of inhibitor presence. 

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