Coil density

It is well-known that the coil density of macromolecules decreases with increasing molar mass. Due to cyclization this decrease in density becomes less or even disappears because the macromolecules of higher molar mass are more strongly contracted than those of lower molar mass. After a certain conversion of pendant vinyl groups, the influence of the intermolecular reaction on [r ]... 

We can now ask the question What is the magnitude of the coil density How far is the statistical coil, which we have considered so far, diluted How many monomer units are present in a unit volume It is possible to calculate how the density, p, depends on the distance to the centre of gravity and on the number of links n. It appears that the volume fraction in the centre equals /o = Ihfn, i.e. ... 

Considering the calculation of coil density, this is not surprising. A concentration of 1% in a solution seems small, but when the coil is more than 100 times diluted, considerable mutual penetrations of the coils can be expected, and, therefore, strong deviations from the behaviour of single, separate coils. 

Deriving molecular dimensions in solution from viscosities depends on the model assumed for the conformations of the free molecules. Since any a- or - triple helical sections of our gelatins vrc>uld be melted at 30 C. we assume near randomness for the chains, and a lew ellipticity for the molecular envelopes. Further, the success of Flory s viscosity theory (17) has shown that the hydrodynamically effective volume of randomly coiled (and of many other) chain molecules is not very different from the volume encompassed by the meandering segments. Thus we treated our data as if they pertained to random coil molecules. The measured layer thicknesses then describe the level within the adsorbed interphase below v ich the segmental density is equal to, or larger, than the effective coil density of the free molecules. 

FIGURE 76 The dependence of macromolecular coil density p (in relative units) on average viscous molecular weight Afl/ for PDMDAAC (D =l. 65). 

In Fig. 21 the kinetic curves conversion degree—reaction duration Q-t for two polyols on the basis of ethyleneglycole (PO-1) and propylene-glycole (PO-2) are adduced. As it was to be expected, these curves had autodecelerated character, that is, reaction rate was decreased with time. Such type of kinetic curves is typical for fractal reactions, to which either fractal objects reactions or reactions in fractal spaces are attributed [85], In case of Euclidean reactions the linear kinetics (i> =const) is observed. The general Eq. (2.107) was used for the description of fractal reactions kinetics. From this relationship it follows, that the plot Q t) construction in double logarithmic coordinates allows to determine the exponent value in this relationship and, hence, the fractal dimension value. In Fig. 3.22 such dependence for PO-1 is adduced, from which it follows, that it consists of two linear sections, allowing to perform the indicated above estimation. For small t t 50 min) the linear section slope is higher and A =2.648 and for i>50 min A =2.693. Such A increase or macromolecular coil density enhancement in reaction course is predicted by the irreversible... 

Obviously, excimer formation represents a serious obstacle to energy migration, since the excimer site itself functions as a trap, and, after excitation, is mostly deactivated by emission of a photon rather than by energy transfer to a neighboring donor moiety (Texc< z h)- Moreover, any effect on coil density exerted by the choice of temperature or solvent can dramatically effect the efficiency of energy trapping. 

Completely statistical (random) arrangements of the macromolecules without a regular order or orientation, i.e., without constant distances, are known as amorphous states. There is no long-range order whatsoever. The valid model for such states is the statistical coil. This is the dominating secondary structure in synthetic polymers and polymeric solutions. Its determinant parameter is coil density. 

The condition is chosen by two reasons. Firstly, used at Ph-2 synthesis C(, values are relatively small and for diluted solutions the value grows as and in the limit of very diluted solutions [90], Secondly, at the obtained for polyarylate Ph-2 values D =1.65 in dichloroethane and D=1.81 in acetone [87] macromolecular coils density is large enough and exceeds density of surrounding them solution [88], These densities become equal at reaction cessation, as it was noted above. Since for the same polymer then for MM reaching reac-... 

The stated above results on APESF example have shown, that copolymers molecular weight systematic reduction at aromatic polyformal blocks contents increase has key reasons. Molecular coil growth and, hence, molecular weight increase ceases, when coil density reduces up to the environment density. This transition is defined by macromolecular coil fractal dimension D. and polymer elementary link average weight m,. 

In the end the conclusion can be made, that reaction cessation in low-temperature polycondensation process is limited by pnrely physical factor, namely, by macromolecular coil density reaching of reactive medium density (mixture monomer — polymer solution) [121], that is possible for fractal objects only. Such conclusion follows from the simple analysis, adduced below. As it is known [122], the fractal object density pfr can be calculated according to the Eq. (73) ... 

FIGURE 3 The dependences of macromolecular coil density pfr on TMACh contents cTMACh for copolymers PAA-TMACh. Calculation according to the Eq. (73) of Chapter 1 at real values (1) and at the condition R = const (2). 

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. 

Results obtained from conformational studies on POE-bound p tides and from investigations on analogous compounds under identical experimraital conditicms revealed that POE does not significantly influence the peptide conformation >. This property can be rationalized by the random coil conformaticm of POE in solution. Both low coil density and high segment flexibility hamper specific interactions between peptide and polymer . 

Lakatos et al. (1979) found that the level of HPAM retention for a 500 ppm solution in the sandpack decreased slightly with increasing molecular mass but decreased even more sharply as the degree of hydrolysis increased. This point is shown in Figure 5.16 (Lakatos et al, 1979), and this trend agrees with earlier results presented by Martin and Sherwood (1975). They correlated these results with the more fundamental molecular properties of equivalent coil diameter and coil density of the flexible chain molecules. In a good solvent, the coil diameter is proportional to ([>/] as discussed in... 

Viscosimetric data yield information about the coil density, i.e., the polymer mass per unit volume of the polymer particles. PEC formation often leads to a decrease of coil density in comparison to the dissolved components and therefore it can be studied by this method. However, the main contribution of the viscosity is given by the dissolved excess component. 

Substance density in a single coil (density given in units of excluded volume) decreases with the increase of the Kuhn segment length as well as with the increase of the chain length ... 

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