Statistical segments number

The parameter Cr expresses the effectiveness of the hindrance release by segment fluctuation and varies between 0 and 1. An empirical expression for it as a function of the Kuhn statistical segment number N is given in Sect. 8. Although Cr contributes only to the correction terms in de/Le, fr(de/Le) changes from 1 to 2.56 in the range of allowable values of de/Le. Thus, the factor fr (de/Le) is more important than the factor f (de/Le) in Dx. 

Thus, the statistical segments number per polymer volume unit is equal to [191] ... 

Figure 1. The dependence of limiting draw ratio X on statistical segments number on chain part between clusters for carbon plastics at testing temperatures 293 (1), 313 (2), 333 (3) and 353 K (4)...

Let us consider further diffiisive processes influence on interfacial regions formation in the studied nanocomposites. In Refs. [12, 13], the treatment of depositions structure formation on fibers and surfaces within the frameworks of irreversible aggregation models was proposed. Within the framework of this treatment the relationship between mean-square deposition (interfacial layer) thickness and particles (statistical segments) number . in it atwas proposed [13] ... 

In its turn, the statistical segments number in interfacial layer n. can be calculated according to the equation [14] ... 

FIGURE 7.4 The dependence of interfacial layer thickness /jj on statistical segments number n. in it for nanocomposites on the basis of BSR in double logarithmic coordinates. 

For the solution of the first from the indicated problems the statistical segments number in one nano cluster j and its variation at nanofiller contents change should be estimated. The parameter calculation consistency includes the following stages. At first the nanocomposite stmcture fractal dimension is calculated according to the equation [12] ... 

FIGU RE 8.1 The dependences of elasticity modulus on Statistical segments number per... 

Further the Eq. (9) allows to estimate the value (p In Fig. 8.2 the dependence j((p.j.) for nanocomposites LLDPE/MMT is adduced. As one can see, reduction at (Pjj, increasing is observed, that is, formed on organoclay surface densely packed (and, possibly, subjecting to epitaxial crystallization [9]) interfacial regions as if pull apart nanoclusters, reducing statistical segments number in them. As it follows from the Eqs. (9) and (8), these processes have the same direction, namely, nanocomposite elasticity modulus increase. 

FIGURE 8.2 The dependence of statistical segments number per one nano cluster on interfacial regions relative fraction for nano composites LLDPE/MMT. Horizontal shaded line indicates the minimum value n =2. 

Hence, this chapter results demonstrated common reinforcement mechanism of natural and artificial (filled with inorganic nanofiller) polymer nanocomposites. The statistical segments number per one nanocluster reduction at nanofiller contents growth is such a mechanism on suprasegmental level. The indicated effect physical foundation is the densely packed interfacial regions formation in artificial nanocomposites. 

The statistical segment number per chain part between chemical crosslinking... 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

Fig. 3. The dependence of % on the volume fraction of the dry polymer tp2 for i - 0.012 and c = 0. Numbers at curves denote the number of monomers in the statistical segment, s. From Ilavsky [34]...

N is the number of statistical segments in a chain, 1 is their length and m the number of submolecules. This model includes the front factor only in C, but the parameter K0 is also temperature dependent it depends on the thermal expansion. Thus, the Priss tube model predicts different temperature dependences of C, and C.. It means that the entropy and energy contribution have to be dependent on X and include a considerable intermolecular part. 

The dependence of T2 values on the molecular parameters is explained by a simple model for the chain with both ends fixed, and defined by the number of statistical segments, Z, in the chain between the crosslinks108) ... 

AMJhj is a function 6f a) the orientation of the inter-crosslink vector h. with the respect to the magnetic field B0 and b) the time-averaged value of the sum over k, which is the actual measure of the motional restrictions induced by crosslinking. In lightly crosslinked networks, presented by the freely-jointed model of the polymer chain 108), the residual part also can be described by the number of statistical segments in the chain section between crosslinks (Z) (Eq. (24)) ... 

Here, vmech is the mechanically effective chain density specified, e.g., in [168], Ac 0.67 [170] is a microstructure factor which describes the fluctuations of network junctions, Na the Avogadro number, p mass density, Ms and Zs molar mass and length of a statistic segment, respectively, kB the Boltzmann constant, and T absolute temperature. 

---