Macromolecular entanglements

A number of features of the behaviour of the oriented polymers, that fits weakly to the version of macromolecular entanglement network, has been revealed during detailed revision of some results of [5-9, 14, 15]. Thereby, the direct application of the two deformation schemes mentioned previously is prohibited. These features are ... 

Some possible approximations have been considered by Cates [56], who concentrated attention on macromolecular entanglements, which play an important role in the description of the behaviour of block polymers [86-89]. Cates believes that the fact that the concept of polymer fractal neglects the effects of macromolecular entanglements is the main drawback of this theory. Nevertheless, Cates [56] introduced several simplifications that make it possible to ignore these effects for dilute solutions and relatively low molecular masses. However, in the opinion of Cates, even in the case of predominant influence of entanglements, theoretical interpretation of this phenomenon is impossible without preliminary investigation of the properties of the system in terms of Rouse-Zimm dynamics, which can serve as the basis for a more complex theory. It was assumed [56] that the effects of entanglement can be due to the substantially enhanced local friction of macromolecules. 

Let us consider the procedure for estimation of the and values in terms of the cluster model [15, 89]. A cluster is regarded as a multifunctional unit in a fluctuation net-work of macromolecular entanglements therefore, according to Flory [43], the reduced molecular mass M per cluster is estimated from Equation (11.4). By dividing M into the molecular mass of a statistical segment, we obtain the number of particles (statistical segments) (NJ per cluster. 

Condensed systems start to behave as polymers after a certain molecular mass has been attained and a network of macromolecular entanglements or chemical nodes has been formed [57]. In consideration of condensed polymers, it is especially important to describe the sections of the macromolecule between the points of chemical crosslinking or entanglements [56]. The deformability and mobility of these sections largely determine the macroscopic properties of polymers [57, 104]. The general physical grounds that account for the fractality of these chain sections are considered next in relation to epoxy polymers. 

Below we consider practical aspects of the estimation of the fractal dimension D of a macromolecule section between chemical crosslinking points with allowance for these statements as well as for those considered in the preceding Sections. This approach differs fundamentally from that of the Cates [56] and Vilgis models [61, 62]. All the foregoing is valid not only for a network of chemical bonds but also for a network of macromolecular entanglements in linear polymers. 

For linear polymers, the network of macromolecular entanglements is the analogue of... 

At present a parameters number exists, with the aid of which polymer melts viscosity is estimated [3], In the present chapter with this purpose the most simple and easily measured from them—melt flow index (MFI) will be used. Excepting the merits, noted above, it is connected with a polymer key characteristics number, namely, with molecular weight and macromolecular entanglements network density [4],... 

Further it is supposed that the macromolecular entanglements (traditional macromolecular binary hookings [10]) network is formed by just such contacts of fractals (macromolecular coils), therefore the indicated network... 

FIGURE 1 The dependence of macromolecular entanglements network density on... 

FIGURE 2 The dependence of intrinsic viscosity [t ] on macromolecular entanglements network density for APESF. 

Let us make in conclusion one comment. Quite many conceptions exist, defining polymer melt viscosity only as a fimction of MM. For example, in Ref. [14] the relationship, received within the framework of the thermofluctuation concept of macromolecular entanglements network, was proposed ... 

Let us consider in conclusion the reason of macromolecular entanglements network formation at the transition to the autoacceleration section. It is obvious, that such network formation requires contact of macromolecular coils in solution and their interpenetration. It should be supposed, that the higher coils interpenetration distance 1 is the denser, the network of macromolecular entanglements is. Within the frameworks of fractal analysis the value 1 is determined as follows [41] ... 

Assuming b = 1, the value 1 at D = 2.45 (initial section) and D = 1.65 (autoacceleration section) can be calculated. In this case the values 1, equal to 5.3 and 90.9 relative units, accordingly, were obtained. Hence, change at the transition to the autoacceleration section results to 1 growth in about 17 times, that should tell accordingly on macromolecular entanglements density increasing. 

Kowalski, T., E. Brundrett, "Macromolecular entanglement hypothesis in drag reduction flows". Int. Conf. on Drag Reduction, Cambridge, (1974) Paper Cl. 

If the solution is too concentrated, macromolecular entanglements will scatter radiation at different time scales than single polymer coils. To prevent this, DLS is done on dilute solutions and results are extrapolated to zero concentration conditions. 

Macromolecular entanglements cluster network density v j can be estimated as follows [8] ... 

As it is known [5], in amorphous phase two types of macromolecular entanglements are present traditional macromolecular binary hooking and entanglements, formed by nano clusters, networks density of which is equal to and v, respectively. value is determined within the framework of mbber high-elasticity conception [2] ... 

The value knowledge allows formally to calculate the density of macromolecular entanglements network in polymeric medium according to the well-known expressions of high-elasticity theory [23] ... 

FIGURE 2.5 The dependences of elasticity modulus E (1) and equilibrium modulus (2) on macromolecular entanglements cluster network density n, for PC [47],... 

The plotted according to the experimental data dependencies of elasticity modulus E on macromolecular entanglements cluster network density (Figs. 2.5 and 2.6) break down into two linear parts, the boundary of which serves loosely packed matrix glass transition temperature which is lower on about 50K of polymer glass transition temperature [50]. Below the value E is defined by the total contribution of both clusters and loosely packed matrix and above - only by clusters contribution. It becomes clear, if to taken into consideration, that above the elasticity modulus value of devitrificated loosely packed matrix has the order of 1 MPa [51], that is, negligible small. It is an extremely interesting the observation, that loosely packed matrix in the value E, determined by the plot E (v, ) extrapolation to = 0, is independent on temperature. Such situation is not occasional and deserves individual consideration. 

Kozlov, G. V, Sanditov, D. S., Mil man, L. D., Serdyuk, V. D. (1993). The Cluster Network of Macromolecular Entanglements and Network Connectivity in Polymers. Iz-vestiya VUZov, Severo-Kavkazsk. Region, estestv. Nauki, 3-4, 88-92. 

Lately the large attention is given to macromolecular entanglements fluctuation network influence on crazes formation process in polymers [20], Much less is known about entanglements network influence on shear deformation zones (ZD) formation processes, which by their essence are crazes, without microvoids. The authors of Ref [21] fulfilled quantitative estimation of such influence on deformation processes in ZD on the example of polyarylatesulfone (PASF) samples in the form of films with a sharp notch. In this analysis two models of macromolecular entanglements network were used of binary hooking s [20] and cluster ones [22], The PASF films were prepared with the aid of nine various solvents that allows their structure wide enough variation [21]. 

As it is known [39], the ability to conduct current with definite conductivity level g mixtures metal-insulator are acquired at percolation threshold reaching, that is, in the case, when conductive bonds form continuous percolation network. As it was noted above, macroscopic polymer samples are acquired ability to bear stress at formation in them of macromolecular entanglements continuous network. This obvious analogy allows to use modem physical models of conductivity in disordered systems for description of the dependence of cold flow plateau stress Gp on macromolecular entanglements network density in amorphous polymers. As it is known [40], the dependent on length scale L conductivity g L) is described by the relationship ... 

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