Network junction factor

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

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. 

Nevertheless, a value of a = -2 does not guarantee the presence of an entangled regime when H = Af as pointed out in previous section. Studying chain diffusion in a crosslinked matrix helps avoid the tube-renewal factor, the presence of permanent topological constraints is assured, and an independent measure of the diffusion coefficient for the free chain can be obtained but mechanisms in addition to reptation could still appear, i.e., fluctuations of network Junctions. 

A5.1.3 Strain Amplification Factor from the Network Junction Theory... 

A mechanistic argument yields this factor (1 — 2/f) in a simple way [24]. The N strands of the rubberlike network are not independent, since they are linked with their ends in the junctions. The sum of the forces operating at each junction has to cancel in order to guarantee the mechanical equilibrium of the network. The number C of junctions with functionality f is ... 

IR dichroism has also been particularly helpful in this regard. Of predominant interest is the orientation factor S=( 1/2)(3—1) (see Chapter 8), which can be obtained experimentally from the ratio of absorbances of a chosen peak parallel and perpendicular to the direction in which an elastomer is stretched [5,249]. One representation of such results is the effect of network chain length on the reduced orientation factor [S]=S/(72—2 1), where X is the elongation. A comparison is made among typical theoretical results in which the affine model assumes the chain dimensions to change linearly with the imposed macroscopic strain, and the phantom model allows for junction fluctuations that make the relationship nonlinear. The experimental results were found to be close to the phantom relationship. Combined techniques, such as Fourier-transform infrared (FTIR) spectroscopy combined with rheometry (see Chapter 8), are also of increasing interest [250]. 

In order to enable these fluctuations to occur, the network chains are assumed to be "phantom" in nature i.e. their material properties are dismissed and they act only to exert forces on the junctions to which they are attached. With common networks having tetrafunctional junctions, the results of the two approaches differ by a factor of two. Identical results are only obtained from both theories, when the functionality is infinite. From a practical viewpoint, however, a value of about 20 for f can already be equated to infinity because crosslink densities can hardly be obtained with an accuracy better than 10%. 

Ronca and Allegra (12) and Flory ( 1, 2) assume explicitly in their new rubber elasticity theory that trapped entanglements make no contribution to the equilibrium elastic modulus. It is proposed that chain entangling merely serves to suppress junction fluctuations at small deformations, thereby making the network deform affinely at small deformations. This means that the limiting value of the front factor is one for complete suppression of junction fluctuations. 

Freshly isolated or subcultured brain microvascular endothelial cells offer a notable in vitro tool to study drug transport across the blood-brain barrier. Cells can be grown to monolayers on culture plates or permeable membrane supports. The cells retain the major characteristics of brain endothelial cells in vivo, such as the morphology, specific biochemical markers of the blood-brain barrier, and the intercellular tight junctional network. Examples of these markers are y-glutamyl transpeptidase, alkaline phosphatase, von-Willebrandt factor-related antigen, and ZO-1 tight junctional protein. The methods of... 

Figure 9. Reduced equilibrium modulus of polyurethane networks from POP trlols and MDI in dependence on the sol fraction. networks from POP triol Mjj - 708, o networks from POP triol Mjj = 2630. C-) calculated dependence using Flory junction fluctuation theory for the value of the front factor A indicated. (Reproduced from Ref. 57. Copyright 1982 American Chemical Society.)...

Figure 1, Ratio of molar mass between elastically effective junctions to front factor (M(-/A) relative to molar mass between junctions of the perfect network (M ) versus extent of intramolecular reaction at gelation (pj- (.) Polyurethane networks from hexamethylene diisocyanate (HDI) reacted with polyoxpropylene (POP) triols at 80°C in bulk and in nitrobenzene solution(5-7,12). Systems 1 and 2 HDI/POP triols >i= 33, V2= 61. Systems 3-6 ...

The positive intercepts in Figure 7 show that post-gel(inelastic) loop formation is influenced by the same factors as pre-gel intramolecular reaction but is not determined solely by them. The important conclusion is that imperfections still occur in the limit of infinite reactant molar masses or very stiff chains (vb - ). They are a demonstration of a law-of-mass-action effect. Because they are intercepts in the limit vb - >, spatial correlations between reacting groups are absent and random reaction occurs. Intramolecular reaction occurs post-gel simply because of the unlimited number of groups per molecule in the gel fraction. The present values of p , (0.06 for f=3 and 0.03 for f=4 are derived from modulus measure- ments, assuming two junction points per lost per inelastic loop in f=3 networks and one junction point lost per loop in f=4 networks. 

The front factor g as defined above5 is unity in all the earlier theories (17). Recently Duiser and Staverman (233) have obtained g = j and Imai and Gordon (259) g — 0.54 with Rouse model theories which make no a priori assumptions about the junction point locations after deformation. Edwards (260) also arrives at and Freed (261) deduces that g= 1 is an upper bound by similar approaches. The front factor usually assumed in the shifted relaxation theory of the plateau modulus is g = 1, although Chompff and Duiser (232) obtain g = j through their extension of the Duiser-Staverman result to entanglement networks. The physical reasons for the different values of g in different treatments are not clear at present. 

The distribution of drugs depends on both the physicochemical properties of the drug molecules and the composition of tissue membranes. These factors can either result in a uniform or uneven distribution of dmgs into the various body compartments and fluids. In the extreme, distribution may tend toward an accumulation of drugs in particular tissues or to an almost complete exclusion of the drag from a particular compartment in a defined length of time. One unique compartment that has to be considered in this respect is the brain, which is separated from the capillary system of the blood by the blood-brain barrier, whose membrane has a special structure. It consists of a cerebral capillary network formed by a capillary endothelium that consists of a cell layer with continuous compact intercellular junctions. It has no pores, but special cells, astrocytes, which support the stability of the tissues, are situated at the bases of the endothelial membrane separating the brain and CSF from the blood. The astrocytes form an envelope around the capillaries. 

K is a numerical factor which accounts essentially for chain flexibility. The 2H NMR spectrum might be simulated by superposing the contributions of all chains, considered independently [35]. If the macroscopic deformation is transmitted affinely to crosslink junctions, P(R) may be written in the deformed network (the strain being along z) ... 

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