Network dilution

The net effect is that tackifiers raise the 7g of the blend, but because they are very low molecular weight, their only contribution to the modulus is to dilute the elastic network, thereby reducing the modulus. It is worth noting that if the rheological modifier had a 7g less than the elastomer (as for example, an added compatible oil), the blend would be plasticized, i.e. while the modulus would be reduced due to network dilution, the T also would be reduced and a PSA would not result. This general effect of tackification of an elastomer is shown in the modulus-temperature plot in Fig. 4, after the manner of Class and Chu. Chu [10] points out that the first step in formulating a PSA would be to use Eqs. 1 and 2 to formulate to a 7g/modulus window that approximates the desired PSA characteristics. Windows of 7g/modulus for a variety of PSA applications have been put forward by Carper [35]. 

TPS-polyester) and the composite (TPS fibres), without synergetic effect between them. In fact, the fibres embedded in the polyester phase did not participate to the cellulose-TPS network (dilution effect). 

This assumes mutual network dilution and co-continuity, with no added internetwork physical crosslinks, and since the final material has only the two networks,... 

The second term of equation (4.11) will also be analogous to previous results because of the assumption that the two networks are elastically independent. Thus, the two networks dilute each other. From rubber elasticity... 

As the quinone stabilizer is consumed, the peroxy radicals initiate the addition chain propagation reactions through the formation of styryl radicals. In dilute solutions, the reaction between styrene and fumarate ester foUows an alternating sequence. However, in concentrated resin solutions, the alternating addition reaction is impeded at the onset of the physical gel. The Hquid resin forms an intractable gel when only 2% of the fumarate unsaturation is cross-linked with styrene. The gel is initiated through small micelles (12) that form the nuclei for the expansion of the cross-linked network. 

Crystallization-based separation of multi-component mixtures has widespread application. The technique consists of sequences of heating, cooling, evaporation, dilution, diluent addition and solid-liquid separation. Berry and Ng (1996, 1997), Cisternas and Rudd (1993), Dye and Ng (1995), Ng (1991) and Oyander etal. (1997) proposed various schemes based on the phase diagram. Cisternas (1999) presented an alternate network flow model for synthesizing crystallization-based separations for multi-component systems. The construction... 

The scaling analysis, mentioned in Sec. IIIB, predicts that one should observe a different kind of distribution in the dilute regime for chains which are smaller than the blob size [32] and thus behave essentially as isolated chains. These chains, which are fully swollen and may slip through the network made up from the chains of average size (L) without being seriously... 

In general, greatly reduced rates of attack are observed for impure or dilute nickel alloys compared with pure nickel when exposed to SO2 + O2 atmospheres. Haflan et al. have attributed this to the segregation of impurities at the sulphide/oxide interface causing breakup of the sulphide network. For example in the case of silicon additions, it has been shown that silicates form and it has been proposed that these alter the wetting characteristics of the sulphide and prevent the establishment of an interconnected sulphide network. 

Serious deviations of the polymer network structure from the ideal one can have several causes. One of them is the crosslinking agent involvement in intramolecular cycle formation. The contribution of this reaction grows with the system dilution as well as when the crosslinker units in the chain are close one to the other, i.e. its fraction in the copolymer increases. All this is in good agreement with the observed trend. 

In sodium bis(2-ethylhexyl) phosphate microemulsions, which are composed of cylindrical micelles in the dilute region, it has been observed that the formation of micellar clusters is characterized by a branched structure as the volume fraction (<1>) of the aggregates increases. At d> > 0.2, these clusters mutually overlap, forming a network expanded overall [283]. 

Another type of network imperfection, resulting from cross-linking of two units not distantly related structurally, is indicated in Fig. 94. Cross-linkages such as B are wasted (except insofar as the loop may be involved in entanglements not otherwise operative). The proportion of these short path cross-linkages should be small ordinarily but could become very large if the cross-linking process were carried out in a dilute solution of the polymer. 

While the condition of stoichiometric neutrality invariably must hold for a macroscopic system such as a space-network polyelectrolyte gel, its application to the poly electrolyte molecule in an infinitely dilute solution may justifiably be questioned. In a polyelectrolyte gel of macroscopic size the minute excess charge is considered to occur in the surface layer (the gel being conductive), which is consistent with the assumption that the potential changes abruptly at the surface. This change is never truly abrupt, for it must take place throughout a layer extending to a depth which is of the order of magnitude of the... 

Simha [53] made the first attempts to model the transition from a dilute to a concentrated solution. He assumed that in the range from lscaling laws a theory has been developed which allows for the prediction of the influence of Mw c and the solvent power on the screening length [54,55]. This theory is founded on the presumption that above a critical concentration, c, the coils overlap and interpenetrate. Furthermore it is assumed that in a thermody-... 

In a 0-solvent no semi-dilute network solution occurs, as free interpenetrability is present with overlapping. Figure 3 reproduces the individual states of solution with respect to the molar mass and the concentration [22]. 

The range of validity of a semi-dilute network lies between the two critical values c (transition between semi-dilute particle solution and semi-dilute net-... 

A very convenient method for determining c is provided by the t 0-Mw-c relationship. In complete analogy to Bueche, r 0 is also found to correlate in semi-dilute solutions with M3 4. Consequently, the onset of a polymeric network is that point at which the first two terms of Eq. (9) are equal to the third term, which represents the influence of couplings on r 0. 

The longest mode (p=l) should be identical to the motion of the chain. The fundamental correctness of the model for dilute solutions has been shown by Ferry [74], Ferry and co-workers [39,75] have shown that,in concentrated solutions, the formation of a polymeric network leads to a shift of the characteristic relaxation time A,0 (X0=l/ ycrit i.e. the critical shear rate where r becomes a function of y). It has been proposed that this time constant is related to the motion of the polymeric chain between two coupling points. 

The range of semi-dilute network solutions is characterised by (1) polymer-polymer interactions which lead to a coil shrinkage (2) each blob acts as individual unit with both hydrodynamic and excluded volume effects and (3) for blobs in the same chain all interactions are screened out (the word blob denotes the portion of chain between two entanglements points). In this concentration range the flow characteristics and therefore also the relaxation time behaviour are not solely governed by the molar mass of the sample and its concentration, but also by the thermodynamic quality of the solvent. This leads to a shift factor, hm°d, is a function of the molar mass, concentration and solvent power. 

Fig. 5.20 shows the instrument with the addition of the ion-selective electrode (ISE) module, which performs Na, K and C02 analyses (240 samples or 720 tests per hour) as requested and without interruption of the other analyses. The sample for electrolyte determination is also placed on the sample tray and a third probe aspirates diluted sample from the reaction tray for processing by the ISE module. Finally, the Technicon SRA-2000 system is a computer-controlled network of the subsystems SMAC II and RA-1000. 

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