Cross-links density determinations

In addition to the above techniques, inverse gas chromatography, swelling experiments, tensile tests, mechanical analyses, and small-angle neutron scattering have been used to determine the cross-link density of cured networks (240—245). Si soHd-state nmr and chemical degradation methods have been used to characterize cured networks stmcturaHy (246). H- and H-nmr and spin echo experiments have been used to study the dynamics of cured sihcone networks (247—250). 

Cross-Link Density. Cross-link density measurements were determined on samples swollen to equilibrium in toluene after 24 h. Five specimens were tested for each sample. The volume fraction... 

Determination of cross-link density from compression experiments is perhaps the most effective means of determining cross-link density as long as samples of the appropriate geometry can be prepared. When a hydrogel is subjected to an external force, it undergoes elastic deformation which can be related to the effective cross-link density of the network [63,99], Here the measurements made to extract cross-link density from polymer deformation are briefly discussed. 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

Actually, crosslinks control the molecular packing and indeed significantly affect the elastic modulus of the material. As the intermolecular energy of kink formation is also determined by elastic modulus, the yield stress will definitely vary with modulus and thus the cross -linking density. In other words, crosslinks may not seriously affect the activation segment configuration in the molecular chain but will indirectly control the yield stress. 

The cross-link density can be determined by equilibrium swelling or from equilibrium stress-strain measurements at low strain rate, elevated temperature, and sometimes in the swollen state3 °... 

When using equilibrium stress-strain measurements, the cross-link density is determined from the Mooney-Rivlin equation ... 

Swelling tests and determination of tensile properties. The procedure for estimating cross-link density from equilibrium swelling data is described in detail in a previous paper (6). The tensile properties of the PU films were carried out at 23°C and 60% relative humidity. The crosshead speed and distance were 10 mm/min and 30 mm, respectively. A more detailed description of the tensile tests is given elsewhere (6). 

The description of the physical properties of fluoroelastomers is necessarily less precise than that of fluoroplastics because of the major effect of adding curatives and fillers to achieve useful cross-linked materials of a given hardness and specific mechanical properties Generally, two parameters are varied increasing cross-link density increases modulus and decreases elongation, and raising filler levels increases hardness and decreases solvent swell because of the decreased volume fraction of the elastomer In addition to these two major vanables, the major determinants of vulcanizate behavior are the chemical and thermal stabilities of its cross-links The selection of elastomer, of course, places limits on the overall resistance to fluids and chemicals and on its service temperature range... 

The permselectivity is the product of ion-exchange selectivity and mobility selectivity. The mobility of different ions is determined mainly by steric effects, that is, the size of the ions and the cross-linking density of the membrane [4],... 

From a fit of Equation (10) to spatially resolved relaxation curves, images of the parameters A, B, T2, q M2 have been obtained [3- - 32]. Here A/(A + B) can be interpreted as the concentration of cross-links and B/(A + B) as the concentration of dangling chains. In addition to A/(A + B) also q M2 is related to the cross-link density in this model. In practice also T2 has been found to depend on cross-link density and subsequently strain, an effect which has been exploited in calibration of the image in Figure 7.6. Interestingly, carbon-black as an active filler has little effect on the relaxation times, but silicate filler has. Consequently the chemical cross-link density of carbon-black filled elastomers can be determined by NMR. The apparent insensitivity of NMR to the interaction of the network chains with carbon black filler particles is explained with paramagnetic impurities of carbon black, which lead to rapid relaxation of the NMR signal in the vicinity of the filler particles. 

Conventionally, cross-link density is determined by measurements of the modulus, the glass transition temperature T, and by solvent uptake in swelling experiments. In these procedures, the chemical cross-link density cannot be discriminated from network-... 

In elastomer samples with macroscopic segmental orientation, the residual dipolar couplings are oriented as well, so that also the transverse relaxation decay depends on orientation. Therefore, the relaxation rate 1/T2 of a strained rubber band exhibits an orientation dependence, which is characteristic of the orientational distribution function of the residual dipolar interactions in the network. For perfect order the orientation dependence is determined by the square of the second Legendre polynomial [14]. Nearly perfect molecular order has been observed in porcine tendon by the orientation dependence of 1/T2 [77]. It can be concluded, that the NMR-MOUSE appears suitable to discriminate effects of macroscopic molecular order from effects of temperature and cross-link density by the orientation dependence of T2. 

For certain clearcoat systems a partial healing of scratches can be observed on the time scale. In literature this is known as the reflow effect [21], Thermal relaxation phenomena may be used for a physical explanation of this effect. In connection with scratch resistance the cross-linking density of clearcoats is also a decisive factor. Meanwhile, dynamic mechanical analysis (DMA) has been established as a method to determine cross-linking density [21-23],... 

In this paper the recently developed techniques to characterize the mar resistance of coating systems were presented. The techniques base on methods that create a single scratch onto a surface. Characteristic values like the critical load as a measure for the transition from plastic behaviour to brittle fracture can be determined and used to rank different clearcoat systems and to compare these results with other physical properties. In the field of mar resistance the cross-linking density of the... 

The formation of a polymer networks starts with an increase in molecular weight and formation of branched structures. At a typical extent of reaction, the gelation point is that point at which a network is first formed. The extent of reaction as well as the cross-linking density in radiation-induced cross-linking processes is determined by the radiation dose. The term dose means the quantity of radiation applied to or absorbed accidentally by a given volume or mass of sample. The absorbed dose is measured in Gray (Gy), 1 Gy = 1J kg-1. Therefore, the formation of a polymeric network needs a certain dose, the gelation dose Dg, which can be determined by sol-gel analysis. ... 

Typically, a cross-linked polymer is insoluble. During the cross-linking reaction, the amount of polymer chains being connected by chemical bonds increases. The determination of the insoluble fraction (gel) and the soluble fraction (sol) of a polymer is done by the sol-gel analysis. In general, the cross-linking density increases and the sol content decreases with increasing dose. But, it is necessary to determine these correlations for each polymer at the conditions during irradiation. 

Glass transition temperature, Tg, and storage modulus, E , were measured to explore how the pigment dispersion affects the material (i.e. cross-link density) and mechanical properties. Both Tg and E were determined from dynamic mechanical analysis method using a dynamic mechanical thermal analyzer (DMTA, TA Instruments RSA III) equipped with transient testing capability. A minimum of 3 to 4 specimens were analyzed from each sample. The estimated uncertainties of data are one-standard deviation. 

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