Interphase thickness

Several methods are used to detennine the thickness of the interphase. Table 7.1 lists the most important methods and the results of the thickness of an interphase 

This equation includes the parameters used in Table 7.1 to characterize the interphase thickness. The results presented are much affected by the method of measurement. The methods of measurement are indirect therefore it is quite difficult to estimate what the potential error of measurement may be. There are 

The thickness of the interphase depends on the reactivity of the filler surface with the matrix material. It also depends on their physical affinity.Increased acid-base interaction between chlorinated polyethylene and titanium dioxide increases the thickness of the adsorbed layer. There is a maximum of thickness of interphase which depends on the properties of polymer bulk. The acid-base interaction is more dependent on how the filler is modified than on the matrix properties themselves. Both filler and matrix are responsible for the formation of an equilibrium, although each contributes in a different way. 

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Rheological methods of measuring the interphase thickness have become very popular in science [50, 62-71]. Usually they use the viscosity versus concentration relationships in the form proposed by Einstein for the purpose [62-66], The factor K0 in Einstein s equation typical of particles of a given shape is evaluated from measurements of dispersion of the filler in question in a low-molecular liquid [61, 62], e.g., in transformer oil [61], Then the viscosity of a suspension of the same filler in a polymer melt or solution is determined, the value of Keff is obtained, and the adsorbed layer thickness is calculated by this formula [61,63,64] ... 

Kuznetsov et al. s methodological approach [72-75] provides another example of attempts to evalue the interphase thickness experimentally. Their approach was based on the hypothesis that the mesophase remains glassy while the bulk of the binder has already passed to the highly elastic state. Investigating the concentration... 

Other methods for estimating the volume percentage of the interphases in a composition have been proposed, too, for example, measurements of density variations [76, 77], volume of compressed sample [78], the dielectric constant [77], etc. The important thing is that the interphase thickness determined in one way or another is an effective value dependent upon the conditions and type of the experiment by which it was determined [51]. 

The Takayanagi model parameters are related with filler concentration and interphase thickness by the following simple relationships ... 

It was concluded that the filler partition and the contribution of the interphase thickness in mbber blends can be quantitatively estimated by dynamic mechanical analysis and good fitting results can be obtained by using modified spline fit functions. The volume fraction and thickness of the interphase decrease in accordance with the intensity of intermolecular interaction. 

Note 1 Estimates of the degree of compatibility are often based upon the mechanical performance of the composite, the interphase thickness, or the sizes of the phase domains present in the composite, relative to the corresponding properties of composites lacking compatibility. 

The thickness of the interphase is a similarly intriguing and contradictory question. It depends on the type and strength of the interaction and values from 10 Ato several microns have been reported in the hterature for the most diverse systems [47,49,52,58-60]. Since interphase thickness is calculated or deduced indirectly from some measured quantities, it depends also on the method of determination. Table 3 presents some data for different particulate filled systems. The data indicate that interphase thicknesses determined from some mechanical properties are usually larger than those deduced from theoretical calculations or from extraction of filled polymers [49,52,59-63]. The data supply further proof for the adsorption of polymer molecules onto the filler surface and for the decreased mobility of the chains. Thermodynamic considerations and extraction experiments yield data which are not influenced by the extent of deformation. In mechanical measurements, however, deformation of the material takes place in all cases. The specimen is deformed even during the determination of modulus. With increasing deformations the role and effect of the immobilized chain ends increase and the determined interphase thickness also increases (see Table 3) [61]. 

The thickness of the interphase must depend on the strength of the interaction. As was pointed out previously, interaction is created by secondary, van der Waals forces. Although the range of these forces is small, the volume affected by the decreased mobility of the chains attached to the surface is much larger when the material is deformed, shown also by the larger interphase thicknesses determined by indirect, mechanical measurements (see Table 3). This volume and the thickness of the interphase can be estimated by a semi-empirical correlation de-... 

Table 3. Interphase Thickness in niques Particulate Filled Polymers Determined by Different Tech- ...

Interphase thicknesses are plotted as a function of in Fig. 7 for CaCOj composites prepared with four different matrices PVC, plasticized PVC (pPVC), PP and HDPE. The thickness of the interphase linearly changes with increasing adhesion. The figure proves several of the points mentioned above. The reversible work of adhesion adequately describes the strength of the interaction, or at least it is proportional to it, interaction is created mostly by secondary forces and, finally, the thickness of the interphase strongly depends on the strength of interaction. 

A blend between two highly immiscible polymers, 20% PDMS in Nylon 6 (PA6) has a very thin interphase thickness of 2A, as shown on Table 11.1, and, as a result a coarse dispersed morphology of about 10pm. Similarly coarse morphology in obtained when PDMS is blended with PA 6 amine-functionalized at each chain end to form PA 6/diamine. 

TABLE 11.1 Calculated Interphase Thicknesses <5/ for Four Pairs of Immiscible Polymers... 

Apparently, with a very small interphase thickness the two end-cap groups are too few and not easily accessible to affect compatibilization. On the other hand, when four anhydride (An) groups are attached, randomly on each PDMS chain, then the blend of 20% PDMS/4-An and PA 6/di-amine have a very fine and stable morphology (ca 0.5 pm). Thus, the amount of interfacial reaction product, although diminished by small < / values of the unmodified polymer components, is promoted by the larger number and more accessible functional groups in either or both of the reactive components. Finally, Macosko and co-workers (62) have estimated that the minimum fraction of the interphase that has to be covered by reacted compatibilization products to achieve fine and stable morphologies is about 0.2. 

Figure 2.1. Fraction of interphase polymer as a function of volume fraction of fiber inclusion, where t is the interphase thickness and r, is the radius of the nanotube/ fiber inclusion. Reproduced from reference 1 with permission from Elsevier.

Shang et al. (1995) show that the work of adhesion between a silica filler surface and a polymer matrix is directly related to the dynamic viscosity and moduli. Additionally, at lower frequencies there is a greater influence of the work of adhesion. The influence is shown to be described well by an effective increase in interphase thickness due to the increase in the work of adhesion, such that polymer chains are effectively immobilized around the filler, and the friction between the immobilized layer and the polymer then governs the dynamic rheology. It was noted that the immobilized layer could be reduced in extent at higher frequencies. 

Figure 4.1. Representation of the interface, with the definition of the interphase thickness, Al % and b are respectively the binary interaction and the lattice parameters [Helfand and Tagami, 1971].

Theories of block copolymers are usually complex, involving computation of the domain size, the interphase thickness between the blocks, the stmc-ture, and the order-disorder transitions. Helfand and Wasserman [1976, 1978, 1980] using the narrow interphase approximation, showed that Eq 4.4 is valid in the limit of infinitely immiscible blocks having (i.e., the strong segrega-... 

Figure 4.4. Interphase thickness in styrene-isoprene block copolymers vs. total molecular weight. Points are experimental [Hashimoto et al., 1980 Richars and Thomason, 1983], the hne was computed from Eq 4.13 using Al = 1.9 nm and X = 1000 Xae o = 0-6.

The interfacial thickness, Al , and the interfacial tension coefficient, v , are both related to the square root of the thermodynamic binary interaction parameter, — Al directly, whereas inversely, thus their product , Al. v , is to be independent of thermodynamic interactions. The latter conclusion may have limited validity, but the general tendency — the reciprocity between the interfacial tension coefficient and the interphase thickness — is correct. The theory correctiy predicted the magnitude of the interphasial thickness, Al = 1-4 nm. Note that the theory is for A/B binary systems, thus extending these predictions to compatibilized systems, where Al < 65 nm may lead to erroneous expectations. For the latter system the reciprocity between v and Al is not to be expected. 

These and more recent theories can be considered as guides for the expected dependencies, but they can not be used directly to calculate either the interfacial tension coefficient or the interphase thickness. Since there is a significant disagreement between the theoretical relationships derived... 

In contrast to measurements of the interfacial tension coefficient, only few measurements of the interphase thickness have been reported [Wlochowicz and Janicki, 1989 Janicki et al, 1986]. For example, domain boundary thickness were measured in PS/PMMA blends [Foster et al, 1990 Fernandez et al, 1988 Russel et al, 1991 Perrin and Prud homme, 1994]. Generally, values in the range of 2-6 nm were reported for the interface thickness. 

There are fewer methods available to measure the interphase thickness, e.g., ellipsometry, microscopy, and scattering. A summary of the measured Al is given in Table 7.3. The temperature dependence of Al in PMMA/SAN and PMMA/PS blends is presented in Figure 7.6. More information on the fundamentals, methods of measurements, and numerical values of the interfacial ten-... 

Figure 7.6. Interphase thickness vs. temperature for polymethylmethacrylate blends with (from top) styrene-acrylonitrile copolymer and polystyrene [Kressler et al., 1993].

For proper understanding of the immiscible polymer blends it is important to take into account the interphase. In binary blends, the interphase thickness, is inversely proportional to the interfacial tension coefficient, thus, poorer the miscibility, larger the interfacial tension coefficient and smaller the interphase thickness. Owing to the thermodynamic forces the polymeric chain-ends concentrate at the interface and the low molecular weight components difiuse to it as well. Thus,... 

The interphase thickness depends on the miscibility of the polymeric component as well as on the compatibilization. For uncompatibilized binary, strongly immiscible systems, the interphase thickness Al - 2 nm. The thickest interphase has been observed for reactively compatibilized polymer alloys Al = 65 nm. For most blends, the interphase thickness is in between these two limits. The importance on the interphase can be appreciated noting that its volume will be the same as that of the dispersed phase when the drop diameter (without interphase) is about 500 nm. It is noteworthy that in most commercial polymer alloys the drop diameter is about five times smaller, making the importance of the interphase much greater. 

Estimation of the interphase thickness and permeability in polymer-zeolite mixed matrix membranes... 

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