Interphase thickness, effect

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 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]. 

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. 

A method for determining the effect of particle size on the effective permeability values of zeolite-polymer mixed matrix membranes has been developed in this study. The model presented is a modified form of the effective medium theory, including the permeability and thickness of an additional phase, the interphase, which is assumed to surround the zeolite particles in the polymer environment. The interphase thickness and permeability values were determined by taking into consideration the assumptions that in case the size of the zeolite particles is held constant, the interphase thickness should be equal for different gases and in case the zeolite particle size is varied, the interphase permeability should remain constant for the same gas. The model seems to fit the experimental permeability data for O2, N2 and CO2 in the silicalite-PDMS mixed matrix membranes well. 

The slip factor, k, depends on the interphase property, expressed as a product of the interphase thickness, dl, and its viscosity, /. Thus, Eq. (2.56) indicates that the effective viscosity, decreases with the reduction of the interphase thickness and viscosity. While it is expected that reduction of /i will augment the interlayer slip the effect of /d I is best discussed in terms of the Helfand et al. model [25-27], which suggests high concentration of low molecular weight components in decreasing interphase thickness, which increases the slip. 

Eiber lengths between 5 and 10 mm are conveniently selected for the microindentation test (111). Eor a carbon fiber/epoxy system, as the fiber volume fraction increases from 10 to 50 vol%, the indentation displacement distance decreases from 44 to 36 pm but the interfacial shear strength increases from 33 to 46 MPa. When the interphase-to-matrix modulus ratio increases from 1.0 to 7.5, the interfacial shear stress increases by only 10%. Likewise, the interphase thickness and fiber diameter have marginal effects on the interfacial shear stress. Three types of thermoplastic polymers (polyester, polyamide, and polypropylene) were tested for their interfacial shear strength to the glass fiber by Desaeger and... 

Unlike in the case of spherical inclusions where the rigid inclusions cause stiffening of the composite by excluding volume of a deformable mattix, the presence of an interphase layer affects the tme reinforcing efficiency of the inclusions. Hence, the effective filler modulus of the inclusions have to be calculated as a function of interphase thickness and elastic modulus. This can be done effectively using simple rule of mixture ... 

Lipatov (22) investigated the effects of interphase thickness on the calorimetric response of particulate-filled polymer composites. Based on experimental evidence, his analysis led to the conclusion that the interphase region surrounding filler particles had sufficient thickness to give rise to measurable calorimetric response. The proposed existence of a thick interphase region correlates with limitations of molecular mobihty for supermolecular structures extending beyond the two-dimensional filler boundary surface. 

The resulting empirical expression for particulate filler reinforcement for the Lipatov model can be used to calculate the effective interphase thickness Ar, using given values of filler volume fraction, filler particle radius, and measured calorimetric evaluation of X ... 

The evaluation of interphase thickness of the immobilized polymer layer surrounding glass fibers provides quantitative means for gauging the relative effectiveness of given interphase design. After obtaining necessary input data from DSC measurements, the following sequence of calculations is followed ... 

Therefore, based on classic shear lag analysis (also based on definition of shear strain), it can be shown that for a fixed strain rate (function) the effect of increased cross-head rate can be induced by increasing the interphase thickness (i.e., application of fiber sizing). Indeed, the experimental results reveal shorter fragment lengths for increased cross-head rate and/or presence of fiber sizing. Based on this premise, the following superposition relations can be written for the interfacial strength, Tc ... 

The boundary layers, or interphases as they are also called, form the mesophase with properties different from those of the bulk matrix and result from the long-range effects of the solid phase on the ambient matrix regions. Even for low-molecular liquids the effects of this kind spread to liquid layers as thick as tens or hundreds or Angstrom [57, 58], As a result the liquid layers at interphases acquire properties different from properties in the bulk, e.g., higher shear strength, modified thermophysical characteristics, etc. [58, 59], The transition from the properties prevalent in the boundary layers to those in the bulk may be sharp enough and very similar in a way to the first-order phase transition [59]. 

In this conceptual framework it is naturally impossible to simulate the effect of the interphases of complex structure on the composite properties. A different approach was proposed in [119-123], For fiber-filled systems the authors suggest a model including as its element a fiber coated with an infinite number of cylinders of radius r and thickness dr, each having a modulus Er of its own, defined by the following equation ... 

Lipatov et al. [116,124-127] who simulated the polymeric composite behavior with a view to estimate the effect of the interphase characteristics on composite properties preferred to break the problem up into two parts. First they considered a polymer-polymer composition. The viscoelastic properties of different polymers are different. One of the polymers was represented by a cube with side a, the second polymer (the binder) coated the cube as a homogeneous film of thickness d. The concentration of d-thick layers is proportional to the specific surface area of cubes with side a, that is, the thickness d remains constant while the length of the side may vary. The calculation is based on the Takayanagi model [128]. From geometric considerations the parameters of the Takayanagi model are related with the cube side and film thickness by the formulas ... 

The interphase can be considered as a particular phase s of thickness h. This phase differs from the homogeneous phases only in that the effect of pressure is accompanied by the effect of the interfacial tension y. Consider a rectangle with sides h (perpendicular to the interphase) and / (parallel with the interphase) located perpendicular to the interphase. The force acting on the rectangle is not equal to the product phi (as for an area in the bulk of the solution) but phi — yl. If the volume of the interphase V(s) is increased by dV(s) by increasing the thickness of the interphase by dh, then area A = V(s)lh increases by cL4. The overall work, W, connected with this process consists of volume work accompanying the increase in the thickness of the interphase and volume and surface work connected with an increase of the surface area ... 

One possible, although speculative explanation of the effect of the addition of sulfamic acid or sodium sulfate may be based on Eq. (4.9). According to this equation, the variation in the concentration c of a nonreacting electrolyte changes the thickness of the metal-solution interphase, the double-layer thickness It appears that as the thickness of the double layer, decreases, the coercivity of the Co(P) deposited decreases as well. 

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