Density strand

The combined effects of a divalent Ca counterion and thermal treatment can be seen from studies of PMMA-based ionomers [16]. In thin films of Ca-salts of this ionomer cast from methylene chloride, and having an ion content of only 0.8 mol%, the only observed deformation was a series of long, localized crazes, similar to those seen in the PMMA homopolymer. When the ionomer samples were subject to an additional heat treatment (8 h at 100°C), the induced crazes were shorter in length and shear deformation zones were present. This behavior implies that the heat treatment enhanced the formation of ionic aggregates and increased the entanglement strand density. The deformation pattern attained is rather similar to that of Na salts having an ion content of about 6 mol% hence, substitution of divalent Ca for monovalent Na permits comparable deformation modes, including some shear, to be obtained at much lower ion contents. 

The mechanical properties of ionomers are generally superior to those of the homopolymer or copolymer from which the ionomer has been synthesized. This is particularly so when the ion content is near to or above the critical value at which the ionic cluster phase becomes dominant over the multiplet-containing matrix phase. The greater strength and stability of such ionomers is a result of efficient ionic-type crosslinking and an enhanced entanglement strand density. 

Glad [37] studied the micro deformations of thin films prepared from DGE-BA/MDA by electron microscopy. His results are also shown in Fig. 7.5. The deformation of the sample with high strand density was small and consequently its image in the EM rather blurred. Therefore, the result on Mc = 0.5 kg/mol should perhaps have been omitted. 

The solutions to Equation 9 are those values of g for which the functional f=(l- ) intersects the functional f=(l-ag), where r=fcn[CQ,k, k, nQ,eQ,k, k ] and a in general also is a function of the same variables. Actin binding protein (ABP) joins contiguous chains and a therefore depends on strand density and network topology in addition to the intrinsic rate constants for attachment of ABP to an available binding site. 

Langley, N. R. Elastically effective strand density in polymer networks. Macromolecules... 

The surface tension F of the void ceiling that appears in the capOlarity equation (Eq. (12)) is the key quantity to be specified in understanding the effects of network strand density v on the craze widening stress. For the moment suppose this network is comprised entirely of crosslinked drains. Then to create a surface requires the scission of a certain number of strands per unit area, a geometricaUy necessary strand loss, which is given by (1/2) vd. The energy required to create this surface is then... 

Effects of Network Strand Density at Room Temperature... 

One of the great successes of the craze growth model is that it predicts a transition from scission-dominated crazing to shear deformation as the strand density of the network is increased. While the shear yield stress is essentially unaffected by dian ... 

Fig. 11a. A summary of the dominant mode of plastic deformation observed in crosslinked PS films as a function of the strand density v and the temperature at which the deformation was carried out. The open squares, half-filled squares and filled squares represent crazing only, crazing plus shear, and shear only, respectively (From Ref. courtesy of J. Mat. Sci. (Chapman and Hall), b The temperature dependence of the shear yield stress Oy and the crazing stress S (for two values of v)...

From X and X, together with stress-strain measurements in extension from the state of ease, or simply from the equilibrium stress at X, the concentration of trapped entanglement strands can be calculated and compared with the entanglement strand density estimated from transient measurements on the uncrosslinked polymer. To obtain consistent results, especially for stress-strain relations in large extensions of the dual network from its state of ease, it is necessary to attribute deviations from neo-Hookean elasticity to the trapped entanglement network, as described by the... 

As described previously, t ne N network of strands is assigned the CKF Theory Coefficients and Cpf, the Y network of Vy strands is taken as neo-Hookean with the CKF Co-efficient C-y only, since it is in compression, following similar reasoning as used previously for the Vy network for conditions when = 0. Reservations concerning use of the Mooney-Rivlin formulation and its justification for convenience have been described elsewhere. Then assuming front factors of unity, the strand densities are related to the CKF Theory Coefficients as follows ... 

Deformation behavior of amorphous polymers has been studied for years, and explained in terms of structure of polymers. Especially, great progress has been made by using the concept of " network (strand) density" to understand the deformation behavior (such as crazing and shear deformation) [1,2]. When the concept of a critical thickness of the polymer layer, below which a sample behaves in a ductile manner even for normally brittle polymers like polystyrene (PS), has been added to the network density concept, more comprehensive understanding has become possible [3-8] and it provides a great opportunity for developing ductility of otherwise brittle... 

There has been considerable progress over recent years in the study of molecular mechanisms involved in crazing and shear yielding [1,2]. When sample preparation and test conditions (temperature, stress state, strain, strain rate, and thermal history) are chosen to be the same, the effect of molecular variables can be determined. It is now well established that (network) strand density plays an important role in determining the deformation mechanism and in affecting the craze-shear deformation transition. Polymers are... 

The idea described above for glassy amorphous homopolymers can be extended to include miscible amorphous polymer blends, such as PS/PPO. Furthermore, a low degree of covalent cross-links can be considered as equivalent to entanglements for controlling the deformation mode. The strand density of cross-linked polymers is defined as the sum of the entanglement density and the covalent cross-link density [18] as... 

Figure 18.5 True strain ratio in craze and shear deformation zones as a function of network strand density. The open squares and open diamonds represent homopolymers and copolymers, open triangles and hexagons uncross-linked blends of PS and PPO, and fiUed triangles and circles cross-linked PS. Henkee and Kramer [18], Reproduced with permission of John WUey and Sons.

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