Forced compatibility

At a phase separation of a real system, the level of mixing of the components in the separating phases, corresponding to a higher temperature (if the phase separation has heen caused by the lowering of temperature) or to other initial conditions of the separation, causes molecules to get frozen at some stage of the latter. Such a system is in a state of forced compatibility". In this case, the expression for (XAslexp may be written as ... 

Eq 6.9 differs from Eq 6.8 because it allows for the contribution of an interphase region and because (%ab)i and (Xab)ii can be either negative, or positive. The latter means that the separated phases are at non-equilibrium state and are in the state of forced compatibility. As seen from Eq 6.9, the experimental value of the interaction parameter (the same relates to the free energy) consists of three terms, the value of each is determined by conditions of the microphase separation and the degree of the deviation from the equilibrium which was attained. Thus, a system which is in a non-equilibrium state may be characterized by a set of values of the three components of the experimentally-found parameter Xab-... 

Binary filled (reinforced) polymer alloy shordd be considered as conventionally consisting of four phases two separated phases near the interface and two phases in the brdk. Their compositions differ from the average composition of an alloy. It is pertinent that these are not the equihbrirun states, and the phase structure may be considered as a result of forced compatibility. 

The influence of the fillers on the phase structure of the obtained semi-IPNs was studied by DMA. For the 50/50 semi-IPN a wide single peak on the temperature dependence of E has been observed. The authors of [44, 45] explain this fact by forced compatibility of the components. This apparent compatibility appears as a result of a competition between the rates of the chemical processes between the components and phase separation (diffusion). As it was shown above, the rate of polycyanmate network formation increases by 4 times at introducing the LPU to the cyanate monomer. Thus, phase separation does not occur. The... 

Calculations have shown that in almost all cases the values of AHi,2 are positive. It is known that positive values of the enthalpy of mixing show that such a pair is thermodynamically incompatible. Thus, in spite of forming the monolithic system, two constituent networks are not compatible, and formation of IPNs as a whole is the result of synthesis in the regime of forced compatibility. Only in the regions where the amount of one of the network... 

Analysis of the behavior of some IPNs shows that such a system may not only be in a state of forced compatibility, but also in a state of forced microphase separation [86]. If such systems have an UCST, the end of the transition to the one-phase system corresponds to the curve located above... 

The analysis of the thermodynamic behavior of some IPNs shows [88,90] that two states may exist a state of forced compatibility and a state of forced microphase separation. It should also be noted that the most probable mechanism of phase separation is nucleation and growth for sequential IPNs and spinodal decomposition for simultaneous formation. 

Both the chemical reactions and the phase separation proceed under nonequilibrium conditions simply because they proceed simultaneously. After some degree of chemical conversion and cross-linking is reached, microphase separation is impeded and the system freezes in a nonequilibrium structure characterized by incomplete phase separation. Thus, by the completion of IPN formation, reactions proceed in two evolved phases. The real structure of an IPN is a multiphase one, which is determined by the coexistence of at least three phases (not in a true thermodynamic sense). Two phases are formed by networks due to phase separation. Each phase may be considered as an independent IPN in which phase separation did not take place (the state of forced compatibility), and in which mixing on the molecular level is preserved. The composition of these two phases is determined by the reaction rate and the temperature. Each phase has an average composition that does not correspond to the network ratio in the entire IPN. The third phase is the nonequilibrium transition zone from one phase to another its size depends on the conditions of phase separation. This zone may be called mesophase and may be considered as a nonequilibrium IPN of some transition composition, since the molecular level of mixing should also be preserved. For spinodal decomposition there is no sharp border between coexisting phases. The transition zone may be arbitrarily chosen in such a way that its composition corresponds to the average composition of the IPN. 

DMPPO and polystyrene form compatible blends. The two components are miscible in all proportions (59). Reported dynamic—mechanical results that indicate the presence of two phases in some blends apparendy are caused by incomplete mixing (60). Transition behavior of thoroughly mixed blends indicates that the polymers are truly compatible on a segmental level (61). CompatibiUty may be attributed to a %— % interaction between the aromatic rings of the two polymers sufficient to produce a negative heat of mixing. However, the forces are very small, ie, = ca40 J/mol (9.6 cal/g), and any... 

Preparation of Emulsions. An emulsion is a system ia which one Hquid is coUoidaHy dispersed ia another (see Emulsions). The general method for preparing an oil-ia-water emulsion is to combine the oil with a compatible fatty acid, such as an oleic, stearic, or rosia acid, and separately mix a proportionate quantity of an alkah, such as potassium hydroxide, with the water. The alkah solution should then be rapidly stirred to develop as much shear as possible while the oil phase is added. Use of a homogenizer to force the resulting emulsion through a fine orifice under pressure further reduces its oil particle size. Liquid oleic acid is a convenient fatty acid to use ia emulsions, as it is readily miscible with most oils. 

As indicated earlier, the vaUdity of the method of dimensional analysis is based on the premise that any equation that correcdy describes a physical phenomenon must be dimensionally homogeneous. An equation is said to be dimensionally homogeneous if each term has the same exponents of dimensions. Such an equation is of course independent of the systems of units employed provided the units are compatible with the dimensional system of the equation. It is convenient to represent the exponents of dimensions of a variable by a column vector called dimensional vector represented by the column corresponding to the variable in the dimensional matrix. In equation 3, the dimensional vector of force F is [1,1, —2] where the prime denotes the matrix transpose. 

The solubiHty parameter of a polymer is a measure of its iatermolecular forces, and provides an estimate of the compatibiHty of a polymer with another polymer or a polymer with a solvent. Two components are compatible if they have similar solubiHty parameters. The solubiHty parameter can be determined by various methods, such as intrinsic viscosity and swelling measurements. The solubiHty parameters of various polymers and solvents are tabulated ia refereace handbooks (146,147). It also can be estimated from the stmcture of the polymer (148). 

Polymers used for seat and plug seals and internal static seals include PTFE (polytetrafluoroeth ene) and other fluorocarbons, polyethylene, nylon, polyether-ether-ketone, and acetal. Fluorocarbons are often carbon or glass-filled to improve mechanical properties and heat resistance. Temperature and chemical compatibility with the process fluid are the key selec tion criteria. Polymer-lined bearings and guides are used to decrease fric tion, which lessens dead band and reduces actuator force requirements. See Sec. 28, Materials of Construction, for properties. 

Oil, water, grease, or any liquid or substance compatible with the tluid are forced under pressure into the paeking through the lantern ring by means of a connection on the stuffing box wall to provide these three hinetions. 

Lubricated cylinders use a separate mechanical lubricator to force feed, in metered droplet form, a very precise amount of lubricant to specified points. This minimizes the amount of lubricant in the cylinder and allows a lubricant most compatible with the gas to be selected without compromising the frame lubrication system. Lubricant is fed to a point or points on the cylinder to service the piston rings and the packing when required. In a few cases, as in air compressors, the packing is lubricated from the crankcase. On some applications involving wet CO7 or H2S m the gas stream, special materials may be avoided if one of the lubrication points IS connected to the suction pulsation dampener. 

A chemical will be a solvent for another material if the molecules of the two materials are compatible, i.e. they can co-exist on the molecular scale and there is no tendency to separate. This statement does not indicate the speed at which solution may take place since this will depend on additional considerations such as the molecular size of the potential solvent and the temperature. Molecules of two different species will be able to co-exist if the force of attraction between different molecules is not less than the forces of attraction between two like molecules of either species. If the average force of attraction between dissimilar molecules A and B is and that between similar molecules of type B Fbb and between similar molecules of type A F a then for compatibility Fab - bb and AB - P/KA- This is shown schematically in Figure 5.5 (a). 

It has a low solubility parameter (15.3 MPa ) which differs considerably from that of the cellulose dinitrate (21.8 MPa ). This indicates that compatibility is not simply due to similarities of cohesive forces but also to some form of interaction probably involving the carbonyl group. 

The fundamental analysis of a laminate can be explained, in principle, by use of a simple two-layered cross-ply laminate (a layer with fibers at 0° to the x-direction on top of an equal-thickness layer with fibers at 90° to the x-direction). We will analyze this laminate approximately by considering what conditions the two unbonded layers in Figure 4-3 must satisfy in order for the two layers to be bonded to form a laminate. Imagine that the layers are separate but are subjected to a load in the x-direction. The force is divided between the two layers such that the x-direction deformation of each layer is identical. That is, the laminae in a laminate must deform alike along the interface between the layers or else fracture must existl Accordingly, deformation compatibility of layers is a requirement for a laminate. Because of the equal x-direction deformation of each layer, the top (0°) layer has the most x-direction ress because it is stiffer than the bottom (90°) layer in the x-direction./ Trie x-direction stresses in the top and bottom layers can be shown to have the relation... 

That is, although we required equal x-direction displacements of the two layers (the proportion of N in each layer was adjusted to create that equal-displacement condition), the lateral displacfiments arfi guitfijjjffer-ent. Those different displacements are a violation of the requireddeToT- mation compatibility of laminae in a laminatir Tolemedy this violation, the top layer must get wider by application of a lateral tensile stress aj, and the bottom layer must get narrower by application of a compressive stress Oy. The two deformations must result in equal-width laminae to satisfy deformation compatibility. Moreover, the lateral stresses in each layer must satisfy force equilibrium in the y-direction, i.e.,... 

Miscibility or compatibility provided by the compatibilizer or TLCP itself can affect the dimensional stability of in situ composites. The feature of ultra-high modulus and low viscosity melt of a nematic liquid crystalline polymer is suitable to induce greater dimensional stability in the composites. For drawn amorphous polymers, if the formed articles are exposed to sufficiently high temperatures, the extended chains are retracted by the entropic driving force of the stretched backbone, similar to the contraction of the stretched rubber network [61,62]. The presence of filler in the extruded articles significantly reduces the total extent of recoil. This can be attributed to the orientation of the fibers in the direction of drawing, which may act as a constraint for a certain amount of polymeric material surrounding them. 

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