Mutual solution

By a similar usage in petrology, a euleeltc is a discrete mixture of two or more minerals, in definite proportions, which have simultaneously crystallized front the mutual solution of their constituents The eutectic point is the lowest temperature at any given pressure at which the above physical-chemical process may lake pluce, The eutectic ratio is the ratio hy weight of two minerals dial originate bv the above process. 

The essence of the basic model is then to describe the process of mutual solute-solvent interaction, and to extract from the final solute wavefunction, all the... 

Many investigators have opted to study polymer compatibility in solution in mutual solvents, because of uncertainty as to whether a bulk mixture is actually in an equilibrium stale. Compatible components form a single, transparent phase in mutual solution, while incompatible polymers exhibit phase separation if the solution is not extremely dilute. 

If three different substances are to be dealt with, and, chemical action being excluded, the possibilities of mutual solution, c., are to be considered, the problem is an extensive one, and its scope and partial solution may best be given by means of a definite example. 

From a thermodynamic point of view, phase diagrams may be constructed by changing the temperature (ii), pressure (12). or composition of a material. The present experiments are concerned with changes in composition at constant temperature and pressure, leading to a ternary phase diagram with polymer network I at one corner, monomer II at the second corner, and polymer network II at the third corner. According to classical concepts, at first there should be a mutual solution of monomer II in network I, followed by the binodal (nucleation and growth kinetics) and finally the spinodal (spinodal decomposition kinetics). 

Dependence of the total overpotential of the electrode reaction on current can be found by the mutual solution of Equations (1.54) and (1.58). However, this solution cannot be found by analytical calculation. The curves turn of this dependence is defined by the 7°gm/ °me ratio. The calculated polarization curves are presented in Figure 1.20. The cathode current was restricted by the value of /°gm> and the polarization curves become similar to the Taffel dependencies with the increase of Tj. 

Thus if A is albite and B is anorthite, then (A,B) is plagioclase, and we say that the plagioclase solid solution is more stable than a mechanical mixture of grains of albite and anorthite. On the other hand if A is diopside and B is anorthite, little or no mutual solution takes place because in this case... 

Next, consider the case where the mineral standard states are of the variable pressure type, that is, the standard states for brucite and periclase are taken to be the pure phase at the system P and T, while water continues to have a standard state of ideal gaseous water at T and one bar. Because there is essentially no mutual solution between the three phases they are essentially pure when at mutual equilibrium, and the mineral activities are therefore 1.0 at all Ps and Ts. This is only an apparent simplification, because now the equilibrium constant varies with pressure. Its value at 2000 bars, 25°C can be calculated from equation (13.42), thus... 

If both polymer networks are chemically identical, the naive viewpoint suggests that a mutual solution will result with few ways to distinguish network I from network II. As will be shown below, this is emphatically not the case. 

When components do mutually dissolve to form a solution. Equation (10.4) still works for volumes if the solution is ideal, but even for ideal solutions, it does not work for G. The Gibbs energy of the solution must be less than the weighted average of the G of the two pure end-members for mutual solution to take place, and it is represented by the festoon, or convex-downward loop. Therefore, the liquid solution formed when liquid Di and liquid are mixed together is represented by such a loop. It is shown in all sections, even when the liquid is not the stable phase. 

As the temperature of the paste rises during cure, the plasticizer penetrates into the polymer particles, which swell and merge. If the temperature is sufficiently high and the time adequate, the process culminates in complete mutual solution of polymer and plasticizer. This is represented by the formation of a homogeneous plasticized PVC melt that on cooling solidifies to a solid plasticized PVC material. 

Care must be taken during distribution experiments to avoid reference solvents which are miscible with water the calculation of the activity coefficients can be distorted by any mutual solution of water and the... 

The enthalpy of mixing of the networks, calculated from equation (6.52), is shown in Figure 6.25. At low concentrations of network II, A//i2 is observed to be negative. Although it is not a general criterion, thermodynamic mutual solution may be possible in this region. However, the enthalpy of mixing increases as the concentration of the second network is increased and becomes positive at a value of W2 = 0.3. 

From a fundamental point of view, different underlying morphologies are sensed differently for various properties. Thus mechanical measurements might be more responsive to, say, phase continuity, while thermal measurements might be more sensitive to the extent of actual molecular mutual solution. It is therefore interesting to bring to bear barrier properties as another class of molecular probes by which an IPN can be studied. The behavior of permeating small molecules can yield much information... 

Strictly speaking, the use of the term network refers to the crosslinking of the single polymer chains. Therefore, an IPN implies a mutual solution of the two networks. While this problem was dealt with in Section 1.2, a brief review is instructive. 

Over the years, people have discovered many different ways of synthesizing IFN s. Figure 2 Illustrates the sequential IPN synthesis, top, and the simultaneous Interpenetrating network, SIN, synthesis, bottom. In the sequential synthesis, polymer network I Is swollen with monomer II plus crosslinker and activator, and polymerized In situ. The SIN synthesis begins with a mutual solution of both monomers or prepolymers and their respective crosslinkers, which are then polymerized simultaneously by noninterfering modes, such as stepwise and chain polymerizations. These methods have been used In the bulk, suspension, and latex states. Each will yield a distinguishable composition, even for the same polymer pair. 

Figure 2.10 Six basic modes of linking two or more polymers are identified (20). (a) A polymer blend, constituted by a mixture or mutual solution of two or more polymers, not chemically bonded together, (b) A graft copolymer, constituted by a backbone of polymer I with covalently bonded side chains of polymer II. (c) A block copolymer, constituted by linking two polymers end on end by covalent bonds, (d) A semi-interpenetrating polymer network constituted by an entangled combination of two polymers, one of which is cross-linked, that are not bonded to each other, (e) An interpenetrating polymer network, abbreviated IPN, is an entangled combination of two cross-linked polymers that are not bonded to each other, (f) AS-cross-linked copolymer, constituted by having the polymer II species linked, at both ends, onto polymer I. The ends may be grafted to different chains or the same chain. The total product is a network composed of two different polymers.

Polystyrene Poly(2,6-dimethyl-l,4- phenyleneoxide) Mutual solution toughens polystyrene Impact-resistant objects, such as appliances... 

Not every polymer will dissolve in every solvent, however. When one attempts to dissolve a polymer in solvents selected at random, many, perhaps most, will not work. The experimenter rapidly discovers that the higher the molecular weight of the polymer, the more difficult it is to select a good solvent. Polymer-polymer mutual solutions are even more difficult to attain. 

Attempts to understand polymer-solvent and polymer-polymer mutual solution behavior led to many new theoretical developments, particularly in thermodynamics. To an increasing extent, the polymer scientist is now able to predict phase relationships involving polymers. The development of polymer solution and phase separation behavior is the subject of this chapter. 

There are two major mechanisms by which two components of a mutual solution can phase-separate nucleation and growth, and spinodal decomposition ... 

Random types of cross-linking are of special interest for real systems. Clough et al. (100,101) blended anionically polymerized polystyrene with PS-dg and cross-linked the mutual solution with Co y-radiation. Bars of the cross-linked polystyrene were elongated at 145°C and cooled. Specimens were cut in both the longitudinal and transverse directions and characterized by SANS. The quantity... 

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