Pseudo ideal

Note 1 In some respects, a polymer solution in the theta state resembles an ideal solution and the theta state may he referred to as a pseudo-ideal state. However, a solution in the theta state must not be identified with an ideal solution. 

The fundamental cause of the "pseudo-ideal deton vels that are observed in the progress by stages of the reaction at the deton wave front of mixed HE s is due to the kinetics of the decompn of the expl components. A whole series of factors have an influence on the rate of liberation of energy in the wave... 

The measured velocity, called the "pseudo-ideal velocity , results from an intermediate reaction state in the wave front of the detonation. The intermediate state is caused by the differences in the decompn rates of the components. 

Proton chemical shifts, 369 Pseudo ideal state, 247 Pulling rod, 810... 

Agreement with Raoult s Law is not a sufficient condition for ideality —though it is a necessary one (627). Occasionally a mixture capable of H bonding will form a pseudo-ideal system which obeys the equation. Pyridine-ethanol is an example (227) which must include H bonding, both in association of the alcohol and between the two components. The observed ideal behavior surely results from a fortuitous cancellation of effects. 

Vapor pressure pseudo-ideal H bond system, pyridine-ethanol. 

It has become international practice to employ the mixtures n-heptane-inethyl-uyclohexane, 1.2-dichloroethane-benzene, benzene-carbon tetrachloride und benzene-ethylene dichloride (for plate numbers up to 50 or 60) and benzene-carbon tetrachloride (for plate numbers up to 30) for tests at atmospheric pressure. Brandt and Rock [196] examined the system n-heptane-methylcyclohexane as regards its ideality of behaviour. It was found that the mixture must be classed as a separate typo, termed pseudo-ideal , because the heats of mixing are not negligible in spite of the constancy of the relative volatility. The system is also very suitable for testing under reduced pressure. A further advantage is that the molar heats of evaporation of the components are almost the same (7.575 kcal/mole). For plate numbers from 100 to 500 heavy water is suitable as a test substance [214]. The system... 

This prediction is well illustrated with the classic data of Rahage and collaborators [26]. Figure 7-5 shows those for polystyrene in cyclohexane above and below the 9 temperature. At the indicated temperatures the system is close to the 6 state (some authors call it the pseudo-ideal state), so that dYl/dc stays nearly constant in the region of low concentration. Flence, the initial decline in D as seen in the figure can be attributed to an increase in / with c. The rise in D after a minimum indicates the suppression of a continuous increase in / by a sharp increase in 511/5c. 

With the change of temperature or with the addition of a poor solvent, the transition of the single chain from an expanded coU to a hard sphere is called collapse transition. Meanwhile, the scaling exponent of the coU size reduces from 0.6 to 0.33. Therefore, v = 0.5 exists during the collapse transition, representing a scaling relationship for ideal cods. We defined the thermodynamic condition for this transient pseudo-ideal state as the theta point. 

Kj and will compensate with each other, leading to the pseudo-ideal state of the single-chain system. Flory defined the temperate 6 = Kjlxj/i x T. Accordingly,... 

To approach the pseudo-ideal state, one can either adjust the temperature to the theta temperature, or use the theta solvent. 

Correlation between end to end distance and radius of gyration in pseudo-ideal conditions and for good solvent qualities. 

Fig. 1.1. Schematic representation of the different stages of the solution conformation of dissolved polymers compact a=0), pseudo-ideal unperturbed dimensions (theta conditions, a=05), good solvent (a<0.5), rigid rod (a<2)...

Theoretical approaches to determine solution structures of neutral polymers act on the assumption of the pseudo ideal state. Here the solvation forces from the solvent and the aggregation forces of the chain segments are in an equilibrium where the coil appears to be unaffected by forces. This pseudo ideal state is called the theta state. Theta conditions exist when the exponent a of the [q]-M-relationship has the value a=0.5 and at the same time the value of the second virial coefficient is A2=0 (see the chapter "The [q]-M-relationship in this monograph). Accordingly, a pseudo ideal solvent is called theta solvent and the corresponding temperature is called theta temperature. As Flory showed in his Nobel price lecture [1], the theta state can be described mathematically exactly from the chemical structure of the chain. 

When large differences in the CEDs of the components occur, x exceeds the critical value and the two components segregate into two macroscopic phases. Values of x < 5 characterize instead thermodynamically good solvents in which polymer segments experience chain expansion and solvation. The term j — x describes the excess mixing (dilution) free energy, which attains pseudo ideal values when [48]... 

Such a state is called the 0 state (theta state). At the 9 state, the excluded volume effect vanishes and the dimensions of the polymer molecule are called unperturbed dimensions. Thus, the 0 state is also called the unperturbed state or the (pseudo) ideal state. 

It is found that polymer solutions only approach ideality at infinite dilution although under certain circumstances (0 condition) they can exhibit pseudo-ideal behaviour. 

It has been mentioned earlier that polymer solutions can sometimes exhibit pseudo-ideal behaviour and this will obviously be when the excess partial molarJree energy of mixing is zero. For this to happen A//f must be equal to TASi and therefore k, equal to. The temperature at which this is so is called the Flory or Theta temperature, 0, which can be defined as... 

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