Volume change polymers

We might be tempted to equate the forces given by Eqs. (9.61) and (3.38) and solve for a from the resulting expression. However, Eq. (3.38) is not suitable for the present problem, since it was derived for a cross-linked polymer stretched in one direction with no volume change. We are concerned with a single, un-cross-linked molecule whose volume changes in a spherically symmetrical way. The precursor to Eq. (3.36) in a more general derivation than that presented in Chap. 3 is... 

Crystal Structure. The crystal stmcture of PVDC is fairly well estabhshed. Several unit cells have been proposed (63). The unit cell contains four monomer units with two monomer units per repeat distance. The calculated density, 1.96 g/cm, is higher than the experimental values, which are 1.80—1.94 g/cm at 25°C, depending on the sample. This is usually the case with crystalline polymers because samples of 100% crystallinity usually cannot be obtained. A dkect calculation of the polymer density from volume changes during polymerization yields a value of 1.97 g/cm (64). If this value is correct, the unit cell densities may be low. 

Fig. 22.8. (a) The volume change when a simple melt (like a liquid metal) crystallises defines the melting point, T (b) the spread of molecular weights blurs the melting point when polymers crystallise ( ) when a polymer solidifies to a gloss the melting point disappears completely, but a new temperature at which the free volume disappears (the gloss temperature, TJ con be defined and measured. 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

Two basic approaches to this problem have been developed. One is to correlate the volume change using Fick s law in a polymer-fixed reference frame, and... 

BG Kabra, MK Akhtar, SH Gehrke. Volume change kinetics of temperature-sensitive poly(vinylmethylether) gel. Polymer 33 990-995, 1992. 

Patterson D. Role of Free Volume Changes in Polymer Solutions Thermodynamics II J. Polym. Sci. C, 1968, 16, p. 3379-3389. 

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

Molecular rotors allow us to study changes in free volume of polymers as a function of polymerization reaction parameters, molecular weight, stereoregularity, crosslinking, polymer chain relaxation and flexibility. Application to monitoring of polymerization reactions is illustrated in Box 8.1. 

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