Entropy polymer thermodynamics

The ring-opening polymerization of is controUed by entropy, because thermodynamically all bonds in the monomer and polymer are approximately the same (21). The molar cycHzation equihbrium constants of dimethyl siloxane rings have been predicted by the Jacobson-Stockmayer theory (85). The ring—chain equihbrium for siloxane polymers has been studied in detail and is the subject of several reviews (82,83,86—89). The equihbrium constant of the formation of each cycHc is approximately equal to the equihbrium concentration of this cycHc, [(SiR O) Thus the total... 

In an attempt to clarify the mechanism whereby electrolytes influence the solvency of water for a polymer, Garvey and Robb (1979) measured the heats of dilution of poly(vinyl pyrrolidone) in aqueous electrolyte solutions. The heat of dilution was found to be negative (i.e. mixing is favoured by the enthalpy changes) so that phase separation must inevitably be controlled by entropy effects. Thermodynamics demands that in the salting-out of a polymer by a second component, this component must be negatively adsorbed from the polymer. This can be expressed mathematically by... 

In Chap. 8 we discuss the thermodynamics of polymer solutions, specifically with respect to phase separation and osmotic pressure. We shall devote considerable attention to statistical models to describe both the entropy and the enthalpy of mixtures. Of particular interest is the idea that the thermodynamic... 

The thermodynamic ceiling temperature (26) T for a polymerization is computed by dividing the AfTp by the standard entropy of polymerization, The T is the temperature at which monomer and polymer are in equHibrium in their standard states at 25°C (298.15 K) and 101.3... 

Most polymer pairs are thermodynamically incompatible, in the sense that their free energy of mixing is positive. This does not mean that there is absolutely no interdiffusion at all at the interface between them adjacent to the interface limited interdiffusion occurs, which can be seen as an increasing of the low surface entropy implied by a smooth surface [30-33]. This nanoscale roughening of an interface can increase the adhesion between the polymers. 

Polymerization thermodynamics has been reviewed by Allen and Patrick,323 lvin,JM [vin and Busfield,325 Sawada326 and Busfield/27 In most radical polymerizations, the propagation steps are facile (kp typically > 102 M 1 s l -Section 4.5.2) and highly exothermic. Heats of polymerization (A//,) for addition polymerizations may be measured by analyzing the equilibrium between monomer and polymer or from calorimetric data using standard thermochemical techniques. Data for polymerization of some common monomers are collected in Table 4.10. Entropy of polymerization ( SP) data are more scarce. The scatter in experimental numbers for AHp obtained by different methods appears quite large and direct comparisons are often complicated by effects of the physical state of the monomei-and polymers (i.e whether for solid, liquid or solution, degree of crystallinity of the polymer). 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

Microdomain stmcture is a consequence of microphase separation. It is associated with processability and performance of block copolymer as TPE, pressure sensitive adhesive, etc. The size of the domain decreases as temperature increases [184,185]. At processing temperature they are in a disordered state, melt viscosity becomes low with great advantage in processability. At service temperamre, they are in ordered state and the dispersed domain of plastic blocks acts as reinforcing filler for the matrix polymer [186]. This transition is a thermodynamic transition and is controlled by counterbalanced physical factors, e.g., energetics and entropy. 

If peptide residues are converted to peptoid residues, the conformational heterogeneity of the polymer backbone is likely to increase due to cis/trans isomerization at amide bonds. This will lead to an enhanced loss of conformational entropy upon peptoid/protein association, which could adversely affect binding thermodynamics. A potential solution is the judicious placement of bulky peptoid side chains that constrain backbone dihedral angles. 

These two examples show that regular patterns can evolve but, by definition, dissipative structures disappear once the thermodynamic equilibrium has been reached. When one wants to use dissipative structures for patterning of materials, the dissipative structure has to be fixed. Then, even though the thermodynamic instability that led to and supported the pattern has ceased, the structure would remain. Here, polymers play an important role. Since many polymers are amorphous, there is the possibility to freeze temporal patterns. Furthermore, polymer solutions are nonlinear with respect to viscosity and thus strong effects are expected to be seen in evaporating polymer solutions. Since a macromolecule is a nanoscale object, conformational entropy will also play a role in nanoscale ordered structures of polymers. 

Another quasi-thermodynamical model of ion transport in polymers is based on the concept of minimum configurational entropy required for rearrangement of the polymer, giving practically identical o—T and D — T dependences as the preceding model. 

The third law of thermodynamics states that the entropy of a perfect crystal is zero at a temperature of absolute zero. Although this law appears to have limited use for polymer scientists, it is the basis for our understanding of temperature. At absolute zero (-273.14 °C = 0 K), there is no disorder or molecular movement in a perfect crystal. One caveat must be introduced for the purist - there is atomic movement at absolute zero due to vibrational motion across the bonds - a situation mandated by quantum mechanical laws. Any disorder creates a temperature higher than absolute zero in the system under consideration. This is why absolute zero is so hard to reach experimentally ... 

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