Question number 1 2 3 4 5 6 7 8 9 10 11 Answer D B C B A D A B E C D Based on calculations Question number #1 To have miscibility, i.e., a homogeneous phase, it is necessary for the free energy of mixing to be negative. The importance of specific interactions in yielding a negative heat of mixing ΔHm is due to the negligible contribution of the entropy of mixing ΔSm for higher molecular weight polymers in the following expression: βπΊπππ₯ = βπ»πππ₯ + πβππππ₯ < 0 The free energy of mixing has both enthalphic (ΔHmix) and entropic (ΔSmix) contributions. These contributions are generally functions of composition, temperature and in the case of ΔSmix, molecular weight. Polymers undergoing dissolution show much smaller entropies of mixing (ΔSm) than do conventional solutes of low relative molar mass. The reason for this is the size of the polymer molecules: when segments of a molecule are covalently bonded to each other, they cannot adopt any position in the liquid and must remain nearby. Thus, when such big molecules are dissolved in solvent, the disordering effect is much less than for molecules of, say, a typical low molar mass organic compound. If a low-molecular-mass solute is involved, then each point of the lattice can be occupied by either a solvent or solute molecule. The possible arrangements of solvent and solute molecules in an extensive lattice are very numerous. According to Boltzmann, the entropy is defined as: S = π ∗ ln(π) π − Boltzmann’s constant ; W − probability of states When we put a polymer into this lattice, we can no longer put one molecule of solute at each lattice site; instead, we can put one segment of the polymer molecule at every lattice site. As a result, we see that there are fewer possible arrangements for the system. The value of W is therefore much lower than for the low molar mass solute, and thus is S. Question number #2 Question number #3 Polystyrene πΏππ = 9.5 [ π = ππ» + ππ = Polybutadiene πππ 1/2 ] ππ3 πΏππ΅ = 8.1 [ πππ 1/2 ] ππ3 Styrene butadiene rubber (SBR) πΏππ΅π = 0.5 ∗ 9.5 + 0.5 ∗ 8.1 πππ 1/2 = 8.8 [ 3 ] ππ ππ 2 ∗ (πΏπ − πΏπ ) + 0.34 π π ππ3 ππ − πππππ π£πππ’ππ ππ π πππ£πππ‘ [ ] πππ π − π’πππ£πππ ππ πππ ππππ π‘πππ‘ = 1.987 [ πππ ] ; π − π‘πππ = 298 [πΎ] πππ − πΎ ππ π < 0.5 → π πππ£πππ‘ − ππππ¦πππ πππ πππππππ‘π¦ As much as solubility parameter of the solvent and polymer close / identical, (πΏπ − πΏπ )2 ≅ 0 will be miscible in all proportions. Polystyrene: Solvent δs [cal/cm3]^1/2 δps [cal/cm3]^1/2 Vs [cm3/mol] n-Hexane 7.2 9.5 132 Carbon tetrachloride 8.6 9.5 97 Benzene 9.2 9.5 89 Acetone 9.7 9.5 73.3 Methanol 14.5 9.5 40.4 R [cal/mol-K] 1.987 1.987 1.987 1.987 1.987 T [K] 298 298 298 298 298 χ [interaction parameter] 1.519 0.473 0.354 0.345 2.046 Polybutadiene: Solvent n-Hexane Carbon tetrachloride Benzene Acetone Methanol δs [cal/cm3]^1/2 7.2 8.6 9.2 9.7 14.5 δps [cal/cm3]^1/2 Vs [cm3/mol] R [cal/mol-K] 8.1 132 1.987 8.1 97 1.987 8.1 89 1.987 8.1 73.3 1.987 8.1 40.4 1.987 T [K] 298 298 298 298 298 χ [interaction parameter] 0.521 0.381 0.522 0.657 3.135 Styrene butadiene rubber (SBR): Solvent n-Hexane Carbon tetrachloride Benzene Acetone Methanol δs [cal/cm3]^1/2 7.2 8.6 9.2 9.7 14.5 solvents n-Hexane Carbon tetrachloride Benzene Acetone Methanol δStyrene [cal/cm3]^1/2 δbutadiene [cal/cm3]^1/2 8.1 9.5 8.1 9.5 8.1 9.5 8.1 9.5 8.1 9.5 Polystyrene Phase separation critical point Miscible mixture Miscible mixture Phase separation δSBR [cal/cm3]^1/2 8.8 8.8 8.8 8.8 8.8 Polybutadiene critical point Miscible mixture critical point Phase separation Phase separation Vs [cm3/mol] R [cal/mol-K] 132 1.987 97 1.987 89 1.987 73.3 1.987 40.4 1.987 T [K] 298 298 298 298 298 χ [interaction parameter] 0.911 0.347 0.364 0.440 2.557 Styrene butadiene rubber (SBR) Phase separation Miscible mixture Miscible mixture Miscible mixture Phase separation Styrene butadiene rubber (SBR) with Carbon tetrachloride solvent will be miscible, contrary to Polystyrene. This can be seen by solubility parameter of solvent and polymer, solubility parameter of SBR (8.8) more close to solubility parameter of Carbon tetrachloride (8.6), than solubility parameter of PS (9.5). Question number #4 Question number #5 ln ππ = ππ + ππ 0 1 1 = ln ππ + ππ ∗ (1 + ) + πππ2 = ππ π (πππππ π£πππ’ππ πππ‘πππ)πππππ → (1 + ) ≅ 1 π π π π Values of ln ππ were obtained at 34 [β°] πππ π − π’πππ£πππ ππ πππ ππππ π‘πππ‘ = 1.987 [ ] ; π − π‘πππ = 34 + 273.15 = 302.15 [πΎ] πππ − πΎ ln ππ = X= ππ + ππ 0 = ln ππ + ππ + πππ2 π π ππππ −ln ππ − ππ 2 ππ =[ Φp [volum fraction] 0.343 0.388 0.435 0.485 0.543 0.637 0.69 0.768 0.818 0.902 ln( ππ )−ππ 1−ππ 2 ππ ln (as) -0.004 -0.0042 -0.013 -0.018 -0.024 -0.063 -0.089 -0.151 -0.232 -0.46 ] as 0.991 0.990 0.971 0.959 0.946 0.865 0.815 0.706 0.586 0.347 1-Φ 0.657 0.612 0.565 0.515 0.457 0.363 0.31 0.232 0.182 0.098 ln(as/1-Φ)-Φ 0.067861 0.093352 0.105996 0.137142 0.184810 0.231290 0.276253 0.345328 0.351549 0.361599 χ polystyrene/cyclohexane 0.577 0.620 0.560 0.583 0.627 0.570 0.580 0.585 0.525 0.444 Minimum in energy occurs at F3 when the representative points on the free energy curve are joined by the lowest straight line. In this case, have phase separation into compositions cA and cB, with phase's ο‘ and ο’. For compositions c < cA have ο‘ phase ο cA < c < cB have ο‘ + ο’ cB<c have just ο’. Proportions of ο‘ and ο’ given by Lever rule: For c<cA A dissolves B For cB<c B dissolves A cA and cB define solubility limits. Question number #6 Below LCST, PNIPA exhibits hydrophilicity by absorbing water, while the hydrophobicity becomes dominant above the LCST as they release much of the absorbed water. In the case of phase separation of polymer solution occur with increase in temp, the bimodal and spinodal curve coincide at a temp and composition called the LCST, one serious limitation of the Flory-Huggins theory, is that it fails to predict LCST behavior. Flory–Huggins theory, ignores changes to volume upon mixing, there in fact are discernible changes to the volume per residue upon mixing - packing interactions of solvent around the chain or of chain around chain. χ can be empirically recast as: π≈π΄+ π΅ π A is the temperature-independent entropic part (ΔS) and B/T is the temperature-dependent enthalpy part (ΔH) Question number #7 The Flory-Huggins equation is used in describing the thermodynamics of polymer solution, however, there a number of important limitation, the most important are the following: 1. Applicability only to solution those are sufficiently concentrated that they have uniform segment density. 2. There is no volume change of mixing (whereas favorable interaction between polymer and solvent molecules should result in a negative volume change) 3. There are no energetically-preferred arrangements of polymer segments and solvent molecules in the lattice 4. The interaction parameter, χ, is independent of composition. When we discuss polymer solubility, we need to remember that the basis is thermodynamics. In other words, this approach gives information about the energetics of solubility, but does not give any insight in the kinetics of the process. In order to promote rapid dissolution, it may be more helpful to employ a solvent that is less good thermodynamically, but that consists of small, compact molecules that readily diffuse into the polymer and hence dissolve the polymer more quickly. Let's look at a specific example of "water-soluble polymer": Many synthetic polymers that are widely used commercially are soluble in water. These tend to have very polar functional groups; polar functional groups alone do not guarantee water-solubility. Presence of few relatively non-polar groups makes polymer more water-soluble; the reason is that the non-polar groups interrupt the regularity of the structure in the solid polymer, thus making possible the entry of water on this material. This in turn paves the way for solvation of the polar functional groups of the individual molecules leading to dissolution. Such insolubility arises for kinetic rather than thermodynamic reasons. In the case of water-soluble polymers, there is another factor that has to be taken into account when considering solubility, namely the possibility of hydrophobic interactions. If we take into account a polymer that is soluble in water, if it is made up of two types of chemical species, polar functional groups and the non-polar backbone. Typically, polymers have an organic backbone that consists of C—C chains with the majority of valence sites on the carbon atoms occupied by hydrogen atoms. In other words, this kind of polymer partially exhibits the nature of a hydrocarbon, and as such resists dissolution in water. This kind of hydrophobic interaction originates when the hydrocarbon components are attempted to dissolve. Hydrogen bonds between water molecules create cage structures around the non-polar solute. This increase in the regularity of the solvent would result in an overall reduction in entropy of the system, and therefore is not favored. In general, the solution behavior of water-soluble polymers represents a balance between the polar and the non-polar components of the molecules. Hydrophobic properties provide the lower temperature behavior, while hydrophilic properties provide the higher temperature behavior due to the swamping effects of polar (hydrophilic) functional groups.
