Exam 1

1. Four problems • Answers: • Typed • length < ½ page per problem • single space • Any graphics by chemdraw or other software, not harvested off web • Pdf file • Problem in finding or creating answers, assembling and communicating a reasonable solution to the customer. • Exam due Feb 6th at 11:59 PM. • Drop box in D2L Exam 1

2. Two Homework assignments due Feb 7th. • Bibliography (references for paper): at least 10 citations to primary literature or patents in J. Am. Chem. Soc. style with paper or patent titles. • D2L problems due next week

3. Chapter 3 Polymer Solutions How do you know if something is soluble???

5. Industrial Relevance of Polymer Solubility

6. Polymer Solubility • When two hydrocarbons such as dodecane and 2,4,6,8,10-pentamethyldodecane are combined, we (not surprisingly) generate a homogeneous solution: • It is therefore interesting that polymeric analogues of these compounds, poly(ethylene) and poly(propylene) do not mix, but when combined produce a dispersion of one material in the other.

7. Polymer solutions: Definitions • Configuration: arrangement of atoms through bonds • Inter-change requires bond breaking and making (>200 kJ/mol) • Different compositions of polymers • Different isomers or stereochemistries • Conformation: within the constraints of a configuration, the possible arrangement(s) of atoms in space • Interchange requires bond rotations, but no bonds are broken or made (can have non-bonding , ie. hydrogen bonding)

8. Polyethylene coil Fully stretched Polyethylene What are the dimensions of a polymer? • In a solution, in the solid state, in its melt, in vacuum?

9. Factors Affecting Macromolecule Dimensions

10. Flexible coil Polymer Conformations Rigid rod And everything in between

11. l . . . 1 2 3 n How to describe conformations with models: The freely jointed chain • Simplest measure of a chain is the length along the backbone • For n monomers each of length l, the contour length is nl

12. First, Most Primative Model: Freely Jointed Chain Any bond angles & orientations are possible

13. A useful measure of the size of macromolecules: end-to-end distance r • For an isolated polymer in a solvent the end-to-end distance will change continuously due to molecular motion • But many conformation give rise to the same value of r, and some values of r are more likely than others e.g., • Only one conformation with r = nl - a fully extended chain • Many conformation have r = 0, (cyclic polymers) • Define the root mean square end-to-end distance • Permits statistical treatments But we still don’t know the shape; need something more Free rotation model: Infinite number of conformations

15. Example of a “low resolution” polymer coil RW. Contour length = lct, unit vectors to describe the length = e(l), a = vectors that connect the junction points on the chain, r = end-to-end distance of the chain Random Walk Model for linear polymers A freely jointed chain in 2D from a random walk of 50 steps. # of steps based on number atoms in chain Complications: excluded volume & steric limitations

16. What does this all mean?? • An ideal polymer chain with 106 repeat units (not unusual), each unit about 6Å will have: • a rms end-to-end distance R of 600 nm • a contour length of 600 μm

17. R A better measure of Polymer dimensions: Radius of Gyration of a Polymer Coil The radius of gyration Rg is defined as the RMS distance of the collection of atoms from their common centre of gravity. For a solid sphere of radius R; For a polymer coil with rms end-to-end distance R ; Rg Can be related directly to statistical distributions from polymer characterizations

18. Restrict the bond angles to what we see in the polymer: Valence Angle Model

19. Valence angle model • Simplest modification to the freely jointed chain model • Introduce bond angle restrictions • Allow free rotation about bonds • Neglecting steric effects (for now) • If all bond angles are equal to q, indicates that the result is for the valence angle model • E.g. for polyethylene q = 109.5° and cos q ~ -1/3, hence,

20. Finite Number of Conformations due to torsional & steric interactions: Restricted Rotation Angle The energy barrier between gauche and trans is about 2.5 kJ/mol RT~8.31*300 J/mol~2.5 kJ/mol

26. Equivalent Freely Jointed Chain Model C∞ C∞ is a function of the stiffness of the chain. Higher is stiffer

27. Steric parameter and the characteristic ratio • In general • where s is the steric parameter, which is usually determined for each polymer experimentally • A measure of the stiffness of a chain is given by the characteristic ratio • C typically ranges from 5 - 12

28. Flexible coil Polymer Conformations <r2>1/2 ~ N1/2 Rigid rod <r2>1/2 ~ N The shape of the polymers can therefore only be usefully described statistically.

29. Calculate size of macromolecules!

30. Excluded volume • Freely jointed chain, valence angle and rotational isomeric states models all ignore • long range intramolecular interactions (e.g. ionic polymers) • polymer-solvent interactions • Such interactions will affect • Define where is the expansion parameter

31. Space filling? The random walk and the steric limitations makes the polymer coils in a polymer melt or in a polymer glass “expanded”. However, the overlap between molecules ensure space filling

32. Expansion Factors: Measure of solvent -Polymer Interactions

33. : mean-square average distance between chain ends for a linear polymer : square average radius of gyration about the center of gravity for a branched polymer Better solvent  stronger interaction between solvent and polymer  larger hydrodynamic volume r0, s0: unperturbed dimension (i.e. the size of the macromolecule exclusive of solvent effects)  : an expansion factor

34. (for a linear polymer) greater  better solvent  = 1  ideal statistical coil Solubility vary with temperature in a given solvent  is temperature dependent Theta (θ) temperature (Flory temperature) • For a given polymer in a given solvent, the lowest temperature at which  = 1 •  state /  solvent • Polymer in a  state • having a minimal solvation effect • on the brink of becoming insoluble • further diminution of solvation effect  polymer precipitation

35. The expansion parameter ar Solvent Effects on the Macromolecules • ar depends on balance between i) polymer-solvent and ii) polymer-polymer interactions • If polymer-polymer are more favourable than polymer-solvent • ar < 1 • Chains contract • Solvent is poor • If polymer-polymer are less favourable than polymer-solvent • ar > 1 • Chains expand • Solvent is good • If these interactions are equivalent, we have theta condition • ar = 1 • Same as in amorphous melt

36. The theta temperature • For most polymer solutions ar depends on temperature, and increases with increasing temperature • At temperatures above some theta temperature, the solvent is good, whereas below the solvent is poor, i.e., What determines whether or not a polymer is soluble? Often polymers will precipitate out of solution, rather than contracting

37. Solubility of Polymers • Encyclopedia of Polymer Science, Vol 15, pg 401 says it best... • A polymer is often soluble in a low molecular weight liquid if: • •the two components are similar chemically or are so constituted that specific attractive interactions such as hydrogen bonding take place between them; • •the molecular weight of the polymer is low; • •the bulk polymer is not crystalline; • •the temperature is elevated (except in systems with LCST). • The method of solubility parameters can be useful for identifying potential solvents for a polymer. • Some polymers that are not soluble in pure liquids can be dissolved in a multi-component solvent mixture. • Binary polymer-polymer mixtures are usually immiscible except when they possess a complementary dissimilarity that leads to negative heats of mixing.

38. DGmix < 0 DGmix > 0 Another way of looking at Solubility: Thermodynamics of Mixing mA moles mB moles material A material B A-B solution + immiscible blend DGmix (Joules/gram) is defined by: DGmix = DHmix -T DSmix where DHmix = HAB - (xAHA + xBHB) DSmix = SAB - (xASA + xBSB) and xA, xB are the mole fractions of each material. Polymer-solvent: volume fraction of polymers

39. Thermodynamics of Mixing: Small Molecules Ethanol(1) / n-heptane(2) at 50ºC Ethanol(1) / chloroform(2) at 50ºC Ethanol(1) / water(2) at 50ºC

40. Solvent-Solvent Solutions vs Polymer-Solvent Solutions Solvents can easily replace one another. Polymers are thousands of solvent sized monomers connected together. Monomers can not be placed randomly! • Entropy of mixing is generally positive • Enthalpy is also often positive: smaller the better Ideal = 0

41. ENTROPY OF MIXING • The total configurational entropy of mixing (J/K) created in forming a solution from n1 moles of solvent and n2 moles of solute (polymer) is: • where fi is the component volume fraction in the mixture: • and • xi represents the number of segments in the species • for a usual monomeric solvent, xi = 1 • xi for a polymer corresponds roughly (but not exactly) to the repeat unit • On the previous slide, f1, f2 and n1 are equivalent in the two lattice representations, but n2 = 20 for the monomeric solute, while n2 = 1 for the polymeric solute.

42. Enthalpy of Mixing • DHmix can be a positive or negative quantity • If A-A and B-B interactions are stronger than A-B interactions, then DHmix > 0 (unmixed state is lower in energy) • If A-B interactions are stronger than pure component interactions, then DHmix < 0 (solution state is lower in energy) • An ideal solution is defined as one in which the interactions between all components are equivalent. As a result, • DHmix = HAB - (wAHA + wBHB) = 0 for an ideal mixture • In general, most polymer-solvent interactions produce DHmix > 0, the exceptional cases being those in which significant hydrogen bonding between components is possible. • Predicting solubility in polymer systems often amounts to considering the magnitude of DHmix > 0. • If the enthalpy of mixing is greater than TDSmix, then we know that the lower Gibbs energy condition is the unmixed state.

43. Gibbs Energy of Mixing: Flory-Huggins Theory • Combining expressions for the enthalpy and entropy of mixing generates the free energy of mixing: • The two contributions to the Gibbs energy are configurational • entropy as well as an interaction entropy and enthalpy • (characterized by c ; “chi” pronounced “Kigh”). • Note that for complete miscibility over all concentrations, c for the • solute-solvent pair at the T of interest must be less than 0.5. • • If c > 0.5, then DGmix > 0 and phase separation occurs • • If c < 0.5, then DGmix < 0 over the whole composition range. • • The temperature at which c = 0.5 is the theta temperature.

44. Flory-Huggins Theory • Flory-Huggins theory, originally derived for small molecule systems, was expanded to model polymer systems by assuming the polymer consisted of a series of connected segments, each of which occupied one lattice site. • Assuming segments are randomly distributed and that all lattice sites are occupied, the free energy of mixing per mole of lattice sites is DGmix=RT[(fA/NA)lnfA+(fB/NB)lnfB+cFHfAfB] (3) • fi is the volume fraction of polymer i • Ni is the number of segments in polymer i • cHF is the Flory-Huggins interaction parameter

45. Characterization of polymers: Length and time scales are important [Reproduced from G. M. Kavanagh and S. B. Ross-Murphy, “Rheological characterisation of polymer gels”, Prog. Polym. Sci. 23, 533 (1998).]

46. Polymer solubility • In solvent, other polymer(s) or plasticizer • Non-Newtonian properties: Viscosity, rheology • Need to understand the configuration, conformation, and dynamics of macromolecules • Statistical mechanics • Series of mathematical models • Tied to experiment (viscosity, light scattering)

47. Thermodynamics of Mixing: (Free energy) DG = DH -TDS For solution DG < 0 -TDS Polymers are more sensitive to DH Entropy > 0, so –TDS < 0 DH can be negative or positive

48. Spinoidal decomposition of a solution into two phases • Quenching (rapid cooling) of solution • Polymer rich & polymer poor phases Careful removal of polymer poor phase “microporous” Foams.

49. Any solution process is governed by the free energy relationship G = H－TS G＜0  polymer dissolves spontaneously S＞0  arising from increased conformational mobility of the polymer chain For a binary system, Hmix: heat of mixing V1,V2: molar volumes 1, 2: volume fractions E1,E2 : energies of vaporization E1/V1, E2/V2: cohesive energy densities

50. Enthalpy of Mixing • DHmix can be a positive or negative quantity • If A-A and B-B interactions are stronger than A-B interactions, then DHmix > 0 (unmixed state is lower in energy) • If A-B interactions are stronger than pure component interactions, then DHmix < 0 (solution state is lower in energy) • An ideal solution is defined as one in which the interactions between all components are equivalent. As a result, • DHmix = HAB - (wAHA + wBHB) = 0 for an ideal mixture • In general, most polymer-solvent interactions produce DHmix > 0, the exceptional cases being those in which significant hydrogen bonding between components is possible. • Predicting solubility in polymer systems often amounts to considering the magnitude of DHmix > 0. • If the enthalpy of mixing is greater than TDSmix, then we know that the lower Gibbs energy condition is the unmixed state.