Chap 6. Characterization of MW Unlike small molecules, polymers are typically a mixture of differently sized molecules. Only an average molecular weight can be defined. In case of Low MW

Measurements of average molecular weight (M.W.) Number average M.W. (Mn): Total weight of all chains divided by # of chains Weight average M.W. (Mw): Weighted average. Always larger than Mn Viscosity average M.W. (Mv): Average determined by viscosity measurements. Closer to Mw than Mn Weight Average Molecular Weight Mw: Since most of the polymer mass is in the heavier fractions, this gives the average molecular weight of the most abundant polymer fraction by mass.

Number average molecular weight Mn

Surfing to the internet High MW sensitive Low MW sensitive Surfing to the internet For further details, Click next homepage. http://www.pslc.ws/mactest/weight.htm

Determination of Molecular Weight Absolute Method End-group Analysis Colligative Property Measurements Relative Method Viscosity Measurements The concentration dependence is observed to follow this functional dependence: Neglect higher order term in c. Plot of hsp/c vs c will yield [h] as y-intercept. y-intercept k = Huggins constant k=2 for rigid uncharged spheres k=0.35 for flexible polymers

Determination of Molecular Weight Virtual Experiment Case Western Reserve Univ. Polymer and Liquid Crystals Viscosity Measurements Click the next homepage, experiment part http://plc.cwru.edu/tutorial/enhanced/lab/visco/visco.htm If you have the trouble viewing this site, See this page http://plc.cwru.edu/tutorial/enhanced/software.html http://www.macromedia.com/shockwave/download/triggerpages_mmcom/default.html K and a are empirical parameters characteristic of a polymer and a solvent - a=0.5 for a well-coiled polymer in a poor solvent - a=1.7 for rigid rod-like polymer

Molecular Weight Distribution

Surfing to the internet Gel Permeation Chromatography Solvent flow carries molecules from left to right; big ones come out first while small ones get caught in the pores. It is thought that particle volume controls the order of elution. But what about shape? For further details Click next homepage. http://www.pslc.ws/mactest/sec.htm Surfing to the internet Size Exclusion Principle

Simple GPC c log10M log10M c Ve c log10M DRI degas pump injector It is all smoke and mirrors to the physical chemist, but darned if it doesn’t work! Then again, if I have to be a plumber, shouldn’t I be paid more? degas pump injector

Chap 7. Polymer Solubility and Solutions Three factors are of general interest 1. What Solvents will dissolve what polymer? 2. How does the polymer-solvent interaction influence the solution properties/ 3. To what applications do the interesting properties of polymer solutions lead? General rules foe polymer solubility 1. Like dissolve like; Polar polymers- polar solvents Nonpolar polymer-nonpolar solvent. ex) PVA in water, PS in toluene 2. Solubility will decrease with increasing molecular weight at const. temp. 3. Crystallinity decreases solubility. 4. Crosslinking eliminates solubility. 5. The rate of solubility increases with short branches, allowing the solvent molecules to penetrate more easily. 6. The rate of solubility decreases with longer branches, because the entanglement makes it harder for individual molecules to separate.

Thermodynamics of polymer solubility ΔGm=ΔHm-TΔSm < 0 Where ΔGm = the change in Gibbs free energy in the process ΔHm = the change in enthalpy in the process ΔSm = the change in entropy in the process Only if ΔGm is negative will the solution process be feasible. AB solution + Immicible A positive ΔH – solvent and polymer “prefer their own company”, the pure materials are in a lower energy state. A negative ΔH – the solution is in the lower energy state, specific interactions are formed between the solvents and polymer molecules. (ref) H.Tompa; polymer solutions, Butterworths,London, 1956,chapter 7 DGmix < 0 DGmix > 0 A B

For Small Molecules No = N1 + N2 Ω = No! / N1!·N2! S = klnΩ Smix = -R[n1lnx1 + n2lnx2] Two-dimensional lattice representation of a solution

Vi+1 = (No-xi) · Z(1-fi) · (Z-1)(1-fi) · (Z-1)(1-fi)··· For Macromolecules No = N1 + xN2 Vi+1 = (No-xi) · Z(1-fi) · (Z-1)(1-fi) · (Z-1)(1-fi)··· 1st segment 2nd 3rd 4th Vi+1 = (No-xi)Z(Z-1)x-2(1-fi)x-1 Ω = 1 / N2! (∏ vi) = 1 / N2! (∏ vi+1) N2 i=1 N2-1 i=0 ∆Smix = -k(N1 ln N1/N1 +xN2) + (N2ln xN2/N1+XN2) ∆Smix = -R(n1lnØ1 + n2lnØ2) Two-dimensional lattice representation of a polymer molecule in solution

Surfing to the internet Solubility Parameter The solubility parameter is defined as: H  E = 12(1  2)2 (cal/cm3soln) 1, 2 : vol. frac. 1 : polymer solubility parameter. 2 : solvent solubility parameter.  = (CED)1/2 = (Ev/v)1/2 = (cal/cm3)1/2 Ev/v : molar vol. of liq. rule of thumb 1  2  0.5 for solubility. Surfing to the internet For further details, Click next homepage. http://palimpsest.stanford.edu/byauth/burke/solpar/

Hansen’s 3-D Solubility Parameter internal energy on vaporization Ev = Eh + Ed + Ep The cohesive energy, δ 2 , is divided into three parts: dispersion forces (δd ) 2) polar forces ( δp ) 3) hydrogen bonding ( δH )

Properties of dilute solutions -Good solvent : Solubility parameter closely matches that of the polymer. The secondary forces between polymer segments and solvent molecules are strong, and the polymer molecules are strong, and the polymer molecules will assume a spread-out conformation in solution. -Poor solvent : the attractive forces between the segments of the polymer chain are greater than those between the chain segments and the solvent. Ex) polystyrene (δ = 9.0 ~ 9.3 ) Chloroform (δ = 9.2 ) Then non-solvent is added , methanol( δ = 14.5 ),the mixed solvent(Chloroform + methanol) becomes too”poor” to sustain solution, and the polymer precipitates out. When ΔG = 0 and ΔH = TΔS (θ condition)

Chap 8. Transitions in Polymers Glass Transition PMMA, PS  hard, rigid glassy plastics at RT when heated to 125C, become rubbery Polybutadiene Polyethylacrylate rubbery at RT, when cooled in Liq. N2 Polyisoprene become rigid and glassy, shatters when break • At low temperatures, all amorphous polymers are stiff and glassy, sometimes called as the Vitreous State, especially for inorganic polymers. • On Warming, polymers soften in a characteristic temperature range known as the glass-rubber transition region. • The glass transition temperature (Tg), is the temperature at which the amorphous phase of the polymer is converted between rubbery and glassy states. • Tg constitutes the most important mechanical property for all polymers. In fact, upon synthesis of a new polymer, the glass transition temperature is among the first properties measured.

Molecular Motions in an Amorphous Polymer Amorphous regions of the material begin to exhibit long-range, cooperative segmental motion Molecular motion available to polymer chains below their Tg are restricted primarily to vibrational modes. Above Tg there is sufficient thermal energy for the chains, through cooperative rotational motion about the backbone bonds, to flow under an applied stress. The presence of this large-scale segmental motion (20–50 atoms moving in concert) above Tg produces an increase in the free volume of the polymer.

Differential Thermal Analysis (DTA) Principal components of the experiment include: • an oven for the controlled heating of the samples • separate temperature sensing transducers for both the analysis and reference samples

Surfing to the internet Differential Scanning Calorimeter (DSC) Two samples, each heated independently. Temperature difference is monitored. Control heat flow into analysis sample (adjusting heater power) to keep the temperature difference ∆T = 0. This is a null experiment with feedback. Surfing to the internet For further details, Click next homepage. http://www.pslc.ws/mactest/dsc.htm

DTA & DSC Images and Sample data DSC sample data DTA sample data

Main factor of Tg Free volume of the polymer vf. Free volume vf = v vs v: specific volume of polymer mass vs: volume of solidly packed molecules * Pressure가 높아지면 vf가 작아짐. Tg 2. Attractive forces between molrcules.  Tg

 Tg Eo Silicone 7.3 -120 ~ 0 PE 7.9 -85 3.3 PTFE 6.2 >20 4.7 3. Internal mobility of chains (= freedom to rotate about bond)  Tg Eo Silicone 7.3 -120 ~ 0 PE 7.9 -85 3.3 PTFE 6.2 >20 4.7

4. Stiffness of the materials Young’s Modulus E may be written as: σ = Tensile stress; ε = Tensile strain Young’s modulus is a fundamental measure of the stiffness of the material. The higher its value, the more resistant the material is to being stretched. Unit of E: dynes/cm2 (10 dynes/cm2 = 1 Pascal) 5. Chain Length.

Surfing to the internet For further details about Tg, Tg of Copolymer T : Kelvin temperature 1, 2 : polymer 1 and 2 Surfing to the internet For further details about Tg, Click next homepage. http://www.pslc.ws/mactest/tg.htm & http://plc.cwru.edu/tutorial/enhanced/files/polymers/therm/therm.htm

Example 4) Nylon n Tm  TS water cont

Example 5) H-bonding Hm PU : O (Swivel)  flexibility Extra NH in polyurea  more extensive H-bond. Hm

Example 6)  300 C , PET rapidly cooled to RT  rigid and transparent  heated to 100 C maintained at that temp  and becomes translucent  then cooled down to RT again now, it is translucent rather than transparent.

Influence of Copolymerization on Properties  homogeneous, amorphous  amorphous and glassy, rigid