Begin Chapter 3 Osmotic pressure used to find number-average molecular weight Scattered-light intensity used to find weight-average molecular weights Remember isotactic, syndiotactic, atactic Conformation is same as saying chain-orientations. r=nxL (simplest form) r is the distance from origin (0,0) to the end tip of the polymer (end to end distance) n = the number of links (think: kind of like how many links are in an iron-chain/bike chain) L= the equal length of each of those links, each link is the same length and it equals L *there are some probability equations, but I do not see that being on the test, or so I hope* In general to express end to end distance, this formula is used: I think that can be rewritten for simplicity as: =nl2 Polymer Solutions Solution: any phase containing more than one component (gas, liquid or solid) it was discovered that dilute polymer solutions deviated strongly from idweal-solution behavior. Polymers are studied while in solution for these reasons:
size exclusion, chromatography, osmometry, viscosimetry, light scattering, and important measurements such as Molecular weight are discovered WHILE the polymer is IN Solution.
Polymers are usually formed while in solution, such as polystyrene
Whether or not a polymer and solvent are mutually soluble, or miscible, is governed by the sign of the Gibbs free energy of mixing, (delta Gmix as shown above in equation) if it satisfies the equation above, then the sign will be negative but it isn’t only condition that has to be met for miscibility. Another condition has to be met, and that is located on page 109, equation 3.63 (I don’t get that equation…) *looking at all those graphs on the slideshow (slides 19,20,21,22)…..i don’t have a darn clue what they mean (spinodal, bimodal curve, etc) * Polymer-Solvent Interaction
Size of polymer molecule greatly depends on its interaction with the solvent that was used to make it.
In good solvents Molecules assume expanded conformations
In poor solvents intramolecular interactions become more significant
In solvents chains assume their “unperturbed dimensions”
Alpha is the linear coil expansion, this is how it is related from that “equivalent radius” equation to determining what is a good/bad solvent…I think this also ‘might’ have something to do with “radius of gyration” as she mentioned in class once. Polymer Characterization FOUR ways to calculate Molecular Weight of a polymer: (look at pages starting with page 129) -Osmometry -Light Scattering -Intrinsic Viscosity -Gel-Permeation Chromatography……. (In addition to these accurate but time-consuming techniques, there are a number of secondary methods by which average molecular weight can be determined. The most important method is called gel permeation chromatography (GPC) The osmotic pressure is the additional pressure that must be imposed to keep solvent and solution sections at the same level. This static method requires a long time to reach equilibrium. Pi/c=RT/MN + RTA2c always linear. Y = C1 + C2 X A reproduction of a graph I had in my notes……: In class, she said something about this being important: -Absolute (or primary) method -Measures number average molecular weight -Lower limit is about 20,000 due to permeability of low molecular weight polymer fraction -Upper limit is about 500,000 due to inaccuracy in measuring small osmotic pressure *Important*……..maybe, study Osmotic pressure, its effect on quality Light Scattering Method: The weight average molecular weight (Mw) can be obtained directly by scattering experiments. This techniques is not used routinely used for molecular weight determination because of the difficulty and expense sample preparation. This method has these characteristics: -Absolute (or primary) method -Measures weight average molecular weight -Applicable from 10,000 to 10,000,000 -Limitation for copolymers due to difference in refractive indexes between two types of repeat units -No problems for branched polymers -Can measure radius of gyration *It would be a good idea to highlight the differences between light scattering and Osmometry* For the Zimm Method, I do not know if it will be that important since she didn’t underscore much from it, but it is def. worth a look: The most rigorous approach top determine Mw from light scattering data is a Zimm plot. A double extrapolation to both zero concentration and zero angle is used to obtain information concerning molecular weight , second virial coefficient, and chain dimensions In addition to this, from me: this procedure has the advantage that the “chain conformation” does not need to be known in advance. Also, you need to tediously measure the scattered light at many angles, which is a disadvantage because it is laborious (extra work). Intrinsic Viscosity Measurements A method widely used for routine molecular weight determination is based upon the determination of the intrinsic viscosity , of a polymer in solution through measurements of the solution viscosity. Molecular weight is related to  by the Mark-Houwink-Sakurada equation I think this is really important Used to find molecular weight That “n” looking symbol stands for intrinsic viscosity, The v stands for viscosity And if you know both constants a and K, you can use this equation to find Molecular Weight based on viscosity. “a” tells you how the polymer is….? (that’s what she said in class….) The intrinsic viscosity can be found by finding the y-intercept of this graph, or a graph similar that has the same xy axis And from the notes above and on other pages, I think an equation similar to this was used for this graph: π /c=RT/MN + RTA2c always linear. π /c= [n] + Kx[n]2c remember: Y=mx+b y= π /c ……m=slope= RTA2 & Kx[n]2 …… x= c ……..b=y intercept= RT/MN & [n] Chromatography/Gel Permeation Chromatography Chromatography is a separations method that relies on differences in partitioning behavior between a flowing mobile phase and a stationary phase to separate the components in a mixture. A mixture of different size solute molecules is eluted through a column of porous particles. Large molecules are swept through unhindered, while small molecules are retarded in the pores END TOPIC/CHAPTER 3 Begin Topic/Chapter 4 Solid State Properties of Polymers Recap on Thermoplastics & Thermosets… Here is stuff on this topic from last test’s notes: Thermoplastics-------amorphous---------only Tg --------semicrystalline------Tm & Tg Thermoset------amorphous-----only Tg Amorphous -random chain entanglements -most transparent resins are amorphous -greater impact strength, less shrink and warp -only Tg Spaghetti Like Semi-Crystalline -ordered crystalline structure -Crystallinity affected by processing -Exhibits both a Tc and a Tg Linear and branched polymers are thermoplastics Crosslinked network, are ultimately branched are thermoset. Polymer Morphology Morphology involves the study of the arrangement of polymer molecules into crystalline and amorphous regions. -Polymer with high crystallinity are dense, stiffer , harder, tougher and more resistant to solvents. -Amorphous domains add flexibility and promote ease of processing below the melting temperature. Presence of crystalline structure have a significant influence on the physical, thermal and mechanical properties of the polymer Example of amorphous polymer is atactic polystyrene. “as the melt is cooled, a temperature is reached at which all long-range segmental motion ceases, and this called the glass-transition temperature, Tg” In the glassy state, at TMc is the minimum polymer chain-length or critical molecular weight for the formation of stable entanglements which depends on the flexibility of a polymer chain……? (from book) According to slides: Mc= minimum molecular weight for the formation of entanglements Me=average molecular weight between entanglements The minimum polymer chain length for the formation of stable entanglements depends upon the flexibility of a polymer chain. Relatively flexible polymer chains, such as PS, have a high Mc, while more rigid chain polymers, such as those whit aromatic backbones (PC) have a relatively low Mc Reptation: Back to talking about the glass-transition……: The temperature that marks the transition from the amorphous solid sate to the melt state is called the glass transition temperature. *each polymer has a Tg, the Tg itself depends on molecular weight* Something I modified on Paint to show Tg where it is graphically…..: Also, look over stress=F/A, youngs modulus, strain, elongation, their relation to graph…. (10/20/09) The Crystalline State Under favorable conditions, some polymers cooled from the melt can organize into regular crystalline structures The basic units of crystalline polymer morphology include crystalline lamellae consisting of arrays of folded chains. Reentry of each chain in the folded structure can be adjacent (regular folding chain) or nonadjacent (irregular chain folding). Spherulites: For some polymer crystallized from the melt or from concentrated solutions, crystallites can organize into large spherical structures called spherulites. Each spherulites contains arrays of lamellar crystallites that are typical oriented with the chain axis perpendicular to the radial (growth) direction of the spherulite (i.e.PP). Ok….back to Tg/Tm…… For most polymers Tg is approximately 1/ 2 or 1/3 of Tm The chemical structure of a polymer determines whether it will be crystalline or amorphous in the solid state. Talking about crystallinity again…..: Increasing the degree of Crystallinity Produces a Stiffer, Harder, Stronger Material. But the impact Resistance Decreases Eg: Think about the differences in the physical properties of a polyethylene bucket (relatively high crystallinity ) and a garbage bag (relatively low crystallinity)
Crystalline melting temperature the free energy of fusion per repeating unit of the polymer: This equation below is pretty much the same as the one above. Only difference is that this is in equilibrium, and in equilibrium, Gu =0, so then when you rearrange what you have left, you get: Hu is the enthalpy of fusion per repeating unit Su is the entropy of fusion per repeating unit Tm0 is melting temperature. Note this: In general, the observed crystalline-melting temperature, Tm, is always lower than the equilibrium value (Tm°). Crystallization Kinetics She said this in class, kinda random, but may help: When plastic/polymer is transparent, that means it is Amorphous. ….The rate of crystallization depends upon the crystallization temperature The extent of crystallization attained during melt processing depends upon the rate of crystallization and the time during which melt temperatures are maintained. Thermal Transitions and Properties Cp= specific heat at constant pressure Glass transition is a second order transition that is affected by the rate of heating or cooling. Dilatometry: change in volume Remember, if not mistaken: endothermic=getting more heat, heating up Exothermic: giving off heat, losing heat, therefore, it is cooling Slides 41, 42, 43 in Topic 4 are good to look at maybe. They are below as well: Probably Important: Mechanical Properties σ stands for stress ε I think stands for percent change in length??? Another equation for stress: σ = E ε where E is strain, and ε is ∆L/L o (this is also called Hooke’s Law) extension is like elongating, stretching something shear is stressing something by shaking, like an earthquake on a building? These might be handy to look at She said in class: steep slope = young’s modulus? Don’t know if this is important….hmmmm IZOD Impact: -Swinging pendulum looses energy after impact ? I guess this is what I deem relevant for the test, might be wrong, might be right, Good Luck anyways! This is def. not 100% complete by any means. Def. more to look over