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Lecture10notes - Polymers in the Solid State Lecture 10 1...

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Unformatted text preview: Polymers in the Solid State Lecture 10 1 Monday, November 1, 2010 Todays concepts • In the solid state, polymers are typically amorphous or semi-crystalline, and rarely 100% crystalline • The more regular a polymer structure, the easier it is to pack into crystalline subdomains • Polymers crystallize into chain-folded structures (lamellae) (if they crystallize) • Crystallinity affects physical properties • Kinetics are important in polymer crystallization • Crystallinity can be characterized using XRD 2 Monday, November 1, 2010 Polymers in the Solid State semi-crystalline amorphous glassy rubbery How does polymer structure relate to its physical properties? 3 Monday, November 1, 2010 Polymer Morphology • • • Biologists and botanists use the term morphology to study the structure and form of living things (for example, we often talk about cell morphology and sometimes relate it to cell function) The term morphology, when applied to polymers, more typically means the study of order within macromolecular solids - polymer crystallinity Morphology is also used to describe the structures formed by block copolymers 4 Monday, November 1, 2010 Ordered Chain Conformations • • • • We previously described the minimum energy (enthalpy) conformation of a chain, in which all the bonds are trans (no gauche or eclipsing interactions) This is entropically not as favorable as the statistical distribution of chain conformations found in the melt If we take a polymer melt and cool it down, ordered structures can start to form as a result of crystallization What do the crystals look like? What is the conformation of the chains and how are they arranged relative to one another? 5 Monday, November 1, 2010 Amorphous vs. Semi-Crystalline • • Semi-crystalline implies order; there are different ways to order chains, and different levels of order Amorphous polymers are not ordered 6 Monday, November 1, 2010 Small molecules vs polymers • Crystalline materials (typically small molecules) are either 100% crystalline, neglecting defects, or amorphous at a particular temperature; they melt at a sharp, well-defined temperature • Crystallizable polymers are never 100% crystalline, and melt over a range of temperatures • According to the phase rule a single component mixture should be either crystalline (neglecting defects) or amorphous at a particular temperature, and the transition between them should be sharp and first order (rather than over a range of temperatures) “ ey laid upon them the curse of not obeying thermodynamics” J.D. Hoffman, G.T. Davis, and J.I. Lauritzen Jr. in Treatise on Solid State Chemistry Vol 3 (Editor: Hannay, N.B.), Plenum Press, New York, p. 497, 1976 7 Monday, November 1, 2010 Polymer Crystallization • • • What is the conformation of the chains in the crystalline domains and how are they stacked relative to one another? What is the overall shape and form of the crystals? What are the relative arrangements of the crystalline and amorphous parts? 8 Monday, November 1, 2010 Crystallization • • XRD gives us information about the unit cell of a crystal, but what is meant by “unit cell”? If we know the structure of the unit cell, we can obtain a picture of the entire crystal by repeating the unit cell over and over and over… 9 Monday, November 1, 2010 Polyethylene Unit Cell • The unit cell contains small segments of different chains side view top view 10 Monday, November 1, 2010 Tacticity and Crystallinity • • • • Atactic poly(propylene) does not crystallize, while isotactic poly(propylene) does In order to be able to crystallize, a polymer must have an ordered chain microstructure Regularity of structure makes a polymer capable of crystallizing, but that doesn’t mean it will! Crystallization occurs if there is a sufficient enthalpic gain from maximizing interactions through ordered close packing to offset the entropic loss of restricting conformation 11 Monday, November 1, 2010 Polymer Crystallinity • • • The minimum free energy for a polymer is going to be combination of intermolecular and intramolecular interactions Certain polymers can fold into a number of different conformations of nearly equal energy leading to a variety of crystal forms The form you get (or distribution of the forms) depends on the crystallization conditions 12 Monday, November 1, 2010 How do polymers crystallize? • • The crystalline domains within a polymer are arranged in a regular ordered form in the same manner as small molecules, but these crystals coexist with amorphous material In the fringed micelle model, individual chains traverse regions of both order and disorder, going from small crystallite to an amorphous region, into another crystallite 13 Monday, November 1, 2010 How do polymers crystallize? • • • • In 1957 Keller, Till and Fischer independently grew single crystal lamellae of PE by cooling from a solution of hot xylene Because the chains were not all tangled up (were in dilute solution), a simple crystal form was obtained This appears on an electron micrograph as a flat diamond, although in solution these crystals are more like hollow pyramids (gash) Electron micrographs show that the chains are perpendicular to the large flat faces, and parallel to the thin faces 14 Monday, November 1, 2010 How do polymers crystallize? • • • Electron micrographs show that the chains are perpendicular to the large flat faces, and parallel to the thin faces) The thickness of the sheets is only about 100 Å, but the extended length of the chain is at east 5 times that! “as the parallel alignment of chains is almost perfect, we are forced to conclude that the molecules must sharply fold upon themselves” (Keller and O’Connor) Is this a good picture of what is happening? 15 Monday, November 1, 2010 Adjacent Re-entry vs. Random Re-entry While Keller proposed that folding occurred in a tight, regular manner (adjacent re-entry), Flory argued that the fold surface should be disordered, with chains entering and leaving at random (switchboard model) (big fights, big meeting in 1979, still controversial) CONCLUSION: for a single crystal all chains re-enter within about three lattice sites of the surface 16 Monday, November 1, 2010 Polymer Crystallization • • • The previous examples really concern polymers that have been crystallized from dilute solution Crystals grown from the melt are less ordered Let’s take a look: 17 Monday, November 1, 2010 What does polymer crystallization look like? Spherulites nucleate grow Overlap and impinge Grow more to cover all space 18 Monday, November 1, 2010 Spherulites Isotactic Polypropylene Spherulites, MW=129000 g/mol (polarized light microscopy) 19 Monday, November 1, 2010 Spherulites Each “arm” of the spherulite is a lamellar sheet of polymer Initially, a central lamellae is thought to form, which subsequently branches to form the spherulite The space between the arms is amorphous material The lamellar arms consist of chain-folded material, but the nature of the folding here is thought to be less regular than crystals grown from solution There are a certain number of chains that cross from one arm to another 20 Monday, November 1, 2010 Polymer Crystal Size 21 Monday, November 1, 2010 Crystallization and Polymer Properties • • • • • • As the material crystallizes, it becomes more dense Strength, stiffness and toughness generally increase with density Optical clarity often decreases with increasing crystallinity, depending on the size of the crystalline domains Crystalline materials have better barrier properties – small molecules cannot usually penetrate or diffuse though the crystalline domains Solvent resistance generally increases with increasing crystallinity Increasing the degree of crystallinity produces a stiffer, harder, stronger material, but impact resistance decreases 22 Monday, November 1, 2010 Polymer Fibers • • • Drawing a polymer into a fiber can align the chains “Drawing” means taking the polymer above it Tg but below Tm, and stretching The preferred orientation of chains is parallel to the draw direction 23 Monday, November 1, 2010 Polymer Crystallization Polymer melting is usually reported as the temperature at which the last crystals disappear, as melting can occur over a broad temperature range If we melt a polymer, and then cool it back down to the Tm, crystallization does not occur; typically, we have to go 15-50 °C below Tm (undercooling) For most polymers crystallization is a slow process, and the growth rate can be observed using an optical microscope Crystallization depends on concentration fluctuations within the melt which results in the formation of a primary nucleus, from which the crystals grow There is an energy barrier for all materials that prevents the formation of a stable nucleus at Tm, but it is much more difficult for polymers than other molecules Polymers crystallize into chain-folded structures, so the thickness of the structure is also important The size of undercooling affects the thickness of the lamellae 24 Monday, November 1, 2010 Crystallization and Free Energy 25 Monday, November 1, 2010 Polymer Crystallization Small molecules typically exhibit little undercooling (not universal though) Polymers typically exhibit undercooling (large difference between crystallization temperature and melting temperature) cool Specific volume cool Specific volume heat heat Tc Tm Monday, November 1, 2010 temp Tc Tm temp 26 Crystallization Volume changes as a function of temperature Specific volume (1/d) is discontinuous at the melting/crystallization transition cool Specific volume heat Tc Monday, November 1, 2010 Tm temp 27 Differential Scanning Calorimetry (DSC) A DSC plot showing a change in the specific heat (ΔCp) at the glass transition temperature (Tg) and an endothermic peak at the melting temperature (Tm) for linear polyethylene 28 Monday, November 1, 2010 Polymer Crystallization and Free Energy The free energy of a crystal is the sum of the free energy of the surface and the free energy of the bulk Surface free energy is larger than bulk free energy In a lamellar structure, chains are not in the minimum energy conformation If a polymer is annealed between its Tm and the crystallization temperature, l increases In the bulk, the segments stack to minimize their interactions (minimize the sum of free energy, both conformation and interaction contributions) On the surface, there is typically a higher energy conformation, and there is a difference between what the chains at the surface see inside the crystal versus outside the surface ΔGc = ΔGs + ΔGb ΔGc = 4 xlσ + 2 x 2σ e − x 2 lΔg Sides of crystal Surface Bulk 29 Monday, November 1, 2010 Free Energy of a Crystal ΔGc = 4 xlσ + 2 x 2σ e − x 2 lΔg Sides of crystal Surface Bulk Δg is the bulk free energy of fusion σ is the free energy per unit area of the side surface σe is the free energy per unit area of the top surface The crystal minimizes its free energy by getting thicker (maximizing bulk, minimizing surface) Minimum free energy is obtained for a crystal where the chains are fully extended 30 Monday, November 1, 2010 Free Energy of a Crystal Free energy is minimized when the surface area is minimized Compare fully extended chains to folded chains Folded chains increase their fold period upon annealing 31 Monday, November 1, 2010 Why do polymers crystallize as folded chains? Kinetics! The crystal must first form by a process of nucleation from the melt or solution What is the probability of obtaining one chain with the fully extended state? What is the probability of getting a bunch of chains to form an extended chain nucleus? 32 Monday, November 1, 2010 Critical nucleus size • The critical nucleus size is determined by determining the values of x and l that minimize ΔGc: ∂ΔG ∂ΔG = =0 ∂l ∂x • This leads to an expression for the most probable size of the critical nucleus: 4σ e l* = Δg • This expression for Δg isn’t as useful as something more measurable, like degree of undercooling • We can use some of these equations to obtain an expression for the equilibrium melting point (which is always higher than the observed melting point) • We can use some of these equations to obtain an expression for the fold period and its dependence on surface energy and Tm 33 Monday, November 1, 2010 Free energy of fusion • Consider a perfect extended chain crystal in equilibrium with its melt At equilibrium, the change in the free energy of fusion is: Δg = 0 o Δg = Δh f − Tm Δs f = 0 Δs f = Δh f o Tm Consider a temperature T where Δg≠0, so we can substitute Δsf to obtain: ⎛T ⎞ Δg = Δh f − Tc Δs f = Δh f ⎜ c ⎟ o ⎝ Tm ⎠ Error in text? (PC Essentials p 302) o ⎛ ⎛ Tm − Tc ⎞ Tc ⎞ Δg = Δh f − Tc Δs f = Δh f ⎜1 − o ⎟ = Δh f ⎜ ⎟ o Tm ⎠ ⎝ ⎝ Tm ⎠ 34 Monday, November 1, 2010 Crystallization We have our previous expression for thickness: l* = 4σ e Δg We can combine it with the expression for Δg: o ⎛ Tm − Tc ⎞ Δg = Δh f ⎜ ⎟ o Tm ⎠ ⎝ The expression for the minimum fold period, lmin is obtained from this: o 4σ e ⎛ Tm ⎞ l= ⎜o ⎟ Δh f ⎝ Tm − Tc ⎠ * For crystallization close to Tm, only crystals with infinite fold periods can grow Random concentration fluctuations to get a collection of fully extended chains is vanishingly small, so polymers don’t crystallize close to Tm 35 Monday, November 1, 2010 Crystallization • • • • This expression for l* really only applies to pure polymers In most practical cases, crystallization starts on the surface of impurities, deliberately added nucleating agents, surface irregularities in the mold, etc… These act by further reducing the interfacial free energy, σ, and lower the degree of undercooling necessary for crystallization We can therefore look at the process of secondary nucleation 36 Monday, November 1, 2010 Kinetics of Crystallization An initial nucleus of folded chains is formed that is then locked in by subsequent growth There are two distinguishable stages: primary nucleation with subsequent growth on the sides of this nucleus by a process of secondary nucleation Primary nucleation Secondary nucleation 37 Monday, November 1, 2010 Secondary Nucleation ΔGstem = (2 al)σ + n (2 a 2 )σ e − n ( a 2 l)Δg Δg is the bulk free energy of fusion σ is the free energy per unit area of the side surface σe is the free energy per unit area of the top surface * min l o 2σ e ⎛ Tm ⎞ = ⎜o ⎟ Δh f ⎝ Tm − Tc ⎠ 38 Monday, November 1, 2010 Fold Period and Crystal Growth Rate • The thickness of the secondary nucleus must be bigger than the minimum size (by δl) if further growth is to occur: o 2σ e ⎛ Tm ⎞ * lg = ⎜o ⎟ + δl Δh f ⎝ Tm − Tc ⎠ • The growth rate is exponential, and depends on a number of things − GrowthRate e • 0 C σσ e ⎡Tm ⎤ ⎣⎦ 2 0 Δh f kTc ⎡Tm − Tc ⎤ ⎣ ⎦ × otherterms Theory predicts that the fold period or thickness of the crystals increases with decreasing undercooling, while the rate of primary crystallization increases with decreasing temperature Growth rate ~ e − Kg TΔT 39 Monday, November 1, 2010 Fold Period and Crystal Growth Rate 40 Monday, November 1, 2010 Crystallization Kinetics Bell shaped curves are obtained for primary and secondary nucleation because of a balance between two factors: a) the formation of the nucleus (increases as T decreases) b) the transport of chains to the growth front (decreases as T decreases) A larger number of smaller crystals are formed as the crystallization temperature is decreased, which affects material properties 41 Monday, November 1, 2010 Crystallization Regimes Regime I: occurs at low supercoolings Regime II: High supercoolings Regime III: Prolific multiple nucleation (ignore) Growth rate in regimes I and II: Growth rate ~ e − Kg TΔT o 2σ e ⎛ Tm ⎞ l= ⎜o ⎟ + δl Δh f ⎝ Tm − Tc ⎠ * g Growth rate depends on balance between diffusion and nucleation terms 42 Monday, November 1, 2010 Polymer Crystallization Polymers would like to crystallize in the extended chain form but cannot get there The initial nucleus is folded and its formation is governed by kinetic factors Subsequent crystal growth proceeds by a secondary nucleation process that locks the crystal into its folded chain form The lower the crystallization temperature, the more crystals are formed, and the shorted the folding period This theory accounts for the thin character of polymer crystals A stable crystal with a fold period of lg* is formed and this grows laterally There is no crystallization on the high energy fold surface 43 Monday, November 1, 2010 Characteristics of the Crystalline Melting Point The term melting is used to describe the transition from an ordered crystalline phase to a disordered liquid phase, usually at a well-defined temperature 44 Monday, November 1, 2010 Crystallization vs. melting • Lamallae of different sizes melt at different temperatures ΔGc = 4 xlσ + 2 x 2σ e − x 2 lΔg ⎧ 2l ⎫ ΔGc = 2 x 2 ⎨ σ + σ e ⎬ − ( x 2 l)Δg ⎩x ⎭ ΔGc ~ 2 x 2σ e − ( x 2 l)Δg 0 Tm − T ΔGc ~ 2 x σ e − ( x l)Δh f =0 0 Tm 2 2 At eqm. ⎡ 2σ ⎤ e T = T ⎢1 − ⎥ ⎣ lΔh f ⎦ 0 m 45 Monday, November 1, 2010 Melting ⎡ 2σ ⎤ e T = T ⎢1 − ⎥ ⎣ lΔh f ⎦ 0 m 46 Monday, November 1, 2010 Melting, Free Energy and Eqm At equilibrium between the liquid and solid state, the change in free energy is zero This means the enthalpy put into the system perfectly offsets the entropic gain of melting, or that the enthalpy gained from the system perfectly offsets the entropy lost in crystallization ΔG f = ΔH f − TΔS f at equilibrium ΔG f = 0 Tm = ΔH f ΔS f How do we relate this to molecular properties? Monday, November 1, 2010 47 Chemical Structure and Enthalpy We assume enthalpy is related to the force of attraction between chains ΔHm must be related to the difference in the forces of attraction between polymers packed in a regular array in the crystalline domains, and the forces between those chains when randomly intertwined in the melt The forces of attraction between simple hydrocarbons segments found in PE are weak dispersion forces (~0.2 kcal/mol) In contrast, nylon 6 contains amide groups which form hydrogen bonds that are an order of magnitude stronger (~5 kcal/mol) 48 Monday, November 1, 2010 Entropy and Crystallization Recall that enthalpic arguments favor extended chain crystallization, but that polymers simply don’t get there Entropically, the extended chain conformation is disfavored anyway, as it restricts the total number of possible conformations of the chain In the crystalline state, a polymer chain is a single ordered conformation Upon melting the chain escapes the cage of the crystalline lattice and now has the freedom of many more conformations ΔS f = k (ln Ωmelt − ln Ωcryst ) 49 Monday, November 1, 2010 Entropy and side-chain stiffness Bond rotations are sterically hindered and the number of configurations available to the chain becomes limited 50 Monday, November 1, 2010 Why does crystallinity matter in biomaterials? 51 Monday, November 1, 2010 “High-throughput investigation of osteoblast response to polymer crystallinity: influence of nanometer-scale roughness on proliferation” N. R. Washburn, K. M. Yamada, CG. Simon Jr., S.B. Kennedy, E.J. Amis. Biomaterials 2004, 25, 1215-1224 52 Monday, November 1, 2010 “High-throughput investigation of osteoblast response to polymer crystallinity: influence of nanometer-scale roughness on proliferation” N. R. Washburn, K. M. Yamada, CG. Simon Jr., S.B. Kennedy, E.J. Amis. Biomaterials 2004, 25, 1215-1224 53 Monday, November 1, 2010 “High-throughput investigation of osteoblast response to polymer crystallinity: influence of nanometer-scale roughness on proliferation” N. R. Washburn, K. M. Yamada, CG. Simon Jr., S.B. Kennedy, E.J. Amis. Biomaterials 2004, 25, 1215-1224 54 Monday, November 1, 2010 “High-throughput investigation of osteoblast response to polymer crystallinity: influence of nanometer-scale roughness on proliferation” N. R. Washburn, K. M. Yamada, CG. Simon Jr., S.B. Kennedy, E.J. Amis. Biomaterials 2004, 25, 1215-1224 55 Monday, November 1, 2010 Next time • The glass transition temperature, liquid crystalline behavior, and relating these and Tm to biological systems and biomedical applications 56 Monday, November 1, 2010 ...
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