Lecture 8 Polymers and Gels
Variety of polymeric materials Polymer molecule made by repeating of covalently joint units. Many of physical properties of polymers have universal characteristic related to generic properties of long string-like molecules
Variety of polymeric materials Polymers are predominantly based on carbons though often contain other elements in the chain and sometimes don t involve carbon at all.
Stereochemistry of polymers If polymer has more than one type of side groups different arrangement are possible Atactic arrangement involves quenched disorder and therefore prevents crystallization: polymer will form glass at low temperature
Architecture of polymers quenched disorder linear or branched average number of units in the chain: degree of polymerization N or molecular mass M distribution of lengths: polydispersity formed of the same units: homopolymers or several types of units: copolymers quenched disorder copolymers: random, sequenced copolymers (DNA, proteins), block copolymers strictly prescribed sequence leading to self-assembly microphase separation with complex morphologies
Block copolymers in nanotechnology polymers where repeat units come in blocks: can be combination of different polymers, e.g. amorphous (rubbery) and crystalline (hard) microphase separation leads to a zoo of possible structures
Phase diagram of a block copolymer The structures formed depend on the relative length of blocks and compatibility of polymers
Nanopatterning with block copolymers provides cheap way to produce nanostructures, e.g. for magnetic storage
Creating nanodots
Pluronics copolymers for drug delivery Symmetrical hydrophobically associating triblock copolymers, Poly(propylene oxide) and poly(ethylene oxide) CH 3 HO (CH -CH -0) n (CH -CH -O) m (CH -CH -0) n H
Poly(propylen oxide) Pluronics copolymers Central hydrophobic core Folds in aqueous solution CH 3 groups interact by Van der Waals Binds hydrophobic proteins Poly(ethylen oxide) Hydrophilic Soluble in water Protein Hydrogen bonding interaction More PEO in Pluronic, easier to dissolve Moves freely in aqueous solution High entropy low protein adsorption Protein S < 0
Drug encapsulation by Pluronics Form after passing critical micelle concentration (CMC) or critical micelle temperature (CMT) Suspensions can encapsulate drugs Drug Pluronic Aqueous Solution Pluronic Encapsulated Drug Aqueous Solution
Physical state of polymers Liquid: often very viscous with particular viscoelastic properties Glass: very common due to quenched disorder Crystalline: often semi-crystalline: micro crystallites in amorphous matrix Liquid crystalline: can be formed in a case of rigid molecules, e.g. Kevlar
Random walk and polymer chain freely joint chain polymer model equivalent of random work end-to-end distance r N = ai i= 1 mean end-to-end distance r r = a a = a a N N N N i j i j i= 1 j= 1 i= 1 j= 1 N r = Na + ai aj i j 0, as different links are uncorrelated
Entropy of a polymer chain Entropy of a macrostate is related to the number of available microstates (statistical weight): S = k B ln Ω
Entropy of a polymer chain In a case of 1D walk: R = ( N N ) a ; Ω = x + x x N N!! N! + [ ] ln x! = xln x x; ln Ω = N f ln f + (1 f) ln(1 f), f = N N x function has a maximum at f=1/, let s make Taylor expansion around the maximum: dln Ωx 1 d ln Ω ln Ω x = ln Ω x(1 ) + (1 f) + 1 +... df R ln Ωx N ln N( 1 f ) ; ln Ωx Na 3Rx in 3D: ln Ω= ln ΩxΩyΩz Na x ( f ) df f = 1 f = 1 x x x +
Entropy of a polymer chain Configurational entropy of a freely joint polymer chain: Sr () 3kR B + const Na x x Gibbs energy G = T S = 3kT F = r Na B x 3kTR B Na x x
More realistic model: short range correlations realistically, correlation will not disappear for nearest neighbors due to e.g. bond angle ( ) m a a 1 = a cos θ; a a = a cosθ i i i i m the chain will behave as its subunits are effectively longer N r = c = Nb g correlations can be characterized by characteristic ratio C = b a
Excluded volume: Flory s approach Consider a molecule that occupies volume r 3 : segment concentration: c This leads to reduction of entropy: N 3 r kvn B kvn B G = T = T 3 V r Total energy including configurational energy: ktr Na ktvn r B B G = Grep + Gel = + 3 assuming excluded volume v ~ a 3 and minimizing energy: r an 35
Interaction between polymer segments Number of contacts for a polymer molecule: 1 1 N znvc N znv c N N znvc znv c 0 pp = ; ps = (1 ); ss = ss (1 ) z number of neighbors for any polymer segment or solvent molecule The interaction energy: 1 Uint = znvc( ε + ε ε ) + zn( ε + ε ) + N ε 0 pp ss ps ps ss ss ss 1 Uint = kbtχ v N + const; k ( ) 3 BTχ = z ε pp + εss ε ps r The total energy: N Grep + Uint = kbtv(1 χ) + const; 3 r
Interaction between polymer segments The total energy: N Grep + Uint = kbtv(1 χ) + const; 3 r We expect different behavior according to value x: 1. x<1/ polymer chain is expanded (swollen) good solvent behavior. x=1/ repulsive effects are cancelled by attractive effects of polymersolvent interaction. Polymer behaves as ideal random walk: theta condition 3. x>1/ attractive effect prevail, polymer forms a globule e.g. change in temperature could induce coil-globule transition
Polymers grated on a surface The case of polymer densely grafted on the surface: polymer brush with the density of s/a and height h. N h Grep = kbtv = k 3 BTv r Na σ N Grep + U = k Tb(1 χ) ha int B [ σ (1 χ) ] 13 h b N
Gels and gelation Gelation or sol-gel transition - formation of a material with non-zero shear modulus Gels chemical termosetting resins (e.g. epoxy) sol-gel glasses (silane polymerisation) physical via microcrystalline regions via microphase separation
Theory of gelation Gelation occurs when an infinitely size cluster is formed
Gelation theory: Flory-Stockmayer model
Gelation theory: Flory-Stockmayer model Let s suppose that the probability to form a bond is f and number of neighbors is z each monomer in nth generation is bound to f(z-1) monomers in (n+1)th generation. So, number of bonds for a cluster in Nth generation is: N f( z 1) n [ ] f c 1 = z 1