BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 Lecture 2: Molecular Design and Synthesis of Biomaterials I: Biodegradable Solid Polymeric Materials(continued) hemistry and physical chemistry of degrading polymeric solids for biomaterials Today Theory of polymer erosion Enzymatic degradation of synthetic biomaterials Designing degradable materials Reading A. Gopferich, "Mechanisms of polymer degradation and erosion, Biomaterials 17, 103 (1996) Ratner p. 243-259 Supplementary Reading R.J. Young and P A. Lovell, "Introduction to Polymers, ch. 4 Polymer Structure pp 241 309(crystallization of polymers, Tm, glass transition, etc. Surface vs. Bulk Hydrolysis: GOpferich's theory for polymer erosion4 Biodegradable solids may have differing modes of degradation Surface erosion -degradation from exterior only with little/no water penetration into bulk Bulk erosion- water penetrates entire structure and degrades entire device simultaneously surface erosion bulk-erosion degree of degradation Fig. I. Schematic illustration of the changes a polymer matrix undergoes during surface erosion and bulk erosion. Polymers hydrolyzing by mechanisms ll or Ill can be either surface or bulk eroding Assuming that a polymer is water insoluble(initially) and that hydrolysis is the only mechanism of breakdown, the factors listed above all vary two rates of importance rate of water diffusion into polymer rate of chain cleavage by water ions The balance of these rates determines whether a polymer erodes from the surface in or by simultaneous degradation throughout the materia Comparing velocities of water diffusion and chain cleavage Lecture 2- Biodegradable Solid Polymers1 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Lecture 2: Molecular Design and Synthesis of Biomaterials I: Biodegradable Solid Polymeric Materials (continued) Last time: chemistry and physical chemistry of degrading polymeric solids for biomaterials Today: Theory of polymer erosion Enzymatic degradation of synthetic biomaterials Designing degradable materials Reading: A. Gopferich, “Mechanisms of polymer degradation and erosion,’ Biomaterials 17, 103 (1996) Ratner p. 243-259 Supplementary Reading: R.J. Young and P.A. Lovell, “Introduction to Polymers,” ch. 4 Polymer Structure pp. 241- 309 (crystallization of polymers, Tm, glass transition, etc.) Surface vs. Bulk Hydrolysis: Göpferich’s theory for polymer erosion1-4 Biodegradable solids may have differing modes of degradation: Surface erosion – degradation from exterior only with little/no water penetration into bulk Bulk erosion – water penetrates entire structure and degrades entire device simultaneously Polymers hydrolyzing by mechanisms II or III can be either surface or bulk eroding.5-7 Assuming that a polymer is water insoluble (initially) and that hydrolysis is the only mechanism of breakdown, the factors listed above all vary two rates of importance: rate of water diffusion into polymer rate of chain cleavage by water ions The balance of these rates determines whether a polymer erodes from the surface in or by simultaneous degradation throughout the material: Comparing velocities of water diffusion and chain cleavage: Lecture 2 – Biodegradable Solid Polymers1 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 Accounting for rate of water diffusion Time required for water to diffuse a mean distance into the solid polymer: tdm=2/4D20 DH20=effective diffusivity of water in polymer See Atkins Phys. Chem p 770 for derivatio Random walk Fig. 10. 18 One possible path of a random walk in three dimensions In this general case, the step length is also a random variable Mean distance from origin traveled by water molecule after time t= =(2D:20t)12 Mean distance traveled in x direction =<>= 2(DH2otarl/I) EXPLAIN Number of bonds in depth ( 2)n=(NAvp/Mo) NAv Avogadro's number polymer density Mo= molecular weight of polymer repeat unit Accounting for rate of chain cleavage( k): probability that a bonds breaks in the interval (o, t) (3)p(t)=ke where we have assumed that chain cleavage is a random event following Poisson kinetics k= rate constant for bond hydrolysis Therefore the mean lifetime of a single bond is given by t>=【pd=【edt=1(kt+1e=1 k Time to degrade n bonds is a zero-order waiting time distributed according to a zero-order Erlang distribution (5)=(1/k)∑[=1ton](1/≈(1/k)ln(n) (1/k)[In +(1/3)In(NAvp/Mo) (substituting(2)) Lecture 2-Biodegradable Solid Polymers2 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Accounting for rate of water diffusion: Time required for water to diffuse a mean distance into the solid polymer: (1) tdiff = 2 π/4DH2O DH2O = effective diffusivity of water in polymer See Atkins Phys. Chem p. 770 for derivation Random walk: Mean distance from origi (Atkins8 ) n traveled by water molecule after time t = = (2DH2Ot)1/2 Mean distance traveled in x direction = = 2(DH2Otdiff/π) 1/2 EXPLAIN Number of bonds in depth : (2) n = (bonds/cm3 ) 1/3 = (NAvρ/M0) 1/3 NAv = Avogadro’s number ρ = polymer density M0 = molecular weight of polymer repeat unit Accounting for rate of chain cleavage (k): probability that a bonds breaks in the interval (0,t): (3) p(t) = ke-kt where we have assumed that chain cleavage is a random event following Poisson kinetics k = rate constant for bond hydrolysis Therefore the mean lifetime of a single bond is given by: � � � = �t p(t) dt = �t e-kt dt = -1 (kt + 1)e-kt = 1 (4) 0 0 k 0 k Time to degrade n bonds is a zero-order waiting time distributed according to a zero-order Erlang distribution: (5) = (1/k)Σ[i=1 to n] (1/i) ≈ (1/k)ln (n) = (1/k)[ln + (1/3)ln (NAvρ/M0)] (substituting (2)) Lecture 2 – Biodegradable Solid Polymers2 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 Mechanism(surface vs bulk) is controlled by ratio of time for diffusion to time for hydrolysis, a dimensionless parameter analogous to a Deborah number Erosion number s (5)s=taifl=keT/[4DH20(In +(1/3)In(NAvp/Mo)11 note in denominator In should have same units as p, i.e. cm if p is in g/cm If ex> is replaced by the total thickness of a degrading sample, we can predict the mechanism of erosion: bulk erosion change in erosion mechanism surface erosion surface erosion 10 bulk erosion 30 10 Fig 2. Dependence of the erosion number, s, on the diffusivity of water inside the polymer, D,, the dimensions of a polymer matrix, L, and the polymer bond reactivity, i, calculated from equation 7. The white plane represents the area of surface erosion, the gray one the area of bulk erosion Lecture 2- Biodegradable Solid Polymers3 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Mechanism (surface vs. bulk) is controlled by ratio of time for diffusion to time for hydrolysis, a dimensionless parameter analogous to a Deborah number: Erosion number = ε (5) ε ≡ tdiff/ = 2 kcπ/[4DH2O{ln + (1/3)ln (NAvρ/M0)}] • note in denominator ln should have same units as ρ, i.e. cm if ρ is in g/cm3 If is replaced by the total thickness of a degrading sample, we can predict the mechanism of erosion: ε > 1 bulk erosion ε = 1 change in erosion mechanism ε < 1 surface erosion Lecture 2 – Biodegradable Solid Polymers3 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 mass loss is linear for surface-eroding Table I Estimated values of s and Lentical for selected degradable polymers Chemical structure i(s") Poly(anhydrides) 1.9×10-3Ref.30 75 um C-O-C 64×10-3Ref.0 04 mt Polyfortho esters 48×10Ref:3 0.6mm =0-R 27×108Rer,130l O-R Poly( caprolactone) 97×10Re.3 H Poly(z-hydroxy-esters) 66x·10Ref.3ol 40x10- Poly(amides) 2.6×1013Ref.t3l 1.5x10 13.4m For a lcm thick device. D=10-'cm's"(estimated from Ref [32) and InVM/NA(N =-16.5. D= estimated from Ref. 3 2D) and in/VM/NA(N-19[--165 surface bulk eroding polyacetals oolyketals polyesters polyan. poly(ortho- hydrides esters) polyure polyamide 102 10 10 Fig 3. Critical thickness, Leritical, that a polymer device has to exceed to undergo surface erosion (calculated from Eq (7). data shown in Lecture 2- Biodegradable Solid Polymers of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 • mass loss is linear for surface-eroding devices only “surface eroding” “bulk eroding” Lecture 2 – Biodegradable Solid Polymers4 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 Experimental demonstration of theory: Transition of pl ga erosion from bulk to surface mode degraded at basic pH (12)-increased kc, thus decreasing s 12) Erosion profiles of poly( a-hydroxy esters)at PH 7.4:(a) lh() and PLAs017(-),(b)PLA2sGAs沿h(◆).PAs (·) and PLA2GAs47h(■) 2p8P21 SEM shown previously(Fig. 13)confirms transition to surface mode Synthesizing biodegradable macromolecules to tailor properties Approaches to molecular design o Control polymer hydrophobicity -> degradation rate o Control concentration of reactive groups o Alter biocompatibility What are the degradation products? Acidity/basicity? Toxicity? Biological effects? Lecture 2-Biodegradable Solid Polymers5 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Experimental demonstration of theory: Transition of PLGA erosion from bulk to surface mode: degraded at basic pH (>12)- increased kc, thus decreasing ε 12): SEM shown previously (Fig. 13) confirms transition to surface mode Synthesizing biodegradable macromolecules to tailor properties Approaches to molecular design • Copolymerization o Control polymer hydrophobicity -> degradation rate o Control concentration of reactive groups o Alter biocompatibility What are the degradation products? Acidity/basicity? Toxicity? Biological effects? Lecture 2 – Biodegradable Solid Polymers5 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 o Vary Tm, Tg,(mechanical properties) (SLIDE) 练 HANTION Table 3. Properties of poly( CLco-DXO) Poly(VL co DXO), and poly(LLA..DXO) N DXO in copolymer I. DSQ IC] Im(Iso[C] 56.8 -55.5 VDO -599 60705 D10 111 PIGURE 2. variation of gI 83.8 tion temperature (Tg) Polymer36,1009(1995) Reactions on polymers/Polymer functionalization Controlling Molecular Architecture Ve wont undertake an exhaustive description, but some of the important methods to be aware of Condensation polymerization o Not very efficient, produces low molecular weight polymers(usually s 10K g/mole) HO-CI cha e HO Lecture 2-Biodegradable Solid Polymers6 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Vary Tm, Tg9 , (mechanical properties) (SLIDE) Polymer 36, 1009 (1995) • Reactions on polymers/Polymer functionalization Controlling Molecular Architecture We won’t undertake an exhaustive description, but some of the important methods to be aware of: • Condensation polymerization o Not very efficient, produces low molecular weight polymers (usually ≤ 10K g/mole) HO-CH-C-OH CH3 O ∆ -(CH -C-O) n CH3 O - -H2O Lecture 2 – Biodegradable Solid Polymers6 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 o Has been found useful for growing dendritic polyme Prepared using AB2-type monomers (SLIDE) H CHOH CHOH scheme 22. a) The dit Ring-opening polymerization o Catalysis by stannous octoate(tin 2-ethyl hexanoate, FDA-approved Useful for polyesters(PLA, PCL, PGA, and their copolymers )To (SLIDE) Tin(U)2-ethylhexanoateT1 Lecture 2-Biodegradable Solid Polymers7 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 o Has been found useful for growing dendritic polymers: • Prepared using AB2-type monomers (SLIDE) • Ring-opening polymerization o Catalysis by stannous octoate (tin 2-ethyl hexanoate, FDA-approved) Useful for polyesters (PLA, PCL, PGA, and their copolymers)10 Polymerization initiates from alcohol co-initiator groups by a coordination-insertion mechanism: Tin(II) 2-ethylhexanoate11: (SLIDE) Lecture 2 – Biodegradable Solid Polymers7 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 Proposed mechanisms:(on board) insertion a) snoc:.R-OH+ Hc-C O-CH2 CH H Caprolactone snot,120°c E) 570c:+R-OH Oc5n-oR+=C 0-CH-CH ofC CH, CH CH2 CH-CH2 o) me& The main ROP mechanism proposals with sa(oct) as catat, a) compleat H a monomer and akohol prior tD ROP and b) formation of a tim-alloride before ROP of sheme 17. a Methacryloyl amo-hndroryl-poly(e-caprolactone)macromonom For lactide and glycolide, each ring monomer opens to 2 lactic acid/glycolic acid moieties lg. 8. The chemical structure of glycolide and the resulting repeating unit A variety of similar catalysts can be used to polymerize lactone ring monomers: ( SLIDEJ ladle 1. Structure and designation at vanous lactones Y-butyrolacto B-BL VL P-CL 1.5-dioxepan -2 DXO Lecture 2-Biodegradable Solid Polymers8 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Proposed mechanisms: (on board) example insertion: For lactide and glycolide, each ring monomer opens to 2 lactic acid/glycolic acid moieties: A variety of similar catalysts can be used to polymerize lactone ring monomers: (SLIDE) Lecture 2 – Biodegradable Solid Polymers8 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 Multi-alcohol initiators permit synthesis of multi-armed polymers HO OH o Living ring-opening polymerization Coordination- insertion catalysts: e.g. aluminum isopropoxide Provide control over molecular weight and MWD 20000 13 15000 Liing chain end dEad end goup 5000 arnwersicn[9 FIg. 2. The influence of L-LA mon n on the number- menage molecular cheme 15. Aluminum isopropoxide initiated polymerization of 1, 5dinxepan--one miil(O)and the MWD().Aolym anomer-toinitiator ratio of 100: 1 Allows the synthesis of block copolymers Hg.5. A schemati Presentation of an AHA tri-block copolymer with two A blocks (gray circles with dark centers)and one B-block(gray circles with light centers) Monomers polymerized sequentially, when block A is formed, monomer B is injected, etc pendant peptide groups Lecture 2-Biodegradable Solid Polymers 9 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Multi-alcohol initiators permit synthesis of multi-armed polymers: OH HO OH OH o Living ring-opening polymerization Coordination-insertion catalysts: e.g. aluminum isopropoxide10 Provide control over molecular weight and MWD: Allows the synthesis of block copolymers: • Monomers polymerized sequentially, when block A is formed, monomer B is injected, etc. pendant peptide groups Lecture 2 – Biodegradable Solid Polymers9 of 12
BEH.462/3. 962J Molecular Principles of Biomaterials Spring 2003 Copolymerization of ring peptides with biodegradable monomers Scheme 2, Synthesis of Poly(L-lactie acid-co-L-lysine) e t s At and Protected e-lysinmer Stannous octoate cH一 CaN-C.C CHAiN 人 HCla. " fus PoCh SEtH, NEt, I t, 5 daya ·cHcN arrera et a 12-14 Poly (L-Lactic Acid- co-L Lysine) o monomers must be synthesized from scratch o bulky substituents make for highly inefficient ring-opening polymerization Table 2. Effect of the Concentration of 5 on Polymerizations Conducted at 136C for 48 h Using a Catalyst to Monomer Ratio of 1/1000a mole%5° 00 8513200022300061.61694 5326711450036700575155.3° 2300055.8152.8F 201230015000524none a All the molecular weight data were obtained on protected polymers. Determined by H NMR. Incorporated of 10 mol% 5 actually yields only 5 mol lysine since each molecule of 5 contains one lysine residue and one lactic acid residue. Indicates 2 or more melting endotherms Network polymerization copolymerization of liquid pi Allows formation of polymeric solids in situ from liquid precursors Curable through fiber optics or by shining light through tissue gineering Useful for dental restorations bone fixation tissue en UV or visible light initiators available Lecture 2- Biodegradable Solid Poly mers10 of 12
BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 • Copolymerization of ring peptides with biodegradable monomers e.g. Barrera et al12-14 : o monomers must be synthesized from scratch o bulky substituents make for highly inefficient ring-opening polymerization15 • Network polymerization o Photopolymerization of liquid precursors E.g. polyanhydrides16,17 Allows formation of polymeric solids in situ from liquid precursors • Useful for dental restorations, bone fixation, tissue engineering Curable through fiber optics or by shining light through tissue UV or visible light initiators available Lecture 2 – Biodegradable Solid Polymers10 of 12