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: G?pferich’s theory for polymer erosion 1-4 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 <x> into the solid polymer: (1) t diff = <x> 2 π/4D H2O D H2O = effective diffusivity of water in polymer See Atkins Phys. Chem p. 770 for derivation Random walk: Mean distance from origi (Atkins 8 ) n traveled by water molecule after time t = <r> = (2D H2O t) 1/2 Mean distance traveled in x direction = <x> = 2(D H2O t diff /π) 1/2 EXPLAIN Number of bonds in depth <x>: (2) n = <x>(bonds/cm 3 ) 1/3 = <x>(N Av ρ/M 0 ) 1/3 N Av = Avogadro’s number ρ = polymer density M 0 = 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 c > = ?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) <t c (n)> = (1/k)Σ[i=1 to n] (1/i) ≈ (1/k)ln (n) = (1/k)[ln <x> + (1/3)ln (N Av ρ/M 0 )] (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 = ε (5) ε ≡ t diff /<t c (n)> = <x> 2 k c π/[4D H2O {ln <x> + (1/3)ln (N Av ρ/M 0 )}] ? note <x> in denominator ln should have same units as ρ, i.e. cm if ρ is in g/cm 3 If <x> 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 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 PLGA erosion from bulk to surface mode: degraded at basic pH (>12)- increased k c , thus decreasing ε << 1 Bulk (normal erosion at pH 7.4): Surface (pH > 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 null 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 9 , (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 CH 3 O ? -(CH -C-O) n CH 3 O - -H 2 O 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 polymers: ? Prepared using AB 2 -type monomers (SLIDE) ? Ring-opening polymerization o Catalysis by stannous octoate (tin 2-ethyl hexanoate, FDA-approved) null Useful for polyesters (PLA, PCL, PGA, and their copolymers) 10 null Polymerization initiates from alcohol co-initiator groups by a coordination-insertion mechanism: Tin(II) 2-ethylhexanoate 11 : (SLIDE) Lecture 2 – Biodegradable Solid Polymers7 of 12 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Proposed mechanisms: (on board) example insertion: null 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 null Multi-alcohol initiators permit synthesis of multi-armed polymers: OH OH HO OH o Living ring-opening polymerization null Coordination-insertion catalysts: e.g. aluminum isopropoxide 10 Provide control over molecular weight and MWD: null 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 e.g. Barrera et al 12-14 : o monomers must be synthesized from scratch o bulky substituents make for highly inefficient ring-opening polymerization 15 ? Network polymerization o Photopolymerization of liquid precursors null E.g. polyanhydrides 16,17 null Allows formation of polymeric solids in situ from liquid precursors ? Useful for dental restorations, bone fixation, tissue engineering null Curable through fiber optics or by shining light through tissue null UV or visible light initiators available Lecture 2 – Biodegradable Solid Polymers10 of 12 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 Benefit of rapid polymerization: network properties can be tuned at the molecular level by copolymerizing monofunctional monomers: cholesterol a vital component of cell membranes; stearic acid a natural fatty acid Lecture 2 – Biodegradable Solid Polymers11 of 12 BEH.462/3.962J Molecular Principles of Biomaterials Spring 2003 References 1. Gopferich, A. & Langer, R. Modeling of Polymer Erosion. Macromolecules 26, 4105-4112 (1993). 2. Gopferich, A. Polymer bulk erosion. Macromolecules 30, 2598-2604 (1997). 3. Gopferich, A. Mechanisms of polymer degradation and erosion. Biomaterials 17, 103-14 (1996). 4. von Burkersroda, F., Schedl, L. & Gopferich, A. Why degradable polymers undergo surface erosion or bulk erosion. Biomaterials 23, 4221-31 (2002). 5. Agrawal, C. M. & Athanasiou, K. A. Technique to control pH in vicinity of biodegrading PLA-PGA implants. J Biomed Mater Res 38, 105-14 (1997). 6. Lu, L., Garcia, C. A. & Mikos, A. G. In vitro degradation of thin poly(DL-lactic-co-glycolic acid) films. J Biomed Mater Res 46, 236-44 (1999). 7. Tsuji, H. & Nakahara, K. Poly(L-lactide). IX. Hydrolysis in acid media. Journal of Applied Polymer Science 86, 186-194 (2002). 8. Atkins, P. The Elements of Physical Chemistry (W.H. Freeman, New York, 1997). 9. Pitt, C. G., Marks, T. A. & Schindler, A. in Controlled Release of Bioactive Materials (ed. Baker, R. W.) 19-43 (Academic Press, New York, 1980). 10. Albertsson, A. C. & Varma, I. K. in Degradable Aliphatic Polyesters 1-40 (2002). 11. Stridsberg, K. M., Ryner, M. & Albertsson, A. C. in Degradable Aliphatic Polyesters 41-65 (2002). 12. Barrera, D. A., Zylstra, E., Lansbury, P. T. & Langer, R. Synthesis and RGD peptide modification of a new biodegradable copolymer: poly(lactic acid-co-lysine). J. Am. Chem. Soc. 115, 11010-11011 (1993). 13. Barrera, D. A., Zylstra, E., Lansbury, P. T. & Langer, R. Copolymerization and degradation of poly(lactic acid-co- lysine). Macromolecules 28, 425-432 (1995). 14. Cook, A. D. et al. Characterization and development of RGD-peptide-modified poly(lactic acid-co-lysine) as an interactive, resorbable biomaterial. J Biomed Mater Res 35, 513-23 (1997). 15. Ivin, K. J. Ring-opening polymerization (Elsevier, London, 1984). 16. Burkoth, A. K. & Anseth, K. S. A review of photocrosslinked polyanhydrides: in situ forming degradable networks. Biomaterials 21, 2395-404 (2000). 17. Burkoth, A. K., Burdick, J. & Anseth, K. S. Surface and bulk modifications to photocrosslinked polyanhydrides to control degradation behavior. J Biomed Mater Res 51, 352-9 (2000). Lecture 2 – Biodegradable Solid Polymers12 of 12