DOC PREVIEW
MIT 3 052 - ELASTICITY OF SINGLE POLYMER CHAINS

This preview shows page 1-2-3 out of 8 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 8 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 8 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 8 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 8 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

REVIEW : LECTURE 18 NANOMECHANICS AND BIOCOMPATIBILITY : PROTEIN-BIOMATERIAL INTERACTIONS 2SUMMARY : THEORETICAL MODELS FOR SINGLE POLYMER CHAIN ELASTICITYVARIOUS MATHEMATICAL FORMS FOR THE (INEXTENSIBLE) FREELY JOINTED CHAIN (FJC) MODELCOMPARISON OF VARIOUS MATHEMATICAL FORMS FOR THE INEXTENSIBLE FREELY JOINTED CHAIN (FJC) MODELEXTENSIBLE FREELY JOINTED CHAIN (FJC) MODELWORM LIKE CHAIN (WLC) MODEL(*Kratky-Porod Model)APPENDIX : THEORETICAL MODELS FOR THE ELASTICITY OF SINGLE POLYMERCHAINS : FULL CITATIONS OF ORIGINAL REFERENCES3.052 Nanomechanics of Materials and Biomaterials Thursday 04/26/07 Prof. C. Ortiz, MIT-DMSEILECTURE 19: ELASTICITY OF SINGLE POLYMER CHAINS :THEORETICAL FORMULATIONSOutline :REVIEW LECTURE #18 : NANOMECHANICS AND BIOCOMPATIBILITY 2............................................2SUMMARY : THEORETICAL MODELS FOR SINGLE POLYMER ELASTICITY.......................................3VARIOUS MATHEMATICAL FORMS FOR THE INEXTENSIBLE FREELY JOINTED CHAIN (FJC).........4 Graphical Comparison...................................................................................................................5 EXTENSIBLE FJC.....................................................................................................................................6 WORM LIKE CHAIN (WLC) MODEL..........................................................................................................7APPENDIX : FULL CITATIONS..................................................................................................................8 Objectives: To understand the theoretical formulations of single macromolecule elasticityReadings: Course Reader Document 31, CR Documents 32-39 are the original theoretical papers for reference, English translations of CR 33 and 36 are available on Stellar Multimedia : Podcast : Elasticity of fibronectin; Abu-Lail, et al. Matrix Biology 2006 25 17513.052 Nanomechanics of Materials and Biomaterials Thursday 04/26/07 Prof. C. Ortiz, MIT-DMSEREVIEW : LECTURE 18 NANOMECHANICS AND BIOCOMPATIBILITY : PROTEIN-BIOMATERIAL INTERACTIONS 2-Two examples of biomaterials : vascular graft and endotracheal tube (materials, design issues, relation to nanomechanics)-Kinetics of protein adsorption; contributions to diffusion; ideal and activated (Szleifer model-CR 29,30); initial and secondary stage of protein adsorption-Modes of protein adsorption : (I.) adsorption of proteins to the top boundary of the polymer brush (II.) localcompression of the polymer brush by a strongly adsorbed protein (III.) protein interpenetration into the brush followed bythe non-covalent complexation of the protein and polymer chain (IV.) adsorption of proteins to the underlying biomaterialsurface via interpenetration with little disturbance of the polymer brush-Use of steric repulsion (conformational entropy) to inhibit protein adsorption (Halperin model for polymer brushes-posted on stellar- Polymer brush is a layer of polymers attached with one end to a surface whereby the distance between neighboring chains, s<Rg where Rg is the radius of gyration of an isolated chain; this condition causes extension of the chains away from the surface)(Halperin, Langmuir 1999) For a protein interacting with a planar surface : eff bare brush= +U (z) U (z) U (z)U*=activation barrier determining rate of primary adsorptionkads= adsorption rate constantKramers rate theory: ads- *expkT� ��� �� �0U DkαLD= diffusion constant= width of barrier at U*-kTLo= uncompressed height of polymer brush-Polyethylene oxide (PEO, PEG) - hydrophilic and water-soluble at RT, forms an extensive H-bonding network; intramolecular H-bond bridges between -O- groups and HOH→ large excluded volume, locally (7/2) helical supramolecular structure (tgt axial repeat = 0.278 nm), high flexibility, molecular mobility, low van der Waals attraction, neutral. However: poor mechanical stability,protein adhesion reported under certain conditions (long implant times), maintains some hydrophobic character.23.052 Nanomechanics of Materials and Biomaterials Thursday 04/26/07 Prof. C. Ortiz, MIT-DMSESUMMARY : THEORETICAL MODELS FOR SINGLE POLYMER CHAIN ELASTICITY 33.052 Nanomechanics of Materials and Biomaterials Thursday 04/26/07 Prof. C. Ortiz, MIT-DMSEVARIOUS MATHEMATICAL FORMS FOR THE (INEXTENSIBLE) FREELY JOINTED CHAIN (FJC) MODEL( )B B2contourBB-13k T 3k T=na aL1 aAnalytical Formula : ) = na coth x - where : x = (2)x k Tk TLangevin Expansion : = (3)a= Inverse Lange� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �� �=� �� �f(r) r = r (1)fr(ff(r)nabbGaussian :Non - Gaussian :rL3 5 7-1Bcontourvin Function9 297 1539= 3 ...5 na 175 na 875 naHigh Stretch Approximation : k T= 1- (4)a L� � � � � �� � � � � � � �+ + + +� � � � � �� � � � � � � �� � � � � �� � � � � � � �� � � � � �� �� �� �� �� �� �narf(r)r r r r-entropic elasticity; chain wants to maximum # of conformations (random coil), when stretched;links rotate to uncoil, align, extend, polymer chain along stretching axis# available conformations ↓disorder and entropy ↓restoring force driving back to random coil↑assume no enthalpy change (no stretching of backbone bonds)Two molecular level parameters (can be used as fitting parameters) :a= statistical segment length (local chain stiffness)n= number of statistical segmentsLcontour = na= fully extended length of polymer chain43.052 Nanomechanics of Materials and Biomaterials Thursday 04/26/07 Prof. C. Ortiz, MIT-DMSECOMPARISON OF VARIOUS MATHEMATICAL FORMS FOR THE INEXTENSIBLE FREELY JOINTED CHAIN (FJC) MODELSurface separation distance, D= r, chain end-to-end distance; sign convention (-) for attractive back force, however some scientists plot as (+); e.g. Zauscher (podcast)(1) Gaussian physically unrealistic; force continues to increase forever beyond Lcontour, valid for r<1/3 Lcontour(3) Langevin Series Expansion; finite force beyond Lcontour (physically unrealistic); valid for r<3/4 Lcontour(4) High stretch approximation underestimates force for r<3/4Lcontour, valid for r>3/4Lcontour53.052 Nanomechanics of Materials and Biomaterials Thursday 04/26/07


View Full Document

MIT 3 052 - ELASTICITY OF SINGLE POLYMER CHAINS

Documents in this Course
SURFACES

SURFACES

30 pages

Load more
Download ELASTICITY OF SINGLE POLYMER CHAINS
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view ELASTICITY OF SINGLE POLYMER CHAINS and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view ELASTICITY OF SINGLE POLYMER CHAINS 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?