‘Tracer diffusion in confined media’

APOSTOLOS VAGIAS

Stuttgart, 24th November 2011

Max Planck Institute for Polymer Research, Mainz

Department of Materials Science and Technology, University of

Crete, Greece

Institute of Electronic Structure and Laser (IESL), Greece

The logo of the University of Crete is designed by Ms. Aspasia Papadoperaki (The figure is originally reported in: http://www.uoc.gr) The copyright holder of the F.O.R.T.H. emblem, is F.O.R.T.H. (2007).All rights reserved.

The copyright holder of the M.P.I.P. emblem, is Mr. Jürgen Worm: Max Planck institute for Polymers, Mainz

A few words about me… • Born in Athens, Hellas

• Hellenic, German, English, Italian

• Sept. 2002-May 2007: M.Sc. Chemical Engineering (National Technical University of Athens!)

• September 2007-February 2010: M.Sc. Chemical Engineering University of Minneapolis, Minnesota, Twin Cities (-35°C!) –publications submitted/under submission (advisors: H. Ted Davis, Alon McCormick, Yiannis Kaznessis)

• September 2010-now:PhD student at the MPIP-Mainz (Profs: George Fytas, Hans-Jürgen Butt; Project leader: Dr. Kaloian Koynov)!

Copyright holder of the logo of N.T.U.A: 2009 National Technical University of Athens (The figure is originally reported in: http:www.ntua.gr) The figure of the N.T.U.A historic building, is originally reported in: http://www. http://www.arch.ntua.gr/studies/studies.htm

PREVIEW

• Objectives

• Definition of a nanostructured environment

• Importance of our study

• FCS-the technique

• Examples of environments and tracer molecules; structures and features

• Results & outlook

• Acknowledgements

OPENING

• Motivation: 1. How does the penetrant’s mobility get affected

as R →ξ (increasing ‘frustration’)? By penetrant’s shape? Temperature?

2. Why is this study important? • Objectives: • a. To present FCS & examples of nanostructured

environments examined. • b. To demonstrate how changes in chemistry can

affect the penetrants’ mobility.

NANOSTRUCTURED ENVIRONMENTS..

• A bicontinuous porous environment-the pores are interconnected.

• P.H. Hermans (1949) about ‘gels’: ‘…The gels exhibit mechanical properties, characteristic of the solid-like phase...Both the dispersed and the continuous phase extend continuously throughout the whole system…’

Macroporous: >50 [nm]

Mesoporous:

2-50 [nm]

Microporous: <2 [nm]

WHY THESE MEDIA ARE IMPORTANT?

Tissue engineering

Optimal mechanical properties

i.e. cartilage (Jin R. et al., 2010)

Separation membranes

Selectivity between molecules

(Huang R. et al., 2009)

Drug delivery of pharmaceuticals

Controlled kinetics of drug release

(Peppas N.A. et al. 2006)

Biosensors

Specific binding

(Vaisocherova et al., 2008)

Jin, R.; Teixeira, L. S. M.; Krouwels, A.; Dijkstra, P. J.; van Blitterswijk, C. A.; Karperien, M.; Feijen, J., Synthesis and characterization of hyaluronic acid-poly(ethylene glycol) hydrogels via Michael addition: An injectable biomaterial for cartilage repair. Acta Biomater. 2010, 6 (6), 1968-1977.

Huang, R.; Kostanski, L. K.; Filipe, C. D. M.; Ghosh, R., Environment-responsive hydrogel-based ultrafiltration membranes for protein bioseparation. J. Membr. Sci. 2009, 336 (1-2), 42-49. Peppas, N. A.; Serra, L.; Domenech, J., Drug transport mechanisms and release kinetics from molecularly designed poly(acrylic acid-/i g/-ethylene glycol) hydrogels. Biomaterials 2006, 27

(31), 5440-5451. Vaisocherova H.; Yang W.; Zhang Z.; Cao Z.Q.; Cheng G.; Piliarik M.; Homola J.; Jiang S. Y., Ultralow fouling and functionalizable surface chemistry based on a zwitterionic polymer enabling

sensitive and specific protein detection in undiluted blood plasma. Anal. Chem. 2008, 80 (20), 7804-7901

Importance of penetrant dynamics’ studies →mapping of the confined environment

HOW DOES FCS WORK?

,)(

)()()(

2tF

tFtFG

1 1/ 2

* 2

1( ) 1 1 1

D D

GN S

S=zo/ro

t4

t2

t3

F(t

) <

kH

z>

F(t) [k

Hz]

Time [s]

F(t) [k

Hz]

Time [s]

t5

t1

t2

t3

t4

t5

t1

1E-5 1E-4 1E-3 0.010.0

0.2

0.4

0.6

0.8

1.0

1.2 Autocorrelation curve G(t)

G(t

)

Time (s)

tracer molecule

From the fit: τD & local concentration

WHY FCS? -ADVANTAGES

• Very sensitive-Single molecule detection (~1 nM)

• Very specific –only to fluorescent molecules

• Small observation volume (<1 μm³): local mobility measurements

• Mobility (diffusion and flow velocity) of different tracers can be studied simultaneously, over a broad range

THE CONFINED MEDIA..

Well-defined systems

i-Opals (Inorganic porous matrix)

Tetra-PEG (Hydrogel)

Aqueous PEO solutions

Hierarchical system

PNIPAAm (Hydrogel grafted

on glass)

WELL-DEFINED SYSTEM: INVERSE OPALS

• I-opals: Inorganic bicontinuous porous nanostructure (Li Q. et al.)

• Formation: Codeposition of colloidal PS & Silica nanoparticles (Li Q. et al.)

• Technique: Vertical lifting deposition (20°C, 50% RH, 400 nm/sec) on (pre-cleaned with plasma) glass slides.

Li, Q.; Retsch, M.; Wang, J.; Knoll, W.; Jonas, U., Porous Networks Through Colloidal Templates. In Templates in Chemistry III, Broekmann, P.; Dötz, K.-H.; Schalley, C., Eds. Springer Berlin / Heidelberg: 2009; Vol. 287, pp 135-180.

All the original figures of i-Opals and Diagrams of slowdown and G(t) vs t functions, have been originally reported by: Raccis, R.; Nikoubashman, A.; Retsch, M.; Jonas, U.; Koynov, K.; Butt, H.-J. r.; Likos, C. N.; Fytas, G., Confined Diffusion in Periodic Porous Nanostructures. ACS Nano 2011

DYNAMICS IN i-OPALS

• Tracers:Alexa647, Q- Dots (525,545,585)

• Study in aqueous buffer solution

All the original figures of i-Opals and Diagrams of slowdown and G(t) vs t functions, have been originally reported by: Raccis, R.; Nikoubashman, A.; Retsch, M.; Jonas, U.; Koynov, K.; Butt, H.-J. r.; Likos, C. N.; Fytas, G., Confined Diffusion in Periodic Porous Nanostructures. ACS Nano 2011

WELL-DEFINED SYSTEMS:TETRA-PEG

Tetra-Polyethylene-Glycol Hydrogel (Tetra-PEG)

Synthesized and mechanically characterized by Shibayama M. et al.

1. Minor presence of defects (i.e. entanglements and/or dangling chains)

2. Very high yield stress -Excellent mechanical abilities

3.Mesh size: defined by the overlapping chains (>30 [A°], as-prepared state)

Original figure of Tetra-PEG repeat unit reported by: Matsunaga, T.; Sakai, T.; Akagi, Y.; Chung, U.-i.; Shibayama, M., SANS and SLS Studies on Tetra-Arm PEG Gels in As-Prepared and Swollen States. Macromolecules 2009, 42 (16), 6245-6252.

Sakai, T.; Matsunaga, T.; Yamamoto, Y.; Ito, C.; Yoshida, R.; Suzuki, S.; Sasaki, N.; Shibayama, M.; Chung, U.-i., Design and Fabrication of a High-Strength Hydrogel with Ideally Homogeneous Network Structure from Tetrahedron-like Macromonomers. Macromolecules 2008, 41 (14), 5379-5384.

ALEXA 647 IN TETRA-PEG OF THREE DIFFERENT MWs (10k, 20k,40k): RESULTS

0 50 100 150 200 250 300 350 400

0.7

0.8

0.9

1.0

1.1

1.2

1.3

normalized_intensity_z-scans

norm

aliz

ed inte

nsity (

in g

el over

free s

olu

tio

n)

Z-distance from gel (µm)

10k

20k

40k

1E-5 1E-4 1E-3 0.01

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Gel_vs_free_solution G

(t)

Time (s)

free_solution

40k

20k

10k

gel

solution

Increasing slowdown

DIFFUSION IN Tetra-PEG

y = 2.7293e2.4472x

R² = 0.9896

1

10

100

1000

0 0.5 1 1.5 2

Diffusion slowdownζ (ζ=Do/D)

α' (α' = 2*R/ξ')

QD525/PEG 10k

A647/PEG 10k;PEG 20k; PEG 40kQD525/PEG 20k

QD525/PEG 40k

QD585/PEG 20k

QD585/PEG 40k

QD545/PEG 40k

𝜁 =𝐷_𝑜

𝐷= 1.1209 ∙ 𝑒2.6879∙𝛼′

; 𝑅2 = 0.9823 y = 2.7293e2.4472x

R² = 0.9896

1

10

100

1000

0 1 2 3 4

Diffusion slowdown ζ

(ζ=Do/D)

α* (α* = 2*R/ξ*)

A647/PEG10k;PEG 20k;PEG40kQD525/PEG 40k

QD525/PEG 20k

QD525/PEG 10k

QD545/PEG 40k

QD585/PEG 40k

QD585/PEG 20k

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

1 2 3 4 5 6 7

Permeability coefficient , (P)

Position

10k;QD525

20k;QD525

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4

Permeability coefficient, (P)

Position

40k;QD525

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

1 2 3 4 5 6 7

Permeability coefficient , (P)

Position

10k;QD525

20k;QD525

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4

Permeability coefficient, (P)

Position

40k;QD525

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0.01

0.1

1

D/D

0

c (g/ml)

QD525 (RH= 5.3nm) in PEO (Mw: g/mol)

QD525 (RH=5.3nm) in PEO (Mw:g/mol)

QD525 (RH=5.3nm) in PEO (Mw:g/mol)

lexa (RH=0.78 nm) in Tetra-PEG 10k,20k,40k

QD525 (RH=5.3nm) in Tetra-PEG 10k,20k,40k

DIFFUSION IN PEO SOLUTIONS

T. Cherdhirankorn, A.Best, K. Koynov, K.Peneva, K. Müllen, G. Fytas in 'Diffusion in Polymer Solutions studied by Fluorescence Correlation Spectroscopy', J. Phys. Chem. B, 2009, 113 (11), pp 3355–3359

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0.01

0.1

1

D/D

0

c (g/ml)

Small tracers: 1-2 [nm]

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0.01

0.1

1

D/D

0

c (g/ml)10

-710

-610

-510

-410

-310

-210

-110

0

0.01

0.1

1

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

0.01

0.1

1

D/D

0

c (g/ml)

Equat i on

y = I nt er cept + B1*x

^1 + B2*x^2 + B3*x^3

+ B4*x^4 + B5*x^5

Wei ght No Wei ght i ng

Resi dual Sum of

Squar es

0. 00771

Adj . R- Squar e 0. 996

Val ue St andar d Er r or

( D/ Do) I nt er cept - 3. 11598 0. 49895

( D/ Do) B1 - 4. 56009 2. 62762

( D/ Do) B2 - 4. 73025 4. 8505

( D/ Do) B3 - 2. 7073 4. 00694

( D/ Do) B4 - 0. 66892 1. 51593

( D/ Do) B5 - 0. 05154 0. 21372

circles: QD525 (RH= 5.3nm) in PEO (Mw: g/mol)

triangles: PS beads (RH= 14nm) in PEO (Mw: g/mol)

QD525 (RH=5.3nm) in PEO (Mw:g/mol)

circles:QD525 (RH=5.3nm) in PEO (Mw:g/mol)

squares:QD545 (RH=6.35nm) in PEO (Mw:g/mol)

triangles:PS beads (RH=14nm) in PEO (Mw:20400 g/mol)

lexa (RH=0.78 nm) in Tetra-PEG 10k,20k,40k

QD525 (RH=5.3nm) in Tetra-PEG 10k,20k,40k

‘ADDED ELECTROLYTE’ EFFECT

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

0.01

0.1

1

D/D

0

c (g/ml)

DYNAMICS IN THE DIFFERENT MEDIA

1E-5 1E-4 1E-3 0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

G'(t)

Time (sec)

10k

20k

40k

no gel

QD525_in_Tetra-PEG_10k_20k_40k

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

QD525_in_3c*_at_different Mw of PEO

G'(t)

Time (s)

Mw_PEO:102,000 g/mol

Mw_PEO: 20,400 g/mol

Mw_PEO:481,000 g/mol

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

G'(t)

Time (s)

15c*

6c*

3c*

0.5c*

QD525_in_PEO (Mw=481,000 g/mol) AQUEOUS SOLUTION

Tetra-PEG

PEO Solutions

PNIPAAm ON GLASS

Sample preparation:

1.Slide functionalization (benzophenone/silane solution)

2. 50 [°C] in vacuum ,1 hour

3.Spin coating (1000 rpm, 60 sec)

4.Drying overnight (50 [°C] in vacuum ,8 hours)

5. Annealing (170 [°C], in vacuum, 1 hour)

6. UV-crosslinking for different irradiation times

(energy dose, 6.28 *J/cm²+ →1 hour)

Mesh size: 3-50 [A°]

The original photo of the molecular structure of Alexa 488 structure ,is reported by Invitrogen: http://www.invitrogen.com/ Orginal source of PNIPAAm structural repeat unit, hydrogel drawings and Alexa 647: Riccardo Raccis, ‘Characterization of Structure and Dynamics of Submicrometric Systems via

Fluorescence Correlation Spectroscopy’, PhD Thesis, University of Mainz, Physics Department, November 2010

T<LCST T> LCST

Repeat unit of PNIPAAm, Mw: 260 kg/mol Anionic charge, PDI:2.7

Lower Critical Solution Temperature in water:32 [°C]

Alexa 488, MW: 880 g/mol Alexa 647, MW: 1250 g/mol, weakly anionic

PNIPAAm IN AQUEOUS SOLUTIONS

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

G(t

)

Time(s)

10c*

2c*

4c*

6c*

8c*

stretched exponent decreases:

down to ~0.7

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

G'(t)

Time (s)

x1_y1

x2_y2

x3_y3

A647

8c*

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

G'(t)

Time (s)

x1_y1

x2_y2

x3_y3

A647

c*

SIMULTANEOUS DIFFUSION OF A488 and A647 IN GRAFTED PNIPAAm:

RESULTS

• T=16 [°C] to T>LCST

• Difference in dynamic behavior:

• a. between tracers

• b. at different T

-10 -5 0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

110

120

15'_UV-irradiated_& annealed_PNIPAAm

Count

rate

(kH

z)

Z-position (m)

A647

A488

1E-5 1E-4 1E-3 0.01 0.1 1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

15'_UV-irradiated & annealed_PNIPAAmG

'(t)

Time (s)

A647-outside

A488-outside

A488-gel

A647-gel

Glass

Gel

Water

Increasing slowdown

DYNAMICS IN PNIPAAm

1E-5 1E-4 1E-3 0.01 0.1 1

0.0

0.2

0.4

0.6

0.8

1.0

G'(t)

Time (s)

16C

20C

25C

29C

32C

35C

A488_60'_irradiated_different_T

1E-5 1E-4 1E-3 0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

G'(t)

time (sec)

A488

A647

30'_irradiated

1E-5 1E-4 1E-3 0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

G'(t)

time (sec)

A647

A488

A647_free

A488_free

60'_irradiated

1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

G(t

)

Time(s)

10c*

2c*

4c*

6c*

8c*

stretched exponent decreases:

down to ~0.7

CONCLUSION- OUTLOOK

• i-Opals: non-Fickian slowdown only in most ‘frustrated’ particle and most ‘confined’ environment.

• PEO solutions & Tetra-PEG: Q-Dots do not follow small tracer slowdown; [D/Do]=[D/Do](ξ)-for PEO physical networks and Tetra-PEG.

• PNIPAAm grafted on glass: A488 interacts with the gel (A647 does not); Temperature effect on the dynamics.

Still, interested to examine the effect in tracer’s mobility of: • Simultaneous transport (Flow) and Diffusion? • Other network systems? • Different Polydispersity index of PNIPAAm? • Opportunity to experience other techniques (SPR-EDLS, NMR, EPR).

ACKNOWLEDGEMENTS • DFG SPP 1259 ‘ Intelligente Hydrogele’ • Prof. Dr. Christian Holm • Dr. Peter Kosovan • Deutsche Forschungsgemeinschaft DFG (Funding source) • Max Planck Institute für Polymerforschung (MPIP) • Department of Materials Science and Technology, University of Crete • F.O.R.T.H., Heraklion, Greece • Professor Dr. George Fytas • Professor Dr. Hans- Jürgen Butt-Director of Polymer Physics in MPIP • Dr. Kaloian Koynov-Max Planck Institute for Polymer Research, Mainz, Germany • Professor Mitsuhiro Shibayama group (University of Tokyo, Japan) • Dr. Riccardo Raccis • Mr. Andreas Best

• MY FAMILY (for everything!) • To anyone not included in the list and….TO THE WHOLE AK BUTT (!)

THANK YOU!

WHAT IS A GEL?

• T. Tanaka (1987):’…Gel is a cross-linked polymer network, swollen in a liquid medium. The gel’s properties depend on the interactions between network and liquid medium…’

• P.H. Hermans (1949): ‘…The gels exhibit mechanical properties, characteristic of the solid-like phase...Both the dispersed and the continuous phase extend continuously throughout the whole system…’

• Phase transitions in gels: De Gennes P. G. (1972), Lifshitz M.(1978)

Hermans P. H., Gels. In ‘Colloid Science’, Vol.2, ed. H. R. Kruyt. Elsevier Publishing Company, Inc., Amsterdam, The Netherlands 1949, pp.483-651

Original figure of reversible swelling of hydrogels (left) belongs to Patrick Beines .The figure is originally reported in Robert Roskamp’s PhD Thesis: ‘Functional Hydrogels’, University of Mainz, Chemistry Department, July 2009

Tanaka T., Gels.In 'Encyclopedia of Polymer Science and Engineering', Vol.7, Ed. A.Klingsberg & A.Piccininni. John Wiley & Sons, New York, 1987, p.514

DIFFERENCE OF GELS FROM POLYMER SOLUTIONS

According to Clark A.H. & Ross-Murphy S.B. (1987):

Clark A.H., Ross-Murphy S.B. Advancements in Polymer Science 1987, Vol. 83, p.57 Original figure for non-entangled & entangled solutions and mesh size, reported by : ‘Gianneli M. ‘Local and global dynamics of free polymer solutions and swollen gels anchored to solid surfaces’. Half-time practice talk in

Max Planck Institute for Polymers

Types of systems Characteristic property

Example

Non-entangled polymer solution

C < C*, G’<< G’’

Entangled polymer solution

C > C*-At high ω: G’ > G’’

→

Weak gels C > C*, G’ ≥ G’’ Xanthan gel

Strong gels C > C*, G’>> G’’ Agar gel

Correlation

length or

mesh size,

C~C* C > C*

C*: polymer chain overlap concentration ω: oscillating frequency

WHAT METHODS COULD BE USED? Methods

(elasticity)

Atomic Force Microscope-

AFM

(‘frozen’ structure)-

Neutron Scattering

(Dynamics)

Nuclear Magnetic

Resonance -NMR(pulse-

field gradient,

using labelled tracers)

(Dynamics)

Optical techniques (Rayleigh-Thermal Diffusion Forced

Rayleigh /Light/Surface Plasmon Enhanced

Scattering, Fluorescence recovery after photobleaching)

(Dynamics) Optical

techniques Fluorescence Correlation

Spectroscopy –FCS

Plum,M.; Steffen,W.; Fytas,G.; Knoll ,W.; Menges B. Probing Dynamics at Interfaces: Dynamic Light Scattering Field Enhanced by Surface Plasmon Polaritons ".Optics Express 177,10364 (2009) Gianneli, M.; Beines, P. W.; Roskamp, R. F.; Koynov, K.; Fytas, G.; Knoll, W., Local and global dynamics of transient polymer networks and swollen gels anchored on solid surfaces. J. Phys.

Chem. C 2007, 111 (35), 13205-13211. Gianneli, M.; Roskamp, R. F.; Jonas, U.; Loppinet, B.; Fytas, G.; Knoll, W., Dynamics of swollen gel layers anchored to solid surfaces. Soft Matter 2008, 4 (7), 1443-1447.

Cappella, B.; Butt, H. J.; Kappl, M., Force measurements with the atomic force microscope: Technique, interpretation and applications. Surf. Sci. Rep. 2005, 59 (1-6), 1-152. Saalwachter, K., Proton multiple-quantum NMR for the study of chain dynamics and structural constraints in polymeric soft materials. Prog. Nucl. Magn. Reson. Spectrosc. 2007, 51 (1), 1-35. Modesti, G.; Zimmermann, B.; Borsch, M.; Herrmann, A.; Saalwachter, K., Diffusion in Model Networks as Studied by NMR and Fluorescence Correlation Spectroscopy. Macromolecules 2009,

42 (13), 4681-4689. Fatin-Rouge, N.; Wilkinson, K. J.; Buffle, J., Combining small angle neutron scattering (SANS) and fluorescence correlation spectroscopy (FCS) measurements to relate diffusion in agarose gels

to structure. J. Phys. Chem. B 2006, 110 (41), 20133-20142. Zustiak, S. P.; Boukari, H.; Leach, J. B., Solute diffusion and interactions in cross-linked poly(ethylene glycol) hydrogels studied by Fluorescence Correlation Spectroscopy. Soft Matter 2010, 6

(15), 3609-3618. R. Kita, S. Wiegand, J. Luettmer-Strathmann, Sign change of the Soret coefficient of poly(ethylene oxide) in water/ethanol mixtures observed by thermal diffusion forced Rayleigh

scattering.Journal of Chemical Physics. 121(8), 3874-3885 (2004)

HYDROGEL’S FEATURE: SWELLING

• ‘ύδρο’ (‘hydro’ from greek:water)

• Characteristic feature of hydrogels: Large uptake of solvent (water)

• At swelling equilibrium:

• balance

• Swelling ratio: Volume of the system in the swollen state (gel+solvent)/Volume of dry gel

• Advantage? Tune mechanical properties of the gel→ tremendous applications→IMPORTANT

Retractive forces due to the

crosslinking points

Thermodynamically driven swelling forces

CLASSIFICATION OF GELS & CROSSLINKS

Physically crosslinked

→Reason?

Favorable polymer-polymer interactions &unfavorable polymer-

solvent interactions

Electrostatic interactions, Van der Waals forces, Hydrogen bonds)

Chemically crosslinked (permanent, covalent crosslinks)

Crosslinkers: Small MW, multifunctional monomers (in small mass fraction) that

contain crosslinking units.

→During polymerization: Copolymerization-crosslinking between

monomers and the multifunctional monomers

→After polymerization:

By providing energy through e⁻ beams, γ-rays, X-rays, UV-irradiation.

Organic (polymer) gels

Original figure for crosslinking (upper, left) reported by : Associate Professor Ozan Akkus, Purdue University on the lecture BIOE 2200 : Biomaterials, lecture 9: hydrogels (2005)

Original figure for crosslinking (upper, right) reported by : ‘Gianneli M. ‘Local and global dynamics of free polymer solutions and swollen gels anchored to solid surfaces’. Half-time practice talk in Max Planck Institute for Polymers