The diffusion of small molecules through hydrogels is of great importance for many applications. Especially in biological contexts, the diffusion of nutrients through hydrogel networks defines whether cells can survive inside the hydrogel or not. In this contribution, hydrogels based on poly(ethylene glycol) diacrylate with mesh sizes ranging from ξ = 1.1 to 12.9 nm are prepared using polymers with number-average molecular weights between Mn = 700 and 8000 g/mol. Precise measurements of diffusion coefficients D of adenosine triphosphate (ATP), an important energy carrier in biological systems, in these hydrogels are performed by pulsed field gradient nuclear magnetic resonance. Depending on the mesh size, ξ, and on the polymer volume fraction of the hydrogel after swelling, ϕ, it is possible to tune the relative ATP diffusion coefficient D/D0 in the hydrogels to values between 0.14 and 0.77 compared to the ATP diffusion coefficient D0 in water. The diffusion coefficients of ATP in these hydrogels are compared with predictions of various mathematical expressions developed under different model assumptions. The experimental data are found to be in good agreement with the predictions of a modified obstruction model or the free volume theory in combination with the sieving behavior of the polymer chains. No reasonable agreement was found with the pure hydrodynamic model.

1.
N. A.
Peppas
,
J. Z.
Hilt
,
A.
Khademhosseini
, and
R.
Langer
,
Adv. Mater.
18
,
1345
1360
(
2006
).
2.
T.
Canal
and
N. A.
Peppas
,
J. Biomed. Mater. Res.
23
,
1183
1193
(
1989
).
3.
P. J.
Flory
and
J.
Rehner
,
J. Chem. Phys.
11
,
521
526
(
1943
).
4.
P. J.
Flory
and
J.
Rehner
,
J. Chem. Phys.
11
,
512
520
(
1943
).
5.
M. L.
Oyen
,
Int. Mater. Rev.
59
,
44
59
(
2014
).
6.
K. S.
Anseth
,
C. N.
Bowman
, and
L.
Brannon-Peppas
,
Biomaterials
17
,
1647
1657
(
1996
).
7.
A.
Southan
,
E.
Hoch
,
V.
Schönhaar
,
K.
Borchers
,
C.
Schuh
,
M.
Müller
,
M.
Bach
, and
G. E. M.
Tovar
,
Polym. Chem.
5
,
5350
5359
(
2014
).
8.
A.
Southan
,
V.
Hagel
,
M.
Mateescu
,
M.
Bach
,
C.
Schuh
,
C.
Kleinhans
,
P. J.
Kluger
,
S.
Tussetschläger
,
I.
Nuss
,
T.
Haraszti
,
S. V.
Wegner
,
J. P.
Spatz
,
H.
Böhm
,
S.
Laschat
, and
G. E. M.
Tovar
,
Macromol. Chem. Phys.
214
,
1865
1873
(
2013
).
9.
J.
Zheng
,
L. A.
Smith Callahan
,
J.
Hao
,
K.
Guo
,
C.
Wesdemiotis
,
R. A.
Weiss
, and
M. L.
Becker
,
ACS Macro Lett.
1
,
1071
1073
(
2012
).
10.
T.
Potta
,
C.
Chun
, and
S.-C.
Song
,
Biomaterials
30
,
6178
6192
(
2009
).
11.
K. M.
Schultz
,
A. D.
Baldwin
,
K. L.
Kiick
, and
E. M.
Furst
,
Macromolecules
42
,
5310
5316
(
2009
).
12.
M. H.
Smith
and
L. A.
Lyon
,
Macromolecules
44
,
8154
8160
(
2011
).
13.
J. P.
Schillemans
,
W. E.
Hennink
, and
C. F.
van Nostrum
,
Eur. J. Pharm. Biopharm.
76
,
329
335
(
2010
).
14.
S. H.
Gehrke
,
J. P.
Fisher
,
M.
Palasis
, and
M. E.
Lund
,
Ann. N. Y. Acad. Sci.
831
,
179
184
(
1997
).
15.
O.
Lieleg
and
K.
Ribbeck
,
Trends Cell Biol.
21
,
543
551
(
2011
).
16.
T. G.
Kim
,
H.
Shin
, and
D. W.
Lim
,
Adv. Funct. Mater.
22
,
2446
2468
(
2012
).
17.
C.
Bastiancich
,
P.
Danhier
,
V.
Préat
, and
F.
Danhier
,
J. Controlled Release
243
,
29
42
(
2016
).
18.
L.
Jin
,
P.
Lu
,
H.
You
,
Q.
Chen
, and
J.
Dong
,
Int. J. Pharm.
371
,
82
88
(
2009
).
19.
J.
Kobayashi
,
A.
Kikuchi
,
K.
Sakai
, and
T.
Okano
,
J. Chromatogr. A
958
,
109
119
(
2002
).
20.
Q. T.
Nguyen
,
Y.
Hwang
,
A. C.
Chen
,
S.
Varghese
, and
R. L.
Sah
,
Biomaterials
33
,
6682
6690
(
2012
).
21.
L. A.
Hockaday
,
K. H.
Kang
,
N. W.
Colangelo
,
P. Y. C.
Cheung
,
B.
Duan
,
E.
Malone
,
J.
Wu
,
L. N.
Girardi
,
L. J.
Bonassar
,
H.
Lipson
,
C. C.
Chu
, and
J. T.
Butcher
,
Biofabrication
4
,
035005
(
2012
).
22.
V. T.
Michael
,
S.
Sonja
,
C. L.
Jeffery
, and
P.
Georgia
,
Biomed. Mater.
8
,
025001
(
2013
).
23.
B.
Yañez-Soto
,
S. J.
Liliensiek
,
C. J.
Murphy
, and
P. F.
Nealey
,
J. Biomed. Mater. Res., Part A
101A
,
1184
1194
(
2013
).
24.
M. L.
Cuchiara
,
S.
Coşkun
,
O. A.
Banda
,
K. L.
Horter
,
K. K.
Hirschi
, and
J. L.
West
,
Biotechnol. Bioeng.
113
,
870
881
(
2016
).
25.
G. M.
Cruise
,
D. S.
Scharp
, and
J. A.
Hubbell
,
Biomaterials
19
,
1287
1294
(
1998
).
26.
K.
Engberg
and
C. W.
Frank
,
Biomed. Mater.
6
,
055006
(
2011
).
27.
A.
Cavallo
,
M.
Madaghiele
,
U.
Masullo
,
M. G.
Lionetto
, and
A.
Sannino
,
J. Appl. Polym. Sci.
134
,
44380
(
2017
).
28.
V.
Hagel
,
T.
Haraszti
, and
H.
Böhm
,
Biointerphases
8
,
36
(
2013
).
29.
K.
Tomić
,
W. S.
Veeman
,
M.
Boerakker
,
V. M.
Litvinov
, and
A. A.
Dias
,
J. Pharm. Sci.
97
,
3245
3256
(
2008
).
30.
H.
Lin
,
T.
Kai
,
B. D.
Freeman
,
S.
Kalakkunnath
, and
D. S.
Kalika
,
Macromolecules
38
,
8381
8393
(
2005
).
31.
B.
Amsden
,
Macromolecules
31
,
8382
8395
(
1998
).
32.
B.
Amsden
,
Macromolecules
32
,
874
879
(
1999
).
33.
34.
E. O.
Stejskal
and
J. E.
Tanner
,
J. Chem. Phys.
42
,
288
292
(
1965
).
35.
J. E.
Tanner
,
J. Chem. Phys.
52
,
2523
2526
(
1970
).
36.
P.
Stilbs
,
Prog. Nucl. Magn. Reson. Spectrosc.
19
,
1
45
(
1987
).
37.
W. S.
Price
,
NMR Studies of Translational Motion: Principles and Applications
(
University Press
,
Cambridge
,
2009
).
38.
P. T.
Callaghan
,
Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR
(
University Press
,
Oxford
,
2011
).
39.
M.
Piotto
,
V.
Saudek
, and
V.
Sklenar
,
J. Biomol. NMR
2
,
661
665
(
1992
).
40.
W. S.
Price
,
F.
Elwinger
,
C.
Vigouroux
, and
P.
Stilbs
,
Magn. Reson. Chem.
40
,
391
395
(
2002
).
41.
G.
Majer
and
K.
Zick
,
J. Chem. Phys.
142
,
164202
(
2015
).
42.
J. E.
Mark
and
P. J.
Flory
,
J. Am. Chem. Soc.
87
,
1415
1423
(
1965
).
43.
N. A.
Peppas
and
E. W.
Merrill
,
J. Appl. Polym. Sci.
21
,
1763
1770
(
1977
).
44.
E. W.
Merrill
,
K. A.
Dennison
, and
C.
Sung
,
Biomaterials
14
,
1117
1126
(
1993
).
46.
C. H.
Neuman
,
J. Chem. Phys.
60
,
4508
4511
(
1974
).
47.
W. S.
Price
and
P. W.
Kuchel
,
J. Magn. Reson.
94
,
133
139
(
1991
).
48.
M.
Peter
and
P.
Tayalia
,
RSC Adv.
6
,
40878
40885
(
2016
).
49.
P.
Malo de Molina
,
S.
Lad
, and
M. E.
Helgeson
,
Macromolecules
48
,
5402
5411
(
2015
).
50.
H.
Zhang
,
L.
Wang
,
L.
Song
,
G.
Niu
,
H.
Cao
,
G.
Wang
,
H.
Yang
, and
S.
Zhu
,
J. Appl. Polym. Sci.
121
,
531
540
(
2011
).
51.
D. J.
Munoz-Pinto
,
S.
Samavedi
,
B.
Grigoryan
, and
M. S.
Hahn
,
Polymer
77
,
227
238
(
2015
).
52.
X.
Dai
,
X.
Chen
,
L.
Yang
,
S.
Foster
,
A. J.
Coury
, and
T. H.
Jozefiak
,
Acta Biomater.
7
,
1965
1972
(
2011
).
53.
H.
Huang
,
M.
Liu
, and
X.-A.
Mao
,
Spectrochim. Acta, Part A
54
,
999
1005
(
1998
).
54.
W. M.
Haynes
,
CRC Handbook of Chemistry and Physics
, 95th ed. (
CRC
,
2014
).
55.
C. T. W.
Moonen
,
P. C. M.
Van Zijl
,
D. L.
Bihan
, and
D.
Despres
,
Magn. Reson. Med.
13
,
467
477
(
1990
).
56.
M. J.
Hubley
,
B. R.
Locke
, and
T. S.
Moerland
,
Biochim. Biophys. Acta, Gen. Subj.
1291
,
115
121
(
1996
).
57.
W. J.
Bowen
and
H. L.
Martin
,
Arch. Biochem. Biophys.
107
,
30
36
(
1964
).
58.
J. P.
Melchior
,
G.
Majer
, and
K. D.
Kreuer
,
Phys. Chem. Chem. Phys.
19
,
601
612
(
2017
).
59.
H.
Yasuda
,
A.
Peterlin
,
C. K.
Colton
,
K. A.
Smith
, and
E. W.
Merrill
,
Makromol. Chem.
126
,
177
186
(
1969
).
60.
S. R.
Lustig
and
N. A.
Peppas
,
J. Appl. Polym. Sci.
36
,
735
747
(
1988
).
61.
J. S.
Mackie
and
P.
Meares
,
Proc. R. Soc. A
232
,
510
518
(
1955
).
62.
R. I.
Cukier
,
Macromolecules
17
,
252
255
(
1984
).
63.
J. S.
Vrentas
and
J. L.
Duda
,
J. Polym. Sci., Polym. Phys. Ed.
15
,
403
416
(
1977
).
64.
N. A.
Peppas
and
C. T.
Reinhart
,
J. Membr. Sci.
15
,
275
287
(
1983
).
65.
C. T.
Reinhart
and
N. A.
Peppas
,
J. Membr. Sci.
18
,
227
239
(
1984
).
66.
N. A.
Peppas
and
S. L.
Wright
,
Macromolecules
29
,
8798
8804
(
1996
).
67.
D. S.
Clague
and
R. J.
Phillips
,
Phys. Fluids
8
,
1720
1731
(
1996
).
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