The primary goal of this work is to assess the effect of excluded volume interactions on the diffusion controlled release of drug molecules from a spherical, neutral, inert, and cross-linked device of nanometric size. To this end, coarse-grained simulations of the release process were performed. In this way, the inner structure and topology of the polymer network can be explicitly taken into account as well. Our in silico experiments reveal that the boundary condition of constant surface concentration is not appropriate for nanogels. In particular, the predictions based on the perfect sink condition clearly overestimate the fraction of drug released. In addition, these simulations provide values for the release exponent that depends on both the diameter of drug molecules and the number of drug molecules loaded in the matrix, which clearly contrasts with the classical prediction of a constant release exponent. Consequently, the widely used classification of drug release mechanisms based on this kinetic exponent must be extended to include new situations.

1.
R.
Pelton
,
Adv. Colloid Interface Sci.
85
,
1
(
2000
).
2.
J. K.
Oh
,
R.
Drumright
,
D. J.
Siegwart
, and
K.
Matyjaszewski
,
Prog. Polym. Sci.
33
,
448
(
2008
).
3.
K.
Raemdonck
,
J.
Demeester
, and
S.
De Smedt
,
Soft Matter
5
,
707
(
2009
).
4.
A. V.
Kabanov
and
S. V.
Vinogradov
,
Angew. Chem., Int. Ed.
48
,
5418
(
2009
).
5.
R. T.
Chacko
,
J.
Ventura
,
J.
Zhuang
, and
S.
Thayumanavan
,
Adv. Drug Delivery Rev.
64
,
836
(
2012
).
6.
X.
Zhang
,
S.
Malhotra
,
M.
Molina
, and
R.
Haag
,
Chem. Soc. Rev.
44
,
1948
(
2015
).
7.
M.
Molina
,
M.
Asadian-Birjand
,
J.
Balach
,
J.
Bergueiro
,
E.
Miceli
, and
M.
Calderon
,
Chem. Soc. Rev.
44
,
6161
(
2015
).
8.
S.
Merino
,
C.
Martin
,
K.
Kostarelos
,
M.
Prato
, and
E.
Vazquez
,
ACS Nano
9
,
4686
(
2015
).
9.
M.
Karimi
,
A.
Ghasemi
,
P. S.
Zangabad
,
R.
Rahighi
,
S. M. M.
Basri
,
H.
Mirshekari
,
M.
Amiri
,
Z. S.
Pishabad
,
A.
Aslani
,
M.
Bozorgomid
,
D.
Ghosh
,
A.
Beyzavi
,
A.
Vaseghi
,
A. R.
Aref
,
L.
Haghani
,
S.
Bahrami
, and
M. R.
Hamblin
,
Chem. Soc. Rev.
45
,
1457
(
2016
).
10.
A.
Fernandez-Barbero
,
I. J.
Suarez
,
B.
Sierra-Martin
,
A.
Fernandez-Nieves
,
F.
de las Nieves
,
M.
Marquez
,
J.
Rubio-Retama
, and
E.
Lopez-Cabarcos
,
Adv. Colloid Interface Sci.
147-148
,
88
(
2009
).
11.
J.
Ramos
,
A.
Imaz
,
J.
Callejas-Fernandez
,
L.
Barbosa-Barros
,
J.
Estelrich
,
M.
Quesada-Perez
, and
J.
Forcada
,
Soft Matter
7
,
5067
(
2011
).
12.
D.
Klinger
and
K.
Landfester
,
Polymer
53
,
5209
(
2012
).
13.
C. C.
Lin
and
A. T.
Metters
,
Adv. Drug Delivery Rev.
58
,
1379
(
2006
).
14.
T.
Casalini
and
G.
Perale
,
Gels
5
,
28
(
2019
).
15.
K.
Kosmidis
,
P.
Argyrakis
, and
P.
Macheras
,
Pharm. Res.
20
,
988
(
2003
).
16.
P. L.
Ritger
and
N. A.
Peppas
,
J. Controlled Release
5
,
23
(
1987
).
17.
P. L.
Ritger
and
N. A.
Peppas
,
J. Controlled Release
5
,
37
(
1987
).
18.
R.
Villalobos
,
E. V.
Garcia
,
D.
Quintanar
, and
P. M.
Young
,
Curr. Drug Delivery
14
,
65
(
2017
).
19.
A.
Bunde
,
S.
Havlin
,
R.
Nossal
,
H. E.
Stanley
, and
G. H.
Weiss
,
J. Chem. Phys.
83
,
5909
(
1985
).
20.
M.
Quesada-Perez
and
A.
Martin-Molina
,
Soft Matter
9
,
7086
(
2013
).
21.
A.
Martín-Molina
and
M.
Quesada-Pérez
,
J. Mol. Liq.
280
,
374
(
2019
).
22.
L.
Rovigatti
,
N.
Gnan
,
L.
Tavagnacco
,
A. J.
Moreno
, and
E.
Zaccarelli
,
Soft Matter
15
,
1108
(
2019
).
23.
B.
Cichocki
and
K.
Hinsen
,
Physica A
166
,
473
(
1990
).
24.
R. S.
Dias
and
A.
Pais
,
Adv. Colloid Interface Sci.
158
,
48
(
2010
).
25.
S. C. C.
Nunes
,
T.
Cova
, and
A.
Pais
,
J. Chem. Phys.
139
,
054906
(
2013
).
26.
M.
Seijo
,
M.
Pohl
,
S.
Ulrich
, and
S.
Stoll
,
J. Chem. Phys.
131
,
174704
(
2009
).
27.
G.
Luque-Caballero
,
A.
Martín-Molina
, and
M.
Quesada-Pérez
,
J. Chem. Phys.
140
,
174701
(
2014
).
28.
J.
Jin
and
J.
Wu
,
J. Chem. Phys.
128
,
074901
(
2008
).
29.
L.
Wang
,
H.
Liang
, and
J.
Wu
,
J. Chem. Phys.
133
,
044906
(
2010
).
30.
J.
Kim
and
J.
Wu
,
J. Chem. Phys.
140
,
235101
(
2014
).
31.
L.
Rovigatti
,
F.
Bomboi
, and
F.
Sciortino
,
J. Chem. Phys.
140
,
154903
(
2014
).
32.
M.
Quesada-Pérez
,
S.
Ahualli
, and
A.
Martín-Molina
,
J. Chem. Phys.
141
,
124903
(
2014
).
33.
G. C.
Claudio
,
K.
Kremer
, and
C.
Holm
,
J. Chem. Phys.
131
,
094903
(
2009
).
34.
P. K.
Jha
,
J. W.
Zwanikken
,
F. A.
Detcheverry
,
J. J.
de Pablo
, and
M. O.
de la Cruz
,
Soft Matter
7
,
5965
(
2011
).
35.
R.
Schroeder
,
A. A.
Rudov
,
L. A.
Lyon
,
W.
Richtering
,
A.
Pich
, and
I. I.
Potemkin
,
Macromolecules
48
,
5914
(
2015
).
36.
H.
Kobayashi
and
R.
Winkler
,
Polymers
6
,
1602
(
2014
).
37.
H.
Kobayashi
and
R. G.
Winkler
,
Sci. Rep.
6
,
19836
(
2016
).
38.
H.
Kobayashi
,
R.
Halver
,
G.
Sutmann
, and
R. G.
Winkler
,
polymers
9
,
15
(
2017
).
39.
N.
Gnan
,
L.
Rovigatti
,
M.
Bergman
, and
E.
Zaccarelli
,
Macromolecules
50
,
8777
(
2017
).
40.
A. J.
Schmid
,
J.
Dubbert
,
A. A.
Rudov
,
J. S.
Pedersen
,
P.
Lindner
,
M.
Karg
,
I. I.
Potemkin
, and
W.
Richtering
,
Sci. Rep.
6
,
22736
(
2016
).
41.
M.
Quesada-Pérez
,
I.
Adroher-Benítez
, and
J. A.
Maroto-Centeno
,
J. Chem. Phys.
140
,
204910
(
2014
).
42.
M.
Quesada-Perez
,
J.
Ramos
,
J.
Forcada
, and
A.
Martin-Molina
,
J. Chem. Phys.
136
,
244903
(
2012
).
43.
M.
Daeihamed
,
A.
Haeri
,
S. N.
Ostad
,
M. F.
Akhlaghi
, and
S.
Dadashzadeh
,
Nanomedicine
12
,
1187
(
2017
).
44.
G.
Wieczorek
and
P.
Zielenkiewicz
,
Biophys. J.
95
,
5030
(
2008
).
45.
J. S.
Rothman
,
L.
Kocsis
,
E.
Herzog
,
Z.
Nusser
, and
R. A.
Silver
,
eLife
5
,
e15133
(
2016
).
46.
J. R.
Houser
,
D. J.
Busch
,
D. R.
Bell
,
B.
Li
,
P.
Ren
, and
J. C.
Stachowiak
,
Soft Matter
12
,
2127
(
2016
).
47.
S.
Smith
and
R.
Grima
,
J. Chem. Phys.
146
,
024105
(
2017
).
48.
J.
Crank
,
The Mathematics of Diffusion
, 2nd ed. (
Clarendon Press
,
Oxford
,
1975
), 1979.
49.
J.
Siepmann
and
F.
Siepmann
,
J. Controlled Release
161
,
351
(
2012
).
50.
S. R.
Lustig
and
N. A.
Peppas
,
J. Appl. Polym. Sci.
36
,
735
(
1988
).
51.
G. K.
Batchelor
,
J. Fluid Mech.
74
,
1
(
1976
).
52.
B. J.
Ackerson
and
L.
Fleishman
,
J. Chem. Phys.
76
,
2675
(
1982
).
53.
C. W. J.
Beenakker
and
P.
Mazur
,
Physica A
120
,
388
(
1983
).
54.
J. F.
Brady
,
J. Fluid Mech.
272
,
109
(
1994
).
56.
M.-H.
Hsiao
,
M.
Larsson
,
A.
Larsson
,
H.
Evenbratt
,
Y.-Y.
Chen
,
Y.-Y.
Chen
, and
D.-M.
Liu
,
J. Controlled Release
161
,
942
(
2012
).
57.
G.
Aguirre
,
E.
Villar-Alvarez
,
A.
Gonzalez
,
J.
Ramos
,
P.
Taboada
, and
J.
Forcada
,
J. Polym. Sci., Part A: Polym. Chem.
54
,
1694
(
2016
).
58.
M. D.
Blanco
,
S.
Guerrero
,
C.
Teijón
,
R.
Olmo
,
L.
Pastrana
,
I.
Katime
, and
J. M.
Teijón
,
Polym. Int.
57
,
1215
(
2008
).
59.
B.
Kaoui
,
M.
Lauricella
, and
G.
Pontrelli
,
Comput. Biol. Med.
93
,
149
(
2018
).
60.
E. J.
Carr
and
G.
Pontrelli
,
Math. Biosci.
303
,
1
(
2018
).
62.
K.
Sangeetha
and
E. K.
Girija
,
Mater. Sci. Eng., C
78
,
1046
(
2017
).
63.
M.
Zandi
,
N.
Dardmeh
,
S.
Pirsa
, and
H.
Almasi
,
J. Food Process Eng.
40
,
e12314
(
2017
).
64.
G.
Batôt
,
V.
Dahirel
,
G.
Mériguet
,
A. A.
Louis
, and
M.
Jardat
,
Phys. Rev. E
88
,
043304
(
2013
).
You do not currently have access to this content.