We introduce a comprehensive model of a mucin-like polyelectrolyte gel swelling-deswelling which includes the ion-mediated crosslinking of polymer strands and the exchange of divalent and monovalent ions in the gel. The gel is modeled as a multi-phase mixture which accounts for the polymer and solvent volume fractions and velocities as well as ionic species concentrations. Motion is determined by force balances involving viscous, drag, and chemical forces. The chemical forces are derived from a free energy which includes entropic contributions as well as the chemical and electrostatic interactions among the crosslinked polymer, uncrosslinked polymer, and the ionic solvent. The unified derivation produces all the classical effects (van't Hoff osmotic pressure, Donnan equilibrium potential, Nernst-Planck motion of ions) as well as expressions for Flory interaction parameter and the standard free energy parameters that explicitly depend on the gel chemistry and crosslink structure. For this model, we show how the interplay between ionic bath concentrations, ionic binding, and transient divalent crosslinking leads to a variety of swelled and deswelled phases/phase transitions. In particular, we show how the absorption of divalent ions can lead to a massive deswelling of the gel. We conclude that the unique properties of mucin-like gels can be explained by their ionic binding affinities and transient divalent crosslinking.

1.
P.
Verdugo
,
Adv. Polym. Sci.
110
,
145
156
(
1993
).
2.
P.
Verdugo
,
I.
Deyrup-Olsen
,
A. W.
Martin
, and
D. L.
Luchtel
,
Mechanics of Swelling
,
NATO ASI Series
Vol.
H 64
, edited by
T. K.
Karalis
(
Springer-Verlag
,
1992
), pp.
671
681
.
3.
J.
Barasch
,
B.
Kiss
,
A.
Prince
,
L.
Saiman
,
D.
Gruenert
, and
Q.
Awqati
,
Lett. Nature
352
,
70
74
(
1991
).
4.
P. W.
Cheng
,
T. F.
Boat
,
K.
Cranfill
,
J. R.
Yankaskas
, and
R.
Boucher
,
J. Clin. Invest.
84
,
68
72
(
1989
).
5.
R.
Kuver
,
J. H.
Klinkspoor
,
W. R. A.
Osborne
, and
S. P.
Lee
,
Glycobiology
10
,
149
157
(
2000
).
6.
J. P.
Vilar
,
Am. J. Respir. Cell Mol. Biol.
36
,
183
190
(
2007
).
7.
R.
Bansil
and
B. S.
Turner
,
Curr. Opin. Colloid and Interface Sci.
11
,
164
170
(
2006
).
8.
P.
Verdugo
,
Chap. 19 in
Cilia, Mucus, and Mucociliary Interactions
(
Marcel Decker
,
New York
,
1998
), pp.
167
189
.
9.
P.
Verdugo
,
M.
Aitken
,
L.
Langley
, and
M.
Villalon
,
Biorheology
24
,
625
633
(
1987
).
10.
J.
Cohen
and
Z.
Priel
,
Macromolecules
22
,
2356
(
1989
).
11.
F.
Horkay
,
P. J.
Basser
,
A.-M.
Hecht
, and
E.
Geissler
,
Macromolecules
45
,
2882
(
2012
).
12.
F.
Horkay
,
P. J.
Basser
,
D. J.
Londono
,
A.-M.
Hecht
, and
E.
Geissler
,
J. Chem. Phys.
131
,
184902
(
2009
).
13.
D.-W.
Yin
,
F.
Horkay
,
J. F.
Douglas
, and
J. J.
de Pablo
,
J. Chem. Phys.
129
,
154902
(
2008
).
14.
Y.
Zhang
,
J. F.
Douglas
,
B. D.
Ermi
, and
E. J.
Amis
,
J. Chem. Phys.
114
,
3299
(
2001
).
15.
T.
Tanaka
,
D.
Filmore
,
S. T.
Sun
,
I.
Nishio
,
G.
Swislow
, and
A.
Saha
,
Phys. Rev. Lett.
45
,
1636
(
1980
).
16.
A. E.
English
,
S.
Mafe
,
J.
Manzanares
,
X.
Yu
,
A. Y.
Grosberg
, and
T.
Tanaka
,
J. Chem. Phys.
104
,
8713
8720
(
1996
).
17.
C.
Wolgemuth
,
A.
Mogilner
, and
G.
Oster
,
Eur. Biophys. J.
33
,
146
158
(
2004
).
18.
S. K.
De
,
N. R.
Aluru
,
B.
Johnson
,
W. C.
Crone
,
D. J.
Beebe
, and
J.
Moore
,
J. Microelectromech. Syst.
11
,
544
555
(
2002
).
19.
E.
Kokufuta
,
Langmuir
21
,
10004
10015
(
2005
).
20.
O. V.
Zribi
,
H.
Kyung
,
R.
Golestanian
,
T. B.
Liverpool
, and
G. C. L.
Wong
,
Phys. Rev. E
73
,
031911
(
2006
).
21.
S.
Hirotsu
,
J. Chem. Phys.
94
,
3949
3957
(
1990
).
22.
M.
Doi
,
J. Phys. Condens. Matter
23
,
284118
(
2011
).
23.
J. P.
Keener
,
S.
Sircar
, and
A. L.
Fogelson
,
SIAM J. Appl. Math.
71
,
854
875
(
2011
).
24.
C. W.
Wolgemuth
,
Biophys. J.
95
,
1564
1574
(
2008
).
25.
M.
Doi
,
Introduction to Polymer Dynamics
(
Oxford University Press
,
Oxford, England
,
1996
).
26.
P. J.
Flory
,
Principles of Polymer Chemistry
(
Cornell University Press
,
Ithaca, NY
,
1953
).
27.
P. J.
Flory
,
Proc. R. Soc. Lond., Ser. A.
351
,
351
380
(
1976
).
28.
J. P.
Keener
,
S.
Sircar
, and
A.
Fogelson
,
Phys. Rev. E
83
,
041802
(
2011
).
29.
S.
Hirotsu
,
Y.
Hirokawa
, and
T.
Tanaka
,
J. Chem. Phys.
87
,
1392
1395
(
1987
).
30.
This corrects the interface conditions used in Ref. 23.
You do not currently have access to this content.