A. AKYÜZ: INVESTIGATION OF A POLYELECTROLYTE DEGRADATION WITH VISCOMETRY
769–774
INVESTIGATION OF A POLYELECTROLYTE DEGRADATION
WITH VISCOMETRY
RAZISKAVA DEGRADACIJE POLIELEKTROLITA Z
VISKOZIMETRIJO
Ali Akyüz
Mehmet Akif Ersoy University, Bucak Emin Gulmez Technical Sciences Vocational Higher School, 310 Street, 15300 Burdur, Turkey
aakyuz@mehmetakif.edu.tr
Prejem rokopisa – received: 2018-05-13; sprejem za objavo – accepted for publication: 2018-06-28
doi:10.17222/mit.2018.106
Ultrasonic degradation of a cationic polyelectrolyte, polydiallyl dimethylammonium chloride in aqueous solutions was
investigated at 25 °C for the first time according to the literature. Degradations were performed at a varying molar concentration
of NaCl (0.05-0.50-1.00 M), using different sodium salts with constant molar concentrations (Na2SO4, NaNO3, NaBr) in the
solution and at medium pH values of 1, 3 and 5. The ultrasound frequency (20 kHz), intensity and polymer concentration were
kept constant (0.005 g/mL). By doing so, only the effect of the solvent quality was studied. The degradation process was
characterized with viscometry and the Ovenall/Harrington/Madras model was successfully applied to predict the degradation
parameters. The results show that the degradation efficiency depends strongly on the solvent quality.
Keywords: polyelectrolyte, polydiallyl dimethylammonium chloride, sonication, degradation, viscosity
Avtorji so raziskovali ultrazvo~no degradacijo kationskega polielektrolita, to je polidialnega dimetilamonijevega klorida v vodni
raztopini pri 25
0
C. Poudarjajo, da gre glede na doslej objavljeno literaturo za prvo tovrstno raziskavo. Degradacije so izvajali v
razli~nih molarnih koncentracijah NaCl (0,05-0,50-1.00 M), razli~nih Na soli s konstantno molarno koncentracijo (Na2SO4,
NaNO3, NaBr) v raztopini in pri srednji kislosti pH 1, 3 in 5. Ultrazvo~no frekvenco (20 kHz), intenziteto in koncentracijo
polimera (0,005 g/mL) so ohranjali konstantne. Tako so lahko raziskovali samo kvaliteto topila. Proces degradacije so okarakte-
rizirali z viskozimetrijo. Uspe{no so uporabili Ovenall/Harrington/Madras-ov model za napoved degradacijskih parametrov.
Rezultati so pokazali, da je u~inkovitost degradacije mo~no odvisna od kvalitete topila.
Klju~ne besede: polielektrolit, polidialni dimetilamonijev klorid, sonikacija (ultrazvo~enje), degradacija, viskoznost
1 INTRODUCTION
Polyelectrolytes (PEs) are polymers having many
covalently bonded ionizable groups. These groups
dissociate in polar solvents into macro-ions and small
counterions. Electrostatic forces between macro-ions and
small ions determine the characteristics of a PE in the
solution. In recent years, water-soluble PE studies have
increased considerably because of their diverse appli-
cations such as water purification, film coating, paper
processing and biomedicine. Besides many studies about
PEs, it is widely accepted that physicochemical proper-
ties of PEs are not fully understood and the subject still
presents challenges.
1–5
The conformation of macro-
molecules identified by the persistence length is formed
by the combination of the bare persistence length and the
electrostatic contribution. The electrostatic contribution
is proportional to the square of the Debye length, which
is simply the length over which the electrostatic forces
are screened. Barrat, Joanny and Dobrynin stated that the
electrostatic persistence length of charged flexible chains
scales on the order of the Debye screening length.
6–10
Polydiallyl dimethylammonium chloride (PDADMAC)
is a cationic polymer, which has a backbone of cyclic
units including a cationic quaternary ammonium struc-
ture within every chain that gives the polymer a better
solubility comparable to that of strong PEs. PDADMAC
polymers have been preferred for numerous industrial
applications. They are recommended in wastewater treat-
ment as coagulants and flocculants used for the removal
of contaminants. PDADMAC homopolymers are also
commonly utilized for strengthening and fixing the
agents in the paper and textile industries. They are also
widely used in cosmetic, medicine and food products.
For that reason, PDADMAC has attracted a lot of interest
recently and significant researches have focused on the
understanding of physicochemical or solution charac-
teristics and the polymerization mechanism.
11–16
When high-intensity ultrasound (US) passes through
a liquid and a sufficiently strong negative pressure is
applied during the expansion phase, the critical distance
between the liquid molecules is exceeded and cavitation
bubbles form in the liquid and collapse severely at one
point. The collapse of cavitation bubbles results in very
short periods of enormous local temperature and pres-
sure. In addition, cavitation results in sonophysical
effects such as shear forces, velocity gradients, micro-
streaming, micro-jets and shock waves.
17–19
The first
effect of applying US to polymer solutions (sonication)
is polymer degradation (polymer-chain scission). Solvo-
dynamic forces resulting from the cavitation cause the
Materiali in tehnologije / Materials and technology 52 (2018) 6, 769–774 769
UDK 620.1:544.6.018.47-036.5:542.9:532.13 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 52(6)769(2018)

polymer chain to become divided and the molecular
weight to decrease. Polymer chains in a solution tend to
become extended conformations under the forces per-
forming chain cleavages to lower the chain lengths. The
degradation proceeds more rapidly for longer chains and
after long sonication times, the chain length reaches the
limiting value. The degradation is influenced by different
experimental factors including intensity, frequency,
temperature, polymer concentration, dissolved gas, and
initial molecular weight of the polymer. Solution charac-
teristics have an important role in the chain scission
because the effect of solvodynamic forces on polymer
chains depends on the conformations of the molecules in
the solution.
18–25
An analysis of the literature shows that there has
been no research on the ultrasonic degradation of
PDADMAC and only limited research has been carried
out for ultrasonic polyelectrolyte degradation. In this
study, the salt and pH effect of the ultrasonic
PDADMAC degradation in a solution were investigated
using viscosity measurements. Viscosity measurement is
one of the suitable and widely used techniques for
describing the behavior of polymer chains in solutions.
As the salt concentration or pH of the medium were
changed, the conformation of PDADMAC chains in the
solution changed and therefore the degradation effect of
US also changed. A number of researchers presented
various theoretical models for ultrasonic polymer degra-
dation to explain the kinetics of this process. The
polymer molecular weight or viscosity decreases rapidly
at the beginning of the degradation and then approaches
a fixed value. For the kinetic analysis of the PDADMAC
degradation, the Ovenall/Harrington/Madras (OHM)
model, which provided good results in determining the
change in the molecular weight and viscosity, was
used.
20,22
In the present study, the PDADMAC degra-
dation is basically monitored in terms of intrinsic visco-
sity.
2 EXPERIMENTAL PART
Commercial PDADMAC (Aldrich Mw
400,000-500,000-20 w/% in H
2
O) was used in this study.
NaCl, NaBr, Na
2
SO
4
, NaNO
3
, HCl were obtained from
Merck and distilled water was used for the solutions.
Sonication was performed in a 50-mL glass flat-bottom
vessel using the Bandelin GM 3100 (Bandelin Electro-
nic, Berlin-Germany) ultrasonic homogenizer (20 kHz
fixed frequency) with a MS73 micro-tip probe (3-mm
diameter, 175-mm length). The initial PDADMAC con-
centration was kept constant at 0.001 g/mL, which was
lower than the overlap concentration for all the sonica-
tion experiments.
12
The vessel was kept in an ice-water
bath at 25±1 °C during all the experiments. The soni-
cation of the PDADMAC solutions was performed from
250 s to 8000 s to prevent a volume change as an alter-
native to the withdrawal of the samples from the reaction
medium. It was considered that the volume change
would have an effect on the sonication medium and on
the results. To provide for a precise comparison, the
setting was maintained during all the experiments. The
experiments were repeated twice and the experimental
errors were around 2 %. The viscosity measurements of
the PDADMAC samples were carried out at room tem-
perature with a differential viscometer. The viscometer
system was formed by connecting a stainless steel tube
(0.1/0.00025 m length/radius) from two ends to a diffe-
rential pressure transducer (Validyne Engineering
DP15-28, USA) using a T junction and a Validyne CD
15 indicator.
The voltage of the pressure transducer is correlative
to the pressure change through the tube. The pressure
change is proportional to the PDADMAC solution
viscosity ($
solution
) according to Poisseuille’s formula. The
specific viscosity ($
sp
) is the increase in the viscosity
caused by the polymer in the solution. Normalization of
the specific viscosity to the polymer concentration (c) is
the influence of the polymer causing the solution vis-
cosity to increase, i.e., the viscosity ($
red
) to reduce. $
sp
and$
red
are directly calculated from the voltage output of
the transducer using Equations (1) and (2). The intrinsic
viscosity [$], is known as the size of one polymer chain
in the solution. The intrinsic viscosity provides more
knowledge about the characteristics of the polymer and
its interaction with the solvent. Single-point procedures
for determining the intrinsic viscosity as outlined by the
Solomon-Ciuta formula (Equation (3)) are generally
suggested as a useful method for polymer-degradation
experiments.
21,26
The intrinsic viscosities are determined
from Equation (3). Table 1 presents an overview of the
experimental conditions. The initial intrinsic ([$]
0
) and
reduced viscosities ($
red,0
) are determined using
Equations (2) and (3).
$
$$
$
sp
solution solvent
solvent
=
− ()
(1)
$
$
red
sp
=
c
(2)
[]
[]
$
$ $
=
−+
sp sp
ln( ))
.
1
05
c
(3)
Table 1: Conditions for the experiments
Condition [$]
0
(mL/g) $
red,0
(mL/g)
0.05 M NaCl
0.50 M NaCl
1.00 M NaCl
0.50 M Na 2
SO
4
0.50 M NaNO
3
0.50 M NaBr
pH 1
pH 3
pH 5
359
146
103
155
218
82
194
386
464
404
151
107
166
235
85
215
425
514
A. AKYÜZ: INVESTIGATION OF A POLYELECTROLYTE DEGRADATION WITH VISCOMETRY
770 Materiali in tehnologije / Materials and technology 52 (2018) 6, 769–774

The adapted expression of the OHM model is given
in Equation (4).
21,22
For the model, [$]
t
is the intrinsic
viscosity as a function of time, [$]
lim
is the limiting value
and k is the degradation constant. In order to plot
ln([$]
–1
lim
– [$]
t
–1
) against the sonication time, t gives a
linear correlation and the degree of slope yields the
OHM degradation constant. Here, instead of this
approach, [$]
t
was fitted using nonlinear techniques for a
meaningful analysis. In addition, in this study, an index
(Equation (5)) called the degradation index (DI)w a s
used to compare the sonication experiments.
[] [] () [] [] () ln ln
lim lim
$$ $$
−− −−
−=−−
11 1
0
1
t
kt (4)
[] [] ()
[]
DI =
− 100
0
0
$$
$
lim
(5)
3 RESULTS AND DISCUSSION
3.1 Effect of the NaCl concentration
To investigate the effect of the NaCl concentration on
the ultrasonic PDADMAC degradation, samples with a
0.05-0.50-1.00 M NaCl concentration before the sonica-
tion were prepared. Figure 1 shows the variation of the
experimental intrinsic viscosity data (represented by
points) versus the sonication time and in line with the
OHM model. In this figure, solid lines represent the
OHM curve-fitting function. It is noted that for each
experiment, the intrinsic viscosity leveled off quickly
within the first 1000 s, but a quick decrease in the
sonication slowed it down during 5000–8000 s towards
the limiting value. It is also observed that the beginning
of the decrease in the viscosity is the most effective for
the lowest amount of NaCl and the slowest for the
highest NaCl concentration. Quantitatively, DI dropped
from 82.89 % to 67.28 % and k from 0.001830 to
0.000945 s
–1
for an increase in the concentration of NaCl
from 0.050 M to 1.00 M. The OHM degradation con-
stants, [$]
lim
and degradation index are given in Table 2.
The existence of NaCl in the PDADMAC solution pre-
vents the Coulombic forces of ions on the chains, addi-
tionally increasing intrapolymer associations. With the
increase of the Cl
–
ions in the solution, the electrostatic
screening group of N(CH
3
)
2
increases and PDADMAC
chains become a more coiled formation (from 0.05 M to
1.00 M NaCl). It is generally accepted that the effect of
degradation is greater in good solvents where the
polymer chains form an expanded conformation. The
degradation impact of solvodynamic forces like the shear
strain are more effective for expanded PDADMAC
chains (0.05 M NaCl) than coiled chain conformations
(0.50–1.00 M NaCl). The result is consistent with the
studies on the effect of salt concentration on polyelec-
trolyte such as xanthan, polystyrene sulfonate degrada-
tion.
21,27
3.2 Effect of different sodium salts
The influence of particular sodium salts such as
NaCl, Na
2
SO
4
, NaNO
3
and NaBr on the degradation of
PDADMAC was investigated for a fixed 0.50-M salt
concentration. Figure 2 shows the effect of sodium salts
on the degradation details of the PDADMAC solution for
an 8000-s sonication. In this set of experiments, the
intrinsic viscosity underwent a quick initial reduction,
approaching the limiting value. Figure 2 also shows the
intrinsic viscosity data (points) fitted to the OHM model
(solid lines in the figure). The model presents a proper
explanation of the evaluation of the intrinsic viscosity.
When the Na
2
SO
4
–PDADMAC solution was sonicated,
the intrinsic viscosity decreased efficiently from 155 to
46 mL/g in 8000 s. DI was 75.24 % and k was 0.000994 s
–1
.
When the NaNO
3
–PDADMAC solution was irradiated
A. AKYÜZ: INVESTIGATION OF A POLYELECTROLYTE DEGRADATION WITH VISCOMETRY
Materiali in tehnologije / Materials and technology 52 (2018) 6, 769–774 771
Figure 2: Effects of different salts on the PDADMAC degradation and
the prediction of the OHM model
Figure 1: Effect of NaCl concentration on the PDADMAC degrada-
tion and the prediction of the OHM model

by the ultrasound, the intrinsic viscosity decreased from
218 mL/g to 48 mL/g, DI was 78.23 % and k was
0.001220 s
–1
. In the case of the NaBr–PDADMAC soni-
cation, the initial and limiting intrinsic viscosities were
82 mL/g and 41 mL/g, respectively. DIwas55%andkwas
0.000715 s
–1
. The results of the 0.50 M NaCl–PDA-
DMAC experiment are given above. A summary of the
results obtained for this set of experiments is given in
Table 2. Particularly, for the 0.50-M salt concentration, it
can be noticed that the initial intrinsic viscosity increases
the most with the presence of NaNO
3
, followed by NaCl,
Na
2
SO
4
and NaBr.
The change in the initial viscosity can be enforced by
interaction variations between the PADMAC chains and
the counterions. For the NaCl and NaNO
3
solution (mo-
novalent counterions), the intrinsic viscosity increases
with the increasing counterion size as bigger ions are
weakly associated with PDADMAC chains.
13
In the case
of the Na
2
SO
4
solution (bivalent counterions), PDAD-
MAC chains have a higher charge affinity than NaCl and
NaNO
3
; therefore, polymer chains had a coiled confor-
mation. Using NaBr in the PDADMAC solution reduces
the solvent quality as it causes a lower intrinsic viscosity
and the PDADMAC chains exhibit a more coiled con-
formation than in the cases of NaCl, Na
2
SO
4
and NaNO
3
.
The increasing interactions between the polymer chain
and counterions shows that the counterion binding is not
supported by remarkable dehydration and the counterion
binding is not specific for halides.
28
Li and Feke inves-
tigated the effect of NaCl and Na
2
SO
4
on the nonionic
locust-bean-gum degradation due to ultrasound. They
showed that when NaCl was used, the degradation was
more effective compared to the Na
2
SO
4
usage.
29
In
another study of Li and Feke, it was concluded that an
addition of NaCl to the solution was more effective than
Na
2
SO
4
during the ultrasonic xanthan degradation. They
reported that xanthan exhibited a more compacted form
in the Na
2
SO
4
solution.
30
Their results are consistent
within this study.
3.3 Effect of pH
Sonications were carried out at medium pH values of
1, 3 and 5. pKa’s of the monomer, low and high mole-
cular weight of PDADMAC were 7.0, 6.7, and 6.3, res-
pectively; they were positively charged in an acidic
media.
16
The pH was adjusted with HCl. The pH of the
solution was determined for the duration of sonication
and it did not change during sonication. The evolutions
of the intrinsic viscosities for this set are shown in
Figure 3. This figure also shows the prediction of the
OHM model (solid lines). The intrinsic viscosity for the
pH of 1 decreased rapidly during the initial 1000 s from
194 mL/g to 44 mL/g, slightly inclining toward the limit-
ing viscosity of 43 after 7000 s. In this experiment, k and
DI were determined as 0.001395 s
–1
and 77.70 %, res-
pectively. For the pH of 3, the intrinsic viscosity
decreased from 386 mL/g to 90 mL/g during 1000 s and
finally the viscosity approached the value of 67 mL/g.
The values of k and DI were calculated as 0.001950 s
–1
and 83.75 %, respectively. The initial intrinsic viscosity
reduced from 464 mL/g to 107 mL/g during 1000 s and
reached 74 mL/g at the end of 8000 s for the pH of 5.
The values of k and DI were calculated as 0.002150 s
–1
and 83.90 %, respectively. A higher degradation efficien-
cy was obtained at the pH of 5 and the lowest degra-
dation efficiency was observed at the pH of 1 (Table 2).
The pH of the medium changed the solution charac-
teristics of PDADMAC because the dissociation of the
ionic groups of the polymer chains was also affected by
the pH of the medium. At the pH of 1, the number of Cl
ions was higher than at the pH values of 3 and 5.
Therefore, at the pH of 1, the Coulomb repulsion forces
were higher due to the electrostatic screening of the Cl
ions and the PDADMAC chains had a more compact
A. AKYÜZ: INVESTIGATION OF A POLYELECTROLYTE DEGRADATION WITH VISCOMETRY
772 Materiali in tehnologije / Materials and technology 52 (2018) 6, 769–774
Figure 4: Variation in the OHM degradation constants and DI with the
initial intrinsic viscosity
Figure 3: Effect of pH on the PDADMAC degradation and the
prediction of the OHM model

form than at the pH values of 3 and 5, at which the
PDADMAC chains exhibited an expanded conformation.
It is easier to break polymer chains in an expanded form.
Vijayalakshmi and Madras investigated the pH effect on
the polyvinyl-alcohol degradation. They concluded that a
degradation at pH values of 2 and 12 was more effective
than at a pH of 7. It was also concluded that the poly-
vinyl-alcohol degradation was more efficient in the
expanded form of polymer chains.
19
Mehrdad studied the
effect of the HCl concentration on the polyethylene
oxide sonication and reported that the degradation
efficiency was reduced at a higher HCl concentration.
31
It
should be noted that polyvinyl alcohol and polyethylene
oxide are not polyelectrolytes. The correlation coeffi-
cients (R
2
) from the OHM model for all the experiments
are given in Table 2.
Table 2: Degradation parameters
Condition
k (s
–1
)×
10
–4
[$]
lim
(mL/g)
R
2
DI
0.05 M NaCl
0.50 M NaCl
1.00 M NaCl
0.50 M Na 2
SO
4
0.50 M NaNO
3
0.50 M NaBr
pH 1
pH 3
pH 5
18.30
9.58
9.45
9.94
12.20
7.15
13.95
19.50
21.50
61.40
47.76
48.44
46.12
48.12
41.00
43.26
65.70
74.70
0.996
0.989
0.979
0.992
0.994
0.987
0.989
0.994
0.995
82.89
69.26
57.06
71.72
79.22
43.52
77.70
83.75
83.90
The obtained results with regard to the initial intrinsic
viscosity, which was a measure of the solvent quality, are
given in Figure 4. The right side of the figure shows k
and the left side shows DI. The values of k and DI
monotonically increase when the initial viscosity, i.e.,
the solvent quality is increased.
4 CONCLUSIONS
Ultrasonic techniques are useful for producing well-
designed polymers with different characteristics, scaling
down the heterogeneity index of polymers, generating
chemical structures for different reactions and modifying
polymers for desired properties. To figure out and learn
how to control these types of processes, the mechanism
of the influence of US and parameters need to be inves-
tigated. That is why ultrasonic degradation continues to
be studied intensively. In this study, ultrasonic poly-
diallyl dimethylammonium chloride degradation in
aqueous solutions was studied for the first time accord-
ing to the literature. The ultrasonic degradation of
PDADMAC in sodium salts and HCl solutions was me-
thodically investigated. It was shown that the sonication
efficiently leads to a scission of PDADMAC chains. The
most effective degradation occurred within the first 1000
s of the sonication for all the experiments. The solvent
quality was controlled with the salt content in the
solution and pH was the predominant influence during
the ultrasonic PDADMAC degradation. The effect of
solvodynamic forces on PDADMAC chains is higher in a
better solvent, in which the chains exhibit expanded
conformations. The experimental results agree with the
studies by Vijayalakshmi and the previous study about
the polystyrene-sulfonate degradation, indicating that the
polymer-chain conformation in a solution is an important
factor for the degradation. This study is also consistent
with Schaefer’s results, according to which the contour
length is the main parameter for the ultrasonic polymer
degradation.
18,19,21,24
Acknowledgements
This study was partly supported by the TUBÝTAK
project, number 115Z421.
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