2009 )4 (22 مجلة ابن الهیثم للعلوم الصرفة والتطبیقیة          المجلد  

     

دراسة الخواص المیكانیكیة والریولوجیة لبولیمر بولي اكریلك اسید لمحالیل بولي اكریلك 

  اسید

  

  

  خالدة حسین حبیب المیالي

   جامعة الكوفة،كلیة التربیة للبنات ،قسم الفیزیاء 
 

  

  لخالصةا

 وسـعة ، وزمـن االسـترخاء، وكـذلك معامـل االمتـصاص،وسـرعة الموجـات فـوق الـسمعیة،االمتصاص عین معامل 

ـه وبنـسب المـاء المـذاب فــي   أسـیدكاكـر یلــبــولیمر بـولي ل  واالنـضغاطیة،واللزوجـة،االسـترخاء   مختلفـة باسـتخدام تقنیــة وزنیـ

    .ºC 30وفي درجة حرارة )  26kHz( تردد يالموجات فوق السمعیة ذ

 وسـعة االسـترخاء تـزداد ، وزمـن االسـترخاء ، ومعامـل االمتـصاص النتائج ان كل من قیم السرعة واللزوجـةأظهرت

 لهذا البولیمر وبالعكس فان قیم االنضغاطیة تتناقص بزیادة التركیز وهذه النتیجة تقترح وجود انـدماج  لمحالیل بزیادة التركیز

  .نفسهاأك بین جزیئات البولیمر داخلي بین جزیئات البولیمر وجزئیات المذیب وكذل

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 



  

IBN AL- HAITHAM J. FO R PURE & APPL. SC I        VO L.22 (4) 2009  

 
Ultrasonic and Viscosity Studies of Poly  

( Acrylic Acid ) Solutions 
 

K. H.H.  AL-Mayali  
Department of Physics, College of Education for Girls, University of Kufa  

  
 

Abstract 
Ultrasonic absorption, velocity, viscosity , adiabatic compressibility , relaxation time 

and relaxation amplitude measurements are reported on different concentrations of 
poly(acrylic acid) solutions in common solvent water using pulsed ultrasonic apparatus 
technique operating at 26 kHz and 30 ºC. 

Results show an increase of velocity, viscosity, and absorption coefficient ،relaxation 

time and relaxation amplitude values with the increasing concentrations of the poly(acrylic 
acid) solutions, which might be the result of structural fluctuations of polymer molecules such 
as the segmental motions of the polymer chains. In contrast the compressibility  decreases with 
the increasing concentration of this polymer. This study suggests there is an association 
between polymer and solvent molecules and also there is association between polymer 
molecules itself. 

  

Introduction  
     Poly(acrylic acid) is an unsaturated carboxylic acid. It readily undergoes 

polymerization and addition reactions from the monomer -CH2CH(CO2H)- . 
     PAA is innoxious and soluble in water, it can be used in situations of alkaline and high 

concentration without scale sediment. PAA can disperse the microcrystals or microsand of 
calcium carbonate, calcium phosphate and calcium sulfate. PAA is used as scale inhibitor and 
dispersant for circulating cool water system, papermaking, weave, dyeing, ceramic, painting, 
etc. 

 
  
 

 
 
 

PAA can be used as a scale inhibitor and dispersant in circulating cool water systems 

in power plants, iron & steel factories, chemical fertilizer plants, refineries and air 

conditioning systems. Dosage should be in accordance with water quality  and equipment 

materials[1,2]. 

 



  

IBN AL- HAITHAM J. FO R PURE & APPL. SC I        VO L.22 (4) 2009  
 
Ultrasonic absorption and velocity measurements provide useful information on the 

behaviour of polymers in solutions. It is, therefore, important to obtain fundamental 
information on how this important and valuable polymer acts in asolution, especially in 
water[3,4]. 

 
 

Experimental 
Poly(acrylic acid) a fine white powder has a molecular weight of 2,000g. Its solutions 

were prepared by adding a known weight of the polymer to a fixed volume of water, it was 
stirred for at least 20 hrs, at the temperature 30°C . The ultrasonic velocity measurements 
were obtained by using the pulsed ultrasonic technique of sender-receiver type (PHYWE-
WEST GERMANY) Ultrasonic generator with constant frequency of 26kHz [5]. The 
temperature is maintained at 30

oC circulating water from a thermostat with a thermal stability 
of 

+
 0.05

o
C through the double wall jaket of the ultrasonic experimental cell. The viscosity  of  

solutions was measured at 30
oC by using an Ostwald viscometer, the method of measurement  

was described elsewhere[6]. The accuracy of the viscosity measurement was +0.015%. 
 

Theoretical Calculation 
Theoretical values of adiabatic compressibility  () relaxation time (), relaxation 

amplitude (/f2), viscosity  (), absorption coefficient (), and specific acoustic impedance 
(Z) for the solutions were determined by using the following equations (5, 6, 7). 

 
 
 =  (2)-1      …(1) 

23

4




      …(2) 

32 3

8

f 





     …(3) 

ooo t

t









     …(4) 

T

X
       …(5) 

Z       …(6) 
 
Where  and o are the viscosity  for the solution and solvent respectively,  and o 

are the densities of the solution and the solute respectively,  is ultrasonic wave velocity in 
the solution, t, to are flow times of solution and solvent respectively. T is the delay time of 
ultrasonic waves and x is the crystal moving distance.  

 

Results and Discussion 
The variation of the  viscosity , ultrasonic velocity, absorption coefficient, relaxation 

time, relaxation amplitude and specific acoustic impedance of Poly(acrylic acid) solutions 
with composition were shown in   figures 1, 2, 3, 4, 5 and respectively 6 .  

From these figures it is clearly evident that the values of these properties are 
increasing with the increasing concentrations of this polymer. Figure

 (7) shows the results for   
the adiabatic compressibility  of ultrasonic waves at 26 kHz and 30 ºC as a function of  
poly(acrylic acid) concentrations .  



  

IBN AL- HAITHAM J. FO R PURE & APPL. SC I        VO L.22 (4) 2009  
 
The interaction causing association between defferent concentrations of  Poly(acrylic 

acid) and water may be responsible for the increase in velocity, viscosity , relaxation time and 
relaxation amplitude

 [7,8,9]. The increase in the values of the acoustic attenuation with the 
increase in the concentration can be attributed to modification in the nature of the 
intermolecular interactions. These measurements suggest the formation of a more rigid 
structure with the increase of poly(acrylic acid) concentration, possibly due to the polymer-
water hydrogen bonding at sites on the polymer's carboxyl(CO2H) group. The behaviour 
observed in the poly(acrylic acid) aqueous solutions was observed in other polymer-water 
solutions [10]. 

 The attenuation of ultrasonic energy depends on viscosity , thermal conductivity, 
scattering and inter molecular processes, the thermal conductivity and scattering effects are 
known to be negligible

 [4,7] therefore, the inter molecular is responsible for the increase of 
the high values of the acoustic attenuation [7,9,11], indicating an increase in the overall size 
of the molecule in the path of ultrasonic waves as a result of complex formation between 
several polymer  macromolecules and solvent molecules

 
[4, 12]. 

Considering viscosity  as a relaxation phenomenon, the increase in the value of 
viscosity  versus concentration of solute supports the complex formation

 [4,7]. 
In Figure 7,at 1,5,10% and 15% poly(acrylic acid) concentration, the adiabatic 

compressibility  of poly(acrylic acid) aqueous solutions increase, from 20%, compressibility  
suddenly decreases with concentrations. This could be interpreted in terms of change in the 
structure of water and in the interaction between the polymer and water. This relaxation 
phenomenon in poly(acrylic acid) aqueous solutions might be the result of structural 
fluctuations of polymer molecules, such as the segmental motion of polymer chains and this 
behaviour suggests the formation of more structures [9,7,13].   
 

Conclustion 
This study shows that intermolecular processes are responsible for the relaxation and 

indicating an increase in the overall size of the molecules in the path of ultrasonic waves as a 
result of complex formation between Poly(acrylic acid) and solvents molecules. An ultrasonic 
relaxation in poly(acrylic acid) aqueous solutions, which may be the result of structural 
actuations of polymer molecules, such as the segmental motions of the polymer chains, was  
observed for the first time. 

 

References 
1.Blmeer, F., ( 1971), “Fundamental of polymer Sciences”, Joho wily and sons, Inc.. 
2.Shaghayegh J. and Hamid M., ( 2005), “ A Study on Swelling and Complex  
     Formationof Acrylic Acid and Methacrylic Acid Hydrogels with Polyethylene  

     Glycol”  ،“Iranian Polymer Journal”,14 (10):863-873. 

3.Hiroyasu, N.; Tatsuro, M. and Shinobu, K. ( 2004), “Ultrasonically induced  
      birefringence in polymer solutions”, “ Pure Appl. Chem. ”,. 76(1): 97–104. 
4.Hassun, S. and Rahman, K., (1989)Ultrasonic Study of Molecularer association  
      of high Impact Polystyrene Solutions in Toluene (1990)Iraqi J. Sci. 30:3-24. 
5.Blitz, J. (1967).Fundamental of Ultrasonic 2nd eedion,  
6.Khalida, H.H.; Alaa, F. and Salh, H. (2006) Study of Temperature Effect of  
      some Rheological and Electrical Properties of Poly isobutylene ,Journal of  
      Babylon University”, 13(3):530-538. 
7.Khalida, H. H., (2004), Study  of Structural and Visco-Relaxation of  
      Polycarbonates Solutions by Ultrasonic Technique”,“Journal of Al-Qadisiya  
       of Pure Sciences 9(3):118-122. 
8.Massoumeh, F. ( 2006) Density Dependence of the Viscosity  and Excess  
       Volume of Aqueous Solutions of Polyvinylpyrrolidone”, “Acta Chim. Slov.,  



  

IBN AL- HAITHAM J. FO R PURE & APPL. SC I        VO L.22 (4) 2009 
  

     53:219–222 .  
9.Syal ,V.K.;Anita ,Ch. and Suvarcha, Ch.. (2005), Ultrasonic velocity, viscosity  
      and density studies of poly (ethylene glycols)(PEG - 8,000, PEG - 20,000) in  
      acetonitrile (AN) and water (H2O) mixtures at 250C, J. Pure Appl Ultrason  
       27:  61-69. 
10.Jong ,R.B.  (2002) Ultrasonic Velocity and Absorption Measurements in  
     Binary Solutions, Journal of the Korean Physical Society, 41(1):171-174. 
11.Rajulu, A.V. and Redlody, R.L.,  (2000) Miscibility  Studies of Polystyrene  
       Blends as M easured by Viscosity, Ultrsonic, and Refractiv Index Methods, J.  
        Polymeric Mater, 5:467. 
12.Maffezzoli, A.; Tarziq, A. and Cannoletta, D.(1999) Ultrasonic  
       Characterization of the Kineties of Water Sorption in Hydrogels, M acromol  
       Symp. 138(144): 149-154. 
13.Hassun, S.K. and Isa, S.O. (1989) Visco-Relaxation Study of Poly (Vinyl a  
       lcohol) aqueous Solution (A M ethod for the Determination of Molecular  
       Weight)”,“British polymer Journal, 21: 333. 

  

Fig.( 1): The variation of Viscosity with Concentration of 

Poly(acrylic acid )  at 30 هC .

1.E-02

2.E-02

4.E-02

5.E-02

7.E-02

8.E-02

9.E-02

0 5 10 15 20 25 30 35
Concentration wt% of Poly(acrylic acid)

V
is

c
o

s
it
y

 (p
o

is
e)

 
 
 

  
 
 
 
 
 
 
 
 
 
 
 
 
 



  

IBN AL- HAITHAM J. FO R PURE & APPL. SC I        VO L.22 (4) 2009 
 

Fig.( 2) The variation of Velocity with Concentration  of 

Poly(acrylic acid )  at 30 
ه
C .

1500

1520

1540

1560

1580

1600

0 5 10 15 20 25 30 35
Co ncentration wt%

V
e

lo
c

it
y

 (
m

/s
)

 

Fig.( 3): The variation of absorption coefficient of ultrasonic 

waves with the Concentration of Poly(acrylic acid)  at 30
ه 
C .

1.0E-05

2.1E-04

4.1E-04

6.1E-04

8.1E-04

1.0E-03

1.2E-03

1.4E-03

0 5 10 15 20 25 30 35
Concentration wt% of Poly(acrylic acid .

A
b
s

o
rp

ti
o

n
 c

o
ef

fi
ci

e
n

t 
( 

m
-1

 )

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 



  

IBN AL- HAITHAM J. FO R PURE & APPL. SC I        VO L.22 (4) 2009 
 

Fig.( 4): The variation of relaxation time with the Concentration of 

Poly(acrylic acid)  at 30 
ه
C .

3.E-12

2.E-11

4.E-11

6.E-11

8.E-11

1.E-10

1.E-10

1.E-10

0 5 10 15 20 25 30 35

Concentration wt% of Poly(acrylic acid

R
e
L

a
x
a

ti
o

n
 t

im
e
 (
 s

  
) 

 

Fig.( 5) The variation of relaxation amplitude with 

the Concentration of Poly(acrylic acid) at 30
ه 
C .

2 .0E-14

3 .2E-13

6 .2E-13

9 .2E-13

1 .2E-12

1 .5E-12

1 .8E-12

2 .1E-12

0 5 10 15 20 25 30 35
C onc entr ation wt% of Poly(acrylic acid .

R
e

la
x

a
ti

o
n 

A
m

p
lit

u
d

e
 (

 s
2
 /

 m
 )

 .

 
 
 
 
 
 
 
 
 
 
 
 
 
 



  

 IBN AL- HAITHAM J. FO R PURE & APPL. SC I        VO L.22 (4) 2009 
 
 
 

Fig.( 6):The variation of specific acoustic impedance with 

the Concentration of Poly(acrylic acid) at 30 
ه
C .

25000

33000

41000

49000

57000

65000

73000

81000

89000

97000

0 5 10 15 20 25 30 35

Concentration wt% of Poly(acrylic acid ( g / ml ) .

S
p

e
c

if
ic

 A
c

o
u

st
ic

 I
m

p
e

d
a

n
ce

 (
 k

g
 /

 m
2
 .

 
s

 )

 

Fig.( 7): The variation of compressibility with 

the Concentration of Poly(acrylic acid ) at 30 
ه
C .

6.E-09

9.E-09

1.E-08

2.E-08

2.E-08

2.E-08

2.E-08

0 5 10 15 20 25 30 35

Concentration wt% of Poly(acrylic acid ( g / ml ) .

C
o

m
p

re
s

s
ib

il
it

y 
( 

m
 . 

s
2
 /

 k
g

 )