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 

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

    .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  
Departme nt of Physics, College of Education for Girls, Unive rsity of Kufa  

  
 

Abstract 
Ultrasonic absorp tion, velocity , viscosity , adiabatic comp ressibility , relaxation time 

and relaxation amp litude measurements are reported on different concentrations of 
p oly(acry lic acid) solutions in common solvent water using p ulsed ultrasonic app aratus 
technique op erating at 26 kHz and 30 ºC. 

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

time and relaxation amp litude values with the increasin g concentrations of the p oly (acry lic 
acid) solutions, which might be the result of structural fluctuations of p oly mer molecules such  
as the segmental motions of t he poly mer chains. In contrast  the compressibility  decreases with 
the increasin g concentration of this p olymer. This study  suggests there is an association 
between p olymer and solvent molecules and also there is association between  p olymer 
molecu les itself. 

  

Introduction  
     Poly (acry lic acid) is an unsaturated carbo xy lic acid. It read ily  undergoes  

p oly merization 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 disp erse the microcry stals or microsand of 
calcium carbonate, calcium p hosp hate and calciu m sulfate. PAA is used as sc ale inhib itor and  
disp ersant for circulating cool water system, p apermaking, weave, dy ein g, ceramic, p ainting,  
etc. 

 
  
 

 
 
 

PAA can be used as a scale inhib itor and disp ersant in circulating cool water sy stems 

in p ower p lants, iron & st eel factories, chemical f ertilizer p lants, refineries and air 

conditionin g sy stems. Dosage should be in accordance with water quality  and equip ment 

materials[1,2]. 

 



  

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

behaviour of p olymers in solutions. It is, therefore, imp ortant to obtain fundamental 
information on how this imp ortant and valuable p olymer acts in asolution, esp ecially  in 
water[3,4]. 

 
 

Experimental 
Poly (acry lic acid)  a fine white p owder has a molecular weight of 2,000 g.  Its solutions 

were p repared by  adding a known weight of the p olymer to a fixed volume of water, it was 
st irred for at least 20 hrs, at the temp erature 30°C . The ultrasonic velocity  measurements 
were obtained by  using the p ulsed ultrasonic technique of sender-receiver typ e (PHYWE-
WEST GERM ANY) Ultrasonic generator with constant frequency of 26kHz  [5]. The 
temp erature is maintained at 30

o
C circulatin g water from a t hermost at with a thermal st ability  

of 
+
 0.05

o
C through the double wall jak et of t he ultrasonic e xp erimental cell. The viscosity  of  

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

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

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

amp litude (/f
2
), viscosity  (), absorp tion coefficient (), and sp ecific acoust ic imp edance 

(Z) for the solutions were determined by using the following equations
 
(5, 6, 7). 

 
 
 =  (

2
)
-1

      …(1) 

2
3

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 resp ectively,  and o 

are the densities of the solution and the solute resp ectively,  is ultrasonic wave velocity  in 
the solution, t, to are flow times of solution and solvent resp ectively. T is the delay time of 
ultrasonic waves and x is the cry st al moving distance.  

 

Re sults and Discussion 
The variation of the  viscosity , ultrasonic velocity , absorp tion coefficient, relaxation 

time, relaxation amp litude and sp ecific acoust ic imp edance of Poly (acry lic acid) solutions 
with comp osition were shown in   figures 1, 2, 3, 4, 5 and resp ectively 6 .  

From these figures it is clearly  evident that the values of these p rop erties are 
increasin g with the increasin g concentrations of this p olymer. Figure

 
(7) shows t he results for   

the adiabatic comp ressibility  of ultrasonic waves at 26 kHz and 30 ºC as a function of  
p oly (acry lic acid) concentrations .  



  

IBN AL- HAITHAM J. FO R PURE & APPL. SC I        VO L.22 (4)  2009  
 
The interaction causin g association between deffer ent concentrations of  Poly (acry lic 

acid) and water may  be resp onsible for the increase in velocity , viscosity , relaxation time and 
relaxation amp litude

 
[7,8,9]. The increase in the values of the acoust ic att enuation with the 

increase in the concentration can be att ributed to modification in the nature of the 
intermolecu lar interactions. These measurements suggest the formation of a more rigid 
st ructure with the increase of p oly(acry lic acid) concentration, p ossibly  due to the p oly mer-
water hy drogen bonding at sites on the p olymer's carboxy l(CO2H) group . The behaviour 
observed in the p oly(acry lic acid) aqueous solutions was observed in other p oly mer-water 
solutions [10]. 

 The att enuation of ultrasonic energy  depends on viscosity , thermal conductivity , 
scatt ering and inter molecular p rocesses, the thermal conductivity  and scatt ering effects are 
known to be negligible

 
[4,7] therefore, the inter molecular is resp onsible for the increase of 

the high values of the acoust ic att enuation [7,9,11], indicating an increase in the overall size 
of the molecule in the p ath of ultrasonic waves as a result of comp lex formation between 
several polymer  macromolecules and solvent molecules

 
[4, 12]. 

Considering viscosity  as a relaxation p henomenon, the increase in the value of 
viscosity  versus concentration of solute sup p orts t he complex formation

 
[4,7]. 

In Figure 7,at 1,5,10% and 15% p oly(acry lic acid) concentration, the adiabatic 
comp ressibility  of p oly(acry lic acid) aqueous solutions increase, from 20%, comp ressibility  
suddenly decreases with concentrations. This could be interp reted in terms of change in the 
st ructure of water and in the interaction between the p olymer and water. This relaxation 
p henomenon in p oly(acry lic acid) aqueous solutions might be the result of st ructural 
fluctuations of p olymer molecules, such as the segmental motion of p olymer chains and this 
behaviour suggests t he formation of more st ructures [9,7,13].   
 

Conclustion 
This study  shows that intermolecular p rocesses are resp onsible for the relaxation and 

indicating an increase  in the overall size of the mo lecules in the p ath of ultrasonic wav es as a 
result of complex formation between Poly(acry lic acid) and solvents molecules. An u ltrasonic 
relaxation in p oly(acry lic acid) aqueous solutions, which may  be the result of structural 
actuations of p oly mer molecules, such as the segmental motions of the p oly mer chains, was  
observed for the first time. 

 

Re ferences 
1.Blmeer, F., ( 1971), “ Fundamental of p olymer Sciences”, Joho wily and sons, Inc.. 
2.Shaghayegh J. and Hamid M ., ( 2005), “ A Study  on Swelling and Comp lex  
     Formationof Acry lic Acid and M ethacrylic Acid Hy drogels with Poly ethy lene  

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

3.Hiroy asu, N.; Tatsuro, M. and Shinobu, K. ( 2004), “Ultrasonically induced  
      birefringence in polymer solutions”, “ Pure App l. Chem. ”,. 76(1): 97–104. 
4.Hassun, S. and Rahman, K., (1989)Ultrasonic Study  of M olecularer association  
      of high I mpact Polysty rene 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 Temp erature Effect of  
      some Rheological and Electrical Prop erties of Poly  isobutylene ,Journal of  
      Babylon University”, 13(3):530-538. 
7.Khalida, H. H., (2004), Study  of Structural and Visco-Relaxation of  
      Poly carbonates Solutions by  Ultrasonic Technique”,“Journal of Al-Qadisiya  
       of Pure Sciences 9(3):118-122. 
8.M assoumeh, F. ( 2006) Density Dep endence of the Viscosity  and Excess  
       Volume of Aqueous Solutions of Poly vinylpy rrolidone”, “Acta Chim. Slov.,  



  

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

     53:219–222 .  
9.Sy al ,V.K.;Anita ,Ch. and Suvarch a, Ch.. (2005), Ultrasonic velocity , viscosity   
      and density  studies of p oly (ethy lene gly cols)(PEG - 8,000, PEG - 20,000) in  
      acetonitrile (AN) and water (H2O) mixtures at 250C, J. Pure App l Ultrason  
       27:  61-69. 
10.Jong ,R.B.  (2002) Ultrasonic Velocity  and Absorption M easurements in  
     Binary  Solutions, Journal of the Korean Phy sical Society , 41(1):171-174. 
11.Rajulu, A.V. and Redlody, R.L.,  (2000) M iscibility  Studies of Polystyrene  
       Blends as M easured by  Viscosity , Ultrsonic, and Refractiv Index M ethods, J.  
        Poly meric M ater, 5:467. 
12.M affezzoli, A.; Tarziq, A. and Cannoletta, D.(1999) Ultrasonic  
       Characterization of the Kineties of Water Sorp tion in Hy drogels, M acromol  
       Sy mp. 138(144): 149-154. 
13.Hassun, S.K. and Isa, S.O. (1989) Visco-R elaxation Study  of Poly  (Vinyl a  
       lcohol) aqu eous Solution (A M ethod for the Determination of M olecular  
       Weight)”,“British p oly mer Journal, 21: 333. 

  

Fig.( 1): The variati on of Viscosity wi th Concen tration of 

Po ly(acr ylic 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
Conc entration w t% of P oly(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 vari ation of Veloci ty with Concentration  of 

Poly(acrylic aci d )  at 30 
ه
C .

1500

1520

1540

1560

1580

1600

0 5 10 15 20 25 30 35
Co ncentrati on wt%

V
e

lo
c

it
y

 (
m

/s
)

 

Fig. ( 3): The variation of absorption c oefficient of ultrasonic 

w aves 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
e
ff

ic
ie

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 aci d)  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

Concentrat ion wt% of Pol y(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(acr ylic acid .

R
e

la
x

a
ti

o
n
 A

m
p

li
tu

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 specifi c acoustic impedance with 

the Concentration of P oly(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(a cryli c acid ( g / ml  ) .

S
p

e
c

if
ic

 A
c

o
u

s
ti

c
 I

m
p

e
d

a
n

c
e

 (
 k

g
 /

 m
2
 .

 
s

 )

 

Fig .( 7):  T he variatio n o f compressibility with 

the Concentration of Po ly(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

Concentra tion wt% of Poly(acrylic acid ( g / m l ) .

C
o

m
p

re
s

s
ib

il
it

y
 (

 m
 .
 s

2
 /

 k
g

 )