REFERENCES - mqa.ogpta.polsl.plmqa.ogpta.polsl.pl/files-articles/28/pdf/293-298.pdfREFERENCES 1....

Molecular and Quantum Acoustics vol. 28 (2007) 239

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– S. Mørup, M.F. Hansen, Handbook of Magnetism and Advanced Magnetic Materials, Wiley, New York, 2007, Vol. 4, 2159-2176.

– W.A. Urs, H.R. Hergt, R. Misri, Handbook of Magnetism and Advanced Magnetic Materials, Wiley, New York, 2007, Vol. 4, 2536-2569.

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– B. Payet, D. Vincent, L. Delaunay, G. Noyel, J. Magn. Magn. Mater. 186, 168–174 (1998).

– R.E. Rosensweig, J. Magn. Magn. Mater. 252, 370-374 (2002).

– E. Blums, A. Cebers, M.M. Maiorov, Magnetic Fluids, Walter de Gruyter, Berlin, New York 1997, 14-48.

– R.H. Kodama, J. Magn. Magn. Mater. 200, 359-372 (1999).

– Y. Wang, S. Maksimuk, R. Shen, H. Yang, Green Chemistry 9, 1051-1056 (2007).

– N. Fan, X. Ma, X. Liu, L. Xu, Y. Qian, Carbon 45, 1839-1846 (2007).

– L. Zhang, Y.H. Dou, H.C. Gu, Journal of Crystal Growth 296, 221-226 (2006).

– A. Skumiel, J. Magn. Magn. Mater. 307, 85-90 (2006).

– E. Zorebski, Molecular and Quantum Acustics 24, 261-270 (2004).

– B. Linde, Molecular and Quantum Acoustics 27, 169-188 (2006).

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– M. Ma, Y. Wu, J. Zhou, Y. Sun, Y. Zhang, N. Gu, J. Magn. Magn. Mater. 268, 33-39 (2004).

– R. Hiergeist, et al., J. Magn. Magn. Mater. 201, 420-422 (1999).


SOUND WAVES DIFFRACTION PHENOMENA AT OPENING OF

SOFT CYLINDRICAL DUCTS

Anna SNAKOWSKA

University of Rzeszow, Institute of Physics, 16 RejtanaStr, 35-959 Rzeszów, POLAND

[email protected]

The paper presents analytical description of diffraction phenomena at the

opening of an acoustically soft cylindrical duct and solution of the wave equation

with adequate boundary condition imposed by the duct wall. Mathematical tools

which were applied are the Green’s first theorem and the Green’s free-space

function in cylindrical co-ordinates. As a result, the velocity potential was

expressed as a surface integral, containing discontinuity of the normal component

of the particle velocity on the duct wall. The solution of the problem consists in

calculating this discontinuity by means of the Wiener-Hopf technique and results

in formulas for the velocity potential inside and outside the duct.

1. INTRODUCTION

The duct-like elements are frequently met in many technical and industrial devices,

where they are sources of harmful and undesired noise. Thus the phenomena occurring at the

duct outlet are presented in numerous scientific papers, long list of which is included in [1,2].

Account for diffraction at the outlet substantially complicates the solution of the wave

equation. To avoid that, the solution obtained for the duct with the outlet placed in an infinite

baffle is applied most often, even though it does not reflect the practice. The baffle changes

the area into which the energy is radiated and so it influences the reflection coefficients, the

directivity characteristics, the impedance of the outlet and other physical quantities describing

the sound field inside and outside the duct. For that reason the solution counting for

diffraction has not only theoretical, but also practical meaning. Hard and soft ducts [3,4]

represent limiting cases (wall impedance equal to infinity or zero) of real ducts which, in

general, have complex wall impedance [5].

The approach presented in this paper is analogous to the one applied by the author for

the hard duct [3] and is based on the Wiener-Hopf method [5-9].

242 Snakowska A.

2. THE WIENER-HOPF METHOD

The assumptions under which the problem is considered are as follows: the duct is

acoustically soft, its wall is described in the cylindrical co-ordinates system as

and is filled with non-absorbing and non-dispersive medium excited

to harmonic vibrations with angular frequency ω. To solve the wave equation for the velocity

potential , with the boundary condition for the acoustic pressure

, corresponding to the Dirichlet condition , the first Green theorem for

scalar functions is applied, what results in integral equation [6]

(1)

where denotes the free-space Green function and is the jump of the normal velocity

on the duct surface

(2)

interpreted as the effect of appearance, due to diffraction of the incident wave, of the so called

image-sources.

Assume the incident wave to have the form of the single mode propagating without

energy dissipation in an infinite soft duct [9]

(3)

where is the axial wave number, is the wave number, is the m-th

order Bessel function and is its l-th root ( =0. K is a constant, (the

prime sign denotes derivative) ensuring unit velocity amplitude at the duct wall and simple

form of succeeding equations, analogues to equations derived for the hard duct, which will be

recalled in what follows.

Analysing the function one sees that its dependence on must be the same as in

(3), so that Denoting the first term describes the

velocity of the incident wave, while the second one the diffracted term. Introducing the

explicit form of the Green’s function in the cylindrical co-ordinates [6], one can express the

potential (1) and the boundary conditions

(4)

(5)


where and is the m-th order first kind Hankel function [7]. The integration

limits in the last two expressions were expanded to , because on elongation of the

duct wall the particle velocity must be continuous function and thus .

Next step of the Wiener-Hopf technique [6, 7] consists in deriving the Fourier transform

of the diffraction term (image-sources function)

(6)

The boundary condition has the form of integral equation of the Wiener-Hopf type, with the

kernel of translated argument

(7)

where is the second integral in equation (4) and has the form of the inverse Fourier

transform. Finally, introducing

(8)

one may express the two conditions imposed on the solution by means of the Fourier

transforms and

(9)

(10)

The last two integral equations, corresponding to similar pair met in a hard duct theory [3],

are true under the following conditions:

– the function is analytic in the lower complex half plane , except for one

point , in which its residue is equal to imaginary unit and on the semicircle in

the upper half-plane ∞, , tends uniformly to zero,

– the product of Fourier transforms is an analytic function in the lower half

plane , and tends uniformly to zero on a semicircle lying in that area.

3. FACTORIZATION OF THE LM TRANSFORM

To introduce analytic functions into the theory, the wave number is assumed to have a

small, positive imaginary part . Thus, the factor is analytic and has no roots

in the domain while the factor has the same properties for . The

function is similar to the one obtained by Weinstein [10] for electromagnetic waves of

TM type. Following his calculations one obtains

244 Snakowska A.

where denotes number of modes of m-th circumferential order for which (axial

wave numbers are real). The real and imaginary part of function

are equal to

where stands for the main value of the integrand (13), and

The explicit form of the derived factors , allows to calculate the Fourier

transform as

what ensures fulfillment of both equations (9, 10) and leads to the velocity potential formula,

based on results presented in [3,10].

4. THE VELOCITY POTENTIAL

As was mentioned before, the explicit form of the transform (6), which

represents the diffracted field, i.e. the image-sources appearing on the duct wall as an effect of

diffraction, allows to calculate the velocity potential, which one can write as

where, according to (4) and (9), the diffracted term takes the form

(16)


Fig. 1. Contour of integration to calculate the potential inside the duct.

The last integral will be calculated by closing the contour of integration with a

semicircle , located on upper or lower complex half-plane (Fig.1) It

passes around the cut-line , on which singularities of the integrand are situated at

.

As a result, the velocity potential inside the duct takes the form

where the first term represents the incident wave, while the sum – modes appearing as a result

of diffraction, among which one can identify the propagating modes ( real, .

The factor stands for the reflection or transformation coefficients, equal to

the ratio of the amplitude of the mode excited at the outlet to the amplitude of the

incident mode

where .

To calculate the field outside the duct one has to consider three areas: ,

, proceeding calculations applying upper ) or lower

form of expression (4) and closing the contour of integration in the upper or lower

half-plane. Finally, the potential outside the duct takes the form of integral over the cut-

line

246 Snakowska A.

situated in the upper ), or lower ), half-plane. Thus, for real the limits of

integration are equal to and .

5. CONCLUSION

Analytical solution of the sound field of a semi-infinite duct, accounting for diffraction

at the outlet, have been obtained applying the Wiener-Hopf method. The velocity potential

inside the duct has a form of a sum of the incident wave and duct modes excited due to

diffraction which propagate backward from the opening. The velocity potential outside has

the form suitable for applying the saddle point method to calculate the far field and the

directivity characteristics. The presented solution allows to derive explicit formulas for the

reflection coefficients, the impedance of the outlet, the power radiated outside and returned to

the duct etc.

Because of complicated form of the solution, especially the function, further

analysis can be proceed only by means of numerical methods.

REFERENCES

1. L.M.B.C. Campos , J.M.G.S. Oliveira , J. Acoust. Soc. Am. 116/6, 3336-3347 (2004).

2. Encyclopedia of Acoustics, Edited by M. J. Crocker, Chapter 8: Davies P.O.A.L. “Waveguides” J. Villey & Sons, Vol. 1, 91-105 (1997).

3. A. Snakowska, R. Wyrzykowski, Archives of Acoustics 11/3, 261-285 (1986).

4. E.J. Rice, “Modal propagation angles in ducts with soft walls and their connection with suppressor performance”, AIAA 5th Aero-acoustics Conference, Seattle (1979).

5. A.D. Rawlins, “Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface”, Proc. R. Soc. London A 361, 65-91 (1978).

6. P. Kaniewski, Molecular and Quantum Acoustics 26, 129-148 (2005).

7. P.M. Morse, H. Feshbach. “Methods of theoretical physics” Mc Graw Hill, New York 1961.

8. V. Petrov, S. Lapin, V. Chirkov, Molecular and Quantum Acoustics 24, 141-148 (2003).

9. L. Leniowska, Molecular and Quantum Acousics 24, 109-124 (2003).

10. L.A. Weinstein, “The theory of diffraction and the factorization method (Generalised Wiener-Hopf technique)”, Golem Press, Boulder, Colorado, 1969.


ULTRASONIC CAVITATION IN SEWAGE SLUDGE

Piotr SORYS, Ewa ZIELEWICZ-MADEJ

Institute of Water and Wastewater Engineering, Silesian University of Technology,

Konarskiego 18A, 44-100 Gliwice, POLAND

The study revealed considerable differences in the susceptibility of the sludge to

preliminary treatment by two kind of mixing and expressed as changes in the

initial properties of the sludge and thus conditions for the occurrence of

ultrasonic disintegration in particular sludge from wastewater treatment plants

G, K and Z. The susceptibility of sludge to ultrasounds which depends on the

sludge properties was explained by the higher COD of dissolved matter after

ultrasonic disintegration of sludge.

1. INTRODUCTION

The diversified effect of ultrasounds enables their application to the physicochemical

processing of excess sludge produced during biological treatment of wastewater.

The possibility for intensifying the hydrolytic phase of excess sludge digestion which

limits further processes of biochemical decomposition of organic compounds by bacteria in

subsequent phases (acidogenic, acetogenic and methanogenic) has become one of the most

interesting and extensively analyzed research problems in the technology of wastewater and

sewage sludge treatment. It may be carried out via the preliminary treatment of the sludge by

thermal, chemical and mechanical methods or a combination of those [1]. The treatment is

aimed at dispersing the solid phase of the sludge and destroying microorganism cells with

concomitant release of substrates and enzymes into the sludge fluid for further biochemical

decomposition of organic matter. The Institute of Water and Wastewater Engineering at the

Silesian University of Technology has investigated the application of ultrasounds to the

disintegration of activated excess sludge for many years. Its objective was the intensification

of the acidogenic and acetogenic phases of digestion to obtain short-chain organic acids

(VFA) [2,3].

2. THEORETICAL ASSUMPTIONS

The majority of research staff and engineers or specialist in ultrasonic technology

express the opinion that active reaction of ultrasounds in liqids is, first of all, the result of

ultrasonic cavitation. The rapid implosion of the cavitation bubbles causes a local pressure

248 Sorys P., Zielewicz-Madej E.

increase and elastic shock waves [4]. Since the collapse of the bubbles is very short (a few

μs), it is assumed that a simultaneous adiabatic compression occurs coupled with a quasi-

adiabatic temperature increase of about several thousand K [5]. The occurrence of ultrasonic

cavitation depends on a number of factors (temperature, surface tension, medium viscosity,

hydrostatic pressure, the degree of gas saturation, gas type and others), therefore they are

different for different mediums and experimental conditions. Because cavitation takes place

primarily on the phase boundary, the presence of gas bubbles and the ones suspended in the

medium, called the germ of cavitation, increases the susceptibility of the liquid to the process.

All factors which decrease the viscosity of the liquid and break up the continuity of its

structure, all solid, liquid and gaseous waste, as well as the roughness of the walls of the

chambers in which ultrasonic treatment is carried out bring about a decrease in the cavitation

threshold [5]. The use of ultrasounds in the aqueous environment offers a lot of technological

opportunities for the treatment of water, wastewater and sewage sludge [6,7]. Local

occurrence of high pressures and temperatures during bubbles collapse explains possible,

deep, diversified and often irreversible changes in the structure and other physicochemical

properties of sewage sludge subjected to ultrasounds [8,9].The mechanical and sonochemical

treatment of excess sludge may result in the destruction of the flocculent structure of excess

sludge, increase in particle dispersion, destruction of the cell membranes of microorganisms

and release of cell matter into sludge liquid [2,10-14].The investigations carried out by us and

other researchers for the last several years have shown that the disintegration of sewage

sludge should be conducted using ultrasounds generated at a relatively narrow range of 16

kHz - 50 kHz.

3. OBJECTIVE, SCOPE AND METHODOLOGY OF THE RESEARCH

The research aimed at comparing the conditions for occurrence of disintegrating

cavitation in several excess sludge characterized by different consistency, hydration,

concentration of organic matter and different initial CODnn of the compounds dissolved in

the total CODo of the sludge. They were collected in wastewater treatment plants (denoted as

G, K and Z) only after the mechanical thickening process aided by introducing appropriate

polyelectrolyte doses. The concentrations of the dry weight of the sludge showed that the

efficiency of the thickeners differed 1.3 - 2-fold (Table 1).


Tab. 1. Parameters of sludge and sludge liquid prior to ultrasonic treatment.

Lp. Symbol of

sludge

Parameters of sludges (aerated of mixes) before sound

amplificationDrymass

concentatrion

Organic

compound

s

COD0 CODnn CODnn/

COD0

x x % % mg/l mg/l %1 2 3 4 5 6 72 Z 5,7 69 86432 89 0,103 Z-aerated 5,7 69 86432 105 0,124 Z-mixed 5,7 69 86432 368 0,435 K 3,1 71 56470 116 0,216 K-aerated 3,1 71 56470 116 0,217 K-mixed 3,1 71 56470 112 0,208 G 3,8 70 42340 71 0,179 G-aerated 3,8 70 42340 129 0,3010 G-mixed 3,8 70 42340 181 0,43

The study also examined the effect of sludge preparation (preliminary mechanical or

compressed air stirring) for ultrasonic disintegration on the results obtained. The preparation

of the sludge prior to ultrasonic treatment involved a short (5 min) stirring of 1-litre sludge

sample with a paddle stirrer (1450 rpm) or 1-h aeration with compressed air at 6 l/min. Both

types of stirring were used to increase the susceptibility of the sludge to ultrasounds by

dispersing of particles and introduction of gas bubbles which break up the liquid phase. The

sludge were treated with ultrasounds in a laboratory employing an experimental system

equipped with a WK-2000 disintegrator produced at the Silesian University of Technology

(Fig.1). 300-ml sludge samples were placed in a cylindrical steel chamber of 8 cm in

diameter, the ultrasound transducer head being submerged in the sludge at a depth of h=1.0

cm below the surface. The sonotrodes transmitted ultrasounds to the sludge samples at

frequencies of 10, 23 and 30 kHz, changeable ultrasonic treatment time in the range of 0.5 –

10 min and constant electrical power of the disintegrator of PG = 450 W. CODnd of the liquid

(the basic parameter used to monitor the effects of ultrasonic disintegration) was assayed

after it had been centrifuged (20 000 rpm) and filtered through cellulose acetate membrane

0.45μm (COD of dissolved fraction showed the disintegration of microorganism cells and

sonolysis) [1,2]. The extent of ultrasonic disintegration was measured on the basis of process

variables:

kd1 = CODnd/CODnn (bw) (1)

CODnd - COD of liquid phase of sludge treated with ultrasounds

CODnn - COD of liquid phase of sludge not treated with ultrasounds


02468

1012141618202224262830323436

0 1 2 3 4 5 6 7 8 9 10 11Time of sonification (min)

kd

1 (

-)

kd1-G

kd1-K

kd1-Z

Fig. 1. Ultrasonic disintegrator WK-2000. Fig. 2. The influence of time on degree of disintegration.

3. RESULTS

The susceptibility of sludge to ultrasounds depends on the sludge properties which are a

function of its formation during wastewater treatment The study revealed considerable

differences in the susceptibility of the sludge to stirring by compressed air or mechanical

stirrer expressed as changes in the initial properties of the sludge (Table 1), and thus

conditions for the occurrence of ultrasonic cavitation in particular sludge. For instance,

aeration substantially changed the properties of sludge G, while those of sludge Z and K

remained almost unchanged. The mechanical stirring increased the amount of dissolved

matter (CODnn) in sludge Z and G 4-fold and 3-fold respectively, producing no increase in

sludge K. However, sludge K, not susceptible to the preliminary treatment, which might be

explained by its homogenous consistency and a relatively high initial hydrolysis ( CODnn/

CODo) was most susceptible to ultrasounds alone, which may result from the favourable, low

initial concentration of dry weight ( about 4%).Despite the different susceptibility of sludge

G, Z and K to ultrasounds, an increase in ultrasonic treatment time affected ultrasonic

disintegration (expressed as kd1). of all the sludge. The correlations, however, are neither

directly proportional to ultrasonic treatment time, and thus energy used, nor identical for all

the sludge (Fig.2). Although the ultrasonic treatment time of 10 min was the most favourable

for all the sludge, the effects obtained for the time of 5 min were only slightly worse and the

differences did not justify the use of twice (from 125 kWh/m3 to 250 kWh/m3) as much of

energy. The characteristic correlations between the ultrasonic treatment and the effect of

aeration and stirring (for the time of 5 min and frequency of 23 kHz) are shown in the

diagrams (Fig.3). Most tests revealed a favourable effect of combined preliminary stirring and

ultrasonic treatment on final disintegration. Fig.4 depicts a correlation between disintegration

degree kd1and ultrasound frequency typical of all the sludge. The efficiency of ultrasounds of


23 kHz proved to be the highest, which is another confirmation of the conclusions drawn by

us and other authors [3,12] that the frequency of 20-25 kHz is the most favourable for

ultrasonic disintegration of excess sludge.

0

100

200

300

400

500

600

700

800

900

CO

D [

mg

O 2/d

m3 ]

G

G-s

tirre

d

G-a

erate

dZ

Z-stir

red

Z-aera

ted

K

K-s

tirre

d

K-a

erat

ed

increase of COD in liquid phase of sound desintegratedsludgeCOD of liquid phase in untreated sludge

Fig. 3. The final effect of CODnd production in disintegrated sludge.

0

5

10

15

20

25

30

0 10 20 30 40

Frequency (kHz)

kd

1 (

-)

G

Z

K

Fig. 4. Correlation of disintegration coefficient kd1 and ultrasound frequency at time 5 min.

4. CONCLUSIONS

– The susceptibility of sludge (collected at the three different treatment plants) to the

disintegrating effect of ultrasounds depended greatly on their initial properties.

– Each sludge displayed too different susceptibility to the preliminary treatment of stirring

or aeration, sludge K showing the most negligible effect of preliminary treatment on the

final results of disintegration; the preliminary mechanical stirring is favourable for sludge

Z while compressed air proved to be better for sludge G.

– Sludge K characterized by the lowest initial CODnn/ CODo and lowest concentration of

dry weight (3.1%) turned out to be the most susceptible to ultrasonic disintegration.


– The total disintegrating effect of combined preliminary treatment by mixing and ultrasonic

disintegration was higher than the ultrasonic treatment alone.

– The frequency of 23 kHz produced the most favourable disintegration effect for all the

sludge.

REFERENCES

11. J. Müller, Water Science Technology 38, 425-433 (1998).

12. A. Tiehm, K. Nickel, U. Neis, Water Science Technology 36, 121-128 (1997).

13. E. Zielewicz-Madej, Molecular and Quantum Acoustics 21, 319-327 (2000).

14. A. Śliwiński, Ultradźwięki i ich zastosowanie, 347-372 (WNT, Warszawa, 1993).

15. H. Destaillats, M. Hoffman, H. Wallace, Sonochemical degradation of pollutants, Environmental and Industrial Application, 201-234 (Marcel Dekker Inc., NewYork-Basel, 2001).

16. T. Mason, E. Joyce, S. Phull, J. Lorimer, Ultrason. Sonochem 10, 319-323 (2003) .

17. O. Schlafer, et al., Ultrasonics 40, 25-29 (2002).

18. E. Kowalska, J. Bień, E. Zielewicz-Madej, Drying Technology 6, 447-471 (1988).

19. J. Bień, E. Kowalska, E. Zielewicz, Acustica 40 99-103 (1978).

20. A. Szpakowski, T. Pustelny, Molecular and Quantum Acoustics 26, 261-266 (2005).

21. E. Zielewicz-Madej, Inżynieria i Ochrona Środowiska 4, 231-237 (2001).

22. T. Pustelny, Ultrasonics 33/4, 289-294 (1995).

23. C. Chu, et al., Water Research 35, 1038-1046 (2001).

24. E. Zielewicz-Madej, Molecular and Quantum Acoustics 26, 299-308 (2005).


PIEZOELECTRICAL PROPERTIES OF X/65/35 PLZT CERAMICS

DEPENDED OF THE LANTHANUM (X) IONS CONTENTS

Zygmunt SUROWIAK, Malgorzata PLONSKA

Department of Material Science, Faculty of Computer Science and Material Science,

University of Silesia, 2 Śnieżna Str., 41-200 Sosnowiec, POLAND

[email protected]; [email protected]

For many years the PLZT ceramics have been known as a ferroelectric material

which has various electro-optic and piezoelectric properties. The aim of this work

was to study how the lanthanum dopant (x) influences on the piezoelectric

properties of x/65/35 PLZT ceramics. All samples were sintered by the hot

uniaxial pressing method, from the sol-gel derived powders. The measurements

enclose the complex of electric parameters, such as: ε, tgδ, kp, k31, d31, SE11,

g31, VR. The domain structures of unpoled and poled samples were conducted on

the FESEM HITACHI S-4700.

1. INTRODUCTION

The ferroelectric ceramics have a number of properties, which make them very useful in

a variety of applications. As an example of such materials the lanthanum – doped PZT

systems, represented also as PLZT. Solid - state nature of PLZT material is based on: the

simple PbZrO3-PbTiO3 solid solution system, the function of the lanthanum concentration as

well as the Zr/Ti ratio. Donor dopants of higher charge, like a La3+ ions, enhance domain wall

mobility and result in improved remanent polarization, coupling factors, dielectric constants,

dielectric loss tangent and increased of optical transparency of electrically “soft” PZT

material [1, 2]. The result of such doping is also attributed to the creation of vacancies (V) in

the A site of perovskite crystal structure, thus the chemical composition of PLZT is given by

the formula [3]:

Pb1-xLax(Zr1-yTiy)1-x/4V0,25x O3, (1)

Creations of such vacancies ensure electric neutrality of the lead lanthanum zirconate

titanate system. The composition of PLZT is routinely represented by the notation x/(1-y)/y,

which denotes the amount of La/Zr/Ti, given in mole fractions or mole per cent.

254 Surowiak Z., Plonska M.

The goal of this study was: to obtained PLZT materials, from sol-gel derived powders

by the hot uniaxial sintering method (HUP), subjected all samples to polarization by the low

temperature method, and to study the influence of La3+ dopant on their basic dielectric and

piezoelectric properties.

2. MATERIALS AND EXPERIMENTAL PROCEDURE

Based on the PLZT phase diagram [4] to the study the chosen materials had chemical

compositions corresponding to x/65/35 ratio, with different amount of lanthanum (x), for

x=0-12 mol%. The technological fabrication process of the all ceramic samples included two

stages, described in more details in previous works, i.e. [4-7]. Firstly, a modified low

temperature sol-gel synthesis was employed to obtain PLZT nanopowders, from the

organometallic precursors of Pb(OAc)2, La(OAc)3,Zr(O-nPr)4 and Ti(O-nPr)4, in the suitable

solvent – n-propyl alcohol and stabilizing agent - acetyloacetone. The second stage involved

consolidation of such prepared powders and obtaining high density ceramics by the hot

uniaxial pressing method. All samples were received at the experimentally verified

temperature, Ts = 1473 K for t = 2 h, as a shape of discs about (10×1) mm2 of dimension. The

flow chart of the preparation of PLZT bulk ceramics is showed in Fig.1.

Fig. 1. Flow chart of the PLZT ceramics fabrication process.

After sintering each of PLZT samples were ground, polished and than stress relief

annealed at T = 873 K for t = 0.5 h. Before the dielectric and piezoelectric measurements on

the ceramics surface were deposited electrodes by the silver paste burning method. Such

prepared samples were subjected next to polarization by the low temperature method in

silicone oil, with the feeder of high voltage HEOPS-5B6. Polarized conditions were Tp = 423

K, Ep = 20 kV/cm, t = 30 min. Piezoelectric parameters of poled samples were determined by

resonance – antiresonance method. Dielectric permittivity ε and dielectric loss tangent tgδ were measured during the cooling cycles with Quadtech 1920 impedance meter, for the non-

poled samples with temperatures T (T = Tm = TC, Tm is temperature at which ε(T) reaches its

maximum – the Curie point) [6-9].


3. RESULTS AND DISCUSSIONS

Dielectric measurements exhibited the influence of lanthanum dopant on the dielectric

parameters of the x/65/35 PLZT system. Figure 2 shows, that already with the small amount

of lanthanum dopping ε growth to the value of εm2= 28955 for 2/65/35 PLZT, while for PZT

65/35, without dopant, εm1 = 27299. Further increase of La3+ content reduced the maximum of

dielectric constant peak (Curie point) and displaced them to the low temperature, make their

more diffuse. The maximum of loss tangent overlap with maximum of the dielectric

permittivity, and increased with the increase of La content. Observed characteristics are

typical for the relaxor materials, exhibiting diffuse phase transitions. The influence of

lanthanum amounts on Curie point - εm and Tm is shown in Fig.3.

Fig. 2. Temperature dependence of the dielectric permittivity ε and loss tangent tgδ for x/65/35 PLZT compositions with x= 0–12 La3+ at.%.

Fig. 3. Influence of amount of lanthanum dopant on Curie point, for x/65/35 PLZT with x = 0 – 12 La3+ at. %.

Figure 4 illustrates the effect of the poling process on the PZT 65/35 samples. In the

unpoled ceramics (Fig.4a) each grain contains a number of domains, and the net polarization

is zero. After poling, as can be seen in Fig.4b, the domains are oriented with net polarization

along the direction of applied field. Such effect confirmed that material is piezoelectrically

active.

Fig. 4. SEM morphologies of the chemically etched fracture surface of: (a) unpoled PZT 65/35 ceramic; (b) poled PZT 65/35 ceramic.

256 Surowiak Z., Plonska M.

Basing on the measured data’s the important piezoelectric parameters were calculated.

A summary of parameters of some selected PLZT compositions is given in table. As can also

be seen in Fig.5, the influence on each of piezoelectric factors with lanthanum amount was

observed. The acoustic velocity - VR decreases, when the elastic susceptibility - SE11 increases

with the growth of applied dopant (x = 0-9 La at.%). In case of the electromechanical

coupling coefficient -kp, the cross electromechanical coupling coefficient - k31, and the

piezoelectric modulus - d31, all values increase to the 6 at.% La, and for larger contents the

significant decrease of those parameters can be observed. The piezoelectric constant - g31

characteristic was variable independence on lanthanum ions in x/65/35 PLZT. It decreases for

x = 0, 2, 6, 9. But for 8/65/35 PLZT unexpected growth of value happened.

The x/65/35 PLZT compositions with x larger than 9 at.% quantity of La3+ the polarized

state for applied poling conditions was not observed, therefore they were not considered in the

results.

Fig. 5. The influence of La3+ dopant on piezoelectric parameters x/65/35 PLZT.

Table. The piezoelectric parameters of some selected PLZT compositions.

PLZT

x/65/35

VR ×103

[m/s]

g31×10-3

[Vm/N]

k31 kp d31×10-11

[C/N]

SE11×10-11

[m2/N]

0/65/35 2,356 12,08 0,23 0,41 4,45 1,02

2/65/35 2,147 10,49 0,24 0,46 6,91 1,27

6/65/35 2,096 8,05 0,29 0,53 14,39 1,31

8/65/35 1,934 8,8 0,14 0,33 4,12 11,77

9/65/35 1,344 6,12 0,06 0.23 2,43 39,46


4. CONCLUSION

As a donor dopant, La3+ makes PLZT x/65/35 electrically “soft” materials. Results have

shown that a growth of x in x/65/35 compositions exhibited diffuse phase transition in

temperature dependence of ε and tgδ. Also the piezoelectric properties were considerably

depended on the lanthanum contents, and for the PLZT compositions above the 9 at.% La the

polarized state were not achieved.

REFERENCES

1. C. Galassi, et al., NATO ASI Series 3: High Technology, Kluwer Academic Publishers 76, 87 (2000).

2. Y. Xu, Ferroelectric materials and their applications, North-Holland, New York, 1991.

3. G.H. Haertling, Ferroelectrics 75, 25 (1987).

4. B. Brus, et al., Molecular and Quantum Acoustics 27, 63 (2006).

5. M. Płońska, et al., Ceramics 71, 424 (2002).

6. R. Zachariasz, M. Czerwiec, J. Ilczuk, Molecular and Quantum Acoustics 27, 307 (2006).

7. M. Płońska, et al., Material Science Poland 21/4, 431 (2003).

8. Z. Surowiak, D. Czekaj, Molecular and Quantum Acoustics 24, 183 (2003).

9. B. Brus, R. Zachariasz, J. Ilczuk, Molecular and Quantum Acoustics 26, 55 (2005).


INVESTIGATION OF ACOUSTO-OPTIC DIFFRACTION IN BIAXIAL

CRYSTALS

A. TCHERYATIAN and E. NAZAROVA

Department of Physics, M. V. Lomonosov Moscow State University,

119992 Moscow, Russia

Influence of optic wavelength dispersion on phase matching conditions of

acousto-optic interaction in optically biaxial media is considered for the first

time. Diffraction of light by ultrasound is examined in basic optical plane of a

biaxial crystal by the example of monoclinic double lead molybdate single crystal

(Pb2MoO5). Frequency dependences of Bragg angle have been analysed taking

into account wavelength dispersion of light. It is shown that a considerable

transformation of the characteristics of the acousto-optic interaction is caused by

a change of the directions of optic and dielectric axes in a biaxial medium with a

tuning of optic wavelength.

1. INTRODUCTION

Optically anisotropic materials are widely used in modern acoustooptic devices such as

modulators, deflectors and filters. Application of peculiar regimes of optical wave diffraction

by ultrasound in crystals facilitated to a significant improvement of parameters of these

devices [1]. Absolute majority of the optical crystalline materials, so far applied in the

acousto-optic devices, belongs to the uniaxial crystals. At the same time, the biaxial crystals

seem very promising with respect to the acousto-optic applications. These crystals possess

unique geometries of light and sound interaction, which cannot be observed in uniaxial

crystals [2]. However, the biaxial media are much more complicated for analysis of optic,

elastic and acousto-optic properties while the acousto-optic interaction in such media still has

not been investigated adequately. In particular, the phenomenon of optic wavelength

dispersion occurs more intricate due to the low symmetry of the biaxial crystals. The paper is

devoted to analysis of Bragg acousto-optic diffraction in biaxial media in presence of the

dispersion of optic waves.

260 Tcheryatian A., Nazarova E.

2. WAVELENGTH DISPERSION IN BIAXIAL CRYSTALS

The acoustooptic scattering is considered in the socalled basic optical plane, which

contains both optical axes of a biaxial media. The crosssection of the surface of refraction

indices by this plane represents intersecting a circle and an ellipse. In a case of application of

nonmonocromatic light or a tuning of optical wavelength, an appreciable difficulty of the

analysis of the acoustooptic diffraction is caused by the phenomenon of the optical

dispersion. It is notable that the optical dispersion in the biaxial crystals qualitatively differs

from the case of the uniaxial media [3]. The first difference appears due to a change of basic

refraction indices with the optic wavelength λ. In the biaxial media, variation of the indexes

of refraction results in a change of an angle 2v between the optic axes, where v is the angle

between an optical axis and the dielectric Z axis:

22

222sin −−

−−

−−

=zx

yx

nn

nnν . (1)

The basic refraction indices nx, ny and nz in Eq. (1) correspond to the directions of

dielectric (optic indicatrix) axes X, Y, and Z respectively and change with the wavelength.

Therefore, contrary to the case of a uniaxial crystal, the directions of the optic axes in a

biaxial material are not fixed in space. This circumstance can dramatically influence the phase

matching condition.

The second principal difference from the uniaxial media is observed for the biaxial

crystals of low symmetrical classes that belong to the monoclinic and triclinic syngonies. In

these crystals, not only the optic axes change their directions with the wavelength λ but the

directions of the dielectric axes X, Y, and Z also depend on the value λ.

3. PHASE MATCHING CONDITIONS IN BIAXIAL CRYSTALS WITH CONSIDERABLE DISPERSION

It is known that Bragg acoustooptic scattering may be observed only if the phase

matching condition

kd = k i + K (2)

is satisfied [1]. Here, k i and kd are wave vectors of an incident and a diffracted optic beams

correspondingly, k = 2πn/λ, where the refraction index n should be taken for the appropriate

direction and the optic mode. An absolute value of an acoustic wave vector K may be

expressed via acoustic velocity V and frequency of ultrasound f, K = 2πf /V .


The phase matching condition (2) of the acoustooptic interaction in the case of the

biaxial media results in extremely complicated dependences of Bragg angle θB on the

frequency f of ultrasound. Moreover, a general view of these dependences is determined by a

choice of a propagation direction of ultrasound as well as by a selection of orientation of the

interaction plane. The dependences θB(f) occur very important since they make it possible

evaluation of basic parameters of the acoustooptic diffraction. These parameters are the

operating acoustic frequency and the required angle of light incidence as well as the acoustic

bandwidth and the angular aperture of an acoustooptic device.

Figure 1 presents an example of the dependences θB(f) calculated for the biaxial crystal

double lead molybdate (Pb2MoO5), which belongs to the monoclinic syngony. The crystal

Pb2MoO5 is promising for the acoustooptic application [4] due to its optic and acoustooptic

characteristics. During the calculation, data on the optical dispersion were used from [5,6,7]

while the acoustic parameters of the material were taken from [6]. The basic optical (XZ)

plane of this crystal does not change its position with the tuning of optic wavelength due to

the existence of the axis of twofold symmetry, which is normal to the XZ plane.

In the case presented on Fig. 1 (a), the acoustic vector K is directed along X axis, where

the orientation of the X axis corresponds to the optic wavelength λ1 = 633 nm. The frequency

angle characteristics θB(f) of four types of the diffraction is shown in Fig. 1. The first two

types designated as sf + and sf – correspond to the scattering of a slow optic wave with the

conversion into a fast wave and taking place in a plus and minus first diffraction orders

correspondingly. On the other hand, the diffraction processes fs + and fs – represent the

interaction of the fast wave with the conversion of the mode. Top and bottom scales of the

graphs correspond to quasishear (QS) and quasilongitudinal (QL) acoustic waves differing

by their velocities VQS and VQL respectively [8].

The figures 1 (a) and 1 (b) demonstrate the significant difference between the curves

corresponding to the various values of the wavelength λ1 = 633 nm and λ2 = 413 nm, which

is caused, to a grate extent, by the dispersion of both the optic and dielectric axes of the

medium. It should be noted that both figures correspond to exactly the same direction of

propagation of ultrasound relatively to the crystal structure although the vector K is not

parallel to the X axis in the case (b) due to the axes dispersion.


a) b)

Fig. 1. Frequency dependencies of Bragg angle for the diffraction with conversion of the modes; a) λ1 = 633 nm, b) λ2 = 413 nm.

At the same time, it may be concluded that the particular case of the collinear diffraction

(points A and A* as well as B and B*) demonstrates relatively weak dependence on the

dispersion of the axes. In this case, the wavelength dispersion, to a great extent, appears only

due to the traditional scaling factor λ2/λ1. On the other hand, the points C and C*

corresponding to the optimal geometry of a deflector are situated very close to each other, in

spite of the scaling factor λ2/λ1. Such a peculiar situation occurs possible only due to the

particular rotation of the dielectric and optic axes with the tuning of the optic wavelength. In a

given case, this rotation compensates the traditional shift of the acoustic frequency which

takes place in accordance with the condition λ1f1 ≈ λ2f2 (f1 and f2 are the frequencies of the

phase matching at the wavelengths λ1 and λ2 correspondingly). It is notable that similar

phenomenon cannot be observed in a uniaxial or optically isotropic medium because the

change of the refraction indices is moderate in all media.

Another peculiarity mainly related to the movement of the axes appears as a sufficient

change of the Bragg angle θB. As may be seen from Fig. 1, especially strong deviation of the

angle θB is observed in the area of moderate frequencies f around the point O1. The

considerable movement of one of the optical axis exceeding 10º (!) provides this deviation

while another optical axes does not change its position dramatically (point O).

Finally, one more investigated case of the diffraction is of interest in respect to a design

of wideaperture acoustooptic filters for the image processing. The wideaperture geometry


of the diffraction corresponds to the point of the frequencyangle dependence θB(f)

characterized by a vertical tangent (df / dθB = 0). The most wide angle aperture is obtained

when both the first and the second derivatives are equal to zero, df / dθB = 0 and

d2f / dθB 2 = 0. The latter case of the diffraction is presented in Fig. 2 for the wavelength λ1=

633 nm (solid curves). It may be observed if the angle between the vector K and X axis is

equal to α = 23.2o.

The same figure demonstrates the dependencies θB(f) for the wavelength λ2 = 413 nm

(dotted curves) where the condition d2f / dθB 2 = 0 is violated because of the wavelength

dispersion of the axes. Moreover, the point with the vertical tangent is divided into two points,

which occur displaced not only by the frequency f but also by the Bragg angle θB. Such

behaviour of the frequencyangle dependencies θB(f) may cause the additional difficulty in

design of the wideaperture acoustooptic filters since the transmission function of the device

occurs dependent on the wavelength. On the other hand, a new possibility of control of the

transmission function appears that may find an application in the adaptive devices controlled

by an optic radiation with a tunable wavelength.

Fig. 2. Frequency dependencies of Bragg angle for the wideangle diffraction at wavelength λ = 633 nm (solid curves) and λ = 413 nm (dotted curves).

4. CONCLUSION

Phase matching conditions of acoustooptic interaction in optically biaxial crystals have

been investigated by the example of double lead molybdate (Pb2MoO5) crystal taking into


account optical dispersion. It was revealed that phase matching conditions in the crystal of

Pb2MoO5 sufficiently change because of the wavelength dispersion. Considerable

transformation of the characteristics of the acoustooptic interaction is caused by a change of

the directions of optic and dielectric axes with a tuning of the optic wavelength. The obtained

results may be directly applied to design of acoustooptic devices based on biaxial crystals

and possessing optimal operation characteristics.

The work has been supported in part by the Russian Ministry of Education and Science,

grant RNP.2.1.2.8698 and also by the Russian Foundation for Basic Research,

grant 060789309.

REFERENCES

1. V. Balakshy, V. Parygin, L. Chirkov, Physical Principles of AcoustoOptics (Radio and Communication, Moscow, 1985).

2. E. Nazarova, A. Tchernyatin, in Abstracts of IX International Conference for Young Researchers: Wave Electronics and Its Applications in Information and Telecommunication Systems, Nondestructive Testing, Security and Medicine, 13 (St. Petersburg, Russia, 2006).

3. Yu. Sirotin, M. Shaskolskaya, Basics of Physics of Crystal, (Nauka Publ., Moscow, 1979)

4. A. Tchernyatin, in Proceedings SPIE of International Congress on Optics and Optoelectronics 5953, 228 (2005).

5. N. Uchida, S. Miyazawa, K. Ninomiya, J. of Opt. Society of America 60/10, 1375 (1970).

6. V. Balakshy, B. Linde, A. Vostrikova, Molecular and Quantum Acoustics 27, 7 (2006).

7. V. Volochinov, N. Polikarpova, Molecular and Quantum Acoustics 24, 225 (2003).

8. Y. Ohmachi, N. Uchida, J. of Appl. Phys. 42/2, 521 (1971).


ANALYSIS OF BRAGG DIFFRACTION OF LIGHT IN

PERIODICALLY INHOMOGENEOUS ACOUSTIC FIELD

Anna N. VOSTRIKOVA, Vladimir I. BALAKSHY

Department of Physics, M.V.Lomonosov Moscow State University,

19992 Moscow, Russia

Peculiarities of the Bragg diffraction of light in a periodically inhomogeneous

acoustic field are studied. Different variants of amplitude and phase spatial

modulation of the acoustic field are analyzed. Amplitude, angular and frequency

characteristics are calculated for case of strong acousto-optic interaction.

1. INTRODUCTION

For many years the problem of light diffraction by acoustic waves was solved mainly in

assumption of a homogeneous and non-divergent acoustic field [1,2]. Therefore, great efforts

of acousticians worked in the field of ultrasonic technology were turned to development and

fabrication of perfect piezoelectric transducers that would generate homogeneous ultrasound

beams. However, at the present time, the situation has significantly changed. The ultrasonic

technology has become so perfect that piezotransducers of almost any structure can be

fabricated [3,4]. This new level of technology development opens up novel possibilities for

applied acousto-optics (AO) and poses the problem of studying light diffraction in spatially

inhomogeneous acoustic fields.

In the given paper, we present results of theoretical investigations of AO interaction in

cells where amplitude or phase of acoustic wave varies periodically along the direction of

optical wave propagation. Such an acoustic field creates a two-dimensional grating for light:

the first grating has a period equal to the acoustic wavelength, whereas the period of the

second grating is defined by the period of spatial modulation. Most attention is concentrated

on the case of the sinusoidal law of spatial modulation of the acoustic amplitude and phase as

well as on strong AO interaction in cells with phased array transducers.

The aim of the research was to study light diffraction in spatially inhomogeneous

acoustic fields and to understand, how amplitude and phase inhomogeneity can change basic

characteristics of AO interaction. It is well known that in case of homogeneous acoustic field

the maximal intensity of light in the first diffraction order is attained when the incidence angle

266 Vostrikova A.N., Balakshy V.I.

iθ is equal to the Bragg angle Bθ . Inhomogeneity of the acoustic field results in changing the

Bragg condition and diffraction efficiency.

2. AMPLITUDE INHOMOGENEITY

Firstly, consider the situation when the acoustic field amplitude is modulated according

to the sine law:

),2

cos1()( 0 xd

maxaπ+= (1)

where 0a is the average magnitude of the amplitude, m is the spatial modulation depth, d is

the spatial period of modulation. Fig. 1 presents a set of curves, which demonstrate the

diffraction efficiency ξ as a function of AO phase mismatch η , which is proportional to the

magnitude Bi θθ − . The calculation is carried out for 4=N periods of the spatial variation,

fixed amplitude modulation depth 1=m , and for different values of the Raman-Nath

parameter A , which is proportional to 0a . These dependences have a symmetrical structure

relative to Bi θθ = and consist of three lobes. Central lobe is typical for the Bragg diffraction in

the homogeneous acoustic field. Two lateral lobes appear because of the sinusoidal amplitude

inhomogenity. The diffraction efficiency and the location of lateral lobes depend on

parameters m and d .

40 20 0 200

0.2

0.4

0.6

0.8

1

η

ξ

π=A

3

π=A

π2=A

Fig. 1. Diffraction efficiency ξ as a function of AO phase mismatch η for fixed magnitude of amplitude modulation depth 1=m .

The matter of a particular interest concerns a maximal value of diffraction efficiency

that can be got in the lateral lobes. Fig. 2 demonstrates the diffraction efficiency as a function

of the Raman-Nath parameter for two cases: the solid and dashed lines correspond to the

lateral and central lobes respectively. It is seem that the dependence for the central lobe

repeats the analogous dependence for the homogeneous field: 100% diffraction efficiency is

attained at π=A . An unexpected result demonstrates the other curve: in spite of a significant


phase mismatch between the interacting waves, the diffraction efficiency in the lateral lobes

approaches about 100% as well.

However, it requires more acoustic power than in case of homogeneous acoustic field.

0 1 2 3 4 50

0.5

1

A

ξ

lobes

lateral

lobe

central

Fig. 2. Diffraction efficiency ξ as a function of Raman-Nath parameter A in case of sinusoidal modulation of acoustic amplitude for 1=m .

3. PHASE INHOMOGENEITY

Light diffraction in a phase-inhomogeneous acoustic field has a more complicated

character. We have studied the case of sinusoidal phase modulation with the amplitude 0ϕ :

),2

cosexp()( 00 xd

jaxaπϕ= (2)

0 1 2 3 4 50

0.5

1

A

ξ

1

23

Fig. 3. Diffraction efficiency ξ as a function of A in case of sinusoidal modulation of

acoustic phase with 20πϕ = .


The theoretical analysis has shown that the dependence )(ηξ has form like that

displayed in Fig. 1. However, the number of the principal lateral lobes is more than two; it

depends on the magnitude of 0ϕ .

Fig. 3 demonstrates the diffraction efficiency as a function of the Raman-Nath

parameter for three cases: plot 1 corresponds to the case of the homogeneous acoustic field

(this curve is shown for comparison), plot 2 refers to the central lobe, and plot 3 conforms to

the first lateral lobes. These calculations show that the diffraction efficiency in case of

sinusoidal modulation of the acoustic phase can also attain 100% in every lobe.

Next graph expresses the peculiarity of phase-inhomogeneous acoustic field. The

diffraction efficiency as a function of 0ϕ for fixed magnitude of A is presented in Fig. 4. The

diffraction efficiency in central lobe at some values of phase modulation depth 4.20 =ϕ and

5.50 =ϕ does not exceed zero.

0 1 2 3 4 50

0.5

1ξ

0ϕ

lobe

central

lobes

lateral

Fig. 4. Diffraction efficiency ξ as a function of phase modulation amplitude 0ϕ for fixed magnitude of Raman-Nath parameter π=A .

4. PHASED ARRAY TRANSDUCERS

Besides AO interactions in cells with sinusoidal spatial variations of the acoustic

amplitude and phase, we have analyzed strong AO interaction in cells with phased array

transducers [5,6]. The acoustic field excited by such transducers has a complicated structure

and can simultaneously have both amplitude and phase inhomogeneity. In the near wave zone,

acoustic field consists of separate parallel acoustic beams excited by every section. An optical

wave passing through the AO cell diffracts successively on these beams. The partial diffracted

waves then interfere and the result depends on their mutual phases. It should be taken into

account that the phase of the acoustic wave is transferred into the optical wave. Therefore, the

structure of the diffraction pattern depends on phase shift between sections and on the period

of the transducer array.


Nowadays the sectional transducers are widely used, especially for facilitation of

generator-transducer electrical matching. Varying the number and the length of electrode

sections, as well as the value of the gap and the phase shift between adjacent elements, one

can get an acoustic field with different types of inhomogeneity. In case of antiphase excitation

of adjacent sections and the gap equal to zero, the excited acoustic field has only phase

inhomogeneity. If this transducer has the gap not equal to zero, the excited acoustic field has

both amplitude and phase inhomogeneity.

35 40 45 500

5

10

gradi ,θ

MHzf ,

Fig. 5. Fragment of the intensity distribution as a function of light incident angle and acoustic frequency for case of homogeneity acoustic field.

35 40 45 500

5

10

gradi ,θ

MHzf ,

Fig. 6. Fragment of the intensity distribution as a function of light incident angle and acoustic frequency for case of amplitude inhomogeneity of acoustic field.


Consider more carefully how these various inhomogeneities change the Bragg angle

frequency dependence. This dependence plays very important role in AO devices. It is not

overstated to say that all advantages of anisotropic diffraction in comparison with isotropic

one result from quite complicated and very diverse form of this dependence.

The fragment of the intensity distribution (for the extraordinary polarization of incident

light) as a function of incident angle and acoustical frequency for different types of

inhomogeneity of acoustic field is presented in Figs. 5, 6, 7.

Different brightness of diagrams is used for intensity denomination. Transition from

light zone to dark one is corresponding to the reduction of the intensity. Diffraction efficiency

of the brightest parts attained 100%.

35 40 45 500

5

10

gradi ,θ

MHzf ,

Fig. 7. Fragment of the intensity distribution as a function of light incident angle and acoustic frequency for case of phase inhomogeneity of acoustic field.

These diagrams show that the working area of the cell in case of inhomogeneity

acoustic field is split into two or even into three parts. This peculiarity opens up new

possibilities for improving and optimizing parameters of AO devices.

REFERENCES

1. V.I. Balakshy, V.N. Parygin, L.E. Chirkov, Physical Principles of Acousto-Optics (Radio i Svyaz, Moscow, 1985).

2. A. Korpel, Acousto-Optics (Marcel Dekker, New York, 1988).

3. C.S. Tsai, IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control UFFC-39, 529 (1992) .

4. V. Balakshy, B. Linde, A. Vostrikova, Molecular and Quantum Acoustics 27, 7 (2006).

5. V. Volochinov, N. Polikarpova, Molecular and Quantum Acoustics 24, 225 (2003).

6. G.A. Alphonse, Appl.Opt. 14, 201-207 (1975).


DECOMPOSITION OF FREQUENCY CHARACTERISTICS OF

ACOUSTIC EMISSION SIGNALS FOR DIFFERENT TYPES

OF PARTIAL DISCHARGES SOURCES

Franciszek WITOS*, Zbigniew GACEK**, Paweł PADUCH*

** Institute of Physics, Silesian University of Technology,

2 KrzywoustegoStr, 44-100 Gliwice, POLAND

** Institute of Power Systems and Control, Silesian University of Technology,

2 KrzywoustegoStr, 44-100 Gliwice, POLAND

The problem touched in the article is decomposition of frequency characteristic of

AE signals into elementary form of three-parametrical Gauss function. At the first

stage, for modelled curves in form of sum of three-parametrical Gauss peaks,

accordance of modelled curve and a curve resulting from a solutions obtained

using method with dynamic windows, Levenberg-Marquardt algorithm, genetic

algorithms and differential evolution algorithm are discussed. It is founded that

analyses carried out by means differential evolution algorithm are effective and

the computer system served an analysis of AE signal frequency characteristics

was constructed. Decomposition of frequency characteristics for selected AE

signals coming from modelled PD sources using different ends of the bushing,

and real PD sources in generator coil bars are carried out.

1. INTRODUCTION

According to theoretical description proposed by Malen, Bolin, Ono, Shibata,

Takashima and others [1-5] dynamic AE sources are describes by: additional inelastic

deformation ),( ** txnm

β or additional mass forces ),( ** txF

related to a mass unit

)()(),(: ******** tfxtx ijijij

βββ == (1)

)()(),(: ******** tfxFtxFF iii

== (2)

They generate a stress field in the form so called elementary bipolar stress impulse:

)4

)/(exp(

2

/

8),(

2

2

222/3

*

τττπσ tvrtvr

rv

Dtr

−−−= (3)

272 Witos F., Gacek Z., Paduch P.

Detection of AE vawes by the sensor having a flat frequency characteristic lets to the

following output voltage of the sensor:

)exp(4

2|)(| 22*

3

**33 τωπρ

ελεµω −

∆+∆= o

qq PVra

V (4)

Quantity ∆τ=4τ, named as dynamic AE source rise time, changes its value depending on

phenomenon scale from nanoseconds to milliseconds. Expression (4) is biparametric Gauss

function with two parameters: amplitude and width of a curve connected with the source rise

time. Expression (4) is a model description in which single AE source is occurred.

Actual frequencies characteristic are composed rather of triparametric Gauss function

with parameters: amplitude, width of a curve connected with the source rise time and

frequency characteristic for the source (5). Additionally, there are often many sources

occurring simultaneously, hence our proposition relative to decomposition takes the form of

linear combination of triparametric Gauss functions (5-6):

]2

)(exp[)(

2

2

k

kkk AG

σωωω −−= (5)

)()(1

0ωω k

Nk

kGf ∑ −=

== (6)

Expressions (5) and (6) are a base of proposed and searched decomposition of frequency

characteristics.

2. DECOMPOSITION OF FREQUENCY CHARACTERISTICS’

2.1. INITIAL STAGE

A possibility of searching and describing of local maximums has been programmed for

a signal frequency characteristic. Analysis is composed of two stages: smoothing of the curve

aimed at elimination of local fluctuation of neighbouring data and data search using a window

method (during such a stage the window parameters should be determined: width and level of

a discrimination and next one should be started to data search using a window which occupies

successive positions in a transfer band). For each window position the principal maximum of

a curve is founded and localised in such a way that searched curve is approximated locally by

means of triparametric Gauss functions

)2/)exp(( 220 ∆−= ffAy (7)

containing the following parameters: A – amplitude, f0 – frequency of principal maximum,

∆−half width of the approximated curve.

Analysis results of frequency characteristics of AE signals relating to the first stage of

decomposition obtained from windows analysis are presented in Fig. 1. In the case of signals


coming from modelled AE sources, when different bushing ends were used [6,7] the dominant

band in the signal is 22-44 kHz. For AE signal s coming from real sources (PD real sources

within generator coil bars [7,8]) there are the following frequency bands: predominant

230kHz-240kHz and remaining 205kHz–210kHz. Presented decomposition is not précised;

therefore more detailed analysis should be needed.

2.2. SEARCHED SOLUTION

In order to find solution two problems have been separated: determination of number of

Gauss peaks (with approximated values of their describing parameters) as well as

optimization of parameters of searched Gauss peaks.

Finally number of peaks is determined by means of the inflexion point method, defined

by the authors. In such a method each Gauss peak is described by two inflexion points of

analysed spectrum curve. Number of pair of inflexion points corresponds with number of

Gauss peaks. Variation intervals of Gauss peaks parameters are determined basing on

positions and values of inflexion points (Fig.2).

Optimization of parameters of searched linear combination of Gauss peaks has been

made using in turn Levenberg-Marquardt algorithm, genetic algorithms and differential

evolution algorithms [9]. In the case of L-M algorithm its implementation in LabView packet

was used. Application of the algorithm to obtain searched form of decomposition turned out

impossible because of frequent incorrect results [9,10]. According to authors, it is caused by

local searching property of solution. Application of genetic algorithm to find a searched

decomposition has been made using own and developed processing programs as well as

advanced numerical library concerning components of GAlib genetic algorithms [11].

Obtained results were low-stable and even application of multicriterial optimization [12-15]

does not cause of a decided improvements. Good results have been obtained using differential

evolutions algorithms [16] when mutation operators have been defined as follows:

)(: ,3,2,11, GrGrGrGi XXFXX ++=+ (8)

)(: ,3,2,1, GrGrGbestGi XXFXX ++=+ (9)

(where Xi,G+1 – mutated vector, Xj,G – vectors of solution in G generation, F – scale factor

whose values are in the interval (0,2) but the best approximation results are obtained for

values from (0.55, 0.9) interval, G – number of generation/iteration of the algorithm) as well

as using the following selections condition: selection is made between tentative vector

creating during mutation and solution vector (one should ever choice the vector with better

value of objective function [9].


Fmax= 324,8 [kHz]; U^2rms(Fmax)= 2,83E-8[V]^2

Figure 1. Frequency characteristics of AE signals together with analysis results by using of windows method registered within: a/ modelled PD sources with different bushing ends [6,7], b/ real PD sources occurring in generator coils bars [7,8])

Figure 2. Global spectrum and its components in the form of triparametric Gauss function together with marked inflexion points.

a

b

2.3 ANALYSIS SYSTEM OF AE SIGNAL FREQUENCY CHARACTERISTICS

Basing on founded solutions, represented in the preceding section, a computer system

served an analysis of AE signal frequency characteristics was constructed. The system is

composed of program which analyse AE signals and processing program for scrolling of data

generating by analysing program. Both programs have been written in LabView environment.

Analysing program contains the following procedures: signal preparation (filtration,

smoothing and decimation), calculation of power density spectrum, determination of number

of Gauss peaks and intervals of their variability (determination of a source model) as well as

optimization (modulus written in C++ language).

Input data are AE signals obtained from the program used to data registration. They

have the form of binary files coming from three measuring lines and referring line, in which

the supply voltage is registered. Fourier transform (using Hanning window) treated as power

spectrum density of a signal is calculated for data coming from measuring lines. Such a

spectrum is smoothed and then number of Gauss peaks is determined as well as optimization

is carried out. It is proper to add that determination of of number of Gauss peaks and intervals

of their variability is made for a spectrum calculated for one period of the supply voltage (not

to the whole signal). This enable us to more detailed analyse.

Example results relating to AE signal, registered in the case of modelled PD source as

the bushing with thread are presented in Fig. 3.


b

c

d

e

a

Fig. 3. AE signal (a), the supply voltage (b), Power Spectrum Density of signal (c), PSD of signal after its smoothing by means of walking average 4x400, fitted spectrum and its components (d) for PD source in the form of the bushing end with a threat [6].

3. ANAYSIS OF SELECTED AE SIGNALS

3.1. SIGNALS COMING FROM MODELLED SOURCES

Analyses deals with AE signal coming from PD sources occurring within modelled

measuring object with the bushing whose open end not contain additional elements [6].

Modelled PD sources are recognised as surface PD. Frequency characteristics of selected AE

signals are presented in Fig. 4: (a), (c), (e) concern spectrums and spectrums after smoothing,

(b), (d), (f) concern smoothed spectrums, fitted spectrums and components of fitted spectrum

for different values of apparent electric charge introduced by the PD source. More detailed

analysis gives following features of spectrums:

a/ for whole group of sources there are very closed characteristic frequencies,

b/ there are not tendency to change for frequencies of component spectrum in function of

apparent electric charge introduced by the PD source,

c/ changes of relation between amplitudes of components spectrums for particular signal are

inconsiderable,

d/ half-widths (for spectrum of maximum amplitude) extends when apparent electric charge

introduced by the PD source increases.

Analysis results prove that in every analysed cased - independently of the value of

apparent electric charge introduced by a modelled source – there are only sources of the one

type.


Fig. 4. Frequency characteristics of selected AE signal for PD source in the form of the bushing end [6]. Power Spectrum Density of signals - (a),(c),(e). PSD of signal after its smoothing, fitted spectrum and its components – (b),(d),(f).Measuring conditions: (a) – “A” measuring point, 220pC (apparent electric charge introduced by PD source), (b) - “A” measuring point, 890pC, (c) - “B” measuring point, 890pC.

3.2. SIGNALS COMING FROM SOURCES OCCURRING WITHIN REAL OBJECTS

Analyses deals with AE signal coming from PD sources occurring within generator

coils bars (generator of 120MW and UN=13,8kV[7,8]. Frequency characteristics of selected

AE signals are presented in Fig. 5: (a), (c), (e) concern spectrums and spectrums after

smoothing, (b), (d), (f) concern smoothed spectrums, fitted spectrums and components of

fitted spectrum for different values of supply voltage. Analysed signals were registered at P2,

P5 measuring points, in vicinity where PD sources with maximum activity have been located

[8].


Fig. 5. Frequency characteristics of selected AE signal for PD source within generator coils bars [7,8]. Power Spectrum Density of signals - (a),(c),(e). PSD of signal after its smoothing, fitted spectrum and its components – (b),(d),(f).Measuring conditions: (a) – “P2” measuring point, 11,8kV (value of the supply voltage), (b) - “P2” measuring point, 19,0kV, (c) - “P5” measuring point, 20,5kV.

The detailed analysis results prove a complete variety of features of components

spectrum as well as prove that there are different types of PD sources in different measuring

points and for different values of the supply voltage.

4. CONCLUSIONS

The problem touched in the article is decomposition of frequency characteristic of AE

signals into elementary form of three-parametrical Gauss function. Solution of the problem

has been obtained in two stages.

At the first stage, for modelled curves (in form of sum of three-parametrical Gauss

peaks), accordance of modelled curve and a curve resulting from a solution obtained from


particular analysis method is discussed. Possibilities of application to analyse the following

method are considered: a method with dynamic windows, Levenberg-Marquardt algorithm,

genetic algorithms and differential evolution algorithm. It is founded that analyses carried out

by means differential evolution algorithm are effective and the computer system served an

analysis of AE signal frequency characteristics was constructed.

At the second stage, frequency characteristic for selected AE signals obtained for the

following types of PD sources have been analysed: modelled sources using different ends of

the bushing, and real sources in generator coil bars. Experimental curves have been smoothed

by a method of modified walking mean and they have analysed using of a solution proposed

at the first stage. This way for each type of PD sources the sets parameters for Gauss peaks

components have been obtained. The detailed analysis results prove:

a/ in every analysed cases for surface PD - independently of the value of apparent electric

charge introduced by a modelled source – there are only sources of the one type,

b/ a complete variety of features of components spectrum - there are different types of PD

sources in different measuring points and for different values of the supply voltage.

REFERENCES

1. K. Malen, L. Bolin, Physica Status Solidi (B) 61, 637-645 (1974).

2. K. Ono, AE arising from plastic deformation and Fracture, Fundamentals of AE, University of California, Los Angeles 1979, 167-207.

3. M. Shibata, Materials Evaluation 42/1, 107-115 (1984).

4. T. Takashima, Y. Higo, S. Nunomura, Philosophical Magazine A 49/2, 221-229 (1984).

5. I. Malecki, F. Witos, A. Opilski, Acustica 79/2, 112-116 (1993).

6. F. Witos, Z. Gacek, A. Opilski, Archives of Acoustic 27/1, 65-77 (2002).

7. Z. Gacek, F. Witos, Acta Electrotechnica et Informatica 3/2, 15-20 (2003).

8. F. Witos, Molecular and Quantum Acoustics 23, 433-442 (2002).

9. P. Paduch P., Analiza częstotliwościowa sygnałów EA pochodzących od sygnałów wnz, praca magisterska, Instytut Fizyki Politechniki Śląskiej, 2005.

10. J.R. Parker, Computing 65, 291-312 (2000).

11. M. Wall, A. Gali, C++ library of genetic algorithms components, Massachusetts Institute of Technology, 2004 (http://lancet.mit.edu.ga).

12. E. Zitzler, Evolutionary algorithms for multiobjective optimizations: methods and applications, PhD works, Zurich 1999 (http://www.tik.ee.ethzet.ch/zitzler).

13. F. Witos, Z. Gacek, Z. Opilski, Molecular and Quantum Acoustics 24, 237-248 (2003).

14. T. Boczar, D. Zmarzly, Molecular and Quantum Acoustics 25, 45-68 (2004).

15. T. Boczar, et al., Molecular and Quantum Acoustics 26, 35-44 (2005).

16. N. Storn, K. Price, Journal of Global Optimization 11, 341-359 (1999).

http://www.tik.ee.ethzet.ch/zitzler

http://lancet.mit.edu.ga/


NUMERICAL ANALYZE AND EXPERIMENTAL RESULTS OF

ULTRASONIC WAVES SCATTERING ON A MODEL OF THE

ARTERY

Janusz WOJCIK, Tadeusz POWALOWSKI, Zbigniew TRAWINSKI

Ultrasonic Department, Institute of Fundamental Technological Research,

Polish Academy of Science, 21 Swietokrzska str., 00-049 Warsaw, POLAND

The aim of this paper is to compare the results of the mathematical modeling and

experimental results of the ultrasonic waves scattering in the inhomogeneous

dissipative medium. The research was carried out for an artery model (a pipe

made of a latex), with internal diameter of 5 mm and wall thickness of 1.25 mm.

The numerical solver was created for calculation of the fields of ultrasonic beams

and scattered fields under different boundary conditions, different angles and

transversal displacement of ultrasonic beams with respect to the position of the

arterial wall. The investigations employed the VED ultrasonic apparatus. The

good agreement between the numerical calculation and experimental results was

obtained.

1. INTRODUCTION

The pathological process of atherosclerosis development and its connection with

alterations that occur in walls of blood vessels present a matter of interest for numerous

scientific and clinical centers worldwide. In case of non-invasive investigations, the ultrasonic

measurements for momentary diameters of arteries over the entire cardiac cycle serve as the

basis enabling to determine elasticity of arterial walls. Maximum and minimum values for the

vessel diameter are associated with respective systolic and diastolic blood pressures measured

by a sphygmomanometer. Based on the above measurements, the elasticity factors of the

arterial wall are determined [1,2]. In case of non-invasive ultrasonic measurement,

reproducibility of the obtained results is an extremely important parameter, since it is used to

define sensitivity of the diagnostic tool [3]. The major objective of the thesis was to develop a

mathematical model that would be capable of describing spatial and time-dependent

distribution of an ultrasonic beam that is emitted by a piezoelectric ring transducer and then

backscattered on cylindrical surfaces of the walls in artery models. The developed model was

280 Wojcik J., Powalowski T., Trawinski Z.

tested for results of experiments when an elastic pipe was immersed in water. The

investigations were carried out using the VED equipment, designed and constructed in the

Ultrasonic Department of the Institute of Fundamental Technological Research of the Polish

Academy of Sciences, purposefully dedicated for elasticity examination of arterial walls in

human body.

2. PHYSICAL MODEL

With use of non-dimensional variables, the equation that defines the propagation of

sonic waves in a homogenous (with undisturbed parameters of the material) non-linear and

absorbing medium, can be expressed by the following equation [4]:

( ) 02 2 =∂+∂−∂−∆ PqPPP ttttt βA (1)

where ( )tPtAP ,)( xA ⊗≡ , [ ])()( 1 naFtA −= , ),( tP x is the pressure in the 3D coordinate system x

at the moment of time t; A is a convolutiontype operator that defines absorption; q is the

Mach number (in our case the Mach number is calculated for velocities on the surface of the

disturbance); 2/)1( +≡ γβ ; 1)( +≡ ABγ or γ adiabatic exponent, 0ffn ≡ nondimensional

frequency; f , 0f respectively: frequency and characteristic frequency; )(na the small

signal coefficient of absorption, [ ])(F 1 na−=A , [ ]⋅F Fourier transform.

For the medium with disturbed materials parameters the equation of the scattered field

scP can be developed from the formula 1 (more details see [58]) end takes the form:

)(2 insctt

sct

sctt

sc PPPPP +∂Π−=∂−∂−∆ A (2)

where inP incident field which fulfils the equation (1), 2/11)( rc−≡Π x scattering potential,

2rc disturbed dimensionless sound velocity.

3. SOLVER

Construction of a solver for backscattered fields is the fundamental issue for setting up a

numerical model of an experiment that is aimed to reflect real situations that occur in

ultrasonography practice. The solver that we constructed is composed of three parts:

1. Solver for the incident field. It is the solver that bases on codes JWNUT2D and

JWNUT3D [9], which we have been using for many years. The first code solves the

equation in the axially symmetrical cases, the second one is applicable to whichever one

sided boundary conditions.

2. Solver for the backscattered field. It is the tool that is able to calculate parameters of

backsscattered fields and their pressures on the detector surface, whereas the tool uses


numerically determined incident field and information on geometrical and material

parameters of the target as the basis for calculations.

3. Simulator of the electronic receiver channel that is used for calculation of pulse responds

)(th of this unit. Distribution of pressure on the surface of the probe is averaged over the

entire probe surface (the theory of piezoelectric phenomena says that electric signals at

probe output are proportional to the aforementioned average value).

∫=)(

))(()),((1

)(x

xxS

sc dSSAptSPS

tPE (3)

where )(xS denotes a point on the transducer surface, S stands for the transducer surface area

and ))(( xSAp is the apodization function for the transducer surface. In this study )(tPE is

referred to as the echo. The RF signal )(tPRF represents a single line of scanning and is

calculated as follows:

)()()( tPthtP ERF ⊗= , )]([F 1 nHh −= (4)

where )(nH is the system transmittance.

4. RESULTS

Experimental setup is shown on Fig. 1. The research was carried out for a pipe made of

latex, with internal diameter of 5 mm and wall thickness of 1.25 mm. The investigations

employed the VED ultrasonic apparatus. The frequency of the transmitted ultrasound was

6.75 MHz. The pulses were measured by means of the hydrophone of the type: Sonic

Technologies Model 800 Bilaminar Hydrophone. During the performed research the front

surface of the pipe wall was positioned in the focus of the ultrasonic probe. The RF electric

signal, )(tPRF , corresponding to echoes reflected by the pipe walls, was recorded at the output

of the RF receiver by means of the digital oscilloscope AGILENT 54641D. To highlight

relationships between target (pipe) dimensions and wavelength of the echoed signals (both

acoustic waves and corresponding electric waveforms) the scales were converted all the time

into 3D ones and expressed in millimetres. Signal amplitudes were presented as relative

values. Results for calculations and measurements are presented in Fig. 2, 3 and 4.

282 Wojcik J., Powalowski T., Trawinski Z.

Fig. 1. Experimental setup.

Fig. 2. a) The RF signal )(tPRF calculated from the numerical model by means of the formula 2; b) the expanded RF signal, from the first pipe wall. Ar – the relative amplitude (with respect to the maximum value of the RF signal amplitude).

Fig. 3. a) The RF signal )(tPRF measured by means of the VED apparatus; b) the expanded RF signal from the first pipe wall, Ar – the relative amplitude (with respect to the maximum value of the RF signal amplitude).


Fig. 4. Changes of the maximal RF-signal amplitude as a function of angle α and the transversal displacement L of the ultrasonic beam axis x1, with respect to the arterial model axis x2 (see Fig.1). Ar - maximal RF-signal amplitude with respect to the maximal RF – signal amplitude for the angle α = 90deg and transversal displacement L = 0mm.

5. CONCLUSIONS

Comparison between the results that were obtained from numerical calculations and

from measurements (Fig. 2 – 4) serves as a proof that the numerical model that was developed

by our own enables simulation of the experiments with a good coherence, which was the

actual objective of the study. It is the matter of high importance when the designing process of

measurement equipment is to be optimized.

REFERENCES

1. T. Powalowski, Z. Trawinski, L. Hilgertner, Archives of Acoustics 28, 325–337 (2003).

2. T. Kawasaki, S. Sasayama, S. YagI, T. Asakawa, T. Hirai, Cardiovascular Research 21, 678–687 (1987).

3. T. Szymonski, M. Lapinski, T. Powalowski, Z. Trawinski, Acta Angiologica 3, 83–91 (1997).

4. J. Wojcik, J. Acoust. Soc. Am. 104, 2654–2663 (1998).

5. J. Wojcik, Archives of Acoustics 29, 607–632 (2004).

6. M. Gawlikowski, M. Darlak, T. Pustelny, R. Kustosz, Molecular and Quantum Acoustics 27, 89-96 (2006).

7. M. Gawlikowski, T. Pustelny, R. Kustosz, M. Darlak, Molecular and Quantum Acoustics 27, 97-106 (2006).

8. H. Sorvoja, R. Myllyla, Molecular and Quantum Acoustics 27, 239-264 (2006).

9. J. Wojcik, A. Nowicki, P.A. Lewin, P.E. Bloomfield, T. Kujawska, L. Filipczynski†, Ultrasonics 44, 310–329 (2006).


ULTRASOUND INVESTIGATIONS OF THE EFFECT OF

4-HYDROXYCOUMARIN AND UMBELLIFERONE ON LIPID

BILAYERS

Krzysztof WOJTOWICZ

Department of Biophysics Medical University of Lublin,

Al. Racławickie 1, 20-059 Lublin, POLAND

Ultrasound absorption technique was applied to compare the influence of two

coumarines: 4-hydroxycoumarin and umbe1liferone (7-hydroxycoumarin) on the

phase transition of lipid membranes. There was examined the effect of these

coumarines on lipid membranes obtained on the basis of three lecithins differing

from each other by the length of acyl chain: dimirystoylphosphatidylcholine

(DMPC), dipalmitoylphosphatidylcholine (DPPC) and

distearoylphosphatidylcholine (DSPC). 4-hydroxycoumarin was found to change

both phase transition temperature of this transition, and cooperativity more than

umbelliferone in the case of all the three lecithins.

Keywords: ultrasound absorption, phase transition, lipids, 4-hydroxycoumarin,

umbelliferone.

1. INTRODUCTION

Phosphocholines, due to their amphiphilic character, easily form in water surrounding

c1osed structures - liposomes, which are commonly examined as simple models of cellular

membranes. Bilamellar phospholipids with chains of saturated carbohydrates, including

DPPC, are characterized by phase transition. The main phase transition Pβ’ - Lα of lecithin

layers, called gel-liquid crystalline transition, consists, among others, in an increase of trans -

gauche isomerization speed of acyl chains making up the hydrophobic part of lipid layers.

Trans-gauche isomerization is a relaxation process due to which the measurement of

ultrasound absorption enables monitoring of phase transition [1]. The parameters of this

transition depend on acyl lipid chains length, membrane shape and addition of modifiers to

the lipid. Used phosphocholines have lengths of acyl chains: DMPC chain contains 14 carbon

atoms, DPPC -16 and DSPC - 18. The temperature of the main phase transition amounts in

286 Wojtowicz K.

the case of big liposomes without additives to about 24°C for DMPC, 41°C for DPPC and

54°C for DSPC.

A change of phase transition parameters under the influence of addition of modifiers

provides information on the interactions of added modifiers with lipids and about the

organization of modifier in lipid bilayer.

In the presented study we used coumarines as modifiers: 4-hydroxycoumarin and 7-

hydroxycoumarin.

A lot of coumarines have pharmaceutical application. Derivatives of 4-

hydroxycoumarin are usually anticoagulant drugs, but they also have antitumor effect [2].

Umbelliferone is a multi-effect drug. It exhibits spasmolytic, antitumor, immunomodulatory

[3] and antidiabetic effect [4, 5]. It also has antifungal properties [6]. Coumarines make up a

big group of compounds whosemolecular structure is based on a common skeleton of benzo-

α-piron, whose chemical structure is presented in Fig.1.

Fig. 1. Chemical structure of the benzo-α-piron molecule.

Nearly all coumarines have ligands. These are most often –OH, -OCH3 groups and

aliphatic lateral chains. 4-HC and umbelliferone, examined in this study, have a hydroxygroup

at C-4 and at C-7 position respectively. The result is that 4-HC molecules are amphiphilic

“along” the molecule – molecules have one of the shorter sides polar and the other apolar, and

umbelliferone molecules have amphiphilic character „across” the molecule – longer sides of

the umbelliferone molecule are amphiphilic.

The effect of these differences in the structure of both coumarines on phase transition of

lipid membranes and on the organization of coumarines in membranes is the aim of this study.

2. MATERIALS AND METHODS

DL-α dimyristoylphosphatidylcholine (DMPC), DL-α dipalmitoylphosphatidylcholine

(DPPC), DL-α distearoylphosphatidylcholine (DSPC) manufactured by Sigma (St.Louis, MO,

USA) were used. 4-hydroxycoumarin, umbelliferone and Tricine buffer were also purchased


from this company. Spectrally pure methanol and chloroform made by POCh S.A. (Gliwice,

Poland) were used as lipid and coumarins solvents.

Liposomes with and without coumarin were obtained according to the following

procedure. Lipid was dissolved in 1:1 chloroform-methanol solutions possibly with an

additive of either 4 - hydroxycoumarin or umbelliferone. Then, a thin film of lipid was

obtained by evaporating the solvent in the atmosphere of dry nitrogen. Residues of solvents

were removed in a vacuum.

Liposomes were obtained by adding to the film 10 mM buffer Tricine (pH=7,6) and

shaking for 1 h at a temperature above that of the phase transition. Liposome solutions at 1.5

mM concentration with the addition of one of the coumarins in the amount of 1-30mol% ratio

to DPPC were analyzed and compared with liposomes without coumarins. Liposomes with a

diameter of 400 nm were prepared by extruding part of the stock suspension with an extruder

using filters.

The measurements of ultrasound absorption were carried out using accustom made

resonance system similar to that described by Eggers and Funck [7]. Ultrasound absorption

was determined in the frequency range 1.1 to 1.4 MHz. Ultrasound absorption coefficients per

wavelength were measured in liposome solutions and in a buffer and next, they were

subtracted giving excess of ultrasound absorption Δαλ. The maximum position of temperature

dependence of this excess determined the temperature of phase transition. Half-width of the

peak of this dependence gave information about cooperativity of this transition. The smaller

the cooperativity the wider the peak of absorption.

The accuracy of measurement of excess absorption, as determined on the basis of data

scattering in several measurements, is 3-7% of an excess absorption at the phase transition

temperature. Phase transition temperature can be determined with the accuracy of 0.2oC, as

judged from several samples of the same type.

3. RESULTS AND DISCUSSION

Fig. 2 and 3 present temperature profiles of ultrasound absorption of DMPC liposomes

admixtures with 4-hydroxycoumarin and umbelliferone respectively.

In pure DMPC we recorded the main phase transition at about 24oC and with the

increase of 4-hydroxycoumarin concentration a decrease of phase transition temperature to

about 20oC at 30mol% addition of coumarin is observed, see Fig.4.

288 Wojtowicz K.

0

1

2

3

4

5

6

7

10 20 30 40T(oC)

104 ∆α

λ

pure DMPC

2mol%4HC

5mol%4HC

10mol%4HC

20mol%4HC

Fig. 2. The excess of the ultrasound absorption of DMPC liposomes with various concentrations of 4-hydroxycoumarin as a function of temperature.

0

1

2

3

4

5

6

7

10 20 30 40T(oC)

104 ∆α

λ

pure DMPC

5mol%umb

10mol%umb

20mol%umb

Fig. 3. The excess of the ultrasound absorption of DMPC liposomes with various umbelliferone concentrations as a function of temperature.


19

20

21

22

23

24

0 10 20 30 40c(mol%)

T(o

C)

umb

4-HC

Fig. 4. Plots of the transition temperature of DMPC bilayers as a function of coumarin concentrate.

As can be seen in Fig. 4 coumarine concentrations above 5 mol/% disproportionately

more decrease the temperature of phase transition than concentrations within the range l-5

mol/%. In the case of umbelliferone additive change of transition temperature is considerably

smaller from 23oC to about 22oC. It should be noted that small umbelliferone concentrations

(1-2 mol%) slightly increase phase transition temperature. Both coumarines affect DPPC [8]

and DSPC membranes in a similar way they affect DMPC membranes - Fig. 5 and 6. No

distinct influence of the length of lipid hydrocarbon chain can be seen here.

290 Wojtowicz K.

37

38

39

40

41

42

0 10 20 30 40c(mol%)

T(oC

)

umb

4-HC

Fig. 5. Plots of the transition temperature of DPPC bilayers as a function of coumarin concentrate.

50

51

52

53

54

55

0 10 20 30 40c(mol%)

T(o

C)

4-HC

umb

Fig. 6. Plots of the transition temperature of DSPC bilayers as a function of coumarin concentrate.

Fig. 7 presents dependencies of peak half-width on coumarines concentration. It can be

seen here that the additive of hydroxycoumarines causes widening of ultrasound suppression

peak i.e. these coumarines decrease cooperativeness of phase transition. An especially distinct

effect is observable for concentrations over 10 mol%. Umbelliferone, however, does not

change so distinctly the cooperativeness of phase transition; small concentrations, below or 5


mol% slightly increase cooperativeness and bigger than 5 mol% slightly decrease it. Similar

relationships were obtained in the case of all three lipids.

0

1

2

3

0 10 20 30 40

c (mol%)

∆T

1/2(

oC

)4-HC

umb

Fig. 7. Half peak width of the excess of ultrasound absorption of DPPC liposomes depending on concentrations.

Broadening of transition peaks, and lowering of transition temperature, that we can

observe in the case of 4-HC, are induced by addition of a modifier that localizes in C1 –C8

hydrocarbon region of lipid bilayer [9-12]. In 4-HC molecules, shorter sides are amphiphilic -

one of the shorter sides of molecules is polar and the other apolar, due to the fact that the

hydroxygroup is located next to the fourth carbon atom (see Fig.1). Owing to this, it can build

itself into the lipid membrane hitching with its polar sides at the lipid polar heads, while the

apolar part will be located between acyl chains disturbing their interactions and, consequently,

decreasing the temperature and enthalpy of membrane phase transition, and doing away with

this transition at high concentrations.

An umbelliferone molecule has one of the longer sides polar and the other apolar which

is the result of locating a hydroxygroup next to the seventh carbon atom, and it can be said to

have the amhiphilic character “across” the molecule. It is hard for such a molecule to

incorporate itself into the lipid membrane and if it does, this occurs very close to polar heads

almost without interaction with lipid acyl chains and thus only slightly affecting phase

transition parameters. This is at concentrations of umbelliferone below 10 mol%. It is difficult

to express unequivocally the organization of umbelliferone in lipid bilayers at concentrations

above 10 mol%. At this concentrations can be observed slight but noticeable lowering of

phase transition parameters and broadening of transition peak which may mean partial

location of umbelliferone in the acyl chain region. This may be associated with the

292 Wojtowicz K.

aggregation of umbelliferone which, as we presume, occurs at its higher concentrations

[11,12].

REFERENCES

1. R.P.D.II Morse, L.D. Ma, R. L. Magin, F. Dunn, Chem. Phys. Lipids 103, 1-10 (1999).

2. J.C. Jung, J. H. Lee, S. Oh, J. G. Lee, O.S. Park, Bioorg. Med. Chem. Lett. 14(22), 5527-5534 (2004).

3. T. H. Stefanova, N. J. Nikolova, R. A. Toshkova, H.O. Neychev J. Exp. Theor. Oncol., 6(2), 107-115 (2007).

4. B. Ramesh, K.V. Pugalendi, Yale J. Biol. Med. 78(4), 189-196 (2005).

5. B. Thati, A. Noble, R. Rowan, B.S. Creaven , M. Walsh, M. Mc Cann, D. Egan, K. Kavanagh, Toxicol. in Vitro 21, 801-808 (2007).

6. F. Eggers, Th. Funck, Naturwissenschaften 63, 280-289 (1976).

7. K. Wojtowicz, H. Gawda, Molecular and Quantum Acoustics, vol. 25. 243-248 (2004).

8. M. K. Jain, N. M. Wu, J. Membrane Biol. 34, 157-201 (1977).

9. H. Sorvoja, J. Hast, R. Myllyla, Molecular and Quantum Acoustics 24, 169-182 (2003).


11. O. Wesołowska, A. B. Hendrich, N. Motohashi, M. Kawase, P. Dobryszycki, A. Ożyhar, K. Michalak, Biophys. Chem. 109, 399-412 (2004).

12. S. Biswas, S.C. Bhattacharya, B.B. Bhowmik, S.P. Moulik, J. Coll. Interface Sci. 244, 145-155 (2001).


THE EFFECT OF 4-HYDROXYCOUMARIN

AND UMBELLIFERONE ON DPPC BILAYERS.

ULTRASOUND STUDY

Krzysztof WOJTOWICZ

Department of Biophysics Medical University of Lublin,

Al. Racławickie 1, 20-059 Lublin, POLAND

The organisation of two coumarins, 4-hydroxycoumarin and 7-hydroxycoumarin

(umbelliferone) in dipalmitolyphosphatidylcholine (DPPC) was examined in the

study. Ultrasound absorption technique was applied to study the effect of the

presence in DPPC membranes of one of the coumarines on the parameters of

phase transition. 4-hydroxycoumarin was found to change both phase transition

temperature of this transition, and cooperativity more than umbelliferone.

Different influence of these examined compounds is associated with their different

location in the DPPC membrane, what results from different distribution of

amphyphilness in molecules of both compounds.

1. INTRODUCTION

Coumarins, make up a big group of compounds whose molecular structure is based on a

common skeleton of benzo-α-piron. A lot of them have pharmaceutic value, among others,

umbelliferone (7-hydroxycoumarin) examined in this paper. Its most important properties

include: spasmolytic, antitumor [1] and antidiabetic effect [2] and absorption of UV radiation

which lets use it in skin protection radiation filters. However, it is toxic [3], has hepatoxic

effect damaging endoplasmatic membranes of hepatic cells and, hence, the usefulness of

examining its influence on lipid membranes.

Derivatives of the other compound, 4-hydroxycoumarin are usually anticoagulant drugs,

but they also have antitumor effect [4]. Molecules of umbelliferone and those of 4-

hydroxycoumarin differ in their location of hydroxygroups (Fig.1). The aim of the study was

to examine the effect of this location on thermodynamic properties of lipid membranes

modified by one of these compounds.

294 Wojtowicz K.

Fig. 1. Chemical structures of coumarins: 4-hydroxycoumarin – left, umbelliferone – right.

Lipid bilayers in the form of liposomes are a simple model of a cellular membrane

Much attention has therefore been paid to their properties of bilayers. This paper describes

studies of liposomes obtained on the basis of dipalmitoylphosphatidylcholine (DPPC).

Bilamellar phospholipids with chains of saturated carbohydrates, including DPPC, are

characterized by phase transition. The main phase transition Pβ’ - Lα of lecithin layers, called

gel-fluid transition, consists, among others, in an increase of trans - gauche isomarisation

speed of acyl chains making up the hydrophobic part of lipid layers. In the case of

multilamellar DPPC liposomes, phase transition occurs at about 41oC. The addition of a

modifier usually changes this temperature.

Examinations were carried out by measuring the coefficients of ultrasound absorption

and also using a microcalorimetric method. The ultrasound method is used for the monitoring

of phase transition in lipid membranes [5]. The basis for using the ultrasound method is the

fact that trans-gauche isomerisation is a relaxation process, thus, the measurement of

ultrasound absorption examines phase transition in lipid membranes.

These measurements give basis for conclusions about changes resulting from the

addition of modifiers, temperature of phase transition (Tt), and cooperativity of this transition.

2. MATERIALS AND METHODS

For preparation of liposomes, DL-α dipalmitoylphosphatidylcholine (DPPC)

manufactured by Sigma Chem. Co. was used. 4 - and 7 - hydroxycoumarin and Tricine buffer

were also purchased from this company. Spectrally pure methanol and chloroform made by

POCh Gliwice were used as lipid and coumarin solvents.

Multilamellar liposomes with and without coumarin were obtained according to the

following procedure. Lipid was dissolved in 1:1 chloroform-methanol solutions with an

appropriate coumarin. Then, a thin film of lipid was obtained, in the atmosphere of dry

nitrogen, by evaporating the solvent, possibly with an additive of the either

4-hydroxycoumarin or umbelliferone. Residues of solvents were removed in a vacuum.

Liposomes were obtained by adding to the film 10 mM buffer Tricine (pH=7,6) and

shaking for 1 h at a temperature above that of the phase transition. Liposome solutions at 1.5


mM concentration with the addition of one of the coumarins in the amount of 1-30mol% ratio

to DPPC were analyzed and compared with liposomes without coumarins.

The measurements of ultrasound absorption were carried out using accustom made

resonance system similar to that described by Eggers and Funck [6]. The ultrasound

absorption was determined in the frequency range 1.1 to 1.4 MHz. Ultrasound absorption

coefficients per wavelength were measured in liposome solutions and in a buffer and next,

they were subtracted giving excess of ultrasound absorption Δαλ. The maximum position of

temperature dependence of this excess determined the temperature of phase transition. Half-

width of the peak of this dependence gave information about cooperativity of this transition.

3. RESULTS AND DISCUSSION

The Fig. 2 presents temperature profiles of ultrasound absorption of DPPC liposomes

admixtures with 4-hydroxycoumarin. With the increase of coumarin concentration a decrease

of phase transition temperature is observed. In the case of umbelliferone additive (Fig. 3)

change of transition temperature is considerably smaller (see Fig. 4).

The presented dependencies show that an additive of 4-hydroxycoumarin causes

gradual, a decrease of phase transition temperature from about 410C to about 370C with the

increase of coumarin concentration from 0 mol% to 30 mol%. 7-hydroxycoumarin affects

phase transition temperature in a slightly more complex manner. Thus, small concentrations

(1-2 mol%) increase the temperature of phase transition by about 0.30C. From the 2 mol%

concentration, the temperature of phase transition is decreased, from 10mol% to 30 mol%

remains almost constant and at 30mol% reaches the value of about 40.50C.

The effect on phase transition cooperativity of each of the discussed coumarins is

different. 4-hydroxyoumarin decreases cooperativity to a greater extent than umbelliferone,

which is accounted for by a greater widening of the peak of absorption profile with increased

coumarin concentration.

296 Wojtowicz K.

DPPC+4HC

0

2

4

6

8

10

25 30 35 40 45 50T(oC)

104 ∆

αλ

DPPC

1mol%

2mol%

5mol%

10mol%

20mol%0

Fig. 2. Effects of 4-hydroxycoumarine on the excess of the ultrasound absorption of DPPC versus temperature.

DPPC+umb

0

2

4

6

8

10

25 30 35 40 45 50T(oC)

104 ∆

αλ

DPPC

1mol%

2mol%

5mol%

10mol%

20mol%

Fig. 3. Effects of umbelliferone on the excess of the ultrasound absorption of DPPC versus temperature.

As for the effect of umbelliferone on cooperativity, the results of this study differ from

hose of paper [7]. In the latter paper umbelliferone was found to cause an increase of phase

transition cooperativity. This different action of umbelliferone on the lipid membrane is

associated with pH effect. In paper [7] a phosphate buffer with pH=8 was used while in the

present paper Tricine buffer with pH=7.6 was applied. As can be concluded from paper

[8-13], at pH=8 umbelliferone molecules are mostly in the monomeric form, while at pH=7.6

both monomers and dimmers occur.


36

37

38

39

40

41

42

0 10 20 30 40c(mol%)

T(o

C)

umb

4-HC

Fig. 4. Plots of the transition temperature of DPPC bilayers as a function of coumarins concentrate. Curves refer to umbelliferone (umb) and 4-hydroxycoumarin (4-HC).

Similar dependences were obtained in work [10] by microcalorimetric measurements.

Enthalpy determined in this work decreases with the increase of each coumarins

concentration, and can also observe a greater effect of 4-hydroxycoumarin than the effect of

umbelliferone addition.

All these results indicate that the additive of 4-hydroxycoumarin to DPPC membranes

modifies these membranes more strongly than umbelliferone. An umbelliferone molecules by

has one of the longer sides polar and the other apolar what results from locating a

hydroxygroup next to a seventh carbon atom (see Fig.1), and it can be said to have the

amhyphilic character “across” the molecule. It is hard for such a molecule to incorporate itself

into the lipid membrane and if it does, this occurs very close to polar heads almost without

interaction with lipid acyl chains and thus only slightly affecting phase transition parameters.

The fact that an increase of umbelliferone concentration above 10 mol% does not result in a

further considerable change of phase transition parameters may account for an aggregation of

umbelliferone molecules as well as a limited degree of incorporation of its molecules into the

lipid membrane. In 4-hydroxycoumarin molecules shorter sides is amphyphilic, due to the fact

that the hydroxygroup is located next to the fourth carbon atom. Owing to this it can build

itself into the lipid membrane hitching with its polar sides at the lipid polar heads, while the

apolar part will be located between acyl chains disturbing their interactions and, consequently,

decreasing the cooperativity of membrane phase transition, temperature and enthalpy of this

transition and doing away with his transition at high concentrations.

298 Wojtowicz K.

REFERENCES

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5. R.P.D.II Morse, L.D. Ma, R. L. Magin, F.Dunn, Chem. Phys. Lipids 103, 1 (1999).

6. F. Eggers, Th. Funck, Naturwissenschaften 63, 280 (1976)/

7. K.Wojtowicz, Inst. Sci.& Techn. 27, 290 (1999).

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12. M. Gawlikowski, T. Pustelny, R. Kustosz, J.Phys.IV France 137, 73-78 (2006).

13. K. Wojtowicz, to be published in Annales UMCS sectio DDD.

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