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Optik 122 (2011) 99–104

Contents lists available at ScienceDirect

Optik

journa l homepage: www.e lsev ier .de / i j leo

olarimetric characterization of ultra-high molecular weight polyethyleneUHMWPE) for bone substitute biomaterials

. Firdousa,∗, M. Fuzailb, M. Atif a, M. Nawaza

Biophotonics Laboratory, Photonics Division, National Institute of Lasers and Optronics (NILOP), P.O. Nilore 45650, Islamabad, PakistanApplied Chemistry Laboratory (ACL), P.O. Nilore 45650, Islamabad, Pakistan

r t i c l e i n f o

rticle history:eceived 5 May 2009ccepted 20 October 2009

eywords:

a b s t r a c t

In this work the UHMWPE is characterized for their optical properties with Mueller matrix polarimeter.The transmittance birefringence, retardance, polarizance, linear and circular polarization and absorbanceof polarized light at different wavelengths ranging 400–800 nm are measured. The presented Muellermatrix elements along with depth resolve polarization decrease in intensity with the change in thewavelength. Linear retardance increases compared to circular through highly scattering polyethylene.

iomaterialHMWPEolarizationcatteringepolarizationueller matrix

High refractive index and low mean free path; and close bonding of particles of material rotates theincoming photons and circular polarization which is dominant as compared to the linear one. Thereforethe average intensity increases with both the optical depth and the scattered concentration in UHMWPE,which would accordingly decrease the apparent degree of polarization.

The extracted results in terms of linear and circular retardances prove that UHMWPE is compati-ble, strong, and compact. This research work provides an optical characterization technique for bone

the h

substitute biomaterial in

. Introduction

Advances in artificial joint technology have resulted in success-ul surgical treatments for the debilitating loss of mobility caused byoint disease, traumatic injury, and overuse of native joint. Variousngineering materials have been used in orthopedic applicationsor bone replacement or repair in a variety of surgical procedures1,2]. Ultra-high molecular weight polyethylene (UHMWPE) is anown biomaterial which is self-lubricating, has light weight ands machineable that can be shaped by compression molding; it canbsorb shock easily as well. Other excellent properties, such asow density, high strength, high modulus, good abrasion, chemicalsesistance and low frictional coefficient [7–9] make it the materialf choice for hip joints and knee joints. It is expected to with-tand any anticipated physiological loading without dimensionalhanges, catastrophic brittle fracture or fracture in the longer termue to creep, fatigue or stress corrosion [3,4]. The molecular weightf UHMWPE is typically ∼6 million and the material comprisesoth crystalline and amorphous parts. The large size molecules are

inked together by Vander vaal bonds [5,6].UHMWPE has already been characterized with the time of

ight (TOF), atomic force microscopy (AFM) and force modulationicroscopy (FMM) [10–12]. Raman spectroscopy studied by Barron

∗ Corresponding author.E-mail addresses: shamaraz@gmail.com, shamaraz@nilop.edu.pk (S. Firdous).

030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2009.10.008

ealth care industry.© 2010 Elsevier GmbH. All rights reserved.

[13] demonstrated that the material consists of three phases, fullycrystalline, fully amorphous and an intermediate non-crystallinephase [13]. A recent thermal degradation study report shows thatthe powder sample has the thermal activation energy of 131 kJ/moland it has only one major step of degradation between 200 and500 ◦C [14].

In the present work Mueller matrix polarimetric technique wasused for the first time to characterize UHMWPE with respect tooptical characteristics. It has already been proved that this type ofmaterial is suitable for (low-weight) bearing joints replacement,bone reconstruction, vertebral bodies, and in plastic surgery. Since1962, UHMWPE has also been used in surgical implants as thebearing surface in artificial joints [15,16] and at present, about 2million joint replacements are performed around the world eachyear. However, UHMWPE has a finite lifetime, and the wear anddamage of the components is one of the limiting factors of implants[17,18].

In addition to other characterization techniques used, the polari-metric method is the technique of measuring the polarization stateof a light beam and the diattenuating, retarding, and depolarizingproperties of materials. The polarimeter is an optical instrumentfor the determination of the polarization state of a light beam, or

the polarization altering properties of a sample. We used a Muellermatrix formalism for characterizing polarization elements becauseit contains within its elements all of the polarization properties:diattenuation, retardance, depolarization, and linear and circular[19–21]. When the Mueller matrix is known, then the exiting polar-

1 ptik 122 (2011) 99–104

itisvbmIclc

wewg

S

wppdtttt

D

g

[

we

[

wcbmcpa[

⎤⎥⎥⎥⎥⎦ , [QW] = 1

2

⎡⎢⎣

1 −1 0 0−1 1 0 00 0 0 00 0 0 0

⎤⎥⎦ ,

Fig. 1. Experimental setup for the measurement of Mueller matrix polarizationproperties through UHMWPE, biomaterial. The polarimetric system consists of

surements were made on low crystalline (∼30%) powder samples.The molecular weight was in the range of 3–5 million as per themanufacturer’s data. The apparent density was 0.94–0.96 g/cc forthe powder UHMWP [28]. One percent solution of UHMWPE was

00 S. Firdous et al. / O

zation state is known for all incident polarization states. In general,he interaction of light with optical elements such as lenses, polar-zer, filters, surfaces, and scattering media, changes the polarizationtate of the light. When light is described by a four-componentector, this interaction with any optical element or material cane described as a multiplication of the Stokes vector with a 4 × 4atrix, this sixteen-element matrix is a Mueller matrix [22,23].

f scattering is involved, this matrix completely characterizes anyomponent or material in terms of its optical properties. For theight propagating along the z axis, we obtain the two orthogonalomplex electric field components as [24]:

Ex(t) = Eixei�x(t)e−iKzeiωt,

Ey(t) = Eiyei�y(t)e−iKzeiωt,(1)

here the phases ϕx (t), ϕy (t) and amplitudes Eix(t) and Eiy(t) ofach component are the functions of time. The Stokes parameters,hich are used to describe the polarization state of the light, are

iven in the vector form by [24]

=

⎡⎢⎣

S0

S1

S2

S3

⎤⎥⎦ =

⎡⎢⎢⎣

% E20x + % E2

0y

% E20x − % E2

0y

2% E0xE0y cos ı

2% E0xE0y sin ı

⎤⎥⎥⎦ , (2)

here S0 is the total input intensity, S1 and S2 represent the linearlyolarized components of the beam, S3 represents the circularlyolarized component and ı(t) = ϕx(t) − ϕy(t) is the relative phaseifference between the two orthogonal components. For an arbi-rary light beam, these terms are related by S0

2 ≥ S12 + S2

2 + S32,

he equality holds for fully polarized light and the inequality applieso partially polarized light. The degree of polarization (DOP) for theurbid medium is defined as [25]

OP =√

S21 + S2

2 + S23

S20

. (3)

The transformation of the Stokes vector by an optical system isiven by [25]:

Sout] = [Msystem][Sin], (4)

here [Msystem] is the Mueller matrix representing the entirexperimental optical system given as

Msystem] = [QW][AM][M][QW][PM]. (5)

To model the polarization effects of various optical componentsere represented by Mueller matrices [26,27]. Using Mueller cal-

ulus, an optical element that acts on a light beam is representedy multiplication of the incident light Stokes vector by the Muelleratrix for that optical element. The output stokes vector can be

alculated by relation in Eq. (4), where the Mueller matrix forolarizer [P], UHMWPE [M], analyzer [A] quarter wave plate [QW]t horizontal fast axis and Stokes input vector [Sin] are given as26]

[PM] = 12

⎡⎢⎢⎢⎢⎣

1 C2i S2i 0

C2i C22i

S4i

20

S2iS4i

2S2

2i0

0 0 0 0

⎤⎥⎥⎥⎥⎦ , [AM] = 1

2

⎡⎢⎢⎢⎢⎣

1 C2o S2o 0

C2o C22o

S4o

20

S2oS4o

2S2

2o 0

0 0 0 0⎡ ⎤ ⎡ ⎤

[M] = ⎢⎣

m11 m12 m13 m14

m21 m22 m23 m24

m31 m32 m33 m34

m41 m42 m43 m44

⎥⎦ , Sin = ⎢⎣S0

S1

S2

S3

⎥⎦ ,

polarizers and retarders for polarization change.

where C2i = cos (2�i), S2i = sin (2�i), S4i = sin (4�i), C2o = cos (2�o),S2o = sin (2�o), S4o = sin (4�o). All the Mueller matrix elements canbe determined experimentally [see Fig. 1]. It can be shown that 49intensity measurements with various orientations of polarizers andanalyzers are necessary to obtain the 16 elements of the Muellermatrix [21].

2. Materials and methods

The ultra-high molecular weight polyethylene used in thepresent work was from Beijing Chemical Company and the mea-

(6)

S. Firdous et al. / Optik 122 (2011) 99–104 101

pt

2

m5loglttrw

2

ttu−oscborfi

3

tuslSifm

mDT

The retardance of light through the material is shown in Fig. 4. Itis a polarization-dependent phase change associated with a polar-ization element or system. The phase (optical path length) of theoutput beam depends upon the polarization state of the input beam.

Fig. 2. Differential scanning calorimetry (DSC) scan of UHMWPE powder.

repared in the boiling xylene. For polarimetric study, solution wasaken in the quartz tube of 3 cm × 1 cm length.

.1. The Mueller matrix polarimetry

In Experimental setup for measurements of transmitted Muelleratrix elements, a Halogen lamp beam with an output power of

0 W at a wavelength of 400–800 nm for hot solution is used as theight source (see Fig. 1). The light beam is focused on polarizer P1 forbtaining linearly polarized light. The circularly polarized light isenerated, by inserting a quarter mica retardation plate behind theinear polarizer. The output polarized light is focused to UHMWPEurbid medium, by lens L1 (f = 15 cm) and after sample it passeshrough quarter wave plate and analyzer. The output intensity isecorded on photodiode detector, which is controlled and operatedith Lab software.

.2. Differential scanning calorimetry (DSC)

Differential scanning calorimetry, or DSC, was used to measurehe degree of crystallinity and the melting point of a material. Inhis study, a Module DSC 822e, Mettler Toledo, Switzerland wassed for differential scanning calorimetry. A temperature range of50 to 450 ◦C was run; the heating rate of 10 ◦C/min under streamf nitrogen with flow rate of 50 ml/min was taken. Samples wereealed in aluminum standard 40 �l pan and a single heating andooling scan was used. The degree of crystallinity was determinedy comparing the measured heat of fusion with the theoretical heatf fusion of 100% crystalline polyethylene of 293 J/g. For polarimet-ic study, sample was dissolved in boiling xylene and solution wasltered and kept at 80 ◦C.

. Results and discussions

The polarizance measured for UHMWP with Mueller polarime-er is a property of an optical element or system wherebynpolarized light is transformed into polarized light. It can behown by its magnitude (equal to the degree of polarization ofight exiting the system when unpolarized light is input) and thetokes vector of the output light. The objective of the Mueller matrixmaging polarimeter is to measure the characteristics of UHMWProm the Mueller matrix distribution and optical properties of

aterial.The DSC technique was employed to analyze the material’s ther-

al behavior and to assess the crystallinity of the material. TheSC traces for UHMWPE powder in Fig. 2, show two key features.he melting peak (Tm), which corresponds to the point at which

Fig. 3. The transmittance of polarized light passing through UHMWPE, usingMueller matrix polarimeter. It increases up to 600 nm and then slowly decreases.

almost all of the crystalline regions have melted, was sharp andfound at 125.55 C. The enthalpy of melting was 88.01 kJ/mol andthe crystallinity was found to be ∼30%.

In Fig. 3 the polarized transmittance behavior of materialdescribes an increase in polarized intensity with change of wave-length. It is maximum on 600 nm and then starts decreasing, whichdescribes that after 600 nm the scattering is saturated. UHMWPEparticles describe Rayleigh scattering behavior and starts satura-tion on higher wavelength. Due to its smaller grain size compared tolight wavelength and compact shape, the scattering above 600 nmdecreases.

The UHMWPE is birefringent material and the retardance asso-ciated with propagation through an anisotropic medium. For eachpropagation direction within a birefringent medium there are twomodes of propagation with different refractive indices n1 and n2.The birefringence Dn is:

Dn = |n1 − n2|. (7)

The larger the refractive index of the material provides higherscattering for light passing it. The polarizer is used with an intensitytransmittance of one for its principal state and an intensity trans-mittance of zero for the orthogonal state. The linear polarizer hasa property that when placed in front of an incident unpolarizedbeam produces a beam of light whose electric field vector is oscil-lating primarily in one plane, with only a small component in theperpendicular plane.

Fig. 4. Total retardance in degree of polarized light through UHMWPE, from 400to 800 nm wavelength of light. There is decrease in intensity up to 500 nm andincreases.

102 S. Firdous et al. / Optik 122 (2011) 99–104

FUci

Tap

aqsrcalwwodid

iiiop

iiaaadw

msTmoimMsto

am

has very less azimuthal dependence, it decreases with increasingmaterial concentration.

The increase in light intensity from 400 to 800 nm passingthrough UHMWPE as shown in Fig. 2, increases in the random scat-

Table 1The Mueller matrix element of UHMWPE at 450 nm wavelength.

M11 M12 M13 M14

0.033179 0.000864 0.000789 −0.000912

M21 M22 M23 M24

0.001006 0.037604 0.000909 0.000470

M31 M32 M33 M34

0.000099 −0.000469 0.038356 0.000229

M41 M42 M43 M44

0.000500 0.000848 −0.00007 0.036060

Table 2The Mueller matrix element of UHMWPE at 550 nm wavelength.

M11 M12 M13 M14

0.039760 0.000343 −0.00070 0.000584

M21 M22 M23 M24

0.000060 0.041653 0.000751 −0.000004

M31 M32 M33 M34

ig. 5. The linear and circular polarization of polarized light on passing throughHMWPE, using Mueller matrix polarimeter. For both the polarizations althoughircular signal is weak but they show increasing behavior compared to linear polar-zation.

he transmitted phase is a maximum for one eigenpolarization,nd a minimum for the other eigenpolarization. Other states showolarization coupling and an intermediate phase.

The total retardance in degree decreases from 400 to 500 nmnd then starts increasing up to 800 nm wavelength. Higher fre-uency and lower wavelength light passes frequently throughmall particles of the material and drops at higher wavelengthegion. This means that the UHMWPE is composite, strong andompact. The light depolarized on passing through the materialnd during the process it couples polarized light into unpolarizedight. Depolarization is intrinsically associated with scattering and

ith diattenuation and retardance which vary in space, time, andavelength. During the diattenuation, the intensity transmittance

f the exiting beam depends on the polarization state of the inci-ent beam. The intensity transmittance is a maximum Pmax for one

ncident state, and a minimum Pmin for the orthogonal state. Theiattenuation is then:

Pmax − Pmin

Pmax + Pmin. (8)

The linear and circular retardance from UHMWPE is shownn Fig. 5. The circular polarization is increasing and linear dropsncrease in wavelength. This behavior presents dominant scatter-ng through material. Lower mean free path and close bondingf particles of material rotates the incoming photons and circularolarization is dominant as compared to the linear one.

The analyzer collects output light, whose intensity transmissions proportional to the content of a specific polarization state in thencident beam. The transmitted polarization state emerging fromn analyzer is not necessarily the same as the state which is beingnalyzed. As the UHMWPE is inhomogeneous polarization elementnd its eigenpolarizations are not orthogonal. Such a material willisplay different polarization characteristics for forward and back-ard propagating beams.

The Mueller matrix through UHMWPE is shown in Fig. 6. Theseatrices can be measured through 49 different polarization mea-

urements with Mueller matrix polarimeter setup shown in Fig. 1.he mathematical calculations of 16 elements out of 49 measure-ents can be performed through literature [25]. The M11 element

f the Mueller matrix corresponds to the polarization independentmage, as acquired through non-polarized configuration. The other

atrices Mij (i and j = 1, 2, 3, 4) are normalized through M11. The11 (total intensity matrix) reveals less information then other

trong layered structure, like M13, M22, M33, and M44. We have

aken multi-images and readings of different polarizations statesf UHMWPE.

All the other elements except M11 (identity matrix) can be neg-tive due to intensity addition and subtraction. All the Muelleratrices of UHMWPE show azimuthally variation in relative inten-

Fig. 6. The 16 element of Mueller matrix for UHMWPE, measured by Mueller matrixpolarimeter. Linear polarization and direct light component is dominant as com-pared to circular polarization elements.

sity, and the intensity decay and increase depend upon scatteringand absorption of sample.

In transmitted light shown in Fig. 3, most of the regions preserveoriginal polarizations states due to stronger co polarized signalinstead of the cross-polarized. The entire matrix elements fromTables 1–4 provide comprehensive and detailed information of thesample. Analyzing only the diagonal elements or images M11, M22,M33, and M44 of the Mueller matrix, one can extract useful informa-tions and characterize the sample under investigation. M11 is unityand unpolarized matrix provides less information comparable toothers but the maximum intensity pattern is achieved through thismatrix. M22 and M33 show the linear polarization effect of lightthrough sample. M44 involves on circular polarized light only and

0.001031 −0.001425 0.043473 −0.001718

M41 M42 M43 M44

−0.000649 0.000479 −0.00099 0.041513

S. Firdous et al. / Optik 1

Table 3The Mueller matrix element of UHMWPE at 650 nm wavelength.

M11 M12 M13 M14

0.041369 0.000303 0.000163 −0.000020

M21 M22 M23 M24

0.000318 0.042683 0.000257 0.000218

M31 M32 M33 M34

−0.000173 −0.000426 0.043048 −0.000646

M41 M42 M43 M44

0.000364 −0.000053 −0.00062 0.041580

Table 4The Mueller matrix element of UHMWPE at 750 nm wavelength.

M11 M12 M13 M14

0.041430 0.000376 −0.00006 −0.000660

M21 M22 M23 M24

0.000693 0.043550 0.000736 −0.000353

M31 M32 M33 M34

−0.000020 −0.000121 0.043164 −0.000060

tistitd

ppoaboctmtet

4

pitipmtcold

[

[

[

[

[

[

[

[[

[

[

[

M41 M42 M43 M44

0.000205 0.000182 −0.00043 0.042418

ering that the light undergoes per unit optical depth. An increasen the optical depth means that the scattered light undergoes morecattering events, which causes more fluctuation because each scat-ering event has Brownian motion. Therefore the average intensityncreases with both the optical depth and the scatterer concentra-ion in UHMWPE, which would accordingly decrease the apparentegree of polarization.

In the centre of Mueller matrix the output images show strongolarization effect, due to less scattering of light. The symmetryattern of the Mueller matrix element is very dominant and thenly sizes of the numerical value of the matrix are opposite. M22nd M33 are quite sensitive to the material aspect ratios and maye useful for determining particle morphology. The Mueller matrixf upper left corner is associated only with the linear polarizationonfiguration and easer to quantify by lab measurements than byhe circular polarization. The results in Figs. 2–6 are in good agree-

ent between theory and experiment for the intensity pattern ofhree- and two-dimensional transmitted light. This technique canxtract or decode useful information about the sample under inves-igation.

. Conclusion

The UHMWPE proves to be a suitable option for use in ortho-edic implants. Constant improvements are being researched to

ncrease the life of implants. The UHMWPE is characterized forheir optical properties with Mueller matrix polarimetry. The polar-zed transmittance behavior of material describes an increase inolarized intensity with change of wavelength. It shows maxi-um value on 600 nm and then starts decreasing, which shows

hat after 600 nm the scattering is saturated. UHMWPE parti-les describe Rayleigh scattering behavior and starts saturationn higher wavelength. Due to its smaller grain size compared toight wavelength and compact shape, the scattering above 600 nmecreases. Higher frequency and lower wavelength light passes

[

[

[

22 (2011) 99–104 103

frequently through small particles of the material and drops athigher wavelength. Lower mean free path and close bonding ofparticles of material rotate the incoming photons and circularpolarization is dominant as compared to the linear one. There-fore the average intensity increases with both the optical depthand the scatterer concentration in UHMWPE, which would accord-ingly decrease the apparent degree of polarization. All the sixteenMueller matrix components give a detailed and comprehensiveknowledge about the birefringent medium. It provides the changein morphology and needs detailed analysis of each single Muellermatrix.

In this work we present a method and general framework for thestudy of transmitted, depolarized and other polarization propertiesto characterize highly scattering UHMWPE for its optical activity.The transmittance, retardance and linear and circular depolariza-tion of light through UHMWPE, proves its high compatibility, as astrong and dense scattering medium, which is suitable for hip andknee joint biomaterial.

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[

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