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554 Lubricant Additives: Chemistry and Applications

the peak assignments given in Table 22.11 [1]. Similar IR spectra and peak assignments are reported

for mechanically stressed grease by Cann et al. [57]. The IR peak assignments, in conjunction

with XPS measurements on the residue given in Table 22.12 [1], show electrochemical oxidation

of the grease. The ratio of carbonyl groups increased following the electrochemistry. For the pure

thickener, the ratio of carbonyl to Li is 1.07, whereas aged grease and electrochemically oxidized

grease have increased carbonyl due to oxidation. For black grease from a failed bearing, residue in a

noisy bearing and a pin on disk wear test track also show increased carbonyl relative to the original

thickener.

In summary, for the longest lifetime and best performance under all conditions, lithium grease

should be kept free of metallic impurities and diluents. When electrochemical oxidation does occur,

it forms a residue from the soap thickener on the raceway.

22.3.2 BALL BEARING SPINDLE MOTOR FERROFLUID SEAL

As mentioned earlier, the return path from the rotor to the stator for charge generated by the ball

bearings is through the ferro uid seal (Figure 22.14b). The ferro uid is held in place by magnets

in the seal housing, and the primary function of the ferro uid seal is to prevent air ow through the

motor into the disk drive enclosure. The typical ferro uid is a suspension of 10–30 wt% subdomain

magnetite particles 10 nm in diameter in a trimellitic/trimethylol propane ester oil with 10–20 wt%

dispersing agent and up to 10 wt% antioxidant.

10× Lens

Composition

(a)

(b)

100 µm scale bar

20× Lens

FIGURE 22.21 Optical micrographs showing the  lm deposits on the negative electrode plate following

electrochemical oxidation of contaminated grease at two different levels of magni cation. The residue was

insoluble in chloroform and isopropanol, whereas the initial grease was easily removed from the plates by

rinsing with chloroform. SRL grease + 300 ppm Zn for 336 h (a), and SRL grease + 16% prelube A for 576

h (b). (Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chemistry and

Technology, Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.)

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Lubricants for the Disk Drive Industry 555

Ferro uid is a mature technology, and these  uids are highly stable. The most recent effort to

modify the properties of the ferro uid was intended to increase the electrical conductivity so as to

reduce the electrical potential between the rotor and stator of the spindle motor. The development

of conductivity additives for ferro uids is described later.

Additives to increase the conductivity of the carrier oil were investigated. A number of conductivity

enhancing compounds were incorporated in a model carrier oil, trioctyltrimellitate (TOTM), and the

conductivity was measured by DEA, as described in Section 22.2.1.2. The results of the initial screening

are given in Table 22.13 [1]. Most of the additives reduced the conductivity. This probably indicates that

the additives were associating with impurities that were the primary charge carriers in the oil. The most

promising initial results were obtained with a micellar solution of succinimide and dodecylbenzenesul-

fonic acid [58]. Variations of the organic acid and the succinimide/acid ratio were explored to optimize

the conductivity of the TOTM carrier oil. The results are summarized in Table 22.14 [1]. The mixtures

of succinimide and acid provided the highest conductivity to the oil. The most promising conductivity

additives based on the tests in the model oil are shown in Figure 22.23 [1]. Even the best combination of

conductivity additives in TOTM still had lower conductivity than any of the ferro uids.

Dielectric spectroscopy was performed to determine the conductivity mechanism of the

ferro uid. The ferro uid has three dielectric relaxation times: 260, 43, and 6.3 ms. These relaxation

TABLE 22.10

Grease Electrochemical Cell Test Results for Grease on a 160 µm Thick

Filter Paper between 1 in. Diameter Electrode Plates

Sample Initial Conductance (nS) Time (h) Film Deposit

SRL grease alone 4 960 Light

SRL grease 28 336 Medium

+ 36% prelube A

+ 300 ppm Zn

+ 100 ppm Fe

SRL grease 7 336 Heavy

+ 300 ppm Zn

SRL grease 8 576 Heavy

+ 16% prelube A

SRL grease 20 336 Light

+ 16% prelube A

+ 300 ppm Zn

SRL grease 52 576 Light

+ 16% prelube B

SRL grease 93 336 Heavy

+ 16% prelube B

+ 300 ppm Zn

SRL grease 9 336 Light

+ 12.5% SRL base oil

SRL grease 16 336 Heavy

+ 12.5% SRL base oil

+ 300 ppm Zn

Note: The initial conductance was calculated from the linear region of the current–voltage data

measured between 1 and 25 V (Figure 22.19). Prelube is de ned in the text. The right-hand

column gives the appearance of the  lm deposit on the negative electrode plate after application

of 25 V for the amount of time listed in the third column.

Source: Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chem-

istry and Technology, Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.

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556 Lubricant Additives: Chemistry and Applications

modes probably comprise the phoretic motion of the magnetite particles, phoretic motion of ions,

and electronic hopping, respectively. The activation energy for conductivity is close to the viscous

 ow activation energy, so the conductivity of the ferro uid is mostly due to the phoretic motion of

the magnetite particles. The relaxation times were unchanged by the conductivity additives.

As it became apparent that conventional additives used to enhance the conductivity of the carrier

oil are of no bene t, or reduce the conductivity of the ferro uid, a different approach was needed.

Ferro uid is signi cantly more conductive than the carrier oil, due to the presence of the magne-

tite particles. The conductivity of a ferro uid can only be enhanced by improving the ef ciency

of charge transfer between the suspended magnetite particles. This may be done by incorporating

17362921

1581

1451

5001000150020002500300035004000

Wavenumber (cm

−1

)

Absorbance

(a)

1712

1456

1587

2922

5001000150020002500300035004000

Wavenumber (cm

−1

)

Absorbance

(b)

1718

1456

1587

2922

5001000150020002500300035004000

Wavenumber

(

−1

)

Absorbance

(c)

SRL grease

+ 36% Prelube A

+ 300 ppm Zn

+ 100 ppm Fe

SRL grease

+ 300 ppm Zn

SRL grease

+ 16% Prelube A

FIGURE 22.22 Re ection FTIR spectra of residue deposited on the negative electrode plates from grease con-

taining various contaminants: (a) Prelube A, Zn, and Fe, (b) Zn, and (c) prelube A. Oil was removed by washing

with solvent before measurement. (Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based

Lubricants Chemistry and Technology, Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.)

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Lubricants for the Disk Drive Industry 557

TABLE 22.11

FTIR Peak Assignments

Absorbance

Wavenumber (cm

−1

)

Broad dimer hydrogen-bonded carbonyl O–H stretch in 12-hydroxy stearic acid 3500–2500

Hydrogen-bonded O–H stretch in alcohol 3500–3200

Asymmetrical methylene C–H stretch 2928–2917

Aliphatic aldehyde or ester C=O stretch 1740

Aliphatic methyl ketone C=O stretch 1730

Alphatic internal ketone C=O stretch 1725

Carboxylic acid dimer C=O stretch in 12-hydroxy stearic acid 1695

C–O–H in-plane bend in 2-hydroxy stearic acid 1470

Carboxylate anion, asymmetrical stretch 1589–1581

Carboxylate anion, symmetrical stretch 1456–1442

Ester C–C(=O)–O in base oil 1166

Note: The carboxylate anion is formed with Li or Zn and 12-hydroxy stearic acid. The ratio (C=O)

salt

/C(–H)

was measured

using the carboxylate anion, asymmetrical stretching, and the asymmetrical methylene C–H stretching.

Source: Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chemistry and Technology,

Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.

TABLE 22.12

The Ratio of Carboxylic Acid to Methylene from FTIR, the Ratio of Total Carbonyl Carbon

to Methylene Carbon and to Li, and Atomic Percent of Li and Zn from XPS, in Model

Compounds, Electrochemically Deposited Films, Inner Race Deposits, and Black Grease

from Failed Motor Bearings

FTIR XPS

Film

Hydrogen-

Bonded OH

(C=O)

salt

C(–H)

C=O)

total

C(–H)

C=O)

total

(%)

Li 12-hydroxy stearate Yes 0.067 (exact) 0.067 1.07 4.3 0.09

Li 12-hydroxy stearate from grease (brown,

stored 8 years)

Yes 0.035 0.079 1.5 3.6 —

Zn (12-hydroxy stearate)

— — 0.063 — <0.3 3.0

Zn (12-hydroxy stearate)

after 10 min at 130°C Yes 0.049 — — — —

eChem SRL grease + 36% prelube A Yes 0.17, 0.05,

0.054

0.097 1.3 5.1 0.06

+ 300 ppm Zn

+ 100 ppm Fe

eChem SRL grease + 300 ppm Zn Yes 0.086, 0.082 0.11 1.4 4.7 0.12

eChem SRL grease + 16% prelube A Yes 0.072, 0.077 0.11 1.4 5.3 —

Black grease No 0.076 0.14 0.5 15.8 0.16

In-plane residue No, yes 0.10, 0.06 — — — —

Ball track residue No 0.12, 0.20,

0.31, 0.13

————

Note: The extinction coef cient ratio, ε

C(–H)

/ε

C=O

= 0.0475, was calculated from FTIR spectra of methylene C(–H)

asym-

metric stretch and carboxylic acid (C=O–O) anion asymmetric stretch measured for Li 12-hydroxy stearate and Li

stearate. Grease samples were rinsed with solvent to remove the oil. For Li 12 hydroxy stearate, the exact ratio of

C=O/C(–H)

is 1/15 = 0.067, and the exact ratio of C(=O)/Li is 1, the exact atomic percent of Li = 4.8, and for

Zn= 2.4; 300 ppm of Zn corresponds to 0.06 atomic percent of the lithium 12-hydroxy stearate. These results show

evidence for electrochemical oxidation of the 12 hydroxy stearate thickener.

Source: Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chemistry and Technology,

Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.

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558 Lubricant Additives: Chemistry and Applications

particles coated with conducting polymer, conducting polymer oligomers, or nanowires in the form

of multiwall carbon nanotubes. Conducting polymer-coated carbon black particles (Eeonomer,

Eeonyx Corp., Pinole, California, United States [59]) and multiwall nanotubes (BU200, Bucky USA,

Houston, Texas, United States) were evaluated in the TOTM model oil. As shown in Table 22.15

[1], the Eeonomers and nanotubes increased the oil conductivity by about  ve orders of magnitude.

A stable mixed suspension of the nanotubes could not be adequately dispersed in the ferro uid.

TABLE 22.13

Trial Matrix of Potential Conductivity Additives in Triocytyltrimellitate Model Carrier Oil

Additive Concentration (wt%) Comments Conductivity (pS/m)

None — — 250–300

Disodium sebacate (Ciba DSSG) 1 Milky 5–7

Succinimide (2,5-pyrrolidenedione) 2 Mostly insoluble 80–100

Dodecylbenzenesulfonic acid 2 Clear solution 180–230

Butylated hydroxy toluene (BHT, or Ionol) 2 Clear solution 50–70

Ciba Irgamet 30 2 Clear solution 170–180

Dicyclohexylammonium benzoate 2 Milky 200–260

PMC Cobratec 911S 2 Clear solution 130–150

Mellitic acid 2 Mostly insoluble 8–17

Mixtures

Succinimide (2,5-pyrrolidenedione) 1.6 Hazy 860–990

Dodecylbenzenesulfonic acid 1

Succinimide (2,5-pyrrolidenedione) 7.6 Hazy/Gel 3000–5000

Dodecylbenzenesulfonic acid 4.8

Note: Conductivity measured at 1 Hz and 50°C.

Source: Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chemistry and Technology,

Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.

TABLE 22.14

Optimization Matrix of Succinimide/Sulfonate Conductivity Additives in

Tricoctyltrimellitate Model Carrier Oil

Permittivity (1 Hz) Conductivity (pS/m)

Additive Concentration (wt%) Comments 5°C50°C5°C50°C

None — — 3.9 6.3 15 250–300

Succinimide 2 Mostly insoluble — 4.0 — 80–100

DDBSA 2 Clear solution — 4.0 — 180–230

Succinimide 1.6 Hazy 4.9 6.5 140 860–990

DDBSA 1

Succinimide 7.6 Hazy/Gel — 26.0 — 3000–5000

DDBSA 4.8

Succinimide 1.5 Brownish, hazy 3.0–3.2 4.8–5.6 160–220 4400

DNNSA 1.4

Succinimide 1.5 Whitish, hazy, looks

good

— 2.9–3.2 — 5–8

DNNDSA 0.8

Note: Succinimide is 2,5-pyrrolidenedione (99.1 g/mol). DDBSA is dodecylbenzenesulfonic acid (326.5 g/mol). DNNSA

is dinonyl naphthalenesulfonic acid (460.71 g/mol). DNNDSA is dinonyl naphthalene disulfonic acid (540.79 g/mol).

Amounts of DNNSA and DNNDSA adjusted for molecular weight and normality.

Source: Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chemistry and Technology,

Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.

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Lubricants for the Disk Drive Industry 559

The conductivity of the ferro uid increased with the Eeonomer concentration and was nearly

independent of temperature between 5 and 50°C, as shown in Figure 22.24 [1]. The conductivity as

a function of temperature for ferro uid 1 containing Eeonomers is shown in Figure 22.25a [1]. The

conduction mechanism seems to be limited by electronic transport through the Eeonomers, rather

than by diffusive contacts between the particles, as the product of the conductivity and viscosity of the

ferro uid-containing Eeonomers decreased with temperature (Figure 22.25b). The metallic-like con-

ductivity of the conducting polymer sheath is decreased by scattering because lattice vibrations faster

than the transport between particles are increased by Brownian motion with increasing temperature.

Although the Eeonomers appear to be the most effective means to increase the ferro uid con-

ductivity, the long-term stability may be degraded by reaction of the dodecylbenzenesulfonic acid

with the ester carrier oil. Furthermore, the conducting polymer sheath may also be crushed off of

the carbon black in milling during the initial dispersion phase of ferro uid manufacturing.

0 10203040506070

Temperature (°C)

Conductivity (S/m)

Ferrofluid 1

Ferrofluid 2

Ferrofluid 3

Ferrofluid 4

Pure TOTM

TOTM

+1.6% Succinimide

+1% DDBSDA

TOTM

+7.6% Succinimide

+4.8% DDBSDA

Ferrofluid 1

+3% Succinimide

+2% DDBSDA

Ferrofluid 2

particles

Redispersed

in DOS

1×10

−6

1×10

−7

1×10

−8

1×10

−9

1×10

−10

1×10

−11

FIGURE 22.23 Conductivity of several types of ferro uid, conductivity additives in model carrier oil, and

ferro uid 1 combined with one of the most promising conductivity additives. (Adapted from Rudnick, L.R.

(ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chemistry and Technology, Chapter 38, CRC Press,

Taylor & Francis Group, Boca Raton, FL, 2006.)

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560 Lubricant Additives: Chemistry and Applications

TABLE 22.15

Conductivity Evaluation of Multiwall Nanotubes and Eeonomers

in TOTM Model Carrier Oil

Additive

Conductivity (σ [S/m])

None 2.5–3 × 10

−10

2% Eeonomer 200F 6.1 × 10

−4

3.1 × 10

−4

2% Eeonomer 610F 2.0 × 10

−4

2.3 × 10

−4

1% BS200 multiwall nanotubes 9.0 × 10

−4

9.0 × 10

−4

10% BU200 multiwall nanotubes 8.8 × 10

−4

8.6 × 10

−4

Note: The results of two separate measurements are shown for the mixtures.

Source: Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based

Lubricants Chemistry and Technology, Chapter 38, CRC Press, Taylor & Francis

Group, Boca Raton, FL, 2006.

0 0.5 1 1.5 2 2.5 3

Eeonomer concentration (wt%)

Conductivity (S/m)

Eeonomer 610F, 50°C

Eeonomer 200F, 50°C

Eeonomer 610F, 25°C

Eeonomer 200F, 25°C

Eeonomer 610F, 10°C

Eeonomer 200F, 10°C

Eeonomer 610F, 5°C

Eeonomer 200F, 5°C

1×10

−2

1×10

−3

1×10

−4

1×10

−5

1×10

−6

1×10

−7

1×10

−8

FIGURE 22.24 Conductivity of Eeonomers in ferro uid 1 as a function of Eeonomer concentration and

temperature. (Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chem-

istry and Technology, Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.)

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Lubricants for the Disk Drive Industry 561

22.3.3 FLUID BEARING MOTOR OIL

Disk drive motor bearing dynamics determine the precision of the spindle rotation. As the sleeve

spins relative to the stator, the spin axis traces out an orbit. The spin axis motion has a component

that is in phase and at the same frequency as the spindle rotation. This is repeatable run out. There

is also a component of spin axis motion that is random. This is nonrepeatable run out (NRRO).

Increasing computer magnetic recording disk drive data storage density is potentially limited by

NRRO. The spindle bearing is the primary contributor to NRRO. Improved NRRO improves the

seek time and ability to track follow for a given track pitch and servomechanism. A disk drive with

a low-NRRO spindle bearing accommodates higher track density, allowing higher areal density.

Nearly all disk drives are now being built with  uid dynamic bearing motors (Figure 22.14c).

These replace ball bearing spindle motors, because their lower NRRO allows the servomechanism to

follow narrower data tracks. At the heart of a  uid dynamic bearing are a shaft in a sleeve for radial

thrust and a thrust plate and bushing for axial thrust. Embossed on one face of the radial and axial

thrust members are grooves that force the oil inward, creating the internal pressure that provides the

0102030405060

Conductivity (S/m)

Temperature (°C)

2% Eeonomer 610F

0.5% Eeonomer 610F

0.1% Eeonomer 610F

Ferrofluid 1 alone

(a)

010203040506

Viscosity × conductivity

(Pa s S/m)

Temperature (°C)

2% Eeonomer 610F 2% Eeonomer 200F

0.5% Eeonomer 610F 0.5 Eeonomer 200F

0.1% Eeonomer 610F 0.1% Eeonomer 200F

Ferrofluid 1 alone

(b)

1×10

−2

1×10

−4

1×10

−6

1×10

−8

1×10

−10

1×10

−2

1×10

−4

1×10

−6

1×10

−8

1×10

−10

FIGURE 22.25 Conductivity of Eeonomers in ferro uid 1 as a function of Eeonomer temperature (a) and the

product of conductivity and viscosity as a function of temperature (b) with additives in ferro uid 1. (Adapted

from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chemistry and Technology,

Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.)

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562 Lubricant Additives: Chemistry and Applications

bearing stiffness [60]. The  uid dynamic bearing achieves lower levels of NRRO because a relatively

thick  lm of lubricant separates the sleeve and stator. The oil  lm thickness in high-performance

motors for 10–15 krpm is typically 5–10 µm. The  lm provides viscous damping that attenuates

NRRO below that achievable in ball bearings. The forces generated on the sleeve by the  uid dynamic

bearing are of a lower frequency and amplitude than with ball bearings. The reduction in the excitation

bandwidth and power allows the servo to seek and hold on a higher track density.

However, the bearing must be designed to avoid cavitation [61] and air ingestion [62]; two fun-

damental requirements of  uid dynamic bearing oil are low viscosity and low vapor pressure. The

viscosity must be thin enough to allow for spin-up in a reasonably short period of time at temperatures

approaching 0°C. For example, the spin-up time for prototype disk drives with  uid bearing motors is

shown in Figure 22.26 [1]. The viscosity dominates the spin-up time when it is higher than ∼25 mPa s.

For lower viscosities, the spin-up time is limited by inertia of the disk pack and peak motor power.

The oil vapor pressure must be low enough so that there is no appreciable evaporation over the

5 to 7 year lifetime of the motor at its maximum internal operating temperature of ∼80°C. In addi-

tion, the  uid bearing oil must be suf ciently conductive to dissipate static charge accumulation

due to air shear, electrical double-layer shear [63], and work function difference between the slider

and disk [64]. The oil must also have a low dc dielectric permittivity to minimize charge storage by

ionic separation or dipole orientation. Finally, well-formulated oil should contain antioxidants and

other additives to inhibit oxidation and corrosion. Formulation and testing of antioxidants for  uid

bearing oil is described in Ref. 50. Oil oxidation kinetics is discussed in Section 22.3.4.

Various model oils were investigated with the goal of providing guidelines for selection of the oil

with the lowest possible viscosity and vapor pressure. The oils studied were diesters (Table 22.16) [1],

triesters (Table 22.17) [1], and nonpolar hydrocarbons (Table 22.18) [1]. The  rst  ve model oils are

0102030405060

Viscosity (mPa s)

Spin-up time (s)

Base oil

Base oil + conductivity additive

FIGURE 22.26 Spin-up time for prototype disk drives as a function of  uid bearing oil viscosity measured

between 1 and 25°C. The conductivity additive was mixed polymers, as described in Ref. 50. The base oil is a com-

mercially available diester. (Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubri-

cants Chemistry and Technology, Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.)

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Lubricants for the Disk Drive Industry 563

diesters made from alkanedioic acids and alcohols with a range of diacid chain lengths and several alco-

hol molecular weights and branched isomers. The di(n-butyl)sebacate (DBS), di(2-ethylhexyl)adipate

(DOA), and di(2-ethylhexyl)sebacate (DOS) were obtained form Aldrich Chemical Company (Saint

Louis, MO, USA). The di(2-ethylhexyl)azelate (DOZ) is Emery 2958 and the di(4,4-diethylhexyl)adipate

(DIA) is Emery 2970. The Emery oil samples were provided by Henkel Corporation (Emery Group,

Cincinnati, OH, USA). The next four model oils are triesters made from triols and alkanoic acids with

a range of acid chain length. The triglycerides, glycerol tributanoate (TRIB), glycerol trihexanoate

(TRIH), and glycerol trioctanoate (TRIO) (also referred to as tributyrin, tricaproin, and tricaprylin,

respectively) were obtained from Aldrich Chemical Company. About 8% of low-molecular-weight

impurities were evaporated from tricaproin by vacuum baking at 6.3 kPa for 96 h. The level of impuri-

ties in the other model ester oils was less than 0.2% during vacuum baking at the same conditions and

did not show up in the NMR spectra. The trimethylol propane C7 ester, trimethylolpropane triheptano-

ate (TMP), is Emkarate 1510 from ICI Americas, Inc. (Wilmington, DE, USA). The branched alkane,

a low-molecular-weight poly(alphaole n), was NYE 167A from Nye Lubricants, Inc. (Fairhaven, MA,

USA). Some of the oils are isomers, having the same molecular weight and composition but differing

only in molecular structure. More details of the oil properties are given in Ref. 40.

TABLE 22.16

Molecular Structures of the Diester Oils Investigated for Fluid Dynamic Bearing Motors

Acronym

Molecular

Weight (g/mol) Structure

DBS 314

DOA 371

DOZ 413

DOS 427

DIA 427

Source: Adapted from Rudnick, L.R. (ed.), Synthetics, Mineral Oils, and Bio-Based Lubricants Chemistry and Technology,

Chapter 38, CRC Press, Taylor & Francis Group, Boca Raton, FL, 2006.

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