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564 Lubricant Additives: Chemistry and Applications

Representative proton NMR spectra for the diester oils are shown for DBS and DOS in

Figure 22.27. These are most similar to the oils that are widely used in disk drive  uid dynamic

bearing spindle motors. The NMR measurements were done on a Bruker Aspect 3000 Nuclear

Magnetic Resonance Spectrometer attached to a 250 MHz superconducting magnet with an

automatic sample changer. The samples for proton NMR were 10% w/w oil in chloroform-d1. The

solution spectra were measured in 5 mm NMR tubes from Kontes Scienti c Glassware (Grade 6,

5 pack, #897235). The proton NMR measurements were done using a spectral width of 5 kHz, 45°

pulse width of 3.0 µs, 1 s relaxation delay, and 512 scans.

The proton corresponding to each peak in the NMR spectra in Figure 22.27 [1] is indicated by a

letter, and an arrow shows the location of the corresponding proton on the molecular structure. Peak

TABLE 22.17

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

Acronym

Molecular

Weight (g/mol) Structure

TRIB 302

TRIH 387

TRIO 471

TMP 471

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

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

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Lubricants for the Disk Drive Industry 565

assignments corresponding to these structures are listed in Table 22.19 [1]. The peak area is proportional

to the number of protons at each chemical shift. The peak areas were calculated from the NMR spectra

with commercial software (NUTS NMR Data Processing Software, Version 4.27, Acorn NMR, Inc.,

Fremont, California, United States). The reference peak area (indicated by “a” in the  rst column of the

peak assignment tables) was assigned to the expected area. The rest of the integrated areas are relative

to the reference peak area. Both the integrated peak areas and the peak areas expected from the abun-

dance of each type of proton in the model chemical structure agree within 10%. Small changes in the

chemical shifts are due to differences in the chemical environment of the protons.

22.3.3.1 Viscosity and Vapor Pressure

Oil viscosity and vapor pressure are thermodynamically interrelated by the dispersion and dipolar

forces between the molecules. All of the intermolecular potential energy must be surmounted to evap-

orate a molecule from the liquid, and part of the intermolecular potential energy must be surmounted

for  ow. To  rst order, the dispersion force is proportional to the number and type of atoms, thus to

molecular weight. For the relatively low-molecular-weight oils useful in  uid bearings, the  ow is

mostly by the whole molecule, rather than segments of the molecule. Thus, increasing the molecular

weight, or polarity, to reduce the vapor pressure increases the viscosity. The relationship between oil

vapor pressure and viscosity is thoroughly investigated with Eyring’s chemical reaction rate theory of

evaporation and  ow (Karis and Nagaraj [40]). The essence of their  ndings is summarized later.

TABLE 22.18

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

Acronym

Molecular

Weight

(g/mol) Structure

2,2-DPP 196

1,3-DPP 196

PAO 240

PRS 269

SQL 423

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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566 Lubricant Additives: Chemistry and Applications

According to the Eyring Equation 22.6, a plot of ln(η) versus 1/T is a straight line with slope,

∆E

vis

/R and intercept ln(Nh

) − ∆S

vis

/R. The viscosity of several low-molecular-weight ester and

hydrocarbon oils is shown plotted as ln(η) versus 1/T i n F i g u r e 2 2 . 2 8 [1]. T h e r e i s s o m e s ys t e m a t i c d e v i -

ation from linearity, but overall the general trend is  t by the Eyring equation between −20 and 100°C.

4.5 4.0

3.5

3.0 2.5 2.0 1.5 1.0 0.5

4.5 4.0

3.5

3.0 2.5 2.0 1.5 1.0 0.5 ppm

ppm

(a)

(b)

(c)

(d)

(e)

(A)

(B)

(e)

(b)

(a)

(c)

(d)

(c)

(e)

FIGURE 22.27 Proton NMR spectrum of diester  uid dynamic bearing oil (A) DBS and (B) DOS. The peak

assignments are indicated on the molecular structures. (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 567

The  ow activation entropy ∆S

vis

= ∆S

vis

trans

+ ∆S

rot

vis

is the sum of the translational and rotational

contributions. The slope and intercept of the ln(η) versus 1/T plot is employed to calculate ∆S

vis

and

∆E

vis

for each of the oils. These thermodynamic properties for  ow are listed in Table 22.20 [1].

A similar analysis was performed for the vapor pressure of these oils. According to the Claperyron

Equation 22.15, a plot of ln(P

) versus 1/T is a straight line with slope −∆E

vap

/R and intercept

ln(P) − 1 + ∆S

vap

/R. The vapor pressure of several low-molecular-weight ester and hydrocarbon

oil is shown plotted as ln(P

) versus 1/T in Figure 22.29 [1]. The vaporization entropy ∆S

vap

∆S

trans

vap

+ ∆S

rot

vap

is approximately the sum of the translational and rotational contributions. The inter-

cept of the ln(P

) versus 1/T plot is then employed to calculate ∆S

vap

and ∆E

vap

for each of the oils.

The translational component of the vaporization is approximately equal to the vapor-phase entropy

given by Equa tion 22.16, and the rotational component is similarly calculated in the vapor phase

with Equa tion 22.17 [40]. The vaporization entropy and the calculated vapor-phase translational and

rotational entropy are employed to estimate the liquid-phase entropy as S

liq

≈ S

vap

− ∆S

vap

. These

thermodynamic  ow properties for vaporization are listed in Table 22.20.

Further insight into the relationship between the evaporation and  ow properties of the poten-

tial  uid bearing motor oils is obtained by combining the results together within the framework

of thermodynamics and the reaction rate model for evaporation and  ow [65,66]. The ratio of the

vaporization energy to the  ow activation energy n = ∆E

vap

/∆E

vis

measures the partial decoupling

of intermolecular forces between molecules during  ow relative to the complete decoupling that

takes place upon vaporization [67]. Another thermodynamic quantity that plays a key role in the

 ow process is the  ow activation rotational entropy. The  ow activation rotational entropy, ∆S

rot

vis

was calculated from the combined vapor pressure and viscosity versus temperature, given in Karis

and Nagaraj [40]. If there is a way to lower the viscosity without increasing the vapor pressure, it

seems that it can be done only by increasing the  ow activation entropy, ∆S

vis

. For the oils shown

here, ∆S

vis

is proportional to ∆S

rot

vis

, as shown in Figure 22.30a [1]. However, ∆S

rot

vis

decreases with n,

as shown in Figure 22.30b. Thus, the  ow activation rotational entropy decreases with the amount

of decoupling or asymmetry between vaporization and  ow. For example, spherical molecules are

TABLE 22.19

Proton NMR Chemical Shifts and Peak Assignments

for the Spectra in Figure 22.27

Proton

Chemical Shift

(ppm) Measured Expected

Peak Area for DBS

(a)

4.01 4 4

(b) 2.23 4.2 4

(d) 1.36 12.4 12

(e) 0.91 6.1 6

Peak Area for DOS

(a)

3.97 4 4

(b) 2.27 4.1 4

(d) 1.28 24.6 24

(e) 0.86 12.1 12

Reference peak used as the basis for the other peak areas.

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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568 Lubricant Additives: Chemistry and Applications

more freely rotating in the  ow-activated state, whereas rotation of rod-like molecules becomes less

likely in the  ow-activated state, as they surmount the energy barrier between adjacent molecules

in the surrounding liquid.

Although the preceding discussion shows how the thermodynamic properties of vaporization

and  ow govern the oil vapor pressure and viscosity, little can be said about speci cally what

molecular structure and compositions can be synthesized to provide an improved  uid bearing

−7

−6

−5

−4

−3

−2

−1

0.0025 0.0030 0.0035 0.004

1/Temperature (K

−1

)

ln (Viscosity) (Pa s)

DBS

DOA

DOZ

DOS

DIA

Diesters

(a)

−7

−6

−5

−4

−3

−2

−1

0.0025 0.003 0.0035 0.004

1/Temperature (K

−1

)

ln (Viscosity) (Pa s)

TRIB

TRIH

TRIO

TMP

Triesters

(b)

−8

−6

−4

−2

0.0025 0.003 0.0035 0.004

Temperature (°C)

ln (Viscosity) (Pa s)

2,2-DPP

1,3-DPP

PAO

PRS

SQL

Nonpolar

(c)

FIGURE 22.28 Natural logarithm of viscosity as a function of inverse temperature of (a) diesters, (b) tri-

esters, and (c) hydrocarbon oils. The line is a  t to the Eyring equation. (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 569

motor. Recent developments on molecular dynamic simulation promise to bridge this gap between

molecular structure and thermodynamics. For example, Bair et al. [68] have demonstrated good

agreement between high shear viscosity measurements and predictions from a molecular dynam-

ics simulation. Yet, the model requires input of a particular molecular structure, in their case,

squalane, and numerically intensive computations that are required to predict the viscosity. Even

more complexity is involved if one tries to similarly predict the viscosity of a more complex polar

molecule such as diesters.

Oil blends, or viscosity-reducing additives, have also been considered. Blending oils change the

pressure–viscosity coef cient [55] and provide an intermediate viscosity [69,70]. The vaporization

energy and entropy and  ow activation energy and entropy are shown for a blend of polar diester

oil in nonpolar poly alpha ole n (PAO) oil in Figure 22.31 [1]. In this case, the vaporization energy

of the blend was less than that of the pure components. The entropy of the blend was higher than

that of the pure components. The reduction in the vaporization energy outweighed the effect of the

increase in liquid entropy, and the vapor pressure of the blend was higher than that of the pure com-

ponents. There is, however, an interesting dip in the properties near 95% DOS, which was reproduc-

ible. The  ow activation energy and entropy of the blends are shown in Figures 22.31c and 22.31d.

The  ow activation energy is approximately given by a linear combination of the weight fractions

of blend components. While the blend viscosity is actually less than the linear combination due

to an increase in the  ow activation entropy near 50%. Taking the analysis one step further, the

 ow activation rotational entropy has a sharp maximum near 95% DOS in Figure 22.32a. The ratio

n = ∆E

vap

/∆E

vis

has a sharp minimum near 95% DOS (Figure 22.32b). This unusual behavior near

95% DOS suggests that synergistic effects are possible in oil blends. These probably arise from clus-

tering of the nonpolar oil with the aliphatic chains of the diester. Perhaps, this type of effect could be

exploited to develop viscosity-reducing additives that have a lower vapor pressure than the base oil.

TABLE 22.20

Evaporation and Flow Thermodynamic Properties Calculated from Vapor Pressure and

Viscosity Data for Model Fluid Dynamic Bearing Oils

Evaporation Flow

Oil

∆E

vap

(kJ/mol)

∆S

vap

(J/mol K)

liq

(J/mol K)

∆E

vis

(kJ/mol)

∆S

vis

(J/mol K)

∆S

vis

rot

(J/mol K) n

DBS 90.7 160 114 20.6 −4.2 −3.1 4.4

DOA 94.4 160 117 24.7 4.1 6.61 3.8

DOZ 84.5 125 154 26.7 6.8 19.8 3.2

DOS 108.6 175 105 26.7 5.8 2.6 4.1

DIA 94.1 143 137 28.9 11.2 18.1 3.3

TRIB 81.8 154 163 25.1 10.5 12.5 3.3

TRIH 93.3 156 167 23.2 −1.5 2.4 4.0

TRIO 116.3 185 143 26.2 3.5 −1.4 4.4

TMP 81.0 110 218 28.9 10.4 30.3 2.8

2,2-DPP 59.1 120 144 25.5 17.0 30.4 2.3

1,3-DPP 74.2 159 105 22.3 8.4 6.6 3.4

PAO 89.6 188 80 22.7 4.5 −4.2 3.9

PRS 78.5 166 104 22.8 4.6 2.6 3.5

SQL 82.8 124 156 32.9 21.2 36.6 2.5

Note: Evaporation properties are referenced to 100°C and atmospheric pressure (100 kPa). Flow properties are referenced

to 40°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.

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570 Lubricant Additives: Chemistry and Applications

However, for a blend to be useful, it would also need to be capable of forming an azeotrope, and

then it could only be used in motors at the azeotropic composition. Otherwise, the evaporation of

the oil component with the highest vapor pressure would gradually change the oil blend viscosity

and vapor pressure with time.

−15

−10

−5

0.0020 0.0025 0.0030 0.0035

1/Temperature (K

−1

)

1/Temperature (K

−1

)

0.0020 0.0025 0.0030 0.0035

1/Temperature (K

−1

)

ln (P

) (Pa)

−15

−10

−5

ln (P

) (Pa)

−15

−10

−5

ln (P

) (Pa)

Diesters

(a)

(b)

(c)

DBS

DOA

DOZ

DIA

DOS

Triesters

TRIB

TRIH

TMP

TRIO

Nonpolar

2,2-DPP

1,3-DPP

PRS

PAO

SQL

FIGURE 22.29 Natural logarithm of vapor pressure as a function of inverse temperature of (a) diesters,

(b) triesters, and (c) hydrocarbon oils. The line is a  t to the Clapeyron equation. Ambient pressure P =

100 kPa. (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 571

22.3.4 OIL FORMULATION CHEMISTRY

Thermal stability is imparted to grease and oil through formulation with additives. Over the past

two decades, we employed the principles of oil oxidation chemistry in developing formulations for

ball bearing grease [71] and  uid dynamic bearing [72] spindle motors at the leading edge of the

industry in our laboratory. The general outline of the chemical mechanisms for oxidation and stabi-

lization, potential additives, and accelerated test results is published in Ref. 50. Here, we summarize

the low-temperature elementary reactions for each type of oxidation pathway including inhibition

by antioxidants. The rate equations are solved numerically in nondimensional form, and the model

results are compared with thermal oxidation life test data to illustrate the synergistic effects of pri-

mary antioxidant PriAOX and secondary antioxidant SecAOX and metal catalysis.

Diesters

Triesters

Nonpolar

−10

−5

−10

01020304050

(a)

(

)

∆S

vis

(J/mol K)

∆S

vis

(J/mol K)

rot

∆S

vis

(J/mol K)

rot

234

FIGURE 22.30 Flow activation entropy versus  ow activation rotational entropy (a) and the  ow activation

rotational entropy versus the ratio of the vaporization energy to the  ow activation energy (b) for the oils listed in

Tables 22.16 through 22.18. (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.)

Diesters

Triesters

Nonpolar

−10

−5

−10

01020304050

(a)

(

)

∆S

vis

(J/mol K)

∆S

vis

(J/mol K)

rot

∆S

vis

(J/mol K)

rot

234

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572 Lubricant Additives: Chemistry and Applications

FIGURE 22.31 Vaporization activation energy and entropy change (a, b) and  ow activation and entropy change (c, d) for blends of DOS in PAO. (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.)

wt% DOS in PAO

∆E

vap

(kJ/mol)

∆E

vis

(kJ/mol)

∆S

vis

(J/mol K)

(a)

(d)(c)

0 20406080100

wt% DOS in PAO

0 20 40 60 80 100

wt% DOS in PAO

0 20 40 60 80 100

∆S

vap

(J/mol K)

(b)

100

120

140

160

180

wt% DOS in PAO

0 20406080100

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Lubricants for the Disk Drive Industry 573

The following sets of elementary reactions, derived from schemes in Refs 50 and 73, are employed

to model the data. Intrachain proton abstraction and self-termination are not included. Some of the

non-rate-controlling reactants and products are not shown. The initiation reactions and the propo-

gation reactions are shown in Figures 22.33a and 22.33b, respectively. The dot denotes a carbon

radical. Only interchain proton abstraction (no cleavage reaction) is considered because this is the

dominant reaction pathway that we observed with ester oils. Proton abstraction from RH by thermal

or mechanical excitation is the rate-limiting step in the initiation mechanism. Decomposition of the

hydroperoxide ROOH is the rate-limiting step in the propagation mechanism.

PriAOX protonates radicals, as shown in Figure 22.34a. Examples of PriAOX are butylated

hydroxy toluene (BHT), dioctyldiphenyl amine (DDA), and phenyl naphthylamine (PNA).

SecAOX decomposes hydroperoxide, as shown in Figure 22.34b. Examples of SecAOX are zinc

−10

−5

0 20 40 60 80 100

wt% DOS in PAO

0 20 40 60 80 100

wt% DOS in PAO

(a)

(

)

2.0

2.5

3.0

3.5

4.0

∆S

vis

(J/mol K)

rot

FIGURE 22.32 The rotational component of the  ow activation entropy (a) and the ratio of the vaporization

energy to the  ow activation energy, n, (b) for blends of DOS in PAO.

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