Siloxane-based polymers (polysiloxanes) exhibit a range of volume, viscosity, and pressure-viscosity behaviors that are strongly influenced by the macromolecular structure. In this report, a combination of extant rheological models is applied to develop a molecular-rheological modeling formalism that predicts polysiloxane rheological properties, such as specific volume, which means density, viscosity, and pressure-viscosity index variations with macromolecular structure, pressure, and temperature. Polysiloxane molecular features are described in terms of alkyl branch length L, pendant type J, density of branch functional monomers Q, and degree of polymerization DP. Both new and published data are used for model parameter determination and validation. Several siloxane-based polymers with alkyl, aryl, alkyl-aryl, cycloalkyl, and halogenated branches were synthesized to examine the modeled relationship between their molecular structures and rheological behaviors.

References

References
1.
Baker
,
E.
,
Barry
,
A.
, and
Hunter
,
M.
,
1946
, “
Dielectric Constants of Dimethyl Siloxane Polymers
,”
Ind. Eng. Chem.
,
38
(
11
), pp.
1117
1120
.10.1021/ie50443a011
2.
Brophy
,
J. E.
,
Militz
,
R. O.
, and
Zisman
,
W. A.
,
1946
, “
Dimethyl-Silicone-Polymer Fluids and Their Performance Characteristics in Unilaterally Loaded Journal Bearings
,”
Trans. ASME
,
68
(
4
), pp.
355
360
.
3.
Hunter
,
M.
,
Warrick
,
E.
,
Hyde
,
J.
, and
Currie
,
C.
,
1946
, “
Organosilicon Polymers. II. The Open Chain Dimethylsiloxanes With Trimethylsiloxy End Groups1
,”
J. Am. Chem. Soc.
,
68
(
11
), pp.
2284
2290
.10.1021/ja01215a048
4.
Hurd
,
C.
,
1946
, “
Studies on Siloxanes. I. The Specific Volume and Viscosity in Relation to Temperature and Constitution
,”
J. Am. Chem. Soc.
,
68
(
3
), pp.
364
370
.10.1021/ja01207a005
5.
Patnode
,
W.
, and
Wilcock
,
D.
,
1946
, “
Methylpolysiloxanes1
,”
J. Am. Chem. Soc.
,
68
(
3
), pp.
358
363
.10.1021/ja01207a004
6.
Sauer
,
R. O.
, and
Mead
,
D. J.
,
1946
, “
Dipole Moments of Linear and Cyclic Polymethylpolysiloxanes
,”
J. Am. Chem. Soc.
,
68
(
9
), pp.
1794
1797
.10.1021/ja01213a034
7.
Dickens
,
P.
,
Sullivan
,
J.
, and
Lancaster
,
J.
,
1986
, “
Speed Effects on the Dry and Lubricated Wear of Polymers
,”
Wear
,
112
(
3–4
), pp.
273
289
.10.1016/0043-1648(86)90175-4
8.
Wilcock
,
D.
,
1946
, “
Vapor Pressure-Viscosity Relations in Methylpolysiloxanes
,”
J. Am. Chem. Soc.
,
68
(
4
), pp.
691
696
.10.1021/ja01208a050
9.
Fox
,
H.
,
Taylor
,
P.
, and
Zisman
,
W.
,
1947
, “
Polyorganosiloxanes. Surface Active Properties
,”
Ind. Eng. Chem.
,
39
(
11
), pp.
1401
1409
.10.1021/ie50455a607
10.
Lewis
,
G.
,
1916
, “
The Atom and the Molecule
,”
J. Am. Chem. Soc.
,
38
(
4
), pp.
762
785
.10.1021/ja02261a002
11.
Flory
,
P.
,
1969
,
Statistical Mechanics of Chain Molecules
,
Interscience
,
New York
.
12.
Brandup
,
J.
,
Immergut
,
E.
, and
Grulke
,
E.
,
1975
,
Polymer Handbook
,
Interscience
,
New York
.
13.
De Jaeger
,
R.
, and
Gleria
,
M.
,
2007
,
Inorganic Polymers
,
Nova Science Pub Inc.
,
New York
.
14.
Mackenzie
,
K.
, and
Jemmett
,
A.
,
1971
, “
Polymer Shear Stability
,”
Wear
,
17
(
5–6
), pp.
389
398
.10.1016/0043-1648(71)90045-7
15.
Ziegler
,
M.
, and
Fearon
,
F.
,
1990
,
Silicon-Based Polymer Science: A Comprehensive Resource (Advances in Chemistry Series, 224)
,
American Chemical Society
,
Washington DC
.
16.
Rochow
,
E.
,
1987
,
Silicon and Silicones
,
Springer
Berlin
.
17.
Zolper
,
T. J.
,
Li
,
Z.
,
Chen
,
C.
,
Jungk
,
M.
,
Marks
,
T. J.
,
Chung
,
Y.-W.
, and
Wang
,
Q.
,
2012
, “
Lubrication Properties of Poly-alpha-olefin and Polysiloxane Lubricants: Molecular Structure-Tribology Relationships
,”
Tribol. Lett.
,
48
, pp.
355
365
.
18.
Zolper
,
T. J.
,
Li
,
Z.
,
Jungk
,
M.
,
Stammer
,
A.
,
Stoegbauer
,
H.
,
Marks
,
T. J.
,
Chung
,
Y.-W.
, and
Wang
,
Q.
,
2013
, “
Traction Characteristics of Siloxanes With Aryl and Cyclohexyl Branches
,”
Tribol. Lett.
,
49
(
2
), pp.
301
311
.10.1007/s11249-012-0066-x
19.
Zolper
,
T. J.
,
Seyam
,
A. M.
,
Chen
,
C.
,
Jungk
,
M.
,
Stammer
,
A.
,
Stoegbauer
,
H.
,
Marks
,
T. J.
,
Chung
,
Y.-W.
, and
Wang
,
Q.
,
2013
, “
Energy Efficient Siloxane Lubricants Utilizing Temporary Shear-Thinning
,”
Tribol. Lett.
,
49
(
3
), pp.
525
538
.10.1007/s11249-012-0093-7
20.
Zolper
,
T. J.
,
Seyam
,
A.
,
Li
,
Z.
,
Chen
,
C.
,
Jungk
,
M.
,
Stammer
,
A.
,
Marks
,
T. J.
,
Chung
,
Y.-W.
, and
Wang
,
Q.
,
2013
, “
Friction and Wear Protection Performance of Synthetic Siloxane Lubricants
,”
Tribol. Lett.
,
51
, pp.
365
376
.10.1007/s11249-013-0169-z
21.
Jakobsen
,
J.
,
Sanborn
,
D.
, and
Winer
,
W.
,
1974
, “
Pressure Viscosity Characteristics of a Series of Siloxane Fluids
,”
ASME J. Lub. Technol.
,
96
(
3
), pp.
410
417
.10.1115/1.3451980
22.
Kuss
,
E.
,
1974
,
“Viskositats-Druckverhalten von flussigen Methyl-Phenylmethyl- und Cyclohexylmethyl-Siloxeanen
,
” Erdol und Kohle-Erdgas-Petrochemie vereinigt mit Brennstoff-Chemie
,
27
(
8
), pp.
416
422
.
23.
ASME
,
1953
,
Viscosity and Density of Over 40 Lubricating Fluids of Known Composition at Pressures to 150,000 psi and Temperatures to 425 F
, Vol.
1
,
American Society of Mechanical Engineers
,
New York
.
24.
Winer
,
W. O.
,
1977
,
A Study of the Elastohydrodynamic Lubrication and High Pressure Rheological Behavior of a Series of Silicone Fluids
,
Georgia Tech
,
Atlanta, GA
.
25.
Bridgman
,
P.
,
1949
, “
Viscosities to 30,000 Kg/Cm
,”
Proc. Am. Aca. Arts Sci.
,
77
(
4
), pp.
117
128
.
26.
Bondi
,
A.
,
1964
, “
van der Waals Volumes and Radii
,”
J. Phys. Chem.
,
68
(
3
), pp.
441
451
.10.1021/j100785a001
27.
Bondi
,
A.
,
1968
,
Physical Properties of Molecular Crystals, Liquids, and Glasses
,
Wiley
,
New York
.
28.
Slonimskii
,
G.
,
Askadskii
,
A.
, and
Kitaigorodskii
,
A.
,
1970
, “
The Packing of Polymer Molecules
,”
Polym. Sci. USSR
,
12
(
3
), pp.
556
577
.10.1016/0032-3950(70)90345-X
29.
Van Krevelen
,
D. W.
,
1990
,
Properties of Polymers. Their Correlation with Chemical Structure, Their Numerical Estimation and Prediction From Additive Group Contribution
,
3rd ed.
,
Elsevier
,
New York
.
30.
Zhao
,
Y.
,
Abraham
,
M.
, and
Zissimos
,
A.
,
2003
, “
Fast Calculation of van der Waals Volume as a Sum of Atomic and Bond Contributions and Its Application to Drug Compounds
,”
J. Org. Chem.
,
68
(
19
), pp.
7368
7373
.10.1021/jo034808o
31.
Schaffer
,
J. P.
,
Saxena
,
A.
,
Antolovich
,
S. D.
,
Sanders
,
T.
, and
Warner
,
S. B.
,
1995
,
The Science and Design of Engineering Materials
,
Irwin
,
Toronto
.
32.
Callister
,
W. D.
, and
Rethwisch
,
D. G.
,
2011
,
Fundamentals of Materials Science and Engineering: An Integrated Approach
,
Wiley
,
New York
.
33.
Lee
,
W.
,
1980
, “
Selection of Barrier Materials From Molecular Structure
,”
Polym. Eng. Sci.
,
20
(
1
), pp.
65
69
.10.1002/pen.760200111
34.
Mathews
,
A.
,
1916
, “
Physiological Chemistry
,”
William Wood and Company
,
New York
,
35.
Sugden
,
S.
1927
, “
Molecular Volumes at Absolute Zero II. Zero Volumes and Chemical Composition
,”
J. Chem. Soc.
,
2
, pp.
1786
1798
.10.1039/jr9270001786
36.
Biltz
,
W.
,
Rohlffs
,
G.
, and
Vogel
,
H.
,
1934
, “
Beiträge zur systematischen Verwandtschaftslehre. 61. Bau und Verwendung eines Hochtemperaturkalorimeters mit geschlossenem Reaktionsraum
,”
Z. anorg. allg. Chem
,
220
, pp.
113
141
.10.1002/zaac.19342200202
37.
Asano
,
T.
,
1973
, “
Void and Expansion Volume Contributions to Reaction and Activation Volumes of Nearly Nonpolar Reactions
,”
Rev. Phys. Chem. Jap.
,
43
(
2
), pp.
82
91
.
38.
Flory
,
P.
,
1940
, “
Viscosities of Linear Polyesters. An Exact Relationship Between Viscosity and Chain Length
,”
J. Am. Chem. Soc.
,
62
(
5
), pp.
1057
1070
.10.1021/ja01862a020
39.
Berry
,
G.
, and
Fox
,
T.
,
1968
, “
The Viscosity of Polymers and Their Concentrated Solutions
,”
Adv. Polymer Sci.
,
5
, pp.
261
357
.10.1007/BFb0050984
40.
Lee
,
M. K.
, and
Meier
,
D. J.
,
1994
, “
Synthesis and Properties of Diarylsiloxane and (Aryl/methyl) Siloxane Polymers: 2. Solution and Rheological Properties
,”
Polymer
,
35
(
15
), pp.
3282
3284
.10.1016/0032-3861(94)90135-X
41.
Mandík
,
L.
,
Foksová
,
A.
, and
Foltyn
,
J.
,
1979
, “
Gel Permeation Chromatography of Poly (Dimethyl Siloxane). I. The Universal Calibration
,”
J. Appl. Polym. Sci.
,
24
(
2
), pp.
395
404
.10.1002/app.1979.070240208
42.
Van Krevelen
,
D.
, and
Hoftyzer
,
P.
,
1976
, “
Newtonian Shear Viscosity of Polymeric Melts
,”
Die Angewandte Makromolekulare Chemie
,
52
(
1
), pp.
101
109
.10.1002/apmc.1976.050520109
43.
Orrah
,
D.
,
Semlyen
,
J.
, and
Ross-Murphy
,
S.
,
1988
, “
Studies of Cyclic and Linear Poly (Dimethylsiloxanes): 27. Bulk Viscosities Above the Critical Molar Mass for Entanglement
,”
Polymer
,
29
(
8
), pp.
1452
1454
.10.1016/0032-3861(88)90310-2
44.
Orrah
,
D.
,
Semlyen
,
J.
, and
Ross-Murphy
,
S.
,
1988
, “
Studies of Cyclic and Linear Poly (Dimethylsiloxanes): 28. Viscosities and Densities of Ring and Chain Poly (Dimethylsiloxane) Blends
,”
Polymer
,
29
(
8
), pp.
1455
1458
.10.1016/0032-3861(88)90311-4
45.
Fox
,
T.
, and
Allen
,
V.
,
1964
, “
Dependence of the Zero Shear Melt Viscosity and the Related Friction Coefficient and Critical Chain Length on Measurable Characteristics of Chain Polymers
,”
J. Chem. Phys.
,
41
, pp.
344
352
.10.1063/1.1725872
46.
Schaefgen
,
J.
, and
Flory
,
P.
,
1948
, “
Synthesis of Multichain Polymers and Investigation of their Viscosities 1
,”
J. Am. Chem. Soc.
,
70
(
8
), pp.
2709
2718
.10.1021/ja01188a026
47.
Fox
,
T.
,
1962
, “
Properties of Dilute Polymer Solutions III: Intrinsic Viscosity/Temperature Relationships for Conventional Polymethyl Methacrylate
,”
Polymer
,
3
, pp.
111
128
.10.1016/0032-3861(62)90069-1
48.
Ferry
,
J.
,
1980
,
Viscoelastic Properties of Polymers
,
John Wiley & Sons Inc.
,
New York
.
49.
Arrighi
,
V.
,
Gagliardi
,
S.
,
Dagger
,
A.
,
Semlyen
,
J.
,
Higgins
,
J.
, and
Shenton
,
M.
,
2004
, “
Conformation of Cyclics and Linear Chain Polymers in Bulk by SANS
,”
Macromolecules
,
37
(
21
), pp.
8057
8065
.10.1021/ma049565w
50.
Dvornic
,
P.
,
Jovanovic
,
J.
, and
Govedarica
,
M.
,
1993
, “
On the Critical Molecular Chain Length of Polydimethylsiloxane
,”
J. Appl. Polym. Sci.
,
49
(
9
), pp.
1497
1507
.10.1002/app.1993.070490901
51.
Beltzung
,
M.
,
Picot
,
C.
,
Rempp
,
P.
, and
Herz
,
J.
,
1982
, “
Investigation of the Conformation of Elastic Chains in Poly (Dimethylsiloxane) Networks by Small-Angle Neutron Scattering
,”
Macromolecules
,
15
(
6
), pp.
1594
1600
.10.1021/ma00234a026
52.
Edwards
,
C.
,
Rigby
,
D.
,
Stepto
,
R.
,
Dodgson
,
K.
, and
Semlyen
,
J.
,
1983
, “
Studies of Cyclic and Linear Poly (Dimethyl Siloxanes): 10. Calculations of Radii of Gyration
,”
Polymer
,
24
(
4
), pp.
391
394
.10.1016/0032-3861(83)90023-X
53.
Fetters
,
L.
,
Lohse
,
D.
,
Richter
,
D.
,
Witten
,
T.
, and
Zirkel
,
A.
,
1994
, “
Connection Between Polymer Molecular Weight, Density, Chain Dimensions, and Melt Viscoelastic Properties
,”
Macromolecules
,
27
(
17
), pp.
4639
4647
.10.1021/ma00095a001
54.
Zhou
,
Z.
, and
Yan
,
D.
,
1997
, “
Mean-Square Radius of Gyration of Polymer Chains
,”
Macromol. Theory Sim.
,
6
(
3
), pp.
597
611
.10.1002/mats.1997.040060302
55.
Zang
,
Y.
, and
Carreau
,
P.
,
1991
, “
A Correlation Between Critical End to End Distance for Entanglements and Molecular Chain Diameter of Polymers
,”
J. Appl. Polym. Sci.
,
42
(
7
), pp.
1965
1968
.10.1002/app.1991.070420721
56.
Patel
,
A.
,
Cosgrove
,
T.
, and
Semlyen
,
J.
,
1991
, “
Studies of Cyclic and Linear Poly (Dimethylsiloxanes): 30. Adsorption Studies on Silica in Solution
,”
Polymer
,
32
(
7
), pp.
1313
1317
.10.1016/0032-3861(91)90237-D
57.
McGuiggan
,
P.
,
Gee
,
M.
,
Yoshizawa
,
H.
Hirz
,
S.
and
Israelachvili
,
J.
,
2007
, “
Friction Studies of Polymer Lubricated Surfaces
,”
Macromolecules
,
40
(
6
), pp.
2126
2133
.10.1021/ma061750h
58.
Zilliox
,
J.
,
Roovers
,
J.
, and
Bywater
,
S.
,
1975
, “
Preparation and Properties of Polydimethylsiloxane and Its Block Copolymers With Styrene
,”
Macromolecules
,
8
(
5
), pp.
573
578
.10.1021/ma60047a002
59.
Villegas
,
J.
,
Olayo
,
R.
, and
Cervantes
,
J.
,
2003
, “
Effect of Side Groups on the Conformation of a Series of Polysiloxanes in Solution
,”
J. Inorganic Organometal. Polym.
,
13
(
4
), pp.
205
222
.10.1023/A:1026191926742
60.
Büyüktanir
,
E. A.
, and
Küçükyavuz
,
Z.
,
2000
, “
Solution Properties of Poly (Dimethyl siloxane)
,”
J. Polym. Sci. B Polym. Phys.
,
38
(
20
), pp.
2678
2686
.10.1002/1099-0488(20001015)38:20<2678::AID-POLB80>3.0.CO;2-H
61.
Evmenenko
,
G.
,
Dugan
,
S.
,
Kmetko
,
J.
, and
Dutta
,
P.
,
2001
, “
Molecular Ordering in Thin Liquid Films of Polydimethylsiloxanes
,”
Langmuir
,
17
(
13
), pp.
4021
4024
.10.1021/la0017734
62.
Buch
,
R. R.
,
Klimisch
,
H. M.
, and
Johannson
,
O.
,
1969
, “
Light Scattering and Intrinsic Viscosity Investigation of Polymethyl - 3, 3, 3 - Trifluoropropylsiloxamer
,”
J. Polym. Sci. A Polym. Phys.
,
7
(
3
), pp.
563
574
.10.1002/pol.1969.160070310
63.
Buch
,
R. R.
,
Klimisch
,
H. M.
, and
Johannson
,
O.
,
1970
, “
Dilute Solution Parameters of Polymethylphenylsiloxamers
,”
J. Polym. Sci. A Polym. Phys.
,
8
(
4
), pp.
541
554
.10.1002/pol.1970.160080406
64.
Crescenzi
,
V.
, and
Flory
,
P.
,
1964
, “
Configuration of the Poly-(Dimethylsiloxane) Chain. II. Unperturbed Dimensions and Specific Solvent Effects
,”
J. Am. Chem. Soc.
,
86
(
2
), pp.
141
146
.10.1021/ja01056a006
65.
Ma
,
H.
,
Sun
,
T.
, and
Ye
,
G.
,
2008
, “
Mean-Square Radius of Gyration and Dipole Moment of Poly (Methylphenylsiloxane) Chains
,”
Chin. J. Polym. Sci.
,
26
(
6
), pp.
741
749
.10.1142/S0256767908003497
66.
Granick
,
S.
, and
Hu
,
H. W.
,
1994
, “
Nanorheology of Confined Polymer Melts. 1. Linear Shear Response at Strongly Adsorbing Surfaces
,”
Langmuir
,
10
(
10
), pp.
3857
3866
.10.1021/la00022a076
67.
Clarson
,
S.
,
Dodgson
,
K.
, and
Semlyen
,
J.
,
1987
, “
Cyclic Polysiloxanes: 2. Neutron Scattering From Poly (Phenylmethylsiloxane)
,”
Polymer
,
28
(
2
), pp.
189
192
.10.1016/0032-3861(87)90402-2
68.
Rim
,
P. B.
,
Rasoul
,
H. A. A.
,
Hurley
,
S. M.
,
Orler
,
E. B.
, and
Scholsky
,
K. M.
,
1987
, “
Rheological and Thermal Properties of Poly (Methylalkylsiloxane)
,”
Macromolecules
,
20
(
1
), pp.
208
211
.10.1021/ma00167a037
69.
Huglin
,
M. B.
,
1972
,
Light Scattering From Polymer Solutions
, Vol.
27
,
Academic Press
,
New York
.
70.
Bonchev
,
D.
,
Markel
,
E.
, and
Dekmezian
,
A.
,
2002
, “
Long Chain Branch Polymer Chain Dimensions: Application of Topology to the Zimm–Stockmayer model* 1
,”
Polymer
,
43
(
1
), pp.
203
222
.10.1016/S0032-3861(01)00589-4
71.
Wiener
,
H.
,
1947
, “
Structural Determination of Paraffin Boiling Points
,”
J. Am. Chem. Soc.
,
69
(
1
), pp.
17
20
.10.1021/ja01193a005
72.
Zimm
,
B.
, and
Stockmayer
,
W.
,
1949
, “
The Dimensions of Chain Molecules Containing Branches and Rings
,”
J. Chem. Phys.
,
17
, pp.
1301
1314
.10.1063/1.1747157
73.
Tait
,
P.
,
1888
, “
Physics and Chemistry of the Voyage of HMS Challenger
,”
Cambridge University Press
,
Cambridge, UK
.
74.
Dymond
,
J.
, and
Malhotra
,
R.
,
1988
, “
The Tait Equation: 100 Years on
,”
Int. J. Thermophys.
,
9
(
6
), pp.
941
951
.10.1007/BF01133262
75.
Habchi
,
W.
,
Eyheramendy
,
D.
,
Bair
,
S.
,
Vergne
,
P.
, and
Morales-Espejel
,
G.
,
2008
, “
Thermal Elastohydrodynamic Lubrication of Point Contacts Using a Newtonian/Generalized Newtonian Lubricant
,”
Tribol. Lett.
,
30
(
1
), pp.
41
52
.10.1007/s11249-008-9310-9
76.
Dlubek
,
G. N.
,
De
,
U.
,
Pionteck
,
J. R.
,
Arutyunov
,
N. Y.
,
Edelmann
,
M.
, and
Krause-Rehberg
,
R.
,
2005
, “
Temperature Dependence of Free Volume in Pure and Silica-Filled Poly(Dimethyl Siloxane) From Positron Lifetime and PVT Experiments
,”
Macromol. Chem. Phys.
,
206
(
8
), pp.
827
840
.10.1002/macp.200400546
77.
Prigogine
,
I.
,
Trappeniers
,
N.
, and
Mathot
,
V.
,
1953
, “
Statistical Thermodynamics of r-mers and r-mer Solutions
,”
Discuss. Faraday Soc.
,
15
, pp.
93
107
.10.1039/df9531500093
78.
Prigogine
,
I.
,
Bellemans
,
A.
, and
Mathot
,
V.
,
1957
,
The Molecular Theory of Solutions
,
North-Holland
,
Amsterdam
,
79.
Flory
,
P.
,
Orwoll
,
R.
, and
Vrij
,
A.
,
1964
, “
Statistical Thermodynamics of Chain Molecule Liquids. I. An Equation of State for Normal Paraffin Hydrocarbons
,”
J. Am. Chem. Soc.
,
86
(
17
), pp.
3507
3514
.10.1021/ja01071a023
80.
Dee
,
G.
,
Ougizawa
,
T.
, and
Walsh
,
D.
,
1992
, “
The Pressure-Volume-Temperature Properties of Polyethylene, Poly (Dimethyl Siloxane), Poly (Ethylene Glycol) and Poly (Propylene Glycol) as a Function of Molecular Weight
,”
Polymer
,
33
(
16
), pp.
3462
3469
.10.1016/0032-3861(92)91104-A
81.
Sanchez
,
I.
, and
Lacombe
,
R.
,
1976
, “
An Elementary Molecular Theory of Classical Fluids. Pure Fluids
,”
J. Phys. Chem.
,
80
(
21
), pp.
2352
2362
.10.1021/j100562a008
82.
Sanchez
,
I.
, and
Lacombe
,
R.
,
1977
, “
An Elementary Equation of State for Polymer Liquids
,”
J. Polym. Sci. Polym. Lett.
,
15
(
2
), pp.
71
75
10.1002/pol.1977.130150202.
83.
Chiew
,
Y.
,
Ting
,
S.
, and
Leong
,
K.
,
2000
, “
A Perturbed Lennard–Jones Chain Equation of State for Polymer Liquids
,”
Fluid Phase Equilibria
,
168
(
1
), pp.
19
29
.10.1016/S0378-3812(99)00329-5
84.
Simha
,
R.
, and
Somcynsky
,
T.
,
1969
, “
On the Statistical Thermodynamics of Spherical and Chain Molecule Fluids
,”
Macromolecules
,
2
(
4
), pp.
342
350
.10.1021/ma60010a005
85.
Simha
,
R.
,
Wilson
,
P.
, and
Olabisi
,
O.
,
1973
, “
Pressure-Volume-Temperature Properties of Amorphous Polymers: Empirical and Theoretical Predictions
,”
Colloid Polym. Sci.
,
251
(
6
), pp.
402
408
.
86.
Beret
,
S.
, and
Prausnitz
,
J.
,
1975
, “
Densities of Liquid Polymers at High Pressure. Pressure-Volume-Temperature Measurements for Polyethylene, Polyisobutylene, Poly (Vinyl Acetate), and Poly (Dimethylsiloxane) to 1 kbar
,”
Macromolecules
,
8
(
4
), pp.
536
538
.10.1021/ma60046a028
87.
Dee
,
G.
, and
Walsh
,
D.
,
1988
, “
Equations of State for Polymer Liquids
,”
Macromolecules
,
21
(
3
), pp.
811
815
.10.1021/ma00181a043
88.
Fakhreddine
,
Y.
, and
Zoller
,
P.
,
1990
, “
The Equation of State of a Polydimethylsiloxane Fluid
,”
J. Appl. Polym. Sci.
,
41
(
5–6
), pp.
1087
1093
.10.1002/app.1990.070410518
89.
Sachdev
,
V.
,
Yahsi
,
U.
, and
Jain
,
R.
,
1998
, “
Equation of State of Poly (Dimethylsiloxane) Melts
,”
J. Polym. Sci. B Polym. Phys.
,
36
(
5
), pp.
841
850
.10.1002/(SICI)1099-0488(19980415)36:5<841::AID-POLB11>3.0.CO;2-9
90.
Rodgers
,
P.
,
1993
, “
Pressure–Volume–Temperature Relationships for Polymeric Liquids: A Review of Equations of State and Their Characteristic Parameters for 56 Polymers
,”
J. Appl. Polym. Sci.
,
48
(
6
), pp.
1061
1080
.10.1002/app.1993.070480613
91.
Sedlacek
,
T.
,
Zatloukal
,
M.
,
Filip
,
P.
,
Boldizar
,
A.
, and
Saha
,
P.
,
2004
, “
On the Effect of Pressure on the Shear and Elongational Viscosities of Polymer Melts
,”
Polym. Eng. Sci.
,
44
(
7
), pp.
1328
1337
.10.1002/pen.20128
92.
Utracki
,
L.
, and
Simha
,
R.
,
2001
, “
Analytical Representation of Solutions to Lattice-Hole Theory
,”
Macromol. Theory Sim.
,
10
(
1
), pp.
17
24
.10.1002/1521-3919(20010101)10:1<17::AID-MATS17>3.0.CO;2-B
93.
Bridgman
,
P.
,
1949
, “
Further Rough Compressions to 40,000 Kg/Cm, Especially Certain Liquids
,” Proceedings of the American Academy of Arts and Sciences,
77
, pp.
129
146
.
94.
Vogel
,
H.
,
1921
, “
Das Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten
,”
Phys. Z
,
22
, pp.
645
646
.
95.
Andrade
,
E.
,
1930
, “
The Viscosity of Liquids
,”
Nature
,
125
(
3148
), pp.
309
310
.10.1038/125309b0
96.
Glasstone
,
S.
,
Laidler
,
K.
, and
Eyring
,
H.
,
1941
,
The Theory of Rate Process
,
Mc Graw-Hill
,
New York
,
97.
Eyring
,
H.
,
Henderson
,
D.
,
Stover
,
B.
, and
Eyring
,
E.
,
1964
,
Statistical Mechanics and Dynamics
,
John Wiley & Sons
,
New York
.
98.
LaFountain
,
A. R.
,
Johnston
,
G. J.
, and
Spikes
,
H. A.
,
2001
, “
The Elastohydrodynamic Traction of Synthetic Base Oil Blends
,”
Tribol. Trans.
,
44
(
4
), pp.
648
656
.10.1080/10402000108982506
99.
Ferguson
,
J.
,
Wright
,
B.
, and
Haward
,
R.
,
1964
, “
The Flow Properties of Polyethylene Whole Polymers and Fractions
,”
J. Appl. Chem.
,
14
(
2
), pp.
53
63
.10.1002/jctb.5010140201
100.
Marshall
,
D. I.
,
1956
, “
Effects of Branching on the Temperature Coefficient of Viscosity of Ethylene Polymers
,”
130 National Meeting ACS
,
Atlantic City, NJ
.
101.
Williams
,
M.
,
Landel
,
R.
, and
Ferry
,
J.
,
1955
, “
The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids
,”
J. Am. Chem. Soc.
,
77
(
14
), pp.
3701
3707
.10.1021/ja01619a008
102.
Doolittle
,
A.
,
1951
, “
Studies in Newtonian Flow. II. The Dependence of the Viscosity of Liquids on Free Space
,”
J. Appl. Phys.
,
22
(
12
), pp.
1471
1475
.10.1063/1.1699894
103.
Bair
,
S.
,
2001
, “
The High-Pressure, High-Shear Stress Rheology of a Polybutene
,”
J. Non-Newton. Fluid Mech.
,
97
(
1
), pp.
53
65
.10.1016/S0377-0257(00)00197-X
104.
Bair
,
S.
, and
Winer
,
W.
,
2007
, “
A Quantitative Test of the Einstein–Debye Relation for Low Molecular Weight Liquids Using the Shear Dependence of Viscosity
,”
Tribol. Lett.
,
26
(
3
), pp.
223
228
.10.1007/s11249-007-9195-z
105.
Bair
,
S.
, and
Qureshi
,
F.
,
2002
, “
Accurate Measurements of Pressure-Viscosity Behavior in Lubricants
,”
Tribol. Trans.
,
45
(
3
), pp.
390
396
.10.1080/10402000208982564
106.
Bair
,
S.
, and
Kottke
,
P.
,
2003
, “
Pressure-Viscosity Relationships for Elastohydrodynamics
,”
Tribol. Trans.
,
46
(
3
), pp.
289
295
.10.1080/10402000308982628
107.
Bair
,
S.
,
Liu
,
Y.
, and
Wang
,
Q. J.
,
2006
, “
The Pressure-Viscosity Coefficient for Newtonian EHL Film Thickness With General Piezoviscous Response
,”
ASME J. Tribol.
,
128
(
3
), pp.
624
631
.10.1115/1.2197846
108.
Liu
,
Y.
,
Wang
,
Q.
,
Krupka
,
I.
,
Hartl
,
M.
, and
Bair
,
S.
,
2008
, “
The Shear-Thinning Elastohydrodynamic Film Thickness of a Two-Component Mixture
,”
ASME J. Tribol.
,
130
(
2
), p.
021502
.10.1115/1.2842298
109.
Bair
,
S.
,
1998
, “
Elastohydrodynamic Film Forming With Shear Thinning Liquids
,”
ASME J. Tribol.
,
120
, pp.
173
178
.10.1115/1.2834405
110.
Bair
,
S.
,
2006
, “
Reference Liquids for Quantitative Elastohydrodynamics: Selection and Rheological Characterization
,”
Tribol. Lett.
,
22
(
2
), pp.
197
206
.10.1007/s11249-006-9083-y
111.
Bair
,
S.
,
Roland
,
C.
, and
Casalini
,
R.
,
2007
, “
Fragility and the Dynamic Crossover in Lubricants
,”
Proc. IMechE J: J. Eng. Tribol.
,
221
(
7
), pp.
801
811
.10.1243/13506501JET278
112.
Bair
,
S.
, and
Casalini
,
R.
,
2008
, “
A Scaling Parameter and Function for the Accurate Correlation of Viscosity With Temperature and Pressure Across Eight Orders of Magnitude of Viscosity
,”
ASME J. Tribol.
,
130
, p.
041802
.10.1115/1.2959116
113.
Habchi
,
W.
,
Eyheramendy
,
D.
,
Vergne
,
P.
, and
Morales-Espejel
,
G.
,
2012
, “
Stabilized Fully-Coupled Finite Elements for Elastohydrodynamic Lubrication Problems
,”
Adv. Eng. Software
,
46
(
1
), pp.
4
18
.10.1016%2Fj.advengsoft.2010.
114.
Johnston
,
W.
,
1981
, “
A Method to Calculate the Pressure-Viscosity Coefficient From Bulk Properties of Lubricants
,”
Tribol. Trans.
,
24
(
2
), pp.
232
238
.
115.
So
,
B.
, and
Klaus
,
E.
,
1980
, “
Viscosity-Pressure Correlation of Liquids
,”
Tribol. Trans.
,
23
(
4
), pp.
409
421
.
116.
Wu
,
C.
,
Klaus
,
E.
, and
Duda
,
J.
,
1989
, “
Development of a Method for the Prediction of Pressure-Viscosity Coefficients of Lubricating Oils Based on Free-Volume Theory
,”
ASME J. Tribol.
,
111
(
1
), pp.
121
128
.10.1115/1.3261861
117.
Foord
,
C.
,
Hammann
,
W.
, and
Cameron
,
A.
,
1968
, “
Evaluation of Lubricants Using Optical Elastohydrodynamics
,”
Tribol. Trans.
,
11
(
1
), pp.
31
43
.
118.
Johnston
,
G.
,
Wayte
,
R.
, and
Spikes
,
H.
,
1991
, “
The Measurement and Study of Very Thin Lubricant Films in Concentrated Contacts
,”
Tribol. Trans.
,
34
(
2
), pp.
187
194
.10.1080/10402009108982026
119.
Aderin
,
M.
,
Johnston
,
G.
,
Spikes
,
H.
, and
Caporiccio
,
G.
,
1992
, “
The Elastohydrodynamic Properties of Some Advanced Non Hydrocarbon-Based Lubricants
,”
Lub. Eng.
,
48
(
8
), pp.
633
638
.
120.
Gunsel
,
S.
,
Korcek
,
S.
,
Smeeth
,
M.
, and
Spikes
,
H.
,
1999
, “
The Elastohydrodynamic Friction and Film Forming Properties of Lubricant Base Oils
,”
Tribol. Trans.
,
42
(
3
), pp.
559
569
.10.1080/10402009908982255
121.
Yokoyama
,
F.
, and
Spikes
,
H.
,
2000
, “
Film-Forming Properties of Polyol Esters, Polyphenyl Ethers and Their Mixtures Over a Wide Range of Temperature
,”
Tribol. Trans.
,
43
(
1
), pp.
130
136
.10.1080/10402000008982322
122.
Guangteng
,
G.
, and
Spikes
,
H.
,
1996
, “
Boundary Film Formation by Lubricant Base Fluids
,”
Tribol. Trans.
,
39
(
2
), pp.
448
454
.10.1080/10402009608983551
123.
Jones
,
W. R.
,
Johnson
,
R. L.
,
Winer
,
W. O.
, and
Sanborn
,
D. M.
,
1975
, “
Pressure-Viscosity Measurements for Several Lubricants to 5.5 × 108 Newtons per Square Meter (8 × 104 psi) and 149 °C (300°F)
,”
Tribol. Trans.
,
18
(
4
), pp.
249
262
.
124.
Bair
,
S.
, and
Qureshi
,
F.
,
2003
, “
The High Pressure Rheology of Polymer-Oil Solutions
,”
Tribol. Int.
,
36
(
8
), pp.
637
645
.10.1016/S0301-679X(03)00008-2
125.
Bair
,
S. S.
,
2007
,
High-Pressure Rheology for Quantitative Elastohydrodynamics
, Vol.
54
,
Elsevier Science
,
Oxford, UK
.
126.
Blok
,
H.
,
1964
, “
Inverse Hydrodynamics
,”
Proceedings of the International Symposium on Lubrication and Wear
,
McCutchan Publ. Corp.
,
Berkeley, CA
, pp.
1
151
.
127.
Roelands
,
C. J. A.
,
1966
, “
Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils
,” Ph.D. thesis,
Technical University Delft, Delft, The Netherlands
(
V. R. B., Groningen, The Netherlands
).
128.
Hamrock
,
B.
, and
Dowson
,
D.
,
1976
, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts. I—Theoretical Formulation
,”
ASME J. Lubr. Technol.
,
98
(
2
), pp.
223
228
.10.1115/1.3452801
129.
Hamrock
,
B.
, and
Dowson
,
D.
,
1976
, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts. II—Ellipticity Parameter Results
,”
ASME J. Lubr. Technol.
,
98
(
3
), pp.
375
381
.10.1115/1.3452861
130.
Hamrock
,
B.
, and
Dowson
,
D.
,
1977
, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts. III—Fully Flooded Results
,”
ASME J. Lubr. Technol.
,
99
(
2
), pp.
264
275
.10.1115/1.3453074
131.
Bair
,
S.
, and
Qureshi
,
F.
,
2003
, “
The Generalized Newtonian Fluid Model and Elastohydrodynamic Film Thickness
,”
ASME J. Tribol.
,
125
(
1
), pp.
70
75
.10.1115/1.1504086
132.
Kumar
,
P.
,
Bair
,
S.
,
Krupka
,
I.
, and
Hartl
,
M.
,
2010
, “
Newtonian Quantitative Elastohydrodynamic Film Thickness With Linear Piezoviscosity
,”
Tribol. Int.
,
43
(
11
), pp.
2159
2165
.10.1016/j.triboint.2010.06.005
133.
Mills
,
N.
,
1969
, “
The Rheological Properties and Molecular Weight Distribution of Polydimethylsiloxane
,”
Eur. Polym. J.
,
5
(
5
), pp.
675
695
.10.1016/0014-3057(69)90130-X
134.
Rahalkar
,
R.
,
Lamb
,
J.
,
Harrison
,
G.
,
Barlow
,
A.
,
Hawthorne
,
W.
, and
Semlyen
,
J.
,
North
,
A.
, and
Pethrick
,
R.
,
1983
, “
Viscoelastic Studies of Reptational Motion of Linear Polydimethylsiloxanes
,”
Faraday Symposium, Chem. Soc
,
18
, pp.
103
114
.10.1039/fs9831800103
135.
Kissi
,
N.
,
Piau
,
J.
,
Attané
,
P.
, and
Turrel
,
G.
,
1993
, “
Shear Rheometry of Polydimethylsiloxanes. Master Curves and Testing of Gleissle and Yamamoto Relations
,”
Rheolog. Acta
,
32
(
3
), pp.
293
310
.10.1007/BF00434194
136.
Barry
,
A. J.
,
1946
, “
Viscometric Investigation of Dimethylsiloxane Polymers
,”
J. Appl. Phys.
,
17
(
12
), pp.
1020
1024
.10.1063/1.1707670
137.
Lee
,
C.
,
Polmanteer
,
K.
, and
King
,
E.
,
1970
, “
Flow Behavior of Narrow-Distribution Polydimethylsiloxane
,”
J. Polym. Sci. A Polym. Phys.
,
8
(
11
), pp.
1909
1916
.10.1002/pol.1970.160081106
138.
Debye
,
P. J. W.
,
1929
,
Polar Molecules
,
Dover
,
New York
.
139.
Hu
,
H.
,
Carson
,
G.
, and
Granick
,
S.
,
1991
, “
Relaxation Time of Confined Liquids Under Shear
,”
Phys. Rev. Lett.
,
66
(
21
), pp.
2758
2761
.10.1103/PhysRevLett.66.2758
140.
Macosko
,
C.
,
1994
,
Rheology: Principles, Measurements, and Applications
,
Wiley-VCH
,
Poughkeepsie, NY
.
141.
Strohriegl
,
P.
,
1986
, “
Polymers With Pendant Carbazole Groups, 1. Synthesis and Characterization of Some Novel Polysiloxanes
,”
Die Makromolekulare Chemie, Rapid Commun.
,
7
(
12
), pp.
771
775
.10.1002/marc.1986.030071204
142.
Bahar
,
I.
,
Zuniga
,
I.
,
Dodge
,
R.
, and
Mattice
,
W.
,
1991
, “
Conformational Statistics of Poly (Dimethylsiloxane). 1. Probability Distribution of Rotational Isomers From Molecular Dynamics Simulations
,”
Macromolecules
,
24
(
10
), pp.
2986
2992
.10.1021/ma00010a054
143.
Höglund
,
E.
,
1999
, “
Influence of Lubricant Properties on Elastohydrodynamic Lubrication
,”
Wear
,
232
(
2
), pp.
176
184
.10.1016/S0043-1648(99)00143-X
You do not currently have access to this content.