A Monte Carlo model is applied to determinate the steady state, solar-weighted optical properties of potential thermotropic composite materials for overheat protection of polymer solar absorbers. The key results are dimensionless plots of normal-hemispherical transmittance, reflectance and absorptance as a function of particle size parameter, scattering albedo, and overall optical thickness. The optical behavior of thermotropic materials at different temperatures is represented by a change in the relative refractive index which affects the scattering albedo and optical thickness. At low temperatures where overheat protection is not required, referred to as the clear state, the overall optical thickness should be less than 0.3 to ensure high transmittance for the preferred particle size parameter of 2. At higher temperatures where overheat protection is required, referred to as the translucent state, the overall optical thickness should be greater than 10 and the scattering albedo should be greater than 0.995 to achieve 50% reflectance. A case study of low molecular weighted polyethylene in poly(methyl methacrylate) is presented to illustrate use of the results to guide the design of thermotropic materials.

References

1.
U.S. Energy Information Agency
,
2009
, “
2009 Residential Energy Consumption Survey—Consumption and Expenditure Tables (by End use)
,” 2013(07/31) http://www.eia.gov/consumption/residential/data/2009/index.cfm?view=consumption#end-use
2.
Buckles
,
W. E.
, and
Klein
,
S. A.
,
1980
, “
Analysis of Solar Domestic Hot Water Heaters
,”
Sol. Energy
,
25
(
5
), pp.
417
424
.10.1016/0038-092X(80)90448-X
3.
Hudon
,
K.
,
Merrigan
,
T.
,
Burch
,
J.
, and
Maguire
,
J.
,
2012
, “
Low-Cost Solar Water Heating Research and Development Roadmap
,” National Renewable Energy Laboratory (NREL), Technical Report No. NREL/TP-550054793.
4.
Merrigan
,
T.
,
2007
, “
Solar Heating & Lighting: Solar Water Heating R&D—DOE Solar Energy Technologies Program
,”
DOE Solar Energy Technologies Program Peer Review Meeting
, Apr. 17–19,
Denver, CO
.
5.
Tsilingiris
,
P. T.
,
1999
, “
Towards Making Solar Water Heating Technology feasible—The Polymer Solar Collector Approach
,”
Energy Convers. Manage.
,
40
(
12
), pp.
1237
1250
.10.1016/S0196-8904(99)00032-1
6.
Kohl
,
M.
,
Meir
,
M. G.
, and
Papillon
,
P.
,
2012
,
Polymeric Materials for Solar Thermal Applications
,
Wiley-VCH Verlag & Co.
,
Weinheim, German
, pp.
73
106
.
7.
Rhodes
,
R. O.
,
2010
, “
Polymer Thin-Film Design Reduces Installed Cost of Solar Water Heater
,”
Proceedings of the 39th ASES National Solar Conference
, May 17–20,
Phoenix, AZ
.
8.
Kearney
,
M.
,
Davidson
,
J.
, and
Mantell
,
S.
,
2005
, “
Polymeric Absorbers for Flat-Plate Collectors: Can Venting Provide Adequate Overheat Protection?
,”
ASME J. Sol. Energy Eng.
,
127
(
3
), pp.
421
424
.10.1115/1.1979518
9.
Resch
,
K.
,
Hausner
,
R.
, and
Wallner
,
G. M.
,
2009
, “
All Polymeric Flat-Plate Collector—Potential of Thermotropic Layers to Prevent Overheating
,”
Proceedings of ISES World Conference 2007
, pp.
561
565
.
10.
Resch
,
K.
, and
Wallner
,
G. M.
,
2009
, “
Thermotropic Layers for Flat-Plate Collectors—A Review of Various Concepts for Overheating Protection With Polymeric Materials
,”
Sol. Energy Mater. Sol. Cells
,
93
(
1
), pp.
119
128
.10.1016/j.solmat.2008.09.004
11.
UL746B
,
1998
,
Polymeric Materials—Long Term Property Evaluations
,
Underwriters Laboratories, Inc.
,
Northbrook, IL
.
12.
Raman
,
R.
,
Mantell
,
S.
, and
Davidson
,
J.
,
2000
, “
A Review of Polymer Materials for Solar Water Heating Systems
,”
ASME J. Sol. Energy Eng.
,
122
(
2
), pp.
92
100
.10.1115/1.1288214
13.
Kohl
,
M.
,
Meir
,
M. G.
, and
Papillon
,
P.
,
2012
,
Polymeric Materials for Solar Thermal Applications
,
Wiley-VCH Verlag & Co.
,
Weinheim, German
, pp.
187
210
.
14.
Gladen
,
A. C.
,
Davidson
,
J. H.
, and
Mantell
,
S. C.
,
2013
, “
Selection of Thermotropic Materials for Overheat Protection of Polymer Absorbers
,”
Sol. Energy
, (in press).10.1016/j.solener.2013.10.026
15.
Wallner
,
G. M.
,
Resch
,
K.
, and
Hausner
,
R.
,
2008
, “
Property and Performance Requirements for Thermotropic Layers to Prevent Overheating in an All Polymeric Flat-Plate Collector
,”
Sol. Energy Mater. Sol. Cells
,
92
(
6
), pp.
614
620
.10.1016/j.solmat.2007.12.005
16.
Nitz
,
P.
, and
Hartwig
,
H.
,
2005
, “
Solar Control With Thermotropic Layers
,”
Sol. Energy
,
79
(
6
), pp.
573
582
.10.1016/j.solener.2004.12.009
17.
Seeboth
,
A.
,
Ruhmann
,
R.
, and
Muehling
,
O.
,
2010
, “
Thermotropic and Thermochromic Polymer Based Materials for Adaptive Solar Control
,”
Materials
,
3
(
12
), pp.
5143
5168
.10.3390/ma3125143
18.
Resch
,
K.
,
Wallner
,
G. M.
, and
Hausner
,
R.
,
2009
, “
Phase Separated Thermotropic Layers Based on UV Cured Acrylate Resins—Effect of Material Formulation on Overheating Protection Properties and Application in a Solar Collector
,”
Sol. Energy
,
83
(
9
), pp.
1689
1697
.10.1016/j.solener.2009.06.006
19.
Resch
,
K.
, and
Wallner
,
G. M.
,
2009
, “
Morphology of Phase-Separated Thermotropic Layers Based on UV Cured Acrylate Resins
,”
Polym. Adv. Technol.
,
20
(
12
), pp.
1163
1167
.10.1002/pat.1393
20.
Weber
,
A.
, and
Resch
,
K.
,
2012
, “
Thermotropic Glazings for Overheating Protection
,”
Energy Procedia
,
30
, pp.
471
477
.10.1016/j.egypro.2012.11.056
21.
Schael
,
G. W.
,
1964
, “
Determination of Polyolefin Film Properties From Refractive Index Measurements
,”
J. Appl. Polym. Sci.
,
8
(
6
), pp.
2717
2722
.10.1002/app.1964.070080617
22.
Krevelen
,
D. W. V.
, and
Nijenhuis
,
K.
,
2009
,
Properties of Polymers—Their Correlation With Chemical Structure; Their Numerical Estimation and Prediction From Additive Group Contributions (4th Completely Revised Edition)
,
Elsevier
,
New York
, pp. 287–318.
23.
Buehler
,
D. F. S. R.
,
2004
, “
Reversible Thermotropic Composition
, Its Preparation and Use,” EPO Patent No. EP0985709.
24.
Dabisch
,
W.
,
1981
, “
Bodies With Reversibly Variable Temperature-Dependent Light Absorbence
,” U.S. Patent No. 4,268,413.
25.
Muehling
,
O.
,
Seeboth
,
A.
, and
Haeusler
,
T.
,
2009
, “
Variable Solar Control Using Thermotropic Core/Shell Particles
,”
Sol. Energy Mater. Sol. Cells
,
93
(
9
), pp.
1510
1517
.10.1016/j.solmat.2009.03.029
26.
Errico
,
M.
,
Greco
,
R.
, and
Laurienzo
,
P.
,
2006
, “
Acrylate/EVA Reactive Blends and Semi-IPN: Chemical, Chemical–Physical, and Thermo-Optical Characterization
,”
J. Appl. Polym. Sci.
,
99
(
6
), pp.
2926
2935
.10.1002/app.22788
27.
Takahashi
,
S.
,
Okada
,
H.
, and
Nobukawa
,
S.
,
2012
, “
Optical Properties of Polymer Blends Composed of Poly(Methyl Methacrylate) and Ethylene–Vinyl Acetate Copolymer
,”
Eur. Polym. J.
,
48
(
5
), pp.
974
980
.10.1016/j.eurpolymj.2012.02.009
28.
Bernini
,
U.
,
Malinconico
,
M.
, and
Martuscelli
,
E.
,
1995
, “
Ultra-Tough Synthetic Glasses Made by Reactive Blending of PMMA and EVA Rubbers: Opto-Thermal Characterization
,”
J. Mater. Process. Technol.
,
55
(
3–4
), pp.
224
228
.10.1016/0924-0136(95)02010-1
29.
Weber
,
A.
, and
Resch
,
K.
,
2014
, “
Thermotropic Glazings for Overheating Protection. I. Material Preselection, Formulation, and Light-Shielding Efficiency
,”
J. Appl. Polym. Sci.
,
131
(
4
).10.1002/app.39950
30.
Weber
,
A.
,
Schmid
,
A.
, and
Resch
,
K.
,
2014
, “
Thermotropic Glazings for Overheating Protection. II. Morphology and Structure–Property Relationships
,”
J. Appl. Polym. Sci.
,
131
(
4
).10.1002/app.39910
31.
Weber
,
A.
, and
Resch
,
K.
,
2012
, “
Effect of Temperature-Cycling on the Morphology of Polymeric Thermotropic Glazings for Overheating Protection Applications
,”
J. Polym. Res.
,
19
(
6
), pp.
1
8
.10.1007/s10965-012-9888-3
32.
Weber
,
A.
,
Schlögl
,
S.
, and
Resch
,
K.
,
2013
, “
Effect of Formulation and Processing Conditions on Light Shielding Efficiency of Thermotropic Systems With Fixed Domains Based on UV Curing Acrylate Resins
,”
J. Appl. Polym. Sci.
,
130
(
5
), pp.
3299
3310
.10.1002/app.39571
33.
Nitz
,
P.
,
Ferber
,
J.
, and
Stangl
,
R.
,
1998
, “
Simulation of Multiply Scattering Media
,”
Sol. Energy Mater. Sol. Cells
,
54
(
1–4
), pp.
297
307
.10.1016/S0927-0248(98)00081-6
34.
Kasarova
,
S. N.
,
Sultanova
,
N. G.
, and
Ivanov
,
C. D.
,
2007
, “
Analysis of the Dispersion of Optical Plastic Materials
,”
Opt. Mater.
,
29
(
11
), pp.
1481
1490
.10.1016/j.optmat.2006.07.010
35.
Filmetrics
,
2012
, “
Refractive Index of Polyethylene, PE
,” 2013(01/25) http://www.filmetrics.com/refractive-index-database/Polyethylene/PE-Polyethene
36.
Dell'Erba
,
R.
,
Groeninckx
,
G.
, and
Maglio
,
G.
,
2001
, “
Immiscible Polymer Blends of Semicrystalline Biocompatible Components: Thermal Properties and Phase Morphology Analysis of PLLA/PCL Blends
,”
Polymer
,
42
(
18
), pp.
7831
7840
.10.1016/S0032-3861(01)00269-5
37.
Gupta
,
A. K.
,
Ratnam
,
B. K.
, and
Srinivasan
,
K. R.
,
1992
, “
Impact Toughening of Polypropylene by Ethylene Vinyl Acetate Copolymer
,”
J. Appl. Polym. Sci.
,
45
(
7
), pp.
1303
1312
.10.1002/app.1992.070450718
38.
Tien
,
C. L.
, and
Drolen
,
B.
,
1987
, “
Thermal Radiation in Particulate Media With Dependent and Independent Scattering
,”
Annual Review of Numerical Fluid Mechanics and Heat Transfer
, Vol.
1
(A88-18971 06-34),
Hemisphere Publishing Corp.
,
Washington, DC
, pp.
1
32
.
39.
Gooch
,
J. W.
,
2011
,
Encyclopedic Dictionary of Polymers
, 2nd ed.,
Springer Science & Business Media
,
New York, NY
, p.
520
.
40.
Viskanta
,
R.
, and
Mengüç
,
M. P.
,
1987
, “
Radiation Heat Transfer in Combustion Systems
,”
Prog. Energy Combust. Sci.
,
13
(
2
), pp.
97
160
.10.1016/0360-1285(87)90008-6
41.
Mishchenko
,
M. I.
,
Travis
,
L. D.
, and
Lacis
,
A. A.
,
2006
,
Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering
,
Cambridge University Press
,
New York
, p.
478
.
42.
Modest
,
M.
,
2003
,
Radiative Heat Transfer
, 2nd ed.,
Academic Press
,
New York
, pp.
263
287
.
43.
Randrianalisoa
,
J.
, and
Baillis
,
D.
,
2010
, “
Radiative Properties of Densely Packed Spheres in Semitransparent Media: A New Geometric Optics Approach
,”
J. Quant. Spectrosc. Radiat. Transfer
,
111
(
10
), pp.
1372
1388
.10.1016/j.jqsrt.2010.01.014
44.
Dombrovskii
,
L. A.
,
2004
, “
The Propagation of Infrared Radiation in a Semitransparent Liquid Containing Gas Bubbles
,”
High Temp.
,
42
(
1
), pp.
146
153
.10.1023/B:HITE.0000020103.82678.13
45.
Bohren
,
C. F.
, and
Huffman
,
D. R.
,
1998
,
Absorption and Scattering of Light by Small Particles
,
Wiley-Interscience
,
New York
, p.
530
.
46.
Randrianalisoa
,
J.
,
Baillis
,
D.
, and
Pilon
,
L.
,
2006
, “
Modeling Radiation Characteristics of Semitransparent Media Containing Bubbles or Particles
,”
J. Opt. Soc. Am. A
,
23
(
7
), pp.
1645
1656
.10.1364/JOSAA.23.001645
47.
Baneshi
,
M.
,
Maruyama
,
S.
, and
Komiya
,
A.
,
2010
, “
Infrared Radiative Properties of Thin Polyethylene Coating Pigmented With Titanium Dioxide Particles
,”
ASME J. Heat Transfer
,
132
(
2
),
p. 023306
.10.1115/1.4000235
48.
Modest
,
M.
,
2003
,
Radiative Heat Transfer
, 2nd ed.,
Academic Press
,
New York
, pp.
644
679
.
49.
Farmer
,
J. T.
, and
Howell
,
J. R.
,
1998
,
Advances in Heat Transfer
,
Elsevier
,
New York
, pp.
333
429
.
50.
Modest
,
M.
,
2003
,
Radiative Heat Transfer
, 2nd ed.,
Academic Press
, New York, pp.
31
60
.
51.
Busbridge
,
I.
, and
Orchard
,
S.
,
1967
, “
Reflection and Transmission of Light by a Thick Atmosphere According to a Phase Function: 1—χ COS θ
,”
Astrophys. J.
,
149
, pp.
655
664
.10.1086/149294
52.
Sutton
,
W.
, and
Özişik
,
M.
,
1979
, “
An Iterative Solution for Anisotropic Radiative Transfer in a Slab
,”
ASME J. Heat Transfer
,
101
, pp.
695
698
.10.1115/1.3451059
53.
Lee
,
H.
, and
Buckius
,
R.
,
1982
, “
Scaling Anisotropic Scattering in Radiation Heat Transfer for a Planar Medium
,”
ASME Trans. J. Heat Transfer
,
104
, pp.
68
75
.10.1115/1.3245070
54.
Maruyama
,
S.
,
1998
, “
Radiative Heat Transfer in Anisotropic Scattering Media With Specular Boundary Subjected to Collimated Irradiation
,”
Int. J. Heat Mass Transfer
,
41
(
18
), pp.
2847
2856
.10.1016/S0017-9310(98)00055-6
55.
Baumer
,
S.
,
2010
,
Handbook of Plastic Optics
,
Wiley-VCH, Weinheim
,
Germany
, pp.
123
160
.
56.
Lens
,
U. S. P.
,
1973
,
The Handbook of Plastic Optics
,
U.S. Precision Lens, Inc.
,
Cincinnati, OH
, pp.
11
23
.
57.
Dombrovsky
,
L.
,
Randrianalisoa
,
J.
, and
Baillis
,
D.
,
2005
, “
Use of Mie Theory to Analyze Experimental Data to Identify Infrared Properties of Fused Quartz Containing Bubbles
,”
Appl. Opt.
,
44
(
33
), pp.
7021
7031
.10.1364/AO.44.007021
58.
Rubin
,
M.
,
1985
, “
Optical Properties of Soda Lime Silica Glasses
,”
Sol. Energy Mater.
,
12
(
4
), pp.
275
288
.10.1016/0165-1633(85)90052-8
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