### Abstract

We have developed a parametric analysis of diffuse scattering (haze) measured by integrating sphere, based on power law ('B') representation of changes in scattering intensity vs. NIR to UV wavelengths. The standard haze quantification method involves integration over the visible band, and so prevents interpreting the important B-dependency relative to its physical characteristic. Integration also removes proper interpretation of the physiological response to human vision by considering the diffuse signal as constant. Our B-modeling of diffuse scattering allows a closer connection between haze and both physical and physiological quantities, while yielding the same quantification of haze as the standard method. In particular, the measured B dependence on scattering size (a) can be related by Rayleigh-Gans (R-G) (4.0 to 2.0), and Mie (as formulated by van de Hulst, "Mie_{vdH}") (2.0 to 0.0) scattering theories. While mathematically, the large size limit of R-G asymptotically equals the small size limit of Mie_{vdH}, large discontinuities exist predicting B(a) between R-G and Mie_{vdH} theories due to differences in the way that refractive index (n) is used, showing a need to develop a more unified scattering theory. As an intermediate fix to this problem, we find that the Mie_{vdH} (n=1.3) B(a) trend matches well with the R-G B(a) trend, establishing continuity in B(a) over its entire range. This Mie_{vdH} (1.3) assumption is therefore used as a parametric tool to estimate a. We find for glass, a ≈20nm, while for polymers, a ranges from about 10nm to over 200nm. By comparing this average size with the associated scattering efficiencies, we deduce the number of scattering centers. We thus obtain a quantitative handle on why haze differs for various glass and polymer materials.

Original language | English (US) |
---|---|

Journal | Surface and Coatings Technology |

DOIs | |

State | Accepted/In press - 2017 |

### Profile

### Keywords

- Diffuse scattering
- Glass
- Haze
- Mie
- Polymers
- Rayleigh
- Rayleigh-Gans
- Windows

### ASJC Scopus subject areas

- Chemistry(all)
- Condensed Matter Physics
- Surfaces and Interfaces
- Surfaces, Coatings and Films
- Materials Chemistry

### Cite this

*Surface and Coatings Technology*. DOI: 10.1016/j.surfcoat.2017.08.054

**Quantification of diffuse scattering in glass and polymers by parametric power law analysis of UV to NIR light.** / Tsu, David V.; Muehle, Matthias; Becker, Michael; Schuelke, Thomas; Slagter, John.

Research output: Contribution to journal › Article

*Surface and Coatings Technology*. DOI: 10.1016/j.surfcoat.2017.08.054

}

TY - JOUR

T1 - Quantification of diffuse scattering in glass and polymers by parametric power law analysis of UV to NIR light

AU - Tsu,David V.

AU - Muehle,Matthias

AU - Becker,Michael

AU - Schuelke,Thomas

AU - Slagter,John

PY - 2017

Y1 - 2017

N2 - We have developed a parametric analysis of diffuse scattering (haze) measured by integrating sphere, based on power law ('B') representation of changes in scattering intensity vs. NIR to UV wavelengths. The standard haze quantification method involves integration over the visible band, and so prevents interpreting the important B-dependency relative to its physical characteristic. Integration also removes proper interpretation of the physiological response to human vision by considering the diffuse signal as constant. Our B-modeling of diffuse scattering allows a closer connection between haze and both physical and physiological quantities, while yielding the same quantification of haze as the standard method. In particular, the measured B dependence on scattering size (a) can be related by Rayleigh-Gans (R-G) (4.0 to 2.0), and Mie (as formulated by van de Hulst, "MievdH") (2.0 to 0.0) scattering theories. While mathematically, the large size limit of R-G asymptotically equals the small size limit of MievdH, large discontinuities exist predicting B(a) between R-G and MievdH theories due to differences in the way that refractive index (n) is used, showing a need to develop a more unified scattering theory. As an intermediate fix to this problem, we find that the MievdH (n=1.3) B(a) trend matches well with the R-G B(a) trend, establishing continuity in B(a) over its entire range. This MievdH (1.3) assumption is therefore used as a parametric tool to estimate a. We find for glass, a ≈20nm, while for polymers, a ranges from about 10nm to over 200nm. By comparing this average size with the associated scattering efficiencies, we deduce the number of scattering centers. We thus obtain a quantitative handle on why haze differs for various glass and polymer materials.

AB - We have developed a parametric analysis of diffuse scattering (haze) measured by integrating sphere, based on power law ('B') representation of changes in scattering intensity vs. NIR to UV wavelengths. The standard haze quantification method involves integration over the visible band, and so prevents interpreting the important B-dependency relative to its physical characteristic. Integration also removes proper interpretation of the physiological response to human vision by considering the diffuse signal as constant. Our B-modeling of diffuse scattering allows a closer connection between haze and both physical and physiological quantities, while yielding the same quantification of haze as the standard method. In particular, the measured B dependence on scattering size (a) can be related by Rayleigh-Gans (R-G) (4.0 to 2.0), and Mie (as formulated by van de Hulst, "MievdH") (2.0 to 0.0) scattering theories. While mathematically, the large size limit of R-G asymptotically equals the small size limit of MievdH, large discontinuities exist predicting B(a) between R-G and MievdH theories due to differences in the way that refractive index (n) is used, showing a need to develop a more unified scattering theory. As an intermediate fix to this problem, we find that the MievdH (n=1.3) B(a) trend matches well with the R-G B(a) trend, establishing continuity in B(a) over its entire range. This MievdH (1.3) assumption is therefore used as a parametric tool to estimate a. We find for glass, a ≈20nm, while for polymers, a ranges from about 10nm to over 200nm. By comparing this average size with the associated scattering efficiencies, we deduce the number of scattering centers. We thus obtain a quantitative handle on why haze differs for various glass and polymer materials.

KW - Diffuse scattering

KW - Glass

KW - Haze

KW - Mie

KW - Polymers

KW - Rayleigh

KW - Rayleigh-Gans

KW - Windows

UR - http://www.scopus.com/inward/record.url?scp=85029443135&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029443135&partnerID=8YFLogxK

U2 - 10.1016/j.surfcoat.2017.08.054

DO - 10.1016/j.surfcoat.2017.08.054

M3 - Article

JO - Surface and Coatings Technology

T2 - Surface and Coatings Technology

JF - Surface and Coatings Technology

SN - 0257-8972

ER -