Advances in the Development of Cool Materials for the Built Environment

Modeling Cool Materials’ Properties

Author(s): Dionysia-Denia Kolokotsa, Vassilis Dimitriou and Afroditi Synnefa

Pp: 195-230 (36)

DOI: 10.2174/9781608054718113010011

* (Excluding Mailing and Handling)

Abstract

Optical properties (i.e., reflectance, transmittance, etc.) of light scattering materials can be described using two approaches. In the first approach, the interaction of light with the matter’s particles is modeled (microscopic approach) while in the second, the light fluxes into and out of bulked considered matter is modeled (macroscopic approach). Kubelka-Munk (KM) is the most common theory of macroscopic modeling, for calculating the change of light fluxes (two-flux theory) as a function of scattering, absorption, and distance. Modified KM Models, for calculating the optical properties of rough surfaces, revised KM theories as well as, inversion methods from KM analysis are presented. A KM and Mie microscopic model is used for emmitance calculations of coating layers. Three flux models track two diffuse fluxes and one collimated flux, while four flux models track two diffuse and two collimated fluxes. Maheu- Letoulouzan-Gouesbet (M-L-G), multilayered, and other generalized four-flux models are shown. A number of applications of the discussed models in pigments (such us polymer coatings), light scattering from TiO2 and red particles are also presented.


Keywords: Kubelka-munk model, four flux model, N-flux model, opticalproperties models.

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      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51271243 and j.to_ip >=51271243 )) and ((j.from_date <= 1739848348 and j.to_date >= 1739848348 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 4890) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51271243 and j.to_ip >=51271243 )) and ((j.from_date <= 1739848348 and j.to_date >= 1739848348 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 4890) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51271243 and j.to_ip >=51271243 )) and ((j.from_date <= 1739848348 and j.to_date >= 1739848348 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 4890)
      640μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 1207 and `b`.`banner_from_date` <= 1739848348 and `b`.`banner_to_date` >= 1739848348 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.1msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 1207
      • 3: 1739848348
      • 4: 1739848348
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='44089d207f3ceacf2a37af0496261510'
      250μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    4Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        qwZxsr6naS7sl5yel43WMmyYX3zvnRbX3XHTkrys
        uc_cart_id
        44089d207f3ceacf2a37af0496261510
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/4890" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/4890
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6IjliNWUxMlRwRnJZdXlueUxMYXFEMVE9PSIsInZhbHVlIjoiZEJDZ1JZbGxDRkM4enFUdWZHdWJSM0lqMEZXTWJGK2NPYmFPYkNRYWFFbz0iLCJtYWMiOiI2OTg4MzkyODAxNTQwMmRiZDI2MzJkZjk0ZjkzMjRmYmMxZGNhZDcyNjRlMjA2YjRhOWQ2NGU2MDc5MjAwZTg0IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6IjliNWUxMlRwRnJZdXlueUxMYXFEMVE9PSIsInZhbHVlIjoiZEJDZ1JZbGxDRkM4enFUdWZHdWJSM0lqMEZXTWJGK2NPYmFPYkNRYWFFbz0iLCJtYWMiOiI2OTg4MzkyODAxNTQw" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 18 Feb 2025 03:12:28 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Ik1zeDdiTHVwL0tjVkUwTmFlK2kxb3c9PSIsInZhbHVlIjoicS9TY0RpY0p1VkhoVmdKa00rMko2eXFWTGRla3dsUkFtQWRrbU5DTFF6TC9nYUh4cngzUlRKSmcyQU9oVldLbkwxR1hhWkZnMzR6NHhVT2hKM2JKbEhCRFViYjdXN1ZEd1B4Z1M4V2U0dW1DaDBWVkJaRlhMSWZSM1VwOFViWGsiLCJtYWMiOiJmMmVlNDkwMjYxODE1Zjk0Yzk5MWZhNDIyNmMxY2ZhZGY0YzNmMDQ3NjUzOTYxYWM5YTkwNWVhNmI5ZTRkNGJmIiwidGFnIjoiIn0%3D; expires=Thu, 20 Feb 2025 15:12:28 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6Ik1zeDdiTHVwL0tjVkUwTmFlK2kxb3c9PSIsInZhbHVlIjoicS9TY0RpY0p1VkhoVmdKa00rMko2eXFWTGRla3dsUkFtQWRrbU5DTFF6TC9nYUh4cngzUlRKSmcyQU9oVldLbkwxR1hhW" 1 => "alphaeurekaselectnet_session=eyJpdiI6Img2NGNoNmlNa2l4ejFKbjVTeDR4Q0E9PSIsInZhbHVlIjoiQ1NreVlWd3J3SHlJOWNTQUlPV0lxRythYTdwZGJkS2NCamdrV0xLN3RjU0R5K1E2M0NHNlRZM1hoTitRei92SW8xM256TDgvMmJmV0lJVjkzSmEvOXpSRE1vZzlpM3JVcmtzbGdnQzVnVFk4R2xsd2dzU1FrYm5QZEFUdjB4TzIiLCJtYWMiOiI1NzAyOWU4MWQ2MGU5MmMzYjM0OGIwYjUzOGQ3NWIyMjhhZDYwMzE0NGY4NTViZDQ3ZjVhMWQ4N2I4ZDM2YmIyIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6Img2NGNoNmlNa2l4ejFKbjVTeDR4Q0E9PSIsInZhbHVlIjoiQ1NreVlWd3J3SHlJOWNTQUlPV0lxRythYTdwZGJkS2NCamdrV0xLN3RjU0R5K1E2M0NHNlRZM1h" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Ik1zeDdiTHVwL0tjVkUwTmFlK2kxb3c9PSIsInZhbHVlIjoicS9TY0RpY0p1VkhoVmdKa00rMko2eXFWTGRla3dsUkFtQWRrbU5DTFF6TC9nYUh4cngzUlRKSmcyQU9oVldLbkwxR1hhWkZnMzR6NHhVT2hKM2JKbEhCRFViYjdXN1ZEd1B4Z1M4V2U0dW1DaDBWVkJaRlhMSWZSM1VwOFViWGsiLCJtYWMiOiJmMmVlNDkwMjYxODE1Zjk0Yzk5MWZhNDIyNmMxY2ZhZGY0YzNmMDQ3NjUzOTYxYWM5YTkwNWVhNmI5ZTRkNGJmIiwidGFnIjoiIn0%3D; expires=Thu, 20-Feb-2025 15:12:28 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6Ik1zeDdiTHVwL0tjVkUwTmFlK2kxb3c9PSIsInZhbHVlIjoicS9TY0RpY0p1VkhoVmdKa00rMko2eXFWTGRla3dsUkFtQWRrbU5DTFF6TC9nYUh4cngzUlRKSmcyQU9oVldLbkwxR1hhW" 1 => "alphaeurekaselectnet_session=eyJpdiI6Img2NGNoNmlNa2l4ejFKbjVTeDR4Q0E9PSIsInZhbHVlIjoiQ1NreVlWd3J3SHlJOWNTQUlPV0lxRythYTdwZGJkS2NCamdrV0xLN3RjU0R5K1E2M0NHNlRZM1hoTitRei92SW8xM256TDgvMmJmV0lJVjkzSmEvOXpSRE1vZzlpM3JVcmtzbGdnQzVnVFk4R2xsd2dzU1FrYm5QZEFUdjB4TzIiLCJtYWMiOiI1NzAyOWU4MWQ2MGU5MmMzYjM0OGIwYjUzOGQ3NWIyMjhhZDYwMzE0NGY4NTViZDQ3ZjVhMWQ4N2I4ZDM2YmIyIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6Img2NGNoNmlNa2l4ejFKbjVTeDR4Q0E9PSIsInZhbHVlIjoiQ1NreVlWd3J3SHlJOWNTQUlPV0lxRythYTdwZGJkS2NCamdrV0xLN3RjU0R5K1E2M0NHNlRZM1h" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "qwZxsr6naS7sl5yel43WMmyYX3zvnRbX3XHTkrys" "uc_cart_id" => "44089d207f3ceacf2a37af0496261510" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/4890" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-18 03:12:28GET/chapter/4890112196