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Energy and Buildings 71 (2014) 95–103

Contents lists available at ScienceDirect

Energy and Buildings

j ourna l ho me page: www.elsev ier .com/ locate /enbui ld

ffective reflectivity and heat generation in sucrosend PMMA mixtures

aria Paz Gutierreza,∗, Tarek I. Zohdib,1

Department of Architecture, University of California, Berkeley, United StatesDepartment of Mechanical Engineering, University of California, Berkeley, United States

r t i c l e i n f o

rticle history:eceived 24 May 2013eceived in revised form 11 October 2013ccepted 14 November 2013

eywords:ucroseMMA mixtureeflectivityeat generationhermal mass

a b s t r a c t

Recent efforts in the construction sector to develop panels made of agricultural waste and polymer mix-tures are becoming more frequent. These panels are usually developed in pursuit of low embodied energy,biodegradability and energy efficiency. PMMA’s transparency and structural advantages over other ther-moplastics is making this material progressively more common in faç ades. While advances in PMMA’srecyclability are under development, the process still presents multiple challenges regarding environ-mental efficiency and resulting structural integrity. It is important, therefore, to establish mixtures wherePMMA’s structural advantages are balanced with low carbon emission substrates, such as agriculturalwastes. Typically, agricultural waste in architectural panels is used for structural reinforcement (i.e.fibers). However, agro-derived materials such as sucrose have additional and/or alternative potentials inconstruction applications. Sucrose’s unique optical properties can be implemented for light and thermalcontrol. Additionally, since the energy losses of buildings concentrate in the envelopes another majorchallenge of cladding substrates pertains to how the faç ade material can improve energy efficiency, i.e.

acting as thermal mass while providing light transmission control avoiding conditions such as glare.Faç ade materials that can minimize environmental impact while supporting energy savings and appro-priate natural light conditions bear strong potential for advancing sustainable building technologies. Thisanalysis provides an expression for the overall reflectivity of combinations of sucrose and PMMA, as wellas, estimates of the thermal heating rate, as a function of the relative volume fractions and materialproperties.

. Introduction

.1. PMMA properties and building enclosures

From MIT/Monsanto’s House of the Future (1957) to Matti Suuro-en’s Futuro (1968), the earliest investigations of polymers inhe building industry primarily took a single-solution perspective,here polymers were used in every component possible [1, pp.

–24]. Since the 1970s, however, the increasing cost of petroleum

s well as an awareness of the environmental impact of polymersed to a reevaluation of their use in buildings. The enormously wideariety of properties and available characteristics led to a leveraging

∗ Corresponding author at: Department of Architecture, University of California,erkeley, 353 Wurster Hall, Berkeley, CA 94720-1820, United States.el.: +1 510 642 4942.

E-mail addresses: mpazgut@berkeley.edu, mpazgut@hotmail.comM.P. Gutierrez), zohdi@me.berkeley.edu (T.I. Zohdi).

1 Address: Department of Mechanical Engineering, University of California, Berke-ey, 6117 Etcheverry Hall, Berkeley, CA 94720-1740, United States.el.: +1 510 642 9172.

378-7788/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.enbuild.2013.11.046

© 2013 Elsevier B.V. All rights reserved.

of the strengths of individual polymers whose use became tailoredfor very specialized applications [2, pp. 10–16]. These uses rangefrom vapor barriers, protective coverings, paints, and insulation(Fig. 1A) applications. Amongst the most used thermoplastics inthese applications are polyethylene (PE), polyvinyl chlorine (PVC),and polystyrene (PS).

In the last decade, we have seen a rising interest in increas-ing the use of thermoplastics as building enclosures as films,surface cladding, and structural modules. From a more frequentuse of PC to EFTE, buildings with thermoplastics exteriors arebecoming increasingly ubiquitous. The desire to work with sub-strates of comparative transparency to glass that can also beeasily fabricated through digital processes for variable formaland esthetic effects in building faç ades is taking architects toexperiment with thermoplastics traditionally not used for exte-rior applications. With this purpose, architects are turning towardimplementing PMMA onto faç ades due to the material’s optic

and mechanical properties, as well as, easy forming and sur-facing characteristics (Fig. 1B). Acrylic faç ades currently cladlarge buildings in applications that reach over 500 m length(Fig. 1C).

dx.doi.org/10.1016/j.enbuild.2013.11.046http://www.sciencedirect.com/science/journal/03787788http://www.elsevier.com/locate/enbuildhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.enbuild.2013.11.046&domain=pdfmailto:mpazgut@berkeley.edumailto:mpazgut@hotmail.commailto:zohdi@me.berkeley.edudx.doi.org/10.1016/j.enbuild.2013.11.046

96 M.P. Gutierrez, T.I. Zohdi / Energy and Buildings 71 (2014) 95–103

Fig. 1. (A) Summary diagram by of typical applications of commonly used polymers in buildings based on [1,2,53]; (B) PMMA onto building faç ade fabricatedt and o ry Buh ing-by

irrtfcaeam

hrough CNC milling for variable translucency [2] (copyright 2007 by Squiref 6 mm thickness and 11 m height (reprinted from Enigmatic Curtain: Factottp://www.detail-online.com/architecture/topics/enigmatic-curtain-factory-build

The physical properties of PMMA give it a distinct advantagen selection over other thermoplastics currently used in exte-ior applications in buildings. One of its chief advantages is itselatively high weathering resistance (Fig. 2A). PC, often charac-erized as comparable to PMMA (mechanical and optic properties)or construction applications, does not weather well. PC typi-ally requires additives to prevent yellowing through time. ETFE,

progressively common material in high-performance buildings

nclosures, on the other hand weathers extremely well and isdvantageous as thermal barrier [3]. Nevertheless, ETFE’s ther-al performance is still arguable regarding typical glass and its

Fig. 2. Properties of thermoplastics used in exterior bu

Partners, reprinted with permission); (C) and (D) corrugated PMMA panelsilding by SANAA, In DETAIL-Online, n.d., Retrieved December 6, 2013, from-sanaa-021171.html, copyright 2013 by DETAIL, reprinted with permission).

structural properties render the material more suitable for thinmembrane applications (often air compression-based) rather thanas structural panels [4, pp. 486–495, 5]. It is important to notethat the mechanical properties of thermoplastics tend to be highlydependent on temperature and have a relatively narrow servicetemperature range. PMMA, for example, has a coefficient of ther-mal expansion nearly seven times that of steel. While it has theundesirable characteristic of a brittle failure mode, PMMA has a

high enough upper stress limit that renders it suitable for faç ade(panel) applications [2, pp. 225–285]. By contrast, the ductile PCand PE deform plastically under low stress (Fig. 2B).

ilding applications diagram by author from [2].

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M.P. Gutierrez, T.I. Zohdi / Ene

.2. Environmental and cost potential of PMMA and agriculturalaste mixtures

While PMMA offers multiple mechanical and weathering advan-ages when compared to other thermoplastics currently used inuilding enclosures it is a material that as most synthetic polymersequires high energy for manufacturing and have strong long termsnvironmental impacts. Literature has discussed largely this topicn life cycle analysis research [6, pp. 3436–3445]. In response to arowing awareness toward environmentally sensitive constructionaterials, research in bioplastics and natural waste-synthetic poly-er mixtures has been growing particularly since the past decade

7, pp. 19–26]. A significant field of research in biodegradableolymers pertains to the incorporation of agriculturally derivedarticles [8, pp. 822–825]. These mixtures offer various sustainabledvantages including biodegradability.

PMMA based mixtures are common to many industrial applica-ions (see http://www.marketsandmarkets.com/Market-Reports/olymethyl-methacrylate-pmma-market-715.html). In fact, thisompound has a higher blending compatibility with other thermo-lastics when compared to most common typical faç ade substratesPC, PE, PET) (Fig. 3) The broad range of compatibility of PMMA witharious naturally derived fillers, i.e. plant fibers, has led to expan-ive experimentation for construction applications. However, theseave concentrated fundamentally on interior finishes uses. Thexperimentation of naturally derived particles or fibers into PMMAatrices for exterior building applications remains largely unex-

lored. Nevertheless, this frontier can yield significant advantageshat range from weight to cost.

Advancements in PMMA and naturally derived particles mix-ures can also be highly beneficial from an environmentaltandpoint. Significant progress has occurred in plastic recy-lability particularly in the last decade [9]. However, PMMAecycling still presents some crucial challenges. For one part,MMA cannot be easily recycled to monomer by simple chem-cal methods unlike condensation polymers as PET [10, pp.564–2575]. The required processes for depolymerization ofMMA, including that the raw condensate of PMMA, may resultn contamination by the metal used or other byproducts ofhe recycling procedure. Research points toward advances inhe preservation of mechanical properties after the recycling ofhermoplastics. Tensile strain at break in PMMA and mixturesith this material [9] remains an exception to this progress.hile to some industries this may not be a relevant factor

n a faç ade application, tensile strain weaknesses are impor-ant for decrease in structural stability [2, pp. 134–150, 11, pp.0–119].

.2.1. Agricultural waste: sucrose potential for constructionLiterature has discussed extensively in the recent years the

otential advantages of incorporating agriculturally derived mate-ials including waste in construction. For most part researchersave focused in evaluating the structural advantages of mate-ials such as flax, hemp, rice husks, sugar cane bagasse, inoncrete [12,13]. In few cases, the structural advantages havelso been co-evaluated with thermal conductivity [14]. How-ver, other significant innovation fronts from agro-based materialsn construction (i.e. optical) remain largely unexplored. Sucroseistinguishes itself in this front due to its highly unique opti-al properties with a refractive index of equivalent ranges1.4–1.55) to clear glass or PMMA [15]. The use of agricul-ural waste in construction panels for optical control has strong

romise for various architectural applications. A key componentf human comfort pertains to balancing daylight transmis-ion to interior spaces without excess heat and preventinglare.

d Buildings 71 (2014) 95–103 97

Glare is defined as the excessive luminance and/or excessiveluminance ratios in the field of vision, fundamental in the determi-nation of visual comfort that must be prevented in daylit spaces.On the other hand, visual comfort on a work plane depends onboth the illuminance level and its distribution. These can be eitherdirect or discomfort glare, and reflected glare or veiling glare [16].If the light source is in the field of vision, we refer to it as directglare. Conversely, if caused by the reflection of a light source ona surface, literature refers to the phenomenon as reflected glare.Current building standards and codes require indoor illuminancelevels on the working plane, which vary widely among countriesand depend on the activity levels [17]. Several luminescence rec-ommendation ranges for tasks exist. Depending on the types ofbuildings and rooms, these ranges span from 200 to 2000 (lux)[38]. Literature estimates ∼50 foot candles on the working faceplane for appropriate light comfort levels [17]. In parallel, glazingincorporates through multiple advances in building technologiesand simulation, which span from films to electrochromic win-dows, new methods to control reflectivity effectively [18]. Intensiveresearch in this frontier points toward the need to improvingdaylight strategies and daylight availability metrics in buildings[19].

While large fenestrations provide good amounts of light andpleasant outdoor views they also contribute significantly to heatgains and/or losses, as well as, potential glare. Advances in trans-parent conductors with spectral selectivity, angular selectivity,and temporal chromatic variability, as well as double and tripleglazing have been widely discussed in literature [20–26]. IGDB(http://windowoptics.lbl.gov/data/igdb/igdb) provides an exten-sive optical data update for glazing (monolithic, laminate, appliedfilms, and coating) products. These products present a wide arrayof variations ranging from extremely low solar reflectance i.e. clearfloat glass (0.077 front and back-3 mm Optiglass) or commercialPMMA (0.07 front and back-3 mm Atofina) to coated glazing (0.438-front/0.535-back, ClimaGuard-on 3 mm clear glass). Fig. 4 presentsa sampling of current products in each category (monolithic, lam-inate, coating, and film) indexing the wide surface variabilityfrom ∼90% to 10% light absorption. The aforementioned literaturediscusses the integration of efficient reflectivity and thermal con-ductivity through various coating films technologies, double andtriple glazing systems. Mohelnikova [23] study presents new glaz-ing technologies with IR reflective thin film (45 nm TiO2–25 nmAg–45 nmTiO2) with reflectivity ∼0.3 used for effective reflectanceand thermal control. Glazing systems currently have a heat transfercoefficient of ∼1 W/m2 K. However, values of as ∼0.2 W/m2 K maybe possible by combining vacuum insulation with low-emittance-coated glass enabling a reduction of 80% of thermal conductivity[26].

More recently, researchers are developing models whichaddress the large impact in heat transfer of long wave radiation[heat exchange] between inside and outside surfaces through glaz-ing [27]. Wang et al. model defines that when the long radiationtransmittance of glass reaches 0.1 the effect of long-wave trans-parence radiation is substantial. This is comparable to the spectralradiation of low-e glazing ∼0.1 [23]. Advances in this area areimportant to typical transparent glass and a broad array of poly-meric glazing including PMMA [27].

In Table 1, we see a projection of the potential of a PMMA–sucrose mixture regarding material cost, embodied energyand carbon emission for a panel of a standard enclosuresize of: 3′ × 6′ × 1/4′′. We have chosen to compare thePMMA–sucrose mixture with transparent glass, pure PMMA,

PC, PE, and PMMA–bamboo mixture. The choice to evaluatea bamboo mixture stems from the fact that this substanceis recognized as the plant with probably the lowest embod-ied energy and carbon emission in construction. Bamboo’s

http://www.marketsandmarkets.com/Market-Reports/polymethyl-methacrylate-pmma-market-715.htmlhttp://www.marketsandmarkets.com/Market-Reports/polymethyl-methacrylate-pmma-market-715.htmlhttp://windowoptics.lbl.gov/data/igdb/igdb

98 M.P. Gutierrez, T.I. Zohdi / Energy and Buildings 71 (2014) 95–103

Fig. 3. PMMA blending capacities with polymers typically used in industry, diagram by author from Knippers et al. [2] and Rybnicek et al. [9].

Fig. 4. (A) Comparison of front surface reflectance of glazing types; (B) Comparison of back surface reflectance of glazing types; (C) Comparison of back and front surfacer indow

facc

t4mcasel

TS(w

F

=i

eflectance of glazing by types, diagram by author plotted from IGDB data (http://w

ootprint is lower than hemp or flax, which are widelycknowledged as extremely low carbon footprints materials inonstruction (http://www.eurostar-ep.com/en-us/news/12-149/arbonfootprint.aspx).

The PMMA–sucrose mixture panel (60% sucrose) has the poten-ial of a material cost of approximately 25% of the cost of glass and0% of the cost of a PMMA panel. In addition, the PMMA–sucroseixture panel (60% sucrose) would cost approximately 25% of the

ost of a PMMA and bamboo particle (60% bamboo) mixture. From

n environmental perspective, the PMMA–sucrose mixture (60%ucrose) panel has the potential of being 24% of the total embodiednergy of glass and 40% of a PMMA panel. Since bamboo has theowest carbon emission of all construction materials the fact that

able 1ucrose–PMMA mixture comparative projections (cost/panel, weight, embodied energy) wcost/panel, weight, embodied energy) for sucrose–PMMA mixture in comparison to tranith sucrose mixture [12–17].f

Cost Cost/ft2 Density (g/cm3

Transparent glassa $180.00 $10.00 2.5 PC $193.71 $10.76 1.2 PE $143.81 $7.99 0.92 PMMA $115.00 $6.40 1.19 Bamboo $230.00 $12.80 0.95 Sucrose $1.08 $0.06 1.55 40% PMMA/60% bamboo $184.00 $10.24 1.046 40% PMMA/60% sucrose $46.65 $2.62 1.35

rames vary substantially and so are not included in the weight for this comparison.a AGC – Planibel glass, 8 mm, mid-high end glass from one of the largest glass manufacb Estimate of embodied energy based on organic component (100% bamboo pulp).c Estimate of embodied energy based on organic component (100% sucrose).d Estimate of embodied energy based on organic component of panel at 60% bamboo pe Estimate of embodied energy based on organic component of panel at 60% sucrose cof See http://www.marketsandmarkets.com/Market-Reports/polymethyl-methacrylate-

sugar, http://comtrade.un.org/db/ce/ceSnapshot.aspx?px=H3&cc=441210, http://wwnterplastic.com.

optics.lbl.gov/data/igdb/igdb).

the PMMA–sucrose mixture at 60% sucrose concentration is threetimes higher and of equal low embodied energy is advantageous.This is particularly the case if we consider that the mixture useslow-grade sucrose crystals, costs only a quarter fraction, and hasthe potential significant energy savings derived from thermal massand optical properties for effective reflectivity.

1.3. Thermal storage and reflectivity potential of PMMA andsucrose mixture

In Table 2 we see that a PMMA panel has a significantly lowerthermal conductivity (0.18 W/mK) than a typical transparent glass(0.8 W/mK) or in comparison to typical thermoplastics used in

ith typical thermoplastics for building enclosures and PMMA mixtures. Projectionssparent glass, translucent glass, PC, PE, PMMA, PMMA with bamboo sheets, PMMA

) Panel size Embodied Energy GWP (kg CO2/kg)

3′ × 6′ × 0.25′′ 349.65 21.83′ × 6′ × 0.25′′ 78.92 11.663′ × 6′ × 0.25′′ 87.1 33′ × 6′ × 0.25′′ 207.3 14.73′ × 6′ × 0.25′′ 0.015b 0.23′ × 6′ × 0.25′′ 0.037c 313′ × 6′ × 0.25′′ 82.80d 63′ × 6′ × 0.25′′ 82.94e 24.48

turers worldwide.

articles.ncentration.pmma-market-715.html, http://www.indexmundi.com/commodities/?commodityw.eurostar-ep.com/en-us/news/12-149/carbonfootprint.aspxand http://www.

http://windowoptics.lbl.gov/data/igdb/igdbhttp://www.eurostar-ep.com/en-us/news/12-149/carbonfootprint.aspxhttp://www.eurostar-ep.com/en-us/news/12-149/carbonfootprint.aspxhttp://www.marketsandmarkets.com/Market-Reports/polymethyl-methacrylate-pmma-market-715.htmlhttp://www.indexmundi.com/commodities/?commodity=sugar, http://comtrade.un.org/db/ce/ceSnapshot.aspx?px=H3&cc=441210http://www.indexmundi.com/commodities/?commodity=sugar, http://comtrade.un.org/db/ce/ceSnapshot.aspx?px=H3&cc=441210http://www.eurostar-ep.com/en-us/news/12-149/carbonfootprint.aspxhttp://www.interplastic.com/http://www.interplastic.com/

M.P. Gutierrez, T.I. Zohdi / Energy and Buildings 71 (2014) 95–103 99

Table 2PMMA–sucrose mixture comparative projections (thermal conductivity, reflectivity) with typical thermoplastics for building enclosures and PMMA mixtures, and transparentglass. Comparative projection of PMMA–sucrose mixture panel (thermal conductivity, reflectivity) in relation to transparent glass, PMMA, PC, PET [2].

Thermal and optical properties

Thermal conductivity (W/m K) Reflectivity Transmissivity Refractive indexd

Transparent glassc 0.8–1.0 0.08 0.87 1.52PCb 0.32–0.40 0.09 0.76 1.585PE (film) 0.42–0.51 0.09 0.05e 1.575PMMAb 0.18 0.07 0.8 1.489PMMA with bamboo 0.031

a AGC – Planibel glass, 8 mm, mid-high end glass from one of the largest glass manufacturers worldwide.b t = 8 mm.

bstmciMrptgs1

mscpafo

eatrc

2

ttd

t(otf

R

wi

R∗ = IrIi

= �̂∗ − �̂∗√

�̂∗ −√

�̂∗(2.1)

c t = 3 mm.d At standard sodium doublet � = 589 nm.e Very low transmissivity at UV and visible spectrums.

uilding enclosures, i.e. PC (0.35 W/mK) and PE (0.45 W/mK) corre-pondingly. For internal climatic comfort and energy savings, thehermal conductivity of architectural enclosures is crucial. As afore-

entioned, building envelopes is the zone where energy losses areoncentrated [28,29]. Thermal mass is pivotal for energy efficiencyn buildings envelopes for various climate zones [30, pp. 763–773].

oreover, climate regions that benefit from thermal mass oftenequire decrease in transparency for internal spaces due to glareroduced by direct light [31, pp. 139–145]. In Table 2, we also seehat PMMA has a refractive index comparative or higher than clearlass ranging typically from 1.4 to 1.55 [32,33]. As aforementioned,ucrose also typically fits within a comparative refractive index of.4–1.5 [15] similar to clear glass and PMMA.

In an attempt to provide thermal insulation and daylight trans-ission control in building enclosures, architects, engineers, and

cientists are researching systems that can be translucent and effi-ient insulators, such as, PC with aerogel granules [34]. Hence, aanel system that can provide the weight, cost, and environmentaldvantages of a PMMA–sucrose substrate projected in Table 1 andunction as a thermal mass with effective reflectivity has strongverall potential for future energy efficient enclosures.

This paper evaluates synchronously the thermal storage andffective reflectivity potential of PMMA and sucrose mixtures for

future building material panel (Fig. 5). This study is set to narrowhe range of experiments (i.e. structural and weathering resistance)equired to evaluate this mixture’s potential for future faç ade appli-ations.

. Theory and calculation

Consider a beam of light incident upon a boundary separatingwo different materials, which produces a reflected wave and aransmitted (refracted/absorbed) wave (Fig. 5). The amount of inci-ent electromagnetic energy (Ii) that is reflected (Ir) is given by the

otal reflectance Rdef= Ir/Ii where 0 ≤ R ≤ 1, where R is given by Eq.1.1) for unpolarized electromagnetic radiation, where n̂ is the ratiof the refractive indices of the ambient (incident) medium (ni) andransmitted (absorbing) medium (nt), n̂ = nt/ni (see Gross et al. [35]or example)

= IrIi

= 12

⎛⎝( (n̂2/ �̂) cos �i + (n̂2 − sin2 �i)1/2(n̂2/ �̂) cos �i + (n̂2 − sin2 �i)

1/2

)2

+(

cos �i + (1/ �̂)(n̂2 − sin2 �i)1/2)2⎞⎠ , (1.1)

cos �i + (1/ �̂)(n̂2 − sin2 �i)1/2

here the refractive index is defined as the ratio of the speed of lightn a vacuum (c) to that of the medium (v), where c = 1/√�0�0 ≈

2.99792458 × 108 ± 1.1 m/s, � = 1/√��, (�) is the electric per-mittivity and (�) is the magnetic permeability.2 In Eq. (1.1), �̂is the ratio of the magnetic permeabilities of the surroundingincident medium (�i), and transmitted (absorbing) medium (�t),�̂ = �t/�i. We consider application where the magnetic perme-ability is, within experimental measurements, virtually the samefor both the matrix and particle phases. Thus, for the remain-der of the work, we shall take �̂ = 1(�0 = �i = �t) and, thus,n̂ = (nt/ni) =

√�t�t/�i�i ⇒ �t�t = (n̂)2�i�i ⇒ �t = (n̂)2�i, where

�i = �0 (vacuum permittivity). Notice that as n → 1 we have com-plete absorption, while as n → ∞ we have complete reflection. Thetotal amount of absorbed power by the material is (1 − R)Ii. Theangle between the point of contact of a beam (Fig. 5) and the out-ward normal to the surface at that point is the angle of incidence(�i).

The classical reflection law states that the angle at which abeam is reflected is the same as the angle of incidence and thatthe incoming (incident, �i) and outgoing (reflected, �r) beam laysin the same plane, and �i = �r. Furthermore, refraction law statesthat, if the beam passes from one medium into a second one (witha different index of refraction), and if the index of refraction ofthe second medium is less than that of the first, the angle the ray

makes with the normal to the interface ndef= (c/v) =√

��/�0�0 =(sin �i/ sin �t), �t being the angle of the transmitted ray (Fig. 5), c isthe propagation speed in the incident medium. Specifically, if thebeam is directly incident (�i = 0)

R = IrIi

=(

n̂ − �̂n̂ + �̂

)2=(√

�t/�i −√

�t/�i√�t/�i +

√�t/�i

)2

=(√

�̂ −√

�̂√�̂ +√

�̂

)2(1.2)

For more details see the cited literature [35–39, pp. 3125–3131,40–42, pp. 256–277, 43, pp. 969–981; 44–46].

2.1. Effective reflectivity of mixture

For mixtures of the chosen materials, we use the effective elec-tric permittivity �∗ and magnetic permeability �∗ to construct theeffective reflectivity:(√ √ )2

2 The free space electric permittivity is �0 = 1/c2�0 = 8.8542 × 10−12 C2N−1 m−2and the free space magnetic permeability is �0 = 4� × 10−7 WbA−1m−1.

100 M.P. Gutierrez, T.I. Zohdi / Energy and Buildings 71 (2014) 95–103

F gram o

an(wp((wmb

�︸

a

�︸

d

�

a

�

F

2

fe

m

cient strategies of energy saving and visual comfort researchersmust consider multiple aspects of daylighting and lighting control

ig. 5. (A) Mixture sucrose PMMA panel prototype; (B) incoming beam of light diaf PMMA–sucrose mixture.

For example, for a two-phase medium, relatively simple uppernd lower estimates for the effective electric permittivity and mag-etic permeability are the so-called Wiener [42] bounds:

�2�2

+ 1 − �2�1

)−1≤ �∗ ≤ �2�2 + (1 − �2)�1 (2.2)

here �2 is the volume fraction of the particles (phase 2), �2 is theermittivity of the particles, �1 is the permittivity of the matrixphase 1) and

�2�2

+ 1 − �2�1

)−1≤ �∗ ≤ �2�2 + (1 − �2)�1 (2.3)

here �2 is the permeability of the particles and �1 is the per-eability of the matrix. Hashin and Shtrikman [39] gave sharper

ounds of the electric permittivity and magnetic permeability:

1 +�2

(1/�2 − �1) + (1 − �2/3�1) ︷︷ ︸

�∗,−

≤ �∗ ≤ �2 +1 − �2

(1/�1 − �2) + (�2/3�2)︸ ︷︷ ︸�∗,+

(2.4)

nd

1 +�2

(1/�2 − �1) + (1 − �2/3�1) ︷︷ ︸

�∗,−

≤ �∗ ≤ �2 +1 − �2

(1/�1 − �2) + (�2/3�2)︸ ︷︷ ︸�∗,+

(2.5)

Simple approximations for the effective parameters can beetermined by taking the average of the bounds:

∗ ≈ 12

(�∗,+ + �∗,−) (2.6)

nd

∗ ≈ 12

(�∗,+ + �∗,−) (2.7)

or more details see Zohdi [47].

.2. Heat generation

The amount of heat absorbed by a wall can be approximated

rom an energy balance where we assume that all of the absorbednergy is converted into heat, ignoring convection and conduction:

CdT

dt= IabsorbedA = (1 − R∗)IiA, (2.8)

of PMMA–sucrose mixture; and (C) convective and radiative heat transfer diagram

where A is the area of the wall, m is the mass of the wall mixture, Cis the heat capacity of the wall mixture given by:

mC ≈ ((�C)1�1 + (�C)2�2)V (2.9)where V is the volume of the wall and � is the density. Solving forthe rate of temperature increase yields

dT

dt= (1 − R

∗)IiA((�C)1�1 + (�C)2�2)V

(2.10)

2.3. Sucrose–PMMA mixture panel example

Below we provide an example of the heat generation andreflectivity of a wall with typical faç ade panel characteristics. Theselected data is approximated from existing literature [48,49].3

• Relative electric permittivity for phase 1 (PMMA binder): �1r =�1�0

= 2.5• Relative electric permittivity for phase 2 (sucrose particles): �2r =

�2�0

= 3.5• Relative magnetic permeability for phase 1 (PMMA binder): �1r =

�1�0

= 1.0• Relative magnetic permeability for phase 2 (sucrose particles):

�2r = �2�0 = 1.0• The density for phase 1 (PMMA binder): �1 = 1200 kg/m3• The density for phase 2 (sucrose particles): �2 = 1150 kg/m3• The heat capacity for phase 1 (PMMA binder): C1 = 1466 W/kg• The heat capacity for phase 2 (sucrose particles): C2 =

1244 W/kg K• The incident radiation is Ii = 1367 W/m2 (maximum intensity)• Wall dimensions are L × W × t = 10 m × 3 m × 0.0254 m

In the case that the magnetic permeabilities are equal, we simplyuse the common value.

See Fig. 6 for results for R∗ and the normalized effective heatingrate, defined as:

H∗def= (dT/dt)(�2)(dT/dt)(v2 = 0)

(3.1)

3. Results and discussion

The energy for spatial cooling amounts to more than 75% of theelectrical peak load in hot climates [50]. Thus, the need to advancethermal conductivity in envelopes is fundamental. To achieve effi-

(i.e. daylight factor, illuminance and luminance, and glare index).

3 See http://www.rgpballs.com.

M.P. Gutierrez, T.I. Zohdi / Energy an

Fig. 6. Parameter study for R∗ and H∗ varying the volume fraction of phase 2 (sucroseparticles).

Fig. 7. Comparison diagram of reflectivity of monolithic panels (glazing, PMMA, PC,

d Buildings 71 (2014) 95–103 101

Daylighting provides ample benefits for productivity and poten-tial energy savings when combined with artificial lighting systemsthrough lighting control techniques [51]. The primary sources forluminance distribution are the sun, sky, buildings, and ground [52].Daylighting design must take in consideration latitude, climate, andbuilding orientation, since all these factors affect daylight availabil-ity. This term refers specifically to the amount of daylight availablefrom the sun and the sky at a specific location, time, date, and skycondition [52].

New materials and simulation advances evidence the needand awareness to advance glazing systems with integrative ther-mal and reflectivity advantages including in polymeric substrates.With this basis, we evaluate a material mixture that decreasesheat gains while providing efficient reflectivity contributing toglare prevention and potential energy savings. This paper providessimple estimates for the overall reflectivity and the overall heatabsorption rate as a function of Sucrose and PMMA properties. ThePMMA–sucrose mixture could be used as the material matrix offaç ade panels in combination with reduced transparent glazing todecrease heat gains and losses and minimize or eradicate glare

through effective reflectivity. For our first estimates of reflectivityof the PMMA–sucrose mixture, we assume an incident radiation of1367 W/m2.

and estimates of PMMA/sucrose mixtures of 20%, 40% and 60% concentration).

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An understanding of the combination effect between opticalnd thermal properties is important to achieve the applicabilityf the PMMA–sucrose structure. In this simulation, we com-ared the reflectivity and normalized heating rate as a functionf the volumetric fraction of sucrose in the mixture. As seen inig. 6, the fraction of sucrose in the wall assembly significantlyffects its potential performance as an applied material. Basedn the increased reflectivity and absorption as the percentage ofucrose increases, transmission of electromagnetic radiation mustecrease. Varying the percentage of sucrose should therefore affecthe direct transfer of light and heat.

Fig. 6 presents that the mixture would have an 83% light absorp-ion (Pure PMMA) at 0% sucrose with an decrease to 65% [40%ucrose concentration] and to 45% [80% sucrose concentration] cor-espondingly. Hence, the effective reflectivity increases around 50%ith a concentration of approximately 80% of sucrose.

Fig. 7 shows the relatively high values of reflectance (visibleavelength) for various concentrations of sucrose in the mixture.

his allows the mixture to reduce the amount of transmitted lighto the interior space without absorbing and reemitting the excessnergy. The projections presented in Fig. 7 point a 28% reflectiv-ty for 20% sucrose concentration; 35% reflectivity for 40% sucroseoncentration and 42% reflectivity for 60% sucrose concentrationor the panels. Commercial PMMA (Plexiglass) of 6 mm averages% reflectivity based on IGDB data. Utilizing this strategy allowsor relatively high thermal insulation without a reliance on low-Eoatings or multiple-pane window systems. For areas that requireaylight control this system could be a very cost-effective solution.

The normalized heat rate in Fig. 6 projects a 15% reduction at 20%ucrose concentration. The heating rate reduction at 60% and 80%ucrose concentration is of 20% and 25% correspondingly. At a fulloncentration of sucrose the table presents a reduction of approxi-ately one third (heating rate) in comparison to pure PMMA. Fig. 6

resents a potential range of optimized reduction between 15% and0% in heating rate and an effective reflectivity between 65% and0% at 60% sucrose concentration in comparison to pure PMMA.

The incorporation of substrates as monolithic aerogel is present-ng promising results in higher effective reflectivity and thermaleduction of glazing. Buratti and Moretti [53] demonstrated thatonolithic aerogel glazing has the best performance with respect

o granular aerogel for light transmittance (0.62 between two 4 mmoat glasses) and thermal insulation (0.6 W m−2 K−1) under a solar

actor of 0.74. The study presents that monolithic aerogel betweenwo 4 mm float glasses enabled a 62% reduction in heat losses, and

17% reduction in light transmittance when compared to a doublelazing with a low-e coating [53]. The concentration range between0% and 60% sucrose appears to be the most promising in the PMMAucrose mixture, concerning heating decrease potential and effec-ive reflectivity. The next phase of research will focus on this range40–60% sucrose concentration) to test empirically the heating rate,eflectivity and mechanical properties of the mixture.

. Conclusions

Significant advances in thermal efficiency of transparent faç adesave been made in recent years particular through surface treat-ent technologies, such as high-performance films or active dyes.owever, research in heat generation in exterior glazing derived

rom agricultural waste mixtures remains largely uncharted terri-ory. In addition, while transparent substrates can be excellent foright conservation in buildings, often, there is need to control glarer increase privacy. Hence, research in new faç ade panels that can

upport energy generation and efficient reflectivity bear a strongotential for future building technologies.

The heating storage potential of the PMMA–sucrose mix-ure depends significantly in the concentration of sucrose. Our

d Buildings 71 (2014) 95–103

simulation results indicate that the best condition to achieve opticaland thermal advantages for heat storage and effective reflectivityin faç ade applications is ∼0.5 of sucrose concentration. In this zone,the normalized heating rate is of a 20% reduction with a decrease inlight absorption to 60% in comparison to 83% in pure PMMA. In par-allel, if a higher need of reflectivity comparable or above existingIR thin film coatings or monolithic aerogel is required, a concentra-tion range (60–75% sucrose) would be suitable. This would providean advantageous normalized heating rate with almost a one thirdreduction in regards to pure PMMA. However, this range in prin-ciple presents more structural challenges. These simple simulationestimates present that the incorporation of sucrose into a PMMAsubstrate can potentially yield a substrate that operates as thermalmass and diffuses natural sunlight for combined energy savings andvisual comfort.

When compared to alternative research of granular or particle-based infill for integrated thermal and optical performance ofbuilding enclosure panels our study provides a first indication of theadvantages of agricultural waste in lieu of synthetic compounds forlow cost and environmentally sensitive solutions. The knowledgeprovided by this study is valuable since it opens up new opportu-nities for incorporating agricultural waste in building compositesthat can act as thermal mass and have effective reflectivity with lowmaterial cost and low manufacturing energy. Projected estimatesindicate that the use of the PMMA–sucrose mixture can providecost-effective energy savings (thermal mass) and glare control forhuman comfort occupation. In combination, the mixture has thepotential of significant low embodied energy decreasing the needfor recycling pure PMMA, which up to date still presents multiplechallenges.

The simulations presented in this paper enable a significantdecrease in future physical testing of the PMMA–sucrose mixtureswhere additional parameters, such as fatigue and compressivestrength, must be integrated for a comprehensive evaluation ofconstruction suitability of the resulting material. The definitionof a significantly smaller test is advantageous for time efficiencyand decrease of unnecessary material waste. Future research willseek to: (i) test the fatigue behavior of PMMA–sucrose mixturesfor a range of 40–60% concentration (sucrose); (ii) evaluate energysavings benefits for thermal mass and effective reflectivity ofPMMA–sucrose mixtures for a range of 40–60% concentration foroffice buildings situated in cold and temperate climates in compar-ison to low-e and coated glazing panels; (iii) identify the structuralpotential of PMMA–sucrose in comparison to existing panels ofrecycled PMMA; (iv) identify the greatest potential for CO2 sav-ings over the life cycle of PMMA–sucrose in comparison to existingpanels of recycled PMMA.

References

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[2] J. Knippers, J. Cremers, M. Gabler, J. Lienhard, Construction Manual for Poly-mers + Membranes, Birkhauser Architecture, Basel, 2011.

[3] A.W. LeCuyer, I. Liddell, S. Lehnert, B. Morris, ETFE: Technology and Design,Birkhäuser, Basel, Boston, 2008.

[4] A. Watts, Modern Construction Envelopes, Springer, New York, 2011.[5] E. Dimitriadou, A. Shea, Experimental Assessment and Thermal Characteriza-

tion of ETFE Foil, 2012.[6] K.-H. Kim, A comparative life cycle assessment of a transparent composite

faç ade system and a glass curtain wall system, Energy and Buildings 43 (12)(2011) 3436–3445.

[7] A.K. Mohanty, M. Misra, L.T. Drzal, Sustainable bio-composites from renewableresources: opportunities and challenges in the green materials world, Journalof Polymers and the Environment 10 (1–2) (2002) 19–26.

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