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注塑成型中顆粒填充物聚丙烯的冷卻情況
摘要：聚丙烯復(fù)合材料的冷卻情況被用于在同一注塑成型過(guò)程中，對(duì)影響散熱性能的各種填料（磁鐵礦，重晶石，銅，滑石，玻璃纖維和鍶鐵氧體）于不同比例下的調(diào)查。注塑成型期間，分別對(duì)室溫和高溫時(shí)熱電偶在型腔模具表面的測(cè)量記錄和對(duì)斜坡冷卻曲線的熱擴(kuò)散分析中發(fā)現(xiàn)：該注射成型的工藝和該模具的填充材料使冷卻曲線顯示出不同的合并路段。所以說(shuō)熱擴(kuò)散系數(shù)是個(gè)暫時(shí)性的系數(shù)。熱擴(kuò)散表明，最高值為30％的滑石粉填充聚丙烯，在最短的冷卻時(shí)間可以發(fā)現(xiàn)35％銅填充聚丙烯。系統(tǒng)性變化的具有熱傳遞性能的復(fù)合材料，在不同的填充材料和填充比例中使注塑過(guò)程優(yōu)化，并以此來(lái)定制熱流性能。此外，滑石粉填充聚丙烯使設(shè)計(jì)的復(fù)合材料與預(yù)定的最高熱流相附，是熱傳遞的首選方向。
關(guān)鍵詞：聚丙烯 ;熱性能;注塑成型;微粒填料
1 .導(dǎo)言
常用的塑料，如聚丙烯和聚酰胺都有一個(gè)低導(dǎo)熱系數(shù)。不過(guò)在汽車行業(yè)，如傳感器或執(zhí)行器，需要新的材料或具有高導(dǎo)熱性。通過(guò)增加合適的填料，比如塑料，其熱行為聚合物是可以改變的。系統(tǒng)的熱擴(kuò)散大于1.2/秒，從0.2/秒多為補(bǔ)聚丙烯。這種填充聚合物具有較高的熱導(dǎo)率，由于廣泛的應(yīng)用在電子封裝上而成為一個(gè)越來(lái)越重要的研究領(lǐng)域。較高的熱導(dǎo)率可以通過(guò)使用一個(gè)合適的填料達(dá)到，如鋁，碳纖維和石墨，鋁氮化物或磁鐵礦顆粒。此外，在注塑機(jī)上模具的冷卻反應(yīng)，是受聚合物填料的熱性能影響。然而，填充材料比較能體現(xiàn)出熱導(dǎo)率的價(jià)值觀。大幅比較不同的材料，是很困難的，甚至可以說(shuō)是不可能的。 因此，聚丙烯樣品不同的填充劑（四氧化三鐵，硫酸鋇，銅，玻璃纖維， 滑石粉）的擠出和注射成型用各種體積分?jǐn)?shù)（ 0-50 ％ ）來(lái)表示 。
磁鐵礦重晶石一般是用來(lái)增加重量的聚丙烯，如：為一瓶措施，鍶鐵氧體是用聚合物粘結(jié)磁鐵，玻璃纖維是用于加固新材料，滑石粉是一種反阻斷劑。然而， 銅被選為額外灌裝機(jī)，因?yàn)樗哂懈叨鹊臒釋?dǎo)率相對(duì)于其他材料。 熱性能，這些注射成型樣品和注塑成型行為人調(diào)查和相關(guān)的金額和種填充材料。
2 .理論思考
傅立葉法的熱量傳遞，在一維給出
與溫度T ，時(shí)間t ，位置x和熱擴(kuò)散在一個(gè)均質(zhì)體，熱擴(kuò)散率A和熱導(dǎo)率L是相互關(guān)聯(lián)的，由具體密度r 和具體的熱容量Cp根據(jù)
假設(shè)一名注射成型工藝與恒溫灌漿期為聚合物的溫度TP和相對(duì)恒定的溫度Tm及作為溫度獨(dú)立的熱擴(kuò)散，解析解決式（ 1 ）結(jié)果
在式（ 3 ） ,S是指壁厚注射模壓部分和T的溫度zai 時(shí)間t后注射。忽略高階計(jì)算，式（ 3 ） 可以減少為
式（ 4 ）給出的關(guān)系冷卻速度和熱擴(kuò)散率，在注射成型過(guò)程中，凡高熱擴(kuò)散導(dǎo)致更高的冷卻速度和短周期的過(guò)程。
3 .實(shí)驗(yàn)
3.1 材料
試驗(yàn)材料供應(yīng)合作編寫RTP的有限公司（法國(guó)）幾種聚丙烯（ PP ）化合物與各種填料（四氧化三鐵，硫酸鋇，銅，玻璃纖維，滑石粉）在擠出過(guò)程中講到的類似在式 [ 2 ] 。填充物材料是常用材料在工業(yè)產(chǎn)品。填料粒子不具備表面涂層可以影響熱性能。一些選定的性能灌裝材料列在表1
圖1.模具注塑成型實(shí)驗(yàn)。
圖 2 .模具與腔準(zhǔn)備測(cè)試樣本，在一個(gè)注塑機(jī)。立場(chǎng)與熱電偶溫度測(cè)量標(biāo)志是一個(gè)箭頭。
3.2 熱擴(kuò)散率測(cè)量
熱擴(kuò)散的高分子材料，是衡量一個(gè)瞬態(tài)法，與雷射閃光實(shí)驗(yàn)有密切的關(guān)系。溫度信號(hào)由熱電偶轉(zhuǎn)移到上側(cè)的抽樣檢驗(yàn)和注冊(cè),被轉(zhuǎn)讓溫度信號(hào)啟動(dòng)一個(gè)熱平衡過(guò)程該標(biāo)本，記錄由熱電偶作為區(qū)別樣品的背面和恒定溫度，用來(lái)為評(píng)價(jià)的熱擴(kuò)散率。最小二乘算法是用來(lái)確定熱擴(kuò)散率，而變系統(tǒng)地?zé)釘U(kuò)散值在一個(gè)特別設(shè)計(jì)差分計(jì)劃。精確的測(cè)量多于總量的3 ％ 。 為熱擴(kuò)散率測(cè)量，小缸10毫米直徑5-6毫米的身高，剪下的注射成型棒（參見(jiàn)圖1 ） 。
3.3 注塑成型
與注塑機(jī)標(biāo)準(zhǔn)樣品測(cè)量拉伸性能連同一棒熱測(cè)量10毫米直徑和130毫米的長(zhǎng)度分別準(zhǔn)備在一模（參見(jiàn)圖1 ） 。在腔的拉伸試驗(yàn)棒鉻（ K型）熱電偶中的應(yīng)用。 在注塑成型實(shí)驗(yàn)溫度記錄每0.5秒一個(gè)數(shù)字萬(wàn)用表和儲(chǔ)存在一臺(tái)個(gè)人電腦。熱電偶s大約0.2毫米成空腔。因此，一個(gè)良好的熱之間的接觸聚合物和熱電偶，甚至后縮的成型，是為了保證錄得更好的溫度時(shí)間。用過(guò)的注射液成型參數(shù)列于表2 。由此時(shí)代特征的注塑成型周期提交見(jiàn)表3 。
4 結(jié)果與討論
圖 3 比較冷卻曲線填補(bǔ)聚丙烯與聚丙烯復(fù)合材料的各種填料組分的四氧化三鐵。
在圖 3 中，聚丙烯的冷卻過(guò)程在一個(gè)時(shí)間在溫度測(cè)量所熱電偶達(dá)到最高值約。 隨著越來(lái)越多的時(shí)間觀測(cè)到溫度下降。 經(jīng)過(guò)在模具打開(kāi)，冷卻行為記錄與熱電偶變化，因?yàn)樗菬o(wú)較長(zhǎng)的接觸與注射成型的材料。由于以大直徑的棒，這個(gè)時(shí)間（） ，直到模具是打開(kāi)及注射成型零件跳傘選擇相對(duì)較高，以確保該部分肯定凝固。 可以看出，在圖 3斜率曲線變化顯著后，這對(duì)應(yīng)于時(shí)間那里后，壓力是拆除。此外，圖。三指出這種復(fù)合材料在腔降溫快隨著越來(lái)越多的磁鐵礦分。要達(dá)到的溫度條-溫度遠(yuǎn)遠(yuǎn)低于凝固的采樣聚丙烯需求，在描述實(shí)驗(yàn)的時(shí)候，，而冷卻時(shí)間聚丙烯的Fe3O4減至（參看表四） 。減少冷卻時(shí)間，是在好的協(xié)議所增加的熱擴(kuò)散的磁鐵礦填充復(fù)合材料由于高的熱擴(kuò)散粒子（參見(jiàn)附表一） ，其中的線索，就式（ 4 ） ，以一個(gè)增加冷卻速度。溫度時(shí)間依賴性圖。 3條不遵循一個(gè)簡(jiǎn)單的線性行為預(yù)期溫度-時(shí)間曲線由式（ 4 ）在對(duì)數(shù)計(jì)。 只為填補(bǔ)聚丙烯實(shí)測(cè)值可安裝一個(gè)單一的直線之間大約15 和第54秒的這條路線通往一個(gè)擴(kuò)散（參見(jiàn)式（ 4 ） ） 。其他測(cè)量冷卻曲線的聚丙烯復(fù)合材料的磁鐵礦裝有在每個(gè)個(gè)案，兩直線，為高溫第和低溫的地區(qū)。熱擴(kuò)散估計(jì)從斜坡上的回歸直線
計(jì)算熱擴(kuò)散系數(shù)的的溫度較高部分的冷卻曲線有一點(diǎn)點(diǎn)低于擴(kuò)散系數(shù)測(cè)量暫態(tài)技術(shù)，而計(jì)算熱擴(kuò)散酶的溫度越低，部分地區(qū)的冷卻曲線滿足實(shí)測(cè)值擴(kuò)散圖 3 比較冷卻曲線填補(bǔ)聚丙烯與聚丙烯復(fù)合材料的各種填料組分的四氧化三鐵。該符號(hào)字里行間都回歸直線（參見(jiàn)文） 。
圖 4顯示測(cè)得的熱擴(kuò)散率數(shù)據(jù)的調(diào)查樣本中可以看出， 該熱擴(kuò)散的磁鐵礦-聚丙烯復(fù)合材料是由為填補(bǔ)聚丙烯截至 增加磁鐵礦負(fù)荷。因此，冷卻時(shí)間變短為高磁鐵礦填料餾分（圖三） 。 原因之一，為改變?cè)谶吰碌睦鋮s曲線顯示圖3是改變熱擴(kuò)散率隨溫度的，其中就表現(xiàn)在是圖 5 磁鐵礦和重晶石聚丙烯復(fù)合材料隨著溫度的升高熱擴(kuò)散率降低。因此，價(jià)值觀來(lái)自模實(shí)驗(yàn)應(yīng)小于測(cè)值的復(fù)合材料在室溫。 熱擴(kuò)散的PP基體中，主要是所造成的聲子，是關(guān)系到等于無(wú)害速度v和平均自由程長(zhǎng)度L聲據(jù)上述凝固溫度的影響PP基體（約條，測(cè)量的DSC ） ，熱擴(kuò)散的基質(zhì)減少，以致降低了體積彈性模量k ，因而減少了聲子速度 ，并降低平均自由程的長(zhǎng)短 。此外，上述凝固溫度日Ts無(wú)晶在聚丙烯矩陣是在低于Ts結(jié)晶下在聚丙烯基體中出現(xiàn)的。存在或缺乏微晶影響體積彈性模量K和聲子自由的道路。其原因是不同實(shí)驗(yàn)都是非等壓條件在注塑成型過(guò)程和非等溫條件樣品的厚度的冷靜過(guò)程，磁鐵礦，重晶石，玻璃纖維， 滑石，永磁鐵氧體和銅填料比較空聚丙烯圖 6 冷卻的過(guò)程與銅填充聚丙烯存在差異。
圖 4 在室溫下熱擴(kuò)散價(jià)值觀注射成型聚丙烯樣品中不同填料和各種填料的比重來(lái)衡量暫態(tài)技術(shù)（參見(jiàn)文）
圖 5 溫度依賴性的熱擴(kuò)散的磁鐵礦和重晶石填充聚丙烯的填料含量
圖 6聚丙烯復(fù)合材料的填料在30vol%后
銅填充復(fù)合降溫速度遠(yuǎn)遠(yuǎn)超過(guò)其他調(diào)查材料。該溫度的影響剩余聚丙烯是，在整個(gè)注射液成型工藝高于氣溫其他調(diào)查材料。冷靜的過(guò)程與其他復(fù)合材料沒(méi)有顯示有較大的差別。該氣溫的磁鐵礦裝聚丙烯是一種比溫度低一點(diǎn)的重晶石填充聚丙烯。氣溫的鍶鐵氧體聚丙烯復(fù)合材料，再次是低于那些該磁鐵礦填充聚合物。 而測(cè)得的熱擴(kuò)散率的滑石粉填充聚丙烯是遠(yuǎn)高于熱擴(kuò)散其他調(diào)查材料，甚至遠(yuǎn)高于這對(duì)銅填充聚丙烯，冷卻行為滑石粉是較小較其他調(diào)查材料。魏登費(fèi)勒等人研究出該滑石粉沿著自己的方向填充復(fù)合一個(gè)對(duì)齊的滑石粉。測(cè)量的熱擴(kuò)散率是平行于這個(gè)主軸的最高熱導(dǎo)率，而溫度測(cè)量在注塑成型過(guò)程中揭示擴(kuò)散垂直流方向發(fā)展。這意味著，該滑石粉填充聚丙烯樣品中有強(qiáng)烈各向異性最高并在流動(dòng)方向低垂直于水流。盡管出現(xiàn)了高導(dǎo)熱的銅（參看表1 ）相對(duì)于其他用于填充材料， 冷靜是相對(duì)的測(cè)氣溫的。結(jié)果表明：這是一個(gè)相對(duì)的措施，一個(gè)最理想的互聯(lián)網(wǎng)絡(luò)的高導(dǎo)電粒子在聚丙烯基體，低于1 ％ 和極差相比，互聯(lián)磁鐵礦55 ％或互聯(lián)的重晶石46 ％。 作者還討論了影響顆粒大小和形狀的聚丙烯矩陣[ 2,3 ] 。
圖 7 各種聚丙烯復(fù)合材料的冷卻時(shí)間（從200下降到60度）
冷卻時(shí)間是線性依賴于填料量分?jǐn)?shù)在聚丙烯基體中，數(shù)據(jù)計(jì)算回歸系列于表6 。它可以清楚看出，銅填充聚丙烯降溫下降速度，遠(yuǎn)遠(yuǎn)超過(guò)其他調(diào)查材料。冷卻的情況，聚丙烯重晶石， 鍶氧體和磁鐵礦是相似的，而磁鐵礦降溫一點(diǎn)點(diǎn)速度比所有其他材料。
5 結(jié)論
冷靜的過(guò)程中聚丙烯在注塑成型工藝可以減少所使用的磁鐵礦重晶石，鍶鐵氧體，玻璃纖維，滑石粉和銅填料。 冷卻過(guò)程中，由于的依賴了傳熱和潛熱凝固溫度，所以不能完全解釋由簡(jiǎn)單指數(shù)律來(lái)自傅立葉的法熱傳導(dǎo)。此外，在注射成型周期，的注射液成型周期和熱擴(kuò)散的聚丙烯矩陣周期，冷卻曲線顯示不同的合并路段。 此外，各向異性的熱傳導(dǎo)性，例如： 為滑石粉填充物，或低互聯(lián)的粒子影響冷卻行為，如銅。 為使用的材料和在調(diào)查范圍填料冷卻時(shí)間冷卻下來(lái)注射成型復(fù)合材料，從溫度200 降至60是線性依賴于填料。銅在聚丙烯基體中的冷卻時(shí)間可縮短從50.5 至20，9秒。在這個(gè)過(guò)程循環(huán)中，具有較高熱傳遞性能的一些復(fù)合材料，可以用來(lái)優(yōu)化模具進(jìn)程提高冷卻速度。
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Cooling behaviour of particle filled polypropylene during injection moulding process
Abstract
The effects of thermal properties of various fillers (magnetite, barite, copper, talc, glass fibres and strontium ferrite) in various proportions on the cooling behaviour of polypropylene matrix composites are investigated in an injection moulding process. A thermocouple in the cavity of the mould records the temperatures at the surface of the composite during injection moulding. From the slope of the cooling curves the thermal diffusivities of the composites are estimated and compared with thermal diffusivities at room temperature and elevated temperatures measured with a transient technique. The cooling curves show different merging sections affected by the after pressure, the diffusivity of the composite and the diffusivity of polypropylene matrix. The cooling behaviour depends on the anisotropic thermal diffusivity of the used composite, which is caused by the alignment of filler material due to the injection moulding process and the interconnectivity of the filler particles. The thermal diffusivity shows the highest value for 30 vol% talc filled polypropylene, whereas the shortest cooling time was found for 35 vol% copper filled polypropylene. The knowledge of the systematic variation of thermal transport properties of composites due to different filler material andfiller proportionsallows to optimizethe mould process and tocustomize the heat flow properties. Furthermore,the strongly anisotropic thermal transport properties of talc filled polypropylene allow the design of composites with a predefined maximum heat flow capability to transport heat in a preferred direction.
Keywords: A. Polymer–matrix composites (PMCs); B. Thermal properties; E. Injection moulding; Particulate filler
1. Introduction
Commonly used plastics, such as polypropylene and polyamide, have a low thermal conductivity. However, new applications, mainly in automotive industries, e.g. for sensors or actuators, require new materials with an enhanced or high thermal conductivity [1]. By the addition of suitable fillers to plastics, the thermal behaviour of polymers can be changed systematically up to significant higher thermal diffusivity of O1.2 mm2/s from 0.2 mm2/s for unfilled polypropylene [2,3]. Such filled polymers with higher thermal conductivities than unfilled ones become more and more an important area of study because of the wide range of applications, e.g. in electronic packaging [4–6]. The higher thermal conductivity can be achieved by the use of a suitable filler such as aluminium [1], carbon fibres and graphite [7], aluminium nitrides [6,8] or magnetite particles [2]. Also, the cooling behaviour in the mould of the injection moulding machine is influenced by the thermal properties of the polymer-filler composite. However, published values of thermal conductivities of the same filler materials in different polymer matrices vary drastically and a comparison of different materials is difficult or at least impossible [2]. Therefore, polypropylene samples with different com- mercially available fillers (Fe3O4, BaSO4, Cu, glass fibres, talcandSrFe12O19)werepreparedbyextrusionandinjection moulding using various volume fractions (0–50%). Magne- tite and barite are generally used to increase the weight of
polypropylene, e.g. for bottle closures (cosmetics industry,cf. Ref. [10]), strontium ferrite is used in polymer bonded magnets, glass fibres are used for the reinforcement of materials, and talc is an anti-blocking agent. However,copper was chosen as additional filler because of its high thermal conductivity compared to the other materials.The thermal properties of these injection moulded
samples and the injection moulding behaviour were investigated and correlated to the amount and the kind of filler material.
2. Theoretical considerations
The Fourier law of heat transport in one dimension is given by
withtemperatureT,timet,positionxandthermaldiffusivitya.In an homogeneous body, thermal diffusivity a and thermal conductivity l are interrelated by specific density r and specific heat capacity cpaccording to
Assuming an injection moulding process with an isothermal filling stage for a polymer with a temperature TPand a constant temperature of the mould TMas well as a temperature independent thermal diffusivity a, an analytical solution of Eq. (1) results in [9]
In Eq. (3), s denotes the wall thickness of the injection moulded part and T the temperature of the moulding after time t after injection. Neglecting higher order terms, Eq. (3) can be reduced for the position xZs/2 to
Eq. (4) gives a relation between cooling rate and thermal diffusivity in an injection moulding process, where high thermal diffusivities result in a higher cooling rate and shorter process cycles.
3. Experimental
3.1. Materials
Test materials were supplied by Minelco B.V. (The Netherlands). Minelco B.V. prepared in cooperation with RTP s.a.r.l (France) several polypropylene (PP) compounds with various fillers (Fe3O4, BaSO4, Cu, glass fibres, talc and SrFe12O19) in an extrusion process similar to that described in Ref. [2]. The filler materials are commonly used materials in industrial products. The filler particles do not have a surface coating which can affect thermal properties. Some selected properties of the filler materials are listed in Table 1.
Fig. 1. Photograph of the used mould for the injection moulding experiments. The mould consists of a standard tensile test sample and a test bar for the measurement of thermal diffusivity.
Fig. 2. Mold with cavity for preparing test samples in an injection moulding machine. The position of the thermocouple for temperature measurements is marked by an arrow.
3.2. Thermal diffusivity measurements
The thermal diffusivity of the polymers is measured by a transient method [12], closely related to laser-flash experi-ments [11]. The used transient technique is especially optimized for measurements of polyphase aggregates. A temperature signal is transferred to the upper side of the
sample and registered by a thermocouple. The transferred temperature signal starts a thermal equilibration process in the specimen, which is recorded by a thermocouple as the difference between sample’s rear surface and a constant temperature in a furnace and which is used for the evaluation of thermal diffusivity. A least squares algorithm is used to determine the thermal diffusivity, while varying systematically the thermal diffusivity value in an especially designed finite-difference scheme. A detailed description of the apparatus is given by Schilling [12]. The accuracy of the measurements of the polyphase aggregates is 3%. For thermal diffusivity measurements, small cylinders of 10 mm diameter and 5–6 mm height were cut out of the injection-moulded rods (cf. Fig. 1).
3.3. Injection moulding
With an injection moulding machine (Allrounder 320C 600-250, Arburg, Germany) standard samples for measuring tensile properties together with a rod for thermal measure-ments of 10 mm diameter and 130 mm length were prepared in one mould (cf. Fig. 1). Inthe cavity of the tensile test bar a chromel alumel (Type K) thermocouple was applied.During injection moulding experiments the temperature was recorded every 0.5 s by a digital multimeter and stored in a personal computer. The position of the thermocouple at the sample surface and its position in the cavity of the ejector are shown in Figs. 1 and 2, respectively. The thermocouple submerges approximately 0.2 mm intothe cavity. Therefore, a good thermal contact between polymer and thermocouple even after shrinkage [10] of the moulding is ensured. For a better comparison of the recorded temperature–time curves the same injection moulding parameters for all composite materials were chosen. The used injection moulding parameters are listed in Table 2. The resultant
characteristic times of the injection moulding cycle are tabled in Table 3.
4. Results and discussion
In Fig. 3, the cooling behaviour of polypropylene without and with various fractions of magnetite filler are presented.
Fig. 3. Comparisonof coolingcurves ofunfilledpolypropylene with polypropylene compositeswith variousfillerfractionsof Fe3O4. The symbolsare measured values; the lines are regression lines (cf. text).
At a time the temperature measured by the thermocouple reaches a maximum value around .With increasing time the observed temperature decreases.After the mould opens and the cooling behaviour recorded with the thermocouple changes because it is no longer in contact with the injection moulded material. Due to the large diameter of the rod, the time (54 s) until the mould is opened and the injection moulded parts are ejected is chosen relatively high to ensure that the parts are surely solidified.It can be seen in Fig. 3 that the slope of the curve changes significantly after , which corresponds to the time where the after pressure is removed. Additionally, Fig. 3 points out that the composite in the cavity cools down faster
withincreasingmagnetitefraction.Toreachatemperatureof —a temperature far below the solidification of the sample—the polypropylene needs in the described exper-iment a time of , whereas cooling time of polypropylene with Fe3O4is reduced to (cf. Table 4). The reduced cooling time is in good agreement with the increased thermal diffusivity of magnetite filled composites due to the high thermal diffusivity of
theparticles(cf.Table1)whichleads,regardingEq.(4),toan increased cooling rate. The temperature time dependence in Fig. 3 doesnotfollow asimplelinear behaviour expected for temperature–time curves by Eq. (4) in a logarithmic plot. Only for the unfilled polypropylene the measured values can befittedwithasinglestraightlinebetweenapproximately15 and 54 s. The slope of this line leads to a diffusivity of (cf. Eq. (4)). The other measured cooling curves of the polypropylene-magnetite composites are fitted in each case with two straight lines, for the high temperature and low temperature () region. The thermal diffusiv-ities estimated from the slopes of the regression lines are
It is remarkable that the calculated thermal diffusivities of the higher temperature parts of the cooling curves are a little bit lower than the diffusivities measured with the transient technique, while the calculated thermal diffusivities of the lower temperature parts of the cooling curves meet the measured diffusivity values
The temperature values in parenthesis give the temperature region of the regression lines and the ambient temperature during the measurement with the transient technique.of unfilled polypropylene quite well (cf. Table 5 and Fig. 4).Fig. 4 shows the measured thermal diffusivity data of the investigated samples at ambient conditions. It can be seen that the thermal diffusivity of the magnetite-polypropylene composite is increased from for unfilled poly-propylene up towith increasing magnetite loading. Therefore, the cooling time becomes shorter for higher magnetite filler fractions(Fig. 3).One reason for the change in the slope of the cooling curves shown in Fig. 3 is a change of the thermal diffusivity with temperature which is shown in Fig. 5 for magnetite and barite polypropylene composites with filler fraction. With increasing temperature thermal diffusivity decreases. Therefore, the values derived from mould experiments should be smaller than the measured values of the composites at room tempera-tures. Thermal diffusivity of the PP matrix is mainly caused by phonons and is related to the mean sound velocity v and mean free path length l of phonons according to
Fig. 4. Thermal diffusivity values of injection moulded polypropylene samples with different fillers and various filler proportions measured by a transient technique at room temperature (cf. text). Solid lines are plotted to guide eyes. Above the solidification temperature of the PP matrix (around,DSC measurements)the thermal diffusivity of the matrix is reduced due to the lowered bulk modulus K which results in a reduced phonon velocity and reduced mean free path length of phonons in a liquid (Einstein approximation). Furthermore, above solidification temperature TSno crystallites in the poly-propylene matrix are present, but below TSa crystallization in the polypropylene matrix appears, and the degree of crystallization as well as the bulk modulus of the composite is dependent on the amount of filler [16]. The presence or absence of crystallites affects the bulk modulus K and the phonon free path. Other reasons for the discrepancy between diffusivity values of the different experiments are the non-isobaric conditions in the injection moulding process and the non-isothermal conditions along the sample’s thickness.
The cooling behaviour of magnetite, barite, glass fibre,talc, hard ferrite and copper fillers in comparison with the unfilled polypropylene are plotted in Fig. 6. Only the cooling behaviour of the unfilled and the copper filled polypropylene show significant differences