ISO/TR 22007-5:2011
(Main)Plastics — Determination of thermal conductivity and thermal diffusivity — Part 5: Results of interlaboratory testing of poly(methyl methacrylate) samples
Plastics — Determination of thermal conductivity and thermal diffusivity — Part 5: Results of interlaboratory testing of poly(methyl methacrylate) samples
ISO/TR 22007-5:2011 presents the results of interlaboratory testing for the determination of thermal conductivity and thermal diffusivity of two poly(methyl methacrylate) (PMMA) materials by means of the transient and the modulated methods presented in ISO 22007 parts 2 to 4 and additional transient and steady state methods.
Plastiques — Détermination de la conductivité thermique et de la diffusivité thermique — Partie 5: Résultats d'essais interlaboratoires du poly(méthacrylate de méthyle)
General Information
Standards Content (Sample)
TECHNICAL ISO/TR
REPORT 22007-5
First edition
2011-04-01
Plastics — Determination of thermal
conductivity and thermal diffusivity —
Part 5:
Results of interlaboratory testing of
poly(methyl methacrylate) samples
Plastiques — Détermination de la conductivité thermique et de la
diffusivité thermique —
Partie 5: Résultats d'essais interlaboratoires du poly(méthacrylate de
méthyle)
Reference number
©
ISO 2011
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2011
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2011 – All rights reserved
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Symbols and definitions.1
3 Specimen preparation and characterization .1
4 Measurement apparatus .2
5 Measurement procedure.3
6 Calculations .3
7 Results and conclusions .3
8 Results.3
9 Uncertainty and repeatability .4
10 Acknowledgment.4
Annex A (informative) Instructions sent to interlaboratory comparison participants: Procedure
for thermal conductivity and diffusivity intercomparison in support of the development of
ISO 22007 parts 1-4 .9
Annex B (informative) Laboratory 1 results .12
Annex C (informative) Laboratory 2 results .18
Annex D (informative) Laboratory 3 results .22
Annex E (informative) Laboratory 4 results.29
Annex F (informative) Laboratory 5 results.31
Bibliography.34
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an international Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or such patent rights.
ISO/TR 22007-5 was prepared by Technical Committee ISO/TC 61, Plastics, Subcommittee SC 5, Physical-
chemical properties.
ISO 22007 consists of the following parts under the general title Plastics — Determination of thermal
conductivity and thermal diffusivity:
⎯ Part 1: General principles
⎯ Part 2: Transient plane heat source (hot disc) method
⎯ Part 3: Temperature wave analysis method
⎯ Part 4: Laser flash method
⎯ Part 5: Results of interlaboratory testing of poly(methyl methacrylate) samples [Technical Report]
iv © ISO 2011 – All rights reserved
Introduction
The purpose of this document is to record the results of the interlaboratory comparison of measurements of
the thermal conductivity and thermal diffusivity of poly(methyl methacrylate) PMMA specimens, as a source of
information in support of the development of the series of standards on thermal conductivity and diffusivity of
[1 - 4]
plastics, ISO 22007 .
TECHNICAL REPORT ISO/TR 22007-5:2011(E)
Plastics — Determination of thermal conductivity and thermal
diffusivity —
Part 5:
Results of interlaboratory testing of poly(methyl methacrylate)
samples
IMPORTANT — The electronic file of this document contains colours which are considered to be
useful for the correct understanding of the document. Users should therefore consider printing this
document using a colour printer.
1 Scope
This Technical Report presents the results of interlaboratory testing for the determination of thermal
conductivity and thermal diffusivity of two poly(methyl methacrylate) (PMMA) materials by means of the
[1 - 4]
transient and the modulated methods presented in ISO 22007 parts 2 to 4 and additional transient and
steady state methods.
The instructions for the intercomparison are presented in Annex A with key items reproduced in the main part
of this Technical Report.
The detailed results of individual laboratories are presented in Annexes B to F.
2 Symbols and definitions
Symbol Meaning Unit
α Thermal diffusivity m /s
d Thickness of specimen m
λ Thermal conductivity W/(m⋅K)
[5] [1]
For definitions of the terms used, the reader is referred to ISO 472 and ISO 22007-1 .
3 Specimen preparation and characterization
3.1 Specimens
Two types of PMMA material were used in the intercomparison:
[6]
• Sumipex 000 (cast grade), Lot. 6621114, supplied by Sumitomo Chemical Co. Ltd, Japan .
Referred to as "Sumipex cast PMMA" herein. Sheet thickness ≈ 2 mm.
• AAJHF (extruded grade), supplied via NPL, UK. Referred to as "extrusion grade PMMA" herein.
Sheet thickness ≈ 3 mm.
The Sumipex cast PMMA was supplied in sheet form only whereas the extrusion grade PMMA was supplied
in both sheet and pellet forms.
3.2 Specimen preparation
Depending on the test method, test specimens needed to be prepared from the sheet samples. For the
temperature wave analysis the specimens were reduced in thickness. For laser flash testing they were
reduced in thickness by one laboratory, but not by the second laboratory. For transient line source testing the
specimens were prepared by cutting small pieces from the sheet for insertion into the barrel of the instrument.
For Hot Disk testing, most of the data reported are for measurements on single sheets, although two sheets
were stacked in some cases to form the test specimen (see Table 1).
4 Measurement apparatus
The experimental apparatus is described in ISO 22007 Parts 1 - 4 and in further detail in references 7 − 17.
Table 1 - The measured thermal properties and various specimen sizes
for the methods used in this study.
Measured
parameter Nominal
Specimen size
specimen Additional
(thermal
Method / Lab No. mm
conductivity thickness pre-treatments
(φ : diameter)
and/or thermal mm
diffusivity)
2, 3
Hot Disk / 1 λ, α, (ρ C ) φ 5, φ 10
p
(4, 6: stacked)
silver paint
Laser flash / 2 2
α φ 10
(30 µm)
1,14 – cast, sputtered
Laser flash / 3 α φ 12,7
1,49 – extruded graphite
Transient line-
moulded in-situ 50 moulded in-situ
λ
source probe / 3
Heat flow meter / 3 2, 3
λ φ 50
Heat flow meter / 4 2, 3 φ 80
λ
Temperature wave
0,01 3 x 5
α
analysis / 5
1 3
The factor ρ C , the specific heat per unit volume J/(m .K), is determined from the ratio of the measured
p
thermal conductivity λ and thermal diffusivity α values where ρ is the density (kg/m ) and C is the specific
p
heat capacity per unit mass (J/kg.K).
2 © ISO 2011 – All rights reserved
5 Measurement procedure
[2 - 4]
The procedures used were as specified in the relevant parts of ISO 22007 for the methods covered by
[7]
that standard. The other methods are specified by ASTM D5930 for the line source probe technique, by
[8]
ASTM E1530 for the guarded heat flow meter method, and as described by [9] for the second heat flux
meter method. Experimental details and variations from these references are reported in the intercomparison
instructions, Annex A, and in the individual laboratory test reports, Annexes B to F.
6 Calculations
All laboratories carried out the necessary analyses of their raw data to determine thermal conductivity, thermal
diffusivity and heat capacity values.
7 Results and conclusions
The test reports of the individual laboratories are presented in Annexes B to F along with tabulated data as
provided or abbreviated as appropriate.
8 Results
The results of the measurements are presented in Figures 1 - 4. In addition, in each of these figures, values of
thermal diffusivity have been calculated from thermal conductivity, or vice-versa, to demonstrate the level of
agreement between the two types of measurement.
The individual results were typically within a range of approximately ± 10 % of the mean value at any given
[18]
temperature for both thermal conductivity and thermal diffusivity .
The reasons for the discrepancy in results are not entirely clear from the intercomparison and require further
examination to reduce further the variation in results.
Three particular issues highlighted by the intercomparison that should be covered by good measurement
practice are:
• Need to ensure that the specimens are of the appropriate thickness for the test method, satisfying
any criteria on thickness that the method imposes. This may necessitate machining of the specimen
to an appropriate thickness.
• Effect of anisotropy of the sample. When using the Hot Disk method, testing can yield either
anisotropic properties or bulk properties depending on the specific method used. As properties of
polymers can be anisotropic, normally due to processing induced effects, it may be necessary to take
this into account in testing, depending on the application for the data.
• When calculating thermal diffusivity from thermal conductivity, and vice-versa, it is important to
assess the uncertainties in the specific heat capacity values used as these can contribute significantly
to the overall uncertainty in calculated values. In the testing carried out here the specific heat capacity
values varied by up to approximately ± 10 % from the mean, and density values by ± 1 % from the
mean. This would contribute an uncertainty of approximately 10 % to the calculation of thermal
diffusivity (see Table 2).
9 Uncertainty and repeatability
Estimates of the uncertainties or repeatabilities of the experimentally measured and calculated values are
presented in Table 2. The uncertainty of measurement (coverage factor k = 2) was calculated according to the
[19]
Guide to the expression of uncertainty in measurement . The expanded uncertainty was calculated when
thermal diffusivity was calculated from thermal conductivity, or vice-versa, by the use of the equation λ = α C ρ
p
according to the Guide to the expression of uncertainty in measurement. In Table 2 the uncertainties are shown
with the k-numbers in parenthesis; values without k-numbers are the repeatabilities.
Table 2 - Estimates of the uncertainties or repeatability for the experimental and calculated values.
Sumipex cast PMMA
ρ C α λ
p
*
Lab. 1 - 0,25 % - 2,89 % 0,32 % - 3,16 % 0,12 % - 0,52 %
(ISO 22007-2) (ISO 22007-2) (ISO 22007-2)
Lab. 2 1 % 4 % 8 % (k = 2) 9 % (k = 2)
(ISO 1183-1) (ISO 11357-4) (ISO 22007-4) (calc, ISO 22007-4)
Lab. 3 per standard - 0,49 % - 2,9 % 3 %
ASTM D792 (ASTM E1269-05) (ASTM E1461-01) (ASTM E1530)
Lab. 4 0,08 % 1,8 % - 4,8 % - 3 %
**
Lab. 5 - - 2,6 % (k = 2) 8,4 % (k = 2)
(ISO22007-3) (calc, ISO22007-3)
Extrusion grade PMMA
C
ρ α λ
p
*
Lab. 1 - 0,12 % - 1,95 % 0,16 % - 1,6 % 0,07 % - 0,35 %
(ISO 22007-2) (ISO 22007-2) (ISO 22007-2)
Lab. 3 per standard - 0,87 % - 5,6 % per standard
ASTM D792 (ASTM E1269-05) (ASTM E1461-01) ASTM D5930
Lab. 4 0,22 % 3,2 % - 4,3 % - 3 %
***
Lab. 5 - - 5,0 % (k = 2) 9,5 % (k = 2)
(ISO 22007-3) (calc, ISO 22007-3)
*
apparent value as ρ C
p
**
calculated with Lab. 2 C and density data
p
***
calculated with Lab. 2 and Lab. 4 C and density data
p
10 Acknowledgment
We express our special thanks to Sumitomo Chemical Co. Ltd. for supplying us the cast PMMA.
4 © ISO 2011 – All rights reserved
1.6
Lab. 1 / HD stacked
Sumipex cast PMMA
Lab. 1 / HD axial
Lab. 2 / LF
Lab. 3 / LF
Lab. 5 / TWA
1.2
0.8
0.4
0 50 100 150 200
T / °C
Figure 1 - Thermal diffusivity of Sumipex cast PMMA in the through-thickness direction
measured by the different laboratories at various temperatures T:
(i) directly measured values:- Lab. 2 by the Laser flash method (LF) (thickness d = 2 mm),
Lab. 3 by LF (d = 1,14 mm), and Lab. 5 by the Temperature wave analysis method (TWA)
(d = 0,011 mm);
(ii) calculated values from thermal conductivity:- Lab. 1 by the Hot disk method (HD) (d = 2 mm
for axial measurement, d = 4 mm for isotropic measurement).
-7
2 -1
α / 10 m s
Lab.1 / HD axial Lab.1 / HD stack
Lab.3 / LS heat
Lab.2 / LF
Lab.4 / HFM
Lab.3 / LF
Lab.3 / HFM Lab.5 / TWA
Lab.3 / LS cool
0.24
cast grade PMMA
0.22
0.20
0.18
0.16
0.14
0 50 100 150 200
T / °C
Figure 2 - Thermal conductivity of Sumipex cast PMMA in the through-thickness direction measured
by the different laboratories at various temperatures T:
(i) directly measured values:- Lab. 1 by the Hot disk method (HD) (thickness d = 2 mm for axial
measurement, d = 4 mm for isotropic measurement), Lab. 3 by the Heat flow meter method (HFM)
(d = 2 mm) and the Line source method (LS) (d = 2 mm), and Lab. 4 by HFM (d = 2 mm);
(ii) calculated values from thermal diffusivity:- Lab. 2 by the Laser flash method (LF) (d = 2 mm), Lab. 3
by LF (d = 1,14 mm), and Lab. 5 by the Temperature wave analysis method (TWA) (d = 0,011 mm).
6 © ISO 2011 – All rights reserved
-1 -1
λ / Wm K
1.6
Extruding grade PMMA
Lab. 1 / HD stacked
Lab. 3 / LS
Lab. 3 / LF
Lab. 5 / TWA
1.2
0.8
0.4
0 50 100 150 200
T / °C
Figure 3 - Thermal diffusivity of the extrusion grade PMMA in the through-thickness direction
measured by the different laboratories at various temperatures T:
(i) directly measured values: Lab. 3 by the Laser flash method (LF) (thickness d = 1,49 mm), and Lab. 5
by the Temperature wave analysis method (d = 0,012 mm);
(ii) calculated values from thermal conductivity:- Lab. 1 by the Hot disk (HD) method (d = 6 mm with
two pieces stacked), and Lab. 3 by the Line source (LS) method (d = 3 mm).
-7
2 -1
α / 10 m s
Lab. 3 / LS cool
Lab. 1 / HD stacked
Lab. 4 / HFM
Lab. 3 / LS heat
Lab. 3 / LF Lab. 5 / TWA
0.22
extrusion grade PMMA
0.20
0.18
0.16
0.14
0 50 100 150 200
T / °C
Figure 4 - Thermal conductivity of the extrusion grade PMMA in the through-thickness
direction measured by the different laboratories at various temperatures T:
(i) directly measured values: Lab. 1 by the Hot disk method (HD) (thickness d = 6 mm with
two species stacked), Lab. 3 by the Line source method ((LS) (d = 3 mm), and Lab. 4 by the
Heat flow meter method (HFM) (d = 3 mm);
(ii) calculated values from thermal diffusivity: Lab. 3 by the Laser flash method (LF)
(d = 1,49 mm), and Lab. 5 by the Temperature wave method (TWA) (d = 0,012 mm).
8 © ISO 2011 – All rights reserved
-1
-1
λ / Wm K
Annex A
(informative)
Instructions sent to interlaboratory comparison participants:
Procedure for thermal conductivity and diffusivity intercomparison
in support of the development of ISO 22007 parts 1-4
A.1 IMPORTANT INFORMATION
If you have any comments or questions concerning this intercomparison (the procedure, sample preparation
etc) please send them to us before 25 February 2007 so that the issue(s) can be discussed BEFORE any
participants prepare specimens or commence testing.
All results and associated documentation to be returned by 14 April 2007 if possible, please. If there are any
problems with this schedule, please contact us as soon as possible.
A.2 INTRODUCTION
A.2.1 Thank you for agreeing to participate in this intercomparison on the measurement of thermal
conductivity and diffusivity of polymers. This is a preliminary intercomparison amongst the project leaders that
will shortly be expanded to a larger intercomparison including other organisations. The purpose of this
preliminary intercomparison is to resolve any major issues that become apparent before involving the larger
number of participants.
A.2.2 In summary, the objectives of this intercomparison are to assess the repeatability, reproducibility and
comparability of the transient and the modulated techniques covered by ISO 22007 Parts 1 - 4 and of other
techniques that may also be incorporated into this series in the future. The intention is that the findings of the
intercomparison will be incorporated into ISO 22007 (or at least Part 1) as part of the precision statements,
and will contribute to the development of all parts of this Standard.
A.2.3 This intercomparison is based on testing of PMMA materials to obtain thermal conductivity and
thermal diffusivity data at a range of temperatures. Information that may be of use on the materials are given
below.
Sumipex cast PMMA: T transition range starts around 100 °C, completed by approx 130 °C (at 10 °C/min);
g
degrades above 220 °C; drying time should be 80 °C for 5 hours. A percentage of water absorption of PMMA
is 0,3 %/24Hr (depending on the relative humidity), and the saturated water absorption is 2 %.
NPL thermoplastic PMMA: extrusion grade PMMA; MFI 1,6 g/10 mins (230 °C/ 3,8 kg); drying conditions
75 °C for 4 hours; Tg transition range by DSC approx 90 °C to 130 °C; typical die process temperatures
220 °C to 240 °C; decompose above 280 °C BUT may degrade at lower temperatures - recommend keep to
below 240 °C.
A.2.4 This document prescribes the procedure to be followed for those measurements.
A.2.5 Tests shall be performed in accordance with the appropriate parts of ISO 22007. The latest versions
of the relevant documents shall be used. Please contact myself if you need a copy.
A.2.6 Where testing using a method not currently covered by ISO 22007, state which Standard/procedure
was used. If an in-house method was used please provide documentation describing the procedure and
equipment.
A.3 THERMAL CONDUCTIVITY / DIFFUSIVITY TEST PLAN
A.3.1 Condition the material using the standard atmosphere (ISO 291) of (23 +/- 1)°C and relative humidity
(50 % +/- 5 %) for at least 4 hours before testing.
A.3.2 The recommended test temperatures:
Cast Sumipex PMMA:
Recommended measurement temperatures are 23 °C, 30 °C (with repeats at this temperature), 60 °C and
90 °C and additional optional temperatures of 140 °C and 180 °C.
Thermoplastic NPL PMMA: (i.e. extrusion grade PMMA):
Recommended measurement temperatures are 30 °C (with repeats at this temperature), 140 °C and 180 °C,
with additional optional temperatures of 23 °C, 60 °C and 80 °C.
PLEASE NOTE IT IS HIGHLY DESIRABLE THAT DATA ARE OBTAINED AT ATLEAST 30 °C FOR BOTH
MATERIALS BY ALL TECHNIQUES
Participants are encouraged to test at other temperatures and, if possible, above the Tg for the thermoplastic
PMMA
A.3.3 At the test temperature of 30 °C repeat the test at least a further 4 times using identical test
conditions. These repeat tests should involve the complete procedure to be a true repeat test including, for
example, re-conditioning the sample, measuring the specimen dimensions and re-loading the sample into the
instrument. Re-testing without going through the whole procedure is not correct practice to determine the true
repeatability of the method.
A.3.4 Where possible, measure the sample density and/or mass before and after testing to assess
moisture uptake during the test.
A.4 ADDITONAL TESTING / DATA REQUIREMENT
A.4.1 Conversion from thermal conductivity values to thermal diffusivity values, and similarly from thermal
diffusivity to thermal conductivity, requires density and specific heat capacity values. All participants should (if
possible) each measure these values and convert their own results (i.e. from thermal conductivity to diffusivity
or vice-versa) using those values. On analysis of all of the participants’ results, further analysis will be carried
out using average values for both density and specific heat capacity. The measurement of these parameters
is a part of the overall measurement of thermal conductivity and/or thermal diffusivity and so is considered a
valid part of this intercomparison. It will enable correct comparison of the thermal conductivity with thermal
diffusivity results.
A.4.2 Measure the density of the material at the same temperature(s).
A.4.3 Measure the specific heat capacity of the material at the same temperature(s).
Note: if resourcing is an issue for any particular laboratory then the emphasis should be on the thermal
conductivity/diffusivity testing.
PLEASE KEEP ALL SPECIMENS FOR FUTURE REFERENCE / USE UNTIL OTHERWISE INSTRUCTED
A.5 REPORTING RESULTS
A.5.1 Provide all information, raw data ~(e.g. plot files) and results as requested in the excel spreadsheet.
The spreadsheet may be used for this purpose. Alternatively, other means of saving the information can be
used (e.g. where information is provided in text or image files direct from the instrument’s software). Where
the information requested is “not applicable” please enter N/A.
A.5.2 Consult ISO 22007-1 and the appropriate Part of ISO 22007 for additional reporting requirements.
A.5.3 Where thermal diffusivity has been measured give values of density and specific heat capacity used
for conversion to thermal conductivity, and vice-versa. Report what methods were used for measurements of
density and specific heat capacity, and provide information on the standards / procedures / techniques /
instruments used. Report both thermal conductivity and thermal diffusivity data, but provide clear indication as
to which is/are measured and which is derived.
10 © ISO 2011 – All rights reserved
A.5.4 Enter comments where the current wording of the standard causes difficulties in carrying out testing,
or is deficient in instruction, etc.
NOTE: Please ensure that you have documented all the information necessary to enable another person to
duplicate the measurement. Much of this is likely to be in the outputs from the instrument.
A.6 REPORT ADDITIONAL INFORMATION
In addition to the results please provide additional information on the following, where available:
A.6.1 Calibration procedures
· Details of calibration procedures
A.6.2 Reference materials
· Details of reference materials used and reference values
A.6.3 Calibration data
· Results of calibrations
A.6.4 Uncertainty analysis
· Provide uncertainty analyses where available.
· Give details of tolerances on measurement parameters, e.g. on dimensions, temperature measurements.
· Provide any further repeatability data on you r measurement system that you may have.
A.7 RETURNING RESULTS
A.7.1 All results and documentation to be returned in electronic format that is readable in either Excel or
Word (e.g. please do not provide files that can only be read by the instrument’s software).
Annex B
(informative)
Laboratory 1 results
B.1 Hot Disk report on the ISO group Round Robin test on two types of PMMA
The two samples were received, heat treated and measured as agreed. In addition to the agreed
measurements, measurements were made of the anisotropic properties as these are very different for the two
materials.
[2, 10, 11, 12]
The Hot Disk method measures thermal conductivity and thermal diffusivity independently in each
measurement in the basic set up (using two equal samples, one on each side of the sensor). Having these
two values the specific heat per unit volume ρ C can be calculated by dividing the thermal conductivity by the
p
thermal diffusivity. It must be understood that this value of ρ C is only correct for isotropic materials. When the
p
sample is anisotropic, this ratio is simply
½
λ ⋅λα/
()
ac a
where the subscripts indicate the axis directions of the properties (e.g. λ is the thermal conductivity along the
a
a-axis). It is assumed here that the properties along the a- and b-axes (mapping out the plane of the sensor)
are the same but different from those along the c-axis.
By introducing an independently measured ρ C value for an anisotropic sample, it is possible to calculate the
p
thermal conductivity and thermal diffusivity for the two directions, normal and parallel to the sensor surface. A
[10]
method for independently measuring the heat capacity has been developed by Gustavsson et al but it is
not a part of the standard ISO 22007-2. This method measures ρ C at room temperature only, which means
p
that other methods, like a drop-calorimeter or a precise DSC must be used at other temperatures. (An
advantage with DSC is that it can be measured as a function of temperature).
For these measurements, where anisotropy is so clearly distinguishing the two samples, it was judged that
this should be investigated. The samples' anisotropic properties as-received and after drying, have been
measured at room temperature.
B.2 Hot Disk measurements on Sumipex cast PMMA – preliminary exploratory
results
Two sheets of Sumipex cast PMMA were supplied from Japan. From these, two circular samples of diameter
50 mm were cut and used for the measurements. The thickness was measured at 2 mm.
First, the material was measured as-received at room temperature (RT), with the standard method and also
with the anisotropic method. A value for ρ C was measured on a smaller sample, cut with a diameter of
p
12 mm.
After the initial measurements, the recommended drying process was carried out: 80 °C in a furnace for
5 hours. After this treatment the samples were stored in desiccators.
The two 50 mm diameter samples were then mounted in a special metal sample holder together with the
sensor (radius 2,001 mm), and put into an oil bath thermostat with temperature regulation.
12 © ISO 2011 – All rights reserved
The following measurements were performed:
Standard at 23 °C, 5 s measuring time, as-received sample
Anisotropic at 23 °C, with ρ C measured on the as-received 12 mm sample
p
Anisotropic at 23 °C, with ρ C measured on the dried 12 mm sample
p
Standard at 23 °C, 5 s
Standard at 30 °C, 5 s
Standard at 60 °C, 5 s
Standard at 60 °C, 10 s
Standard at 90 °C, 10 s
Standard at 90 °C, 5 s
Standard at 60 °C, 10 s
Standard at 60 °C, 5 s
Standard at 30 °C, 5 s
Standard at 23 °C, 5 s
All measurements were done with a sensor 7577, radius 2,001 mm. The power was 0,075 W in all cases. At
lower temperatures the time was 5 s, but as temperature increased, the thermal diffusivity was lower and
allowed for a longer measuring time of 10 s. This is why both 5 s and 10 s were tried at 60 °C and 90 °C. In
both cases the probing depth was always below 2 mm.
Table B.1 - Sumipex cast PMMA, as-received sample
TC StDev. Diff StDev. Apparent ρ C StDev.
p
2 3
W/(m.K) % mm /s % MJ/(m K) %
Front Side* 0,2063 0,31 0,135 0,62 1,52 0,47
Back Side* 0,2065 0,12 0,134 0,32 1,54 0,25
NOTE: StDev. is used as the abbreviation for standard deviation.
Table B.2 - Sumipex cast PMMA, anisotropic properties of as-received sample
(ρ C = 1,733 MJ/(m K) StDev. 0,36 %)
p
TC Axial StDev. Diff Axial StDev. TC Radial StDev. Diff Radial StDev.
2 2
W/(m.K) % mm /s % W/(m.K) % mm /s %
0,1863 0,35 0,108 0,32 0,2302 0,52 0,133 0,51
Table B.3 - Sumipex cast PMMA, anisotropic properties of dried sample
(ρ C = 1,730 MJ/(m K) StDev. 0,27 %)
p
TC Axial StDev. Diff Axial StDev. TC Radial StDev. Diff Radial StDev.
2 2
W/(m.K) % mm /s % W/(m.K) % mm /s %
0,1897 0,87 0,110 0,86 0,2246 1,03 0,130 1,03
Table B.4 - Sumipex cast PMMA
Temperature Time TC StDev. Diff StDev. Apparent ρ C StDev.
p
o 2 3
C s W/(m.K) % mm /s % MJ/(m K) %
23 5 0,2051 0,15 0,132 0,99 1,55 0,82
30 5 0,2064 0,16 0,127 0,49 1,62 0,35
60 5 0,2113 0,52 0,123 2,60 1,72 2,08
60 10 0,2117 0,22 0,120 1,18 1,77 1,00
90 5 0,2156 0,36 0,117 1,47 1,85 1,14
90 10 0,2159 0,28 0,115 3,16 1,88 2,89
60 10 0,2121 0,15 0,120 0,71 1,77 0,53
60 5 0,2121 0,14 0,124 0,77 1,72 0,66
30 5 0,2038 0,08 0,126 0,54 1,63 0,46
23 5 0,2020 0,13 0,126 1,10 1,60 0,95
140 10 0,2109 0,17 0,091 1,01 2,32 0,98
*The first measurements on as-received samples, front side and back side facing the sensor, showed that the
samples do not have a difference due to up/down, through the thickness.
These results indicate that the material is strongly anisotropic. The measured thermal conductivity and thermal
diffusivity are some 20 % lower in the through (thickness) direction than in the plane. Even after annealing the
anisotropic property remains, meaning that at 80 °C no re-organisation of the material has taken place. It is
too far from the melting point. Measurements of standard or bulk samples (all the other measurements) show
an effective average of thermal conductivity and thermal diffusivity over the sampled volume.
Since the material is obviously anisotropic, the expressions used in the table column headers should be
understood as follows:
½
TC = λλ⋅
()
ac
Diff = α
a
and
½
Apparent ρ C = λ ⋅λα/
p()
ac a
where TC is the apparent thermal conductivity and α is the apparent thermal diffusivity, accounting for
a
specimen anisotropy.
There is a very clear trend that TC and Apparent ρ C increase and Diff decreases with temperature, and that
p
the changes are reversible.
Taking into account the very low standard deviations (based on 5 measurements and given for each value in
the table) even the small differences in thermal conductivity are significant.
The changing of material properties due to heating cycles can be observed in Table B.5.
Table B.5 - Sumipex cast PMMA
TC Diff Apparent ρ C
p
2 3
W/(m.K) mm /s MJ/(m K)
As-received Front Side 0,2063 0,135 1,52
As-received Back Side 0,2065 0,134 1,54
o
After heating to 80 C, 5H
0,2051 0,132 1,55
measured at RT
Followed by a full cycle to
0,2020 0,126 1,60
o
90 C measured at RT
14 © ISO 2011 – All rights reserved
B.3 Hot Disk measurements on the extrusion grade PMMA – preliminary
exploratory results
Two sheets of PMMA were supplied by NPL. From these, two circular samples with diameter 50 mm were cut
and used for the measurements. The thickness was measured at 3 mm.
First, the material was measured as-received at room temperature, with the standard method and also with
the anisotropic method. A value for ρ C was measured on a smaller sample, cut with a diameter of 12 mm.
p
After the initial measurements, the recommended drying process was carried out: 75 °C in a furnace for 4
hours. After this treatment the samples were stored in desiccators.
The two 50 mm diameter samples were then mounted in a special metal sample holder together with the
sensor (radius 3,189 mm) and put into an oil bath thermostat with temperature regulation. The following
measurements were performed:
Standard at 23 °C, 20 s measuring time, as-received sample
Anisotropic at 23 °C, 20 s, with ρ C measured on the as-received 12 mm sample
p
Anisotropic at 23 °C, 20 s, after drying (with ρ C measured on a dried 12 mm sample
p
Standard at 23 °C, 20 s
Standard at 30 °C, 20 s
Standard at 60 °C, 20 s
Standard at 80 °C, 20 s
Standard at 80 °C, 20 s
Standard at 60 °C, 20 s
Standard at 30 °C, 20 s
Standard at 23 °C, 20 s
Standard at 140 °C, 20 s
All measurements were done with a sensor 5465, radius 3,189 mm. The power was 0,075 W in all cases. At
all temperatures the measuring time was 20 s. Using this sensor and measuring time, the probing depth was
always below 3 mm (compared to the Sumipex cast PMMA sample, which was only 2 mm thick; this required
a smaller sensor and shorter time).
Table B.6 - Extrusion grade PMMA, as-received sample
TC StDev. Diff StDev. Apparent ρ C StDev.
p
2 3
W/(m.K) % mm /s % MJ/(m K) %
0,2022 0,35 0,121 20,1 1,66 1,95
Table B.7 - Extrusion grade PMMA, anisotropic properties of as-received sample
(ρ C = 1,615 MJ/(m K), StDev 0,52 %)
p
TC Axial StDev. Diff Axial StDev. TC Radial StDev. Diff Radial StDev.
2 2
W/(m.K) % mm /s % W/(m.K) % mm /s %
0,2010 0,29 0,125 0,39 0,2004 0,26 0,125 0,25
Table B.8 - Extrusion grade PMMA, anisotropic properties of dried sample
(ρ C = 1,604 MJ/(m K), StDev. 0,25 %)
p
TC Axial StDev. Diff Axial StDev. TC Radial StDev. Diff Radial StDev.
2 2
W/(m.K) % mm /s % W/(m.K) % mm /s %
0,2048 0,99 0,127 0,98 0,2094 1,33 0,130 1,35
Table B.9 - Extrusion grade PMMA
Temperature Time TC StDev. Diff StDev. Apparent ρ C StDev.
p
o 2 3
C s W/(m.K) % mm /s % MJ/(m K) %
23 20 0,2057 0,07 0,132 0,16 1,56 0,12
30 20 0,2074 0,27 0,131 1,60 1,59 1,35
60 20 0,2090 0,18 0,121 0,51 1,73 0,35
80 20 0,2127 0,09 0,116 0,30 1,84 0,30
down
80 20 0,2126 0,05 0,116 0,18 1,84 0,14
60 20 0,2078 0,27 0,123 1,20 1,69 0,91
30 20 0,2067 0,08 0,131 0,36 1,58 0,35
23 20 0,2069 0,13 0,134 0,59 1,54 0,48
140 20 0,2135 0,16 0,088 0,72 2,43 0,58
These results indicate that this material is much less anisotropic than the Sumipex cast PMMA. The measured
thermal conductivity and thermal diffusivity are about 2 % lower in the through (thickness) direction than in the
plane for the sample.
Measurements of standard or bulk samples (all the other measurements) show an effective average of
thermal conductivity and thermal diffusivity over the sampled volume, which therefore is reported as apparent
ρ C .
p
Due to the fact that the material is almost isotropic, the value for ρ C given in a standard measurement is very
p
close to the measured value.
There is a very clear trend that thermal conductivity and heat capacity increases and thermal diffusivity
decreases with temperature, and that the changes are reversible.
Taking into account the very low standard deviations (based on 5 measurements and given for each value in
the table) even the small differences in thermal conductivity are significant. The difference between thermal
conductivity in axial and radial direction in the anisotropic analysis of the sample is not significant, considering
the standard deviation in the ρ C measurement.
p
The changing of material properties due to heating cycles can be followed, Table B.10:
Table B.10 – Extrusion grade PMMA
TC StDev. Diff StDev. Apparent ρ C StDev.
p
2 3
W/(m.K) % mm /s % MJ/(m K) %
As-received 0,2022 0,35 0,121 20,1 1,66 1,95
o
After drying 75 C, 4 h 0,2057 0,07 0,132 0,16 1,56 0,12
o
After heating cycle to 80 C 0,2069 0,13 0,134 0,59 1,54 0,48
B.4 Stacked specimens results
The results of stacking sheets, to respect specimen thickness criteria, are presented in Tables B.11 and B.12.
Two stacked sheets were necessary to get a thickness sufficient to use a time that was long enough to get a
Total to Characteristic time ratio of 0,45, which is within the analysis model range (0,3 - 1,0).
16 © ISO 2011 – All rights reserved
Table B.11 – Sumipex cast PMMA
Temperature TC StDev. Diff StDev. Apparent ρ C StDev.
p
2 3
°C W/(m.K) % m /s % MJ/(m K) %
23 0,2033 1,1 1,141E-07 1,2 1,78 1,9
30 0,2008 0,2 1,102E-07 0,2 1,82 0,3
60 0,2007 0,3 1,097E-07 2,4 1,83 2,7
90 0,2095 0,4 1,031E-07 1,7 2,03 2,1
Table B.12 – Extrusion grade PMMA
Temperature TC StDev. Diff StDev. Apparent ρ C StDev.
p
2 3
°C W/(m.K) % m /s % MJ/(m K) %
23 0,1998 0,12 1,114E-07 0,55 1,75 0,7
30 0,2027 0,4 1,109E-07 0,8 1,83 0,8
60 0,2006 0,14 1,104E-07 0,8 1,9 1,0
90 0,2087 0,4 1,041E-07 1,5 2,01 1,7
Annex C
(informative)
Laboratory 2 results
C.1 Laser flash specimen preparation
Two sheets of PMMA having a thickness of 2 mm (reference: Sumipex 000 lot 6621114) were received from
one source and two sheets of PMMA having a thickness of 3 mm (reference: AAJHF002-3A) from a second
source. Specimens for density, thermal expansion, specific heat and thermal diffusivity measurements were
machined from one sheet of each type of PMMA. All specimens were dried at a temperature of 80 °C for 5
hours, and were stored in a desiccator.
As PMMA is not opaque to the laser wavelength (1,054 µm) used to measure thermal diffusivity, a thin layer (1
µm to 3 µm) of metallic coating was deposited on both faces of the thermal diffusivity specimens. Due to the
low thermal diffusivity of PMMA and the relatively large thickness of the specimens, the energy deposited by
the laser beam on the front face of the specimen had to be increased, in order to obtain a thermogram having
a good signal/noise ratio. After some thermal diffusivity measurements, it appeared that the metallic coating
did not resist to the repetition of laser impacts. It was then decided to change the coating and to apply a thin
layer (≈ 30 µm) of silver paint. It was, however, not possible to acquire “good” thermograms with the 3 mm
thick specimens. In consequence, the results presented hereafter were obtained on 2 mm thick sheets
(Sumipex 000 lot 6621114).
C.2 Density measurements
C.2.1 Density measurements at 23 °C
[20]
The density is determined at 23°C according to the immersion method (ISO 1183-1 ) and is calculated by
the following formula:
m ⋅ ρ
1 A
ρ =
23°C
()mm−
where m is the apparent mass of the specimen in air, m is the apparent mass of the specimen in the
1 2
immersion liquid (distilled water at 23 °C ± 0,1 °C) and ρ is the density of the immersion liquid at 23 °C.
A
Measurements where performed on six specimens of Sumipex cast PMMA.
Table C.1 - Sumipex cast PMMA: density at 23 °C
Specimen Density
kg/m
1 1186
2 1183
3 1183
4 1185
5 1185
6 1184
Mean value 1184
18 © ISO 2011 – All rights reserved
C.2.2 Density measurements at T >23 °C
For an isotropic material, the density is determined by:
ρ
23°C
ρ =
T
T
1+⋅α ⎤ ()TT−
()L ⎦ 0
T
T
where α ⎤ is the mean linear thermal expansion coefficient between T (23 °C) and T.
L ⎦ 0
T
Table C.2 - Sumipex cast PMMA: density
Temperature Density
°C kg/m
23 1184
60 1174
90 1163
(1)
120 1152
(1)
using the mean thermal expansion coefficient between 23 °C and
100 °C (see C.3)
The uncertainty on density measurements is estimated to be ± 1 %.
C.3 Linear thermal expansion coefficient measurements
[21]
The linear thermal expansion coefficient was determined with a TMA according to ISO 11359-2 standard.
The tests were performed from -10 °C to 120 °C in a high purity helium atmosphere with a heating rate of
5 °C/min. Before the test, the TMA was calibrated under identical test conditions (temperature range, heating
rate, atmosphere…) with reference specimens of known thermal expansion.
T
The mean linear thermal expansion coefficient α ] between T and T is given by the following formula:
L
T
T
ΔL
⎤
⎦
1 T
T
α =⋅
⎤
L ⎦
T
()TT− L
0 T
T
where ΔL] is the expansion measured between T to T and L is the length of the specimen at room
T T
0 0
temperature T (usually T =
...
TECHNICAL ISO/TR
REPORT 22007-5
First edition
2011-04-01
Plastics — Determination of thermal
conductivity and thermal diffusivity —
Part 5:
Results of interlaboratory testing of
poly(methyl methacrylate) samples
Plastiques — Détermination de la conductivité thermique et de la
diffusivité thermique —
Partie 5: Résultats d'essais interlaboratoires du poly(méthacrylate de
méthyle)
Reference number
©
ISO 2011
PDF disclaimer
PDF files may contain embedded typefaces. In accordance with Adobe's licensing policy, such files may be printed or viewed but shall
not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading a PDF file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create the PDF file(s) constituting this document can be found in the General Info relative to
the file(s); the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the files are suitable for
use by ISO member bodies. In the unlikely event that a problem relating to them is found, please inform the Central Secretariat at the
address given below.
This CD-ROM contains the publication ISO/TR 22007-5:2011 in portable document format (PDF), which can
be viewed using Adobe® Acrobat® Reader.
Adobe and Acrobat are trademarks of Adobe Systems Incorporated.
IMPORTANT — The electronic file of this document contains colours which are considered to be
useful for the correct understanding of the document. Users should therefore consider printing this
document using a colour printer.
© ISO 2011
All rights reserved. Unless required for installation or otherwise specified, no part of this CD-ROM may be reproduced, stored in a retrieval
system or transmitted in any form or by any means without prior pe
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.
Loading comments...