WO1993003352A1 - A method for determining the thermal conductivity of anisotropic plastic films and its usage - Google Patents

A method for determining the thermal conductivity of anisotropic plastic films and its usage Download PDF

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Publication number
WO1993003352A1
WO1993003352A1 PCT/FI1992/000226 FI9200226W WO9303352A1 WO 1993003352 A1 WO1993003352 A1 WO 1993003352A1 FI 9200226 W FI9200226 W FI 9200226W WO 9303352 A1 WO9303352 A1 WO 9303352A1
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WO
WIPO (PCT)
Prior art keywords
plastic film
thermic
diffusivity
thermal conductivity
film sample
Prior art date
Application number
PCT/FI1992/000226
Other languages
French (fr)
Inventor
Jussi Jaarinen
Bert Skagerberg
Jukka Rantala
Original Assignee
Neste Oy
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Neste Oy filed Critical Neste Oy
Publication of WO1993003352A1 publication Critical patent/WO1993003352A1/en

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/44—Resins; rubber; leather
    • G01N33/442—Resins, plastics
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00—Investigating or analyzing materials by the use of thermal means
    • G01N25/18—Investigating or analyzing materials by the use of thermal means by investigating thermal conductivity

Definitions

  • the invention relates to a method for determining the thermal conductivity of anisotropic plastic films.
  • the thermic diffusivity is obtained from the equation (1)
  • p C is independent of the orientation degree of the plastic film.
  • Plastic films generally obtain orientation e.g. by stretching. It is a known fact that an orientated plastic film has in the values of the thermal conductivity in different directions considerable differences. The thermal conductivity is even 2-20-fold in certain directions. In the literature of the art is presented even such a fact that the difference in the thermal conductivity could be even 100-fold.
  • the control and determination of the thermic diffusivity of polymers is extremely important when preparing high-class polymers.
  • the thermic diffusivity is import ⁇ ant also in the sense that the structural properties of the polymer depend on the thermic diffusivity. In this sense, the orientation of polymers is also of import- ance with respect to the mechanical properties of the final product.
  • the object of the invention is to provide a method, by means of which the thermal conductivity of anisotropic plastic films may be determined sufficiently reliably.
  • an optical beam deflection known per se.
  • This method has been used for determining the thermal conductivity of metals and ceramics, but this method cannot as such be applied to the determination of the thermal conductivity of anisotropic plastic films.
  • OBD optical beam deflection
  • the data analysis is performed by means of a chemometric analysis method. In this analysis method is used a so- called projection method.
  • a certain especially applicable method is a method of partial least squares regression (PLS), in which the measured thermic wave represents in the analysis a matrix X and the thermic diffusivity is contained as one factor in a matrix Y.
  • PLS partial least squares regression
  • the inventive method may be applied to the determination of the orientation degree of plastic films. As a result of this determination, the mechanical prop ⁇ erties of the plastic film may be adjusted and controlled for achieving the desired mechanical properties.
  • Fig. 1 shows as an axonometric view the principle of the OBD method.
  • Fig. 2A shows graphically the phase and magnitude curves obtained by means of the OBD method for the vertical deviation signals.
  • Fig.2B shows graphically the phase and magnitude curves obtained by means of the OBD method for the horizontal deviation signals.
  • Fig. 3 shows a PLS model in a matrix form.
  • Fig. 1 shows the principle of the OBD method.
  • the method is also called a Mirage method.
  • a laser 11 is a focused and modulated thermal beam, by means of which a plastic film sample 10 is heated.
  • a laser 12 is a measuring beam.
  • the reference number 13 denotes a diagrammatical representation of a thermal profile of the sample 10 and a medium surrounding it, which medium is gen ⁇ erally gas, generally air.
  • a transversal offset 14 is a perpendicular distance of the measuring beam 12 from the central point of the thermal beam 11.
  • a normal offset 15 is a height of the measuring beam 12 from a surface of the sample 10.
  • ⁇ (normal) and ⁇ t (transverse) represent the deviations in the vertical and horizontal direction caused by the deflection of the measuring beam 12.
  • Fig. 2A and 2B show the phase and magnitude curves as a function of the transversal offset 14 both for the vertical and horizontal deviations. Said curves are typical for a polyethylene sample.
  • the temperature profile 13 shown in Fig. 1 is a cyclical temperature distribution according to an equation (3)
  • n index of refraction of a medium, e.g a gas (generally air) at a tempera ⁇ ture T Q
  • T Q average temperature of the medium
  • the projection method refers to methods, in which a math ⁇ ematical projection is made of one or more data blocks for a couple of latent variables (LV).
  • the latent variable is essentially a linear combination of the initial variables.
  • the latent variables indicate the systematic information included in the data.
  • the PLS method partial least squares regression or projections to latent structures
  • two data blocks X and Y are projected, with the intention to simultaneously model X and to predict Y at as high an accuracy as possible.
  • the PLS corresponds to the PCR (principal component regression) and to the PCA (principal component analysis).
  • the PCA in turn resembles an SVD method (singular value decomposition), an eigenvector analysis, and a factor analysis (FA).
  • a particularly applicable method is based on the method of partial least squares regression (PLS).
  • Fig. 3 shows the PLS model in a matrix form.
  • the matrixes T and P model the- X block similar to the actual PC model.
  • the matrixes U and Q model the Y block.
  • connection between the block is modelled as a ratio between the matrixes U and T by means of diagonal matrix B.
  • the remainder matrixes of the block are E and F and the vector describing the internal dependencies is h.
  • the measured thermic wave represents the matrix X and the thermic diffusivity ⁇ is contained as one factor in the matrix Y (cf. Fig. 3).
  • a predictive model PLS
  • the functionability of the model is tested with known test sets, the values of the Y matrix of which are tended to be predicted.
  • the model may be applied to real samples.
  • the PLS model is formed of known samples. The reliability of the PLS model is tested by means of some new samples, whose thermic diffusivity ⁇ is known.

Abstract

The invention relates to a method for determining the thermal conductivity of anisotropic plastic films. A focused and modulated heating beam (11) is directed to a plastic film sample (10), whereby a thermal profile (13) is obtained for the plastic film sample (10) and a medium surrounding it. The thermal profile (13) is inspected by means of a measuring beam (12), whereby a phase and magnitude information (Ζn, Ζt) is obtained for the thermal profile (13) as a function of a transversal offset (14) both for vertical and horizontal deviations. The vertical and horizontal deviation signals of the phase and magnitude information (Ζn, Ζt) are analyzed by means of a projection method, such as a method of partial least squares regression PLS, whereby said thermic wave represents in the analysis a certain matrix (X) and the thermic diffusivity (α) of the plastic film sample (10) is contained as one factor in another matrix (Y). By using known samples or a simulated training set, a PLS model (predictive model) is formed, by means of which the thermic diffusivity (α) of unknown plastic film samples and the thermal conductivity (K) on the basis of the formulas (1): α = K / (ςC) and (2): K = α . ςC are determined.

Description

A method for determining the thermal conductivity of anisotropic plastic films and its usage
The invention relates to a method for determining the thermal conductivity of anisotropic plastic films.
The thermic diffusivity is obtained from the equation (1)
a = _K_ (1) P C
in which
K = thermal conductivity p = density
C = specific heat
From the equation (1) follows that
K = α • p C (2)
It is commonly known that on one certain plastic film, p C is independent of the orientation degree of the plastic film. Plastic films generally obtain orientation e.g. by stretching. It is a known fact that an orientated plastic film has in the values of the thermal conductivity in different directions considerable differences. The thermal conductivity is even 2-20-fold in certain directions. In the literature of the art is presented even such a fact that the difference in the thermal conductivity could be even 100-fold. The control and determination of the thermic diffusivity of polymers is extremely important when preparing high-class polymers. The thermic diffusivity is import¬ ant also in the sense that the structural properties of the polymer depend on the thermic diffusivity. In this sense, the orientation of polymers is also of import- ance with respect to the mechanical properties of the final product.
Currently, there is no good and reliable method for determining the anisotropic thermic diffusivity of orientated polymers. The thermal conductivity of plastic films has been measured with different measuring methods according to the standard ASTM, but the methods known currently do not apply to the measure¬ ment of the thermal conductivity of anisotropic films, since by means of these known methods, it is not possible to measure the thermal conductivity in the direction of the film.
The object of the invention is to provide a method, by means of which the thermal conductivity of anisotropic plastic films may be determined sufficiently reliably.
The objects of the invention are achieved by means of a method, which is characterized in that a focused and modulated heating beam is directed to a plastic film sample, whereby a thermal profile is obtained for the plastic film sample and a medium surrounding it, that said thermal profile is inspected by means of a measuring beam, whereby a phase and magnitude information is obtained for said thermal profile as a function of transversal offset both for vertical and horizontal deviations, that the vertical and horizontal signals of said phase and magnitude information are analyzed by means of a projection method, such as a method of partial least squares regression PLS, whereby said thermic wave represents in the analysis a certain matrix and the thermic diffusivity of the plastic film sample is contained as one factor in another matrix, and that by using known samples or a simulated training set, a PLS model (predictive model) is formed, by means of which the thermic diffusivity of unknown plastic film samples and the thermal conductivity on the basis of the formulas (1) and (2) β = J (i)
P C
K = α • p C (2)
are determined.
In the inventive method, it has been realized to apply an optical beam deflection (OBD) known per se. This method has been used for determining the thermal conductivity of metals and ceramics, but this method cannot as such be applied to the determination of the thermal conductivity of anisotropic plastic films. By means of the OBD method, e.g. for a polyethylene sample is obtained phase and magnitude curves as a function of the transversal offset both for vertical and horizontal deviations. In the inventive method, the data analysis is performed by means of a chemometric analysis method. In this analysis method is used a so- called projection method. A certain especially applicable method is a method of partial least squares regression (PLS), in which the measured thermic wave represents in the analysis a matrix X and the thermic diffusivity is contained as one factor in a matrix Y. By using the known samples or a simulated training set, it is possible to form a predictive model (PLS-model), by means of which the thermic diffusivity α of unknown samples may be determined. The functionability of the model is tested by means of known test sets, in connection of which attempts are made to predict the values of this Y matrix. When the functionability of the model is indicated by means of the test set, the model may be applied to real samples.
The inventive method may be applied to the determination of the orientation degree of plastic films. As a result of this determination, the mechanical prop¬ erties of the plastic film may be adjusted and controlled for achieving the desired mechanical properties.
' The invention is illustrated in detail with reference to a principal solution shown in the figures of the accompanying drawings, to which the invention is however not intended solely to be limited.
Fig. 1 shows as an axonometric view the principle of the OBD method.
Fig. 2A shows graphically the phase and magnitude curves obtained by means of the OBD method for the vertical deviation signals.
Fig.2B shows graphically the phase and magnitude curves obtained by means of the OBD method for the horizontal deviation signals.
Fig. 3 shows a PLS model in a matrix form.
Fig. 1 shows the principle of the OBD method. The method is also called a Mirage method. A laser 11 is a focused and modulated thermal beam, by means of which a plastic film sample 10 is heated. A laser 12 is a measuring beam. The reference number 13 denotes a diagrammatical representation of a thermal profile of the sample 10 and a medium surrounding it, which medium is gen¬ erally gas, generally air. A transversal offset 14 is a perpendicular distance of the measuring beam 12 from the central point of the thermal beam 11. A normal offset 15 is a height of the measuring beam 12 from a surface of the sample 10. φ (normal) and Φt (transverse) represent the deviations in the vertical and horizontal direction caused by the deflection of the measuring beam 12.
Fig. 2A and 2B show the phase and magnitude curves as a function of the transversal offset 14 both for the vertical and horizontal deviations. Said curves are typical for a polyethylene sample.
The temperature profile 13 shown in Fig. 1 is a cyclical temperature distribution according to an equation (3)
T(x,y,z,t) (3) The magnitude curves shown in Fig. 2A and 2B are mathematically based on a formula (4)
in which
n = index of refraction of a medium, e.g a gas (generally air) at a tempera¬ ture TQ
TQ = average temperature of the medium
dl = difference along the measuring beam 12
The inventive data analysis is principally as follows:
known samples — > model
test set --> model testing
real samples - > determination of diffusivity
In this connection, the projection method refers to methods, in which a math¬ ematical projection is made of one or more data blocks for a couple of latent variables (LV). The latent variable is essentially a linear combination of the initial variables. The latent variables indicate the systematic information included in the data. In the PLS method (partial least squares regression or projections to latent structures) two data blocks X and Y are projected, with the intention to simultaneously model X and to predict Y at as high an accuracy as possible. The PLS corresponds to the PCR (principal component regression) and to the PCA (principal component analysis). The PCA in turn resembles an SVD method (singular value decomposition), an eigenvector analysis, and a factor analysis (FA).
In the inventive data analysis method is thus used a projection method. A particularly applicable method is based on the method of partial least squares regression (PLS).
Fig. 3 shows the PLS model in a matrix form. The matrixes T and P model the- X block similar to the actual PC model. The matrixes U and Q model the Y block.
The connection between the block is modelled as a ratio between the matrixes U and T by means of diagonal matrix B. The remainder matrixes of the block are E and F and the vector describing the internal dependencies is h.
In the analysis, the measured thermic wave represents the matrix X and the thermic diffusivity α is contained as one factor in the matrix Y (cf. Fig. 3). By using known samples or a simulated training set, a predictive model (PLS) is formed, by means of which the thermic diffusivity α of unknown samples 10 may be determined. The functionability of the model is tested with known test sets, the values of the Y matrix of which are tended to be predicted. When the functionability of the model has been indicated, the model may be applied to real samples.
The PLS model is formed of known samples. The reliability of the PLS model is tested by means of some new samples, whose thermic diffusivity α is known.
Enclosed are the patent claims, which define the protective scope of the inven- five method.

Claims

Claims
1. A method for determining the thermal conductivity of anisotropic plastic films, c h a r a c t e r i z e d in that a focused and modulated heating beam (11) is directed to a plastic film sample (10), whereby a thermal profile (13) is obtained for the plastic film sample (10) and a medium surrounding it, that said thermal profile (13) is inspected by means of a measuring beam (12), whereby a phase and magnitude information (φ , ø.) is obtained for said thermal profile (13) as a function of a transversal offset (14) both for vertical and horizontal deviations, that the vertical and horizontal signals of said phase and magmtude information ( n, øt) are analyzed by means of a projection method, such as a method of partial least squares regression PLS, whereby said thermic wave represents in the analysis a certain matrix (X) and the thermic diffusivity (α) of the plastic film sample (10) is contained as one factor in another matrix (Y), and that by using known samples or a simulated training set, a PLS model (predictive model) is formed, by means of which the thermic diffusivity ( ) of unknown plastic film samples and the thermal conductivity (K) on the basis of the formulas (1) and (2)
= J (1) P C
K = α • pC (2)
are determined.
2. A method according to Claim 1, c h a r a c t e r i z e d in that the reliability of the PLS model is tested by means of a couple of new samples, whereby the thermic diffusivity (α) is known.
3. A usage of a method according to Claim 1 or 2 for determining the orienta¬ tion degree of plastic films.
4. A usage of a method according to Claim 1 or 2 for adjusting and controlling the mechanical properties of the plastic film.
PCT/FI1992/000226 1991-08-09 1992-08-07 A method for determining the thermal conductivity of anisotropic plastic films and its usage WO1993003352A1 (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
FI913780 1991-08-09
FI913780A FI89633C (en) 1991-08-09 1991-08-09 Method for determining the thermal conductivity of anisotropic plastic films and use thereof

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5586824A (en) * 1994-06-14 1996-12-24 The United States Of America As Represented By The Secretary Of The Navy Method of measuring the thermal conductivity of microscopic graphite fibers
WO2005066875A1 (en) * 2002-09-20 2005-07-21 General Electric Company Systems and methods for developing a predictive continuous product space from an existing discrete product space

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4468136A (en) * 1982-02-12 1984-08-28 The Johns Hopkins University Optical beam deflection thermal imaging
US4521118A (en) * 1982-07-26 1985-06-04 Therma-Wave, Inc. Method for detection of thermal waves with a laser probe
US4589783A (en) * 1984-04-04 1986-05-20 Wayne State University Thermal wave imaging apparatus

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4468136A (en) * 1982-02-12 1984-08-28 The Johns Hopkins University Optical beam deflection thermal imaging
US4521118A (en) * 1982-07-26 1985-06-04 Therma-Wave, Inc. Method for detection of thermal waves with a laser probe
US4589783A (en) * 1984-04-04 1986-05-20 Wayne State University Thermal wave imaging apparatus

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
DERWENT'S ABSTRACT, No. 86-318 020/48; & SU,A,1 226 235, publ. week 8648. *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5586824A (en) * 1994-06-14 1996-12-24 The United States Of America As Represented By The Secretary Of The Navy Method of measuring the thermal conductivity of microscopic graphite fibers
WO2005066875A1 (en) * 2002-09-20 2005-07-21 General Electric Company Systems and methods for developing a predictive continuous product space from an existing discrete product space

Also Published As

Publication number Publication date
FI89633C (en) 1993-10-25
FI913780A (en) 1993-02-10
FI89633B (en) 1993-07-15
FI913780A0 (en) 1991-08-09

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