FI89633C - Method for determining the thermal conductivity of anisotropic plastic films and use thereof - Google Patents

Description

89633

Method for the determination of the thermal conductivity of an isotropic plastic films and its use Förfarande för bestämning av värmeledningsförmägan hos anisotropa plastfilmer och användning av detta 5

The invention relates to a method for determining the thermal conductivity of an isotropic plastic films.

10 Thermal diffusivity a is obtained from equation (1) K ...

• - Jc (1) where K = thermal conductivity p = density 15 C = specific heat

It follows from Equation (1) that K = a · pC (2) 20 It is generally known that for a given plastic film, pC is independent of the degree of orientation of the plastic film. Orientation to plastic films is usually obtained, for example, by stretching. It is a known fact that in an oriented plastic film there are considerable differences in the values of thermal conductivity in different directions. Thermal conductivity is up to 2-20 times in certain directions. There is even information in the art that the difference in thermal conductivity could be as much as 100-fold.

The control and determination of the thermal diffusivity of polymers is very important in the preparation of high quality polymers. Thermal diffusivity is also important in the sense that the structural properties of the polymer depend on the thermal diffusivity. In this sense, the orientation of the polymers is also important for the mechanical properties of the final product.

5 There is currently no good and reliable method for determining the anisotropic thermal diffusivity of oriented polymers. The thermal conductivity of plastic films has been measured by various measurement methods according to the ASTM standard, but currently known methods are not suitable for measuring the thermal conductivity of anisotropic films because these known methods cannot measure the thermal conductivity in the direction of the film.

The object of the invention is to provide a method by which the thermal conductivity of anisotropic plastic films can be determined with sufficient reliability.

The objects of the invention are achieved by a method characterized in that a focused and modulated heating beam is applied to a plastic film sample, thereby providing a thermal profile on the plastic film sample and the surrounding medium, examining said thermal profile with a measuring beam, giving said thermal profile a phase and magnitude as a function of both vertical and 20 horizontal deviations, that the vertical and horizontal deviation signals of said phase and magnitude information are analyzed by a projection method, such as a partial least squares regression (PLS) method, whereby the measured thermal wave represents in the analysis of one matrix and the thermal diffusivity of the plastic film sample is included as one factor in another matrix, 25 and that using known samples or simulated data (training set) aan PLS model (predictive model), which allows the thermal diffusivity and thermal conductivity of unknown plastic film samples according to formulas (1) and (2) K, 1Λ “'7c (1) i 8 9 6 3 3 3 K = a · pC (2) determined.

In the method according to the invention, it has been realized to apply an optical beam deflection (OBD) known per se. This method has been used to determine the thermal conductivity of metals and ceramics, but as such is not suitable for determining the thermal conductivity of anisotropic plastic films. With the help of the OBD method, for example, phase and magnitude curves are obtained for a polyethylene sample as a function of the transverse offset for both vertical and horizontal deviations. In the method according to the invention, the data analysis is performed by means of a chemometric analysis method 10. This method of analysis uses the so-called projection method. One particularly suitable is the partial least squares regression (PLS) method, in which the measured thermal wave represents matrix X in the analysis and thermal diffusivity a is included as one factor in matrix Y. Using known samples or simulated data (training set) a PLS-15 model can be formed. (predictive model), which can be used to determine the thermal diffusivity a of unknown samples. The functionality of the model is tested with known samples (test set), the Y-matrix values of which are sought to be predicted. Once the functionality of the model in a series of tests has been demonstrated, the model can be applied to actual samples.

The method according to the invention can be applied to determine the degree of orientation of plastic films. As a result of this determination, the mechanical properties of the plastic film can be regulated and controlled to provide the desired mechanical properties.

The invention will be explained in detail with reference to the principle solution of the invention shown in the figures of the accompanying drawings, to which, however, the invention is not intended to be exclusively limited.

Figure 1 shows an axonometric diagram of the principle of the OBD method.

B 9 6 4 ό 4

Figure 2Α shows graphically the phase and magnitude curves obtained by the OBD method for vertical deviation signals.

Figure 2B shows graphically the phase and magnitude curves 5 obtained by the OBD method for horizontal deviation signals.

Figure 3 shows the PLS model in matrix form.

Figure 1 shows the principle of the OBD method. The method is also referred to as the 10 Mirage method. The laser 11 is a focused and modulated heating beam with which the plastic film sample 10 is heated. Laser 12 is a measuring beam. Reference numeral 13 denotes a diagram showing the thermal profile of the sample 10 and the surrounding medium, such as, for example, gas, in general air. The transverse offset 14 is the perpendicular distance of the measuring beam 12 from the center of the heating beam 11. The normal offset 15 is the height of the measuring beam 12 15 from the surface of the sample 10. <pn (normal) and <pt (transverse) are the vertical and horizontal deviations due to the bending of the measuring beam 12.

Figures 2A and 2B show phase and magnitude curves as a function of transverse offset 14 for both vertical and horizontal deviations. Ko. the curves are typical of a polyethylene sample.

20

The heat profile 13 shown in Fig. 1 is the periodic temperature distribution T (x, y, z, t) according to Equation (3) (3). 25 The magnitude curves shown in Figs. 2A and 2B are mathematically based on Equation (4).

M

Φ = f vnj / (4)

n dTo L

i 5 B9663 where n = refractive index of a medium such as a gas (usually air) at temperature T0 5 T0 = average temperature of the medium dl = difference along the measuring radius 12

The data analysis of the method according to the invention is basically as follows: 10 known samples -> model test time -> model testing actual samples -> determination of diffusivity a In this context, the projection method refers to methods in which one or more data blocks are mathematically projected to a few latent variables (LV). The latent variable is essentially a linear combination of the original variables. Latent variables indicate the systematic information contained in the data. The PLS method (partial least squares regression or projections to latent structures) projects two data blocks, X and Y, for the purpose of simultaneously modeling X and predicting Y with the greatest possible accuracy. PLS is similar to PCR (principal component regression) and PCA (principal component analysis). PCA, in turn, is similar to the SVD (singular value decomposition) method, eigenvector analysis, and factor analysis (FA).

25

Thus, in the data analysis method according to the invention, a projection method is used. One very suitable is the partial least squares regression (PLS) method.

Figure 3 shows the PLS model in matrix form. The matrices T and P model the X-block similar to the actual PC model. The matrices U and Q model the Y block.

6 B 9 6 3 p

The connection between the blocks is modeled as the relationship between the U and T matrices using the diagonal matrix B. The residual matrices of the block are E and F and the vector describing the internal dependencies is h.

5 The measured thermal wave represents the matrix X in the analysis and the thermal diffusivity a is included as one factor in the matrix Y (compare Figure 3). Using known samples or simulated training (training set), a PLS (predictive model) is generated, by means of which the thermal diffusivity α of the unknown samples 10 can be determined. The functionality of the model is tested with known samples (test set), the Y-matrix values of which are sought to be predicted. Once the functionality of the model with the test time has been demonstrated, the model can be applied to actual samples.

The PLS model is formed from known samples. The reliability of the PLS model is tested with a few new samples with known thermal diffusivity a.

15

The following claims define the scope of the method according to the invention.

Claims (4)

7 89635 A method for determining the thermal conductivity of anisotropic plastic films, characterized in that a focused modulated heating beam (11) is applied to the plastic film sample (10), thereby providing a thermal profile (13) to the plastic film sample (10) and the surrounding medium. (12), whereby said thermal profile (13) is provided with phase and magnitude information (Φη, Φ {) as a function of the transverse offset (14) for both vertical and horizontal deviations, so that said phase and magnitude information (φη, φ,) can be - and 10 horizontal deviation signals are analyzed by a projection method, such as a partial least squares regression PLS, where the measured thermal wave represents a matrix (X) in the analysis and the thermal diffusivity (a) of the plastic film sample (10) is included as one. as a factor in another matrix (Y) , and that using known samples or simulated data 15 (training set) a PLS model (predictive model) is formed, which allows the thermal diffusivity (a) of unknown plastic film samples and the formulas (1) and (2) • 'Jd (1) K = a · Based on pC (2), the thermal conductivity (K) is determined. 20 A method according to claim 1, characterized in that the reliability of the PLS model is tested with a few new samples whose thermal diffusivity (cr) is known. Use of a method according to claim 1 or 2 for determining the degree of orientation of plastic films. --- τ ~. 8 9 6 3 ό 8 Use of a method according to claim 1 or 2 for adjusting and controlling the mechanical properties of a plastic film. 9 b 9 61 j