JP4228080B2 - Method for calculating the crystal length distribution of crystals in a material from differential scanning calorimetry data of the polymer material - Google Patents

Description

  The present invention corrects the melting temperature from a melting peak curve obtained by differential scanning calorimetry (hereinafter referred to as “DSC”) of a polymer material, thereby correcting crystals in the polymer material. (Hereinafter, referred to as “polymer crystal”).

It has been reported that the DSC melting peak curve of a polymer substance can be converted into the distribution of the crystal length ζ of the polymer crystal, and the distribution agrees well with the result of X-ray analysis (see, for example, Non-Patent Document 1). ).
In Non-Patent Document 1, the initial gradient of the melting peak of pure benzoic acid is used to correct the melting temperature Tm indicating the melting peak curve. That is, a straight line having an initial gradient of the melting peak of benzoic acid is drawn from the measured point on the melting peak curve of the polymer substance, and the temperature crossing the temperature axis is the melting temperature Tm at the point on the melting peak curve. It is said that there is. However, benzoic acid is characterized by a slight decrease in purity and a slow rise in melting peak (see Non-Patent Document 2, for example). Therefore, high-purity benzoic acid is required for temperature correction.

However, since the melting method of benzoic acid crystals, which are low molecular weights, is different from the melting of polymer crystals that coexist with non-crystalline parts, the melting temperature Tm of the polymer crystals is corrected by the rising slope of the melting peak of benzoic acid. There is a lack of strictness for doing this. Furthermore, the crystal length calculated in Non-Patent Document 1 (zeta) distribution because not standardized in temperature, i.e., the unit of the distribution function is a rather "nm ^-1 K ^-1" "nm ^-1" Therefore, it cannot be compared with the ζ distribution of other samples. Further, the crystal end surface free energy σ per unit area necessary for calculating the ζ distribution must be cited from other documents (for example, see Non-Patent Document 3). In this case, the crystal end surface free energy σ is merely a temporary value, not the value of the sample used.
Polymer, Vol.25, pp1268-1270 (1984) Principles of Thermal Analysis and Calorimetry, RSC Paperbacks, P87 (2002) Thermochimica Acta, Vol.396, PP79-85 (2003)

  However, even if the crystal end surface free energy σ necessary for calculating the crystal length (ζ) distribution is cited from other documents as in the study of Non-Patent Document 3, it is sensitive to heat and has a delicate structure and properties. Analysis of DSC melting peak of high molecular weight material is difficult with only X-ray analyzer, that is, even if X-ray analyzer is used, the crystal length distribution is close to the actual due to the effect of irradiating the sample with X-rays There was a problem that could not be obtained. Further, when calculating the crystal length distribution, there is an inconvenience that the melting temperature Tm must be corrected using high-purity benzoic acid.

  The object of the present invention is to convert the DSC melting peak of a polymer material into a crystal length distribution that is close to the actual one, so that the structure of a sensitive and sensitive polymer material, which is different from the distribution obtained by X-ray analysis, It is an object of the present invention to provide a method for calculating a crystal length distribution reflecting properties based on DSC data without using high-purity benzoic acid for correction of an X-ray analyzer and a melting temperature Tm.

In the invention according to claim 1 of the present application, as shown in FIGS. 1 to 2, the crystal length distribution of the substance is calculated from the differential scanning calorimetry data of the polymer substance including the following steps (a) to (i). Is the method.
(a) a step of performing differential scanning calorimetry of the polymer material by heat-treating the polymer material at a plurality of given temperatures (Ta1, Ta2, ... Tan);
(b) From the calorimetry, a plurality of melting start temperatures (Tb1, Tb2, ... Tbn) corresponding to each temperature at the plurality of given temperatures (Ta1, Ta2, ... Tan) and a plurality of melting ends The process of determining the temperature (Te1, Te2, ... Ten),
(c) In the figure where the vertical axis is the melting temperature Tm of the polymer material and the horizontal axis is the heat treatment temperature Ta, the plurality of melting start temperatures (Tb1, Tb2, ... Tbn) and the plurality of the melting points Plotting melting end temperatures (Te1, Te2, ... Ten) respectively (see Fig. 1),
(d) A straight line P1 obtained from the plurality of plotted melting start temperatures (Tb1, Tb2,... Tbn) is a straight line P2 obtained from the plurality of plotted melting end temperatures (Te1, Te2,... Ten). To obtain a temperature Tb ⁰ corresponding to the intersection M (see FIG. 1),
(e) drawing a virtual line P3 of Tm = Ta in the figure, the step of obtaining an equilibrium melting temperature Tm ^x corresponding to the intersection N by intersecting a straight line P3 by extending the straight line P2 (see FIG. 1),
(f) The weight of the polymer substance is W, the melting endotherm per gram of the substance of the melting peak A actually measured by differential scanning calorimetry in the step (a) is Q, and the rate of temperature rise is dT / dt (T temperature, t is the time), the (by using the temperature Tb ⁰ and the temperature Tm ^x obtained respectively d) and (e) step, the heat at the peak point P of the virtual melting peak B from the following equation (1) flow seek (dQ / dt) _p, obtaining a rising slope C of the virtual melting peak B from both sides of (Tm ^x -Tb ⁰⁾ in dividing the resulting equation by the formula (1) (2) ( (See Fig. 2)
(dQ / dt) _p = 2QW (dT / dt) / (Tm ^x −Tb ⁰ ) (1)
C = (dQ / dt) _p / (Tm ^x −Tb ⁰ ) = 2QW (dT / dt) / (Tm ^x −Tb ⁰ ) ² (2)
(g) Obtain the area ∫ _Tb ^Te (dQ / dt) dT corresponding to the endothermic amount Q surrounded by the curve of the melting peak A and the temperature axis, and further change the endotherm per unit temperature at each temperature from Tb to Te. corresponds to the ratio Delta] Q / Q to Q quantity ΔQ (dQ / dt) / ∫ Tb Te obtaining a (dQ / dt) dT,
(h) When σ is the crystal end surface free energy per unit area of the crystal in the polymer material and hu is the heat of fusion per unit volume, using the temperature-corrected Tm, the following equation (3) A step of obtaining a crystal length ζ of the polymer crystal, and
ζ = (2σ / hu) [Tm ^x / (Tm ^x −Tm)] (3)
(i) ΔQ / Q obtained in the step (g) and the crystal length ζ obtained in the step (h) are substituted into the following equation (4) to standardize the crystal length at the corrected temperature. A step of obtaining a distribution function F (ζ) and obtaining a crystal length distribution from the function F (ζ).
F (ζ) = (ΔQ / Q) / ζ (4)
However, in the steps (a) to (d), n is a positive integer.

In the method according to claim 1 of the present application, the melting temperature Tm, which is a variable of the DSC melting peak curve, is temperature-corrected based on the equations (1) and (2) using the DSC data of the polymer substance, and the temperature Tb ⁰ and the temperature By calculating the crystal length distribution function F (ζ) from Eqs. (3) and (4) using Tm ^x , the DSC melting peak of the polymer substance can be converted into a crystal length distribution close to actuality, The structure and properties of sensitive and sensitive polymer substances can be predicted from the crystal length distribution. Further, the crystal length distribution of the polymer substance can be calculated easily and inexpensively without using high-purity benzoic acid for the correction of the X-ray analyzer and the melting temperature Tm.

Hereinafter, the best mode of the present invention will be described for each step.
(a) Implementation of DSC A plurality of identical polymer materials are prepared, and each polymer material is heat-treated at a plurality of given temperatures (Ta1, Ta2,... Tan) to obtain DSC data. When setting a plurality of given temperatures, a melting end temperature Te and a melting start temperature Te in a temperature range in which Tb-Ta is substantially constant are selected by avoiding a temperature range in which the crystal form changes by heat treatment. Te is generally not related to the value of Tb. The polymer substance has a crystal structure in the substance.

(b) Measurement of each melting start temperature and each melting end temperature From a plurality of DSC data, a plurality of melting start temperatures (Tb1, Tb2, ... Tbn for each of a plurality of heat treatment temperatures (Ta1, Ta2, ... Tan). ) And a plurality of melting end temperatures (Te1, Te2,... Ten). These temperatures are obtained from a plurality of DSC data as follows. Draw an extension line to the high temperature side from the straight line part before the melting peak rises, set the rising temperature of the peak from the straight line to Tb, and draw an extension line from the straight line part after the melting peak to the low temperature side, Te is the junction of the straight line and the peak curve at the end of melting.

(c) Plot in the figure As shown in FIG. 1, in the figure where the vertical axis is the melting temperature Tm of the polymer substance and the horizontal axis is the heat treatment temperature Ta, a plurality of heat treatment temperatures (Ta1, Ta2,. .. Tan, a plurality of melting start temperatures (Tb1, Tb2,... Tbn) and a plurality of melting end temperatures (Te1, Te2,... Ten) are respectively plotted.

(d) Determination of temperature Tb ^{0 As} shown in FIG. 1, a straight line P1 is first obtained from a plurality of plotted melting start temperatures (Tb1, Tb2,... Tbn). Next, a straight line P2 is obtained from the plotted melting end temperatures (Te1, Te2,... Ten). Next, the straight line P1 is intersected with the straight line P2, and the intersection M is obtained. The point M is read by the temperature axis of the horizontal axis, and the temperature Tb ⁰ corresponding to the intersection M is obtained. This temperature Tb ⁰ is a melting start temperature, a melting end temperature of a virtual melting peak B (see FIG. 2) described later, and a peak B peak temperature.

(e) subtracting the virtual straight line P3 of Tm = Ta in first determined Figure 1 equilibrium melting temperature Tm ^x. Then the intersection point N determined by intersecting a straight line P3 by extending the straight line P2 obtained in step (d), by reading this point N at a temperature axis of abscissa, obtaining the temperature Tm ^x corresponding to the intersection N. The Tm ^x is an equilibrium melting temperature. That is, it is the melting temperature of the polymer substance when the crystal length is infinite, and is also the temperature when all the crystals are melted and the crystallinity is 0 (zero). As is apparent from FIG. 1, the straight line P1 obtained from a plurality of melting start temperatures (Tb1, Tb2,... Tbn) is generally located above the virtual straight line P3 of Tm = Ta. That is, each melting start temperature is usually several degrees higher than the respective heat treatment temperature Ta.
In the high-temperature heat treatment sample may melting completion temperature Te increases beyond equilibrium melting temperature Tm ^x with increasing annealing temperature Ta. This is generally considered as an overshoot due to delayed melting of the crystal, and the melting end temperature Te at this time cannot be used for data for drawing the P2 straight line.

(f) Determination of gradient from virtual melting peak of polymer substance FIG. 2 shows the melting peak A measured by DSC in the step (a) and the temperature Tb ⁰ obtained in the step (d) and the above ( virtual melting peak B plotting by the following procedure using the temperature Tm ^x obtained in step e).
First, the weight of the polymer substance is W, the melting endotherm per gram of the substance having the melting peak A is Q, the heating rate is dT / dt (T is temperature, t is time), temperature Tb ⁰ and temperature Tm ^x 2, the heat flow (dQ / dt) _p at the peak point P of the virtual melting peak B is obtained from the following equation (1), as shown in FIG.
(dQ / dt) _p = 2QW (dT / dt) / (Tm ^x −Tb ⁰ ) (1)
Next, the rising gradient C of the virtual melting peak B is obtained from the equation (2) obtained by dividing both sides of the equation (1) by (Tm ^x -Tb ⁰ ). Thus, as shown in FIG. 2, it is possible to draw a right triangle consisting of points Tb ⁰ and the point Tm ^x and the point P. The area of this triangle corresponds to the endothermic amount Q.
C = (dQ / dt) _p / (Tm ^x −Tb ⁰ ) = 2QW (dT / dt) / (Tm ^x −Tb ⁰ ) ² (2)

(g) Determination of specific endothermic change ΔQ / Q per unit temperature Obtain an area ∫ _Tb ^Te (dQ / dt) dT corresponding to the endothermic amount Q surrounded by the curve of the melting peak A and the temperature axis. corresponding to Delta] Q / Q at each temperature up Te Request _{(dQ / dt) / ∫ Tb} Te (dQ / dt) dT. The temperature correction for each temperature from Tb to Te is performed as follows. From the peak point of the melting peak A to the temperature axis, a straight line of the gradient C obtained in the step (f) is drawn from the peak point. The intersection temperature with the temperature axis is the true melting peak temperature at the peak point. Next, a difference ΔT between the pre-correction melting peak temperature and the true melting peak temperature is obtained. The temperature correction value for each temperature from Tb to Te is given by -ΔT (dQ / dt) / (dQ / dt) p. Here, (dQ / dT) p is the heat flow at the peak point, and (dQ / dT) is the heat flow at each temperature before temperature correction.

(h) Determination of crystal length of crystal in polymer material As shown in Non-Patent Document 1 mentioned above, σ is the crystal free surface energy per unit area of crystal in the polymer material, and hu is its unit volume. When the heat of fusion is per unit, the crystal length ζ of this polymer crystal is obtained from the following equation (3). As Tm in the equation (3), Tm whose temperature is corrected is used.
ζ = (2σ / hu) [Tm ^x / (Tm ^x −Tm)] (3)

(i) Determination of crystal length distribution by crystal length distribution function F (ζ) The specific endothermic change ΔQ / Q obtained in the step (g) and the crystal length ζ obtained in the step (h) are expressed by the following formula ( Substituting into 4), the crystal length distribution function F (ζ) normalized by temperature is obtained, and the crystal length distribution is obtained from the crystal length ζ obtained in the step (h) and the function F (ζ).
F (ζ) = (ΔQ / Q) / ζ (4)

This equation (4) is expressed as the crystal length distribution function F (ζ) normalized by temperature, as shown in the NATAS Annual Conference Proceedings (0.29.26p in CD), Albuquerque, (2003) (Non-Patent Document 4), 39th. Also defined in the following equation (4 ′) in the collection of lectures on thermal measurement discussion, Hiroshima, p282 (2003) (non-patent document 5).
F (ζ) = (ΔQ / Q) / ζ = nζ / [Nc (Te−Tb)] (4 ′)
Here, nζ is the number of crystal chains having the length of ζ, and Nc is the number of structural units of crystals melted in the range of the melting start temperature Tb and the melting end temperature Te.

Also, σ in equation (3) is calculated by the following equation (5). This equation (5) is shown in J. Macromol. Sci., Phys., B42 , 621 (2003) (Non-Patent Document 6) in addition to Non-Patent Documents 4 and 5 above.
_{σ / h u = b [RTm} 2 + (Hx-hx) (Tm x -Tm)] / [2 (Hx-hx) Tm x] ... (5)
Here, Hx = 2 (w / ρ) hu-wQ, b is the fiber axis length of the crystal unit cell, hx is the transition enthalpy per mole of structural unit due to the pseudocrystal in the amorphous region, and w is The molecular weight per mole of structural unit, ρ, is the density of the crystal.

Next, examples of the present invention will be described.
<Example 1>
As the polymer material, eight polyhexamethylene adipamide (nylon 66) films were prepared, and each film was subjected to eight different temperatures using a heat flux type DSC apparatus (DSC3200S manufactured by Bruker AXS). That is, heat treatment was performed at Ta1 = 220 ° C., Ta2 = 225 ° C., Ta3 = 230 ° C., Ta4 = 240 ° C., Ta5 = 250 ° C., Ta6 = 253 ° C., Ta7 = 256 ° C. and Ta7 = 258 ° C. for 60 minutes.

  From the above 8 types of DSC data, the melting start temperature (Tb1, Tb2, Tb3, Tb4, Tb5, Tb6, Tb7, Tb8) and the melting end temperature (Te1, Te2, Te3, Te4, Te5, Te6, Te7, Te8) were obtained. In this example, Tb-Ta was approximately 4 ° C in the heat treatment up to 240 ° C, and Tb-Ta was approximately 2 ° C in the heat treatment at 250 ° C or higher. In the heat treatment from 240 ° C. to 250 ° C., the crystal form formed was predicted to have changed from β-type to α-type, and Tb and Te in this range were excluded from the data. FIG. 3 shows a DSC melting peak curve of the nylon 66 film when heat-treated for 60 minutes at 256 ° C. where Tb-Ta is approximately 2 ° C.

Next, as shown in FIG. 1, the eight melting start temperatures (Tb1, Tb2, Tb3, Tb4, Tb5) are shown in the figure where the vertical axis is the melting temperature Tm of the polymer material and the horizontal axis is the heat treatment temperature Ta. , Tb6, Tb7, Tb8) and eight melting end temperatures (Te1, Te2, Te3, Te4, Te5, Te6, Te7, Te8), respectively. A straight line P1 was obtained from these melting start temperatures (Tb1, Tb2, Tb3, Tb4, Tb5, Tb6, Tb7, Tb8). Next, a straight line P2 was obtained from the plotted melting end temperatures (Te1, Te2, Te3, Te4, Te5, Te6, Te7, Te8). Next, the intersection point M is obtained by intersecting the straight line P1 with the straight line P2, and this point M is read on the temperature axis of the horizontal axis, and is also the melting start temperature of the virtual melting peak B shown in FIG. The temperature Tb ⁰ which is also the melting end temperature was determined. In this example, Tb ⁰ = 267 ° C.

Subsequently, after drawing a virtual straight line P3 of Tm = Ta in FIG. 1, the straight line P2 obtained in the step (d) is extended and intersected with the straight line P3 to obtain the intersection N. read at a temperature axis of the shaft to determine the equilibrium melting temperature Tm ^x corresponding to the intersection N. In this example, Tm ^x = 269 ° C.
Against 2 that actually measured melting peak A by DSC indicated, was plotted virtual melting peak B by the following procedure using the temperature Tb ⁰ and the temperature Tm ^x. First, the heat flow (dQ / dt) _p at the peak point P of the virtual melting peak B was determined from the above-described equation (1). In this example, the endothermic amount Q = 21.62 cal / g, the weight of the polymer material W = 0.28 mg, the rate of temperature increase dT / dt = 10 ° C./min, and (dQ / dt) _p = 1009 μcal / second. Met. Then determine the rising slope C of the virtual melting peak B from equation (2) described above, as shown in FIG. 2, and a point Tb ⁰ and the point Tm ^x and the point P, painted right triangle corresponding to the heat absorption amount Q It was. In this example, the gradient C was 504.5 μcal / (sec · K).

  Subsequently, in this embodiment, ΔQ / Q at each temperature is obtained in a temperature range from Tb = 258 ° C. to Te = 269 ° C. Each temperature is determined by the setting of the sampling time of the DSC apparatus. In this example, the temperature interval was automatically set to 0.1 ° C. or 0.2 ° C. for each temperature.

  On the other hand, the temperatures corrected in accordance with the step (g) from Tb to Te are substituted for Tm in the above-described equation (3), and the crystal lengths ζ1, ζ2, ζ3,,, of the nylon 66 film at each temperature are substituted. , ζn was obtained. n is the number of sampling temperatures determined by the setting of the sampling time of the DSC device. .DELTA.Q1 / Q, .DELTA.Q2 / Q, .DELTA.Q3 / Q,..., .DELTA.Qn / Q and .zeta.1, .zeta.2, .zeta.3,. The crystal length distribution was determined by the crystal length distribution function F (ζ). The result is shown in FIG. This crystal length distribution could be obtained simply and inexpensively without using high-purity benzoic acid for correcting the X-ray analyzer and the melting temperature Tm.

It is a diagram illustrating a method for determining the melting temperature Tb ⁰ and Tm ^x from multiple melting initiation temperature and melting completion temperature obtained by heat-treating the polymer material at a plurality of temperatures. Built using the melting peak A and the temperature Tb ⁰ and the temperature Tm ^x actually measured for obtaining the crystal length distribution, have the same area and peak A and a model diagram of a virtual melting peak B corresponding to the heat absorption amount Q is there. It is a figure which shows the DSC melting peak curve of the nylon 66 film heat-processed for 60 minutes at the temperature of 256 degreeC. It is a figure which shows the crystal length distribution curve of the nylon 66 film converted by the temperature correction by the Example of this invention, and converting from the actual melting peak curve of FIG.

Claims (1)

(a) performing a differential scanning calorimetry of the polymer material by heat-treating the polymer material at a plurality of given temperatures (Ta1, Ta2, ... Tan);
(b) From the calorimetry, a plurality of melting start temperatures (Tb1, Tb2, ... Tbn) corresponding to each temperature at the plurality of given temperatures (Ta1, Ta2, ... Tan) and a plurality of melting ends A process for obtaining temperatures (Te1, Te2, ... Ten);
(c) In the figure where the vertical axis is the melting temperature Tm of the polymer material and the horizontal axis is the heat treatment temperature Ta, the plurality of melting start temperatures (Tb1, Tb2, ... Tbn) and the plurality of the melting points Plotting melting end temperatures (Te1, Te2, ... Ten) respectively;
(d) A straight line P1 obtained from the plurality of plotted melting start temperatures (Tb1, Tb2,... Tbn) is a straight line P2 obtained from the plurality of plotted melting end temperatures (Te1, Te2,... Ten). And obtaining a temperature Tb ⁰ corresponding to the intersection M,
drawing a virtual line P3 of Tm = Ta in (e) the figure, a step of determining the equilibrium melting temperature Tm ^x corresponding to the intersection N by intersecting a straight line P3 by extending the straight line P2,
(f) The weight of the polymer substance is W, the melting endotherm per gram of the substance of the melting peak A actually measured by differential scanning calorimetry in the step (a) is Q, and the rate of temperature rise is dT / dt (T temperature, t is the time), the (by using the temperature Tb ⁰ and the temperature Tm ^x obtained respectively d) and (e) step, the heat at the peak point P of the virtual melting peak B from the following equation (1) calculated flow (dQ / dt) _p, and obtaining a rise slope C of the virtual melting peak B from both sides of (Tm ^x -Tb ⁰⁾ in dividing equation obtained by the equation (1) (2) ,
(dQ / dt) _p = 2QW (dT / dt) / (Tm ^x −Tb ⁰ ) (1)
C = (dQ / dt) _p / (Tm ^x −Tb ⁰ ) = 2QW (dT / dt) / (Tm ^x −Tb ⁰ ) ² (2)
(g) Obtain the area ∫ _Tb ^Te (dQ / dt) dT corresponding to the endothermic amount Q surrounded by the curve of the melting peak A and the temperature axis, and further change the endotherm per unit temperature at each temperature from Tb to Te. corresponds to the ratio Delta] Q / Q to Q of the amount Delta] Q and obtaining a _{(dQ / dt) / ∫ Tb} Te (dQ / dt) dT,
(h) When σ is the crystal end surface free energy per unit area of the crystal in the polymer material and hu is the heat of fusion per unit volume, using the temperature-corrected Tm, the following equation (3) A step of obtaining a crystal length ζ of the polymer crystal,
ζ = (2σ / hu) [Tm ^x / (Tm ^x −Tm)] (3)
(i) ΔQ / Q obtained in the step (g) and the crystal length ζ obtained in the step (h) are substituted into the following equation (4) to standardize the crystal length at the corrected temperature. Obtaining a distribution function F (ζ) and obtaining a crystal length distribution from the function F (ζ);
F (ζ) = (ΔQ / Q) / ζ (4)
A method for calculating the crystal length distribution of crystals in the material from differential scanning calorimetry data of the polymer material characterized by comprising:

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