JP3195090B2 - Method and apparatus for determining aspect ratio of powder - Google Patents
Method and apparatus for determining aspect ratio of powderInfo
- Publication number
- JP3195090B2 JP3195090B2 JP35172992A JP35172992A JP3195090B2 JP 3195090 B2 JP3195090 B2 JP 3195090B2 JP 35172992 A JP35172992 A JP 35172992A JP 35172992 A JP35172992 A JP 35172992A JP 3195090 B2 JP3195090 B2 JP 3195090B2
- Authority
- JP
- Japan
- Prior art keywords
- aspect ratio
- powder
- average particle
- specific surface
- surface area
- Prior art date
- Legal status (The legal status 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 status listed.)
- Expired - Fee Related
Links
Landscapes
- Length Measuring Devices With Unspecified Measuring Means (AREA)
- Length Measuring Devices By Optical Means (AREA)
Description
【０００１】[0001]
【産業上の利用分野】本発明は粉体のアスペクト比を求
める方法および測定装置に関するものであり、更に詳し
くは粉体の平均粒径、比表面積など実測可能な測定値を
用いて、簡単な計算式により算出して、容易に精度の高
いアスペクト比を求めることができる方法および測定装
置に関するものである。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for determining the aspect ratio of a powder, and more particularly, to a method and a method for measuring the aspect ratio of a powder by using measured values such as the average particle diameter and the specific surface area of the powder. The present invention relates to a method and a measuring apparatus that can easily calculate a high-accuracy aspect ratio by calculating using a calculation formula.
【０００２】[0002]
【従来の技術】従来、雲母などの粉体の形状指数である
アスペクト比は粉体の性状を表す重要な特性であるので
光学顕微鏡や電子顕微鏡を用いて、あるいは光学顕微鏡
や電子顕微鏡を用いて写真撮影を行って粉体の長径と厚
みを測定し、平均値を求め、平均粒径／平均厚みの比か
らアスペクト比を求めていた。その際、粉体の形状が比
較的均一であれば、少ない試料数の測定ですむので、時
間さえかければアスペクト比を求めることができるが、
実際には粉体の形状は均一ではなく、アスペクト比を求
めるためには数多くの測定が必要で、時間がかかるとい
う問題がある以外に、粉体の厚み方向の測定を行うこと
が難しく精度の高いアスペクト比を求めることができな
かった。2. Description of the Related Art Conventionally, the aspect ratio, which is the shape index of powder such as mica, is an important characteristic that represents the properties of powder. Therefore, the aspect ratio is determined by using an optical microscope or an electron microscope, or by using an optical microscope or an electron microscope. Photographs were taken to measure the major axis and thickness of the powder, the average value was determined, and the aspect ratio was determined from the ratio of average particle diameter / average thickness. At that time, if the shape of the powder is relatively uniform, only a small number of samples need to be measured.
Actually, the shape of the powder is not uniform, and many measurements are required to determine the aspect ratio. A high aspect ratio could not be obtained.
【０００３】このような光学顕微鏡や電子顕微鏡を用い
る方法の欠点を避けるために、水面粒子膜法（「材料」
第２７巻、第２９８号、昭和５３年７月、頁９４〜９８
に記載の方法など）により、厚みの測定が行われている
が、時間がかかり、極めて煩わしいという問題がある以
外に、小さな薄片状マイカなどの粉体の場合には粉体同
志が重なり合って単粒子層になっていない場合があり、
特に粉砕した粉体などの場合は正確なアスペクト比を求
めることができなかった。従って、最近は画像処理装置
を用いて粒径を測定し、データ処理をして、平均粒径を
求めることが可能になっているにもかかわらず、厚みの
測定が困難であるため、容易に精度の高いアスペクト比
を求めることができなかった。一方、粉体の平均粒径と
しては、最も長い径の平均値、フレークの面積相当
円直径平均値、レーザーを利用した方法で求める平均
粒径、コールター原理と呼ばれる電気抵抗法による平
均粒径などが現在使われているが、それぞれ測定法が違
うので平均粒径の値が異なってくる上、平均値の計算の
仕方も、個数平均、重量平均、メジアン（中央値）など
があり、どの平均粒径の値を用いるかによってアスペク
ト比の値が違ってくるという問題がある。In order to avoid the drawbacks of the method using an optical microscope and an electron microscope, a water particle film method (“material”) is used.
Vol. 27, No. 298, July, 1978, pp. 94-98
The measurement of the thickness is carried out by the method described in (1), but it is time-consuming and extremely troublesome. In addition, in the case of powder such as small flaky mica, the powders are overlapped with each other. It may not be a particle layer,
In particular, in the case of pulverized powder or the like, an accurate aspect ratio could not be obtained. Therefore, recently, although it has become possible to measure the particle size using an image processing device and perform data processing to obtain the average particle size, it is difficult to measure the thickness, so A highly accurate aspect ratio could not be obtained. On the other hand, as the average particle diameter of the powder, the average value of the longest diameter, the average value of the circle diameter equivalent to the area of the flakes, the average particle diameter obtained by a method using a laser, the average particle diameter by the electric resistance method called the Coulter principle, etc. Is currently used, but the measurement method is different, so the value of the average particle size is different, and the method of calculating the average value is number average, weight average, median (median), etc. There is a problem that the value of the aspect ratio differs depending on whether the value of the particle size is used.
【０００４】[0004]
【発明が解決しようとする課題】本発明の目的は、繊維
状、板状、燐片状、フレーク状、球状など種々の形状を
有する粉体の平均粒径、比表面積など実測可能な測定値
を用いて、容易に精度の高いアスペクト比を求めること
ができる方法および測定装置を提供することである。SUMMARY OF THE INVENTION An object of the present invention is to measure measured values such as the average particle size and specific surface area of powders having various shapes such as fiber, plate, flake, flake, and sphere. The present invention provides a method and a measuring apparatus that can easily obtain a high-accuracy aspect ratio by using the method.
【０００５】[0005]
【課題を解決するための手段】本発明者らは、上記問題
に鑑み鋭意研究した結果、粉体の平均粒径（Ｒ）、比表
面積（Ａ）など容易に実測可能な測定値を用いて、予め
作成した（Ｒ）と（Ａ）を変数とする簡単な計算式によ
り算出することにより容易に精度の高いアスペクト比を
求めることができることを見いだして、本発明を成すに
到った。Means for Solving the Problems The inventors of the present invention have conducted intensive studies in view of the above problems, and as a result, have been able to use easily measured values such as the average particle diameter (R) and the specific surface area (A) of the powder. The present invention has been accomplished by finding that it is possible to easily obtain a high-accuracy aspect ratio by calculating with a simple calculation formula using (R) and (A) as variables, which are prepared in advance.
【０００６】本発明の請求項１の発明は、粉体の平均粒
径（Ｒ）と比表面積（Ａ）を変数とする関数［アスペク
ト比（Ｙ）＝ｆ（Ｒ，Ａ）］によりアスペクト比（Ｙ）
を計算して求めることを特徴とする粉体のアスペクト比
を求める方法である。According to the first aspect of the present invention, the aspect ratio is determined by a function [aspect ratio (Y) = f (R, A)] having the average particle size (R) and the specific surface area (A) of the powder as variables. (Y)
Is obtained by calculating the aspect ratio of the powder.
【０００７】本発明の請求項２の発明は、粉体の平均粒
径（Ｒ）と比表面積（Ａ）を測定し、次式（１）により
アスペクト比（Ｙ）を計算して求めることを特徴とする
請求項１記載の粉体のアスペクト比を求める方法であ
る。 Ｙ＝ｍ・Ｒ・Ａ＋ｎ （１） （但し、ｍ、ｎは粉体の性状により決められる常数）According to a second aspect of the present invention, the average particle diameter (R) and the specific surface area (A) of the powder are measured, and the aspect ratio (Y) is calculated and obtained by the following equation (1). A method according to claim 1, wherein the aspect ratio of the powder is obtained. Y = m · R · A + n (1) (where m and n are constants determined by the properties of the powder)
【０００８】本発明の請求項３の発明は、アスペクト比
（Ｙ）を粉体の最長辺（ａ）の平均値（Ｒ’）と粉体の
最短辺の平均値（ｃ）との比［（Ｒ’）／（ｃ）］で表
す場合は、次式（２）でアスペクト比（Ｙ）を計算して
求めることを特徴とする請求項２記載の方法である。 Ｙ＝０．５Ｒ’・Ａ−４ （２） （但し、Ｒ’はμｍ単位で求めた平均粒径、Ａはｍ2 ／
ｍｌ単位で求めた比表面積）According to a third aspect of the present invention, the aspect ratio (Y) is defined as a ratio of an average value (R ') of the longest side (a) of the powder to an average value (c) of the shortest side of the powder [c]. (R ′) / (c)], wherein the aspect ratio (Y) is calculated and calculated by the following equation (2). Y = 0.5R ′ · A-4 (2) (where R ′ is the average particle diameter obtained in μm unit, and A is m 2 /
Specific surface area determined in ml)
【０００９】本発明の請求項４の発明は、アスペクト比
（Ｙ）を粉体の面積相当円の直径の平均値（Ｒ”）と粉
体の最短辺の平均値（ｃ）との比［（Ｒ”）／（ｃ）］
で表す場合（例えば、「工業材料」第２６巻、第２号、
１９７８年、「マイカ」に関する総説中の頁１６、右欄
５〜６行目に記載されている）は、次式（３）でアスペ
クト比（Ｙ）を計算して求めることを特徴とする請求項
２記載の方法である。 Ｙ＝０．５Ｒ”・Ａ−２．７５ （３） （但し、Ｒ”はμｍ単位で求めた平均粒径、Ａはｍ2 ／
ｍｌ単位で求めた比表面積）According to a fourth aspect of the present invention, the aspect ratio (Y) is defined as the ratio of the average value (R ″) of the diameter of a circle corresponding to the area of the powder to the average value (c) of the shortest side of the powder [c]. (R ") / (c)]
(For example, "Industrial Materials" Vol. 26, No. 2,
1916, described in page 16 in the review on "mica", right column, 5th to 6th line), the aspect ratio (Y) is calculated by the following equation (3). Item 2. The method according to Item 2. Y = 0.5R ″ · A−2.75 (3) (where R ″ is the average particle diameter determined in μm unit, and A is m 2 /
Specific surface area determined in ml)
【００１０】本発明の請求項５の発明は、少なくとも粉
体の平均粒径測定装置、粉体の比表面積測定装置および
測定された平均粒径と比表面積を用いてアスペクト比を
算出する計算手段から成る装置であり、あるいはさらに
これらの装置が一体化した装置であって、該計算手段は
粉体の平均粒径（Ｒ）と比表面積（Ａ）を変数とする関
数［アスペクト比（Ｙ）＝ｆ（Ｒ，Ａ）］によりアスペ
クト比（Ｙ）を計算して求めることを特徴とする粉体の
アスペクト比測定装置である。前記関数［アスペクト比
（Ｙ）＝ｆ（Ｒ，Ａ）］としては特に限定されるもので
はないが、前記（１）式［Ｙ＝ｍ・Ｒ・Ａ＋ｎ］を挙げ
ることができ、アスペクト比（Ｙ）を［（Ｒ’）／
（ｃ）］で表す場合は、前記（２）式［Ｙ＝０．５Ｒ’
・Ａ−４］、アスペクト比（Ｙ）を［（Ｒ”）／
（ｃ）］で表す場合は前記（３）式［Ｙ＝０．５Ｒ”・
Ａ−２．７５］などを挙げることができる。According to a fifth aspect of the present invention, there is provided an apparatus for measuring at least an average particle diameter of a powder, an apparatus for measuring a specific surface area of a powder, and a calculating means for calculating an aspect ratio using the measured average particle diameter and the specific surface area. Or an apparatus in which these apparatuses are integrated, wherein the calculating means uses a function [aspect ratio (Y)] in which the average particle diameter (R) and the specific surface area (A) of the powder are variables. = F (R, A)], which is an aspect ratio measuring apparatus for powder, wherein the aspect ratio (Y) is calculated and obtained. The function [aspect ratio (Y) = f (R, A)] is not particularly limited, but the function [Y = m · R · A + n] (1) can be used. Y) is [(R ') /
(C)], the formula (2) [Y = 0.5R ′]
A-4] and the aspect ratio (Y) is [(R ″) /
(C)], the formula (3) [Y = 0.5R ″ ·
A-2.75].
【００１１】本発明の方法を適用することができる粉体
の材質や形状は特に限定されず、例えば、材質は無機
物、有機物あるいはこれらの混合物などのいずれでもよ
く、また繊維状、板状、燐片状、フレーク状、球状など
種々の形状を有する粉体に適用できる。しかし、アスペ
クト比を求めようとする粉体の表面が滑らかで、直方体
かそれに近い形状の粉体に適用することが好ましく、粉
体が多孔質であったり、凹凸があるような場合は、コー
テイング厚みを無視しうる適当な方法によりコーテイン
グするなどの前処理を施せば本発明の方法を適用するこ
とができる。粉体の粒度分布が正規分布かそれに近い場
合は、信頼性が高い値が得られるが、正規分布からずれ
ている場合でも、実用上さしつかえない程度の値が得ら
れる。本発明で使用する平均粒径測定装置、粉体の比表
面積測定装置および計算手段などは特に限定されるもの
ではなく、公知のものを使用することができる。レーザ
ー方式やコールター原理による平均粒径測定法では針状
に近ずくと長径の平均値が実際と大きなずれを生ずる
（短くなる）ようになるため、（電子）顕微鏡で拡大し
て画像処理（肉眼観察）した最も長い径の平均あるいは
フレークの面積相当円直径の平均を求めるのが望まし
い。The material and shape of the powder to which the method of the present invention can be applied are not particularly limited. For example, the material may be any of inorganic materials, organic materials and mixtures thereof, and may be fibrous, plate-like, phosphorous, etc. It can be applied to powders having various shapes such as flakes, flakes, and spheres. However, it is preferable to apply to a powder having a smooth rectangular surface or a shape close to a rectangular parallelepiped for which the aspect ratio is to be determined. The method of the present invention can be applied by performing a pretreatment such as coating by an appropriate method that can ignore the thickness. When the particle size distribution of the powder is a normal distribution or close to the normal distribution, a highly reliable value is obtained. However, even when the powder distribution deviates from the normal distribution, a value practically insignificant is obtained. The apparatus for measuring the average particle size, the apparatus for measuring the specific surface area of the powder, the calculating means, and the like used in the present invention are not particularly limited, and known ones can be used. In the average particle diameter measurement method based on the laser method or the Coulter principle, the average value of the major axis becomes significantly different (shorter) from the actual one when approaching a needle shape. It is desirable to obtain the average of the observed longest diameters or the average of the circle diameters equivalent to the flake area.
【００１２】アスペクト比（Ｙ）を粉体の最長辺（ａ）
の平均値（Ｒ’）と粉体の最短辺の平均値（ｃ）との比
［（Ｒ’）／（ｃ）］で表す場合は、平均粒径（Ｒ’）
と比表面積（Ａ）を変数とする関数として前記（２）式
を用いてアスペクト比（Ｙ）を計算して求めることが好
ましいが、粉体を直方体と見なした場合（理想的な直方
体で、同一形状、同一の大きさの集合体より成ると仮定
した場合）、直方体［ａ×ｂ×ｃ、但しａは最長辺、ｃ
は最短辺（厚み）］の各辺の相対的な長さ関係がａ≧ｂ
≧０．２ａである場合には、ＹはＹ≒ａ／ｃ±２となっ
て、実際とよく一致する。しかし、各辺の相対的な長さ
関係がａ≧ｂ≧ｃである場合には、（２）式によるＹの
計算値は次に示すように粉体の形状が針状になるに従っ
て誤差が大きくなる。 ａ／ｃ （２）式によるＹの計算値 ５ ３〜７ １０ ８〜１７ ２０ １８〜３７ ３０ ２８〜５７ ５０ ４８〜９７ １００ ９８〜１９７The aspect ratio (Y) is set to the longest side (a) of the powder.
Is expressed by the ratio [(R ′) / (c)] between the average value (R ′) of the powder and the average value (c) of the shortest side of the powder, the average particle size (R ′)
It is preferable to calculate and obtain the aspect ratio (Y) using the equation (2) as a function having the specific surface area (A) as a variable, but when the powder is regarded as a rectangular parallelepiped (ideal rectangular parallelepiped). , Assuming that they consist of an aggregate of the same shape and the same size), a rectangular parallelepiped [a × b × c, where a is the longest side, c
Is the shortest side (thickness)].
If ≧ 0.2a, Y is Y ≒ a / c ± 2, which is in good agreement with the actual situation. However, when the relative length relation of each side is a ≧ b ≧ c, the calculated value of Y by the equation (2) shows an error as the powder shape becomes acicular as shown below. growing. a / c Calculated value of Y according to equation (2) 53 3-7 108 8-17 20 18-37 30 28-57 50 48-97 100 98-197
【００１３】アスペクト比（Ｙ）を［（Ｒ’）／
（ｃ）］で表す場合であって、各辺の相対的な長さ関係
がａ≧ｂ≧０．８ａである場合は、前記関数として次式
（４）を使用した方が実際とよく一致する。 Ｙ＝０．５Ｒ’・Ａ−２ （４） （但し、Ｒ′はμｍ単位で求めた平均粒径、Ａはｍ2 ／
ｍｌ単位で求めた比表面積）When the aspect ratio (Y) is [(R ′) /
(C)], and when the relative length relationship of each side is a ≧ b ≧ 0.8a, it is better to use the following equation (4) as the function and to better match the actual situation. I do. Y = 0.5R ′ · A-2 (4) (where R ′ is the average particle diameter obtained in μm unit, and A is m 2 /
Specific surface area determined in ml)
【００１４】また、アスペクト比（Ｙ）を［（Ｒ’）／
（ｃ）］で表す場合であって、各辺の相対的な長さ関係
がｂ≒ｃである場合は、前記関数として次式（５）を使
用した方が実際とよく一致する。 Ｙ＝０．２５Ｒ’・Ａ−０．５ （５） （但し、Ｒ′はμｍ単位で求めた平均粒径、Ａはｍ2 ／
ｍｌ単位で求めた比表面積）The aspect ratio (Y) is set to [(R ') /
(C)], and when the relative length relationship of each side is b ≒ c, using the following equation (5) as the function better matches the actual case. Y = 0.25R ′ · A−0.5 (5) (where R ′ is the average particle diameter determined in μm unit, and A is m 2 /
Specific surface area determined in ml)
【００１５】アスペクト比（Ｙ）を粉体の面積相当円の
直径の平均値（Ｒ”）と粉体の最短辺（ｃ）の平均値と
の比［（Ｒ”）／（ｃ）］で表す場合は、平均粒径
（Ｒ”）と比表面積（Ａ）を変数とする関数として前記
（３）式を用いてアスペクト比（Ｙ）を計算して求める
が、この場合のａとｂの相対的な長さ関係はａ≧ｂ≧
０．１ａを満足すると、Ｙ≒（４ａ・ｂ／π）1/2 ／Ｃ
＝±１．５となって、実際とよく一致する。The aspect ratio (Y) is defined as the ratio [(R ″) / (c)] between the average value of the diameter (R ″) of the circle corresponding to the area of the powder and the average value of the shortest side (c) of the powder. In this case, the aspect ratio (Y) is calculated by using the above equation (3) as a function having the average particle size (R ″) and the specific surface area (A) as variables. The relative length relationship is a ≧ b ≧
When 0.1a is satisfied, Y ≒ (4a · b / π) 1/2 / C
= ± 1.5, which is in good agreement with the actual situation.
【００１６】[0016]
【作用】粉体の平均粒径（Ｒ）、比表面積（Ａ）など容
易に実測可能な測定値を用いて、予め作成した（Ｒ）と
（Ａ）を変数とする簡単な関数（計算式）により算出す
ることにより容易に精度の高いアスペクト比を求めるこ
とができる。アスペクト比（Ｙ）を粉体の最長辺（ａ）
の平均値（Ｒ’）と粉体の最短辺の平均値（ｃ）との比
［（Ｒ’）／（ｃ）］で表す場合は、予め作成した前記
関数として簡単な計算式である上記（２）式により計算
することにより容易に精度の高いアスペクト比を求める
ことができる。アスペクト比（Ｙ）を［（Ｒ’）／
（ｃ）］で表す場合に用いることができる前記関数とし
ての上記（４）式あるいは（５）式は、（２）式の場合
に比べ、ａ〜ｂの狭い条件でしか適用されないが、両式
を用いた場合、粉体の各辺の相対的な長さ関係が前記の
所定範囲にあれば、得られるアスペクト比の値のばらつ
きの程度は、（２）式の場合に比べ小さいと推定され
る。アスペクト比（Ｙ）を粉体の面積相当円の直径の平
均値（Ｒ”）と粉体の最短辺の平均値（ｃ）との比
［（Ｒ”）／（ｃ）］で表す場合は、予め作成した前記
関数である簡単な上記（３）式により計算することによ
り容易に精度の高いアスペクト比を求めることができ
る。公知の平均粒径測定装置や比表面積測定装置を用い
て測定された平均粒径と比表面積の値から、コンピュー
タなどの計算手段により簡単な前記関数によりアスペク
ト比を計算することにより簡便に、迅速に、精度の高い
アスペクト比を求めることができる。A simple function (calculation formula) using previously prepared (R) and (A) as variables using easily measured values such as the average particle diameter (R) and specific surface area (A) of the powder. ), A highly accurate aspect ratio can be easily obtained. Change the aspect ratio (Y) to the longest side of powder (a)
Is expressed by the ratio [(R ′) / (c)] between the average value (R ′) of the powder and the average value (c) of the shortest side of the powder, a simple calculation formula is used as the function prepared in advance. By calculating using the equation (2), a highly accurate aspect ratio can be easily obtained. When the aspect ratio (Y) is [(R ′) /
The above equation (4) or (5) as the function that can be used in the case represented by (c)] is applied only under narrower conditions of a and b as compared with the case of equation (2). When the equation is used, if the relative length relationship of each side of the powder is within the above-mentioned predetermined range, it is estimated that the degree of variation of the obtained aspect ratio value is smaller than that of the equation (2). Is done. When the aspect ratio (Y) is represented by the ratio [(R ″) / (c)] between the average value (R ″) of the diameter of the circle corresponding to the area of the powder and the average value (c) of the shortest side of the powder By calculating with the simple formula (3), which is the function created in advance, a highly accurate aspect ratio can be easily obtained. From the values of the average particle diameter and the specific surface area measured using a known average particle diameter measuring device or specific surface area measuring device, the aspect ratio is calculated by the above-mentioned function by a simple calculation means such as a computer, thereby easily and quickly. In addition, a highly accurate aspect ratio can be obtained.
【００１７】[0017]
【実施例】次に実施例により本発明をさらに詳しく説明
するが、本発明はこれらによって限定されるものではな
い。 （実施例１）（既知の直方体粒子単体のアスペクト比の
計算） 粉体を直方体と見なし（理想的な直方体で、同一形状、
同一の大きさの集合体より成ると仮定した場合）、直方
体［ａ×ｂ×ｃ、但しａは最長辺、ｃは最短辺（厚
み）］の各辺のａ＝１〜１００μｍ、ｂ＝０．１〜５０
μｍ、ｃ＝０．１〜１００μｍとした場合であって、か
つ粉体の最長辺（ａ）の平均値（Ｒ’）と粉体の最短辺
の平均値（ｃ）との比［（Ｒ’）／（ｃ）］が１〜１０
０の範囲にあり、粉体の面積相当円の直径の平均値
（Ｒ”）と粉体の最短辺の平均値（ｃ）との比
［（Ｒ”）／（ｃ）］が１〜１１２．８の範囲にある場
合において、上記計算式（２）式、（４）式および
（５）式を用いて粉体のアスペクト比（Ｙ）を計算した
結果、および上記計算式（３）式を用いてアスペクト比
（Ｙ）を計算した結果を表１〜３に合わせて示す。The present invention will be described in more detail with reference to the following Examples, which should not be construed as limiting the present invention. (Example 1) (Calculation of aspect ratio of known rectangular parallelepiped particles) The powder is regarded as a rectangular parallelepiped (ideal rectangular parallelepiped, same shape,
(Assuming that they consist of an aggregate having the same size), a = 1 to 100 μm, b = 0 of each side of a rectangular parallelepiped [a × b × c, where a is the longest side and c is the shortest side (thickness)] .1 to 50
μm, c = 0.1 to 100 μm, and the ratio of the average value (R ′) of the longest side (a) of the powder to the average value (c) of the shortest side of the powder [(R ') / (C)] is 1 to 10
0, and the ratio [(R ″) / (c)] between the average value (R ″) of the diameter of the circle corresponding to the area of the powder and the average value (c) of the shortest side of the powder is 1 to 112. .8, the result of calculating the aspect ratio (Y) of the powder using the above equations (2), (4) and (5), and the equation (3) The results of calculating the aspect ratio (Y) using are also shown in Tables 1 to 3.
【００１８】[0018]
【表１】 [Table 1]
【００１９】[0019]
【表２】 [Table 2]
【００２０】[0020]
【表３】 [Table 3]
【００２１】表１〜３に示した計算の結果から、アスペ
クト比（Ｙ）を［（Ｒ’）／（ｃ）］で表す場合は、粉
体の各辺の相対的な長さ関係がａ≧ｂ≧０．２ａである
場合には、ＹはＹ≒ａ／ｃ±２となって、（２）式の計
算結果とよく一致することが判る。しかし、各辺の相対
的な長さ関係がａ≧ｂ≧ｃである場合には、（２）式に
よるＹの計算値は粉体の形状が針状になるに従って誤差
が大きくなる。このような場合でｂ≒ｃである時は、
（５）式の計算結果とよく一致することが判る。また、
各辺の相対的な長さ関係がａ≧ｂ≧０．８ａである場合
は、（４）式の計算結果とよく一致することが判る。一
方、アスペクト比（Ｙ）を［（Ｒ”）／（ｃ）］で表す
場合は、ａとｂの相対的な長さ関係がａ≧ｂ≧０．１ａ
である場合には、（３）式の計算結果とよく一致するこ
とが判る。 （実施例２）（既知の直方体粒子混合物のアスペクト比
の計算） 表１〜３に示した直方体粒子の中の適当なものを混合し
た混合物を仮に作成し、その直方体粒子混合物の計算平
均比表面積およびアスペクト比を算出し、（２）式を用
いて計算したアスペクト比や（３）式を用いて計算した
アスペクト比と比較検討した結果をまとめて表４に示
す。From the calculation results shown in Tables 1 to 3, when the aspect ratio (Y) is represented by [(R ') / (c)], the relative length relationship of each side of the powder is a When ≧ b ≧ 0.2a, Y becomes YＹa / c ± 2, and it can be seen that the result agrees well with the calculation result of Expression (2). However, when the relative length relation of each side is a ≧ b ≧ c, the error of the calculated value of Y by the equation (2) increases as the powder becomes acicular. When b ≒ c in such a case,
It can be seen that the result agrees well with the calculation result of equation (5). Also,
When the relative length relationship of each side is a ≧ b ≧ 0.8a, it can be seen that the calculation result of Expression (4) is well matched. On the other hand, when the aspect ratio (Y) is represented by [(R ″) / (c)], the relative length relationship between a and b is a ≧ b ≧ 0.1a.
In the case of, it can be seen that the result well matches the calculation result of the equation (3). (Example 2) (Calculation of aspect ratio of known rectangular parallelepiped particle mixture) A temporary mixture was prepared by mixing appropriate ones among the rectangular parallelepiped particles shown in Tables 1 to 3, and the calculated average specific surface area of the rectangular parallelepiped particle mixture was calculated. And the aspect ratio calculated using the equation (2) and the aspect ratio calculated using the equation (3) are shown in Table 4.
【００２２】[0022]
【表４】 [Table 4]
【００２３】表４に示した計算の結果から、粒度分布が
正規分布かそれに近い場合（Ｎｏ．６１、６３、６４お
よび６５）、（２）式を用いて計算したアスペクト比や
（３）式を用いて計算したアスペクト比は直方体粒子の
アスペクト比とよく一致し、データの信頼性が高いこと
が判る。正規分布から大きくずれている場合（Ｎｏ．６
２）、（２）式を用いて計算したアスペクト比や（３）
式を用いて計算したアスペクト比はやや誤差を生じ、デ
ータの信頼性は低くなるが、実用的な範囲にあることが
判る。From the results of the calculation shown in Table 4, when the particle size distribution is normal or close to the normal distribution (Nos. 61, 63, 64 and 65), the aspect ratio calculated using the equation (2) and the equation (3) The aspect ratio calculated by using the equation well matches the aspect ratio of the rectangular parallelepiped particles, and it can be seen that the reliability of the data is high. When there is a large deviation from the normal distribution (No. 6)
Aspect ratios calculated using equations (2) and (2) and (3)
It can be seen that the aspect ratio calculated using the formula causes a slight error and the reliability of the data is low, but is in a practical range.
【００２４】（実施例３〜６）市販の比表面積測定装置
［湯浅アイオニックス株式会社製、クオンタソーブ９ｆ
Ｆ−１６（Quantasorb 9F-16) ］および市販の平均粒径
測定装置［画像処理解析装置／画像ファイリング装置、
株式会社ニレコ、ルーゼックス］を使用して市販の合成
マイカ（Ａ）および（Ｂ）、市販の天然マイカ（Ａ）お
よび（Ｂ）の比表面積および平均粒径を測定し、測定結
果をマイコンに入力して（２）式および（３）式により
アスペクト比を算出した。結果を表５に示す。(Examples 3 to 6) A commercially available specific surface area measuring device [Quantasorb 9f, manufactured by Yuasa Ionics Co., Ltd.]
F-16 (Quantasorb 9F-16)] and a commercially available average particle size measuring device [image processing analyzer / image filing device,
The specific surface area and average particle size of commercially available synthetic mica (A) and (B) and commercially available natural mica (A) and (B) are measured using Nireco, Luzex Corporation, and the measurement results are input to a microcomputer. Then, the aspect ratio was calculated by the equations (2) and (3). Table 5 shows the results.
【００２５】[0025]
【表５】 [Table 5]
【００２６】[0026]
【発明の効果】本発明の方法および測定装置を用いるこ
とにより、粉体の平均粒径（Ｒ）、比表面積（Ａ）など
容易に実測可能な測定値を用いて、予め作成した（Ｒ）
と（Ａ）を変数とする関数である簡単な計算式により計
算することにより容易に精度の高いアスペクト比を求め
ることができる。従来、雲母などの粉体のアスペクト比
は粉体の性状を表す重要な特性であるにもかかわらず、
厚さの測定が困難であるなどのため、簡単に精度の高い
アスペクト比を求めることはできなかったので、本発明
の産業上の利用価値は高い。According to the method and the measuring apparatus of the present invention, (R) is prepared in advance by using easily measured values such as the average particle diameter (R) and specific surface area (A) of the powder.
By calculating with a simple calculation formula which is a function having (A) and (A) as variables, a highly accurate aspect ratio can be easily obtained. Conventionally, although the aspect ratio of powder such as mica is an important property that indicates the properties of powder,
Since it is difficult to measure the thickness and the like, it was not possible to easily obtain a high-accuracy aspect ratio, and thus the industrial utility of the present invention is high.
Claims (5)
を変数とする関数［アスペクト比（Ｙ）＝ｆ（Ｒ，
Ａ）］によりアスペクト比（Ｙ）を計算して求めること
を特徴とする粉体のアスペクト比を求める方法。1. An average particle size (R) and a specific surface area (A) of a powder.
[Aspect ratio (Y) = f (R,
A)] A method for calculating the aspect ratio of a powder, wherein the aspect ratio is calculated by calculating the aspect ratio (Y).
を測定し、次式（１）によりアスペクト比（Ｙ）を計算
して求めることを特徴とする請求項１記載の粉体のアス
ペクト比を求める方法。 Ｙ＝ｍ・Ｒ・Ａ＋ｎ （１） （但し、ｍ、ｎは粉体の性状により決められる常数）2. An average particle size (R) and a specific surface area (A) of a powder.
2. The method according to claim 1, wherein the aspect ratio (Y) is calculated by the following equation (1). Y = m · R · A + n (1) (where m and n are constants determined by the properties of the powder)
（ａ）の平均値（Ｒ’）と粉体の最短辺の平均値（ｃ）
との比［（Ｒ’）／（ｃ）］で表す場合は、次式（２）
でアスペクト比（Ｙ）を計算して求めることを特徴とす
る請求項２記載の方法。 Ｙ＝０．５Ｒ’・Ａ−４ （２） （但し、Ｒ’はμｍ単位で求めた平均粒径、Ａはｍ2 ／
ｍｌ単位で求めた比表面積）3. The average value (R ') of the longest side (a) of the powder and the average value (c) of the shortest side of the powder are determined by the aspect ratio (Y).
Is expressed by the ratio [(R ′) / (c)] with the following formula (2)
3. The method according to claim 2, wherein the aspect ratio (Y) is calculated and obtained by: Y = 0.5R ′ · A-4 (2) (where R ′ is the average particle diameter obtained in μm unit, and A is m 2 /
Specific surface area determined in ml)
の直径の平均値（Ｒ”）と粉体の最短辺の平均値（ｃ）
との比［（Ｒ”）／（ｃ）］で表す場合は、次式（３）
でアスペクト比（Ｙ）を計算して求めることを特徴とす
る請求項２記載の方法。 Ｙ＝０．５Ｒ”・Ａ−２．７５ （３） （但し、Ｒ”はμｍ単位で求めた平均粒径、Ａはｍ2 ／
ｍｌ単位で求めた比表面積）4. The aspect ratio (Y) is defined as the average value (R ″) of the diameter of a circle corresponding to the area of the powder and the average value (c) of the shortest side of the powder.
Is expressed by the ratio [(R ″) / (c)] with the following equation (3).
3. The method according to claim 2, wherein the aspect ratio (Y) is calculated and obtained by: Y = 0.5R ″ · A−2.75 (3) (where R ″ is the average particle diameter determined in μm unit, and A is m 2 /
Specific surface area determined in ml)
体の比表面積測定装置および測定された平均粒径と比表
面積を用いてアスペクト比を算出する計算手段から成る
装置であり、あるいはさらにこれらの装置が一体化した
装置であって、該計算手段は粉体の平均粒径（Ｒ）と比
表面積（Ａ）を変数とする関数［アスペクト比（Ｙ）＝
ｆ（Ｒ，Ａ）］によりアスペクト比（Ｙ）を計算して求
めることを特徴とする粉体のアスペクト比測定装置。5. An apparatus comprising at least an apparatus for measuring an average particle diameter of a powder, an apparatus for measuring a specific surface area of a powder, and a calculating means for calculating an aspect ratio by using the measured average particle diameter and the specific surface area. An apparatus in which these apparatuses are integrated, and the calculating means uses a function [Aspect ratio (Y) =
f (R, A)] to calculate the aspect ratio (Y).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP35172992A JP3195090B2 (en) | 1992-12-08 | 1992-12-08 | Method and apparatus for determining aspect ratio of powder |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP35172992A JP3195090B2 (en) | 1992-12-08 | 1992-12-08 | Method and apparatus for determining aspect ratio of powder |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH06174627A JPH06174627A (en) | 1994-06-24 |
| JP3195090B2 true JP3195090B2 (en) | 2001-08-06 |
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ID=18419218
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|---|---|---|---|
| JP35172992A Expired - Fee Related JP3195090B2 (en) | 1992-12-08 | 1992-12-08 | Method and apparatus for determining aspect ratio of powder |
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| US9346023B2 (en) | 2012-08-21 | 2016-05-24 | General Electric Company | Flux enhancing agent for improving composite polyamide reverse osmosis membrane performance |
| CN114235649A (en) * | 2021-12-20 | 2022-03-25 | 珠海真理光学仪器有限公司 | Particle diameter-thickness ratio measuring method and device based on laser particle sizer and storage medium |
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