2. Rate of dyeing (absorption ) curve

Information on the rate of dyeing (absorption) curve is provided by dye manufacturers as an absorption curve at a constant temperature or with a temperature rise.

For example, an absorption curve of 2:1 metal complex acid dye on wool at constant temperatures (without acid) and that with a temperature rise (with acid, rate of temperature rise =1°C/min.) are shown in Figure 1. The dyeing behavior of three dyes with different absorption properties can be seen more clearly in the curve with temperature rise than in the curves at constant temperatures.

The evaluation of the dyeing behavior from the curve at constant temperature looks very easy at first sight, but it is not sufficient to understand practical dyeing behavior, nor easy to draw necessary information from these curves.

On the other hand, the rate of dyeing curve with temperature rise is very effective for obtaining useful information on controlling the dyeing conditions including temperature rise in dyeing.

The rate of dyeing curve with temperature rise can be practically divided into three types, Ⅰ, Ⅱ and Ⅲ.

Figure 1 Three types of absorption curves

Dye with the absorption curve of typeⅠcan be controlled with the most ease.

The characteristics of three types of absorption curves are discussed below.

a) Absorption curve of typeⅠ

In this case, the absorption curve is close to linear as shown in Figure 1. The decrease of rate of dyeing by the decrease of dye in the dyebath with the progression of dyeing and the increase of the rate of dyeing by temperature rise is balanced, therefore, the rate of dyeing is proportional to the rate of temperature rise.

The factor of decreasing the rate of dyeing with an increase in dyebath temperature is a decrease of probability of contact of the dye to the fiber, because the amount of dye in the dyebath decreases as the dyeing proceeds.

On the other hand, the factor of increasing the rate of dyeing is the increase of the rate of diffusion of dye into the fiber. In the case of natural fibers, the number of dye-sites in the fiber is independent of the dyeing temperature, but in the case of synthetic fibers, the number of dye-sites increases with the increase of dyeing temperature so that both the increase of diffusion and increase of dye-sites by temperature rise synergistically increase the rate of dyeing.

Because the rate of dyeing increases progressively with the increase of the dyeing temperature, the rate of dyeing curve of linear type can not be obtained in a strict sense by balancing the increase of the rate of dyeing due to the increase of dyeing temperature with the decrease of the amount of dye in the dyebath. However, in the practical case where the curve may be deemed to be approximately linear, the slope of this linear line (%/℃) may be regarded as the rate of dyeing.

b) Absorption curve of type Ⅱ

The absorption curve at constant temperature shows this figure in all dyeing systems. However, this type of absorption curve with temperature rise is mainly obtained in the case where the activation energy of diffusion is low such as in the case of the dyeing of cellulosic fibers or dyeing of wool with leveling type acid dye.

In this case, the problem is that the rate of dyeing is so fast at the early stage of dyeing that the controll of dyeing speed only with the rate of temperature rise is very difficult.

If the activation energy of diffusion is high, the rate of dyeing at room temperature could be low, so that the rate of dyeing can be controlled by decreasing the starting temperature. However, the control of rate of dyeing in such a dyeing system can not rely on the dyebath temperature but on other measures such as the dyebath pH or a portion-wise addition of inorganic salts.

To analyze the rate of dyeing with this type of absorption curve, the curve should be subdivided into many small parts, enough to regard as a linear line, then the slope of each line is summed up and the average is calculated. For example, the concept of critical rate of dyeing, Vsig can be applied.

c) Absorption curve of type Ⅲ

This type of absorption curve (S-shaped curve) is observed in cases where the activation energy is relatively high. Although in the dyeing of natural fibers it is seen only in the case of wool dyeing with premetallized or super milling acid dye, in the dyeing of other natural fibers it is very popular.

A typical example is dyeing polyester with disperse dye.

In this case, the complex effect of two factors induced by the temperature rise over its glass transition point;

1) an increase of the number of dye-sites in polyester fiber and an increase of the rate of diffusion

2) a decrease of the amount of dye in the finite dyebath

may produce a S-shaped absorption curve.

This type of absorption curve is also obtained in the dyeing of acrylic fiber with cationic dye. The activation energy of diffusion of cationic dye into acrylic fiber is about twice of that of disperse dye into polyester fiber, that means the rate of dyeing is more influenced by the dyeing temperature, and its absorption curve becomes S-shaped one with steep slope where about 70% of cationic dye is absorbed in the temperature range of 80～90℃.

Therefore very strict temperature control is required to achieve level dyeing in this dyeing system, however, the temperature variation during the temperature rise is rather large in bulk dyeing machines so that a constant temperature dyeing method using a cationic retarder as an auxiliary making the absorption speed favorable is employed. In this dyeing system, the absorption curve becomes similar to typeⅡ.

A semi-S-shaped curve is observed in the dyeing of nylon with milling type acid dye.

An average rate of dyeing (Vs) can be effectively utilized to make a numerical approach on the rate of dyeing with these S-shaped absorption curves.

The type of absorption curve with temperature rise for each dyeing system is classified as shown in Table 1.

The practical dyeing recipe and conditions can be reasonably determined by making a numerical approach according to the type of absorption curve and utilizing the concept of liquor circulation and leveling or area exchange as mentioned before.