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Dyeing kinetics, (diffusion, pore model, free volume model)

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Md. Abdul Hannan

This document discusses dyeing kinetics and diffusion models for dye uptake in fibers. It describes the exhaustion curve which defines the rate of dyeing over time. The initial rate is called the strike. Diffusion occurs through three transport zones: flow, absorption, and diffusion into the fiber. Two main diffusion models are described: the pore model which considers diffusion through pores filled with dye liquor, and the free volume model which involves diffusion through amorphous, mobile regions of the polymer chain. The document contrasts these models and discusses how temperature affects dyeing rates.

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Dyeing Kinetics, (Diffusion, Pore Model, Free volume model) 1. Exhaustion 2. Slope of a dyeing exhaustion 3. Effects 4. Diffusion 5. Diffusion mechanisms 6. Transport zones 7. Dyeing rate 8. Diffusion models Md. Abdul Hannan Associate Prof. DUET Hannan_tex62@yahoo.com 01913354913
Exhaustion • The degree of dyebath exhaustion as a function of time describes the rate and extent of the dyeing process. • For a single dye, the exhaustion is defined as the ratio of • i)mass of dye taken up by the material and • Ii)the total initial mass of dye in the bath, • but for a bath of constant volume: • where C0 =concentrations of dye in the dyebath initially • and Cs =concentrations of dye during the process, respectively. • For many dyeings, a gradual increase of the dyeing temperature controls the rate of exhaustion
Exhaustion The slope of a dyeing exhaustion curve (Figure) defines the rate of dyeing at any instant during the process An equilibrium is reached where no more dye is taken up by the fibres. There is now a balance between the rates of dye absorption and desorption. Typical exhaustion curves show the initial rate of dyeing, the gradual decrease in dyeing rate as the bath becomes exhausted and the equilibrium position Figure : Dye bath exhaustion as a function of time at a constant dyeing temperature Exhaustion curves at different temperatures show how the dyeing rate increases with increasing temperature
Effects • Exhaustion curves characterise the dyeing properties of a dye and are useful for selecting compatible dyes. • They should have very similar rates of exhaustion when used in mixtures under the given dyeing conditions • The adsorption equilibrium is usually rapid, and the overall rate of dyeing depends on the rate of diffusion of the dye into the fibres.
Diffusion Molecular movement of a substrate due to its natural intrinsic mobility, i.e. without the participation of external forces. A substance in solution will migrate at constant temperature from zones of higher to lower concentration until a concentration equilibrium is established within the entire system. Diffusion is thus a general characteristic of the dilution tendency of a solution which is accelerated by elevation of temperature. Diffusion coefficient: A proportionality factor which gives the number of moles of a dissolved substance diffusing through a cross sectional area of I cm2 per unit time for a given temperature and solvent when the concentration gradient is (-l) measurement of concentration changes
Diffusion mechanisms in dyeing • Dyeing processes are very dynamic as they involve the transport of diverse products from the dyeing medium into the fibres. • Seldom reach a genuine state of thermodynamic equilibrium. • Only gives a transient picture of the distribution of dye between the medium and the fibre after a certain dyeing time. • Three transport zones which depend on three different transport carriers and transport effects have been defined.
Three transport zones 1. The zone of transport due to flow, determined by the machine or flow pump. 2. The zone of transport due to absorption, which is mainly dependent on the chemistry of the dye and the ancillary agents on the liquid side. 3. The zone of transport due to diffusion, which is mainly dependent on the chemistry of the dye and the substrate.
Dyeing Rate • If the dye is delivered at a sufficiently high rate through the laminar boundary layer on the surface of the fibre, then it will get into the fibre by a process of absorption and slow diffusion. • Accesses of a dye into the fibre via a transition interface is the key to understanding the dye interactions in the area of dye kinetics. • The rate of diffusion of the dye into the fibre interior is controlled by its concentration at the fibre surface. • The dye kinetics and resulting concentration profile are determined by -the rates of diffusion, -adsorption and -immobilisation. • In the case of reactive dyes, for example, the process of immobilisation (fixation) is a chemical reaction.
• The initial rate of dyeing (the initial slope of exhaustion versus time) is called the strike. Rapid strike by a dye often results in initial unlevelness . • The strike depends on : • dyeing temperature, pH and the addition of chemicals. • Even for dyes of moderate and low strike, the objective of uniform dyeing of the fibre mass is rarely achieved during the initial stages of the operation. • This is because of a) irregularities - inthe material’s construction, - in the fibre packing, - in the distribution of residual impurities, b) differences in temperature c) flow rate of the solution in contact with the fibres.
Materials composed of finer fibres have a much larger specific surface (m2 /kg) and a higher dyeing rate, even though the equilibrium exhaustion may not be significantly different from that of a material made of courser fibres of the same polymer. If the dyeing rate is proportional to the fibre surface area per unit mass, it will be inversely proportional to the fibre radius, r, and thus inversely proportional to the square root of the fibre tex.
• The rate of dyeing is of greater practical importance than dyeing equilibrium because few commercial dyeing processes reach equilibrium. • Dyeing rates are quite sensitive to : • -The degree of agitation of the bath, • - The liquor ratio, • - The type and construction of the material, • -The dyebath temperature and pH, • -The concentration of dyeing assistants, • -The dye substantivity.
• Practical dyeing rates depend upon the way dye bath exhaustion changes as a function of time at a constant temperature for most practical purposes, the temperature may vary useful for selecting compatible dyes that exhaust at about the same rate under the same conditions. • Typical exhaustion curves show the initial rate of • dyeing, the gradual decrease in dyeing rate as the bath becomes exhausted and the equilibrium position (Figure 10.2).
Relation between surface area &pick-up This equation gives a linear relationship between the mass-specific surface area of the fibre and the dye pick- up. The dyeing speed, therefore, increases with increasing fibre fineness. The even distribution of the dye over the fibre cross section among other things may be regarded as a measurement standard for successful dyeing. After adsorption onto the fibre surface, the dye must migrate into the interior through the fibre mass or through existing channels and distribute itself there in the optimum manner.
• At the same time, the diffusion medium has a vital influence on the rate of diffusion. This becomes evident in the variable order of magnitude of the true diffusion coefficient. • The diffusion coefficient is significantly greater in the gas phase than in liquid or solid phases. • The main driving force behind diffusion is the difference in concentration.
Dyeing kinetics, (diffusion, pore model, free volume model)
Dyeing kinetics, (diffusion, pore model, free volume model)
Diffusion Models • Theories of dye kinetics arc concerned with the nature of dye diffusion in solid polymers. • Essentially they are based on two important fundamentally different models of dye diffusion in fibres namely: 1) The pore diffusion model and 2) The free-volume or mobile segment model
The Pore Model • The pore model represents the fibre as a solid structure with a network of interconnected channels or pores which are filled with the dyeing liquid, which is normally water. • The dissolved dye diffuses through these pores, where it can be simultaneously adsorbed on the walls of the pores. For quantitative expressions of the rate of diffusion, the porosity P is of primary importance as well as the adsorption equilibrium. • P is the proportion of pores in relation to the total volume of the fibre available under the conditions of dyeing. • In I966, Weisz developed a mathematical model for diffusion processes which is overlaid by an adsorption/desorption equilibrium of the dye liquor at the external and internal boundary layers of the fibre. The pore model presupposes, of course, that the pores are connected to each other as well as to the external dye bath and that their diameter is sufficiently large for the dye molecules to find rooms in them.
• Model concepts for dye uptake on cellulosic fibres are generally based on the pore model. According to this, a network of pores swollen and filled with water is present in the fibres within which dye diffusion and sorption takes place followed, if applicable, by chemical reactions as in the case of reactive dyes. • The first mechanistic hypotheses on the uptake of anionic direct dyes soon after their discovery were based on the assumption that these dyes form colloidal particles in the fibre voids. • It was concluded that substantivity is largely based on the fact that the dye molecules which have diffused into the fibre form aggregates in the cellulose pores. • Likewise assisted by experimental findings, the mechanism of monomolecular adsorption in the pores has found support for low to medium depth dyeings at least.
The Free Volume Model • The free volume model describes the dyeing process as diffusion of the dye through the less ordered ("amorphous") regions of the polymer matrix . • The rate of diffusion is therefore determined by the mobility of the polymer chain segments. • The most important support : the temperature dependence of the rates of dyeing for a particular type of fibre is less above a certain temperature. • The resistance of the solid structure of the fibre to the penetration of dye is much lower above this temperature. This is referred to as the glass transition temperature of the fibre in question (Tg), or more precisely, the glass transition temperature under dyeing conditions or the dyeing transition point (Td), since the classical glass transition temp. is a parameter which is measured in the dry state.
• Both parameters, Tg and Td, correspond to those temperatures at which, from a microscopic perspective. • the less ordered component of the polymer is converted from a glass-like state into the viscoelastic state, or. at a molecular level, at which the less ordered segments of the macromolecule move against each other, i.e.. become, in effect, like "micro fluids". • The glass transition temperature plays an important role here. It corresponds. At a molecular level, to the temperature at which the amorphous regions of a polymer are converted from a glass- like state to a gummy (i.e., viscoelastic) state. • Above this temperature, parts of the polymer chain (thread) molecule become mobile.
• This segment change in the spatial arrangement of the chain moleculesmobility causes an uninterrupted in these regions. • "Holes“ are formed above Tg and disappear again or occur at neighbouling sites of the polymer segment involved. • In the viscoelastic state. therefore. The polymer structure cannot be conceived in static terms: the structure changes constantly. • The possibility for the diffusion of relatively small molecules through such a structure is a problem of probability (or expressed in physical terms, it is a question of entropy) as to whether "holes", "channels“ and adsorption sites for small molecules are formed by segment mobility.

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Dyeing kinetics, (diffusion, pore model, free volume model)

  • 1. Dyeing Kinetics, (Diffusion, Pore Model, Free volume model) 1. Exhaustion 2. Slope of a dyeing exhaustion 3. Effects 4. Diffusion 5. Diffusion mechanisms 6. Transport zones 7. Dyeing rate 8. Diffusion models Md. Abdul Hannan Associate Prof. DUET Hannan_tex62@yahoo.com 01913354913
  • 2. Exhaustion • The degree of dyebath exhaustion as a function of time describes the rate and extent of the dyeing process. • For a single dye, the exhaustion is defined as the ratio of • i)mass of dye taken up by the material and • Ii)the total initial mass of dye in the bath, • but for a bath of constant volume: • where C0 =concentrations of dye in the dyebath initially • and Cs =concentrations of dye during the process, respectively. • For many dyeings, a gradual increase of the dyeing temperature controls the rate of exhaustion
  • 3. Exhaustion The slope of a dyeing exhaustion curve (Figure) defines the rate of dyeing at any instant during the process An equilibrium is reached where no more dye is taken up by the fibres. There is now a balance between the rates of dye absorption and desorption. Typical exhaustion curves show the initial rate of dyeing, the gradual decrease in dyeing rate as the bath becomes exhausted and the equilibrium position Figure : Dye bath exhaustion as a function of time at a constant dyeing temperature Exhaustion curves at different temperatures show how the dyeing rate increases with increasing temperature
  • 4. Effects • Exhaustion curves characterise the dyeing properties of a dye and are useful for selecting compatible dyes. • They should have very similar rates of exhaustion when used in mixtures under the given dyeing conditions • The adsorption equilibrium is usually rapid, and the overall rate of dyeing depends on the rate of diffusion of the dye into the fibres.
  • 5. Diffusion Molecular movement of a substrate due to its natural intrinsic mobility, i.e. without the participation of external forces. A substance in solution will migrate at constant temperature from zones of higher to lower concentration until a concentration equilibrium is established within the entire system. Diffusion is thus a general characteristic of the dilution tendency of a solution which is accelerated by elevation of temperature. Diffusion coefficient: A proportionality factor which gives the number of moles of a dissolved substance diffusing through a cross sectional area of I cm2 per unit time for a given temperature and solvent when the concentration gradient is (-l) measurement of concentration changes
  • 6. Diffusion mechanisms in dyeing • Dyeing processes are very dynamic as they involve the transport of diverse products from the dyeing medium into the fibres. • Seldom reach a genuine state of thermodynamic equilibrium. • Only gives a transient picture of the distribution of dye between the medium and the fibre after a certain dyeing time. • Three transport zones which depend on three different transport carriers and transport effects have been defined.
  • 7. Three transport zones 1. The zone of transport due to flow, determined by the machine or flow pump. 2. The zone of transport due to absorption, which is mainly dependent on the chemistry of the dye and the ancillary agents on the liquid side. 3. The zone of transport due to diffusion, which is mainly dependent on the chemistry of the dye and the substrate.
  • 8. Dyeing Rate • If the dye is delivered at a sufficiently high rate through the laminar boundary layer on the surface of the fibre, then it will get into the fibre by a process of absorption and slow diffusion. • Accesses of a dye into the fibre via a transition interface is the key to understanding the dye interactions in the area of dye kinetics. • The rate of diffusion of the dye into the fibre interior is controlled by its concentration at the fibre surface. • The dye kinetics and resulting concentration profile are determined by -the rates of diffusion, -adsorption and -immobilisation. • In the case of reactive dyes, for example, the process of immobilisation (fixation) is a chemical reaction.
  • 9. • The initial rate of dyeing (the initial slope of exhaustion versus time) is called the strike. Rapid strike by a dye often results in initial unlevelness . • The strike depends on : • dyeing temperature, pH and the addition of chemicals. • Even for dyes of moderate and low strike, the objective of uniform dyeing of the fibre mass is rarely achieved during the initial stages of the operation. • This is because of a) irregularities - inthe material’s construction, - in the fibre packing, - in the distribution of residual impurities, b) differences in temperature c) flow rate of the solution in contact with the fibres.
  • 10. Materials composed of finer fibres have a much larger specific surface (m2 /kg) and a higher dyeing rate, even though the equilibrium exhaustion may not be significantly different from that of a material made of courser fibres of the same polymer. If the dyeing rate is proportional to the fibre surface area per unit mass, it will be inversely proportional to the fibre radius, r, and thus inversely proportional to the square root of the fibre tex.
  • 11. • The rate of dyeing is of greater practical importance than dyeing equilibrium because few commercial dyeing processes reach equilibrium. • Dyeing rates are quite sensitive to : • -The degree of agitation of the bath, • - The liquor ratio, • - The type and construction of the material, • -The dyebath temperature and pH, • -The concentration of dyeing assistants, • -The dye substantivity.
  • 12. • Practical dyeing rates depend upon the way dye bath exhaustion changes as a function of time at a constant temperature for most practical purposes, the temperature may vary useful for selecting compatible dyes that exhaust at about the same rate under the same conditions. • Typical exhaustion curves show the initial rate of • dyeing, the gradual decrease in dyeing rate as the bath becomes exhausted and the equilibrium position (Figure 10.2).
  • 13. Relation between surface area &pick-up This equation gives a linear relationship between the mass-specific surface area of the fibre and the dye pick- up. The dyeing speed, therefore, increases with increasing fibre fineness. The even distribution of the dye over the fibre cross section among other things may be regarded as a measurement standard for successful dyeing. After adsorption onto the fibre surface, the dye must migrate into the interior through the fibre mass or through existing channels and distribute itself there in the optimum manner.
  • 14. • At the same time, the diffusion medium has a vital influence on the rate of diffusion. This becomes evident in the variable order of magnitude of the true diffusion coefficient. • The diffusion coefficient is significantly greater in the gas phase than in liquid or solid phases. • The main driving force behind diffusion is the difference in concentration.
  • 17. Diffusion Models • Theories of dye kinetics arc concerned with the nature of dye diffusion in solid polymers. • Essentially they are based on two important fundamentally different models of dye diffusion in fibres namely: 1) The pore diffusion model and 2) The free-volume or mobile segment model
  • 18. The Pore Model • The pore model represents the fibre as a solid structure with a network of interconnected channels or pores which are filled with the dyeing liquid, which is normally water. • The dissolved dye diffuses through these pores, where it can be simultaneously adsorbed on the walls of the pores. For quantitative expressions of the rate of diffusion, the porosity P is of primary importance as well as the adsorption equilibrium. • P is the proportion of pores in relation to the total volume of the fibre available under the conditions of dyeing. • In I966, Weisz developed a mathematical model for diffusion processes which is overlaid by an adsorption/desorption equilibrium of the dye liquor at the external and internal boundary layers of the fibre. The pore model presupposes, of course, that the pores are connected to each other as well as to the external dye bath and that their diameter is sufficiently large for the dye molecules to find rooms in them.
  • 19. • Model concepts for dye uptake on cellulosic fibres are generally based on the pore model. According to this, a network of pores swollen and filled with water is present in the fibres within which dye diffusion and sorption takes place followed, if applicable, by chemical reactions as in the case of reactive dyes. • The first mechanistic hypotheses on the uptake of anionic direct dyes soon after their discovery were based on the assumption that these dyes form colloidal particles in the fibre voids. • It was concluded that substantivity is largely based on the fact that the dye molecules which have diffused into the fibre form aggregates in the cellulose pores. • Likewise assisted by experimental findings, the mechanism of monomolecular adsorption in the pores has found support for low to medium depth dyeings at least.
  • 20. The Free Volume Model • The free volume model describes the dyeing process as diffusion of the dye through the less ordered ("amorphous") regions of the polymer matrix . • The rate of diffusion is therefore determined by the mobility of the polymer chain segments. • The most important support : the temperature dependence of the rates of dyeing for a particular type of fibre is less above a certain temperature. • The resistance of the solid structure of the fibre to the penetration of dye is much lower above this temperature. This is referred to as the glass transition temperature of the fibre in question (Tg), or more precisely, the glass transition temperature under dyeing conditions or the dyeing transition point (Td), since the classical glass transition temp. is a parameter which is measured in the dry state.
  • 21. • Both parameters, Tg and Td, correspond to those temperatures at which, from a microscopic perspective. • the less ordered component of the polymer is converted from a glass-like state into the viscoelastic state, or. at a molecular level, at which the less ordered segments of the macromolecule move against each other, i.e.. become, in effect, like "micro fluids". • The glass transition temperature plays an important role here. It corresponds. At a molecular level, to the temperature at which the amorphous regions of a polymer are converted from a glass- like state to a gummy (i.e., viscoelastic) state. • Above this temperature, parts of the polymer chain (thread) molecule become mobile.
  • 22. • This segment change in the spatial arrangement of the chain moleculesmobility causes an uninterrupted in these regions. • "Holes“ are formed above Tg and disappear again or occur at neighbouling sites of the polymer segment involved. • In the viscoelastic state. therefore. The polymer structure cannot be conceived in static terms: the structure changes constantly. • The possibility for the diffusion of relatively small molecules through such a structure is a problem of probability (or expressed in physical terms, it is a question of entropy) as to whether "holes", "channels“ and adsorption sites for small molecules are formed by segment mobility.