The implementation of UV-technologies has revealed problems associated with the migration of harmful components of the ink layer to the back of the packaging in contact with the packaged products. The reason for this migration is the incomplete reaction of the UV-ink components due to a decrease in the intensity of UV-radiation, the mismatch between the absorption spectrum of the photoinitiator and the spectrum of the UV-source and the inhibitory effect of oxygen. It has been established that the decay products of photoinitiators, which occupy the third position in terms of concentration content in the ink composition, have a potential ability to migrate. To prevent such migration, polymerized photoinitiators have been developed that differ from conventional ones by higher molecular weight. Accordingly, a study of the effect of the photopolymerization degree of UV-ink on the presence of residual odor, as a direct characteristic of the ability of ink components to migrate has been done. It has been found that at the photopolymerization degree of 84%, the average value of the residual odor level is 4 points, and at the photopolymerization degree of 96%, it is 2.8 points. Using the obtained data on the presence of residual odor and the data on the influence of molecular weight of photoinitiators, a knowledge base has been formed with the condition "if-then", a logical scheme has been formed and fuzzy logical equations of influence of established factors on the migration capacity of UV-ink have been constructed. The establishment of a universal set and evaluation terms has made it possible to form a quantitative indicator of migration of UV-ink components. The formed fuzzy knowledge base has been checked when modeling with the help of the Fuzzy Logic Toolbox system of the Matlab technological calculation environment according to Mamdani principle, using the method "Center of gravity" for the dephasification operation. The suggested method of calculating the migration capacity of UV-inks has made it possible to construct a two-factor forecasting model.
The development of photopolymerizable inks (UV-inks) has given the impetus to the improvement
of printing processes. Instant drying of imprints under the influence of actinic UV-radiation has made
it possible to further process them without additional technological downtime, and the imprints
themselves have high optical and operational performance parameters [
In the recent past, the detection of residues of the photoinitiator Isopropyl Thioxantone in
packaged products [
In the technological process of packaging printing and manufacturing, as well as during its
operation, the following options of migration of printing ink components are possible (Fig. 1): the
contact of the front and back of the imprints, evaporation and penetration (diffusion) [
Manufacturers of UV-inks and their chemical components have found that decay products of
photoinitiators which occupy the third position in terms of concentration in the ink composition have
the potential for migration [
Therefore, forecasting the effect of the molecular weight of the photoinitiator and the
polymerization degree of the UV-ink layer of on the migration amount of its components is relevant.
In the forecasting area, there are publications related to the application of fuzzy logic to ensure the
quality of technological processes [
To develop a model for forecasting the potential harmful contamination of packaging during the migration of UV-ink components with a radical photoinitiated polymerization mechanism.
The development of systems capable of adequately reproducing human reasoning requires a
mathematical apparatus that would interpret ambiguous statements into the language of clear and
formal mathematical formulas. This principle was introduced by Latfi Zadeh, who developed the
basics of fuzzy logic and introduced the concept of a universal set for a particular problem area [
To determine the effect of the photopolymerization degree on the migration capacity of the ink
layer, a model photopolymerizable UV-ink binder was developed based on epoxyacrylate oligomer
and photoinitiator 1-hydroxycyclohexyl-phenyl ketone (Omnirad 184, IGM Resin). UV-ink binder
was applied with the thickness of 10 μm on the surface of coated paper, weighing 200 g/m2 of Magno
Gloss brand, (Sappi Group) and was irradiated with a UV-lamp DRT-400 with UV intensity of 95
W/m2. The polymerization degree of the UV-ink binder at different irradiation times was evaluated by
the method of determining the gel-sol fraction [
The migration of the components of UV-printing inks depends primarily on the molecular weight of its components and the photopolymerization degree of the applied ink layer. Accordingly, the migration amount of the UV ink components is defined as:
М К = f (M, P), (1) where M is a linguistic valuable which characterizes the molecular weight of the photoinitiator; Р is a linguistic valuable which characterizes the photopolymerization degree of the ink layer.
Migration capacity of UV-inks
М К = f (M, P)
Influence of the molecular weight of
PI
Influence of the photopolymerization degree of the ink layer
According to the results of expert judgments and experimental studies, one will form a block diagram of a logical conclusion about the influence of the molecular weight of the components and the photopolymerization degree of the ink on its migration capacity (Fig. 2).
One can evaluate the values of linguistic variables using a system of qualitative concepts that make up the corresponding fuzzy set, i.e. some property of the factor, which is considered as a linguistic term. For our membership functions, you can apply the division into three members of each input variable with a symmetric Gaussian membership function:
µ (х) = e− (x2−ch2)2 , (2) № where х is an element of a universal set; h is a parameter of a membership function (maximum coordinate); с is a parameter of a membership function (concentration ratio).
Selected samples with a certain photopolymerization degree were simultaneously evaluated by the odor amount as a characteristic of the migration potential of UV-ink. The results of the study are shown in Table 1.
Linguistic variables, on which the migration capacity of ink components and assessment terms depend, are presented in Table 2.
Based on the results of the influence of the molecular weight of the photoinitiator [
For a linguistic assessment of this parameter, one can use a set of fuzzy terms: M (x) = <low, medium, high>. In accordance with these terms, one obtains the membership functions of the linguistic variable "Molecular weight of PI" (Fig. 3, a).
For the variable "Photopolymerization degree of IL", one can set the universal set: u1 = 84% ; u2 = 87%; u3 = 90%; u4 = 93%; u5 = 96%. For a linguistic assessment of the variable, one uses a set of fuzzy terms: P(y) = <low, medium, high>. Therefore, taking into account the results of determining the residual odor, for the indicator "Photopolymerization degree of IL" in relation to these terms, one can construct membership functions (Fig. 3, b).
One can form a fuzzy knowledge base on the selected parameters of the quality of the digitization process: 1. For the term “low” migration: • if the molecular weight of PI is "high", the photopolymerization degree of IL is "high", the migration is "low" or • if the molecular weight of PI is "high", the photopolymerization degree of IL is "medium", the migration is "low". 2. For the term “medium” migration: • if the molecular weight of PI is "high", the photopolymerization degree of IL is "low", the migration is "medium" or • if the molecular weight of PI is "medium", the photopolymerization degree of IL is "medium", then migration is "medium". 3. For the term “high” migration: • if the molecular weight of PI is "low", the photopolymerization degree of IL is "low", then the migration is "high" or • if the molecular weight of PI is "medium", the photopolymerization degree of IL is "low", then migration is "high".
Logical equations for forecasting the migration amount of UV-ink components are: µ l = µ h (x) ∧ µ h ( y) ∨ µ h (x) ∧ µ m ( y) , µ m = µ h (x) ∧ µ l ( y) ∨ µ m (x) ∧ µ m ( y) , µ h = µ l (x) ∧ µ l ( y) ∨ µ m (x) ∧ µ н ( y) . (3) (4) (5)
The notations and are the operations of determining the minimum and maximum in logical equations. Using the membership functions and substituting the membership degrees into the system of fuzzy logical equations, one can forecast the migration options of the ink components
The formed fuzzy knowledge base has been checked when modelling with the help of the Fuzzy
Logic Toolbox system of the Matlab technological calculation environment according to Mamdani
principle [
According to the formed logical equations and the constructed model, several variants of the dependence of the migration capacity of the UV-ink components on its degree of photopolymerization and the molecular weight of the photoinitiator are calculated (Table 3).
The simulation results have shown the possibilities of applying the developed knowledge base for forecasting assessment of the migration capacity of UV-ink components.
Therefore, the influence of the photopolymerization degree of the UV-composition on the value of the residual odor as a direct characteristic of the migration capacity of unreacted components has been established in the paper. Using data on the influence of the photopolymerization degree and the molecular weight of the photoinitiator, the analysis has been performed using fuzzy expert-linguistic information and the rule "if-then", which allowed one to obtain fuzzy logical equations of the influence of linguistic variables on migration capacity and, accordingly, to quantify it. The suggested calculation of the migration capacity of UV-ink components allows the development of a simulation model for forecasting the possible harmful contamination of packaging.