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Title:
METHOD FOR REGULATING MIGRATION OF INSECTICIDE OR ACARICIDE IN A POLYMER FIBRE BY STRETCHING
Document Type and Number:
WIPO Patent Application WO/2012/149933
Kind Code:
A1
Abstract:
Method for regulating migration of insecticide/acaricide in a polymer fibre by stretching A method for producing an insecticidal or acaricidal polymer filament, where the retention effect of Carbon Black on the migration of the insecticide/acaricide is counteracted by a low draw ratio. The method comprising mixing insecticide/acaricide and Carbon Black into a molten thermoplastic polymer, extruding the insecticidal or acaricidal polymer with the insecticide/acaricide and the Carbon Black into a filament, drawing the filament at a draw ratio of 3 to 7.7and thereby obtaining a stretched filament with 80 to 1000 denier.

Inventors:
VESTERGAARD FRANDSEN MIKKEL (CH)
GOUIN SEBASTIEN (CH)
HOANG HUYEN THANH (VN)
ZELLWEGER MATTHIEU (CH)
Application Number:
PCT/DK2011/050148
Publication Date:
November 08, 2012
Filing Date:
May 02, 2011
Export Citation:
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Assignee:
VESTERGAARD FRANDSEN SA (CH)
VESTERGAARD FRANDSEN MIKKEL (CH)
GOUIN SEBASTIEN (CH)
HOANG HUYEN THANH (VN)
ZELLWEGER MATTHIEU (CH)
International Classes:
A01N25/34; A01N25/10
Foreign References:
US5856271A1999-01-05
Attorney, Agent or Firm:
PATRADE A/S (Aarhus C, DK)
Download PDF:
Claims:
CLAIMS

1. A method for producing an insecticidal or acaricidal polymer filament, the method comprising mixing insecticide or acaricide and Carbon Black into a molten thermoplas- tic polymer; wherein the Carbon Black is included in the molten polymer to an amount of 2-10% by weight of the molten polymer in order to form a matrix containing the polymer, the Carbon Black, as well as the insecticide or acaricide; extruding the matrix into a filament; and stretching the filament to a mass per length of 80 to 1000 denier at a draw ratio of 3 to 7.5.

2. A method according to claim 1, wherein for a mass per length D in units of denier for filaments of between 100 and 350 denier, the draw ratio is lower than according to the formula [8.7- 0.01 I'D]. 3. A method according to claim 2, wherein for a mass per length D in units of denier for filaments of between 100 and 350 denier, the draw ratio is higher than according to the formula [7.1- 0.01 I'D].

4. A method according to claim 1, wherein the draw ratio is 5 to 7.5 for filaments hav- ing a thickness of 80- 150 denier.

5. A method according to claim 1, wherein the draw ratio is 4.5 to 6.5 for a filament having a thickness of 150-250 denier. 6. A method according to claim 1, wherein the draw ratio is 3.5 to 5 for a filament having a thickness of 250-350 denier.

7. A method according to any preceding claim, wherein the draw ratio is 3 to 4.5 for filaments of more than 350 denier.

8. A method according to claim 1, wherein the draw ratio is

- 6 to 7.5 for a filament having a thickness of 80-150 denier, or - 5.5 to 6.5 for a filament having a thickness of 150-250 denier, or

- 4 to 6 for a filament having a thickness of 250-350 denier, or

- 3.5 to 4.5 for a filament having a thickness of 350-1000 denier. 9. A method according to any preceding claim, wherein the polymer comprises poly- olefin.

10. A method according to claim 8, wherein the polymer comprises polyethylene (PE) or polypropylene (PP) or both.

11. A method according to claim 8, wherein the polymer comprises HDPE and LDPE or LLDPE or both.

12. A method according to claim 10, wherein the polymer comprises more than 50% HDPE and at least 25% LDPE or LLDPE.

13. A method according to claim 11, wherein the polymer comprises least twice as much HDPE than LDPE or LLDPE. 14. A method according to any preceding claim, wherein the content of Carbon Black is 2-5%.

15. A method according to claim 1 , wherein the draw ratio is

- 5 to 7 for a filament having a mass per length of 80-150 denier or

- 4.5 to 6 for a filament having a mass per length of 150-250 denier or

- 3.5 to 5 for a filament having a mass per length of 250-350 denier or

- 3 to 4 for a filament having a mass per length of 350-1000 denier or

16. A method according to claim 1, wherein for a mass per length D in units of denier for filaments of between 100 and 350 denier, the draw ratio is lower than according to the formula [8.2- 0.011»D].

17. A method according to claim 15, wherein for a mass per length D in units of denier for filaments of between 100 and 350 denier, the draw ratio is higher than according to the formula [7.1- 0.011»D].

18. A method according to claim 1, 14, 15, or 16, wherein the carbon content is 5-10% by weight of the polymer.

19. A method according to claim 1, 14, 15, 16, or 17, wherein the polymer comprises more than 75% HDPE.

20. A method according to claim 18, wherein the polymer comprises more than 10% LLDPE or LDPE.

21. A method according to any preceding claim, wherein the insecticide/acaricide is a pyrethroid, a pyrrole, a pyrazole, a neonicotinoid, a carbamate, an organophos- phate, or a combination of these.

22. A method according to claim 20, wherein the insecticide or acaricide is del- tamethrin, chlorfenapyr, fipronil, or dinotefuran, or a combination of these.

23. A method according to claim 21, wherein the insecticide or acaricide is del- tamethrin at a concentration of 0.2-1% by weight of the polymer.

24. A method according to any preceding claim, wherein the filament is woven or knitted into a fabric.

25. A method according to claim 24, wherein the fabric is a net.

Description:
Method for regulating migration of insecticide or acaricide in a polymer fibre by stretching

FIELD OF THE INVENTION

The present invention relates to regulation of the migration of insecticides or acaricides in a polymer fibre by stretching. Especially, it relates to a method for regulating the migration of insecticide or acaricide in a polymer filament that also contains Carbon Black.

BACKGROUND OF THE INVENTION

Stretching of polymers is a well known measure for adjusting the physical properties, especially for fibres. Different draw ratios are disclosed in US patent applications and patents US2007/134305, US7291669, US3418200, US429720, US4369156, US4245001, US6444312, US6465095, US6743506, and US7560159.

WO2008/032842 by Sumitomo discloses advantages of an elongation percentage of 25% to 40% in a matrix of high density polyethylene (HDPE) and linear low density polyethylene (LLDPE) containing porous particles with insecticide. The advantage of the elongation percentage is a reduction of the tendency to crease. The elongation in this interval of 25-40% is achieved with a draw ratio of 7-9.

WO2008/032844 by Sumitomo discloses an insect-repellent fiber comprising a mixture of LLDPE and HDPE with a preferable weight ratio of 5-30:70-95 and a pyrethroid. Furthermore, the insect-repellent fiber may comprise a UV absorber, antistatic agent, lubricant, anti-blocking agent, pigment, nucleator, metal soap. A draw ratio of 8 is mentioned in example 1.

WO2009/75373 by Sumitomo discloses a 270 deniers 24-filament yarn extruded from a mixture of a polypropylene (PP) and PP-l-butene copolymer as a permethrin matrix and drawn by a factor of 3 to a 90 deniers yarn. No other examples are given for draw ratios. Preferred mass per length for fibres are 50-500 deniers (page 21 line 4).

WO2008/047604 by Sumitomo discloses a polymer fibres containing a pesticide on a pesticide support. A stretching rate ratio of 5 or more is disclosed.

US6770356 by Procter & Gamble discloses fibres, for example with insecticide (col. 20 line 2), in which the draw ratio is less than 4 (col. 7 line 62), preferably between 1.2- 2.5 for poly(lactic acid) in order to obtain soft fibres with low degree of shrinkage.

US4935232 by Interface Research Corporation discloses a biocidal polymeric composition. In example XV microbiocidal fiber composed for example of polyethylene and combined with biocidally effective amount of a phosphate ester is disclosed. A draw ratio of 3 is mentioned in relation to tensile properties. Examples of fibre mass per lengths are given for PP as 179 deniers and as 280 deniers for nylon yarn.

US4957943 by Minnesota Mining discloses a particle-filled microporous material such as films and fibres. High density polyethylene (HDPE) and low density polyethylene (LDPE) are mentioned as materials, however, not in combination. Pesticides can be trapped in the microporous structure. A draw ratio of 3 is mentioned for films.

For polymers containing insecticide, stretching is also known to be used for adjusting the migration rate. WO2003/063587 by Vestergaard.Frandsen discloses the influence of drawing on the migration rate, as described on page line 14-17, "in-line drawing of the yarn to a draw ratio of 5 to 1 1 , 5 to 10, or 8 to 10, thus, achieving the crystallinity of the yarn/matrix associated with the state of "fully drawn yarn", and the desired migration rate and as well as other suitable physical properties." From this disclosure, it is also known that Carbon Black (colloidal carbon particles) is a migration inhibitor apart from being a UV protector. WO2008/004711 by Sumitomo concerns mainly the bleed coefficient caused by and a powdery carrier material for the insecticide, for example with fine powdery carriers of carbon. Further, the migration rate is determined by a large number of factors including the draw ratio. It discloses a draw ratio of 8 for a monofilament of HDPE and LLDPE containing permethrin. The preferred fibres are made of HDPE/LDPE with a mass per length of 100-350 deniers but rather 130-230 denier.

The patent applications Wo2010/015256 and Wo2010/015257 by Vestergaard Frand- sen refer to draw ratios between 5 and 11 for proper migration rate and physical prop- erties of a matrix containing HDPE/LDPE at a ratio of 8 to 10. The preferred fibre mass per length is 50-100 denier.

EP582823B1 by Sumitomo (patent family with US5476652) discloses a stretch ratio of 1.1-10 related to the bleeding coefficient (page 4 lines 32-36) in connection with mi- cro -voids caused by a substantial amount of filler and formed by stretching polymer sheets with the right draw ratio. The microvoids are believed to be filled with insecticide, like a reservoir. An example of a stretch ratio of 4 is given in the Examples for a LLDPE resin containing a filler, for example calcium carbonate, and drugs, for example the synthetic pyrethroid empethrin or allothrin.

US2009/041820 by Exxon discloses functional polymer compositions, for example an insect repellent fabric, see paragraph [0147]). For the fibre preparation, draw ratios of 3 or more are used, see paragraph [0184]. UV stabilizers are mentioned in [0024] and a discussion on the complex nature of migration is found in [0028], which reads, "For a given class of polymer, the molecular weight, molecular weight distribution, polymer density, degree of crystallinity, crystallite size and shape, method of fabrication, etc. may have an effect on the degree and the rate of release or migration of the fluids and or active substrate components.". The preferred mass per length range is 0.5 to 10 deniers (page 20 right column line 5). Deltamethrin (DM) or pyrethroids in general are not mentioned and neither a HDPE/LLDPE blend of the polymer.

Apart from the above mentioned disclosure WO2008/004711 by Sumitomo and WO2003/063587 by Vestergaard Frandsen, the use of Carbon Black for migration con- trol of insecticide in polymer matrices has been reported repeatedly by Battelle, for example in US5856271 and WO2002/043487 published. Also, US4680328 by Dow discloses an insecticidal PE composition for a cable with Carbon Black as compatibility additive which increases the retention time; an example (No. 5) is given with 2.6% Carbon Black in a matrix of 37% HDPE, 60% LLDPE. US2002/192259 by Syngenta discloses release of insecticide from a matrix being controlled by Carbon Black. The matrix is used as barrier for buildings to protect wood against pests.

Thus, in addition to the use of Carbon Black to regulate the migration, it is known to apply various draw ratios to polyethylene fibres and sheets. However, the interplay between the content of Carbon Black and the draw ratio has not been explicitly discussed. As Carbon Black is desired in fibres, especially insecticidal nets, for its UV protection of the insecticide, it would be desirable to find suitable draw ratios for insecticidal or acaricidal fibres in dependence of their thickess and content of Carbon Black.

DESCRIPTION / SUMMARY OF THE INVENTION

It is therefore the object of the invention to provide an improvement in the art of stretched polymer filaments containing insecticide or acaricide and Carbon Black (colloidal carbon particles). Especially, it is the purpose to provide polymer filaments containing insecticide or acaricide and a substantial concentration of Carbon Black and still having a useful migration rate for the insecticide or acaricide. This purpose is achieved with a method for producing an insecticidal or acaricidal polymer filament, the method comprising

- mixing insecticide/acaricide and Carbon Black into a molten thermoplastic polymer to obtain a matrix for extrusion, wherein the Carbon Black is added to the molten polymer at an amount of 2-10% by weight of the molten polymer,

- extruding the insecticidal or acaricidal matrix with the Carbon Black into a filament,

- stretching the filament at a draw ratio of 3 to 7.5 to obtain a stretched filament with a mass per length of 80 to 1000 denier. For example, a draw ratio of 3 to 6.5 is used for a mass per length for a filament of 150 to 1000 denier. Another example is a draw ratio of 3 to 5 for a mass per length for a filament of 250 to 1000 denier. A further example is a draw ratio of 3 to 4.5 is used for a mass per length for a filament of between 350 to 1000 denier.

The term "filament" is restricted to monofilaments and does not include multifilaments. The term "polymer" is used for polymer or the blend of polymers without insecti- cide/acaricide, Carbon Black and further additives. The term "matrix" is used for the blend of polymers and the additives, including Carbon Black and insecticide/acaricide, and optionally synergists and other additives.

The term "insect or acari" has to be read as "insect or acari or both". The term "insec- ticide'V'acaricide" is not meant as only one single insecticide/acaricide and does not exclude the insecticide/acaricide being part of a group of insecticides/acaricide. It should also be pointed out that many specific insecticides are also acaricides, as they act against insects as well as acari; thus, the expression "an insecticide or an acaricide" is not meant as one of them excluding the other.

Typically, filaments for mosquito nets are fully drawn at a draw ratio of around 8. This appears from

- the draw ratio of 8 in Sumitomo's WO2008/032844 and WO2008/004711

- the drawing interval of 7-9 in Sumitomo's WO2008/032842

- the preferred draw ratio interval of 8 to 10 and the preference of fully drawn yarn in the International patent applications WO2003/063587, WO2010/015256 and WO2010/015257 by Vestergaard Frandsen,

However, as it has turned out, a reduced stretching of the filaments efficiently counteracts the retention effect by Carbon Black on the insecticide/acaricide, for example del- tamethrin. In this connection, it should be emphasized that the retention properties of Carbon Black on deltamethrin (DM) in polyethylene (PE) filaments is very pronounced. For example, experiments have shown that for a 325 denier PE filament, the Carbon Black content has to be as low as 1% by weight in order to have a satisfactory migration of DM. However, this is too low a Carbon Black content for a proper UV protection. By reducing the draw ratio, a relatively high concentration of Carbon Black, for example, 5%, can be retained while still having a satisfactory migration speed for replenishing the insecticide/acaricide on the surface of the filaments. Advantageous polymers for the filaments are polyolefms, especially polyethylene (PE) and polypropylene (PP). The term polyethylene comprises the different types of PE, including high density polyethylene (HDPE), medium density polyethylene (MDPE), low density polyethylene (LDPE), and linear low density polyethylene (LLDPE). In some embodiment, the filament has at least 150 denier or at least 250 or at least 350 denier.

Examples of draw ratios in dependence of the mass per length of the filament in units of denier are the following:

- 5 to 7.5, for example 6 to 7.5 or 5 to 7, for a filament having a mass per length of 80-150 denier,

- 4.5 to 6.5, for example 5.5 to 6.5 or 4.5 to 6, for a filament having a mass per length of 150-250 denier,

- 3.5 to 6, for example 4 to 6 or 3.5 to 5, for a filament having a mass per length of 250-350 denier,

- 3 to 4.5, for example 3.5 to 4.5 or 3 to 4, for a filament having a mass per length of 350-1000 denier,

For example, the polymer matrix contains at least 75% or at least 90% of PE or PP. A non limiting example of polymer matrices for which the above stated values are considered advantageous is a polyethylene polymer that contains a mixture including HDPE and LDPE or HDPE and LLDPE or HDPE and LDPE and LLDPE. An advantageous polymer for the above draw ratios contains more HDPE than LDPE or LLDPE, for example, at least 50% HDPE and at least 20% LDPE or LLDPE. In further embodi- ments, the polymer contains at least 50% HDPE and at least twice as much HDPE than LDPE or LLDPE. As insecticide/acaricide, a large variety of migrating insecticide/acaricides can be used. Non-limiting examples are pyrethroids, pyrroles, pyrazoles, neonicotinoids, carbamates, or organophosphates, or a combination of these. Examples thereof are del- tamethrin, chlorfenapyr, fipronil, and dinotefuran. For example, the filament contains insecticide/acaricide, optionally deltamethrin (DM), at an amount of 0.2-1% by weight of the polymer or 0.3-0.6% or 0.3-0.4%.

In addition to the insecticide/acaricide, the filament may also contain synergists, for example piperonyl butoxide (PBO). For example, the filament contains DM and PBO. The insecticide/acaricide and the synergist may be provided in the same polymer matrix of the filament.

Alternatively, filaments with DM and filaments with PBO may be combined to a multifilament yarn. In this case, the migration and surface concentration of the DM and the migration and surface concentration of the PBO can be better controlled, as it is described in International patent applications WO2009/003468 by Vestergaard Frandsen and WO2010 046348 by Intelligent Insect Control.

A further alternative is a yarn, which is co-extruded to comprise in a single yarn a first polymer with a specific insecticide/acaricide but not PBO and a second polymer with PBO and not the specific insecticide/acaricide, for example as disclosed in Wo2009/003468 by Vestergaard Frandsen, where a side-by-side configuration is disclosed with one half of the yarn being made of the first polymer and the other half by the second, or where the yarn has two quarters of the first polymer and two quarters of the second polymer. A further alternative is this respect is a yarn with a core having a polymer with the one agent and a sheath around the cores having a polymer with the other agent.

Considerations on the extrusion of fibres with a synergist and an insecticide/acaricide have been published in International patent application WO2008/098572. Especially, the considerations about the design of the extrusion apparatus and about the temperature of the extruder being higher than the temperature throughout the material and the influence of the extrusion time on the insecticide/acaricides and synergists can be transferred to this invention as well.

The filaments are useful for a variety of fabrics. Special attention have filaments for nets, for example bed nets, greenhouse nets, nets for crop coverage, or fences surrounding at least partly an agricultural open air area for preventing low flying insects to enter the area. The latter is explained in more detail in the International patent application WO2003003827 by Vestergaard Frandsen. Insect nets, typically, have a mesh size of 1-5 mm, for example 1.5-2.5 mm. Yarns for nets advantageously have a thickness of 75-900 denier. Useful examples for greenhouse nets are yarns with 150-600 denier. For fencing, typically, thicker yarns are used, for example 500-900 denier yarns. Other examples are nets or other fabrics, for example for covering walls; examples of wall linings are explained in International patent application WO2009/059607 by Vestergaard Frandsen, where it is also explained that a dark colour may be advantageous for wall linings; such a dark colour is achieved with Carbon Black. As also disclosed in International patent application WO2009/059607, the product may be used for covering spaces where mosquitoes or other insects or acari can enter dwellings; for example, it can be used as a net or other kind of fabric to close the space between the upper edge of a wall in a hut and the roof of the hut. The latter has great importance in Africa, where huts are constructed with such open spaces. A further example is protection of harvested crops, for example during storage of grain. For example, in India, large parts of crops are lost during storage because of pest attack, why it is important to protect the harvested crops, for example grains in storage. For this reason, pesticidal films or textiles including sacks, bags, and nets, can successfully be used to enclose the harvested crops. In addition, pesticidal textiles can be used to surround crops, such as banana, while still connected to the plant itself. An advantageous concentration for insecticide/acaricide, for example DM, in products, especially, fabrics, including nets, is between 10 and 500 mg/m 2 or between 20 and 250 mg/m 2 or between 50 and 150 mg/m 2 of the fabric. For example, the concentration is of the insecticide/acaricide is 2-10 g/kg of the polymer or 3-4g/kg of the polymer.

Other non exclusive applications include curtains, window screens and door screens in livestock, horse blankets, wrapping sacks, paper, construction materials, and leathers.

Other beneficial ingredients for a product according to the above include biocides, acaricides, repellents, and additives of various kinds, for example synergists, bactericides, bacteriostatics, herbicides, UV protecting agents, preservatives, anti-hydrolysis agents, detergents, fillers, impact modifiers, anti-fogging agents, blowing agents, clari- fiers, nucleating agents, coupling agents, conductivity-enhancing agents to prevent static electricity, stabilizers such as anti-oxidants, carbon and oxygen radical scavengers and peroxide decomposing agents, flame retardants, mould release agents, optical brighteners, spreading agents, antiblocking agents, other anti-migrating agents, migration promoters, foam-forming agents, anti-soiling agents, antifouling agents, thicken- ers, wetting agents, plasticizers adhesive or anti-adhesive agents, fragrance, pigments, dyestuffs, and oils and waxes, for example polymer oil and polymer waxes.

In intervals given between two values or from one value to a second value, the end points are included or, optionally, excluded.

DETAILED DESCRIPTION / PREFERRED EMBODIMENT

The effect of the draw ratio was investigated for polyethylene monofilament yarn experimentally. The yarn was a monofilament comprising about 60% HDPE and 25-35% LLDPE and containing 0.5% w/w DM and varying loads of Carbon Black. The stretching targeted a 325 denier yarn. Bioefficacies against mosquitoes were measured after 4 and 8 weeks. Results are shown in the table below.

It is seen from the results that the bioefficacy was remarkably higher for the yarn S2 with a draw ratio of 4.0 and a Carbon Black load of 5%. Especially, the S2 yarn has a much higher bioefficacy than the fully drawn yarn S 1 with the same load of 5% of Carbon Black. It occurs from the table that S5 with a draw ratio of 8.4 and a Carbon Black load as low as 1% cannot even compete in bioefficacy with S2 with a draw ratio of 4.0 and a Carbon Black load of 5%. This illustrates that a reduced draw ratio is an efficient measure to counteract the retention effect of Carbon Black. The optimum draw ratio depends on the material, the mass per length of the fibre and the concentration of Carbon Black. In the following, a few examples are given for draw ratios.

For example, the following draw ratios in dependence of the mass per length have been found advantageous for an insecticidal or acaricidal polyolefin filament containing 2- 10% Carbon Black:

- 5 to 7.5 for a filament having a mass per length of 80-150 denier

- 4.5 to 6.5 for a filament having a mass per length of 150-250 denier

- 3.5 to 6 for a filament having a mass per length of 250-350 denier

- 3 to 4.5 for a filament having a mass per length of 350-1000 denier For a restricted amount of 2-5% Carbon Black and a content of HDPE of more than 50% and at least 20% LLDPE or LDPE, the draw ratio is advantageously

- 6 to 7.5 for a filament having a mass per length of 80-150 denier

- 5.5 to 6.5 for a filament having a mass per length of 150-250 denier

- 4 to 6 for a filament having a mass per length of 250-350 denier

- 3.5 to 4.5 for a filament having a mass per length of 350-1000 denier

For a restricted amount of 5-10% Carbon Black and a content of HDPE of more than 50% and at least 20% LLDPE or LDPE, or for an amount of 2-10% and a content of HDPE of more than 75% and with at least 10% LLDPE or LDPE the draw ratio is advantageously

- 5 to 7 for a filament having a mass per length of 80-150 denier

- 4.5 to 6 for a filament having a mass per length of 150-250 denier

- 3.5 to 5 for a filament having a mass per length of 250-350 denier

- 3 to 4 for a filament having a mass per length of 350-1000 denier

For greenhouse nets, the following yarn has turned out to be beneficial. It is a thermoplastic polymer filament, for example PE or PP filament, with 150 to 350 denier containing 2-10% Carbon Black, for example 3-8% Carbon Black, and having been stretched with a draw ratio of between 4 and 6.5. Optionally, it may comprise at least 50% HDPE and at least 20% LDPE or LLDPE. As a further option, the polymer comprises 0.2-1 % by weight DM.

Mathematically, the relationship between an advantageous draw ratio and the mass per length of the filaments in denier can surprisingly be expressed by a very simple approximate mathematical expression as follows: For a mass per length D (in denier) of filaments having a mass per length of between 100 and 350 denier, the draw ratio should be lower than [8.7- 0.011*D]. For example, according to this formula for a 100 denier yarn, the draw ratio should be less than 8.7-0.011*100=7.6;

for a 200 denier yarn, the draw ratio should be less than 8.7-0.011*200=6.5, for a 325 denier yarn, the draw ratio should be less than 8.7-0.011*325=5.1

for a 350 denier yarn, the draw ratio should be less than 8.7-0.011*325=4.85. However, for a mass per thickness larger than 350 denier, the optimum draw ratio does not change much any more and should be below 4.5.

For most applications, the draw ratio should be higher than [7.1-0.011 » D] for filaments having a mass per length of between 100 and 350 denier. For example, according to this formula,

for a 100 denier yarn, the draw ratio should be higher than 7.1-0.011*100=6, for a 200 denier yarn, the draw ratio should be higher than 7.1-0.011*200=4.9;

for a 325 denier yarn, the draw ratio should be higher than 7.1-0.011*325=3.5, for a 350 denier yarn, the draw ratio should be higher than 7.1-0.011 ·350=3.25.

However, for a mass per thickness larger than 350 denier, the optimum draw ratio does not change much any more and should be higher than 3. The values for the draw ratio, achieved with the approximate formulae, are within an uncertainty +/- 0.1 when comparing with the above ranges, which illustrates the relatively preciseness despite the simple nature of the approximation.

The two formulae also express implicitly the low-denier limit corresponding to a full drawing, which is typically around 8 or slightly higher. With increasing mass per length, the draw ratio should decrease in order to achieve proper migration properties for the insecticide/ acaricide .

This very simple approximative scaling law for proper migration of insecti- cide/acaricides in thermoplastic matrices can be made even more precise in dependence on the material and the amount of Carbon Black.

For example, the above approximation for the upper limit of [8.7- 0.011 » D] for filaments having a mass per length of between 100 and 350 denier is valid for a thermo- plastic matrix containing a restricted concentration of 2-5% Carbon Black and at least 50% HDPE and more than 25% LLDPE. For example, the lower limit of the draw ratio in this case may be restricted to higher than [7.6- 0.011 » D] for filaments having a mass per length of between 100 and 350 denier and higher than 3.5 for filaments having a mass per length higher than 350 denier.

For example, for a relatively high amount of Carbon Black of 5-10%, the draw ratio should be lower. The upper limit for the draw ratio may be expressed by the simple formulae [8.2- 0,011 D]. The same formula applies for a thermoplastic matrix with a relatively high content of more than 75% HDPE, optionally with at least 10% LLDPE or LDPE. Also in this case, for most applications, the draw ratio should be higher than [7.1- 0.011 » D] for filaments having a mass per length of between 100 and 350 denier and higher than 3.5 for filaments heavier than 350 denier.