A selective hopping method for hit avoidance in a frequency hopping spread spectrum communication system utilizing an original hopping sequence, having a plurality of available channels for receiving signal packet traffic utilizing a plurality of receiving signal slots are disclosed. The plurality of available channels all are available for use in frequency hopping. The method includes the steps of dividing the plurality of available channels into a plurality of partitions; distributing the available channels in each of the plurality of partitions into a predetermined distribution; forming a partition sequence by assigning a predetermined number of channels to a plurality of selected receiving signal slot sets; generating a generated hopping sequence by partition mapping, in which the partition mapping is responsive to the partition sequence; and managing the receiving signal packet traffic, in which the receiving signal packet traffic is transmitted only in the selected receiving signal slot sets.

The short-range wireless communication specification in the 2.4 GHz Industrial Scientific Medicine (ISM) band known as "Bluetooth" has been adopted as the basis of the first part of the Wireless Personal Area Network (WPAN) specifications (IEEE Std 802.15.1). Being designed as a low-cost replacement for wires and cables, Bluetooth aims to provide a unified and convenient wireless interface for applications within a "personal area" of approximately 10 meters. Bluetooth utilizes frequency hopping (FH) as its spread spectrum approach, a requirement in the ISM band. The ISM band, however, is an unlicensed shared band that may have interference from many different systems operating concurrently. The Wireless Local Area Network (WLAN) specification known as IEEE Std 802.11(b), and its higher-speed extension, is another wireless communication specification in the ISM band. WLAN is targeted for high-speed data exchange in a local area network (LAN) environment. Clearly, there is a high probability that WPAN and WLAN devices will be utilized at the same time, a situation known as co-existence. The problems arising from co-existence have drawn so much attention that a special task group, TG2, under the auspices of the IEEE 802.15 has been formed to model the resulting performance degradation and study possible solutions. Adaptive frequency hopping (AFH) (HongBing Gan and Bijan Treister, Adaptive Frequency Hopping Implementation Proposals for IEEE 802.15.1/2 WPAN, IEEE P802.15 Working Group Contribution, IEEE 802.15-00/367r0, Nov. 1, 2000) has been one proposed solution to the co-existent problem. AFH removes the channels which experience interference from the hopping sequence thus providing hops to the clean, non-interfered channels only. However, one problem with AFH is that the Federal Communications Commission (FCC) has placed a restriction on the channel usage of frequency-hopping systems in the 2.4 GHz band. The system must have at least 75 channels and the occupation time of each channel not exceed 0.4 second in 30 seconds. This implies that at least 75 channels should be kept and used uniformly to achieve full-time usage. Removal of 22 channels occupied by an 802.11b device from the 79 hopping channels of Bluetooth would be unfeasible. This restriction applies to Bluetooth type 1 and type 2 devices but not to type 3 devices due to their relatively lower transmission power (Bluetooth Special Interest Group, Specifications of the Bluetooth System, vol. 1, v.1.0B 'Core' and vol. 2 v1.0B 'Profiles', December 1999). The design of a new hopping sequence is also critical to integrate AFH into Bluetooth. Two recent proposals in the AFH section of TG2 (Hongbing Gan, Bijan Treister, et al, Adaptive Frequency Hopping, a Non-collaborative Coexistence Mechanism, IEEE P802.15 Working Group Contribution, IEEE 802.15-00/367r1, March 2001; Kwang-Cheng Chen, Hung-Kun Chen, and Chi-Chao Chao, Selective Hopping for Hit Avoidance, IEEE P802.15 Working Group Contribution, IEEE 802.15-01/057r2, March 2001; Anuj Batra, Kofi Anim-Appiah, and Jin-Meng Ho, An Intelligent Frequency Hopping Scheme for Improved Bluetooth Throughput in an Interference-Limited Environment, IEEE P802.15 Working Group Contribution, IEEE 802.15-01/082r1, March 2001; and Oren Eliezer and Dan Michael, Adaptive Frequency Hopping for FHS S Systems, IEEE P802.15 Working Group Contribution, IEEE 802.15-01/169r0, March 2001) to solve this problem are by Gan and Eliezer, respectively. However, Gan and Eliezer's schemes do not comply with the FCC regulation of using at least 75 hopping channels. Gan's number of channels in the new hopping sequence is equal to that of the good channels, which is adaptive according to the environment. The bad channels in the original hopping sequence are redirected to the pool of good channels in a circular order, while the good channels remain unchanged. This circular order redirection, however, does not maintain the pseudo-randomness of the original hopping sequence and is thus considered a weakness. Eliezer's number of channels in the new hopping sequence is equal to a prime number, 23, selected from the pool of good channels. The sequence has a very short period and also provides no pseudo-randomness. The reduction of the number of hopping channels and shortened period of the hopping sequence is claimed by Eliezer to be suitable for AFH. Another approach to the co-existence problem is so-called intelligent frequency hopping (IFH) (Anuj Batra, Kofi Anim-Appiah, and Jin-Meng Ho, An Intelligent Frequency Hopping Scheme for Improved Bluetooth Throughput in an Interference-Limited Environment, IEEE P802.15 Working Group Contribution, IEEE 802.15-01/082r1, March 2001) which uses all the hopping channels and generates a new hopping sequence based on traffic requirements. In IFH, the number of channels used in the new hopping sequence can be equal to the number of all the channels. The new hopping sequence comprises good windows and bad windows. Each good window is followed by a bad window and vice-versa. The length of good windows and bad windows are fixed and optimized for data or voice traffic. IFH generates good channels within the good windows utilizing a look-ahead algorithm; however, the repetition of good and bad channels is not well suited to voice traffic. Furthermore, the look-ahead algorithm requires searching through the sequence and is more complex than other hop-by-hop mapping algorithms, such as in Gan.

Selective frequency hopping for hit avoidance in wireless communications system and method


An electrostatically force balanced accelerometer employs electrostatic, single sided square law forcing after filtering and scaling the pickoff signal to determine a restoring force required to bring the pendulous mass (10) of the accelerometer back to its null position. A signal (44,48) proportional to the square root of the restoring force is applied to an electrostatic square law forcing circuit (50) that applies a restoring force to one side or the other of the pendulum (10). A system output signal (42) is proportional to the calculated restoring force, and thus linearly proportional to the sensed acceleration. The transfer function of the forcing circuit (50) is empirically determined by applying a series of known accelerations and measuring the balancing signal required to restore the pendulous mass (10) to its null position. A feedback signal (44,48) is then generated which has a relation to the pickoff signal that is the inverse of the empirically determined transverse function of the forcing circuit.

The present invention relates to force balanced instruments of the closed loop type, and more particularly concerns control of a force balanced instrument having a linear output proportional to sensed input and in which a processed feedback signal provides a forcing signal to a selected side of the sensitive element.
Force balanced sensing instruments often use a sensing member that is movable from a nominal position in response to an input condition that is to be sensed. A position pickoff provides an indication of sensing member position and a feedback signal, based on the pickoff signal, applies a force to the sensing member that tends to return it to its nominal position The feedback signal may provide an instrument output signal representing the sensed input condition. It is generally desired that the instrument output signal be proportional to the input condition, and thus in many types of electrostatic and electromagnetic force balance sensing instruments special techniques are provided or required to obtain a linear relation between the instrument output and the sensed input. In electrostatic and electromagnetic instruments the forces applied by the instrument forcer are not linearly related to the feedback voltage or current supplied to the forcer. Furthermore, for optimum operation of the instrument itself, it is preferred that the feedback force applied by the feedback control network have a linear relation to the sensed input. Thus special techniques have been employed for obtaining such linearity.
For example, in an electrostatic force balanced accelerometer of the type shown in U.S. Pat. No. 4,679,434, for Integrated Force Balanced Accelerometer of Robert E. Stewart, electrostatic forcing in a closed loop system is employed to position and obtain an output from a pendulous inertial mass. The electrostatic forcing system employs a capacitative pickoff electrode on each side of a pendulous member that has been etched from a silicon substrate. The electrodes also apply nominally equal and opposite bias forces to the pendulous member, to which is applied a control voltage. In another control arrangement for an accelerometer of this type, a fixed bias voltage, V, is applied to the pendulous inertial mass, and feedback voltages +v and -v, are applied concurrently to pickoff and forcing electrodes on opposite sides of the mass. Accordingly, omitting factors such as gap variation, parallelism, dielectric constants and the like, which may also affect force, the force applied by each electrode to the pendulous mass is proportional to (V+v).sup.2 and (V-v).sup.2, respectively. The net force on the pendulum applied by this control system then is the difference between the two forces, which is effectively proportional to 4 vV. As the bias voltage V is a constant, the feedback voltage, v, is proportional to the feedback force applied, and is also linearly related to the input acceleration experienced by the pendulous inertial mass.
This system has a number of problems, including the large negative spring effect associated with the required bias electrical fields. Even in the absence of any input acceleration to be sensed, the bias fields are required, and, since the bias field may vary and the pickoff null position may vary, the instrument may have poor null stability and repeatability. In the described prior system, many factors, such as gap variation, aging of components, temperature variations and the like provide sources of error that may result in a spurious output and decreased null stability. Potentially this spurious bias error is a large error. Small variations in electric field are exacerbated by the large negative spring effect in voltage biased systems. This negative spring effect is caused by the two large bias fields and may be quite large for typical ranges of accelerometer inputs
The problems described above that exist in this oppositely biased electrostatically forced silicon accelerometer may also exist in other types of electrostatic or electromagnetic force balanced instruments where the applied feedback force is not linearly related to the feedback signal.
Accordingly, it is an object of the present invention to provide a closed loop force balanced instrument that avoids or minimizes above-mentioned problems.

Square law controller for an electrostatic force balanced accelerometer


The polyisocyanate polyaddition products comprise hydrophobic compounds plus at least one further compound selected from the group consisting of: (i) organic, cyclic compounds having a molecular weight of from 200 to 3000 g/mol, (ii) salts of metals of transition groups I, II and/or VIII, (iii) organic and/or inorganic acid anhydrides, (iv) cyclic sulfonic esters and/or sulfones, (v) lactones, lactams and/or cyclic esters and/or (vi) xcex1,xcex2-unsaturated carboxylic acids, xcex1,xcex2-unsaturated carboxylic acid derivatives, xcex1,xcex2-unsaturated ketones and/or xcex1,xcex2-unsaturated aldehydes.

The present invention relates to polyisocyanate polyaddition products comprising hydrophobic compounds plus at least one further compound selected from the group consisting of: (i) organic, cyclic compounds having a molecular weight of from 200 to 3000 g/mol, (ii) salts of metals of transition groups I, II and/or VIII, (iii) organic and/or inorganic acid anhydrides, (iv) cyclic sulfonic esters and/or sulfones, (v) lactones, lactams and/or cyclic esters and/or (vi) xcex1,xcex2-unsaturated carboxylic acids, xcex1,xcex2-unsaturated carboxylic acid derivatives, xcex1,xcex2-unsaturated ketones and/or xcex1,xcex2-unsaturated aldehydes, preferably selected from the group consisting of: (i), (iii), (iv), (v) and/or (vi), particularly preferably selected from the group consisting of (iii), (iv) and/or (vi). Furthermore, the invention relates to a process for producing these polyisocyanate polyaddition products, in particular mattresses or furniture upholstery and/or carpet backing. The invention also relates to the use of hydrophobic compounds for reducing the formation and/or the content of primary amines in polyisocyanate polyaddition products and/or for reducing the water uptake of polyisocyanate polyaddition products, in particular flexible polyurethane foams.
The production of polyisocyanate polyaddition products by reacting polyisocyanates with compounds which are reactive toward isocyanates in the presence of catalysts which accelerate the reaction of the substances which are reactive toward isocyanates with isocyanates and, if desired, blowing agents, additives and/or auxiliaries is generally known.
Like other plastics, polyisocyanate polyaddition products are subject to aging processes which generally lead to a deterioration in the use properties as time goes on. Important aging influences are, for example, hydrolysis, photooxidation and thermal oxidation which lead to rupture of bonds in the polymer chains. In the case of polyisocyanate polyaddition products, for example polyurethanes, hereinafter also referred to as PURs, especially the action of moisture and even more the combination of moisture and elevated temperature results in hydrolytic cleavage of the urethane and urea bonds.
This cleavage is not only reflected in a significant deterioration in the use properties but also leads to formation of primary aromatic amines, e.g. toluenediamine (TDA) and diaminodiphenylmethane (MDA), or primary aliphatic amines such as hexamethylenediamine or isophoronediamine.
As experiments have found, amine formation is influenced by a series of parameters. In particular, high temperatures above 80xc2x0 C. in combination with high atmospheric humidity lead to hydrolytic cleavage of the urethane and urea bonds. Such conditions are of importance in some specific applications of flexible PUR foams.
A further parameter which has a significant influence on the formation of primary amines is the type and amount of catalysts used. As has been able to be shown in various experiments, the catalysts which are present in polyurethane systems and are necessary for the urethanization and blowing reaction also catalyze the hydrolytic redissociation reaction to a considerable extent. The presence of catalysts is thus a critical precondition for the hydrolysis of the urethane and urea bonds. Furthermore, it has been able to be shown that the efficiency of the hydrolysis is highly dependent on the activity and the type of catalyst, and also on whether the catalyst remains in the system or can migrate out of the material. In particular, tertiary amine catalysts having reactive functional groups such as OH and NH2 considerably accelerate amine formation by lowering the activation energy for the cleavage reaction. The functional groups result in incorporation of the catalysts into the PUR network formed and the products produced using them have the advantage of lower odor and fogging problems since the catalysts cannot escape by diffusion after production of the PUR product. The same applies to formulations comprising polyols which have been prepared using primary or secondary amines as initiator molecules and thus have catalytically active centers. Such polyols have been increasingly used in recent times. In the case of formulations which comprise such constituents and are exposed to particularly hot and humid conditions in specific applications, the formation of primary amines as dissociation products cannot be ruled out. In contrast, in the case of foams produced using amine catalysts which contain no functional groups capable of being built into the structure, the catalysts are generally given off only a short time after manufacture or during aging of the foam. In the case of such foams, hot and humid conditions lead to significantly lower amine contents.
As compounds which reduce the aromatic amine content of flexible polyurethane foams, U.S. Pat. No. 4,211,847, GB 1 565 124 and DE-A 29 46 625 make use of sterically hindered cycloaliphatic monoisocyanates and monothioisocyanates. Owing to their steric hindrance and their lower reactivity compared to aromatic isocyanates, these isocyanates react to only a slight extent during the foaming reaction, so that free isocyanate is available for reaction with any aromatic amines present after the foaming reaction is complete. Disadvantages of these known teachings are that the compounds mentioned are relatively expensive and, especially the two last-named compounds, also participate at least partially in the urethanization reaction despite their steric hindrance and do not react only after the foaming reaction with aromatic amine formed. In addition, these isocyanates tend to migrate out of the finished foam because of their low vapor pressure and thus pose a further health hazard due to the occurrence of free isocyanate.
DE-A 42 32 420 discloses the use of xcex1,xcex2-unsaturated ester carboxylates for producing polyurethane foams which have an improved compressive strength and elongation at break. In that document, salts of xcex1,xcex2-unsaturated ester carboxylates are used as catalysts for the NCO/water reaction. In an aside, it is stated that the compounds are, due to the presence of olefinic double bonds adjacent to the carboxylate groups, capable of addition of amino groups which are formed during the slow aging of the foam. A disadvantage of these compounds is their catalytic action which has an adverse effect on the foaming reaction. A catalytic action of additives for reducing the amine contents of finished PUR foams is, however, not desirable since this leads, as described above, to further and accelerated formation of primary amines.
Hydrolysis inhibitors for polyurethanes containing ester groups are described in DE-A 23 31 796, FR 1 550 562 and GB 1 014 974. The increase in the hydrolysis resistance of the PUR products is usually based on an improvement in the mechanical properties after storage under hot and humid conditions. DE-A 23 31 796 describes the addition of epoxy compounds in order to avoid hydrolysis of the ester groups in PUR products. For the same purpose, FR 1 550 562 claims alkyl carbonates and GB 1 014 974 claims carbodiimides in combination with a compound containing enol groups.
DD 238 992 describes epoxidized synthetic products such as triglycerides, alkyl epoxystearates, etc., and epoxidized natural products such as soya oil as hydrolysis inhibitors for polyurethane elastomers. However, the improvement in the hydrolysis resistance (increased hardness, tensile strength and elongation at break) is restricted to polyurethane elastomers containing polyesters as polyol component. DD 298 246 claims a polyol component for producing noncellular polyurethane moldings having an improved hydrolysis resistance. The improvement in the hydrolysis resistance is achieved here by addition of fatty amines.
A similar reaction mixture is claimed in DE-A 3 443 341. The improvement in the elongation at break of possibly cellular polyurethanes is achieved here by means of a mixture of an inorganic filler, a metal salt of a fatty acid and a hydrophobicizing agent such as a fatty acid amide, fatty alcohol or a natural or synthetic wax.
GB 2 313 128 discloses castor oil and derivatives and also polyols based on polybutadiene and saturated hydrocarbons ( greater than C10) for increasing the resistance of polyurethanes to discoloration. It is also possible to use hydrophobic compounds without OH groups, for example olefins, paraffins and also animal and vegetable oils.
U.S. Pat. No. 5,549,841 claims a process for producing flexible PUR foams having an improved compressive set for use in a tropical or subtropical climate. This improvement is achieved by the use of polyols having a variable ethylene oxide content or a variable ethylene oxide end cap in combination with polymer polyols. The polymer polyol comprises a vinyl polymer dispersion in a polyoxyalkylene base polyol.
EP-A 672 698 describes a process for producing polyurethanes by addition of reaction products of polyalkylenepolyamines and natural fats or oils. The foams produced using these products are largely closed-celled and therefore have a rigid foam character. Such formulations are unsuitable for flexible foam applications.
A further document in which hydrophobic PUR foams are described is EP-A 933. The foams produced with addition of fatty acids, fatty acid esters, adducts of fatty acids and EO/PO and also fatty acid amides have a high absorption capability in respect of oil and possibly halogen-containing, hydrophobic compounds.
WO 99/00428 discloses flexible polyurethane foams which are produced using hydroxylated polydienes.
It is an object of the present invention to modify polyisocyanate polyaddition products, in particular polyurethane foams, in such a way that the hydrolytic cleavage of urethane and urea bonds and thus, in particular, the formation of aromatic amines is prevented or at least reduced. The compounds should be inexpensive and readily available and should be able to display their effect in the finished foam without further after-treatment. In addition, they should affect the foam properties as little as possible.
We have found that this object is achieved by the polyisocyanate polyaddition products described at the outset and the use of the hydrophobic compounds likewise described at the outset.
It has been found that the extent of hydrolytic redissociation of urethane and urea bonds is dependent to a considerable degree on the penetration of moisture into the foam matrix. It was thus necessary to find additives which hinder the penetration of moisture, especially in foams which are exposed to hot and humid conditions. These additives should have no significant effect on the foaming reaction and the properties of the foams.
The penetration of moisture into the foam matrix was able to be influenced by the degree of hydrophilicity or hydrophobicity of the foams. It was found that, because of its water-repellent properties, a hydrophobic foam takes up less moisture than a hydrophilic foam. The problem described could accordingly be solved by increasing the hydrophobicity of the foams. Surprisingly, it was found that these technical teachings according to the present invention not only enable the penetration of water into, in particular, the flexible polyurethane foam to be prevented but also enable the formation of primary amines to be reduced.
The hydrophobic compounds used according to the present invention are preferably employed in the generally known processes for producing polyisocyanate polyaddition products, preferably polyurethanes which may contain isocyanurate and/or urea structures, particularly preferably flexible polyurethane foams. The present invention therefore also provides a process for producing flexible polyurethane foams having the properties according to the present invention in respect of water uptake and/or water adsorption by producing the flexible polyurethane foam in the presence of the hydrophobic compounds used according to the present invention.
The hydrophobic compounds used according to the present invention preferably contain groups which are reactive toward isocyanates, more preferably from 2 to 4 reactive groups, in particular hydroxyl groups.
Preferred hydrophobic compounds have a molecular weight of from 500 to 8000 g/mol and have at least one continuous carbon framework, i.e. a carbon framework connected by means of carbon-carbon bonds, having at least 8, preferably at least 10, carbon atoms.
The hydrophobic compounds used are therefore preferably reaction products of castor oil with alkylene oxides, epoxidized fatty acid esters, low molecular weight hydroxy-functional polyolefins preferably having a molecular weight from 500 to 8000 g/mol and/or oleochemical polyols based on a C9-C22-fatty acid and prepared by ring opening of epoxidized triglycerides.
In particular, it is possible to use modified, where the term modified refers, for example, to ring-opened fatty acid esters, or unmodified fatty acid esters, oils, in particular vegetable oils, and/or polyolefins, for example:
oleochemical polyols, e.g. triglycerides, based on a C9-C22-fatty acid and prepared, for example, by ring opening of epoxidized fatty acid esters, for example triglycerides, and preferably having a hydroxyl number (OHN) of from 50 to 300 mg KOH/g, where the epoxy content can be varied from 0% to 10% depending on the completeness of ring opening;
fatty acid esters, preferably epoxidized fatty acid esters, preferably having a hydroxyl number (OHN) of from 30 to 500 mg KOH/g, particularly preferably from 100 to 200 mg KOH/g, preferably based on a C9-C22-fatty acid, e.g. prepared by transesterification of oleochemical polyols with C1-C30-alkanols, e.g. alkyl epoxystearates, alkyl epoxytallates, alkyl epoxytetrahydrophthalates, alkyl oleates, dialkyl adipates, dialkyl sebacates, di(methylcyclohexyl) phthalate, dicyclohexyl phthalate, diisotridecyl phthalate, hexyl oleylcetyl phthalate, di(oleylcetyl) phthalate, dioctyl adipate, diisodecyl adipate, dibutyl sebacate, dioctyl sebacate, isobutyl stearate, the 2-ethylhexyl ester of epoxidized soya oil, isobutyl esters of fatty acids, the isobutyl ester of tallow acid, 2-ethylhexyl stearate and/or tetrahydrofurfuryl oleate;
reaction products of natural vegetable oils, e.g. castor oil, linseed oil and/or soya oil, with ethylene oxide and/or propylene oxide, preferably propylene oxide, advantageously having an OHN of from 50 to 200, particularly preferably from 80 to 90, mg KOH/g and/or
low molecular weight polyolefins, preferably having a molecular weight of from 500 to 8000 g/mol, which are preferably hydroxy-functionalized at both ends and/or have an epoxidized isoprene unit at one or both ends.
Replacement of part of the polyol component, for example in the production of flexible polyurethane foams, by the hydrophobic compounds described enables the hydrophobicity of the foams to be increased so that the penetration of moisture is significantly inhibited. This is a tremendous advantage for, in particular, foams which are exposed to hot and humid conditions (hot steam disinfection or in future sterilization of hospital mattresses, hot steam cleaning of upholstered furniture and carpets). In the case of foams which have been produced using such polyols, the entry of moisture is inhibited to such a degree that the occurrence of hydrolytic cleavage of urethane and urea bonds under hot and humid conditions is significantly reduced.
The formation of primary aromatic amines such as toluenediamine or diaminodiphenylmethane associated with this cleavage reaction is likewise significantly reduced by this measure. The stabilizing action of the polyols used according to the present invention is advantageously based on a prevention of the formation of primary amines, while the addition of other additives, e.g. the abovementioned sterically hindered isocyanates, results in only primary amine which has already been formed being chemically bound. The hydrophobic compounds used according to the present invention do not pose a health hazard and can be easily incorporated into the polyol component because of their good compatibility with the constituents of the polyol component. The hydrophobic compounds used according to the present invention counter both a deterioration in the mechanical properties, particularly when exposed to hot and humid conditions, and also the formation of primary amines, in particular primary aromatic amines, for example 2,2xe2x80x2-, 2,4xe2x80x2- and/or 4,4xe2x80x2-MDA and/or 2,4- and/or 2,6-TDA.
The use of oleochemical polyols, in particular, gives open-celled foams. Varying the proportion of these polyols allows the open cell content of PUR foams to be set in a targeted manner.
The use of the hydrophobic compounds described makes it possible to obtain foams which consist in large part of natural, i.e. regenerating, raw materials. Since the production of molded PUR foams and slabstock foams is increasingly looked at from an ecological perspective, finished products containing a relatively high proportion of recyclable components should be produced in future so as to conserve resources.
To produce the polyisocyanate polyaddition products, the hydrophobic compounds are preferably used in an amount of from 0.2 to up to 100.0% by weight, based on the weight of all the isocyanate-reactive compounds employed.
To produce the polyisocyanate polyaddition products, it is also advantageous to use (i) organic, cyclic compounds having a molecular weight of from 200 to 3000 g/mol, preferably from 200 to 1300 g/mol, hereinafter also referred to as xe2x80x9cmacrocyclesxe2x80x9d.
As a result of the use of the macrocycles, the macrocycles form complexes with tertiary amines which have been used as catalysts in the production of the polyisocyanate polyaddition products, in particular in the finished polyisocyanate polyaddition product, and the tertiary amines in the complex with the macrocycles can no longer display their catalytic activity, i.e. they are blocked. Since the complexed amine catalysts in the finished polyisocyanate polyaddition products are no longer capable of catalyzing the abovementioned hydrolytic redissociation of urethane and urea bonds, the macrocycles counter both a deterioration in the mechanical properties, in particular on exposure to hot and humid conditions, and also the formation of primary amines, in particular primary aromatic amines, for example 2,2xe2x80x2-, 2,4xe2x80x2- and/or 4,4xe2x80x2-MDA and/or 2,4- and/or 2,6-TDA. Furthermore, the formation of complexes of the macrocycles used according to the present invention with primary amines, for example primary aromatic amines, can hinder migration or extraction of these amines from the polyisocyanate polyaddition product. Migration or extraction of the amine catalysts, too, from the product is hindered by such complexation. The resulting reduction in odor and fogging problems is reinforced, in particular, by the additives used according to the present invention being able to be at least partially incorporated into the polyurethane network due to the presence of OH groups. The inclusion of primary and/or tertiary amines by the macrocycles which have been fixed in this way leads to the amines being immobilized in the foam matrix.
Macrocycles, e.g. cyclodextrins, are capable of the inclusion of water molecules as well as amines, which further reduces the occurrence of hydrolytic cleavage reactions and thus additionally counters the formation of primary amines.
As macrocycles, it is possible to use generally known compounds, for example cyclodextrins, resorcinarenes, cyclophanes and/or cyclocalixarenes, each of which may be in modified form.
Such cyclodextrins, which may also have a branched structure, are mentioned in, for example, U.S. Pat. No. 5,063,251, column 2, lines 55 to 63, and DE-A 1 96 14 441, page 2, lines 46 and 47. Suitable cyclocalixarenes are described in U.S. Pat. No. 4,642,362, column 2, line 34 to column 7, line 68.
Preference is given to using xcex1-cyclodextrin, xcex2-cyclodextrin, xcex3-cyclodextrin, reaction products of these cyclodextrins with alkylene oxides, 4-tert-butylcalix[4]arene, 4-tert-butylcalix [6]arene, 4-tert-butylcalix[8]arene, 4-sulfocalix[4]arene, 4-sulfocalix[6]arene, 4-sulfocalix[8]arene, C-methylcalix[4]resorcinarene, C-undecylcalix[4]resorcinarene, tetra-N-pentylcalix[4]resorcinarene and/or [2.2]paracyclophane, particularly preferably xcex2-cyclodextrin, 4-tert-butylcalix[6]arene, 4-sulfocalix[6]arene and/or [2.2]paracyclophane.
The macrocycles can be used in the A and/or B components or in the constituents of these components, preferably in the isocyanate component in order to avoid complexation of the amine catalysts which are customarily present in the A component before the polyurethane product has been produced. If the macrocycles are not soluble in either the A component or the B component, they are dispersed in powder form in one of the two components and subsequently processed in this form.
To produce the polyisocyanate polyaddition products, the macrocycles are preferably used in an amount of from 0.2 to 5% by weight, based on the weight of the compounds which are reactive toward isocyanates.
Furthermore, (ii) salts of metals of transition groups I, II and/or VIII, hereinafter also referred to generally as xe2x80x9cmetal saltsxe2x80x9d, are also advantageously used for producing the polyisocyanate polyaddition products. For the purposes of the present invention, the terms xe2x80x9csalts of metalsxe2x80x9d or xe2x80x9cmetal saltsxe2x80x9d also include the cations of the metals specified in complexed form.
As a result of the use of the metal salts, the metal ions form complexes with tertiary amines used as catalysts in the production of the polyisocyanate polyaddition products, and the tertiary amines in the complex with the metals can no longer display their catalytic activity, i.e. they are blocked. Since the complexed amine catalysts in the finished polyisocyanate polyaddition products are no longer capable of catalyzing the abovementioned hydrolytic redissociation of urethane and urea bonds, the metal salts counter both a deterioration in the mechanical properties, in particular on exposure to hot and humid conditions, and also the formation of primary amines, in particular primary aromatic amines, for example 2,2xe2x80x2-, 2,4xe2x80x2- and/or 4,4xe2x80x2-MDA and/or 2,4- and/or 2,6-TDA. Furthermore, the formation of complexes of the metal salts used according to the present invention with primary amines, for example primary aromatic amines, can hinder migration or extraction of these amines from the polyisocyanate polyaddition product. Such complexation prevents migration or extraction of the amine catalysts, too, from the product, which is reflected in improved fogging behavior of the foams. In addition, the metal salts can act as oxidation catalysts and accelerate oxidative degradation of any aromatic amines formed.
As metal salts, it is possible to use generally known salts of metals, for example salts of inorganic and/or organic acids, e.g. mineral acids, of the transition groups indicated, for example salts of the following metals: Cu, Ni, Co, Fe, Zn, Ag, Pd and Rh, preferably Cu, Ni and/or Fe salts, where the metals can be in any stable oxidation state.
As anion in the metal salts, it is possible for generally customary anions to be present, for example, chloride, sulfate, nitrate and/or carboxylates having from 1 to 20 carbon atoms. Furthermore, it is possible to use salts of complexed cations of the same metals with known ligands, for example monoalkylamines, alkylenediamines, phenanthroline, acetylacetone, aromatic phosphines such as triphenylphosphine, aliphatic phosphines such as tributylphosphine, salicylaldehyde and/or 1,4-diazabutadiene derivatives; it is preferred that no tertiary amines are used as ligands. Examples of metal salts or salts of their complex cations are the following compounds: Cu(II) sulfate, Cu(II) chloride, Ni(II) sulfate, Co(II) chloride, Cu(II) naphthenate, Fe(II) chloride, Cu(I) chloride, Fe(III) chloride, Cu(II) acetate-ethylenediamine complex, Fe(II) phenanthroline complex (generally known as a redox indicator under the name ferroin) Cu(I)-nitratobistriphenylphosphine complex, [glyoxal bis(cyclohexylimine)]chlorocopper(I) complex.
The central atom and ligand of the metal-ligand complex are preferably chosen so that the central atom of the complex can form complexes with primary aromatic amines or tertiary aliphatic amines or catalyze their oxidation. The complex between MDA and/or TDA or the amine catalysts and the metal cation of the complex used is preferably more stable, i.e. the dissociation constant is greater, than the complex cation used.
Preference is given to using Cu(II) sulfate, Ni(II) sulfate, Cu(II) acetate, Fe(II) phenanthroline complex, Cu(II)-acetate-ethylenediamine complex, Cu(II) naphthenate and/or Cu(I)-nitratobistriphenylphosphine complex as metal salt.
To produce the polyisocyanate polyaddition products, the metal salts are preferably used in an amount of from 0.05 to 5% by weight, based on the weight of the sum of the metal salts and the compounds which are reactive toward isocyanates.
The metal salts can be used in the A and/or B components or in the constituents of these components, preferably in the isocyanate component.
Furthermore, it can be useful to use (iii) organic and/or inorganic acid anhydrides, particularly preferably at least one carboxylic anhydride, for producing the polyisocyanate polyaddition products. The acid anhydride(s) is/are preferably used in an amount of from 0.01 to 20% by weight, based on the weight of the isocyanates and the acid anhydrides.
When acid anhydrides are employed, the anhydrides in the polyisocyanate polyaddition products are hydrolyzed to the acids, particularly under hot and humid conditions. These acids resulting from the hydrolysis block the amine catalysts which may be present in the products, for example by protonation or reaction, and thus prevent acceleration of the redissociation of the urethane bonds. In addition, the acid anhydrides used according to the present invention bind any free amino groups formed by undesired cleavage of urethane bonds.
The acid anhydrides are thus used in polyisocyanate polyaddition products to stabilize the polyisocyanate polyaddition products, in particular polyurethanes, against cleavage of the urethane and urea bonds, for example by blocking amine catalysts by protonating the catalysts or by reaction with the catalysts. In addition, the acid anhydrides can be employed in polyisocyanate polyaddition products to react with amino groups in the polyisocyanate polyaddition products, for example to form amides.
In this way, the diffusion of amines out of the polyisocyanate polyaddition products and the redissociation of the urethane bond, for example by amine catalysts present in the polyisocyanate polyaddition products, can be reduced.
It was surprisingly found that acid anhydrides used in the production of polyisocyanate polyaddition products survive the production process almost unscathed and do not participate significantly in the reaction. This is particularly true when the acid anhydrides are used in admixture with isocyanates, since this component is usually free of water and hydrolysis of the anhydrides can thus be avoided. Use of the acid anhydrides in admixture with compounds which are reactive toward isocyanates can be particularly advantageously carried out by adding the acid anhydrides to this mixture only just before production of the polyisocyanate polyaddition products, since the compounds which are reactive toward isocyanates usually contain small amounts of water. The acid anhydrides used according to the present invention can also be stable in the isocyanate-reactive compounds over a prolonged period of time.
Surprisingly, it has been found that the acid anhydrides are stable in admixture with isocyanates at room temperature, i.e. 25xc2x0 C., and the isocyanate groups do not react or do not react significantly with the anhydride groups.
As anhydrides, it is possible to use organic or inorganic acid anhydrides, for example also polyanhydrides, preferably carboxylic anhydrides, for example anhydrides of aliphatic, cycloaliphatic, araliphatic and/or aromatic carboxylic acids having usually from 1 to 10, preferably 1 or 2, carboxyl groups, with mixed anhydrides prepared from at least two different carboxylic acids also being able to be used. Polyanhydrides obtainable from dicarboxylic and/or polycarboxylic acids or copolymers of anhydrides and various alkenes can also be used as anhydrides. The carboxyl groups of the compounds are preferably converted to a large extent, particularly preferably completely, into the corresponding anhydrides. The compounds (ii) usually have a molecular weight of from 60 to 1000000 g/mol. Examples which may be mentioned are: acetic anhydride, propionic anhydride, butyric anhydride, pentanoic anhydride, hexanoic anhydride, heptanoic anhydride, octanoic anhydride, dimethylolpropionic anhydride, adipic anhydride, fumaric anhydride, mesaconic anhydride, methylenemalonic anhydride, trimellitic anhydride, ethylene glycol 4,4xe2x80x2-bis(anhydrotrimellitate), 2-acetyl-1,3-glyceryl 40 4,4xe2x80x2-bisanhydrotrimellitate, decanedioic anhydride, dodecanedioic anhydride, azelaic anhydride, pimelic anhydride, brassylic anhydride, citraconic anhydride, itaconic anhydride, naphthalene-1,8-dicarboxylic anhydride, naphthalene-1,2-dicarboxylic anhydride, chlorendic anhydride, 1,2,3,6-tetrahydrophthalic anhydride, mellophanic anhydride, benzene-1,2,3,4-tetracarboxylic anhydride, benzene-1,2,3-tricarboxylic anhydride, benzoic anhydride, biphenyl-3,3xe2x80x2-4,4xe2x80x2-tetracarboxylic anhydride, biphenyl-2,2xe2x80x2-3,3xe2x80x2-tetracarboxylic anhydride, naphthalene-2,3,6,7-tetracarboxylic anhydride, naphthalene-1,2,4,5-tetracarboxylic anhydride, naphthalene-1,4,5,8-tetracarboxylic anhydride, decahydronaphthalene-1,4,5,8-tetracarboxylic anhydride, 4,8-dimethyl-1,2,3,5,6,7-hexahydronaphthalene-1,2,5,6-tetra-carboxylic anhydride, 2,6-dichloronaphthalene-1,4,5,8-tetra-carboxylic anhydride, 2,7-dichloronaphthalene-1,4,5,8-tetra-carboxylic anhydride, 2,3,6,7-tetrachloronaphthalene-1,4,5,8-tetracarboxylic anhydride, phenanthrene-1,3,9,10-tetracarboxylic anhydride, perylene-3,4,9,10-tetracarboxylic anhydride, bis(2,3-dicarboxyphenyl)methane anhydride, bis(3,4-dicarboxyphenyl)methane anhydride, 1,1-bis(2,3-dicarboxyphenyl)ethane anhydride, 1,1-bis(3,4-dicarboxyphenyl)ethane anhydride, 2,2-bis(2,3-dicarboxyphenyl)propane anhydride, 2, 2-bis(3,4-dicarboxyphenyl)propane anhydride, bis(3,4-dicarboxyphenyl) sulfone anhydride, bis(3,4-dicarboxyphenyl) ether anhydride, ethylenetetracarboxylic anhydride, butane-1,2,3,4-tetracarboxylic anhydride, cyclopentane-1,2,3,4-tetracarboxylic anhydride, pyrrolidine-2,3,4,5-tetracarboxylic anhydride, pyrazine-2,3,5,6-tetracarboxylic anhydride, mellitic anhydride, thiophene-2,3,4,5-tetracarboxylic anhydride, benzophenone-3,3xe2x80x2,4,4xe2x80x2-tetracarboxylic anhydride, maleic anhydride, glutaric anhydride, pyromellitic anhydride, phthalic anhydride, isophthalic and/or terephthalic anhydride, benzoic anhydride, phenylacetic anhydride, cyclohexylalkane anhydrides, malonic anhydride, succinic anhydride, polymaleic anhydride, anhydrides based on adducts of maleic acid and styrene, dodecenylsuccinic anhydride, anhydrides of maleic acid and any alkylenes, for example n-octylenesuccinic anhydride, n-dodecylenesuccinic anhydride and/or copolymers of anhydrides and any further monomers such as isobutene and maleic anhydride, poly(ethylene-co-butyl acrylate-co-maleic dianhydride) and/or poly(styrene-co-maleic anhydride), where the diacids or polyacids are partially or preferably completely in the form of anhydrides. The anhydrides of the diacids or polyacids can, insofar as it is sterically possible, be either intermolecular or intramolecular.
Preference is given to using anhydrides based on the following compounds: pyromellitic acid, succinic acid, maleic acid, polymaleic anhydride, glutaric acid, which may also contain a variety of side groups, and/or copolymers of these anhydrides with all conceivable monomers which are polymerizable with anhydrides or acids.
Very particular preference is generally given to anhydrides which dissolve readily in the isocyanates and/or the compounds which are reactive toward isocyanates, preferably the isocyanates.
Furthermore, it is possible to use (iv) cyclic sulfonic esters, also known as sultones, and/or sulfones, i.e. compounds containing sulfonyl groups, preferably unsaturated sulfones. The cyclic sulfonic esters and sulfones are hereinafter also referred to collectively as xe2x80x9csulfur compoundsxe2x80x9d. It has surprisingly been found that the addition of the sulfur compounds leads to significantly reduced primary amine contents. The reaction of primary amines can occur under relatively mild conditions. Apart from the reaction of primary amine already formed to give less problematical compounds, the addition of sulfur compounds, in particular sultones, prevents the formation of the primary amines. The mechanism leading to this reduced amine formation is based on the deactivation of the tertiary amine catalysts present, which, after the polyurethane product has been produced, contribute to catalysis of the hydrolytic cleavage of urethane and urea bonds and thus to the formation of primary amines.
The added sultones, in particular, are hydrolyzed during the foaming reaction as a result of the heat generated to form the corresponding sulfonic acids. These sulfonic acids are in turn capable of reacting with tertiary amines by protonating the catalytically active nitrogen atom. This counters not only the formation of primary amines but also the associated deterioration in the mechanical properties during aging of the polyurethane product. As a particular advantage of the additives used according to the present invention, it has surprisingly been found that there is even an improvement in the mechanical properties before aging. A further positive effect associated with this hydrolysis of the sultones is that a major part of the water which penetrates is consumed in this reaction and is no longer available for the cleavage of urethane and urea bonds. In order to prevent premature hydrolysis of the sultones prior to the foaming reaction, they are preferably dissolved in the isocyanate component.
In unsaturated sulfones, the sulfonyl group causes, as a result of the partial positive charge on the sulfur atom, such a strong polarization of the Cxe2x95x90C double bond that this is capable of adding primary amines under very mild conditions. The primary amine content of polyisocyanate polyaddition products can be significantly reduced by the addition of unsaturated sulfones as a result of reaction to form unproblematical compounds. In addition, sulfones also lead to an improvement in the mechanical properties of the polyisocyanate polyaddition products.
The addition of sultones and sulfones can reduce the diffusion or migration of primary amines out of the polyurethane products. In hydrolyzed form, sultones improve the fogging behavior by preventing diffusion of tertiary amine catalysts as a result of the reaction of these with the hydrolyzed sultones.
In the case of brominated sultones (e.g. tetrabromo-2-sulfobenzoic anhydride) and sulfones, an increase in the flame resistance of the foams produced therewith has also been found.
Accordingly, the sulfur compounds counter both a deterioration in the mechanical properties, particularly on exposure to hot and humid conditions, and also the formation of primary amines, in particular primary aromatic amines, for example 2,2xe2x80x2-, 2,4xe2x80x2- and/or 4,4xe2x80x2-MDA and/or 2,4- and/or 2,6-TDA.
The additives used according to the present invention have been found to be particularly effective in PUR formulations which contain tertiary amines having reactive functional groups as catalysts.
As sulfur compounds, it is possible to use generally known compounds, preferably sultones and/or unsaturated sulfones.
Examples are: cyclic esters of aliphatic and aromatic sulfonic acids, known as sultones, e.g. 1,3-propanesultone, 1,4-butanesultone, 2,4-butanesultone, 2,3-benzopropanesultone, tolylsultone, 2-sulfobenzoic cycloanhydride, tetrabromo-2-sulfobenzoic cycloanhydride, tetraiodo-2-sulfobenzoic cycloanhydride, 1-naphthol-8-sulfonic sultone, carbyl sulfate and/or triphenylmethane dyes containing sultone groups, e.g. phenol red, pyrogallol red, pyrocatechol violet, thymol blue, bromothymol blue, p-xylenol blue, bromoxylenol blue, bromocresol green, bromophenol blue, tetrabromophenol blue, chlorophenol red, cresol red, xylenol orange, bromophenol red, nitrophenolsulfonephthalein, sulfonefluorescein and/or bromopyrogallol red, preferably 1,3-propanesultone, 1,4-butanesultone, 2,4-butanesultone, 2-sulfobenzoic cycloanhydride, tetrabromo-2-sulfobenzoic cycloanhydride and 1-naphthol-8-sulfonic sultone.
Unsaturated sulfones which can be used are, for example, butadiene sulfone, divinyl sulfone, benzyl allyl sulfone, allyl sulfone, thionaphthene 1,1-dioxide and/or p-tolyl vinyl sulfone, preferably butadiene sulfone.
To produce the polyisocyanate polyaddition products, the sulfur compounds are preferably used in an amount of from 0.01 to 20% by weight, based on the weight of the polyisocyanate polyaddition product.
Furthermore, it is possible to use (v) lactones, lactams and/or cyclic esters, hereinafter also referred to as xe2x80x9cinhibitorsxe2x80x9d.
The addition of the inhibitors in PUR foam formulations surprisingly leads to significantly reduced contents of primary amines. As inhibitors to be used according to the present invention for reducing the primary amine content in polyurethane products, we have accordingly found lactones or cyclic esters and lactams. As experiments have shown, there are various mechanisms which contribute to this reduction. The hydrolysis of lactones in the presence of moisture to form hydroxycarboxylic acids is known from the literature. The carboxylic acid formed by hydrolysis of the inhibitor is capable of protonating the tertiary N atom in the amine catalyst. As a result of the catalytically active N atom being blocked with formation of a quaternary N atom, the amine catalyst loses its catalytic activity in respect of the hydrolytic redissociation of urethane and urea bonds. This counters a deterioration in the mechanical properties of the polyisocyanate polyaddition products, in particular the flexible foams, especially when exposed to hot and humid conditions, and also the formation of primary amines, in particular primary aromatic amines, for example 2,2xe2x80x2-, 2,4xe2x80x2- and/or 4,4xe2x80x2-MDA and/or 2,4- and/or 2,6-TDA. The addition of the inhibitors reduces the hydrolysis of urethane and urea bonds in two ways: as mentioned by deactivating the amine catalysts present and also as a result of a major part of the water which penetrates being consumed in the hydrolysis of the lactones and lactams added and no longer being available for the cleavage of urethane and urea bonds. Moreover, the inhibitors are also capable of reacting with primary amine which has already been formed to give hydroxycarboxamides or aminocarboxamides.
The addition of the inhibitors can reduce the diffusion or migration of primary amines out of the polyurethane products by converting the primary amines into hydroxycarboxamides or aminocarboxamides. The relatively high molecular weight of the reaction products, in particular when using lactones of higher carboxylic acids, e.g. of hydroxydecanoic acid or of hydroxydodecanoic acid, reduces diffusion or migration out of the polyurethane matrix so that the fogging behavior is improved.
After they have been hydrolyzed, lactams and lactones also effect an improvement in the fogging behavior of polyurethane products by preventing diffusion of the tertiary amine catalysts used by protonating them. Furthermore, in some applications it is desirable to increase the crosslinking density of polyurethane foams, in particular flexible polyurethane foams, by modification of the formulation (increasing the proportion of crosslinker, use of multiring MDI, increasing the index) without, however, increasing the hardness too much at the same time. The addition of lactones and lactams, which also function as plasticizers, makes it possible to compensate for this undesired increase in hardness.
Examples of inhibitors which can be used according to the present invention are the following compounds:
Lactones, for example those having a molecular weight of from 70 to 300 g/mol, e.g. xcex2-propiolactone, xcex3-butyrolactone, xcex3-valerolactone, xcex5-caprolactone, xcex3-decanolactone, xcex4-decanolactone, xcex4-dodecanolactone, xcex3xcex3-dimethylbutyrolactone and/or xcex1-ethyl-xcex3-methylbutyrolactone.
Lactams, for example those having a molecular weight of from 70 to 300 g/mol, e.g. xcex2-propiolactam, 2-pyrrolidone, N-methylpyrrolidone and 2-piperidone.
Cyclic esters, for example those having a molecular weight of from 150 to 500 g/mol, preferably condensation products of aliphatic, cycloaliphatic, araliphatic and/or aromatic dicarboxylic acids having from 4 to 15 carbon atoms and aliphatic, cycloaliphatic, araliphatic and/or aromatic dialcohols having from 2 to 15 carbon atoms, particularly preferably condensation products based on diethylene glycol (DEG) and adipic acid (ADA). These cyclic esters, for example the cyclic DEG-ADA ester and the cyclic ADA-DEG-ADA-DEG ester, are found, along with DEG and low molecular weight linear esters, in an amount of about 40-50% by mass in a distillation residue obtained in the synthesis of polyester polyols based on ADA-DEG-trimethylolpropane and are accordingly particularly economically advantageous to use.
To produce the polyisocyanate polyaddition products, the inhibitors are preferably used in an amount of from 0.01 to 20.0% by weight, based on the weight of the compounds which are reactive toward isocyanates.
Furthermore, generally known xcex1,xcex2-unsaturated carboxylic acids, xcex1,xcex2-unsaturated carboxylic acid derivatives, xcex1,xcex2-unsaturated ketones and/or xcex1,xcex2-unsaturated aldehydes as (vi) can advantageously be used.
As a result of the use of (vi), any free amino groups formed by undesired cleavage of urethane and/or urea groups are bound by reaction with the compounds (vi) used according to the present invention.
Both primary and secondary amines are capable of addition to Cxe2x95x90C double bonds, particularly if these are adjacent to a carbonyl group. This Michael addition of the amine occurs onto the unsaturated system in which the xcfx80-electrons are delocalized over the carbonyl group. As has been found in experiments, temperatures of from 70 to 120xc2x0 C. as can be encountered under hot and humid conditions, for example in hot steam sterilization or cleaning with hot steam, are very surprisingly sufficient to react at least some of the primary amine formed in the PUR foam by hydrolytic cleavage of urethane and urea bonds with the compounds (vi). The amino groups are bound to the xcex1,xcex2-unsaturated carbonyl compounds used according to the present invention by addition onto the Cxe2x95x90C double bonds with formation of a covalent bond. The diffusion or migration of primary amines out of the polyurethane foams can thus be reduced according to the present invention. This is particularly true when the compounds (vi) are built into the polyurethane network being formed as a result of the presence of groups such as OH or NH2 capable of being incorporated into the polyurethane structure. In this way, not only are the compounds (vi) fixed and their diffusion from the polyurethane foams is thereby prevented, but the primary amine bound to the compound (vi) is likewise immobilized.
Preference is given to compounds (vi) which have the following structural feature:
where the radicals R1 to R4 have the following meanings:
R1: H, C1-C12-alkyl, C6-C20-aryl,
R2: H, C1-C12-alkyl, C6-C20-aryl,
R3: H, C1-C12-alkyl, C6-C20-aryl,
R4: H, C1-C12-alkyl, C6-C20-aryl, xe2x80x94Oxe2x80x94C1-C12-alkyl, xe2x80x94Oxe2x80x94C1-C12-alkyl-OH, xe2x80x94C1-C12-alkyl-OH, xe2x80x94Oxe2x80x94C1-C12-alkyl, xe2x80x94C1-C12-alkyl-NH2, xe2x80x94Oxe2x80x94C1-C12-alkyl-NH2, xe2x80x94O-benzyl, xe2x80x94O-aryl, xe2x80x94Oxe2x80x94C1-C12-alkyl-COOH, xe2x80x94Oxe2x80x94C1-C1-C12-alkyl-CH(OH)xe2x80x94CH2xe2x80x94Oxe2x80x94(CO)xe2x80x94CHCH2, xe2x80x94Oxe2x80x94C1-C12-alkyl-Oxe2x80x94(CO)xe2x80x94CHCH2.
As (vi), particular preference is given to the following compounds: acrylic acid, crotonic acid, isocrotonic acid, sorbic acid, fumaric acid, cinnamic acid, hydroxyethyl acrylate, 3-(acryloyloxy)-2-hydroxypropyl methacrylate, benzyl cinnamate, trans-3-nonen-2-one, benzalacetone, dibenzalacetone, benzalacetophenone, l-methylbenzalacetophenone, crotonaldehyde, cinnamaldehyde, methyl vinyl ketone and/or xcex1,xcex2-unsaturated polyester diols prepared by polycondensation of maleic acid, fumaric acid and/or acrylic acid with oligomeric diols such as butanediol, diethylene glycol, propylene glycol, 1,3-propanediol and/or triols such as glycerol and having a molecular weight factor per double bond of from 150 to 3000, a functionality of from 2 to 6, a hydroxyl number of from 20 to 800 mg KOH/g and an acid number of from 0 to 15.
In particular, the following compounds are used as (vi): hydroxyethyl acrylate, 3-(acryloyloxy)-2-hydroxypropyl-methacrylate, trans-3-nonen-2-one, benzyl cinnamate, crotonic acid and/or xcex1,xcex2-unsaturated polyester diols (A) prepared by polycondensation of maleic acid, fumaric acid or acrylic acid with oligomeric diols such as butanediol, diethylene glycol, propylene glycol, 1,3-propanediol and/or triols such as glycerol and having a molecular weight factor per double bond of from 150 to 3000, a functionality of from 2 to 6, a hydroxyl number of from 20 to 800 mg KOH/g and an acid number of from 0 to 15.
xcex1,xcex2-unsaturated carbonyl compounds having additional functional groups such as OH and NH2 which are built into the PUR network lead to a particularly significant reduction in the MDA and TDA contents. Examples which may be mentioned are hydroxyethyl acrylate and 3-(acryloyloxy)-2-hydroxypropyl methacrylate. Polyols containing integrated Cxe2x95x90C double bonds conjugated with the carbonyl group act in a similar way.
In general, particular preference is given to compounds (vi) which dissolve readily in the isocyanates or the compounds which are reactive toward isocyanates. The compounds (vi) are preferably used in admixture with the isocyanates.
In the process of the present invention for producing polyurethane foams, (vi) is preferably used in an amount of from 0.1 to 20% by weight, particularly preferably from 0.5 to 10% by weight, based on the weight of the polyisocyanate polyaddition products.
The polyurethane foams obtainable according to the present invention have the particular advantage that any primary amines, in particular primary aromatic amines, formed by hydrolysis are converted into an unproblematical form by means of the compounds (vi). The polyurethane foams, in particular mattresses, furniture upholstery or foam backing for carpets, thus particularly preferably contain products of the reaction of primary and/or secondary amines, preferably aromatic amines, with the abovementioned compounds (vi), i.e. the xcex1,xcex2-unsaturated carboxylic acids, xcex1,xcex2-unsaturated carboxylic acid derivatives, xcex1,xcex2-unsaturated ketones and/or xcex1,xcex2-unsaturated aldehydes.
The compounds described above, i.e. the hydrophobic compounds and also (i) organic, cyclic compounds having a molecular weight of from 200 to 3000 g/mol, (ii) salts of metals of transition groups I, II and/or VIII, (iii) organic and/or inorganic acid anhydrides, (iv) cyclic sulfonic esters and/or sulfones, (v) lactones, lactams and/or cyclic esters and/or (vi) xcex1,xcex2-unsaturated carboxylic acids, xcex1,xcex2-unsaturated carboxylic acid derivatives, xcex1,xcex2-unsaturated ketones and/or xcex1,xcex2-unsaturated aldehydes, can be used for producing polyisocyanate polyaddition products by generally known methods, for example by reacting isocyanates with compounds which are reactive toward isocyanates in the presence or absence of catalysts, blowing agents, additives and/or auxiliaries. For example, compact or cellular, for example microcellular, flexible, semirigid or rigid polyurethane foams, thermoplastic polyurethanes or polyurethane elastomers can be produced as polyisocyanate polyaddition products by customary methods using the inhibitors employed according to the present invention. The compounds described are preferably used in processes for producing polyurethane elastomers or foamed polyisocyanate polyaddition products, in particular flexible polyurethane foams having a density of from 15 to 300 kg/m3, preferably from 2 to 70 kg/m3, preferably mattresses and/or furniture upholstery or carpet backing, in particular hospital mattresses, by reacting isocyanates with compounds which are reactive toward isocyanates in the presence of catalysts, blowing agents and, if desired, additives and/or auxiliaries. These products, i.e. in particular the furniture upholstery and/or carpet backing or the mattresses, are increasingly treated with hot steam for the purpose of cleaning or disinfection, so that it is precisely these products in which the advantages obtained according to the present invention are particularly pronounced.
The generally customary starting materials for producing the polyisocyanate polyaddition products are described below by way of example.
As isocyanates, it is possible to use the aliphatic, cycloaliphatic, araliphatic and preferably aromatic organic isocyanates known per se, preferably polyfunctional isocyanates, particularly preferably diisocyanates.
Specific examples are: alkylene diisocyanates having from 4 to 12 carbon atoms in the alkylene radical, e.g. dodecane 1,12-diisocyanate, 2-ethyltetramethylene 1,4-diisocyanate, 2-methylpentamethylene 1,5-diisocyanate, tetramethylene 1,4-diisocyanate and preferably hexamethylene 1,6-diisocyanate; cycloaliphatic diisocyanates such as cyclohexane 1,3- and 1,4-diisocyanate and also any mixtures of these isomers, 1-isocyanato-3,3,5-trimethyl-5-isocyanatomethylcyclohexane (isophorone diisocyanate), hexahydrotolylene 2,4- and 2,6-diisocyanate and also the corresponding isomer mixtures, dicyclohexylmethane 4,4xe2x80x2-, 2,2xe2x80x2- and 2,4xe2x80x2-diisocyanate and also the corresponding isomer mixtures, aromatic diisocyanates and polyisocyanates, e.g. tolylene 2,4- and 2,6-diisocyanate (TDI) and the corresponding isomer mixtures, diphenylmethane 4,4xe2x80x2-, 2,4xe2x80x2- and 2,2xe2x80x2-diisocyanate (MDI) and the corresponding isomer mixtures, naphthalene 1,5-diisocyanate (NDI), mixtures of diphenylmethane 4,4xe2x80x2- and 2,4xe2x80x2-diisocyanates, mixtures of NDI and diphenylmethane 4,4xe2x80x2- and/or 2,4xe2x80x2-diisocyanates, 3,3xe2x80x2-dimethyl-4,4xe2x80x2-diisocyanatobiphenyl (TODI), mixtures of TODI and diphenylmethane 4,4xe2x80x2- and/or 2,4xe2x80x2-diisocyanates, polyphenylpolymethylene polyisocyanates, mixtures of diphenylmethane 4,4xe2x80x2-, 2,4xe2x80x2- and 2,2xe2x80x2-diisocyanates and polyphenylpolymethylene polyisocyanates (crude MDI) and mixtures of crude MDI and tolylene diisocyanates. The organic diisocyanates and polyisocyanates can be used individually or in the form of their mixtures.
Use is frequently also made of modified polyfunctional isocyanates, i.e. products which are obtained by chemical reaction of organic diisocyanates and/or polyisocyanates. Examples which may be mentioned are diisocyanates and/or polyisocyanates containing ester, urea, biuret, allophanate, carbodiimide, isocyanurate, uretdione and/or urethane groups. Specific examples of suitable modified isocyanates are: organic, preferably aromatic polyisocyanates containing urethane groups and having NCO contents of from 33.6 to 15% by weight, preferably from 31 to 21% by weight, based on the total weight, modified diphenylmethane 4,4xe2x80x2-diisocyanate, modified diphenylmethane 4,4xe2x80x2- and 2,4xe2x80x2-diisocyanate mixtures, modified NDI, modified TODI, modified crude MDI and/or tolylene 2,4- or 2,6-diisocyanate, with examples of dialkylene glycols or polyoxyalkylene glycols which can be used individually or as mixtures being: diethylene glycol, dipropylene glycol, polyoxyethylene, polyoxypropylene and polyoxypropylene-polyoxyethylene glycols, triols and/or tetrols. Also suitable are prepolymers containing NCO groups, having NCO contents of from 25 to 3.5% by weight, preferably from 21 to 14% by weight, based on the total weight, and prepared from, for example, polyester polyols and/or preferably polyether polyols and diphenylmethane 4,4xe2x80x2-diisocyanate, mixtures of diphenylmethane 2,4xe2x80x2- and 4,4xe2x80x2-diisocyanate, NDI, TODI, mixtures of NDI and isomers of MDI, tolylene 2,4- and/or 2,6-diisocyanates or crude MDI. Further modified isocyanates which have been found to be useful are liquid polyisocyanates containing carbodiimide groups and/or isocyanurate rings and having NCO contents of from 33.6 to 15% by weight, preferably from 31 to 21% by weight, based on the total weight, e.g. ones based on diphenylmethane 4,4xe2x80x2-, 2,4xe2x80x2- and/or 2,2xe2x80x2-diisocyanate, NDI, TODI and/or tolylene 2,4xe2x80x2- and/or 2,6-diisocyanate.
The modified polyisocyanates may, if desired, be mixed with one another or with unmodified organic polyisocyanates such as diphenylmethane 2,4xe2x80x2- and/or 4,4xe2x80x2-diisocyanate, NDI, TODI, crude MDI and tolylene 2,4- and/or 2,6-diisocyanate.
Isocyanates which are preferably used in the mixtures employed according to the present invention or the process of the present invention are diphenylmethane 4,4xe2x80x2-, 2,4xe2x80x2- and/or 2,2xe2x80x2-diisocyanate, tolylene 2,4- and/or 2,6-diisocyanate, NDI, hexamethylene diisocyanate and/or isophorone diisocyanate, with these isocyanates being able to be used in any mixtures or in modified form as described above.
As isocyanate-reactive compounds, if desired in addition to the hydrophobic compounds used according to the present invention, insofar as the latter are reactive toward isocyanates, usually having at least two reactive hydrogen atoms, usually hydroxyl and/or amino groups, use can advantageously be made of those having a functionality of from 2 to 8, preferably from 2 to 6, and a molecular weight of usually from 60 to 10000. Compounds which have been found to be useful are, for example, polyetherpolyamines and/or preferably polyols selected from the group consisting of polyether polyols, polyester polyols, polythioether polyols, polyesteramides, hydroxyl-containing polyacetals and hydroxyl-containing aliphatic polycarbonates or mixtures of at least two of the polyols mentioned. Preference is given to using polyester polyols and/or polyether polyols which can be prepared by known methods.
The polyester polyols preferably have a functionality of from 2 to 4, in particular from 2 to 3, and a molecular weight of usually from 500 to 3000 g/mol, preferably from 1200 to 3000 g/mol and in particular from 1800 to 2500 g/mol.
The polyether polyols have a functionality of preferably from 2 to 6 and usually have molecular weights of from 500 to 8000.
Suitable polyether polyols also include, for example, polymer-modified polyether polyols, preferably graft polyether polyols, in particular those based on styrene and/or acrylonitrile which can be prepared by in situ polymerization of acrylonitrile, styrene or preferably mixtures of styrene and acrylonitrile.
Like the polyester polyols, the polyether polyols can be used individually or in the form of mixtures. They can also be mixed with the graft polyether polyols or polyester polyols or with hydroxyl-containing polyesteramides, polyacetals and/or polycarbonates.
Polyol components used for rigid polyurethane foams which may contain isocyanurate structures are high-functionality polyols, in particular polyether polyols based on high-functionality alcohols, sugar alcohols and/or saccharides as initiator molecules while polyols used for flexible foams are 2- and/or 3-functional polyether polyols and/or polyester polyols based on glycerol and/or trimethylolpropane and/or glycols as initiator molecules or alcohols to be esterified. The polyether polyols are prepared using a known technology. Suitable alkylene oxides for preparing the polyols are, for example, tetrahydrofuran, 1,3-propylene oxide, 1,2- or 2,3-butylene oxide, styrene oxide and preferably ethylene oxide and 1,2-propylene oxide. The alkylene oxides can be used individually, alternately in succession or as mixtures. Preference is given to using alkylene oxides which lead to primary hydroxyl groups in the polyol. Particular preference is given to using polyols which have been alkoxylated using ethylene oxide at the conclusion of the alkoxylation and therefore have primary hydroxyl groups. For producing thermoplastic polyurethanes, preference is given to using polyols having a functionality of from 2 to 2.2 and no crosslinker.
As compounds which are reactive toward isocyanates, it is also possible to use chain extenders and/or crosslinkers. The addition of chain extenders, crosslinkers or, if desired, mixtures thereof can prove to be advantageous for, for example, modifying the mechanical properties, e.g. the hardness, of the polyisocyanate polyaddition products produced using these substances. Chain extenders and/or crosslinkers which can be used are water, diols and/or triols having molecular weights of from 60 to  less than 500, preferably from 60 to 300. Examples of suitable chain extenders/crosslinkers are aliphatic, cycloaliphatic and/or araliphatic diols having from 2 to 14, preferably from 4 to 10, carbon atoms, for example ethylene glycol, 1,3-propanediol, 1,10-decanediol, o-, m-, p-dihydroxycyclohexane, diethylene glycol, dipropylene glycol and preferably 1,4-butanediol, 1,6-hexanediol and bis(2-hydroxyethyl)hydroquinone, triols such as 1,2,4- or 1,3,5-trihydroxycyclohexane, glycerol and trimethylolpropane and low molecular weight hydroxyl-containing polyalkylene oxides based on ethylene oxide and/or 1,2-propylene oxide and diols and/or triols as initiator molecules.
If chain extenders, crosslinkers or mixtures thereof are employed for producing the polyisocyanate polyaddition products, they are advantageously used in an amount of from 0 to 20% by weight, preferably from 2 to 8% by weight, based on the weight of the compounds which are reactive toward isocyanates; thermoplastic polyurethanes are preferably produced without a crosslinker.
Suitable catalysts are generally customary compounds, for example organic amines such as triethylamine, triethylenediamine, tributylamine, dimethylbenzylamine, N,N,Nxe2x80x2,Nxe2x80x2-tetramethylethylenediamine, N,N,Nxe2x80x2,Nxe2x80x2-tetramethylbutanediamine, N,N,Nxe2x80x2,Nxe2x80x2-tetramethylhexane-1,6-diamine, dimethylcyclohexylamine, pentamethyldipropylenetriamine, pentamethyldiethylenetriamine, 3-methyl-6-dimethylamino-3-azapentol, dimethylaminopropylamine, 1,3-bis(dimethylamino)butane, bis(2-dimethylaminoethyl) ether, N-ethylmorpholine, N-methylmorpholine, N-cyclohexylmorpholine, 2-dimethylaminoethoxyethanol, dimethylethanolamine, tetramethylhexamethylenediamine, dimethylamino-N-methylethanolamine, N-methylimidazole, N- (3-aminopropyl) imidazole, N- (3-aminopropyl) -2-methylimidazole, 1-(2-hydroxyethyl)imidazole, N-formyl-N,Nxe2x80x2-dimethylbutylenediamine, N-dimethylaminoethylmorpholine, 3,3xe2x80x2-bis(dimethylamino)-di-n-propylamine and/or 2,2xe2x80x2-bis(2-piperazinoisopropyl) ether, dimethylpiperazine, N,Nxe2x80x2-bis(3-aminopropyl)ethylenediamine and/or tris(N,N-dimethylaminopropyl)-s-hexahydrotriazine, or mixtures comprising at least two of the amines mentioned. Also possible are relatively high molecular weight tertiary amines as are described, for example, in DE-A 28 12 256. Further catalysts which can be used for this purpose are customary organic metal compounds, preferably organic tin compounds such as tin(II) salts of organic carboxylic acids, e.g. tin(II) acetate, tin(II) octoate, tin(II) ethylhexanoate and tin(II) laurate and the dialkyltin(IV) salts of organic carboxylic acids, e.g. dibutyltin diacetate, dibutyltin dilaurate, dibutyltin maleate and dioctyltin diacetate. Tertiary aliphatic and/or cycloaliphatic amines are preferably present in the mixtures, particularly preferably triethylenediamine.
As blowing agents, it is possible to use, if desired, preferably for producing foamed polyurethanes, generally known blowing agents such as materials which have a boiling point at atmospheric pressure in the range from xe2x88x9240xc2x0 C. to 120xc2x0 C., gases and/or solid blowing agents and/or water in customary amounts, for example carbon dioxide, alkanes and/or cycloalkanes, e.g. isobutane, propane, n- or iso-butane, n-pentane and cyclopentane, ethers such as diethyl ether, methyl isobutyl ether and dimethyl ether, nitrogen, oxygen, helium, argon, nitrous oxide, halogenated hydrocarbons and/or partially halogenated hydrocarbons, e.g. trifluoromethane, monochlorotrifluoroethane, difluoroethane, pentafluoroethane or tetrafluoroethane, or mixtures comprising at least two of the blowing agents mentioned by way of example.
Examples of auxiliaries and/or additives are surface-active substances, foam stabilizers, cell regulators, fillers, dyes, pigments, flame retardants, hydrolysis inhibitors, fungistatic and bacteriostatic substances.
The organic polyisocyanates and the isocyanate-reactive compounds having a molecular weight of from 60 to 10000 g/mol are usually reacted in such amounts that the equivalence ratio of NCO groups of the polyisocyanates to the sum of the reactive hydrogen atoms of the isocyanate-reactive compounds is 0.5-5:1, preferably 0.9-3:1 and in particular 0.95-2:1.
It may be advantageous for the polyurethanes to contain at least some bound isocyanurate groups. In these cases, the ratio of NCO groups of the polyisocyanates to the sum of the reactive hydrogen atoms is advantageously 1.5-60:1, preferably 1.5-8:1.
The polyisocyanate polyaddition products can, for example, be produced by the one-shot method or the known prepolymer method, for example with the aid of the high-pressure or low-pressure technique in open or closed molds, reaction extruders or belt units.
The mixtures used according to the present invention are preferably employed for producing foamed polyisocyanate polyaddition products, for example foamed polyurethanes and/or polyisocyanurates.
It has been found to be advantageous to produce the polyisocyanate polyaddition products by the two-component process and to combine the compounds which are reactive toward isocyanates and, if desired, the catalysts, blowing agents and/or auxiliaries and/or additives as the A component and to use the isocyanates and catalysts and/or blowing agents as the B component. The hydrophobic compounds can, if they have no groups which are reactive toward isocyanates, be used in the A and/or B component or in the constituents of these components. Hydrophobic compounds which have groups which are reactive toward isocyanates, for example hydroxyl groups, are preferably used in the polyol component.
The invention is illustrated by the following examples.


The present disclosure relates to a pixel cell circuit of compensation feedback voltage. The pixel cell circuit is provided with the compensation capacitance (C_co), one end of the compensation capacitance (C_co) electrically connects to the compensation level wirings G(m)_co, and the other end of the compensation capacitance (C_co) electrically connects to the drain of the TFT (T1) and the pixel electrode (P). A level of the compensation signals transmitted by the compensation level wirings G(m)_co is opposite to the level of the scanning signals transmitted by the scanning lines G(m). When the pixel electrode has been fully charged, the compensation capacitance generates a pull-up feedback voltage for compensating the pull-down voltage caused by the parasitic capacitance so as to eliminate the effects toward the pixel electrodes caused by the scanning signals transmitted by the scanning lines. This configuration not only decreases the flickers, but also the image sticking. In brief, the display uniformity and the display performance are enhanced.

1. Field of the Invention
The present disclosure relates to liquid crystal display technology, and more particularly to a pixel cell circuit of compensation feedback voltage.
2. Discussion of the Related Art
LCDs typically are characterized by attributes including thin, power-saving, and low radiation, and thus have been widely adopted by electronic devices, such as liquid crystal televisions, mobile phones, personal digital assistant (PDA), digital cameras, and monitors for computers and notebooks. The LCD is dominant in the flat display field.
Currently, LCDs are mainly backlight type, which may include a housing, a liquid crystal panel and a backlight module arranged within the housing. The liquid crystal panel is the key component of the LCD. However, the liquid crystal panel needs the light source provided by the backlight module to display images.
The liquid crystal panel usually includes a color filter (CF), a Thin Film Transistor Array Substrate (TFT Array Substrate), and a liquid Crystal Layer between the two substrates. Pixel electrodes and common electrodes are arranged at internal surfaces of the two substrates facing toward each other. The alignment of the liquid crystal molecules may be changed by applying the voltage to the liquid crystal molecules such that the light beams from the backlight module are reflected to generate the images. The array substrate may include a plurality of pixels arranged in a matrix. Each of the pixels includes Thin Film Transistor (TFT) to control the voltage of the pixel electrode so as to change the rotating angle of the liquid crystal. As such, the density of the optical field may be controlled.
There are a variety of structures of the TFTs. Currently, most of the LCDs adopt bottom-gate structure. The gate and the source/drain are overlapped in the bottom of the TFT, and parasitic capacitance (Cgs) may be generated in the overlapped area.
FIG. 1 is a circuit diagram of the conventional pixel cell circuit. The pixel cell circuit includes the TFT (T1). The gate of the TFT (T1) electrically connects with the scanning line G(m) corresponding to row of the pixel cell, the source of the TFT (T1) electrically connects with the data line D(n) corresponding to the column of the pixel cell, and the drain electrically connects with the pixel electrode (P). Two ends of the parasitic capacitance (Cgs) electrically connects with the gate and the drain of the TFT (T1). One end of a storage capacitance (Cst) electrically connects with the drain of the TFT (T1), and the other end of the storage capacitance (Cst) connects with a constant voltage. One end of the liquid crystal capacitor (Clc) electrically connect to the drain of the TFT (T1), and the other end of the liquid crystal capacitor (Clc) connects with the constant voltage.
The voltage of the pixel electrode (P) may be interfered by the level of the gate of the TFT (T1) due to the parasitic capacitance (Cgs). Also referring to FIG. 2, when the pixel electrode (P) has been charged fully, the level of the gate of the TFT (T1) is pulled down instantly. The voltage of the pixel electrode (P) may also be pulled down due to the capacitance coupling effect. As such, one feedthrough voltage (Vft1) is generated, and the magnitude of the feedthrough voltage (Vft1) may be represented by the equation below:Vft1=(Vgh−Vgl)×Cgs/Ctotal
Wherein Vgh represents the high level of the scanning signals transmitted by the scanning line G(m), Vgl represents the low level of the scanning signals transmitted by the scanning line G(m), Ctotal represents a sum of the capacitance connected by the pixel electrode (P), including the liquid crystal capacitor (Clc), the storage capacitance (Cst), and the parasitic capacitance (Cgs).
The voltage of the positive and negative frames of the pixel electrode (P) may be affected by the parasitic capacitance (Cgs), which results in asymmetric voltage of the positive and negative frames. This may cause problems such as flicker and image sticking, and thus the display performance may be affected. In addition, the RC delay with respect to different areas of the panel may also cause the difference of the feedback voltage. This may result in non-uniform voltage of the common electrode (Vcom), and may cause serious flicker.

Pixel cell circuits of compensation feedback voltage

SHENZHEN CHINA STAR OPTOELECTRONICS TECHNOLOGY CO., LTD.


Computer implemented techniques for simulating a fluid flow about a surface of a solid, include receiving a coordinate system for representation of a curvilinear mesh that conforms to the surface of the solid, simulating, with a lattice velocity set transport of particles in a volume of fluid, with the transport causing collision among the particles, executing a distribution function for transport of the particles, with the distribution function including a particle collision determination and a change in particle distribution associated with the curvilinear mesh, performing by the computing system, advection operations in the coordinate system under constraints applied to particle momentum values and mapping by the computer system values resulting from simulating onto the curvilinear mesh by translation of the particle momentum values and spatial coordinates determined in the coordinate system into momentum and spatial values in the curvilinear space.

This description relates to computer simulation of physical processes, such as physical fluid flows.
The so called "Lattice Boltzmann Method" (LBM) is an advantageous technique for use in computational fluid dynamics. The underlying dynamics of a lattice Boltzmann system resides in the fundamental physics of kinetic theory that involves motion of many particles according to the Boltzmann equation. There are two fundamental dynamical processes in a basic Boltzmann kinetic system collision and advection. The collision process involves interactions among particles obeying conservation laws and to relax to an equilibrium. The advection process involves modeling movement of particles from one location to another according to the particles microscopic velocities.
In a standard LBM model, particle velocity takes on a discrete set of constant values, and the latter form exact links from one lattice site to its neighboring sites on a simple Bravais lattice corresponding to a three dimensional (3D) uniform cubical Cartesian mesh.
Various attempts have been made to extend LBM to meshes based on arbitrary coordinate systems (arbitrary mesh(es)). One of the main representative approaches is to relax a one-to-one advection mapping between a pair of lattice sites. On such arbitrary meshes, a particle after advection from its original mesh site does not in general land on a single neighboring site. In those solutions, the location of the particle is represented by those mesh sites by interpolation.

Computer simulation of physical fluids on a mesh in an arbitrary coordinate system


A multi-channel signal compressor for compressing digital sound signals in the respective channels of a multi-channel sound system. The apparatus comprises a first-stage compression system and a second-stage compression system. In the first-stage compression system, a coupling circuit performs coupling between the digital sound signals of at least two of the channels to generate coupling-processed signals, one for each of the channels. A compressor circuit receives the coupling-processed signals from the coupling circuit and frequency divides each coupling-processed signal into frequency range signals in respective frequency ranges, and compresses the frequency range signals obtained by dividing each coupling-processed signal to generate a first-stage compressed signal. In the second-stage compression system, a determining circuit receives the first-stage compressed signal for each channel from the first-stage compression system and determines an energy for each channel from the first-stage compressed signal of the respective channel. A channel bit apportionment decision circuit operates in response to the determining circuit, and apportions a predetermined number of bits among the channels to apportion a number of bits to each channel. Finally, an additional compressor additionally compresses the first-stage compressed signal of each channel using, for each channel, the number of bits apportioned to the respective channel by the channel bit apportionment decision circuit.

Many techniques for compressing digital audio or speech signals are known. For example, in sub-band coding, a non block-forming frequency band dividing system, in which the input audio signal is not divided in time into blocks, but is divided in frequency by a filter into plural frequency bands for quantizing. In a block-forming frequency band dividing system, such as a transform coding system, the input audio signal in the time domain is converted into spectral coefficients in the frequency domain by an orthogonal transform. The resulting spectral coefficients are divided by frequency into plural frequency bands, and the spectral coefficients in each band are quantized.
A technique consisting of a combination of sub-band coding and transform coding is also known. In this, frequency range signals produced by dividing the input audio signal in frequency without dividing it into blocks are individually orthogonally transformed into spectral coefficients. The spectral coefficients are then divided by frequency into plural frequency bands, and the spectral coefficients in each band are then quantized.
Among the filters useful for dividing a digital audio input signal into frequency ranges without dividing it into blocks is the quadrature mirror (QMF) filter, which is described, for example, in R. E. Crochiere, Digital Coding of Speech in Sub-bands, 55 BELL SYST. TECH. J. No.8, (1976). A technique of dividing the audio input signal in frequency into frequency bands of an equal width is discussed in Joseph H. Rothweiler, Polyphase Quadrature Filers-a New Sub-band Coding Technique, ICASSP 83, BOSTON (1983).
Known techniques for orthogonally transforming an input signal include the technique of dividing the digital input audio signal in time into blocks having a predetermined duration, and processing the resulting blocks using a fast Fourier transform (FFT), a discrete cosine transform (DCT), or a modified DCT (MDCT) to convert each block of the digital audio signal in the time domain into a set of spectral coefficients in the frequency domain. A modified DCT is discussed in J. P. Princen and A. B. Bradley, Subband/Transform Coding Using Filter Bank Based on Time Domain Aliasing Cancellation, ICASSP 1987.
As a technique for quantizing the spectral coefficients obtained by frequency division, it is known to divide the spectral coefficients by frequency into bands to take account of the frequency resolution characteristics of the human sense of hearing. The audio frequency range of 0 Hz to 20 or 22 kHz may be divided in frequency into bands, such as 25 critical bands, which have a bandwidth that increases with increasing frequency. The spectral coefficients in each of the bands are quantized by adaptive bit allocation applied to each band. For example, the spectral coefficients resulting from a modified discrete cosine transform (MDCT) are divided by frequency into bands, and the spectral coefficients in each band are quantized using an adaptively-determined number of bits.
Two known adaptive bit allocation techniques will be now be described. First, in the technique described in ASSP-25, IEEE TRANSACTIONS OF ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, No.4, August 1977, bit allocation is carried out on the basis of the magnitude of the signals of the respective bands. Although this system provides a flat quantizing noise spectrum, and minimizes noise energy, noise perceived by the listener is not minimized because this technique does not exploit the masking characteristics of the human sense of hearing.
On the other hand, the technique described in M. A. Kransner, The Critical Band Coder-Digital Encoding of the Perceptual Requirements of the Auditory System, ICASSP 1980, uses the masking characteristics of the human sense of hearing to determine the signal-to-noise ratio necessary for each band to make a fixed quantizing bit allocation. However, this technique provides relatively poor results with a single sine-wave input because of its fixed bit allocation.
As a high-efficiency system for compressing digital audio signals, employing, for example, the above-mentioned sub-band coding system, a high-efficiency compression system called ATRAC is already used in practical applications. This system compresses digital audio signals to about 20% of their original bit requirement by taking advantage of the characteristics of the human sense of hearing using adaptive transform acoustic coding. ATRAC is a registered trademark of one of the present assignees (Sony Corporation).
Multi-channel audio or speech signals in four to eight channels are not only encountered in, for example, commonplace audio equipment, but are also encountered in stereo or multi-channel sound systems, such as those found in motion picture theaters, high-quality television systems, video tape recorders, and video disc players. In such cases, the use of high-efficiency compression is desirable to reduce the bit rate required to represent the large number of audio signals.
In particular, in commercial applications, a tendency towards multi-channel digital sound signals and equipment handling eight-channel digital sound signals has developed. Typical of the equipment handling eight-channel digital sound signals are motion picture theater sound systems, and the apparatus that electronically reproduces the pictures and sound of a motion picture film via various electronic media, in particular apparatus such as high-quality television systems, video tape recorders, and video disc players. In the sound systems of such apparatus, the tendency is towards multi-channel sound systems of between four and eight channels.
Motion picture theater sound systems have recently been proposed that record on a motion picture film the digital sound signals for the following eight channels: left, left-center, center, right-center, right, left surround, right surround, and sub-woofer. These sound channels are respectively reproduced by left loudspeaker, a left-center loudspeaker, a center loudspeaker, a right-center loudspeaker, and a right loudspeaker, all arranged behind the screen; a sub-woofer located behind or in front of the screen; and a left-surround loudspeaker and a right-surround loudspeaker. For the left-surround speaker and the right-surround speaker, two groups of loudspeakers are respectively arranged on the left side wall and the left part of the back wall of the auditorium, and on the right side wall and the right part of the back wall of the auditorium. The two groups of loudspeakers on the sides and back of the auditorium generate a sound field rich in ambience to accompany spectacular optical effects on the large-format screen of the motion picture theater. For simplicity, these two groups of loudspeakers will from now on be referred to as the "left-surround loudspeaker" and the "right-surround loudspeaker."
It is difficult to record on a motion picture film eight channels of 16-bit linear-quantized digital audio with the sampling frequency of 44.1 kHz, such as is employed in a compact disc (CD), because the film lacks an area capable of accommodating a soundtrack wide enough for such a signal. The width of the motion picture film and the width of the picture area on the film are standardized. The width of the film cannot be increased, or the width of the picture area cannot be decreased to accommodate a soundtrack of the width required for digital audio signals of this type. A standard-width film, with a standard picture area, a standard analog sound track, and standard perforations, has only a narrow area in which digital audio signals can be recorded. Accordingly, eight channels of digital sound can only be recorded if the digital sound signals are compressed prior to recording on the film. The eight channels of digital sound may be compressed using the above-mentioned ATRAC high-efficiency compression system.
Motion picture films are susceptible to scratches, which can cause drop-outs if digital sound signals are recorded without any form of error detection and correction. Therefore, the use of error correction codes is essential, and this must be taken into account when the signal compression is performed.
Optical discs have become popular as a medium for providing motion pictures in the home. It is desirable to be able to record multi-channel sound with four to eight channels on an optical disc to provide more realistic sound than conventional stereo sound. On an optical disc, the data volume of the video signal is as many as ten times that of the sound signal, and only a limited recording area is provided for the sound signal. Especially when the picture signal is required to provide a high picture quality, as is required with the current trend towards larger-size screens, as much of the recording area as possible is devoted to the picture signal. Thus, the sound signal must be subject to a high degree of compression if the desired number of channels is to be provided in the recording area available for the sound signal.
When the above-mentioned ATRAC high-efficiency compression system proposed by one of the present assignees (Sony Corporation) is used in a stereo (two-channel) audio system, the audio signal in each channel is compressed independently of the other. This enables each channel to be used independently, and simplifies the processing algorithm used to compress the audio signals. Operated this way, the ATRAC system provides sufficient compression for most applications, and the sound quality obtained when an audio signal is compressed and expanded using the ATRAC system is well regarded.
However, because it compresses each audio signal independently, it cannot be said that the bit allocation process by which the present ATRAC system performs its compression operates at highest efficiency. For example, if the signal level in one of the channels is very low, the signal can be represented adequately using a small number of bits. On the other hand, the signal in another channel may require a much larger number of bits to represent it adequately. Yet the present ATRAC system allocates the same number of bits to each channel, irrespective of the number of bits actually required to adequately represent the signal in the channel. Thus, to provide its high quality of reproduction, there must be some redundancy in the bit allocation performed by the present system.

Two-stage compression and expansion of coupling processed multi-channel sound signals for transmission and recording