Calix resorcinarenes bearing four hydrophobic side chains ( Ar-Rn, Ar-Ph, and Ar-N) orient stably on water oil interface and show high solubilization capacities for organic compounds, such as long chain alcohols...Calix resorcinarenes bearing four hydrophobic side chains ( Ar-Rn, Ar-Ph, and Ar-N) orient stably on water oil interface and show high solubilization capacities for organic compounds, such as long chain alcohols, benzene, toluene and dyes. The capacities are high even near the cmc of polyalkylated calix resorcinarenes, but the solubilities of organic compounds(solubilizates) decrease with the increase of the size of the solubilizates. Ar-R 6, with a chain length of six carbons, is the most effective among Ar-R n , Ar-Ph, and Ar-N; 11 fold mol of hexanol is dissolved in 2×10 -3 mol/L Ar-R 6. Moreover, Ar-R n bearing four alkyl side chains solubilizes the chain alcohols of the same chain length mostly. The solubilization capacities are presumably brought by inclusion in a large cavity of the polyalkylated calix resorcinarenes and by an efficient orientation of the solubilizates.展开更多
Eight-arm star-shaped poly（■-caprolactone）-block-poly（ethylene glycol）s（SPCL-b-PEG） have been prepared by a combination of controlled ring-opening polymerization（CROP） and coupling reaction. First, eight-arm ...Eight-arm star-shaped poly（■-caprolactone）-block-poly（ethylene glycol）s（SPCL-b-PEG） have been prepared by a combination of controlled ring-opening polymerization（CROP） and coupling reaction. First, eight-arm star-shaped poly（■-caprolactone）s（SPCL） with a resorcinarene core were synthesized using octamethyl tetraundecylresorcinarene octaacetate as octa-initiator and yttrium tris（2,6-di-tert-butyl-4-methylphenolate） [Y（DBMP）3] as catalyst. Then the coupling reaction was carried out between SPCLs and carboxyl-terminated methoxy poly（ethylene glycol）s（mP EG-COOH） in the presence of N,N′-dicyclohexylcarbodiimide（DCC） and 4-dimethylaminopyridine（DMAP）, resulting in eight-arm star-shaped SPCL-b-PEGs with controlled molecular weight and well-defined architecture. Furthermore, these amphiphilic eight-arm SPCL-b-PEGs could self-assemble into micelles with low critical micellar concentrations（CMC）, which was characterized by fluorescent spectroscopy. Moreover, indomethacin loaded micelles with high drug loading content and high encapsulation efficiency can be prepared, which is probably due to the highly branched architecture. The morphologies of micelles were characterized by transmission electron microscopy（TEM）, which exhibited diverse nanostructures as the drug loading contents varied. In vitro drug release of indomethacin from SPCL-b-PEG micelles was carried out in PBS, from which a sustained release behavior was observed. SPCL-b-PEG micelles did not show significant cytotoxicity at copolymer concentrations up to 1000 mg/L, making them very promising for drug delivery.展开更多
A simple synthesis of novel and known calix[4]resorcinarenes derivatives has been achieved by the condensation of resorcinol and different aromatic aldehydes in the presence of catalytic amounts of Fe_3O_4 nanoparticl...A simple synthesis of novel and known calix[4]resorcinarenes derivatives has been achieved by the condensation of resorcinol and different aromatic aldehydes in the presence of catalytic amounts of Fe_3O_4 nanoparticles under solvent-free conditions.The experimental conditions have been thoroughly optimized and established,allowing significant rate enhancements and good to excellent yields.The reactions can be run safely without using any toxic organic solvents under mild reaction conditions.The Fe_3O_4 nanoparticles were characterized by powdered X-ray diffraction（XRD）,transmission electron microscopy（TEM） and FT-IR spectroscopy.展开更多
Compartmentalization in the biological world brings excellent efficiency and specificity to the formation of complex compounds,inspiring supramolecular chemists to continuously search for defined spaces that can mimic...Compartmentalization in the biological world brings excellent efficiency and specificity to the formation of complex compounds,inspiring supramolecular chemists to continuously search for defined spaces that can mimic such natural binding sites.Bowl-shaped cavitands built up from resorcinarenes(RA)present rigid and preorganized concave surfaces,which are capable of mimicking the molecular recognition properties of enzymes.The versatile scaffold of RA endows the cavitand with terrific variety and excellent binding behavior.This review provides a comprehensive overview over the structural modification to date in the high attention field of RA-based cavitands development.Different strategies for synthesizing diverse cavitands,such as small cavity cavitands,wider cavity cavitands,deep cavity cavitands,biscavitands,and asymmetric cavitands,are discussed in details.Furthermore,insights into their applications including catalysis,separations and sensing are provided.展开更多
First to third-generation calix[4] resorcinarene core dendrimers, compounds 4a, 4b, 7a, 7b, 10a and 10b, were prepared via the divergent method in seven steps with the corresponding tetraphenyl- and tetra （hydroxyphe...First to third-generation calix[4] resorcinarene core dendrimers, compounds 4a, 4b, 7a, 7b, 10a and 10b, were prepared via the divergent method in seven steps with the corresponding tetraphenyl- and tetra （hydroxyphenyl） calix[4] resorcinarenes （compounds 1a, 1b） as the starting material. The repeat units of the polyamidoamines of these dendrimers were obtained by the ammonolysis of ethyl calixarylacetates 2a and 2b with 1,3-diaminopropane, that is, amide derivatives with terminal amino groups, which in turn reacted with ethyl acrylate to give a higher generation of ester derivatives. The structures of these dendrimers were characterized by IR, ^1H and ^13C NMR spoctrometries. The crystal structure of compound 2b with 12 ethoxycarbonylmethoxy groups was determined by X-ray analysis.展开更多
Novel tetra-methoxy resorcinarene tetra-hydrazide（TMRTH） has been synthesized and used as a reducing agent and a capping agent for the synthesis of water-dispersible stable palladium nanoparticles（PdNPs）.The TMRTH...Novel tetra-methoxy resorcinarene tetra-hydrazide（TMRTH） has been synthesized and used as a reducing agent and a capping agent for the synthesis of water-dispersible stable palladium nanoparticles（PdNPs）.The TMRTH-PdNPs were characterized by UV-Vis spectroscopy,transmission electron microscopy,energy-dispersive X-ray spectroscopy,and powder X-ray diffraction.The synthesized nanoparticles are polydispersible with a size of 5 ± 2 nm and were found to be recyclable over five cycles maintaining a catalytic activity in the Suzuki-Miyuara cross-coupling reaction.The nanocatalyst was superior in catalytic performance to conventional palladium catalysts with respect to reaction time,catalyst loading and recyclability.TMRTH-PdNPs show promise for their use in biological applications as they exhibit good antibacterial activity against gram-positive bacteria.展开更多
An octa-functional acrylate of C-tetramethyl calix[4]resorcinarene（CMC-4-RA） was facilely synthesized and characterized with ^1H NMR, ^13C NMR and FTIR spectroscopy. The CMC-4-RA was added to a thiol-acrylate system...An octa-functional acrylate of C-tetramethyl calix[4]resorcinarene（CMC-4-RA） was facilely synthesized and characterized with ^1H NMR, ^13C NMR and FTIR spectroscopy. The CMC-4-RA was added to a thiol-acrylate system with different mass ratios, and exposed to a middle pressure mercury lamp. The maximum photopolymerization rate and final vinyl group conversion in the cured film increased greatly along with CMC-4-RA addition that was monitored with Photo-DSC. The tensile strength and pendulum hardness were improved significantly after the addition of CMC-4-RA. With increasing the content of CMC-4-RA to 60%（mass fraction）, the glass transition temperature increased from 34.2 ℃ to 84.1 ℃; the cross-link density was calculated to be increased from 23.83 mmol/cm^3 to 82.40 mmol/cm^3 according to dynamic mechanical thermal analysis; the thermostability was greatly improved.展开更多
Three different synthetic routes were developed to introduce carbamoyloxy functional groups at the upper periphery of two calix[4]resorcinarenes. By treating activated esters 2a-b with excess corresponding amine such...Three different synthetic routes were developed to introduce carbamoyloxy functional groups at the upper periphery of two calix[4]resorcinarenes. By treating activated esters 2a-b with excess corresponding amine such as 3-(dimethylamino)propylamine 3, -phenethylamine 4 and triethylenetetramine 5, six amide derivatives 6a^8b were obtained in high yield (Route 1). The pyridine-linked amide derivatives 9a-b were prepared by using acid chloride intermediate (Route 2). The amide derivatives 10a-b were obtained in moderate yields by direct alkylation of phenolic hydroxyl groups of 1a-b with N,N-dipropylchloroacetoamide in the presence of K2CO3/KI in acetone (Route 3).展开更多
The technique of supported liquid membranes was used to achieve the facilitated transport of Cr(III) ions, using tow amphiphilic carriers, the methyl cholate and resorcinarene. For prepared SLMs, toluene as organic ph...The technique of supported liquid membranes was used to achieve the facilitated transport of Cr(III) ions, using tow amphiphilic carriers, the methyl cholate and resorcinarene. For prepared SLMs, toluene as organic phase and film of polyvinylidene difluoride, as hydrophobic polymer support with 100 μm in thickness and 0.45 μm as the diameter of the pores. The macroscopic parameters (P and J0) on the transport of these ions were determined for different medium temperatures. For these different environments, the prepared SLMs were highly permeable and a clear evolution of these parameters was observed. The parameter J0 depended on the temperature according to the Arrhenius equation. The activation parameters, Ea, ΔH≠ and ΔS≠, for the transition state on the reaction of complex formation (ST) , were determined. To explain these results for this phenomenon, and achieve a better extraction of the substrate, a model based on the substrate complexation by the carrier and the diffusion of the formed complex (ST) was developed. The experimental results verify this model and determine the microscopic parameters (Kass and D*). These studies show that these parameters Kass and D* are specific to facilitated transport of Cr(III) ions by each of the carriers and they are changing significantly with temperature.展开更多
In this work, the transport and removal of Cr(Ⅵ) were achieved through supported liquid membrane(SLM) by using a 5,17, di-tert-butyl-11,23-bis[(1,4-dioxa-8-azaspiro [4,5]decanyl)methyl]-25,26,27,28-tetrahydroxy calix...In this work, the transport and removal of Cr(Ⅵ) were achieved through supported liquid membrane(SLM) by using a 5,17, di-tert-butyl-11,23-bis[(1,4-dioxa-8-azaspiro [4,5]decanyl)methyl]-25,26,27,28-tetrahydroxy calix[4]arene carrier, dissolved in 2-nitrophenyl octyl ether dichloromethane.The studied parameters are the solvent effect in the membrane phase, the effect of carrier concentration, and the acid type in the donor phase.The Celgard 2500 was used as a membrane support.We used the Danesi mass transfer model to calculate the permeability coefficients for each studied parameter.In addition, AFM and SEM techniques were used to characterize the surface morphology of the prepared Celgard 2500 membrane that included the calix[4]arene carrier.展开更多
A C-iso-butyl-cavitand bowl with trimethyl and methylol groups was isolated from the acetoxymethyl hydrolysis of mono-methylbromo-cavitand in THF. The molecular structure of the present cavitand compound was determi...A C-iso-butyl-cavitand bowl with trimethyl and methylol groups was isolated from the acetoxymethyl hydrolysis of mono-methylbromo-cavitand in THF. The molecular structure of the present cavitand compound was determined by single-crystal X-ray diffraction. The compound (C56H70N2O9) crystallizes in orthorhombic, space group Pnma with a = 19.5060(15), b = 19.8136(15), c = 12.9508(10) ?, V = 5005.3(7) ?3, Z = 4, Mr = 915.14, Dc = 1.214 g/cm3, F(000) = 1968, μ = 0.081 mm?1, S = 1.012, the final R = 0.0789 and wR = 0.1488 for 2298 observed reflections with I > 2σ(I) and 322 variable parameters. The structure exhibits a rigid bowl-cavity with an available functional hydroxyl group. The bowl of cavitand contains a CH3CN solvent molecule, and the depth of the bowl-shaped cavity is ca. 2.42 ?.展开更多
Treatment of tetra-iso-butyl-resorcin[4]arene 1 with propargyl bromide in the presence of K2CO3 as base gave an octopus-like octapropargyl tetra-iso-butyl-resorcin[4]arene 2 （C68H72O8, Mr = 1017.26） in a quantitativ...Treatment of tetra-iso-butyl-resorcin[4]arene 1 with propargyl bromide in the presence of K2CO3 as base gave an octopus-like octapropargyl tetra-iso-butyl-resorcin[4]arene 2 （C68H72O8, Mr = 1017.26） in a quantitative yield. Single-crystal structure of 2 was determined by X-ray crystallography. 2 crystallizes in the monoclinic system, space group P21/n with a =13.3247（6）, b = 24.7929（11）, c = 19.1810（9）A°, β = 109.272（1）°, V= 5981.5（5） A°^3, Dc = 1.130g/cm^3,μ = 0.073 mm^-1, F（000） = 2176 and Z = 4. Overall structure of 2 reveals an octopus-like resorcinarene with eight propargyl groups in different directions. The resorcinarene adopts the boat conformation where the iso-butyl residues act as four-legged piano stool. The two opposite aryl rings of the macrocyclic framework are almost coplanar, and the two others facing each other are perpendicular to this plane.展开更多
文摘Calix resorcinarenes bearing four hydrophobic side chains ( Ar-Rn, Ar-Ph, and Ar-N) orient stably on water oil interface and show high solubilization capacities for organic compounds, such as long chain alcohols, benzene, toluene and dyes. The capacities are high even near the cmc of polyalkylated calix resorcinarenes, but the solubilities of organic compounds(solubilizates) decrease with the increase of the size of the solubilizates. Ar-R 6, with a chain length of six carbons, is the most effective among Ar-R n , Ar-Ph, and Ar-N; 11 fold mol of hexanol is dissolved in 2×10 -3 mol/L Ar-R 6. Moreover, Ar-R n bearing four alkyl side chains solubilizes the chain alcohols of the same chain length mostly. The solubilization capacities are presumably brought by inclusion in a large cavity of the polyalkylated calix resorcinarenes and by an efficient orientation of the solubilizates.
基金supported by the National Natural Science Foundation of China(Nos.20704036 and 21274121)the Major State Basic Research Project(No.2011CB606001)
文摘Eight-arm star-shaped poly（■-caprolactone）-block-poly（ethylene glycol）s（SPCL-b-PEG） have been prepared by a combination of controlled ring-opening polymerization（CROP） and coupling reaction. First, eight-arm star-shaped poly（■-caprolactone）s（SPCL） with a resorcinarene core were synthesized using octamethyl tetraundecylresorcinarene octaacetate as octa-initiator and yttrium tris（2,6-di-tert-butyl-4-methylphenolate） [Y（DBMP）3] as catalyst. Then the coupling reaction was carried out between SPCLs and carboxyl-terminated methoxy poly（ethylene glycol）s（mP EG-COOH） in the presence of N,N′-dicyclohexylcarbodiimide（DCC） and 4-dimethylaminopyridine（DMAP）, resulting in eight-arm star-shaped SPCL-b-PEGs with controlled molecular weight and well-defined architecture. Furthermore, these amphiphilic eight-arm SPCL-b-PEGs could self-assemble into micelles with low critical micellar concentrations（CMC）, which was characterized by fluorescent spectroscopy. Moreover, indomethacin loaded micelles with high drug loading content and high encapsulation efficiency can be prepared, which is probably due to the highly branched architecture. The morphologies of micelles were characterized by transmission electron microscopy（TEM）, which exhibited diverse nanostructures as the drug loading contents varied. In vitro drug release of indomethacin from SPCL-b-PEG micelles was carried out in PBS, from which a sustained release behavior was observed. SPCL-b-PEG micelles did not show significant cytotoxicity at copolymer concentrations up to 1000 mg/L, making them very promising for drug delivery.
文摘A simple synthesis of novel and known calix[4]resorcinarenes derivatives has been achieved by the condensation of resorcinol and different aromatic aldehydes in the presence of catalytic amounts of Fe_3O_4 nanoparticles under solvent-free conditions.The experimental conditions have been thoroughly optimized and established,allowing significant rate enhancements and good to excellent yields.The reactions can be run safely without using any toxic organic solvents under mild reaction conditions.The Fe_3O_4 nanoparticles were characterized by powdered X-ray diffraction（XRD）,transmission electron microscopy（TEM） and FT-IR spectroscopy.
基金supported by the Natural Science Foundation of Jiangsu Province(Nos.BK20200432,BK20211179)National Natural Science Foundation of China(Nos.22271154,M-0411)the Fundamental Research Funds for the Central Universities(No.NG2022003).
文摘Compartmentalization in the biological world brings excellent efficiency and specificity to the formation of complex compounds,inspiring supramolecular chemists to continuously search for defined spaces that can mimic such natural binding sites.Bowl-shaped cavitands built up from resorcinarenes(RA)present rigid and preorganized concave surfaces,which are capable of mimicking the molecular recognition properties of enzymes.The versatile scaffold of RA endows the cavitand with terrific variety and excellent binding behavior.This review provides a comprehensive overview over the structural modification to date in the high attention field of RA-based cavitands development.Different strategies for synthesizing diverse cavitands,such as small cavity cavitands,wider cavity cavitands,deep cavity cavitands,biscavitands,and asymmetric cavitands,are discussed in details.Furthermore,insights into their applications including catalysis,separations and sensing are provided.
文摘First to third-generation calix[4] resorcinarene core dendrimers, compounds 4a, 4b, 7a, 7b, 10a and 10b, were prepared via the divergent method in seven steps with the corresponding tetraphenyl- and tetra （hydroxyphenyl） calix[4] resorcinarenes （compounds 1a, 1b） as the starting material. The repeat units of the polyamidoamines of these dendrimers were obtained by the ammonolysis of ethyl calixarylacetates 2a and 2b with 1,3-diaminopropane, that is, amide derivatives with terminal amino groups, which in turn reacted with ethyl acrylate to give a higher generation of ester derivatives. The structures of these dendrimers were characterized by IR, ^1H and ^13C NMR spoctrometries. The crystal structure of compound 2b with 12 ethoxycarbonylmethoxy groups was determined by X-ray analysis.
基金financial assistance provided by UGC(University Grant Commission)DRDO (Defence Research Development Organisation),New Delhi
文摘Novel tetra-methoxy resorcinarene tetra-hydrazide（TMRTH） has been synthesized and used as a reducing agent and a capping agent for the synthesis of water-dispersible stable palladium nanoparticles（PdNPs）.The TMRTH-PdNPs were characterized by UV-Vis spectroscopy,transmission electron microscopy,energy-dispersive X-ray spectroscopy,and powder X-ray diffraction.The synthesized nanoparticles are polydispersible with a size of 5 ± 2 nm and were found to be recyclable over five cycles maintaining a catalytic activity in the Suzuki-Miyuara cross-coupling reaction.The nanocatalyst was superior in catalytic performance to conventional palladium catalysts with respect to reaction time,catalyst loading and recyclability.TMRTH-PdNPs show promise for their use in biological applications as they exhibit good antibacterial activity against gram-positive bacteria.
基金Supported by the National Natural Science Foundation of China(No.50233030)Granted by China NKBRSF Project (No.2001CB409600)
文摘An octa-functional acrylate of C-tetramethyl calix[4]resorcinarene（CMC-4-RA） was facilely synthesized and characterized with ^1H NMR, ^13C NMR and FTIR spectroscopy. The CMC-4-RA was added to a thiol-acrylate system with different mass ratios, and exposed to a middle pressure mercury lamp. The maximum photopolymerization rate and final vinyl group conversion in the cured film increased greatly along with CMC-4-RA addition that was monitored with Photo-DSC. The tensile strength and pendulum hardness were improved significantly after the addition of CMC-4-RA. With increasing the content of CMC-4-RA to 60%（mass fraction）, the glass transition temperature increased from 34.2 ℃ to 84.1 ℃; the cross-link density was calculated to be increased from 23.83 mmol/cm^3 to 82.40 mmol/cm^3 according to dynamic mechanical thermal analysis; the thermostability was greatly improved.
文摘Three different synthetic routes were developed to introduce carbamoyloxy functional groups at the upper periphery of two calix[4]resorcinarenes. By treating activated esters 2a-b with excess corresponding amine such as 3-(dimethylamino)propylamine 3, -phenethylamine 4 and triethylenetetramine 5, six amide derivatives 6a^8b were obtained in high yield (Route 1). The pyridine-linked amide derivatives 9a-b were prepared by using acid chloride intermediate (Route 2). The amide derivatives 10a-b were obtained in moderate yields by direct alkylation of phenolic hydroxyl groups of 1a-b with N,N-dipropylchloroacetoamide in the presence of K2CO3/KI in acetone (Route 3).
基金All authors thank the Agence Universitaire de la Fran-cophonie(AUF)for financial support(PCSI 59113PS 014)Professor Jean-François Verchère from the University of Rouen(France)for his advice,fruitful dis-cussions,strong encouragement and exemplary coopera-tion.
文摘The technique of supported liquid membranes was used to achieve the facilitated transport of Cr(III) ions, using tow amphiphilic carriers, the methyl cholate and resorcinarene. For prepared SLMs, toluene as organic phase and film of polyvinylidene difluoride, as hydrophobic polymer support with 100 μm in thickness and 0.45 μm as the diameter of the pores. The macroscopic parameters (P and J0) on the transport of these ions were determined for different medium temperatures. For these different environments, the prepared SLMs were highly permeable and a clear evolution of these parameters was observed. The parameter J0 depended on the temperature according to the Arrhenius equation. The activation parameters, Ea, ΔH≠ and ΔS≠, for the transition state on the reaction of complex formation (ST) , were determined. To explain these results for this phenomenon, and achieve a better extraction of the substrate, a model based on the substrate complexation by the carrier and the diffusion of the formed complex (ST) was developed. The experimental results verify this model and determine the microscopic parameters (Kass and D*). These studies show that these parameters Kass and D* are specific to facilitated transport of Cr(III) ions by each of the carriers and they are changing significantly with temperature.
基金supported financially by the Scientific Research Projects (BAP) of Pamukkale University, Denizli-Turkey (2013 FBE 045)
文摘In this work, the transport and removal of Cr(Ⅵ) were achieved through supported liquid membrane(SLM) by using a 5,17, di-tert-butyl-11,23-bis[(1,4-dioxa-8-azaspiro [4,5]decanyl)methyl]-25,26,27,28-tetrahydroxy calix[4]arene carrier, dissolved in 2-nitrophenyl octyl ether dichloromethane.The studied parameters are the solvent effect in the membrane phase, the effect of carrier concentration, and the acid type in the donor phase.The Celgard 2500 was used as a membrane support.We used the Danesi mass transfer model to calculate the permeability coefficients for each studied parameter.In addition, AFM and SEM techniques were used to characterize the surface morphology of the prepared Celgard 2500 membrane that included the calix[4]arene carrier.
基金This project was supported by the Key Scientific Research Foundation of State Education Ministry of China (No. 204067)
文摘A C-iso-butyl-cavitand bowl with trimethyl and methylol groups was isolated from the acetoxymethyl hydrolysis of mono-methylbromo-cavitand in THF. The molecular structure of the present cavitand compound was determined by single-crystal X-ray diffraction. The compound (C56H70N2O9) crystallizes in orthorhombic, space group Pnma with a = 19.5060(15), b = 19.8136(15), c = 12.9508(10) ?, V = 5005.3(7) ?3, Z = 4, Mr = 915.14, Dc = 1.214 g/cm3, F(000) = 1968, μ = 0.081 mm?1, S = 1.012, the final R = 0.0789 and wR = 0.1488 for 2298 observed reflections with I > 2σ(I) and 322 variable parameters. The structure exhibits a rigid bowl-cavity with an available functional hydroxyl group. The bowl of cavitand contains a CH3CN solvent molecule, and the depth of the bowl-shaped cavity is ca. 2.42 ?.
基金This project was supported by the Natural Science Foundation of Anhui Province (No. 050460303)
文摘Treatment of tetra-iso-butyl-resorcin[4]arene 1 with propargyl bromide in the presence of K2CO3 as base gave an octopus-like octapropargyl tetra-iso-butyl-resorcin[4]arene 2 （C68H72O8, Mr = 1017.26） in a quantitative yield. Single-crystal structure of 2 was determined by X-ray crystallography. 2 crystallizes in the monoclinic system, space group P21/n with a =13.3247（6）, b = 24.7929（11）, c = 19.1810（9）A°, β = 109.272（1）°, V= 5981.5（5） A°^3, Dc = 1.130g/cm^3,μ = 0.073 mm^-1, F（000） = 2176 and Z = 4. Overall structure of 2 reveals an octopus-like resorcinarene with eight propargyl groups in different directions. The resorcinarene adopts the boat conformation where the iso-butyl residues act as four-legged piano stool. The two opposite aryl rings of the macrocyclic framework are almost coplanar, and the two others facing each other are perpendicular to this plane.
