Weak epitaxy growth of metal-free phthalocyanine on p-sexiphenyl monolayer and double-layer films

Weak epitaxy growth (WEG) can afford high-mobility thin films of disk-like organic semiconductor of which mobility is up to the level of the corresponding single crystals. We investigated the WEG behavior and mechanism of planar phthalocyanine in the model system of metal-free phthalocyanine (H2Pc) grown on p-sexiphenyl (p-6P) ultrathin films (monolayers and double layers). Highly oriented H2Pc films with molecules standing up exhibited two kinds of different in-plane orientations, i.e., three sets of in-plane orientations and only one set of in-plane orientation, on p-6P monolayer and double-layer films, respectively. The surface geometrical channels of p-6P substrate dominated the oriented nucleation and growth of H2Pc film. Consequently, the H2Pc film showed incommensurate and commensurate epitaxy on p-6P ultrathin films.     

Ultrathin-film growth of para-sexiphenyl (I): submonolayer thin-film growth as a function of the substrate temperature

The para-sexiphenyl (p-6P) monolayer film induces weak epitaxy growth (WEG) of disk-like organic semiconductors, and their charge mobilities are increased dramatically to the level of the corresponding single crystals [Wang et al., Adv. Mater. 2007, 19, 2168]. The growth behavior and morphology of p-6P monolayer film play decisive roles on WEG. Here, we investigated the growth behavior of p-6P submonolayer film as a function of the substrate temperature. Its growth exhibited two different mechanisms at high and low substrate temperature. At high substrate temperature (>60 degrees C), the mechanism of diffusion-limited aggregation controlled the growth of submonolayer thin film with fractal islands, whereas at low substrate temperature (< or =60 degrees C), the submonolayer thin film was composed of the compact islands. Its growth exhibited another growth mechanism in which the stable compact islands were formed by dissociation and reorganization of the metastable disordered film. The substrate temperature of about 180 degrees C may be optimal to fabricate high-quality p-6P monolayer film with large-size domains and low saturated island density of about 0.018 microm(-2).     

Ultrathin-film growth of para-sexiphenyl (II): formation of large-size domain and continuous thin film

The large-size domain and continuous para-sexiphenyl (p-6P) ultrathin film was fabricated successfully on silicon dioxide (SiO2) substrate and investigated by atomic force microscopy and selected area electron diffraction. At the optimal substrate temperature of 180 degrees C, the first-layer film exhibits the mode of layer growth, and the domain size approaches 100 microm(2). Its saturated island density (0.018 microm(-2)) is much smaller than that of the second-layer film (0.088 microm(-2)), which begins to show the Volmer-Weber growth mode. The characteristic of liquid-like crystal of p-6P monolayer film and the adequate diffusion of p-6P molecules dominate the formation of large-size domain. The coalescence of large-size domains offers the possibility to grow high-quality p-6P monolayer film which provides excellent substrate for weak epitaxy growth of phthalocyanine compounds.     

Growth modes of organic semiconductor thin films using organic molecular beam deposition: epitaxy,van der Waals epitaxy,and quasi-epirtaxy

We compare the ultrahigh vacuum growth of several different archetype organic molecular compounds on a variety of substrates, and find that the resulting thin films can form epitaxial, van der Waals epitaxial (vdWE) or quasi-epitaxial (QE) structures. Epitaxial and vdWE films form lattices commensurate with that of the substrate, where epitaxy refers to chemisorbed films while vdWE refers to purely vdW-bonded, physisorbed films. In contrast, QE films are incommensurate with the substrate lattice. In spite of this incommensurability, QE films can exhibit long range order, and have a unique orientational relationship with the substrate lattice. Quasi-epitaxial growth can result in strained structures, where the strain energy is relieved by variations in the internal lattice degrees of freedom. It has been found that QE growth can thus result in stable, quasi-equilibrium film structures which are different than the bulk structure of that same material. Organic thin films such as the phthalocyanines, 3,4,9,10-perylenetetracar☐ylic dianhydride, and the fullerenes grown on graphite, alkali halide crystals, Au, semiconductors and other substrates are all discussed.     

Gas sensing mechanism in chemiresistive cobalt and metal-free phthalocyanine thin films

The gas sensing behaviors of cobalt phthalocyanine (CoPc) and metal-free phthalocyanine (H2Pc) thin films were investigated with respect to analyte basicity. Chemiresistive sensors were fabricated by deposition of 50 nm thick films on interdigitated gold electrodes via organic molecular beam epitaxy (OMBE). Time-dependent current responses of the films were measured at constant voltage during exposure to analyte vapor doses. The analytes spanned a range of electron donor and hydrogen-bonding strengths. It was found that, when the analyte exceeded a critical base strength, the device responses for CoPc correlated with Lewis basicity, and device responses for H2Pc correlated with hydrogen-bond basicity. This suggests that the analyte-phthalocyanine interaction is dominated by binding to the central cavity of the phthalocyanine with analyte coordination strength governing CoPc sensor responses and analyte hydrogen-bonding ability governing H2Pc sensor responses. The interactions between the phthalocyanine films and analytes were found to follow first-order kinetics. The influence of O2 on the film response was found to significantly affect sensor response and recovery. The increase of resistance generally observed for analyte binding can be attributed to hole destruction in the semiconductor film by oxygen displacement, as well as hole trapping by electron donor ligands.     

Role of coordinated metal ions on the orientation of phthalocyanine based coatings

In the present work, we have investigated the molecular orientation of phthalocyanine films deposited on polycrystalline gold. Three films built from the following molecules are investigated: phthalocyanine (H(2)Pc), cobalt phthalocyanine (CoPc) and copper phthalocyanine (CuPc). The films are prepared by spin coating and drop casting methods. Orientation analysis has been performed using polarization dependent Fourier transform infrared (FTIR) spectroscopy using transmission and grazing angle reflectance mode. The FTIR study suggests that each phthalocyanine film contains both alpha- and beta-phases. H(2)Pc based films demonstrate deposition method dependence on the molecular orientation, while the CuPc and CoPc films preserve their molecular orientation independent of deposition method. Grazing angle analysis also suggests that CoPc films show negligible preferred orientation irrespective of film deposition methods. In literature, the band at 878cm(-1) in CuPc has been assigned to out-of-plane bending of C-H. Our grazing angle experiments suggest that this band cannot be assigned to out-of-plane bending vibrations of C-H. Accurate band assignments are also described here for the phthalocyanine system.     

Electron-donating alkoxy-group-driven synthesis of heteroleptic tris(phthalocyaninato) lanthanide(III) triple-deckers with symmetrical molecular structure

Reaction of heteroleptic bis(phthalocyaninato) lanthanide compounds [(Pc)M{Pc(OC8H17)8}] [H2Pc=unsubstituted phthalocyanine; H2Pc(OC8H17)8 = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine] with monomeric complexes [(Pc)M(acac)] (Hacac=acetylacetone), both of which generated in situ, led to the isolation of heteroleptic phthalocyaninato-[2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato] lanthainde(III) triple-decker complexes [(Pc)M{Pc(OC8H17)8}] (M=Gd-Lu) (1-8) as the sole product. Heterodinuclear analogues [(Pc)Lu{Pc(OC8H17)8}M(Pc)] (M=Gd-Yb) (9-15) were obtained in a similar manner from the reaction of [(Pc)M{Pc(OC8H17)8}] (M=Gd-Yb) and [(Pc)Lu(acac)]. The molecular structures of the herterodinuclear compound [(Pc)Lu{Pc(OC8H17)8}Er(Pc)] (13) and its homodinuclear counterparts [(Pc)M{Pc(OC8H17)8}M(Pc)] (M=Er, Lu) (5, 8) have been determined by X-ray diffraction analysis; these structures exhibit a symmetrical molecular structure with one inner planar Pc(OC8H17)8 ligand and two outer domed Pc ligands. In addition to various spectroscopic analyses, the electrochemistry of these compounds has also been studied by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) methods, revealing the gradually enhanced pi-pi interactions among the phthalocyanine rings in the triple-deckers along with the lanthanide contraction.     

Aggregation behavior of heteroleptic tris(phthalocyaninato) dysprosium complexes with different alkoxy chains in monolayer or multilayer solid films

Three heteroleptic tris(phathlocyaninato) dysprosium triple-decker complexes with different alkoxy groups at the peripheral positions of the medium phthalocyanine ligand (Pc)Dy[Pc(OCnH(2n+1))8]Dy(Pc) (n = 4, 8, 16) (I-III) {Pc = unsubstituted phthalocyaninate; Pc(OC4H9)8 = 2,3,9,10,16,17,23,24-octakis(butyloxy)phthalocyaninate; Pc(OC8H17)8 = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninate; Pc(OC16H33)8 = 2,3,9,10,16,17,23,24-octakis(hexadecyloxy)phthalocyaninate} have been synthesized, and their aggregate behaviors in monolayer and multilayer solid films have been comparatively studied. The pure compounds and their 1:4 mixtures with stearic acid (SA) have been found to form a stable monolayer at the air/water interface with a tilted edge-on orientation of (Pc)Dy[Pc(OCnH(2n+1))8]Dy(Pc) molecules. In the pure monolayers of the three triple-decker compounds, wirelike molecular aggregates were observed by high-resolution transmission electron microscopy (HRTEM). Adding SA has been found to prevent triple-decker compounds (Pc)Dy[Pc(OC4H9)8]Dy(Pc) (I) and (Pc)Dy[Pc(OC8H17)8]Dy(Pc) (II) from forming large aggregates, and small domains with a diameter of ca. 10 nm were observed in the mixed monolayers. HRTEM studies revealed that two crystalline phases with rectangular and hexagonal lattice structure are present in the small domains. However, both pi-A isotherms and HRTEM studies indicated that the mixed monolayer of compound (Pc)Dy[Pc(OC16H33)8]Dy(Pc) (III) with SA did not show a difference from the corresponding pure monolayer. The SA molecules were pressed into the cavity above the phthalocyanine ring formed by the eight long hexadecyloxy side chains of the medium macrocycle ligand in III. The multilayer LB films of all of these triple deckers fabricated by the vertical dipping method showed very good layered structure as revealed by the multiple-order diffraction peaks in low-angle X-ray diffraction (LAXRD) patterns.     

酞菁铜化合物LB膜的制备及结构形态研究

利用LB技术研究了带有4个长碳氢链的酞菁铜化合物(CuC12Pc)的单分子膜及它与十八胺(ODA)、二十酸(AA)的混合LB膜的聚集结构形态. 结果表明这种酞菁铜化合物在气液界面上可以形成比较稳定有序的双层Langmuir膜, 且可以转移质量较好的多层LB膜. 利用原子力显微镜(AFM)研究了酞菁铜分子的聚集体结构, 发现CuC12Pc/AA混合膜表现为网状的聚集结构, 而CuC12Pc/ODA混合膜形成长岛颗粒状聚集, 并结合UV-Vis吸收光谱讨论了酞菁铜分子形成不同聚集结构的原因.     

Thin-film transistors based on Langmuir-Blodgett films of heteroleptic bis(phthalocyaninato) rare earth complexes

An ordered molecular assembly of heteroleptic bis(phthalocyaninato) rare earth complexes M(Pc)[Pc(OC8H17)8] [M = Tb, Lu; H2Pc = phthalocyanine; H2Pc(OC8H17)8 = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine] has been fabricated by the Langmuir-Blodgett (LB) technique and characterized by surface pressure-area isotherms, electronic absorption and polarized electronic absorption spectroscopy, low-angle X-ray diffraction, and atomic force microscopy. The molecular ordering in the LB multilayer film on SiO2 substrate was made into a p-channel field effect transistor (FET), which was generally operated in the enhanced mode. The energy levels of the highest occupied molecular orbital and the lowest unoccupied molecular orbital as well as the energy band diagram can be deduced from the electrochemical measurement results. The charge mobilities of Tb(Pc)[Pc(OC8H17)8] and Lu(Pc)[Pc(OC8H17)8] were calculated to be about 6.4 x 10(-4) and 1.7 x 10(-3) cm2 V(-1) s(-1), respectively.     

Arrangement of tris(phthalocyaninato) gadolinium triple-decker complexes with multi-octyloxy groups on water surface

A series of five carefully designed tris(phthalocyaninato) gadolinium triple-decker complexes [Pc(R)8]Gd[Pc(R')8]Gd[Pc(R')8] (R=R'=R'=H; R=R'=H, R'=OC8H17; R=R'=H, R'=OC8H17; R=H, R'=R'=OC8H17; R=R'=R'=OC8H17) (1-5) were prepared and the film forming properties on water surface were systematically investigated. The limited mean molecular area obtained by pi-A isotherms revealed an "edge-on" conformation for all these compounds. UV-vis absorption spectra showed red-shifted Q bands, indicating the formation of J aggregates and effective intermolecular interaction in solid film. Phthalocyanine rings were found to take tilted orientation with respect to the normal of substrate according to the polarized absorption spectroscopic measurements. Low angle X-ray diffraction results provide direct evidence and therefore clearly clarify the point, for the first time, that unsymmetrical triple-decker molecules pack on the water surface with the unsubstituted phthalocyanine ring set close to the water surface and the substituted phthalocyanine ligand with octyloxy groups lies on the top.     

Effect of peripheral hydrophobic alkoxy substitution on the organic field effect transistor performance of amphiphilic tris(phthalocyaninato) europium triple-decker complexes

A series of four amphiphilic heteroleptic tris(phthalocyaninato) europium complexes with different lengths of hydrophobic alkoxy substituents on one outer phthalocyanine ligand [Pc(15C5)4]Eu[Pc(15C5)4]Eu[Pc(OCnH(2n+1))8] (n = 4, 6, 10,12) (1, 2, 4, and 5) was designed and prepared. Their film forming and organic field effect transistor properties have been systematically studied in comparison with analogous [Pc(15C5)4]Eu[Pc(15C5)4]Eu[Pc(OC8H17)8] (3). Experimental results showed that all these typical amphiphilic sandwich triple-decker molecules have been fabricated into highly ordered films by the Langmuir-Blodgett (LB) technique, which displays carrier mobility in the direction parallel to the aromatic phthalocyanine rings in the range of 0.0032-0.60 cm2 V(-1) s(-1) depending on the length of the hydrophobic alkoxy substituents. This is rationalized on the basis of comparative morphology analysis results of the LB films by the atomic force microscopy technique.     

Highly ordered thin films of 5,5'-bis(3'-fluoro-biphenyl-4-yl)-2,2' : 5',2'-terthiophene with two meso-phases

The growth process and phase state of 5,5'-bis(3'-fluoro-biphenyl-4-yl)-2,2'?:?5',2'- terthiophene (m-F2BP3T) thin films were investigated by atomic force microscopy (AFM), in-plane and out-of-plane X-ray diffraction (XRD), and selected area electron diffraction (SAED). Two meso-phases (thin film phases) of m-F2BP3T films on SiO(2) surface were obtained in the early stages. The m-F2BP3T films initially exhibited two-dimensional (2D) layers (≤4 ML) followed by three-dimensional (3D) island growth. The film structure evolved two thin film phases in the first four layers and the bulk phase was formed from the fifth layer, which occurred concomitantly with the change of the growth mode. Moreover, the variation of weak epitaxy growth behavior of ZnPc from 2D to 3D growth further reflects that the phase state of the first three layers is different from that of the fourth layer, in spite of ZnPc crystals showing just one orientation corresponding to commensurate epitaxy. The novel phase behavior is closely related to the synergistic effects of the outstanding soft matter properties, limited elasticity of organic molecules, and strain originating from the SiO(2) substrate. This study investigates novel phase behavior in organic thin films and provides significant insight into the mechanism of the phase transition.     

Air-stable spin-coated naphthalocyanine transistors for enhanced chemical vapor detection

Air-stable organic thin-film transistor (OTFT) sensors fabricated using spin-cast films of 5,9,14,18,23,27,32,36-octabutoxy-2,3-naphthalocyanine (OBNc) demonstrated improved chemical vapor sensitivity and selectivity relative to vacuum-deposited phthalocyanine (H(2)Pc) OTFTs. UV-vis spectroscopy data show that annealed spin-cast OBNc films exhibit a red-shift in the OBNc Q-band λ(max) which is generally diagnostic of improved π-orbital overlap in phthalocyanine ring systems. Annealed OBNc OTFTs have mobilities of 0.06 cm(2) V(-1) s(-1), low threshold voltages (|V(th)| < 1 V), and on/off ratios greater than 10(6). These air-stable device parameters are utilized for sensing modalities which enhance the sensitivity and selectivity of OBNc OTFTs relative to H(2)Pc OTFTs. While both sensors exhibit mobility decreases for all analytes, only OBNc OTFTs exhibit V(th) changes for highly polar/nonpolar analytes. The observed mobility decreases for both sensors are consistent with electron donation trends via hydrogen bonding by basic analytes. In contrast, V(th) changes for OBNc sensors appear to correlate with the analyte's octanol-water partition coefficient, consistent with polar molecules stabilizing charge in the organic semiconductor film. The analyte induced V(th) changes for OBNc OTFTs can be employed to develop selective multiparameter sensors which can sense analyte stabilized fixed charge in the film.     

Two-dimensional "nano-ring and nano-crystal" morphologies in Langmuir monolayer of phthalocyaninato nickel complexes

Three 1,8,15,22-tetrasubstituted phthalocyaninato nickel complexes Ni[Pc(alpha-OR)(4)] [H(2)Pc(alpha-OC(5)H(11))(4) = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine; H(2)Pc(alpha-OC(7)H(15))(4) = 1,8,15,22-tetrakis(2,4-dimethyl-3-pentyloxy)phthalocyanine; H(2)Pc(alpha-OC(10)H(7))(4) = 1,8,15,22-tetrakis(2-naphthyloxy)phthalocyanine] (1-3) have been prepared by treating the corresponding metal-free phthalocyanines H(2)Pc(alpha-OR)(4) with Ni(acac)(2)2H(2)O in refluxing n-pentanol. Structures of the Langmuir monolayers of these compounds at different temperature have been investigated. Compound 1 formed nano-ring structures with the outer diameter of 70-150 nm and inner diameter of 50 nm at 25.0 degrees C while 2 and 3 formed round particles. This difference can be ascribed to the different substituents at alpha position. The morphologies of the aggregates of 1 in monolayers have been found to change with temperature. Decreasing in temperature induced the formation of regular quadrate crystals. UV-vis absorption spectra revealed strong intermolecular interactions in the nano-ring aggregates. Polarized UV-vis absorption spectra suggest a titled orientation with respect to the surface of substrate for phthalocyanine macrocycles in the nano-ring aggregates.     

Fabrication of Micro‐ and Nanoscale Crystals and Thin Films of a Phthalocyanine

Micro‐ and nanosized crystals of 1, 4, 8, 11, 15, 18, 22, 25–octabutoxy–29H, 31H–phthalocyanine (Pc) were successfully fabricated through the reprecipitation approach followed by ultrasonication treatment from acetone solution. Phthalocyanine thin films were prepared by vacuum sublimation, spin‐coating and drop‐cast methods, respectively. Field emission scanning electron microscopy (FESEM), UV/VIS/NIR spectroscopy, polarizing optical microscopy and luminescence spectrometry were applied to study phthalocyanine crystal's surface morphology, electronic absorption, birefringence and light emission properties accordingly. The electronic absorption maximum of Pc nanocrystals shifts to longer wavelength compared to that in acetone solution. Birefringence phenomena exist for Pc crystals with different sizes. Fluorescence is observed for both the Pc in acetone solution and thin film.     

Site-specific intermolecular interaction in α-phase crystalline films of phthalocyanines studied by soft x-ray emission spectroscopy

The local electronic structures of crystalline and amorphous films of zinc phthalocyanine (ZnPc) and metal-free phthalocyanine (H(2)Pc) have been studied by soft x-ray emission spectroscopy (XES). We found a clear crystalline structure dependence of the elastic-peak shape in the resonant XES spectra. The elastic peaks of both ZnPc and H(2)Pc are found to show an asymmetric shape due to resonant inelastic x-ray scattering (RIXS) at the nitrogen sites for the α-crystalline films, but not for the amorphous films. The observed RIXS feature is ascribed to the charge transfer excitation due to the Raman-active intermolecular interaction, which dominates the excited-electron dynamics in α-crystalline phthalocyanine films.     

Layer-by-layer electrostatic assembly with a control over orientation of molecules: anisotropy of electrical conductivity and dielectric properties

While forming layer-by-layer (LbL) electrostatic assembly of a magnetic organic molecule, namely, nickel phthalocyanine (NiPc), we apply a magnetic field. The field orients the magnetic moment of the molecules on a monolayer along the direction of magnetic field. Such an orientation of the molecules is then electrostatically immobilized with a monolayer of a polycation. By repeating the dipping cycle, we form LbL films with planar NiPc molecules facing a particular direction. With NiPc's moment perpendicular to the molecular plane, two types of LbL films were formed: (a) NiPc's molecular plane parallel to the substrate (moment is perpendicular) and (b) molecules perpendicular to the substrate and facing one particular direction, the direction of magnetic field. Such films, with the molecules lying either (a) parallel or (b) perpendicular to the substrate, provide unique systems to study anisotropy of optical, dielectric, and electrical characteristics in these planar organic molecules. The latter film responds to the polarization of incident beam in electronic absorption spectroscopy. Here we show methods to obtain an orientation of molecules in LbL films and study anisotropy of dielectric constant and conductivity of the molecules in ultrathin films.     

Facile electrochemical growth of nanostructured copper phthalocyanine thin film via simultaneous anodic oxidation of copper and dilithium phthalocyanine for photoelectrochemical hydrogen evolution

We present a novel electrochemical approach to grow copper phthalocyanine (CuPc) thin-film photoelectrodes through anodic oxidation of copper and dilithium phthalocyanine (Li₂Pc). This circumvents the challenges associated with the electrochemical processing of unsubstituted CuPc from solution. The potentiostatic co-electrooxidation reaction at the heterogeneous interface favors the growth of CuPc thin film. The surface morphology of thin film exhibits nanorod-like features. UV-Vis, grazing angle Fourier transform infrared (FTIR), and grazing angle X-ray diffraction patterns reveal that the nanocrystalline phase corresponds only to α-CuPc and no admixture of other polymorphs. Photocurrent measurement shows a stable photoresponse in neutral medium. The photoelectrochemical hydrogen evolution on p-type CuPc coated copper photocathode shows an enhanced activity over bare copper and indium tin oxide (ITO) electrodeposited with CuPc and monolithium phthalocyanine radical (LiPc) thin films.     

Synthesis, structure, spectroscopic properties, and electrochemistry of (1,8,15,22-tetrasubstituted phthalocyaninato)lead complexes

Three (1,8,15,22-tetrasubstituted phthalocyaninato)lead complexes Pb[Pc(alpha-OR)(4)] [H(2)Pc(alpha-OC(5)H(11))(4) = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine; H(2)Pc(alpha-OC(7)H(15))(4) = 1,8,15,22-tetrakis(2,4-dimethyl-3-pentyloxy)phthalocyanine; H(2)Pc(alpha-OC(10)H(7))(4) = 1,8,15,22-tetrakis(2-naphthyloxy)phthalocyanine] (1-3) have been prepared as racemic mixtures by treating the corresponding metal-free phthalocyanines H(2)Pc(alpha-OR)(4) (4-6) with Pb(OAc)(2).3H(2)O in refluxing n-pentanol. The molecular structure of Pb[Pc(alpha-OC(5)H(11))(4)] (1) in the solid state has been determined by single-crystal X-ray diffraction analysis. This compound, having a nonplanar structure, crystallizes in the monoclinic system with a P2(1)/c space group. Each unit cell contains two pairs of enantiomeric molecules, which are linked by weak coordination of the Pb atom of one molecule with an aza nitrogen atom and its neighboring oxygen atom from the alkoxy substituent of another molecule, forming a pseudo-double-decker supramolecular structure in the crystals with a short ring-to-ring separation, 2.726 A, and thus a strong ring-ring pi-pi interaction. The decreased molecular symmetry for these complexes has also been revealed by the NMR spectra of 1 and 2. The methyl protons of the 3-pentyloxy and 2,4-dimethyl-3-pentyloxy side chains of 1 and 2, respectively, are chemically inequivalent. In addition to the elemental analysis and various spectroscopic characterizations, these compounds have also been electrochemically studied. Two one-electron oxidations and up to five one-electron reductions have been revealed by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) methods.