Self‐assembled complexes of poly(acrylic acid) and poly(styrene)‐block‐poly(4‐vinyl pyridine)

Polymer complexes were prepared from high molecular weight poly(acrylic acid) (PAA) and poly(styrene)‐block‐poly(4‐vinyl pyridine) (PS‐b‐P4VP) in dimethyl formamide (DMF). The hydrogen bonding interactions, phase behavior, and morphology of the complexes were investigated using Fourier transform infrared (FTIR) spectroscopy, differential scanning calorimetry (DSC), dynamic light scattering (DLS), atomic force microscopy (AFM), and transmission electron microscopy (TEM). In this A‐b‐B/C type block copolymer/homopolymer system, P4VP block of the block copolymer has strong intermolecular interaction with PAA which led to the formation of nanostructured micelles at various PAA concentrations. The pure PS‐b‐P4VP block copolymer showed a cylindrical rodlike morphology. Spherical micelles were observed in the complexes and the size of the micelles increased with increasing PAA concentration. The micelles are composed of hydrogen‐bonded PAA/P4VP core and non‐bonded PS corona. Finally, a model was proposed to explain the microphase morphology of complex based on the experimental results obtained. The selective swelling of the PS‐b‐P4VP block copolymer by PAA resulted in the formation of different micelles. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1192–1202, 2009     

Segregation of Coronal Chains in Micelles Formed by Supramolecular Interactions

Summary: Spherical micelles have been formed by mixing, in DMF, a poly(styrene)‐block‐poly(2‐vinylpyridine)‐block‐poly(ethylene oxide) (PS‐block‐P2VP‐block‐PEO) triblock copolymer with either poly(acrylic acid) (PAA) or a tapered triblock copolymer consisting of a PAA central block and PEO macromonomer‐based outer blocks. Noncovalent interactions between PAA and P2VP result in the micellar core while the outer corona contains both PS and PEO chains. Segregation of the coronal chains is observed when the tapered copolymer is used.

Inclusion of comb‐like chains with short PEO teeth in the corona triggers the nanophase segregation of PS and PEO as illustrated here (PS = polystyrene; PEO = poly(ethylene oxide)).     

Self‐assembly of a triblock terpolymer mediated by hydrogen‐bonded complexes

A poly(methyl methacrylate)‐block‐poly(4‐vinylpyridine)‐block‐polystyrene (PMMA‐b‐P4VP‐b‐PS) triblock terpolymer is synthesized by ATRP to study its self‐assembly with PAA in organic solvents. The self‐assembly behavior of this system is compared with the one of a mixture of two diblocks, namely polystyrene‐block‐poly(4‐vinylpyridine) (PS‐b‐P4VP) and poly(methyl methacrylate)‐block‐poly(methacrylic acid) (PMMA‐b‐PMAA). For both systems, formation of hydrogen‐bonded complexes between the P4VP and PMAA or PAA blocks occurs. These complexes become insoluble in the solvent used and micelles with a P4VP/P(M)AA complexes core surrounded by PS and PMMA coronal chains are obtained in both cases. These micelles are analyzed by DLS and TEM. Spherical micelles are formed for both systems but the hydrodynamic radii obtained for the two types of micelles are different. Indeed, the micelles formed by the PMMA‐b‐P4VP‐b‐PS + PAA system are smaller than those observed for the PS‐b‐P4VP + PMMA‐b‐PMAA system. Finally, the effect of the molar ratio of the P4VP/PMAA complexing blocks is investigated. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 459–467     

Double‐hydrophilic block copolymer for encapsulation and two‐way pH change‐induced release of metalloporphyrins

A double hydrophilic block copolymer composed of poly(acrylic acid) (PAA) and poly(4‐vinyl pyridine) (P4VP) was obtained through hydrolysis of diblock copolymer of poly(tert‐butyl acrylate) (PtBA) and P4VP synthesized using atom transfer radical polymerization. Water‐soluble micelles with PAA core and P4VP corona were observed at low (acidic) pH, while micelles with P4VP core and PAA corona were formed at high (basic) pH. Two metalloporphyrins, zinc tetraphenylporphyrin (ZnTPP) and cobalt tetraphenylporphyrin (CoTPP), were used as model compounds to investigate the encapsulation of hydrophobic molecules by both types of micelles. UV–vis spectroscopic measurements indicate that micelles with P4VP core are able to entrap more ZnTPP and CoTPP as a result of the axial coordination between the transition metals and the pyridine groups. The study found that metalloporphyrins encapsulated by the micelles with PAA core could be released on pH increase, while those entrapped by the micelles with P4VP core could be released on pH decrease. This behavior originates from the two‐way pH change‐induced disruption of PAA‐b‐P4VP micelles. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1734–1744, 2006     

Nanometer‐Scaled Hollow Spherical Micelles with Hydrophilic Channels and the Controlled Release of Ibuprofen

PS‐b‐PAA spherical micelles with a liquid core and a PAA shell are prepared with the assistance of 1,2‐dichloroethane. During the process of adding a mixture of PNIPAM‐b‐P4VP and PEG‐b‐P4VP, multi‐layered micelles with a mixed corona that consists of both PNIPAM and PEG chains are constructed through the electrostatic interaction and hydrogen bonding between the PAA block and the P4VP block. When heating above the LCST, the PNIPAM chains collapse onto the PAA/P4VP complex layer while the PEG chains still stretch into the solution through the collapsed PNIPAM layer, which leads to the formation of hydrophilic channels around the PEG chains. The ibuprofen encapsulated in the hollow space can diffuse through the channels and its release rate can be controlled by changing the ratio of PEG chains to PNIPAM chains in the corona.

     

Preparation of polymeric vesicles through ultrasonic treatment of poly(styrene‐block‐2‐vinylpyridine) micelles under alkaline conditions

An approach for the preparation of block copolymer vesicles through ultrasonic treatment of polystyrene‐block‐poly(2‐vinyl pyridine) (PS‐b‐P2VP) micelles under alkaline conditions is reported. PS‐b‐P2VP block copolymers in toluene, a selective solvent for PS, form spherical micelles. If a small amount of NaOH solution is added to the micelles solution during ultrasonic treatment, organic‐inorganic Janus‐like particles composed of the PS‐b‐P2VP block copolymers and NaOH are generated. After removal of NaOH, block copolymer vesicles are obtained. A possible mechanism for the morphological transition from spherical micelles to vesicles or Janus‐like particles is discussed. If the block copolymer micelles contain inorganic precursors, such as FeCl₃, hybrid vesicles are formed, which may be useful as biological and chemical sensors or nanostructured templates. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 953–959     

Contractive Polymeric Complex Micelles as Thermo‐Sensitive Nanopumps

Complex micelles were obtained from PS‐b‐PNIPAM‐b‐PAA micelles and PEG‐b‐P4VP block copolymers via the strong electrostatic interaction and hydrogen bonding between PAA and P4VP blocks in water. The PS block formed the core and the PAA/P4VP complex shell functioned as a semi‐permeable membrane which could control the permeation of small molecules. Between the core and shell, the large fluid‐filled space that was formed with the thermoresponsive PNIPAM gel could retain the loaded drug for a long period of time. With increasing temperature, the shrinkage of the PNIPAM coils pumped the drug out of the complex micelles. The complex micelles functioned as a contractive “nanopump”, which could potentially be applied as a thermosensitive controlled release system.

     

Ultrathin and Large‐area Macroporous Polymeric Membranes Formed Through Self‐assembly of Sub‐10 nm Elastic Nanoparticles

A variety of sub‐10 nm nanoparticles are successfully prepared by crosslinking of polystyrene‐b‐poly(1,3‐butadiene) (PS‐b‐PB) and polystyrene‐b‐poly(4‐vinyl pyridine) (PS‐b‐P4VP) block copolymer micelles and inverse micelles. Among them, the core‐crosslinked PS‐b‐PB micelles can self‐assemble into ultrathin (< 10 nm) macroporous (pore size <1 µm) membranes in a facile way, i.e., by simply drop‐coating the particle solution onto a mica surface. No continuous/porous membranes are produced from shell‐crosslinked PS‐b‐PB micelles and both forms of PS‐b‐P4VP micelles. This suggests that the unique structure of the block copolymer precursor, including the very flexible core‐forming block and the glassy corona‐forming block and the specific block length ratio, directly determines the formation of the macroporous membrane.

     

Core extractable nano‐objects: Manipulating triblock copolymer micelles

We report manipulation of polymer nano‐objects by changing solvents through chemically crosslinking the spherical micelles of poly(3‐(triethoxysilyl)propyl methacrylate)‐block‐polystyrene‐block‐poly(2‐vinylpyridine) (PTEPM‐b‐PS‐b‐P2VP). In methanol, which is a common solvent of PTEPM and P2VP but poor of PS, PTEPM‐b‐PS‐b‐P2VP forms micelles with a PS core. When changing the medium into acidic water, the PTEPM segments further collapse and gelate to form a crosslinked shell outside of the PS core. When the particles are re‐dispersed into tetrahydrofuran (THF), the PS segments are extracted out, producing uniform small cavity of few nanometers in each particle. Thus one sample can be used to generate well‐defined nano‐objects with different appearance by solvent manipulation. The particle structure development has been characterized by transmission electron microscope (TEM), DLS, and ¹H NMR. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Self‐assembly of thermo‐ and pH‐responsive poly(acrylic acid)‐b‐poly(N‐isopropylacrylamide) micelles for drug delivery

Self‐assembled thermo‐ and pH‐responsive poly(acrylic acid)‐b‐poly(N‐isopropylacrylamide) (PAA‐b‐PNIPAM) micelles for entrapment and release of doxorubicin (DOX) was described. Block copolymer PAA‐b‐PNIPAM associated into core‐shell micelles in aqueous solution with collapsed PNIPAM block or protonated PAA block as the core on changing temperature or pH. Complexation of DOX with PAA‐b‐PNIPAM triggered by the electrostatic interaction and release of DOX from the complexes due to the changing of pH or temperature were studied. Complex micelles incorporated with DOX exhibited pH‐responsive and thermoresponsive drug release profile. The release of DOX from micelles was suppressed at pH 7.2 and accelerated at pH 4.0 due to the protonation of carboxyl groups. Furthermore, the cumulative release of DOX from complex micelles was enhanced around LCST ascribed to the structure deformation of the micelles. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5028–5035, 2008     

Synthesis and self‐assembly of diblock copolymers bearing 2‐nitrobenzyl photocleavable side groups

The light‐responsive behavior in solution and in thin films of block copolymers bearing 2‐nitrobenzyl photocleavable esters as side groups is discussed in this article. The polymers were synthesized by grafting 2‐nitrobenzyl moieties onto poly(acrylic acid)‐block‐polystyrene (PAA‐b‐PS) precursor polymers, leading to poly(2‐nitrobenzyl acrylate‐random‐acrylic acid)‐block‐polystyrene (P(NBA‐r‐AA)‐b‐PS) block copolymers. The UV irradiation of the block copolymers in a selective solvent for PS led to the formation of micelles that were used to trap hydrophilic molecules inside their core (light‐induced encapsulation). In addition, thin films consisting of light‐responsive P(NBA‐r‐AA) cylinders surrounded by a PS matrix were achieved by the self‐assembly of P(NBA‐r‐AA)‐b‐PS copolymers onto silicon substrates. Exposing these films to UV irradiation generates nanostructured materials containing carboxylic acids inside the cylindrical nanodomains. The availability of these chemical functions was demonstrated by reacting them with a functional fluorescent dye. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Composite Worm‐Like Aggregates Formed from a Pair of Block‐Copolymers Containing Hydrogen‐Bonding Donor and Acceptor

Worm‐like aggregates with a PAA/P4VP complex core and a PEG/PNIPAM mixed shell were prepared in ethanol by the comicellization of poly(ethylene glycol)‐block‐poly(acrylic acid) (PEG‐b‐PAA) and poly(N‐isopropylacrylamide)‐block‐poly(4‐vinylpyridine) (PNIPAM‐b‐P4VP) through hydrogen‐bonding. The formed aggregates were studied by dynamic light scattering, static light scattering, ¹H NMR, and transmission electron microscopy. The length of worm‐like aggregates could be adjusted by changing the weight ratio of W(PNIPAM‐b‐P4VP)/W(PEG‐b‐PAA). When the ratio changed from 20 to 150%, the length changed from about 100 nm to several microns, and the diameter stayed almost unchanged at about 15 nm.

     

Complex micelles formed from two diblock copolymers for applications in controlled drug release

Double‐responsive core‐shell‐corona complex micelles for applications in drug release were formed from self‐assembly of two diblock copolymers PtBA‐b‐ PNIPAM and PtBA‐b‐P4VP. The two diblock copolymers coaggregated into core‐shell complex micelles in acidic water with the hydrophobic PtBA blocks as the common core and soluble PNIPAM/P4VP blocks as the mixed shell. Increasing temperature or pH value, the micelles converted into core‐shell‐corona micelles because of the collapse of PNIPAM or P4VP blocks as the inner shell and soluble P4VP or PNIPAM chains stretching outside as the outer corona. The anti‐inflammation drug naproxen (NAP) was loaded as the model drug in micelles in acidic water and released because of the ionization of NAP in alkaline solutions. Compared with pure core‐shell micelles, release of NAP from core‐shell‐corona complex micelles avoided the burst diffusion and the release rate is more easily controlled by tuning the composition of the mixtures or by adjusting the pH of the medium. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1804–1810, 2009     

Enhanced stability of ZnTPPS by polymeric gold nanoparticles in acidic aqueous solutions

Novel kind of core-shell corona complex micelles were prepared, which enhanced both the hydrolytic stability and the photostability of water-soluble zinc tetrakis(4-sulfonatophenyl) porphyrin (ZnTPPS) in acidic aqueous solutions. The core-shell gold nanoparticles (AuNPS) were synthesized by reducing HAuCl₄ and di-thioester terminated block copolymer, poly(Nisopropylacrylamide)-block-poly(4-vinylpyridine) (PNIPAM-b-P4VP). The complex micelles with gold core, P4VP/ZnTPPS shell and PNIPAM corona were formed by simple mixing of gold nanoparticles and ZnTPPS. The photochemical properties of the complex micelles were studied by UV–Visiblespectroscopy and fluorescence spectroscopy. The results showed trapping of ZnTPPS in the positively charged micellar shell that effectively prevented demetallation of the ZnTPPS that would occur in acidic aqueous solutions. Furthermore, with appropriate concentration of gold nanoparticles, ZnTPPS in the complex micelle had excellent photostability by suppression of generation of reactive oxygen species (ROS). The enhanced stability of ZnTPPS in acidic aqueous media could be extensively used for photocatalysis and in solar cells.     

Micelles‐Encapsulated Microcapsules for Sequential Loading of Hydrophobic and Water‐Soluble Drugs

Layer‐by‐layer (LbL) assembly was conducted on CaCO₃ microparticles pre‐doped with polystyrene‐block‐poly(acrylic acid) (PS‐b‐PAA) micelles, and resulted in micelles encapsulation in the microcapsules after core removal. Distribution of the micelles in the templates and capsules was characterized by transmission electron microscopy and confocal laser scanning microscopy. The micelles inside the capsules connected with each other to form a chain and network‐like structure with a higher density near the capsule walls. The hydrophobic PS cores were then able to load small uncharged hydrophobic drugs while the negatively charged PAA corona could induce spontaneous deposition of water‐soluble positively charged drugs such as doxorubicin.

     

Synthesis of arborescent polystyrene‐g‐[poly(2‐vinylpyridine)‐b‐polystyrene] core–shell–corona copolymers

Arborescent copolymers with a core‐shell‐corona (CSC) architecture, incorporating a polystyrene (PS) core, an inner shell of poly(2‐vinylpyridine), P2VP, and a corona of PS chains, were obtained by anionic polymerization and grafting. Living PS‐b‐P2VP‐Li block copolymers serving as side chains were obtained by capping polystyryllithium with 1,1‐diphenylethylene before adding 2‐vinylpyridine. A linear or arborescent (generation G0 – G3) PS substrate, randomly functionalized with acetyl or chloromethyl coupling sites, was then added to the PS‐b‐P2VP‐Li solution for the grafting reaction. The grafting yield and the coupling efficiency observed in the synthesis of the arborescent PS‐g‐(P2VP‐b‐PS) copolymers were much lower than for analogous coupling reactions previously used to synthesize arborescent PS homopolymers and PS‐g‐P2VP copolymers from the same types of coupling sites. It was determined from static and dynamic light scattering analysis that PS‐b‐P2VP formed aggregates in THF, the solvent used for the synthesis. This presumably hindered coupling of the macroanions with the substrate, and explains the low grafting yield and coupling efficiency observed in these reactions. Purification of the crude products was also problematic due to the amphipolar character of the CSC copolymers and the block copolymer contaminant. A new fractionation method by cloud‐point centrifugation was developed to purify copolymers of generations G1 and above. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1075–1085     

Synthesis of PEG‐PNIPAM‐PLys hetero‐arm star polymer and its variation of thermo‐responsibility after the formation of polyelectrolyte complex micelles with PAA

A hetero‐arm star polymer, poly(ethylene glycol)‐poly(N‐isopropylacrylamide)‐poly(L‐lysine) (PEG‐PNIPAM‐PLys), was synthesized by “clicking” the azide group at the junction of PEG‐b‐PNIPAM diblock copolymer with the alkyne end‐group of poly(L‐lysine) (PLys) homopolymer via 1,3‐dipolar cycloaddition. The resultant polymer was characterized by gel permeation chromatography, proton nuclear magnetic resonance, and Fourier transform infrared spectroscopes. Surprisingly, the PNIPAM arm of this hetero‐arm star polymer nearly lose its thermal responsibility. It is found that stable polyelectrolyte complex micelles are formed when mixing the synthesized polymer with poly(acrylic acid) (PAA) in water. The resultant polyelectrolyte complex micelles are core‐shell spheres with the ion‐bonded PLys/PAA chains as core and the PEG and PNIPAM chains as shell. The PNIPAM shell is, as expected, thermally responsive. However, its lower critical solution temperature is shifted to 37.5 °C, presumably because of the existence of hydrophilic components in the micelles. Such star‐like PEG‐PNIPAM‐PLys polymer with different functional arms as well as its complexation with anionic polymers provides an excellent and well‐defined model for the design of nonviral vectors to deliver DNA, RNA, and anionic molecular medicines. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1450–1462, 2009     

Dimensional Control of Block Copolymer Nanofibers with a π‐Conjugated Core: Crystallization‐Driven Solution Self‐Assembly of Amphiphilic Poly(3‐hexylthiophene)‐b‐poly(2‐vinylpyridine)

With the aim of accessing colloidally stable, fiberlike, π‐conjugated nanostructures of controlled length, we have studied the solution self‐assembly of two asymmetric crystalline–coil, regioregular poly(3‐hexylthiophene)‐b‐poly(2‐vinylpyridine) (P3HT‐b‐P2VP) diblock copolymers, P3HT₂₃‐b‐P2VP₁₁₅ (block ratio=1:5) and P3HT₄₄‐b‐P2VP₁₁₅ (block ratio=ca. 1:3). The self‐assembly studies were performed under a variety of solvent conditions that were selective for the P2VP block. The block copolymers were prepared by using Cu‐catalyzed azide–alkyne cycloaddition reactions of azide‐terminated P2VP and alkyne end‐functionalized P3HT homopolymers. When the block copolymers were self‐assembled in a solution of a 50 % (v/v) mixture of THF (a good solvent for both blocks) and an alcohol (a selective solvent for the P2VP block) by means of the slow evaporation of the common solvent; fiberlike micelles with a P3HT core and a P2VP corona were observed by transmission electron microscopy (TEM). The average lengths of the micelles were found to increase as the length of the hydrocarbon chain increased in the P2VP‐selective alcoholic solvent (MeOH<iPrOH<nBuOH). Very long (>3 μm) fiberlike micelles were prepared by the dialysis of solutions of the block copolymers in THF against iPrOH. Furthermore the widths of the fibers were dependent on the degree of polymerization of the chain‐extended P3HT blocks. The crystallinity and π‐conjugated nature of the P3HT core in the fiberlike micelles was confirmed by a combination of UV/Vis spectroscopy, photoluminescence (PL) measurements, and wide‐angle X‐ray scattering (WAXS). Intense sonication (iPrOH, 1 h, 0 °C) of the fiberlike micelles formed by P3HT₂₃‐b‐P2VP₁₁₅ resulted in small (ca. 25 nm long) stublike fragments that were subsequently used as initiators in seeded growth experiments. Addition of P3HT₂₃‐b‐P2VP₁₁₅ unimers to the seeds allowed the preparation of fiberlike micelles with narrow length distributions (L_w/L_n <1.11) and lengths from about 100‐300 nm, that were dependent on the unimer‐to‐seed micelle ratio.     

Coassembly of Metal and Titanium Dioxide Nanocrystals Directed by Monolayered Block Copolymer Inverse Micelles for Enhanced Photocatalytic Performance

Functional nanostructures of self‐assembled block copolymers (BCPs) incorporated with various inorganic nanomaterials have received considerable attention on account of their many potential applications. Here we demonstrate the two‐dimensional self‐assembly of anisotropic titanium dioxide (TiO₂) nanocrystals (NCs) and metal nanoparticles (NPs) directed by monolayered poly(styrene)‐block‐poly(4‐vinylpyridine) (PS‐b‐P4VP) copolymer inverse micelles. The independent position‐selective assembly of TiO₂ NCs and silver nanoparticles (AgNPs) preferentially in the intermicelle corona regions and the core of micelles, respectively, for instance, was accomplished by spin‐coating a mixture solution of PS‐b‐P4VP and ex situ synthesized TiO₂ NCs, followed by the reduction of Ag salts coordinated in the cores of micelles into AgNPs. Hydrophobic TiO₂ NCs with a diameter and length of approximately 3 nm and 20–30 nm, respectively, were preferentially sequestered in the intermicelle nonpolar PS corona regions energetically favorable with the minimum entropic packing penalty. Subsequent high‐temperature annealing at 550 °C not only effectively removed the block copolymer but also transformed the TiO₂ NCs into connected nanoparticles, thus leading to a two‐dimensionally ordered TiO₂ network in which AgNPs were also self‐organized. The enhanced photocatalytic activity of the AgNP‐decorated TiO₂ networks by approximately 27 and 44 % over that of Ag‐free TiO₂ networks and randomly deposited TiO₂ nanoparticles, respectively, was confirmed by the UV degradation property of methylene blue.     

Cancer‐associated pH‐responsive tetracopolymeric micelles composed of poly(ethylene glycol)‐b‐poly(L‐histidine)‐b‐poly(L‐lactic acid)‐b‐poly(ethylene glycol)

To create a novel vector for specifically delivering anticancer therapy to solid tumors, we used diafiltration to synthesize pH‐sensitive polymeric micelles. The micelles, formed from a tetrablock copolymer [poly(ethylene glycol)‐b‐poly(L ‐histidine)‐b‐poly(L ‐lactic acid)‐b‐poly(ethylene glycol)] consisted of a hydrophobic poly(L ‐histidine) (polyHis) and poly(L ‐lactic acid) (PLA) core and a hydrophilic poly(ethylene glycol) (PEG) shell, in which we encapsulated the model anticancer drug doxorubicin (DOX). The robust micelles exhibited a critical micellar concentration (CMC) of 2.1–3.5 µg/ml and an average size of 65–80 nm pH 7.4. Importantly, they showed a pH‐dependent micellar destabilization, due to the concurrent ionization of the polyHis and the rigidity of the PLA in the micellar core. In particular, the molecular weight of PLA block affected the ionization of the micellar core. Depending on the molecular weight of the PLA block, the micelles triggering released DOX at pH 6.8 (i.e. cancer acidic pH) or pH 6.4 (i.e. endosomal pH), making this system a useful tool for specifically treating solid cancers or delivering cytoplasmic cargo in vivo. Copyright © 2008 John Wiley & Sons, Ltd.