The influences of α/β compound nucleating agents based on octamethylenedicarboxylic dibenzoylhydrazide on crystallization and melting behavior of isotactic polypropylene

The influences of α/β compound nucleating agents based on octamethylenedicarboxylic dibenzoylhydrazide on crystallization and melting behavior of isotactic polypropylene (iPP) were analyzed. It is found that the crystallization temperatures of nucleated iPP were increased by above 11.0°C and the relative contents of β‐crystals (K_β ) in iPP reached above 0.40 after addition of compound nucleating agents. The K_β values depend on cooling rate, crystallization temperature in isothermal crystallization, and the difference between the crystallization temperatures of iPP nucleated by two individual nucleating agents. The nonisothermal crystallization kinetics were studied by Caze method and Mo method, respectively. The effective activation energy was calculated by the Friedman's method. The results illustrate that the half crystallization time was shortened and the crystallization rate was increased obviously after addition of nucleating agents, and the effective activation energy was increased with the relative crystallinity.     

Synthesis and crystallization behavior study of syndiotactic polystyrene‐g‐isotactic polypropylene (sPS‐g‐iPP) graft copolymers

Based on coordination polymerization mechanism only, novel stereoregular graft copolymers with syndiotactic polystyrene main chain and isotactic polypropylene side chain (sPS‐g‐iPP) were synthesized via two steps of catalytic reactions. First, a chain transfer reaction was initiated by a chain transfer complex composed of a styrene derivative, 1,2‐bis(4‐vinylphenyl)ethane, and hydrogen in propylene polymerization mediated by rac‐Me₂Si[2‐Me‐4‐Ph(Ind)]₂ZrCl₂ and MAO, which gave iPP macromonomer bearing a terminal styryl group (iPP‐t‐St). Then the iPP‐t‐St macromonomers of varied molecular mass were engaged in syndiospecific styrene polymerization over a typical mono‐titanocene catalyst (CpTiCl₃/MAO) under different conditions to produce sPS‐g‐iPP graft copolymers of varied structure. With an effective purification process, well‐defined sPS‐g‐iPP copolymers were obtained, which were then subjected to differential scanning calorimetry (DSC) and polarized optical micrograph (POM) studies. The graft copolymers were generally found with dual melting and crystallization temperatures, which were ascribable respectively to the sPS backbone and iPP graft. However, it was revealed that the two segments displayed largely different melting and crystallization behaviors than sPS homopolymer and the precursory iPP‐t‐St macromonomer. Consequently, the graft copolymer exhibited much distinctive crystalline morphologies when compared with their individual components. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

Semicrystalline blends of polyethylene and isotactic polypropylene: Improving mechanical performance by enhancing the interfacial structure

The low‐temperature mechanical behavior of semicrystalline polymer blends is investigated. Isotactic polypropylene (iPP) is blended with both Zeigler–Natta polyethylene (PE) and metallocene PE. Transmission electron microscopy (TEM) on failed tensile bars reveals that the predominate failure mode in the Zeigler–Natta blend is interfacial, while that in the metallocene blend is failure of the iPP matrix. The observed change in failure mode is accompanied by a 40% increase in both tensile toughness and elongation at −10 °C. We argue that crystallite anchoring of interfacially entangled chains is responsible for this dramatic property improvement in the metallocene blend. The interfacial width between PE and iPP melts is approximately 40 Å, allowing significant interfacial entanglement in both blends. TEM micrographs illustrate that the segregation of low molecular weight amorphous material in the Zeigler–Natta blend reduces the number and quality of crystallite anchors as compared with the metallocene blend. The contribution of anchored interfacial structure was further explored by introducing a block copolymer at the PE/iPP interface in the metallocene blend. Small‐angle X‐ray scattering (SAXS) experiments show the block copolymer dilutes the number of crystalline anchors, decoupling the interface. Increasing the interfacial coverage of the block copolymer reduces the number of anchored interfacial chains. At 2% block copolymer loading, the low‐temperature failure mode of the metallocene blend changes from iPP failure to interfacial failure, reducing the blend toughness and elongation to that of the Zeigler–Natta blend. This work demonstrates that anchored interfacial entanglements are a critical factor in designing semicrystalline blends with improved low‐temperature properties. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 108–121, 2000     

Partial melting and recrystallization of isotactic polypropylene

<正>A relatively high predetermined crystallization temperature(135℃) was chosen to grow well developed iPP spherulites,then the partial melting was carried out at a temperature of 165℃,where the preformed spherulites were seen to only decrease their size but not completely melted.The crystallization behavior of partially melted isotactic polypropylene (iPP) has been carefully examined by different scanning calorimetry(DSC) and polarized light microscopy(PLM).The experimental results show that at a special annealing temperature(165℃) the melting behavior of iPP includes two parts with different mechanism,one part is the melting of iPP spherulite outside,another is the partial lamellae perfection during longer annealing time in the unmelted spherulite.The conformational orders of the iPP melt decrease with the increase of the annealing temperature.     

Epitaxial and graphoepitaxial growth of isotactic polypropylene (iPP) from the melt on highly oriented high density polyethylene (HDPE) substrates

Although under normal conditions only the crystallization behavior of PE on oriented iPP substrates can be studied due to the higher melting point of iPP, the faster crystallization rate of a molten, oriented HDPE film compared to a nonoriented iPP layer was used to study the crystallization of iPP on the oriented HDPE film by means of transmission electron microscopy (TEM) and electron diffraction (ED). Besides the known epitaxial relationship of HDPE/iPP with their chains 50° apart, two new orientation relationships with (a) chains of both polymers parallel and (hk0)_iPP in contact with the HDPE substrate, and (b) the a‐axis of iPP crystals parallel to the chain direction of HDPE but (001)_iPP in contact with the HDPE substrate were observed. Both orientations are assumed as graphoepitaxy. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1893–1898, 1999     

Investigations of morphological changes during annealing of polyethylene single crystals

The morphological evolution of isolated individual single crystals deposited on solid substrates was investigated during annealing experiments using in situ and ex situ atomic force microscopy techniques. The crystal morphology changed during annealing at temperatures slightly above the original crystallization temperature of the crystals, far below their melting temperature. Evenly distributed cavities penetrated the crystals, and the number of cavities increased with a rising annealing temperature until the adjacent cavities coalesced. The thickness of the crystals increased during annealing at temperatures slightly above the crystallization temperature. Annealing experiments at fixed temperatures showed that the reorganization process (cavity formation and single‐crystal thickening) was fast. Depending on the annealing temperature, the final morphology was formed in seconds. This behavior suggests high chain mobility as well as a homogeneous solid‐state reorganization of the entire single crystal at low annealing temperatures. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 763–770, 2001     

Isothermal crystallization kinetics of polypropylene latex–based nanocomposites with organo‐modified clay

The effect of organo‐modified clay (Cloisite 93A) on the crystal structure and isothermal crystallization behavior of isotactic polypropylene (iPP) in iPP/clay nanocomposites prepared by latex technology was investigated by wide angle X‐ray diffraction, differential scanning calorimetry and polarized optical microscopy. The X‐ray diffraction results indicated that the higher clay loading promotes the formation of the β‐phase crystallites, as evidenced by the appearance of a new peak corresponding to the (300) reflection of β‐iPP. Analysis of the isothermal crystallization showed that the PP nanocomposite (1% C93A) exhibited higher crystallization rates than the neat PP. The unfilled iPP matrix and nanocomposites clearly shows double melting behavior; the shape of the melting transition progressively changes toward single melting with increasing crystallization temperature. The fold surface free energy (σ_e) of polymer chains in the nanocomposites was lower than that in the PP latex (PPL). It should be reasonable to treat C93A as a good nucleating agent for the crystallization of PPL, which plays a determinant effect on the reduction in σ_e during the isothermal crystallization of the nanocomposites. The activation energy, ΔE_a, decreased with the incorporation of clay nanoparticles into the matrix, which in turn indicates that the nucleation process is facilitated by the presence of clay. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1927–1938, 2010     

Effects of β‐nucleating agent and crystallization conditions on the crystallization behavior and polymorphic composition of isotactic polypropylene/multi‐walled carbon nanotubes composites

In this study, the effects of crystallization conditions (cooling rate and end temperature of cooling) on crystallization behavior and polymorphic composition of isotactic polypropylene/multi‐walled carbon nanotubes (iPP/MWCNTs) composites nucleated with different concentrations of β‐nucleating agent (tradename TMB‐5) were investigated by differential scanning calorimetry (DSC), wide‐angle X‐ray diffraction (WAXD) and scanning electronic microscopy (SEM). The results of DSC, WAXD and SEM revealed that the addition of MWCNTs and TMB‐5 evidently elevates crystallization temperatures and significantly decreases the crystal sizes of iPP. Because of the competition between α‐nucleation (provided by MWCNTs) and β‐nucleation (induced by TMB‐5), the β‐phase crystallization takes place only when 0.15 wt% and higher concentration of TMB‐5 is added. Non‐isothermal crystallization kinetics study showed that the crystallization activation energy ΔE of β‐nucleated iPP/MWCNTs composites is obviously higher than that of pure iPP, which slightly increases with the increase of TMB‐5 concentration, accompanying with the transition of its polymorphic crystallization behavior. The results of non‐isothermal crystallization and melting behavior suggested that the cooling rate and end temperature of cooling (T_end) are important factors in determining the proportion and thermal stability of β‐phase: Lower cooling rate favors the formation of less amount of β‐phase with higher thermal stability, while higher cooling rate encourages the formation of higher proportion of β‐phase with lower thermal stability. The T_end = 100°C can eliminate the β–α recrystallization during the subsequent heating and therefore enhance the thermal stability of the β‐phase. By properly selecting TMB‐5 concentration, cooling rate and T_end, high β‐phase proportion of 88.9% of the sample was obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Insight into understanding the evolution of the epitaxy crystallization in isotactic polypropylene and polyethylene blends

In this article, epitaxial structures have been successfully obtained in the isotactic polypropylene (iPP)/polyethylene (PE) blends by an accessible injection molding methods. By studying a series of iPP/PE blends, the evolution of the epitaxial growth of PE lamellae on the oriented iPP lamellae has been detailedly discussed via wide‐angle X‐ray diffraction, small‐angle X‐ray scattering, scanning electron microscopy and differential scanning calorimetry. Unexpectedly, the exactly epitaxial angles between peculiarly arranged PE lamellae and oriented PP lamellae are all larger than the classical epitaxy theory value of 50°, and it even increases gradually with increasing PP content. It is inferred that the special crystallization of PE is the consequence of joint construction of the oriented PP crystals and the continuous intense shear field provided by pressure vibration injection molding. The epitaxial structures play a positive role in the interfacial connection between two components; thus, the mechanical properties of the blends are improved. This work provides an insight understanding on the formation mechanism of the epitaxy crystallization under shear field. Copyright © 2017 John Wiley & Sons, Ltd.     

Epitaxial recrystallization of HDPE-quenched ultrathin films on oriented iPP substrates

The recrystallization behavior of high-density polyethylene (HDPE) on the highly oriented isotactic polypropylene (iPP) substrates at temperatures below the melting temperature of HDPE has been investigated by means of transmission electron microscopy. The results obtained by the bright-field observation and the electron diffraction show that upon annealing the HDPE-quenched films on the oriented iPP substrates at temperatures below 125°C, only a small amount of HDPE recrystallizes on the iPP substrate with [001]_HDPE//[001]_iPP, while annealing the HDPE-quenched films at temperatures above 125°C, all of the HDPE crystallites recrystallize epitaxially on the iPP substrate with [001]_HDPE//[101]_iPP. © 1997 John Wiley & Sons, Inc. J Polym Sci B: 35 : 1415–1421, 1997     

Melting behavior of linear polyethylene crystallized by solution stirring

Calorimetric and dilatometric studies have been made of the fusion process of linear polyethylene crystals precipitated by high speed stirring from solution. It is shown that long-time annealing at elevated temperatures alleviates the superheating observed when rapid heating rates are employed. By the annealing procedures that have been adopted, a small but demonstrable fraction of high melting material can be produced whose melting temperature depends on the crystallization temperature. For crystallization at 105°C, followed by annealing at 142°C, a melting temperature of 146.0 ± 0.5°C is observed. The dissolution temperature in xylene, determined for the same sample, is consistent with the high melting temperature observed for the pure polymer. It is recognized that a state of high axial orientation need not necessarily be identified with extended chain crystals. Consequently, the increased melting temperature can result from either an increase in the crystallite size or a reduced interfacial free energy relative to crystallites produced by the more conventional mode of crystallization.     

Probing Liquid-Liquid Phase Separation of a Polyethylene Blend with Thermal Analysis

Summary: A series of polyethylene (PE) blends consisting of a high density polyethylene (HDPE) and a linear low density polyethylene (LLDPE) with a butene-chain branch density of 77/1000 carbon was prepared at different concentrations. The LLDPE only crystallized below 50 °C, therefore, above 80 °C and below the melting temperature of HDPE, only HDPE crystallized in the PE blends. A specifically designed multi-step experimental procedure based on thermal analysis technique was utilized to monitor the liquid–liquid phase separation (LLPS) of this set of PE blends. The main step was first to quench the system from the homogeneous temperatures and isothermally anneal them at a prescribed temperature higher than the equilibrium melting temperature of the HDPE for the purpose of allowing the phase morphology to develop from LLPS, and then cool the system at constant rate to record the non-isothermal crystallization. The crystallization peak temperature (T_p) was used to character the crystallization rate. Because LLPS results in HDPE-rich domains where the crystallization rates are increased, this technique provided an experimental measure to identify the binodal curve of the LLPS for the system indicated by increased T_p. The result showed that the LLPS boundary of the blend measured by this method was close to that obtained by phase contrast optical microscopy method. Therefore, we considered that the thermal analysis technique based on the non-isothermal crystallization could be effective to investigate the LLPS of PE blends.     

Extensional Flow‐Induced Dynamic Phase Transitions in Isotactic Polypropylene

With a combination of fast extension rheometer and in situ synchrotron radiation ultra‐fast small‐ and wide‐angle X‐ray scattering, flow‐induced crystallization (FIC) of isotactic polypropylene (iPP) is studied at temperatures below and above the melting point of α crystals (Tmα). A flow phase diagram of iPP is constructed in strain rate–temperature space, composing of melt, non‐crystalline shish, α and α&β coexistence regions, based on which the kinetic and dynamic competitions among these four phases are discussed. Above T_mα, imposing strong flow reverses thermodynamic stabilities of the disordered melt and the ordered phases, leading to the occurrence of FIC of β and α crystals as a dynamic phase transition. Either increasing temperature or stain rate favors the competiveness of the metastable β over the stable α crystals, which is attributed to kinetic rate rather than thermodynamic stability. The violent competitions among four phases near the boundary of crystal‐melt may frustrate crystallization and result in the non‐crystalline shish winning out.

     

Specificity and versatility of nucleating agents toward isotactic polypropylene crystal phases

Nucleating agents with an ≈6.5 Å lattice parameter induced the α phase of isotactic polypropylene (iPP, α‐iPP). A 6.5 Å periodicity is also involved in the nucleating agents for the β phase of iPP (β‐iPP). The similarity in substrate periodicities suggests that some nucleating agents may induce either the α or β phase under different crystallization conditions. 4‐Fluorobenzoic acid, dicyclohexylterephthalamide, and γ‐quinacridone (the latter two are known as β‐iPP nucleators) were tested over a wide range of crystallization temperatures [up to crystallization temperature (T_c) > 145 °C]. The two former nucleating agents induce exclusively α‐iPP and β‐iPP, respectively. γ‐Quinacridone on the contrary is a versatile agent with respect to the crystal phase generated. More specifically, the same crystal face of γ‐quinacridone induces either β‐iPP or α‐iPP when T_c is below or above ≈140 °C. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2504–2515, 2002     

Thermal analysis and X‐ray scattering study of metallocene isotactic polypropylene prepared by partial melting

In this study, we examine the effects of heating, nucleation, cooling, and reheating on the thermal properties and structure of metallocene isotactic polypropylene (m‐iPP) that had been prepared initially in a standard state containing nearly equal amounts of the crystallographic α and γ phases. Heat treatment was achieved through partial melting and annealing by the heating of samples to self‐nucleation temperatures (T_n's) that spanned and exceeded the entire range of melting of the standard state, from 122 to 160 °C. The relative amounts of α and γ crystals are determined from the area under the unique wide‐angle X‐ray reflections. The lower and upper endotherms are caused by the melting of γ and α crystals, respectively. Four distinct regions of T_n were identified on the basis of the thermal and structural parameters of m‐iPP. In region I, T_n is below the peak melting temperature of the γ phase. Here, γ crystals are annealed and α crystals are barely affected by T_n. In region II, T_n is above the peak of the lower endotherm but below the peak of the upper endotherm. γ crystals melt, and α crystals anneal. In both regions I and II, the portion of the sample melted at T_n recrystallizes epitaxially with existing parent α lamellae as the substrates, and the amount of α always exceeds the amount of γ. In region III, T_n is above the peak of the upper endotherm, and all γ crystals and some or all α crystals are melted at T_n. The number of α‐crystal nuclei steadily decreases as T_n increases, causing systematic depression of the crystallization and melting temperatures seen during cooling. Finally, in region IV, T_n exceeds the upper endotherm, and only small self‐nuclei or heterogeneous nuclei remain. Recrystallization is now suppressed to lower temperatures. For regions III and IV, a crossover behavior in the relative amounts of α and γ is observed during cooling from T_n. Because of the effective nucleating ability of α toward γ, as the temperature drops, the amount of γ increases and then exceeds the amount of α. With subsequent reheating, the reverse crossover occurs because of the lower melting point of γ. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1644–1660, 2002     

等规聚丙烯/二元乙丙橡胶合金相分离对结晶动力学的影响

用小角激光光散射(SALLS)、相差显微镜(PCM)、示差扫描量热仪(DSC)和偏光显微镜(POM)研究了聚丙烯/二元乙丙橡胶(iPP/EPR)共混体系的相分离行为和等温结晶行为.发现iPP/EPR(50/50,W/W)发生的液-液相分离遵循spinodal机理.通过Cahn-Hilliard方程求得了不同实验温度下iPP/EPR的表观扩散系数(Dapp)以及spinodal温度(Ts).考察了不同相分离程度的iPP/EPR体系结晶动力学,发现延长相分离时间(tps)或提高相分离温度(Tps)均会导致半结晶时间(t1/2)增大,即结晶速率降低.这被归于EPR成核作用的降低.动力学分析结果表明Avrami模型适用于描述该体系的等温结晶过程,其结晶机理基本不受相分离程度的影响,结晶均以瞬时成核和三维生长为主.     

Isotactic polypropylene reversible crystallization investigated by modulated temperature and quasi‐isothermal FTIR

Modulated temperature techniques allow to separate the reversing and non‐reversing contributions of material transitions. To investigate reversible crystallization and melting of isotactic polypropylene (iPP) at microstructural level, in this research, modulated temperature Fourier transform infrared (MTFTIR) and quasi‐isothermal FTIR (QIFTIR) analyses are used. By following the intensity variation of iPP regularity bands, associated with 3₁ helix structures of different lengths (n repeating units), MTFTIR evidences that, independently from helix length, a reversing coil–helix transition takes place few degrees below the non‐reversing crystallization onset. By comparing spectroscopic and differential scanning calorimetry experiments performed in quasi‐isothermal conditions, the reversing transition was found to be associated with the reversible melting‐crystallization phenomenon. Moreover, QIFTIR evidences that helices of different lengths contribute differently to the reversible transition: the helices composed of n = 10 and n = 12 are active into all the explored temperature range (30–130 °C) whereas the shortest (n = 6) and the longest (n > 15) helices contribute to reversibility at T > 100 °C. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 922–931     

Crystallization and melting behaviors of isotactic polypropylene nucleated with compound nucleating agents

Crystallization and melting behaviors of isotactic polypropylene (iPP) nucleated with compound nucleating agents of sodium 2,2′‐methylene‐bis (4,6‐di‐tert‐butylphenyl) phosphate (hereinafter called as NA40)/dicyclohexylterephthalamide (hereinafter called as NABW) (weight ratio of NA40 to NABW is 1:1) were studied by differential scanning calorimetry and wide‐angle X‐ray diffraction (WAXD), the relative β‐amount of iPP nucleated with these compound nucleating agents was also calculated in Turner‐Jones equation by using wide‐angle X‐ray diffraction data. Under isothermal crystallization, there exists a temperature range favorable for formation of β‐iPP. When the concentration of compound nucleating agents is 0.2 wt %, the temperature range is from 100 to 140 °C. While in nonisothermal crystallization, lower cooling rate is favorable for form of β‐iPP and the relative β‐amount of iPP increases with the decreasing of cooling rate in crystallization process. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 911–916, 2008     

STRUCTURAL CHARACTERIZATION OF POLYETHYLENES BY DSC ANALYSIS AFTER CRYSTALLIZATION SEGREGATION*

The molecular structure of polyethylene (PE) samples with various comonomers including propylene, 1-buteneand 1-hexene was investigated by DSC and ~(13)C-NMR techniques. The density of the samples varies from 0.948 g/cm~3 to0.917 g/cm~3, and the molecular weight determined by the GPC method is in the range of 1～2×10~5. The branch point contentof the samples was determined by ~(13)C-NMR measurements and was found to be less than 20 per 1000 C atoms along themain chain. Crystallization segregation DSC technique (CSDSC) was used to characterize the branch point distribution or thesegment length distribution of PEs. The crystallization segregation was performed in a successive annealing process atdecreasing temperatures. The interval of two successive annealing temperatures was 6 K, and the time length of eachannealing step was 2.5 h. The CSDSC results clearly indicate that all the PE samples used, including some metallocene PEs,more or less exhibit their non-uniformity in segment length distribution, and bimodal or multimodal CSDSC curves wereusually observed. For quantitative characterization of the CSDSC curves and the segment length distribution two parameters,the average melting point, T_(mAV), and the root-mean-square deviation of melting temperature, (ΔT_(mAV)~2)~(1/2), were proposed.T_(mAV) is corresponding to the average segment length due to branching and (ΔT_(mAV)~2)~(1/2) gives information about the width ofthe segment length distribution. Experimental results show that both the degree of average melting temperature depressionand the width of the distribution seem to increase with increasing the branching content and are dependent on the type ofcomonomers. Very good reproducibility and additivity of the CSDSC method were evidenced experimentally. It wasconcluded that the CSDSC technique is a sensitive and convenient method for characterizing the segment length distribution of branched polyethylenes and will be of great interest in structure-property relationship studies of crystalline polymers.     

Investigation on the dynamic crystallization and melting behavior of β‐nucleated isotactic polypropylene with different stereo‐defect distribution—the role of dual‐selective β‐nucleation agent

The selectivities of different β‐nucleating agents might be quite different from each other, which is important in determining the crystallization and properties of the obtained β‐isotactic polypropylene (β‐iPP). However, the relationship between molecular structure and dynamic crystallization behavior of β‐iPP nucleated by dual‐selective β‐nucleating agent (DS‐β‐NA) is still not clear. In this study, the dynamic crystallization and melting behavior of two β‐iPP with nearly same average isotacticity but different stereo‐defect distribution, nucleated by a DS‐β‐NA (N,N′‐dicyclohexyl‐2,6‐naphthalenedicarboxamide; trade name TMB‐5), were studied by differential scanning calorimetry, wide‐angle X‐ray diffraction, and scanning electronic microscopy. The results indicated that in the presence of TMB‐5, the dynamic crystallization and melting behavior of the samples are quite different because the joint effects of the dual selectivity of TMB‐5 and stereo‐defect distribution of the iPP under different cooling rates. Two important roles were observed: (i) slow cooling rate favors the formation of high β‐fraction; and (ii) high crystallization temperature favors the crystallization of α‐phase accelerated by TMB‐5. Generally, the dual selectivity of the DS‐β‐NA, the stereo‐defect distribution of iPP, and the cooling rate were important factors in determining the formation of β‐crystal. Copyright © 2013 John Wiley & Sons, Ltd.