Liquid-crystalline medium

09822302 · 2017-11-21

Assignee

Inventors

Cpc classification

International classification

Abstract

The compounds of the formula I, and a liquid-crystalline medium, preferably having a nematic phase and negative dielectric anisotropy, which comprises a) one or more compounds of the formula I ##STR00001## and b) one or more compounds of the formulae II-1 to II-4, ##STR00002##
in which the parameters have the meanings defined herein, are suitable for use in an electro-optical display, particularly in an active-matrix display based on the VA, ECB, PALC, FFS or IPS effect.

Claims

1. A liquid-crystalline medium comprising a) one or more compounds of the formula I, ##STR00230## in which n denotes 3 or 4, m denotes (4−n), ##STR00231## denotes an organic radical having 4 bonding sites, in which, in addition to the m groups R.sup.12 present in the molecule, but independently thereof, a further H atom may be replaced by R.sup.12 or a plurality of further H atoms may each be replaced by R.sup.12 and in which one —CH.sub.2— group or a plurality of —CH.sub.2— groups may each be replaced by —O— or —(C═O)— in such a way that two O atoms are not bonded directly to one another, or denotes a substituted or unsubstituted aromatic or heteroaromatic hydrocarbon radical having 4 bonding sites, in which, in addition to the m groups 12.sup.12 present in the molecule, but independently thereof, a further H atom may be replaced by R.sup.12 or a plurality of further H atoms may each be replaced by R.sup.12, Z.sup.11 and Z.sup.12, independently of one another, denote —O—, —(C═O)—, —(N—R.sup.14)— or a single bond, but do not both simultaneously denote —O—, r and s, independently of one another, denote 0 or 1, Y.sup.11 to Y.sup.14 each, independently of one another, denote alkyl having 1 to 4 C atoms, and alternatively, independently of one another, one or both of the pairs (Y.sup.11 and Y.sup.12) and (Y.sup.13 and Y.sup.14) together also denote a divalent group having 3 to 6 C atoms, R.sup.12 on each occurrence, independently of one another, denotes H, F, OR.sup.14, NR.sup.14R.sup.15, a straight-chain or branched alkyl chain having 1-20 C atoms, in which one —CH.sub.2— group or a plurality of —CH.sub.2— groups may each be replaced by —O— or —C(═O)—, but two adjacent —CH.sub.2— groups cannot be replaced by —O—, denotes a hydrocarbon radical which contains a cycloalkyl or alkylcycloalkyl unit and in which one —CH.sub.2— group or a plurality of —CH.sub.2— groups may each be replaced by —O— or —C(═O)—, but two adjacent —CH.sub.2— groups cannot be replaced by —O—, and in which one H atom or a plurality of H atoms may each be replaced by OR.sup.14, N(R.sup.14)(R.sup.15) or R.sup.16, or denotes an aromatic or heteroaromatic hydrocarbon radical, in which one H atom or a plurality of H atoms may each be replaced by OR.sup.14, N(R.sup.14)(R.sup.15) or R.sup.16, R.sup.14 on each occurrence, independently of one another, denotes a straight-chain or branched alkyl or acyl group having 1 to 10 C atoms, or an aromatic hydrocarbon or carboxyl radical having 6-12 C atoms, R.sup.15 on each occurrence, independently of one another, denotes a straight-chain or branched alkyl or acyl group having 1 to 10 C atoms, or an aromatic hydrocarbon or carboxyl radical having 6-12 C atoms, R.sup.16 on each occurrence, independently of one another, denotes a straight-chain or branched alkyl group having 1 to 10 C atoms, in which one —CH.sub.2— group or a plurality of —CH.sub.2— groups may each be replaced by —O— or —C(═O)—, but two adjacent —CH.sub.2— groups cannot be replaced by —O—, b) one or more compounds selected from the group of the compounds of the formulae II-1 to II-4, ##STR00232## in which R.sup.21 denotes an unsubstituted alkyl radical having 1 to 7 C atoms, R.sup.22 denotes an unsubstituted alkyl radical having 1 to 7 C atoms or an unsubstituted alkoxy radical having 1 to 6 C atoms, and m, n and o each, independently of one another, denote 0 or 1, and c) one or more compounds of formula III-3, ##STR00233## in which alkoxy, alkoxy′, independently of one another, denote an alkoxy radical having 1 to 5 C atoms.

2. The medium according to claim 1, wherein the group ##STR00234## in formula I on each occurrence denotes ##STR00235##

3. The medium according to claim 1, wherein said medium comprises one or more compounds of the formula I selected from the compounds of the formulae I-1 and I-2, ##STR00236##

4. The medium according to claim 1, wherein the total concentration of the compounds of the formula I in the medium as a whole is 1 ppm or more to 1000 ppm or less.

5. The medium according to claim 1, wherein said medium additionally comprises one or more compounds of the formula IV, ##STR00237## in which R.sup.41 denotes an unsubstituted alkyl radical having 1 to 7 C atoms or an unsubstituted alkenyl radical having 2 to 7 C atoms, and R.sup.42 denotes an unsubstituted alkyl radical having 1 to 7 C atoms, an unsubstituted alkoxy radical having 1 to 6 C atoms or an unsubstituted alkenyl radical having 2 to 7 C atoms.

6. The medium according to claim 1, wherein the total concentration of the compounds of the formulae II-1 to II-4 in the medium as a whole is 10% or more to 80% or less.

7. The medium according to claim 1, wherein said medium comprises one or more compounds of the formula II-3.

8. An electro-optical display or electro-optical component comprising a liquid-crystalline medium according to claim 1.

9. The display according to claim 8, wherein said display is based on the VA or ECB effect.

10. The display according to claim 8, wherein said display has an active-matrix addressing device.

11. A method of generating an electro-optical effect comprising applying a voltage to a display according to claim 8.

12. A process for the preparation of a liquid-crystalline medium according to claim 1, comprising mixing one or more compounds of formula I with one or more compounds of the formulae II-1 to II-4 and one or more compounds of formulae III-3.

13. The medium according to claim 1, wherein ##STR00238## denotes ##STR00239## (benzene-1,2,4,5-tetrayl) or straight-chain or branched tetravalent alkyl having 2 to 24 C atoms.

14. The medium according to claim 1, wherein —[Z.sup.11—].sub.r—[z.sup.12—].sub.s on each occurrence, independently of one another, denotes —O—, —(C═O)—O— or —O—(C≡O)—, —(N-R.sup.14)- or a single bond.

15. The medium according to claim 14, wherein —[Z.sup.11—].sub.r—[Z.sup.12—], on each occurrence, independently of one another, denotes —O— or —(C═O)—O— or —O—(C═O)—.

16. The medium according to claim 1, wherein R.sup.12, if present, denotes alkyl or alkoxy.

17. The medium according to claim 1, wherein said medium comprise one or more compounds of formula II-1.

18. The medium according to claim 1, wherein said one or more compounds of formula II-1 are selected from the compounds of formulae II-1-1 and II-1-2, ##STR00240##

19. The medium according to claim 1, wherein said medium comprise one or more compounds of formula II-2.

20. The medium according to claim 19, wherein said one or more compounds of formula II-2 are selected from the compounds of formulae II-2-1 and II-2-2, ##STR00241##

21. The medium according to claim 7, wherein said one or more compounds of formula II-3 are selected from the compounds of formulae II-3-1 and II-3-2, ##STR00242##

22. The medium according to claim 1, wherein said medium comprise one or more compounds of formula II-4.

23. The medium according to claim 22, wherein said one or more compounds of formula II-4 are selected from the compounds of formula II-4-a, ##STR00243## in which alkyl and alkyl′, independently of one another, denote alkyl having 1 to 7 C atoms.

24. The medium according to claim 5, wherein said one or more compounds of the formula IV arc selected from the compounds of the formulae IV-1 to IV-4, ##STR00244## in which alkyl and alkyl′, independently of one another, denote alkyl having 1 to 7 C atoms. alkenyl denotes an alkenyl radical having 2 to 5 C atoms, alkenyl′ denotes an alkenyl radical having 2 to 5 C atoms, and alkoxy denotes alkoxy having 1 to 5 C atoms.

25. The medium according to claim 24, wherein said one or more compounds of the formula IV are selected from the compounds of formulae IV-1 and IV-2.

26. The medium according to claim 4, wherein the total concentration of the compounds of the formulae II-1 to II-4 in the medium as a whole is 10% or more to 80% or less.

Description

EXAMPLES

(1) The following examples explain the present invention without restricting it in any way. However, the physical properties make it clear to the person skilled in the art what properties can be achieved and in what ranges they can be modified. In particular, the combination of the various properties which can preferably be achieved is thus well defined for the person skilled in the art.

(2) Liquid-crystal mixtures having the compositions and properties as indicated in the following tables are prepared and investigated. The improved stability of the mixtures comprising compounds of the formula I is demonstrated by comparison with unstabilized base mixtures as reference (Ref.).

Examples 1.1 to 1.3

(3) The following mixture (M-1) is prepared and investigated.

(4) TABLE-US-00009 Mixture M-1 Composition Compound Concentration/ No. Abbreviation % by weight 1 CY-3-O2 12.0 2 CY-3-O4 2.0 3 CY-5-O2 12.0 4 CCY-3-O1 6.0 5 CCY-3-O2 8.0 6 CCY-4-O2 8.0 7 CPY-2-O2 9.0 8 CPY-3-O2 9.0 9 PYP-2-3 5.0 10 CC-3-V1 5.0 11 CC-3-V 19.0 12 CPP-3-2 5.0 Σ 100.0 Physical properties T(N, I) = 86.5° C. n.sub.e(20° C., 589 nm) = 1.5924 Δn(20° C., 589 nm) = 0.1092 ∈⊥(20°, 1 kHz) = 7.9 Δ∈(20°, 1 kHz) = −4.2 γ.sub.1(20° C.) = 155 mPa .Math. s k.sub.11(20° C.) = 14.6 pN k.sub.33(20° C.) = 16.6 pN V.sub.0(20° C.) = 2.08 V

(5) Mixture M-1 is divided into four parts and investigated as described below.

(6) Firstly, the stability of the voltage holding ratio of mixture (M-1) itself is determined. Mixture M-1 is investigated for its stability to UV exposure in a test cell having an alignment material for homeotropic alignment and flat ITO electrodes. To this end, corresponding test cells are irradiated in the sun test for 30 min. The voltage holding ratio is then determined in each case after 5 minutes at a temperature of 100° C. The results are summarized in Table 1. Here, as below, six test cells are filled and investigated for each individual mixture. The values indicated are the average of the six individual values.

(7) Next, 100 ppm, 200 ppm and 300 ppm of compound I-1 are in each case added to the remaining three parts of mixture M-1, and the resultant mixtures (M-1-1, M-1-2, M-1-3) are investigated for their stability as described above. The results are shown in Table 1 below.

(8) The relative deviations of the voltage holding ratio values in the case of various measurement series are typically in the range from about 3 to 4%.

(9) TABLE-US-00010 TABLE 1 Stabi- c(stab.)/ VHR(t)/% Ex. Mixture liser ppm t = 0 h t = 30 min (Ref.) M-1 none 0 98.3 ± 0.3 91 ± 0.2 1.1 M-1-1 I-1 100 98.7 ± 0.3 97 ± 0.5 1.2 M-1-2 I-1 200 97.6 ± 0.3 95 ± 0.5 1.3 M-1-3 I-1 300 97.8 ± 0.3 96 ± 0.5

(10) It can readily be seen here that compound I-1, even in relatively low concentrations, exhibits clearly stabilizing properties.

(11) Compound I-1 has excellent stabilization activity in a concentration of 100 ppm. This results in a reduction in the risk of image sticking on exposure to the backlight.

Example 1.4

(12) Mixture M-1 is prepared and divided into two parts. 150 ppm of compound I-1 are added to one part (mixture M-1-4).

(13) Firstly, the stability of the voltage holding ratio of the mixtures as such is determined. The two mixtures are subsequently investigated for their stability to illumination by means of a cold cathode (CCFL) LCD backlight in a test cell having an alignment material for homeotropic alignment and flat ITO electrodes. To this end, corresponding test cells are exposed to the illumination for 900 h. The voltage holding ratio is then determined in each case after 5 minutes at a temperature of 100° C. The results are summarized in Table 2.

(14) TABLE-US-00011 TABLE 2 Stabi- c(stab.)/ VHR(t)/% Ex. Mixture liser ppm t = 0 h t = 900 h (Ref.) M-1 none 0 98.9 ± 0.3 89 ± 2.sup.  1.4 M-1-4 I-1 150 97.5 ± 0.5 97 ± 0.3

(15) As can be seen from Table 2, even a low concentration of compound I-1 results in a considerable improvement in the final value for the VHR after exposure to light of an LCD backlight.

Example 2

(16) The following mixture (M-2) is prepared and investigated.

(17) TABLE-US-00012 Mixture M-2 Composition Compound Concentration/ No. Abbreviation % by weight 1 CPP-3-2 4.5 2 CC-3-V 23.5 3 CC-3-O1 4.0 4 CCY-3-O2 4.0 5 CCY-3-O3 7.0 6 CCY-4-O2 8.0 7 CLY-3-O2 8.0 8 CPY-2-O2 7.0 9 CPY-3-O2 11.0 10 CY-3-O2 11.0 11 PY-3-O2 12.0 Σ 100.0 Physical properties T(N, I) = 86° C. n.sub.e(20° C., 589 nm) = 1.5962 Δn(20° C., 589 nm) = 0.1118 ∈.sub.⊥(20°, 1 kHz) = 8.0 Δ∈(20°, 1 kHz) = −4.3 γ.sub.1(20° C.) = 143 mPa .Math. s k.sub.11(20° C.) = 15.0 pN k.sub.33(20° C.) = 16.7 pN V.sub.0(20° C.) = 2.08 V

(18) Mixture M-2 is divided into two parts, 100 ppm of compound I-2 are added to one part (mixture M-2-1), and the two mixtures are investigated in test cells for their stability to UV exposure in the sun test analogously to the procedure described in Examples 1.1 to 1.3. The results of the VHR measurements after irradiation for 30 min are summarized in Table 3.

(19) TABLE-US-00013 TABLE 3 Stabi- c(stab.)/ VHR(t)/% Ex. Mixture liser ppm t = 0 h t = 30 min (Ref.) M-2 none 0 87.5 ± 2 78 ± 4 2 M-2-1 I-2 100 82.7 ± 2 84 ± 2 (VHR: 60° C., 1 V, 60 Hz)

(20) As can be seen from Table 3, even a low concentration of compound I-2 results in a considerable improvement in the final value for the VHR after UV exposure.

Example 3 and Comparative Example 3-V

(21) The following mixture (M-3) is prepared and investigated.

(22) TABLE-US-00014 Mixture M-3 Composition Compound Concentration/ No. Abbreviation % by weight 1 CCY-3-O1 8.0 2 CCY-4-O2 3.0 3 CLY-3-O2 8.0 4 CLY-3-O3 4.0 5 CPY-2-O2 6.5 6 CPY-3-O2 4.0 7 B-2O—O5 4.0 8 CC-3-V 41.5 9 PY-1-O4 5.0 10 PY-3-O2 11.5 11 CCY-3-O2 4.5 Σ 100.0 Physical properties T(N, I) = 76.1° C. n.sub.e(20° C., 589 nm) = 1.5856 Δn(20° C., 589 nm) = 0.1025 ∈⊥(20°, 1 kHz) = 7.4 Δ∈(20°, 1 kHz) = −3.7 γ.sub.1(20° C.) = 91 mPa .Math. s k.sub.11(20° C.) = 13.9 pN k.sub.33(20° C.) = 14.8 pN V.sub.0(20° C.) = 2.10 V

(23) Mixture M-3 is prepared and divided into three parts. 150 ppm of compound I-1 are added to one part (mixture M-3-1). For comparison, 150 ppm of a stabilizer from the prior art (compound VII, mixture V-1) are added to a further part.

(24) ##STR00229##

(25) The VHR before and after irradiation for 476 h by means of a cold cathode (CCFL) LCD backlight is investigated analogously to the experiments described above. The results are summarized in Table 4 (the low measurement frequency should be noted).

(26) TABLE-US-00015 TABLE 4 Stabi- c(stab.)/ VHR(t)/% Ex. Mixture lizer ppm t = 0 h t = 476 h (Ref.) M-3 none 0 91.9 ± 1 60 ± 4 3 M-3-1 I-1 150 83.7 ± 2 87 ± 2 3-V V-1 VII 150 83.7 ± 2 78 ± 4 (VHR: 20° C., 1 V, 1 Hz)

(27) As can be seen from Table 4, even a low concentration of compound I-1 results in a considerable improvement in the final value for the VHR after exposure by means of an LCD backlight. Furthermore, comparison of the VHR values of mixtures M-3-1 and V-1 shows that the use of compound I-1 results in even better values for the VHR after exposure than the use of compound VII from the prior art.

Example 4

(28) The following mixture (M-4) is prepared and investigated.

(29) TABLE-US-00016 Mixture M-4 Composition Compound Concentration/ No. Abbreviation % by weight 1 CC-3-V 30.5 2 CC-3-V1 4.5 3 CCY-3-O1 6.0 4 CCY-3-O2 8.0 5 CLY-3-O2 8.0 6 CPY-2-O2 8.0 7 CPY-3-O2 12.0 8 CY-3-O2 15.0 9 PY-3-O2 8.0 Σ 100.0 Physical properties T(N, I) = 80.1° C. n.sub.e(20° C., 589 nm) = 1.5858 Δn(20° C., 589 nm) = 0.1033 ∈⊥(20°, 1 kHz) = 7.6 Δ∈(20°, 1 kHz) = −4.0 γ.sub.1(20° C.) = 113 mPa .Math. s k.sub.11(20° C.) = 14.4 pN k.sub.33(20° C.) = 17.0 pN V.sub.0(20° C.) = 2.16 V

(30) Mixture M-4 is divided into three parts, and 100 ppm of compound I-1 or I-2 are in each case added to two of them. The mixtures are subsequently subjected to an exposure test by means of an LCD backlight as described in Example 1.4, and comparably good results are obtained.

Example 5 and Comparative Example 5-V

(31) The following mixture (M-5) is prepared and investigated.

(32) TABLE-US-00017 Mixture M-5 Composition Compound Concentration/ No. Abbreviation % by weight 1 CCY-3-O1 7.5 2 CLY-3-O2 10.0 3 CPY-2-O2 10.0 4 CPY-3-O2 10.0 5 PGIY-2-O4 2.5 6 CC-3-V 35.0 7 PY-1-O4 9.0 8 PY-3-O2 8.0 9 PY-4-O2 3.0 10 CCY-3-O2 5.0 Σ 100.0 Physical properties T(N, I) = 80.0° C. n.sub.e(20° C., 589 nm) = 1.6010 Δn(20° C., 589 nm) = 0.1150 ∈⊥(20°, 1 kHz) = 7.7 Δ∈(20°, 1 kHz) = −4.0 γ.sub.1(20° C.) = 114 mPa .Math. s k.sub.11(20° C.) = 14.9 pN k.sub.33(20° C.) = 15.7 pN V.sub.0(20° C.) = 2.09 V

(33) Mixture M-5 is prepared and divided into three parts. 100 ppm of compound I-1 are added to one part (mixture M-5-1). For comparison, 100 ppm of the stabilizer of the formula VII are added to a further part (mixture V-5). The VHR before and after irradiation for 168 h by means of a cold cathode (CCFL) LCD backlight is determined analogously to the experiments described above. The results are summarized in Table 5.

(34) TABLE-US-00018 TABLE 5 Stabi- c(stab.)/ VHR(t)/% Ex. Mixture liser ppm t = 0 h t = 168 h (Ref.) M-5 none 0 83.4 ± 2 54.6 ± 4 5 M-5-1 I-1 100 82.7 ± 2 84.4 ± 2 5-V V-5 VII 100 82.5 ± 2 79.7 ± 2 (VHR: 100° C., 1 V, 60 Hz)

(35) As can be seen from Table 5, even a low concentration of compound I-1 results in a considerable improvement in the final value for the VHR after exposure by means of an LCD backlight. Furthermore, comparison of the VHR values of mixtures M-5-1 and V-5 shows that the use of compound I-1 results in even better values for the VHR after exposure than the use of compound VII from the prior art.

Example 6 and Comparative Example 6-V

(36) The following mixture (M-6) is prepared and investigated.

(37) TABLE-US-00019 Mixture M-6 Composition Compound Concentration/ No. Abbreviation % by weight 1 CCY-3-O2 7.5 2 CPY-2-O2 10.0 3 CPY-3-O2 11.0 4 CLY-3-O2 5.0 5 PGIY-2-O4 4.0 6 PYP-2-3 3.5 7 CC-3-V 36.5 8 PP-1-2V1 3.0 9 CY-3-O2 16.5 10 B-2O—O5 3.0 Σ 100.0 Physical properties T(N, I) = 74.6° C. n.sub.e(20° C., 589 nm) = 1.5962 Δn(20° C., 589 nm) = 0.1110 ∈⊥(20° 1 kHz) = 7.4 Δ∈(20°, 1 kHz) = −3.7 γ.sub.1(20° C.) = 96 mPa .Math. s k.sub.11(20° C.) = 13.3 pN k.sub.33(20° C.) = 15.0 pN V.sub.0(20° C.) = 2.13 V

(38) Mixture M-6 is prepared and divided into three parts. 100 ppm of compound I-1 are added to one part (mixture M-6-1). For comparison, 100 ppm of the stabilizer of the formula VII are added to a further part (mixture V-6). The VHR before and after irradiation for 1000 h by means of a cold cathode (CCFL) LCD backlight is determined analogously to the experiments described above. The results are summarized in Table 6.

(39) TABLE-US-00020 TABLE 6 Stabi- c(stab.)/ VHR(t)/% Ex. Mixture liser ppm t = 0 h t = 1000 h (Ref.) M-6 none 0 79.1 ± 2 61.5 ± 2 6 M-6-1 I-1 100 79.2 ± 2 66.2 ± 2 6-V V-6 VII 100 80.7 ± 2 62.3 ± 2 (VHR: 100° C., 1 V, 60 Hz)

(40) As can be seen from Table 6, even a low concentration of compound I-1 results in a considerable improvement in the final value for the VHR after exposure by means of an LCD backlight. Furthermore, comparison of the VHR values of mixtures M-6-1 and V-6 shows that the use of compound I-1 results in even better values for the VHR after exposure than the use of compound VII from the prior art.

Example 7

(41) The following mixture (M-7) is prepared and investigated.

(42) TABLE-US-00021 Mixture M-7 Composition Compound Concentration/ No. Abbreviation % by weight 1 CC-3-V 35.5 2 CCP-3-1 2.5 3 CCY-3-O2 9.5 4 CLY-3-O2 8.0 5 CPY-2-O2 4.5 6 CPY-3-O2 10.5 7 CY-3-O2 14.5 8 PGIY-2-O4 6.0 9 PYP-2-3 2.0 10 B(S)-2O—O5 4.0 11 B(S)-2O—O4 3.0 Σ 100.0 Physical properties T(N, I) = 85.4° C. n.sub.e(20° C., 589 nm) = 1.5883 Δn(20° C., 589 nm) = 0.1116 ∈⊥(20° 1 kHz) = 7.9 Δ∈(20°, 1 kHz) = −4.3 γ.sub.1(20° C.) = 113 mPa .Math. s k.sub.11(20° C.) = 15.0 pN k.sub.33(20° C.) = 16.7 pN V.sub.0(20° C.) = 2.09 V

(43) Mixture M-7 is prepared and divided into two parts. 100 ppm of compound I-1 are added to one part (mixture M-6-1). The VHR before and after irradiation for 1000 h by means of a cold cathode (CCFL) LCD backlight is determined analogously to the experiments described above. The results are summarized in Table 7.

(44) TABLE-US-00022 TABLE 7 Stabi- c(stab.)/ VHR(t)/% Ex. Mixture liser ppm t = 0 h t = 1000 h (Ref.) M-7 none 0 93.6 ± 1 72.1 ± 2 M-7 M-7-1 I-1 100 92.2 ± 1 86.2 ± 2 (VHR: 60° C., 5 V, 1 Hz)

(45) As can be seen from Table 7, even a low concentration of compound I-1 results in a considerable improvement in the final value for the VHR after exposure to light of an LCD backlight.

(46) Without further elaboration, it is believed that one skilled in the art can, using the preceding description, utilize the present invention to its fullest extent. The preceding preferred specific embodiments and examples are, therefore, to be construed as merely illustrative, and not limitative of the remainder of the disclosure in any way whatsoever.

(47) From the foregoing description, one skilled in the art can easily ascertain the essential characteristics of this invention and, without departing from the spirit and scope thereof, can make various changes and modifications of the invention to adapt it to various usages and conditions.

(48) The entire disclosures of all applications, patents and publications, cited herein and of corresponding German Application No. 102015006013.9, filed May 13, 2015, are incorporated by reference herein.