STAIN-RESISTANT BRANCHED POLYAMIDES

1 . A polyamide composition comprising the following formula:

wherein M is a lithium ion, a sodium ion, a potassium ion, or a hydrogen ion;

a=6 to 10;

b=6 to 10;

c=4 to 10;

d=4 to 10;

n=1 to 20;

p=1 to 1000;

m=1 to 400 and

x=4-200.

2 . The polyamide composition of claim 1 , wherein the polyamide composition includes a residue of a salt of 5-sulfoisophthalic acid.

3 . The polyamide composition of claim 2 , wherein the salt of 5-sulfoisophthalic acid is selected from the group consisting of sodium 5-sulfoisophthalate, lithium 5-sulfoisophthalate and potassium 5-sulfoisophthalate.

4 . The polyamide composition of claim 2 , wherein a concentration of the residue of the salt of 5-sulfoisophthalic acid is from 0.1 wt. % to 15 wt. % based on a total weight of the polyamide composition.

5 . The polyamide composition of claim 1 , wherein the polyamide composition includes a residue of a dimer acid, the dimer acid including two carbon chains each having more than 5 carbons.

6 . The polyamide composition of claim 5 , wherein a concentration of the residue of dimer acid is from 6 wt. % to 18 wt. % based on a total weight of the polyamide composition.

7 . The polyamide composition of claim 1 , wherein a total amine end group concentration of the polyamide composition is from about 5 millimoles per kilogram to about 50 millimoles per kilogram.

8 . The polyamide composition of claim 1 , wherein a relative viscosity (RV) of the polyamide composition is from about 2.0 to about 7.0 RV, as determined by GB/T 12006.1-2009/ISO 307:2007.

9 . The polyamide composition of claim 1 , wherein a formic acid viscosity of the polyamide composition is from about 200 FAV to about 950 FAV, as measured by ASTM D-789-07.

10 . The polyamide composition of claim 1 , wherein a color difference ΔE is less than 10, per CIE DE2000.

11 . A fiber formed from the polyamide compositions according to claim 1 , the fiber having a tenacity from 3.0 to 7.0 grams per denier.

12 . The fiber of claim 11 having a tenacity of from 6.0 to 7.0 grams per denier.

13 . A method of making a polyamide composition having the formula:

wherein M is a lithium ion, a sodium ion, a potassium ion, or a hydrogen ion, a=6 to 10, b=6 to 10, c=4 to 10, d=4 to10, n=1 to 20, p=1 to 1000, m=1 to 400 and x=4-200, the method comprising:

providing caprolactam, a dimer acid, a diamine and at least one of: a 5-sulfoisophthalic acid salt or 5-sulfoisophthalic acid to a reactor;

mixing the caprolactam, the dimer acid, the diamine and the at least one of: 5-sulfoisophthalic acid salt and 5-sulfoisophthalic acid together in the reactor; and

reacting the caprolactam, the dimer acid, the diamine and the at least one of: 5-sulfoisophthalic acid salt and 5-sulfoisophthalic acid within the reactor at a reaction temperature.

14 . The method of claim 13 , wherein, in the providing step, the at least one of: 5-sulfoisophthalic acid salt and 5-sulfoisophthalic acid is from 0.1 wt. % to 15 wt. % based on a total weight of the polyamide composition.

15 . The method of claim 13 , wherein, in the providing step, the at least one of: 5-sulfoisophthalic acid salt and 5-sulfoisophthalic acid is a 5-sulfoisophthalic acid salt selected from the group consisting of: sodium 5-sulfoisophthalate, lithium 5-sulfoisophthalate and potassium 5-sulfoisophthalate.

16 . The method of claim 13 , wherein, in the providing step, the diamine includes hexamethylenediamine.

17 . The method of claim 13 , wherein, in the providing step, the dimer acid is from 6 wt. % to 18 wt. % based on a total weight of the polyamide composition.

18 . The method of claim 13 , wherein, in the reacting step, the reactor is pressurized for a portion of the reacting step.

19 . The method of claim 13 , wherein, in the reacting step, the reactor is under vacuum for a portion of the reacting step.

20 . The method of claim 13 , wherein, in the reacting step, the reaction temperature is from about 225° C. to about 290° C.