POLYMER COMPOSITION, CROSS-LINKED PRODUCT AND TIRE

1 - 8 . (canceled)

9 . A polymer composition comprising:

a paraffin wax (B) having a melting point of 75° C. or more; and

a polymer (A), which is a random copolymer and having a value α represented by formula (i) of 0.60 or more:

α=( p +(0.5× r ))/( p+q +(0.5× r )+ s )  (i)

wherein p is a molar composition ratio of a structural unit of formula (1)

in the polymer (A),

q is a molar composition ratio of a structural unit of formula (2)

in the polymer (A),

r is a molar composition ratio of a structural unit of formula (3)

—CH 2 —CH 2 —  (3),

in the polymer (A), and

s is a molar composition ratio of a structural unit of formula (4)

—CH 2 —CH═CH—CH 2 —  (4),

in the polymer (A),

wherein the polymer (A) has a weight average molecular weight (Mw) of 1.0×10 5 to 2.0×10 6 in terms of polystyrene measured by gel permeation chromatography, and

wherein the polymer (A) comprises a carbon-carbon unsaturated bond.

10 . The composition of claim 9 , wherein the polymer (A) has one or more functional groups selected from the group consisting of an amino group, a nitrogen-containing heterocyclic group, a phosphino group, a hydroxyl group, a thiol group, and a hydrocarbyloxysilyl group.

11 . The composition of claim 9 , wherein the polymer (A) has a partial structure derived from at least one selected from the group consisting of a compound of formula (9), a compound of formula (10), a compound of formula (11), and a compound of formula (12):

wherein A 1 is a monovalent functional group having at least one atom selected from the group consisting of N, P, O, S, and Si, and bonding to R 5 through the N, P, O, S, Si, or a carbon atom in a carbonyl group, or a (thio)epoxy group, R 3 and R 4 are each independently a hydrocarbyl group, and R 5 is a hydrocarbylene group, and r is 0, 1, or 2;

wherein A 2 is a monovalent functional group having at least one atom selected from the group consisting of N, P, O, S, and Si, having no active hydrogen, and bonding to R 9 through the N, P, O, S, Si, or a hydrocarbyl group having 1 to 20 carbon atoms, R 6 and R 7 are each independently a hydrocarbyl group, R 8 is a hydrocarbylene group, R 9 is a single bond or a hydrocarbylene group, and m is 0 or 1;

wherein A 3 represents a monovalent group bonding to L 2 through an imino group, an amido group, a(thio)carbonyl group, a (thio)carbonyloxy group, a sulfide group, or a polysulfide group, or a protected primary amino group, a protected secondary amino group, a tertiary amino group, a nitrile group, a pyridyl group, a (thio)epoxy group, a (thio)isocyanate group, a (thio)formyl group, a (thio)carboxylic acid ester group, a metal salt of (thio)carboxylic acid ester group, —COX 1 with X 1 being a halogen atom, an imidazolyl group, or a group of formula (11a), L 2 and L 3 are each independently a single bond or a hydrocarbylene group having 1 to 20 carbon atoms, R 9 and R 10 are each independently a hydrocarbyl group, k is independently 0, 1, or 2, and j is 0 or 1;

wherein L 4 is independently a single bond or a hydrocarbylene group having 1 to 20 carbon atoms, R 11 and R 12 are each independently a hydrocarbyl group, i is independently 0, 1, 2, or 3, “*” is a site that binds to L 2 ; and

wherein A 4 is independently an imino group, an amido group, a (thio)carbonyl group or a (thio)carbonyloxy group, Z 1 is a t-valent group having or not having a nitrogen atom and having 1 to 20 carbon atoms, L 5 is independently a single bond or a hydrocarbylene group having 1 to 20 carbon atoms, L 6 is independently a hydrocarbylene group having 1 to 20 carbon atoms, and R 13 and R 14 are each independently a hydrocarbyl group; h is independently 0 or 1, and t is 2 or 3.

12 . The composition of claim 9 , wherein the paraffin wax (B) is present in a range of from 0.5 to 5 parts by mass with respect to 100 parts by mass of the rubber component comprising the polymer (A) in the polymer composition.

13 . The composition of claim 9 , wherein the paraffin wax (B) has a melting point of 140° C. or less.

14 . The composition of claim 9 , further comprising:

a cross-linking agent.

15 . A cross-linked product, produced by using the polymer composition of claim 9 .

16 . A tire, comprising:

a tread and/or a sidewall, formed from the polymer composition of claim 9 .